%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SWW370+1 : TPTP v8.2.0. Released v5.2.0. % Transfm : none % Format : tptp:raw % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % Computer : n002.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 18:08:38 EDT 2024 % Result : Theorem 187.68s 187.62s % Output : CNFRefutation 187.94s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.12 % Problem : SWW370+1 : TPTP v8.2.0. Released v5.2.0. % 0.04/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % 0.13/0.34 % Computer : n002.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Wed Jun 19 08:17:24 EDT 2024 % 0.13/0.34 % CPUTime : % 0.55/0.59 start to proof:theBenchmark % 187.32/187.47 %------------------------------------------- % 187.32/187.47 % File :CSE---1.7 % 187.32/187.47 % Problem :theBenchmark % 187.32/187.47 % Transform :cnf % 187.32/187.47 % Format :tptp:raw % 187.32/187.47 % Command :java -jar mcs_scs.jar %d %s % 187.32/187.47 % 187.32/187.47 % Result :Theorem 172.460000s % 187.32/187.47 % Output :CNFRefutation 172.460000s % 187.32/187.47 %------------------------------------------- % 187.32/187.48 %------------------------------------------------------------------------------ % 187.32/187.48 % File : SWW370+1 : TPTP v8.2.0. Released v5.2.0. % 187.32/187.48 % Domain : Software Verification % 187.32/187.48 % Problem : Hoare's Logic with Procedures 435490, 5000 axioms selected % 187.32/187.48 % Version : Especial. % 187.32/187.48 % English : % 187.32/187.48 % 187.32/187.48 % Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day % 187.32/187.48 % : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe % 187.32/187.48 % Source : [Bla11] % 187.32/187.48 % Names : hoare_435490.5000.p [Bla11] % 187.32/187.48 % 187.32/187.48 % Status : ContradictoryAxioms % 187.32/187.48 % Rating : 0.78 v8.2.0, 0.75 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, 0.79 v6.2.0, 0.88 v6.1.0, 0.90 v6.0.0, 0.87 v5.5.0, 0.89 v5.4.0, 0.93 v5.3.0, 0.96 v5.2.0 % 187.32/187.48 % Syntax : Number of formulae : 5241 (1699 unt; 0 def) % 187.32/187.48 % Number of atoms : 12717 (4494 equ) % 187.32/187.48 % Maximal formula atoms : 13 ( 2 avg) % 187.32/187.48 % Number of connectives : 8493 (1017 ~; 155 |; 723 &) % 187.32/187.48 % ( 887 <=>;5711 =>; 0 <=; 0 <~>) % 187.32/187.48 % Maximal formula depth : 22 ( 6 avg) % 187.32/187.48 % Maximal term depth : 19 ( 2 avg) % 187.32/187.48 % Number of predicates : 146 ( 145 usr; 2 prp; 0-7 aty) % 187.32/187.48 % Number of functors : 360 ( 360 usr; 55 con; 0-6 aty) % 187.32/187.48 % Number of variables : 16684 (16536 !; 148 ?) % 187.32/187.48 % SPC : FOF_CAX_RFO_SEQ % 187.32/187.48 % 187.32/187.48 % Comments : This file was generated by Isabelle (most likely Sledgehammer) % 187.32/187.48 % 2011-03-01 12:43:28 % 187.32/187.48 %------------------------------------------------------------------------------ % 187.32/187.48 %----Relevant facts (4986) % 187.32/187.48 fof(fact_ext,axiom, % 187.32/187.48 ! [V_g_2,V_f_2] : % 187.32/187.48 ( ! [B_x] : hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) % 187.32/187.48 => V_f_2 = V_g_2 ) ). % 187.32/187.48 % 187.32/187.48 fof(fact_empty,axiom, % 187.32/187.48 ! [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))) ). % 187.32/187.48 % 187.32/187.48 fof(fact_hoare__derivs_Oequations_I1_J,axiom, % 187.32/187.48 ! [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))) ). % 187.32/187.48 % 187.32/187.48 fof(fact_triple_Oinject,axiom, % 187.32/187.48 ! [V_fun2_H_2,V_com_H_2,V_fun1_H_2,V_fun2_2,V_com_2,V_fun1_2,T_a] : % 187.32/187.48 ( 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) % 187.32/187.48 <=> ( V_fun1_2 = V_fun1_H_2 % 187.32/187.48 & V_com_2 = V_com_H_2 % 187.32/187.48 & V_fun2_2 = V_fun2_H_2 ) ) ). % 187.32/187.48 % 187.32/187.48 fof(fact_cut,axiom, % 187.32/187.48 ! [V_Ga_2,V_ts_2,V_G_H_2,T_a] : % 187.32/187.48 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_H_2,V_ts_2) % 187.32/187.48 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,V_G_H_2) % 187.32/187.48 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,V_ts_2) ) ) ). % 187.32/187.48 % 187.32/187.48 fof(fact_hoare__derivs_Oinsert,axiom, % 187.32/187.48 ! [V_ts_2,V_t_2,V_Ga_2,T_a] : % 187.32/187.48 ( 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)))) % 187.32/187.48 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,V_ts_2) % 187.32/187.48 => 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)) ) ) ). % 187.32/187.48 % 187.32/187.48 fof(fact_derivs__insertD,axiom, % 187.32/187.48 ! [V_ts_2,V_t_2,V_Ga_2,T_a] : % 187.32/187.48 ( 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)) % 187.32/187.48 => ( 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)))) % 187.32/187.48 & c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,V_ts_2) ) ) ). % 187.32/187.48 % 187.32/187.48 fof(fact_weak__Body,axiom, % 187.32/187.48 ! [V_Q_2,V_pna_2,V_P_2,V_Ga_2,T_a] : % 187.32/187.48 ( 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_pna_2))),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) % 187.32/187.48 => 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_pna_2)),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) ). % 187.32/187.48 % 187.32/187.48 fof(fact_BodyN,axiom, % 187.32/187.48 ! [V_Ga_2,V_Q_2,V_pna_2,V_P_2,T_a] : % 187.32/187.48 ( 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_pna_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_pna_2))),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) % 187.32/187.48 => 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_pna_2)),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) ). % 187.32/187.48 % 187.32/187.48 fof(fact_evalc__elim__cases_I6_J,axiom, % 187.32/187.48 ! [V_s1,V_s,V_P] : % 187.32/187.48 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,V_P)),V_s),V_s1)) % 187.32/187.48 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_P))),V_s),V_s1)) ) ). % 187.32/187.48 % 187.32/187.48 fof(fact_evalc_OBody,axiom, % 187.32/187.48 ! [V_s1,V_s0,V_pn] : % 187.32/187.48 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn))),V_s0),V_s1)) % 187.32/187.48 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,V_pn)),V_s0),V_s1)) ) ). % 187.32/187.48 % 187.32/187.48 fof(fact_evalc_Oequations_I9_J,axiom, % 187.32/187.48 ! [V_a3_2,V_a2_2,V_a1_2] : % 187.32/187.48 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,V_a1_2)),V_a2_2),V_a3_2)) % 187.32/187.48 <=> 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)) ) ). % 187.32/187.48 % 187.32/187.48 fof(fact_triple_Orecs,axiom, % 187.32/187.48 ! [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) ). % 187.32/187.48 % 187.32/187.48 fof(fact_triple_Osimps_I2_J,axiom, % 187.32/187.48 ! [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) ). % 187.32/187.48 % 187.32/187.48 fof(fact_empty__not__insert,axiom, % 187.32/187.48 ! [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) ). % 187.32/187.48 % 187.32/187.48 fof(fact_insert__not__empty,axiom, % 187.32/187.48 ! [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)) ). % 187.32/187.48 % 187.32/187.48 fof(fact_doubleton__eq__iff,axiom, % 187.32/187.48 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] : % 187.32/187.48 ( hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(T_a),V_c_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_d_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) % 187.32/187.48 <=> ( ( V_a_2 = V_c_2 % 187.32/187.48 & V_b_2 = V_d_2 ) % 187.32/187.48 | ( V_a_2 = V_d_2 % 187.32/187.48 & V_b_2 = V_c_2 ) ) ) ). % 187.32/187.48 % 187.32/187.48 fof(fact_singleton__inject,axiom, % 187.32/187.48 ! [V_b_2,V_a_2,T_a] : % 187.32/187.48 ( 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))) % 187.32/187.48 => V_a_2 = V_b_2 ) ). % 187.32/187.48 % 187.32/187.48 fof(fact_bot__apply,axiom, % 187.32/187.48 ! [V_x_2,T_b,T_a] : % 187.32/187.48 ( class_Orderings_Obot(T_a) % 187.32/187.48 => hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,T_a)),V_x_2) = c_Orderings_Obot__class_Obot(T_a) ) ). % 187.32/187.48 % 187.32/187.48 fof(fact_MGF__complete,axiom, % 187.32/187.48 ! [V_Q_2,V_P_2,V_c_2] : % 187.32/187.48 ( c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_OMGT(V_c_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) % 187.32/187.48 => ( c_Hoare__Mirabelle_Ohoare__valids(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),V_P_2),V_c_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) % 187.32/187.48 => c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),V_P_2),V_c_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) ) ) ). % 187.32/187.48 % 187.32/187.48 fof(fact_hoare__derivs_OSkip,axiom, % 187.32/187.48 ! [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)))) ). % 187.32/187.48 % 187.32/187.48 fof(fact_evalc__elim__cases_I1_J,axiom, % 187.32/187.48 ! [V_t,V_s] : % 187.32/187.48 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),V_s),V_t)) % 187.32/187.48 => V_t = V_s ) ). % 187.32/187.48 % 187.32/187.48 fof(fact_evalc_OSkip,axiom, % 187.32/187.48 ! [V_s] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),V_s),V_s)) ). % 187.32/187.48 % 187.32/187.48 fof(fact_evalc_Oequations_I1_J,axiom, % 187.32/187.48 ! [V_a] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),V_a),V_a)) ). % 187.32/187.48 % 187.32/187.48 fof(fact_hoare__sound,axiom, % 187.32/187.48 ! [V_ts_2,V_Ga_2,T_a] : % 187.32/187.48 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,V_ts_2) % 187.32/187.48 => c_Hoare__Mirabelle_Ohoare__valids(T_a,V_Ga_2,V_ts_2) ) ). % 187.32/187.48 % 187.32/187.48 fof(fact_insert__code,axiom, % 187.32/187.48 ! [V_x_2,V_A_2,V_y_2,T_a] : % 187.32/187.48 ( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(T_a),V_y_2),V_A_2),V_x_2)) % 187.32/187.48 <=> ( V_y_2 = V_x_2 % 187.32/187.48 | hBOOL(hAPP(V_A_2,V_x_2)) ) ) ). % 187.32/187.48 % 187.32/187.48 fof(fact_insert__commute,axiom, % 187.32/187.48 ! [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)) ). % 187.32/187.48 % 187.32/187.48 fof(fact_insert__absorb2,axiom, % 187.32/187.48 ! [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) ). % 187.32/187.48 % 187.32/187.48 fof(fact_com__det,axiom, % 187.32/187.48 ! [V_u,V_t,V_s,V_c] : % 187.32/187.48 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c),V_s),V_t)) % 187.32/187.48 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c),V_s),V_u)) % 187.32/187.48 => V_u = V_t ) ) ). % 187.32/187.48 % 187.32/187.48 fof(fact_hoare__derivs_Oequations_I7_J,axiom, % 187.32/187.48 ! [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)))) ). % 187.32/187.48 % 187.32/187.48 fof(fact_the__elem__eq,axiom, % 187.32/187.48 ! [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 ). % 187.32/187.48 % 187.32/187.48 fof(fact_com_Osimps_I19_J,axiom, % 187.32/187.48 ! [V_pname_H] : hAPP(c_Com_Ocom_OBODY,V_pname_H) != c_Com_Ocom_OSKIP ). % 187.32/187.48 % 187.32/187.48 fof(fact_com_Osimps_I18_J,axiom, % 187.32/187.48 ! [V_pname_H] : c_Com_Ocom_OSKIP != hAPP(c_Com_Ocom_OBODY,V_pname_H) ). % 187.32/187.48 % 187.32/187.48 fof(fact_conseq1,axiom, % 187.32/187.48 ! [V_P_2,V_Q_2,V_c_2,V_P_H_2,V_Ga_2,T_a] : % 187.32/187.48 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_H_2),V_c_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) % 187.32/187.48 => ( ! [B_Z,B_s] : % 187.32/187.48 ( hBOOL(hAPP(hAPP(V_P_2,B_Z),B_s)) % 187.32/187.48 => hBOOL(hAPP(hAPP(V_P_H_2,B_Z),B_s)) ) % 187.32/187.48 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),V_c_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) ) ). % 187.32/187.48 % 187.32/187.48 fof(fact_conseq2,axiom, % 187.32/187.48 ! [V_Q_2,V_Q_H_2,V_c_2,V_P_2,V_Ga_2,T_a] : % 187.32/187.48 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),V_c_2),V_Q_H_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) % 187.32/187.48 => ( ! [B_Z,B_s] : % 187.32/187.48 ( hBOOL(hAPP(hAPP(V_Q_H_2,B_Z),B_s)) % 187.32/187.48 => hBOOL(hAPP(hAPP(V_Q_2,B_Z),B_s)) ) % 187.32/187.48 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),V_c_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) ) ). % 187.32/187.48 % 187.32/187.48 fof(fact_Comp,axiom, % 187.32/187.48 ! [V_R_2,V_d_2,V_Q_2,V_c_2,V_P_2,V_Ga_2,T_a] : % 187.32/187.48 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),V_c_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) % 187.32/187.48 => ( 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)))) % 187.32/187.48 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),c_Com_Ocom_OSemi(V_c_2,V_d_2)),V_R_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) ) ). % 187.32/187.48 % 187.32/187.48 fof(fact_com_Osimps_I6_J,axiom, % 187.32/187.48 ! [V_pname_H_2,V_pname_2] : % 187.32/187.48 ( hAPP(c_Com_Ocom_OBODY,V_pname_2) = hAPP(c_Com_Ocom_OBODY,V_pname_H_2) % 187.32/187.48 <=> V_pname_2 = V_pname_H_2 ) ). % 187.32/187.48 % 187.32/187.48 fof(fact_Body__triple__valid__Suc,axiom, % 187.32/187.48 ! [V_Q_2,V_pna_2,V_P_2,V_n_2,T_a] : % 187.32/187.48 ( 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_pna_2))),V_Q_2)) % 187.32/187.48 <=> 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_pna_2)),V_Q_2)) ) ). % 187.32/187.48 % 187.32/187.48 fof(fact_conseq12,axiom, % 187.32/187.48 ! [V_Q_2,V_P_2,V_Q_H_2,V_c_2,V_P_H_2,V_Ga_2,T_a] : % 187.32/187.48 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_H_2),V_c_2),V_Q_H_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) % 187.32/187.48 => ( ! [B_Z,B_s] : % 187.32/187.48 ( hBOOL(hAPP(hAPP(V_P_2,B_Z),B_s)) % 187.32/187.48 => ! [B_s_H] : % 187.32/187.48 ( ! [B_Z_H] : % 187.32/187.48 ( hBOOL(hAPP(hAPP(V_P_H_2,B_Z_H),B_s)) % 187.32/187.48 => hBOOL(hAPP(hAPP(V_Q_H_2,B_Z_H),B_s_H)) ) % 187.32/187.48 => hBOOL(hAPP(hAPP(V_Q_2,B_Z),B_s_H)) ) ) % 187.32/187.48 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),V_c_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) ) ). % 187.32/187.48 % 187.32/187.48 fof(fact_MGT__alternI,axiom, % 187.32/187.48 ! [V_c_2,V_Ga_2] : % 187.32/187.48 ( c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_OMGT(V_c_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) % 187.32/187.49 => 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_c_2))))),c_fequal))),V_c_2),c_fequal)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) ) ). % 187.32/187.49 % 187.32/187.49 fof(fact_MGF__lemma1,axiom, % 187.32/187.49 ! [V_c_2,V_Ga_2] : % 187.32/187.49 ( c_Hoare__Mirabelle_Ostate__not__singleton % 187.32/187.49 => ( ! [B_x] : % 187.32/187.49 ( hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),B_x),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody))) % 187.32/187.49 => c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_OMGT(hAPP(c_Com_Ocom_OBODY,B_x))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) ) % 187.32/187.49 => ( hBOOL(hAPP(c_Com_OWT,V_c_2)) % 187.32/187.49 => c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_OMGT(V_c_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) ) ) ) ). % 187.32/187.49 % 187.32/187.49 fof(fact_MGT__alternD,axiom, % 187.32/187.49 ! [V_c_2,V_Ga_2] : % 187.32/187.49 ( c_Hoare__Mirabelle_Ostate__not__singleton % 187.32/187.49 => ( 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_c_2))))),c_fequal))),V_c_2),c_fequal)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) % 187.32/187.49 => c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_OMGT(V_c_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) ) ) ). % 187.32/187.49 % 187.32/187.49 fof(fact_evalc_OSemi,axiom, % 187.32/187.49 ! [V_s2,V_c1,V_s1,V_s0,V_c0] : % 187.32/187.49 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c0),V_s0),V_s1)) % 187.32/187.49 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c1),V_s1),V_s2)) % 187.32/187.49 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(V_c0,V_c1)),V_s0),V_s2)) ) ) ). % 187.32/187.49 % 187.32/187.49 fof(fact_WTs__elim__cases_I4_J,axiom, % 187.32/187.49 ! [V_c2,V_c1] : % 187.32/187.49 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(V_c1,V_c2))) % 187.32/187.49 => ~ ( hBOOL(hAPP(c_Com_OWT,V_c1)) % 187.32/187.49 => ~ hBOOL(hAPP(c_Com_OWT,V_c2)) ) ) ). % 187.32/187.49 % 187.32/187.49 fof(fact_triple__valid__Suc,axiom, % 187.32/187.49 ! [V_t,V_n,T_a] : % 187.32/187.49 ( c_Hoare__Mirabelle_Otriple__valid(T_a,hAPP(c_Nat_OSuc,V_n),V_t) % 187.32/187.49 => c_Hoare__Mirabelle_Otriple__valid(T_a,V_n,V_t) ) ). % 187.32/187.49 % 187.32/187.49 fof(fact_WT_OSemi,axiom, % 187.32/187.49 ! [V_c1,V_c0] : % 187.32/187.49 ( hBOOL(hAPP(c_Com_OWT,V_c0)) % 187.32/187.49 => ( hBOOL(hAPP(c_Com_OWT,V_c1)) % 187.32/187.49 => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(V_c0,V_c1))) ) ) ). % 187.32/187.49 % 187.32/187.49 fof(fact_com_Osimps_I3_J,axiom, % 187.32/187.49 ! [V_com2_H_2,V_com1_H_2,V_com2_2,V_com1_2] : % 187.32/187.49 ( c_Com_Ocom_OSemi(V_com1_2,V_com2_2) = c_Com_Ocom_OSemi(V_com1_H_2,V_com2_H_2) % 187.32/187.49 <=> ( V_com1_2 = V_com1_H_2 % 187.32/187.49 & V_com2_2 = V_com2_H_2 ) ) ). % 187.32/187.49 % 187.32/187.49 fof(fact_WT_Oequations_I4_J,axiom, % 187.32/187.49 ! [V_a2_2,V_a1_2] : % 187.32/187.49 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSemi(V_a1_2,V_a2_2))) % 187.32/187.49 <=> ( hBOOL(hAPP(c_Com_OWT,V_a1_2)) % 187.32/187.49 & hBOOL(hAPP(c_Com_OWT,V_a2_2)) ) ) ). % 187.32/187.49 % 187.32/187.49 fof(fact_WT_Oequations_I1_J,axiom, % 187.32/187.49 hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSKIP)) ). % 187.32/187.49 % 187.32/187.49 fof(fact_WT_OSkip,axiom, % 187.32/187.49 hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OSKIP)) ). % 187.32/187.49 % 187.32/187.49 fof(fact_com_Osimps_I49_J,axiom, % 187.32/187.49 ! [V_com2,V_com1,V_pname_H] : hAPP(c_Com_Ocom_OBODY,V_pname_H) != c_Com_Ocom_OSemi(V_com1,V_com2) ). % 187.32/187.49 % 187.32/187.49 fof(fact_com_Osimps_I48_J,axiom, % 187.32/187.49 ! [V_pname_H,V_com2,V_com1] : c_Com_Ocom_OSemi(V_com1,V_com2) != hAPP(c_Com_Ocom_OBODY,V_pname_H) ). % 187.32/187.49 % 187.32/187.49 fof(fact_bot__fun__def,axiom, % 187.32/187.49 ! [V_x_2,T_b,T_a] : % 187.32/187.49 ( class_Orderings_Obot(T_a) % 187.32/187.49 => hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,T_a)),V_x_2) = c_Orderings_Obot__class_Obot(T_a) ) ). % 187.32/187.49 % 187.32/187.49 fof(fact_com_Osimps_I13_J,axiom, % 187.32/187.49 ! [V_com2_H,V_com1_H] : c_Com_Ocom_OSemi(V_com1_H,V_com2_H) != c_Com_Ocom_OSKIP ). % 187.32/187.49 % 187.32/187.49 fof(fact_com_Osimps_I12_J,axiom, % 187.32/187.49 ! [V_com2_H,V_com1_H] : c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(V_com1_H,V_com2_H) ). % 187.32/187.49 % 187.32/187.49 fof(fact_evalc_Oequations_I4_J,axiom, % 187.32/187.49 ! [V_a5_2,V_a2_2,V_a4_2,V_a1_2] : % 187.32/187.49 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(V_a1_2,V_a4_2)),V_a2_2),V_a5_2)) % 187.32/187.49 <=> ? [B_s1] : % 187.32/187.49 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a1_2),V_a2_2),B_s1)) % 187.32/187.49 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a4_2),B_s1),V_a5_2)) ) ) ). % 187.32/187.49 % 187.32/187.49 fof(fact_MGT__def,axiom, % 187.32/187.49 ! [V_c_2] : c_Hoare__Mirabelle_OMGT(V_c_2) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),c_fequal),V_c_2),c_Natural_Oevalc(V_c_2)) ). % 187.32/187.49 % 187.32/187.49 fof(fact_escape,axiom, % 187.32/187.49 ! [V_Q_2,V_c_2,V_Ga_2,T_a,V_P_2] : % 187.32/187.49 ( ! [B_Z,B_s] : % 187.32/187.49 ( hBOOL(hAPP(hAPP(V_P_2,B_Z),B_s)) % 187.32/187.49 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),T_a),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ostate,tc_HOL_Obool),c_fequal),B_s))),V_c_2),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),T_a),hAPP(V_Q_2,B_Z)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) % 187.32/187.49 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),V_c_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) ). % 187.32/187.49 % 187.32/187.49 fof(fact_the__elem__def,axiom, % 187.32/187.49 ! [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))))) ). % 187.32/187.49 % 187.32/187.49 fof(fact_evaln_OBody,axiom, % 187.32/187.49 ! [V_s1,V_n,V_s0,V_pn] : % 187.32/187.49 ( 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)) % 187.32/187.49 => 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)) ) ). % 187.32/187.49 % 187.32/187.49 fof(fact_LoopF,axiom, % 187.32/187.49 ! [V_c_2,V_b_2,V_P_2,V_Ga_2,T_a] : c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),T_a),c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fconj)),V_P_2))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate),c_fNot),V_b_2))),c_Com_Ocom_OWhile(V_b_2,V_c_2)),V_P_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ). % 187.32/187.49 % 187.32/187.49 fof(fact_evaln_Oequations_I9_J,axiom, % 187.32/187.49 ! [V_a4_2,V_a3_2,V_a2_2,V_a1_2] : % 187.32/187.49 ( 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)) % 187.32/187.49 <=> 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)) ) ). % 187.32/187.49 % 187.32/187.49 fof(fact_triple__valid__def,axiom, % 187.32/187.49 ! [V_t_2,V_n_2,T_a] : % 187.32/187.49 ( c_Hoare__Mirabelle_Otriple__valid(T_a,V_n_2,V_t_2) % 187.32/187.49 <=> 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)) ) ). % 187.32/187.49 % 187.32/187.49 fof(fact_Body__triple__valid__0,axiom, % 187.32/187.49 ! [V_Q_2,V_pna_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_pna_2)),V_Q_2)) ). % 187.32/187.49 % 187.32/187.49 fof(fact_evalc__elim__cases_I4_J,axiom, % 187.32/187.49 ! [V_t,V_s,V_c2,V_c1] : % 187.32/187.49 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(V_c1,V_c2)),V_s),V_t)) % 187.32/187.49 => ~ ! [B_s1] : % 187.32/187.49 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c1),V_s),B_s1)) % 187.32/187.49 => ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c2),B_s1),V_t)) ) ) ). % 187.32/187.49 % 187.32/187.49 fof(fact_finite__dom__body,axiom, % 187.32/187.49 hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Com_Opname),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody))) ). % 187.32/187.49 % 187.32/187.49 fof(fact_WT_OBody,axiom, % 187.32/187.49 ! [V_pn] : % 187.32/187.49 ( hAPP(c_Com_Obody,V_pn) != c_Option_Ooption_ONone(tc_Com_Ocom) % 187.32/187.49 => hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_pn))) ) ). % 187.32/187.49 % 187.32/187.49 fof(fact_WTs__elim__cases_I8_J,axiom, % 187.32/187.49 ! [V_a_2,V_P_2,V_X_2] : % 187.32/187.49 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(V_X_2,V_P_2,V_a_2))) % 187.32/187.49 => hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_P_2))) ) ). % 187.32/187.49 % 187.32/187.49 fof(fact_evaln_OWhileTrue,axiom, % 187.32/187.49 ! [V_s2_2,V_s1_2,V_n_2,V_c_2,V_s0_2,V_b_2] : % 187.32/187.49 ( hBOOL(hAPP(V_b_2,V_s0_2)) % 187.32/187.49 => ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c_2),V_s0_2),V_n_2),V_s1_2)) % 187.32/187.49 => ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(V_b_2,V_c_2)),V_s1_2),V_n_2),V_s2_2)) % 187.32/187.49 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(V_b_2,V_c_2)),V_s0_2),V_n_2),V_s2_2)) ) ) ) ). % 187.32/187.49 % 187.32/187.49 fof(fact_evaln_OWhileFalse,axiom, % 187.32/187.49 ! [V_n_2,V_c_2,V_s_2,V_b_2] : % 187.32/187.49 ( ~ hBOOL(hAPP(V_b_2,V_s_2)) % 187.32/187.49 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(V_b_2,V_c_2)),V_s_2),V_n_2),V_s_2)) ) ). % 187.32/187.49 % 187.32/187.49 fof(fact_evalc_OWhileTrue,axiom, % 187.32/187.49 ! [V_s2_2,V_s1_2,V_c_2,V_s0_2,V_b_2] : % 187.32/187.49 ( hBOOL(hAPP(V_b_2,V_s0_2)) % 187.32/187.49 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c_2),V_s0_2),V_s1_2)) % 187.32/187.49 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_b_2,V_c_2)),V_s1_2),V_s2_2)) % 187.32/187.49 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_b_2,V_c_2)),V_s0_2),V_s2_2)) ) ) ) ). % 187.32/187.49 % 187.32/187.49 fof(fact_evalc_OWhileFalse,axiom, % 187.32/187.49 ! [V_c_2,V_s_2,V_b_2] : % 187.32/187.49 ( ~ hBOOL(hAPP(V_b_2,V_s_2)) % 187.32/187.49 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_b_2,V_c_2)),V_s_2),V_s_2)) ) ). % 187.32/187.49 % 187.32/187.49 fof(fact_WTs__elim__cases_I6_J,axiom, % 187.32/187.49 ! [V_c_2,V_b_2] : % 187.32/187.49 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(V_b_2,V_c_2))) % 187.32/187.49 => hBOOL(hAPP(c_Com_OWT,V_c_2)) ) ). % 187.32/187.49 % 187.32/187.49 fof(fact_evaln_OSemi,axiom, % 187.32/187.49 ! [V_s2,V_c1,V_s1,V_n,V_s0,V_c0] : % 187.32/187.49 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c0),V_s0),V_n),V_s1)) % 187.32/187.49 => ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c1),V_s1),V_n),V_s2)) % 187.32/187.49 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OSemi(V_c0,V_c1)),V_s0),V_n),V_s2)) ) ) ). % 187.32/187.49 % 187.32/187.49 fof(fact_evaln_OSkip,axiom, % 187.32/187.49 ! [V_n,V_s] : hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OSKIP),V_s),V_n),V_s)) ). % 187.32/187.49 % 187.32/187.49 fof(fact_evaln__elim__cases_I1_J,axiom, % 187.32/187.49 ! [V_t,V_n,V_s] : % 187.32/187.49 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OSKIP),V_s),V_n),V_t)) % 187.32/187.49 => V_t = V_s ) ). % 187.32/187.49 % 187.32/187.49 fof(fact_com_Osimps_I7_J,axiom, % 187.32/187.49 ! [V_fun_H_2,V_pname_H_2,V_vname_H_2,V_fun_2,V_pname_2,V_vname_2] : % 187.32/187.49 ( c_Com_Ocom_OCall(V_vname_2,V_pname_2,V_fun_2) = c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2) % 187.32/187.49 <=> ( V_vname_2 = V_vname_H_2 % 187.32/187.49 & V_pname_2 = V_pname_H_2 % 187.32/187.49 & V_fun_2 = V_fun_H_2 ) ) ). % 187.32/187.49 % 187.32/187.49 fof(fact_com_Osimps_I5_J,axiom, % 187.32/187.49 ! [V_com_H_2,V_fun_H_2,V_com_2,V_fun_2] : % 187.32/187.49 ( c_Com_Ocom_OWhile(V_fun_2,V_com_2) = c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) % 187.32/187.49 <=> ( V_fun_2 = V_fun_H_2 % 187.32/187.49 & V_com_2 = V_com_H_2 ) ) ). % 187.32/187.49 % 187.32/187.49 fof(fact_com_Osimps_I61_J,axiom, % 187.32/187.49 ! [V_com_2,V_fun_2,V_fun_H_2,V_pname_H_2,V_vname_H_2] : c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2) != c_Com_Ocom_OWhile(V_fun_2,V_com_2) ). % 187.32/187.49 % 187.32/187.49 fof(fact_com_Osimps_I60_J,axiom, % 187.32/187.49 ! [V_fun_H_2,V_pname_H_2,V_vname_H_2,V_com_2,V_fun_2] : c_Com_Ocom_OWhile(V_fun_2,V_com_2) != c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2) ). % 187.32/187.49 % 187.32/187.49 fof(fact_evaln_Oequations_I8_J,axiom, % 187.32/187.49 ! [V_a6_2,V_a4_2,V_a2_2,V_a3_2,V_a1_2] : % 187.32/187.49 ( 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)) % 187.32/187.49 <=> ( ( V_a6_2 = V_a2_2 % 187.32/187.49 & ~ hBOOL(hAPP(V_a1_2,V_a2_2)) ) % 187.32/187.49 | ( hBOOL(hAPP(V_a1_2,V_a2_2)) % 187.32/187.49 & ? [B_s1] : % 187.32/187.49 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a3_2),V_a2_2),V_a4_2),B_s1)) % 187.32/187.49 & 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)) ) ) ) ) ). % 187.32/187.49 % 187.32/187.49 fof(fact_evaln_Oequations_I7_J,axiom, % 187.32/187.49 ! [V_a4_2,V_a2_2,V_a3_2,V_a1_2] : % 187.32/187.49 ( 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)) % 187.32/187.49 <=> ( hBOOL(hAPP(V_a1_2,V_a2_2)) % 187.32/187.49 => ? [B_s1] : % 187.32/187.49 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a3_2),V_a2_2),V_a4_2),B_s1)) % 187.32/187.49 & 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)) ) ) ) ). % 187.32/187.49 % 187.32/187.49 fof(fact_evaln__Suc,axiom, % 187.32/187.49 ! [V_s_H,V_n,V_s,V_c] : % 187.32/187.49 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c),V_s),V_n),V_s_H)) % 187.32/187.49 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c),V_s),hAPP(c_Nat_OSuc,V_n)),V_s_H)) ) ). % 187.32/187.49 % 187.32/187.49 fof(fact_evaln__evalc,axiom, % 187.32/187.49 ! [V_t,V_n,V_s,V_c] : % 187.32/187.49 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c),V_s),V_n),V_t)) % 187.32/187.49 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c),V_s),V_t)) ) ). % 187.32/187.49 % 187.32/187.49 fof(fact_eval__eq,axiom, % 187.32/187.49 ! [V_t_2,V_s_2,V_c_2] : % 187.32/187.49 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c_2),V_s_2),V_t_2)) % 187.32/187.49 <=> ? [B_n] : hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c_2),V_s_2),B_n),V_t_2)) ) ). % 187.32/187.49 % 187.32/187.49 fof(fact_evaln_Oequations_I4_J,axiom, % 187.32/187.49 ! [V_a6_2,V_a3_2,V_a2_2,V_a5_2,V_a1_2] : % 187.32/187.49 ( 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)) % 187.32/187.49 <=> ? [B_s1] : % 187.32/187.49 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a1_2),V_a2_2),V_a3_2),B_s1)) % 187.32/187.49 & hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a5_2),B_s1),V_a3_2),V_a6_2)) ) ) ). % 187.32/187.49 % 187.32/187.49 fof(fact_evaln_Oequations_I1_J,axiom, % 187.32/187.49 ! [V_a2,V_a1] : hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OSKIP),V_a1),V_a2),V_a1)) ). % 187.32/187.49 % 187.32/187.49 fof(fact_evalc_Oequations_I8_J,axiom, % 187.32/187.49 ! [V_a5_2,V_a2_2,V_a3_2,V_a1_2] : % 187.32/187.49 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),V_a2_2),V_a5_2)) % 187.32/187.49 <=> ( ( V_a5_2 = V_a2_2 % 187.32/187.49 & ~ hBOOL(hAPP(V_a1_2,V_a2_2)) ) % 187.32/187.49 | ( hBOOL(hAPP(V_a1_2,V_a2_2)) % 187.32/187.49 & ? [B_s1] : % 187.32/187.49 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a3_2),V_a2_2),B_s1)) % 187.32/187.49 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),B_s1),V_a5_2)) ) ) ) ) ). % 187.32/187.49 % 187.32/187.49 fof(fact_evalc_Oequations_I7_J,axiom, % 187.32/187.49 ! [V_a2_2,V_a3_2,V_a1_2] : % 187.32/187.49 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),V_a2_2),V_a2_2)) % 187.32/187.49 <=> ( hBOOL(hAPP(V_a1_2,V_a2_2)) % 187.32/187.49 => ? [B_s1] : % 187.32/187.49 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a3_2),V_a2_2),B_s1)) % 187.32/187.49 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),B_s1),V_a2_2)) ) ) ) ). % 187.32/187.49 % 187.32/187.49 fof(fact_WT_Oequations_I6_J,axiom, % 187.32/187.49 ! [V_a1_2,V_a2_2] : % 187.32/187.49 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(V_a2_2,V_a1_2))) % 187.32/187.49 <=> hBOOL(hAPP(c_Com_OWT,V_a1_2)) ) ). % 187.32/187.49 % 187.32/187.49 fof(fact_While,axiom, % 187.32/187.49 ! [V_b_2,V_c_2] : % 187.32/187.49 ( hBOOL(hAPP(c_Com_OWT,V_c_2)) % 187.32/187.49 => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OWhile(V_b_2,V_c_2))) ) ). % 187.32/187.49 % 187.32/187.49 fof(fact_com_Osimps_I58_J,axiom, % 187.32/187.49 ! [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) ). % 187.32/187.49 % 187.32/187.49 fof(fact_com_Osimps_I59_J,axiom, % 187.32/187.49 ! [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) ). % 187.32/187.49 % 187.32/187.49 fof(fact_com_Osimps_I46_J,axiom, % 187.32/187.49 ! [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) ). % 187.32/187.49 % 187.32/187.49 fof(fact_com_Osimps_I47_J,axiom, % 187.32/187.49 ! [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) ). % 187.32/187.49 % 187.32/187.49 fof(fact_com_Osimps_I16_J,axiom, % 187.32/187.49 ! [V_com_H_2,V_fun_H_2] : c_Com_Ocom_OSKIP != c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) ). % 187.32/187.49 % 187.32/187.49 fof(fact_com_Osimps_I17_J,axiom, % 187.32/187.49 ! [V_com_H_2,V_fun_H_2] : c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) != c_Com_Ocom_OSKIP ). % 187.32/187.49 % 187.32/187.49 fof(fact_com_Osimps_I63_J,axiom, % 187.32/187.49 ! [V_pname_2,V_fun_H_2,V_pname_H_2,V_vname_H_2] : c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2) != hAPP(c_Com_Ocom_OBODY,V_pname_2) ). % 187.32/187.49 % 187.32/187.49 fof(fact_com_Osimps_I62_J,axiom, % 187.32/187.49 ! [V_fun_H_2,V_pname_H_2,V_vname_H_2,V_pname_2] : hAPP(c_Com_Ocom_OBODY,V_pname_2) != c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2) ). % 187.32/187.49 % 187.32/187.49 fof(fact_com_Osimps_I50_J,axiom, % 187.32/187.49 ! [V_fun_H_2,V_pname_H_2,V_vname_H_2,V_com2_2,V_com1_2] : c_Com_Ocom_OSemi(V_com1_2,V_com2_2) != c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2) ). % 187.32/187.49 % 187.32/187.49 fof(fact_com_Osimps_I51_J,axiom, % 187.32/187.49 ! [V_com2_2,V_com1_2,V_fun_H_2,V_pname_H_2,V_vname_H_2] : c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2) != c_Com_Ocom_OSemi(V_com1_2,V_com2_2) ). % 187.32/187.49 % 187.32/187.49 fof(fact_com_Osimps_I20_J,axiom, % 187.32/187.49 ! [V_fun_H_2,V_pname_H_2,V_vname_H_2] : c_Com_Ocom_OSKIP != c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2) ). % 187.32/187.49 % 187.32/187.49 fof(fact_com_Osimps_I21_J,axiom, % 187.32/187.49 ! [V_fun_H_2,V_pname_H_2,V_vname_H_2] : c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2) != c_Com_Ocom_OSKIP ). % 187.32/187.49 % 187.32/187.49 fof(fact_triple__valid__def2,axiom, % 187.32/187.49 ! [V_Q_2,V_c_2,V_P_2,V_n_2,T_a] : % 187.32/187.49 ( c_Hoare__Mirabelle_Otriple__valid(T_a,V_n_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),V_c_2),V_Q_2)) % 187.32/187.49 <=> ! [B_Z,B_s] : % 187.32/187.49 ( hBOOL(hAPP(hAPP(V_P_2,B_Z),B_s)) % 187.32/187.49 => ! [B_s_H] : % 187.32/187.49 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c_2),B_s),V_n_2),B_s_H)) % 187.32/187.49 => hBOOL(hAPP(hAPP(V_Q_2,B_Z),B_s_H)) ) ) ) ). % 187.32/187.49 % 187.32/187.49 fof(fact_WT_Oequations_I8_J,axiom, % 187.32/187.49 ! [V_a3_2,V_a1_2,V_a2_2] : % 187.32/187.49 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(V_a2_2,V_a1_2,V_a3_2))) % 187.32/187.49 <=> hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_a1_2))) ) ). % 187.32/187.49 % 187.32/187.49 fof(fact_WT_OCall,axiom, % 187.32/187.49 ! [V_a_2,V_X_2,V_pna_2] : % 187.32/187.49 ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_pna_2))) % 187.32/187.49 => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCall(V_X_2,V_pna_2,V_a_2))) ) ). % 187.32/187.49 % 187.32/187.49 fof(fact_finite_OinsertI,axiom, % 187.32/187.49 ! [V_a_2,V_A_2,T_a] : % 187.32/187.49 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.32/187.49 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2))) ) ). % 187.32/187.49 % 187.32/187.49 fof(fact_finite_OemptyI,axiom, % 187.32/187.50 ! [T_a] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ). % 187.32/187.50 % 187.32/187.50 fof(fact_triple_Osize_I1_J,axiom, % 187.32/187.50 ! [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) ). % 187.32/187.50 % 187.32/187.50 fof(fact_dom__eq__empty__conv,axiom, % 187.32/187.50 ! [V_f_2,T_b,T_a] : % 187.32/187.50 ( c_Map_Odom(T_a,T_b,V_f_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.32/187.50 <=> V_f_2 = hAPP(c_COMBK(tc_Option_Ooption(T_b),T_a),c_Option_Ooption_ONone(T_b)) ) ). % 187.32/187.50 % 187.32/187.50 fof(fact_dom__empty,axiom, % 187.32/187.50 ! [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)) ). % 187.32/187.50 % 187.32/187.50 fof(fact_triple_Osize_I2_J,axiom, % 187.32/187.50 ! [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) ). % 187.32/187.50 % 187.32/187.50 fof(fact_evaln__elim__cases_I6_J,axiom, % 187.32/187.50 ! [V_s1,V_n,V_s,V_P] : % 187.32/187.50 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,hAPP(c_Com_Ocom_OBODY,V_P)),V_s),V_n),V_s1)) % 187.32/187.50 => ~ ! [B_n] : % 187.32/187.50 ( V_n = hAPP(c_Nat_OSuc,B_n) % 187.32/187.50 => ~ 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)) ) ) ). % 187.32/187.50 % 187.32/187.50 fof(fact_Zero__not__Suc,axiom, % 187.32/187.50 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m) ). % 187.32/187.50 % 187.32/187.50 fof(fact_nat_Osimps_I2_J,axiom, % 187.32/187.50 ! [V_nat_H] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_nat_H) ). % 187.32/187.50 % 187.32/187.50 fof(fact_Suc__not__Zero,axiom, % 187.32/187.50 ! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 187.32/187.50 % 187.32/187.50 fof(fact_nat_Osimps_I3_J,axiom, % 187.32/187.50 ! [V_nat_H_1] : hAPP(c_Nat_OSuc,V_nat_H_1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 187.32/187.50 % 187.32/187.50 fof(fact_Zero__neq__Suc,axiom, % 187.32/187.50 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m) ). % 187.32/187.50 % 187.32/187.50 fof(fact_finite__code,axiom, % 187.32/187.50 ! [V_A_2,T_a] : % 187.32/187.50 ( class_Finite__Set_Ofinite(T_a) % 187.32/187.50 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ). % 187.32/187.50 % 187.32/187.50 fof(fact_finite,axiom, % 187.32/187.50 ! [V_A_2,T_a] : % 187.32/187.50 ( class_Finite__Set_Ofinite(T_a) % 187.32/187.50 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ). % 187.32/187.50 % 187.32/187.50 fof(fact_bot__nat__def,axiom, % 187.32/187.50 c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 187.32/187.50 % 187.32/187.50 fof(fact_Suc__inject,axiom, % 187.32/187.50 ! [V_y,V_x] : % 187.32/187.50 ( hAPP(c_Nat_OSuc,V_x) = hAPP(c_Nat_OSuc,V_y) % 187.32/187.50 => V_x = V_y ) ). % 187.32/187.50 % 187.32/187.50 fof(fact_nat_Oinject,axiom, % 187.32/187.50 ! [V_nat_H_2,V_nat_2] : % 187.32/187.50 ( hAPP(c_Nat_OSuc,V_nat_2) = hAPP(c_Nat_OSuc,V_nat_H_2) % 187.32/187.50 <=> V_nat_2 = V_nat_H_2 ) ). % 187.32/187.50 % 187.32/187.50 fof(fact_Suc__n__not__n,axiom, % 187.32/187.50 ! [V_n] : hAPP(c_Nat_OSuc,V_n) != V_n ). % 187.32/187.50 % 187.32/187.50 fof(fact_n__not__Suc__n,axiom, % 187.32/187.50 ! [V_n] : V_n != hAPP(c_Nat_OSuc,V_n) ). % 187.32/187.50 % 187.32/187.50 fof(fact_finite_Oequations_I1_J,axiom, % 187.32/187.50 ! [T_a] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ). % 187.32/187.50 % 187.32/187.50 fof(fact_finite__insert,axiom, % 187.32/187.50 ! [V_A_2,V_a_2,T_a] : % 187.32/187.50 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2))) % 187.32/187.50 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ). % 187.32/187.50 % 187.32/187.50 fof(fact_Suc__neq__Zero,axiom, % 187.32/187.50 ! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 187.32/187.50 % 187.32/187.50 fof(fact_folding__one__idem_Oinsert__idem,axiom, % 187.32/187.50 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_a] : % 187.32/187.50 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2) % 187.32/187.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.32/187.50 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.32/187.50 => 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)) ) ) ) ). % 187.32/187.50 % 187.32/187.50 fof(fact_the__sym__eq__trivial,axiom, % 187.32/187.50 ! [V_x_2,T_a] : c_HOL_OThe(T_a,hAPP(c_fequal,V_x_2)) = V_x_2 ). % 187.32/187.50 % 187.32/187.50 fof(fact_the__eq__trivial,axiom, % 187.32/187.50 ! [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 ). % 187.32/187.50 % 187.32/187.50 fof(fact_ran__empty,axiom, % 187.32/187.50 ! [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)) ). % 187.32/187.50 % 187.32/187.50 fof(fact_folding__image__simple__idem_Oinsert__idem,axiom, % 187.32/187.50 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 187.32/187.50 ( c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 187.32/187.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.32/187.50 => 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)) ) ) ). % 187.32/187.50 % 187.32/187.50 fof(fact_fold1Set__sing,axiom, % 187.32/187.50 ! [V_b_2,V_a_2,V_f_2,T_a] : % 187.32/187.50 ( 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)) % 187.32/187.50 <=> V_a_2 = V_b_2 ) ). % 187.32/187.50 % 187.32/187.50 fof(fact_folding__one_Osingleton,axiom, % 187.32/187.50 ! [V_x_2,V_F_2,V_f_2,T_a] : % 187.32/187.50 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2) % 187.32/187.50 => 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 ) ). % 187.32/187.50 % 187.32/187.50 fof(fact_finite_Osimps,axiom, % 187.32/187.50 ! [V_a_2,T_a] : % 187.32/187.50 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_a_2)) % 187.32/187.50 <=> ( V_a_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.32/187.50 | ? [B_A] : % 187.32/187.50 ( ? [B_a] : V_a_2 = hAPP(hAPP(c_Set_Oinsert(T_a),B_a),B_A) % 187.32/187.50 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),B_A)) ) ) ) ). % 187.32/187.50 % 187.32/187.50 fof(fact_Loop__sound__lemma,axiom, % 187.32/187.50 ! [V_c_2,V_b_2,V_P_2,V_Ga_2,T_a] : % 187.32/187.50 ( c_Hoare__Mirabelle_Ohoare__valids(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),c_Hoare__Mirabelle_Opeek__and(T_a,V_P_2,V_b_2)),V_c_2),V_P_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) % 187.32/187.50 => c_Hoare__Mirabelle_Ohoare__valids(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),c_Com_Ocom_OWhile(V_b_2,V_c_2)),c_Hoare__Mirabelle_Opeek__and(T_a,V_P_2,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),V_b_2)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) ). % 187.32/187.50 % 187.32/187.50 fof(fact_evaln__elim__cases_I4_J,axiom, % 187.32/187.50 ! [V_t,V_n,V_s,V_c2,V_c1] : % 187.32/187.50 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OSemi(V_c1,V_c2)),V_s),V_n),V_t)) % 187.32/187.50 => ~ ! [B_s1] : % 187.32/187.50 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c1),V_s),V_n),B_s1)) % 187.32/187.50 => ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c2),B_s1),V_n),V_t)) ) ) ). % 187.32/187.50 % 187.32/187.50 fof(fact_Least__Suc,axiom, % 187.32/187.50 ! [V_n_2,V_P_2] : % 187.32/187.50 ( hBOOL(hAPP(V_P_2,V_n_2)) % 187.32/187.50 => ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) % 187.32/187.50 => c_Orderings_Oord__class_OLeast(tc_Nat_Onat,V_P_2) = hAPP(c_Nat_OSuc,c_Orderings_Oord__class_OLeast(tc_Nat_Onat,hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_HOL_Obool,tc_Nat_Onat),V_P_2),c_Nat_OSuc))) ) ) ). % 187.32/187.50 % 187.32/187.50 fof(fact_LeastI__ex,axiom, % 187.32/187.50 ! [V_P_2,T_a] : % 187.32/187.50 ( class_Orderings_Owellorder(T_a) % 187.32/187.50 => ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) % 187.32/187.50 => hBOOL(hAPP(V_P_2,c_Orderings_Oord__class_OLeast(T_a,V_P_2))) ) ) ). % 187.32/187.50 % 187.32/187.50 fof(fact_folding__one__idem_Oidem,axiom, % 187.32/187.50 ! [V_x_2,V_F_2,V_f_2,T_a] : % 187.32/187.50 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2) % 187.32/187.50 => hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2 ) ). % 187.32/187.50 % 187.32/187.50 fof(fact_folding__image__simple__idem_Oidem,axiom, % 187.32/187.50 ! [V_x_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 187.32/187.50 ( c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 187.32/187.50 => hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2 ) ). % 187.32/187.50 % 187.32/187.50 fof(fact_LeastI,axiom, % 187.32/187.50 ! [V_k_2,V_P_2,T_a] : % 187.32/187.50 ( class_Orderings_Owellorder(T_a) % 187.32/187.50 => ( hBOOL(hAPP(V_P_2,V_k_2)) % 187.32/187.50 => hBOOL(hAPP(V_P_2,c_Orderings_Oord__class_OLeast(T_a,V_P_2))) ) ) ). % 187.32/187.50 % 187.32/187.50 fof(fact_peek__and__def,axiom, % 187.32/187.50 ! [V_s_2,V_Z_2,V_p_2,V_P_2,T_a] : % 187.43/187.50 ( hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(T_a,V_P_2,V_p_2),V_Z_2),V_s_2)) % 187.43/187.50 <=> ( hBOOL(hAPP(hAPP(V_P_2,V_Z_2),V_s_2)) % 187.43/187.50 & hBOOL(hAPP(V_p_2,V_s_2)) ) ) ). % 187.43/187.50 % 187.43/187.50 fof(fact_fold1Set__nonempty,axiom, % 187.43/187.50 ! [V_x_2,V_A_2,V_f_2,T_a] : % 187.43/187.50 ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_a,V_f_2,V_A_2),V_x_2)) % 187.43/187.50 => V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 187.43/187.50 % 187.43/187.50 fof(fact_empty__fold1SetE,axiom, % 187.43/187.50 ! [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)) ). % 187.43/187.50 % 187.43/187.50 fof(fact_Loop,axiom, % 187.43/187.50 ! [V_c_2,V_b_2,V_P_2,V_Ga_2,T_a] : % 187.43/187.50 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),c_Hoare__Mirabelle_Opeek__and(T_a,V_P_2,V_b_2)),V_c_2),V_P_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) % 187.43/187.50 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),c_Com_Ocom_OWhile(V_b_2,V_c_2)),c_Hoare__Mirabelle_Opeek__and(T_a,V_P_2,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),V_b_2)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) ). % 187.43/187.50 % 187.43/187.50 fof(fact_hoare__derivs_OIf,axiom, % 187.43/187.50 ! [V_d_2,V_Q_2,V_c_2,V_b_2,V_P_2,V_Ga_2,T_a] : % 187.43/187.50 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),c_Hoare__Mirabelle_Opeek__and(T_a,V_P_2,V_b_2)),V_c_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) % 187.43/187.50 => ( 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)))) % 187.43/187.50 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),c_Com_Ocom_OCond(V_b_2,V_c_2,V_d_2)),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) ) ). % 187.43/187.50 % 187.43/187.50 fof(fact_folding__idem_Oinsert__idem,axiom, % 187.43/187.50 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 187.43/187.50 ( c_Finite__Set_Ofolding__idem(T_a,T_b,V_f_2,V_F_2) % 187.43/187.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.43/187.50 => 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)) ) ) ). % 187.43/187.50 % 187.43/187.50 fof(fact_o__def,axiom, % 187.43/187.50 ! [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)) ). % 187.43/187.50 % 187.43/187.50 fof(fact_K__record__comp,axiom, % 187.43/187.50 ! [V_x_2,V_f_2,V_c_2,T_c,T_a,T_b] : hAPP(hAPP(c_Fun_Ocomp(T_b,T_a,T_c,hAPP(c_COMBK(T_a,T_b),V_c_2)),V_f_2),V_x_2) = V_c_2 ). % 187.43/187.50 % 187.43/187.50 fof(fact_folding__one_Oinsert,axiom, % 187.43/187.50 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_a] : % 187.43/187.50 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2) % 187.43/187.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.43/187.50 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 187.43/187.50 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.43/187.50 => 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)) ) ) ) ) ). % 187.43/187.50 % 187.43/187.50 fof(fact_Least__Suc2,axiom, % 187.43/187.50 ! [V_m_2,V_Q_2,V_n_2,V_P_2] : % 187.43/187.50 ( hBOOL(hAPP(V_P_2,V_n_2)) % 187.43/187.50 => ( hBOOL(hAPP(V_Q_2,V_m_2)) % 187.43/187.50 => ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) % 187.43/187.50 => ( ! [B_k] : % 187.43/187.50 ( hBOOL(hAPP(V_P_2,hAPP(c_Nat_OSuc,B_k))) % 187.43/187.50 <=> hBOOL(hAPP(V_Q_2,B_k)) ) % 187.43/187.50 => c_Orderings_Oord__class_OLeast(tc_Nat_Onat,V_P_2) = hAPP(c_Nat_OSuc,c_Orderings_Oord__class_OLeast(tc_Nat_Onat,V_Q_2)) ) ) ) ) ). % 187.43/187.50 % 187.43/187.50 fof(fact_folding__one_Oinsert__remove,axiom, % 187.43/187.50 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_a] : % 187.43/187.50 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2) % 187.43/187.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.43/187.50 => ( ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.43/187.50 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = V_x_2 ) % 187.43/187.50 & ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.43/187.50 => 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)))))) ) ) ) ) ). % 187.43/187.50 % 187.43/187.50 fof(fact_finite__nonempty__imp__fold1Set,axiom, % 187.43/187.50 ! [V_f_2,V_A_2,T_a] : % 187.43/187.50 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.43/187.50 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.43/187.50 => ? [B_x1] : hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_a,V_f_2,V_A_2),B_x1)) ) ) ). % 187.43/187.50 % 187.43/187.50 fof(fact_com_Osize_I1_J,axiom, % 187.43/187.50 c_Com_Ocom_Ocom__size(c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 187.43/187.50 % 187.43/187.50 fof(fact_com_Osize_I8_J,axiom, % 187.43/187.50 ! [V_fun_2,V_pname_2,V_vname_2] : c_Com_Ocom_Ocom__size(c_Com_Ocom_OCall(V_vname_2,V_pname_2,V_fun_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 187.43/187.50 % 187.43/187.50 fof(fact_folding__one__idem_Osubset__idem,axiom, % 187.43/187.50 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_a] : % 187.43/187.50 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2) % 187.43/187.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.43/187.50 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.43/187.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 187.43/187.50 => 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) ) ) ) ) ). % 187.43/187.50 % 187.43/187.50 fof(fact_order__refl,axiom, % 187.43/187.50 ! [V_x,T_a] : % 187.43/187.50 ( class_Orderings_Opreorder(T_a) % 187.43/187.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_x)) ) ). % 187.43/187.50 % 187.43/187.50 fof(fact_equalityCE,axiom, % 187.43/187.50 ! [V_c_2,T_a,V_B_2,V_A_2] : % 187.43/187.50 ( V_A_2 = V_B_2 % 187.43/187.50 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) % 187.43/187.50 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2)) ) % 187.43/187.50 => ~ ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) % 187.43/187.50 => hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2)) ) ) ) ). % 187.43/187.50 % 187.43/187.50 fof(fact_equalityI,axiom, % 187.43/187.50 ! [V_B_2,V_A_2,T_a] : % 187.43/187.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 187.43/187.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 187.43/187.50 => V_A_2 = V_B_2 ) ) ). % 187.43/187.50 % 187.43/187.50 fof(fact_emptyE,axiom, % 187.43/187.50 ! [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)))) ). % 187.43/187.50 % 187.43/187.50 fof(fact_insertE,axiom, % 187.43/187.50 ! [V_A_2,V_b_2,V_a_2,T_a] : % 187.43/187.50 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),V_A_2))) % 187.43/187.50 => ( V_a_2 != V_b_2 % 187.43/187.50 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ). % 187.43/187.50 % 187.43/187.50 fof(fact_insertCI,axiom, % 187.43/187.50 ! [V_b_2,V_B_2,V_a_2,T_a] : % 187.43/187.50 ( ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_B_2)) % 187.43/187.50 => V_a_2 = V_b_2 ) % 187.43/187.50 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),V_B_2))) ) ). % 187.43/187.50 % 187.43/187.50 fof(fact_subsetD,axiom, % 187.43/187.50 ! [V_c_2,V_B_2,V_A_2,T_a] : % 187.43/187.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 187.43/187.50 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) % 187.43/187.50 => hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2)) ) ) ). % 187.43/187.50 % 187.43/187.50 fof(fact_empty__subsetI,axiom, % 187.43/187.50 ! [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)) ). % 187.43/187.50 % 187.43/187.50 fof(fact_DiffI,axiom, % 187.43/187.50 ! [V_B_2,V_A_2,V_c_2,T_a] : % 187.43/187.50 ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) % 187.43/187.50 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2)) % 187.43/187.50 => hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ). % 187.43/187.50 % 187.43/187.50 fof(fact_DiffE,axiom, % 187.43/187.50 ! [V_B_2,V_A_2,V_c_2,T_a] : % 187.43/187.50 ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 187.43/187.50 => ~ ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) % 187.43/187.50 => hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2)) ) ) ). % 187.43/187.50 % 187.43/187.50 fof(fact_finite__Diff,axiom, % 187.43/187.50 ! [V_B_2,V_A_2,T_a] : % 187.43/187.50 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.43/187.50 => 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))) ) ). % 187.43/187.50 % 187.43/187.50 fof(fact_evaln_OIfFalse,axiom, % 187.43/187.50 ! [V_c0_2,V_s1_2,V_n_2,V_c1_2,V_s_2,V_b_2] : % 187.43/187.50 ( ~ hBOOL(hAPP(V_b_2,V_s_2)) % 187.43/187.50 => ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c1_2),V_s_2),V_n_2),V_s1_2)) % 187.43/187.50 => 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)) ) ) ). % 187.43/187.50 % 187.43/187.50 fof(fact_evaln_OIfTrue,axiom, % 187.43/187.50 ! [V_c1_2,V_s1_2,V_n_2,V_c0_2,V_s_2,V_b_2] : % 187.43/187.50 ( hBOOL(hAPP(V_b_2,V_s_2)) % 187.43/187.50 => ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c0_2),V_s_2),V_n_2),V_s1_2)) % 187.43/187.50 => 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)) ) ) ). % 187.43/187.50 % 187.43/187.50 fof(fact_evaln__elim__cases_I5_J,axiom, % 187.43/187.50 ! [V_t_2,V_n_2,V_s_2,V_c2_2,V_c1_2,V_b_2] : % 187.43/187.50 ( 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)) % 187.43/187.50 => ( ( hBOOL(hAPP(V_b_2,V_s_2)) % 187.43/187.50 => ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c1_2),V_s_2),V_n_2),V_t_2)) ) % 187.43/187.50 => ~ ( ~ hBOOL(hAPP(V_b_2,V_s_2)) % 187.43/187.50 => ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c2_2),V_s_2),V_n_2),V_t_2)) ) ) ) ). % 187.43/187.50 % 187.43/187.50 fof(fact_evalc_OIfFalse,axiom, % 187.43/187.50 ! [V_c0_2,V_s1_2,V_c1_2,V_s_2,V_b_2] : % 187.43/187.50 ( ~ hBOOL(hAPP(V_b_2,V_s_2)) % 187.43/187.50 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c1_2),V_s_2),V_s1_2)) % 187.43/187.50 => 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)) ) ) ). % 187.43/187.50 % 187.43/187.50 fof(fact_evalc_OIfTrue,axiom, % 187.43/187.50 ! [V_c1_2,V_s1_2,V_c0_2,V_s_2,V_b_2] : % 187.43/187.50 ( hBOOL(hAPP(V_b_2,V_s_2)) % 187.43/187.50 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c0_2),V_s_2),V_s1_2)) % 187.43/187.50 => 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)) ) ) ). % 187.43/187.50 % 187.43/187.50 fof(fact_evalc__elim__cases_I5_J,axiom, % 187.43/187.50 ! [V_t_2,V_s_2,V_c2_2,V_c1_2,V_b_2] : % 187.43/187.50 ( 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)) % 187.43/187.50 => ( ( hBOOL(hAPP(V_b_2,V_s_2)) % 187.43/187.50 => ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c1_2),V_s_2),V_t_2)) ) % 187.43/187.50 => ~ ( ~ hBOOL(hAPP(V_b_2,V_s_2)) % 187.43/187.50 => ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c2_2),V_s_2),V_t_2)) ) ) ) ). % 187.43/187.50 % 187.43/187.50 fof(fact_WTs__elim__cases_I5_J,axiom, % 187.43/187.50 ! [V_c2_2,V_c1_2,V_b_2] : % 187.43/187.50 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(V_b_2,V_c1_2,V_c2_2))) % 187.43/187.50 => ~ ( hBOOL(hAPP(c_Com_OWT,V_c1_2)) % 187.43/187.50 => ~ hBOOL(hAPP(c_Com_OWT,V_c2_2)) ) ) ). % 187.43/187.50 % 187.43/187.50 fof(fact_subset__refl,axiom, % 187.43/187.50 ! [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)) ). % 187.43/187.50 % 187.43/187.50 fof(fact_Diff__subset,axiom, % 187.43/187.50 ! [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)) ). % 187.43/187.50 % 187.43/187.50 fof(fact_le__fun__def,axiom, % 187.43/187.50 ! [V_g_2,V_f_2,T_a,T_b] : % 187.43/187.50 ( class_Orderings_Oord(T_b) % 187.43/187.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_f_2),V_g_2)) % 187.43/187.50 <=> ! [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))) ) ) ). % 187.43/187.50 % 187.43/187.50 fof(fact_mem__def,axiom, % 187.43/187.50 ! [V_A_2,V_x_2,T_a] : % 187.43/187.50 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 187.43/187.50 <=> hBOOL(hAPP(V_A_2,V_x_2)) ) ). % 187.43/187.50 % 187.43/187.50 fof(fact_linorder__linear,axiom, % 187.43/187.50 ! [V_y,V_x,T_a] : % 187.43/187.50 ( class_Orderings_Olinorder(T_a) % 187.43/187.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 187.43/187.50 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ). % 187.43/187.50 % 187.43/187.50 fof(fact_set__eq__subset,axiom, % 187.43/187.50 ! [T_a,V_B_2,V_A_2] : % 187.43/187.50 ( V_A_2 = V_B_2 % 187.43/187.50 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 187.43/187.50 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) ) ) ). % 187.43/187.50 % 187.43/187.50 fof(fact_order__eq__iff,axiom, % 187.43/187.50 ! [V_y_2,V_x_2,T_a] : % 187.43/187.50 ( class_Orderings_Oorder(T_a) % 187.43/187.50 => ( V_x_2 = V_y_2 % 187.43/187.50 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 187.43/187.50 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) ) ) ) ). % 187.43/187.50 % 187.43/187.50 fof(fact_Diff__iff,axiom, % 187.43/187.50 ! [V_B_2,V_A_2,V_c_2,T_a] : % 187.43/187.50 ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 187.43/187.50 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) % 187.43/187.50 & ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2)) ) ) ). % 187.43/187.50 % 187.43/187.50 fof(fact_Diff__idemp,axiom, % 187.43/187.50 ! [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) ). % 187.43/187.50 % 187.43/187.50 fof(fact_equalityD1,axiom, % 187.43/187.50 ! [T_a,V_B_2,V_A_2] : % 187.43/187.50 ( V_A_2 = V_B_2 % 187.43/187.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 187.43/187.50 % 187.43/187.50 fof(fact_equalityD2,axiom, % 187.43/187.50 ! [T_a,V_B_2,V_A_2] : % 187.43/187.50 ( V_A_2 = V_B_2 % 187.43/187.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) ) ). % 187.43/187.50 % 187.43/187.50 fof(fact_order__eq__refl,axiom, % 187.43/187.50 ! [V_y,V_x,T_a] : % 187.43/187.50 ( class_Orderings_Opreorder(T_a) % 187.43/187.50 => ( V_x = V_y % 187.43/187.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ). % 187.43/187.50 % 187.43/187.50 fof(fact_le__funD,axiom, % 187.43/187.50 ! [V_x_2,V_g_2,V_f_2,T_a,T_b] : % 187.43/187.50 ( class_Orderings_Oord(T_b) % 187.43/187.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_f_2),V_g_2)) % 187.43/187.50 => 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))) ) ) ). % 187.43/187.50 % 187.43/187.50 fof(fact_eqset__imp__iff,axiom, % 187.43/187.50 ! [V_x_2,T_a,V_B_2,V_A_2] : % 187.43/187.50 ( V_A_2 = V_B_2 % 187.43/187.50 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 187.43/187.50 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) ) ) ). % 187.43/187.50 % 187.43/187.50 fof(fact_eqelem__imp__iff,axiom, % 187.43/187.50 ! [V_A_2,T_a,V_y_2,V_x_2] : % 187.43/187.50 ( V_x_2 = V_y_2 % 187.43/187.50 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 187.43/187.50 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) ) ) ). % 187.43/187.50 % 187.43/187.50 fof(fact_in__mono,axiom, % 187.43/187.50 ! [V_x_2,V_B_2,V_A_2,T_a] : % 187.43/187.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 187.43/187.50 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 187.43/187.50 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) ) ) ). % 187.43/187.50 % 187.43/187.50 fof(fact_order__antisym__conv,axiom, % 187.43/187.50 ! [V_x_2,V_y_2,T_a] : % 187.43/187.50 ( class_Orderings_Oorder(T_a) % 187.43/187.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) % 187.43/187.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 187.43/187.50 <=> V_x_2 = V_y_2 ) ) ) ). % 187.43/187.50 % 187.43/187.50 fof(fact_eq__mem__trans,axiom, % 187.43/187.50 ! [V_A_2,T_a,V_b_2,V_a_2] : % 187.43/187.50 ( V_a_2 = V_b_2 % 187.43/187.50 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),V_A_2)) % 187.43/187.50 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ). % 187.43/187.50 % 187.43/187.50 fof(fact_ord__eq__le__trans,axiom, % 187.43/187.50 ! [V_c,V_b,V_a,T_a] : % 187.43/187.50 ( class_Orderings_Oord(T_a) % 187.43/187.50 => ( V_a = V_b % 187.43/187.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c)) % 187.43/187.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) ) ) ) ). % 187.43/187.50 % 187.43/187.50 fof(fact_xt1_I3_J,axiom, % 187.43/187.50 ! [V_c,V_b,V_a,T_a] : % 187.43/187.50 ( class_Orderings_Oorder(T_a) % 187.43/187.50 => ( V_a = V_b % 187.43/187.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_b)) % 187.43/187.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_a)) ) ) ) ). % 187.43/187.50 % 187.43/187.50 fof(fact_set__rev__mp,axiom, % 187.43/187.50 ! [V_B_2,V_A_2,V_x_2,T_a] : % 187.43/187.50 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 187.43/187.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 187.43/187.50 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) ) ) ). % 187.43/187.50 % 187.43/187.50 fof(fact_set__mp,axiom, % 187.43/187.50 ! [V_x_2,V_B_2,V_A_2,T_a] : % 187.43/187.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 187.43/187.50 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 187.43/187.50 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) ) ) ). % 187.43/187.50 % 187.43/187.50 fof(fact_subset__trans,axiom, % 187.43/187.50 ! [V_C_2,V_B_2,V_A_2,T_a] : % 187.43/187.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 187.43/187.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) % 187.43/187.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ). % 187.43/187.50 % 187.43/187.50 fof(fact_ord__le__eq__trans,axiom, % 187.43/187.50 ! [V_c,V_b,V_a,T_a] : % 187.43/187.50 ( class_Orderings_Oord(T_a) % 187.43/187.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 187.43/187.50 => ( V_b = V_c % 187.43/187.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) ) ) ) ). % 187.43/187.50 % 187.43/187.50 fof(fact_xt1_I4_J,axiom, % 187.43/187.50 ! [V_c,V_a,V_b,T_a] : % 187.43/187.50 ( class_Orderings_Oorder(T_a) % 187.43/187.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 187.43/187.50 => ( V_b = V_c % 187.43/187.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_a)) ) ) ) ). % 187.43/187.50 % 187.43/187.50 fof(fact_order__antisym,axiom, % 187.43/187.50 ! [V_y,V_x,T_a] : % 187.43/187.50 ( class_Orderings_Oorder(T_a) % 187.43/187.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 187.43/187.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 187.43/187.50 => V_x = V_y ) ) ) ). % 187.43/187.50 % 187.43/187.50 fof(fact_order__trans,axiom, % 187.43/187.50 ! [V_z,V_y,V_x,T_a] : % 187.43/187.50 ( class_Orderings_Opreorder(T_a) % 187.43/187.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 187.43/187.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_z)) % 187.43/187.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z)) ) ) ) ). % 187.43/187.50 % 187.43/187.50 fof(fact_xt1_I5_J,axiom, % 187.43/187.50 ! [V_x,V_y,T_a] : % 187.43/187.50 ( class_Orderings_Oorder(T_a) % 187.43/187.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 187.43/187.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 187.43/187.50 => V_x = V_y ) ) ) ). % 187.43/187.50 % 187.43/187.50 fof(fact_xt1_I6_J,axiom, % 187.43/187.50 ! [V_z,V_x,V_y,T_a] : % 187.43/187.50 ( class_Orderings_Oorder(T_a) % 187.43/187.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 187.43/187.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_y)) % 187.43/187.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x)) ) ) ) ). % 187.43/187.50 % 187.43/187.50 fof(fact_Diff__mono,axiom, % 187.43/187.50 ! [V_B_2,V_D_2,V_C_2,V_A_2,T_a] : % 187.43/187.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) % 187.43/187.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_D_2),V_B_2)) % 187.43/187.50 => 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))) ) ) ). % 187.43/187.50 % 187.43/187.50 fof(fact_double__diff,axiom, % 187.43/187.50 ! [V_C_2,V_B_2,V_A_2,T_a] : % 187.43/187.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 187.43/187.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) % 187.43/187.50 => 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 ) ) ). % 187.43/187.50 % 187.43/187.50 fof(fact_equalityE,axiom, % 187.43/187.50 ! [T_a,V_B_2,V_A_2] : % 187.43/187.50 ( V_A_2 = V_B_2 % 187.43/187.50 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 187.43/187.50 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) ) ) ). % 187.43/187.50 % 187.43/187.50 fof(fact_le__funE,axiom, % 187.43/187.50 ! [V_x_2,V_g_2,V_f_2,T_a,T_b] : % 187.43/187.50 ( class_Orderings_Oord(T_b) % 187.43/187.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_f_2),V_g_2)) % 187.43/187.50 => 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))) ) ) ). % 187.43/187.50 % 187.43/187.50 fof(fact_DiffD1,axiom, % 187.43/187.50 ! [V_B_2,V_A_2,V_c_2,T_a] : % 187.43/187.50 ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 187.43/187.50 => hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) ) ). % 187.43/187.50 % 187.43/187.50 fof(fact_DiffD2,axiom, % 187.43/187.50 ! [V_B_2,V_A_2,V_c_2,T_a] : % 187.43/187.50 ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 187.43/187.50 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2)) ) ). % 187.43/187.50 % 187.43/187.50 fof(fact_linorder__le__cases,axiom, % 187.43/187.50 ! [V_y,V_x,T_a] : % 187.43/187.50 ( class_Orderings_Olinorder(T_a) % 187.43/187.50 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 187.43/187.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ). % 187.43/187.50 % 187.43/187.50 fof(fact_com_Osimps_I4_J,axiom, % 187.43/187.50 ! [V_com2_H_2,V_com1_H_2,V_fun_H_2,V_com2_2,V_com1_2,V_fun_2] : % 187.43/187.50 ( 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) % 187.43/187.50 <=> ( V_fun_2 = V_fun_H_2 % 187.43/187.50 & V_com1_2 = V_com1_H_2 % 187.43/187.50 & V_com2_2 = V_com2_H_2 ) ) ). % 187.43/187.50 % 187.43/187.50 fof(fact_insert__Diff1,axiom, % 187.43/187.50 ! [V_A_2,V_B_2,V_x_2,T_a] : % 187.43/187.50 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) % 187.43/187.50 => 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) ) ). % 187.43/187.50 % 187.43/187.50 fof(fact_insert__Diff__if,axiom, % 187.43/187.50 ! [V_A_2,V_B_2,V_x_2,T_a] : % 187.43/187.50 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) % 187.43/187.50 => 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) ) % 187.43/187.50 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) % 187.43/187.50 => 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)) ) ) ). % 187.43/187.50 % 187.43/187.50 fof(fact_subset__insert,axiom, % 187.43/187.50 ! [V_B_2,V_A_2,V_x_2,T_a] : % 187.43/187.50 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 187.43/187.50 => ( 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))) % 187.43/187.50 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ). % 187.43/187.50 % 187.43/187.50 fof(fact_insert__subset,axiom, % 187.43/187.50 ! [V_B_2,V_A_2,V_x_2,T_a] : % 187.43/187.50 ( 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)) % 187.43/187.50 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) % 187.43/187.50 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ). % 187.43/187.50 % 187.43/187.50 fof(fact_subset__insert__iff,axiom, % 187.43/187.50 ! [V_B_2,V_x_2,V_A_2,T_a] : % 187.43/187.50 ( 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))) % 187.43/187.50 <=> ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 187.43/187.50 => 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)) ) % 187.43/187.50 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 187.43/187.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ). % 187.43/187.50 % 187.43/187.50 fof(fact_diff__single__insert,axiom, % 187.43/187.50 ! [V_B_2,V_x_2,V_A_2,T_a] : % 187.43/187.50 ( 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)) % 187.43/187.50 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 187.43/187.50 => 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))) ) ) ). % 187.43/187.50 % 187.43/187.50 fof(fact_Diff__insert__absorb,axiom, % 187.43/187.50 ! [V_A_2,V_x_2,T_a] : % 187.43/187.50 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 187.43/187.50 => 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 ) ). % 187.43/187.50 % 187.43/187.50 fof(fact_insert__Diff,axiom, % 187.43/187.50 ! [V_A_2,V_a_2,T_a] : % 187.43/187.50 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 187.43/187.50 => 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 ) ). % 187.43/187.50 % 187.43/187.50 fof(fact_empty__Diff,axiom, % 187.43/187.50 ! [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)) ). % 187.43/187.50 % 187.43/187.50 fof(fact_Diff__empty,axiom, % 187.43/187.50 ! [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 ). % 187.43/187.50 % 187.43/187.50 fof(fact_Diff__cancel,axiom, % 187.43/187.50 ! [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)) ). % 187.43/187.50 % 187.43/187.50 fof(fact_finite__Diff2,axiom, % 187.43/187.50 ! [V_A_2,V_B_2,T_a] : % 187.43/187.50 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 187.43/187.50 => ( 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))) % 187.43/187.50 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ) ). % 187.43/187.50 % 187.43/187.50 fof(fact_bot__least,axiom, % 187.43/187.50 ! [V_x,T_a] : % 187.43/187.50 ( class_Orderings_Obot(T_a) % 187.43/187.50 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x)) ) ). % 187.43/187.50 % 187.43/187.50 fof(fact_all__not__in__conv,axiom, % 187.43/187.50 ! [V_A_2,T_a] : % 187.43/187.50 ( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 187.43/187.50 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 187.43/187.50 % 187.43/187.50 fof(fact_ex__in__conv,axiom, % 187.43/187.50 ! [V_A_2,T_a] : % 187.43/187.50 ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 187.43/187.50 <=> V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 187.43/187.50 % 187.43/187.50 fof(fact_empty__iff,axiom, % 187.43/187.50 ! [V_c_2,T_a] : ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ). % 187.43/187.50 % 187.43/187.50 fof(fact_equals0D,axiom, % 187.43/187.50 ! [V_a_2,T_a,V_A_2] : % 187.43/187.50 ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.43/187.50 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ). % 187.43/187.50 % 187.43/187.50 fof(fact_subset__empty,axiom, % 187.43/187.50 ! [V_A_2,T_a] : % 187.43/187.50 ( 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)))) % 187.43/187.50 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 187.43/187.50 % 187.43/187.50 fof(fact_finite__subset,axiom, % 187.43/187.50 ! [V_B_2,V_A_2,T_a] : % 187.43/187.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 187.43/187.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 187.43/187.50 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ) ). % 187.43/187.50 % 187.43/187.50 fof(fact_rev__finite__subset,axiom, % 187.43/187.50 ! [V_A_2,V_B_2,T_a] : % 187.43/187.50 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 187.43/187.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 187.43/187.50 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ) ). % 187.43/187.50 % 187.43/187.50 fof(fact_insertI1,axiom, % 187.43/187.50 ! [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))) ). % 187.43/187.50 % 187.43/187.50 fof(fact_insert__iff,axiom, % 187.43/187.50 ! [V_A_2,V_b_2,V_a_2,T_a] : % 187.43/187.50 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),V_A_2))) % 187.43/187.50 <=> ( V_a_2 = V_b_2 % 187.43/187.50 | hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ). % 187.43/187.50 % 187.43/187.50 fof(fact_insert__ident,axiom, % 187.43/187.50 ! [V_B_2,V_A_2,V_x_2,T_a] : % 187.43/187.50 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 187.43/187.50 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) % 187.43/187.50 => ( 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) % 187.43/187.50 <=> V_A_2 = V_B_2 ) ) ) ). % 187.43/187.50 % 187.43/187.50 fof(fact_insertI2,axiom, % 187.43/187.50 ! [V_b_2,V_B_2,V_a_2,T_a] : % 187.43/187.50 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_B_2)) % 187.43/187.50 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),V_B_2))) ) ). % 187.43/187.50 % 187.43/187.50 fof(fact_insert__absorb,axiom, % 187.43/187.50 ! [V_A_2,V_a_2,T_a] : % 187.43/187.50 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 187.43/187.50 => hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2) = V_A_2 ) ). % 187.43/187.50 % 187.43/187.50 fof(fact_subset__insertI,axiom, % 187.43/187.50 ! [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))) ). % 187.43/187.50 % 187.43/187.50 fof(fact_subset__insertI2,axiom, % 187.43/187.50 ! [V_b_2,V_B_2,V_A_2,T_a] : % 187.43/187.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 187.43/187.50 => 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))) ) ). % 187.43/187.50 % 187.43/187.50 fof(fact_insert__mono,axiom, % 187.43/187.50 ! [V_a_2,V_D_2,V_C_2,T_a] : % 187.43/187.50 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_D_2)) % 187.43/187.50 => 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))) ) ). % 187.43/187.50 % 187.43/187.50 fof(fact_asm,axiom, % 187.43/187.50 ! [V_Ga_2,V_ts_2,T_a] : % 187.43/187.50 ( 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)) % 187.43/187.50 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,V_ts_2) ) ). % 187.43/187.50 % 187.43/187.50 fof(fact_weaken,axiom, % 187.43/187.50 ! [V_ts_2,V_ts_H_2,V_Ga_2,T_a] : % 187.43/187.50 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,V_ts_H_2) % 187.43/187.50 => ( 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)) % 187.43/187.50 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,V_ts_2) ) ) ). % 187.43/187.50 % 187.43/187.50 fof(fact_thin,axiom, % 187.43/187.50 ! [V_Ga_2,V_ts_2,V_G_H_2,T_a] : % 187.43/187.50 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_H_2,V_ts_2) % 187.43/187.50 => ( 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)) % 187.43/187.50 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,V_ts_2) ) ) ). % 187.43/187.50 % 187.43/187.50 fof(fact_folding__idem_Oin__comp__idem,axiom, % 187.43/187.50 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 187.43/187.50 ( c_Finite__Set_Ofolding__idem(T_a,T_b,V_f_2,V_F_2) % 187.43/187.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.43/187.50 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 187.43/187.50 => 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) ) ) ) ). % 187.43/187.50 % 187.43/187.50 fof(fact_folding__idem_Osubset__comp__idem,axiom, % 187.43/187.50 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 187.43/187.50 ( c_Finite__Set_Ofolding__idem(T_a,T_b,V_f_2,V_F_2) % 187.43/187.50 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.43/187.50 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 187.43/187.50 => 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) ) ) ) ). % 187.43/187.50 % 187.43/187.50 fof(fact_evaln_Oequations_I5_J,axiom, % 187.43/187.50 ! [V_a5_2,V_a4_2,V_a2_2,V_a6_2,V_a3_2,V_a1_2] : % 187.43/187.50 ( 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)) % 187.43/187.50 <=> ( ( hBOOL(hAPP(V_a1_2,V_a2_2)) % 187.43/187.50 & hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a3_2),V_a2_2),V_a4_2),V_a5_2)) ) % 187.43/187.50 | ( ~ hBOOL(hAPP(V_a1_2,V_a2_2)) % 187.43/187.50 & hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a6_2),V_a2_2),V_a4_2),V_a5_2)) ) ) ) ). % 187.43/187.50 % 187.43/187.50 fof(fact_evaln_Oequations_I6_J,axiom, % 187.43/187.50 ! [V_a5_2,V_a4_2,V_a2_2,V_a3_2,V_a6_2,V_a1_2] : % 187.43/187.50 ( 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)) % 187.43/187.50 <=> ( ( hBOOL(hAPP(V_a1_2,V_a2_2)) % 187.43/187.50 & hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a6_2),V_a2_2),V_a4_2),V_a5_2)) ) % 187.43/187.50 | ( ~ hBOOL(hAPP(V_a1_2,V_a2_2)) % 187.43/187.50 & hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a3_2),V_a2_2),V_a4_2),V_a5_2)) ) ) ) ). % 187.43/187.50 % 187.43/187.50 fof(fact_evalc_Oequations_I5_J,axiom, % 187.43/187.51 ! [V_a4_2,V_a2_2,V_a5_2,V_a3_2,V_a1_2] : % 187.43/187.51 ( 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)) % 187.43/187.51 <=> ( ( hBOOL(hAPP(V_a1_2,V_a2_2)) % 187.43/187.51 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a3_2),V_a2_2),V_a4_2)) ) % 187.43/187.51 | ( ~ hBOOL(hAPP(V_a1_2,V_a2_2)) % 187.43/187.51 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a5_2),V_a2_2),V_a4_2)) ) ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_evalc_Oequations_I6_J,axiom, % 187.43/187.51 ! [V_a4_2,V_a2_2,V_a3_2,V_a5_2,V_a1_2] : % 187.43/187.51 ( 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)) % 187.43/187.51 <=> ( ( hBOOL(hAPP(V_a1_2,V_a2_2)) % 187.43/187.51 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a5_2),V_a2_2),V_a4_2)) ) % 187.43/187.51 | ( ~ hBOOL(hAPP(V_a1_2,V_a2_2)) % 187.43/187.51 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a3_2),V_a2_2),V_a4_2)) ) ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_WT_OIf,axiom, % 187.43/187.51 ! [V_b_2,V_c1_2,V_c0_2] : % 187.43/187.51 ( hBOOL(hAPP(c_Com_OWT,V_c0_2)) % 187.43/187.51 => ( hBOOL(hAPP(c_Com_OWT,V_c1_2)) % 187.43/187.51 => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(V_b_2,V_c0_2,V_c1_2))) ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_WT_Oequations_I5_J,axiom, % 187.43/187.51 ! [V_a2_2,V_a1_2,V_a3_2] : % 187.43/187.51 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OCond(V_a3_2,V_a1_2,V_a2_2))) % 187.43/187.51 <=> ( hBOOL(hAPP(c_Com_OWT,V_a1_2)) % 187.43/187.51 & hBOOL(hAPP(c_Com_OWT,V_a2_2)) ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_com_Osimps_I55_J,axiom, % 187.43/187.51 ! [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) ). % 187.43/187.51 % 187.43/187.51 fof(fact_com_Osimps_I54_J,axiom, % 187.43/187.51 ! [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) ). % 187.43/187.51 % 187.43/187.51 fof(fact_com_Osimps_I53_J,axiom, % 187.43/187.51 ! [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) ). % 187.43/187.51 % 187.43/187.51 fof(fact_com_Osimps_I52_J,axiom, % 187.43/187.51 ! [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) ). % 187.43/187.51 % 187.43/187.51 fof(fact_com_Osimps_I45_J,axiom, % 187.43/187.51 ! [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) ). % 187.43/187.51 % 187.43/187.51 fof(fact_com_Osimps_I44_J,axiom, % 187.43/187.51 ! [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) ). % 187.43/187.51 % 187.43/187.51 fof(fact_com_Osimps_I57_J,axiom, % 187.43/187.51 ! [V_com2_2,V_com1_2,V_fun_2,V_fun_H_2,V_pname_H_2,V_vname_H_2] : c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2) != c_Com_Ocom_OCond(V_fun_2,V_com1_2,V_com2_2) ). % 187.43/187.51 % 187.43/187.51 fof(fact_com_Osimps_I56_J,axiom, % 187.43/187.51 ! [V_fun_H_2,V_pname_H_2,V_vname_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_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2) ). % 187.43/187.51 % 187.43/187.51 fof(fact_com_Osimps_I15_J,axiom, % 187.43/187.51 ! [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 ). % 187.43/187.51 % 187.43/187.51 fof(fact_com_Osimps_I14_J,axiom, % 187.43/187.51 ! [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) ). % 187.43/187.51 % 187.43/187.51 fof(fact_Least__le,axiom, % 187.43/187.51 ! [V_k_2,V_P_2,T_a] : % 187.43/187.51 ( class_Orderings_Owellorder(T_a) % 187.43/187.51 => ( hBOOL(hAPP(V_P_2,V_k_2)) % 187.43/187.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Orderings_Oord__class_OLeast(T_a,V_P_2)),V_k_2)) ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_Diff__insert,axiom, % 187.43/187.51 ! [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)))) ). % 187.43/187.51 % 187.43/187.51 fof(fact_Diff__insert2,axiom, % 187.43/187.51 ! [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) ). % 187.43/187.51 % 187.43/187.51 fof(fact_insert__Diff__single,axiom, % 187.43/187.51 ! [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) ). % 187.43/187.51 % 187.43/187.51 fof(fact_finite__Diff__insert,axiom, % 187.43/187.51 ! [V_B_2,V_a_2,V_A_2,T_a] : % 187.43/187.51 ( 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)))) % 187.43/187.51 <=> 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))) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_folding__one_Oremove,axiom, % 187.43/187.51 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_a] : % 187.43/187.51 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2) % 187.43/187.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.43/187.51 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 187.43/187.51 => ( ( 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)) % 187.43/187.51 => hAPP(V_F_2,V_A_2) = V_x_2 ) % 187.43/187.51 & ( 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)) % 187.43/187.51 => 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)))))) ) ) ) ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_singleton__iff,axiom, % 187.43/187.51 ! [V_a_2,V_b_2,T_a] : % 187.43/187.51 ( 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))))) % 187.43/187.51 <=> V_b_2 = V_a_2 ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_singletonE,axiom, % 187.43/187.51 ! [V_a_2,V_b_2,T_a] : % 187.43/187.51 ( 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))))) % 187.43/187.51 => V_b_2 = V_a_2 ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_subset__singletonD,axiom, % 187.43/187.51 ! [V_x_2,V_A_2,T_a] : % 187.43/187.51 ( 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))))) % 187.43/187.51 => ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.43/187.51 | 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))) ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_domIff,axiom, % 187.43/187.51 ! [V_m_2,T_b,V_a_2,T_a] : % 187.43/187.51 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Map_Odom(T_a,T_b,V_m_2))) % 187.43/187.51 <=> hAPP(V_m_2,V_a_2) != c_Option_Ooption_ONone(T_b) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_folding__idem_Oidem__comp,axiom, % 187.43/187.51 ! [V_x_2,V_F_2,V_f_2,T_b,T_a] : % 187.43/187.51 ( c_Finite__Set_Ofolding__idem(T_a,T_b,V_f_2,V_F_2) % 187.43/187.51 => 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) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_folding__idem_Oidem__left__comp,axiom, % 187.43/187.51 ! [V_g_2,V_x_2,T_c,V_F_2,V_f_2,T_b,T_a] : % 187.43/187.51 ( c_Finite__Set_Ofolding__idem(T_a,T_b,V_f_2,V_F_2) % 187.43/187.51 => 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) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_folding__one__idem_Oin__idem,axiom, % 187.43/187.51 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_a] : % 187.43/187.51 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2) % 187.43/187.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.43/187.51 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 187.43/187.51 => hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,V_A_2)) = hAPP(V_F_2,V_A_2) ) ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_folding__image__simple__idem_Oin__idem,axiom, % 187.43/187.51 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 187.43/187.51 ( c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 187.43/187.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.43/187.51 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 187.43/187.51 => 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) ) ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_folding__image__simple__idem_Osubset__idem,axiom, % 187.43/187.51 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 187.43/187.51 ( c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 187.43/187.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.43/187.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 187.43/187.51 => 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) ) ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_dom__minus,axiom, % 187.43/187.51 ! [V_A_2,T_b,T_a,V_x_2,V_f_2] : % 187.43/187.51 ( hAPP(V_f_2,V_x_2) = c_Option_Ooption_ONone(T_a) % 187.43/187.51 => 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) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_o__eq__elim,axiom, % 187.43/187.51 ! [V_d_2,V_c_2,T_d,V_b_2,V_a_2,T_a,T_b,T_c] : % 187.43/187.51 ( hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_a_2),V_b_2) = hAPP(c_Fun_Ocomp(T_d,T_b,T_a,V_c_2),V_d_2) % 187.43/187.51 => ! [B_v] : hAPP(V_a_2,hAPP(V_b_2,B_v)) = hAPP(V_c_2,hAPP(V_d_2,B_v)) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_o__eq__dest,axiom, % 187.43/187.51 ! [V_v_2,V_d_2,V_c_2,T_d,V_b_2,V_a_2,T_a,T_b,T_c] : % 187.43/187.51 ( hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_a_2),V_b_2) = hAPP(c_Fun_Ocomp(T_d,T_b,T_a,V_c_2),V_d_2) % 187.43/187.51 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_c_2,hAPP(V_d_2,V_v_2)) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_o__eq__dest__lhs,axiom, % 187.43/187.51 ! [V_v_2,V_c_2,V_b_2,V_a_2,T_a,T_b,T_c] : % 187.43/187.51 ( hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_a_2),V_b_2) = V_c_2 % 187.43/187.51 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_c_2,V_v_2) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_o__apply,axiom, % 187.43/187.51 ! [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)) ). % 187.43/187.51 % 187.43/187.51 fof(fact_o__assoc,axiom, % 187.43/187.51 ! [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) ). % 187.43/187.51 % 187.43/187.51 fof(fact_com_Osize_I7_J,axiom, % 187.43/187.51 ! [V_pname] : c_Com_Ocom_Ocom__size(hAPP(c_Com_Ocom_OBODY,V_pname)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 187.43/187.51 % 187.43/187.51 fof(fact_le__iff__diff__le__0,axiom, % 187.43/187.51 ! [V_b_2,V_a_2,T_a] : % 187.43/187.51 ( class_Groups_Oordered__ab__group__add(T_a) % 187.43/187.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) % 187.43/187.51 <=> 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))) ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_folding_Oremove,axiom, % 187.43/187.51 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 187.43/187.51 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 187.43/187.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.43/187.51 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 187.43/187.51 => 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)) ) ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_folding__image__simple_Oremove,axiom, % 187.43/187.51 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 187.43/187.51 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 187.43/187.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.43/187.51 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 187.43/187.51 => 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)))))) ) ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_fun__diff__def,axiom, % 187.43/187.51 ! [V_x_2,V_B_2,V_A_2,T_b,T_a] : % 187.43/187.51 ( class_Groups_Ominus(T_a) % 187.43/187.51 => 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)) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_pred__subset__eq,axiom, % 187.43/187.51 ! [V_S_2,V_R_2,T_a] : % 187.43/187.51 ( 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))) % 187.43/187.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_R_2),V_S_2)) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_flat__lub__def,axiom, % 187.43/187.51 ! [V_b_2,V_A_2,T_a] : % 187.43/187.51 ( ( 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))))) % 187.43/187.51 => c_Partial__Function_Oflat__lub(T_a,V_b_2,V_A_2) = V_b_2 ) % 187.43/187.51 & ( ~ 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))))) % 187.43/187.51 => 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)))))) ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_bot__empty__eq,axiom, % 187.43/187.51 ! [V_x_2,T_a] : % 187.43/187.51 ( hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),V_x_2)) % 187.43/187.51 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_folding_Oinsert__remove,axiom, % 187.43/187.51 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 187.43/187.51 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 187.43/187.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.43/187.51 => 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)) ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_folding__image__simple_Oinsert__remove,axiom, % 187.43/187.51 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 187.43/187.51 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 187.43/187.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.43/187.51 => 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)))))) ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_minus__apply,axiom, % 187.43/187.51 ! [V_x_2,V_B_2,V_A_2,T_b,T_a] : % 187.43/187.51 ( class_Groups_Ominus(T_a) % 187.43/187.51 => 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)) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_right__minus__eq,axiom, % 187.43/187.51 ! [V_b_2,V_a_2,T_a] : % 187.43/187.51 ( class_Groups_Ogroup__add(T_a) % 187.43/187.51 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a) % 187.43/187.51 <=> V_a_2 = V_b_2 ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_le0,axiom, % 187.43/187.51 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ). % 187.43/187.51 % 187.43/187.51 fof(fact_diff__is__0__eq_H,axiom, % 187.43/187.51 ! [V_n,V_m] : % 187.43/187.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 187.43/187.51 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_diff__is__0__eq,axiom, % 187.43/187.51 ! [V_n_2,V_m_2] : % 187.43/187.51 ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 187.43/187.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_Suc__diff__le,axiom, % 187.43/187.51 ! [V_m,V_n] : % 187.43/187.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 187.43/187.51 => 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)) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_diff__0__eq__0,axiom, % 187.43/187.51 ! [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) ). % 187.43/187.51 % 187.43/187.51 fof(fact_minus__nat_Odiff__0,axiom, % 187.43/187.51 ! [V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ). % 187.43/187.51 % 187.43/187.51 fof(fact_diff__self__eq__0,axiom, % 187.43/187.51 ! [V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 187.43/187.51 % 187.43/187.51 fof(fact_diffs0__imp__equal,axiom, % 187.43/187.51 ! [V_n,V_m] : % 187.43/187.51 ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 187.43/187.51 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 187.43/187.51 => V_m = V_n ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_diff__Suc__Suc,axiom, % 187.43/187.51 ! [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) ). % 187.43/187.51 % 187.43/187.51 fof(fact_Suc__diff__diff,axiom, % 187.43/187.51 ! [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) ). % 187.43/187.51 % 187.43/187.51 fof(fact_less__eq__nat_Osimps_I1_J,axiom, % 187.43/187.51 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ). % 187.43/187.51 % 187.43/187.51 fof(fact_le__0__eq,axiom, % 187.43/187.51 ! [V_n_2] : % 187.43/187.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) % 187.43/187.51 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_Suc__n__not__le__n,axiom, % 187.43/187.51 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n)),V_n)) ). % 187.43/187.51 % 187.43/187.51 fof(fact_not__less__eq__eq,axiom, % 187.43/187.51 ! [V_n_2,V_m_2] : % 187.43/187.51 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 187.43/187.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_le__Suc__eq,axiom, % 187.43/187.51 ! [V_n_2,V_m_2] : % 187.43/187.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) % 187.43/187.51 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 187.43/187.51 | V_m_2 = hAPP(c_Nat_OSuc,V_n_2) ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_Suc__le__mono,axiom, % 187.43/187.51 ! [V_m_2,V_n_2] : % 187.43/187.51 ( 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))) % 187.43/187.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_le__SucI,axiom, % 187.43/187.51 ! [V_n,V_m] : % 187.43/187.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 187.43/187.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_le__SucE,axiom, % 187.43/187.51 ! [V_n,V_m] : % 187.43/187.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) % 187.43/187.51 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 187.43/187.51 => V_m = hAPP(c_Nat_OSuc,V_n) ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_Suc__leD,axiom, % 187.43/187.51 ! [V_n,V_m] : % 187.43/187.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) % 187.43/187.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_evaln__nonstrict,axiom, % 187.43/187.51 ! [V_m,V_t,V_n,V_s,V_c] : % 187.43/187.51 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c),V_s),V_n),V_t)) % 187.43/187.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 187.43/187.51 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c),V_s),V_m),V_t)) ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_folding_Ocommute__left__comp,axiom, % 187.43/187.51 ! [V_g_2,V_x_2,V_y_2,T_c,V_F_2,V_f_2,T_b,T_a] : % 187.43/187.51 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 187.43/187.51 => 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)) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_folding_Ocommute__comp,axiom, % 187.43/187.51 ! [V_x_2,V_y_2,V_F_2,V_f_2,T_b,T_a] : % 187.43/187.51 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 187.43/187.51 => 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)) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_folding_Ocommute__comps_I1_J,axiom, % 187.43/187.51 ! [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] : % 187.43/187.51 ( c_Finite__Set_Ofolding(T_a,T_b,V_fa_2,V_F_2) % 187.43/187.51 => 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) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_folding__image__simple_Oempty,axiom, % 187.43/187.51 ! [V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 187.43/187.51 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 187.43/187.51 => hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = V_z_2 ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_eq__mem,axiom, % 187.43/187.51 ! [V_y_2,V_x_2,T_a] : % 187.43/187.51 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_fequal,V_y_2))) % 187.43/187.51 <=> V_x_2 = V_y_2 ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_zero__reorient,axiom, % 187.43/187.51 ! [V_x_2,T_a] : % 187.43/187.51 ( class_Groups_Ozero(T_a) % 187.43/187.51 => ( c_Groups_Ozero__class_Ozero(T_a) = V_x_2 % 187.43/187.51 <=> V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_folding_Ocommute__left__comp_H_H,axiom, % 187.43/187.51 ! [V_g_2,T_c,V_B_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 187.43/187.51 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 187.43/187.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.43/187.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 187.43/187.51 => 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)) ) ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_folding_Ocommute__comp_H_H,axiom, % 187.43/187.51 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 187.43/187.51 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 187.43/187.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.43/187.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 187.43/187.51 => 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)) ) ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_folding_Ocommute__left__comp_H,axiom, % 187.43/187.51 ! [V_g_2,V_x_2,T_c,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 187.43/187.51 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 187.43/187.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.43/187.51 => 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)) ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_folding_Ocommute__comp_H,axiom, % 187.43/187.51 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 187.43/187.51 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 187.43/187.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.43/187.51 => 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)) ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_diff__eq__diff__eq,axiom, % 187.43/187.51 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] : % 187.43/187.51 ( class_Groups_Oab__group__add(T_a) % 187.43/187.51 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_c_2),V_d_2) % 187.43/187.51 => ( V_a_2 = V_b_2 % 187.43/187.51 <=> V_c_2 = V_d_2 ) ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_rev__predicate1D,axiom, % 187.43/187.51 ! [V_Q_2,T_a,V_x_2,V_P_2] : % 187.43/187.51 ( hBOOL(hAPP(V_P_2,V_x_2)) % 187.43/187.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_P_2),V_Q_2)) % 187.43/187.51 => hBOOL(hAPP(V_Q_2,V_x_2)) ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_predicate1D,axiom, % 187.43/187.51 ! [V_x_2,V_Q_2,V_P_2,T_a] : % 187.43/187.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_P_2),V_Q_2)) % 187.43/187.51 => ( hBOOL(hAPP(V_P_2,V_x_2)) % 187.43/187.51 => hBOOL(hAPP(V_Q_2,V_x_2)) ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_pred__equals__eq,axiom, % 187.43/187.51 ! [V_S_2,V_R_2,T_a] : % 187.43/187.51 ( 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) % 187.43/187.51 <=> V_R_2 = V_S_2 ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_folding__image__simple_Oinsert,axiom, % 187.43/187.51 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 187.43/187.51 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 187.43/187.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.43/187.51 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 187.43/187.51 => 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)) ) ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_folding_Oinsert,axiom, % 187.43/187.51 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 187.43/187.51 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 187.43/187.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.43/187.51 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 187.43/187.51 => 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)) ) ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_diff__eq__diff__less__eq,axiom, % 187.43/187.51 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] : % 187.43/187.51 ( class_Groups_Oordered__ab__group__add(T_a) % 187.43/187.51 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_c_2),V_d_2) % 187.43/187.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) % 187.43/187.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c_2),V_d_2)) ) ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_diff__0__right,axiom, % 187.43/187.51 ! [V_a,T_a] : % 187.43/187.51 ( class_Groups_Ogroup__add(T_a) % 187.43/187.51 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_diff__self,axiom, % 187.43/187.51 ! [V_a,T_a] : % 187.43/187.51 ( class_Groups_Ogroup__add(T_a) % 187.43/187.51 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_eq__iff__diff__eq__0,axiom, % 187.43/187.51 ! [V_b_2,V_a_2,T_a] : % 187.43/187.51 ( class_Groups_Oab__group__add(T_a) % 187.43/187.51 => ( V_a_2 = V_b_2 % 187.43/187.51 <=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_folding__one_Oclosed,axiom, % 187.43/187.51 ! [V_A_2,V_F_2,V_f_2,T_a] : % 187.43/187.51 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2) % 187.43/187.51 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.43/187.51 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.43/187.51 => ( ! [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)))))) % 187.43/187.51 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(V_F_2,V_A_2)),V_A_2)) ) ) ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_finite__empty__induct,axiom, % 187.43/187.51 ! [V_P_2,V_A_2,T_a] : % 187.43/187.51 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.43/187.51 => ( hBOOL(hAPP(V_P_2,V_A_2)) % 187.43/187.51 => ( ! [B_a,B_A] : % 187.43/187.51 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),B_A)) % 187.43/187.51 => ( hBOOL(hAPP(hAPP(c_member(T_a),B_a),B_A)) % 187.43/187.51 => ( hBOOL(hAPP(V_P_2,B_A)) % 187.43/187.51 => 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)))))) ) ) ) % 187.43/187.51 => hBOOL(hAPP(V_P_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ) ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_finite__subset__induct,axiom, % 187.43/187.51 ! [V_P_2,V_A_2,V_F_2,T_a] : % 187.43/187.51 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) % 187.43/187.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_F_2),V_A_2)) % 187.43/187.51 => ( hBOOL(hAPP(V_P_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) % 187.43/187.51 => ( ! [B_a,B_F] : % 187.43/187.51 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),B_F)) % 187.43/187.51 => ( hBOOL(hAPP(hAPP(c_member(T_a),B_a),V_A_2)) % 187.43/187.51 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),B_a),B_F)) % 187.43/187.51 => ( hBOOL(hAPP(V_P_2,B_F)) % 187.43/187.51 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Set_Oinsert(T_a),B_a),B_F))) ) ) ) ) % 187.43/187.51 => hBOOL(hAPP(V_P_2,V_F_2)) ) ) ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_card__Suc__Diff1,axiom, % 187.43/187.51 ! [V_x_2,V_A_2,T_a] : % 187.43/187.51 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.43/187.51 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 187.43/187.51 => 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) ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_fun__left__comm__idem__remove,axiom, % 187.43/187.51 ! [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))))) ). % 187.43/187.51 % 187.43/187.51 fof(fact_fold1Set_Ointros,axiom, % 187.43/187.51 ! [V_x_2,V_A_2,V_a_2,V_f_2,T_a] : % 187.43/187.51 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_a,V_f_2,V_a_2,V_A_2),V_x_2)) % 187.43/187.51 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 187.43/187.51 => 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)) ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_dom__fun__upd,axiom, % 187.43/187.51 ! [V_x_2,V_f_2,T_b,T_a,V_y_2] : % 187.43/187.51 ( ( V_y_2 = c_Option_Ooption_ONone(T_a) % 187.43/187.51 => 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)))) ) % 187.43/187.51 & ( V_y_2 != c_Option_Ooption_ONone(T_a) % 187.43/187.51 => 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)) ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_psubset__insert__iff,axiom, % 187.43/187.51 ! [V_B_2,V_x_2,V_A_2,T_a] : % 187.43/187.51 ( 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))) % 187.43/187.51 <=> ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) % 187.43/187.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) % 187.43/187.51 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) % 187.43/187.51 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 187.43/187.51 => 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)) ) % 187.43/187.51 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 187.43/187.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_finite__induct,axiom, % 187.43/187.51 ! [V_P_2,V_F_2,T_a] : % 187.43/187.51 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) % 187.43/187.51 => ( hBOOL(hAPP(V_P_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) % 187.43/187.51 => ( ! [B_x,B_F] : % 187.43/187.51 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),B_F)) % 187.43/187.51 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),B_F)) % 187.43/187.51 => ( hBOOL(hAPP(V_P_2,B_F)) % 187.43/187.51 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Set_Oinsert(T_a),B_x),B_F))) ) ) ) % 187.43/187.51 => hBOOL(hAPP(V_P_2,V_F_2)) ) ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_fold__graph_H_Ointros_I2_J,axiom, % 187.43/187.51 ! [V_y_2,V_z_2,V_f_2,T_b,V_A_2,V_x_2,T_a] : % 187.43/187.51 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 187.43/187.51 => ( 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) % 187.43/187.51 => 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)) ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_fun__upd__triv,axiom, % 187.43/187.51 ! [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 ). % 187.43/187.51 % 187.43/187.51 fof(fact_le__refl,axiom, % 187.43/187.51 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_n)) ). % 187.43/187.51 % 187.43/187.51 fof(fact_diff__le__self,axiom, % 187.43/187.51 ! [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)) ). % 187.43/187.51 % 187.43/187.51 fof(fact_nat__le__linear,axiom, % 187.43/187.51 ! [V_n,V_m] : % 187.43/187.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 187.43/187.51 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_diff__commute,axiom, % 187.43/187.51 ! [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) ). % 187.43/187.51 % 187.43/187.51 fof(fact_eq__imp__le,axiom, % 187.43/187.51 ! [V_n,V_m] : % 187.43/187.51 ( V_m = V_n % 187.43/187.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_diff__le__mono2,axiom, % 187.43/187.51 ! [V_l,V_n,V_m] : % 187.43/187.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 187.43/187.51 => 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))) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_diff__le__mono,axiom, % 187.43/187.51 ! [V_l,V_n,V_m] : % 187.43/187.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 187.43/187.51 => 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))) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_diff__diff__cancel,axiom, % 187.43/187.51 ! [V_n,V_i] : % 187.43/187.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_n)) % 187.43/187.51 => 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 ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_le__trans,axiom, % 187.43/187.51 ! [V_k,V_j,V_i] : % 187.43/187.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 187.43/187.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_k)) % 187.43/187.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_k)) ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_le__antisym,axiom, % 187.43/187.51 ! [V_n,V_m] : % 187.43/187.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 187.43/187.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 187.43/187.51 => V_m = V_n ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_eq__diff__iff,axiom, % 187.43/187.51 ! [V_n_2,V_m_2,V_k_2] : % 187.43/187.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2)) % 187.43/187.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2)) % 187.43/187.51 => ( 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) % 187.43/187.51 <=> V_m_2 = V_n_2 ) ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_Nat_Odiff__diff__eq,axiom, % 187.43/187.51 ! [V_n,V_m,V_k] : % 187.43/187.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_m)) % 187.43/187.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) % 187.43/187.51 => 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) ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_le__diff__iff,axiom, % 187.43/187.51 ! [V_n_2,V_m_2,V_k_2] : % 187.43/187.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2)) % 187.43/187.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2)) % 187.43/187.51 => ( 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))) % 187.43/187.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_fun__left__comm__idem_Ofun__left__idem,axiom, % 187.43/187.51 ! [V_z_2,V_x_2,V_f_2,T_b,T_a] : % 187.43/187.51 ( c_Finite__Set_Ofun__left__comm__idem(T_a,T_b,V_f_2) % 187.43/187.51 => 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) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_order__less__irrefl,axiom, % 187.43/187.51 ! [V_x,T_a] : % 187.43/187.51 ( class_Orderings_Opreorder(T_a) % 187.43/187.51 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_x)) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_linorder__neq__iff,axiom, % 187.43/187.51 ! [V_y_2,V_x_2,T_a] : % 187.43/187.51 ( class_Orderings_Olinorder(T_a) % 187.43/187.51 => ( V_x_2 != V_y_2 % 187.43/187.51 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 187.43/187.51 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_x_2)) ) ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_not__less__iff__gr__or__eq,axiom, % 187.43/187.51 ! [V_y_2,V_x_2,T_a] : % 187.43/187.51 ( class_Orderings_Olinorder(T_a) % 187.43/187.51 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 187.43/187.51 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_x_2)) % 187.43/187.51 | V_x_2 = V_y_2 ) ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_linorder__less__linear,axiom, % 187.43/187.51 ! [V_y,V_x,T_a] : % 187.43/187.51 ( class_Orderings_Olinorder(T_a) % 187.43/187.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 187.43/187.51 | V_x = V_y % 187.43/187.51 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_linorder__antisym__conv3,axiom, % 187.43/187.51 ! [V_x_2,V_y_2,T_a] : % 187.43/187.51 ( class_Orderings_Olinorder(T_a) % 187.43/187.51 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_x_2)) % 187.43/187.51 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 187.43/187.51 <=> V_x_2 = V_y_2 ) ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_linorder__neqE,axiom, % 187.43/187.51 ! [V_y,V_x,T_a] : % 187.43/187.51 ( class_Orderings_Olinorder(T_a) % 187.43/187.51 => ( V_x != V_y % 187.43/187.51 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 187.43/187.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_less__imp__neq,axiom, % 187.43/187.51 ! [V_y,V_x,T_a] : % 187.43/187.51 ( class_Orderings_Oorder(T_a) % 187.43/187.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 187.43/187.51 => V_x != V_y ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_order__less__not__sym,axiom, % 187.43/187.51 ! [V_y,V_x,T_a] : % 187.43/187.51 ( class_Orderings_Opreorder(T_a) % 187.43/187.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 187.43/187.51 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_order__less__imp__not__less,axiom, % 187.43/187.51 ! [V_y,V_x,T_a] : % 187.43/187.51 ( class_Orderings_Opreorder(T_a) % 187.43/187.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 187.43/187.51 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_order__less__imp__not__eq,axiom, % 187.43/187.51 ! [V_y,V_x,T_a] : % 187.43/187.51 ( class_Orderings_Oorder(T_a) % 187.43/187.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 187.43/187.51 => V_x != V_y ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_order__less__imp__not__eq2,axiom, % 187.43/187.51 ! [V_y,V_x,T_a] : % 187.43/187.51 ( class_Orderings_Oorder(T_a) % 187.43/187.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 187.43/187.51 => V_y != V_x ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_order__less__asym_H,axiom, % 187.43/187.51 ! [V_b,V_a,T_a] : % 187.43/187.51 ( class_Orderings_Opreorder(T_a) % 187.43/187.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 187.43/187.51 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_xt1_I9_J,axiom, % 187.43/187.51 ! [V_a,V_b,T_a] : % 187.43/187.51 ( class_Orderings_Oorder(T_a) % 187.43/187.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 187.43/187.51 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_ord__eq__less__trans,axiom, % 187.43/187.51 ! [V_c,V_b,V_a,T_a] : % 187.43/187.51 ( class_Orderings_Oord(T_a) % 187.43/187.51 => ( V_a = V_b % 187.43/187.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c)) % 187.43/187.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)) ) ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_xt1_I1_J,axiom, % 187.43/187.51 ! [V_c,V_b,V_a,T_a] : % 187.43/187.51 ( class_Orderings_Oorder(T_a) % 187.43/187.51 => ( V_a = V_b % 187.43/187.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_b)) % 187.43/187.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)) ) ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_psubset__trans,axiom, % 187.43/187.51 ! [V_C_2,V_B_2,V_A_2,T_a] : % 187.43/187.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 187.43/187.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) % 187.43/187.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_ord__less__eq__trans,axiom, % 187.43/187.51 ! [V_c,V_b,V_a,T_a] : % 187.43/187.51 ( class_Orderings_Oord(T_a) % 187.43/187.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 187.43/187.51 => ( V_b = V_c % 187.43/187.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)) ) ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_xt1_I2_J,axiom, % 187.43/187.51 ! [V_c,V_a,V_b,T_a] : % 187.43/187.51 ( class_Orderings_Oorder(T_a) % 187.43/187.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 187.43/187.51 => ( V_b = V_c % 187.43/187.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)) ) ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_order__less__trans,axiom, % 187.43/187.51 ! [V_z,V_y,V_x,T_a] : % 187.43/187.51 ( class_Orderings_Opreorder(T_a) % 187.43/187.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 187.43/187.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z)) % 187.43/187.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_xt1_I10_J,axiom, % 187.43/187.51 ! [V_z,V_x,V_y,T_a] : % 187.43/187.51 ( class_Orderings_Oorder(T_a) % 187.43/187.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) % 187.43/187.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y)) % 187.43/187.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_order__less__asym,axiom, % 187.43/187.51 ! [V_y,V_x,T_a] : % 187.43/187.51 ( class_Orderings_Opreorder(T_a) % 187.43/187.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 187.43/187.51 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_linorder__cases,axiom, % 187.43/187.51 ! [V_y,V_x,T_a] : % 187.43/187.51 ( class_Orderings_Olinorder(T_a) % 187.43/187.51 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 187.43/187.51 => ( V_x != V_y % 187.43/187.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_fun__upd__idem__iff,axiom, % 187.43/187.51 ! [V_y_2,V_x_2,V_f_2,T_b,T_a] : % 187.43/187.51 ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_x_2),V_y_2) = V_f_2 % 187.43/187.51 <=> hAPP(V_f_2,V_x_2) = V_y_2 ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_fun__upd__upd,axiom, % 187.43/187.51 ! [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) ). % 187.43/187.51 % 187.43/187.51 fof(fact_fun__upd__same,axiom, % 187.43/187.51 ! [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 ). % 187.43/187.51 % 187.43/187.51 fof(fact_fun__upd__apply,axiom, % 187.43/187.51 ! [V_y_2,V_f_2,T_b,T_a,V_x_2,V_z_2] : % 187.43/187.51 ( ( V_z_2 = V_x_2 % 187.43/187.51 => 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 ) % 187.43/187.51 & ( V_z_2 != V_x_2 % 187.43/187.51 => 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) ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_fun__upd__twist,axiom, % 187.43/187.51 ! [V_d_2,V_b_2,V_m_2,T_b,T_a,V_c_2,V_a_2] : % 187.43/187.51 ( V_a_2 != V_c_2 % 187.43/187.51 => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_m_2),V_a_2),V_b_2)),V_c_2),V_d_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_m_2),V_c_2),V_d_2)),V_a_2),V_b_2) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_fun__upd__other,axiom, % 187.43/187.51 ! [V_y_2,V_f_2,T_b,T_a,V_x_2,V_z_2] : % 187.43/187.51 ( V_z_2 != V_x_2 % 187.43/187.51 => 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) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_fun__upd__idem,axiom, % 187.43/187.51 ! [T_a,T_b,V_y_2,V_x_2,V_f_2] : % 187.43/187.51 ( hAPP(V_f_2,V_x_2) = V_y_2 % 187.43/187.51 => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_a),V_f_2),V_x_2),V_y_2) = V_f_2 ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_fun__upd__def,axiom, % 187.43/187.51 ! [V_b_2,V_f_2,T_b,T_a,V_a_2,V_x_2] : % 187.43/187.51 ( ( V_x_2 = V_a_2 % 187.43/187.51 => 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 ) % 187.43/187.51 & ( V_x_2 != V_a_2 % 187.43/187.51 => 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) ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_fun__left__comm__idem_Ofun__left__comm__idem__apply,axiom, % 187.43/187.51 ! [V_g_2,T_c,V_f_2,T_b,T_a] : % 187.43/187.51 ( c_Finite__Set_Ofun__left__comm__idem(T_a,T_b,V_f_2) % 187.43/187.51 => 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)) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_fold__graph_H_Oequations_I1_J,axiom, % 187.43/187.51 ! [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) ). % 187.43/187.51 % 187.43/187.51 fof(fact_fold__graph_H_Ointros_I1_J,axiom, % 187.43/187.51 ! [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) ). % 187.43/187.51 % 187.43/187.51 fof(fact_less__fun__def,axiom, % 187.43/187.51 ! [V_g_2,V_f_2,T_a,T_b] : % 187.43/187.51 ( class_Orderings_Oord(T_b) % 187.43/187.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b)),V_f_2),V_g_2)) % 187.43/187.51 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_f_2),V_g_2)) % 187.43/187.51 & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_g_2),V_f_2)) ) ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_linorder__not__less,axiom, % 187.43/187.51 ! [V_y_2,V_x_2,T_a] : % 187.43/187.51 ( class_Orderings_Olinorder(T_a) % 187.43/187.51 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 187.43/187.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_linorder__not__le,axiom, % 187.43/187.51 ! [V_y_2,V_x_2,T_a] : % 187.43/187.51 ( class_Orderings_Olinorder(T_a) % 187.43/187.51 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 187.43/187.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_x_2)) ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_linorder__le__less__linear,axiom, % 187.43/187.51 ! [V_y,V_x,T_a] : % 187.43/187.51 ( class_Orderings_Olinorder(T_a) % 187.43/187.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 187.43/187.51 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_order__less__le,axiom, % 187.43/187.51 ! [V_y_2,V_x_2,T_a] : % 187.43/187.51 ( class_Orderings_Oorder(T_a) % 187.43/187.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 187.43/187.51 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 187.43/187.51 & V_x_2 != V_y_2 ) ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_less__le__not__le,axiom, % 187.43/187.51 ! [V_y_2,V_x_2,T_a] : % 187.43/187.51 ( class_Orderings_Opreorder(T_a) % 187.43/187.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 187.43/187.51 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 187.43/187.51 & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) ) ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_order__le__less,axiom, % 187.43/187.51 ! [V_y_2,V_x_2,T_a] : % 187.43/187.51 ( class_Orderings_Oorder(T_a) % 187.43/187.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 187.43/187.51 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 187.43/187.51 | V_x_2 = V_y_2 ) ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_leI,axiom, % 187.43/187.51 ! [V_y,V_x,T_a] : % 187.43/187.51 ( class_Orderings_Olinorder(T_a) % 187.43/187.51 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 187.43/187.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_not__leE,axiom, % 187.43/187.51 ! [V_x,V_y,T_a] : % 187.43/187.51 ( class_Orderings_Olinorder(T_a) % 187.43/187.51 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 187.43/187.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_linorder__antisym__conv1,axiom, % 187.43/187.51 ! [V_y_2,V_x_2,T_a] : % 187.43/187.51 ( class_Orderings_Olinorder(T_a) % 187.43/187.51 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 187.43/187.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 187.43/187.51 <=> V_x_2 = V_y_2 ) ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_order__neq__le__trans,axiom, % 187.43/187.51 ! [V_b,V_a,T_a] : % 187.43/187.51 ( class_Orderings_Oorder(T_a) % 187.43/187.51 => ( V_a != V_b % 187.43/187.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 187.43/187.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_xt1_I12_J,axiom, % 187.43/187.51 ! [V_b,V_a,T_a] : % 187.43/187.51 ( class_Orderings_Oorder(T_a) % 187.43/187.51 => ( V_a != V_b % 187.43/187.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 187.43/187.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_leD,axiom, % 187.43/187.51 ! [V_x,V_y,T_a] : % 187.43/187.51 ( class_Orderings_Olinorder(T_a) % 187.43/187.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 187.43/187.51 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_order__less__imp__le,axiom, % 187.43/187.51 ! [V_y,V_x,T_a] : % 187.43/187.51 ( class_Orderings_Opreorder(T_a) % 187.43/187.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 187.43/187.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_linorder__antisym__conv2,axiom, % 187.43/187.51 ! [V_y_2,V_x_2,T_a] : % 187.43/187.51 ( class_Orderings_Olinorder(T_a) % 187.43/187.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 187.43/187.51 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 187.43/187.51 <=> V_x_2 = V_y_2 ) ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_order__le__imp__less__or__eq,axiom, % 187.43/187.51 ! [V_y,V_x,T_a] : % 187.43/187.51 ( class_Orderings_Oorder(T_a) % 187.43/187.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 187.43/187.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 187.43/187.51 | V_x = V_y ) ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_order__le__neq__trans,axiom, % 187.43/187.51 ! [V_b,V_a,T_a] : % 187.43/187.51 ( class_Orderings_Oorder(T_a) % 187.43/187.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 187.43/187.51 => ( V_a != V_b % 187.43/187.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_xt1_I11_J,axiom, % 187.43/187.51 ! [V_a,V_b,T_a] : % 187.43/187.51 ( class_Orderings_Oorder(T_a) % 187.43/187.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 187.43/187.51 => ( V_a != V_b % 187.43/187.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_order__less__le__trans,axiom, % 187.43/187.51 ! [V_z,V_y,V_x,T_a] : % 187.43/187.51 ( class_Orderings_Opreorder(T_a) % 187.43/187.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 187.43/187.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_z)) % 187.43/187.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_xt1_I7_J,axiom, % 187.43/187.51 ! [V_z,V_x,V_y,T_a] : % 187.43/187.51 ( class_Orderings_Oorder(T_a) % 187.43/187.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) % 187.43/187.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_y)) % 187.43/187.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_order__le__less__trans,axiom, % 187.43/187.51 ! [V_z,V_y,V_x,T_a] : % 187.43/187.51 ( class_Orderings_Opreorder(T_a) % 187.43/187.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 187.43/187.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z)) % 187.43/187.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_xt1_I8_J,axiom, % 187.43/187.51 ! [V_z,V_x,V_y,T_a] : % 187.43/187.51 ( class_Orderings_Oorder(T_a) % 187.43/187.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 187.43/187.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y)) % 187.43/187.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_psubsetD,axiom, % 187.43/187.51 ! [V_c_2,V_B_2,V_A_2,T_a] : % 187.43/187.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 187.43/187.51 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) % 187.43/187.51 => hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2)) ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_not__psubset__empty,axiom, % 187.43/187.51 ! [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)))) ). % 187.43/187.51 % 187.43/187.51 fof(fact_diff__eq__diff__less,axiom, % 187.43/187.51 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] : % 187.43/187.51 ( class_Groups_Oordered__ab__group__add(T_a) % 187.43/187.51 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_c_2),V_d_2) % 187.43/187.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) % 187.43/187.51 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),V_d_2)) ) ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_psubset__eq,axiom, % 187.43/187.51 ! [V_B_2,V_A_2,T_a] : % 187.43/187.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 187.43/187.51 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 187.43/187.51 & V_A_2 != V_B_2 ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_subset__iff__psubset__eq,axiom, % 187.43/187.51 ! [V_B_2,V_A_2,T_a] : % 187.43/187.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 187.43/187.51 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 187.43/187.51 | V_A_2 = V_B_2 ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_psubset__imp__subset,axiom, % 187.43/187.51 ! [V_B_2,V_A_2,T_a] : % 187.43/187.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 187.43/187.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_psubset__subset__trans,axiom, % 187.43/187.51 ! [V_C_2,V_B_2,V_A_2,T_a] : % 187.43/187.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 187.43/187.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) % 187.43/187.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_subset__psubset__trans,axiom, % 187.43/187.51 ! [V_C_2,V_B_2,V_A_2,T_a] : % 187.43/187.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 187.43/187.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) % 187.43/187.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_fold__graph_Oequations_I1_J,axiom, % 187.43/187.51 ! [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)) ). % 187.43/187.51 % 187.43/187.51 fof(fact_fold__graph_OemptyI,axiom, % 187.43/187.51 ! [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)) ). % 187.43/187.51 % 187.43/187.51 fof(fact_empty__fold__graphE,axiom, % 187.43/187.51 ! [V_x_2,V_z_2,V_f_2,T_b,T_a] : % 187.43/187.51 ( 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)) % 187.43/187.51 => V_x_2 = V_z_2 ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_fold__graph__imp__finite,axiom, % 187.43/187.51 ! [V_x_2,V_A_2,V_z_2,V_f_2,T_b,T_a] : % 187.43/187.51 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),V_x_2)) % 187.43/187.51 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_empty__upd__none,axiom, % 187.43/187.51 ! [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) ). % 187.43/187.51 % 187.43/187.51 fof(fact_fun__upd__comp,axiom, % 187.43/187.51 ! [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)) ). % 187.43/187.51 % 187.43/187.51 fof(fact_not__less__Least,axiom, % 187.43/187.51 ! [V_P_2,V_k_2,T_a] : % 187.43/187.51 ( class_Orderings_Owellorder(T_a) % 187.43/187.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_k_2),c_Orderings_Oord__class_OLeast(T_a,V_P_2))) % 187.43/187.51 => ~ hBOOL(hAPP(V_P_2,V_k_2)) ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_fun__left__comm__idem__insert,axiom, % 187.43/187.51 ! [T_a] : c_Finite__Set_Ofun__left__comm__idem(T_a,tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a)) ). % 187.43/187.51 % 187.43/187.51 fof(fact_card_Oempty,axiom, % 187.43/187.51 ! [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) ). % 187.43/187.51 % 187.43/187.51 fof(fact_card__infinite,axiom, % 187.43/187.51 ! [V_A_2,T_a] : % 187.43/187.51 ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.43/187.51 => hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_card__insert__le,axiom, % 187.43/187.51 ! [V_x_2,V_A_2,T_a] : % 187.43/187.51 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.43/187.51 => 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)))) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_card__seteq,axiom, % 187.43/187.51 ! [V_A_2,V_B_2,T_a] : % 187.43/187.51 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 187.43/187.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 187.43/187.51 => ( 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))) % 187.43/187.51 => V_A_2 = V_B_2 ) ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_card__mono,axiom, % 187.43/187.51 ! [V_A_2,V_B_2,T_a] : % 187.43/187.51 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 187.43/187.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 187.43/187.51 => 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))) ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_diff__card__le__card__Diff,axiom, % 187.43/187.51 ! [V_A_2,V_B_2,T_a] : % 187.43/187.51 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 187.43/187.51 => 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)))) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_fun__left__comm__idem_Ofun__comp__idem,axiom, % 187.43/187.51 ! [V_x_2,V_f_2,T_b,T_a] : % 187.43/187.51 ( c_Finite__Set_Ofun__left__comm__idem(T_a,T_b,V_f_2) % 187.43/187.51 => 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) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_less__iff__diff__less__0,axiom, % 187.43/187.51 ! [V_b_2,V_a_2,T_a] : % 187.43/187.51 ( class_Groups_Oordered__ab__group__add(T_a) % 187.43/187.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) % 187.43/187.51 <=> 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))) ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_fold__graph_OinsertI,axiom, % 187.43/187.51 ! [V_y_2,V_z_2,V_f_2,T_b,V_A_2,V_x_2,T_a] : % 187.43/187.51 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 187.43/187.51 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),V_y_2)) % 187.43/187.51 => 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))) ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_card__eq__0__iff,axiom, % 187.43/187.51 ! [V_A_2,T_a] : % 187.43/187.51 ( hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 187.43/187.51 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.43/187.51 | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_card__Diff__subset,axiom, % 187.43/187.51 ! [V_A_2,V_B_2,T_a] : % 187.43/187.51 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 187.43/187.51 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 187.43/187.51 => 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)) ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_card__insert__if,axiom, % 187.43/187.51 ! [V_x_2,V_A_2,T_a] : % 187.43/187.51 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.43/187.51 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 187.43/187.51 => 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) ) % 187.43/187.51 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 187.43/187.51 => 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)) ) ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_card__insert__disjoint,axiom, % 187.43/187.51 ! [V_x_2,V_A_2,T_a] : % 187.43/187.51 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.43/187.51 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 187.43/187.51 => 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)) ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_card__Diff1__le,axiom, % 187.43/187.51 ! [V_x_2,V_A_2,T_a] : % 187.43/187.51 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.43/187.51 => 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))) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_card__insert,axiom, % 187.43/187.51 ! [V_x_2,V_A_2,T_a] : % 187.43/187.51 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.43/187.51 => 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)))))) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_Diff1__fold__graph,axiom, % 187.43/187.51 ! [V_y_2,V_x_2,V_A_2,V_z_2,V_f_2,T_b,T_a] : % 187.43/187.51 ( 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)) % 187.43/187.51 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 187.43/187.51 => 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))) ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_fun__upd__None__restrict,axiom, % 187.43/187.51 ! [V_m_2,T_b,V_D_2,V_x_2,T_a] : % 187.43/187.51 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_D_2)) % 187.43/187.51 => 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))))) ) % 187.43/187.51 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_D_2)) % 187.43/187.51 => 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) ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_card__Suc__eq,axiom, % 187.43/187.51 ! [V_k_2,V_A_2,T_a] : % 187.43/187.51 ( hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = hAPP(c_Nat_OSuc,V_k_2) % 187.43/187.51 <=> ? [B_b,B_B] : % 187.43/187.51 ( V_A_2 = hAPP(hAPP(c_Set_Oinsert(T_a),B_b),B_B) % 187.43/187.51 & ~ hBOOL(hAPP(hAPP(c_member(T_a),B_b),B_B)) % 187.43/187.51 & hAPP(c_Finite__Set_Ocard(T_a),B_B) = V_k_2 % 187.43/187.51 & ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 187.43/187.51 => B_B = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_card__Diff__singleton,axiom, % 187.43/187.51 ! [V_x_2,V_A_2,T_a] : % 187.43/187.51 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.43/187.51 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 187.43/187.51 => 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)) ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_card__Diff__singleton__if,axiom, % 187.43/187.51 ! [V_x_2,V_A_2,T_a] : % 187.43/187.51 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.43/187.51 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 187.43/187.51 => 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)) ) % 187.43/187.51 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 187.43/187.51 => 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) ) ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_fold__graph_H_Oequations_I2_J,axiom, % 187.43/187.51 ! [V_a5_2,V_a1_2,V_a2_2,V_a4_2,V_a3_2,T_b,T_a] : % 187.43/187.51 ( 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)) % 187.43/187.51 <=> ( ( V_a2_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.43/187.51 & hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) = V_a4_2 ) % 187.43/187.51 | ? [B_x,B_y] : % 187.43/187.51 ( hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) = hAPP(hAPP(V_a3_2,B_x),B_y) % 187.43/187.51 & hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_a2_2)) % 187.43/187.51 & 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) ) ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_card__Diff__insert,axiom, % 187.43/187.51 ! [V_B_2,V_a_2,V_A_2,T_a] : % 187.43/187.51 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.43/187.51 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 187.43/187.51 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_B_2)) % 187.43/187.51 => 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)) ) ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_fun__upd__restrict__conv,axiom, % 187.43/187.51 ! [V_y_2,V_m_2,T_b,V_D_2,V_x_2,T_a] : % 187.43/187.51 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_D_2)) % 187.43/187.51 => 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) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_restrict__fun__upd,axiom, % 187.43/187.51 ! [V_y_2,V_m_2,T_b,V_D_2,V_x_2,T_a] : % 187.43/187.51 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_D_2)) % 187.43/187.51 => 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) ) % 187.43/187.51 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_D_2)) % 187.43/187.51 => 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) ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_card__Diff1__less,axiom, % 187.43/187.51 ! [V_x_2,V_A_2,T_a] : % 187.43/187.51 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.43/187.51 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 187.43/187.51 => 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))) ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_card__Diff2__less,axiom, % 187.43/187.51 ! [V_y_2,V_x_2,V_A_2,T_a] : % 187.43/187.51 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.43/187.51 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 187.43/187.51 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) % 187.43/187.51 => 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))) ) ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_less__zeroE,axiom, % 187.43/187.51 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 187.43/187.51 % 187.43/187.51 fof(fact_lessI,axiom, % 187.43/187.51 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_n))) ). % 187.43/187.51 % 187.43/187.51 fof(fact_Suc__mono,axiom, % 187.43/187.51 ! [V_n,V_m] : % 187.43/187.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 187.43/187.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n))) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_zero__less__Suc,axiom, % 187.43/187.51 ! [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))) ). % 187.43/187.51 % 187.43/187.51 fof(fact_less__not__refl,axiom, % 187.43/187.51 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n)) ). % 187.43/187.51 % 187.43/187.51 fof(fact_nat__neq__iff,axiom, % 187.43/187.51 ! [V_n_2,V_m_2] : % 187.43/187.51 ( V_m_2 != V_n_2 % 187.43/187.51 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 187.43/187.51 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_linorder__neqE__nat,axiom, % 187.43/187.51 ! [V_y,V_x] : % 187.43/187.51 ( V_x != V_y % 187.43/187.51 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y)) % 187.43/187.51 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y),V_x)) ) ) ). % 187.43/187.51 % 187.43/187.51 fof(fact_less__irrefl__nat,axiom, % 187.43/187.51 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n)) ). % 187.43/187.51 % 187.43/187.51 fof(fact_less__not__refl2,axiom, % 187.43/187.51 ! [V_m,V_n] : % 187.43/187.51 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m)) % 187.43/187.51 => V_m != V_n ) ). % 187.43/187.51 % 187.43/187.52 fof(fact_less__not__refl3,axiom, % 187.43/187.52 ! [V_t,V_s] : % 187.43/187.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_s),V_t)) % 187.43/187.52 => V_s != V_t ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_nat__less__cases,axiom, % 187.43/187.52 ! [V_P_2,V_n_2,V_m_2] : % 187.43/187.52 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 187.43/187.52 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) ) % 187.43/187.52 => ( ( V_m_2 = V_n_2 % 187.43/187.52 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) ) % 187.43/187.52 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) % 187.43/187.52 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) ) % 187.43/187.52 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) ) ) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_one__reorient,axiom, % 187.43/187.52 ! [V_x_2,T_a] : % 187.43/187.52 ( class_Groups_Oone(T_a) % 187.43/187.52 => ( c_Groups_Oone__class_Oone(T_a) = V_x_2 % 187.43/187.52 <=> V_x_2 = c_Groups_Oone__class_Oone(T_a) ) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_not__less0,axiom, % 187.43/187.52 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 187.43/187.52 % 187.43/187.52 fof(fact_neq0__conv,axiom, % 187.43/187.52 ! [V_n_2] : % 187.43/187.52 ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 187.43/187.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_less__nat__zero__code,axiom, % 187.43/187.52 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 187.43/187.52 % 187.43/187.52 fof(fact_gr__implies__not0,axiom, % 187.43/187.52 ! [V_n,V_m] : % 187.43/187.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 187.43/187.52 => V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_gr0I,axiom, % 187.43/187.52 ! [V_n] : % 187.43/187.52 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 187.43/187.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_not__less__eq,axiom, % 187.43/187.52 ! [V_n_2,V_m_2] : % 187.43/187.52 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 187.43/187.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2))) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_less__Suc__eq,axiom, % 187.43/187.52 ! [V_n_2,V_m_2] : % 187.43/187.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) % 187.43/187.52 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 187.43/187.52 | V_m_2 = V_n_2 ) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_Suc__less__eq,axiom, % 187.43/187.52 ! [V_n_2,V_m_2] : % 187.43/187.52 ( 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))) % 187.43/187.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_not__less__less__Suc__eq,axiom, % 187.43/187.52 ! [V_m_2,V_n_2] : % 187.43/187.52 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) % 187.43/187.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2))) % 187.43/187.52 <=> V_n_2 = V_m_2 ) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_less__antisym,axiom, % 187.43/187.52 ! [V_m,V_n] : % 187.43/187.52 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m)) % 187.43/187.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_m))) % 187.43/187.52 => V_m = V_n ) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_less__SucI,axiom, % 187.43/187.52 ! [V_n,V_m] : % 187.43/187.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 187.43/187.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_Suc__lessI,axiom, % 187.43/187.52 ! [V_n,V_m] : % 187.43/187.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 187.43/187.52 => ( hAPP(c_Nat_OSuc,V_m) != V_n % 187.43/187.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) ) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_less__trans__Suc,axiom, % 187.43/187.52 ! [V_k,V_j,V_i] : % 187.43/187.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 187.43/187.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),V_k)) % 187.43/187.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_i)),V_k)) ) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_less__SucE,axiom, % 187.43/187.52 ! [V_n,V_m] : % 187.43/187.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) % 187.43/187.52 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 187.43/187.52 => V_m = V_n ) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_Suc__lessD,axiom, % 187.43/187.52 ! [V_n,V_m] : % 187.43/187.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) % 187.43/187.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_Suc__less__SucD,axiom, % 187.43/187.52 ! [V_n,V_m] : % 187.43/187.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n))) % 187.43/187.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_less__or__eq__imp__le,axiom, % 187.43/187.52 ! [V_n,V_m] : % 187.43/187.52 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 187.43/187.52 | V_m = V_n ) % 187.43/187.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_le__neq__implies__less,axiom, % 187.43/187.52 ! [V_n,V_m] : % 187.43/187.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 187.43/187.52 => ( V_m != V_n % 187.43/187.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_less__imp__le__nat,axiom, % 187.43/187.52 ! [V_n,V_m] : % 187.43/187.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 187.43/187.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_le__eq__less__or__eq,axiom, % 187.43/187.52 ! [V_n_2,V_m_2] : % 187.43/187.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 187.43/187.52 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 187.43/187.52 | V_m_2 = V_n_2 ) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_nat__less__le,axiom, % 187.43/187.52 ! [V_n_2,V_m_2] : % 187.43/187.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 187.43/187.52 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 187.43/187.52 & V_m_2 != V_n_2 ) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_diff__less__mono2,axiom, % 187.43/187.52 ! [V_l,V_n,V_m] : % 187.43/187.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 187.43/187.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_l)) % 187.43/187.52 => 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))) ) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_less__imp__diff__less,axiom, % 187.43/187.52 ! [V_n,V_k,V_j] : % 187.43/187.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),V_k)) % 187.43/187.52 => 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)) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_restrict__in,axiom, % 187.43/187.52 ! [V_m_2,T_b,V_A_2,V_x_2,T_a] : % 187.43/187.52 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 187.43/187.52 => 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) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_Suc__pred_H,axiom, % 187.43/187.52 ! [V_n] : % 187.43/187.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 187.43/187.52 => 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))) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_Suc__diff__1,axiom, % 187.43/187.52 ! [V_n] : % 187.43/187.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 187.43/187.52 => 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 ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_restrict__map__empty,axiom, % 187.43/187.52 ! [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) ). % 187.43/187.52 % 187.43/187.52 fof(fact_less__Suc__eq__0__disj,axiom, % 187.43/187.52 ! [V_n_2,V_m_2] : % 187.43/187.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) % 187.43/187.52 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 187.43/187.52 | ? [B_j] : % 187.43/187.52 ( V_m_2 = hAPP(c_Nat_OSuc,B_j) % 187.43/187.52 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_n_2)) ) ) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_less__Suc0,axiom, % 187.43/187.52 ! [V_n_2] : % 187.43/187.52 ( 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)))) % 187.43/187.52 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_gr0__conv__Suc,axiom, % 187.43/187.52 ! [V_n_2] : % 187.43/187.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) % 187.43/187.52 <=> ? [B_m] : V_n_2 = hAPP(c_Nat_OSuc,B_m) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_One__nat__def,axiom, % 187.43/187.52 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ). % 187.43/187.52 % 187.43/187.52 fof(fact_Suc__le__lessD,axiom, % 187.43/187.52 ! [V_n,V_m] : % 187.43/187.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) % 187.43/187.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_le__less__Suc__eq,axiom, % 187.43/187.52 ! [V_n_2,V_m_2] : % 187.43/187.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 187.43/187.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2))) % 187.43/187.52 <=> V_n_2 = V_m_2 ) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_Suc__leI,axiom, % 187.43/187.52 ! [V_n,V_m] : % 187.43/187.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 187.43/187.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_le__imp__less__Suc,axiom, % 187.43/187.52 ! [V_n,V_m] : % 187.43/187.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 187.43/187.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_Suc__le__eq,axiom, % 187.43/187.52 ! [V_n_2,V_m_2] : % 187.43/187.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_n_2)) % 187.43/187.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_less__Suc__eq__le,axiom, % 187.43/187.52 ! [V_n_2,V_m_2] : % 187.43/187.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) % 187.43/187.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_less__eq__Suc__le,axiom, % 187.43/187.52 ! [V_m_2,V_n_2] : % 187.43/187.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) % 187.43/187.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_diff__less,axiom, % 187.43/187.52 ! [V_m,V_n] : % 187.43/187.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 187.43/187.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)) % 187.43/187.52 => 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)) ) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_zero__less__diff,axiom, % 187.43/187.52 ! [V_m_2,V_n_2] : % 187.43/187.52 ( 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))) % 187.43/187.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_diff__less__Suc,axiom, % 187.43/187.52 ! [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))) ). % 187.43/187.52 % 187.43/187.52 fof(fact_diff__Suc__eq__diff__pred,axiom, % 187.43/187.52 ! [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) ). % 187.43/187.52 % 187.43/187.52 fof(fact_diff__Suc__1,axiom, % 187.43/187.52 ! [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 ). % 187.43/187.52 % 187.43/187.52 fof(fact_less__diff__iff,axiom, % 187.43/187.52 ! [V_n_2,V_m_2,V_k_2] : % 187.43/187.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2)) % 187.43/187.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2)) % 187.43/187.52 => ( 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))) % 187.43/187.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_diff__less__mono,axiom, % 187.43/187.52 ! [V_c,V_b,V_a] : % 187.43/187.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a),V_b)) % 187.43/187.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_c),V_a)) % 187.43/187.52 => 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))) ) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_less__eq__Suc__le__raw,axiom, % 187.43/187.52 ! [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)) ). % 187.43/187.52 % 187.43/187.52 fof(fact_restrict__out,axiom, % 187.43/187.52 ! [V_m_2,T_b,V_A_2,V_x_2,T_a] : % 187.43/187.52 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 187.43/187.52 => hAPP(c_Map_Orestrict__map(T_a,T_b,V_m_2,V_A_2),V_x_2) = c_Option_Ooption_ONone(T_b) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_restrict__map__insert,axiom, % 187.43/187.52 ! [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)) ). % 187.43/187.52 % 187.43/187.52 fof(fact_restrict__map__def,axiom, % 187.43/187.52 ! [V_m_2,T_b,V_A_2,V_x_2,T_a] : % 187.43/187.52 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 187.43/187.52 => 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) ) % 187.43/187.52 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 187.43/187.52 => hAPP(c_Map_Orestrict__map(T_a,T_b,V_m_2,V_A_2),V_x_2) = c_Option_Ooption_ONone(T_b) ) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_restrict__map__to__empty,axiom, % 187.43/187.52 ! [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) ). % 187.43/187.52 % 187.43/187.52 fof(fact_card__ge__0__finite,axiom, % 187.43/187.52 ! [V_A_2,T_a] : % 187.43/187.52 ( 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))) % 187.43/187.52 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_diff__Suc__less,axiom, % 187.43/187.52 ! [V_i,V_n] : % 187.43/187.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 187.43/187.52 => 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)) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_Suc__pred,axiom, % 187.43/187.52 ! [V_n] : % 187.43/187.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 187.43/187.52 => 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 ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_psubset__card__mono,axiom, % 187.43/187.52 ! [V_A_2,V_B_2,T_a] : % 187.43/187.52 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 187.43/187.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 187.43/187.52 => 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))) ) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_card__gt__0__iff,axiom, % 187.43/187.52 ! [V_A_2,T_a] : % 187.43/187.52 ( 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))) % 187.43/187.52 <=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.43/187.52 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_card__psubset,axiom, % 187.43/187.52 ! [V_A_2,V_B_2,T_a] : % 187.43/187.52 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 187.43/187.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 187.43/187.52 => ( 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))) % 187.43/187.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_fun__upd__restrict,axiom, % 187.43/187.52 ! [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) ). % 187.43/187.52 % 187.43/187.52 fof(fact_not__one__less__zero,axiom, % 187.43/187.52 ! [T_a] : % 187.43/187.52 ( class_Rings_Olinordered__semidom(T_a) % 187.43/187.52 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_zero__less__one,axiom, % 187.43/187.52 ! [T_a] : % 187.43/187.52 ( class_Rings_Olinordered__semidom(T_a) % 187.43/187.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oone__class_Oone(T_a))) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_zero__le__one,axiom, % 187.43/187.52 ! [T_a] : % 187.43/187.52 ( class_Rings_Olinordered__semidom(T_a) % 187.43/187.52 => 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))) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_not__one__le__zero,axiom, % 187.43/187.52 ! [T_a] : % 187.43/187.52 ( class_Rings_Olinordered__semidom(T_a) % 187.43/187.52 => ~ 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))) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_card_Oremove,axiom, % 187.43/187.52 ! [V_x_2,V_A_2,T_a] : % 187.43/187.52 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.43/187.52 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 187.43/187.52 => 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)))))) ) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_termination__basic__simps_I5_J,axiom, % 187.43/187.52 ! [V_y,V_x] : % 187.43/187.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y)) % 187.43/187.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_y)) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_one__neq__zero,axiom, % 187.43/187.52 ! [T_a] : % 187.43/187.52 ( class_Rings_Ozero__neq__one(T_a) % 187.43/187.52 => c_Groups_Oone__class_Oone(T_a) != c_Groups_Ozero__class_Ozero(T_a) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_zero__neq__one,axiom, % 187.43/187.52 ! [T_a] : % 187.43/187.52 ( class_Rings_Ozero__neq__one(T_a) % 187.43/187.52 => c_Groups_Ozero__class_Ozero(T_a) != c_Groups_Oone__class_Oone(T_a) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_card_Oinsert__remove,axiom, % 187.43/187.52 ! [V_x_2,V_A_2,T_a] : % 187.43/187.52 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.43/187.52 => 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)))))) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_diff__Suc,axiom, % 187.43/187.52 ! [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)) ). % 187.43/187.52 % 187.43/187.52 fof(fact_ab__semigroup__add__class_Oadd__ac_I1_J,axiom, % 187.43/187.52 ! [V_c,V_b,V_a,T_a] : % 187.43/187.52 ( class_Groups_Oab__semigroup__add(T_a) % 187.43/187.52 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c)) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_add__left__cancel,axiom, % 187.43/187.52 ! [V_c_2,V_b_2,V_a_2,T_a] : % 187.43/187.52 ( class_Groups_Ocancel__semigroup__add(T_a) % 187.43/187.52 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_c_2) % 187.43/187.52 <=> V_b_2 = V_c_2 ) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_add__right__cancel,axiom, % 187.43/187.52 ! [V_c_2,V_a_2,V_b_2,T_a] : % 187.43/187.52 ( class_Groups_Ocancel__semigroup__add(T_a) % 187.43/187.52 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_a_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_a_2) % 187.43/187.52 <=> V_b_2 = V_c_2 ) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_add__left__imp__eq,axiom, % 187.43/187.52 ! [V_c,V_b,V_a,T_a] : % 187.43/187.52 ( class_Groups_Ocancel__semigroup__add(T_a) % 187.43/187.52 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c) % 187.43/187.52 => V_b = V_c ) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_add__imp__eq,axiom, % 187.43/187.52 ! [V_c,V_b,V_a,T_a] : % 187.43/187.52 ( class_Groups_Ocancel__ab__semigroup__add(T_a) % 187.43/187.52 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c) % 187.43/187.52 => V_b = V_c ) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_add__right__imp__eq,axiom, % 187.43/187.52 ! [V_c,V_a,V_b,T_a] : % 187.43/187.52 ( class_Groups_Ocancel__semigroup__add(T_a) % 187.43/187.52 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_a) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a) % 187.43/187.52 => V_b = V_c ) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_nat__add__commute,axiom, % 187.43/187.52 ! [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) ). % 187.43/187.52 % 187.43/187.52 fof(fact_nat__add__left__commute,axiom, % 187.43/187.52 ! [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)) ). % 187.43/187.52 % 187.43/187.52 fof(fact_nat__add__assoc,axiom, % 187.43/187.52 ! [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)) ). % 187.43/187.52 % 187.43/187.52 fof(fact_nat__add__left__cancel,axiom, % 187.43/187.52 ! [V_n_2,V_m_2,V_k_2] : % 187.43/187.52 ( 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) % 187.43/187.52 <=> V_m_2 = V_n_2 ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_nat__add__right__cancel,axiom, % 187.43/187.52 ! [V_n_2,V_k_2,V_m_2] : % 187.43/187.52 ( 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) % 187.43/187.52 <=> V_m_2 = V_n_2 ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_termination__basic__simps_I1_J,axiom, % 187.43/187.52 ! [V_z,V_y,V_x] : % 187.43/187.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y)) % 187.43/187.52 => 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))) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_termination__basic__simps_I2_J,axiom, % 187.43/187.52 ! [V_y,V_z,V_x] : % 187.43/187.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_z)) % 187.43/187.52 => 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))) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_termination__basic__simps_I4_J,axiom, % 187.43/187.52 ! [V_y,V_z,V_x] : % 187.43/187.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_z)) % 187.43/187.52 => 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))) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_termination__basic__simps_I3_J,axiom, % 187.43/187.52 ! [V_z,V_y,V_x] : % 187.43/187.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_y)) % 187.43/187.52 => 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))) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_add__le__imp__le__left,axiom, % 187.43/187.52 ! [V_b,V_a,V_c,T_a] : % 187.43/187.52 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 187.43/187.52 => ( 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))) % 187.43/187.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_add__le__imp__le__right,axiom, % 187.43/187.52 ! [V_b,V_c,V_a,T_a] : % 187.43/187.52 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 187.43/187.52 => ( 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))) % 187.43/187.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_add__mono,axiom, % 187.43/187.52 ! [V_d,V_c,V_b,V_a,T_a] : % 187.43/187.52 ( class_Groups_Oordered__ab__semigroup__add(T_a) % 187.43/187.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 187.43/187.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d)) % 187.43/187.52 => 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))) ) ) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_add__left__mono,axiom, % 187.43/187.52 ! [V_c,V_b,V_a,T_a] : % 187.43/187.52 ( class_Groups_Oordered__ab__semigroup__add(T_a) % 187.43/187.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 187.43/187.52 => 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))) ) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_add__right__mono,axiom, % 187.43/187.52 ! [V_c,V_b,V_a,T_a] : % 187.43/187.52 ( class_Groups_Oordered__ab__semigroup__add(T_a) % 187.43/187.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 187.43/187.52 => 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))) ) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_add__le__cancel__left,axiom, % 187.43/187.52 ! [V_b_2,V_a_2,V_c_2,T_a] : % 187.43/187.52 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 187.43/187.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_b_2))) % 187.43/187.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) ) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_add__le__cancel__right,axiom, % 187.43/187.52 ! [V_b_2,V_c_2,V_a_2,T_a] : % 187.43/187.52 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 187.43/187.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_c_2))) % 187.43/187.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) ) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_add_Ocomm__neutral,axiom, % 187.43/187.52 ! [V_a,T_a] : % 187.43/187.52 ( class_Groups_Ocomm__monoid__add(T_a) % 187.43/187.52 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_add__0__right,axiom, % 187.43/187.52 ! [V_a,T_a] : % 187.43/187.52 ( class_Groups_Omonoid__add(T_a) % 187.43/187.52 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_double__zero__sym,axiom, % 187.43/187.52 ! [V_a_2,T_a] : % 187.43/187.52 ( class_Groups_Olinordered__ab__group__add(T_a) % 187.43/187.52 => ( c_Groups_Ozero__class_Ozero(T_a) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2) % 187.43/187.52 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_add__0,axiom, % 187.43/187.52 ! [V_a,T_a] : % 187.43/187.52 ( class_Groups_Ocomm__monoid__add(T_a) % 187.43/187.52 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_add__0__left,axiom, % 187.43/187.52 ! [V_a,T_a] : % 187.43/187.52 ( class_Groups_Omonoid__add(T_a) % 187.43/187.52 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_add__less__cancel__right,axiom, % 187.43/187.52 ! [V_b_2,V_c_2,V_a_2,T_a] : % 187.43/187.52 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 187.43/187.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_c_2))) % 187.43/187.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_add__less__cancel__left,axiom, % 187.43/187.52 ! [V_b_2,V_a_2,V_c_2,T_a] : % 187.43/187.52 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 187.43/187.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c_2),V_b_2))) % 187.43/187.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_add__strict__right__mono,axiom, % 187.43/187.52 ! [V_c,V_b,V_a,T_a] : % 187.43/187.52 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 187.43/187.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 187.43/187.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c))) ) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_add__strict__left__mono,axiom, % 187.43/187.52 ! [V_c,V_b,V_a,T_a] : % 187.43/187.52 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 187.43/187.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 187.43/187.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b))) ) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_add__strict__mono,axiom, % 187.43/187.52 ! [V_d,V_c,V_b,V_a,T_a] : % 187.43/187.52 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 187.43/187.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 187.43/187.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) % 187.43/187.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d))) ) ) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_add__less__imp__less__right,axiom, % 187.43/187.52 ! [V_b,V_c,V_a,T_a] : % 187.43/187.52 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 187.43/187.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c))) % 187.43/187.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_add__less__imp__less__left,axiom, % 187.43/187.52 ! [V_b,V_a,V_c,T_a] : % 187.43/187.52 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 187.43/187.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_a)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_c),V_b))) % 187.43/187.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_add__diff__cancel,axiom, % 187.43/187.52 ! [V_b,V_a,T_a] : % 187.43/187.52 ( class_Groups_Ogroup__add(T_a) % 187.43/187.52 => 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 ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_diff__add__cancel,axiom, % 187.43/187.52 ! [V_b,V_a,T_a] : % 187.43/187.52 ( class_Groups_Ogroup__add(T_a) % 187.43/187.52 => 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 ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_add__eq__self__zero,axiom, % 187.43/187.52 ! [V_n,V_m] : % 187.43/187.52 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_m % 187.43/187.52 => V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_add__is__0,axiom, % 187.43/187.52 ! [V_n_2,V_m_2] : % 187.43/187.52 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 187.43/187.52 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 187.43/187.52 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_Nat_Oadd__0__right,axiom, % 187.43/187.52 ! [V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ). % 187.43/187.52 % 187.43/187.52 fof(fact_plus__nat_Oadd__0,axiom, % 187.43/187.52 ! [V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n ). % 187.43/187.52 % 187.43/187.52 fof(fact_add__Suc__shift,axiom, % 187.43/187.52 ! [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)) ). % 187.43/187.52 % 187.43/187.52 fof(fact_add__Suc,axiom, % 187.43/187.52 ! [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)) ). % 187.43/187.52 % 187.43/187.52 fof(fact_add__Suc__right,axiom, % 187.43/187.52 ! [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)) ). % 187.43/187.52 % 187.43/187.52 fof(fact_add__lessD1,axiom, % 187.43/187.52 ! [V_k,V_j,V_i] : % 187.43/187.52 ( 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)) % 187.43/187.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_k)) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_less__add__eq__less,axiom, % 187.43/187.52 ! [V_n,V_m,V_l,V_k] : % 187.43/187.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l)) % 187.43/187.52 => ( 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) % 187.43/187.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_add__less__mono,axiom, % 187.43/187.52 ! [V_l,V_k,V_j,V_i] : % 187.43/187.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 187.43/187.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l)) % 187.43/187.52 => 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))) ) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_add__less__mono1,axiom, % 187.43/187.52 ! [V_k,V_j,V_i] : % 187.43/187.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 187.43/187.52 => 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))) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_trans__less__add2,axiom, % 187.43/187.52 ! [V_m,V_j,V_i] : % 187.43/187.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 187.43/187.52 => 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))) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_trans__less__add1,axiom, % 187.43/187.52 ! [V_m,V_j,V_i] : % 187.43/187.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 187.43/187.52 => 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))) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_nat__add__left__cancel__less,axiom, % 187.43/187.52 ! [V_n_2,V_m_2,V_k_2] : % 187.43/187.52 ( 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))) % 187.43/187.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_not__add__less2,axiom, % 187.43/187.52 ! [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)) ). % 187.43/187.52 % 187.43/187.52 fof(fact_not__add__less1,axiom, % 187.43/187.52 ! [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)) ). % 187.43/187.52 % 187.43/187.52 fof(fact_le__add2,axiom, % 187.43/187.52 ! [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))) ). % 187.43/187.52 % 187.43/187.52 fof(fact_le__add1,axiom, % 187.43/187.52 ! [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))) ). % 187.43/187.52 % 187.43/187.52 fof(fact_le__iff__add,axiom, % 187.43/187.52 ! [V_n_2,V_m_2] : % 187.43/187.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 187.43/187.52 <=> ? [B_k] : V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_nat__add__left__cancel__le,axiom, % 187.43/187.52 ! [V_n_2,V_m_2,V_k_2] : % 187.43/187.52 ( 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))) % 187.43/187.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_trans__le__add1,axiom, % 187.43/187.52 ! [V_m,V_j,V_i] : % 187.43/187.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 187.43/187.52 => 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))) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_trans__le__add2,axiom, % 187.43/187.52 ! [V_m,V_j,V_i] : % 187.43/187.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 187.43/187.52 => 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))) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_add__le__mono1,axiom, % 187.43/187.52 ! [V_k,V_j,V_i] : % 187.43/187.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 187.43/187.52 => 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))) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_add__le__mono,axiom, % 187.43/187.52 ! [V_l,V_k,V_j,V_i] : % 187.43/187.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 187.43/187.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_l)) % 187.43/187.52 => 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))) ) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_add__leD2,axiom, % 187.43/187.52 ! [V_n,V_k,V_m] : % 187.43/187.52 ( 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)) % 187.43/187.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_add__leD1,axiom, % 187.43/187.52 ! [V_n,V_k,V_m] : % 187.43/187.52 ( 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)) % 187.43/187.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_add__leE,axiom, % 187.43/187.52 ! [V_n,V_k,V_m] : % 187.43/187.52 ( 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)) % 187.43/187.52 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 187.43/187.52 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_diff__add__inverse2,axiom, % 187.43/187.52 ! [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 ). % 187.43/187.52 % 187.43/187.52 fof(fact_diff__add__inverse,axiom, % 187.43/187.52 ! [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 ). % 187.43/187.52 % 187.43/187.52 fof(fact_diff__diff__left,axiom, % 187.43/187.52 ! [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)) ). % 187.43/187.52 % 187.43/187.52 fof(fact_diff__cancel,axiom, % 187.43/187.52 ! [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) ). % 187.43/187.52 % 187.43/187.52 fof(fact_diff__cancel2,axiom, % 187.43/187.52 ! [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) ). % 187.43/187.52 % 187.43/187.52 fof(fact_pos__add__strict,axiom, % 187.43/187.52 ! [V_c,V_b,V_a,T_a] : % 187.43/187.52 ( class_Rings_Olinordered__semidom(T_a) % 187.43/187.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 187.43/187.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c)) % 187.43/187.52 => 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))) ) ) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_less__add__one,axiom, % 187.43/187.52 ! [V_a,T_a] : % 187.43/187.52 ( class_Rings_Olinordered__semidom(T_a) % 187.43/187.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Oone__class_Oone(T_a)))) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_zero__le__double__add__iff__zero__le__single__add,axiom, % 187.43/187.52 ! [V_a_2,T_a] : % 187.43/187.52 ( class_Groups_Olinordered__ab__group__add(T_a) % 187.43/187.52 => ( 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))) % 187.43/187.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_double__add__le__zero__iff__single__add__le__zero,axiom, % 187.43/187.52 ! [V_a_2,T_a] : % 187.43/187.52 ( class_Groups_Olinordered__ab__group__add(T_a) % 187.43/187.52 => ( 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))) % 187.43/187.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_add__nonneg__nonneg,axiom, % 187.43/187.52 ! [V_b,V_a,T_a] : % 187.43/187.52 ( class_Groups_Oordered__comm__monoid__add(T_a) % 187.43/187.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 187.43/187.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 187.43/187.52 => 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))) ) ) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_add__nonneg__eq__0__iff,axiom, % 187.43/187.52 ! [V_y_2,V_x_2,T_a] : % 187.43/187.52 ( class_Groups_Oordered__comm__monoid__add(T_a) % 187.43/187.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x_2)) % 187.43/187.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y_2)) % 187.43/187.52 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x_2),V_y_2) = c_Groups_Ozero__class_Ozero(T_a) % 187.43/187.52 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a) % 187.43/187.52 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_add__increasing,axiom, % 187.43/187.52 ! [V_c,V_b,V_a,T_a] : % 187.43/187.52 ( class_Groups_Oordered__comm__monoid__add(T_a) % 187.43/187.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 187.43/187.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c)) % 187.43/187.52 => 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))) ) ) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_add__increasing2,axiom, % 187.43/187.52 ! [V_a,V_b,V_c,T_a] : % 187.43/187.52 ( class_Groups_Oordered__comm__monoid__add(T_a) % 187.43/187.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 187.43/187.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 187.43/187.52 => 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))) ) ) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_add__nonpos__nonpos,axiom, % 187.43/187.52 ! [V_b,V_a,T_a] : % 187.43/187.52 ( class_Groups_Oordered__comm__monoid__add(T_a) % 187.43/187.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 187.43/187.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 187.43/187.52 => 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))) ) ) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_add__le__less__mono,axiom, % 187.43/187.52 ! [V_d,V_c,V_b,V_a,T_a] : % 187.43/187.52 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 187.43/187.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 187.43/187.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) % 187.43/187.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d))) ) ) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_add__less__le__mono,axiom, % 187.43/187.52 ! [V_d,V_c,V_b,V_a,T_a] : % 187.43/187.52 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 187.43/187.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 187.43/187.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d)) % 187.43/187.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_d))) ) ) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_add__neg__neg,axiom, % 187.43/187.52 ! [V_b,V_a,T_a] : % 187.43/187.52 ( class_Groups_Oordered__comm__monoid__add(T_a) % 187.43/187.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 187.43/187.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 187.43/187.52 => 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))) ) ) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_add__pos__pos,axiom, % 187.43/187.52 ! [V_b,V_a,T_a] : % 187.43/187.52 ( class_Groups_Oordered__comm__monoid__add(T_a) % 187.43/187.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 187.43/187.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 187.43/187.52 => 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))) ) ) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_double__add__less__zero__iff__single__add__less__zero,axiom, % 187.43/187.52 ! [V_a_2,T_a] : % 187.43/187.52 ( class_Groups_Olinordered__ab__group__add(T_a) % 187.43/187.52 => ( 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))) % 187.43/187.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_zero__less__double__add__iff__zero__less__single__add,axiom, % 187.43/187.52 ! [V_a_2,T_a] : % 187.43/187.52 ( class_Groups_Olinordered__ab__group__add(T_a) % 187.43/187.52 => ( 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))) % 187.43/187.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_zero__less__two,axiom, % 187.43/187.52 ! [T_a] : % 187.43/187.52 ( class_Rings_Olinordered__semidom(T_a) % 187.43/187.52 => 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)))) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_one__is__add,axiom, % 187.43/187.52 ! [V_n_2,V_m_2] : % 187.43/187.52 ( 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) % 187.43/187.52 <=> ( ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 187.43/187.52 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 187.43/187.52 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 187.43/187.52 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_add__is__1,axiom, % 187.43/187.52 ! [V_n_2,V_m_2] : % 187.43/187.52 ( 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)) % 187.43/187.52 <=> ( ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 187.43/187.52 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 187.43/187.52 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 187.43/187.52 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_add__gr__0,axiom, % 187.43/187.52 ! [V_n_2,V_m_2] : % 187.43/187.52 ( 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))) % 187.43/187.52 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2)) % 187.43/187.52 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_less__add__Suc1,axiom, % 187.43/187.52 ! [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)))) ). % 187.43/187.52 % 187.43/187.52 fof(fact_less__add__Suc2,axiom, % 187.43/187.52 ! [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)))) ). % 187.43/187.52 % 187.43/187.52 fof(fact_less__iff__Suc__add,axiom, % 187.43/187.52 ! [V_n_2,V_m_2] : % 187.43/187.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 187.43/187.52 <=> ? [B_k] : V_n_2 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k)) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_diff__add__0,axiom, % 187.43/187.52 ! [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) ). % 187.43/187.52 % 187.43/187.52 fof(fact_less__diff__conv,axiom, % 187.43/187.52 ! [V_k_2,V_j_2,V_i_2] : % 187.43/187.52 ( 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))) % 187.43/187.52 <=> 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)) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_add__diff__inverse,axiom, % 187.43/187.52 ! [V_n,V_m] : % 187.43/187.52 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 187.43/187.52 => 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 ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_diff__diff__right,axiom, % 187.43/187.52 ! [V_i,V_j,V_k] : % 187.43/187.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 187.43/187.52 => 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) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_le__diff__conv,axiom, % 187.43/187.52 ! [V_i_2,V_k_2,V_j_2] : % 187.43/187.52 ( 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)) % 187.43/187.52 <=> 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))) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_le__add__diff,axiom, % 187.43/187.52 ! [V_m,V_n,V_k] : % 187.43/187.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) % 187.43/187.52 => 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))) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_le__add__diff__inverse,axiom, % 187.43/187.52 ! [V_m,V_n] : % 187.43/187.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 187.43/187.52 => 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 ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_add__diff__assoc,axiom, % 187.43/187.52 ! [V_i,V_j,V_k] : % 187.43/187.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 187.43/187.52 => 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) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_le__diff__conv2,axiom, % 187.43/187.52 ! [V_i_2,V_j_2,V_k_2] : % 187.43/187.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_j_2)) % 187.43/187.52 => ( 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))) % 187.43/187.52 <=> 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)) ) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_le__add__diff__inverse2,axiom, % 187.43/187.52 ! [V_m,V_n] : % 187.43/187.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 187.43/187.52 => 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 ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_le__imp__diff__is__add,axiom, % 187.43/187.52 ! [V_k_2,V_j_2,V_i_2] : % 187.43/187.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) % 187.43/187.52 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2) = V_k_2 % 187.43/187.52 <=> V_j_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_i_2) ) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_diff__add__assoc,axiom, % 187.43/187.52 ! [V_i,V_j,V_k] : % 187.43/187.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 187.43/187.52 => 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)) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_add__diff__assoc2,axiom, % 187.43/187.52 ! [V_i,V_j,V_k] : % 187.43/187.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 187.43/187.52 => 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) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_diff__add__assoc2,axiom, % 187.43/187.52 ! [V_i,V_j,V_k] : % 187.43/187.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 187.43/187.52 => 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) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_Suc__eq__plus1__left,axiom, % 187.43/187.52 ! [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) ). % 187.43/187.52 % 187.43/187.52 fof(fact_Suc__eq__plus1,axiom, % 187.43/187.52 ! [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)) ). % 187.43/187.52 % 187.43/187.52 fof(fact_nat__case__0,axiom, % 187.43/187.52 ! [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 ). % 187.43/187.52 % 187.43/187.52 fof(fact_nat__case__Suc,axiom, % 187.43/187.52 ! [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) ). % 187.43/187.52 % 187.43/187.52 fof(fact_add__pos__nonneg,axiom, % 187.43/187.52 ! [V_b,V_a,T_a] : % 187.43/187.52 ( class_Groups_Oordered__comm__monoid__add(T_a) % 187.43/187.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 187.43/187.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 187.43/187.52 => 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))) ) ) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_add__nonneg__pos,axiom, % 187.43/187.52 ! [V_b,V_a,T_a] : % 187.43/187.52 ( class_Groups_Oordered__comm__monoid__add(T_a) % 187.43/187.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 187.43/187.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 187.43/187.52 => 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))) ) ) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_add__strict__increasing,axiom, % 187.43/187.52 ! [V_c,V_b,V_a,T_a] : % 187.43/187.52 ( class_Groups_Oordered__comm__monoid__add(T_a) % 187.43/187.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 187.43/187.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c)) % 187.43/187.52 => 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))) ) ) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_add__strict__increasing2,axiom, % 187.43/187.52 ! [V_c,V_b,V_a,T_a] : % 187.43/187.52 ( class_Groups_Oordered__comm__monoid__add(T_a) % 187.43/187.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 187.43/187.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c)) % 187.43/187.52 => 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))) ) ) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_add__neg__nonpos,axiom, % 187.43/187.52 ! [V_b,V_a,T_a] : % 187.43/187.52 ( class_Groups_Oordered__comm__monoid__add(T_a) % 187.43/187.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 187.43/187.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 187.43/187.52 => 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))) ) ) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_add__nonpos__neg,axiom, % 187.43/187.52 ! [V_b,V_a,T_a] : % 187.43/187.52 ( class_Groups_Oordered__comm__monoid__add(T_a) % 187.43/187.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 187.43/187.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 187.43/187.52 => 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))) ) ) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_nat__diff__split__asm,axiom, % 187.43/187.52 ! [V_b_2,V_a_2,V_P_2] : % 187.43/187.52 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2))) % 187.43/187.52 <=> ~ ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2)) % 187.43/187.52 & ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) % 187.43/187.52 | ? [B_d] : % 187.43/187.52 ( V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d) % 187.43/187.52 & ~ hBOOL(hAPP(V_P_2,B_d)) ) ) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_nat__diff__split,axiom, % 187.43/187.52 ! [V_b_2,V_a_2,V_P_2] : % 187.43/187.52 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2))) % 187.43/187.52 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2)) % 187.43/187.52 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) % 187.43/187.52 & ! [B_d] : % 187.43/187.52 ( V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d) % 187.43/187.52 => hBOOL(hAPP(V_P_2,B_d)) ) ) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_diff__Suc__diff__eq1,axiom, % 187.43/187.52 ! [V_m,V_j,V_k] : % 187.43/187.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 187.43/187.52 => 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)) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_diff__Suc__diff__eq2,axiom, % 187.43/187.52 ! [V_m,V_j,V_k] : % 187.43/187.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 187.43/187.52 => 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)) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_linorder__neqE__linordered__idom,axiom, % 187.43/187.52 ! [V_y,V_x,T_a] : % 187.43/187.52 ( class_Rings_Olinordered__idom(T_a) % 187.43/187.52 => ( V_x != V_y % 187.43/187.52 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 187.43/187.52 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_comp__cong,axiom, % 187.43/187.52 ! [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] : % 187.43/187.52 ( 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)) % 187.43/187.52 => 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) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_add__eq__if,axiom, % 187.43/187.52 ! [V_n,V_m] : % 187.43/187.52 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 187.43/187.52 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_n ) % 187.43/187.52 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 187.43/187.52 => 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)) ) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_com_Osize_I6_J,axiom, % 187.43/187.52 ! [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))) ). % 187.43/187.52 % 187.43/187.52 fof(fact_com_Osize_I5_J,axiom, % 187.43/187.52 ! [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))) ). % 187.43/187.52 % 187.43/187.52 fof(fact_com_Osize_I4_J,axiom, % 187.43/187.52 ! [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))) ). % 187.43/187.52 % 187.43/187.52 fof(fact_card_Oinsert,axiom, % 187.43/187.52 ! [V_x_2,V_A_2,T_a] : % 187.43/187.52 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.43/187.52 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 187.43/187.52 => 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)) ) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_even__less__0__iff,axiom, % 187.43/187.52 ! [V_a_2,T_a] : % 187.43/187.52 ( class_Rings_Olinordered__idom(T_a) % 187.43/187.52 => ( 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))) % 187.43/187.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_double__eq__0__iff,axiom, % 187.43/187.52 ! [V_a_2,T_a] : % 187.43/187.52 ( class_Groups_Olinordered__ab__group__add(T_a) % 187.43/187.52 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_a) % 187.43/187.52 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_add__0__iff,axiom, % 187.43/187.52 ! [V_a_2,V_b_2,T_a] : % 187.43/187.52 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a) % 187.43/187.52 => ( V_b_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_a_2) % 187.43/187.52 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom, % 187.43/187.52 ! [V_a,T_a] : % 187.43/187.52 ( class_Rings_Ocomm__semiring__1(T_a) % 187.43/187.52 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom, % 187.43/187.52 ! [V_a,T_a] : % 187.43/187.52 ( class_Rings_Ocomm__semiring__1(T_a) % 187.43/187.52 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_card__Plus__conv__if,axiom, % 187.43/187.52 ! [V_B_2,T_b,V_A_2,T_a] : % 187.43/187.52 ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.43/187.52 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) % 187.43/187.52 => 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)) ) % 187.43/187.52 & ( ~ ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.43/187.52 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) % 187.43/187.52 => 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) ) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_com_Osize_I12_J,axiom, % 187.43/187.52 ! [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))) ). % 187.43/187.52 % 187.43/187.52 fof(fact_com_Osize_I13_J,axiom, % 187.43/187.52 ! [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))) ). % 187.43/187.52 % 187.43/187.52 fof(fact_com_Osize_I14_J,axiom, % 187.43/187.52 ! [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))) ). % 187.43/187.52 % 187.43/187.52 fof(fact_finite__Plus__iff,axiom, % 187.43/187.52 ! [V_B_2,V_A_2,T_b,T_a] : % 187.43/187.52 ( 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))) % 187.43/187.52 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.43/187.52 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_finite__Plus,axiom, % 187.43/187.52 ! [V_B_2,T_b,V_A_2,T_a] : % 187.43/187.52 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.43/187.52 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 187.43/187.52 => 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))) ) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_finite__PlusD_I1_J,axiom, % 187.43/187.52 ! [V_B_2,V_A_2,T_b,T_a] : % 187.43/187.52 ( 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))) % 187.43/187.52 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_finite__PlusD_I2_J,axiom, % 187.43/187.52 ! [V_B_2,V_A_2,T_b,T_a] : % 187.43/187.52 ( 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))) % 187.43/187.52 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom, % 187.43/187.52 ! [V_c,V_a,T_a] : % 187.43/187.52 ( class_Rings_Ocomm__semiring__1(T_a) % 187.43/187.52 => 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) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom, % 187.43/187.52 ! [V_d,V_c,V_a,T_a] : % 187.43/187.52 ( class_Rings_Ocomm__semiring__1(T_a) % 187.43/187.52 => 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)) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom, % 187.43/187.52 ! [V_d,V_c,V_a,T_a] : % 187.43/187.52 ( class_Rings_Ocomm__semiring__1(T_a) % 187.43/187.52 => 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) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom, % 187.43/187.52 ! [V_c,V_b,V_a,T_a] : % 187.43/187.52 ( class_Rings_Ocomm__semiring__1(T_a) % 187.43/187.52 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b),V_c)) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom, % 187.43/187.52 ! [V_c,V_b,V_a,T_a] : % 187.43/187.52 ( class_Rings_Ocomm__semiring__1(T_a) % 187.43/187.52 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b)),V_c) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_c)),V_b) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom, % 187.43/187.52 ! [V_d,V_c,V_b,V_a,T_a] : % 187.43/187.52 ( class_Rings_Ocomm__semiring__1(T_a) % 187.43/187.52 => 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)) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_com_Osize_I15_J,axiom, % 187.43/187.52 ! [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) ). % 187.43/187.52 % 187.43/187.52 fof(fact_com_Osize_I16_J,axiom, % 187.43/187.52 ! [V_fun_2,V_pname_2,V_vname_2] : hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OCall(V_vname_2,V_pname_2,V_fun_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 187.43/187.52 % 187.43/187.52 fof(fact_com_Osize_I9_J,axiom, % 187.43/187.52 hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 187.43/187.52 % 187.43/187.52 fof(fact_card__Plus,axiom, % 187.43/187.52 ! [V_B_2,T_b,V_A_2,T_a] : % 187.43/187.52 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.43/187.52 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 187.43/187.52 => 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)) ) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_less__eq__nat_Osimps_I2_J,axiom, % 187.43/187.52 ! [V_n_2,V_m_2] : % 187.43/187.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_n_2)) % 187.43/187.52 <=> 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)) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_Plus__eq__empty__conv,axiom, % 187.43/187.52 ! [V_B_2,V_A_2,T_b,T_a] : % 187.43/187.52 ( 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)) % 187.43/187.52 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.43/187.52 & V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_Ints__odd__less__0,axiom, % 187.43/187.52 ! [V_a_2,T_a] : % 187.43/187.52 ( class_Rings_Olinordered__idom(T_a) % 187.43/187.52 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a))) % 187.43/187.52 => ( 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))) % 187.43/187.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_ex__least__nat__less,axiom, % 187.43/187.52 ! [V_n_2,V_P_2] : % 187.43/187.52 ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) % 187.43/187.52 => ( hBOOL(hAPP(V_P_2,V_n_2)) % 187.43/187.52 => ? [B_k] : % 187.43/187.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_k),V_n_2)) % 187.43/187.52 & ! [B_i] : % 187.43/187.52 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_k)) % 187.43/187.52 => ~ hBOOL(hAPP(V_P_2,B_i)) ) % 187.43/187.52 & 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)))) ) ) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_card__def,axiom, % 187.43/187.52 ! [V_A_2,T_a] : % 187.43/187.52 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.43/187.52 => 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) ) % 187.43/187.52 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.43/187.52 => hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_card_Oeq__fold__g,axiom, % 187.43/187.52 ! [V_A_2,T_a] : % 187.43/187.52 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.43/187.52 => 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) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_fold1Set_Oequations,axiom, % 187.43/187.52 ! [V_a3_2,V_a2_2,V_a1_2,V_f_2,T_a] : % 187.43/187.52 ( 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)) % 187.43/187.52 <=> ? [B_a,B_A] : % 187.43/187.52 ( hAPP(hAPP(c_Set_Oinsert(T_a),V_a1_2),V_a2_2) = hAPP(hAPP(c_Set_Oinsert(T_a),B_a),B_A) % 187.43/187.52 & hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_a,V_f_2,B_a,B_A),V_a3_2)) % 187.43/187.52 & ~ hBOOL(hAPP(hAPP(c_member(T_a),B_a),B_A)) ) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_insert__fold1SetE,axiom, % 187.43/187.52 ! [V_x_2,V_X_2,V_a_2,V_f_2,T_a] : % 187.43/187.52 ( 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)) % 187.43/187.52 => ~ ! [B_a,B_A] : % 187.43/187.52 ( hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_X_2) = hAPP(hAPP(c_Set_Oinsert(T_a),B_a),B_A) % 187.43/187.52 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_a,V_f_2,B_a,B_A),V_x_2)) % 187.43/187.52 => hBOOL(hAPP(hAPP(c_member(T_a),B_a),B_A)) ) ) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_Ints__odd__nonzero,axiom, % 187.43/187.52 ! [V_a_2,T_a] : % 187.43/187.52 ( class_Int_Oring__char__0(T_a) % 187.43/187.52 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a))) % 187.43/187.52 => 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) ) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_dom__eq__singleton__conv,axiom, % 187.43/187.52 ! [V_x_2,V_f_2,T_b,T_a] : % 187.43/187.52 ( 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))) % 187.43/187.52 <=> ? [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)) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_map__upd__Some__unfold,axiom, % 187.43/187.52 ! [V_y_2,V_x_2,V_b_2,V_a_2,V_m_2,T_a,T_b] : % 187.43/187.52 ( 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) % 187.43/187.52 <=> ( ( V_x_2 = V_a_2 % 187.43/187.52 & V_b_2 = V_y_2 ) % 187.43/187.52 | ( V_x_2 != V_a_2 % 187.43/187.52 & hAPP(V_m_2,V_x_2) = hAPP(c_Option_Ooption_OSome(T_a),V_y_2) ) ) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_map__upd__triv,axiom, % 187.43/187.52 ! [T_b,V_x_2,T_a,V_k_2,V_t_2] : % 187.43/187.52 ( hAPP(V_t_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_x_2) % 187.43/187.52 => 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 ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_map__upd__eqD1,axiom, % 187.43/187.52 ! [V_y_2,V_n_2,V_x_2,V_a_2,V_m_2,T_b,T_a] : % 187.43/187.52 ( 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)) % 187.43/187.52 => V_x_2 = V_y_2 ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_fold__image__empty,axiom, % 187.43/187.52 ! [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 ). % 187.43/187.52 % 187.43/187.52 fof(fact_domI,axiom, % 187.43/187.52 ! [T_b,V_b_2,T_a,V_a_2,V_m_2] : % 187.43/187.52 ( hAPP(V_m_2,V_a_2) = hAPP(c_Option_Ooption_OSome(T_a),V_b_2) % 187.43/187.52 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Map_Odom(T_b,T_a,V_m_2))) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_insert__dom,axiom, % 187.43/187.52 ! [T_b,V_y_2,T_a,V_x_2,V_f_2] : % 187.43/187.52 ( hAPP(V_f_2,V_x_2) = hAPP(c_Option_Ooption_OSome(T_a),V_y_2) % 187.43/187.52 => 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) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_ranI,axiom, % 187.43/187.52 ! [T_b,V_b_2,T_a,V_a_2,V_m_2] : % 187.43/187.52 ( hAPP(V_m_2,V_a_2) = hAPP(c_Option_Ooption_OSome(T_a),V_b_2) % 187.43/187.52 => hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Map_Oran(T_b,T_a,V_m_2))) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_map__upd__nonempty,axiom, % 187.43/187.52 ! [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)) ). % 187.43/187.52 % 187.43/187.52 fof(fact_folding__image__simple_Oeq__fold__g,axiom, % 187.43/187.52 ! [V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 187.43/187.52 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 187.43/187.52 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.43/187.52 => 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) ) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_Ints__0,axiom, % 187.43/187.52 ! [T_a] : % 187.43/187.52 ( class_Rings_Oring__1(T_a) % 187.43/187.52 => hBOOL(hAPP(hAPP(c_member(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Int_Oring__1__class_OInts(T_a))) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_Ints__add,axiom, % 187.43/187.52 ! [V_b_2,V_a_2,T_a] : % 187.43/187.52 ( class_Rings_Oring__1(T_a) % 187.43/187.52 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a))) % 187.43/187.52 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Int_Oring__1__class_OInts(T_a))) % 187.43/187.52 => 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))) ) ) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_Ints__diff,axiom, % 187.43/187.52 ! [V_b_2,V_a_2,T_a] : % 187.43/187.52 ( class_Rings_Oring__1(T_a) % 187.43/187.52 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a))) % 187.43/187.52 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Int_Oring__1__class_OInts(T_a))) % 187.43/187.52 => 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))) ) ) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_Ints__1,axiom, % 187.43/187.52 ! [T_a] : % 187.43/187.52 ( class_Rings_Oring__1(T_a) % 187.43/187.52 => hBOOL(hAPP(hAPP(c_member(T_a),c_Groups_Oone__class_Oone(T_a)),c_Int_Oring__1__class_OInts(T_a))) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_WT_Oequations_I7_J,axiom, % 187.43/187.52 ! [V_a_2] : % 187.43/187.52 ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_a_2))) % 187.43/187.52 <=> ? [B_y] : hAPP(c_Com_Obody,V_a_2) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),B_y) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_Ints__double__eq__0__iff,axiom, % 187.43/187.52 ! [V_a_2,T_a] : % 187.43/187.52 ( class_Int_Oring__char__0(T_a) % 187.43/187.52 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a))) % 187.43/187.52 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_a) % 187.43/187.52 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_ran__map__upd,axiom, % 187.43/187.52 ! [V_b_2,T_b,T_a,V_a_2,V_m_2] : % 187.43/187.52 ( hAPP(V_m_2,V_a_2) = c_Option_Ooption_ONone(T_a) % 187.43/187.52 => 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)) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_WT__bodiesD,axiom, % 187.43/187.52 ! [V_b,V_pn] : % 187.43/187.52 ( c_Com_OWT__bodies % 187.43/187.52 => ( hAPP(c_Com_Obody,V_pn) = hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),V_b) % 187.43/187.52 => hBOOL(hAPP(c_Com_OWT,V_b)) ) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_the_Osimps,axiom, % 187.43/187.52 ! [V_x,T_a] : hAPP(c_Option_Othe(T_a),hAPP(c_Option_Ooption_OSome(T_a),V_x)) = V_x ). % 187.43/187.52 % 187.43/187.52 fof(fact_option_Osimps_I2_J,axiom, % 187.43/187.52 ! [V_a_H,T_a] : c_Option_Ooption_ONone(T_a) != hAPP(c_Option_Ooption_OSome(T_a),V_a_H) ). % 187.43/187.52 % 187.43/187.52 fof(fact_option_Osimps_I3_J,axiom, % 187.43/187.52 ! [V_a_H,T_a] : hAPP(c_Option_Ooption_OSome(T_a),V_a_H) != c_Option_Ooption_ONone(T_a) ). % 187.43/187.52 % 187.43/187.52 fof(fact_not__Some__eq,axiom, % 187.43/187.52 ! [T_a,V_x_2] : % 187.43/187.52 ( ! [B_y] : V_x_2 != hAPP(c_Option_Ooption_OSome(T_a),B_y) % 187.43/187.52 <=> V_x_2 = c_Option_Ooption_ONone(T_a) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_not__None__eq,axiom, % 187.43/187.52 ! [T_a,V_x_2] : % 187.43/187.52 ( V_x_2 != c_Option_Ooption_ONone(T_a) % 187.43/187.52 <=> ? [B_y] : V_x_2 = hAPP(c_Option_Ooption_OSome(T_a),B_y) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_option_Osize_I2_J,axiom, % 187.43/187.52 ! [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))) ). % 187.43/187.52 % 187.43/187.52 fof(fact_ran__restrictD,axiom, % 187.43/187.52 ! [V_A_2,V_m_2,T_b,V_y_2,T_a] : % 187.43/187.52 ( 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)))) % 187.43/187.52 => ? [B_x] : % 187.43/187.52 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 187.43/187.52 & hAPP(V_m_2,B_x) = hAPP(c_Option_Ooption_OSome(T_a),V_y_2) ) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_WTs__elim__cases_I7_J,axiom, % 187.43/187.52 ! [V_P] : % 187.43/187.52 ( hBOOL(hAPP(c_Com_OWT,hAPP(c_Com_Ocom_OBODY,V_P))) % 187.43/187.52 => ~ ! [B_y] : hAPP(c_Com_Obody,V_P) != hAPP(c_Option_Ooption_OSome(tc_Com_Ocom),B_y) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_option_Osize_I1_J,axiom, % 187.43/187.52 ! [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) ). % 187.43/187.52 % 187.43/187.52 fof(fact_option_Oinject,axiom, % 187.43/187.52 ! [V_a_H_2,V_a_2,T_a] : % 187.43/187.52 ( hAPP(c_Option_Ooption_OSome(T_a),V_a_2) = hAPP(c_Option_Ooption_OSome(T_a),V_a_H_2) % 187.43/187.52 <=> V_a_2 = V_a_H_2 ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_nat_Osize_I2_J,axiom, % 187.43/187.52 ! [V_nat] : c_Nat_Onat_Onat__size(hAPP(c_Nat_OSuc,V_nat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Nat_Onat_Onat__size(V_nat)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 187.43/187.52 % 187.43/187.52 fof(fact_Option_Oset_Osimps_I2_J,axiom, % 187.43/187.52 ! [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))) ). % 187.43/187.52 % 187.43/187.52 fof(fact_nat_Osize_I4_J,axiom, % 187.43/187.52 ! [V_nat] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_nat)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),V_nat)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 187.43/187.52 % 187.43/187.52 fof(fact_option_Osize_I4_J,axiom, % 187.43/187.52 ! [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) ). % 187.43/187.52 % 187.43/187.52 fof(fact_option_Osize_I3_J,axiom, % 187.43/187.52 ! [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) ). % 187.43/187.52 % 187.43/187.52 fof(fact_Option_Oset_Osimps_I1_J,axiom, % 187.43/187.52 ! [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)) ). % 187.43/187.52 % 187.43/187.52 fof(fact_set__empty__eq,axiom, % 187.43/187.52 ! [V_xo_2,T_a] : % 187.43/187.52 ( c_Option_Oset(T_a,V_xo_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.43/187.52 <=> V_xo_2 = c_Option_Ooption_ONone(T_a) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_elem__set,axiom, % 187.43/187.52 ! [V_xo_2,V_x_2,T_a] : % 187.43/187.52 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Option_Oset(T_a,V_xo_2))) % 187.43/187.52 <=> V_xo_2 = hAPP(c_Option_Ooption_OSome(T_a),V_x_2) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_restrict__upd__same,axiom, % 187.43/187.52 ! [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))))) ). % 187.43/187.52 % 187.43/187.52 fof(fact_ComplI,axiom, % 187.43/187.52 ! [V_A_2,V_c_2,T_a] : % 187.43/187.52 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) % 187.43/187.52 => hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2))) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_minus__minus,axiom, % 187.43/187.52 ! [V_a,T_a] : % 187.43/187.52 ( class_Groups_Ogroup__add(T_a) % 187.43/187.52 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)) = V_a ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_double__compl,axiom, % 187.43/187.52 ! [V_x,T_a] : % 187.43/187.52 ( class_Lattices_Oboolean__algebra(T_a) % 187.43/187.52 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)) = V_x ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_uminus__apply,axiom, % 187.43/187.52 ! [V_x_2,V_A_2,T_b,T_a] : % 187.43/187.52 ( class_Groups_Ouminus(T_a) % 187.43/187.52 => 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)) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_equation__minus__iff,axiom, % 187.43/187.52 ! [V_b_2,V_a_2,T_a] : % 187.43/187.52 ( class_Groups_Ogroup__add(T_a) % 187.43/187.52 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2) % 187.43/187.52 <=> V_b_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) ) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_minus__equation__iff,axiom, % 187.43/187.52 ! [V_b_2,V_a_2,T_a] : % 187.43/187.52 ( class_Groups_Ogroup__add(T_a) % 187.43/187.52 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) = V_b_2 % 187.43/187.52 <=> hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2) = V_a_2 ) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_neg__equal__iff__equal,axiom, % 187.43/187.52 ! [V_b_2,V_a_2,T_a] : % 187.43/187.52 ( class_Groups_Ogroup__add(T_a) % 187.43/187.52 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2) % 187.43/187.52 <=> V_a_2 = V_b_2 ) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_compl__eq__compl__iff,axiom, % 187.43/187.52 ! [V_y_2,V_x_2,T_a] : % 187.43/187.52 ( class_Lattices_Oboolean__algebra(T_a) % 187.43/187.52 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y_2) % 187.43/187.52 <=> V_x_2 = V_y_2 ) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_fun__Compl__def,axiom, % 187.43/187.52 ! [V_x_2,V_A_2,T_b,T_a] : % 187.43/187.52 ( class_Groups_Ouminus(T_a) % 187.43/187.52 => 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)) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_double__complement,axiom, % 187.43/187.52 ! [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 ). % 187.43/187.52 % 187.43/187.52 fof(fact_Compl__eq__Compl__iff,axiom, % 187.43/187.52 ! [V_B_2,V_A_2,T_a] : % 187.43/187.52 ( 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) % 187.43/187.52 <=> V_A_2 = V_B_2 ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_nat__size,axiom, % 187.43/187.52 ! [V_n] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),V_n) = V_n ). % 187.43/187.52 % 187.43/187.52 fof(fact_compl__mono,axiom, % 187.43/187.52 ! [V_y,V_x,T_a] : % 187.43/187.52 ( class_Lattices_Oboolean__algebra(T_a) % 187.43/187.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 187.43/187.52 => 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))) ) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_le__imp__neg__le,axiom, % 187.43/187.52 ! [V_b,V_a,T_a] : % 187.43/187.52 ( class_Groups_Oordered__ab__group__add(T_a) % 187.43/187.52 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 187.43/187.52 => 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))) ) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_compl__le__compl__iff,axiom, % 187.43/187.52 ! [V_y_2,V_x_2,T_a] : % 187.43/187.52 ( class_Lattices_Oboolean__algebra(T_a) % 187.43/187.52 => ( 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))) % 187.43/187.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) ) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_neg__le__iff__le,axiom, % 187.43/187.52 ! [V_a_2,V_b_2,T_a] : % 187.43/187.52 ( class_Groups_Oordered__ab__group__add(T_a) % 187.43/187.52 => ( 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))) % 187.43/187.52 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) ) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_minus__le__iff,axiom, % 187.43/187.52 ! [V_b_2,V_a_2,T_a] : % 187.43/187.52 ( class_Groups_Oordered__ab__group__add(T_a) % 187.43/187.52 => ( 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)) % 187.43/187.52 <=> 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)) ) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_le__minus__iff,axiom, % 187.43/187.52 ! [V_b_2,V_a_2,T_a] : % 187.43/187.52 ( class_Groups_Oordered__ab__group__add(T_a) % 187.43/187.52 => ( 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))) % 187.43/187.52 <=> 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))) ) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_neg__equal__zero,axiom, % 187.43/187.52 ! [V_a_2,T_a] : % 187.43/187.52 ( class_Groups_Olinordered__ab__group__add(T_a) % 187.43/187.52 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) = V_a_2 % 187.43/187.52 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_neg__equal__0__iff__equal,axiom, % 187.43/187.52 ! [V_a_2,T_a] : % 187.43/187.52 ( class_Groups_Ogroup__add(T_a) % 187.43/187.52 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) = c_Groups_Ozero__class_Ozero(T_a) % 187.43/187.52 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_equal__neg__zero,axiom, % 187.43/187.52 ! [V_a_2,T_a] : % 187.43/187.52 ( class_Groups_Olinordered__ab__group__add(T_a) % 187.43/187.52 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) % 187.43/187.52 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_neg__0__equal__iff__equal,axiom, % 187.43/187.52 ! [V_a_2,T_a] : % 187.43/187.52 ( class_Groups_Ogroup__add(T_a) % 187.43/187.52 => ( c_Groups_Ozero__class_Ozero(T_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) % 187.43/187.52 <=> c_Groups_Ozero__class_Ozero(T_a) = V_a_2 ) ) ). % 187.43/187.52 % 187.43/187.52 fof(fact_minus__zero,axiom, % 187.43/187.52 ! [T_a] : % 187.43/187.52 ( class_Groups_Ogroup__add(T_a) % 187.43/187.53 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_less__minus__iff,axiom, % 187.43/187.53 ! [V_b_2,V_a_2,T_a] : % 187.43/187.53 ( class_Groups_Oordered__ab__group__add(T_a) % 187.43/187.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2))) % 187.43/187.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2))) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_minus__less__iff,axiom, % 187.43/187.53 ! [V_b_2,V_a_2,T_a] : % 187.43/187.53 ( class_Groups_Oordered__ab__group__add(T_a) % 187.43/187.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),V_b_2)) % 187.43/187.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2)),V_a_2)) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_neg__less__iff__less,axiom, % 187.43/187.53 ! [V_a_2,V_b_2,T_a] : % 187.43/187.53 ( class_Groups_Oordered__ab__group__add(T_a) % 187.43/187.53 => ( 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))) % 187.43/187.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_minus__add__distrib,axiom, % 187.43/187.53 ! [V_b,V_a,T_a] : % 187.43/187.53 ( class_Groups_Oab__group__add(T_a) % 187.43/187.53 => 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)) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_minus__add,axiom, % 187.43/187.53 ! [V_b,V_a,T_a] : % 187.43/187.53 ( class_Groups_Ogroup__add(T_a) % 187.43/187.53 => 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)) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_add__minus__cancel,axiom, % 187.43/187.53 ! [V_b,V_a,T_a] : % 187.43/187.53 ( class_Groups_Ogroup__add(T_a) % 187.43/187.53 => 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 ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_minus__add__cancel,axiom, % 187.43/187.53 ! [V_b,V_a,T_a] : % 187.43/187.53 ( class_Groups_Ogroup__add(T_a) % 187.43/187.53 => 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 ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_Compl__iff,axiom, % 187.43/187.53 ! [V_A_2,V_c_2,T_a] : % 187.43/187.53 ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2))) % 187.43/187.53 <=> ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_ComplD,axiom, % 187.43/187.53 ! [V_A_2,V_c_2,T_a] : % 187.43/187.53 ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2))) % 187.43/187.53 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_ComplE,axiom, % 187.43/187.53 ! [V_A_2,V_c_2,T_a] : % 187.43/187.53 ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2))) % 187.43/187.53 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_minus__diff__eq,axiom, % 187.43/187.53 ! [V_b,V_a,T_a] : % 187.43/187.53 ( class_Groups_Oab__group__add(T_a) % 187.43/187.53 => 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) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_Compl__subset__Compl__iff,axiom, % 187.43/187.53 ! [V_B_2,V_A_2,T_a] : % 187.43/187.53 ( 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))) % 187.43/187.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_Compl__anti__mono,axiom, % 187.43/187.53 ! [V_B_2,V_A_2,T_a] : % 187.43/187.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 187.43/187.53 => 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))) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_neg__0__le__iff__le,axiom, % 187.43/187.53 ! [V_a_2,T_a] : % 187.43/187.53 ( class_Groups_Oordered__ab__group__add(T_a) % 187.43/187.53 => ( 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))) % 187.43/187.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_le__minus__self__iff,axiom, % 187.43/187.53 ! [V_a_2,T_a] : % 187.43/187.53 ( class_Groups_Olinordered__ab__group__add(T_a) % 187.43/187.53 => ( 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))) % 187.43/187.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_neg__le__0__iff__le,axiom, % 187.43/187.53 ! [V_a_2,T_a] : % 187.43/187.53 ( class_Groups_Oordered__ab__group__add(T_a) % 187.43/187.53 => ( 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))) % 187.43/187.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_minus__le__self__iff,axiom, % 187.43/187.53 ! [V_a_2,T_a] : % 187.43/187.53 ( class_Groups_Olinordered__ab__group__add(T_a) % 187.43/187.53 => ( 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)) % 187.43/187.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_less__minus__self__iff,axiom, % 187.43/187.53 ! [V_a_2,T_a] : % 187.43/187.53 ( class_Rings_Olinordered__idom(T_a) % 187.43/187.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2))) % 187.43/187.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_neg__less__nonneg,axiom, % 187.43/187.53 ! [V_a_2,T_a] : % 187.43/187.53 ( class_Groups_Olinordered__ab__group__add(T_a) % 187.43/187.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),V_a_2)) % 187.43/187.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_neg__less__0__iff__less,axiom, % 187.43/187.53 ! [V_a_2,T_a] : % 187.43/187.53 ( class_Groups_Oordered__ab__group__add(T_a) % 187.43/187.53 => ( 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))) % 187.43/187.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_neg__0__less__iff__less,axiom, % 187.43/187.53 ! [V_a_2,T_a] : % 187.43/187.53 ( class_Groups_Oordered__ab__group__add(T_a) % 187.43/187.53 => ( 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))) % 187.43/187.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_minus__unique,axiom, % 187.43/187.53 ! [V_b,V_a,T_a] : % 187.43/187.53 ( class_Groups_Ogroup__add(T_a) % 187.43/187.53 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a) % 187.43/187.53 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) = V_b ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_ab__left__minus,axiom, % 187.43/187.53 ! [V_a,T_a] : % 187.43/187.53 ( class_Groups_Oab__group__add(T_a) % 187.43/187.53 => 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) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_left__minus,axiom, % 187.43/187.53 ! [V_a,T_a] : % 187.43/187.53 ( class_Groups_Ogroup__add(T_a) % 187.43/187.53 => 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) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_eq__neg__iff__add__eq__0,axiom, % 187.43/187.53 ! [V_b_2,V_a_2,T_a] : % 187.43/187.53 ( class_Groups_Ogroup__add(T_a) % 187.43/187.53 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2) % 187.43/187.53 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_right__minus,axiom, % 187.43/187.53 ! [V_a,T_a] : % 187.43/187.53 ( class_Groups_Ogroup__add(T_a) % 187.43/187.53 => 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) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_diff__0,axiom, % 187.43/187.53 ! [V_a,T_a] : % 187.43/187.53 ( class_Groups_Ogroup__add(T_a) % 187.43/187.53 => 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) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_diff__def,axiom, % 187.43/187.53 ! [V_b,V_a,T_a] : % 187.43/187.53 ( class_Groups_Ogroup__add(T_a) % 187.43/187.53 => 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)) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_ab__diff__minus,axiom, % 187.43/187.53 ! [V_b,V_a,T_a] : % 187.43/187.53 ( class_Groups_Oab__group__add(T_a) % 187.43/187.53 => 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)) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_diff__minus__eq__add,axiom, % 187.43/187.53 ! [V_b,V_a,T_a] : % 187.43/187.53 ( class_Groups_Ogroup__add(T_a) % 187.43/187.53 => 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) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J,axiom, % 187.43/187.53 ! [V_y,V_x,T_a] : % 187.43/187.53 ( class_Rings_Ocomm__ring__1(T_a) % 187.43/187.53 => 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)) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_subset__Compl__self__eq,axiom, % 187.43/187.53 ! [V_A_2,T_a] : % 187.43/187.53 ( 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))) % 187.43/187.53 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_Ints__minus,axiom, % 187.43/187.53 ! [V_a_2,T_a] : % 187.43/187.53 ( class_Rings_Oring__1(T_a) % 187.43/187.53 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a))) % 187.43/187.53 => 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))) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_nat_Osize_I3_J,axiom, % 187.43/187.53 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) ). % 187.43/187.53 % 187.43/187.53 fof(fact_nat_Osize_I1_J,axiom, % 187.43/187.53 c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 187.43/187.53 % 187.43/187.53 fof(fact_restrict__complement__singleton__eq,axiom, % 187.43/187.53 ! [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)) ). % 187.43/187.53 % 187.43/187.53 fof(fact_sgn__1__neg,axiom, % 187.43/187.53 ! [V_a_2,T_a] : % 187.43/187.53 ( class_Rings_Olinordered__idom(T_a) % 187.43/187.53 => ( 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)) % 187.43/187.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_sgn__neg,axiom, % 187.43/187.53 ! [V_a,T_a] : % 187.43/187.53 ( class_Rings_Olinordered__idom(T_a) % 187.43/187.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 187.43/187.53 => c_Groups_Osgn__class_Osgn(T_a,V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_sgn__if,axiom, % 187.43/187.53 ! [V_x,T_a] : % 187.43/187.53 ( class_Groups_Osgn__if(T_a) % 187.43/187.53 => ( ( V_x = c_Groups_Ozero__class_Ozero(T_a) % 187.43/187.53 => c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Ozero__class_Ozero(T_a) ) % 187.43/187.53 & ( V_x != c_Groups_Ozero__class_Ozero(T_a) % 187.43/187.53 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 187.43/187.53 => c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Oone__class_Oone(T_a) ) % 187.43/187.53 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 187.43/187.53 => c_Groups_Osgn__class_Osgn(T_a,V_x) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_fold__graph__permute__diff,axiom, % 187.43/187.53 ! [V_a_2,V_x_2,V_A_2,V_b_2,T_a] : % 187.43/187.53 ( class_Groups_Oab__semigroup__mult(T_a) % 187.43/187.53 => ( 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)) % 187.43/187.53 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 187.43/187.53 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),V_A_2)) % 187.43/187.53 => 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)) ) ) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_card_Oneutral,axiom, % 187.43/187.53 ! [V_A_2,T_a] : % 187.43/187.53 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.43/187.53 => ( ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 187.43/187.53 => c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 187.43/187.53 => hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_expand__Suc,axiom, % 187.43/187.53 ! [V_v] : % 187.43/187.53 ( 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))) % 187.43/187.53 => 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))) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_com_Osize_I3_J,axiom, % 187.43/187.53 ! [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))) ). % 187.43/187.53 % 187.43/187.53 fof(fact_com_Osize_I11_J,axiom, % 187.43/187.53 ! [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))) ). % 187.43/187.53 % 187.43/187.53 fof(fact_option_Osimps_I5_J,axiom, % 187.43/187.53 ! [V_a_2,V_f2_2,V_f1_2,T_b,T_a] : hAPP(c_Option_Ooption_Ooption__case(T_a,T_b,V_f1_2,V_f2_2),hAPP(c_Option_Ooption_OSome(T_b),V_a_2)) = hAPP(V_f2_2,V_a_2) ). % 187.43/187.53 % 187.43/187.53 fof(fact_WTs__elim__cases_I3_J,axiom, % 187.43/187.53 ! [V_c_2,V_a_2,V_Y_2] : % 187.43/187.53 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(V_Y_2,V_a_2,V_c_2))) % 187.43/187.53 => hBOOL(hAPP(c_Com_OWT,V_c_2)) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_diff__number__of__eq,axiom, % 187.43/187.53 ! [V_w,V_v,T_a] : % 187.43/187.53 ( class_Int_Onumber__ring(T_a) % 187.43/187.53 => 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))) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_minus__number__of__mult,axiom, % 187.43/187.53 ! [V_z,V_w,T_a] : % 187.43/187.53 ( class_Int_Onumber__ring(T_a) % 187.43/187.53 => 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) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_sgn__times,axiom, % 187.43/187.53 ! [V_b,V_a,T_a] : % 187.43/187.53 ( class_Rings_Olinordered__idom(T_a) % 187.43/187.53 => 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)) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_sgn__sgn,axiom, % 187.43/187.53 ! [V_a,T_a] : % 187.43/187.53 ( class_Rings_Olinordered__idom(T_a) % 187.43/187.53 => 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) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_com_Osimps_I2_J,axiom, % 187.43/187.53 ! [V_com_H_2,V_fun_H_2,V_loc_H_2,V_com_2,V_fun_2,V_loc_2] : % 187.43/187.53 ( 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) % 187.43/187.53 <=> ( V_loc_2 = V_loc_H_2 % 187.43/187.53 & V_fun_2 = V_fun_H_2 % 187.43/187.53 & V_com_2 = V_com_H_2 ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_ab__semigroup__mult__class_Omult__ac_I1_J,axiom, % 187.43/187.53 ! [V_c,V_b,V_a,T_a] : % 187.43/187.53 ( class_Groups_Oab__semigroup__mult(T_a) % 187.43/187.53 => 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)) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_mult__left__idem,axiom, % 187.43/187.53 ! [V_b,V_a,T_a] : % 187.43/187.53 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 187.43/187.53 => 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) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_mult__idem,axiom, % 187.43/187.53 ! [V_x,T_a] : % 187.43/187.53 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 187.43/187.53 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x) = V_x ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_times_Oidem,axiom, % 187.43/187.53 ! [V_a,T_a] : % 187.43/187.53 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 187.43/187.53 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) = V_a ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,axiom, % 187.43/187.53 ! [V_ry,V_rx,V_ly,V_lx,T_a] : % 187.43/187.53 ( class_Rings_Ocomm__semiring__1(T_a) % 187.43/187.53 => 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)) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,axiom, % 187.43/187.53 ! [V_ry,V_rx,V_ly,V_lx,T_a] : % 187.43/187.53 ( class_Rings_Ocomm__semiring__1(T_a) % 187.43/187.53 => 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)) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J,axiom, % 187.43/187.53 ! [V_ry,V_rx,V_ly,V_lx,T_a] : % 187.43/187.53 ( class_Rings_Ocomm__semiring__1(T_a) % 187.43/187.53 => 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))) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,axiom, % 187.43/187.53 ! [V_rx,V_ly,V_lx,T_a] : % 187.43/187.53 ( class_Rings_Ocomm__semiring__1(T_a) % 187.43/187.53 => 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) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,axiom, % 187.43/187.53 ! [V_rx,V_ly,V_lx,T_a] : % 187.43/187.53 ( class_Rings_Ocomm__semiring__1(T_a) % 187.43/187.53 => 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)) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_mult__number__of__left,axiom, % 187.43/187.53 ! [V_z,V_w,V_v,T_a] : % 187.43/187.53 ( class_Int_Onumber__ring(T_a) % 187.43/187.53 => 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) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_eq__number__of,axiom, % 187.43/187.53 ! [V_y_2,V_x_2,T_a] : % 187.43/187.53 ( ( class_Int_Onumber__ring(T_a) % 187.43/187.53 & class_Int_Oring__char__0(T_a) ) % 187.43/187.53 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2) % 187.43/187.53 <=> V_x_2 = V_y_2 ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_arith__simps_I32_J,axiom, % 187.43/187.53 ! [V_w,V_v,T_a] : % 187.43/187.53 ( class_Int_Onumber__ring(T_a) % 187.43/187.53 => 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)) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_number__of__reorient,axiom, % 187.43/187.53 ! [V_x_2,V_w_2,T_a] : % 187.43/187.53 ( class_Int_Onumber(T_a) % 187.43/187.53 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) = V_x_2 % 187.43/187.53 <=> V_x_2 = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,axiom, % 187.43/187.53 ! [V_ry,V_rx,V_lx,T_a] : % 187.43/187.53 ( class_Rings_Ocomm__semiring__1(T_a) % 187.43/187.53 => 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) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,axiom, % 187.43/187.53 ! [V_ry,V_rx,V_lx,T_a] : % 187.43/187.53 ( class_Rings_Ocomm__semiring__1(T_a) % 187.43/187.53 => 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)) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom, % 187.43/187.53 ! [V_b,V_a,T_a] : % 187.43/187.53 ( class_Rings_Ocomm__semiring__1(T_a) % 187.43/187.53 => 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) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_number__of__mult,axiom, % 187.43/187.53 ! [V_w,V_v,T_a] : % 187.43/187.53 ( class_Int_Onumber__ring(T_a) % 187.43/187.53 => 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)) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_right__diff__distrib__number__of,axiom, % 187.43/187.53 ! [V_c,V_b,V_v,T_b] : % 187.43/187.53 ( ( class_Int_Onumber(T_b) % 187.43/187.53 & class_Rings_Oring(T_b) ) % 187.43/187.53 => 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)) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_left__diff__distrib__number__of,axiom, % 187.43/187.53 ! [V_v,V_b,V_a,T_b] : % 187.43/187.53 ( ( class_Int_Onumber(T_b) % 187.43/187.53 & class_Rings_Oring(T_b) ) % 187.43/187.53 => 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))) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_right__distrib__number__of,axiom, % 187.43/187.53 ! [V_c,V_b,V_v,T_b] : % 187.43/187.53 ( ( class_Int_Onumber(T_b) % 187.43/187.53 & class_Rings_Osemiring(T_b) ) % 187.43/187.53 => 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)) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_left__distrib__number__of,axiom, % 187.43/187.53 ! [V_v,V_b,V_a,T_b] : % 187.43/187.53 ( ( class_Int_Onumber(T_b) % 187.43/187.53 & class_Rings_Osemiring(T_b) ) % 187.43/187.53 => 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))) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_add__number__of__diff2,axiom, % 187.43/187.53 ! [V_w,V_c,V_v,T_a] : % 187.43/187.53 ( class_Int_Onumber__ring(T_a) % 187.43/187.53 => 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) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_le__number__of,axiom, % 187.43/187.53 ! [V_y_2,V_x_2,T_a] : % 187.43/187.53 ( ( class_Int_Onumber__ring(T_a) % 187.43/187.53 & class_Rings_Olinordered__idom(T_a) ) % 187.43/187.53 => ( 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))) % 187.43/187.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),V_y_2)) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_less__number__of,axiom, % 187.43/187.53 ! [V_y_2,V_x_2,T_a] : % 187.43/187.53 ( ( class_Int_Onumber__ring(T_a) % 187.43/187.53 & class_Rings_Olinordered__idom(T_a) ) % 187.43/187.53 => ( 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))) % 187.43/187.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2)) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_add__number__of__left,axiom, % 187.43/187.53 ! [V_z,V_w,V_v,T_a] : % 187.43/187.53 ( class_Int_Onumber__ring(T_a) % 187.43/187.53 => 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) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_add__number__of__eq,axiom, % 187.43/187.53 ! [V_w,V_v,T_a] : % 187.43/187.53 ( class_Int_Onumber__ring(T_a) % 187.43/187.53 => 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)) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_number__of__add,axiom, % 187.43/187.53 ! [V_w,V_v,T_a] : % 187.43/187.53 ( class_Int_Onumber__ring(T_a) % 187.43/187.53 => 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)) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_number__of__diff,axiom, % 187.43/187.53 ! [V_w,V_v,T_a] : % 187.43/187.53 ( class_Int_Onumber__ring(T_a) % 187.43/187.53 => 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)) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_number__of__minus,axiom, % 187.43/187.53 ! [V_w,T_a] : % 187.43/187.53 ( class_Int_Onumber__ring(T_a) % 187.43/187.53 => 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)) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_arith__simps_I30_J,axiom, % 187.43/187.53 ! [V_w,T_a] : % 187.43/187.53 ( class_Int_Onumber__ring(T_a) % 187.43/187.53 => 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)) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom, % 187.43/187.53 ! [V_a,T_a] : % 187.43/187.53 ( class_Rings_Ocomm__semiring__1(T_a) % 187.43/187.53 => 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) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,axiom, % 187.43/187.53 ! [V_a,T_a] : % 187.43/187.53 ( class_Rings_Ocomm__semiring__1(T_a) % 187.43/187.53 => 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) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_mult__zero__left,axiom, % 187.43/187.53 ! [V_a,T_a] : % 187.43/187.53 ( class_Rings_Omult__zero(T_a) % 187.43/187.53 => 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) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_mult__zero__right,axiom, % 187.43/187.53 ! [V_a,T_a] : % 187.43/187.53 ( class_Rings_Omult__zero(T_a) % 187.43/187.53 => 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) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_mult__eq__0__iff,axiom, % 187.43/187.53 ! [V_b_2,V_a_2,T_a] : % 187.43/187.53 ( class_Rings_Oring__no__zero__divisors(T_a) % 187.43/187.53 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a) % 187.43/187.53 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a) % 187.43/187.53 | V_b_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_no__zero__divisors,axiom, % 187.43/187.53 ! [V_b,V_a,T_a] : % 187.43/187.53 ( class_Rings_Ono__zero__divisors(T_a) % 187.43/187.53 => ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 187.43/187.53 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 187.43/187.53 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_divisors__zero,axiom, % 187.43/187.53 ! [V_b,V_a,T_a] : % 187.43/187.53 ( class_Rings_Ono__zero__divisors(T_a) % 187.43/187.53 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a) % 187.43/187.53 => ( V_a = c_Groups_Ozero__class_Ozero(T_a) % 187.43/187.53 | V_b = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J,axiom, % 187.43/187.53 ! [V_z,V_y,V_x,T_a] : % 187.43/187.53 ( class_Rings_Ocomm__semiring__1(T_a) % 187.43/187.53 => 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)) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_crossproduct__noteq,axiom, % 187.43/187.53 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] : % 187.43/187.53 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a) % 187.43/187.53 => ( ( V_a_2 != V_b_2 % 187.43/187.53 & V_c_2 != V_d_2 ) % 187.43/187.53 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_d_2)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_d_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_c_2)) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,axiom, % 187.43/187.53 ! [V_c,V_b,V_a,T_a] : % 187.43/187.53 ( class_Rings_Ocomm__semiring__1(T_a) % 187.43/187.53 => 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)) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J,axiom, % 187.43/187.53 ! [V_b,V_m,V_a,T_a] : % 187.43/187.53 ( class_Rings_Ocomm__semiring__1(T_a) % 187.43/187.53 => 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) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_crossproduct__eq,axiom, % 187.43/187.53 ! [V_z_2,V_x_2,V_y_2,V_w_2,T_a] : % 187.43/187.53 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a) % 187.43/187.53 => ( 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)) % 187.43/187.53 <=> ( V_w_2 = V_x_2 % 187.43/187.53 | V_y_2 = V_z_2 ) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_comm__semiring__class_Odistrib,axiom, % 187.43/187.53 ! [V_c,V_b,V_a,T_a] : % 187.43/187.53 ( class_Rings_Ocomm__semiring(T_a) % 187.43/187.53 => 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)) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_combine__common__factor,axiom, % 187.43/187.53 ! [V_c,V_b,V_e,V_a,T_a] : % 187.43/187.53 ( class_Rings_Osemiring(T_a) % 187.43/187.53 => 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) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,axiom, % 187.43/187.53 ! [V_a,T_a] : % 187.43/187.53 ( class_Rings_Ocomm__semiring__1(T_a) % 187.43/187.53 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,axiom, % 187.43/187.53 ! [V_a,T_a] : % 187.43/187.53 ( class_Rings_Ocomm__semiring__1(T_a) % 187.43/187.53 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_mult_Ocomm__neutral,axiom, % 187.43/187.53 ! [V_a,T_a] : % 187.43/187.53 ( class_Groups_Ocomm__monoid__mult(T_a) % 187.43/187.53 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_mult__1__right,axiom, % 187.43/187.53 ! [V_a,T_a] : % 187.43/187.53 ( class_Groups_Omonoid__mult(T_a) % 187.43/187.53 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_mult__1,axiom, % 187.43/187.53 ! [V_a,T_a] : % 187.43/187.53 ( class_Groups_Ocomm__monoid__mult(T_a) % 187.43/187.53 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_mult__1__left,axiom, % 187.43/187.53 ! [V_a,T_a] : % 187.43/187.53 ( class_Groups_Omonoid__mult(T_a) % 187.43/187.53 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_mult__0,axiom, % 187.43/187.53 ! [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) ). % 187.43/187.53 % 187.43/187.53 fof(fact_mult__0__right,axiom, % 187.43/187.53 ! [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) ). % 187.43/187.53 % 187.43/187.53 fof(fact_mult__is__0,axiom, % 187.43/187.53 ! [V_n_2,V_m_2] : % 187.43/187.53 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 187.43/187.53 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 187.43/187.53 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_mult__cancel1,axiom, % 187.43/187.53 ! [V_n_2,V_m_2,V_k_2] : % 187.43/187.53 ( 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) % 187.43/187.53 <=> ( V_m_2 = V_n_2 % 187.43/187.53 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_mult__cancel2,axiom, % 187.43/187.53 ! [V_n_2,V_k_2,V_m_2] : % 187.43/187.53 ( 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) % 187.43/187.53 <=> ( V_m_2 = V_n_2 % 187.43/187.53 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_square__eq__iff,axiom, % 187.43/187.53 ! [V_b_2,V_a_2,T_a] : % 187.43/187.53 ( class_Rings_Oidom(T_a) % 187.43/187.53 => ( 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) % 187.43/187.53 <=> ( V_a_2 = V_b_2 % 187.43/187.53 | V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2) ) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_minus__mult__minus,axiom, % 187.43/187.53 ! [V_b,V_a,T_a] : % 187.43/187.53 ( class_Rings_Oring(T_a) % 187.43/187.53 => 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) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_minus__mult__commute,axiom, % 187.43/187.53 ! [V_b,V_a,T_a] : % 187.43/187.53 ( class_Rings_Oring(T_a) % 187.43/187.53 => 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)) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_minus__mult__left,axiom, % 187.43/187.53 ! [V_b,V_a,T_a] : % 187.43/187.53 ( class_Rings_Oring(T_a) % 187.43/187.53 => 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) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_minus__mult__right,axiom, % 187.43/187.53 ! [V_b,V_a,T_a] : % 187.43/187.53 ( class_Rings_Oring(T_a) % 187.43/187.53 => 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)) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_Suc__mult__cancel1,axiom, % 187.43/187.53 ! [V_n_2,V_m_2,V_k_2] : % 187.43/187.53 ( 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) % 187.43/187.53 <=> V_m_2 = V_n_2 ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_add__mult__distrib,axiom, % 187.43/187.53 ! [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)) ). % 187.43/187.53 % 187.43/187.53 fof(fact_add__mult__distrib2,axiom, % 187.43/187.53 ! [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)) ). % 187.43/187.53 % 187.43/187.53 fof(fact_mult__le__mono,axiom, % 187.43/187.53 ! [V_l,V_k,V_j,V_i] : % 187.43/187.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 187.43/187.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_l)) % 187.43/187.53 => 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))) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_mult__le__mono2,axiom, % 187.43/187.53 ! [V_k,V_j,V_i] : % 187.43/187.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 187.43/187.53 => 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))) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_mult__le__mono1,axiom, % 187.43/187.53 ! [V_k,V_j,V_i] : % 187.43/187.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 187.43/187.53 => 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))) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_le__cube,axiom, % 187.43/187.53 ! [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)))) ). % 187.43/187.53 % 187.43/187.53 fof(fact_le__square,axiom, % 187.43/187.53 ! [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))) ). % 187.43/187.53 % 187.43/187.53 fof(fact_diff__mult__distrib,axiom, % 187.43/187.53 ! [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)) ). % 187.43/187.53 % 187.43/187.53 fof(fact_diff__mult__distrib2,axiom, % 187.43/187.53 ! [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)) ). % 187.43/187.53 % 187.43/187.53 fof(fact_nat__mult__eq__1__iff,axiom, % 187.43/187.53 ! [V_n_2,V_m_2] : % 187.43/187.53 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 187.43/187.53 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 187.43/187.53 & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_nat__mult__1__right,axiom, % 187.43/187.53 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_n ). % 187.43/187.53 % 187.43/187.53 fof(fact_nat__1__eq__mult__iff,axiom, % 187.43/187.53 ! [V_n_2,V_m_2] : % 187.43/187.53 ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) % 187.43/187.53 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 187.43/187.53 & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_nat__mult__1,axiom, % 187.43/187.53 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n) = V_n ). % 187.43/187.53 % 187.43/187.53 fof(fact_fun__left__comm__idem,axiom, % 187.43/187.53 ! [T_a] : % 187.43/187.53 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 187.43/187.53 => c_Finite__Set_Ofun__left__comm__idem(T_a,T_a,c_Groups_Otimes__class_Otimes(T_a)) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_WT_Oequations_I3_J,axiom, % 187.43/187.53 ! [V_a1_2,V_a3_2,V_a2_2] : % 187.43/187.53 ( hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(V_a2_2,V_a3_2,V_a1_2))) % 187.43/187.53 <=> hBOOL(hAPP(c_Com_OWT,V_a1_2)) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_WT_OLocal,axiom, % 187.43/187.53 ! [V_a_2,V_Y_2,V_c_2] : % 187.43/187.53 ( hBOOL(hAPP(c_Com_OWT,V_c_2)) % 187.43/187.53 => hBOOL(hAPP(c_Com_OWT,c_Com_Ocom_OLocal(V_Y_2,V_a_2,V_c_2))) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_com_Osimps_I40_J,axiom, % 187.43/187.53 ! [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) ). % 187.43/187.53 % 187.43/187.53 fof(fact_com_Osimps_I41_J,axiom, % 187.43/187.53 ! [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) ). % 187.43/187.53 % 187.43/187.53 fof(fact_com_Osimps_I38_J,axiom, % 187.43/187.53 ! [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) ). % 187.43/187.53 % 187.43/187.53 fof(fact_com_Osimps_I39_J,axiom, % 187.43/187.53 ! [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) ). % 187.43/187.53 % 187.43/187.53 fof(fact_com_Osimps_I36_J,axiom, % 187.43/187.53 ! [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) ). % 187.43/187.53 % 187.43/187.53 fof(fact_com_Osimps_I37_J,axiom, % 187.43/187.53 ! [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) ). % 187.43/187.53 % 187.43/187.53 fof(fact_com_Osimps_I42_J,axiom, % 187.43/187.53 ! [V_fun_H_2,V_pname_H_2,V_vname_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_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2) ). % 187.43/187.53 % 187.43/187.53 fof(fact_com_Osimps_I43_J,axiom, % 187.43/187.53 ! [V_com_2,V_fun_2,V_loc_2,V_fun_H_2,V_pname_H_2,V_vname_H_2] : c_Com_Ocom_OCall(V_vname_H_2,V_pname_H_2,V_fun_H_2) != c_Com_Ocom_OLocal(V_loc_2,V_fun_2,V_com_2) ). % 187.43/187.53 % 187.43/187.53 fof(fact_com_Osimps_I35_J,axiom, % 187.43/187.53 ! [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) ). % 187.43/187.53 % 187.43/187.53 fof(fact_com_Osimps_I34_J,axiom, % 187.43/187.53 ! [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) ). % 187.43/187.53 % 187.43/187.53 fof(fact_com_Osimps_I10_J,axiom, % 187.43/187.53 ! [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) ). % 187.43/187.53 % 187.43/187.53 fof(fact_com_Osimps_I11_J,axiom, % 187.43/187.53 ! [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 ). % 187.43/187.53 % 187.43/187.53 fof(fact_sgn0,axiom, % 187.43/187.53 ! [T_a] : % 187.43/187.53 ( class_Groups_Osgn__if(T_a) % 187.43/187.53 => c_Groups_Osgn__class_Osgn(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_sgn__0__0,axiom, % 187.43/187.53 ! [V_a_2,T_a] : % 187.43/187.53 ( class_Rings_Olinordered__idom(T_a) % 187.43/187.53 => ( c_Groups_Osgn__class_Osgn(T_a,V_a_2) = c_Groups_Ozero__class_Ozero(T_a) % 187.43/187.53 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_le__number__of__eq__not__less,axiom, % 187.43/187.53 ! [V_w_2,V_v_2,T_a] : % 187.43/187.53 ( ( class_Int_Onumber(T_a) % 187.43/187.53 & class_Orderings_Olinorder(T_a) ) % 187.43/187.53 => ( 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))) % 187.43/187.53 <=> ~ 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))) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_add__number__of__diff1,axiom, % 187.43/187.53 ! [V_c,V_w,V_v,T_a] : % 187.43/187.53 ( class_Int_Onumber__ring(T_a) % 187.43/187.53 => 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) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_split__mult__neg__le,axiom, % 187.43/187.53 ! [V_b,V_a,T_a] : % 187.43/187.53 ( class_Rings_Oordered__cancel__semiring(T_a) % 187.43/187.53 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 187.43/187.53 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) ) % 187.43/187.53 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 187.43/187.53 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) % 187.43/187.53 => 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))) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_split__mult__pos__le,axiom, % 187.43/187.53 ! [V_b,V_a,T_a] : % 187.43/187.53 ( class_Rings_Oordered__ring(T_a) % 187.43/187.53 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 187.43/187.53 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) % 187.43/187.53 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 187.43/187.53 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) ) ) % 187.43/187.53 => 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))) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_mult__mono,axiom, % 187.43/187.53 ! [V_d,V_c,V_b,V_a,T_a] : % 187.43/187.53 ( class_Rings_Oordered__semiring(T_a) % 187.43/187.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 187.43/187.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d)) % 187.43/187.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 187.43/187.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 187.43/187.53 => 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))) ) ) ) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_mult__mono_H,axiom, % 187.43/187.53 ! [V_d,V_c,V_b,V_a,T_a] : % 187.43/187.53 ( class_Rings_Oordered__semiring(T_a) % 187.43/187.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 187.43/187.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d)) % 187.43/187.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 187.43/187.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 187.43/187.53 => 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))) ) ) ) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_mult__left__mono__neg,axiom, % 187.43/187.53 ! [V_c,V_a,V_b,T_a] : % 187.43/187.53 ( class_Rings_Oordered__ring(T_a) % 187.43/187.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 187.43/187.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 187.43/187.53 => 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))) ) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_mult__right__mono__neg,axiom, % 187.43/187.53 ! [V_c,V_a,V_b,T_a] : % 187.43/187.53 ( class_Rings_Oordered__ring(T_a) % 187.43/187.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 187.43/187.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 187.43/187.53 => 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))) ) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_comm__mult__left__mono,axiom, % 187.43/187.53 ! [V_c,V_b,V_a,T_a] : % 187.43/187.53 ( class_Rings_Oordered__comm__semiring(T_a) % 187.43/187.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 187.43/187.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 187.43/187.53 => 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))) ) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_mult__left__mono,axiom, % 187.43/187.53 ! [V_c,V_b,V_a,T_a] : % 187.43/187.53 ( class_Rings_Oordered__semiring(T_a) % 187.43/187.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 187.43/187.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 187.43/187.53 => 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))) ) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_mult__right__mono,axiom, % 187.43/187.53 ! [V_c,V_b,V_a,T_a] : % 187.43/187.53 ( class_Rings_Oordered__semiring(T_a) % 187.43/187.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 187.43/187.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 187.43/187.53 => 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))) ) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_mult__nonpos__nonpos,axiom, % 187.43/187.53 ! [V_b,V_a,T_a] : % 187.43/187.53 ( class_Rings_Oordered__ring(T_a) % 187.43/187.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 187.43/187.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 187.43/187.53 => 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))) ) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_mult__nonpos__nonneg,axiom, % 187.43/187.53 ! [V_b,V_a,T_a] : % 187.43/187.53 ( class_Rings_Oordered__cancel__semiring(T_a) % 187.43/187.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 187.43/187.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 187.43/187.53 => 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))) ) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_mult__nonneg__nonpos2,axiom, % 187.43/187.53 ! [V_b,V_a,T_a] : % 187.43/187.53 ( class_Rings_Oordered__cancel__semiring(T_a) % 187.43/187.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 187.43/187.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 187.43/187.53 => 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))) ) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_mult__nonneg__nonpos,axiom, % 187.43/187.53 ! [V_b,V_a,T_a] : % 187.43/187.53 ( class_Rings_Oordered__cancel__semiring(T_a) % 187.43/187.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 187.43/187.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 187.43/187.53 => 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))) ) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_mult__nonneg__nonneg,axiom, % 187.43/187.53 ! [V_b,V_a,T_a] : % 187.43/187.53 ( class_Rings_Oordered__cancel__semiring(T_a) % 187.43/187.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 187.43/187.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 187.43/187.53 => 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))) ) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_mult__le__0__iff,axiom, % 187.43/187.53 ! [V_b_2,V_a_2,T_a] : % 187.43/187.53 ( class_Rings_Olinordered__ring__strict(T_a) % 187.43/187.53 => ( 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))) % 187.43/187.53 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) % 187.43/187.53 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),c_Groups_Ozero__class_Ozero(T_a))) ) % 187.43/187.53 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) % 187.43/187.53 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b_2)) ) ) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_zero__le__mult__iff,axiom, % 187.43/187.53 ! [V_b_2,V_a_2,T_a] : % 187.43/187.53 ( class_Rings_Olinordered__ring__strict(T_a) % 187.43/187.53 => ( 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))) % 187.43/187.53 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) % 187.43/187.53 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b_2)) ) % 187.43/187.53 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) % 187.43/187.53 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_zero__le__square,axiom, % 187.43/187.53 ! [V_a,T_a] : % 187.43/187.53 ( class_Rings_Olinordered__ring(T_a) % 187.43/187.53 => 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))) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_not__square__less__zero,axiom, % 187.43/187.53 ! [V_a,T_a] : % 187.43/187.53 ( class_Rings_Olinordered__ring(T_a) % 187.43/187.53 => ~ 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))) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_mult__less__cancel__right__disj,axiom, % 187.43/187.53 ! [V_b_2,V_c_2,V_a_2,T_a] : % 187.43/187.53 ( class_Rings_Olinordered__ring__strict(T_a) % 187.43/187.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_c_2))) % 187.43/187.53 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2)) % 187.43/187.53 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) % 187.43/187.53 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a))) % 187.43/187.53 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),V_a_2)) ) ) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_mult__less__cancel__left__disj,axiom, % 187.43/187.53 ! [V_b_2,V_a_2,V_c_2,T_a] : % 187.43/187.53 ( class_Rings_Olinordered__ring__strict(T_a) % 187.43/187.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2))) % 187.43/187.53 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2)) % 187.43/187.53 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) % 187.43/187.53 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a))) % 187.43/187.53 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),V_a_2)) ) ) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_mult__less__cancel__left__pos,axiom, % 187.43/187.53 ! [V_b_2,V_a_2,V_c_2,T_a] : % 187.43/187.53 ( class_Rings_Olinordered__ring__strict(T_a) % 187.43/187.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2)) % 187.43/187.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2))) % 187.43/187.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_mult__pos__pos,axiom, % 187.43/187.53 ! [V_b,V_a,T_a] : % 187.43/187.53 ( class_Rings_Olinordered__semiring__strict(T_a) % 187.43/187.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 187.43/187.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 187.43/187.53 => 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))) ) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_mult__pos__neg,axiom, % 187.43/187.53 ! [V_b,V_a,T_a] : % 187.43/187.53 ( class_Rings_Olinordered__semiring__strict(T_a) % 187.43/187.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 187.43/187.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 187.43/187.53 => 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))) ) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_mult__pos__neg2,axiom, % 187.43/187.53 ! [V_b,V_a,T_a] : % 187.43/187.53 ( class_Rings_Olinordered__semiring__strict(T_a) % 187.43/187.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 187.43/187.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 187.43/187.53 => 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))) ) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_zero__less__mult__pos,axiom, % 187.43/187.53 ! [V_b,V_a,T_a] : % 187.43/187.53 ( class_Rings_Olinordered__semiring__strict(T_a) % 187.43/187.53 => ( 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))) % 187.43/187.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 187.43/187.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_zero__less__mult__pos2,axiom, % 187.43/187.53 ! [V_a,V_b,T_a] : % 187.43/187.53 ( class_Rings_Olinordered__semiring__strict(T_a) % 187.43/187.53 => ( 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))) % 187.43/187.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 187.43/187.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_mult__less__cancel__left__neg,axiom, % 187.43/187.53 ! [V_b_2,V_a_2,V_c_2,T_a] : % 187.43/187.53 ( class_Rings_Olinordered__ring__strict(T_a) % 187.43/187.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a))) % 187.43/187.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2))) % 187.43/187.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),V_a_2)) ) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_mult__neg__pos,axiom, % 187.43/187.53 ! [V_b,V_a,T_a] : % 187.43/187.53 ( class_Rings_Olinordered__semiring__strict(T_a) % 187.43/187.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 187.43/187.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 187.43/187.53 => 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))) ) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_mult__neg__neg,axiom, % 187.43/187.53 ! [V_b,V_a,T_a] : % 187.43/187.53 ( class_Rings_Olinordered__ring__strict(T_a) % 187.43/187.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 187.43/187.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 187.43/187.53 => 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))) ) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_mult__strict__right__mono,axiom, % 187.43/187.53 ! [V_c,V_b,V_a,T_a] : % 187.43/187.53 ( class_Rings_Olinordered__semiring__strict(T_a) % 187.43/187.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 187.43/187.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 187.43/187.53 => 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))) ) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_mult__strict__left__mono,axiom, % 187.43/187.53 ! [V_c,V_b,V_a,T_a] : % 187.43/187.53 ( class_Rings_Olinordered__semiring__strict(T_a) % 187.43/187.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 187.43/187.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 187.43/187.53 => 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))) ) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_comm__mult__strict__left__mono,axiom, % 187.43/187.53 ! [V_c,V_b,V_a,T_a] : % 187.43/187.53 ( class_Rings_Olinordered__comm__semiring__strict(T_a) % 187.43/187.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 187.43/187.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 187.43/187.53 => 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))) ) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_mult__strict__right__mono__neg,axiom, % 187.43/187.53 ! [V_c,V_a,V_b,T_a] : % 187.43/187.53 ( class_Rings_Olinordered__ring__strict(T_a) % 187.43/187.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 187.43/187.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 187.43/187.53 => 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))) ) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_mult__strict__left__mono__neg,axiom, % 187.43/187.53 ! [V_c,V_a,V_b,T_a] : % 187.43/187.53 ( class_Rings_Olinordered__ring__strict(T_a) % 187.43/187.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 187.43/187.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 187.43/187.53 => 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))) ) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_add__scale__eq__noteq,axiom, % 187.43/187.53 ! [V_d,V_c,V_b,V_a,V_r,T_a] : % 187.43/187.53 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a) % 187.43/187.53 => ( V_r != c_Groups_Ozero__class_Ozero(T_a) % 187.43/187.53 => ( ( V_a = V_b % 187.43/187.53 & V_c != V_d ) % 187.43/187.53 => 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)) ) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_sum__squares__eq__zero__iff,axiom, % 187.43/187.53 ! [V_y_2,V_x_2,T_a] : % 187.43/187.53 ( class_Rings_Olinordered__ring__strict(T_a) % 187.43/187.53 => ( 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) % 187.43/187.53 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a) % 187.43/187.53 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_less__1__mult,axiom, % 187.43/187.53 ! [V_n,V_m,T_a] : % 187.43/187.53 ( class_Rings_Olinordered__semidom(T_a) % 187.43/187.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_m)) % 187.43/187.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_n)) % 187.43/187.53 => 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))) ) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_eq__add__iff1,axiom, % 187.43/187.53 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_a] : % 187.43/187.53 ( class_Rings_Oring(T_a) % 187.43/187.53 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_c_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2) % 187.43/187.53 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2)),V_e_2)),V_c_2) = V_d_2 ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_eq__add__iff2,axiom, % 187.43/187.53 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_a] : % 187.43/187.53 ( class_Rings_Oring(T_a) % 187.43/187.53 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_c_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2) % 187.43/187.53 <=> V_c_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_b_2),V_a_2)),V_e_2)),V_d_2) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J,axiom, % 187.43/187.53 ! [V_m,V_a,T_a] : % 187.43/187.53 ( class_Rings_Ocomm__semiring__1(T_a) % 187.43/187.53 => 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) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J,axiom, % 187.43/187.53 ! [V_a,V_m,T_a] : % 187.43/187.53 ( class_Rings_Ocomm__semiring__1(T_a) % 187.43/187.53 => 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) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J,axiom, % 187.43/187.53 ! [V_m,T_a] : % 187.43/187.53 ( class_Rings_Ocomm__semiring__1(T_a) % 187.43/187.53 => 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) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_square__eq__1__iff,axiom, % 187.43/187.53 ! [V_x_2,T_a] : % 187.43/187.53 ( class_Rings_Oring__1__no__zero__divisors(T_a) % 187.43/187.53 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2) = c_Groups_Oone__class_Oone(T_a) % 187.43/187.53 <=> ( V_x_2 = c_Groups_Oone__class_Oone(T_a) % 187.43/187.53 | V_x_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J,axiom, % 187.43/187.53 ! [V_x,T_a] : % 187.43/187.53 ( class_Rings_Ocomm__ring__1(T_a) % 187.43/187.53 => 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) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_mult__eq__1__iff,axiom, % 187.43/187.53 ! [V_n_2,V_m_2] : % 187.43/187.53 ( 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)) % 187.43/187.53 <=> ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 187.43/187.53 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_mult__less__mono2,axiom, % 187.43/187.53 ! [V_k,V_j,V_i] : % 187.43/187.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 187.43/187.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k)) % 187.43/187.53 => 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))) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_mult__less__mono1,axiom, % 187.43/187.53 ! [V_k,V_j,V_i] : % 187.43/187.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 187.43/187.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k)) % 187.43/187.53 => 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))) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_mult__less__cancel2,axiom, % 187.43/187.53 ! [V_n_2,V_k_2,V_m_2] : % 187.43/187.53 ( 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))) % 187.43/187.53 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 187.43/187.53 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_mult__less__cancel1,axiom, % 187.43/187.53 ! [V_n_2,V_m_2,V_k_2] : % 187.43/187.53 ( 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))) % 187.43/187.53 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 187.43/187.53 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_nat__0__less__mult__iff,axiom, % 187.43/187.53 ! [V_n_2,V_m_2] : % 187.43/187.53 ( 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))) % 187.43/187.53 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2)) % 187.43/187.53 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_Suc__mult__less__cancel1,axiom, % 187.43/187.53 ! [V_n_2,V_m_2,V_k_2] : % 187.43/187.53 ( 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))) % 187.43/187.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_mult__Suc__right,axiom, % 187.43/187.53 ! [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)) ). % 187.43/187.53 % 187.43/187.53 fof(fact_mult__Suc,axiom, % 187.43/187.53 ! [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)) ). % 187.43/187.53 % 187.43/187.53 fof(fact_Suc__mult__le__cancel1,axiom, % 187.43/187.53 ! [V_n_2,V_m_2,V_k_2] : % 187.43/187.53 ( 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))) % 187.43/187.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_Ints__number__of,axiom, % 187.43/187.53 ! [V_w_2,T_a] : % 187.43/187.53 ( class_Int_Onumber__ring(T_a) % 187.43/187.53 => 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))) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_mult__eq__self__implies__10,axiom, % 187.43/187.53 ! [V_n,V_m] : % 187.43/187.53 ( V_m = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) % 187.43/187.53 => ( V_n = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 187.43/187.53 | V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_Ints__mult,axiom, % 187.43/187.53 ! [V_b_2,V_a_2,T_a] : % 187.43/187.53 ( class_Rings_Oring__1(T_a) % 187.43/187.53 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a))) % 187.43/187.53 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Int_Oring__1__class_OInts(T_a))) % 187.43/187.53 => 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))) ) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_mult__left__le__imp__le,axiom, % 187.43/187.53 ! [V_b,V_a,V_c,T_a] : % 187.43/187.53 ( class_Rings_Olinordered__semiring__strict(T_a) % 187.43/187.53 => ( 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))) % 187.43/187.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 187.43/187.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_mult__right__le__imp__le,axiom, % 187.43/187.53 ! [V_b,V_c,V_a,T_a] : % 187.43/187.53 ( class_Rings_Olinordered__semiring__strict(T_a) % 187.43/187.53 => ( 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))) % 187.43/187.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 187.43/187.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_mult__less__imp__less__left,axiom, % 187.43/187.53 ! [V_b,V_a,V_c,T_a] : % 187.43/187.53 ( class_Rings_Olinordered__semiring__strict(T_a) % 187.43/187.53 => ( 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))) % 187.43/187.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 187.43/187.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_mult__left__less__imp__less,axiom, % 187.43/187.53 ! [V_b,V_a,V_c,T_a] : % 187.43/187.53 ( class_Rings_Olinordered__semiring(T_a) % 187.43/187.53 => ( 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))) % 187.43/187.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 187.43/187.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_mult__less__imp__less__right,axiom, % 187.43/187.53 ! [V_b,V_c,V_a,T_a] : % 187.43/187.53 ( class_Rings_Olinordered__semiring__strict(T_a) % 187.43/187.53 => ( 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))) % 187.43/187.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 187.43/187.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_mult__right__less__imp__less,axiom, % 187.43/187.53 ! [V_b,V_c,V_a,T_a] : % 187.43/187.53 ( class_Rings_Olinordered__semiring(T_a) % 187.43/187.53 => ( 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))) % 187.43/187.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 187.43/187.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_mult__le__less__imp__less,axiom, % 187.43/187.53 ! [V_d,V_c,V_b,V_a,T_a] : % 187.43/187.53 ( class_Rings_Olinordered__semiring__strict(T_a) % 187.43/187.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 187.43/187.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) % 187.43/187.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 187.43/187.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 187.43/187.53 => 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))) ) ) ) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_mult__less__le__imp__less,axiom, % 187.43/187.53 ! [V_d,V_c,V_b,V_a,T_a] : % 187.43/187.53 ( class_Rings_Olinordered__semiring__strict(T_a) % 187.43/187.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 187.43/187.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d)) % 187.43/187.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 187.43/187.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 187.43/187.53 => 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))) ) ) ) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_mult__strict__mono_H,axiom, % 187.43/187.53 ! [V_d,V_c,V_b,V_a,T_a] : % 187.43/187.53 ( class_Rings_Olinordered__semiring__strict(T_a) % 187.43/187.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 187.43/187.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) % 187.43/187.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 187.43/187.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 187.43/187.53 => 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))) ) ) ) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_mult__strict__mono,axiom, % 187.43/187.53 ! [V_d,V_c,V_b,V_a,T_a] : % 187.43/187.53 ( class_Rings_Olinordered__semiring__strict(T_a) % 187.43/187.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 187.43/187.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) % 187.43/187.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 187.43/187.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 187.43/187.53 => 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))) ) ) ) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_mult__le__cancel__left__neg,axiom, % 187.43/187.53 ! [V_b_2,V_a_2,V_c_2,T_a] : % 187.43/187.53 ( class_Rings_Olinordered__ring__strict(T_a) % 187.43/187.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a))) % 187.43/187.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2))) % 187.43/187.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_a_2)) ) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_mult__le__cancel__left__pos,axiom, % 187.43/187.53 ! [V_b_2,V_a_2,V_c_2,T_a] : % 187.43/187.53 ( class_Rings_Olinordered__ring__strict(T_a) % 187.43/187.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2)) % 187.43/187.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),V_b_2))) % 187.43/187.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) ) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_sum__squares__le__zero__iff,axiom, % 187.43/187.53 ! [V_y_2,V_x_2,T_a] : % 187.43/187.53 ( class_Rings_Olinordered__ring__strict(T_a) % 187.43/187.53 => ( 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))) % 187.43/187.53 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a) % 187.43/187.53 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_sum__squares__ge__zero,axiom, % 187.43/187.53 ! [V_y,V_x,T_a] : % 187.43/187.53 ( class_Rings_Olinordered__ring(T_a) % 187.43/187.53 => 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)))) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_not__sum__squares__lt__zero,axiom, % 187.43/187.53 ! [V_y,V_x,T_a] : % 187.43/187.53 ( class_Rings_Olinordered__ring(T_a) % 187.43/187.53 => ~ 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))) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_sum__squares__gt__zero__iff,axiom, % 187.43/187.53 ! [V_y_2,V_x_2,T_a] : % 187.43/187.53 ( class_Rings_Olinordered__ring__strict(T_a) % 187.43/187.53 => ( 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)))) % 187.43/187.53 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(T_a) % 187.43/187.53 | V_y_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_mult__left__le__one__le,axiom, % 187.43/187.53 ! [V_y,V_x,T_a] : % 187.43/187.53 ( class_Rings_Olinordered__idom(T_a) % 187.43/187.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 187.43/187.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 187.43/187.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),c_Groups_Oone__class_Oone(T_a))) % 187.43/187.53 => 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)) ) ) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_mult__right__le__one__le,axiom, % 187.43/187.53 ! [V_y,V_x,T_a] : % 187.43/187.53 ( class_Rings_Olinordered__idom(T_a) % 187.43/187.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 187.43/187.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 187.43/187.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),c_Groups_Oone__class_Oone(T_a))) % 187.43/187.53 => 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)) ) ) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_le__add__iff2,axiom, % 187.43/187.53 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_a] : % 187.43/187.53 ( class_Rings_Oordered__ring(T_a) % 187.43/187.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2))) % 187.43/187.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_b_2),V_a_2)),V_e_2)),V_d_2))) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_le__add__iff1,axiom, % 187.43/187.53 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_a] : % 187.43/187.53 ( class_Rings_Oordered__ring(T_a) % 187.43/187.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2))) % 187.43/187.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2)),V_e_2)),V_c_2)),V_d_2)) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_less__add__iff2,axiom, % 187.43/187.53 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_a] : % 187.43/187.53 ( class_Rings_Oordered__ring(T_a) % 187.43/187.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2))) % 187.43/187.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_b_2),V_a_2)),V_e_2)),V_d_2))) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_less__add__iff1,axiom, % 187.43/187.53 ! [V_d_2,V_b_2,V_c_2,V_e_2,V_a_2,T_a] : % 187.43/187.53 ( class_Rings_Oordered__ring(T_a) % 187.43/187.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_c_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2))) % 187.43/187.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2)),V_e_2)),V_c_2)),V_d_2)) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_sgn__greater,axiom, % 187.43/187.53 ! [V_a_2,T_a] : % 187.43/187.53 ( class_Rings_Olinordered__idom(T_a) % 187.43/187.53 => ( 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))) % 187.43/187.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_sgn__less,axiom, % 187.43/187.53 ! [V_a_2,T_a] : % 187.43/187.53 ( class_Rings_Olinordered__idom(T_a) % 187.43/187.53 => ( 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))) % 187.43/187.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_one__less__mult,axiom, % 187.43/187.53 ! [V_m,V_n] : % 187.43/187.53 ( 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)) % 187.43/187.53 => ( 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)) % 187.43/187.53 => 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))) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_n__less__n__mult__m,axiom, % 187.43/187.53 ! [V_m,V_n] : % 187.43/187.53 ( 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)) % 187.43/187.53 => ( 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)) % 187.43/187.53 => 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))) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_n__less__m__mult__n,axiom, % 187.43/187.53 ! [V_m,V_n] : % 187.43/187.53 ( 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)) % 187.43/187.53 => ( 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)) % 187.43/187.53 => 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))) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_one__le__mult__iff,axiom, % 187.43/187.53 ! [V_n_2,V_m_2] : % 187.43/187.53 ( 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))) % 187.43/187.53 <=> ( 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)) % 187.43/187.53 & 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)) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_mult__le__cancel2,axiom, % 187.43/187.53 ! [V_n_2,V_k_2,V_m_2] : % 187.43/187.53 ( 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))) % 187.43/187.53 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 187.43/187.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_mult__le__cancel1,axiom, % 187.43/187.53 ! [V_n_2,V_m_2,V_k_2] : % 187.43/187.53 ( 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))) % 187.43/187.53 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 187.43/187.53 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_fold__graph__insert__swap,axiom, % 187.43/187.53 ! [V_z_2,V_y_2,V_A_2,V_b_2,T_a] : % 187.43/187.53 ( class_Groups_Oab__semigroup__mult(T_a) % 187.43/187.53 => ( 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)) % 187.43/187.53 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),V_A_2)) % 187.43/187.53 => 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))) ) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_fold__image__distrib,axiom, % 187.43/187.53 ! [V_h_2,V_g_2,V_A_2,T_a,T_b] : % 187.43/187.53 ( class_Groups_Ocomm__monoid__mult(T_b) % 187.43/187.53 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.43/187.53 => 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)) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_convex__bound__le,axiom, % 187.43/187.53 ! [V_v,V_u,V_y,V_a,V_x,T_a] : % 187.43/187.53 ( class_Rings_Olinordered__semiring__1(T_a) % 187.43/187.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 187.43/187.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_a)) % 187.43/187.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_u)) % 187.43/187.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_v)) % 187.43/187.53 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) = c_Groups_Oone__class_Oone(T_a) % 187.43/187.53 => 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)) ) ) ) ) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_fold__image__insert,axiom, % 187.43/187.53 ! [V_z_2,V_g_2,V_a_2,V_A_2,T_a,T_b] : % 187.43/187.53 ( class_Groups_Oab__semigroup__mult(T_b) % 187.43/187.53 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.43/187.53 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 187.43/187.53 => 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)) ) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_mult__eq__if,axiom, % 187.43/187.53 ! [V_n,V_m] : % 187.43/187.53 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 187.43/187.53 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 187.43/187.53 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 187.43/187.53 => 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)) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_sgn__1__pos,axiom, % 187.43/187.53 ! [V_a_2,T_a] : % 187.43/187.53 ( class_Rings_Olinordered__idom(T_a) % 187.43/187.53 => ( c_Groups_Osgn__class_Osgn(T_a,V_a_2) = c_Groups_Oone__class_Oone(T_a) % 187.43/187.53 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_sgn__pos,axiom, % 187.43/187.53 ! [V_a,T_a] : % 187.43/187.53 ( class_Rings_Olinordered__idom(T_a) % 187.43/187.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 187.43/187.53 => c_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_convex__bound__lt,axiom, % 187.43/187.53 ! [V_v,V_u,V_y,V_a,V_x,T_a] : % 187.43/187.53 ( class_Rings_Olinordered__semiring__1__strict(T_a) % 187.43/187.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a)) % 187.43/187.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_a)) % 187.43/187.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_u)) % 187.43/187.53 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_v)) % 187.43/187.53 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) = c_Groups_Oone__class_Oone(T_a) % 187.43/187.53 => 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)) ) ) ) ) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_option_Osimps_I4_J,axiom, % 187.43/187.53 ! [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 ). % 187.43/187.53 % 187.43/187.53 fof(fact_nat__less__add__iff1,axiom, % 187.43/187.53 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] : % 187.43/187.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) % 187.43/187.53 => ( 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))) % 187.43/187.53 <=> 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)) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_nat__less__add__iff2,axiom, % 187.43/187.53 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] : % 187.43/187.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) % 187.43/187.53 => ( 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))) % 187.43/187.53 <=> 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))) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_nat__eq__add__iff2,axiom, % 187.43/187.53 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] : % 187.43/187.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) % 187.43/187.53 => ( 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) % 187.43/187.53 <=> 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) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_nat__diff__add__eq2,axiom, % 187.43/187.53 ! [V_n,V_m,V_u,V_j,V_i] : % 187.43/187.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 187.43/187.53 => 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)) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_nat__le__add__iff2,axiom, % 187.43/187.53 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] : % 187.43/187.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) % 187.43/187.53 => ( 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))) % 187.43/187.53 <=> 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))) ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_nat__eq__add__iff1,axiom, % 187.43/187.53 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] : % 187.43/187.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) % 187.43/187.53 => ( 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) % 187.43/187.53 <=> 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 ) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_nat__diff__add__eq1,axiom, % 187.43/187.53 ! [V_n,V_m,V_u,V_i,V_j] : % 187.43/187.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_i)) % 187.43/187.53 => 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) ) ). % 187.43/187.53 % 187.43/187.53 fof(fact_nat__le__add__iff1,axiom, % 187.43/187.53 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] : % 187.43/187.53 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) % 187.43/187.53 => ( 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))) % 187.43/187.54 <=> 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)) ) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_zsgn__def,axiom, % 187.43/187.54 ! [V_i] : % 187.43/187.54 ( ( V_i = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 187.43/187.54 => c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 187.43/187.54 & ( V_i != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 187.43/187.54 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i)) % 187.43/187.54 => c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) % 187.43/187.54 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i)) % 187.43/187.54 => 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)) ) ) ) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_zadd__zminus__inverse2,axiom, % 187.43/187.54 ! [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) ). % 187.43/187.54 % 187.43/187.54 fof(fact_zminus__zadd__distrib,axiom, % 187.43/187.54 ! [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)) ). % 187.43/187.54 % 187.43/187.54 fof(fact_diff__int__def,axiom, % 187.43/187.54 ! [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)) ). % 187.43/187.54 % 187.43/187.54 fof(fact_diff__int__def__symmetric,axiom, % 187.43/187.54 ! [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) ). % 187.43/187.54 % 187.43/187.54 fof(fact_minus__numeral__code_I6_J,axiom, % 187.43/187.54 ! [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))) ). % 187.43/187.54 % 187.43/187.54 fof(fact_zminus__zminus,axiom, % 187.43/187.54 ! [V_z] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)) = V_z ). % 187.43/187.54 % 187.43/187.54 fof(fact_minus__numeral__code_I5_J,axiom, % 187.43/187.54 ! [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)) ). % 187.43/187.54 % 187.43/187.54 fof(fact_zmult__zminus,axiom, % 187.43/187.54 ! [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)) ). % 187.43/187.54 % 187.43/187.54 fof(fact_zminus__0,axiom, % 187.43/187.54 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) ). % 187.43/187.54 % 187.43/187.54 fof(fact_nat__mult__assoc,axiom, % 187.43/187.54 ! [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)) ). % 187.43/187.54 % 187.43/187.54 fof(fact_nat__mult__commute,axiom, % 187.43/187.54 ! [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) ). % 187.43/187.54 % 187.43/187.54 fof(fact_zmult__zless__mono2,axiom, % 187.43/187.54 ! [V_k,V_j,V_i] : % 187.43/187.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j)) % 187.43/187.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k)) % 187.43/187.54 => 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))) ) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_less__number__of__int__code,axiom, % 187.43/187.54 ! [V_l_2,V_k_2] : % 187.43/187.54 ( 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))) % 187.43/187.54 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_zmult__assoc,axiom, % 187.43/187.54 ! [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)) ). % 187.43/187.54 % 187.43/187.54 fof(fact_times__numeral__code_I5_J,axiom, % 187.43/187.54 ! [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)) ). % 187.43/187.54 % 187.43/187.54 fof(fact_zmult__commute,axiom, % 187.43/187.54 ! [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) ). % 187.43/187.54 % 187.43/187.54 fof(fact_zdiff__zmult__distrib2,axiom, % 187.43/187.54 ! [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)) ). % 187.43/187.54 % 187.43/187.54 fof(fact_less__eq__number__of__int__code,axiom, % 187.43/187.54 ! [V_l_2,V_k_2] : % 187.43/187.54 ( 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))) % 187.43/187.54 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_zdiff__zmult__distrib,axiom, % 187.43/187.54 ! [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)) ). % 187.43/187.54 % 187.43/187.54 fof(fact_zadd__zmult__distrib2,axiom, % 187.43/187.54 ! [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)) ). % 187.43/187.54 % 187.43/187.54 fof(fact_plus__numeral__code_I9_J,axiom, % 187.43/187.54 ! [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)) ). % 187.43/187.54 % 187.43/187.54 fof(fact_zadd__zmult__distrib,axiom, % 187.43/187.54 ! [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)) ). % 187.43/187.54 % 187.43/187.54 fof(fact_zmult__1__right,axiom, % 187.43/187.54 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),c_Groups_Oone__class_Oone(tc_Int_Oint)) = V_z ). % 187.43/187.54 % 187.43/187.54 fof(fact_zmult__1,axiom, % 187.43/187.54 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z) = V_z ). % 187.43/187.54 % 187.43/187.54 fof(fact_pos__zmult__eq__1__iff,axiom, % 187.43/187.54 ! [V_n_2,V_m_2] : % 187.43/187.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m_2)) % 187.43/187.54 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint) % 187.43/187.54 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) % 187.43/187.54 & V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_int__one__le__iff__zero__less,axiom, % 187.43/187.54 ! [V_z_2] : % 187.43/187.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)) % 187.43/187.54 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_le__imp__0__less,axiom, % 187.43/187.54 ! [V_z] : % 187.43/187.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 187.43/187.54 => 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))) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_zadd__zless__mono,axiom, % 187.43/187.54 ! [V_z,V_z_H,V_w,V_w_H] : % 187.43/187.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_H),V_w)) % 187.43/187.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_H),V_z)) % 187.43/187.54 => 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))) ) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_zless__imp__add1__zle,axiom, % 187.43/187.54 ! [V_z,V_w] : % 187.43/187.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w),V_z)) % 187.43/187.54 => 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)) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_add1__zle__eq,axiom, % 187.43/187.54 ! [V_z_2,V_w_2] : % 187.43/187.54 ( 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)) % 187.43/187.54 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_zle__diff1__eq,axiom, % 187.43/187.54 ! [V_z_2,V_w_2] : % 187.43/187.54 ( 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)))) % 187.43/187.54 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_zle__add1__eq__le,axiom, % 187.43/187.54 ! [V_z_2,V_w_2] : % 187.43/187.54 ( 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)))) % 187.43/187.54 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_odd__less__0,axiom, % 187.43/187.54 ! [V_z_2] : % 187.43/187.54 ( 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))) % 187.43/187.54 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_int__0__less__1,axiom, % 187.43/187.54 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))) ). % 187.43/187.54 % 187.43/187.54 fof(fact_zadd__strict__right__mono,axiom, % 187.43/187.54 ! [V_k,V_j,V_i] : % 187.43/187.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j)) % 187.43/187.54 => 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))) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_zless__add1__eq,axiom, % 187.43/187.54 ! [V_z_2,V_w_2] : % 187.43/187.54 ( 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)))) % 187.43/187.54 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) % 187.43/187.54 | V_w_2 = V_z_2 ) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_odd__nonzero,axiom, % 187.43/187.54 ! [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) ). % 187.43/187.54 % 187.43/187.54 fof(fact_zadd__0__right,axiom, % 187.43/187.54 ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_z ). % 187.43/187.54 % 187.43/187.54 fof(fact_zadd__0,axiom, % 187.43/187.54 ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z) = V_z ). % 187.43/187.54 % 187.43/187.54 fof(fact_zadd__assoc,axiom, % 187.43/187.54 ! [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)) ). % 187.43/187.54 % 187.43/187.54 fof(fact_zadd__left__commute,axiom, % 187.43/187.54 ! [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)) ). % 187.43/187.54 % 187.43/187.54 fof(fact_zadd__commute,axiom, % 187.43/187.54 ! [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) ). % 187.43/187.54 % 187.43/187.54 fof(fact_zadd__left__mono,axiom, % 187.43/187.54 ! [V_k,V_j,V_i] : % 187.43/187.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j)) % 187.43/187.54 => 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))) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_zle__antisym,axiom, % 187.43/187.54 ! [V_w,V_z] : % 187.43/187.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_w)) % 187.43/187.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_z)) % 187.43/187.54 => V_z = V_w ) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_zle__trans,axiom, % 187.43/187.54 ! [V_k,V_j,V_i] : % 187.43/187.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j)) % 187.43/187.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_j),V_k)) % 187.43/187.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_k)) ) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_zle__linear,axiom, % 187.43/187.54 ! [V_w,V_z] : % 187.43/187.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_w)) % 187.43/187.54 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_z)) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_zle__refl,axiom, % 187.43/187.54 ! [V_w] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_w)) ). % 187.43/187.54 % 187.43/187.54 fof(fact_zless__linear,axiom, % 187.43/187.54 ! [V_y,V_x] : % 187.43/187.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x),V_y)) % 187.43/187.54 | V_x = V_y % 187.43/187.54 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_y),V_x)) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_zless__le,axiom, % 187.43/187.54 ! [V_w_2,V_z_2] : % 187.43/187.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),V_w_2)) % 187.43/187.54 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_2),V_w_2)) % 187.43/187.54 & V_z_2 != V_w_2 ) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_less__bin__lemma,axiom, % 187.43/187.54 ! [V_l_2,V_k_2] : % 187.43/187.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) % 187.43/187.54 <=> 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))) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_nat__mult__eq__cancel__disj,axiom, % 187.43/187.54 ! [V_n_2,V_m_2,V_k_2] : % 187.43/187.54 ( 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) % 187.43/187.54 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 187.43/187.54 | V_m_2 = V_n_2 ) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_left__add__mult__distrib,axiom, % 187.43/187.54 ! [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) ). % 187.43/187.54 % 187.43/187.54 fof(fact_nat__mult__eq__cancel1,axiom, % 187.43/187.54 ! [V_n_2,V_m_2,V_k_2] : % 187.43/187.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 187.43/187.54 => ( 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) % 187.43/187.54 <=> V_m_2 = V_n_2 ) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_nat__mult__less__cancel1,axiom, % 187.43/187.54 ! [V_n_2,V_m_2,V_k_2] : % 187.43/187.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 187.43/187.54 => ( 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))) % 187.43/187.54 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_nat__mult__le__cancel1,axiom, % 187.43/187.54 ! [V_n_2,V_m_2,V_k_2] : % 187.43/187.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 187.43/187.54 => ( 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))) % 187.43/187.54 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_zdiv__mono2__neg__lemma,axiom, % 187.43/187.54 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] : % 187.43/187.54 ( 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) % 187.43/187.54 => ( 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))) % 187.43/187.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) % 187.43/187.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H)) % 187.43/187.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 187.43/187.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b)) % 187.43/187.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),V_q)) ) ) ) ) ) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_unique__quotient__lemma__neg,axiom, % 187.43/187.54 ! [V_r,V_q,V_r_H,V_q_H,V_b] : % 187.43/187.54 ( 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))) % 187.43/187.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 187.43/187.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r)) % 187.43/187.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r_H)) % 187.43/187.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),V_q_H)) ) ) ) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_zdiv__mono2__lemma,axiom, % 187.43/187.54 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] : % 187.43/187.54 ( 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) % 187.43/187.54 => ( 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))) % 187.43/187.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b_H)) % 187.43/187.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) % 187.43/187.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 187.43/187.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b)) % 187.43/187.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),V_q_H)) ) ) ) ) ) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_unique__quotient__lemma,axiom, % 187.43/187.54 ! [V_r,V_q,V_r_H,V_q_H,V_b] : % 187.43/187.54 ( 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))) % 187.43/187.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H)) % 187.43/187.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b)) % 187.43/187.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) % 187.43/187.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),V_q)) ) ) ) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_q__neg__lemma,axiom, % 187.43/187.54 ! [V_r_H,V_q_H,V_b_H] : % 187.43/187.54 ( 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))) % 187.43/187.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H)) % 187.43/187.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 187.43/187.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_q__pos__lemma,axiom, % 187.43/187.54 ! [V_r_H,V_q_H,V_b_H] : % 187.43/187.54 ( 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))) % 187.43/187.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b_H)) % 187.43/187.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 187.43/187.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_q_H)) ) ) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_self__quotient__aux1,axiom, % 187.43/187.54 ! [V_q,V_r,V_a] : % 187.43/187.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 187.43/187.54 => ( 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)) % 187.43/187.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_a)) % 187.43/187.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_q)) ) ) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_self__quotient__aux2,axiom, % 187.43/187.54 ! [V_q,V_r,V_a] : % 187.43/187.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 187.43/187.54 => ( 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)) % 187.43/187.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) % 187.43/187.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_number__of__is__id,axiom, % 187.43/187.54 ! [V_k] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_k) = V_k ). % 187.43/187.54 % 187.43/187.54 fof(fact_int__0__neq__1,axiom, % 187.43/187.54 c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint) ). % 187.43/187.54 % 187.43/187.54 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J,axiom, % 187.43/187.54 ! [V_y,V_x] : % 187.43/187.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 187.43/187.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 187.43/187.54 => 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))) ) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J,axiom, % 187.43/187.54 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))) ). % 187.43/187.54 % 187.43/187.54 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J,axiom, % 187.43/187.54 ! [V_y,V_x] : % 187.43/187.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 187.43/187.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 187.43/187.54 => 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))) ) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J,axiom, % 187.43/187.54 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))) ). % 187.43/187.54 % 187.43/187.54 fof(fact_of__nat__number__of__lemma,axiom, % 187.43/187.54 ! [V_v,T_a] : % 187.43/187.54 ( class_Int_Onumber__ring(T_a) % 187.43/187.54 => ( ( 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))) % 187.43/187.54 => 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) ) % 187.43/187.54 & ( ~ 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))) % 187.43/187.54 => 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) ) ) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_fold1__insert,axiom, % 187.43/187.54 ! [V_x_2,V_A_2,T_a] : % 187.43/187.54 ( class_Groups_Oab__semigroup__mult(T_a) % 187.43/187.54 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.43/187.54 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.43/187.54 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 187.43/187.54 => 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)) ) ) ) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_eq__number__of__eq,axiom, % 187.43/187.54 ! [V_y_2,V_x_2,T_a] : % 187.43/187.54 ( class_Int_Onumber__ring(T_a) % 187.43/187.54 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2) % 187.43/187.54 <=> 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)))) ) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_negative__zle,axiom, % 187.43/187.54 ! [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))) ). % 187.43/187.54 % 187.43/187.54 fof(fact_negative__zless,axiom, % 187.43/187.54 ! [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))) ). % 187.43/187.54 % 187.43/187.54 fof(fact_of__nat__eq__iff,axiom, % 187.43/187.54 ! [V_n_2,V_m_2,T_a] : % 187.43/187.54 ( class_Nat_Osemiring__char__0(T_a) % 187.43/187.54 => ( 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) % 187.43/187.54 <=> V_m_2 = V_n_2 ) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_transfer__int__nat__numerals_I1_J,axiom, % 187.43/187.54 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)) ). % 187.43/187.54 % 187.43/187.54 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J,axiom, % 187.43/187.54 ! [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))) ). % 187.43/187.54 % 187.43/187.54 fof(fact_transfer__int__nat__quantifiers_I2_J,axiom, % 187.43/187.54 ! [V_P_2] : % 187.43/187.54 ( ? [B_x] : % 187.43/187.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 187.43/187.54 & hBOOL(hAPP(V_P_2,B_x)) ) % 187.43/187.54 <=> ? [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_transfer__int__nat__quantifiers_I1_J,axiom, % 187.43/187.54 ! [V_P_2] : % 187.43/187.54 ( ! [B_x] : % 187.43/187.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 187.43/187.54 => hBOOL(hAPP(V_P_2,B_x)) ) % 187.43/187.54 <=> ! [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_transfer__int__nat__relations_I2_J,axiom, % 187.43/187.54 ! [V_y_2,V_x_2] : % 187.43/187.54 ( 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))) % 187.43/187.54 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_transfer__int__nat__relations_I3_J,axiom, % 187.43/187.54 ! [V_y_2,V_x_2] : % 187.43/187.54 ( 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))) % 187.43/187.54 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x_2),V_y_2)) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I1_J,axiom, % 187.43/187.54 ! [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)) ). % 187.43/187.54 % 187.43/187.54 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I2_J,axiom, % 187.43/187.54 ! [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)) ). % 187.43/187.54 % 187.43/187.54 fof(fact_transfer__int__nat__numerals_I2_J,axiom, % 187.43/187.54 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)) ). % 187.43/187.54 % 187.43/187.54 fof(fact_iszero__def,axiom, % 187.43/187.54 ! [V_z_2,T_a] : % 187.43/187.54 ( class_Rings_Osemiring__1(T_a) % 187.43/187.54 => ( c_Int_Oiszero(T_a,V_z_2) % 187.43/187.54 <=> V_z_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_iszero__0,axiom, % 187.43/187.54 ! [T_a] : % 187.43/187.54 ( class_Rings_Osemiring__1(T_a) % 187.43/187.54 => c_Int_Oiszero(T_a,c_Groups_Ozero__class_Ozero(T_a)) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_not__iszero__1,axiom, % 187.43/187.54 ! [T_a] : % 187.43/187.54 ( class_Rings_Osemiring__1(T_a) % 187.43/187.54 => ~ c_Int_Oiszero(T_a,c_Groups_Oone__class_Oone(T_a)) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_int__eq__0__conv,axiom, % 187.43/187.54 ! [V_n_2] : % 187.43/187.54 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 187.43/187.54 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_int__0,axiom, % 187.43/187.54 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) ). % 187.43/187.54 % 187.43/187.54 fof(fact_zero__zle__int,axiom, % 187.43/187.54 ! [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))) ). % 187.43/187.54 % 187.43/187.54 fof(fact_int__less__0__conv,axiom, % 187.43/187.54 ! [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))) ). % 187.43/187.54 % 187.43/187.54 fof(fact_zless__int,axiom, % 187.43/187.54 ! [V_n_2,V_m_2] : % 187.43/187.54 ( 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))) % 187.43/187.54 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_zle__int,axiom, % 187.43/187.54 ! [V_n_2,V_m_2] : % 187.43/187.54 ( 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))) % 187.43/187.54 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_zadd__int,axiom, % 187.43/187.54 ! [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)) ). % 187.43/187.54 % 187.43/187.54 fof(fact_zadd__int__left,axiom, % 187.43/187.54 ! [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) ). % 187.43/187.54 % 187.43/187.54 fof(fact_zle__iff__zadd,axiom, % 187.43/187.54 ! [V_z_2,V_w_2] : % 187.43/187.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) % 187.43/187.54 <=> ? [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)) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_zero__le__imp__of__nat,axiom, % 187.43/187.54 ! [V_m,T_a] : % 187.43/187.54 ( class_Rings_Olinordered__semidom(T_a) % 187.43/187.54 => 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))) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_of__nat__0__le__iff,axiom, % 187.43/187.54 ! [V_n,T_a] : % 187.43/187.54 ( class_Rings_Olinordered__semidom(T_a) % 187.43/187.54 => 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))) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_negative__eq__positive,axiom, % 187.43/187.54 ! [V_m_2,V_n_2] : % 187.43/187.54 ( 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) % 187.43/187.54 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 187.43/187.54 & V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_of__nat__less__0__iff,axiom, % 187.43/187.54 ! [V_m,T_a] : % 187.43/187.54 ( class_Rings_Olinordered__semidom(T_a) % 187.43/187.54 => ~ 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))) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_not__int__zless__negative,axiom, % 187.43/187.54 ! [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)))) ). % 187.43/187.54 % 187.43/187.54 fof(fact_zmult__int,axiom, % 187.43/187.54 ! [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)) ). % 187.43/187.54 % 187.43/187.54 fof(fact_int__mult,axiom, % 187.43/187.54 ! [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)) ). % 187.43/187.54 % 187.43/187.54 fof(fact_of__nat__0,axiom, % 187.43/187.54 ! [T_a] : % 187.43/187.54 ( class_Rings_Osemiring__1(T_a) % 187.43/187.54 => 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) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_of__nat__less__iff,axiom, % 187.43/187.54 ! [V_n_2,V_m_2,T_a] : % 187.43/187.54 ( class_Rings_Olinordered__semidom(T_a) % 187.43/187.54 => ( 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))) % 187.43/187.54 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_less__imp__of__nat__less,axiom, % 187.43/187.54 ! [V_n,V_m,T_a] : % 187.43/187.54 ( class_Rings_Olinordered__semidom(T_a) % 187.43/187.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 187.43/187.54 => 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))) ) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_of__nat__less__imp__less,axiom, % 187.43/187.54 ! [V_n,V_m,T_a] : % 187.43/187.54 ( class_Rings_Olinordered__semidom(T_a) % 187.43/187.54 => ( 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))) % 187.43/187.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_int__1,axiom, % 187.43/187.54 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) ). % 187.43/187.54 % 187.43/187.54 fof(fact_of__nat__le__iff,axiom, % 187.43/187.54 ! [V_n_2,V_m_2,T_a] : % 187.43/187.54 ( class_Rings_Olinordered__semidom(T_a) % 187.43/187.54 => ( 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))) % 187.43/187.54 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_of__nat__add,axiom, % 187.43/187.54 ! [V_n,V_m,T_a] : % 187.43/187.54 ( class_Rings_Osemiring__1(T_a) % 187.43/187.54 => 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)) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_of__nat__mult,axiom, % 187.43/187.54 ! [V_n,V_m,T_a] : % 187.43/187.54 ( class_Rings_Osemiring__1(T_a) % 187.43/187.54 => 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)) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_of__nat__1,axiom, % 187.43/187.54 ! [T_a] : % 187.43/187.54 ( class_Rings_Osemiring__1(T_a) % 187.43/187.54 => 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) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_Ints__of__nat,axiom, % 187.43/187.54 ! [V_n_2,T_a] : % 187.43/187.54 ( class_Rings_Oring__1(T_a) % 187.43/187.54 => 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))) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_fold1__singleton,axiom, % 187.43/187.54 ! [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 ). % 187.43/187.54 % 187.43/187.54 fof(fact_fold1__singleton__def,axiom, % 187.43/187.54 ! [V_a_2,V_f_2,T_a,V_g_2] : % 187.43/187.54 ( V_g_2 = c_Finite__Set_Ofold1(T_a,V_f_2) % 187.43/187.54 => 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 ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_folding__one_Oeq__fold,axiom, % 187.43/187.54 ! [V_A_2,V_F_2,V_f_2,T_a] : % 187.43/187.54 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2) % 187.43/187.54 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.43/187.54 => hAPP(V_F_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_a,V_f_2),V_A_2) ) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_int__le__0__conv,axiom, % 187.43/187.54 ! [V_n_2] : % 187.43/187.54 ( 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))) % 187.43/187.54 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_int__Suc0__eq__1,axiom, % 187.43/187.54 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) ). % 187.43/187.54 % 187.43/187.54 fof(fact_zless__iff__Suc__zadd,axiom, % 187.43/187.54 ! [V_z_2,V_w_2] : % 187.43/187.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) % 187.43/187.54 <=> ? [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))) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_int__zle__neg,axiom, % 187.43/187.54 ! [V_m_2,V_n_2] : % 187.43/187.54 ( 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)))) % 187.43/187.54 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 187.43/187.54 & V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_int__Suc,axiom, % 187.43/187.54 ! [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)) ). % 187.43/187.54 % 187.43/187.54 fof(fact_negative__zle__0,axiom, % 187.43/187.54 ! [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))) ). % 187.43/187.54 % 187.43/187.54 fof(fact_zdiff__int,axiom, % 187.43/187.54 ! [V_m,V_n] : % 187.43/187.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 187.43/187.54 => 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)) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_of__nat__Suc,axiom, % 187.43/187.54 ! [V_m,T_a] : % 187.43/187.54 ( class_Rings_Osemiring__1(T_a) % 187.43/187.54 => 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)) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_of__nat__diff,axiom, % 187.43/187.54 ! [V_m,V_n,T_a] : % 187.43/187.54 ( class_Rings_Oring__1(T_a) % 187.43/187.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 187.43/187.54 => 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)) ) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_fold1__def,axiom, % 187.43/187.54 ! [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)) ). % 187.43/187.54 % 187.43/187.54 fof(fact_zero__less__int__conv,axiom, % 187.43/187.54 ! [V_n_2] : % 187.43/187.54 ( 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))) % 187.43/187.54 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_zmult__zless__mono2__lemma,axiom, % 187.43/187.54 ! [V_k,V_j,V_i] : % 187.43/187.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j)) % 187.43/187.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k)) % 187.43/187.54 => 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))) ) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_not__zle__0__negative,axiom, % 187.43/187.54 ! [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))))) ). % 187.43/187.54 % 187.43/187.54 fof(fact_negative__zless__0,axiom, % 187.43/187.54 ! [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))) ). % 187.43/187.54 % 187.43/187.54 fof(fact_of__nat__0__less__iff,axiom, % 187.43/187.54 ! [V_n_2,T_a] : % 187.43/187.54 ( class_Rings_Olinordered__semidom(T_a) % 187.43/187.54 => ( 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))) % 187.43/187.54 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_fold1__insert__idem,axiom, % 187.43/187.54 ! [V_x_2,V_A_2,T_a] : % 187.43/187.54 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 187.43/187.54 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.43/187.54 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.43/187.54 => 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)) ) ) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_zdiff__int__split,axiom, % 187.43/187.54 ! [V_y_2,V_x_2,V_P_2] : % 187.43/187.54 ( 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)))) % 187.43/187.54 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),V_x_2)) % 187.43/187.54 => 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)))) ) % 187.43/187.54 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) % 187.43/187.54 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_semiring__1__class_Oof__nat__code,axiom, % 187.43/187.54 ! [V_n_2,T_a] : % 187.43/187.54 ( class_Rings_Osemiring__1(T_a) % 187.43/187.54 => 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)) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_fold1__in,axiom, % 187.43/187.54 ! [V_A_2,T_a] : % 187.43/187.54 ( class_Groups_Oab__semigroup__mult(T_a) % 187.43/187.54 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.43/187.54 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.43/187.54 => ( ! [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)))))) % 187.43/187.54 => 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)) ) ) ) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_tsub__def,axiom, % 187.43/187.54 ! [V_x,V_y] : % 187.43/187.54 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x)) % 187.43/187.54 => c_Nat__Transfer_Otsub(V_x,V_y) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y) ) % 187.43/187.54 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x)) % 187.43/187.54 => c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_of__nat__number__of__eq,axiom, % 187.43/187.54 ! [V_v,T_a] : % 187.43/187.54 ( class_Int_Onumber__ring(T_a) % 187.43/187.54 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 187.43/187.54 => 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) ) % 187.43/187.54 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 187.43/187.54 => 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) ) ) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_eq__special_I1_J,axiom, % 187.43/187.54 ! [V_y_2,T_a] : % 187.43/187.54 ( class_Int_Onumber__ring(T_a) % 187.43/187.54 => ( c_Groups_Ozero__class_Ozero(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2) % 187.43/187.54 <=> 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)))) ) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_eq__special_I3_J,axiom, % 187.43/187.54 ! [V_x_2,T_a] : % 187.43/187.54 ( class_Int_Onumber__ring(T_a) % 187.43/187.54 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2) = c_Groups_Ozero__class_Ozero(T_a) % 187.43/187.54 <=> 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)))) ) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_int__int__eq,axiom, % 187.43/187.54 ! [V_n_2,V_m_2] : % 187.43/187.54 ( 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) % 187.43/187.54 <=> V_m_2 = V_n_2 ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_not__neg__int,axiom, % 187.43/187.54 ! [V_n] : ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))) ). % 187.43/187.54 % 187.43/187.54 fof(fact_transfer__int__nat__relations_I1_J,axiom, % 187.43/187.54 ! [V_y_2,V_x_2] : % 187.43/187.54 ( 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) % 187.43/187.54 <=> V_x_2 = V_y_2 ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_not__neg__number__of__Pls,axiom, % 187.43/187.54 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls))) ). % 187.43/187.54 % 187.43/187.54 fof(fact_Pls__def,axiom, % 187.43/187.54 c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ). % 187.43/187.54 % 187.43/187.54 fof(fact_rel__simps_I19_J,axiom, % 187.43/187.54 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ). % 187.43/187.54 % 187.43/187.54 fof(fact_rel__simps_I2_J,axiom, % 187.43/187.54 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ). % 187.43/187.54 % 187.43/187.54 fof(fact_add__Pls,axiom, % 187.43/187.54 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),V_k) = V_k ). % 187.43/187.54 % 187.43/187.54 fof(fact_add__Pls__right,axiom, % 187.43/187.54 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_OPls) = V_k ). % 187.43/187.54 % 187.43/187.54 fof(fact_mult__Pls,axiom, % 187.43/187.54 ! [V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),V_w) = c_Int_OPls ). % 187.43/187.54 % 187.43/187.54 fof(fact_diff__bin__simps_I1_J,axiom, % 187.43/187.54 ! [V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Int_OPls) = V_k ). % 187.43/187.54 % 187.43/187.54 fof(fact_minus__Pls,axiom, % 187.43/187.54 hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls) = c_Int_OPls ). % 187.43/187.54 % 187.43/187.54 fof(fact_not__neg__0,axiom, % 187.43/187.54 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ). % 187.43/187.54 % 187.43/187.54 fof(fact_not__neg__1,axiom, % 187.43/187.54 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint))) ). % 187.43/187.54 % 187.43/187.54 fof(fact_semiring__norm_I112_J,axiom, % 187.43/187.54 ! [T_a] : % 187.43/187.54 ( class_Int_Onumber__ring(T_a) % 187.43/187.54 => c_Groups_Ozero__class_Ozero(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_number__of__Pls,axiom, % 187.43/187.54 ! [T_a] : % 187.43/187.54 ( class_Int_Onumber__ring(T_a) % 187.43/187.54 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_add__numeral__0__right,axiom, % 187.43/187.54 ! [V_a,T_a] : % 187.43/187.54 ( class_Int_Onumber__ring(T_a) % 187.43/187.54 => 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 ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_add__numeral__0,axiom, % 187.43/187.54 ! [V_a,T_a] : % 187.43/187.54 ( class_Int_Onumber__ring(T_a) % 187.43/187.54 => 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 ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_number__of2,axiom, % 187.43/187.54 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))) ). % 187.43/187.54 % 187.43/187.54 fof(fact_bin__less__0__simps_I1_J,axiom, % 187.43/187.54 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ). % 187.43/187.54 % 187.43/187.54 fof(fact_nat__number__of__Pls,axiom, % 187.43/187.54 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 187.43/187.54 % 187.43/187.54 fof(fact_semiring__norm_I113_J,axiom, % 187.43/187.54 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) ). % 187.43/187.54 % 187.43/187.54 fof(fact_zero__is__num__zero,axiom, % 187.43/187.54 c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls) ). % 187.43/187.54 % 187.43/187.54 fof(fact_iszero__Numeral0,axiom, % 187.43/187.54 ! [T_a] : % 187.43/187.54 ( class_Int_Onumber__ring(T_a) % 187.43/187.54 => c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls)) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_not__neg__eq__ge__0,axiom, % 187.43/187.54 ! [V_x_2] : % 187.43/187.54 ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_x_2)) % 187.43/187.54 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_neg__def,axiom, % 187.43/187.54 ! [V_Z_2] : % 187.43/187.54 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_Z_2)) % 187.43/187.54 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_Z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_neg__zminus__int,axiom, % 187.43/187.54 ! [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))))) ). % 187.43/187.54 % 187.43/187.54 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I3_J,axiom, % 187.43/187.54 ! [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)) ). % 187.43/187.54 % 187.43/187.54 fof(fact_of__nat__aux_Osimps_I1_J,axiom, % 187.43/187.54 ! [V_i_2,V_inc_2,T_a] : % 187.43/187.54 ( class_Rings_Osemiring__1(T_a) % 187.43/187.54 => 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 ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_of__nat__aux_Osimps_I2_J,axiom, % 187.43/187.54 ! [V_i_2,V_n_2,V_inc_2,T_a] : % 187.43/187.54 ( class_Rings_Osemiring__1(T_a) % 187.43/187.54 => 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)) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_eq__number__of__0,axiom, % 187.43/187.54 ! [V_v_2] : % 187.43/187.54 ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 187.43/187.54 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_eq__0__number__of,axiom, % 187.43/187.54 ! [V_v_2] : % 187.43/187.54 ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) % 187.43/187.54 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_less__nat__number__of,axiom, % 187.43/187.54 ! [V_v_H_2,V_v_2] : % 187.43/187.54 ( 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))) % 187.43/187.54 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_2),V_v_H_2)) % 187.43/187.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v_H_2)) ) % 187.43/187.54 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_2),V_v_H_2)) ) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_le__nat__number__of,axiom, % 187.43/187.54 ! [V_v_H_2,V_v_2] : % 187.43/187.54 ( 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))) % 187.43/187.54 <=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),V_v_H_2)) % 187.43/187.54 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_neg__imp__number__of__eq__0,axiom, % 187.43/187.54 ! [V_v] : % 187.43/187.54 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 187.43/187.54 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_int__nat__number__of,axiom, % 187.43/187.54 ! [V_v] : % 187.43/187.54 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 187.43/187.54 => 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) ) % 187.43/187.54 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 187.43/187.54 => 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) ) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_le__special_I3_J,axiom, % 187.43/187.54 ! [V_x_2,T_a] : % 187.43/187.54 ( ( class_Int_Onumber__ring(T_a) % 187.43/187.54 & class_Rings_Olinordered__idom(T_a) ) % 187.43/187.54 => ( 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))) % 187.43/187.54 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OPls)) ) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_le__special_I1_J,axiom, % 187.43/187.54 ! [V_y_2,T_a] : % 187.43/187.54 ( ( class_Int_Onumber__ring(T_a) % 187.43/187.54 & class_Rings_Olinordered__idom(T_a) ) % 187.43/187.54 => ( 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))) % 187.43/187.54 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_y_2)) ) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_less__special_I1_J,axiom, % 187.43/187.54 ! [V_y_2,T_a] : % 187.43/187.54 ( ( class_Int_Onumber__ring(T_a) % 187.43/187.54 & class_Rings_Olinordered__idom(T_a) ) % 187.43/187.54 => ( 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))) % 187.43/187.54 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_y_2)) ) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_less__special_I3_J,axiom, % 187.43/187.54 ! [V_x_2,T_a] : % 187.43/187.54 ( ( class_Int_Onumber__ring(T_a) % 187.43/187.54 & class_Rings_Olinordered__idom(T_a) ) % 187.43/187.54 => ( 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))) % 187.43/187.54 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OPls)) ) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_less__0__number__of,axiom, % 187.43/187.54 ! [V_v_2] : % 187.43/187.54 ( 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))) % 187.43/187.54 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v_2)) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_add__nat__number__of,axiom, % 187.43/187.54 ! [V_v_H,V_v] : % 187.43/187.54 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 187.43/187.54 => 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) ) % 187.43/187.54 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 187.43/187.54 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H),c_Int_OPls)) % 187.43/187.54 => 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) ) % 187.43/187.54 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H),c_Int_OPls)) % 187.43/187.54 => 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)) ) ) ) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_eq__nat__number__of,axiom, % 187.43/187.54 ! [V_v_H_2,V_v_2] : % 187.43/187.54 ( 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) % 187.43/187.54 <=> ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2))) % 187.43/187.54 => 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))) ) % 187.43/187.54 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2))) % 187.43/187.54 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2))) % 187.43/187.54 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 187.43/187.54 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2))) % 187.43/187.54 => V_v_2 = V_v_H_2 ) ) ) ) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_nat__number__of__add__left,axiom, % 187.43/187.54 ! [V_k,V_v_H,V_v] : % 187.43/187.54 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 187.43/187.54 => 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) ) % 187.43/187.54 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 187.43/187.54 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 187.43/187.54 => 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) ) % 187.43/187.54 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 187.43/187.54 => 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) ) ) ) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J,axiom, % 187.43/187.54 ! [V_y,V_x] : % 187.43/187.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 187.43/187.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 187.43/187.54 => 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))) ) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_tsub__eq,axiom, % 187.43/187.54 ! [V_x,V_y] : % 187.43/187.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x)) % 187.43/187.54 => c_Nat__Transfer_Otsub(V_x,V_y) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_mult__nat__number__of,axiom, % 187.43/187.54 ! [V_v_H,V_v] : % 187.43/187.54 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 187.43/187.54 => 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) ) % 187.43/187.54 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 187.43/187.54 => 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)) ) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_nat__number__of__mult__left,axiom, % 187.43/187.54 ! [V_k,V_v_H,V_v] : % 187.43/187.54 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 187.43/187.54 => 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) ) % 187.43/187.54 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 187.43/187.54 => 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) ) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_Suc__nat__number__of__add,axiom, % 187.43/187.54 ! [V_n,V_v] : % 187.43/187.54 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 187.43/187.54 => 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) ) % 187.43/187.54 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 187.43/187.54 => 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) ) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_diff__nat__number__of,axiom, % 187.43/187.54 ! [V_v_2,V_v_H_2] : % 187.43/187.54 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H_2),c_Int_OPls)) % 187.43/187.54 => 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) ) % 187.43/187.54 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H_2),c_Int_OPls)) % 187.43/187.54 => 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)) ) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_Suc__nat__number__of,axiom, % 187.43/187.54 ! [V_v] : % 187.43/187.54 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 187.43/187.54 => hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) % 187.43/187.54 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 187.43/187.54 => 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)) ) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_nat__number__of__add__1,axiom, % 187.43/187.54 ! [V_v] : % 187.43/187.54 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 187.43/187.54 => 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) ) % 187.43/187.54 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 187.43/187.54 => 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)) ) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_nat__1__add__number__of,axiom, % 187.43/187.54 ! [V_v] : % 187.43/187.54 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 187.43/187.54 => 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) ) % 187.43/187.54 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 187.43/187.54 => 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)) ) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_nat__number__of__diff__1,axiom, % 187.43/187.54 ! [V_v] : % 187.43/187.54 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v),c_Int_OPls)) % 187.43/187.54 => 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) ) % 187.43/187.54 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v),c_Int_OPls)) % 187.43/187.54 => 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)) ) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_Nats__number__of,axiom, % 187.43/187.54 ! [V_w_2,T_a] : % 187.43/187.54 ( class_Int_Onumber__ring(T_a) % 187.43/187.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_w_2)) % 187.43/187.54 => 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))) ) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_succ__pred,axiom, % 187.43/187.54 ! [V_x] : c_Int_Osucc(c_Int_Opred(V_x)) = V_x ). % 187.43/187.54 % 187.43/187.54 fof(fact_nat__int,axiom, % 187.43/187.54 ! [V_n] : hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = V_n ). % 187.43/187.54 % 187.43/187.54 fof(fact_transfer__nat__int__numerals_I1_J,axiom, % 187.43/187.54 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ). % 187.43/187.54 % 187.43/187.54 fof(fact_nat__0,axiom, % 187.43/187.54 hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 187.43/187.54 % 187.43/187.54 fof(fact_ex__nat,axiom, % 187.43/187.54 ! [V_P_2] : % 187.43/187.54 ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) % 187.43/187.54 <=> ? [B_x] : % 187.43/187.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 187.43/187.54 & hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,B_x))) ) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_all__nat,axiom, % 187.43/187.54 ! [V_P_2] : % 187.43/187.54 ( ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) % 187.43/187.54 <=> ! [B_x] : % 187.43/187.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 187.43/187.54 => hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,B_x))) ) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_transfer__nat__int__relations_I1_J,axiom, % 187.43/187.54 ! [V_y_2,V_x_2] : % 187.43/187.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) % 187.43/187.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2)) % 187.43/187.54 => ( hAPP(c_Int_Onat,V_x_2) = hAPP(c_Int_Onat,V_y_2) % 187.43/187.54 <=> V_x_2 = V_y_2 ) ) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_eq__nat__nat__iff,axiom, % 187.43/187.54 ! [V_z_H_2,V_z_2] : % 187.43/187.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) % 187.43/187.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H_2)) % 187.43/187.54 => ( hAPP(c_Int_Onat,V_z_2) = hAPP(c_Int_Onat,V_z_H_2) % 187.43/187.54 <=> V_z_2 = V_z_H_2 ) ) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_nat__number__of,axiom, % 187.43/187.54 ! [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) ). % 187.43/187.54 % 187.43/187.54 fof(fact_nat__number__of__def,axiom, % 187.43/187.54 ! [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)) ). % 187.43/187.54 % 187.43/187.54 fof(fact_transfer__nat__int__numerals_I2_J,axiom, % 187.43/187.54 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)) ). % 187.43/187.54 % 187.43/187.54 fof(fact_neg__nat,axiom, % 187.43/187.54 ! [V_z] : % 187.43/187.54 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z)) % 187.43/187.54 => hAPP(c_Int_Onat,V_z) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_not__neg__nat,axiom, % 187.43/187.54 ! [V_z] : % 187.43/187.54 ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z)) % 187.43/187.54 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_Suc__eq__number__of,axiom, % 187.43/187.54 ! [V_v_2,V_n_2] : % 187.43/187.54 ( hAPP(c_Nat_OSuc,V_n_2) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) % 187.43/187.54 <=> 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))))) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_eq__number__of__Suc,axiom, % 187.43/187.54 ! [V_n_2,V_v_2] : % 187.43/187.54 ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = hAPP(c_Nat_OSuc,V_n_2) % 187.43/187.54 <=> 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))))) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_nat__case__number__of,axiom, % 187.43/187.54 ! [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))) ). % 187.43/187.54 % 187.43/187.54 fof(fact_le__iff__pred__less,axiom, % 187.43/187.54 ! [V_l_2,V_k_2] : % 187.43/187.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) % 187.43/187.54 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(V_k_2)),V_l_2)) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_pred__def,axiom, % 187.43/187.54 ! [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)) ). % 187.43/187.54 % 187.43/187.54 fof(fact_less__number__of__Suc,axiom, % 187.43/187.54 ! [V_n_2,V_v_2] : % 187.43/187.54 ( 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))) % 187.43/187.54 <=> 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)))) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_less__Suc__number__of,axiom, % 187.43/187.54 ! [V_v_2,V_n_2] : % 187.43/187.54 ( 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))) % 187.43/187.54 <=> 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))))) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_nat__0__iff,axiom, % 187.43/187.54 ! [V_i_2] : % 187.43/187.54 ( hAPP(c_Int_Onat,V_i_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 187.43/187.54 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_nat__le__0,axiom, % 187.43/187.54 ! [V_z] : % 187.43/187.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 187.43/187.54 => hAPP(c_Int_Onat,V_z) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_le__Suc__number__of,axiom, % 187.43/187.54 ! [V_v_2,V_n_2] : % 187.43/187.54 ( 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))) % 187.43/187.54 <=> 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))))) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_le__number__of__Suc,axiom, % 187.43/187.54 ! [V_n_2,V_v_2] : % 187.43/187.54 ( 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))) % 187.43/187.54 <=> 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)))) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_nat__mono__iff,axiom, % 187.43/187.54 ! [V_w_2,V_z_2] : % 187.43/187.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) % 187.43/187.54 => ( 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))) % 187.43/187.54 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_zless__nat__conj,axiom, % 187.43/187.54 ! [V_z_2,V_w_2] : % 187.43/187.54 ( 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))) % 187.43/187.54 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) % 187.43/187.54 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_transfer__nat__int__relations_I3_J,axiom, % 187.43/187.54 ! [V_y_2,V_x_2] : % 187.43/187.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) % 187.43/187.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2)) % 187.43/187.54 => ( 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))) % 187.43/187.54 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),V_y_2)) ) ) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_nat__1,axiom, % 187.43/187.54 hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ). % 187.43/187.54 % 187.43/187.54 fof(fact_nat__0__le,axiom, % 187.43/187.54 ! [V_z] : % 187.43/187.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 187.43/187.54 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_int__eq__iff,axiom, % 187.43/187.54 ! [V_z_2,V_m_2] : % 187.43/187.54 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) = V_z_2 % 187.43/187.54 <=> ( V_m_2 = hAPP(c_Int_Onat,V_z_2) % 187.43/187.54 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_int__nat__eq,axiom, % 187.43/187.54 ! [V_z] : % 187.43/187.54 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 187.43/187.54 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ) % 187.43/187.54 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 187.43/187.54 => 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) ) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_zless__nat__eq__int__zless,axiom, % 187.43/187.54 ! [V_z_2,V_m_2] : % 187.43/187.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Int_Onat,V_z_2))) % 187.43/187.54 <=> 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)) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_nat__zminus__int,axiom, % 187.43/187.54 ! [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) ). % 187.43/187.54 % 187.43/187.54 fof(fact_nat__case__add__eq__if,axiom, % 187.43/187.54 ! [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)))) ). % 187.43/187.54 % 187.43/187.54 fof(fact_succ__def,axiom, % 187.43/187.54 ! [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)) ). % 187.43/187.54 % 187.43/187.54 fof(fact_Nats__0,axiom, % 187.43/187.54 ! [T_a] : % 187.43/187.54 ( class_Rings_Osemiring__1(T_a) % 187.43/187.54 => hBOOL(hAPP(hAPP(c_member(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Nat_Osemiring__1__class_ONats(T_a))) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_Nats__add,axiom, % 187.43/187.54 ! [V_b_2,V_a_2,T_a] : % 187.43/187.54 ( class_Rings_Osemiring__1(T_a) % 187.43/187.54 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Nat_Osemiring__1__class_ONats(T_a))) % 187.43/187.54 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Nat_Osemiring__1__class_ONats(T_a))) % 187.43/187.54 => 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))) ) ) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_Nats__mult,axiom, % 187.43/187.54 ! [V_b_2,V_a_2,T_a] : % 187.43/187.54 ( class_Rings_Osemiring__1(T_a) % 187.43/187.54 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Nat_Osemiring__1__class_ONats(T_a))) % 187.43/187.54 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Nat_Osemiring__1__class_ONats(T_a))) % 187.43/187.54 => 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))) ) ) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_Nats__1,axiom, % 187.43/187.54 ! [T_a] : % 187.43/187.54 ( class_Rings_Osemiring__1(T_a) % 187.43/187.54 => hBOOL(hAPP(hAPP(c_member(T_a),c_Groups_Oone__class_Oone(T_a)),c_Nat_Osemiring__1__class_ONats(T_a))) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_of__nat__in__Nats,axiom, % 187.43/187.54 ! [V_n_2,T_a] : % 187.43/187.54 ( class_Rings_Osemiring__1(T_a) % 187.43/187.54 => 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))) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_zero__less__nat__eq,axiom, % 187.43/187.54 ! [V_z_2] : % 187.43/187.54 ( 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))) % 187.43/187.54 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_transfer__nat__int__relations_I2_J,axiom, % 187.43/187.54 ! [V_y_2,V_x_2] : % 187.43/187.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) % 187.43/187.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2)) % 187.43/187.54 => ( 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))) % 187.43/187.54 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2)) ) ) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_nat__less__eq__zless,axiom, % 187.43/187.54 ! [V_z_2,V_w_2] : % 187.43/187.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 187.43/187.54 => ( 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))) % 187.43/187.54 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_nat__eq__iff2,axiom, % 187.43/187.54 ! [V_w_2,V_m_2] : % 187.43/187.54 ( V_m_2 = hAPP(c_Int_Onat,V_w_2) % 187.43/187.54 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 187.43/187.54 => V_w_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) ) % 187.43/187.54 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 187.43/187.54 => V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_nat__eq__iff,axiom, % 187.43/187.54 ! [V_m_2,V_w_2] : % 187.43/187.54 ( hAPP(c_Int_Onat,V_w_2) = V_m_2 % 187.43/187.54 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 187.43/187.54 => V_w_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) ) % 187.43/187.54 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 187.43/187.54 => V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_nat__le__eq__zle,axiom, % 187.43/187.54 ! [V_z_2,V_w_2] : % 187.43/187.54 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 187.43/187.54 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) % 187.43/187.54 => ( 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))) % 187.43/187.54 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_split__nat,axiom, % 187.43/187.54 ! [V_i_2,V_P_2] : % 187.43/187.54 ( hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,V_i_2))) % 187.43/187.54 <=> ( ! [B_n] : % 187.43/187.54 ( V_i_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n) % 187.43/187.54 => hBOOL(hAPP(V_P_2,B_n)) ) % 187.43/187.54 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 187.43/187.54 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I1_J,axiom, % 187.43/187.54 ! [V_y,V_x] : % 187.43/187.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 187.43/187.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 187.43/187.54 => 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)) ) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_nat__add__distrib,axiom, % 187.43/187.54 ! [V_z_H,V_z] : % 187.43/187.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 187.43/187.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H)) % 187.43/187.54 => 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)) ) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_int__eq__iff__number__of,axiom, % 187.43/187.54 ! [V_v_2,V_m_2] : % 187.43/187.54 ( 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) % 187.43/187.54 <=> ( V_m_2 = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2)) % 187.43/187.54 & 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))) ) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I2_J,axiom, % 187.43/187.54 ! [V_y,V_x] : % 187.43/187.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 187.43/187.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 187.43/187.54 => 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)) ) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_nat__mult__distrib,axiom, % 187.43/187.54 ! [V_z_H,V_z] : % 187.43/187.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 187.43/187.54 => 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)) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_nat__diff__distrib,axiom, % 187.43/187.54 ! [V_z,V_z_H] : % 187.43/187.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H)) % 187.43/187.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_H),V_z)) % 187.43/187.54 => 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)) ) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I3_J,axiom, % 187.43/187.54 ! [V_y,V_x] : % 187.43/187.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 187.43/187.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 187.43/187.54 => 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)) ) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_diff__nat__eq__if,axiom, % 187.43/187.54 ! [V_z_2,V_z_H_2] : % 187.43/187.54 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z_H_2)) % 187.43/187.54 => 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) ) % 187.43/187.54 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z_H_2)) % 187.43/187.54 => 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)) ) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_one__less__nat__eq,axiom, % 187.43/187.54 ! [V_z_2] : % 187.43/187.54 ( 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))) % 187.43/187.54 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_nat__less__iff,axiom, % 187.43/187.54 ! [V_m_2,V_w_2] : % 187.43/187.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 187.43/187.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),V_m_2)) % 187.43/187.54 <=> 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))) ) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_Suc__nat__eq__nat__zadd1,axiom, % 187.43/187.54 ! [V_z] : % 187.43/187.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 187.43/187.54 => 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)) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_number__of__succ,axiom, % 187.43/187.54 ! [V_k,T_a] : % 187.43/187.54 ( class_Int_Onumber__ring(T_a) % 187.43/187.54 => 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)) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_nat__mult__distrib__neg,axiom, % 187.43/187.54 ! [V_z_H,V_z] : % 187.43/187.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 187.43/187.54 => 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))) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_number__of__pred,axiom, % 187.43/187.54 ! [V_w,T_a] : % 187.43/187.54 ( class_Int_Onumber__ring(T_a) % 187.43/187.54 => 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)) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_neg__number__of__pred__iff__0,axiom, % 187.43/187.54 ! [V_v_2] : % 187.43/187.54 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2)))) % 187.43/187.54 <=> hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_Suc__diff__number__of,axiom, % 187.43/187.54 ! [V_m,V_v] : % 187.43/187.54 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v)) % 187.43/187.54 => 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))) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_nat__aux__def,axiom, % 187.43/187.54 ! [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) ). % 187.43/187.54 % 187.43/187.54 fof(fact_nat__rec__add__eq__if,axiom, % 187.43/187.54 ! [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))))) ). % 187.43/187.54 % 187.43/187.54 fof(fact_nat__rec__number__of,axiom, % 187.43/187.54 ! [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)))) ). % 187.43/187.54 % 187.43/187.54 fof(fact_transfer__morphism__nat__int,axiom, % 187.43/187.54 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))) ). % 187.43/187.54 % 187.43/187.54 fof(fact_min__Suc__number__of,axiom, % 187.43/187.54 ! [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)))) ). % 187.43/187.54 % 187.43/187.54 fof(fact_min__number__of__Suc,axiom, % 187.43/187.54 ! [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)))) ). % 187.43/187.54 % 187.43/187.54 fof(fact_of__int__of__nat,axiom, % 187.43/187.54 ! [V_k,T_a] : % 187.43/187.54 ( class_Rings_Oring__1(T_a) % 187.43/187.54 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 187.43/187.54 => 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)))) ) % 187.43/187.54 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 187.43/187.54 => 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)) ) ) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_min__max_Oinf__assoc,axiom, % 187.43/187.54 ! [V_z,V_y,V_x,T_a] : % 187.43/187.54 ( class_Orderings_Olinorder(T_a) % 187.43/187.54 => 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)) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_min__max_Oinf_Oassoc,axiom, % 187.43/187.54 ! [V_c,V_b,V_a,T_a] : % 187.43/187.54 ( class_Orderings_Olinorder(T_a) % 187.43/187.54 => 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)) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_min__max_Oinf__left__commute,axiom, % 187.43/187.54 ! [V_z,V_y,V_x,T_a] : % 187.43/187.54 ( class_Orderings_Olinorder(T_a) % 187.43/187.54 => 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)) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_min__max_Oinf_Oleft__commute,axiom, % 187.43/187.54 ! [V_c,V_a,V_b,T_a] : % 187.43/187.54 ( class_Orderings_Olinorder(T_a) % 187.43/187.54 => 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)) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_min__max_Oinf__left__idem,axiom, % 187.43/187.54 ! [V_y,V_x,T_a] : % 187.43/187.54 ( class_Orderings_Olinorder(T_a) % 187.43/187.54 => 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) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_min__max_Oinf_Oleft__idem,axiom, % 187.43/187.54 ! [V_b,V_a,T_a] : % 187.43/187.54 ( class_Orderings_Olinorder(T_a) % 187.43/187.54 => 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) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_min__max_Oinf__commute,axiom, % 187.43/187.54 ! [V_y,V_x,T_a] : % 187.43/187.54 ( class_Orderings_Olinorder(T_a) % 187.43/187.54 => 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) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_min__max_Oinf_Ocommute,axiom, % 187.43/187.54 ! [V_b,V_a,T_a] : % 187.43/187.54 ( class_Orderings_Olinorder(T_a) % 187.43/187.54 => 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) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_min__max_Oinf_Oidem,axiom, % 187.43/187.54 ! [V_a,T_a] : % 187.43/187.54 ( class_Orderings_Olinorder(T_a) % 187.43/187.54 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_a) = V_a ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_of__int__eq__iff,axiom, % 187.43/187.54 ! [V_z_2,V_w_2,T_a] : % 187.43/187.54 ( class_Int_Oring__char__0(T_a) % 187.43/187.54 => ( 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) % 187.43/187.54 <=> V_w_2 = V_z_2 ) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_min__max_Oinf__le1,axiom, % 187.43/187.54 ! [V_y,V_x,T_a] : % 187.43/187.54 ( class_Orderings_Olinorder(T_a) % 187.43/187.54 => 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)) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_min__max_Oinf__le2,axiom, % 187.43/187.54 ! [V_y,V_x,T_a] : % 187.43/187.54 ( class_Orderings_Olinorder(T_a) % 187.43/187.54 => 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)) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_min__max_Ole__iff__inf,axiom, % 187.43/187.54 ! [V_y_2,V_x_2,T_a] : % 187.43/187.54 ( class_Orderings_Olinorder(T_a) % 187.43/187.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 187.43/187.54 <=> hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),V_y_2) = V_x_2 ) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_min__max_Ole__inf__iff,axiom, % 187.43/187.54 ! [V_z_2,V_y_2,V_x_2,T_a] : % 187.43/187.54 ( class_Orderings_Olinorder(T_a) % 187.43/187.54 => ( 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))) % 187.43/187.54 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 187.43/187.54 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_z_2)) ) ) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_min__max_Ole__infI1,axiom, % 187.43/187.54 ! [V_b,V_x,V_a,T_a] : % 187.43/187.54 ( class_Orderings_Olinorder(T_a) % 187.43/187.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 187.43/187.54 => 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)) ) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_min__max_Ole__infI2,axiom, % 187.43/187.54 ! [V_a,V_x,V_b,T_a] : % 187.43/187.54 ( class_Orderings_Olinorder(T_a) % 187.43/187.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) % 187.43/187.54 => 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)) ) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_min__max_Oinf__absorb1,axiom, % 187.43/187.54 ! [V_y,V_x,T_a] : % 187.43/187.54 ( class_Orderings_Olinorder(T_a) % 187.43/187.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 187.43/187.54 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = V_x ) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_min__max_Oinf__absorb2,axiom, % 187.43/187.54 ! [V_x,V_y,T_a] : % 187.43/187.54 ( class_Orderings_Olinorder(T_a) % 187.43/187.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 187.43/187.54 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = V_y ) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_min__max_Ole__infI,axiom, % 187.43/187.54 ! [V_b,V_a,V_x,T_a] : % 187.43/187.54 ( class_Orderings_Olinorder(T_a) % 187.43/187.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 187.43/187.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) % 187.43/187.54 => 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))) ) ) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_min__max_Oinf__greatest,axiom, % 187.43/187.54 ! [V_z,V_y,V_x,T_a] : % 187.43/187.54 ( class_Orderings_Olinorder(T_a) % 187.43/187.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 187.43/187.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z)) % 187.43/187.54 => 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))) ) ) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_min__max_Oinf__mono,axiom, % 187.43/187.54 ! [V_d,V_b,V_c,V_a,T_a] : % 187.43/187.54 ( class_Orderings_Olinorder(T_a) % 187.43/187.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) % 187.43/187.54 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d)) % 187.43/187.54 => 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))) ) ) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_min__max_Ole__infE,axiom, % 187.43/187.54 ! [V_b,V_a,V_x,T_a] : % 187.43/187.54 ( class_Orderings_Olinorder(T_a) % 187.43/187.54 => ( 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))) % 187.43/187.54 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 187.43/187.54 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) ) ) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_min__le__iff__disj,axiom, % 187.43/187.54 ! [V_z_2,V_y_2,V_x_2,T_a] : % 187.43/187.54 ( class_Orderings_Olinorder(T_a) % 187.43/187.54 => ( 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)) % 187.43/187.54 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_z_2)) % 187.43/187.54 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_z_2)) ) ) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_min__less__iff__disj,axiom, % 187.43/187.54 ! [V_z_2,V_y_2,V_x_2,T_a] : % 187.43/187.54 ( class_Orderings_Olinorder(T_a) % 187.43/187.54 => ( 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)) % 187.43/187.54 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_z_2)) % 187.43/187.54 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_z_2)) ) ) ) ). % 187.43/187.54 % 187.43/187.54 fof(fact_min__less__iff__conj,axiom, % 187.43/187.55 ! [V_y_2,V_x_2,V_z_2,T_a] : % 187.43/187.55 ( class_Orderings_Olinorder(T_a) % 187.43/187.55 => ( 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))) % 187.43/187.55 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z_2),V_x_2)) % 187.43/187.55 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z_2),V_y_2)) ) ) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_min__max_Oless__infI2,axiom, % 187.43/187.55 ! [V_a,V_x,V_b,T_a] : % 187.43/187.55 ( class_Orderings_Olinorder(T_a) % 187.43/187.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_x)) % 187.43/187.55 => 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)) ) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_min__max_Oless__infI1,axiom, % 187.43/187.55 ! [V_b,V_x,V_a,T_a] : % 187.43/187.55 ( class_Orderings_Olinorder(T_a) % 187.43/187.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_x)) % 187.43/187.55 => 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)) ) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_min__add__distrib__left,axiom, % 187.43/187.55 ! [V_z,V_y,V_x,T_a] : % 187.43/187.55 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 187.43/187.55 => 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)) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_min__diff__distrib__left,axiom, % 187.43/187.55 ! [V_z,V_y,V_x,T_a] : % 187.43/187.55 ( class_Groups_Oordered__ab__group__add(T_a) % 187.43/187.55 => 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)) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_min__0L,axiom, % 187.43/187.55 ! [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) ). % 187.43/187.55 % 187.43/187.55 fof(fact_min__0R,axiom, % 187.43/187.55 ! [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) ). % 187.43/187.55 % 187.43/187.55 fof(fact_min__Suc__Suc,axiom, % 187.43/187.55 ! [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)) ). % 187.43/187.55 % 187.43/187.55 fof(fact_min__diff,axiom, % 187.43/187.55 ! [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) ). % 187.43/187.55 % 187.43/187.55 fof(fact_number__of__eq,axiom, % 187.43/187.55 ! [V_k,T_a] : % 187.43/187.55 ( class_Int_Onumber__ring(T_a) % 187.43/187.55 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_k) = hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_k) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_int__number__of__def,axiom, % 187.43/187.55 ! [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) ). % 187.43/187.55 % 187.43/187.55 fof(fact_of__int__int__eq,axiom, % 187.43/187.55 ! [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) ). % 187.43/187.55 % 187.43/187.55 fof(fact_min__max_Ofun__left__comm__idem__inf,axiom, % 187.43/187.55 ! [T_a] : % 187.43/187.55 ( class_Orderings_Olinorder(T_a) % 187.43/187.55 => c_Finite__Set_Ofun__left__comm__idem(T_a,T_a,c_Orderings_Oord__class_Omin(T_a)) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_min__number__of,axiom, % 187.43/187.55 ! [V_v,V_u,T_b] : % 187.43/187.55 ( ( class_Int_Onumber(T_b) % 187.43/187.55 & class_Orderings_Oord(T_b) ) % 187.43/187.55 => ( ( 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))) % 187.43/187.55 => 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) ) % 187.43/187.55 & ( ~ 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))) % 187.43/187.55 => 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) ) ) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_nat__rec__0,axiom, % 187.43/187.55 ! [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 ). % 187.43/187.55 % 187.43/187.55 fof(fact_nat__rec__Suc,axiom, % 187.43/187.55 ! [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)) ). % 187.43/187.55 % 187.43/187.55 fof(fact_of__int__0,axiom, % 187.43/187.55 ! [T_a] : % 187.43/187.55 ( class_Rings_Oring__1(T_a) % 187.43/187.55 => 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) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_of__int__0__eq__iff,axiom, % 187.43/187.55 ! [V_z_2,T_a] : % 187.43/187.55 ( class_Int_Oring__char__0(T_a) % 187.43/187.55 => ( c_Groups_Ozero__class_Ozero(T_a) = hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z_2) % 187.43/187.55 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_of__int__eq__0__iff,axiom, % 187.43/187.55 ! [V_z_2,T_a] : % 187.43/187.55 ( class_Int_Oring__char__0(T_a) % 187.43/187.55 => ( hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z_2) = c_Groups_Ozero__class_Ozero(T_a) % 187.43/187.55 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_of__int__le__iff,axiom, % 187.43/187.55 ! [V_z_2,V_w_2,T_a] : % 187.43/187.55 ( class_Rings_Olinordered__idom(T_a) % 187.43/187.55 => ( 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))) % 187.43/187.55 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_of__int__less__iff,axiom, % 187.43/187.55 ! [V_z_2,V_w_2,T_a] : % 187.43/187.55 ( class_Rings_Olinordered__idom(T_a) % 187.43/187.55 => ( 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))) % 187.43/187.55 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_of__int__add,axiom, % 187.43/187.55 ! [V_z,V_w,T_a] : % 187.43/187.55 ( class_Rings_Oring__1(T_a) % 187.43/187.55 => 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)) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_of__int__number__of__eq,axiom, % 187.43/187.55 ! [V_v,T_a] : % 187.43/187.55 ( class_Int_Onumber__ring(T_a) % 187.43/187.55 => 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) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_of__int__mult,axiom, % 187.43/187.55 ! [V_z,V_w,T_a] : % 187.43/187.55 ( class_Rings_Oring__1(T_a) % 187.43/187.55 => 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)) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_of__int__1,axiom, % 187.43/187.55 ! [T_a] : % 187.43/187.55 ( class_Rings_Oring__1(T_a) % 187.43/187.55 => 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) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_of__int__diff,axiom, % 187.43/187.55 ! [V_z,V_w,T_a] : % 187.43/187.55 ( class_Rings_Oring__1(T_a) % 187.43/187.55 => 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)) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_of__int__of__nat__eq,axiom, % 187.43/187.55 ! [V_n,T_a] : % 187.43/187.55 ( class_Rings_Oring__1(T_a) % 187.43/187.55 => 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) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_of__int__minus,axiom, % 187.43/187.55 ! [V_z,T_a] : % 187.43/187.55 ( class_Rings_Oring__1(T_a) % 187.43/187.55 => 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)) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_Ints__of__int,axiom, % 187.43/187.55 ! [V_z_2,T_a] : % 187.43/187.55 ( class_Rings_Oring__1(T_a) % 187.43/187.55 => 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))) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_min__Suc1,axiom, % 187.43/187.55 ! [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) ). % 187.43/187.55 % 187.43/187.55 fof(fact_min__Suc2,axiom, % 187.43/187.55 ! [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) ). % 187.43/187.55 % 187.43/187.55 fof(fact_of__int__le__0__iff,axiom, % 187.43/187.55 ! [V_z_2,T_a] : % 187.43/187.55 ( class_Rings_Olinordered__idom(T_a) % 187.43/187.55 => ( 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))) % 187.43/187.55 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_of__int__0__le__iff,axiom, % 187.43/187.55 ! [V_z_2,T_a] : % 187.43/187.55 ( class_Rings_Olinordered__idom(T_a) % 187.43/187.55 => ( 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))) % 187.43/187.55 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_of__int__0__less__iff,axiom, % 187.43/187.55 ! [V_z_2,T_a] : % 187.43/187.55 ( class_Rings_Olinordered__idom(T_a) % 187.43/187.55 => ( 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))) % 187.43/187.55 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_of__int__less__0__iff,axiom, % 187.43/187.55 ! [V_z_2,T_a] : % 187.43/187.55 ( class_Rings_Olinordered__idom(T_a) % 187.43/187.55 => ( 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))) % 187.43/187.55 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_of__nat__nat,axiom, % 187.43/187.55 ! [V_z,T_a] : % 187.43/187.55 ( class_Rings_Oring__1(T_a) % 187.43/187.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 187.43/187.55 => 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) ) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_fold1__antimono,axiom, % 187.43/187.55 ! [V_B_2,V_A_2,T_a] : % 187.43/187.55 ( class_Orderings_Olinorder(T_a) % 187.43/187.55 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.43/187.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 187.43/187.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 187.43/187.55 => 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))) ) ) ) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_strict__below__fold1__iff,axiom, % 187.43/187.55 ! [V_x_2,V_A_2,T_a] : % 187.43/187.55 ( class_Orderings_Olinorder(T_a) % 187.43/187.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.43/187.55 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.43/187.55 => ( 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))) % 187.43/187.55 <=> ! [B_x] : % 187.43/187.55 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 187.43/187.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),B_x)) ) ) ) ) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_fold1__strict__below__iff,axiom, % 187.43/187.55 ! [V_x_2,V_A_2,T_a] : % 187.43/187.55 ( class_Orderings_Olinorder(T_a) % 187.43/187.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.43/187.55 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.43/187.55 => ( 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)) % 187.43/187.55 <=> ? [B_x] : % 187.43/187.55 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 187.43/187.55 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),B_x),V_x_2)) ) ) ) ) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_fold1__below__iff,axiom, % 187.43/187.55 ! [V_x_2,V_A_2,T_a] : % 187.43/187.55 ( class_Orderings_Olinorder(T_a) % 187.43/187.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.43/187.55 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.43/187.55 => ( 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)) % 187.43/187.55 <=> ? [B_x] : % 187.43/187.55 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 187.43/187.55 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_x),V_x_2)) ) ) ) ) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_min__max_Obelow__fold1__iff,axiom, % 187.43/187.55 ! [V_x_2,V_A_2,T_a] : % 187.43/187.55 ( class_Orderings_Olinorder(T_a) % 187.43/187.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.43/187.55 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.43/187.55 => ( 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))) % 187.43/187.55 <=> ! [B_x] : % 187.43/187.55 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 187.43/187.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),B_x)) ) ) ) ) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_min__max_Ofold1__belowI,axiom, % 187.43/187.55 ! [V_a_2,V_A_2,T_a] : % 187.43/187.55 ( class_Orderings_Olinorder(T_a) % 187.43/187.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.43/187.55 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 187.43/187.55 => 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)) ) ) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_min__ord__min,axiom, % 187.43/187.55 ! [T_a] : % 187.43/187.55 ( class_Orderings_Oord(T_a) % 187.43/187.55 => c_Orderings_Oord__class_Omin(T_a) = c_Orderings_Oord_Omin(T_a,c_Orderings_Oord__class_Oless__eq(T_a)) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_Min_Oidem,axiom, % 187.43/187.55 ! [V_x,T_a] : % 187.43/187.55 ( class_Orderings_Olinorder(T_a) % 187.43/187.55 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_x) = V_x ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_semilattice__big_OF__eq,axiom, % 187.43/187.55 ! [V_A_2,V_F_2,V_f_2,T_a] : % 187.43/187.55 ( c_Big__Operators_Osemilattice__big(T_a,V_f_2,V_F_2) % 187.43/187.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.43/187.55 => hAPP(V_F_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_a,V_f_2),V_A_2) ) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_dual__max,axiom, % 187.43/187.55 ! [T_a] : % 187.43/187.55 ( class_Orderings_Olinorder(T_a) % 187.43/187.55 => 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) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_comm__monoid__big_OF__eq,axiom, % 187.43/187.55 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_b,T_a] : % 187.43/187.55 ( c_Big__Operators_Ocomm__monoid__big(T_a,T_b,V_f_2,V_z_2,V_F_2) % 187.43/187.55 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.43/187.55 => 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) ) % 187.43/187.55 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.43/187.55 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = V_z_2 ) ) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_Min_Oremove,axiom, % 187.43/187.55 ! [V_x_2,V_A_2,T_a] : % 187.43/187.55 ( class_Orderings_Olinorder(T_a) % 187.43/187.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.43/187.55 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 187.43/187.55 => ( ( 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)) % 187.43/187.55 => c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2) = V_x_2 ) % 187.43/187.55 & ( 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)) % 187.43/187.55 => 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)))))) ) ) ) ) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_min__max_OInf__fin_Oremove,axiom, % 187.43/187.55 ! [V_x_2,V_A_2,T_a] : % 187.43/187.55 ( class_Orderings_Olinorder(T_a) % 187.43/187.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.43/187.55 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 187.43/187.55 => ( ( 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)) % 187.43/187.55 => c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2) = V_x_2 ) % 187.43/187.55 & ( 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)) % 187.43/187.55 => 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)))))) ) ) ) ) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_max__Suc__number__of,axiom, % 187.43/187.55 ! [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)))) ). % 187.43/187.55 % 187.43/187.55 fof(fact_Max_Oidem,axiom, % 187.43/187.55 ! [V_x,T_a] : % 187.43/187.55 ( class_Orderings_Olinorder(T_a) % 187.43/187.55 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_x) = V_x ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_min__max_Osup__assoc,axiom, % 187.43/187.55 ! [V_z,V_y,V_x,T_a] : % 187.43/187.55 ( class_Orderings_Olinorder(T_a) % 187.43/187.55 => 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)) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_min__max_Osup_Oassoc,axiom, % 187.43/187.55 ! [V_c,V_b,V_a,T_a] : % 187.43/187.55 ( class_Orderings_Olinorder(T_a) % 187.43/187.55 => 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)) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_min__max_Osup__left__commute,axiom, % 187.43/187.55 ! [V_z,V_y,V_x,T_a] : % 187.43/187.55 ( class_Orderings_Olinorder(T_a) % 187.43/187.55 => 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)) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_min__max_Osup_Oleft__commute,axiom, % 187.43/187.55 ! [V_c,V_a,V_b,T_a] : % 187.43/187.55 ( class_Orderings_Olinorder(T_a) % 187.43/187.55 => 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)) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_min__max_Osup__left__idem,axiom, % 187.43/187.55 ! [V_y,V_x,T_a] : % 187.43/187.55 ( class_Orderings_Olinorder(T_a) % 187.43/187.55 => 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) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_min__max_Osup_Oleft__idem,axiom, % 187.43/187.55 ! [V_b,V_a,T_a] : % 187.43/187.55 ( class_Orderings_Olinorder(T_a) % 187.43/187.55 => 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) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_min__max_Osup__commute,axiom, % 187.43/187.55 ! [V_y,V_x,T_a] : % 187.43/187.55 ( class_Orderings_Olinorder(T_a) % 187.43/187.55 => 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) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_min__max_Osup_Ocommute,axiom, % 187.43/187.55 ! [V_b,V_a,T_a] : % 187.43/187.55 ( class_Orderings_Olinorder(T_a) % 187.43/187.55 => 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) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_min__max_Osup_Oidem,axiom, % 187.43/187.55 ! [V_a,T_a] : % 187.43/187.55 ( class_Orderings_Olinorder(T_a) % 187.43/187.55 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_a) = V_a ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_max__ord__max,axiom, % 187.43/187.55 ! [T_a] : % 187.43/187.55 ( class_Orderings_Oord(T_a) % 187.43/187.55 => c_Orderings_Oord__class_Omax(T_a) = c_Orderings_Oord_Omax(T_a,c_Orderings_Oord__class_Oless__eq(T_a)) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_le__maxI1,axiom, % 187.43/187.55 ! [V_y,V_x,T_a] : % 187.43/187.55 ( class_Orderings_Olinorder(T_a) % 187.43/187.55 => 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))) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_le__maxI2,axiom, % 187.43/187.55 ! [V_x,V_y,T_a] : % 187.43/187.55 ( class_Orderings_Olinorder(T_a) % 187.43/187.55 => 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))) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_min__max_Ole__iff__sup,axiom, % 187.43/187.55 ! [V_y_2,V_x_2,T_a] : % 187.43/187.55 ( class_Orderings_Olinorder(T_a) % 187.43/187.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 187.43/187.55 <=> hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),V_y_2) = V_y_2 ) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_min__max_Ole__sup__iff,axiom, % 187.43/187.55 ! [V_z_2,V_y_2,V_x_2,T_a] : % 187.43/187.55 ( class_Orderings_Olinorder(T_a) % 187.43/187.55 => ( 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)) % 187.43/187.55 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_z_2)) % 187.43/187.55 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_z_2)) ) ) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_min__max_Ole__supI1,axiom, % 187.43/187.55 ! [V_b,V_a,V_x,T_a] : % 187.43/187.55 ( class_Orderings_Olinorder(T_a) % 187.43/187.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 187.43/187.55 => 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))) ) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_min__max_Ole__supI2,axiom, % 187.43/187.55 ! [V_a,V_b,V_x,T_a] : % 187.43/187.55 ( class_Orderings_Olinorder(T_a) % 187.43/187.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) % 187.43/187.55 => 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))) ) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_min__max_Osup__absorb2,axiom, % 187.43/187.55 ! [V_y,V_x,T_a] : % 187.43/187.55 ( class_Orderings_Olinorder(T_a) % 187.43/187.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 187.43/187.55 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = V_y ) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_min__max_Osup__absorb1,axiom, % 187.43/187.55 ! [V_x,V_y,T_a] : % 187.43/187.55 ( class_Orderings_Olinorder(T_a) % 187.43/187.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 187.43/187.55 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = V_x ) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_min__max_Ole__supI,axiom, % 187.43/187.55 ! [V_b,V_x,V_a,T_a] : % 187.43/187.55 ( class_Orderings_Olinorder(T_a) % 187.43/187.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 187.43/187.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) % 187.43/187.55 => 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)) ) ) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_min__max_Osup__least,axiom, % 187.43/187.55 ! [V_z,V_x,V_y,T_a] : % 187.43/187.55 ( class_Orderings_Olinorder(T_a) % 187.43/187.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 187.43/187.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x)) % 187.43/187.55 => 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)) ) ) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_min__max_Osup__mono,axiom, % 187.43/187.55 ! [V_d,V_b,V_c,V_a,T_a] : % 187.43/187.55 ( class_Orderings_Olinorder(T_a) % 187.43/187.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) % 187.43/187.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d)) % 187.43/187.55 => 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))) ) ) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_min__max_Ole__supE,axiom, % 187.43/187.55 ! [V_x,V_b,V_a,T_a] : % 187.43/187.55 ( class_Orderings_Olinorder(T_a) % 187.43/187.55 => ( 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)) % 187.43/187.55 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 187.43/187.55 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) ) ) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_le__max__iff__disj,axiom, % 187.43/187.55 ! [V_y_2,V_x_2,V_z_2,T_a] : % 187.43/187.55 ( class_Orderings_Olinorder(T_a) % 187.43/187.55 => ( 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))) % 187.43/187.55 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z_2),V_x_2)) % 187.43/187.55 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z_2),V_y_2)) ) ) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_max__less__iff__conj,axiom, % 187.43/187.55 ! [V_z_2,V_y_2,V_x_2,T_a] : % 187.43/187.55 ( class_Orderings_Olinorder(T_a) % 187.43/187.55 => ( 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)) % 187.43/187.55 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_z_2)) % 187.43/187.55 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_z_2)) ) ) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_less__max__iff__disj,axiom, % 187.43/187.55 ! [V_y_2,V_x_2,V_z_2,T_a] : % 187.43/187.55 ( class_Orderings_Olinorder(T_a) % 187.43/187.55 => ( 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))) % 187.43/187.55 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z_2),V_x_2)) % 187.43/187.55 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z_2),V_y_2)) ) ) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_min__max_Oless__supI2,axiom, % 187.43/187.55 ! [V_a,V_b,V_x,T_a] : % 187.43/187.55 ( class_Orderings_Olinorder(T_a) % 187.43/187.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_b)) % 187.43/187.55 => 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))) ) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_min__max_Oless__supI1,axiom, % 187.43/187.55 ! [V_b,V_a,V_x,T_a] : % 187.43/187.55 ( class_Orderings_Olinorder(T_a) % 187.43/187.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a)) % 187.43/187.55 => 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))) ) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_max__add__distrib__left,axiom, % 187.43/187.55 ! [V_z,V_y,V_x,T_a] : % 187.43/187.55 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 187.43/187.55 => 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)) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_max__diff__distrib__left,axiom, % 187.43/187.55 ! [V_z,V_y,V_x,T_a] : % 187.43/187.55 ( class_Groups_Oordered__ab__group__add(T_a) % 187.43/187.55 => 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)) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_max__0L,axiom, % 187.43/187.55 ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n ). % 187.43/187.55 % 187.43/187.55 fof(fact_max__0R,axiom, % 187.43/187.55 ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_n ). % 187.43/187.55 % 187.43/187.55 fof(fact_max__Suc__Suc,axiom, % 187.43/187.55 ! [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)) ). % 187.43/187.55 % 187.43/187.55 fof(fact_min__max_Oinf__sup__distrib2,axiom, % 187.43/187.55 ! [V_x,V_z,V_y,T_a] : % 187.43/187.55 ( class_Orderings_Olinorder(T_a) % 187.43/187.55 => 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)) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_min__max_Osup__inf__distrib2,axiom, % 187.43/187.55 ! [V_x,V_z,V_y,T_a] : % 187.43/187.55 ( class_Orderings_Olinorder(T_a) % 187.43/187.55 => 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)) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_min__max_Oinf__sup__distrib1,axiom, % 187.43/187.55 ! [V_z,V_y,V_x,T_a] : % 187.43/187.55 ( class_Orderings_Olinorder(T_a) % 187.43/187.55 => 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)) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_min__max_Osup__inf__distrib1,axiom, % 187.43/187.55 ! [V_z,V_y,V_x,T_a] : % 187.43/187.55 ( class_Orderings_Olinorder(T_a) % 187.43/187.55 => 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)) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_min__max_Oinf__sup__absorb,axiom, % 187.43/187.55 ! [V_y,V_x,T_a] : % 187.43/187.55 ( class_Orderings_Olinorder(T_a) % 187.43/187.55 => 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 ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_min__max_Osup__inf__absorb,axiom, % 187.43/187.55 ! [V_y,V_x,T_a] : % 187.43/187.55 ( class_Orderings_Olinorder(T_a) % 187.43/187.55 => 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 ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_min__max_Ofun__left__comm__idem__sup,axiom, % 187.43/187.55 ! [T_a] : % 187.43/187.55 ( class_Orderings_Olinorder(T_a) % 187.43/187.55 => c_Finite__Set_Ofun__left__comm__idem(T_a,T_a,c_Orderings_Oord__class_Omax(T_a)) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_min__max_Osup__Inf__absorb,axiom, % 187.43/187.55 ! [V_a_2,V_A_2,T_a] : % 187.43/187.55 ( class_Orderings_Olinorder(T_a) % 187.43/187.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.43/187.55 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 187.43/187.55 => 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 ) ) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_max__number__of,axiom, % 187.43/187.55 ! [V_v,V_u,T_b] : % 187.43/187.55 ( ( class_Int_Onumber(T_b) % 187.43/187.55 & class_Orderings_Oord(T_b) ) % 187.43/187.55 => ( ( 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))) % 187.43/187.55 => 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) ) % 187.43/187.55 & ( ~ 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))) % 187.43/187.55 => 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) ) ) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_min__max_Odistrib__sup__le,axiom, % 187.43/187.55 ! [V_z,V_y,V_x,T_a] : % 187.43/187.55 ( class_Orderings_Olinorder(T_a) % 187.43/187.55 => 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)))) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_min__max_Odistrib__inf__le,axiom, % 187.43/187.55 ! [V_z,V_y,V_x,T_a] : % 187.43/187.55 ( class_Orderings_Olinorder(T_a) % 187.43/187.55 => 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)))) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_minus__max__eq__min,axiom, % 187.43/187.55 ! [V_y,V_x,T_a] : % 187.43/187.55 ( class_Groups_Olinordered__ab__group__add(T_a) % 187.43/187.55 => 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)) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_minus__min__eq__max,axiom, % 187.43/187.55 ! [V_y,V_x,T_a] : % 187.43/187.55 ( class_Groups_Olinordered__ab__group__add(T_a) % 187.43/187.55 => 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)) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_nat__minus__add__max,axiom, % 187.43/187.55 ! [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) ). % 187.43/187.55 % 187.43/187.55 fof(fact_Min_Osingleton,axiom, % 187.43/187.55 ! [V_x_2,T_a] : % 187.43/187.55 ( class_Orderings_Olinorder(T_a) % 187.43/187.55 => 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 ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_max__Suc2,axiom, % 187.43/187.55 ! [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) ). % 187.43/187.55 % 187.43/187.55 fof(fact_max__Suc1,axiom, % 187.43/187.55 ! [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) ). % 187.43/187.55 % 187.43/187.55 fof(fact_dual__min,axiom, % 187.43/187.55 ! [T_a] : % 187.43/187.55 ( class_Orderings_Olinorder(T_a) % 187.43/187.55 => 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) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_min__max_OInf__fin_Oin__idem,axiom, % 187.43/187.55 ! [V_x_2,V_A_2,T_a] : % 187.43/187.55 ( class_Orderings_Olinorder(T_a) % 187.43/187.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.43/187.55 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 187.43/187.55 => 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) ) ) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_Min__le,axiom, % 187.43/187.55 ! [V_x_2,V_A_2,T_a] : % 187.43/187.55 ( class_Orderings_Olinorder(T_a) % 187.43/187.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.43/187.55 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 187.43/187.55 => 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)) ) ) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_min__max_OInf__fin_Osingleton,axiom, % 187.43/187.55 ! [V_x_2,T_a] : % 187.43/187.55 ( class_Orderings_Olinorder(T_a) % 187.43/187.55 => 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 ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_Min__in,axiom, % 187.43/187.55 ! [V_A_2,T_a] : % 187.43/187.55 ( class_Orderings_Olinorder(T_a) % 187.43/187.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.43/187.55 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.43/187.55 => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2)),V_A_2)) ) ) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_Min_Oin__idem,axiom, % 187.43/187.55 ! [V_x_2,V_A_2,T_a] : % 187.43/187.55 ( class_Orderings_Olinorder(T_a) % 187.43/187.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.43/187.55 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 187.43/187.55 => 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) ) ) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_min__max_OInf__fin_OF__eq,axiom, % 187.43/187.55 ! [V_A_2,T_a] : % 187.43/187.55 ( class_Orderings_Olinorder(T_a) % 187.43/187.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.43/187.55 => 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) ) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_Min_OF__eq,axiom, % 187.43/187.55 ! [V_A_2,T_a] : % 187.43/187.55 ( class_Orderings_Olinorder(T_a) % 187.43/187.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.43/187.55 => 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) ) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_min__max_OInf__fin_Oinsert__idem,axiom, % 187.43/187.55 ! [V_x_2,V_A_2,T_a] : % 187.43/187.55 ( class_Orderings_Olinorder(T_a) % 187.43/187.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.43/187.55 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.43/187.55 => 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)) ) ) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_min__max_OInf__fin_Osubset__idem,axiom, % 187.43/187.55 ! [V_B_2,V_A_2,T_a] : % 187.43/187.55 ( class_Orderings_Olinorder(T_a) % 187.43/187.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.43/187.55 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.43/187.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 187.43/187.55 => 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) ) ) ) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_Min__antimono,axiom, % 187.43/187.55 ! [V_N_2,V_M_2,T_a] : % 187.43/187.55 ( class_Orderings_Olinorder(T_a) % 187.43/187.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_M_2),V_N_2)) % 187.43/187.55 => ( V_M_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.43/187.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 187.43/187.55 => 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))) ) ) ) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_Min__insert,axiom, % 187.43/187.55 ! [V_x_2,V_A_2,T_a] : % 187.43/187.55 ( class_Orderings_Olinorder(T_a) % 187.43/187.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.43/187.55 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.43/187.55 => 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)) ) ) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_comm__monoid__big_Oinfinite,axiom, % 187.43/187.55 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_b,T_a] : % 187.43/187.55 ( c_Big__Operators_Ocomm__monoid__big(T_a,T_b,V_f_2,V_z_2,V_F_2) % 187.43/187.55 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.43/187.55 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = V_z_2 ) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_Min_Osubset__idem,axiom, % 187.43/187.55 ! [V_B_2,V_A_2,T_a] : % 187.43/187.55 ( class_Orderings_Olinorder(T_a) % 187.43/187.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.43/187.55 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.43/187.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 187.43/187.55 => 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) ) ) ) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_min__max_OInf__fin_Oinsert,axiom, % 187.43/187.55 ! [V_x_2,V_A_2,T_a] : % 187.43/187.55 ( class_Orderings_Olinorder(T_a) % 187.43/187.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.43/187.55 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 187.43/187.55 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.43/187.55 => 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)) ) ) ) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_min__max_OInf__fin_Oinsert__remove,axiom, % 187.43/187.55 ! [V_x_2,V_A_2,T_a] : % 187.43/187.55 ( class_Orderings_Olinorder(T_a) % 187.43/187.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.43/187.55 => ( ( 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)) % 187.43/187.55 => 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 ) % 187.43/187.55 & ( 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)) % 187.43/187.55 => 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)))))) ) ) ) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_Min_Oinsert,axiom, % 187.43/187.55 ! [V_x_2,V_A_2,T_a] : % 187.43/187.55 ( class_Orderings_Olinorder(T_a) % 187.43/187.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.43/187.55 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 187.43/187.55 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.43/187.55 => 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)) ) ) ) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_Min_Oinsert__remove,axiom, % 187.43/187.55 ! [V_x_2,V_A_2,T_a] : % 187.43/187.55 ( class_Orderings_Olinorder(T_a) % 187.43/187.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.43/187.55 => ( ( 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)) % 187.43/187.55 => c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = V_x_2 ) % 187.43/187.55 & ( 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)) % 187.43/187.55 => 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)))))) ) ) ) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_max__number__of__Suc,axiom, % 187.43/187.55 ! [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)))) ). % 187.43/187.55 % 187.43/187.55 fof(fact_min__max_OInf__fin_Oclosed,axiom, % 187.43/187.55 ! [V_A_2,T_a] : % 187.43/187.55 ( class_Orderings_Olinorder(T_a) % 187.43/187.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.43/187.55 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.43/187.55 => ( ! [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)))))) % 187.43/187.55 => 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)) ) ) ) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_Min_Oclosed,axiom, % 187.43/187.55 ! [V_A_2,T_a] : % 187.43/187.55 ( class_Orderings_Olinorder(T_a) % 187.43/187.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.43/187.55 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.43/187.55 => ( ! [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)))))) % 187.43/187.55 => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2)),V_A_2)) ) ) ) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_Max_Oremove,axiom, % 187.43/187.55 ! [V_x_2,V_A_2,T_a] : % 187.43/187.55 ( class_Orderings_Olinorder(T_a) % 187.43/187.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.43/187.55 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 187.43/187.55 => ( ( 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)) % 187.43/187.55 => c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2) = V_x_2 ) % 187.43/187.55 & ( 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)) % 187.43/187.55 => 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)))))) ) ) ) ) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_min__max_OInf__le__Sup,axiom, % 187.43/187.55 ! [V_A_2,T_a] : % 187.43/187.55 ( class_Orderings_Olinorder(T_a) % 187.43/187.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.43/187.55 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.43/187.55 => 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))) ) ) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_min__max_OSup__fin_Oremove,axiom, % 187.43/187.55 ! [V_x_2,V_A_2,T_a] : % 187.43/187.55 ( class_Orderings_Olinorder(T_a) % 187.43/187.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.43/187.55 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 187.43/187.55 => ( ( 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)) % 187.43/187.55 => c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2) = V_x_2 ) % 187.43/187.55 & ( 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)) % 187.43/187.55 => 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)))))) ) ) ) ) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_decr__mult__lemma,axiom, % 187.43/187.55 ! [V_k_2,V_P_2,V_d_2] : % 187.43/187.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2)) % 187.43/187.55 => ( ! [B_x] : % 187.43/187.55 ( hBOOL(hAPP(V_P_2,B_x)) % 187.43/187.55 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_d_2))) ) % 187.43/187.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 187.43/187.55 => ! [B_x] : % 187.43/187.55 ( hBOOL(hAPP(V_P_2,B_x)) % 187.43/187.55 => 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)))) ) ) ) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_Max_Osingleton,axiom, % 187.43/187.55 ! [V_x_2,T_a] : % 187.43/187.55 ( class_Orderings_Olinorder(T_a) % 187.43/187.55 => 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 ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_min__max_OSup__fin_Oin__idem,axiom, % 187.43/187.55 ! [V_x_2,V_A_2,T_a] : % 187.43/187.55 ( class_Orderings_Olinorder(T_a) % 187.43/187.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.43/187.55 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 187.43/187.55 => 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) ) ) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_Max__ge,axiom, % 187.43/187.55 ! [V_x_2,V_A_2,T_a] : % 187.43/187.55 ( class_Orderings_Olinorder(T_a) % 187.43/187.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.43/187.55 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 187.43/187.55 => 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))) ) ) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_min__max_OSup__fin_Osingleton,axiom, % 187.43/187.55 ! [V_x_2,T_a] : % 187.43/187.55 ( class_Orderings_Olinorder(T_a) % 187.43/187.55 => 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 ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_Max__in,axiom, % 187.43/187.55 ! [V_A_2,T_a] : % 187.43/187.55 ( class_Orderings_Olinorder(T_a) % 187.43/187.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.43/187.55 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.43/187.55 => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2)),V_A_2)) ) ) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_Max_Oin__idem,axiom, % 187.43/187.55 ! [V_x_2,V_A_2,T_a] : % 187.43/187.55 ( class_Orderings_Olinorder(T_a) % 187.43/187.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.43/187.55 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 187.43/187.55 => 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) ) ) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_min__max_OSup__fin_OF__eq,axiom, % 187.43/187.55 ! [V_A_2,T_a] : % 187.43/187.55 ( class_Orderings_Olinorder(T_a) % 187.43/187.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.43/187.55 => 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) ) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_Max_OF__eq,axiom, % 187.43/187.55 ! [V_A_2,T_a] : % 187.43/187.55 ( class_Orderings_Olinorder(T_a) % 187.43/187.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.43/187.55 => 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) ) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_min__max_OSup__fin_Oinsert__idem,axiom, % 187.43/187.55 ! [V_x_2,V_A_2,T_a] : % 187.43/187.55 ( class_Orderings_Olinorder(T_a) % 187.43/187.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.43/187.55 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.43/187.55 => 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)) ) ) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_min__max_OSup__fin_Osubset__idem,axiom, % 187.43/187.55 ! [V_B_2,V_A_2,T_a] : % 187.43/187.55 ( class_Orderings_Olinorder(T_a) % 187.43/187.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.43/187.55 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.43/187.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 187.43/187.55 => 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) ) ) ) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_min__max_Oinf__Sup__absorb,axiom, % 187.43/187.55 ! [V_a_2,V_A_2,T_a] : % 187.43/187.55 ( class_Orderings_Olinorder(T_a) % 187.43/187.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.43/187.55 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 187.43/187.55 => 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 ) ) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_Max__mono,axiom, % 187.43/187.55 ! [V_N_2,V_M_2,T_a] : % 187.43/187.55 ( class_Orderings_Olinorder(T_a) % 187.43/187.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_M_2),V_N_2)) % 187.43/187.55 => ( V_M_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.43/187.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 187.43/187.55 => 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))) ) ) ) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_Max__insert,axiom, % 187.43/187.55 ! [V_x_2,V_A_2,T_a] : % 187.43/187.55 ( class_Orderings_Olinorder(T_a) % 187.43/187.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.43/187.55 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.43/187.55 => 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)) ) ) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_Max_Osubset__idem,axiom, % 187.43/187.55 ! [V_B_2,V_A_2,T_a] : % 187.43/187.55 ( class_Orderings_Olinorder(T_a) % 187.43/187.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.43/187.55 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.43/187.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 187.43/187.55 => 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) ) ) ) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_min__max_OSup__fin_Oinsert,axiom, % 187.43/187.55 ! [V_x_2,V_A_2,T_a] : % 187.43/187.55 ( class_Orderings_Olinorder(T_a) % 187.43/187.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.43/187.55 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 187.43/187.55 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.43/187.55 => 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)) ) ) ) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_min__max_OSup__fin_Oinsert__remove,axiom, % 187.43/187.55 ! [V_x_2,V_A_2,T_a] : % 187.43/187.55 ( class_Orderings_Olinorder(T_a) % 187.43/187.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.43/187.55 => ( ( 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)) % 187.43/187.55 => 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 ) % 187.43/187.55 & ( 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)) % 187.43/187.55 => 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)))))) ) ) ) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_Max_Oinsert,axiom, % 187.43/187.55 ! [V_x_2,V_A_2,T_a] : % 187.43/187.55 ( class_Orderings_Olinorder(T_a) % 187.43/187.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.43/187.55 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 187.43/187.55 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.43/187.55 => 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)) ) ) ) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_Max_Oinsert__remove,axiom, % 187.43/187.55 ! [V_x_2,V_A_2,T_a] : % 187.43/187.55 ( class_Orderings_Olinorder(T_a) % 187.43/187.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.43/187.55 => ( ( 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)) % 187.43/187.55 => c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = V_x_2 ) % 187.43/187.55 & ( 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)) % 187.43/187.55 => 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)))))) ) ) ) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_min__max_OSup__fin_Oclosed,axiom, % 187.43/187.55 ! [V_A_2,T_a] : % 187.43/187.55 ( class_Orderings_Olinorder(T_a) % 187.43/187.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.43/187.55 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.43/187.55 => ( ! [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)))))) % 187.43/187.55 => 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)) ) ) ) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_Max_Oclosed,axiom, % 187.43/187.55 ! [V_A_2,T_a] : % 187.43/187.55 ( class_Orderings_Olinorder(T_a) % 187.43/187.55 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.43/187.55 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.43/187.55 => ( ! [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)))))) % 187.43/187.55 => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2)),V_A_2)) ) ) ) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_nat__number__of__Bit1,axiom, % 187.43/187.55 ! [V_w_2] : % 187.43/187.55 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) % 187.43/187.55 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 187.43/187.55 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) % 187.43/187.55 => 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)))) ) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_negD,axiom, % 187.43/187.55 ! [V_x] : % 187.43/187.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 187.43/187.55 => ? [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))) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_incr__mult__lemma,axiom, % 187.43/187.55 ! [V_k_2,V_P_2,V_d_2] : % 187.43/187.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2)) % 187.43/187.55 => ( ! [B_x] : % 187.43/187.55 ( hBOOL(hAPP(V_P_2,B_x)) % 187.43/187.55 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_d_2))) ) % 187.43/187.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 187.43/187.55 => ! [B_x] : % 187.43/187.55 ( hBOOL(hAPP(V_P_2,B_x)) % 187.43/187.55 => 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)))) ) ) ) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_zero__less__imp__eq__int,axiom, % 187.43/187.55 ! [V_k] : % 187.43/187.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k)) % 187.43/187.55 => ? [B_n] : % 187.43/187.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n)) % 187.43/187.55 & V_k = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n) ) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_rel__simps_I51_J,axiom, % 187.43/187.55 ! [V_l_2,V_k_2] : % 187.43/187.55 ( c_Int_OBit1(V_k_2) = c_Int_OBit1(V_l_2) % 187.43/187.55 <=> V_k_2 = V_l_2 ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_rel__simps_I34_J,axiom, % 187.43/187.55 ! [V_l_2,V_k_2] : % 187.43/187.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit1(V_l_2))) % 187.43/187.55 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_less__eq__int__code_I16_J,axiom, % 187.43/187.55 ! [V_k2_2,V_k1_2] : % 187.43/187.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2))) % 187.43/187.55 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_less__int__code_I16_J,axiom, % 187.43/187.55 ! [V_k2_2,V_k1_2] : % 187.43/187.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2))) % 187.43/187.55 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_rel__simps_I17_J,axiom, % 187.43/187.55 ! [V_l_2,V_k_2] : % 187.43/187.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit1(V_l_2))) % 187.43/187.55 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_rel__simps_I46_J,axiom, % 187.43/187.55 ! [V_k] : c_Int_OBit1(V_k) != c_Int_OPls ). % 187.43/187.55 % 187.43/187.55 fof(fact_rel__simps_I39_J,axiom, % 187.43/187.55 ! [V_l] : c_Int_OPls != c_Int_OBit1(V_l) ). % 187.43/187.55 % 187.43/187.55 fof(fact_bin__less__0__simps_I4_J,axiom, % 187.43/187.55 ! [V_w_2] : % 187.43/187.55 ( 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))) % 187.43/187.55 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_rel__simps_I22_J,axiom, % 187.43/187.55 ! [V_k_2] : % 187.43/187.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k_2))) % 187.43/187.55 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_rel__simps_I12_J,axiom, % 187.43/187.55 ! [V_k_2] : % 187.43/187.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OPls)) % 187.43/187.55 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_Bit1__def,axiom, % 187.43/187.55 ! [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) ). % 187.43/187.55 % 187.43/187.55 fof(fact_neg__number__of__Bit1,axiom, % 187.43/187.55 ! [V_w_2] : % 187.43/187.55 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_w_2)))) % 187.43/187.55 <=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_minus__Bit1,axiom, % 187.43/187.55 ! [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))) ). % 187.43/187.55 % 187.43/187.55 fof(fact_iszero__number__of__Bit1,axiom, % 187.43/187.55 ! [V_w,T_a] : % 187.43/187.55 ( ( class_Int_Onumber__ring(T_a) % 187.43/187.55 & class_Int_Oring__char__0(T_a) ) % 187.43/187.55 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(V_w))) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_succ__Pls,axiom, % 187.43/187.55 c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls) ). % 187.43/187.55 % 187.43/187.55 fof(fact_number__of__Bit1,axiom, % 187.43/187.55 ! [V_w,T_a] : % 187.43/187.55 ( class_Int_Onumber__ring(T_a) % 187.43/187.55 => 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)) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_mult__numeral__1,axiom, % 187.43/187.55 ! [V_a,T_a] : % 187.43/187.55 ( class_Int_Onumber__ring(T_a) % 187.43/187.55 => 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 ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_mult__numeral__1__right,axiom, % 187.43/187.55 ! [V_a,T_a] : % 187.43/187.55 ( class_Int_Onumber__ring(T_a) % 187.43/187.55 => 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 ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_semiring__norm_I110_J,axiom, % 187.43/187.55 ! [T_a] : % 187.43/187.55 ( class_Int_Onumber__ring(T_a) % 187.43/187.55 => c_Groups_Oone__class_Oone(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls)) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_numeral__1__eq__1,axiom, % 187.43/187.55 ! [T_a] : % 187.43/187.55 ( class_Int_Onumber__ring(T_a) % 187.43/187.55 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(T_a) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_rel__simps_I29_J,axiom, % 187.43/187.55 ! [V_k_2] : % 187.43/187.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OPls)) % 187.43/187.55 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_rel__simps_I5_J,axiom, % 187.43/187.55 ! [V_k_2] : % 187.43/187.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k_2))) % 187.43/187.55 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_one__is__num__one,axiom, % 187.43/187.55 c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)) ). % 187.43/187.55 % 187.43/187.55 fof(fact_nat__numeral__1__eq__1,axiom, % 187.43/187.55 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ). % 187.43/187.55 % 187.43/187.55 fof(fact_Numeral1__eq1__nat,axiom, % 187.43/187.55 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) ). % 187.43/187.55 % 187.43/187.55 fof(fact_not__iszero__Numeral1,axiom, % 187.43/187.55 ! [T_a] : % 187.43/187.55 ( class_Int_Onumber__ring(T_a) % 187.43/187.55 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_numeral__1__eq__Suc__0,axiom, % 187.43/187.55 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)) ). % 187.43/187.55 % 187.43/187.55 fof(fact_numeral__3__eq__3,axiom, % 187.43/187.55 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)))) ). % 187.43/187.55 % 187.43/187.55 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J,axiom, % 187.43/187.55 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))))) ). % 187.43/187.55 % 187.43/187.55 fof(fact_Suc3__eq__add__3,axiom, % 187.43/187.55 ! [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) ). % 187.43/187.55 % 187.43/187.55 fof(fact_transfer__int__nat__numerals_I4_J,axiom, % 187.43/187.55 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)))) ). % 187.43/187.55 % 187.43/187.55 fof(fact_transfer__nat__int__numerals_I4_J,axiom, % 187.43/187.55 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)))) ). % 187.43/187.55 % 187.43/187.55 fof(fact_le__special_I2_J,axiom, % 187.43/187.55 ! [V_y_2,T_a] : % 187.43/187.55 ( ( class_Int_Onumber__ring(T_a) % 187.43/187.55 & class_Rings_Olinordered__idom(T_a) ) % 187.43/187.55 => ( 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))) % 187.43/187.55 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2)) ) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_le__special_I4_J,axiom, % 187.43/187.55 ! [V_x_2,T_a] : % 187.43/187.55 ( ( class_Int_Onumber__ring(T_a) % 187.43/187.55 & class_Rings_Olinordered__idom(T_a) ) % 187.43/187.55 => ( 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))) % 187.43/187.55 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls))) ) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_less__special_I2_J,axiom, % 187.43/187.55 ! [V_y_2,T_a] : % 187.43/187.55 ( ( class_Int_Onumber__ring(T_a) % 187.43/187.55 & class_Rings_Olinordered__idom(T_a) ) % 187.43/187.55 => ( 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))) % 187.43/187.55 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2)) ) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_less__special_I4_J,axiom, % 187.43/187.55 ! [V_x_2,T_a] : % 187.43/187.55 ( ( class_Int_Onumber__ring(T_a) % 187.43/187.55 & class_Rings_Olinordered__idom(T_a) ) % 187.43/187.55 => ( 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))) % 187.43/187.55 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls))) ) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_add__special_I3_J,axiom, % 187.43/187.55 ! [V_v,T_a] : % 187.43/187.55 ( class_Int_Onumber__ring(T_a) % 187.43/187.55 => 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))) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_add__special_I2_J,axiom, % 187.43/187.55 ! [V_w,T_a] : % 187.43/187.55 ( class_Int_Onumber__ring(T_a) % 187.43/187.55 => 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)) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_Suc__diff__eq__diff__pred,axiom, % 187.43/187.55 ! [V_m,V_n] : % 187.43/187.55 ( 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)) % 187.43/187.55 => 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)))) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_diff__special_I2_J,axiom, % 187.43/187.55 ! [V_v,T_a] : % 187.43/187.55 ( class_Int_Onumber__ring(T_a) % 187.43/187.55 => 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)))) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_diff__special_I1_J,axiom, % 187.43/187.55 ! [V_w,T_a] : % 187.43/187.55 ( class_Int_Onumber__ring(T_a) % 187.43/187.55 => 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))) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_eq__special_I2_J,axiom, % 187.43/187.55 ! [V_y_2,T_a] : % 187.43/187.55 ( class_Int_Onumber__ring(T_a) % 187.43/187.55 => ( c_Groups_Oone__class_Oone(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2) % 187.43/187.55 <=> 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)))) ) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_eq__special_I4_J,axiom, % 187.43/187.55 ! [V_x_2,T_a] : % 187.43/187.55 ( class_Int_Onumber__ring(T_a) % 187.43/187.55 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2) = c_Groups_Oone__class_Oone(T_a) % 187.43/187.55 <=> 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))))) ) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_of__nat__double,axiom, % 187.43/187.55 ! [V_x,T_a] : % 187.43/187.55 ( class_Rings_Osemiring__1(T_a) % 187.43/187.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 187.43/187.55 => 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))) ) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_power__number__of__odd__number__of,axiom, % 187.43/187.55 ! [V_v_2,V_w_2,T_a] : % 187.43/187.55 ( class_Int_Onumber__ring(T_a) % 187.43/187.55 => ( ( 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))) % 187.43/187.55 => 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))) ) % 187.43/187.55 & ( ~ 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))) % 187.43/187.55 => 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) ) ) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_zpower__number__of__odd,axiom, % 187.43/187.55 ! [V_z_2,V_w_2] : % 187.43/187.55 ( ( 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))) % 187.43/187.55 => 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))) ) % 187.43/187.55 & ( ~ 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))) % 187.43/187.55 => 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) ) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_one__code__numeral__code,axiom, % 187.43/187.55 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)) ). % 187.43/187.55 % 187.43/187.55 fof(fact_power__number__of__odd,axiom, % 187.43/187.55 ! [V_z_2,V_w_2,T_a] : % 187.43/187.55 ( class_Int_Onumber__ring(T_a) % 187.43/187.55 => ( ( 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))) % 187.43/187.55 => 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))) ) % 187.43/187.55 & ( ~ 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))) % 187.43/187.55 => 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) ) ) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_nat__2,axiom, % 187.43/187.55 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))) ). % 187.43/187.55 % 187.43/187.55 fof(fact_int__power,axiom, % 187.43/187.55 ! [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) ). % 187.43/187.55 % 187.43/187.55 fof(fact_zpower__int,axiom, % 187.43/187.55 ! [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)) ). % 187.43/187.55 % 187.43/187.55 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I4_J,axiom, % 187.43/187.55 ! [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)) ). % 187.43/187.55 % 187.43/187.55 fof(fact_code__numeral__zero__minus__one,axiom, % 187.43/187.55 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) ). % 187.43/187.55 % 187.43/187.55 fof(fact_rel__simps_I48_J,axiom, % 187.43/187.55 ! [V_l_2,V_k_2] : % 187.43/187.55 ( c_Int_OBit0(V_k_2) = c_Int_OBit0(V_l_2) % 187.43/187.55 <=> V_k_2 = V_l_2 ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_of__int__power,axiom, % 187.43/187.55 ! [V_n,V_z,T_a] : % 187.43/187.55 ( class_Rings_Oring__1(T_a) % 187.43/187.55 => 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) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J,axiom, % 187.43/187.55 ! [V_q,V_y,V_x,T_a] : % 187.43/187.55 ( class_Rings_Ocomm__semiring__1(T_a) % 187.43/187.55 => 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)) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_power__number__of__even,axiom, % 187.43/187.55 ! [V_w_2,V_z_2,T_a] : % 187.43/187.55 ( class_Int_Onumber__ring(T_a) % 187.43/187.55 => 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))) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_less__eq__int__code_I13_J,axiom, % 187.43/187.55 ! [V_k2_2,V_k1_2] : % 187.43/187.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2))) % 187.43/187.55 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_rel__simps_I31_J,axiom, % 187.43/187.55 ! [V_l_2,V_k_2] : % 187.43/187.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit0(V_l_2))) % 187.43/187.55 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_rel__simps_I14_J,axiom, % 187.43/187.55 ! [V_l_2,V_k_2] : % 187.43/187.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit0(V_l_2))) % 187.43/187.55 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_less__int__code_I13_J,axiom, % 187.43/187.55 ! [V_k2_2,V_k1_2] : % 187.43/187.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2))) % 187.43/187.55 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_Bit0__Pls,axiom, % 187.43/187.55 c_Int_OBit0(c_Int_OPls) = c_Int_OPls ). % 187.43/187.55 % 187.43/187.55 fof(fact_rel__simps_I38_J,axiom, % 187.43/187.55 ! [V_l_2] : % 187.43/187.55 ( c_Int_OPls = c_Int_OBit0(V_l_2) % 187.43/187.55 <=> c_Int_OPls = V_l_2 ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_rel__simps_I44_J,axiom, % 187.43/187.55 ! [V_k_2] : % 187.43/187.55 ( c_Int_OBit0(V_k_2) = c_Int_OPls % 187.43/187.55 <=> V_k_2 = c_Int_OPls ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_rel__simps_I49_J,axiom, % 187.43/187.55 ! [V_l,V_k] : c_Int_OBit0(V_k) != c_Int_OBit1(V_l) ). % 187.43/187.55 % 187.43/187.55 fof(fact_rel__simps_I50_J,axiom, % 187.43/187.55 ! [V_l,V_k] : c_Int_OBit1(V_k) != c_Int_OBit0(V_l) ). % 187.43/187.55 % 187.43/187.55 fof(fact_add__Bit0__Bit0,axiom, % 187.43/187.55 ! [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)) ). % 187.43/187.55 % 187.43/187.55 fof(fact_Bit0__def,axiom, % 187.43/187.55 ! [V_k] : c_Int_OBit0(V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_k) ). % 187.43/187.55 % 187.43/187.55 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J,axiom, % 187.43/187.55 ! [V_q,V_p,V_x,T_a] : % 187.43/187.55 ( class_Rings_Ocomm__semiring__1(T_a) % 187.43/187.55 => 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)) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_zpower__zpower,axiom, % 187.43/187.55 ! [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)) ). % 187.43/187.55 % 187.43/187.55 fof(fact_zpower__number__of__even,axiom, % 187.43/187.55 ! [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))) ). % 187.43/187.55 % 187.43/187.55 fof(fact_mult__Bit0,axiom, % 187.43/187.55 ! [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)) ). % 187.43/187.55 % 187.43/187.55 fof(fact_diff__bin__simps_I7_J,axiom, % 187.43/187.55 ! [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)) ). % 187.43/187.55 % 187.43/187.55 fof(fact_minus__Bit0,axiom, % 187.43/187.55 ! [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)) ). % 187.43/187.55 % 187.43/187.55 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J,axiom, % 187.43/187.55 ! [V_x,T_a] : % 187.43/187.55 ( class_Rings_Ocomm__semiring__1(T_a) % 187.43/187.55 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_x ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_nat__power__eq,axiom, % 187.43/187.55 ! [V_n,V_z] : % 187.43/187.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 187.43/187.55 => 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) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I4_J,axiom, % 187.43/187.55 ! [V_n,V_x] : % 187.43/187.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 187.43/187.55 => 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)) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_power__number__of__even__number__of,axiom, % 187.43/187.55 ! [V_w_2,V_v_2,T_a] : % 187.43/187.55 ( class_Int_Onumber__ring(T_a) % 187.43/187.55 => 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))) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_zero__eq__power2,axiom, % 187.43/187.55 ! [V_a_2,T_a] : % 187.43/187.55 ( class_Rings_Oring__1__no__zero__divisors(T_a) % 187.43/187.55 => ( 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) % 187.43/187.55 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_zero__power2,axiom, % 187.43/187.55 ! [T_a] : % 187.43/187.55 ( class_Rings_Osemiring__1(T_a) % 187.43/187.55 => 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) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J,axiom, % 187.43/187.55 ! [V_x,T_a] : % 187.43/187.55 ( class_Rings_Ocomm__semiring__1(T_a) % 187.43/187.55 => 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)))) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_power2__eq__square,axiom, % 187.43/187.55 ! [V_a,T_a] : % 187.43/187.55 ( class_Groups_Omonoid__mult(T_a) % 187.43/187.55 => 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) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_one__power2,axiom, % 187.43/187.55 ! [T_a] : % 187.43/187.55 ( class_Rings_Osemiring__1(T_a) % 187.43/187.55 => 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) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_power2__minus,axiom, % 187.43/187.55 ! [V_a,T_a] : % 187.43/187.55 ( class_Rings_Oring__1(T_a) % 187.43/187.55 => 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)))) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_power__even__eq,axiom, % 187.43/187.55 ! [V_n,V_a,T_a] : % 187.43/187.55 ( class_Groups_Omonoid__mult(T_a) % 187.43/187.55 => 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)))) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J,axiom, % 187.43/187.55 ! [V_q,V_x,T_a] : % 187.43/187.55 ( class_Rings_Ocomm__semiring__1(T_a) % 187.43/187.55 => 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)) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J,axiom, % 187.43/187.55 ! [V_q,V_x,T_a] : % 187.43/187.55 ( class_Rings_Ocomm__semiring__1(T_a) % 187.43/187.55 => 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)) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J,axiom, % 187.43/187.55 ! [V_q,V_x,T_a] : % 187.43/187.55 ( class_Rings_Ocomm__semiring__1(T_a) % 187.43/187.55 => 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)) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J,axiom, % 187.43/187.55 ! [V_x,T_a] : % 187.43/187.55 ( class_Rings_Ocomm__semiring__1(T_a) % 187.43/187.55 => 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) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J,axiom, % 187.43/187.55 ! [V_q,V_p,V_x,T_a] : % 187.43/187.55 ( class_Rings_Ocomm__semiring__1(T_a) % 187.43/187.55 => 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)) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_bin__less__0__simps_I3_J,axiom, % 187.43/187.55 ! [V_w_2] : % 187.43/187.55 ( 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))) % 187.43/187.55 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J,axiom, % 187.43/187.55 ! [V_n,V_x] : % 187.43/187.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 187.43/187.55 => 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))) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_rel__simps_I21_J,axiom, % 187.43/187.55 ! [V_k_2] : % 187.43/187.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k_2))) % 187.43/187.55 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_rel__simps_I27_J,axiom, % 187.43/187.55 ! [V_k_2] : % 187.43/187.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OPls)) % 187.43/187.55 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_rel__simps_I32_J,axiom, % 187.43/187.55 ! [V_l_2,V_k_2] : % 187.43/187.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit1(V_l_2))) % 187.43/187.55 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_less__eq__int__code_I14_J,axiom, % 187.43/187.55 ! [V_k2_2,V_k1_2] : % 187.43/187.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit1(V_k2_2))) % 187.43/187.55 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_rel__simps_I10_J,axiom, % 187.43/187.55 ! [V_k_2] : % 187.43/187.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OPls)) % 187.43/187.55 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_rel__simps_I4_J,axiom, % 187.43/187.55 ! [V_k_2] : % 187.43/187.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k_2))) % 187.43/187.55 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_less__int__code_I15_J,axiom, % 187.43/187.55 ! [V_k2_2,V_k1_2] : % 187.43/187.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit0(V_k2_2))) % 187.43/187.55 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_rel__simps_I16_J,axiom, % 187.43/187.55 ! [V_l_2,V_k_2] : % 187.43/187.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit0(V_l_2))) % 187.43/187.55 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_add__Bit0__Bit1,axiom, % 187.43/187.55 ! [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)) ). % 187.43/187.55 % 187.43/187.55 fof(fact_add__Bit1__Bit0,axiom, % 187.43/187.55 ! [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)) ). % 187.43/187.55 % 187.43/187.55 fof(fact_zpower__zadd__distrib,axiom, % 187.43/187.55 ! [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)) ). % 187.43/187.55 % 187.43/187.55 fof(fact_diff__bin__simps_I3_J,axiom, % 187.43/187.55 ! [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)) ). % 187.43/187.55 % 187.43/187.55 fof(fact_diff__bin__simps_I9_J,axiom, % 187.43/187.55 ! [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)) ). % 187.43/187.55 % 187.43/187.55 fof(fact_diff__bin__simps_I10_J,axiom, % 187.43/187.55 ! [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)) ). % 187.43/187.55 % 187.43/187.55 fof(fact_Ints__power,axiom, % 187.43/187.55 ! [V_n_2,V_a_2,T_a] : % 187.43/187.55 ( class_Rings_Oring__1(T_a) % 187.43/187.55 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a))) % 187.43/187.55 => 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))) ) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_neg__number__of__Bit0,axiom, % 187.43/187.55 ! [V_w_2] : % 187.43/187.55 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w_2)))) % 187.43/187.55 <=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_pred__Bit0,axiom, % 187.43/187.55 ! [V_k] : c_Int_Opred(c_Int_OBit0(V_k)) = c_Int_OBit1(c_Int_Opred(V_k)) ). % 187.43/187.55 % 187.43/187.55 fof(fact_pred__Bit1,axiom, % 187.43/187.55 ! [V_k] : c_Int_Opred(c_Int_OBit1(V_k)) = c_Int_OBit0(V_k) ). % 187.43/187.55 % 187.43/187.55 fof(fact_iszero__number__of__Bit0,axiom, % 187.43/187.55 ! [V_w_2,T_a] : % 187.43/187.55 ( ( class_Int_Onumber__ring(T_a) % 187.43/187.55 & class_Int_Oring__char__0(T_a) ) % 187.43/187.55 => ( c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(V_w_2))) % 187.43/187.55 <=> c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)) ) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_zero__le__power2,axiom, % 187.43/187.55 ! [V_a,T_a] : % 187.43/187.55 ( class_Rings_Olinordered__idom(T_a) % 187.43/187.55 => 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)))))) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_power2__le__imp__le,axiom, % 187.43/187.55 ! [V_y,V_x,T_a] : % 187.43/187.55 ( class_Rings_Olinordered__semidom(T_a) % 187.43/187.55 => ( 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)))))) % 187.43/187.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 187.43/187.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_power2__eq__imp__eq,axiom, % 187.43/187.55 ! [V_y,V_x,T_a] : % 187.43/187.55 ( class_Rings_Olinordered__semidom(T_a) % 187.43/187.55 => ( 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)))) % 187.43/187.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 187.43/187.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 187.43/187.55 => V_x = V_y ) ) ) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_power2__less__0,axiom, % 187.43/187.55 ! [V_a,T_a] : % 187.43/187.55 ( class_Rings_Olinordered__idom(T_a) % 187.43/187.55 => ~ 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))) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_zero__less__power2,axiom, % 187.43/187.55 ! [V_a_2,T_a] : % 187.43/187.55 ( class_Rings_Olinordered__idom(T_a) % 187.43/187.55 => ( 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)))))) % 187.43/187.55 <=> V_a_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_sum__power2__eq__zero__iff,axiom, % 187.43/187.55 ! [V_y_2,V_x_2,T_a] : % 187.43/187.55 ( class_Rings_Olinordered__idom(T_a) % 187.43/187.55 => ( 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) % 187.43/187.55 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a) % 187.43/187.55 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_power2__eq__square__number__of,axiom, % 187.43/187.55 ! [V_w,T_b] : % 187.43/187.55 ( ( class_Groups_Omonoid__mult(T_b) % 187.43/187.55 & class_Int_Onumber(T_b) ) % 187.43/187.55 => 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)) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_succ__Bit1,axiom, % 187.43/187.55 ! [V_k] : c_Int_Osucc(c_Int_OBit1(V_k)) = c_Int_OBit0(c_Int_Osucc(V_k)) ). % 187.43/187.55 % 187.43/187.55 fof(fact_succ__Bit0,axiom, % 187.43/187.55 ! [V_k] : c_Int_Osucc(c_Int_OBit0(V_k)) = c_Int_OBit1(V_k) ). % 187.43/187.55 % 187.43/187.55 fof(fact_power2__eq__1__iff,axiom, % 187.43/187.55 ! [V_a_2,T_a] : % 187.43/187.55 ( class_Rings_Oring__1__no__zero__divisors(T_a) % 187.43/187.55 => ( 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) % 187.43/187.55 <=> ( V_a_2 = c_Groups_Oone__class_Oone(T_a) % 187.43/187.55 | V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J,axiom, % 187.43/187.55 ! [V_n,V_x,T_a] : % 187.43/187.55 ( class_Rings_Ocomm__semiring__1(T_a) % 187.43/187.55 => 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)) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_power__minus__even,axiom, % 187.43/187.55 ! [V_n,V_a,T_a] : % 187.43/187.55 ( class_Rings_Oring__1(T_a) % 187.43/187.55 => 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)) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_nat__number__of__Bit0,axiom, % 187.43/187.55 ! [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))) ). % 187.43/187.55 % 187.43/187.55 fof(fact_power__nat__number__of,axiom, % 187.43/187.55 ! [V_n,V_v] : % 187.43/187.55 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 187.43/187.55 => 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) ) % 187.43/187.55 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 187.43/187.55 => 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)) ) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_power__nat__number__of__number__of,axiom, % 187.43/187.55 ! [V_w,V_v] : % 187.43/187.55 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 187.43/187.55 => 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)) ) % 187.43/187.55 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 187.43/187.55 => 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))) ) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_power2__less__imp__less,axiom, % 187.43/187.55 ! [V_y,V_x,T_a] : % 187.43/187.55 ( class_Rings_Olinordered__semidom(T_a) % 187.43/187.55 => ( 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)))))) % 187.43/187.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 187.43/187.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_sum__power2__le__zero__iff,axiom, % 187.43/187.55 ! [V_y_2,V_x_2,T_a] : % 187.43/187.55 ( class_Rings_Olinordered__idom(T_a) % 187.43/187.55 => ( 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))) % 187.43/187.55 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a) % 187.43/187.55 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_sum__power2__ge__zero,axiom, % 187.43/187.55 ! [V_y,V_x,T_a] : % 187.43/187.55 ( class_Rings_Olinordered__idom(T_a) % 187.43/187.55 => 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))))))) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_sum__power2__gt__zero__iff,axiom, % 187.43/187.55 ! [V_y_2,V_x_2,T_a] : % 187.43/187.55 ( class_Rings_Olinordered__idom(T_a) % 187.43/187.55 => ( 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))))))) % 187.43/187.55 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(T_a) % 187.43/187.55 | V_y_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_not__sum__power2__lt__zero,axiom, % 187.43/187.55 ! [V_y,V_x,T_a] : % 187.43/187.55 ( class_Rings_Olinordered__idom(T_a) % 187.43/187.55 => ~ 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))) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_power2__sum,axiom, % 187.43/187.55 ! [V_y,V_x,T_a] : % 187.43/187.55 ( class_Int_Onumber__ring(T_a) % 187.43/187.55 => 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)) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_zero__le__even__power_H,axiom, % 187.43/187.55 ! [V_n,V_a,T_a] : % 187.43/187.55 ( class_Rings_Olinordered__idom(T_a) % 187.43/187.55 => 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)))) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_power__odd__eq,axiom, % 187.43/187.55 ! [V_n,V_a,T_a] : % 187.43/187.55 ( class_Groups_Omonoid__mult(T_a) % 187.43/187.55 => 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))))) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I37_J,axiom, % 187.43/187.55 ! [V_n,V_x,T_a] : % 187.43/187.55 ( class_Rings_Ocomm__semiring__1(T_a) % 187.43/187.55 => 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))) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_power__minus1__even,axiom, % 187.43/187.55 ! [V_n,T_a] : % 187.43/187.55 ( class_Rings_Oring__1(T_a) % 187.43/187.55 => 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) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_number__of__Bit0,axiom, % 187.43/187.55 ! [V_w,T_a] : % 187.43/187.55 ( class_Int_Onumber__ring(T_a) % 187.43/187.55 => 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)) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_rel__simps_I15_J,axiom, % 187.43/187.55 ! [V_l_2,V_k_2] : % 187.43/187.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit1(V_l_2))) % 187.43/187.55 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_less__int__code_I14_J,axiom, % 187.43/187.55 ! [V_k2_2,V_k1_2] : % 187.43/187.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit1(V_k2_2))) % 187.43/187.55 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_rel__simps_I33_J,axiom, % 187.43/187.55 ! [V_l_2,V_k_2] : % 187.43/187.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit0(V_l_2))) % 187.43/187.55 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_less__eq__int__code_I15_J,axiom, % 187.43/187.55 ! [V_k2_2,V_k1_2] : % 187.43/187.55 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit0(V_k2_2))) % 187.43/187.55 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_mult__Bit1,axiom, % 187.43/187.55 ! [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) ). % 187.43/187.55 % 187.43/187.55 fof(fact_diff__bin__simps_I8_J,axiom, % 187.43/187.55 ! [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)) ). % 187.43/187.55 % 187.43/187.55 fof(fact_power2__diff,axiom, % 187.43/187.55 ! [V_y,V_x,T_a] : % 187.43/187.55 ( class_Int_Onumber__ring(T_a) % 187.43/187.55 => 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)) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_odd__0__le__power__imp__0__le,axiom, % 187.43/187.55 ! [V_n,V_a,T_a] : % 187.43/187.55 ( class_Rings_Olinordered__idom(T_a) % 187.43/187.55 => ( 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))))) % 187.43/187.55 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) ) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_odd__power__less__zero,axiom, % 187.43/187.55 ! [V_n,V_a,T_a] : % 187.43/187.55 ( class_Rings_Olinordered__idom(T_a) % 187.43/187.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 187.43/187.55 => 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))) ) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_add__Bit1__Bit1,axiom, % 187.43/187.55 ! [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))) ). % 187.43/187.55 % 187.43/187.55 fof(fact_power__minus1__odd,axiom, % 187.43/187.55 ! [V_n,T_a] : % 187.43/187.55 ( class_Rings_Oring__1(T_a) % 187.43/187.55 => 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)) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_zero__code__numeral__code,axiom, % 187.43/187.55 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) ). % 187.43/187.55 % 187.43/187.55 fof(fact_double__number__of__Bit0,axiom, % 187.43/187.55 ! [V_w,T_a] : % 187.43/187.55 ( class_Int_Onumber__ring(T_a) % 187.43/187.55 => 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)) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_power3__eq__cube,axiom, % 187.43/187.55 ! [V_a,T_a] : % 187.43/187.55 ( class_Groups_Omonoid__mult(T_a) % 187.43/187.55 => 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) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_number__of1,axiom, % 187.43/187.55 ! [V_n] : % 187.43/187.55 ( 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))) % 187.43/187.55 => ( 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)))) % 187.43/187.55 & 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)))) ) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_power__eq__if,axiom, % 187.43/187.55 ! [V_p,V_m] : % 187.43/187.55 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 187.43/187.55 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),V_m) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) % 187.43/187.55 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 187.43/187.55 => 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)))) ) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_mult__2,axiom, % 187.43/187.55 ! [V_z,T_a] : % 187.43/187.55 ( class_Int_Onumber__ring(T_a) % 187.43/187.55 => 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) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_mult__2__right,axiom, % 187.43/187.55 ! [V_z,T_a] : % 187.43/187.55 ( class_Int_Onumber__ring(T_a) % 187.43/187.55 => 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) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_one__add__one__is__two,axiom, % 187.43/187.55 ! [T_a] : % 187.43/187.55 ( class_Int_Onumber__ring(T_a) % 187.43/187.55 => 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))) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_semiring__norm_I115_J,axiom, % 187.43/187.55 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))) ). % 187.43/187.55 % 187.43/187.55 fof(fact_numeral__2__eq__2,axiom, % 187.43/187.55 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))) ). % 187.43/187.55 % 187.43/187.55 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J,axiom, % 187.43/187.55 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))))) ). % 187.43/187.55 % 187.43/187.55 fof(fact_add__2__eq__Suc,axiom, % 187.43/187.55 ! [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)) ). % 187.43/187.55 % 187.43/187.55 fof(fact_add__2__eq__Suc_H,axiom, % 187.43/187.55 ! [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)) ). % 187.43/187.55 % 187.43/187.55 fof(fact_nat__mult__2,axiom, % 187.43/187.55 ! [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) ). % 187.43/187.55 % 187.43/187.55 fof(fact_nat__mult__2__right,axiom, % 187.43/187.55 ! [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) ). % 187.43/187.55 % 187.43/187.55 fof(fact_transfer__int__nat__numerals_I3_J,axiom, % 187.43/187.55 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)))) ). % 187.43/187.55 % 187.43/187.55 fof(fact_transfer__nat__int__numerals_I3_J,axiom, % 187.43/187.55 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)))) ). % 187.43/187.55 % 187.43/187.55 fof(fact_nat__1__add__1,axiom, % 187.43/187.55 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))) ). % 187.43/187.55 % 187.43/187.55 fof(fact_less__2__cases,axiom, % 187.43/187.55 ! [V_n] : % 187.43/187.55 ( 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))))) % 187.43/187.55 => ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 187.43/187.55 | V_n = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ). % 187.43/187.55 % 187.43/187.55 fof(fact_power__strict__mono,axiom, % 187.43/187.55 ! [V_n,V_b,V_a,T_a] : % 187.43/187.55 ( class_Rings_Olinordered__semidom(T_a) % 187.43/187.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 187.43/187.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 187.43/187.55 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 187.43/187.56 => 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))) ) ) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_one__less__power,axiom, % 187.43/187.56 ! [V_n,V_a,T_a] : % 187.43/187.56 ( class_Rings_Olinordered__semidom(T_a) % 187.43/187.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 187.43/187.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 187.43/187.56 => 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))) ) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_power__le__imp__le__exp,axiom, % 187.43/187.56 ! [V_n,V_m,V_a,T_a] : % 187.43/187.56 ( class_Rings_Olinordered__semidom(T_a) % 187.43/187.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 187.43/187.56 => ( 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))) % 187.43/187.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_power__increasing__iff,axiom, % 187.43/187.56 ! [V_y_2,V_x_2,V_b_2,T_a] : % 187.43/187.56 ( class_Rings_Olinordered__semidom(T_a) % 187.43/187.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_b_2)) % 187.43/187.56 => ( 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))) % 187.43/187.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x_2),V_y_2)) ) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_power__decreasing,axiom, % 187.43/187.56 ! [V_a,V_N,V_n,T_a] : % 187.43/187.56 ( class_Rings_Olinordered__semidom(T_a) % 187.43/187.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_N)) % 187.43/187.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 187.43/187.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Oone__class_Oone(T_a))) % 187.43/187.56 => 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))) ) ) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_power__strict__decreasing,axiom, % 187.43/187.56 ! [V_a,V_N,V_n,T_a] : % 187.43/187.56 ( class_Rings_Olinordered__semidom(T_a) % 187.43/187.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_N)) % 187.43/187.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 187.43/187.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a))) % 187.43/187.56 => 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))) ) ) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_field__power__not__zero,axiom, % 187.43/187.56 ! [V_n,V_a,T_a] : % 187.43/187.56 ( class_Rings_Oring__1__no__zero__divisors(T_a) % 187.43/187.56 => ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 187.43/187.56 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) != c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_nat__power__eq__Suc__0__iff,axiom, % 187.43/187.56 ! [V_m_2,V_x_2] : % 187.43/187.56 ( 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)) % 187.43/187.56 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 187.43/187.56 | V_x_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_power__Suc__0,axiom, % 187.43/187.56 ! [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)) ). % 187.43/187.56 % 187.43/187.56 fof(fact_nat__power__less__imp__less,axiom, % 187.43/187.56 ! [V_n,V_m,V_i] : % 187.43/187.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_i)) % 187.43/187.56 => ( 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))) % 187.43/187.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_nat__zero__less__power__iff,axiom, % 187.43/187.56 ! [V_n_2,V_x_2] : % 187.43/187.56 ( 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))) % 187.43/187.56 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_x_2)) % 187.43/187.56 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_power__commutes,axiom, % 187.43/187.56 ! [V_n,V_a,T_a] : % 187.43/187.56 ( class_Groups_Omonoid__mult(T_a) % 187.43/187.56 => 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)) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_power__mult__distrib,axiom, % 187.43/187.56 ! [V_n,V_b,V_a,T_a] : % 187.43/187.56 ( class_Groups_Ocomm__monoid__mult(T_a) % 187.43/187.56 => 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)) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_power__one,axiom, % 187.43/187.56 ! [V_n,T_a] : % 187.43/187.56 ( class_Groups_Omonoid__mult(T_a) % 187.43/187.56 => 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) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_of__nat__power,axiom, % 187.43/187.56 ! [V_n,V_m,T_a] : % 187.43/187.56 ( class_Rings_Osemiring__1(T_a) % 187.43/187.56 => 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) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_power__mult,axiom, % 187.43/187.56 ! [V_n,V_m,V_a,T_a] : % 187.43/187.56 ( class_Groups_Omonoid__mult(T_a) % 187.43/187.56 => 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) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_power__one__right,axiom, % 187.43/187.56 ! [V_a,T_a] : % 187.43/187.56 ( class_Groups_Omonoid__mult(T_a) % 187.43/187.56 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_a ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_power__mono,axiom, % 187.43/187.56 ! [V_n,V_b,V_a,T_a] : % 187.43/187.56 ( class_Rings_Olinordered__semidom(T_a) % 187.43/187.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 187.43/187.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 187.43/187.56 => 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))) ) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_zero__le__power,axiom, % 187.43/187.56 ! [V_n,V_a,T_a] : % 187.43/187.56 ( class_Rings_Olinordered__semidom(T_a) % 187.43/187.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 187.43/187.56 => 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))) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_zero__less__power,axiom, % 187.43/187.56 ! [V_n,V_a,T_a] : % 187.43/187.56 ( class_Rings_Olinordered__semidom(T_a) % 187.43/187.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 187.43/187.56 => 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))) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_power__eq__0__iff,axiom, % 187.43/187.56 ! [V_n_2,V_a_2,T_a] : % 187.43/187.56 ( ( class_Power_Opower(T_a) % 187.43/187.56 & class_Rings_Omult__zero(T_a) % 187.43/187.56 & class_Rings_Ono__zero__divisors(T_a) % 187.43/187.56 & class_Rings_Ozero__neq__one(T_a) ) % 187.43/187.56 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_a) % 187.43/187.56 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a) % 187.43/187.56 & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_one__le__power,axiom, % 187.43/187.56 ! [V_n,V_a,T_a] : % 187.43/187.56 ( class_Rings_Olinordered__semidom(T_a) % 187.43/187.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 187.43/187.56 => 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))) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_power__0__Suc,axiom, % 187.43/187.56 ! [V_n,T_a] : % 187.43/187.56 ( ( class_Power_Opower(T_a) % 187.43/187.56 & class_Rings_Osemiring__0(T_a) ) % 187.43/187.56 => 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) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_power__inject__exp,axiom, % 187.43/187.56 ! [V_n_2,V_m_2,V_a_2,T_a] : % 187.43/187.56 ( class_Rings_Olinordered__semidom(T_a) % 187.43/187.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a_2)) % 187.43/187.56 => ( 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) % 187.43/187.56 <=> V_m_2 = V_n_2 ) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_power__Suc2,axiom, % 187.43/187.56 ! [V_n,V_a,T_a] : % 187.43/187.56 ( class_Groups_Omonoid__mult(T_a) % 187.43/187.56 => 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) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_power__Suc,axiom, % 187.43/187.56 ! [V_n,V_a,T_a] : % 187.43/187.56 ( class_Power_Opower(T_a) % 187.43/187.56 => 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)) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_nat__one__le__power,axiom, % 187.43/187.56 ! [V_n,V_i] : % 187.43/187.56 ( 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)) % 187.43/187.56 => 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))) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_power__0,axiom, % 187.43/187.56 ! [V_a,T_a] : % 187.43/187.56 ( class_Power_Opower(T_a) % 187.43/187.56 => 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) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_power__add,axiom, % 187.43/187.56 ! [V_n,V_m,V_a,T_a] : % 187.43/187.56 ( class_Groups_Omonoid__mult(T_a) % 187.43/187.56 => 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)) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_power__less__imp__less__base,axiom, % 187.43/187.56 ! [V_b,V_n,V_a,T_a] : % 187.43/187.56 ( class_Rings_Olinordered__semidom(T_a) % 187.43/187.56 => ( 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))) % 187.43/187.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 187.43/187.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_power__inject__base,axiom, % 187.43/187.56 ! [V_b,V_n,V_a,T_a] : % 187.43/187.56 ( class_Rings_Olinordered__semidom(T_a) % 187.43/187.56 => ( 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)) % 187.43/187.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 187.43/187.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 187.43/187.56 => V_a = V_b ) ) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_power__le__imp__le__base,axiom, % 187.43/187.56 ! [V_b,V_n,V_a,T_a] : % 187.43/187.56 ( class_Rings_Olinordered__semidom(T_a) % 187.43/187.56 => ( 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)))) % 187.43/187.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 187.43/187.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_power__less__power__Suc,axiom, % 187.43/187.56 ! [V_n,V_a,T_a] : % 187.43/187.56 ( class_Rings_Olinordered__semidom(T_a) % 187.43/187.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 187.43/187.56 => 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)))) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_power__gt1__lemma,axiom, % 187.43/187.56 ! [V_n,V_a,T_a] : % 187.43/187.56 ( class_Rings_Olinordered__semidom(T_a) % 187.43/187.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 187.43/187.56 => 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)))) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_power__0__left,axiom, % 187.43/187.56 ! [V_n,T_a] : % 187.43/187.56 ( ( class_Power_Opower(T_a) % 187.43/187.56 & class_Rings_Osemiring__0(T_a) ) % 187.43/187.56 => ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 187.43/187.56 => 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) ) % 187.43/187.56 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 187.43/187.56 => 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) ) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_power__gt1,axiom, % 187.43/187.56 ! [V_n,V_a,T_a] : % 187.43/187.56 ( class_Rings_Olinordered__semidom(T_a) % 187.43/187.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 187.43/187.56 => 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)))) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_power__strict__increasing,axiom, % 187.43/187.56 ! [V_a,V_N,V_n,T_a] : % 187.43/187.56 ( class_Rings_Olinordered__semidom(T_a) % 187.43/187.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_N)) % 187.43/187.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 187.43/187.56 => 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))) ) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_power__less__imp__less__exp,axiom, % 187.43/187.56 ! [V_n,V_m,V_a,T_a] : % 187.43/187.56 ( class_Rings_Olinordered__semidom(T_a) % 187.43/187.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 187.43/187.56 => ( 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))) % 187.43/187.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_power__strict__increasing__iff,axiom, % 187.43/187.56 ! [V_y_2,V_x_2,V_b_2,T_a] : % 187.43/187.56 ( class_Rings_Olinordered__semidom(T_a) % 187.43/187.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_b_2)) % 187.43/187.56 => ( 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))) % 187.43/187.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_power__increasing,axiom, % 187.43/187.56 ! [V_a,V_N,V_n,T_a] : % 187.43/187.56 ( class_Rings_Olinordered__semidom(T_a) % 187.43/187.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_N)) % 187.43/187.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 187.43/187.56 => 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))) ) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_power__minus,axiom, % 187.43/187.56 ! [V_n,V_a,T_a] : % 187.43/187.56 ( class_Rings_Oring__1(T_a) % 187.43/187.56 => 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)) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_power__Suc__less,axiom, % 187.43/187.56 ! [V_n,V_a,T_a] : % 187.43/187.56 ( class_Rings_Olinordered__semidom(T_a) % 187.43/187.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 187.43/187.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a))) % 187.43/187.56 => 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))) ) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_power__eq__imp__eq__base,axiom, % 187.43/187.56 ! [V_b,V_n,V_a,T_a] : % 187.43/187.56 ( class_Rings_Olinordered__semidom(T_a) % 187.43/187.56 => ( 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) % 187.43/187.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 187.43/187.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 187.43/187.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 187.43/187.56 => V_a = V_b ) ) ) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_power__Suc__less__one,axiom, % 187.43/187.56 ! [V_n,V_a,T_a] : % 187.43/187.56 ( class_Rings_Olinordered__semidom(T_a) % 187.43/187.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 187.43/187.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a))) % 187.43/187.56 => 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))) ) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_nat__of__aux__code,axiom, % 187.43/187.56 ! [V_n,V_i] : % 187.43/187.56 ( ( V_i = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 187.43/187.56 => c_Code__Numeral_Onat__of__aux(V_i,V_n) = V_n ) % 187.43/187.56 & ( V_i != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 187.43/187.56 => 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)) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_zmod__number__of__Bit1,axiom, % 187.43/187.56 ! [V_v,V_w] : % 187.43/187.56 ( ( 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))) % 187.43/187.56 => 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)) ) % 187.43/187.56 & ( ~ 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))) % 187.43/187.56 => 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)) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_neg__zmod__mult__2,axiom, % 187.43/187.56 ! [V_b,V_a] : % 187.43/187.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 187.43/187.56 => 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)) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_of__int__num,axiom, % 187.43/187.56 ! [V_k_2,T_a] : % 187.43/187.56 ( class_Rings_Oring__1(T_a) % 187.43/187.56 => ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 187.43/187.56 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_k_2) = c_Groups_Ozero__class_Ozero(T_a) ) % 187.43/187.56 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 187.43/187.56 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 187.43/187.56 => 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))) ) % 187.43/187.56 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 187.43/187.56 => 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))))) ) ) ) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_pos__zmod__mult__2,axiom, % 187.43/187.56 ! [V_b,V_a] : % 187.43/187.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 187.43/187.56 => 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))) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_neg__zdiv__mult__2,axiom, % 187.43/187.56 ! [V_b,V_a] : % 187.43/187.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 187.43/187.56 => 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) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_zmod__zdiv__trivial,axiom, % 187.43/187.56 ! [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) ). % 187.43/187.56 % 187.43/187.56 fof(fact_mod__div__trivial,axiom, % 187.43/187.56 ! [V_b,V_a,T_a] : % 187.43/187.56 ( class_Divides_Osemiring__div(T_a) % 187.43/187.56 => 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) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_DIVISION__BY__ZERO,axiom, % 187.43/187.56 ! [V_a] : % 187.43/187.56 ( 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) % 187.43/187.56 & c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_a ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_zmult__div__cancel,axiom, % 187.43/187.56 ! [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)) ). % 187.43/187.56 % 187.43/187.56 fof(fact_zmod__zdiv__equality_H,axiom, % 187.43/187.56 ! [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)) ). % 187.43/187.56 % 187.43/187.56 fof(fact_mod__self,axiom, % 187.43/187.56 ! [V_a,T_a] : % 187.43/187.56 ( class_Divides_Osemiring__div(T_a) % 187.43/187.56 => c_Divides_Odiv__class_Omod(T_a,V_a,V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_mod__by__0,axiom, % 187.43/187.56 ! [V_a,T_a] : % 187.43/187.56 ( class_Divides_Osemiring__div(T_a) % 187.43/187.56 => c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_mod__0,axiom, % 187.43/187.56 ! [V_a,T_a] : % 187.43/187.56 ( class_Divides_Osemiring__div(T_a) % 187.43/187.56 => c_Divides_Odiv__class_Omod(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_zdiv__zadd1__eq,axiom, % 187.43/187.56 ! [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)) ). % 187.43/187.56 % 187.43/187.56 fof(fact_mod__mod__trivial,axiom, % 187.43/187.56 ! [V_b,V_a,T_a] : % 187.43/187.56 ( class_Divides_Osemiring__div(T_a) % 187.43/187.56 => 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) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_zmod__zdiv__equality,axiom, % 187.43/187.56 ! [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)) ). % 187.43/187.56 % 187.43/187.56 fof(fact_zdiv__zmult1__eq,axiom, % 187.43/187.56 ! [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)) ). % 187.43/187.56 % 187.43/187.56 fof(fact_zdiv__zmod__equality,axiom, % 187.43/187.56 ! [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) ). % 187.43/187.56 % 187.43/187.56 fof(fact_zdiv__zmod__equality2,axiom, % 187.43/187.56 ! [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) ). % 187.43/187.56 % 187.43/187.56 fof(fact_semiring__div__class_Omod__div__equality_H,axiom, % 187.43/187.56 ! [V_b,V_a,T_a] : % 187.43/187.56 ( class_Divides_Osemiring__div(T_a) % 187.43/187.56 => 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 ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_mod__div__equality2,axiom, % 187.43/187.56 ! [V_a,V_b,T_a] : % 187.43/187.56 ( class_Divides_Osemiring__div(T_a) % 187.43/187.56 => 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 ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_mod__div__equality,axiom, % 187.43/187.56 ! [V_b,V_a,T_a] : % 187.43/187.56 ( class_Divides_Osemiring__div(T_a) % 187.43/187.56 => 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 ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_div__mod__equality2,axiom, % 187.43/187.56 ! [V_c,V_a,V_b,T_a] : % 187.43/187.56 ( class_Divides_Osemiring__div(T_a) % 187.43/187.56 => 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) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_div__mod__equality,axiom, % 187.43/187.56 ! [V_c,V_b,V_a,T_a] : % 187.43/187.56 ( class_Divides_Osemiring__div(T_a) % 187.43/187.56 => 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) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_mod__add__self2,axiom, % 187.43/187.56 ! [V_b,V_a,T_a] : % 187.43/187.56 ( class_Divides_Osemiring__div(T_a) % 187.43/187.56 => 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) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_mod__add__self1,axiom, % 187.43/187.56 ! [V_a,V_b,T_a] : % 187.43/187.56 ( class_Divides_Osemiring__div(T_a) % 187.43/187.56 => 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) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_mod__add__right__eq,axiom, % 187.43/187.56 ! [V_c,V_b,V_a,T_a] : % 187.43/187.56 ( class_Divides_Osemiring__div(T_a) % 187.43/187.56 => 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) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_mod__add__left__eq,axiom, % 187.43/187.56 ! [V_c,V_b,V_a,T_a] : % 187.43/187.56 ( class_Divides_Osemiring__div(T_a) % 187.43/187.56 => 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) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_mod__add__eq,axiom, % 187.43/187.56 ! [V_c,V_b,V_a,T_a] : % 187.43/187.56 ( class_Divides_Osemiring__div(T_a) % 187.43/187.56 => 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) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_zmod__simps_I2_J,axiom, % 187.43/187.56 ! [V_c,V_b,V_a,T_a] : % 187.43/187.56 ( class_Divides_Osemiring__div(T_a) % 187.43/187.56 => 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) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_zmod__simps_I1_J,axiom, % 187.43/187.56 ! [V_b,V_c,V_a,T_a] : % 187.43/187.56 ( class_Divides_Osemiring__div(T_a) % 187.43/187.56 => 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) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_mod__add__cong,axiom, % 187.43/187.56 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] : % 187.43/187.56 ( class_Divides_Osemiring__div(T_a) % 187.43/187.56 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c) % 187.43/187.56 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c) % 187.43/187.56 => 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) ) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_mod__mult__cong,axiom, % 187.43/187.56 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] : % 187.43/187.56 ( class_Divides_Osemiring__div(T_a) % 187.43/187.56 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c) % 187.43/187.56 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c) % 187.43/187.56 => 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) ) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_zmod__simps_I4_J,axiom, % 187.43/187.56 ! [V_b,V_c,V_a,T_a] : % 187.43/187.56 ( class_Divides_Osemiring__div(T_a) % 187.43/187.56 => 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) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_mod__mult__mult2,axiom, % 187.43/187.56 ! [V_b,V_c,V_a,T_a] : % 187.43/187.56 ( class_Divides_Osemiring__div(T_a) % 187.43/187.56 => 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) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_mod__mult__mult1,axiom, % 187.43/187.56 ! [V_b,V_a,V_c,T_a] : % 187.43/187.56 ( class_Divides_Osemiring__div(T_a) % 187.43/187.56 => 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)) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_mod__mult__eq,axiom, % 187.43/187.56 ! [V_c,V_b,V_a,T_a] : % 187.43/187.56 ( class_Divides_Osemiring__div(T_a) % 187.43/187.56 => 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) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_mod__mult__left__eq,axiom, % 187.43/187.56 ! [V_c,V_b,V_a,T_a] : % 187.43/187.56 ( class_Divides_Osemiring__div(T_a) % 187.43/187.56 => 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) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_mod__mult__right__eq,axiom, % 187.43/187.56 ! [V_c,V_b,V_a,T_a] : % 187.43/187.56 ( class_Divides_Osemiring__div(T_a) % 187.43/187.56 => 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) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_mod__diff__cong,axiom, % 187.43/187.56 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] : % 187.43/187.56 ( class_Divides_Oring__div(T_a) % 187.43/187.56 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c) % 187.43/187.56 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c) % 187.43/187.56 => 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) ) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_mod__diff__eq,axiom, % 187.43/187.56 ! [V_c,V_b,V_a,T_a] : % 187.43/187.56 ( class_Divides_Oring__div(T_a) % 187.43/187.56 => 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) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_mod__diff__left__eq,axiom, % 187.43/187.56 ! [V_c,V_b,V_a,T_a] : % 187.43/187.56 ( class_Divides_Oring__div(T_a) % 187.43/187.56 => 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) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_mod__diff__right__eq,axiom, % 187.43/187.56 ! [V_c,V_b,V_a,T_a] : % 187.43/187.56 ( class_Divides_Oring__div(T_a) % 187.43/187.56 => 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) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_mod__minus__eq,axiom, % 187.43/187.56 ! [V_b,V_a,T_a] : % 187.43/187.56 ( class_Divides_Oring__div(T_a) % 187.43/187.56 => 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) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_mod__minus__cong,axiom, % 187.43/187.56 ! [V_a_H,V_b,V_a,T_a] : % 187.43/187.56 ( class_Divides_Oring__div(T_a) % 187.43/187.56 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_b) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_b) % 187.43/187.56 => 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) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_zdiv__zero,axiom, % 187.43/187.56 ! [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) ). % 187.43/187.56 % 187.43/187.56 fof(fact_zmod__self,axiom, % 187.43/187.56 ! [V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_a) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ). % 187.43/187.56 % 187.43/187.56 fof(fact_zmod__zero,axiom, % 187.43/187.56 ! [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) ). % 187.43/187.56 % 187.43/187.56 fof(fact_zdiv__zminus2,axiom, % 187.43/187.56 ! [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) ). % 187.43/187.56 % 187.43/187.56 fof(fact_zdiv__zminus__zminus,axiom, % 187.43/187.56 ! [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) ). % 187.43/187.56 % 187.43/187.56 fof(fact_zmod__simps_I3_J,axiom, % 187.43/187.56 ! [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) ). % 187.43/187.56 % 187.43/187.56 fof(fact_zmod__zmult1__eq,axiom, % 187.43/187.56 ! [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) ). % 187.43/187.56 % 187.43/187.56 fof(fact_zdiff__zmod__left,axiom, % 187.43/187.56 ! [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) ). % 187.43/187.56 % 187.43/187.56 fof(fact_zdiff__zmod__right,axiom, % 187.43/187.56 ! [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) ). % 187.43/187.56 % 187.43/187.56 fof(fact_zmod__zminus2,axiom, % 187.43/187.56 ! [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)) ). % 187.43/187.56 % 187.43/187.56 fof(fact_zmod__zminus__zminus,axiom, % 187.43/187.56 ! [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)) ). % 187.43/187.56 % 187.43/187.56 fof(fact_zminus__zmod,axiom, % 187.43/187.56 ! [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) ). % 187.43/187.56 % 187.43/187.56 fof(fact_div__0,axiom, % 187.43/187.56 ! [V_a,T_a] : % 187.43/187.56 ( class_Divides_Osemiring__div(T_a) % 187.43/187.56 => 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) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_div__by__0,axiom, % 187.43/187.56 ! [V_a,T_a] : % 187.43/187.56 ( class_Divides_Osemiring__div(T_a) % 187.43/187.56 => 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) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_div__by__1,axiom, % 187.43/187.56 ! [V_a,T_a] : % 187.43/187.56 ( class_Divides_Osemiring__div(T_a) % 187.43/187.56 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_zpower__zmod,axiom, % 187.43/187.56 ! [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) ). % 187.43/187.56 % 187.43/187.56 fof(fact_mod__mult__self1__is__0,axiom, % 187.43/187.56 ! [V_a,V_b,T_a] : % 187.43/187.56 ( class_Divides_Osemiring__div(T_a) % 187.43/187.56 => 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) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_mod__mult__self2__is__0,axiom, % 187.43/187.56 ! [V_b,V_a,T_a] : % 187.43/187.56 ( class_Divides_Osemiring__div(T_a) % 187.43/187.56 => 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) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_zmod__zmult2__eq,axiom, % 187.43/187.56 ! [V_b,V_a,V_c] : % 187.43/187.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 187.43/187.56 => 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)) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_mod__mult__self1,axiom, % 187.43/187.56 ! [V_b,V_c,V_a,T_a] : % 187.43/187.56 ( class_Divides_Osemiring__div(T_a) % 187.43/187.56 => 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) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_mod__mult__self2,axiom, % 187.43/187.56 ! [V_c,V_b,V_a,T_a] : % 187.43/187.56 ( class_Divides_Osemiring__div(T_a) % 187.43/187.56 => 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) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_mod__by__1,axiom, % 187.43/187.56 ! [V_a,T_a] : % 187.43/187.56 ( class_Divides_Osemiring__div(T_a) % 187.43/187.56 => c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_zdiv__zminus2__eq__if,axiom, % 187.43/187.56 ! [V_a,V_b] : % 187.43/187.56 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 187.43/187.56 => ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 187.43/187.56 => 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)) ) % 187.43/187.56 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 187.43/187.56 => 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)) ) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_zdiv__zminus1__eq__if,axiom, % 187.43/187.56 ! [V_a,V_b] : % 187.43/187.56 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 187.43/187.56 => ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 187.43/187.56 => 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)) ) % 187.43/187.56 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 187.43/187.56 => 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)) ) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_Divides_Otransfer__nat__int__function__closures_I1_J,axiom, % 187.43/187.56 ! [V_y,V_x] : % 187.43/187.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 187.43/187.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 187.43/187.56 => 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))) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_pos__imp__zdiv__neg__iff,axiom, % 187.43/187.56 ! [V_a_2,V_b_2] : % 187.43/187.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2)) % 187.43/187.56 => ( 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))) % 187.43/187.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_neg__imp__zdiv__neg__iff,axiom, % 187.43/187.56 ! [V_a_2,V_b_2] : % 187.43/187.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 187.43/187.56 => ( 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))) % 187.43/187.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_div__neg__pos__less0,axiom, % 187.43/187.56 ! [V_b,V_a] : % 187.43/187.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 187.43/187.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 187.43/187.56 => 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))) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_zdiv__self,axiom, % 187.43/187.56 ! [V_a] : % 187.43/187.56 ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 187.43/187.56 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_a) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_zmod__le__nonneg__dividend,axiom, % 187.43/187.56 ! [V_k,V_m] : % 187.43/187.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m)) % 187.43/187.56 => 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)) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_Divides_Otransfer__nat__int__function__closures_I2_J,axiom, % 187.43/187.56 ! [V_y,V_x] : % 187.43/187.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 187.43/187.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 187.43/187.56 => 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))) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_pos__mod__bound,axiom, % 187.43/187.56 ! [V_a,V_b] : % 187.43/187.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 187.43/187.56 => 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)) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_neg__mod__bound,axiom, % 187.43/187.56 ! [V_a,V_b] : % 187.43/187.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 187.43/187.56 => 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))) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_zdiv__number__of__Bit0,axiom, % 187.43/187.56 ! [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)) ). % 187.43/187.56 % 187.43/187.56 fof(fact_zmod__eq__0__iff,axiom, % 187.43/187.56 ! [V_d_2,V_m_2] : % 187.43/187.56 ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 187.43/187.56 <=> ? [B_q] : V_m_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_d_2),B_q) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_zmod__zminus2__not__zero,axiom, % 187.43/187.56 ! [V_l,V_k] : % 187.43/187.56 ( 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) % 187.43/187.56 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_zmod__zminus1__not__zero,axiom, % 187.43/187.56 ! [V_l,V_k] : % 187.43/187.56 ( 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) % 187.43/187.56 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_div__mult__mult1,axiom, % 187.43/187.56 ! [V_b,V_a,V_c,T_a] : % 187.43/187.56 ( class_Divides_Osemiring__div(T_a) % 187.43/187.56 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 187.43/187.56 => 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) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_div__mult__mult2,axiom, % 187.43/187.56 ! [V_b,V_a,V_c,T_a] : % 187.43/187.56 ( class_Divides_Osemiring__div(T_a) % 187.43/187.56 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 187.43/187.56 => 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) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_div__mult__self1__is__id,axiom, % 187.43/187.56 ! [V_a,V_b,T_a] : % 187.43/187.56 ( class_Divides_Osemiring__div(T_a) % 187.43/187.56 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 187.43/187.56 => 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 ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_div__mult__self2__is__id,axiom, % 187.43/187.56 ! [V_a,V_b,T_a] : % 187.43/187.56 ( class_Divides_Osemiring__div(T_a) % 187.43/187.56 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 187.43/187.56 => 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 ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_div__mult__mult1__if,axiom, % 187.43/187.56 ! [V_b,V_a,V_c,T_a] : % 187.43/187.56 ( class_Divides_Osemiring__div(T_a) % 187.43/187.56 => ( ( V_c = c_Groups_Ozero__class_Ozero(T_a) % 187.43/187.56 => 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) ) % 187.43/187.56 & ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 187.43/187.56 => 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) ) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_div__self,axiom, % 187.43/187.56 ! [V_a,T_a] : % 187.43/187.56 ( class_Divides_Osemiring__div(T_a) % 187.43/187.56 => ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 187.43/187.56 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_split__neg__lemma,axiom, % 187.43/187.56 ! [V_n_2,V_P_2,V_k_2] : % 187.43/187.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 187.43/187.56 => ( 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))) % 187.43/187.56 <=> ! [B_i,B_j] : % 187.43/187.56 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j)) % 187.43/187.56 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 187.43/187.56 & 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) ) % 187.43/187.56 => hBOOL(hAPP(hAPP(V_P_2,B_i),B_j)) ) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_split__pos__lemma,axiom, % 187.43/187.56 ! [V_n_2,V_P_2,V_k_2] : % 187.43/187.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 187.43/187.56 => ( 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))) % 187.43/187.56 <=> ! [B_i,B_j] : % 187.43/187.56 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) % 187.43/187.56 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2)) % 187.43/187.56 & 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) ) % 187.43/187.56 => hBOOL(hAPP(hAPP(V_P_2,B_i),B_j)) ) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_zdiv__eq__0__iff,axiom, % 187.43/187.56 ! [V_k_2,V_i_2] : % 187.43/187.56 ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_i_2),V_k_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 187.43/187.56 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 187.43/187.56 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i_2)) % 187.43/187.56 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),V_k_2)) ) % 187.43/187.56 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 187.43/187.56 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_i_2)) ) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_pos__imp__zdiv__nonneg__iff,axiom, % 187.43/187.56 ! [V_a_2,V_b_2] : % 187.43/187.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2)) % 187.43/187.56 => ( 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))) % 187.43/187.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_pos__imp__zdiv__pos__iff,axiom, % 187.43/187.56 ! [V_i_2,V_k_2] : % 187.43/187.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 187.43/187.56 => ( 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))) % 187.43/187.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_i_2)) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_nonneg1__imp__zdiv__pos__iff,axiom, % 187.43/187.56 ! [V_b_2,V_a_2] : % 187.43/187.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) % 187.43/187.56 => ( 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))) % 187.43/187.56 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),V_a_2)) % 187.43/187.56 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2)) ) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_zdiv__mono2,axiom, % 187.43/187.56 ! [V_b,V_b_H,V_a] : % 187.43/187.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 187.43/187.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 187.43/187.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b)) % 187.43/187.56 => 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))) ) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_div__nonneg__neg__le0,axiom, % 187.43/187.56 ! [V_b,V_a] : % 187.43/187.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 187.43/187.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 187.43/187.56 => 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))) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_div__pos__pos__trivial,axiom, % 187.43/187.56 ! [V_b,V_a] : % 187.43/187.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 187.43/187.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 187.43/187.56 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_neg__imp__zdiv__nonneg__iff,axiom, % 187.43/187.56 ! [V_a_2,V_b_2] : % 187.43/187.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 187.43/187.56 => ( 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))) % 187.43/187.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_div__nonpos__pos__le0,axiom, % 187.43/187.56 ! [V_b,V_a] : % 187.43/187.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 187.43/187.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 187.43/187.56 => 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))) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_zdiv__mono2__neg,axiom, % 187.43/187.56 ! [V_b,V_b_H,V_a] : % 187.43/187.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 187.43/187.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 187.43/187.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b)) % 187.43/187.56 => 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))) ) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_div__neg__neg__trivial,axiom, % 187.43/187.56 ! [V_b,V_a] : % 187.43/187.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 187.43/187.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_a)) % 187.43/187.56 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_zdiv__mono1,axiom, % 187.43/187.56 ! [V_b,V_a_H,V_a] : % 187.43/187.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),V_a_H)) % 187.43/187.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 187.43/187.56 => 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))) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_zdiv__mono1__neg,axiom, % 187.43/187.56 ! [V_b,V_a_H,V_a] : % 187.43/187.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),V_a_H)) % 187.43/187.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 187.43/187.56 => 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))) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_int__div__less__self,axiom, % 187.43/187.56 ! [V_k,V_x] : % 187.43/187.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 187.43/187.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_k)) % 187.43/187.56 => 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)) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_zdiv__zmult2__eq,axiom, % 187.43/187.56 ! [V_b,V_a,V_c] : % 187.43/187.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 187.43/187.56 => 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) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_pos__mod__sign,axiom, % 187.43/187.56 ! [V_a,V_b] : % 187.43/187.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 187.43/187.56 => 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))) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_pos__mod__conj,axiom, % 187.43/187.56 ! [V_a,V_b] : % 187.43/187.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 187.43/187.56 => ( 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))) % 187.43/187.56 & 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)) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_mod__pos__pos__trivial,axiom, % 187.43/187.56 ! [V_b,V_a] : % 187.43/187.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 187.43/187.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 187.43/187.56 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_neg__mod__sign,axiom, % 187.43/187.56 ! [V_a,V_b] : % 187.43/187.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 187.43/187.56 => 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))) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_neg__mod__conj,axiom, % 187.43/187.56 ! [V_a,V_b] : % 187.43/187.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 187.43/187.56 => ( 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))) % 187.43/187.56 & 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))) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_mod__neg__neg__trivial,axiom, % 187.43/187.56 ! [V_b,V_a] : % 187.43/187.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 187.43/187.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_a)) % 187.43/187.56 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_zmod__zminus1__eq__if,axiom, % 187.43/187.56 ! [V_b,V_a] : % 187.43/187.56 ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 187.43/187.56 => 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) ) % 187.43/187.56 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 187.43/187.56 => 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)) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_zmod__zminus2__eq__if,axiom, % 187.43/187.56 ! [V_b,V_a] : % 187.43/187.56 ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 187.43/187.56 => 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) ) % 187.43/187.56 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 187.43/187.56 => 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) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_div__mult__self1,axiom, % 187.43/187.56 ! [V_c,V_a,V_b,T_a] : % 187.43/187.56 ( class_Divides_Osemiring__div(T_a) % 187.43/187.56 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 187.43/187.56 => 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)) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_div__mult__self2,axiom, % 187.43/187.56 ! [V_c,V_a,V_b,T_a] : % 187.43/187.56 ( class_Divides_Osemiring__div(T_a) % 187.43/187.56 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 187.43/187.56 => 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)) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_div__add__self1,axiom, % 187.43/187.56 ! [V_a,V_b,T_a] : % 187.43/187.56 ( class_Divides_Osemiring__div(T_a) % 187.43/187.56 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 187.43/187.56 => 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)) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_div__add__self2,axiom, % 187.43/187.56 ! [V_a,V_b,T_a] : % 187.43/187.56 ( class_Divides_Osemiring__div(T_a) % 187.43/187.56 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 187.43/187.56 => 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)) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_mod__pos__neg__trivial,axiom, % 187.43/187.56 ! [V_b,V_a] : % 187.43/187.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 187.43/187.56 => ( 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))) % 187.43/187.56 => 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) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_divmod__int__rel__div__eq,axiom, % 187.43/187.56 ! [V_r_1,V_y,V_b_1,V_a_1] : % 187.43/187.56 ( 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) % 187.43/187.56 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1)) % 187.43/187.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_1)) % 187.43/187.56 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_1),V_b_1)) ) ) % 187.43/187.56 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1)) % 187.43/187.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_1),V_r_1)) % 187.43/187.56 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r_1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) % 187.43/187.56 => ( V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 187.43/187.56 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_1),V_b_1) = V_y ) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_split__zdiv,axiom, % 187.43/187.56 ! [V_k_2,V_n_2,V_P_2] : % 187.43/187.56 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2))) % 187.43/187.56 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 187.43/187.56 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 187.43/187.56 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 187.43/187.56 => ! [B_i] : % 187.43/187.56 ( ? [B_j] : % 187.43/187.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) % 187.43/187.56 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2)) % 187.43/187.56 & 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) ) % 187.43/187.56 => hBOOL(hAPP(V_P_2,B_i)) ) ) % 187.43/187.56 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 187.43/187.56 => ! [B_i] : % 187.43/187.56 ( ? [B_j] : % 187.43/187.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j)) % 187.43/187.56 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 187.43/187.56 & 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) ) % 187.43/187.56 => hBOOL(hAPP(V_P_2,B_i)) ) ) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_divmod__int__rel__mod__eq,axiom, % 187.43/187.56 ! [V_y,V_q_1,V_b_1,V_a_1] : % 187.43/187.56 ( 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) % 187.43/187.56 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1)) % 187.43/187.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 187.43/187.56 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_y),V_b_1)) ) ) % 187.43/187.56 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1)) % 187.43/187.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_1),V_y)) % 187.43/187.56 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) % 187.43/187.56 => ( V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 187.43/187.56 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a_1,V_b_1) = V_y ) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_zmult2__lemma__aux2,axiom, % 187.43/187.56 ! [V_q,V_r,V_b,V_c] : % 187.43/187.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 187.43/187.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r)) % 187.43/187.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 187.43/187.56 => 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))) ) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_zmult2__lemma__aux1,axiom, % 187.43/187.56 ! [V_q,V_r,V_b,V_c] : % 187.43/187.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 187.43/187.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r)) % 187.43/187.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 187.43/187.56 => 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))) ) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_zmult2__lemma__aux4,axiom, % 187.43/187.56 ! [V_q,V_b,V_r,V_c] : % 187.43/187.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 187.43/187.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) % 187.43/187.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) % 187.43/187.56 => 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))) ) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_zmult2__lemma__aux3,axiom, % 187.43/187.56 ! [V_q,V_b,V_r,V_c] : % 187.43/187.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 187.43/187.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) % 187.43/187.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) % 187.43/187.56 => 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))) ) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_split__zmod,axiom, % 187.43/187.56 ! [V_k_2,V_n_2,V_P_2] : % 187.43/187.56 ( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2))) % 187.43/187.56 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 187.43/187.56 => hBOOL(hAPP(V_P_2,V_n_2)) ) % 187.43/187.56 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 187.43/187.56 => ! [B_i,B_j] : % 187.43/187.56 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) % 187.43/187.56 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2)) % 187.43/187.56 & 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) ) % 187.43/187.56 => hBOOL(hAPP(V_P_2,B_j)) ) ) % 187.43/187.56 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 187.43/187.56 => ! [B_i,B_j] : % 187.43/187.56 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j)) % 187.43/187.56 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 187.43/187.56 & 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) ) % 187.43/187.56 => hBOOL(hAPP(V_P_2,B_j)) ) ) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_zmod__number__of__Bit0,axiom, % 187.43/187.56 ! [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))) ). % 187.43/187.56 % 187.43/187.56 fof(fact_zdiv__number__of__Bit1,axiom, % 187.43/187.56 ! [V_v,V_w] : % 187.43/187.56 ( ( 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))) % 187.43/187.56 => 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)) ) % 187.43/187.56 & ( ~ 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))) % 187.43/187.56 => 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)) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_int__power__div__base,axiom, % 187.43/187.56 ! [V_k,V_m] : % 187.43/187.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)) % 187.43/187.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k)) % 187.43/187.56 => 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)))) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_pos__zdiv__mult__2,axiom, % 187.43/187.56 ! [V_b,V_a] : % 187.43/187.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 187.43/187.56 => 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) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_z3div__def,axiom, % 187.43/187.56 ! [V_k,V_l] : % 187.43/187.56 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 187.43/187.56 => c_SMT_Oz3div(V_k,V_l) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_k),V_l) ) % 187.43/187.56 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 187.43/187.56 => 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))) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_z3mod__def,axiom, % 187.43/187.56 ! [V_k,V_l] : % 187.43/187.56 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 187.43/187.56 => c_SMT_Oz3mod(V_k,V_l) = c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) ) % 187.43/187.56 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 187.43/187.56 => 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)) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_power__power__power,axiom, % 187.43/187.56 ! [T_a] : % 187.43/187.56 ( class_Power_Opower(T_a) % 187.43/187.56 => 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)) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_power__m1__odd,axiom, % 187.43/187.56 ! [V_n,T_a] : % 187.43/187.56 ( class_Int_Onumber__ring(T_a) % 187.43/187.56 => 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) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_power__m1__even,axiom, % 187.43/187.56 ! [V_n,T_a] : % 187.43/187.56 ( class_Int_Onumber__ring(T_a) % 187.43/187.56 => 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) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_one__mod__nat__number__of,axiom, % 187.43/187.56 ! [V_v_H] : % 187.43/187.56 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 187.43/187.56 => 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)) ) % 187.43/187.56 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 187.43/187.56 => 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))) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_Divides_Omod__div__equality_H,axiom, % 187.43/187.56 ! [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)) ). % 187.43/187.56 % 187.43/187.56 fof(fact_mult__div__cancel,axiom, % 187.43/187.56 ! [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)) ). % 187.43/187.56 % 187.43/187.56 fof(fact_div__mod__equality_H,axiom, % 187.43/187.56 ! [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)) ). % 187.43/187.56 % 187.43/187.56 fof(fact_mod__mult2__eq,axiom, % 187.43/187.56 ! [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)) ). % 187.43/187.56 % 187.43/187.56 fof(fact_div__mult1__eq,axiom, % 187.43/187.56 ! [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)) ). % 187.43/187.56 % 187.43/187.56 fof(fact_div__add1__eq,axiom, % 187.43/187.56 ! [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)) ). % 187.43/187.56 % 187.43/187.56 fof(fact_div__le__dividend,axiom, % 187.43/187.56 ! [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)) ). % 187.43/187.56 % 187.43/187.56 fof(fact_div__le__mono,axiom, % 187.43/187.56 ! [V_k,V_n,V_m] : % 187.43/187.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 187.43/187.56 => 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))) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_mod__Suc__eq__Suc__mod,axiom, % 187.43/187.56 ! [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) ). % 187.43/187.56 % 187.43/187.56 fof(fact_div__mult2__eq,axiom, % 187.43/187.56 ! [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) ). % 187.43/187.56 % 187.43/187.56 fof(fact_mod__less,axiom, % 187.43/187.56 ! [V_n,V_m] : % 187.43/187.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 187.43/187.56 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_m ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_mod__less__eq__dividend,axiom, % 187.43/187.56 ! [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)) ). % 187.43/187.56 % 187.43/187.56 fof(fact_mod__mult__distrib2,axiom, % 187.43/187.56 ! [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)) ). % 187.43/187.56 % 187.43/187.56 fof(fact_mod__mult__distrib,axiom, % 187.43/187.56 ! [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)) ). % 187.43/187.56 % 187.43/187.56 fof(fact_rel__simps_I24_J,axiom, % 187.43/187.56 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OMin)) ). % 187.43/187.56 % 187.43/187.56 fof(fact_rel__simps_I7_J,axiom, % 187.43/187.56 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OMin)) ). % 187.43/187.56 % 187.43/187.56 fof(fact_rel__simps_I37_J,axiom, % 187.43/187.56 c_Int_OPls != c_Int_OMin ). % 187.43/187.56 % 187.43/187.56 fof(fact_rel__simps_I40_J,axiom, % 187.43/187.56 c_Int_OMin != c_Int_OPls ). % 187.43/187.56 % 187.43/187.56 fof(fact_rel__simps_I47_J,axiom, % 187.43/187.56 ! [V_k_2] : % 187.43/187.56 ( c_Int_OBit1(V_k_2) = c_Int_OMin % 187.43/187.56 <=> V_k_2 = c_Int_OMin ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_rel__simps_I43_J,axiom, % 187.43/187.56 ! [V_l_2] : % 187.43/187.56 ( c_Int_OMin = c_Int_OBit1(V_l_2) % 187.43/187.56 <=> c_Int_OMin = V_l_2 ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_Bit1__Min,axiom, % 187.43/187.56 c_Int_OBit1(c_Int_OMin) = c_Int_OMin ). % 187.43/187.56 % 187.43/187.56 fof(fact_rel__simps_I45_J,axiom, % 187.43/187.56 ! [V_k] : c_Int_OBit0(V_k) != c_Int_OMin ). % 187.43/187.56 % 187.43/187.56 fof(fact_rel__simps_I42_J,axiom, % 187.43/187.56 ! [V_l] : c_Int_OMin != c_Int_OBit0(V_l) ). % 187.43/187.56 % 187.43/187.56 fof(fact_div__1,axiom, % 187.43/187.56 ! [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 ). % 187.43/187.56 % 187.43/187.56 fof(fact_div__less,axiom, % 187.43/187.56 ! [V_n,V_m] : % 187.43/187.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 187.43/187.56 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_nat__mult__div__cancel__disj,axiom, % 187.43/187.56 ! [V_n,V_m,V_k] : % 187.43/187.56 ( ( V_k = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 187.43/187.56 => 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) ) % 187.43/187.56 & ( V_k != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 187.43/187.56 => 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) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_mod__Suc,axiom, % 187.43/187.56 ! [V_n,V_m] : % 187.43/187.56 ( ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) = V_n % 187.43/187.56 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 187.43/187.56 & ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) != V_n % 187.43/187.56 => 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)) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_mod__1,axiom, % 187.43/187.56 ! [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) ). % 187.43/187.56 % 187.43/187.56 fof(fact_mod__less__divisor,axiom, % 187.43/187.56 ! [V_m,V_n] : % 187.43/187.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 187.43/187.56 => 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)) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_mod__eq__0__iff,axiom, % 187.43/187.56 ! [V_d_2,V_m_2] : % 187.43/187.56 ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 187.43/187.56 <=> ? [B_q] : V_m_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_d_2),B_q) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_mod__geq,axiom, % 187.43/187.56 ! [V_n,V_m] : % 187.43/187.56 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 187.43/187.56 => 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) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_mod__if,axiom, % 187.43/187.56 ! [V_n,V_m] : % 187.43/187.56 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 187.43/187.56 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_m ) % 187.43/187.56 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 187.43/187.56 => 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) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_mod__mult__self3,axiom, % 187.43/187.56 ! [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) ). % 187.43/187.56 % 187.43/187.56 fof(fact_le__mod__geq,axiom, % 187.43/187.56 ! [V_m,V_n] : % 187.43/187.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 187.43/187.56 => 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) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_Divides_Otransfer__int__nat__functions_I1_J,axiom, % 187.43/187.56 ! [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)) ). % 187.43/187.56 % 187.43/187.56 fof(fact_zdiv__int,axiom, % 187.43/187.56 ! [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)) ). % 187.43/187.56 % 187.43/187.56 fof(fact_bin__less__0__simps_I2_J,axiom, % 187.43/187.56 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ). % 187.43/187.56 % 187.43/187.56 fof(fact_rel__simps_I20_J,axiom, % 187.43/187.56 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ). % 187.43/187.56 % 187.43/187.56 fof(fact_rel__simps_I23_J,axiom, % 187.43/187.56 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ). % 187.43/187.56 % 187.43/187.56 fof(fact_rel__simps_I30_J,axiom, % 187.43/187.56 ! [V_k_2] : % 187.43/187.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OMin)) % 187.43/187.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_rel__simps_I26_J,axiom, % 187.43/187.56 ! [V_k_2] : % 187.43/187.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k_2))) % 187.43/187.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_rel__simps_I6_J,axiom, % 187.43/187.56 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ). % 187.43/187.56 % 187.43/187.56 fof(fact_rel__simps_I3_J,axiom, % 187.43/187.56 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ). % 187.43/187.56 % 187.43/187.56 fof(fact_rel__simps_I9_J,axiom, % 187.43/187.56 ! [V_k_2] : % 187.43/187.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k_2))) % 187.43/187.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_rel__simps_I13_J,axiom, % 187.43/187.56 ! [V_k_2] : % 187.43/187.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OMin)) % 187.43/187.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_rel__simps_I28_J,axiom, % 187.43/187.56 ! [V_k_2] : % 187.43/187.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OMin)) % 187.43/187.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_rel__simps_I8_J,axiom, % 187.43/187.56 ! [V_k_2] : % 187.43/187.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k_2))) % 187.43/187.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_Divides_Otransfer__int__nat__functions_I2_J,axiom, % 187.43/187.56 ! [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)) ). % 187.43/187.56 % 187.43/187.56 fof(fact_zmod__int,axiom, % 187.43/187.56 ! [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)) ). % 187.43/187.56 % 187.43/187.56 fof(fact_eq__number__of__Pls__Min,axiom, % 187.43/187.56 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) ). % 187.43/187.56 % 187.43/187.56 fof(fact_Int_OMin__def,axiom, % 187.43/187.56 c_Int_OMin = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) ). % 187.43/187.56 % 187.43/187.56 fof(fact_mult__Min,axiom, % 187.43/187.56 ! [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) ). % 187.43/187.56 % 187.43/187.56 fof(fact_neg__number__of__Min,axiom, % 187.43/187.56 hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin))) ). % 187.43/187.56 % 187.43/187.56 fof(fact_pred__Pls,axiom, % 187.43/187.56 c_Int_Opred(c_Int_OPls) = c_Int_OMin ). % 187.43/187.56 % 187.43/187.56 fof(fact_add__Min__right,axiom, % 187.43/187.56 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_OMin) = c_Int_Opred(V_k) ). % 187.43/187.56 % 187.43/187.56 fof(fact_add__Min,axiom, % 187.43/187.56 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),V_k) = c_Int_Opred(V_k) ). % 187.43/187.56 % 187.43/187.56 fof(fact_pred__Min,axiom, % 187.43/187.56 c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin) ). % 187.43/187.56 % 187.43/187.56 fof(fact_nonzero__number__of__Min,axiom, % 187.43/187.56 ! [T_a] : % 187.43/187.56 ( class_Int_Onumber__ring(T_a) % 187.43/187.56 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_succ__Min,axiom, % 187.43/187.56 c_Int_Osucc(c_Int_OMin) = c_Int_OPls ). % 187.43/187.56 % 187.43/187.56 fof(fact_diff__bin__simps_I2_J,axiom, % 187.43/187.56 ! [V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Int_OMin) = c_Int_Osucc(V_k) ). % 187.43/187.56 % 187.43/187.56 fof(fact_div__le__mono2,axiom, % 187.43/187.56 ! [V_k,V_n,V_m] : % 187.43/187.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)) % 187.43/187.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 187.43/187.56 => 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))) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_div__mult__self1__is__m,axiom, % 187.43/187.56 ! [V_m,V_n] : % 187.43/187.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 187.43/187.56 => 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 ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_div__mult__self__is__m,axiom, % 187.43/187.56 ! [V_m,V_n] : % 187.43/187.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 187.43/187.56 => 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 ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_nat__mult__div__cancel1,axiom, % 187.43/187.56 ! [V_n,V_m,V_k] : % 187.43/187.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k)) % 187.43/187.56 => 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) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_div__less__dividend,axiom, % 187.43/187.56 ! [V_m,V_n] : % 187.43/187.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n)) % 187.43/187.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)) % 187.43/187.56 => 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)) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_mod__le__divisor,axiom, % 187.43/187.56 ! [V_m,V_n] : % 187.43/187.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 187.43/187.56 => 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)) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_mod__mult__self4,axiom, % 187.43/187.56 ! [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) ). % 187.43/187.56 % 187.43/187.56 fof(fact_mult__minus1__right,axiom, % 187.43/187.56 ! [V_z,T_a] : % 187.43/187.56 ( class_Int_Onumber__ring(T_a) % 187.43/187.56 => 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) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_mult__minus1,axiom, % 187.43/187.56 ! [V_z,T_a] : % 187.43/187.56 ( class_Int_Onumber__ring(T_a) % 187.43/187.56 => 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) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_number__of__Min,axiom, % 187.43/187.56 ! [T_a] : % 187.43/187.56 ( class_Int_Onumber__ring(T_a) % 187.43/187.56 => 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)) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_arith__simps_I31_J,axiom, % 187.43/187.56 ! [T_a] : % 187.43/187.56 ( class_Int_Onumber__ring(T_a) % 187.43/187.56 => 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) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_rel__simps_I11_J,axiom, % 187.43/187.56 ! [V_k_2] : % 187.43/187.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OMin)) % 187.43/187.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_rel__simps_I25_J,axiom, % 187.43/187.56 ! [V_k_2] : % 187.43/187.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k_2))) % 187.43/187.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_zmod__minus1__right,axiom, % 187.43/187.56 ! [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) ). % 187.43/187.56 % 187.43/187.56 fof(fact_diff__bin__simps_I4_J,axiom, % 187.43/187.56 ! [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)) ). % 187.43/187.56 % 187.43/187.56 fof(fact_minus__Min,axiom, % 187.43/187.56 hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin) = c_Int_OBit1(c_Int_OPls) ). % 187.43/187.56 % 187.43/187.56 fof(fact_zmult__eq__1__iff,axiom, % 187.43/187.56 ! [V_n_2,V_m_2] : % 187.43/187.56 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint) % 187.43/187.56 <=> ( ( V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) % 187.43/187.56 & V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) % 187.43/187.56 | ( V_m_2 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) % 187.43/187.56 & V_n_2 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_pos__zmult__eq__1__iff__lemma,axiom, % 187.43/187.56 ! [V_n,V_m] : % 187.43/187.56 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m),V_n) = c_Groups_Oone__class_Oone(tc_Int_Oint) % 187.43/187.56 => ( V_m = c_Groups_Oone__class_Oone(tc_Int_Oint) % 187.43/187.56 | V_m = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_diff__bin__simps_I6_J,axiom, % 187.43/187.56 ! [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)) ). % 187.43/187.56 % 187.43/187.56 fof(fact_diff__bin__simps_I5_J,axiom, % 187.43/187.56 ! [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)) ). % 187.43/187.56 % 187.43/187.56 fof(fact_power_Opower_Opower__0,axiom, % 187.43/187.56 ! [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 ). % 187.43/187.56 % 187.43/187.56 fof(fact_power_Opower_Opower__Suc,axiom, % 187.43/187.56 ! [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)) ). % 187.43/187.56 % 187.43/187.56 fof(fact_of__int__m1,axiom, % 187.43/187.56 ! [T_a] : % 187.43/187.56 ( class_Int_Onumber__ring(T_a) % 187.43/187.56 => 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) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_zdiv__minus1__right,axiom, % 187.43/187.56 ! [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) ). % 187.43/187.56 % 187.43/187.56 fof(fact_div__geq,axiom, % 187.43/187.56 ! [V_m,V_n] : % 187.43/187.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 187.43/187.56 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 187.43/187.56 => 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)) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_div__if,axiom, % 187.43/187.56 ! [V_m,V_n] : % 187.43/187.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 187.43/187.56 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 187.43/187.56 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 187.43/187.56 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 187.43/187.56 => 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)) ) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_split__div,axiom, % 187.43/187.56 ! [V_k_2,V_n_2,V_P_2] : % 187.43/187.56 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_n_2),V_k_2))) % 187.43/187.56 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 187.43/187.56 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) % 187.43/187.56 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 187.43/187.56 => ! [B_i,B_j] : % 187.43/187.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2)) % 187.43/187.56 => ( 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) % 187.43/187.56 => hBOOL(hAPP(V_P_2,B_i)) ) ) ) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_nat__div__distrib,axiom, % 187.43/187.56 ! [V_y,V_x] : % 187.43/187.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 187.43/187.56 => 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)) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_Divides_Otransfer__nat__int__functions_I1_J,axiom, % 187.43/187.56 ! [V_y,V_x] : % 187.43/187.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 187.43/187.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 187.43/187.56 => 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)) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_split__mod,axiom, % 187.43/187.56 ! [V_k_2,V_n_2,V_P_2] : % 187.43/187.56 ( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n_2,V_k_2))) % 187.43/187.56 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 187.43/187.56 => hBOOL(hAPP(V_P_2,V_n_2)) ) % 187.43/187.56 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 187.43/187.56 => ! [B_i,B_j] : % 187.43/187.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2)) % 187.43/187.56 => ( 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) % 187.43/187.56 => hBOOL(hAPP(V_P_2,B_j)) ) ) ) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_mod__lemma,axiom, % 187.43/187.56 ! [V_q,V_b,V_r,V_c] : % 187.43/187.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c)) % 187.43/187.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_r),V_b)) % 187.43/187.56 => 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))) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_Suc__times__mod__eq,axiom, % 187.43/187.56 ! [V_m,V_k] : % 187.43/187.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_k)) % 187.43/187.56 => 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) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_nat__mod__distrib,axiom, % 187.43/187.56 ! [V_y,V_x] : % 187.43/187.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 187.43/187.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 187.43/187.56 => 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)) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_Divides_Otransfer__nat__int__functions_I2_J,axiom, % 187.43/187.56 ! [V_y,V_x] : % 187.43/187.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 187.43/187.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 187.43/187.56 => 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)) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_div__eq__minus1,axiom, % 187.43/187.56 ! [V_b] : % 187.43/187.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 187.43/187.56 => 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) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_le__div__geq,axiom, % 187.43/187.56 ! [V_m,V_n] : % 187.43/187.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 187.43/187.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 187.43/187.56 => 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)) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_split__div_H,axiom, % 187.43/187.56 ! [V_n_2,V_m_2,V_P_2] : % 187.43/187.56 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_n_2))) % 187.43/187.56 <=> ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 187.43/187.56 & hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) % 187.43/187.56 | ? [B_q] : % 187.43/187.56 ( 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)) % 187.43/187.56 & 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)))) % 187.43/187.56 & hBOOL(hAPP(V_P_2,B_q)) ) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_split__div__lemma,axiom, % 187.43/187.56 ! [V_m_2,V_q_2,V_n_2] : % 187.43/187.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) % 187.43/187.56 => ( ( 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)) % 187.43/187.56 & 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)))) ) % 187.43/187.56 <=> V_q_2 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_n_2) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_div__Suc__eq__div__add3,axiom, % 187.43/187.56 ! [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)) ). % 187.43/187.56 % 187.43/187.56 fof(fact_Suc__div__eq__add3__div,axiom, % 187.43/187.56 ! [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) ). % 187.43/187.56 % 187.43/187.56 fof(fact_Suc__div__eq__add3__div__number__of,axiom, % 187.43/187.56 ! [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)) ). % 187.43/187.56 % 187.43/187.56 fof(fact_div2__Suc__Suc,axiom, % 187.43/187.56 ! [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))))) ). % 187.43/187.56 % 187.43/187.56 fof(fact_add__self__div__2,axiom, % 187.43/187.56 ! [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 ). % 187.43/187.56 % 187.43/187.56 fof(fact_mod__Suc__eq__mod__add3,axiom, % 187.43/187.56 ! [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)) ). % 187.43/187.56 % 187.43/187.56 fof(fact_Suc__mod__eq__add3__mod,axiom, % 187.43/187.56 ! [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) ). % 187.43/187.56 % 187.43/187.56 fof(fact_Suc__mod__eq__add3__mod__number__of,axiom, % 187.43/187.56 ! [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)) ). % 187.43/187.56 % 187.43/187.56 fof(fact_mod2__Suc__Suc,axiom, % 187.43/187.56 ! [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)))) ). % 187.43/187.56 % 187.43/187.56 fof(fact_div__nat__number__of,axiom, % 187.43/187.56 ! [V_v_H,V_v] : % 187.43/187.56 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 187.43/187.56 => 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) ) % 187.43/187.56 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 187.43/187.56 => 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))) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_mod__nat__number__of,axiom, % 187.43/187.56 ! [V_v_H,V_v] : % 187.43/187.56 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 187.43/187.56 => 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) ) % 187.43/187.56 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 187.43/187.56 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 187.43/187.56 => 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) ) % 187.43/187.56 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 187.43/187.56 => 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))) ) ) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_div__pos__neg__trivial,axiom, % 187.43/187.56 ! [V_b,V_a] : % 187.43/187.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 187.43/187.56 => ( 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))) % 187.43/187.56 => 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) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_zmod__minus1,axiom, % 187.43/187.56 ! [V_b] : % 187.43/187.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 187.43/187.56 => 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)) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_div__2__gt__zero,axiom, % 187.43/187.56 ! [V_n] : % 187.43/187.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n)) % 187.43/187.56 => 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)))))) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_one__div__nat__number__of,axiom, % 187.43/187.56 ! [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))) ). % 187.43/187.56 % 187.43/187.56 fof(fact_mod2__gr__0,axiom, % 187.43/187.56 ! [V_m_2] : % 187.43/187.56 ( 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)))))) % 187.43/187.56 <=> 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) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_Suc__n__div__2__gt__zero,axiom, % 187.43/187.56 ! [V_n] : % 187.43/187.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 187.43/187.56 => 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)))))) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_int__of__code,axiom, % 187.43/187.56 ! [V_k] : % 187.43/187.56 ( ( V_k = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 187.43/187.56 => hAPP(c_Code__Numeral_Oint__of,V_k) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 187.43/187.56 & ( V_k != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 187.43/187.56 => ( ( 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) % 187.43/187.56 => 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)))))) ) % 187.43/187.56 & ( 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) % 187.43/187.56 => 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)) ) ) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_code__numeral_Osize_I1_J,axiom, % 187.43/187.56 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) ). % 187.43/187.56 % 187.43/187.56 fof(fact_divmod__int__rel__def,axiom, % 187.43/187.56 ! [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))))))) ). % 187.43/187.56 % 187.43/187.56 fof(fact_Nitpick_OFrac__def,axiom, % 187.43/187.56 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)))) ). % 187.43/187.56 % 187.43/187.56 fof(fact_setprod__gen__delta,axiom, % 187.43/187.56 ! [V_c_2,V_b_2,V_a_2,V_S_2,T_a,T_b] : % 187.43/187.56 ( class_Groups_Ocomm__monoid__mult(T_b) % 187.43/187.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 187.43/187.56 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) % 187.43/187.56 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),hAPP(hAPP(c_COMBC(T_a,T_b,T_b),hAPP(hAPP(c_COMBS(T_a,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_a),c_If(T_b)),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),V_c_2)),V_S_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(V_b_2,V_a_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_c_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_S_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) % 187.43/187.56 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) % 187.43/187.56 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),hAPP(hAPP(c_COMBC(T_a,T_b,T_b),hAPP(hAPP(c_COMBS(T_a,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_a),c_If(T_b)),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),V_c_2)),V_S_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_c_2),hAPP(c_Finite__Set_Ocard(T_a),V_S_2)) ) ) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_transfer__nat__int__sum__prod2_I2_J,axiom, % 187.43/187.56 ! [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)) ). % 187.43/187.56 % 187.43/187.56 fof(fact_of__nat__setprod,axiom, % 187.43/187.56 ! [V_A_2,V_f_2,T_b,T_a] : % 187.43/187.56 ( ( class_Groups_Ocomm__monoid__mult(T_a) % 187.43/187.56 & class_Rings_Osemiring__1(T_a) ) % 187.43/187.56 => 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) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_int__setprod,axiom, % 187.43/187.56 ! [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) ). % 187.43/187.56 % 187.43/187.56 fof(fact_of__int__setprod,axiom, % 187.43/187.56 ! [V_A_2,V_f_2,T_b,T_a] : % 187.43/187.56 ( ( class_Groups_Ocomm__monoid__mult(T_a) % 187.43/187.56 & class_Rings_Oring__1(T_a) ) % 187.43/187.56 => 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) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_setprod__timesf,axiom, % 187.43/187.56 ! [V_A_2,V_g_2,V_f_2,T_b,T_a] : % 187.43/187.56 ( class_Groups_Ocomm__monoid__mult(T_a) % 187.43/187.56 => 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)) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_setprod__1,axiom, % 187.43/187.56 ! [V_A_2,T_b,T_a] : % 187.43/187.56 ( class_Groups_Ocomm__monoid__mult(T_a) % 187.43/187.56 => 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) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_setprod__zero,axiom, % 187.43/187.56 ! [V_f_2,V_A_2,T_a,T_b] : % 187.43/187.56 ( class_Rings_Ocomm__semiring__1(T_b) % 187.43/187.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.43/187.56 => ( ? [B_x] : % 187.43/187.56 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 187.43/187.56 & hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) ) % 187.43/187.56 => 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) ) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_setprod__zero__iff,axiom, % 187.43/187.56 ! [V_f_2,V_A_2,T_a,T_b] : % 187.43/187.56 ( ( class_Rings_Ocomm__semiring__1(T_b) % 187.43/187.56 & class_Rings_Ono__zero__divisors(T_b) ) % 187.43/187.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.43/187.56 => ( 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) % 187.43/187.56 <=> ? [B_x] : % 187.43/187.56 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 187.43/187.56 & hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_setprod_Oempty,axiom, % 187.43/187.56 ! [V_g_2,T_b,T_a] : % 187.43/187.56 ( class_Groups_Ocomm__monoid__mult(T_a) % 187.43/187.56 => 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) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_setprod__empty,axiom, % 187.43/187.56 ! [V_f_2,T_b,T_a] : % 187.43/187.56 ( class_Groups_Ocomm__monoid__mult(T_a) % 187.43/187.56 => 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) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_setprod_Oinfinite,axiom, % 187.43/187.56 ! [V_g_2,V_A_2,T_a,T_b] : % 187.43/187.56 ( class_Groups_Ocomm__monoid__mult(T_b) % 187.43/187.56 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.43/187.56 => 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) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_setprod__infinite,axiom, % 187.43/187.56 ! [V_f_2,V_A_2,T_a,T_b] : % 187.43/187.56 ( class_Groups_Ocomm__monoid__mult(T_b) % 187.43/187.56 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.43/187.56 => 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) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_setprod__eq__1__iff,axiom, % 187.43/187.56 ! [V_f_2,V_F_2,T_a] : % 187.43/187.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) % 187.43/187.56 => ( 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) % 187.43/187.56 <=> ! [B_x] : % 187.43/187.56 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_F_2)) % 187.43/187.56 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_setprod_Odistrib,axiom, % 187.43/187.56 ! [V_h_2,V_g_2,V_A_2,T_a,T_b] : % 187.43/187.56 ( class_Groups_Ocomm__monoid__mult(T_b) % 187.43/187.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.43/187.56 => 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)) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_setprod__pos__nat__iff,axiom, % 187.43/187.56 ! [V_f_2,V_S_2,T_a] : % 187.43/187.56 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 187.43/187.56 => ( 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))) % 187.43/187.56 <=> ! [B_x] : % 187.43/187.56 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2)) % 187.43/187.56 => 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))) ) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_setprod__delta_H,axiom, % 187.43/187.56 ! [V_b_2,V_a_2,V_S_2,T_a,T_b] : % 187.43/187.56 ( class_Groups_Ocomm__monoid__mult(T_b) % 187.43/187.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 187.43/187.56 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) % 187.43/187.56 => 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) ) % 187.43/187.56 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) % 187.43/187.56 => 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) ) ) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_setprod__delta,axiom, % 187.43/187.56 ! [V_b_2,V_a_2,V_S_2,T_a,T_b] : % 187.43/187.56 ( class_Groups_Ocomm__monoid__mult(T_b) % 187.43/187.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 187.43/187.56 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) % 187.43/187.56 => 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) ) % 187.43/187.56 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) % 187.43/187.56 => 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) ) ) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_setprod__constant,axiom, % 187.43/187.56 ! [V_y_2,V_A_2,T_a,T_b] : % 187.43/187.56 ( class_Groups_Ocomm__monoid__mult(T_b) % 187.43/187.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.43/187.56 => 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)) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_divmod__int__correct,axiom, % 187.43/187.56 ! [V_a,V_b] : % 187.43/187.56 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 187.43/187.56 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_Odivmod__int(V_a,V_b))) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_setprod__insert,axiom, % 187.43/187.56 ! [V_f_2,V_a_2,V_A_2,T_a,T_b] : % 187.43/187.56 ( class_Groups_Ocomm__monoid__mult(T_b) % 187.43/187.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.43/187.56 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 187.43/187.56 => 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)) ) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_setprod_Oinsert,axiom, % 187.43/187.56 ! [V_g_2,V_x_2,V_A_2,T_a,T_b] : % 187.43/187.56 ( class_Groups_Ocomm__monoid__mult(T_b) % 187.43/187.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.43/187.56 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 187.43/187.56 => 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)) ) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_setprod_Oeq__fold,axiom, % 187.43/187.56 ! [V_g_2,V_A_2,T_a,T_b] : % 187.43/187.56 ( class_Groups_Ocomm__monoid__mult(T_b) % 187.43/187.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.43/187.56 => 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) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_setprod_OF__eq,axiom, % 187.43/187.56 ! [V_g_2,V_A_2,T_a,T_b] : % 187.43/187.56 ( class_Groups_Ocomm__monoid__mult(T_b) % 187.43/187.56 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.43/187.56 => 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) ) % 187.43/187.56 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.43/187.56 => 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) ) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_setprod_Oinsert__remove,axiom, % 187.43/187.56 ! [V_x_2,V_g_2,V_A_2,T_a,T_b] : % 187.43/187.56 ( class_Groups_Ocomm__monoid__mult(T_b) % 187.43/187.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.43/187.56 => 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)))))) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_setprod_Oremove,axiom, % 187.43/187.56 ! [V_g_2,V_x_2,V_A_2,T_a,T_b] : % 187.43/187.56 ( class_Groups_Ocomm__monoid__mult(T_b) % 187.43/187.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.43/187.56 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 187.43/187.56 => 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)))))) ) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_code__numeral_Osize_I2_J,axiom, % 187.43/187.56 ! [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))) ). % 187.43/187.56 % 187.43/187.56 fof(fact_zmult2__lemma,axiom, % 187.43/187.56 ! [V_c,V_r,V_q,V_b,V_a] : % 187.43/187.56 ( 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))) % 187.43/187.56 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 187.43/187.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 187.43/187.56 => 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)))) ) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_setprod__diff1,axiom, % 187.43/187.56 ! [V_a_2,V_f_2,V_A_2,T_a,T_b] : % 187.43/187.56 ( class_Fields_Ofield(T_b) % 187.43/187.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.43/187.56 => ( hAPP(V_f_2,V_a_2) != c_Groups_Ozero__class_Ozero(T_b) % 187.43/187.56 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 187.43/187.56 => 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)) ) % 187.43/187.56 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 187.43/187.56 => 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) ) ) ) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_adjust__def,axiom, % 187.43/187.56 ! [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))))))) ). % 187.43/187.56 % 187.43/187.56 fof(fact_adjust__eq,axiom, % 187.43/187.56 ! [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))) ). % 187.43/187.56 % 187.43/187.56 fof(fact_power__divide,axiom, % 187.43/187.56 ! [V_n,V_b,V_a,T_a] : % 187.43/187.56 ( class_Fields_Ofield__inverse__zero(T_a) % 187.43/187.56 => 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)) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_code__numeral_Oinject,axiom, % 187.43/187.56 ! [V_code__numeral_H_2,V_code__numeral_2] : % 187.43/187.56 ( c_Code__Numeral_OSuc__code__numeral(V_code__numeral_2) = c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H_2) % 187.43/187.56 <=> V_code__numeral_2 = V_code__numeral_H_2 ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_pred__subset__eq2,axiom, % 187.43/187.56 ! [V_S_2,V_R_2,T_b,T_a] : % 187.43/187.56 ( 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))) % 187.43/187.56 <=> 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)) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_bot__empty__eq2,axiom, % 187.43/187.56 ! [V_y_2,V_x_2,T_b,T_a] : % 187.43/187.56 ( 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)) % 187.43/187.56 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)))) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_pred__equals__eq2,axiom, % 187.43/187.56 ! [V_S_2,V_R_2,T_b,T_a] : % 187.43/187.56 ( 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) % 187.43/187.56 <=> V_R_2 = V_S_2 ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_minus__divide__left,axiom, % 187.43/187.56 ! [V_b,V_a,T_a] : % 187.43/187.56 ( class_Rings_Odivision__ring(T_a) % 187.43/187.56 => 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) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_divide__1,axiom, % 187.43/187.56 ! [V_a,T_a] : % 187.43/187.56 ( class_Rings_Odivision__ring(T_a) % 187.43/187.56 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_diff__divide__distrib,axiom, % 187.43/187.56 ! [V_c,V_b,V_a,T_a] : % 187.43/187.56 ( class_Rings_Odivision__ring(T_a) % 187.43/187.56 => 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)) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_times__divide__eq__right,axiom, % 187.43/187.56 ! [V_c,V_b,V_a,T_a] : % 187.43/187.56 ( class_Rings_Odivision__ring(T_a) % 187.43/187.56 => 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) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_add__divide__distrib,axiom, % 187.43/187.56 ! [V_c,V_b,V_a,T_a] : % 187.43/187.56 ( class_Rings_Odivision__ring(T_a) % 187.43/187.56 => 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)) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_divide__zero__left,axiom, % 187.43/187.56 ! [V_a,T_a] : % 187.43/187.56 ( class_Rings_Odivision__ring(T_a) % 187.43/187.56 => 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) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_divide__zero,axiom, % 187.43/187.56 ! [V_a,T_a] : % 187.43/187.56 ( class_Rings_Odivision__ring__inverse__zero(T_a) % 187.43/187.56 => 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) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_eq__divide__imp,axiom, % 187.43/187.56 ! [V_b,V_a,V_c,T_a] : % 187.43/187.56 ( class_Rings_Odivision__ring(T_a) % 187.43/187.56 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 187.43/187.56 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c) = V_b % 187.43/187.56 => V_a = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c) ) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_divide__eq__imp,axiom, % 187.43/187.56 ! [V_a,V_b,V_c,T_a] : % 187.43/187.56 ( class_Rings_Odivision__ring(T_a) % 187.43/187.56 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 187.43/187.56 => ( V_b = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c) % 187.43/187.56 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c) = V_a ) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_nonzero__divide__eq__eq,axiom, % 187.43/187.56 ! [V_a_2,V_b_2,V_c_2,T_a] : % 187.43/187.56 ( class_Rings_Odivision__ring(T_a) % 187.43/187.56 => ( V_c_2 != c_Groups_Ozero__class_Ozero(T_a) % 187.43/187.56 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2) = V_a_2 % 187.43/187.56 <=> V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2) ) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_nonzero__eq__divide__eq,axiom, % 187.43/187.56 ! [V_b_2,V_a_2,V_c_2,T_a] : % 187.43/187.56 ( class_Rings_Odivision__ring(T_a) % 187.43/187.56 => ( V_c_2 != c_Groups_Ozero__class_Ozero(T_a) % 187.43/187.56 => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2) % 187.43/187.56 <=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2) = V_b_2 ) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_divide__self__if,axiom, % 187.43/187.56 ! [V_a,T_a] : % 187.43/187.56 ( class_Rings_Odivision__ring__inverse__zero(T_a) % 187.43/187.56 => ( ( V_a = c_Groups_Ozero__class_Ozero(T_a) % 187.43/187.56 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) % 187.43/187.56 & ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 187.43/187.56 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_divide__self,axiom, % 187.43/187.56 ! [V_a,T_a] : % 187.43/187.56 ( class_Rings_Odivision__ring(T_a) % 187.43/187.56 => ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 187.43/187.56 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_right__inverse__eq,axiom, % 187.43/187.56 ! [V_a_2,V_b_2,T_a] : % 187.43/187.56 ( class_Rings_Odivision__ring(T_a) % 187.43/187.56 => ( V_b_2 != c_Groups_Ozero__class_Ozero(T_a) % 187.43/187.56 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a_2),V_b_2) = c_Groups_Oone__class_Oone(T_a) % 187.43/187.56 <=> V_a_2 = V_b_2 ) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_nonzero__minus__divide__divide,axiom, % 187.43/187.56 ! [V_a,V_b,T_a] : % 187.43/187.56 ( class_Rings_Odivision__ring(T_a) % 187.43/187.56 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 187.43/187.56 => 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) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_nonzero__minus__divide__right,axiom, % 187.43/187.56 ! [V_a,V_b,T_a] : % 187.43/187.56 ( class_Rings_Odivision__ring(T_a) % 187.43/187.56 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 187.43/187.56 => 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)) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_nonzero__power__divide,axiom, % 187.43/187.56 ! [V_n,V_a,V_b,T_a] : % 187.43/187.56 ( class_Fields_Ofield(T_a) % 187.43/187.56 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 187.43/187.56 => 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)) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_power__one__over,axiom, % 187.43/187.56 ! [V_n,V_a,T_a] : % 187.43/187.56 ( class_Fields_Ofield__inverse__zero(T_a) % 187.43/187.56 => 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) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_code__numeral_Osimps_I2_J,axiom, % 187.43/187.56 ! [V_code__numeral_H] : c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H) ). % 187.43/187.56 % 187.43/187.56 fof(fact_code__numeral_Osimps_I3_J,axiom, % 187.43/187.56 ! [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) ). % 187.43/187.56 % 187.43/187.56 fof(fact_divmod__int__rel__0,axiom, % 187.43/187.56 ! [V_b] : % 187.43/187.56 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 187.43/187.56 => 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)))) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_self__remainder,axiom, % 187.43/187.56 ! [V_r,V_q,V_a] : % 187.43/187.56 ( 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))) % 187.43/187.56 => ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 187.43/187.56 => V_r = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_unique__quotient,axiom, % 187.43/187.56 ! [V_r_H,V_q_H,V_r,V_q,V_b,V_a] : % 187.43/187.56 ( 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))) % 187.43/187.56 => ( 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))) % 187.43/187.56 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 187.43/187.56 => V_q = V_q_H ) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_unique__remainder,axiom, % 187.43/187.56 ! [V_r_H,V_q_H,V_r,V_q,V_b,V_a] : % 187.43/187.56 ( 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))) % 187.43/187.56 => ( 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))) % 187.43/187.56 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 187.43/187.56 => V_r = V_r_H ) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_setprod__dividef,axiom, % 187.43/187.56 ! [V_g_2,V_f_2,V_A_2,T_a,T_b] : % 187.43/187.56 ( class_Fields_Ofield__inverse__zero(T_b) % 187.43/187.56 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.43/187.56 => 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)) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_divide__eq__eq__number__of1,axiom, % 187.43/187.56 ! [V_a_2,V_w_2,V_b_2,T_a] : % 187.43/187.56 ( ( class_Fields_Ofield__inverse__zero(T_a) % 187.43/187.56 & class_Int_Onumber(T_a) ) % 187.43/187.56 => ( 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 % 187.43/187.56 <=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) != c_Groups_Ozero__class_Ozero(T_a) % 187.43/187.56 => 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)) ) % 187.43/187.56 & ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) = c_Groups_Ozero__class_Ozero(T_a) % 187.43/187.56 => V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_divide__eq__eq__number__of,axiom, % 187.43/187.56 ! [V_w_2,V_c_2,V_b_2,T_a] : % 187.43/187.56 ( ( class_Fields_Ofield__inverse__zero(T_a) % 187.43/187.56 & class_Int_Onumber(T_a) ) % 187.43/187.56 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) % 187.43/187.56 <=> ( ( V_c_2 != c_Groups_Ozero__class_Ozero(T_a) % 187.43/187.56 => V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),V_c_2) ) % 187.43/187.56 & ( V_c_2 = c_Groups_Ozero__class_Ozero(T_a) % 187.43/187.56 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_eq__divide__eq__number__of,axiom, % 187.43/187.56 ! [V_c_2,V_b_2,V_w_2,T_a] : % 187.43/187.56 ( ( class_Fields_Ofield__inverse__zero(T_a) % 187.43/187.56 & class_Int_Onumber(T_a) ) % 187.43/187.56 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2) % 187.43/187.56 <=> ( ( V_c_2 != c_Groups_Ozero__class_Ozero(T_a) % 187.43/187.56 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),V_c_2) = V_b_2 ) % 187.43/187.56 & ( V_c_2 = c_Groups_Ozero__class_Ozero(T_a) % 187.43/187.56 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_eq__divide__eq__number__of1,axiom, % 187.43/187.56 ! [V_w_2,V_b_2,V_a_2,T_a] : % 187.43/187.56 ( ( class_Fields_Ofield__inverse__zero(T_a) % 187.43/187.56 & class_Int_Onumber(T_a) ) % 187.43/187.56 => ( 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)) % 187.43/187.56 <=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) != c_Groups_Ozero__class_Ozero(T_a) % 187.43/187.56 => 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 ) % 187.43/187.56 & ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) = c_Groups_Ozero__class_Ozero(T_a) % 187.43/187.56 => V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_divide__Numeral0,axiom, % 187.43/187.56 ! [V_x,T_a] : % 187.43/187.56 ( ( class_Fields_Ofield__inverse__zero(T_a) % 187.43/187.56 & class_Int_Onumber__ring(T_a) ) % 187.43/187.56 => 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) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_divide__numeral__1,axiom, % 187.43/187.56 ! [V_a,T_a] : % 187.43/187.56 ( ( class_Fields_Ofield(T_a) % 187.43/187.56 & class_Int_Onumber__ring(T_a) ) % 187.43/187.56 => 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 ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_divide__Numeral1,axiom, % 187.43/187.56 ! [V_x,T_a] : % 187.43/187.56 ( ( class_Fields_Ofield(T_a) % 187.43/187.56 & class_Int_Onumber__ring(T_a) ) % 187.43/187.56 => 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 ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_divide__minus1,axiom, % 187.43/187.56 ! [V_x,T_a] : % 187.43/187.56 ( ( class_Fields_Ofield__inverse__zero(T_a) % 187.43/187.56 & class_Int_Onumber__ring(T_a) ) % 187.43/187.56 => 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) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_self__quotient,axiom, % 187.43/187.56 ! [V_r,V_q,V_a] : % 187.43/187.56 ( 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))) % 187.43/187.56 => ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 187.43/187.56 => V_q = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_divmod__int__rel__mod,axiom, % 187.43/187.56 ! [V_r,V_q,V_b,V_a] : % 187.43/187.56 ( 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))) % 187.43/187.56 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 187.43/187.56 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_r ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_divmod__int__rel__div,axiom, % 187.43/187.56 ! [V_r,V_q,V_b,V_a] : % 187.43/187.56 ( 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))) % 187.43/187.56 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 187.43/187.56 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = V_q ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_divmod__int__mod__div,axiom, % 187.43/187.56 ! [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)) ). % 187.43/187.56 % 187.43/187.56 fof(fact_divide__less__eq__number__of1,axiom, % 187.43/187.56 ! [V_a_2,V_w_2,V_b_2,T_a] : % 187.43/187.56 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 187.43/187.56 & class_Int_Onumber(T_a) ) % 187.43/187.56 => ( 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)) % 187.43/187.56 <=> ( ( 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))) % 187.43/187.56 => 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)))) ) % 187.43/187.56 & ( ~ 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))) % 187.43/187.56 => ( ( 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))) % 187.43/187.56 => 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)) ) % 187.43/187.56 & ( ~ 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))) % 187.43/187.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ) ) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_divide__less__eq__number__of,axiom, % 187.43/187.56 ! [V_w_2,V_c_2,V_b_2,T_a] : % 187.43/187.56 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 187.43/187.56 & class_Int_Onumber(T_a) ) % 187.43/187.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))) % 187.43/187.56 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2)) % 187.43/187.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),V_c_2))) ) % 187.43/187.56 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2)) % 187.43/187.56 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a))) % 187.43/187.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),V_c_2)),V_b_2)) ) % 187.43/187.56 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a))) % 187.43/187.56 => 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))) ) ) ) ) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_less__divide__eq__number__of,axiom, % 187.43/187.56 ! [V_c_2,V_b_2,V_w_2,T_a] : % 187.43/187.56 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 187.43/187.56 & class_Int_Onumber(T_a) ) % 187.43/187.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2))) % 187.43/187.56 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2)) % 187.43/187.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),V_c_2)),V_b_2)) ) % 187.43/187.56 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2)) % 187.43/187.56 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a))) % 187.43/187.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),V_c_2))) ) % 187.43/187.56 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a))) % 187.43/187.56 => 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))) ) ) ) ) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_less__divide__eq__number__of1,axiom, % 187.43/187.56 ! [V_w_2,V_b_2,V_a_2,T_a] : % 187.43/187.56 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 187.43/187.56 & class_Int_Onumber(T_a) ) % 187.43/187.56 => ( 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)))) % 187.43/187.56 <=> ( ( 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))) % 187.43/187.56 => 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)) ) % 187.43/187.56 & ( ~ 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))) % 187.43/187.56 => ( ( 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))) % 187.43/187.56 => 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)))) ) % 187.43/187.56 & ( ~ 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))) % 187.43/187.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_power__diff,axiom, % 187.43/187.56 ! [V_m,V_n,V_a,T_a] : % 187.43/187.56 ( class_Fields_Ofield(T_a) % 187.43/187.56 => ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 187.43/187.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 187.43/187.56 => 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)) ) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_minus1__divide,axiom, % 187.43/187.56 ! [V_x,T_a] : % 187.43/187.56 ( ( class_Fields_Ofield__inverse__zero(T_a) % 187.43/187.56 & class_Int_Onumber__ring(T_a) ) % 187.43/187.56 => 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)) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_Suc__code__numeral__minus__one,axiom, % 187.43/187.56 ! [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 ). % 187.43/187.56 % 187.43/187.56 fof(fact_divmod__int__rel__div__mod,axiom, % 187.43/187.56 ! [V_a,V_b] : % 187.43/187.56 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 187.43/187.56 => 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)))) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_divide__le__eq__number__of1,axiom, % 187.43/187.56 ! [V_a_2,V_w_2,V_b_2,T_a] : % 187.43/187.56 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 187.43/187.56 & class_Int_Onumber(T_a) ) % 187.43/187.56 => ( 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)) % 187.43/187.56 <=> ( ( 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))) % 187.43/187.56 => 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)))) ) % 187.43/187.56 & ( ~ 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))) % 187.43/187.56 => ( ( 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))) % 187.43/187.56 => 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)) ) % 187.43/187.56 & ( ~ 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))) % 187.43/187.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ) ) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_divide__le__eq__number__of,axiom, % 187.43/187.56 ! [V_w_2,V_c_2,V_b_2,T_a] : % 187.43/187.56 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 187.43/187.56 & class_Int_Onumber(T_a) ) % 187.43/187.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))) % 187.43/187.56 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2)) % 187.43/187.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),V_c_2))) ) % 187.43/187.56 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2)) % 187.43/187.56 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a))) % 187.43/187.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),V_c_2)),V_b_2)) ) % 187.43/187.56 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a))) % 187.43/187.56 => 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))) ) ) ) ) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_le__divide__eq__number__of,axiom, % 187.43/187.56 ! [V_c_2,V_b_2,V_w_2,T_a] : % 187.43/187.56 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 187.43/187.56 & class_Int_Onumber(T_a) ) % 187.43/187.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2))) % 187.43/187.56 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2)) % 187.43/187.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),V_c_2)),V_b_2)) ) % 187.43/187.56 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2)) % 187.43/187.56 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a))) % 187.43/187.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),V_c_2))) ) % 187.43/187.56 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a))) % 187.43/187.56 => 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))) ) ) ) ) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_le__divide__eq__number__of1,axiom, % 187.43/187.56 ! [V_w_2,V_b_2,V_a_2,T_a] : % 187.43/187.56 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 187.43/187.56 & class_Int_Onumber(T_a) ) % 187.43/187.56 => ( 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)))) % 187.43/187.56 <=> ( ( 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))) % 187.43/187.56 => 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)) ) % 187.43/187.56 & ( ~ 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))) % 187.43/187.56 => ( ( 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))) % 187.43/187.56 => 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)))) ) % 187.43/187.56 & ( ~ 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))) % 187.43/187.56 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_zadd1__lemma,axiom, % 187.43/187.56 ! [V_br,V_bq,V_b,V_ar,V_aq,V_c,V_a] : % 187.43/187.56 ( 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))) % 187.43/187.56 => ( 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))) % 187.43/187.56 => ( V_c != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 187.43/187.56 => 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)))) ) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_zminus1__lemma,axiom, % 187.43/187.56 ! [V_r_2,V_q_2,V_b_2,V_a_2] : % 187.43/187.56 ( 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))) % 187.43/187.56 => 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))))) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_half__gt__zero__iff,axiom, % 187.43/187.56 ! [V_r_2,T_a] : % 187.43/187.56 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 187.43/187.56 & class_Int_Onumber__ring(T_a) ) % 187.43/187.56 => ( 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)))))) % 187.43/187.56 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_r_2)) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_half__gt__zero,axiom, % 187.43/187.56 ! [V_r,T_a] : % 187.43/187.56 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 187.43/187.56 & class_Int_Onumber__ring(T_a) ) % 187.43/187.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_r)) % 187.43/187.56 => 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)))))) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_divmod__int__relI,axiom, % 187.43/187.56 ! [V_r,V_q,V_b,V_a] : % 187.43/187.56 ( 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) % 187.43/187.56 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 187.43/187.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) % 187.43/187.56 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) ) ) % 187.43/187.56 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 187.43/187.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r)) % 187.43/187.56 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) % 187.43/187.56 => 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))) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_zmult1__lemma,axiom, % 187.43/187.56 ! [V_a,V_r,V_q,V_c,V_b] : % 187.43/187.56 ( 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))) % 187.43/187.56 => ( V_c != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 187.43/187.56 => 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)))) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_norm__frac_Osimps,axiom, % 187.43/187.56 ! [V_a_2,V_b_2] : % 187.43/187.56 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 187.43/187.56 => 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)) ) % 187.43/187.56 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 187.43/187.56 => ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 187.43/187.56 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 187.43/187.56 => 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)) ) % 187.43/187.56 & ( ~ ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 187.43/187.56 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 187.43/187.56 => 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))) ) ) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_negDivAlg__eqn__1__number__of,axiom, % 187.43/187.56 ! [V_w] : % 187.43/187.56 ( 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))) % 187.43/187.56 => ( ( 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)))) % 187.43/187.56 => 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))) ) % 187.43/187.56 & ( ~ 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)))) % 187.43/187.56 => 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)))) ) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_splitI,axiom, % 187.43/187.56 ! [T_b,T_a,V_b_2,V_a_2,V_f_2] : % 187.43/187.56 ( hBOOL(hAPP(hAPP(V_f_2,V_a_2),V_b_2)) % 187.43/187.56 => 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))) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_prod__caseI,axiom, % 187.43/187.56 ! [T_b,T_a,V_b_2,V_a_2,V_f1_2] : % 187.43/187.56 ( hBOOL(hAPP(hAPP(V_f1_2,V_a_2),V_b_2)) % 187.43/187.56 => 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))) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_divide__left__mono__neg,axiom, % 187.43/187.56 ! [V_c,V_b,V_a,T_a] : % 187.43/187.56 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 187.43/187.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 187.43/187.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 187.43/187.56 => ( 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))) % 187.43/187.56 => 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))) ) ) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_bot2E,axiom, % 187.43/187.56 ! [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)) ). % 187.43/187.56 % 187.43/187.56 fof(fact_less__by__empty,axiom, % 187.43/187.56 ! [V_B_2,T_a,V_A_2] : % 187.43/187.56 ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)) % 187.43/187.56 => 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)) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_rev__predicate2D,axiom, % 187.43/187.56 ! [V_Q_2,T_b,T_a,V_y_2,V_x_2,V_P_2] : % 187.43/187.56 ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2)) % 187.43/187.56 => ( 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)) % 187.43/187.56 => hBOOL(hAPP(hAPP(V_Q_2,V_x_2),V_y_2)) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_predicate2D,axiom, % 187.43/187.56 ! [V_y_2,V_x_2,V_Q_2,V_P_2,T_b,T_a] : % 187.43/187.56 ( 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)) % 187.43/187.56 => ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2)) % 187.43/187.56 => hBOOL(hAPP(hAPP(V_Q_2,V_x_2),V_y_2)) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_Pair__inject,axiom, % 187.43/187.56 ! [V_b_H,V_a_H,V_b,V_a,T_b,T_a] : % 187.43/187.56 ( 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) % 187.43/187.56 => ~ ( V_a = V_a_H % 187.43/187.56 => V_b != V_b_H ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_Pair__eq,axiom, % 187.43/187.56 ! [V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_b,T_a] : % 187.43/187.56 ( 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) % 187.43/187.56 <=> ( V_a_2 = V_a_H_2 % 187.43/187.56 & V_b_2 = V_b_H_2 ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_split__paired__All,axiom, % 187.43/187.56 ! [T_b,T_a,V_P_2] : % 187.43/187.56 ( ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) % 187.43/187.56 <=> ! [B_a,B_b] : hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_a),B_b))) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_split__weak__cong,axiom, % 187.43/187.56 ! [V_c_2,T_c,T_b,T_a,V_q_2,V_p_2] : % 187.43/187.56 ( V_p_2 = V_q_2 % 187.43/187.56 => hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,T_c),V_c_2),V_p_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,T_c),V_c_2),V_q_2) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_negDivAlg__correct,axiom, % 187.43/187.56 ! [V_b,V_a] : % 187.43/187.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 187.43/187.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 187.43/187.56 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_OnegDivAlg(V_a,V_b))) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_times__divide__times__eq,axiom, % 187.43/187.56 ! [V_w,V_z,V_y,V_x,T_a] : % 187.43/187.56 ( class_Fields_Ofield__inverse__zero(T_a) % 187.43/187.56 => 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)) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_prod_Osimps_I2_J,axiom, % 187.43/187.56 ! [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) ). % 187.43/187.56 % 187.43/187.56 fof(fact_split__conv,axiom, % 187.43/187.56 ! [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) ). % 187.43/187.56 % 187.43/187.56 fof(fact_minus__divide__right,axiom, % 187.43/187.56 ! [V_b,V_a,T_a] : % 187.43/187.56 ( class_Fields_Ofield__inverse__zero(T_a) % 187.43/187.56 => 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)) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_minus__divide__divide,axiom, % 187.43/187.56 ! [V_b,V_a,T_a] : % 187.43/187.56 ( class_Fields_Ofield__inverse__zero(T_a) % 187.43/187.56 => 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) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_splitD,axiom, % 187.43/187.56 ! [V_b_2,V_a_2,V_f_2,T_b,T_a] : % 187.43/187.56 ( 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))) % 187.43/187.56 => hBOOL(hAPP(hAPP(V_f_2,V_a_2),V_b_2)) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_negDivAlg__div__mod,axiom, % 187.43/187.56 ! [V_l,V_k] : % 187.43/187.56 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 187.43/187.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 187.43/187.56 => 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)) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_negDivAlg__minus1,axiom, % 187.43/187.56 ! [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))) ). % 187.43/187.56 % 187.43/187.56 fof(fact_split__eta,axiom, % 187.43/187.56 ! [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 ). % 187.43/187.56 % 187.43/187.56 fof(fact_The__split__eq,axiom, % 187.43/187.56 ! [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) ). % 187.43/187.56 % 187.43/187.56 fof(fact_split__paired__The,axiom, % 187.43/187.56 ! [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)))) ). % 187.43/187.56 % 187.43/187.56 fof(fact_split__twice,axiom, % 187.43/187.56 ! [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) ). % 187.43/187.56 % 187.43/187.56 fof(fact_zero__le__divide__iff,axiom, % 187.43/187.56 ! [V_b_2,V_a_2,T_a] : % 187.43/187.56 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 187.43/187.56 => ( 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))) % 187.43/187.56 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) % 187.43/187.56 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b_2)) ) % 187.43/187.56 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) % 187.43/187.56 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_divide__le__0__iff,axiom, % 187.43/187.56 ! [V_b_2,V_a_2,T_a] : % 187.43/187.56 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 187.43/187.56 => ( 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))) % 187.43/187.56 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) % 187.43/187.56 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),c_Groups_Ozero__class_Ozero(T_a))) ) % 187.43/187.56 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) % 187.43/187.56 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b_2)) ) ) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_divide__right__mono,axiom, % 187.43/187.56 ! [V_c,V_b,V_a,T_a] : % 187.43/187.56 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 187.43/187.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 187.43/187.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 187.43/187.56 => 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))) ) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_divide__right__mono__neg,axiom, % 187.43/187.56 ! [V_c,V_b,V_a,T_a] : % 187.43/187.56 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 187.43/187.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 187.43/187.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 187.43/187.56 => 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))) ) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_divide__strict__right__mono__neg,axiom, % 187.43/187.56 ! [V_c,V_a,V_b,T_a] : % 187.43/187.56 ( class_Fields_Olinordered__field(T_a) % 187.43/187.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 187.43/187.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 187.43/187.56 => 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))) ) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_divide__strict__right__mono,axiom, % 187.43/187.56 ! [V_c,V_b,V_a,T_a] : % 187.43/187.56 ( class_Fields_Olinordered__field(T_a) % 187.43/187.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 187.43/187.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 187.43/187.56 => 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))) ) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_divide__neg__neg,axiom, % 187.43/187.56 ! [V_y,V_x,T_a] : % 187.43/187.56 ( class_Fields_Olinordered__field(T_a) % 187.43/187.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a))) % 187.43/187.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a))) % 187.43/187.56 => 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))) ) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_divide__neg__pos,axiom, % 187.43/187.56 ! [V_y,V_x,T_a] : % 187.43/187.56 ( class_Fields_Olinordered__field(T_a) % 187.43/187.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a))) % 187.43/187.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 187.43/187.56 => 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))) ) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_divide__pos__neg,axiom, % 187.43/187.56 ! [V_y,V_x,T_a] : % 187.43/187.56 ( class_Fields_Olinordered__field(T_a) % 187.43/187.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 187.43/187.56 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a))) % 187.43/187.56 => 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))) ) ) ) ). % 187.43/187.56 % 187.43/187.56 fof(fact_divide__pos__pos,axiom, % 187.68/187.57 ! [V_y,V_x,T_a] : % 187.68/187.57 ( class_Fields_Olinordered__field(T_a) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 187.68/187.57 => 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))) ) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_divide__less__0__iff,axiom, % 187.68/187.57 ! [V_b_2,V_a_2,T_a] : % 187.68/187.57 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 187.68/187.57 => ( 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))) % 187.68/187.57 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) % 187.68/187.57 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),c_Groups_Ozero__class_Ozero(T_a))) ) % 187.68/187.57 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) % 187.68/187.57 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b_2)) ) ) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_zero__less__divide__iff,axiom, % 187.68/187.57 ! [V_b_2,V_a_2,T_a] : % 187.68/187.57 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 187.68/187.57 => ( 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))) % 187.68/187.57 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) % 187.68/187.57 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b_2)) ) % 187.68/187.57 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) % 187.68/187.57 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_frac__eq__eq,axiom, % 187.68/187.57 ! [V_w_2,V_x_2,V_z_2,V_y_2,T_a] : % 187.68/187.57 ( class_Fields_Ofield(T_a) % 187.68/187.57 => ( V_y_2 != c_Groups_Ozero__class_Ozero(T_a) % 187.68/187.57 => ( V_z_2 != c_Groups_Ozero__class_Ozero(T_a) % 187.68/187.57 => ( 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) % 187.68/187.57 <=> 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) ) ) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_mult__divide__mult__cancel__left,axiom, % 187.68/187.57 ! [V_b,V_a,V_c,T_a] : % 187.68/187.57 ( class_Fields_Ofield__inverse__zero(T_a) % 187.68/187.57 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 187.68/187.57 => 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) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_mult__divide__mult__cancel__right,axiom, % 187.68/187.57 ! [V_b,V_a,V_c,T_a] : % 187.68/187.57 ( class_Fields_Ofield__inverse__zero(T_a) % 187.68/187.57 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 187.68/187.57 => 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) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_divide__eq__eq,axiom, % 187.68/187.57 ! [V_a_2,V_c_2,V_b_2,T_a] : % 187.68/187.57 ( class_Fields_Ofield__inverse__zero(T_a) % 187.68/187.57 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2) = V_a_2 % 187.68/187.57 <=> ( ( V_c_2 != c_Groups_Ozero__class_Ozero(T_a) % 187.68/187.57 => V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2) ) % 187.68/187.57 & ( V_c_2 = c_Groups_Ozero__class_Ozero(T_a) % 187.68/187.57 => V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_eq__divide__eq,axiom, % 187.68/187.57 ! [V_c_2,V_b_2,V_a_2,T_a] : % 187.68/187.57 ( class_Fields_Ofield__inverse__zero(T_a) % 187.68/187.57 => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2) % 187.68/187.57 <=> ( ( V_c_2 != c_Groups_Ozero__class_Ozero(T_a) % 187.68/187.57 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2) = V_b_2 ) % 187.68/187.57 & ( V_c_2 = c_Groups_Ozero__class_Ozero(T_a) % 187.68/187.57 => V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_divide__nonneg__pos,axiom, % 187.68/187.57 ! [V_y,V_x,T_a] : % 187.68/187.57 ( class_Fields_Olinordered__field(T_a) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 187.68/187.57 => 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))) ) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_divide__nonneg__neg,axiom, % 187.68/187.57 ! [V_y,V_x,T_a] : % 187.68/187.57 ( class_Fields_Olinordered__field(T_a) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a))) % 187.68/187.57 => 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))) ) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_frac__less2,axiom, % 187.68/187.57 ! [V_z,V_w,V_y,V_x,T_a] : % 187.68/187.57 ( class_Fields_Olinordered__field(T_a) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w)) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_w),V_z)) % 187.68/187.57 => 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))) ) ) ) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_frac__less,axiom, % 187.68/187.57 ! [V_z,V_w,V_y,V_x,T_a] : % 187.68/187.57 ( class_Fields_Olinordered__field(T_a) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w)) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_w),V_z)) % 187.68/187.57 => 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))) ) ) ) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_frac__le,axiom, % 187.68/187.57 ! [V_z,V_w,V_y,V_x,T_a] : % 187.68/187.57 ( class_Fields_Olinordered__field(T_a) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w)) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_w),V_z)) % 187.68/187.57 => 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))) ) ) ) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_divide__nonpos__pos,axiom, % 187.68/187.57 ! [V_y,V_x,T_a] : % 187.68/187.57 ( class_Fields_Olinordered__field(T_a) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a))) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 187.68/187.57 => 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))) ) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_divide__nonpos__neg,axiom, % 187.68/187.57 ! [V_y,V_x,T_a] : % 187.68/187.57 ( class_Fields_Olinordered__field(T_a) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a))) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a))) % 187.68/187.57 => 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))) ) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_less__divide__eq,axiom, % 187.68/187.57 ! [V_c_2,V_b_2,V_a_2,T_a] : % 187.68/187.57 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2))) % 187.68/187.57 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2)) % 187.68/187.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)),V_b_2)) ) % 187.68/187.57 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2)) % 187.68/187.57 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a))) % 187.68/187.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2))) ) % 187.68/187.57 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a))) % 187.68/187.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_divide__less__eq,axiom, % 187.68/187.57 ! [V_a_2,V_c_2,V_b_2,T_a] : % 187.68/187.57 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2)),V_a_2)) % 187.68/187.57 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2)) % 187.68/187.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2))) ) % 187.68/187.57 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2)) % 187.68/187.57 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a))) % 187.68/187.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)),V_b_2)) ) % 187.68/187.57 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a))) % 187.68/187.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ) ) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_pos__less__divide__eq,axiom, % 187.68/187.57 ! [V_b_2,V_a_2,V_c_2,T_a] : % 187.68/187.57 ( class_Fields_Olinordered__field(T_a) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2)) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2))) % 187.68/187.57 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)),V_b_2)) ) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_pos__divide__less__eq,axiom, % 187.68/187.57 ! [V_a_2,V_b_2,V_c_2,T_a] : % 187.68/187.57 ( class_Fields_Olinordered__field(T_a) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2)) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2)),V_a_2)) % 187.68/187.57 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2))) ) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_mult__imp__div__pos__less,axiom, % 187.68/187.57 ! [V_z,V_x,V_y,T_a] : % 187.68/187.57 ( class_Fields_Olinordered__field(T_a) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 187.68/187.57 => ( 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))) % 187.68/187.57 => 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)) ) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_mult__imp__less__div__pos,axiom, % 187.68/187.57 ! [V_x,V_z,V_y,T_a] : % 187.68/187.57 ( class_Fields_Olinordered__field(T_a) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 187.68/187.57 => ( 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)) % 187.68/187.57 => 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))) ) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_neg__less__divide__eq,axiom, % 187.68/187.57 ! [V_b_2,V_a_2,V_c_2,T_a] : % 187.68/187.57 ( class_Fields_Olinordered__field(T_a) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a))) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2))) % 187.68/187.57 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2))) ) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_neg__divide__less__eq,axiom, % 187.68/187.57 ! [V_a_2,V_b_2,V_c_2,T_a] : % 187.68/187.57 ( class_Fields_Olinordered__field(T_a) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a))) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2)),V_a_2)) % 187.68/187.57 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)),V_b_2)) ) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_divide__strict__left__mono,axiom, % 187.68/187.57 ! [V_c,V_a,V_b,T_a] : % 187.68/187.57 ( class_Fields_Olinordered__field(T_a) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 187.68/187.57 => ( 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))) % 187.68/187.57 => 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))) ) ) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_divide__strict__left__mono__neg,axiom, % 187.68/187.57 ! [V_c,V_b,V_a,T_a] : % 187.68/187.57 ( class_Fields_Olinordered__field(T_a) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 187.68/187.57 => ( 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))) % 187.68/187.57 => 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))) ) ) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_add__num__frac,axiom, % 187.68/187.57 ! [V_x,V_z,V_y,T_a] : % 187.68/187.57 ( class_Fields_Ofield__inverse__zero(T_a) % 187.68/187.57 => ( V_y != c_Groups_Ozero__class_Ozero(T_a) % 187.68/187.57 => 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) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_add__divide__eq__iff,axiom, % 187.68/187.57 ! [V_y,V_x,V_z,T_a] : % 187.68/187.57 ( class_Fields_Ofield(T_a) % 187.68/187.57 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 187.68/187.57 => 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) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_add__frac__num,axiom, % 187.68/187.57 ! [V_z,V_x,V_y,T_a] : % 187.68/187.57 ( class_Fields_Ofield__inverse__zero(T_a) % 187.68/187.57 => ( V_y != c_Groups_Ozero__class_Ozero(T_a) % 187.68/187.57 => 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) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_divide__add__eq__iff,axiom, % 187.68/187.57 ! [V_y,V_x,V_z,T_a] : % 187.68/187.57 ( class_Fields_Ofield(T_a) % 187.68/187.57 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 187.68/187.57 => 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) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_add__frac__eq,axiom, % 187.68/187.57 ! [V_w,V_x,V_z,V_y,T_a] : % 187.68/187.57 ( class_Fields_Ofield(T_a) % 187.68/187.57 => ( V_y != c_Groups_Ozero__class_Ozero(T_a) % 187.68/187.57 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 187.68/187.57 => 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)) ) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_diff__frac__eq,axiom, % 187.68/187.57 ! [V_w,V_x,V_z,V_y,T_a] : % 187.68/187.57 ( class_Fields_Ofield(T_a) % 187.68/187.57 => ( V_y != c_Groups_Ozero__class_Ozero(T_a) % 187.68/187.57 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 187.68/187.57 => 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)) ) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_divide__diff__eq__iff,axiom, % 187.68/187.57 ! [V_y,V_x,V_z,T_a] : % 187.68/187.57 ( class_Fields_Ofield(T_a) % 187.68/187.57 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 187.68/187.57 => 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) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_diff__divide__eq__iff,axiom, % 187.68/187.57 ! [V_y,V_x,V_z,T_a] : % 187.68/187.57 ( class_Fields_Ofield(T_a) % 187.68/187.57 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 187.68/187.57 => 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) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_less__half__sum,axiom, % 187.68/187.57 ! [V_b,V_a,T_a] : % 187.68/187.57 ( class_Fields_Olinordered__field(T_a) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 187.68/187.57 => 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))))) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_gt__half__sum,axiom, % 187.68/187.57 ! [V_b,V_a,T_a] : % 187.68/187.57 ( class_Fields_Olinordered__field(T_a) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 187.68/187.57 => 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)) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_negDivAlg_Osimps,axiom, % 187.68/187.57 ! [V_b,V_a] : % 187.68/187.57 ( ( ( 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))) % 187.68/187.57 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 187.68/187.57 => 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)) ) % 187.68/187.57 & ( ~ ( 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))) % 187.68/187.57 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 187.68/187.57 => 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))) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_negDivAlg__eqn,axiom, % 187.68/187.57 ! [V_a,V_b] : % 187.68/187.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 187.68/187.57 => ( ( 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))) % 187.68/187.57 => 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)) ) % 187.68/187.57 & ( ~ 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))) % 187.68/187.57 => 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))) ) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_negDivAlg__eqn__number__of,axiom, % 187.68/187.57 ! [V_w,V_v] : % 187.68/187.57 ( 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))) % 187.68/187.57 => ( ( 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)))) % 187.68/187.57 => 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))) ) % 187.68/187.57 & ( ~ 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)))) % 187.68/187.57 => 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)))) ) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_le__divide__eq,axiom, % 187.68/187.57 ! [V_c_2,V_b_2,V_a_2,T_a] : % 187.68/187.57 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2))) % 187.68/187.57 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2)) % 187.68/187.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)),V_b_2)) ) % 187.68/187.57 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2)) % 187.68/187.57 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a))) % 187.68/187.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2))) ) % 187.68/187.57 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a))) % 187.68/187.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_divide__le__eq,axiom, % 187.68/187.57 ! [V_a_2,V_c_2,V_b_2,T_a] : % 187.68/187.57 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2)),V_a_2)) % 187.68/187.57 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2)) % 187.68/187.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2))) ) % 187.68/187.57 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2)) % 187.68/187.57 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a))) % 187.68/187.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)),V_b_2)) ) % 187.68/187.57 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a))) % 187.68/187.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ) ) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_pos__le__divide__eq,axiom, % 187.68/187.57 ! [V_b_2,V_a_2,V_c_2,T_a] : % 187.68/187.57 ( class_Fields_Olinordered__field(T_a) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2)) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2))) % 187.68/187.57 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)),V_b_2)) ) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_pos__divide__le__eq,axiom, % 187.68/187.57 ! [V_a_2,V_b_2,V_c_2,T_a] : % 187.68/187.57 ( class_Fields_Olinordered__field(T_a) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c_2)) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2)),V_a_2)) % 187.68/187.57 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2))) ) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_mult__imp__div__pos__le,axiom, % 187.68/187.57 ! [V_z,V_x,V_y,T_a] : % 187.68/187.57 ( class_Fields_Olinordered__field(T_a) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 187.68/187.57 => ( 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))) % 187.68/187.57 => 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)) ) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_mult__imp__le__div__pos,axiom, % 187.68/187.57 ! [V_x,V_z,V_y,T_a] : % 187.68/187.57 ( class_Fields_Olinordered__field(T_a) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 187.68/187.57 => ( 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)) % 187.68/187.57 => 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))) ) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_neg__le__divide__eq,axiom, % 187.68/187.57 ! [V_b_2,V_a_2,V_c_2,T_a] : % 187.68/187.57 ( class_Fields_Olinordered__field(T_a) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a))) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2))) % 187.68/187.57 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2))) ) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_neg__divide__le__eq,axiom, % 187.68/187.57 ! [V_a_2,V_b_2,V_c_2,T_a] : % 187.68/187.57 ( class_Fields_Olinordered__field(T_a) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),c_Groups_Ozero__class_Ozero(T_a))) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_c_2)),V_a_2)) % 187.68/187.57 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_c_2)),V_b_2)) ) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_divide__left__mono,axiom, % 187.68/187.57 ! [V_c,V_a,V_b,T_a] : % 187.68/187.57 ( class_Fields_Olinordered__field(T_a) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 187.68/187.57 => ( 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))) % 187.68/187.57 => 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))) ) ) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_in__rel__def,axiom, % 187.68/187.57 ! [V_y_2,V_x_2,V_R_2,T_b,T_a] : % 187.68/187.57 ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(T_a,T_b,V_R_2),V_x_2),V_y_2)) % 187.68/187.57 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),V_R_2)) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_div__mod__code__numeral__def,axiom, % 187.68/187.57 ! [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)) ). % 187.68/187.57 % 187.68/187.57 fof(fact_Nitpick_Orefl_H__def,axiom, % 187.68/187.57 ! [V_r_2,T_a] : % 187.68/187.57 ( c_Nitpick_Orefl_H(T_a,V_r_2) % 187.68/187.57 <=> ! [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)) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_posDivAlg__eqn__1__number__of,axiom, % 187.68/187.57 ! [V_w] : % 187.68/187.57 ( 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))) % 187.68/187.57 => ( ( 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))) % 187.68/187.57 => 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)) ) % 187.68/187.57 & ( ~ 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))) % 187.68/187.57 => 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)))) ) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_posDivAlg_Osimps,axiom, % 187.68/187.57 ! [V_b,V_a] : % 187.68/187.57 ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 187.68/187.57 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 187.68/187.57 => 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) ) % 187.68/187.57 & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 187.68/187.57 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 187.68/187.57 => 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))) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_mem__splitI,axiom, % 187.68/187.57 ! [T_c,T_b,V_b_2,V_a_2,V_c_2,V_z_2,T_a] : % 187.68/187.57 ( hBOOL(hAPP(hAPP(c_member(T_a),V_z_2),hAPP(hAPP(V_c_2,V_a_2),V_b_2))) % 187.68/187.57 => hBOOL(hAPP(hAPP(c_member(T_a),V_z_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_fun(T_a,tc_HOL_Obool)),V_c_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)))) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_splitD_H,axiom, % 187.68/187.57 ! [V_c_2,V_b_2,V_a_2,V_R_2,T_c,T_b,T_a] : % 187.68/187.57 ( hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_fun(T_c,tc_HOL_Obool)),V_R_2),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),V_c_2)) % 187.68/187.57 => hBOOL(hAPP(hAPP(hAPP(V_R_2,V_a_2),V_b_2),V_c_2)) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_posDivAlg__0,axiom, % 187.68/187.57 ! [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)) ). % 187.68/187.57 % 187.68/187.57 fof(fact_posDivAlg__correct,axiom, % 187.68/187.57 ! [V_b,V_a] : % 187.68/187.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 187.68/187.57 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_OposDivAlg(V_a,V_b))) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_posDivAlg__div__mod,axiom, % 187.68/187.57 ! [V_l,V_k] : % 187.68/187.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k)) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 187.68/187.57 => 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)) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_posDivAlg__eqn__number__of,axiom, % 187.68/187.57 ! [V_w,V_v] : % 187.68/187.57 ( 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))) % 187.68/187.57 => ( ( 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))) % 187.68/187.57 => 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)) ) % 187.68/187.57 & ( ~ 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))) % 187.68/187.57 => 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)))) ) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_posDivAlg__eqn,axiom, % 187.68/187.57 ! [V_a,V_b] : % 187.68/187.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 187.68/187.57 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 187.68/187.57 => 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) ) % 187.68/187.57 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 187.68/187.57 => 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))) ) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_divmod__int__def,axiom, % 187.68/187.57 ! [V_b,V_a] : % 187.68/187.57 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 187.68/187.57 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 187.68/187.57 => c_Divides_Odivmod__int(V_a,V_b) = c_Divides_OposDivAlg(V_a,V_b) ) % 187.68/187.57 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 187.68/187.57 => ( ( V_a = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 187.68/187.57 => 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)) ) % 187.68/187.57 & ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 187.68/187.57 => 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))) ) ) ) ) ) % 187.68/187.57 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 187.68/187.57 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 187.68/187.57 => c_Divides_Odivmod__int(V_a,V_b) = c_Divides_OnegDivAlg(V_a,V_b) ) % 187.68/187.57 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 187.68/187.57 => 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))) ) ) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_divmod__nat__step,axiom, % 187.68/187.57 ! [V_m,V_n] : % 187.68/187.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 187.68/187.57 => 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)) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_code__numeral_Osize_I4_J,axiom, % 187.68/187.57 ! [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))) ). % 187.68/187.57 % 187.68/187.57 fof(fact_negDivAlg_Opsimps,axiom, % 187.68/187.57 ! [V_b_2,V_a_2] : % 187.68/187.57 ( 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))) % 187.68/187.57 => ( ( ( 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))) % 187.68/187.57 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 187.68/187.57 => 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)) ) % 187.68/187.57 & ( ~ ( 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))) % 187.68/187.57 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 187.68/187.57 => 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))) ) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_posDivAlg_Opsimps,axiom, % 187.68/187.57 ! [V_b_2,V_a_2] : % 187.68/187.57 ( 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))) % 187.68/187.57 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),V_b_2)) % 187.68/187.57 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 187.68/187.57 => 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) ) % 187.68/187.57 & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),V_b_2)) % 187.68/187.57 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 187.68/187.57 => 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))) ) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_accp_Osimps,axiom, % 187.68/187.57 ! [V_a_2,V_r_2,T_a] : % 187.68/187.57 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_a_2)) % 187.68/187.57 <=> ! [B_x] : % 187.68/187.57 ( hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2)) % 187.68/187.57 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),B_x)) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_accp_Oequations,axiom, % 187.68/187.57 ! [V_a_2,V_r_2,T_a] : % 187.68/187.57 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_a_2)) % 187.68/187.57 <=> ! [B_x] : % 187.68/187.57 ( hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2)) % 187.68/187.57 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),B_x)) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_accp__downward,axiom, % 187.68/187.57 ! [V_a_2,V_b_2,V_r_2,T_a] : % 187.68/187.57 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_b_2)) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2)) % 187.68/187.57 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_a_2)) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_divmod__nat__zero,axiom, % 187.68/187.57 ! [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) ). % 187.68/187.57 % 187.68/187.57 fof(fact_accp__subset,axiom, % 187.68/187.57 ! [V_R2_2,V_R1_2,T_a] : % 187.68/187.57 ( 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)) % 187.68/187.57 => 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))) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_divmod__nat__base,axiom, % 187.68/187.57 ! [V_n,V_m] : % 187.68/187.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 187.68/187.57 => 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) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_negateSnd__eq,axiom, % 187.68/187.57 ! [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)) ). % 187.68/187.57 % 187.68/187.57 fof(fact_divmod__nat__div__mod,axiom, % 187.68/187.57 ! [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)) ). % 187.68/187.57 % 187.68/187.57 fof(fact_divmod__int__rel__neg,axiom, % 187.68/187.57 ! [V_qr,V_b,V_a] : % 187.68/187.57 ( 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)) % 187.68/187.57 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(c_Divides_OnegateSnd,V_qr))) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_code__numeral_Osize_I3_J,axiom, % 187.68/187.57 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) ). % 187.68/187.57 % 187.68/187.57 fof(fact_divmod__nat__if,axiom, % 187.68/187.57 ! [V_m_2,V_n_2] : % 187.68/187.57 ( ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 187.68/187.57 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) % 187.68/187.57 => 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) ) % 187.68/187.57 & ( ~ ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 187.68/187.57 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) % 187.68/187.57 => 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)) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_norm__frac_Opsimps,axiom, % 187.68/187.57 ! [V_b_2,V_a_2] : % 187.68/187.57 ( 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))) % 187.68/187.57 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 187.68/187.57 => 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)) ) % 187.68/187.57 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 187.68/187.57 => ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 187.68/187.57 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 187.68/187.57 => 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)) ) % 187.68/187.57 & ( ~ ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 187.68/187.57 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 187.68/187.57 => 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))) ) ) ) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_negDivAlg_Opinduct,axiom, % 187.68/187.57 ! [V_P_2,V_a1_2,V_a0_2] : % 187.68/187.57 ( 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))) % 187.68/187.57 => ( ! [B_a,B_b] : % 187.68/187.57 ( 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))) % 187.68/187.57 => ( ( ~ ( 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))) % 187.68/187.57 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 187.68/187.57 => 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))) ) % 187.68/187.57 => hBOOL(hAPP(hAPP(V_P_2,B_a),B_b)) ) ) % 187.68/187.57 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_posDivAlg_Opinduct,axiom, % 187.68/187.57 ! [V_P_2,V_a1_2,V_a0_2] : % 187.68/187.57 ( 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))) % 187.68/187.57 => ( ! [B_a,B_b] : % 187.68/187.57 ( 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))) % 187.68/187.57 => ( ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_a),B_b)) % 187.68/187.57 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 187.68/187.57 => 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))) ) % 187.68/187.57 => hBOOL(hAPP(hAPP(V_P_2,B_a),B_b)) ) ) % 187.68/187.57 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_divmod__nat__rel__mult2__eq,axiom, % 187.68/187.57 ! [V_c,V_r,V_q,V_b,V_a] : % 187.68/187.57 ( 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))) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_b)) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c)) % 187.68/187.57 => 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)))) ) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_divmod__nat__rel__mult1__eq,axiom, % 187.68/187.57 ! [V_a,V_r,V_q,V_c,V_b] : % 187.68/187.57 ( 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))) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c)) % 187.68/187.57 => 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)))) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_divmod__nat__rel__unique,axiom, % 187.68/187.57 ! [V_qr_H,V_qr,V_n,V_m] : % 187.68/187.57 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr)) % 187.68/187.57 => ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr_H)) % 187.68/187.57 => V_qr = V_qr_H ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_divmod__nat__eq,axiom, % 187.68/187.57 ! [V_qr,V_n,V_m] : % 187.68/187.57 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr)) % 187.68/187.57 => c_Divides_Odivmod__nat(V_m,V_n) = V_qr ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_divmod__nat__rel__divmod__nat,axiom, % 187.68/187.57 ! [V_n,V_m] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),c_Divides_Odivmod__nat(V_m,V_n))) ). % 187.68/187.57 % 187.68/187.57 fof(fact_divmod__nat__def,axiom, % 187.68/187.57 ! [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)) ). % 187.68/187.57 % 187.68/187.57 fof(fact_mod__eq,axiom, % 187.68/187.57 ! [V_r,V_q,V_n,V_m] : % 187.68/187.57 ( 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))) % 187.68/187.57 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_r ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_div__eq,axiom, % 187.68/187.57 ! [V_r,V_q,V_n,V_m] : % 187.68/187.57 ( 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))) % 187.68/187.57 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = V_q ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_divmod__nat__rel,axiom, % 187.68/187.57 ! [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)))) ). % 187.68/187.57 % 187.68/187.57 fof(fact_divmod__nat__rel__add1__eq,axiom, % 187.68/187.57 ! [V_br,V_bq,V_b,V_ar,V_aq,V_c,V_a] : % 187.68/187.57 ( 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))) % 187.68/187.57 => ( 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))) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c)) % 187.68/187.57 => 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)))) ) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_mod__pos__neg__1__number__of,axiom, % 187.68/187.57 ! [V_w] : % 187.68/187.57 ( 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))) % 187.68/187.57 => 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))))) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_in__measure,axiom, % 187.68/187.57 ! [V_f_2,V_y_2,V_x_2,T_a] : % 187.68/187.57 ( 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))) % 187.68/187.57 <=> 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))) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_norm__frac_Opinduct,axiom, % 187.68/187.57 ! [V_P_2,V_a1_2,V_a0_2] : % 187.68/187.57 ( 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))) % 187.68/187.57 => ( ! [B_a,B_b] : % 187.68/187.57 ( 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))) % 187.68/187.57 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 187.68/187.57 => 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))) ) % 187.68/187.57 => hBOOL(hAPP(hAPP(V_P_2,B_a),B_b)) ) ) % 187.68/187.57 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_div__pos__neg__1__number__of,axiom, % 187.68/187.57 ! [V_w] : % 187.68/187.57 ( 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))) % 187.68/187.57 => 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))))) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_mod__neg__neg,axiom, % 187.68/187.57 ! [V_b,V_a] : % 187.68/187.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 187.68/187.57 => 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)))) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_split__comp,axiom, % 187.68/187.57 ! [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)) ). % 187.68/187.57 % 187.68/187.57 fof(fact_prod__case__beta,axiom, % 187.68/187.57 ! [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)) ). % 187.68/187.57 % 187.68/187.57 fof(fact_split__def,axiom, % 187.68/187.57 ! [V_p_2,V_c_2,T_a,T_c,T_b] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_a),V_c_2),V_p_2) = hAPP(hAPP(V_c_2,hAPP(c_Product__Type_Ofst(T_b,T_c),V_p_2)),hAPP(c_Product__Type_Osnd(T_b,T_c),V_p_2)) ). % 187.68/187.57 % 187.68/187.57 fof(fact_split__comp__eq,axiom, % 187.68/187.57 ! [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)) ). % 187.68/187.57 % 187.68/187.57 fof(fact_split__beta,axiom, % 187.68/187.57 ! [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)) ). % 187.68/187.57 % 187.68/187.57 fof(fact_Pair__fst__snd__eq,axiom, % 187.68/187.57 ! [T_b,T_a,V_t_2,V_s_2] : % 187.68/187.57 ( V_s_2 = V_t_2 % 187.68/187.57 <=> ( hAPP(c_Product__Type_Ofst(T_a,T_b),V_s_2) = hAPP(c_Product__Type_Ofst(T_a,T_b),V_t_2) % 187.68/187.57 & hAPP(c_Product__Type_Osnd(T_a,T_b),V_s_2) = hAPP(c_Product__Type_Osnd(T_a,T_b),V_t_2) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_prod__eqI,axiom, % 187.68/187.57 ! [V_q,V_p,T_b,T_a] : % 187.68/187.57 ( hAPP(c_Product__Type_Ofst(T_a,T_b),V_p) = hAPP(c_Product__Type_Ofst(T_a,T_b),V_q) % 187.68/187.57 => ( hAPP(c_Product__Type_Osnd(T_a,T_b),V_p) = hAPP(c_Product__Type_Osnd(T_a,T_b),V_q) % 187.68/187.57 => V_p = V_q ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_snd__conv,axiom, % 187.68/187.57 ! [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 ). % 187.68/187.57 % 187.68/187.57 fof(fact_snd__eqD,axiom, % 187.68/187.57 ! [V_a,V_y,V_x,T_a,T_b] : % 187.68/187.57 ( 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 % 187.68/187.57 => V_y = V_a ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_fst__eqD,axiom, % 187.68/187.57 ! [V_a,V_y,V_x,T_b,T_a] : % 187.68/187.57 ( 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 % 187.68/187.57 => V_x = V_a ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_pair__collapse,axiom, % 187.68/187.57 ! [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 ). % 187.68/187.57 % 187.68/187.57 fof(fact_fst__conv,axiom, % 187.68/187.57 ! [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 ). % 187.68/187.57 % 187.68/187.57 fof(fact_surjective__pairing,axiom, % 187.68/187.57 ! [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)) ). % 187.68/187.57 % 187.68/187.57 fof(fact_The__split,axiom, % 187.68/187.57 ! [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))) ). % 187.68/187.57 % 187.68/187.57 fof(fact_fst__def,axiom, % 187.68/187.57 ! [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) ). % 187.68/187.57 % 187.68/187.57 fof(fact_snd__def,axiom, % 187.68/187.57 ! [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) ). % 187.68/187.57 % 187.68/187.57 fof(fact_div__int__def,axiom, % 187.68/187.57 ! [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)) ). % 187.68/187.57 % 187.68/187.57 fof(fact_mod__int__def,axiom, % 187.68/187.57 ! [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)) ). % 187.68/187.57 % 187.68/187.57 fof(fact_div__neg__pos,axiom, % 187.68/187.57 ! [V_b,V_a] : % 187.68/187.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 187.68/187.57 => 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)) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_mod__neg__pos,axiom, % 187.68/187.57 ! [V_b,V_a] : % 187.68/187.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 187.68/187.57 => 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)) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_div__pos__pos,axiom, % 187.68/187.57 ! [V_b,V_a] : % 187.68/187.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 187.68/187.57 => 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)) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_mod__pos__pos,axiom, % 187.68/187.57 ! [V_b,V_a] : % 187.68/187.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 187.68/187.57 => 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)) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_div__pos__pos__1__number__of,axiom, % 187.68/187.57 ! [V_w] : % 187.68/187.57 ( 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))) % 187.68/187.57 => 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))) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_mod__pos__pos__1__number__of,axiom, % 187.68/187.57 ! [V_w] : % 187.68/187.57 ( 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))) % 187.68/187.57 => 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))) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_div__pos__neg,axiom, % 187.68/187.57 ! [V_b,V_a] : % 187.68/187.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 187.68/187.57 => 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)))) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_mod__pos__neg,axiom, % 187.68/187.57 ! [V_b,V_a] : % 187.68/187.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 187.68/187.57 => 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)))) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_div__neg__neg,axiom, % 187.68/187.57 ! [V_b,V_a] : % 187.68/187.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 187.68/187.57 => 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)))) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_prod__size__simp,axiom, % 187.68/187.57 ! [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))) ). % 187.68/187.57 % 187.68/187.57 fof(fact_exI__realizer,axiom, % 187.68/187.57 ! [T_a,T_b,V_x_2,V_y_2,V_P_2] : % 187.68/187.57 ( hBOOL(hAPP(hAPP(V_P_2,V_y_2),V_x_2)) % 187.68/187.57 => 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)))) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_conjI__realizer,axiom, % 187.68/187.57 ! [T_b,T_a,V_q_2,V_Q_2,V_p_2,V_P_2] : % 187.68/187.57 ( hBOOL(hAPP(V_P_2,V_p_2)) % 187.68/187.57 => ( hBOOL(hAPP(V_Q_2,V_q_2)) % 187.68/187.57 => ( 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)))) % 187.68/187.57 & 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)))) ) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_mlex__leq,axiom, % 187.68/187.57 ! [V_R_2,T_a,V_y_2,V_x_2,V_f_2] : % 187.68/187.57 ( 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))) % 187.68/187.57 => ( 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)) % 187.68/187.57 => 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))) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_mlex__less,axiom, % 187.68/187.57 ! [V_R_2,T_a,V_y_2,V_x_2,V_f_2] : % 187.68/187.57 ( 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))) % 187.68/187.57 => 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))) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_div__nat__def,axiom, % 187.68/187.57 ! [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)) ). % 187.68/187.57 % 187.68/187.57 fof(fact_mod__nat__def,axiom, % 187.68/187.57 ! [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)) ). % 187.68/187.57 % 187.68/187.57 fof(fact_divmod__nat__rel__def,axiom, % 187.68/187.57 ! [V_qr_2,V_n_2,V_m_2] : % 187.68/187.57 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m_2,V_n_2),V_qr_2)) % 187.68/187.57 <=> ( 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)) % 187.68/187.57 & ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 187.68/187.57 => hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),V_qr_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 187.68/187.57 & ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 187.68/187.57 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) % 187.68/187.57 => ( 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))) % 187.68/187.57 & 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)) ) ) % 187.68/187.57 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) % 187.68/187.57 => ( 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))) % 187.68/187.57 & 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))) ) ) ) ) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_prod_Orecs,axiom, % 187.68/187.57 ! [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) ). % 187.68/187.57 % 187.68/187.57 fof(fact_in__lex__prod,axiom, % 187.68/187.57 ! [V_s_2,V_r_2,V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_b,T_a] : % 187.68/187.57 ( 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))) % 187.68/187.57 <=> ( 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)) % 187.68/187.57 | ( V_a_2 = V_a_H_2 % 187.68/187.57 & 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)) ) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_in__finite__psubset,axiom, % 187.68/187.57 ! [V_B_2,V_A_2,T_a] : % 187.68/187.57 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),c_Wellfounded_Ofinite__psubset(T_a))) % 187.68/187.57 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 187.68/187.57 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_pair__lessI2,axiom, % 187.68/187.57 ! [V_t_2,V_s_2,V_b_2,V_a_2] : % 187.68/187.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_a_2),V_b_2)) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_s_2),V_t_2)) % 187.68/187.57 => 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)) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_pair__lessI1,axiom, % 187.68/187.57 ! [V_t_2,V_s_2,V_b_2,V_a_2] : % 187.68/187.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2)) % 187.68/187.57 => 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)) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_same__fstI,axiom, % 187.68/187.57 ! [T_a,V_R_2,V_y_2,V_y_H_2,T_b,V_x_2,V_P_2] : % 187.68/187.57 ( hBOOL(hAPP(V_P_2,V_x_2)) % 187.68/187.57 => ( 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))) % 187.68/187.57 => 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))) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_pair__leqI2,axiom, % 187.68/187.57 ! [V_t_2,V_s_2,V_b_2,V_a_2] : % 187.68/187.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_a_2),V_b_2)) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_s_2),V_t_2)) % 187.68/187.57 => 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)) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_smin__insertI,axiom, % 187.68/187.57 ! [V_YS_2,V_y_2,V_XS_2,V_x_2] : % 187.68/187.57 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2)) % 187.68/187.57 => ( 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)) % 187.68/187.57 => ( 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)) % 187.68/187.57 => 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)) ) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_smax__insertI,axiom, % 187.68/187.57 ! [V_X_2,V_x_2,V_Y_2,V_y_2] : % 187.68/187.57 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_Y_2)) % 187.68/187.57 => ( 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)) % 187.68/187.57 => ( 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)) % 187.68/187.57 => 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)) ) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_smin__emptyI,axiom, % 187.68/187.57 ! [V_X_2] : % 187.68/187.57 ( V_X_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)) % 187.68/187.57 => 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)) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_smax__emptyI,axiom, % 187.68/187.57 ! [V_Y_2] : % 187.68/187.57 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_Y_2)) % 187.68/187.57 => ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)) % 187.68/187.57 => 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)) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_pair__leqI1,axiom, % 187.68/187.57 ! [V_t_2,V_s_2,V_b_2,V_a_2] : % 187.68/187.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2)) % 187.68/187.57 => 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)) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_wmax__insertI,axiom, % 187.68/187.57 ! [V_XS_2,V_x_2,V_YS_2,V_y_2] : % 187.68/187.57 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_YS_2)) % 187.68/187.57 => ( 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)) % 187.68/187.57 => ( 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)) % 187.68/187.57 => 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)) ) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_wmin__insertI,axiom, % 187.68/187.57 ! [V_YS_2,V_y_2,V_XS_2,V_x_2] : % 187.68/187.57 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2)) % 187.68/187.57 => ( 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)) % 187.68/187.57 => ( 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)) % 187.68/187.57 => 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)) ) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_wmin__emptyI,axiom, % 187.68/187.57 ! [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)) ). % 187.68/187.57 % 187.68/187.57 fof(fact_wmax__emptyI,axiom, % 187.68/187.57 ! [V_X_2] : % 187.68/187.57 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_X_2)) % 187.68/187.57 => 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)) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_min__rpair__set,axiom, % 187.68/187.57 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)) ). % 187.68/187.57 % 187.68/187.57 fof(fact_max__rpair__set,axiom, % 187.68/187.57 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)) ). % 187.68/187.57 % 187.68/187.57 fof(fact_min__strict__def,axiom, % 187.68/187.57 c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ). % 187.68/187.57 % 187.68/187.57 fof(fact_less__than__iff,axiom, % 187.68/187.57 ! [V_y_2,V_x_2] : % 187.68/187.57 ( 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)) % 187.68/187.57 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_pair__less__def,axiom, % 187.68/187.57 c_FunDef_Opair__less = c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_Nat_Onat,c_Wellfounded_Oless__than,c_Wellfounded_Oless__than) ). % 187.68/187.57 % 187.68/187.57 fof(fact_mlex__prod__def,axiom, % 187.68/187.57 ! [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))) ). % 187.68/187.57 % 187.68/187.57 fof(fact_min__weak__def,axiom, % 187.68/187.57 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)))) ). % 187.68/187.57 % 187.68/187.57 fof(fact_intrel__iff,axiom, % 187.68/187.57 ! [V_v_2,V_u_2,V_y_2,V_x_2] : % 187.68/187.57 ( 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)) % 187.68/187.57 <=> 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) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_rp__inv__image__rp,axiom, % 187.68/187.57 ! [V_f_2,T_b,V_P_2,T_a] : % 187.68/187.57 ( c_FunDef_Oreduction__pair(T_a,V_P_2) % 187.68/187.57 => c_FunDef_Oreduction__pair(T_b,hAPP(hAPP(c_FunDef_Orp__inv__image(T_a,T_b),V_P_2),V_f_2)) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_sup1E,axiom, % 187.68/187.57 ! [V_x_2,V_B_2,V_A_2,T_a] : % 187.68/187.57 ( 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)) % 187.68/187.57 => ( ~ hBOOL(hAPP(V_A_2,V_x_2)) % 187.68/187.57 => hBOOL(hAPP(V_B_2,V_x_2)) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_sup1CI,axiom, % 187.68/187.57 ! [T_a,V_A_2,V_x_2,V_B_2] : % 187.68/187.57 ( ( ~ hBOOL(hAPP(V_B_2,V_x_2)) % 187.68/187.57 => hBOOL(hAPP(V_A_2,V_x_2)) ) % 187.68/187.57 => 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)) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_UnE,axiom, % 187.68/187.57 ! [V_B_2,V_A_2,V_c_2,T_a] : % 187.68/187.57 ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 187.68/187.57 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) % 187.68/187.57 => hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2)) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_UnCI,axiom, % 187.68/187.57 ! [V_A_2,V_B_2,V_c_2,T_a] : % 187.68/187.57 ( ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2)) % 187.68/187.57 => hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) ) % 187.68/187.57 => hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_Un__iff,axiom, % 187.68/187.57 ! [V_B_2,V_A_2,V_c_2,T_a] : % 187.68/187.57 ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 187.68/187.57 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) % 187.68/187.57 | hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2)) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_UnI1,axiom, % 187.68/187.57 ! [V_B_2,V_A_2,V_c_2,T_a] : % 187.68/187.57 ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) % 187.68/187.57 => hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_UnI2,axiom, % 187.68/187.57 ! [V_A_2,V_B_2,V_c_2,T_a] : % 187.68/187.57 ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2)) % 187.68/187.57 => hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_Un__insert__right,axiom, % 187.68/187.57 ! [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)) ). % 187.68/187.57 % 187.68/187.57 fof(fact_Un__insert__left,axiom, % 187.68/187.57 ! [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)) ). % 187.68/187.57 % 187.68/187.57 fof(fact_Un__Diff,axiom, % 187.68/187.57 ! [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)) ). % 187.68/187.57 % 187.68/187.57 fof(fact_Un__Diff__cancel2,axiom, % 187.68/187.57 ! [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) ). % 187.68/187.57 % 187.68/187.57 fof(fact_Un__Diff__cancel,axiom, % 187.68/187.57 ! [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) ). % 187.68/187.57 % 187.68/187.57 fof(fact_less__supI2,axiom, % 187.68/187.57 ! [V_a,V_b,V_x,T_a] : % 187.68/187.57 ( class_Lattices_Osemilattice__sup(T_a) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_b)) % 187.68/187.57 => 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))) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_less__supI1,axiom, % 187.68/187.57 ! [V_b,V_a,V_x,T_a] : % 187.68/187.57 ( class_Lattices_Osemilattice__sup(T_a) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a)) % 187.68/187.57 => 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))) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_sup_Oidem,axiom, % 187.68/187.57 ! [V_a,T_a] : % 187.68/187.57 ( class_Lattices_Osemilattice__sup(T_a) % 187.68/187.57 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_a) = V_a ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_sup__idem,axiom, % 187.68/187.57 ! [V_x,T_a] : % 187.68/187.57 ( class_Lattices_Osemilattice__sup(T_a) % 187.68/187.57 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_x) = V_x ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_sup_Ocommute,axiom, % 187.68/187.57 ! [V_b,V_a,T_a] : % 187.68/187.57 ( class_Lattices_Osemilattice__sup(T_a) % 187.68/187.57 => 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) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_inf__sup__aci_I5_J,axiom, % 187.68/187.57 ! [V_y,V_x,T_a] : % 187.68/187.57 ( class_Lattices_Olattice(T_a) % 187.68/187.57 => 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) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_sup__commute,axiom, % 187.68/187.57 ! [V_y,V_x,T_a] : % 187.68/187.57 ( class_Lattices_Osemilattice__sup(T_a) % 187.68/187.57 => 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) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_sup_Oleft__idem,axiom, % 187.68/187.57 ! [V_b,V_a,T_a] : % 187.68/187.57 ( class_Lattices_Osemilattice__sup(T_a) % 187.68/187.57 => 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) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_inf__sup__aci_I8_J,axiom, % 187.68/187.57 ! [V_y,V_x,T_a] : % 187.68/187.57 ( class_Lattices_Olattice(T_a) % 187.68/187.57 => 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) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_sup__left__idem,axiom, % 187.68/187.57 ! [V_y,V_x,T_a] : % 187.68/187.57 ( class_Lattices_Osemilattice__sup(T_a) % 187.68/187.57 => 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) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_sup_Oleft__commute,axiom, % 187.68/187.57 ! [V_c,V_a,V_b,T_a] : % 187.68/187.57 ( class_Lattices_Osemilattice__sup(T_a) % 187.68/187.57 => 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)) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_inf__sup__aci_I7_J,axiom, % 187.68/187.57 ! [V_z,V_y,V_x,T_a] : % 187.68/187.57 ( class_Lattices_Olattice(T_a) % 187.68/187.57 => 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)) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_sup__left__commute,axiom, % 187.68/187.57 ! [V_z,V_y,V_x,T_a] : % 187.68/187.57 ( class_Lattices_Osemilattice__sup(T_a) % 187.68/187.57 => 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)) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_sup_Oassoc,axiom, % 187.68/187.57 ! [V_c,V_b,V_a,T_a] : % 187.68/187.57 ( class_Lattices_Osemilattice__sup(T_a) % 187.68/187.57 => 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)) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_inf__sup__aci_I6_J,axiom, % 187.68/187.57 ! [V_z,V_y,V_x,T_a] : % 187.68/187.57 ( class_Lattices_Olattice(T_a) % 187.68/187.57 => 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)) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_sup__assoc,axiom, % 187.68/187.57 ! [V_z,V_y,V_x,T_a] : % 187.68/187.57 ( class_Lattices_Osemilattice__sup(T_a) % 187.68/187.57 => 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)) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_sup__apply,axiom, % 187.68/187.57 ! [V_x_2,V_g_2,V_f_2,T_b,T_a] : % 187.68/187.57 ( class_Lattices_Olattice(T_a) % 187.68/187.57 => 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)) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_sup1I1,axiom, % 187.68/187.57 ! [V_B_2,T_a,V_x_2,V_A_2] : % 187.68/187.57 ( hBOOL(hAPP(V_A_2,V_x_2)) % 187.68/187.57 => 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)) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_sup1I2,axiom, % 187.68/187.57 ! [V_A_2,T_a,V_x_2,V_B_2] : % 187.68/187.57 ( hBOOL(hAPP(V_B_2,V_x_2)) % 187.68/187.57 => 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)) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_sup__fun__def,axiom, % 187.68/187.57 ! [V_x_2,V_g_2,V_f_2,T_b,T_a] : % 187.68/187.57 ( class_Lattices_Olattice(T_a) % 187.68/187.57 => 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)) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_Un__absorb,axiom, % 187.68/187.57 ! [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 ). % 187.68/187.57 % 187.68/187.57 fof(fact_Un__commute,axiom, % 187.68/187.57 ! [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) ). % 187.68/187.57 % 187.68/187.57 fof(fact_Un__left__absorb,axiom, % 187.68/187.57 ! [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) ). % 187.68/187.57 % 187.68/187.57 fof(fact_Un__left__commute,axiom, % 187.68/187.57 ! [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)) ). % 187.68/187.57 % 187.68/187.57 fof(fact_Un__assoc,axiom, % 187.68/187.57 ! [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)) ). % 187.68/187.57 % 187.68/187.57 fof(fact_bex__Un,axiom, % 187.68/187.57 ! [V_P_2,V_B_2,V_A_2,T_a] : % 187.68/187.57 ( ? [B_x] : % 187.68/187.57 ( 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))) % 187.68/187.57 & hBOOL(hAPP(V_P_2,B_x)) ) % 187.68/187.57 <=> ( ? [B_x] : % 187.68/187.57 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 187.68/187.57 & hBOOL(hAPP(V_P_2,B_x)) ) % 187.68/187.57 | ? [B_x] : % 187.68/187.57 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_B_2)) % 187.68/187.57 & hBOOL(hAPP(V_P_2,B_x)) ) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_ball__Un,axiom, % 187.68/187.57 ! [V_P_2,V_B_2,V_A_2,T_a] : % 187.68/187.57 ( ! [B_x] : % 187.68/187.57 ( 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))) % 187.68/187.57 => hBOOL(hAPP(V_P_2,B_x)) ) % 187.68/187.57 <=> ( ! [B_x] : % 187.68/187.57 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 187.68/187.57 => hBOOL(hAPP(V_P_2,B_x)) ) % 187.68/187.57 & ! [B_x] : % 187.68/187.57 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_B_2)) % 187.68/187.57 => hBOOL(hAPP(V_P_2,B_x)) ) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_Sup__fin_Oidem,axiom, % 187.68/187.57 ! [V_x,T_a] : % 187.68/187.57 ( class_Lattices_Olattice(T_a) % 187.68/187.57 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_x) = V_x ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_sup__max,axiom, % 187.68/187.57 ! [T_a] : % 187.68/187.57 ( ( class_Lattices_Osemilattice__sup(T_a) % 187.68/187.57 & class_Orderings_Olinorder(T_a) ) % 187.68/187.57 => c_Lattices_Osemilattice__sup__class_Osup(T_a) = c_Orderings_Oord__class_Omax(T_a) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_Un__upper1,axiom, % 187.68/187.57 ! [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))) ). % 187.68/187.57 % 187.68/187.57 fof(fact_Un__upper2,axiom, % 187.68/187.57 ! [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))) ). % 187.68/187.57 % 187.68/187.57 fof(fact_subset__Un__eq,axiom, % 187.68/187.57 ! [V_B_2,V_A_2,T_a] : % 187.68/187.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 187.68/187.57 <=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_Un__absorb1,axiom, % 187.68/187.57 ! [V_B_2,V_A_2,T_a] : % 187.68/187.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 187.68/187.57 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_Un__absorb2,axiom, % 187.68/187.57 ! [V_A_2,V_B_2,T_a] : % 187.68/187.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 187.68/187.57 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_Un__least,axiom, % 187.68/187.57 ! [V_B_2,V_C_2,V_A_2,T_a] : % 187.68/187.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) % 187.68/187.57 => 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)) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_Un__mono,axiom, % 187.68/187.57 ! [V_D_2,V_B_2,V_C_2,V_A_2,T_a] : % 187.68/187.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_D_2)) % 187.68/187.57 => 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))) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_le__supE,axiom, % 187.68/187.57 ! [V_x,V_b,V_a,T_a] : % 187.68/187.57 ( class_Lattices_Osemilattice__sup(T_a) % 187.68/187.57 => ( 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)) % 187.68/187.57 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 187.68/187.57 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) ) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_sup__mono,axiom, % 187.68/187.57 ! [V_d,V_b,V_c,V_a,T_a] : % 187.68/187.57 ( class_Lattices_Osemilattice__sup(T_a) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d)) % 187.68/187.57 => 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))) ) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_sup__least,axiom, % 187.68/187.57 ! [V_z,V_x,V_y,T_a] : % 187.68/187.57 ( class_Lattices_Osemilattice__sup(T_a) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x)) % 187.68/187.57 => 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)) ) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_le__supI,axiom, % 187.68/187.57 ! [V_b,V_x,V_a,T_a] : % 187.68/187.57 ( class_Lattices_Osemilattice__sup(T_a) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) % 187.68/187.57 => 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)) ) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_sup__absorb1,axiom, % 187.68/187.57 ! [V_x,V_y,T_a] : % 187.68/187.57 ( class_Lattices_Osemilattice__sup(T_a) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 187.68/187.57 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = V_x ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_sup__absorb2,axiom, % 187.68/187.57 ! [V_y,V_x,T_a] : % 187.68/187.57 ( class_Lattices_Osemilattice__sup(T_a) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 187.68/187.57 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = V_y ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_le__supI2,axiom, % 187.68/187.57 ! [V_a,V_b,V_x,T_a] : % 187.68/187.57 ( class_Lattices_Osemilattice__sup(T_a) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) % 187.68/187.57 => 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))) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_le__supI1,axiom, % 187.68/187.57 ! [V_b,V_a,V_x,T_a] : % 187.68/187.57 ( class_Lattices_Osemilattice__sup(T_a) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 187.68/187.57 => 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))) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_le__sup__iff,axiom, % 187.68/187.57 ! [V_z_2,V_y_2,V_x_2,T_a] : % 187.68/187.57 ( class_Lattices_Osemilattice__sup(T_a) % 187.68/187.57 => ( 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)) % 187.68/187.57 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_z_2)) % 187.68/187.57 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_z_2)) ) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_le__iff__sup,axiom, % 187.68/187.57 ! [V_y_2,V_x_2,T_a] : % 187.68/187.57 ( class_Lattices_Osemilattice__sup(T_a) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 187.68/187.57 <=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x_2),V_y_2) = V_y_2 ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_sup__ge2,axiom, % 187.68/187.57 ! [V_x,V_y,T_a] : % 187.68/187.57 ( class_Lattices_Osemilattice__sup(T_a) % 187.68/187.57 => 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))) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_inf__sup__ord_I4_J,axiom, % 187.68/187.57 ! [V_x,V_y,T_a] : % 187.68/187.57 ( class_Lattices_Olattice(T_a) % 187.68/187.57 => 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))) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_sup__ge1,axiom, % 187.68/187.57 ! [V_y,V_x,T_a] : % 187.68/187.57 ( class_Lattices_Osemilattice__sup(T_a) % 187.68/187.57 => 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))) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_inf__sup__ord_I3_J,axiom, % 187.68/187.57 ! [V_y,V_x,T_a] : % 187.68/187.57 ( class_Lattices_Olattice(T_a) % 187.68/187.57 => 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))) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_sup__eq__bot__iff,axiom, % 187.68/187.57 ! [V_y_2,V_x_2,T_a] : % 187.68/187.57 ( class_Lattices_Obounded__lattice__bot(T_a) % 187.68/187.57 => ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x_2),V_y_2) = c_Orderings_Obot__class_Obot(T_a) % 187.68/187.57 <=> ( V_x_2 = c_Orderings_Obot__class_Obot(T_a) % 187.68/187.57 & V_y_2 = c_Orderings_Obot__class_Obot(T_a) ) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_sup__bot__right,axiom, % 187.68/187.57 ! [V_x,T_a] : % 187.68/187.57 ( class_Lattices_Obounded__lattice__bot(T_a) % 187.68/187.57 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),c_Orderings_Obot__class_Obot(T_a)) = V_x ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_sup__bot__left,axiom, % 187.68/187.57 ! [V_x,T_a] : % 187.68/187.57 ( class_Lattices_Obounded__lattice__bot(T_a) % 187.68/187.57 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x) = V_x ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_Un__empty,axiom, % 187.68/187.57 ! [V_B_2,V_A_2,T_a] : % 187.68/187.57 ( 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)) % 187.68/187.57 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.57 & V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_Un__empty__right,axiom, % 187.68/187.57 ! [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 ). % 187.68/187.57 % 187.68/187.57 fof(fact_Un__empty__left,axiom, % 187.68/187.57 ! [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 ). % 187.68/187.57 % 187.68/187.57 fof(fact_finite__UnI,axiom, % 187.68/187.57 ! [V_Ga_2,V_F_2,T_a] : % 187.68/187.57 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) % 187.68/187.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_Ga_2)) % 187.68/187.57 => 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))) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_finite__Un,axiom, % 187.68/187.57 ! [V_Ga_2,V_F_2,T_a] : % 187.68/187.57 ( 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))) % 187.68/187.57 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) % 187.68/187.57 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_Ga_2)) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_fun__left__comm__idem__sup,axiom, % 187.68/187.57 ! [T_a] : % 187.68/187.57 ( class_Lattices_Osemilattice__sup(T_a) % 187.68/187.57 => c_Finite__Set_Ofun__left__comm__idem(T_a,T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a)) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_sup__Un__eq,axiom, % 187.68/187.57 ! [V_x_2,V_S_2,V_R_2,T_a] : % 187.68/187.57 ( 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)) % 187.68/187.57 <=> 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))) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_insert__is__Un,axiom, % 187.68/187.57 ! [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) ). % 187.68/187.57 % 187.68/187.57 fof(fact_Diff__subset__conv,axiom, % 187.68/187.57 ! [V_C_2,V_B_2,V_A_2,T_a] : % 187.68/187.57 ( 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)) % 187.68/187.57 <=> 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))) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_Diff__partition,axiom, % 187.68/187.57 ! [V_B_2,V_A_2,T_a] : % 187.68/187.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 187.68/187.57 => 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 ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_Compl__Diff__eq,axiom, % 187.68/187.57 ! [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) ). % 187.68/187.57 % 187.68/187.57 fof(fact_rp__inv__image__def,axiom, % 187.68/187.57 ! [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))) ). % 187.68/187.57 % 187.68/187.57 fof(fact_folding__image__simple__idem_Ounion__idem,axiom, % 187.68/187.57 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 187.68/187.57 ( c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 187.68/187.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.68/187.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 187.68/187.57 => 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)) ) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_folding__one__idem_Ounion__idem,axiom, % 187.68/187.57 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_a] : % 187.68/187.57 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2) % 187.68/187.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.57 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 187.68/187.57 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.57 => 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)) ) ) ) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_folding__idem_Ounion__idem,axiom, % 187.68/187.57 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 187.68/187.57 ( c_Finite__Set_Ofolding__idem(T_a,T_b,V_f_2,V_F_2) % 187.68/187.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 187.68/187.57 => 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)) ) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_fold1__Un2,axiom, % 187.68/187.57 ! [V_B_2,V_A_2,T_a] : % 187.68/187.57 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 187.68/187.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.57 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 187.68/187.57 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.57 => 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)) ) ) ) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_Min__Un,axiom, % 187.68/187.57 ! [V_B_2,V_A_2,T_a] : % 187.68/187.57 ( class_Orderings_Olinorder(T_a) % 187.68/187.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.57 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 187.68/187.57 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.57 => 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)) ) ) ) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_Max__Un,axiom, % 187.68/187.57 ! [V_B_2,V_A_2,T_a] : % 187.68/187.57 ( class_Orderings_Olinorder(T_a) % 187.68/187.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.57 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 187.68/187.57 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.57 => 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)) ) ) ) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_min__max_OInf__fin_Ounion__idem,axiom, % 187.68/187.57 ! [V_B_2,V_A_2,T_a] : % 187.68/187.57 ( class_Orderings_Olinorder(T_a) % 187.68/187.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.57 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 187.68/187.57 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.57 => 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)) ) ) ) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_min__max_OSup__fin_Ounion__idem,axiom, % 187.68/187.57 ! [V_B_2,V_A_2,T_a] : % 187.68/187.57 ( class_Orderings_Olinorder(T_a) % 187.68/187.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.57 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 187.68/187.57 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.57 => 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)) ) ) ) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_max__weak__def,axiom, % 187.68/187.57 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)))) ). % 187.68/187.57 % 187.68/187.57 fof(fact_in__inv__image,axiom, % 187.68/187.57 ! [V_f_2,V_r_2,T_b,V_y_2,V_x_2,T_a] : % 187.68/187.57 ( 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))) % 187.68/187.57 <=> 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)) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_Sup__fin_Oremove,axiom, % 187.68/187.57 ! [V_x_2,V_A_2,T_a] : % 187.68/187.57 ( class_Lattices_Olattice(T_a) % 187.68/187.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 187.68/187.57 => ( ( 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)) % 187.68/187.57 => c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2) = V_x_2 ) % 187.68/187.57 & ( 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)) % 187.68/187.57 => 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)))))) ) ) ) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_setprod__mono__one__right,axiom, % 187.68/187.57 ! [V_f_2,V_S_2,V_T_2,T_a,T_b] : % 187.68/187.57 ( class_Groups_Ocomm__monoid__mult(T_b) % 187.68/187.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2)) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2)) % 187.68/187.57 => ( ! [B_x] : % 187.68/187.57 ( 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))) % 187.68/187.57 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_b) ) % 187.68/187.57 => 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) ) ) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_sup__nat__def,axiom, % 187.68/187.57 c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat) = c_Orderings_Oord__class_Omax(tc_Nat_Onat) ). % 187.68/187.57 % 187.68/187.57 fof(fact_Sup__fin_Osingleton,axiom, % 187.68/187.57 ! [V_x_2,T_a] : % 187.68/187.57 ( class_Lattices_Olattice(T_a) % 187.68/187.57 => 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 ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_sup__Un__eq2,axiom, % 187.68/187.57 ! [V_y_2,V_x_2,V_S_2,V_R_2,T_b,T_a] : % 187.68/187.57 ( 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)) % 187.68/187.57 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x_2),V_y_2)),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))) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_Sup__fin_Oin__idem,axiom, % 187.68/187.57 ! [V_x_2,V_A_2,T_a] : % 187.68/187.57 ( class_Lattices_Olattice(T_a) % 187.68/187.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 187.68/187.57 => 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) ) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_Sup__fin_OF__eq,axiom, % 187.68/187.57 ! [V_A_2,T_a] : % 187.68/187.57 ( class_Lattices_Olattice(T_a) % 187.68/187.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.57 => 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) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_Sup__fin_Oinsert__idem,axiom, % 187.68/187.57 ! [V_x_2,V_A_2,T_a] : % 187.68/187.57 ( class_Lattices_Olattice(T_a) % 187.68/187.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.57 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.57 => 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)) ) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_Sup__fin_Osubset__idem,axiom, % 187.68/187.57 ! [V_B_2,V_A_2,T_a] : % 187.68/187.57 ( class_Lattices_Olattice(T_a) % 187.68/187.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.57 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 187.68/187.57 => 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) ) ) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_Sup__fin_Ounion__idem,axiom, % 187.68/187.57 ! [V_B_2,V_A_2,T_a] : % 187.68/187.57 ( class_Lattices_Olattice(T_a) % 187.68/187.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.57 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 187.68/187.57 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.57 => 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)) ) ) ) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_max__strict__def,axiom, % 187.68/187.57 c_FunDef_Omax__strict = c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ). % 187.68/187.57 % 187.68/187.57 fof(fact_measure__def,axiom, % 187.68/187.57 ! [T_a] : c_Wellfounded_Omeasure(T_a) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat,T_a),c_Wellfounded_Oless__than) ). % 187.68/187.57 % 187.68/187.57 fof(fact_Sup__fin_Oinsert,axiom, % 187.68/187.57 ! [V_x_2,V_A_2,T_a] : % 187.68/187.57 ( class_Lattices_Olattice(T_a) % 187.68/187.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.57 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 187.68/187.57 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.57 => 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)) ) ) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_Sup__fin_Oinsert__remove,axiom, % 187.68/187.57 ! [V_x_2,V_A_2,T_a] : % 187.68/187.57 ( class_Lattices_Olattice(T_a) % 187.68/187.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.57 => ( ( 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)) % 187.68/187.57 => 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 ) % 187.68/187.57 & ( 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)) % 187.68/187.57 => 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)))))) ) ) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_max__ext__additive,axiom, % 187.68/187.57 ! [V_D_2,V_C_2,V_R_2,V_B_2,V_A_2,T_a] : % 187.68/187.57 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)),c_Wellfounded_Omax__ext(T_a,V_R_2))) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_D_2)),c_Wellfounded_Omax__ext(T_a,V_R_2))) % 187.68/187.57 => hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),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))) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_max__extp__max__ext__eq,axiom, % 187.68/187.57 ! [V_xa_2,V_x_2,V_R_2,T_a] : % 187.68/187.57 ( c_Wellfounded_Omax__extp(T_a,hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(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) % 187.68/187.57 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool))),hAPP(hAPP(c_Product__Type_OPair(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),V_x_2),V_xa_2)),c_Wellfounded_Omax__ext(T_a,V_R_2))) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_irrefl__def,axiom, % 187.68/187.57 ! [V_r_2,T_a] : % 187.68/187.57 ( c_Relation_Oirrefl(T_a,V_r_2) % 187.68/187.57 <=> ! [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)) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_Body1,axiom, % 187.68/187.57 ! [V_pna_2,V_Procs_2,V_Q_2,V_P_2,V_Ga_2,T_a] : % 187.68/187.57 ( 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)) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),V_pna_2),V_Procs_2)) % 187.68/187.57 => 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_pna_2)),hAPP(c_Com_Ocom_OBODY,V_pna_2)),hAPP(V_Q_2,V_pna_2))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_Field__insert,axiom, % 187.68/187.57 ! [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)) ). % 187.68/187.57 % 187.68/187.57 fof(fact_sup2E,axiom, % 187.68/187.57 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_b,T_a] : % 187.68/187.57 ( 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)) % 187.68/187.57 => ( ~ hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) % 187.68/187.57 => hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_sup2CI,axiom, % 187.68/187.57 ! [T_b,T_a,V_A_2,V_y_2,V_x_2,V_B_2] : % 187.68/187.57 ( ( ~ hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) % 187.68/187.57 => hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) ) % 187.68/187.57 => 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)) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_image__eqI,axiom, % 187.68/187.57 ! [T_a,V_A_2,T_b,V_x_2,V_f_2,V_b_2] : % 187.68/187.57 ( V_b_2 = hAPP(V_f_2,V_x_2) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 187.68/187.57 => hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2))) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_finite__imageI,axiom, % 187.68/187.57 ! [V_h_2,T_b,V_F_2,T_a] : % 187.68/187.57 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) % 187.68/187.57 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Oimage(T_a,T_b,V_h_2),V_F_2))) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_sup2I1,axiom, % 187.68/187.57 ! [V_B_2,T_b,T_a,V_y_2,V_x_2,V_A_2] : % 187.68/187.57 ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) % 187.68/187.57 => 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)) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_sup2I2,axiom, % 187.68/187.57 ! [V_A_2,T_b,T_a,V_y_2,V_x_2,V_B_2] : % 187.68/187.57 ( hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) % 187.68/187.57 => 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)) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_image__Un,axiom, % 187.68/187.57 ! [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)) ). % 187.68/187.57 % 187.68/187.57 fof(fact_image__iff,axiom, % 187.68/187.57 ! [V_A_2,V_f_2,T_b,V_z_2,T_a] : % 187.68/187.57 ( hBOOL(hAPP(hAPP(c_member(T_a),V_z_2),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2))) % 187.68/187.57 <=> ? [B_x] : % 187.68/187.57 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 187.68/187.57 & V_z_2 = hAPP(V_f_2,B_x) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_imageI,axiom, % 187.68/187.57 ! [V_f_2,T_b,V_A_2,V_x_2,T_a] : % 187.68/187.57 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 187.68/187.57 => 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))) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_rev__image__eqI,axiom, % 187.68/187.57 ! [T_b,V_f_2,V_b_2,V_A_2,V_x_2,T_a] : % 187.68/187.57 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 187.68/187.57 => ( V_b_2 = hAPP(V_f_2,V_x_2) % 187.68/187.57 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2))) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_image__compose,axiom, % 187.68/187.57 ! [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)) ). % 187.68/187.57 % 187.68/187.57 fof(fact_image__image,axiom, % 187.68/187.57 ! [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) ). % 187.68/187.57 % 187.68/187.57 fof(fact_image__ident,axiom, % 187.68/187.57 ! [V_Y_2,T_a] : hAPP(c_Set_Oimage(T_a,T_a,c_COMBI(T_a)),V_Y_2) = V_Y_2 ). % 187.68/187.57 % 187.68/187.57 fof(fact_subset__image__iff,axiom, % 187.68/187.57 ! [V_A_2,V_f_2,T_b,V_B_2,T_a] : % 187.68/187.57 ( 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))) % 187.68/187.57 <=> ? [B_AA] : % 187.68/187.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),B_AA),V_A_2)) % 187.68/187.57 & V_B_2 = hAPP(c_Set_Oimage(T_b,T_a,V_f_2),B_AA) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_image__mono,axiom, % 187.68/187.57 ! [V_f_2,T_b,V_B_2,V_A_2,T_a] : % 187.68/187.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 187.68/187.57 => 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))) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_empty__is__image,axiom, % 187.68/187.57 ! [V_A_2,V_f_2,T_b,T_a] : % 187.68/187.57 ( 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) % 187.68/187.57 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_image__empty,axiom, % 187.68/187.57 ! [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)) ). % 187.68/187.57 % 187.68/187.57 fof(fact_image__is__empty,axiom, % 187.68/187.57 ! [V_A_2,V_f_2,T_a,T_b] : % 187.68/187.57 ( 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)) % 187.68/187.57 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_image__insert,axiom, % 187.68/187.57 ! [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)) ). % 187.68/187.57 % 187.68/187.57 fof(fact_insert__image,axiom, % 187.68/187.57 ! [V_f_2,T_b,V_A_2,V_x_2,T_a] : % 187.68/187.57 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 187.68/187.57 => 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) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_finite__surj,axiom, % 187.68/187.57 ! [V_f_2,V_B_2,T_b,V_A_2,T_a] : % 187.68/187.57 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.57 => ( 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))) % 187.68/187.57 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_image__diff__subset,axiom, % 187.68/187.57 ! [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)))) ). % 187.68/187.57 % 187.68/187.57 fof(fact_image__constant__conv,axiom, % 187.68/187.57 ! [V_c_2,T_b,T_a,V_A_2] : % 187.68/187.57 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.57 => hAPP(c_Set_Oimage(T_a,T_b,hAPP(c_COMBK(T_b,T_a),V_c_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) % 187.68/187.57 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.57 => hAPP(c_Set_Oimage(T_a,T_b,hAPP(c_COMBK(T_b,T_a),V_c_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_card__image__le,axiom, % 187.68/187.57 ! [V_f_2,T_b,V_A_2,T_a] : % 187.68/187.57 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.57 => 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))) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_image__constant,axiom, % 187.68/187.57 ! [V_c_2,T_b,V_A_2,V_x_2,T_a] : % 187.68/187.57 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 187.68/187.57 => hAPP(c_Set_Oimage(T_a,T_b,hAPP(c_COMBK(T_b,T_a),V_c_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_Field__empty,axiom, % 187.68/187.57 ! [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)) ). % 187.68/187.57 % 187.68/187.57 fof(fact_mono__Field,axiom, % 187.68/187.57 ! [V_s_2,V_r_2,T_a] : % 187.68/187.57 ( 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)) % 187.68/187.57 => 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))) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_Field__Un,axiom, % 187.68/187.57 ! [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)) ). % 187.68/187.57 % 187.68/187.57 fof(fact_finite__Field,axiom, % 187.68/187.57 ! [V_r_2,T_a] : % 187.68/187.57 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2)) % 187.68/187.57 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Relation_OField(T_a),V_r_2))) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_image__eq__fold__image,axiom, % 187.68/187.57 ! [V_f_2,T_b,V_A_2,T_a] : % 187.68/187.57 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.57 => 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) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_fun__upd__image,axiom, % 187.68/187.57 ! [V_y_2,V_f_2,T_b,V_A_2,V_x_2,T_a] : % 187.68/187.57 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 187.68/187.57 => 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)))))) ) % 187.68/187.57 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 187.68/187.57 => 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) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_minus__Min__eq__Max,axiom, % 187.68/187.57 ! [V_S_2,T_a] : % 187.68/187.57 ( class_Groups_Olinordered__ab__group__add(T_a) % 187.68/187.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 187.68/187.57 => ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.57 => 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)) ) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_minus__Max__eq__Min,axiom, % 187.68/187.57 ! [V_S_2,T_a] : % 187.68/187.57 ( class_Groups_Olinordered__ab__group__add(T_a) % 187.68/187.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 187.68/187.57 => ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.57 => 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)) ) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_hoare__derivs_OBody,axiom, % 187.68/187.57 ! [V_Procs_2,V_Q_2,V_P_2,V_Ga_2,T_a] : % 187.68/187.57 ( 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)) % 187.68/187.57 => 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)) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_Body__sound__lemma,axiom, % 187.68/187.57 ! [V_Procs_2,V_Q_2,V_P_2,V_Ga_2,T_a] : % 187.68/187.57 ( 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)) % 187.68/187.57 => 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)) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_finite__pointwise,axiom, % 187.68/187.57 ! [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] : % 187.68/187.57 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_U_2)) % 187.68/187.57 => ( ! [B_p] : % 187.68/187.57 ( 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)))) % 187.68/187.57 => 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)))) ) % 187.68/187.57 => ( 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)) % 187.68/187.57 => 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)) ) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_Sup__fin_Oclosed,axiom, % 187.68/187.57 ! [V_A_2,T_a] : % 187.68/187.57 ( class_Lattices_Olattice(T_a) % 187.68/187.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.57 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.57 => ( ! [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)))))) % 187.68/187.57 => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2)),V_A_2)) ) ) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_min__max_OSup__fin_Ohom__commute,axiom, % 187.68/187.57 ! [V_N_2,V_h_2,T_a] : % 187.68/187.57 ( class_Orderings_Olinorder(T_a) % 187.68/187.57 => ( ! [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)) % 187.68/187.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 187.68/187.57 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.57 => 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)) ) ) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_min__max_OInf__fin_Ohom__commute,axiom, % 187.68/187.57 ! [V_N_2,V_h_2,T_a] : % 187.68/187.57 ( class_Orderings_Olinorder(T_a) % 187.68/187.57 => ( ! [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)) % 187.68/187.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 187.68/187.57 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.57 => 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)) ) ) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_pair__imageI,axiom, % 187.68/187.57 ! [V_f_2,T_c,V_A_2,V_b_2,V_a_2,T_b,T_a] : % 187.68/187.57 ( 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)) % 187.68/187.57 => 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))) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I3_J,axiom, % 187.68/187.57 ! [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))) ). % 187.68/187.57 % 187.68/187.57 fof(fact_transfer__nat__int__set__relations_I2_J,axiom, % 187.68/187.57 ! [V_A_2,V_x_2] : % 187.68/187.57 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_x_2),V_A_2)) % 187.68/187.57 <=> 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))) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I1_J,axiom, % 187.68/187.57 ! [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)) ). % 187.68/187.57 % 187.68/187.57 fof(fact_transfer__nat__int__set__relations_I3_J,axiom, % 187.68/187.57 ! [V_B_2,V_A_2] : % 187.68/187.57 ( V_A_2 = V_B_2 % 187.68/187.57 <=> 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) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_transfer__nat__int__set__relations_I4_J,axiom, % 187.68/187.57 ! [V_B_2,V_A_2] : % 187.68/187.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2)) % 187.68/187.57 <=> 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))) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_transfer__int__nat__set__return__embed,axiom, % 187.68/187.57 ! [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 ). % 187.68/187.57 % 187.68/187.57 fof(fact_transfer__nat__int__set__relations_I5_J,axiom, % 187.68/187.57 ! [V_B_2,V_A_2] : % 187.68/187.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2)) % 187.68/187.57 <=> 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))) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_transfer__nat__int__set__relations_I1_J,axiom, % 187.68/187.57 ! [V_A_2] : % 187.68/187.57 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_A_2)) % 187.68/187.57 <=> 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))) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I2_J,axiom, % 187.68/187.57 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))) ). % 187.68/187.57 % 187.68/187.57 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I2_J,axiom, % 187.68/187.57 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))) ). % 187.68/187.57 % 187.68/187.57 fof(fact_transfer__nat__int__sum__prod_I2_J,axiom, % 187.68/187.57 ! [V_A_2,V_f_2,T_a] : % 187.68/187.57 ( ( class_Groups_Ocomm__monoid__add(T_a) % 187.68/187.57 & class_Groups_Ocomm__monoid__mult(T_a) ) % 187.68/187.57 => 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)) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_image__map__upd,axiom, % 187.68/187.57 ! [V_y_2,V_m_2,T_b,V_A_2,V_x_2,T_a] : % 187.68/187.57 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 187.68/187.57 => 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) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_Max_Ohom__commute,axiom, % 187.68/187.57 ! [V_N_2,V_h_2,T_a] : % 187.68/187.57 ( class_Orderings_Olinorder(T_a) % 187.68/187.57 => ( ! [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)) % 187.68/187.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 187.68/187.57 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.57 => 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)) ) ) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_Min_Ohom__commute,axiom, % 187.68/187.57 ! [V_N_2,V_h_2,T_a] : % 187.68/187.57 ( class_Orderings_Olinorder(T_a) % 187.68/187.57 => ( ! [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)) % 187.68/187.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 187.68/187.57 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.57 => 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)) ) ) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_Sup__fin_Ohom__commute,axiom, % 187.68/187.57 ! [V_N_2,V_h_2,T_a] : % 187.68/187.57 ( class_Lattices_Olattice(T_a) % 187.68/187.57 => ( ! [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)) % 187.68/187.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 187.68/187.57 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.57 => 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)) ) ) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_hom__fold1__commute,axiom, % 187.68/187.57 ! [V_N_2,V_h_2,T_a] : % 187.68/187.57 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 187.68/187.57 => ( ! [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)) % 187.68/187.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 187.68/187.57 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.57 => 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)) ) ) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I3_J,axiom, % 187.68/187.57 ! [V_B_2,V_A_2] : % 187.68/187.57 ( c_Nat__Transfer_Onat__set(V_A_2) % 187.68/187.57 => ( c_Nat__Transfer_Onat__set(V_B_2) % 187.68/187.57 => 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))) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_transfer__int__nat__sum__prod_I2_J,axiom, % 187.68/187.57 ! [V_f_2,V_A_2,T_a] : % 187.68/187.57 ( ( class_Groups_Ocomm__monoid__add(T_a) % 187.68/187.57 & class_Groups_Ocomm__monoid__mult(T_a) ) % 187.68/187.57 => ( c_Nat__Transfer_Onat__set(V_A_2) % 187.68/187.57 => 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)) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_finite__nat__set__iff__bounded__le,axiom, % 187.68/187.57 ! [V_N_2] : % 187.68/187.57 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_N_2)) % 187.68/187.57 <=> ? [B_m] : % 187.68/187.57 ! [B_x] : % 187.68/187.57 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2)) % 187.68/187.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_x),B_m)) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_finite__nat__set__iff__bounded,axiom, % 187.68/187.57 ! [V_N_2] : % 187.68/187.57 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_N_2)) % 187.68/187.57 <=> ? [B_m] : % 187.68/187.57 ! [B_x] : % 187.68/187.57 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2)) % 187.68/187.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_x),B_m)) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I1_J,axiom, % 187.68/187.57 c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))) ). % 187.68/187.57 % 187.68/187.57 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I2_J,axiom, % 187.68/187.57 ! [V_B_2,V_A_2] : % 187.68/187.57 ( c_Nat__Transfer_Onat__set(V_A_2) % 187.68/187.57 => ( c_Nat__Transfer_Onat__set(V_B_2) % 187.68/187.57 => 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)) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_nat__set__def,axiom, % 187.68/187.57 ! [V_S_2] : % 187.68/187.57 ( c_Nat__Transfer_Onat__set(V_S_2) % 187.68/187.57 <=> ! [B_x] : % 187.68/187.57 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),V_S_2)) % 187.68/187.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I5_J,axiom, % 187.68/187.57 ! [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)) ). % 187.68/187.57 % 187.68/187.57 fof(fact_transfer__int__nat__set__relations_I3_J,axiom, % 187.68/187.57 ! [V_B_2,V_A_2] : % 187.68/187.57 ( c_Nat__Transfer_Onat__set(V_A_2) % 187.68/187.57 => ( c_Nat__Transfer_Onat__set(V_B_2) % 187.68/187.57 => ( V_A_2 = V_B_2 % 187.68/187.57 <=> 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) ) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_Nat__Transfer_Otransfer__nat__int__set__function__closures_I6_J,axiom, % 187.68/187.57 ! [V_x_2,V_A_2] : % 187.68/187.57 ( c_Nat__Transfer_Onat__set(V_A_2) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2)) % 187.68/187.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_transfer__nat__int__set__return__embed,axiom, % 187.68/187.57 ! [V_A_2] : % 187.68/187.57 ( c_Nat__Transfer_Onat__set(V_A_2) % 187.68/187.57 => 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 ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_transfer__int__nat__set__relations_I1_J,axiom, % 187.68/187.57 ! [V_A_2] : % 187.68/187.57 ( c_Nat__Transfer_Onat__set(V_A_2) % 187.68/187.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),V_A_2)) % 187.68/187.57 <=> 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))) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I1_J,axiom, % 187.68/187.57 ! [V_A_2] : % 187.68/187.57 ( c_Nat__Transfer_Onat__set(V_A_2) % 187.68/187.57 => 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)) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_transfer__int__nat__set__relations_I5_J,axiom, % 187.68/187.57 ! [V_B_2,V_A_2] : % 187.68/187.57 ( c_Nat__Transfer_Onat__set(V_A_2) % 187.68/187.57 => ( c_Nat__Transfer_Onat__set(V_B_2) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2)) % 187.68/187.57 <=> 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))) ) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_transfer__int__nat__set__relations_I4_J,axiom, % 187.68/187.57 ! [V_B_2,V_A_2] : % 187.68/187.57 ( c_Nat__Transfer_Onat__set(V_A_2) % 187.68/187.57 => ( c_Nat__Transfer_Onat__set(V_B_2) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2)) % 187.68/187.57 <=> 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))) ) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_transfer__int__nat__set__relations_I2_J,axiom, % 187.68/187.57 ! [V_A_2,V_x_2] : % 187.68/187.57 ( c_Nat__Transfer_Ois__nat(V_x_2) % 187.68/187.57 => ( c_Nat__Transfer_Onat__set(V_A_2) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2)) % 187.68/187.57 <=> 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))) ) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_card__greaterThanLessThan__int,axiom, % 187.68/187.57 ! [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)))) ). % 187.68/187.57 % 187.68/187.57 fof(fact_ord_OatMost__iff,axiom, % 187.68/187.57 ! [V_k_2,V_less__eq_2,V_i_2,T_a] : % 187.68/187.57 ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OatMost(T_a,V_less__eq_2,V_k_2))) % 187.68/187.57 <=> hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_k_2)) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_ord_OatLeast__iff,axiom, % 187.68/187.57 ! [V_k_2,V_less__eq_2,V_i_2,T_a] : % 187.68/187.57 ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OatLeast(T_a,V_less__eq_2,V_k_2))) % 187.68/187.57 <=> hBOOL(hAPP(hAPP(V_less__eq_2,V_k_2),V_i_2)) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_finite__greaterThanLessThan__int,axiom, % 187.68/187.57 ! [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))) ). % 187.68/187.57 % 187.68/187.57 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I5_J,axiom, % 187.68/187.57 c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ). % 187.68/187.57 % 187.68/187.57 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I1_J,axiom, % 187.68/187.57 ! [V_y,V_x] : % 187.68/187.57 ( c_Nat__Transfer_Ois__nat(V_x) % 187.68/187.57 => ( c_Nat__Transfer_Ois__nat(V_y) % 187.68/187.57 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_y)) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I9_J,axiom, % 187.68/187.57 ! [V_z] : c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_z)) ). % 187.68/187.57 % 187.68/187.57 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I6_J,axiom, % 187.68/187.57 c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)) ). % 187.68/187.57 % 187.68/187.57 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I2_J,axiom, % 187.68/187.57 ! [V_y,V_x] : % 187.68/187.57 ( c_Nat__Transfer_Ois__nat(V_x) % 187.68/187.57 => ( c_Nat__Transfer_Ois__nat(V_y) % 187.68/187.57 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y)) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_Divides_Otransfer__int__nat__function__closures_I2_J,axiom, % 187.68/187.57 ! [V_y,V_x] : % 187.68/187.57 ( c_Nat__Transfer_Ois__nat(V_x) % 187.68/187.57 => ( c_Nat__Transfer_Ois__nat(V_y) % 187.68/187.57 => c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_y)) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_Divides_Otransfer__int__nat__function__closures_I1_J,axiom, % 187.68/187.57 ! [V_y,V_x] : % 187.68/187.57 ( c_Nat__Transfer_Ois__nat(V_x) % 187.68/187.57 => ( c_Nat__Transfer_Ois__nat(V_y) % 187.68/187.57 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_y)) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I4_J,axiom, % 187.68/187.57 ! [V_n,V_x] : % 187.68/187.57 ( c_Nat__Transfer_Ois__nat(V_x) % 187.68/187.57 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_n)) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I3_J,axiom, % 187.68/187.57 ! [V_y,V_x] : % 187.68/187.57 ( c_Nat__Transfer_Ois__nat(V_x) % 187.68/187.57 => ( c_Nat__Transfer_Ois__nat(V_y) % 187.68/187.57 => c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(V_x,V_y)) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_is__nat__def,axiom, % 187.68/187.57 ! [V_x_2] : % 187.68/187.57 ( c_Nat__Transfer_Ois__nat(V_x_2) % 187.68/187.57 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_greaterThanLessThan__empty,axiom, % 187.68/187.57 ! [V_k_2,V_l_2,T_a] : % 187.68/187.57 ( class_Orderings_Oorder(T_a) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_k_2)) % 187.68/187.57 => 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)) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_image__uminus__greaterThanLessThan,axiom, % 187.68/187.57 ! [V_y_2,V_x_2,T_a] : % 187.68/187.57 ( class_Groups_Oordered__ab__group__add(T_a) % 187.68/187.57 => 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)) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I6_J,axiom, % 187.68/187.57 ! [V_x_2,V_A_2] : % 187.68/187.57 ( c_Nat__Transfer_Onat__set(V_A_2) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2)) % 187.68/187.57 => c_Nat__Transfer_Ois__nat(V_x_2) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I8_J,axiom, % 187.68/187.57 c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) ). % 187.68/187.57 % 187.68/187.57 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I7_J,axiom, % 187.68/187.57 c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ). % 187.68/187.57 % 187.68/187.57 fof(fact_transfer__int__nat__sum__prod2_I2_J,axiom, % 187.68/187.57 ! [V_f_2,V_A_2,T_a] : % 187.68/187.57 ( ! [B_x] : % 187.68/187.57 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 187.68/187.57 => c_Nat__Transfer_Ois__nat(hAPP(V_f_2,B_x)) ) % 187.68/187.57 => 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)) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_ord_OgreaterThanAtMost__iff,axiom, % 187.68/187.57 ! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_a] : % 187.68/187.57 ( 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))) % 187.68/187.57 <=> ( hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2)) % 187.68/187.57 & hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2)) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_ord_OatLeastLessThan__iff,axiom, % 187.68/187.57 ! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_a] : % 187.68/187.57 ( 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))) % 187.68/187.57 <=> ( hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2)) % 187.68/187.57 & hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2)) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_ord_OgreaterThanLessThan__iff,axiom, % 187.68/187.57 ! [V_u_2,V_l_2,V_less_2,V_i_2,T_a] : % 187.68/187.57 ( 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))) % 187.68/187.57 <=> ( hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2)) % 187.68/187.57 & hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2)) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_finite__greaterThanLessThan,axiom, % 187.68/187.57 ! [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))) ). % 187.68/187.57 % 187.68/187.57 fof(fact_card__greaterThanLessThan,axiom, % 187.68/187.57 ! [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)) ). % 187.68/187.57 % 187.68/187.57 fof(fact_ord_OlessThan__iff,axiom, % 187.68/187.57 ! [V_k_2,V_less_2,V_i_2,T_a] : % 187.68/187.57 ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OlessThan(T_a,V_less_2,V_k_2))) % 187.68/187.57 <=> hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_k_2)) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_ord_OgreaterThan__iff,axiom, % 187.68/187.57 ! [V_k_2,V_less_2,V_i_2,T_a] : % 187.68/187.57 ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OgreaterThan(T_a,V_less_2,V_k_2))) % 187.68/187.57 <=> hBOOL(hAPP(hAPP(V_less_2,V_k_2),V_i_2)) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_ord_OatLeastAtMost__iff,axiom, % 187.68/187.57 ! [V_u_2,V_l_2,V_less__eq_2,V_i_2,T_a] : % 187.68/187.57 ( 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))) % 187.68/187.57 <=> ( hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2)) % 187.68/187.57 & hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2)) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_ivl__disj__un_I4_J,axiom, % 187.68/187.57 ! [V_u_2,V_l_2,T_a] : % 187.68/187.57 ( class_Orderings_Olinorder(T_a) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_l_2),V_u_2)) % 187.68/187.57 => 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) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_finite__greaterThanAtMost,axiom, % 187.68/187.57 ! [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))) ). % 187.68/187.57 % 187.68/187.57 fof(fact_finite__greaterThanAtMost__int,axiom, % 187.68/187.57 ! [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))) ). % 187.68/187.57 % 187.68/187.57 fof(fact_greaterThanAtMost__empty,axiom, % 187.68/187.57 ! [V_k_2,V_l_2,T_a] : % 187.68/187.57 ( class_Orderings_Oorder(T_a) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_k_2)) % 187.68/187.57 => 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)) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_greaterThanAtMost__empty__iff,axiom, % 187.68/187.57 ! [V_l_2,V_k_2,T_a] : % 187.68/187.57 ( class_Orderings_Oorder(T_a) % 187.68/187.57 => ( 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)) % 187.68/187.57 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_k_2),V_l_2)) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_greaterThanAtMost__empty__iff2,axiom, % 187.68/187.57 ! [V_l_2,V_k_2,T_a] : % 187.68/187.57 ( class_Orderings_Oorder(T_a) % 187.68/187.57 => ( 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) % 187.68/187.57 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_k_2),V_l_2)) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_ivl__disj__un_I20_J,axiom, % 187.68/187.57 ! [V_u_2,V_m_2,V_l_2,T_a] : % 187.68/187.57 ( class_Orderings_Olinorder(T_a) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_m_2)) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_m_2),V_u_2)) % 187.68/187.57 => 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) ) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_card__greaterThanAtMost,axiom, % 187.68/187.57 ! [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) ). % 187.68/187.57 % 187.68/187.57 fof(fact_card__greaterThanAtMost__int,axiom, % 187.68/187.57 ! [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)) ). % 187.68/187.57 % 187.68/187.57 fof(fact_ivl__disj__un_I16_J,axiom, % 187.68/187.57 ! [V_u_2,V_m_2,V_l_2,T_a] : % 187.68/187.57 ( class_Orderings_Olinorder(T_a) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_m_2)) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_m_2),V_u_2)) % 187.68/187.57 => 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) ) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_setprod__mono__one__left,axiom, % 187.68/187.57 ! [V_f_2,V_S_2,V_T_2,T_a,T_b] : % 187.68/187.57 ( class_Groups_Ocomm__monoid__mult(T_b) % 187.68/187.57 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2)) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2)) % 187.68/187.57 => ( ! [B_x] : % 187.68/187.57 ( 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))) % 187.68/187.57 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_b) ) % 187.68/187.57 => 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) ) ) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_card__Pow,axiom, % 187.68/187.57 ! [V_A_2,T_a] : % 187.68/187.57 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.57 => 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)) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_ivl__disj__un_I19_J,axiom, % 187.68/187.57 ! [V_u_2,V_m_2,V_l_2,T_a] : % 187.68/187.57 ( class_Orderings_Olinorder(T_a) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_l_2),V_m_2)) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_m_2),V_u_2)) % 187.68/187.57 => 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) ) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_Least__mono,axiom, % 187.68/187.57 ! [V_S_2,V_f_2,T_a,T_b] : % 187.68/187.57 ( ( class_Orderings_Oorder(T_b) % 187.68/187.57 & class_Orderings_Oorder(T_a) ) % 187.68/187.57 => ( c_Orderings_Oorder__class_Omono(T_a,T_b,V_f_2) % 187.68/187.57 => ( ? [B_x] : % 187.68/187.57 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2)) % 187.68/187.57 & ! [B_xa] : % 187.68/187.57 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_S_2)) % 187.68/187.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_x),B_xa)) ) ) % 187.68/187.57 => c_Orderings_Oord__class_OLeast(T_b,hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_S_2))) = hAPP(V_f_2,c_Orderings_Oord__class_OLeast(T_a,hAPP(hAPP(c_COMBC(T_a,tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool),c_member(T_a)),V_S_2))) ) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_finite__atLeastAtMost,axiom, % 187.68/187.57 ! [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))) ). % 187.68/187.57 % 187.68/187.57 fof(fact_finite__atLeastAtMost__int,axiom, % 187.68/187.57 ! [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))) ). % 187.68/187.57 % 187.68/187.57 fof(fact_PowI,axiom, % 187.68/187.57 ! [V_B_2,V_A_2,T_a] : % 187.68/187.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 187.68/187.57 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_a),V_B_2))) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_atLeastSucAtMost__greaterThanAtMost,axiom, % 187.68/187.57 ! [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) ). % 187.68/187.57 % 187.68/187.57 fof(fact_Pow__insert,axiom, % 187.68/187.57 ! [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))) ). % 187.68/187.57 % 187.68/187.57 fof(fact_Cantors__paradox,axiom, % 187.68/187.57 ! [V_A_2,T_a] : % 187.68/187.57 ~ ? [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) ). % 187.68/187.57 % 187.68/187.57 fof(fact_finite__Pow__iff,axiom, % 187.68/187.57 ! [V_A_2,T_a] : % 187.68/187.57 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_OPow(T_a),V_A_2))) % 187.68/187.57 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_PowD,axiom, % 187.68/187.57 ! [V_B_2,V_A_2,T_a] : % 187.68/187.57 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_a),V_B_2))) % 187.68/187.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_Pow__mono,axiom, % 187.68/187.57 ! [V_B_2,V_A_2,T_a] : % 187.68/187.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 187.68/187.57 => 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))) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_Pow__iff,axiom, % 187.68/187.57 ! [V_B_2,V_A_2,T_a] : % 187.68/187.57 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_a),V_B_2))) % 187.68/187.57 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_image__Pow__surj,axiom, % 187.68/187.57 ! [V_B_2,V_A_2,V_f_2,T_a,T_b] : % 187.68/187.57 ( hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2) = V_B_2 % 187.68/187.57 => 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) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_Un__Pow__subset,axiom, % 187.68/187.57 ! [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)))) ). % 187.68/187.57 % 187.68/187.57 fof(fact_Pow__not__empty,axiom, % 187.68/187.57 ! [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)) ). % 187.68/187.57 % 187.68/187.57 fof(fact_Pow__top,axiom, % 187.68/187.57 ! [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))) ). % 187.68/187.57 % 187.68/187.57 fof(fact_Pow__bottom,axiom, % 187.68/187.57 ! [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))) ). % 187.68/187.57 % 187.68/187.57 fof(fact_Pow__empty,axiom, % 187.68/187.57 ! [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))) ). % 187.68/187.57 % 187.68/187.57 fof(fact_image__Suc__atLeastAtMost,axiom, % 187.68/187.57 ! [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)) ). % 187.68/187.57 % 187.68/187.57 fof(fact_image__add__atLeastAtMost,axiom, % 187.68/187.57 ! [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)) ). % 187.68/187.57 % 187.68/187.57 fof(fact_monoD,axiom, % 187.68/187.57 ! [V_y_2,V_x_2,V_f_2,T_a,T_b] : % 187.68/187.57 ( ( class_Orderings_Oorder(T_b) % 187.68/187.57 & class_Orderings_Oorder(T_a) ) % 187.68/187.57 => ( c_Orderings_Oorder__class_Omono(T_a,T_b,V_f_2) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 187.68/187.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,V_x_2)),hAPP(V_f_2,V_y_2))) ) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_mono__Suc,axiom, % 187.68/187.57 c_Orderings_Oorder__class_Omono(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc) ). % 187.68/187.57 % 187.68/187.57 fof(fact_SetInterval_Otransfer__nat__int__set__functions_I2_J,axiom, % 187.68/187.57 ! [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))) ). % 187.68/187.57 % 187.68/187.57 fof(fact_min__of__mono,axiom, % 187.68/187.57 ! [V_n_2,V_m_2,V_f_2,T_a,T_b] : % 187.68/187.57 ( ( class_Orderings_Olinorder(T_b) % 187.68/187.57 & class_Orderings_Olinorder(T_a) ) % 187.68/187.57 => ( c_Orderings_Oorder__class_Omono(T_a,T_b,V_f_2) % 187.68/187.57 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_b),hAPP(V_f_2,V_m_2)),hAPP(V_f_2,V_n_2)) = hAPP(V_f_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_m_2),V_n_2)) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_max__of__mono,axiom, % 187.68/187.57 ! [V_n_2,V_m_2,V_f_2,T_a,T_b] : % 187.68/187.57 ( ( class_Orderings_Olinorder(T_b) % 187.68/187.57 & class_Orderings_Olinorder(T_a) ) % 187.68/187.57 => ( c_Orderings_Oorder__class_Omono(T_a,T_b,V_f_2) % 187.68/187.57 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_b),hAPP(V_f_2,V_m_2)),hAPP(V_f_2,V_n_2)) = hAPP(V_f_2,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_m_2),V_n_2)) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_atLeastPlusOneAtMost__greaterThanAtMost__int,axiom, % 187.68/187.57 ! [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) ). % 187.68/187.57 % 187.68/187.57 fof(fact_SetInterval_Otransfer__int__nat__set__functions,axiom, % 187.68/187.57 ! [V_n_2,V_m_2] : % 187.68/187.57 ( c_Nat__Transfer_Ois__nat(V_m_2) % 187.68/187.57 => ( c_Nat__Transfer_Ois__nat(V_n_2) % 187.68/187.57 => 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))) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_atLeastAtMostSuc__conv,axiom, % 187.68/187.57 ! [V_n_2,V_m_2] : % 187.68/187.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) % 187.68/187.57 => 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)) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_SetInterval_Otransfer__int__nat__set__function__closures,axiom, % 187.68/187.57 ! [V_y_2,V_x_2] : % 187.68/187.57 ( c_Nat__Transfer_Ois__nat(V_x_2) % 187.68/187.57 => c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_x_2,V_y_2)) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_atLeastatMost__empty__iff2,axiom, % 187.68/187.57 ! [V_b_2,V_a_2,T_a] : % 187.68/187.57 ( class_Orderings_Oorder(T_a) % 187.68/187.57 => ( 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) % 187.68/187.57 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_atLeastatMost__empty__iff,axiom, % 187.68/187.57 ! [V_b_2,V_a_2,T_a] : % 187.68/187.57 ( class_Orderings_Oorder(T_a) % 187.68/187.57 => ( 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)) % 187.68/187.57 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_atLeastatMost__empty,axiom, % 187.68/187.57 ! [V_a_2,V_b_2,T_a] : % 187.68/187.57 ( class_Orderings_Oorder(T_a) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),V_a_2)) % 187.68/187.57 => 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)) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_atLeastatMost__subset__iff,axiom, % 187.68/187.57 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] : % 187.68/187.57 ( class_Orderings_Oorder(T_a) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_c_2,V_d_2))) % 187.68/187.57 <=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) % 187.68/187.57 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c_2),V_a_2)) % 187.68/187.57 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_d_2)) ) ) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_atLeastAtMost__singleton_H,axiom, % 187.68/187.57 ! [V_b_2,V_a_2,T_a] : % 187.68/187.57 ( class_Orderings_Oorder(T_a) % 187.68/187.57 => ( V_a_2 = V_b_2 % 187.68/187.57 => 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))) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_atLeastAtMost__singleton__iff,axiom, % 187.68/187.57 ! [V_c_2,V_b_2,V_a_2,T_a] : % 187.68/187.57 ( class_Orderings_Oorder(T_a) % 187.68/187.57 => ( c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2) = hAPP(hAPP(c_Set_Oinsert(T_a),V_c_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) % 187.68/187.57 <=> ( V_a_2 = V_b_2 % 187.68/187.57 & V_b_2 = V_c_2 ) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_atLeastAtMost__singleton,axiom, % 187.68/187.57 ! [V_a_2,T_a] : % 187.68/187.57 ( class_Orderings_Oorder(T_a) % 187.68/187.57 => 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))) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_image__uminus__atLeastAtMost,axiom, % 187.68/187.57 ! [V_y_2,V_x_2,T_a] : % 187.68/187.57 ( class_Groups_Oordered__ab__group__add(T_a) % 187.68/187.57 => 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)) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_mono__Un,axiom, % 187.68/187.57 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 187.68/187.57 ( c_Orderings_Oorder__class_Omono(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),V_f_2) % 187.68/187.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_f_2,V_A_2)),hAPP(V_f_2,V_B_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)))) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_image__Pow__mono,axiom, % 187.68/187.57 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 187.68/187.57 ( 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)) % 187.68/187.57 => 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))) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_mono__iff__le__Suc,axiom, % 187.68/187.57 ! [V_f_2,T_a] : % 187.68/187.57 ( class_Orderings_Oorder(T_a) % 187.68/187.57 => ( c_Orderings_Oorder__class_Omono(tc_Nat_Onat,T_a,V_f_2) % 187.68/187.57 <=> ! [B_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(V_f_2,B_n)),hAPP(V_f_2,hAPP(c_Nat_OSuc,B_n)))) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_mono__sup,axiom, % 187.68/187.57 ! [V_B_2,V_A_2,V_f_2,T_a,T_b] : % 187.68/187.57 ( ( class_Lattices_Osemilattice__sup(T_b) % 187.68/187.57 & class_Lattices_Osemilattice__sup(T_a) ) % 187.68/187.57 => ( c_Orderings_Oorder__class_Omono(T_a,T_b,V_f_2) % 187.68/187.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),hAPP(V_f_2,V_A_2)),hAPP(V_f_2,V_B_2))),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_A_2),V_B_2)))) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_SetInterval_Otransfer__nat__int__set__function__closures,axiom, % 187.68/187.57 ! [V_y_2,V_x_2] : % 187.68/187.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) % 187.68/187.57 => c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_x_2,V_y_2)) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_card__atLeastAtMost,axiom, % 187.68/187.57 ! [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) ). % 187.68/187.57 % 187.68/187.57 fof(fact_atLeastatMost__psubset__iff,axiom, % 187.68/187.57 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] : % 187.68/187.57 ( class_Orderings_Oorder(T_a) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_c_2,V_d_2))) % 187.68/187.57 <=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) % 187.68/187.57 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c_2),V_a_2)) % 187.68/187.57 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_d_2)) % 187.68/187.57 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),V_a_2)) % 187.68/187.57 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),V_d_2)) ) ) ) % 187.68/187.57 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c_2),V_d_2)) ) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_ivl__disj__un_I22_J,axiom, % 187.68/187.57 ! [V_u_2,V_m_2,V_l_2,T_a] : % 187.68/187.57 ( class_Orderings_Olinorder(T_a) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_m_2)) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_m_2),V_u_2)) % 187.68/187.57 => 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) ) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_min__max_Omono__sup,axiom, % 187.68/187.57 ! [V_B_2,V_A_2,V_f_2,T_a,T_b] : % 187.68/187.57 ( ( class_Lattices_Osemilattice__sup(T_b) % 187.68/187.57 & class_Orderings_Olinorder(T_a) ) % 187.68/187.57 => ( c_Orderings_Oorder__class_Omono(T_a,T_b,V_f_2) % 187.68/187.57 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_b),hAPP(V_f_2,V_A_2)),hAPP(V_f_2,V_B_2))),hAPP(V_f_2,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_A_2),V_B_2)))) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_simp__from__to,axiom, % 187.68/187.57 ! [V_i_2,V_j_2] : % 187.68/187.57 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j_2),V_i_2)) % 187.68/187.57 => 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)) ) % 187.68/187.57 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j_2),V_i_2)) % 187.68/187.57 => 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)) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_card__atLeastAtMost__int,axiom, % 187.68/187.57 ! [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))) ). % 187.68/187.57 % 187.68/187.57 fof(fact_ivl__disj__un_I5_J,axiom, % 187.68/187.57 ! [V_u_2,V_l_2,T_a] : % 187.68/187.57 ( class_Orderings_Olinorder(T_a) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2)) % 187.68/187.57 => 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) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_aset_I6_J,axiom, % 187.68/187.57 ! [V_A_2,V_t_2,V_D_2] : % 187.68/187.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 187.68/187.57 => ( 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)) % 187.68/187.57 => ! [B_x] : % 187.68/187.57 ( ! [B_xa] : % 187.68/187.57 ( 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))) % 187.68/187.57 => ! [B_xb] : % 187.68/187.57 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) % 187.68/187.57 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) ) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_x),V_t_2)) % 187.68/187.57 => 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)) ) ) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_bset_I8_J,axiom, % 187.68/187.57 ! [V_B_2,V_t_2,V_D_2] : % 187.68/187.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 187.68/187.57 => ( 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)) % 187.68/187.57 => ! [B_x] : % 187.68/187.57 ( ! [B_xa] : % 187.68/187.57 ( 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))) % 187.68/187.57 => ! [B_xb] : % 187.68/187.57 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) % 187.68/187.57 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) ) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),B_x)) % 187.68/187.57 => 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))) ) ) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_bset_I3_J,axiom, % 187.68/187.57 ! [V_B_2,V_t_2,V_D_2] : % 187.68/187.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 187.68/187.57 => ( 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)) % 187.68/187.57 => ( ! [B_x] : % 187.68/187.57 ( 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))) % 187.68/187.57 => ! [B_xa] : % 187.68/187.57 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),V_B_2)) % 187.68/187.57 => V_t_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xa),B_x) ) ) % 187.68/187.57 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_t_2),V_D_2) = V_t_2 ) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_aset_I3_J,axiom, % 187.68/187.57 ! [V_A_2,V_t_2,V_D_2] : % 187.68/187.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 187.68/187.57 => ( 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)) % 187.68/187.57 => ( ! [B_x] : % 187.68/187.57 ( 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))) % 187.68/187.57 => ! [B_xa] : % 187.68/187.57 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),V_A_2)) % 187.68/187.57 => V_t_2 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xa),B_x) ) ) % 187.68/187.57 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_t_2),V_D_2) = V_t_2 ) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_all__nat__less,axiom, % 187.68/187.57 ! [V_P_2,V_n_2] : % 187.68/187.57 ( ! [B_m] : % 187.68/187.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2)) % 187.68/187.57 => hBOOL(hAPP(V_P_2,B_m)) ) % 187.68/187.57 <=> ! [B_x] : % 187.68/187.57 ( 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))) % 187.68/187.57 => hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_ex__nat__less,axiom, % 187.68/187.57 ! [V_P_2,V_n_2] : % 187.68/187.57 ( ? [B_m] : % 187.68/187.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2)) % 187.68/187.57 & hBOOL(hAPP(V_P_2,B_m)) ) % 187.68/187.57 <=> ? [B_x] : % 187.68/187.57 ( 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))) % 187.68/187.57 & hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_Powp__Pow__eq,axiom, % 187.68/187.57 ! [V_x_2,V_A_2,T_a] : % 187.68/187.57 ( 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)) % 187.68/187.57 <=> hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_x_2),hAPP(c_Set_OPow(T_a),V_A_2))) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_coinduct3__mono__lemma,axiom, % 187.68/187.57 ! [V_B_2,V_X_2,V_f_2,T_b,T_a] : % 187.68/187.57 ( class_Orderings_Oorder(T_a) % 187.68/187.57 => ( c_Orderings_Oorder__class_Omono(T_a,tc_fun(T_b,tc_HOL_Obool),V_f_2) % 187.68/187.57 => c_Orderings_Oorder__class_Omono(T_a,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(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))),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_f_2)),V_X_2))),V_B_2)) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_Powp__mono,axiom, % 187.68/187.57 ! [V_B_2,V_A_2,T_a] : % 187.68/187.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 187.68/187.57 => 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))) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_aset_I5_J,axiom, % 187.68/187.57 ! [V_A_2,V_t_2,V_D_2] : % 187.68/187.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_A_2)) % 187.68/187.57 => ! [B_x] : % 187.68/187.57 ( ! [B_xa] : % 187.68/187.57 ( 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))) % 187.68/187.57 => ! [B_xb] : % 187.68/187.57 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) % 187.68/187.57 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) ) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_x),V_t_2)) % 187.68/187.57 => 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)) ) ) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_bset_I7_J,axiom, % 187.68/187.57 ! [V_B_2,V_t_2,V_D_2] : % 187.68/187.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_B_2)) % 187.68/187.57 => ! [B_x] : % 187.68/187.57 ( ! [B_xa] : % 187.68/187.57 ( 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))) % 187.68/187.57 => ! [B_xb] : % 187.68/187.57 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) % 187.68/187.57 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) ) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),B_x)) % 187.68/187.57 => 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))) ) ) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_bset_I4_J,axiom, % 187.68/187.57 ! [V_B_2,V_t_2,V_D_2] : % 187.68/187.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_B_2)) % 187.68/187.57 => ! [B_x] : % 187.68/187.57 ( ! [B_xa] : % 187.68/187.57 ( 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))) % 187.68/187.57 => ! [B_xb] : % 187.68/187.57 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) % 187.68/187.57 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) ) % 187.68/187.57 => ( B_x != V_t_2 % 187.68/187.57 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2) != V_t_2 ) ) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_aset_I4_J,axiom, % 187.68/187.57 ! [V_A_2,V_t_2,V_D_2] : % 187.68/187.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_A_2)) % 187.68/187.57 => ! [B_x] : % 187.68/187.57 ( ! [B_xa] : % 187.68/187.57 ( 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))) % 187.68/187.57 => ! [B_xb] : % 187.68/187.57 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) % 187.68/187.57 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) ) % 187.68/187.57 => ( B_x != V_t_2 % 187.68/187.57 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2) != V_t_2 ) ) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_aset_I8_J,axiom, % 187.68/187.57 ! [V_t_2,V_A_2,V_D_2] : % 187.68/187.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 187.68/187.57 => ! [B_x] : % 187.68/187.57 ( ! [B_xa] : % 187.68/187.57 ( 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))) % 187.68/187.57 => ! [B_xb] : % 187.68/187.57 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) % 187.68/187.57 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) ) % 187.68/187.57 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),B_x)) % 187.68/187.57 => 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))) ) ) ) ). % 187.68/187.57 % 187.68/187.57 fof(fact_bset_I6_J,axiom, % 187.68/187.57 ! [V_t_2,V_B_2,V_D_2] : % 187.68/187.57 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 187.68/187.57 => ! [B_x] : % 187.68/187.57 ( ! [B_xa] : % 187.68/187.57 ( 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))) % 187.68/187.57 => ! [B_xb] : % 187.68/187.57 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) % 187.68/187.58 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) ) % 187.68/187.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_x),V_t_2)) % 187.68/187.58 => 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)) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_periodic__finite__ex,axiom, % 187.68/187.58 ! [V_P_2,V_d_2] : % 187.68/187.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2)) % 187.68/187.58 => ( ! [B_x,B_k] : % 187.68/187.58 ( hBOOL(hAPP(V_P_2,B_x)) % 187.68/187.58 <=> 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)))) ) % 187.68/187.58 => ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) % 187.68/187.58 <=> ? [B_x] : % 187.68/187.58 ( 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))) % 187.68/187.58 & hBOOL(hAPP(V_P_2,B_x)) ) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_aset_I7_J,axiom, % 187.68/187.58 ! [V_t_2,V_A_2,V_D_2] : % 187.68/187.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 187.68/187.58 => ! [B_x] : % 187.68/187.58 ( ! [B_xa] : % 187.68/187.58 ( 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))) % 187.68/187.58 => ! [B_xb] : % 187.68/187.58 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) % 187.68/187.58 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) ) % 187.68/187.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),B_x)) % 187.68/187.58 => 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))) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_bset_I5_J,axiom, % 187.68/187.58 ! [V_t_2,V_B_2,V_D_2] : % 187.68/187.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 187.68/187.58 => ! [B_x] : % 187.68/187.58 ( ! [B_xa] : % 187.68/187.58 ( 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))) % 187.68/187.58 => ! [B_xb] : % 187.68/187.58 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) % 187.68/187.58 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) ) % 187.68/187.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_x),V_t_2)) % 187.68/187.58 => 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)) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_image__minus__const__atLeastLessThan__nat,axiom, % 187.68/187.58 ! [V_x_2,V_y_2,V_c_2] : % 187.68/187.58 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_c_2),V_y_2)) % 187.68/187.58 => hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_c_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_x_2),V_y_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_x_2),V_c_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_y_2),V_c_2)) ) % 187.68/187.58 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_c_2),V_y_2)) % 187.68/187.58 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) % 187.68/187.58 => hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_c_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_x_2),V_y_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ) % 187.68/187.58 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) % 187.68/187.58 => hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_c_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_x_2),V_y_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_SetInterval_Otransfer__nat__int__set__functions_I1_J,axiom, % 187.68/187.58 ! [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))) ). % 187.68/187.58 % 187.68/187.58 fof(fact_ivl__disj__un_I18_J,axiom, % 187.68/187.58 ! [V_u_2,V_m_2,V_l_2,T_a] : % 187.68/187.58 ( class_Orderings_Olinorder(T_a) % 187.68/187.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_m_2)) % 187.68/187.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_m_2),V_u_2)) % 187.68/187.58 => 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) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_finite__atLeastLessThan__int,axiom, % 187.68/187.58 ! [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))) ). % 187.68/187.58 % 187.68/187.58 fof(fact_finite__atLeastLessThan,axiom, % 187.68/187.58 ! [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))) ). % 187.68/187.58 % 187.68/187.58 fof(fact_finite__atMost,axiom, % 187.68/187.58 ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_k_2))) ). % 187.68/187.58 % 187.68/187.58 fof(fact_atLeastLessThan__inj_I2_J,axiom, % 187.68/187.58 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] : % 187.68/187.58 ( class_Orderings_Olinorder(T_a) % 187.68/187.58 => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2),V_b_2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_c_2),V_d_2) % 187.68/187.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) % 187.68/187.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),V_d_2)) % 187.68/187.58 => V_b_2 = V_d_2 ) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_atLeastLessThan__inj_I1_J,axiom, % 187.68/187.58 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] : % 187.68/187.58 ( class_Orderings_Olinorder(T_a) % 187.68/187.58 => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2),V_b_2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_c_2),V_d_2) % 187.68/187.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) % 187.68/187.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),V_d_2)) % 187.68/187.58 => V_a_2 = V_c_2 ) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_atLeastLessThan__eq__iff,axiom, % 187.68/187.58 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] : % 187.68/187.58 ( class_Orderings_Olinorder(T_a) % 187.68/187.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) % 187.68/187.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c_2),V_d_2)) % 187.68/187.58 => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2),V_b_2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_c_2),V_d_2) % 187.68/187.58 <=> ( V_a_2 = V_c_2 % 187.68/187.58 & V_b_2 = V_d_2 ) ) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_atMost__eq__iff,axiom, % 187.68/187.58 ! [V_y_2,V_x_2,T_a] : % 187.68/187.58 ( class_Orderings_Olinorder(T_a) % 187.68/187.58 => ( hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_x_2) = hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_y_2) % 187.68/187.58 <=> V_x_2 = V_y_2 ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_ex__nat__less__eq,axiom, % 187.68/187.58 ! [V_P_2,V_n_2] : % 187.68/187.58 ( ? [B_m] : % 187.68/187.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2)) % 187.68/187.58 & hBOOL(hAPP(V_P_2,B_m)) ) % 187.68/187.58 <=> ? [B_x] : % 187.68/187.58 ( 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))) % 187.68/187.58 & hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_all__nat__less__eq,axiom, % 187.68/187.58 ! [V_P_2,V_n_2] : % 187.68/187.58 ( ! [B_m] : % 187.68/187.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2)) % 187.68/187.58 => hBOOL(hAPP(V_P_2,B_m)) ) % 187.68/187.58 <=> ! [B_x] : % 187.68/187.58 ( 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))) % 187.68/187.58 => hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_atLeastLessThanSuc__atLeastAtMost,axiom, % 187.68/187.58 ! [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) ). % 187.68/187.58 % 187.68/187.58 fof(fact_atLeastLessThan0,axiom, % 187.68/187.58 ! [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)) ). % 187.68/187.58 % 187.68/187.58 fof(fact_card__atLeastLessThan,axiom, % 187.68/187.58 ! [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) ). % 187.68/187.58 % 187.68/187.58 fof(fact_image__Suc__atLeastLessThan,axiom, % 187.68/187.58 ! [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)) ). % 187.68/187.58 % 187.68/187.58 fof(fact_atLeastLessThan__empty,axiom, % 187.68/187.58 ! [V_a_2,V_b_2,T_a] : % 187.68/187.58 ( class_Orderings_Oorder(T_a) % 187.68/187.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_a_2)) % 187.68/187.58 => 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)) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_atLeastLessThan__empty__iff,axiom, % 187.68/187.58 ! [V_b_2,V_a_2,T_a] : % 187.68/187.58 ( class_Orderings_Oorder(T_a) % 187.68/187.58 => ( 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)) % 187.68/187.58 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_atLeastLessThan__empty__iff2,axiom, % 187.68/187.58 ! [V_b_2,V_a_2,T_a] : % 187.68/187.58 ( class_Orderings_Oorder(T_a) % 187.68/187.58 => ( 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) % 187.68/187.58 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_atLeastLessThan__subset__iff,axiom, % 187.68/187.58 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] : % 187.68/187.58 ( class_Orderings_Olinorder(T_a) % 187.68/187.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2),V_b_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_c_2),V_d_2))) % 187.68/187.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_a_2)) % 187.68/187.58 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c_2),V_a_2)) % 187.68/187.58 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_d_2)) ) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_ivl__disj__un_I17_J,axiom, % 187.68/187.58 ! [V_u_2,V_m_2,V_l_2,T_a] : % 187.68/187.58 ( class_Orderings_Olinorder(T_a) % 187.68/187.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_m_2)) % 187.68/187.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_m_2),V_u_2)) % 187.68/187.58 => 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) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_ivl__diff,axiom, % 187.68/187.58 ! [V_m_2,V_n_2,V_i_2,T_a] : % 187.68/187.58 ( class_Orderings_Olinorder(T_a) % 187.68/187.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_i_2),V_n_2)) % 187.68/187.58 => 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) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_atLeastSucLessThan__greaterThanLessThan,axiom, % 187.68/187.58 ! [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) ). % 187.68/187.58 % 187.68/187.58 fof(fact_atLeast0AtMost,axiom, % 187.68/187.58 ! [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) ). % 187.68/187.58 % 187.68/187.58 fof(fact_image__add__atLeastLessThan,axiom, % 187.68/187.58 ! [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)) ). % 187.68/187.58 % 187.68/187.58 fof(fact_finite__atLeastZeroLessThan__int,axiom, % 187.68/187.58 ! [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))) ). % 187.68/187.58 % 187.68/187.58 fof(fact_card__atMost,axiom, % 187.68/187.58 ! [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) ). % 187.68/187.58 % 187.68/187.58 fof(fact_atMost__Suc,axiom, % 187.68/187.58 ! [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)) ). % 187.68/187.58 % 187.68/187.58 fof(fact_atMost__iff,axiom, % 187.68/187.58 ! [V_k_2,V_i_2,T_a] : % 187.68/187.58 ( class_Orderings_Oord(T_a) % 187.68/187.58 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_k_2))) % 187.68/187.58 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_i_2),V_k_2)) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_atMost__subset__iff,axiom, % 187.68/187.58 ! [V_y_2,V_x_2,T_a] : % 187.68/187.58 ( class_Orderings_Oorder(T_a) % 187.68/187.58 => ( 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))) % 187.68/187.58 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_atLeastLessThan__singleton,axiom, % 187.68/187.58 ! [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))) ). % 187.68/187.58 % 187.68/187.58 fof(fact_atLeastLessThanPlusOne__atLeastAtMost__int,axiom, % 187.68/187.58 ! [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) ). % 187.68/187.58 % 187.68/187.58 fof(fact_ivl__disj__un_I21_J,axiom, % 187.68/187.58 ! [V_u_2,V_m_2,V_l_2,T_a] : % 187.68/187.58 ( class_Orderings_Olinorder(T_a) % 187.68/187.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_m_2)) % 187.68/187.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_m_2),V_u_2)) % 187.68/187.58 => 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) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_atLeastLessThan__add__Un,axiom, % 187.68/187.58 ! [V_k_2,V_j_2,V_i_2] : % 187.68/187.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) % 187.68/187.58 => 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))) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_subset__card__intvl__is__intvl,axiom, % 187.68/187.58 ! [V_k_2,V_A_2] : % 187.68/187.58 ( 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))))) % 187.68/187.58 => 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))) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_image__uminus__atLeastLessThan,axiom, % 187.68/187.58 ! [V_y_2,V_x_2,T_a] : % 187.68/187.58 ( class_Groups_Oordered__ab__group__add(T_a) % 187.68/187.58 => 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)) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_image__uminus__greaterThanAtMost,axiom, % 187.68/187.58 ! [V_y_2,V_x_2,T_a] : % 187.68/187.58 ( class_Groups_Oordered__ab__group__add(T_a) % 187.68/187.58 => 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)) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_image__add__int__atLeastLessThan,axiom, % 187.68/187.58 ! [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) ). % 187.68/187.58 % 187.68/187.58 fof(fact_card__atLeastZeroLessThan__int,axiom, % 187.68/187.58 ! [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) ). % 187.68/187.58 % 187.68/187.58 fof(fact_card__atLeastLessThan__int,axiom, % 187.68/187.58 ! [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)) ). % 187.68/187.58 % 187.68/187.58 fof(fact_atLeastPlusOneLessThan__greaterThanLessThan__int,axiom, % 187.68/187.58 ! [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) ). % 187.68/187.58 % 187.68/187.58 fof(fact_atLeastLessThanSuc,axiom, % 187.68/187.58 ! [V_n_2,V_m_2] : % 187.68/187.58 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 187.68/187.58 => 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)) ) % 187.68/187.58 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 187.68/187.58 => 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)) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_atMost__0,axiom, % 187.68/187.58 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))) ). % 187.68/187.58 % 187.68/187.58 fof(fact_ivl__disj__un_I9_J,axiom, % 187.68/187.58 ! [V_u_2,V_l_2,T_a] : % 187.68/187.58 ( class_Orderings_Olinorder(T_a) % 187.68/187.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2)) % 187.68/187.58 => 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) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_ivl__disj__un_I15_J,axiom, % 187.68/187.58 ! [V_u_2,V_m_2,V_l_2,T_a] : % 187.68/187.58 ( class_Orderings_Olinorder(T_a) % 187.68/187.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_l_2),V_m_2)) % 187.68/187.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_m_2),V_u_2)) % 187.68/187.58 => 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) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_ivl__disj__un_I6_J,axiom, % 187.68/187.58 ! [V_u_2,V_l_2,T_a] : % 187.68/187.58 ( class_Orderings_Olinorder(T_a) % 187.68/187.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2)) % 187.68/187.58 => 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) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_ivl__disj__un_I3_J,axiom, % 187.68/187.58 ! [V_u_2,V_l_2,T_a] : % 187.68/187.58 ( class_Orderings_Olinorder(T_a) % 187.68/187.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_l_2),V_u_2)) % 187.68/187.58 => 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) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_ivl__disj__un_I7_J,axiom, % 187.68/187.58 ! [V_u_2,V_l_2,T_a] : % 187.68/187.58 ( class_Orderings_Olinorder(T_a) % 187.68/187.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_l_2),V_u_2)) % 187.68/187.58 => 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) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_image__atLeastZeroLessThan__int,axiom, % 187.68/187.58 ! [V_u_2] : % 187.68/187.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_u_2)) % 187.68/187.58 => 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))) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_ivl__disj__un_I10_J,axiom, % 187.68/187.58 ! [V_u_2,V_l_2,T_a] : % 187.68/187.58 ( class_Orderings_Olinorder(T_a) % 187.68/187.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2)) % 187.68/187.58 => 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) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_equiv__intrel__iff,axiom, % 187.68/187.58 ! [V_y_2,V_x_2] : % 187.68/187.58 ( 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)))) % 187.68/187.58 <=> 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)) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_finite__lessThan,axiom, % 187.68/187.58 ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_k_2))) ). % 187.68/187.58 % 187.68/187.58 fof(fact_Image__Un,axiom, % 187.68/187.58 ! [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)) ). % 187.68/187.58 % 187.68/187.58 fof(fact_Image__empty,axiom, % 187.68/187.58 ! [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)) ). % 187.68/187.58 % 187.68/187.58 fof(fact_lessThan__eq__iff,axiom, % 187.68/187.58 ! [V_y_2,V_x_2,T_a] : % 187.68/187.58 ( class_Orderings_Olinorder(T_a) % 187.68/187.58 => ( hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_x_2) = hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_y_2) % 187.68/187.58 <=> V_x_2 = V_y_2 ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_card__lessThan,axiom, % 187.68/187.58 ! [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 ). % 187.68/187.58 % 187.68/187.58 fof(fact_Image__mono,axiom, % 187.68/187.58 ! [V_A_2,V_A_H_2,V_r_2,V_r_H_2,T_b,T_a] : % 187.68/187.58 ( 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)) % 187.68/187.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_H_2),V_A_2)) % 187.68/187.58 => 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))) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_Un__Image,axiom, % 187.68/187.58 ! [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)) ). % 187.68/187.58 % 187.68/187.58 fof(fact_atLeast0LessThan,axiom, % 187.68/187.58 ! [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) ). % 187.68/187.58 % 187.68/187.58 fof(fact_lessThan__0,axiom, % 187.68/187.58 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)) ). % 187.68/187.58 % 187.68/187.58 fof(fact_lessThan__Suc,axiom, % 187.68/187.58 ! [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)) ). % 187.68/187.58 % 187.68/187.58 fof(fact_lessThan__Suc__atMost,axiom, % 187.68/187.58 ! [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) ). % 187.68/187.58 % 187.68/187.58 fof(fact_lessThan__iff,axiom, % 187.68/187.58 ! [V_k_2,V_i_2,T_a] : % 187.68/187.58 ( class_Orderings_Oord(T_a) % 187.68/187.58 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_k_2))) % 187.68/187.58 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_i_2),V_k_2)) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_lessThan__subset__iff,axiom, % 187.68/187.58 ! [V_y_2,V_x_2,T_a] : % 187.68/187.58 ( class_Orderings_Olinorder(T_a) % 187.68/187.58 => ( 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))) % 187.68/187.58 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_rev__ImageI,axiom, % 187.68/187.58 ! [V_r_2,V_b_2,T_b,V_A_2,V_a_2,T_a] : % 187.68/187.58 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 187.68/187.58 => ( 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)) % 187.68/187.58 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_OImage(T_a,T_b,V_r_2),V_A_2))) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_Image__iff,axiom, % 187.68/187.58 ! [V_A_2,V_r_2,T_b,V_b_2,T_a] : % 187.68/187.58 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(c_Relation_OImage(T_b,T_a,V_r_2),V_A_2))) % 187.68/187.58 <=> ? [B_x] : % 187.68/187.58 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 187.68/187.58 & 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)) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_lessThan__strict__subset__iff,axiom, % 187.68/187.58 ! [V_n_2,V_m_2,T_a] : % 187.68/187.58 ( class_Orderings_Olinorder(T_a) % 187.68/187.58 => ( 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))) % 187.68/187.58 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_m_2),V_n_2)) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_single__Diff__lessThan,axiom, % 187.68/187.58 ! [V_k_2,T_a] : % 187.68/187.58 ( class_Orderings_Oorder(T_a) % 187.68/187.58 => 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))) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_ivl__disj__un_I8_J,axiom, % 187.68/187.58 ! [V_u_2,V_l_2,T_a] : % 187.68/187.58 ( class_Orderings_Olinorder(T_a) % 187.68/187.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2)) % 187.68/187.58 => 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) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_Image__singleton__iff,axiom, % 187.68/187.58 ! [V_a_2,V_r_2,T_b,V_b_2,T_a] : % 187.68/187.58 ( 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)))))) % 187.68/187.58 <=> 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)) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_lessThan__Suc__eq__insert__0,axiom, % 187.68/187.58 ! [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))) ). % 187.68/187.58 % 187.68/187.58 fof(fact_ivl__disj__un_I2_J,axiom, % 187.68/187.58 ! [V_u_2,T_a] : % 187.68/187.58 ( class_Orderings_Olinorder(T_a) % 187.68/187.58 => 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) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_of__int,axiom, % 187.68/187.58 ! [V_j_2,V_i_2,T_a] : % 187.68/187.58 ( class_Rings_Oring__1(T_a) % 187.68/187.58 => 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)) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_One__int__def,axiom, % 187.68/187.58 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))))) ). % 187.68/187.58 % 187.68/187.58 fof(fact_mult,axiom, % 187.68/187.58 ! [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))))) ). % 187.68/187.58 % 187.68/187.58 fof(fact_le,axiom, % 187.68/187.58 ! [V_v_2,V_u_2,V_y_2,V_x_2] : % 187.68/187.58 ( 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))))))) % 187.68/187.58 <=> 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))) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_minus,axiom, % 187.68/187.58 ! [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))))) ). % 187.68/187.58 % 187.68/187.58 fof(fact_Zero__int__def,axiom, % 187.68/187.58 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))))) ). % 187.68/187.58 % 187.68/187.58 fof(fact_int__def,axiom, % 187.68/187.58 ! [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))))) ). % 187.68/187.58 % 187.68/187.58 fof(fact_add,axiom, % 187.68/187.58 ! [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))))) ). % 187.68/187.58 % 187.68/187.58 fof(fact_nat,axiom, % 187.68/187.58 ! [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) ). % 187.68/187.58 % 187.68/187.58 fof(fact_less,axiom, % 187.68/187.58 ! [V_v_2,V_u_2,V_y_2,V_x_2] : % 187.68/187.58 ( 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))))))) % 187.68/187.58 <=> 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))) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_arith__series__int,axiom, % 187.68/187.58 ! [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)))) ). % 187.68/187.58 % 187.68/187.58 fof(fact_eq__Abs__Integ,axiom, % 187.68/187.58 ! [V_z_2] : % 187.68/187.58 ~ ! [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))))) ). % 187.68/187.58 % 187.68/187.58 fof(fact_arith__series__nat,axiom, % 187.68/187.58 ! [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)))) ). % 187.68/187.58 % 187.68/187.58 fof(fact_arith__series__general,axiom, % 187.68/187.58 ! [V_n_2,V_d_2,V_a_2,T_a] : % 187.68/187.58 ( class_Rings_Ocomm__semiring__1(T_a) % 187.68/187.58 => 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)))) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_setsum__divide__distrib,axiom, % 187.68/187.58 ! [V_r_2,V_A_2,V_f_2,T_b,T_a] : % 187.68/187.58 ( class_Fields_Ofield(T_a) % 187.68/187.58 => 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) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_setsum__negf,axiom, % 187.68/187.58 ! [V_A_2,V_f_2,T_b,T_a] : % 187.68/187.58 ( class_Groups_Oab__group__add(T_a) % 187.68/187.58 => 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)) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_of__int__setsum,axiom, % 187.68/187.58 ! [V_A_2,V_f_2,T_b,T_a] : % 187.68/187.58 ( class_Rings_Oring__1(T_a) % 187.68/187.58 => 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) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_setsum__commute,axiom, % 187.68/187.58 ! [V_A_2,V_B_2,V_f_2,T_c,T_b,T_a] : % 187.68/187.58 ( class_Groups_Ocomm__monoid__add(T_a) % 187.68/187.58 => 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) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_int__setsum,axiom, % 187.68/187.58 ! [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) ). % 187.68/187.58 % 187.68/187.58 fof(fact_of__nat__setsum,axiom, % 187.68/187.58 ! [V_A_2,V_f_2,T_b,T_a] : % 187.68/187.58 ( class_Rings_Osemiring__1(T_a) % 187.68/187.58 => 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) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_transfer__nat__int__sum__prod2_I1_J,axiom, % 187.68/187.58 ! [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)) ). % 187.68/187.58 % 187.68/187.58 fof(fact_setsum__subtractf,axiom, % 187.68/187.58 ! [V_A_2,V_g_2,V_f_2,T_b,T_a] : % 187.68/187.58 ( class_Groups_Oab__group__add(T_a) % 187.68/187.58 => 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)) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_setsum__right__distrib,axiom, % 187.68/187.58 ! [V_A_2,V_f_2,T_b,V_r_2,T_a] : % 187.68/187.58 ( class_Rings_Osemiring__0(T_a) % 187.68/187.58 => 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) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_setsum__left__distrib,axiom, % 187.68/187.58 ! [V_r_2,V_A_2,V_f_2,T_b,T_a] : % 187.68/187.58 ( class_Rings_Osemiring__0(T_a) % 187.68/187.58 => 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) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_setsum__product,axiom, % 187.68/187.58 ! [V_B_2,V_g_2,T_c,V_A_2,V_f_2,T_b,T_a] : % 187.68/187.58 ( class_Rings_Osemiring__0(T_a) % 187.68/187.58 => 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) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_setsum__addf,axiom, % 187.68/187.58 ! [V_A_2,V_g_2,V_f_2,T_b,T_a] : % 187.68/187.58 ( class_Groups_Ocomm__monoid__add(T_a) % 187.68/187.58 => 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)) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_setsum__0,axiom, % 187.68/187.58 ! [V_A_2,T_b,T_a] : % 187.68/187.58 ( class_Groups_Ocomm__monoid__add(T_a) % 187.68/187.58 => 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) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_setsum_Oempty,axiom, % 187.68/187.58 ! [V_g_2,T_b,T_a] : % 187.68/187.58 ( class_Groups_Ocomm__monoid__add(T_a) % 187.68/187.58 => 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) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_setsum__empty,axiom, % 187.68/187.58 ! [V_f_2,T_b,T_a] : % 187.68/187.58 ( class_Groups_Ocomm__monoid__add(T_a) % 187.68/187.58 => 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) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_setsum__infinite,axiom, % 187.68/187.58 ! [V_f_2,V_A_2,T_a,T_b] : % 187.68/187.58 ( class_Groups_Ocomm__monoid__add(T_b) % 187.68/187.58 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.58 => 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) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_setsum_Oinfinite,axiom, % 187.68/187.58 ! [V_g_2,V_A_2,T_a,T_b] : % 187.68/187.58 ( class_Groups_Ocomm__monoid__add(T_b) % 187.68/187.58 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.58 => 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) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_setsum__eq__0__iff,axiom, % 187.68/187.58 ! [V_f_2,V_F_2,T_a] : % 187.68/187.58 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) % 187.68/187.58 => ( 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) % 187.68/187.58 <=> ! [B_x] : % 187.68/187.58 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_F_2)) % 187.68/187.58 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_setsum_Odistrib,axiom, % 187.68/187.58 ! [V_h_2,V_g_2,V_A_2,T_a,T_b] : % 187.68/187.58 ( class_Groups_Ocomm__monoid__add(T_b) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.58 => 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)) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_card__eq__setsum,axiom, % 187.68/187.58 ! [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) ). % 187.68/187.58 % 187.68/187.58 fof(fact_setsum__shift__bounds__Suc__ivl,axiom, % 187.68/187.58 ! [V_n_2,V_m_2,V_f_2,T_a] : % 187.68/187.58 ( class_Groups_Ocomm__monoid__add(T_a) % 187.68/187.58 => 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)) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_setsum__shift__bounds__nat__ivl,axiom, % 187.68/187.58 ! [V_n_2,V_k_2,V_m_2,V_f_2,T_a] : % 187.68/187.58 ( class_Groups_Ocomm__monoid__add(T_a) % 187.68/187.58 => 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)) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_setsum__shift__bounds__cl__Suc__ivl,axiom, % 187.68/187.58 ! [V_n_2,V_m_2,V_f_2,T_a] : % 187.68/187.58 ( class_Groups_Ocomm__monoid__add(T_a) % 187.68/187.58 => 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)) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_setsum__shift__bounds__cl__nat__ivl,axiom, % 187.68/187.58 ! [V_n_2,V_k_2,V_m_2,V_f_2,T_a] : % 187.68/187.58 ( class_Groups_Ocomm__monoid__add(T_a) % 187.68/187.58 => 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)) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_setsum__eq__Suc0__iff,axiom, % 187.68/187.58 ! [V_f_2,V_A_2,T_a] : % 187.68/187.58 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.58 => ( 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)) % 187.68/187.58 <=> ? [B_x] : % 187.68/187.58 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 187.68/187.58 & hAPP(V_f_2,B_x) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 187.68/187.58 & ! [B_xa] : % 187.68/187.58 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_A_2)) % 187.68/187.58 => ( B_x != B_xa % 187.68/187.58 => hAPP(V_f_2,B_xa) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_setsum__eq__1__iff,axiom, % 187.68/187.58 ! [V_f_2,V_A_2,T_a] : % 187.68/187.58 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.58 => ( 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) % 187.68/187.58 <=> ? [B_x] : % 187.68/187.58 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 187.68/187.58 & hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 187.68/187.58 & ! [B_xa] : % 187.68/187.58 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_A_2)) % 187.68/187.58 => ( B_x != B_xa % 187.68/187.58 => hAPP(V_f_2,B_xa) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_setsum__add__nat__ivl,axiom, % 187.68/187.58 ! [V_f_2,V_p_2,V_n_2,V_m_2,T_a] : % 187.68/187.58 ( class_Groups_Ocomm__monoid__add(T_a) % 187.68/187.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 187.68/187.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_p_2)) % 187.68/187.58 => 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)) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_setsum__diff__nat__ivl,axiom, % 187.68/187.58 ! [V_f_2,V_p_2,V_n_2,V_m_2,T_a] : % 187.68/187.58 ( class_Groups_Oab__group__add(T_a) % 187.68/187.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 187.68/187.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_p_2)) % 187.68/187.58 => 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)) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_setsum__shift__lb__Suc0__0,axiom, % 187.68/187.58 ! [V_k_2,V_f_2] : % 187.68/187.58 ( hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 187.68/187.58 => 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)) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_setsum__delta,axiom, % 187.68/187.58 ! [V_b_2,V_a_2,V_S_2,T_a,T_b] : % 187.68/187.58 ( class_Groups_Ocomm__monoid__add(T_b) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 187.68/187.58 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) % 187.68/187.58 => 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) ) % 187.68/187.58 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) % 187.68/187.58 => 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) ) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_setsum__delta_H,axiom, % 187.68/187.58 ! [V_b_2,V_a_2,V_S_2,T_a,T_b] : % 187.68/187.58 ( class_Groups_Ocomm__monoid__add(T_b) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 187.68/187.58 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) % 187.68/187.58 => 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) ) % 187.68/187.58 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) % 187.68/187.58 => 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) ) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_setsum__constant,axiom, % 187.68/187.58 ! [V_A_2,V_y_2,T_b,T_a] : % 187.68/187.58 ( class_Rings_Osemiring__1(T_a) % 187.68/187.58 => 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) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_setsum__lessThan__Suc,axiom, % 187.68/187.58 ! [V_n_2,V_f_2,T_a] : % 187.68/187.58 ( class_Groups_Ocomm__monoid__add(T_a) % 187.68/187.58 => 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)) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_setsum__atMost__Suc,axiom, % 187.68/187.58 ! [V_n_2,V_f_2,T_a] : % 187.68/187.58 ( class_Groups_Ocomm__monoid__add(T_a) % 187.68/187.58 => 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))) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_setsum__insert,axiom, % 187.68/187.58 ! [V_f_2,V_a_2,V_F_2,T_a,T_b] : % 187.68/187.58 ( class_Groups_Ocomm__monoid__add(T_b) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) % 187.68/187.58 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_F_2)) % 187.68/187.58 => 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)) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_setsum_Oinsert,axiom, % 187.68/187.58 ! [V_g_2,V_x_2,V_A_2,T_a,T_b] : % 187.68/187.58 ( class_Groups_Ocomm__monoid__add(T_b) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.58 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 187.68/187.58 => 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)) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_setsum__diff,axiom, % 187.68/187.58 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] : % 187.68/187.58 ( class_Groups_Oab__group__add(T_b) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 187.68/187.58 => 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)) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_setsum_Oeq__fold,axiom, % 187.68/187.58 ! [V_g_2,V_A_2,T_a,T_b] : % 187.68/187.58 ( class_Groups_Ocomm__monoid__add(T_b) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.58 => 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) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_setsum_OF__eq,axiom, % 187.68/187.58 ! [V_g_2,V_A_2,T_a,T_b] : % 187.68/187.58 ( class_Groups_Ocomm__monoid__add(T_b) % 187.68/187.58 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.58 => 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) ) % 187.68/187.58 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.58 => 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) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_setsum__diff__nat,axiom, % 187.68/187.58 ! [V_f_2,V_A_2,V_B_2,T_a] : % 187.68/187.58 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 187.68/187.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 187.68/187.58 => 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)) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_setsum__shift__lb__Suc0__0__upt,axiom, % 187.68/187.58 ! [V_k_2,V_f_2,T_a] : % 187.68/187.58 ( class_Groups_Ocomm__monoid__add(T_a) % 187.68/187.58 => ( hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(T_a) % 187.68/187.58 => 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)) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_setsum__head__upt__Suc,axiom, % 187.68/187.58 ! [V_f_2,V_n_2,V_m_2,T_a] : % 187.68/187.58 ( class_Groups_Ocomm__monoid__add(T_a) % 187.68/187.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 187.68/187.58 => 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))) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_setsum__head__Suc,axiom, % 187.68/187.58 ! [V_f_2,V_n_2,V_m_2,T_a] : % 187.68/187.58 ( class_Groups_Ocomm__monoid__add(T_a) % 187.68/187.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 187.68/187.58 => 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))) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_setsum_Oinsert__remove,axiom, % 187.68/187.58 ! [V_x_2,V_g_2,V_A_2,T_a,T_b] : % 187.68/187.58 ( class_Groups_Ocomm__monoid__add(T_b) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.58 => 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)))))) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_setsum__diff1__nat,axiom, % 187.68/187.58 ! [V_f_2,V_A_2,V_a_2,T_a] : % 187.68/187.58 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 187.68/187.58 => 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)) ) % 187.68/187.58 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 187.68/187.58 => 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) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_setsum__op__ivl__Suc,axiom, % 187.68/187.58 ! [V_f_2,V_m_2,V_n_2,T_a] : % 187.68/187.58 ( class_Groups_Ocomm__monoid__add(T_a) % 187.68/187.58 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) % 187.68/187.58 => 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) ) % 187.68/187.58 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) % 187.68/187.58 => 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)) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_setsum__cl__ivl__Suc,axiom, % 187.68/187.58 ! [V_f_2,V_m_2,V_n_2,T_a] : % 187.68/187.58 ( class_Groups_Ocomm__monoid__add(T_a) % 187.68/187.58 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) % 187.68/187.58 => 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) ) % 187.68/187.58 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) % 187.68/187.58 => 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))) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_setsum__head,axiom, % 187.68/187.58 ! [V_P_2,V_n_2,V_m_2,T_a] : % 187.68/187.58 ( class_Groups_Ocomm__monoid__add(T_a) % 187.68/187.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 187.68/187.58 => 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))) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_setsum__ub__add__nat,axiom, % 187.68/187.58 ! [V_p_2,V_f_2,V_n_2,V_m_2,T_a] : % 187.68/187.58 ( class_Groups_Ocomm__monoid__add(T_a) % 187.68/187.58 => ( 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)))) % 187.68/187.58 => 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)))) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_setsum_Oremove,axiom, % 187.68/187.58 ! [V_g_2,V_x_2,V_A_2,T_a,T_b] : % 187.68/187.58 ( class_Groups_Ocomm__monoid__add(T_b) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.58 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 187.68/187.58 => 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)))))) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_setsum__diff1_H,axiom, % 187.68/187.58 ! [V_f_2,V_a_2,V_A_2,T_a,T_b] : % 187.68/187.58 ( class_Groups_Ocomm__monoid__add(T_b) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.58 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 187.68/187.58 => 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)))))) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_setsum__diff1__ring,axiom, % 187.68/187.58 ! [V_f_2,V_a_2,V_A_2,T_a,T_b] : % 187.68/187.58 ( class_Rings_Oring(T_b) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.58 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 187.68/187.58 => 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)) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_setsum__diff1,axiom, % 187.68/187.58 ! [V_f_2,V_a_2,V_A_2,T_a,T_b] : % 187.68/187.58 ( class_Groups_Oab__group__add(T_b) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.58 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 187.68/187.58 => 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)) ) % 187.68/187.58 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 187.68/187.58 => 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) ) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_geometric__sum,axiom, % 187.68/187.58 ! [V_n_2,V_x_2,T_a] : % 187.68/187.58 ( class_Fields_Ofield(T_a) % 187.68/187.58 => ( V_x_2 != c_Groups_Oone__class_Oone(T_a) % 187.68/187.58 => 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))) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_gauss__sum,axiom, % 187.68/187.58 ! [V_n_2,T_a] : % 187.68/187.58 ( class_Rings_Ocomm__semiring__1(T_a) % 187.68/187.58 => 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))) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_setsum__natinterval__difff,axiom, % 187.68/187.58 ! [V_f_2,V_n_2,V_m_2,T_a] : % 187.68/187.58 ( class_Groups_Oab__group__add(T_a) % 187.68/187.58 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 187.68/187.58 => 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)))) ) % 187.68/187.58 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 187.68/187.58 => 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) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_transfer__int__nat__sum__prod2_I1_J,axiom, % 187.68/187.58 ! [V_f_2,V_A_2,T_a] : % 187.68/187.58 ( ! [B_x] : % 187.68/187.58 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 187.68/187.58 => c_Nat__Transfer_Ois__nat(hAPP(V_f_2,B_x)) ) % 187.68/187.58 => 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)) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_setsum__mono2,axiom, % 187.68/187.58 ! [V_f_2,V_A_2,V_B_2,T_a,T_b] : % 187.68/187.58 ( class_Groups_Oordered__comm__monoid__add(T_b) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 187.68/187.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 187.68/187.58 => ( ! [B_b] : % 187.68/187.58 ( 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))) % 187.68/187.58 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(V_f_2,B_b))) ) % 187.68/187.58 => 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))) ) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_setsum__bounded,axiom, % 187.68/187.58 ! [V_K_2,V_f_2,V_A_2,T_a,T_b] : % 187.68/187.58 ( ( class_Groups_Oordered__ab__semigroup__add(T_b) % 187.68/187.58 & class_Rings_Osemiring__1(T_b) ) % 187.68/187.58 => ( ! [B_i] : % 187.68/187.58 ( hBOOL(hAPP(hAPP(c_member(T_a),B_i),V_A_2)) % 187.68/187.58 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,B_i)),V_K_2)) ) % 187.68/187.58 => 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))) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_setsum__mono3,axiom, % 187.68/187.58 ! [V_f_2,V_A_2,V_B_2,T_a,T_b] : % 187.68/187.58 ( ( class_Groups_Ocomm__monoid__add(T_b) % 187.68/187.58 & class_Groups_Oordered__ab__semigroup__add(T_b) ) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 187.68/187.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 187.68/187.58 => ( ! [B_x] : % 187.68/187.58 ( 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))) % 187.68/187.58 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(V_f_2,B_x))) ) % 187.68/187.58 => 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))) ) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_transfer__nat__int__sum__prod_I1_J,axiom, % 187.68/187.58 ! [V_A_2,V_f_2,T_a] : % 187.68/187.58 ( ( class_Groups_Ocomm__monoid__add(T_a) % 187.68/187.58 & class_Groups_Ocomm__monoid__mult(T_a) ) % 187.68/187.58 => 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)) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_transfer__int__nat__sum__prod_I1_J,axiom, % 187.68/187.58 ! [V_f_2,V_A_2,T_a] : % 187.68/187.58 ( ( class_Groups_Ocomm__monoid__add(T_a) % 187.68/187.58 & class_Groups_Ocomm__monoid__mult(T_a) ) % 187.68/187.58 => ( c_Nat__Transfer_Onat__set(V_A_2) % 187.68/187.58 => 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)) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_setsum__reindex__nonzero,axiom, % 187.68/187.58 ! [T_b,V_h_2,V_f_2,V_S_2,T_a,T_c] : % 187.68/187.58 ( class_Groups_Ocomm__monoid__add(T_c) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 187.68/187.58 => ( ! [B_x] : % 187.68/187.58 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2)) % 187.68/187.58 => ! [B_y] : % 187.68/187.58 ( hBOOL(hAPP(hAPP(c_member(T_a),B_y),V_S_2)) % 187.68/187.58 => ( B_x != B_y % 187.68/187.58 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y) % 187.68/187.58 => hAPP(V_h_2,hAPP(V_f_2,B_x)) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) % 187.68/187.58 => 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) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_setsum__nonneg__0,axiom, % 187.68/187.58 ! [V_i_2,V_f_2,V_s_2,T_a,T_b] : % 187.68/187.58 ( class_Groups_Oordered__ab__group__add(T_b) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_s_2)) % 187.68/187.58 => ( ! [B_i] : % 187.68/187.58 ( hBOOL(hAPP(hAPP(c_member(T_a),B_i),V_s_2)) % 187.68/187.58 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(V_f_2,B_i))) ) % 187.68/187.58 => ( 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) % 187.68/187.58 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),V_s_2)) % 187.68/187.58 => hAPP(V_f_2,V_i_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_setsum__nonneg__leq__bound,axiom, % 187.68/187.58 ! [V_i_2,V_B_2,V_f_2,V_s_2,T_a,T_b] : % 187.68/187.58 ( class_Groups_Oordered__ab__group__add(T_b) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_s_2)) % 187.68/187.58 => ( ! [B_i] : % 187.68/187.58 ( hBOOL(hAPP(hAPP(c_member(T_a),B_i),V_s_2)) % 187.68/187.58 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(V_f_2,B_i))) ) % 187.68/187.58 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_s_2) = V_B_2 % 187.68/187.58 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),V_s_2)) % 187.68/187.58 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,V_i_2)),V_B_2)) ) ) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_sum__diff__distrib,axiom, % 187.68/187.58 ! [V_n_2,V_P_2,V_Q_2] : % 187.68/187.58 ( ! [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))) % 187.68/187.58 => 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)) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_ImageE,axiom, % 187.68/187.58 ! [V_A_2,V_r_2,T_b,V_b_2,T_a] : % 187.68/187.58 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(c_Relation_OImage(T_b,T_a,V_r_2),V_A_2))) % 187.68/187.58 => ~ ! [B_x] : % 187.68/187.58 ( 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)) % 187.68/187.58 => ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_setsum__mono__zero__left,axiom, % 187.68/187.58 ! [V_f_2,V_S_2,V_T_2,T_a,T_b] : % 187.68/187.58 ( class_Groups_Ocomm__monoid__add(T_b) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2)) % 187.68/187.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2)) % 187.68/187.58 => ( ! [B_x] : % 187.68/187.58 ( 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))) % 187.68/187.58 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) ) % 187.68/187.58 => 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) ) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_setsum__mono__zero__right,axiom, % 187.68/187.58 ! [V_f_2,V_S_2,V_T_2,T_a,T_b] : % 187.68/187.58 ( class_Groups_Ocomm__monoid__add(T_b) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2)) % 187.68/187.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2)) % 187.68/187.58 => ( ! [B_x] : % 187.68/187.58 ( 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))) % 187.68/187.58 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) ) % 187.68/187.58 => 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) ) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_setsum__strict__mono,axiom, % 187.68/187.58 ! [V_g_2,V_f_2,V_A_2,T_a,T_b] : % 187.68/187.58 ( ( class_Groups_Ocomm__monoid__add(T_b) % 187.68/187.58 & class_Groups_Oordered__cancel__ab__semigroup__add(T_b) ) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.58 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.58 => ( ! [B_x] : % 187.68/187.58 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 187.68/187.58 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) ) % 187.68/187.58 => 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))) ) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_fold__Un__disjoint,axiom, % 187.68/187.58 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] : % 187.68/187.58 ( class_Groups_Ocomm__monoid__mult(T_b) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 187.68/187.58 => ( 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)) % 187.68/187.58 => 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)) ) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_field__le__mult__one__interval,axiom, % 187.68/187.58 ! [V_y,V_x,T_a] : % 187.68/187.58 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 187.68/187.58 => ( ! [B_z] : % 187.68/187.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),B_z)) % 187.68/187.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),B_z),c_Groups_Oone__class_Oone(T_a))) % 187.68/187.58 => 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)) ) ) % 187.68/187.58 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_transfer__nat__int__sum__prod__cong_I2_J,axiom, % 187.68/187.58 ! [V_g_2,V_f_2,V_B_2,V_A_2,T_a] : % 187.68/187.58 ( ( class_Groups_Ocomm__monoid__add(T_a) % 187.68/187.58 & class_Groups_Ocomm__monoid__mult(T_a) ) % 187.68/187.58 => ( V_A_2 = V_B_2 % 187.68/187.58 => ( c_Nat__Transfer_Onat__set(V_B_2) % 187.68/187.58 => ( ! [B_x] : % 187.68/187.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 187.68/187.58 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) % 187.68/187.58 => 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) ) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_subset__equiv__class,axiom, % 187.68/187.58 ! [V_a_2,V_b_2,V_r_2,V_A_2,T_a] : % 187.68/187.58 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 187.68/187.58 => ( 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)))))) % 187.68/187.58 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),V_A_2)) % 187.68/187.58 => 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)) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_inf1E,axiom, % 187.68/187.58 ! [V_x_2,V_B_2,V_A_2,T_a] : % 187.68/187.58 ( 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)) % 187.68/187.58 => ~ ( hBOOL(hAPP(V_A_2,V_x_2)) % 187.68/187.58 => ~ hBOOL(hAPP(V_B_2,V_x_2)) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_inf1I,axiom, % 187.68/187.58 ! [T_a,V_B_2,V_x_2,V_A_2] : % 187.68/187.58 ( hBOOL(hAPP(V_A_2,V_x_2)) % 187.68/187.58 => ( hBOOL(hAPP(V_B_2,V_x_2)) % 187.68/187.58 => 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)) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_IntE,axiom, % 187.68/187.58 ! [V_B_2,V_A_2,V_c_2,T_a] : % 187.68/187.58 ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 187.68/187.58 => ~ ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) % 187.68/187.58 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2)) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_IntI,axiom, % 187.68/187.58 ! [V_B_2,V_A_2,V_c_2,T_a] : % 187.68/187.58 ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) % 187.68/187.58 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2)) % 187.68/187.58 => hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_finite__Int,axiom, % 187.68/187.58 ! [V_Ga_2,V_F_2,T_a] : % 187.68/187.58 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) % 187.68/187.58 | hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_Ga_2)) ) % 187.68/187.58 => 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))) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_insert__inter__insert,axiom, % 187.68/187.58 ! [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)) ). % 187.68/187.58 % 187.68/187.58 fof(fact_inf__sup__absorb,axiom, % 187.68/187.58 ! [V_y,V_x,T_a] : % 187.68/187.58 ( class_Lattices_Olattice(T_a) % 187.68/187.58 => 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 ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_sup__inf__absorb,axiom, % 187.68/187.58 ! [V_y,V_x,T_a] : % 187.68/187.58 ( class_Lattices_Olattice(T_a) % 187.68/187.58 => 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 ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_inf__sup__distrib1,axiom, % 187.68/187.58 ! [V_z,V_y,V_x,T_a] : % 187.68/187.58 ( class_Lattices_Odistrib__lattice(T_a) % 187.68/187.58 => 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)) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_sup__inf__distrib1,axiom, % 187.68/187.58 ! [V_z,V_y,V_x,T_a] : % 187.68/187.58 ( class_Lattices_Odistrib__lattice(T_a) % 187.68/187.58 => 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)) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_inf__sup__distrib2,axiom, % 187.68/187.58 ! [V_x,V_z,V_y,T_a] : % 187.68/187.58 ( class_Lattices_Odistrib__lattice(T_a) % 187.68/187.58 => 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)) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_sup__inf__distrib2,axiom, % 187.68/187.58 ! [V_x,V_z,V_y,T_a] : % 187.68/187.58 ( class_Lattices_Odistrib__lattice(T_a) % 187.68/187.58 => 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)) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_Int__Un__distrib,axiom, % 187.68/187.58 ! [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)) ). % 187.68/187.58 % 187.68/187.58 fof(fact_Un__Int__distrib,axiom, % 187.68/187.58 ! [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)) ). % 187.68/187.58 % 187.68/187.58 fof(fact_Int__Un__distrib2,axiom, % 187.68/187.58 ! [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)) ). % 187.68/187.58 % 187.68/187.58 fof(fact_Un__Int__distrib2,axiom, % 187.68/187.58 ! [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)) ). % 187.68/187.58 % 187.68/187.58 fof(fact_Un__Int__crazy,axiom, % 187.68/187.58 ! [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)) ). % 187.68/187.58 % 187.68/187.58 fof(fact_Int__iff,axiom, % 187.68/187.58 ! [V_B_2,V_A_2,V_c_2,T_a] : % 187.68/187.58 ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 187.68/187.58 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) % 187.68/187.58 & hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2)) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_IntD1,axiom, % 187.68/187.58 ! [V_B_2,V_A_2,V_c_2,T_a] : % 187.68/187.58 ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 187.68/187.58 => hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_IntD2,axiom, % 187.68/187.58 ! [V_B_2,V_A_2,V_c_2,T_a] : % 187.68/187.58 ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 187.68/187.58 => hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_B_2)) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_inf__bot__right,axiom, % 187.68/187.58 ! [V_x,T_a] : % 187.68/187.58 ( class_Lattices_Obounded__lattice__bot(T_a) % 187.68/187.58 => 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) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_inf__bot__left,axiom, % 187.68/187.58 ! [V_x,T_a] : % 187.68/187.58 ( class_Lattices_Obounded__lattice__bot(T_a) % 187.68/187.58 => 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) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_disjoint__iff__not__equal,axiom, % 187.68/187.58 ! [V_B_2,V_A_2,T_a] : % 187.68/187.58 ( 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)) % 187.68/187.58 <=> ! [B_x] : % 187.68/187.58 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 187.68/187.58 => ! [B_xa] : % 187.68/187.58 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_B_2)) % 187.68/187.58 => B_x != B_xa ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_Int__empty__right,axiom, % 187.68/187.58 ! [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)) ). % 187.68/187.58 % 187.68/187.58 fof(fact_Int__empty__left,axiom, % 187.68/187.58 ! [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)) ). % 187.68/187.58 % 187.68/187.58 fof(fact_inf__sup__ord_I1_J,axiom, % 187.68/187.58 ! [V_y,V_x,T_a] : % 187.68/187.58 ( class_Lattices_Olattice(T_a) % 187.68/187.58 => 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)) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_inf__le1,axiom, % 187.68/187.58 ! [V_y,V_x,T_a] : % 187.68/187.58 ( class_Lattices_Osemilattice__inf(T_a) % 187.68/187.58 => 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)) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_inf__sup__ord_I2_J,axiom, % 187.68/187.58 ! [V_y,V_x,T_a] : % 187.68/187.58 ( class_Lattices_Olattice(T_a) % 187.68/187.58 => 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)) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_inf__le2,axiom, % 187.68/187.58 ! [V_y,V_x,T_a] : % 187.68/187.58 ( class_Lattices_Osemilattice__inf(T_a) % 187.68/187.58 => 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)) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_le__iff__inf,axiom, % 187.68/187.58 ! [V_y_2,V_x_2,T_a] : % 187.68/187.58 ( class_Lattices_Osemilattice__inf(T_a) % 187.68/187.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 187.68/187.58 <=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x_2),V_y_2) = V_x_2 ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_le__inf__iff,axiom, % 187.68/187.58 ! [V_z_2,V_y_2,V_x_2,T_a] : % 187.68/187.58 ( class_Lattices_Osemilattice__inf(T_a) % 187.68/187.58 => ( 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))) % 187.68/187.58 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 187.68/187.58 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_z_2)) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_le__infI1,axiom, % 187.68/187.58 ! [V_b,V_x,V_a,T_a] : % 187.68/187.58 ( class_Lattices_Osemilattice__inf(T_a) % 187.68/187.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 187.68/187.58 => 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)) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_le__infI2,axiom, % 187.68/187.58 ! [V_a,V_x,V_b,T_a] : % 187.68/187.58 ( class_Lattices_Osemilattice__inf(T_a) % 187.68/187.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) % 187.68/187.58 => 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)) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_inf__absorb1,axiom, % 187.68/187.58 ! [V_y,V_x,T_a] : % 187.68/187.58 ( class_Lattices_Osemilattice__inf(T_a) % 187.68/187.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 187.68/187.58 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = V_x ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_inf__absorb2,axiom, % 187.68/187.58 ! [V_x,V_y,T_a] : % 187.68/187.58 ( class_Lattices_Osemilattice__inf(T_a) % 187.68/187.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 187.68/187.58 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = V_y ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_le__infI,axiom, % 187.68/187.58 ! [V_b,V_a,V_x,T_a] : % 187.68/187.58 ( class_Lattices_Osemilattice__inf(T_a) % 187.68/187.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 187.68/187.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) % 187.68/187.58 => 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))) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_inf__greatest,axiom, % 187.68/187.58 ! [V_z,V_y,V_x,T_a] : % 187.68/187.58 ( class_Lattices_Osemilattice__inf(T_a) % 187.68/187.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 187.68/187.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z)) % 187.68/187.58 => 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))) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_inf__mono,axiom, % 187.68/187.58 ! [V_d,V_b,V_c,V_a,T_a] : % 187.68/187.58 ( class_Lattices_Osemilattice__inf(T_a) % 187.68/187.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) % 187.68/187.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d)) % 187.68/187.58 => 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))) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_le__infE,axiom, % 187.68/187.58 ! [V_b,V_a,V_x,T_a] : % 187.68/187.58 ( class_Lattices_Osemilattice__inf(T_a) % 187.68/187.58 => ( 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))) % 187.68/187.58 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 187.68/187.58 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_Int__mono,axiom, % 187.68/187.58 ! [V_D_2,V_B_2,V_C_2,V_A_2,T_a] : % 187.68/187.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) % 187.68/187.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_D_2)) % 187.68/187.58 => 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))) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_Int__greatest,axiom, % 187.68/187.58 ! [V_B_2,V_A_2,V_C_2,T_a] : % 187.68/187.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)) % 187.68/187.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_B_2)) % 187.68/187.58 => 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))) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_Int__absorb1,axiom, % 187.68/187.58 ! [V_A_2,V_B_2,T_a] : % 187.68/187.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 187.68/187.58 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_Int__absorb2,axiom, % 187.68/187.58 ! [V_B_2,V_A_2,T_a] : % 187.68/187.58 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 187.68/187.58 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_Int__lower2,axiom, % 187.68/187.58 ! [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)) ). % 187.68/187.58 % 187.68/187.58 fof(fact_Int__lower1,axiom, % 187.68/187.58 ! [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)) ). % 187.68/187.58 % 187.68/187.58 fof(fact_inf__Int__eq,axiom, % 187.68/187.58 ! [V_x_2,V_S_2,V_R_2,T_a] : % 187.68/187.58 ( 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)) % 187.68/187.58 <=> 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))) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_less__infI2,axiom, % 187.68/187.58 ! [V_a,V_x,V_b,T_a] : % 187.68/187.58 ( class_Lattices_Osemilattice__inf(T_a) % 187.68/187.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_x)) % 187.68/187.58 => 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)) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_less__infI1,axiom, % 187.68/187.58 ! [V_b,V_x,V_a,T_a] : % 187.68/187.58 ( class_Lattices_Osemilattice__inf(T_a) % 187.68/187.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_x)) % 187.68/187.58 => 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)) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_Diff__Int__distrib,axiom, % 187.68/187.58 ! [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)) ). % 187.68/187.58 % 187.68/187.58 fof(fact_Int__Diff,axiom, % 187.68/187.58 ! [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)) ). % 187.68/187.58 % 187.68/187.58 fof(fact_Diff__Int__distrib2,axiom, % 187.68/187.58 ! [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)) ). % 187.68/187.58 % 187.68/187.58 fof(fact_Diff__Int2,axiom, % 187.68/187.58 ! [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) ). % 187.68/187.58 % 187.68/187.58 fof(fact_inf__min,axiom, % 187.68/187.58 ! [T_a] : % 187.68/187.58 ( ( class_Lattices_Osemilattice__inf(T_a) % 187.68/187.58 & class_Orderings_Olinorder(T_a) ) % 187.68/187.58 => c_Lattices_Osemilattice__inf__class_Oinf(T_a) = c_Orderings_Oord__class_Omin(T_a) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_Inf__fin_Oidem,axiom, % 187.68/187.58 ! [V_x,T_a] : % 187.68/187.58 ( class_Lattices_Olattice(T_a) % 187.68/187.58 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_x) = V_x ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_Int__assoc,axiom, % 187.68/187.58 ! [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)) ). % 187.68/187.58 % 187.68/187.58 fof(fact_Int__left__commute,axiom, % 187.68/187.58 ! [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)) ). % 187.68/187.58 % 187.68/187.58 fof(fact_Int__left__absorb,axiom, % 187.68/187.58 ! [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) ). % 187.68/187.58 % 187.68/187.58 fof(fact_Int__commute,axiom, % 187.68/187.58 ! [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) ). % 187.68/187.58 % 187.68/187.58 fof(fact_Int__absorb,axiom, % 187.68/187.58 ! [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 ). % 187.68/187.58 % 187.68/187.58 fof(fact_inf__fun__def,axiom, % 187.68/187.58 ! [V_x_2,V_g_2,V_f_2,T_b,T_a] : % 187.68/187.58 ( class_Lattices_Olattice(T_a) % 187.68/187.58 => 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)) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_inf1D2,axiom, % 187.68/187.58 ! [V_x_2,V_B_2,V_A_2,T_a] : % 187.68/187.58 ( 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)) % 187.68/187.58 => hBOOL(hAPP(V_B_2,V_x_2)) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_inf1D1,axiom, % 187.68/187.58 ! [V_x_2,V_B_2,V_A_2,T_a] : % 187.68/187.58 ( 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)) % 187.68/187.58 => hBOOL(hAPP(V_A_2,V_x_2)) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_inf__apply,axiom, % 187.68/187.58 ! [V_x_2,V_g_2,V_f_2,T_b,T_a] : % 187.68/187.58 ( class_Lattices_Olattice(T_a) % 187.68/187.58 => 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)) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_inf__assoc,axiom, % 187.68/187.58 ! [V_z,V_y,V_x,T_a] : % 187.68/187.58 ( class_Lattices_Osemilattice__inf(T_a) % 187.68/187.58 => 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)) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_inf__sup__aci_I2_J,axiom, % 187.68/187.58 ! [V_z,V_y,V_x,T_a] : % 187.68/187.58 ( class_Lattices_Olattice(T_a) % 187.68/187.58 => 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)) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_inf_Oassoc,axiom, % 187.68/187.58 ! [V_c,V_b,V_a,T_a] : % 187.68/187.58 ( class_Lattices_Osemilattice__inf(T_a) % 187.68/187.58 => 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)) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_inf__left__commute,axiom, % 187.68/187.58 ! [V_z,V_y,V_x,T_a] : % 187.68/187.58 ( class_Lattices_Osemilattice__inf(T_a) % 187.68/187.58 => 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)) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_inf__sup__aci_I3_J,axiom, % 187.68/187.58 ! [V_z,V_y,V_x,T_a] : % 187.68/187.58 ( class_Lattices_Olattice(T_a) % 187.68/187.58 => 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)) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_inf_Oleft__commute,axiom, % 187.68/187.58 ! [V_c,V_a,V_b,T_a] : % 187.68/187.58 ( class_Lattices_Osemilattice__inf(T_a) % 187.68/187.58 => 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)) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_inf__left__idem,axiom, % 187.68/187.58 ! [V_y,V_x,T_a] : % 187.68/187.58 ( class_Lattices_Osemilattice__inf(T_a) % 187.68/187.58 => 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) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_inf__sup__aci_I4_J,axiom, % 187.68/187.58 ! [V_y,V_x,T_a] : % 187.68/187.58 ( class_Lattices_Olattice(T_a) % 187.68/187.58 => 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) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_inf_Oleft__idem,axiom, % 187.68/187.58 ! [V_b,V_a,T_a] : % 187.68/187.58 ( class_Lattices_Osemilattice__inf(T_a) % 187.68/187.58 => 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) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_inf__commute,axiom, % 187.68/187.58 ! [V_y,V_x,T_a] : % 187.68/187.58 ( class_Lattices_Osemilattice__inf(T_a) % 187.68/187.58 => 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) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_inf__sup__aci_I1_J,axiom, % 187.68/187.58 ! [V_y,V_x,T_a] : % 187.68/187.58 ( class_Lattices_Olattice(T_a) % 187.68/187.58 => 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) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_inf_Ocommute,axiom, % 187.68/187.58 ! [V_b,V_a,T_a] : % 187.68/187.58 ( class_Lattices_Osemilattice__inf(T_a) % 187.68/187.58 => 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) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_inf__idem,axiom, % 187.68/187.58 ! [V_x,T_a] : % 187.68/187.58 ( class_Lattices_Osemilattice__inf(T_a) % 187.68/187.58 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_x) = V_x ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_inf_Oidem,axiom, % 187.68/187.58 ! [V_a,T_a] : % 187.68/187.58 ( class_Lattices_Osemilattice__inf(T_a) % 187.68/187.58 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_a) = V_a ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_fun__left__comm__idem__inf,axiom, % 187.68/187.58 ! [T_a] : % 187.68/187.58 ( class_Lattices_Osemilattice__inf(T_a) % 187.68/187.58 => c_Finite__Set_Ofun__left__comm__idem(T_a,T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a)) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_restrict__restrict,axiom, % 187.68/187.58 ! [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)) ). % 187.68/187.58 % 187.68/187.58 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I3_J,axiom, % 187.68/187.58 ! [V_B_2,V_A_2] : % 187.68/187.58 ( c_Nat__Transfer_Onat__set(V_A_2) % 187.68/187.58 => ( c_Nat__Transfer_Onat__set(V_B_2) % 187.68/187.58 => 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)) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_Pow__Int__eq,axiom, % 187.68/187.58 ! [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)) ). % 187.68/187.58 % 187.68/187.58 fof(fact_distrib__inf__le,axiom, % 187.68/187.58 ! [V_z,V_y,V_x,T_a] : % 187.68/187.58 ( class_Lattices_Olattice(T_a) % 187.68/187.58 => 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)))) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_distrib__sup__le,axiom, % 187.68/187.58 ! [V_z,V_y,V_x,T_a] : % 187.68/187.58 ( class_Lattices_Olattice(T_a) % 187.68/187.58 => 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)))) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_inf__compl__bot,axiom, % 187.68/187.58 ! [V_x,T_a] : % 187.68/187.58 ( class_Lattices_Oboolean__algebra(T_a) % 187.68/187.58 => 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) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_compl__inf__bot,axiom, % 187.68/187.58 ! [V_x,T_a] : % 187.68/187.58 ( class_Lattices_Oboolean__algebra(T_a) % 187.68/187.58 => 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) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_diff__eq,axiom, % 187.68/187.58 ! [V_y,V_x,T_a] : % 187.68/187.58 ( class_Lattices_Oboolean__algebra(T_a) % 187.68/187.58 => 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)) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_compl__inf,axiom, % 187.68/187.58 ! [V_y,V_x,T_a] : % 187.68/187.58 ( class_Lattices_Oboolean__algebra(T_a) % 187.68/187.58 => 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)) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_compl__sup,axiom, % 187.68/187.58 ! [V_y,V_x,T_a] : % 187.68/187.58 ( class_Lattices_Oboolean__algebra(T_a) % 187.68/187.58 => 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)) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_Int__insert__right,axiom, % 187.68/187.58 ! [V_B_2,V_A_2,V_a_2,T_a] : % 187.68/187.58 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 187.68/187.58 => 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)) ) % 187.68/187.58 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 187.68/187.58 => 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) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_Int__insert__left,axiom, % 187.68/187.58 ! [V_B_2,V_C_2,V_a_2,T_a] : % 187.68/187.58 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_C_2)) % 187.68/187.58 => 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)) ) % 187.68/187.58 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_C_2)) % 187.68/187.58 => 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) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_Int__insert__right__if0,axiom, % 187.68/187.58 ! [V_B_2,V_A_2,V_a_2,T_a] : % 187.68/187.58 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 187.68/187.58 => 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) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_Int__insert__left__if0,axiom, % 187.68/187.58 ! [V_B_2,V_C_2,V_a_2,T_a] : % 187.68/187.58 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_C_2)) % 187.68/187.58 => 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) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_Int__insert__right__if1,axiom, % 187.68/187.58 ! [V_B_2,V_A_2,V_a_2,T_a] : % 187.68/187.58 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 187.68/187.58 => 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)) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_Int__insert__left__if1,axiom, % 187.68/187.58 ! [V_B_2,V_C_2,V_a_2,T_a] : % 187.68/187.58 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_C_2)) % 187.68/187.58 => 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)) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_mono__inf,axiom, % 187.68/187.58 ! [V_B_2,V_A_2,V_f_2,T_a,T_b] : % 187.68/187.58 ( ( class_Lattices_Osemilattice__inf(T_b) % 187.68/187.58 & class_Lattices_Osemilattice__inf(T_a) ) % 187.68/187.58 => ( c_Orderings_Oorder__class_Omono(T_a,T_b,V_f_2) % 187.68/187.58 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),hAPP(V_f_2,V_A_2)),hAPP(V_f_2,V_B_2)))) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_image__Int__subset,axiom, % 187.68/187.58 ! [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)))) ). % 187.68/187.58 % 187.68/187.58 fof(fact_Diff__disjoint,axiom, % 187.68/187.58 ! [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)) ). % 187.68/187.58 % 187.68/187.58 fof(fact_Diff__triv,axiom, % 187.68/187.58 ! [V_B_2,V_A_2,T_a] : % 187.68/187.58 ( 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)) % 187.68/187.58 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_Un__Int__assoc__eq,axiom, % 187.68/187.58 ! [V_C_2,V_B_2,V_A_2,T_a] : % 187.68/187.58 ( 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)) % 187.68/187.58 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_Diff__Int,axiom, % 187.68/187.58 ! [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)) ). % 187.68/187.58 % 187.68/187.58 fof(fact_Diff__Un,axiom, % 187.68/187.58 ! [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)) ). % 187.68/187.58 % 187.68/187.58 fof(fact_Un__Diff__Int,axiom, % 187.68/187.58 ! [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 ). % 187.68/187.58 % 187.68/187.58 fof(fact_ivl__disj__int_I11_J,axiom, % 187.68/187.58 ! [V_u_2,V_m_2,V_l_2,T_a] : % 187.68/187.58 ( class_Orderings_Oorder(T_a) % 187.68/187.58 => 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)) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I4_J,axiom, % 187.68/187.58 ! [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))) ). % 187.68/187.58 % 187.68/187.58 fof(fact_Compl__disjoint,axiom, % 187.68/187.58 ! [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)) ). % 187.68/187.58 % 187.68/187.58 fof(fact_Compl__disjoint2,axiom, % 187.68/187.58 ! [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)) ). % 187.68/187.58 % 187.68/187.58 fof(fact_Image__Int__subset,axiom, % 187.68/187.58 ! [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)))) ). % 187.68/187.58 % 187.68/187.58 fof(fact_Compl__Int,axiom, % 187.68/187.58 ! [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)) ). % 187.68/187.58 % 187.68/187.58 fof(fact_Compl__Un,axiom, % 187.68/187.58 ! [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)) ). % 187.68/187.58 % 187.68/187.58 fof(fact_Diff__eq,axiom, % 187.68/187.58 ! [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)) ). % 187.68/187.58 % 187.68/187.58 fof(fact_Diff__Compl,axiom, % 187.68/187.58 ! [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) ). % 187.68/187.58 % 187.68/187.58 fof(fact_ivl__disj__int_I14_J,axiom, % 187.68/187.58 ! [V_u_2,V_m_2,V_l_2,T_a] : % 187.68/187.58 ( class_Orderings_Oorder(T_a) % 187.68/187.58 => 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)) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_mono__Int,axiom, % 187.68/187.58 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 187.68/187.58 ( c_Orderings_Oorder__class_Omono(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),V_f_2) % 187.68/187.58 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),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(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_f_2,V_A_2)),hAPP(V_f_2,V_B_2)))) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_dom__restrict,axiom, % 187.68/187.58 ! [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) ). % 187.68/187.58 % 187.68/187.58 fof(fact_equiv__class__nondisjoint,axiom, % 187.68/187.58 ! [V_b_2,V_a_2,V_x_2,V_r_2,V_A_2,T_a] : % 187.68/187.58 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 187.68/187.58 => ( 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))))))) % 187.68/187.58 => 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)) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I4_J,axiom, % 187.68/187.58 ! [V_B_2,V_A_2] : % 187.68/187.58 ( c_Nat__Transfer_Onat__set(V_A_2) % 187.68/187.58 => ( c_Nat__Transfer_Onat__set(V_B_2) % 187.68/187.58 => 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))) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_inf__Sup__absorb,axiom, % 187.68/187.58 ! [V_a_2,V_A_2,T_a] : % 187.68/187.58 ( class_Lattices_Olattice(T_a) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.58 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 187.68/187.58 => 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 ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_min__max_Omono__inf,axiom, % 187.68/187.58 ! [V_B_2,V_A_2,V_f_2,T_a,T_b] : % 187.68/187.58 ( ( class_Lattices_Osemilattice__inf(T_b) % 187.68/187.58 & class_Orderings_Olinorder(T_a) ) % 187.68/187.58 => ( c_Orderings_Oorder__class_Omono(T_a,T_b,V_f_2) % 187.68/187.58 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_A_2),V_B_2))),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_b),hAPP(V_f_2,V_A_2)),hAPP(V_f_2,V_B_2)))) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_disjoint__eq__subset__Compl,axiom, % 187.68/187.58 ! [V_B_2,V_A_2,T_a] : % 187.68/187.58 ( 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)) % 187.68/187.58 <=> 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))) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_ivl__disj__int_I15_J,axiom, % 187.68/187.58 ! [V_u_2,V_m_2,V_l_2,T_a] : % 187.68/187.58 ( class_Orderings_Oorder(T_a) % 187.68/187.58 => 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)) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_Int__atLeastAtMost,axiom, % 187.68/187.58 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] : % 187.68/187.58 ( class_Orderings_Olinorder(T_a) % 187.68/187.58 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a_2),V_c_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b_2),V_d_2)) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_Int__atLeastLessThan,axiom, % 187.68/187.58 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] : % 187.68/187.58 ( class_Orderings_Olinorder(T_a) % 187.68/187.58 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2),V_b_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_c_2),V_d_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a_2),V_c_2)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b_2),V_d_2)) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_ivl__disj__int_I4_J,axiom, % 187.68/187.58 ! [V_u_2,V_l_2,T_a] : % 187.68/187.58 ( class_Orderings_Oorder(T_a) % 187.68/187.58 => 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)) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_ivl__disj__int_I2_J,axiom, % 187.68/187.58 ! [V_u_2,V_l_2,T_a] : % 187.68/187.58 ( class_Orderings_Oorder(T_a) % 187.68/187.58 => 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)) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_ivl__disj__int_I16_J,axiom, % 187.68/187.58 ! [V_u_2,V_m_2,V_l_2,T_a] : % 187.68/187.58 ( class_Orderings_Oorder(T_a) % 187.68/187.58 => 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)) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_ivl__disj__int_I13_J,axiom, % 187.68/187.58 ! [V_u_2,V_m_2,V_l_2,T_a] : % 187.68/187.58 ( class_Orderings_Oorder(T_a) % 187.68/187.58 => 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)) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_ivl__disj__int_I12_J,axiom, % 187.68/187.58 ! [V_u_2,V_m_2,V_l_2,T_a] : % 187.68/187.58 ( class_Orderings_Oorder(T_a) % 187.68/187.58 => 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)) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_equiv__class__self,axiom, % 187.68/187.58 ! [V_a_2,V_r_2,V_A_2,T_a] : % 187.68/187.58 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 187.68/187.58 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 187.68/187.58 => 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)))))) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_Int__greaterThanAtMost,axiom, % 187.68/187.58 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] : % 187.68/187.58 ( class_Orderings_Olinorder(T_a) % 187.68/187.58 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_a_2,V_b_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a_2),V_c_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b_2),V_d_2)) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_ivl__disj__int_I9_J,axiom, % 187.68/187.58 ! [V_u_2,V_m_2,V_l_2,T_a] : % 187.68/187.58 ( class_Orderings_Oorder(T_a) % 187.68/187.58 => 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)) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_Int__greaterThanLessThan,axiom, % 187.68/187.58 ! [V_d_2,V_c_2,V_b_2,V_a_2,T_a] : % 187.68/187.58 ( class_Orderings_Olinorder(T_a) % 187.68/187.58 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_a_2,V_b_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a_2),V_c_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b_2),V_d_2)) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_Int__atLeastAtMostL1,axiom, % 187.68/187.58 ! [V_d_2,V_b_2,V_a_2,T_a] : % 187.68/187.58 ( class_Orderings_Olinorder(T_a) % 187.68/187.58 => 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)) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_Int__atLeastAtMostR1,axiom, % 187.68/187.58 ! [V_d_2,V_c_2,V_b_2,T_a] : % 187.68/187.58 ( class_Orderings_Olinorder(T_a) % 187.68/187.58 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_c_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b_2),V_d_2)) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_ivl__disj__int_I3_J,axiom, % 187.68/187.58 ! [V_u_2,V_l_2,T_a] : % 187.68/187.58 ( class_Orderings_Oorder(T_a) % 187.68/187.58 => 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)) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_ivl__disj__int_I10_J,axiom, % 187.68/187.58 ! [V_u_2,V_m_2,V_l_2,T_a] : % 187.68/187.58 ( class_Orderings_Oorder(T_a) % 187.68/187.58 => 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)) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_ivl__disj__int_I1_J,axiom, % 187.68/187.58 ! [V_u_2,V_l_2,T_a] : % 187.68/187.58 ( class_Orderings_Oorder(T_a) % 187.68/187.58 => 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)) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_folding__image__simple_Ounion__inter,axiom, % 187.68/187.58 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 187.68/187.58 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 187.68/187.58 => 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)) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_fold1__belowI,axiom, % 187.68/187.58 ! [V_a_2,V_A_2,T_a] : % 187.68/187.58 ( class_Lattices_Osemilattice__inf(T_a) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.58 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 187.68/187.58 => 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)) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_below__fold1__iff,axiom, % 187.68/187.58 ! [V_x_2,V_A_2,T_a] : % 187.68/187.58 ( class_Lattices_Osemilattice__inf(T_a) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.58 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.58 => ( 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))) % 187.68/187.58 <=> ! [B_x] : % 187.68/187.58 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 187.68/187.58 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),B_x)) ) ) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_setsum__Un__Int,axiom, % 187.68/187.58 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] : % 187.68/187.58 ( class_Groups_Ocomm__monoid__add(T_b) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 187.68/187.58 => 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)) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_setprod__Un__Int,axiom, % 187.68/187.58 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] : % 187.68/187.58 ( class_Groups_Ocomm__monoid__mult(T_b) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 187.68/187.58 => 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)) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_setprod_Ounion__inter,axiom, % 187.68/187.58 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] : % 187.68/187.58 ( class_Groups_Ocomm__monoid__mult(T_b) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 187.68/187.58 => 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)) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_card__Un__Int,axiom, % 187.68/187.58 ! [V_B_2,V_A_2,T_a] : % 187.68/187.58 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 187.68/187.58 => 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))) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_card_Ounion__inter,axiom, % 187.68/187.58 ! [V_B_2,V_A_2,T_a] : % 187.68/187.58 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 187.68/187.58 => 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)) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_card__Diff__subset__Int,axiom, % 187.68/187.58 ! [V_B_2,V_A_2,T_a] : % 187.68/187.58 ( 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))) % 187.68/187.58 => 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))) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_equiv__class__eq,axiom, % 187.68/187.58 ! [V_b_2,V_a_2,V_r_2,V_A_2,T_a] : % 187.68/187.58 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 187.68/187.58 => ( 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)) % 187.68/187.58 => 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)))) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_setsum__restrict__set,axiom, % 187.68/187.58 ! [V_B_2,V_f_2,V_A_2,T_a,T_b] : % 187.68/187.58 ( class_Groups_Ocomm__monoid__add(T_b) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.58 => 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) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_folding_Ounion__inter,axiom, % 187.68/187.58 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 187.68/187.58 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 187.68/187.58 => 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)) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_folding__image__simple_Ounion__disjoint,axiom, % 187.68/187.58 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 187.68/187.58 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 187.68/187.58 => ( 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)) % 187.68/187.58 => 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)) ) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_folding__one_Ounion__disjoint,axiom, % 187.68/187.58 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_a] : % 187.68/187.58 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.58 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 187.68/187.58 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.58 => ( 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)) % 187.68/187.58 => 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)) ) ) ) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_folding__one_Ounion__inter,axiom, % 187.68/187.58 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_a] : % 187.68/187.58 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 187.68/187.58 => ( 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)) % 187.68/187.58 => 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)) ) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_setsum__Un__disjoint,axiom, % 187.68/187.58 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] : % 187.68/187.58 ( class_Groups_Ocomm__monoid__add(T_b) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 187.68/187.58 => ( 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)) % 187.68/187.58 => 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)) ) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_setsum__Un,axiom, % 187.68/187.58 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] : % 187.68/187.58 ( class_Groups_Oab__group__add(T_b) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 187.68/187.58 => 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))) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_setprod__Un__disjoint,axiom, % 187.68/187.58 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] : % 187.68/187.58 ( class_Groups_Ocomm__monoid__mult(T_b) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 187.68/187.58 => ( 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)) % 187.68/187.58 => 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)) ) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_setprod_Ounion__disjoint,axiom, % 187.68/187.58 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] : % 187.68/187.58 ( class_Groups_Ocomm__monoid__mult(T_b) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 187.68/187.58 => ( 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)) % 187.68/187.58 => 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)) ) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_equiv__class__eq__iff,axiom, % 187.68/187.58 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_a] : % 187.68/187.58 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 187.68/187.58 => ( 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)) % 187.68/187.58 <=> ( 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)))) % 187.68/187.58 & hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 187.68/187.58 & hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_eq__equiv__class,axiom, % 187.68/187.58 ! [V_A_2,V_b_2,V_a_2,V_r_2,T_a] : % 187.68/187.58 ( 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)))) % 187.68/187.58 => ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 187.68/187.58 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),V_A_2)) % 187.68/187.58 => 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)) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_eq__equiv__class__iff,axiom, % 187.68/187.58 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_a] : % 187.68/187.58 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 187.68/187.58 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 187.68/187.58 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) % 187.68/187.58 => ( 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)))) % 187.68/187.58 <=> 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)) ) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_card__Un__disjoint,axiom, % 187.68/187.58 ! [V_B_2,V_A_2,T_a] : % 187.68/187.58 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 187.68/187.58 => ( 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)) % 187.68/187.58 => 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)) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_equiv__class__subset,axiom, % 187.68/187.58 ! [V_b_2,V_a_2,V_r_2,V_A_2,T_a] : % 187.68/187.58 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 187.68/187.58 => ( 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)) % 187.68/187.58 => 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)))))) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_fold__image__Un__Int,axiom, % 187.68/187.58 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] : % 187.68/187.58 ( class_Groups_Ocomm__monoid__mult(T_b) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 187.68/187.58 => 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))) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_fold1__Un,axiom, % 187.68/187.58 ! [V_B_2,V_A_2,T_a] : % 187.68/187.58 ( class_Groups_Oab__semigroup__mult(T_a) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.58 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 187.68/187.58 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.58 => ( 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)) % 187.68/187.58 => 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)) ) ) ) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_Sup__fin_Ounion__inter,axiom, % 187.68/187.58 ! [V_B_2,V_A_2,T_a] : % 187.68/187.58 ( class_Lattices_Olattice(T_a) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 187.68/187.58 => ( 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)) % 187.68/187.58 => 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)) ) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_Sup__fin_Ounion__disjoint,axiom, % 187.68/187.58 ! [V_B_2,V_A_2,T_a] : % 187.68/187.58 ( class_Lattices_Olattice(T_a) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.58 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 187.68/187.58 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.58 => ( 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)) % 187.68/187.58 => 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)) ) ) ) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_Min_Ounion__inter,axiom, % 187.68/187.58 ! [V_B_2,V_A_2,T_a] : % 187.68/187.58 ( class_Orderings_Olinorder(T_a) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 187.68/187.58 => ( 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)) % 187.68/187.58 => 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)) ) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_Min_Ounion__disjoint,axiom, % 187.68/187.58 ! [V_B_2,V_A_2,T_a] : % 187.68/187.58 ( class_Orderings_Olinorder(T_a) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.58 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 187.68/187.58 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.58 => ( 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)) % 187.68/187.58 => 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)) ) ) ) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_Max_Ounion__inter,axiom, % 187.68/187.58 ! [V_B_2,V_A_2,T_a] : % 187.68/187.58 ( class_Orderings_Olinorder(T_a) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 187.68/187.58 => ( 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)) % 187.68/187.58 => 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)) ) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_Max_Ounion__disjoint,axiom, % 187.68/187.58 ! [V_B_2,V_A_2,T_a] : % 187.68/187.58 ( class_Orderings_Olinorder(T_a) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.58 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 187.68/187.58 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.58 => ( 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)) % 187.68/187.58 => 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)) ) ) ) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_min__max_OInf__fin_Ounion__inter,axiom, % 187.68/187.58 ! [V_B_2,V_A_2,T_a] : % 187.68/187.58 ( class_Orderings_Olinorder(T_a) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 187.68/187.58 => ( 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)) % 187.68/187.58 => 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)) ) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_min__max_OInf__fin_Ounion__disjoint,axiom, % 187.68/187.58 ! [V_B_2,V_A_2,T_a] : % 187.68/187.58 ( class_Orderings_Olinorder(T_a) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.58 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 187.68/187.58 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.58 => ( 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)) % 187.68/187.58 => 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)) ) ) ) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_min__max_OSup__fin_Ounion__inter,axiom, % 187.68/187.58 ! [V_B_2,V_A_2,T_a] : % 187.68/187.58 ( class_Orderings_Olinorder(T_a) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 187.68/187.58 => ( 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)) % 187.68/187.58 => 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)) ) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_min__max_OSup__fin_Ounion__disjoint,axiom, % 187.68/187.58 ! [V_B_2,V_A_2,T_a] : % 187.68/187.58 ( class_Orderings_Olinorder(T_a) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.58 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 187.68/187.58 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.58 => ( 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)) % 187.68/187.58 => 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)) ) ) ) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_setsum__Un__nat,axiom, % 187.68/187.58 ! [V_f_2,V_B_2,V_A_2,T_a] : % 187.68/187.58 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 187.68/187.58 => 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))) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_folding_Ounion,axiom, % 187.68/187.58 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 187.68/187.58 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 187.68/187.58 => ( 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)) % 187.68/187.58 => 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)) ) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_card_Ounion__inter__neutral,axiom, % 187.68/187.58 ! [V_B_2,V_A_2,T_a] : % 187.68/187.58 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 187.68/187.58 => ( ( ? [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))) % 187.68/187.58 => c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 187.68/187.58 => 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)) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_setprod__Un,axiom, % 187.68/187.58 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] : % 187.68/187.58 ( class_Fields_Ofield(T_b) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 187.68/187.58 => ( ! [B_x] : % 187.68/187.58 ( 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))) % 187.68/187.58 => hAPP(V_f_2,B_x) != c_Groups_Ozero__class_Ozero(T_b) ) % 187.68/187.58 => 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))) ) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_fold__image__Un__one,axiom, % 187.68/187.58 ! [V_f_2,V_T_2,V_S_2,T_a,T_b] : % 187.68/187.58 ( class_Groups_Ocomm__monoid__mult(T_b) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2)) % 187.68/187.58 => ( ! [B_x] : % 187.68/187.58 ( 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))) % 187.68/187.58 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_b) ) % 187.68/187.58 => 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)) ) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_eq__equiv__class__iff2,axiom, % 187.68/187.58 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_a] : % 187.68/187.58 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 187.68/187.58 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 187.68/187.58 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) % 187.68/187.58 => ( 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) % 187.68/187.58 <=> 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)) ) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_inf__nat__def,axiom, % 187.68/187.58 c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat) = c_Orderings_Oord__class_Omin(tc_Nat_Onat) ). % 187.68/187.58 % 187.68/187.58 fof(fact_inf__Int__eq2,axiom, % 187.68/187.58 ! [V_y_2,V_x_2,V_S_2,V_R_2,T_b,T_a] : % 187.68/187.58 ( 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)) % 187.68/187.58 <=> 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))) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_quotient__is__empty,axiom, % 187.68/187.58 ! [V_r_2,V_A_2,T_a] : % 187.68/187.58 ( 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)) % 187.68/187.58 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_quotient__is__empty2,axiom, % 187.68/187.58 ! [V_r_2,V_A_2,T_a] : % 187.68/187.58 ( 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) % 187.68/187.58 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_quotient__empty,axiom, % 187.68/187.58 ! [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)) ). % 187.68/187.58 % 187.68/187.58 fof(fact_quotient__disj,axiom, % 187.68/187.58 ! [V_Y_2,V_X_2,V_r_2,V_A_2,T_a] : % 187.68/187.58 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 187.68/187.58 => ( 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))) % 187.68/187.58 => ( 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))) % 187.68/187.58 => ( V_X_2 = V_Y_2 % 187.68/187.58 | 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)) ) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_quotientI,axiom, % 187.68/187.58 ! [V_r_2,V_A_2,V_x_2,T_a] : % 187.68/187.58 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 187.68/187.58 => 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))) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_quotient__eqI,axiom, % 187.68/187.58 ! [V_y_2,V_x_2,V_Y_2,V_X_2,V_r_2,V_A_2,T_a] : % 187.68/187.58 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 187.68/187.58 => ( 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))) % 187.68/187.58 => ( 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))) % 187.68/187.58 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_X_2)) % 187.68/187.58 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_Y_2)) % 187.68/187.58 => ( 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)) % 187.68/187.58 => V_X_2 = V_Y_2 ) ) ) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_quotient__eq__iff,axiom, % 187.68/187.58 ! [V_y_2,V_x_2,V_Y_2,V_X_2,V_r_2,V_A_2,T_a] : % 187.68/187.58 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 187.68/187.58 => ( 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))) % 187.68/187.58 => ( 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))) % 187.68/187.58 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_X_2)) % 187.68/187.58 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_Y_2)) % 187.68/187.58 => ( V_X_2 = V_Y_2 % 187.68/187.58 <=> 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)) ) ) ) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_singleton__quotient,axiom, % 187.68/187.58 ! [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))) ). % 187.68/187.58 % 187.68/187.58 fof(fact_quotientE,axiom, % 187.68/187.58 ! [V_r_2,V_A_2,V_X_2,T_a] : % 187.68/187.58 ( 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))) % 187.68/187.58 => ~ ! [B_x] : % 187.68/187.58 ( 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)))) % 187.68/187.58 => ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_setprod__Un__one,axiom, % 187.68/187.58 ! [V_f_2,V_T_2,V_S_2,T_a,T_b] : % 187.68/187.58 ( class_Groups_Ocomm__monoid__mult(T_b) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2)) % 187.68/187.58 => ( ! [B_x] : % 187.68/187.58 ( 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))) % 187.68/187.58 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_b) ) % 187.68/187.58 => 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)) ) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_setprod_Ounion__inter__neutral,axiom, % 187.68/187.58 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] : % 187.68/187.58 ( class_Groups_Ocomm__monoid__mult(T_b) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 187.68/187.58 => ( ! [B_x] : % 187.68/187.58 ( 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))) % 187.68/187.58 => hAPP(V_g_2,B_x) = c_Groups_Oone__class_Oone(T_b) ) % 187.68/187.58 => 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)) ) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_inf2E,axiom, % 187.68/187.58 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_b,T_a] : % 187.68/187.58 ( 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)) % 187.68/187.58 => ~ ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) % 187.68/187.58 => ~ hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_inf2I,axiom, % 187.68/187.58 ! [T_b,T_a,V_B_2,V_y_2,V_x_2,V_A_2] : % 187.68/187.58 ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) % 187.68/187.58 => ( hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) % 187.68/187.58 => 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)) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_inf2D2,axiom, % 187.68/187.58 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_b,T_a] : % 187.68/187.58 ( 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)) % 187.68/187.58 => hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_inf2D1,axiom, % 187.68/187.58 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_b,T_a] : % 187.68/187.58 ( 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)) % 187.68/187.58 => hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_setsum__Un__zero,axiom, % 187.68/187.58 ! [V_f_2,V_T_2,V_S_2,T_a,T_b] : % 187.68/187.58 ( class_Groups_Ocomm__monoid__add(T_b) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2)) % 187.68/187.58 => ( ! [B_x] : % 187.68/187.58 ( 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))) % 187.68/187.58 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) ) % 187.68/187.58 => 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)) ) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_setsum_Ounion__inter__neutral,axiom, % 187.68/187.58 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] : % 187.68/187.58 ( class_Groups_Ocomm__monoid__add(T_b) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 187.68/187.58 => ( ! [B_x] : % 187.68/187.58 ( 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))) % 187.68/187.58 => hAPP(V_g_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) ) % 187.68/187.58 => 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)) ) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_Inf__fin_Oremove,axiom, % 187.68/187.58 ! [V_x_2,V_A_2,T_a] : % 187.68/187.58 ( class_Lattices_Olattice(T_a) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.58 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 187.68/187.58 => ( ( 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)) % 187.68/187.58 => c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2) = V_x_2 ) % 187.68/187.58 & ( 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)) % 187.68/187.58 => 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)))))) ) ) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_Inf__fin_Osingleton,axiom, % 187.68/187.58 ! [V_x_2,T_a] : % 187.68/187.58 ( class_Lattices_Olattice(T_a) % 187.68/187.58 => 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 ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_sup__Inf__absorb,axiom, % 187.68/187.58 ! [V_a_2,V_A_2,T_a] : % 187.68/187.58 ( class_Lattices_Olattice(T_a) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.58 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 187.68/187.58 => 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 ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_Inf__fin_Oin__idem,axiom, % 187.68/187.58 ! [V_x_2,V_A_2,T_a] : % 187.68/187.58 ( class_Lattices_Olattice(T_a) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.58 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 187.68/187.58 => 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) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_Inf__fin_OF__eq,axiom, % 187.68/187.58 ! [V_A_2,T_a] : % 187.68/187.58 ( class_Lattices_Olattice(T_a) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.58 => 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) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_Inf__fin_Oinsert__idem,axiom, % 187.68/187.58 ! [V_x_2,V_A_2,T_a] : % 187.68/187.58 ( class_Lattices_Olattice(T_a) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.58 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.58 => 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)) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_Inf__fin_Osubset__idem,axiom, % 187.68/187.58 ! [V_B_2,V_A_2,T_a] : % 187.68/187.58 ( class_Lattices_Olattice(T_a) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.58 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 187.68/187.58 => 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) ) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_Inf__fin_Ounion__idem,axiom, % 187.68/187.58 ! [V_B_2,V_A_2,T_a] : % 187.68/187.58 ( class_Lattices_Olattice(T_a) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.58 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 187.68/187.58 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.58 => 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)) ) ) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_Inf__le__Sup,axiom, % 187.68/187.58 ! [V_A_2,T_a] : % 187.68/187.58 ( class_Lattices_Olattice(T_a) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.58 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.58 => 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))) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_Inf__fin_Oinsert,axiom, % 187.68/187.58 ! [V_x_2,V_A_2,T_a] : % 187.68/187.58 ( class_Lattices_Olattice(T_a) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.58 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 187.68/187.58 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.58 => 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)) ) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_Inf__fin_Oinsert__remove,axiom, % 187.68/187.58 ! [V_x_2,V_A_2,T_a] : % 187.68/187.58 ( class_Lattices_Olattice(T_a) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.58 => ( ( 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)) % 187.68/187.58 => 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 ) % 187.68/187.58 & ( 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)) % 187.68/187.58 => 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)))))) ) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_Inf__fin_Ounion__disjoint,axiom, % 187.68/187.58 ! [V_B_2,V_A_2,T_a] : % 187.68/187.58 ( class_Lattices_Olattice(T_a) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.58 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 187.68/187.58 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.58 => ( 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)) % 187.68/187.58 => 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)) ) ) ) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_Inf__fin_Ounion__inter,axiom, % 187.68/187.58 ! [V_B_2,V_A_2,T_a] : % 187.68/187.58 ( class_Lattices_Olattice(T_a) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 187.68/187.58 => ( 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)) % 187.68/187.58 => 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)) ) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_Inf__fin_Oclosed,axiom, % 187.68/187.58 ! [V_A_2,T_a] : % 187.68/187.58 ( class_Lattices_Olattice(T_a) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.58 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.58 => ( ! [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)))))) % 187.68/187.58 => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2)),V_A_2)) ) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_card__quotient__disjoint,axiom, % 187.68/187.58 ! [V_r_2,V_A_2,T_a] : % 187.68/187.58 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.58 => ( 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) % 187.68/187.58 => 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) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_quotient__def,axiom, % 187.68/187.58 ! [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)))) ). % 187.68/187.58 % 187.68/187.58 fof(fact_inj__on__empty,axiom, % 187.68/187.58 ! [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))) ). % 187.68/187.58 % 187.68/187.58 fof(fact_inj__uminus,axiom, % 187.68/187.58 ! [V_A_2,T_a] : % 187.68/187.58 ( class_Groups_Oordered__ab__group__add(T_a) % 187.68/187.58 => c_Fun_Oinj__on(T_a,T_a,c_Groups_Ouminus__class_Ouminus(T_a),V_A_2) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_SUP1__I,axiom, % 187.68/187.58 ! [T_b,V_b_2,V_B_2,V_A_2,V_a_2,T_a] : % 187.68/187.58 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 187.68/187.58 => ( hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2)) % 187.68/187.58 => 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)) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_Image__UN,axiom, % 187.68/187.58 ! [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)) ). % 187.68/187.58 % 187.68/187.58 fof(fact_inj__onD,axiom, % 187.68/187.58 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_b,T_a] : % 187.68/187.58 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 187.68/187.58 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) % 187.68/187.58 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 187.68/187.58 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) % 187.68/187.58 => V_x_2 = V_y_2 ) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_inj__on__iff,axiom, % 187.68/187.58 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_b,T_a] : % 187.68/187.58 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 187.68/187.58 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 187.68/187.58 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) % 187.68/187.58 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) % 187.68/187.58 <=> V_x_2 = V_y_2 ) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_inj__on__contraD,axiom, % 187.68/187.58 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_b,T_a] : % 187.68/187.58 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 187.68/187.58 => ( V_x_2 != V_y_2 % 187.68/187.58 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 187.68/187.58 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) % 187.68/187.58 => hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2) ) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_subset__inj__on,axiom, % 187.68/187.58 ! [V_A_2,V_B_2,V_f_2,T_b,T_a] : % 187.68/187.58 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2) % 187.68/187.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 187.68/187.58 => c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_finite__UN,axiom, % 187.68/187.58 ! [V_B_2,T_b,V_A_2,T_a] : % 187.68/187.58 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.58 => ( 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))) % 187.68/187.58 <=> ! [B_x] : % 187.68/187.58 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 187.68/187.58 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_x))) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_inj__on__id2,axiom, % 187.68/187.58 ! [V_A_2,T_a] : c_Fun_Oinj__on(T_a,T_a,c_COMBI(T_a),V_A_2) ). % 187.68/187.58 % 187.68/187.58 fof(fact_SUP1__iff,axiom, % 187.68/187.58 ! [V_b_2,V_B_2,V_A_2,T_b,T_a] : % 187.68/187.58 ( 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)) % 187.68/187.58 <=> ? [B_x] : % 187.68/187.58 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 187.68/187.58 & hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2)) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_inj__on__def,axiom, % 187.68/187.58 ! [V_A_2,V_f_2,T_b,T_a] : % 187.68/187.58 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 187.68/187.58 <=> ! [B_x] : % 187.68/187.58 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 187.68/187.58 => ! [B_xa] : % 187.68/187.58 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_A_2)) % 187.68/187.58 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_xa) % 187.68/187.58 => B_x = B_xa ) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_inj__on__diff,axiom, % 187.68/187.58 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 187.68/187.58 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 187.68/187.58 => 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)) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_inj__on__imageI2,axiom, % 187.68/187.58 ! [V_A_2,V_f_2,V_f_H_2,T_c,T_b,T_a] : % 187.68/187.58 ( 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) % 187.68/187.58 => c_Fun_Oinj__on(T_a,T_c,V_f_2,V_A_2) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_UN__o,axiom, % 187.68/187.58 ! [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) ). % 187.68/187.58 % 187.68/187.58 fof(fact_inj__on__Int,axiom, % 187.68/187.58 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 187.68/187.58 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 187.68/187.58 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2) % 187.68/187.58 => 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)) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_finite__imageD,axiom, % 187.68/187.58 ! [V_A_2,V_f_2,T_b,T_a] : % 187.68/187.58 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2))) % 187.68/187.58 => ( c_Fun_Oinj__on(T_b,T_a,V_f_2,V_A_2) % 187.68/187.58 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_inj__on__Un__image__eq__iff,axiom, % 187.68/187.58 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 187.68/187.58 ( 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)) % 187.68/187.58 => ( 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) % 187.68/187.58 <=> V_A_2 = V_B_2 ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_inj__on__imageI,axiom, % 187.68/187.58 ! [V_A_2,V_f_2,V_g_2,T_c,T_b,T_a] : % 187.68/187.58 ( 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) % 187.68/187.58 => 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)) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_comp__inj__on,axiom, % 187.68/187.58 ! [V_g_2,T_c,V_A_2,V_f_2,T_b,T_a] : % 187.68/187.58 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 187.68/187.58 => ( 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)) % 187.68/187.58 => 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) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_comp__inj__on__iff,axiom, % 187.68/187.58 ! [V_f_H_2,T_c,V_A_2,V_f_2,T_b,T_a] : % 187.68/187.58 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 187.68/187.58 => ( 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)) % 187.68/187.58 <=> 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) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_card__image,axiom, % 187.68/187.58 ! [V_A_2,V_f_2,T_b,T_a] : % 187.68/187.58 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 187.68/187.58 => 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) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_inj__on__strict__subset,axiom, % 187.68/187.58 ! [V_A_2,V_B_2,V_f_2,T_b,T_a] : % 187.68/187.58 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2) % 187.68/187.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 187.68/187.58 => 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))) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_endo__inj__surj,axiom, % 187.68/187.58 ! [V_f_2,V_A_2,T_a] : % 187.68/187.58 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.58 => ( 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)) % 187.68/187.58 => ( c_Fun_Oinj__on(T_a,T_a,V_f_2,V_A_2) % 187.68/187.58 => hAPP(c_Set_Oimage(T_a,T_a,V_f_2),V_A_2) = V_A_2 ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_finite__surj__inj,axiom, % 187.68/187.58 ! [V_f_2,V_A_2,T_a] : % 187.68/187.58 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.58 => ( 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))) % 187.68/187.58 => c_Fun_Oinj__on(T_a,T_a,V_f_2,V_A_2) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_inj__on__image__Int,axiom, % 187.68/187.58 ! [V_B_2,V_A_2,V_C_2,V_f_2,T_b,T_a] : % 187.68/187.58 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_C_2) % 187.68/187.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) % 187.68/187.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) % 187.68/187.58 => 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)) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_inj__on__iff__eq__card,axiom, % 187.68/187.58 ! [V_f_2,T_b,V_A_2,T_a] : % 187.68/187.58 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.58 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 187.68/187.58 <=> 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) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_eq__card__imp__inj__on,axiom, % 187.68/187.58 ! [V_f_2,T_b,V_A_2,T_a] : % 187.68/187.58 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.58 => ( 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) % 187.68/187.58 => c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_inj__on__image__set__diff,axiom, % 187.68/187.58 ! [V_B_2,V_A_2,V_C_2,V_f_2,T_b,T_a] : % 187.68/187.58 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_C_2) % 187.68/187.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) % 187.68/187.58 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) % 187.68/187.58 => 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)) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_setsum__reindex,axiom, % 187.68/187.58 ! [V_h_2,V_B_2,V_f_2,T_b,T_a,T_c] : % 187.68/187.58 ( class_Groups_Ocomm__monoid__add(T_c) % 187.68/187.58 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2) % 187.68/187.58 => 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) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_pigeonhole,axiom, % 187.68/187.58 ! [V_A_2,V_f_2,T_b,T_a] : % 187.68/187.58 ( 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))) % 187.68/187.58 => ~ c_Fun_Oinj__on(T_b,T_a,V_f_2,V_A_2) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_inj__on__fun__updI,axiom, % 187.68/187.58 ! [V_x_2,V_y_2,V_A_2,V_f_2,T_b,T_a] : % 187.68/187.58 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 187.68/187.58 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2))) % 187.68/187.58 => 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) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_setprod__reindex,axiom, % 187.68/187.58 ! [V_h_2,V_B_2,V_f_2,T_b,T_a,T_c] : % 187.68/187.58 ( class_Groups_Ocomm__monoid__mult(T_c) % 187.68/187.58 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2) % 187.68/187.58 => 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) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_setprod__reindex__cong,axiom, % 187.68/187.58 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_b,T_a,T_c] : % 187.68/187.58 ( class_Groups_Ocomm__monoid__mult(T_c) % 187.68/187.58 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 187.68/187.58 => ( V_B_2 = hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2) % 187.68/187.58 => ( V_g_2 = hAPP(c_Fun_Ocomp(T_b,T_c,T_a,V_h_2),V_f_2) % 187.68/187.58 => 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) ) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_Image__eq__UN,axiom, % 187.68/187.58 ! [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))))) ). % 187.68/187.58 % 187.68/187.58 fof(fact_setsum_Oreindex,axiom, % 187.68/187.58 ! [V_g_2,V_h_2,V_A_2,T_a,T_b] : % 187.68/187.58 ( class_Groups_Ocomm__monoid__add(T_b) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.58 => ( c_Fun_Oinj__on(T_a,T_a,V_h_2,V_A_2) % 187.68/187.58 => 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) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_card__bij__eq,axiom, % 187.68/187.58 ! [V_g_2,V_B_2,V_A_2,V_f_2,T_b,T_a] : % 187.68/187.58 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 187.68/187.58 => ( 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)) % 187.68/187.58 => ( c_Fun_Oinj__on(T_b,T_a,V_g_2,V_B_2) % 187.68/187.58 => ( 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)) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 187.68/187.58 => hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = hAPP(c_Finite__Set_Ocard(T_b),V_B_2) ) ) ) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_setprod_Oreindex,axiom, % 187.68/187.58 ! [V_g_2,V_h_2,V_A_2,T_a,T_b] : % 187.68/187.58 ( class_Groups_Ocomm__monoid__mult(T_b) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.58 => ( c_Fun_Oinj__on(T_a,T_a,V_h_2,V_A_2) % 187.68/187.58 => 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) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_inj__on__insert,axiom, % 187.68/187.58 ! [V_A_2,V_a_2,V_f_2,T_b,T_a] : % 187.68/187.58 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) % 187.68/187.58 <=> ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 187.68/187.58 & ~ 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))))))) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_inj__on__Un,axiom, % 187.68/187.58 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 187.68/187.58 ( 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)) % 187.68/187.58 <=> ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 187.68/187.58 & c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2) % 187.68/187.58 & 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)) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_inj__on__iff__card__le,axiom, % 187.68/187.58 ! [V_B_2,T_b,V_A_2,T_a] : % 187.68/187.58 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 187.68/187.58 => ( ? [B_f] : % 187.68/187.58 ( c_Fun_Oinj__on(T_a,T_b,B_f,V_A_2) % 187.68/187.58 & 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)) ) % 187.68/187.58 <=> 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))) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_card__inj__on__le,axiom, % 187.68/187.58 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 187.68/187.58 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 187.68/187.58 => ( 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)) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 187.68/187.58 => 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))) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_fold__image__reindex,axiom, % 187.68/187.58 ! [V_z_2,V_g_2,V_h_2,T_b,V_A_2,T_a,T_c] : % 187.68/187.58 ( class_Groups_Oab__semigroup__mult(T_c) % 187.68/187.58 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.58 => ( c_Fun_Oinj__on(T_a,T_b,V_h_2,V_A_2) % 187.68/187.58 => 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) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_quotient__diff1,axiom, % 187.68/187.58 ! [V_a_2,V_A_2,V_r_2,T_a] : % 187.68/187.58 ( 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) % 187.68/187.58 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 187.68/187.58 => 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)) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_UN__I,axiom, % 187.68/187.58 ! [V_B_2,V_b_2,T_b,V_A_2,V_a_2,T_a] : % 187.68/187.58 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 187.68/187.58 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2))) % 187.68/187.58 => 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))) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_UN__Pow__subset,axiom, % 187.68/187.58 ! [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)))) ). % 187.68/187.58 % 187.68/187.58 fof(fact_image__eq__UN,axiom, % 187.68/187.58 ! [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)))) ). % 187.68/187.58 % 187.68/187.58 fof(fact_inj__Suc,axiom, % 187.68/187.58 ! [V_N_2] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,V_N_2) ). % 187.68/187.58 % 187.68/187.58 fof(fact_inj__Some,axiom, % 187.68/187.58 ! [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) ). % 187.68/187.58 % 187.68/187.58 fof(fact_inj__on__add__nat,axiom, % 187.68/187.58 ! [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) ). % 187.68/187.58 % 187.68/187.58 fof(fact_swap__inj__on,axiom, % 187.68/187.58 ! [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) ). % 187.68/187.58 % 187.68/187.58 fof(fact_ball__UN,axiom, % 187.68/187.58 ! [V_P_2,V_B_2,V_A_2,T_b,T_a] : % 187.68/187.58 ( ! [B_x] : % 187.68/187.58 ( 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))) % 187.68/187.58 => hBOOL(hAPP(V_P_2,B_x)) ) % 187.68/187.58 <=> ! [B_x] : % 187.68/187.58 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 187.68/187.58 => ! [B_xa] : % 187.68/187.58 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),hAPP(V_B_2,B_x))) % 187.68/187.58 => hBOOL(hAPP(V_P_2,B_xa)) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_UN__le__add__shift,axiom, % 187.68/187.58 ! [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) ). % 187.68/187.58 % 187.68/187.58 fof(fact_SUP__commute,axiom, % 187.68/187.58 ! [V_f_2,V_B_2,T_c,V_A_2,T_b,T_a] : % 187.68/187.58 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 187.68/187.58 => 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))) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_UN__UN__flatten,axiom, % 187.68/187.58 ! [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)) ). % 187.68/187.58 % 187.68/187.58 fof(fact_UN__simps_I9_J,axiom, % 187.68/187.58 ! [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)) ). % 187.68/187.58 % 187.68/187.58 fof(fact_UN__extend__simps_I9_J,axiom, % 187.68/187.58 ! [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) ). % 187.68/187.58 % 187.68/187.58 fof(fact_UN__le__eq__Un0,axiom, % 187.68/187.58 ! [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))) ). % 187.68/187.58 % 187.68/187.58 fof(fact_SUP__le__iff,axiom, % 187.68/187.58 ! [V_u_2,V_M_2,V_A_2,T_b,T_a] : % 187.68/187.58 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 187.68/187.58 => ( 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)) % 187.68/187.58 <=> ! [B_x] : % 187.68/187.58 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 187.68/187.58 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(V_M_2,B_x)),V_u_2)) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_less__SUP__iff,axiom, % 187.68/187.58 ! [V_f_2,V_A_2,T_b,V_a_2,T_a] : % 187.68/187.58 ( ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 187.68/187.58 & class_Orderings_Olinorder(T_a) ) % 187.68/187.58 => ( 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))) % 187.68/187.58 <=> ? [B_x] : % 187.68/187.58 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 187.68/187.58 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),hAPP(V_f_2,B_x))) ) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_UN__iff,axiom, % 187.68/187.58 ! [V_B_2,V_A_2,T_b,V_b_2,T_a] : % 187.68/187.58 ( 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))) % 187.68/187.58 <=> ? [B_x] : % 187.68/187.58 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 187.68/187.58 & hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(V_B_2,B_x))) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_SUP__const,axiom, % 187.68/187.58 ! [V_M_2,T_a,V_A_2,T_b] : % 187.68/187.58 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 187.68/187.58 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.58 => 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 ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_UNION__empty__conv_I1_J,axiom, % 187.68/187.58 ! [V_B_2,V_A_2,T_b,T_a] : % 187.68/187.58 ( 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) % 187.68/187.58 <=> ! [B_x] : % 187.68/187.58 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 187.68/187.58 => hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_UN__empty2,axiom, % 187.68/187.58 ! [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)) ). % 187.68/187.58 % 187.68/187.58 fof(fact_UN__constant,axiom, % 187.68/187.58 ! [V_c_2,T_b,T_a,V_A_2] : % 187.68/187.58 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.58 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_c_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) % 187.68/187.58 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.58 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_c_2)) = V_c_2 ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_UNION__empty__conv_I2_J,axiom, % 187.68/187.58 ! [V_B_2,V_A_2,T_a,T_b] : % 187.68/187.58 ( 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)) % 187.68/187.58 <=> ! [B_x] : % 187.68/187.58 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 187.68/187.58 => hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_UN__subset__iff,axiom, % 187.68/187.58 ! [V_B_2,V_A_2,V_I_2,T_b,T_a] : % 187.68/187.58 ( 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)) % 187.68/187.58 <=> ! [B_x] : % 187.68/187.58 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_I_2)) % 187.68/187.58 => 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)) ) ) ). % 187.68/187.58 % 187.68/187.58 fof(fact_UN__extend__simps_I10_J,axiom, % 187.68/187.58 ! [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) ). % 187.68/187.58 % 187.68/187.58 fof(fact_image__UN,axiom, % 187.68/187.58 ! [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)) ). % 187.68/187.58 % 187.68/187.58 fof(fact_UN__simps_I10_J,axiom, % 187.68/187.58 ! [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)) ). % 187.68/187.58 % 187.68/187.58 fof(fact_UN__Un__distrib,axiom, % 187.68/187.58 ! [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)) ). % 187.68/187.58 % 187.68/187.58 fof(fact_UN__Un,axiom, % 187.68/187.58 ! [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)) ). % 187.68/187.58 % 187.68/187.58 fof(fact_UN__simps_I5_J,axiom, % 187.68/187.58 ! [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)) ). % 187.68/187.58 % 187.68/187.58 fof(fact_UN__simps_I4_J,axiom, % 187.68/187.58 ! [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) ). % 187.68/187.58 % 187.68/187.58 fof(fact_UN__extend__simps_I5_J,axiom, % 187.68/187.58 ! [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)) ). % 187.68/187.58 % 187.68/187.58 fof(fact_Int__UN__distrib,axiom, % 187.68/187.58 ! [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)) ). % 187.68/187.58 % 187.68/187.58 fof(fact_UN__extend__simps_I4_J,axiom, % 187.68/187.58 ! [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)) ). % 187.68/187.58 % 187.68/187.58 fof(fact_Int__UN__distrib2,axiom, % 187.68/187.58 ! [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))) ). % 187.68/187.58 % 187.68/187.58 fof(fact_SUPR__apply,axiom, % 187.68/187.58 ! [V_x_2,V_f_2,V_A_2,T_c,T_b,T_a] : % 187.68/187.58 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 187.68/187.59 => 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)) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_UN__extend__simps_I6_J,axiom, % 187.68/187.59 ! [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)) ). % 187.68/187.59 % 187.68/187.59 fof(fact_UN__simps_I6_J,axiom, % 187.68/187.59 ! [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) ). % 187.68/187.59 % 187.68/187.59 fof(fact_SUP__subset,axiom, % 187.68/187.59 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] : % 187.68/187.59 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 187.68/187.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 187.68/187.59 => 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))) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_le__SUPI,axiom, % 187.68/187.59 ! [V_M_2,V_A_2,V_i_2,T_a,T_b] : % 187.68/187.59 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 187.68/187.59 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),V_A_2)) % 187.68/187.59 => 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))) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_UN__insert__distrib,axiom, % 187.68/187.59 ! [V_B_2,V_a_2,T_b,V_A_2,V_u_2,T_a] : % 187.68/187.59 ( hBOOL(hAPP(hAPP(c_member(T_a),V_u_2),V_A_2)) % 187.68/187.59 => 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)) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_UN__upper,axiom, % 187.68/187.59 ! [V_B_2,T_b,V_A_2,V_a_2,T_a] : % 187.68/187.59 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 187.68/187.59 => 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))) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_UN__absorb,axiom, % 187.68/187.59 ! [V_A_2,T_b,V_I_2,V_k_2,T_a] : % 187.68/187.59 ( hBOOL(hAPP(hAPP(c_member(T_a),V_k_2),V_I_2)) % 187.68/187.59 => 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) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_UN__extend__simps_I1_J,axiom, % 187.68/187.59 ! [V_B_2,V_a_2,T_b,T_a,V_C_2] : % 187.68/187.59 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.59 => 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))) ) % 187.68/187.59 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.59 => 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)) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_UN__singleton,axiom, % 187.68/187.59 ! [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 ). % 187.68/187.59 % 187.68/187.59 fof(fact_UN__simps_I1_J,axiom, % 187.68/187.59 ! [V_B_2,V_a_2,T_b,T_a,V_C_2] : % 187.68/187.59 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.59 => 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)) ) % 187.68/187.59 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.59 => 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)) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_UN__extend__simps_I2_J,axiom, % 187.68/187.59 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 187.68/187.59 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.59 => 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 ) % 187.68/187.59 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.59 => 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)) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_UN__extend__simps_I3_J,axiom, % 187.68/187.59 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 187.68/187.59 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.59 => 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 ) % 187.68/187.59 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.59 => 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)) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_UN__simps_I2_J,axiom, % 187.68/187.59 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 187.68/187.59 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.59 => 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)) ) % 187.68/187.59 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.59 => 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) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_UN__simps_I3_J,axiom, % 187.68/187.59 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 187.68/187.59 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.59 => 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)) ) % 187.68/187.59 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.59 => 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)) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_UN__insert,axiom, % 187.68/187.59 ! [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)) ). % 187.68/187.59 % 187.68/187.59 fof(fact_minus__int__def,axiom, % 187.68/187.59 ! [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))))))) ). % 187.68/187.59 % 187.68/187.59 fof(fact_inj__on__iff__surj,axiom, % 187.68/187.59 ! [V_A_H_2,T_b,T_a,V_A_2] : % 187.68/187.59 ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.59 => ( ? [B_f] : % 187.68/187.59 ( c_Fun_Oinj__on(T_a,T_b,B_f,V_A_2) % 187.68/187.59 & 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)) ) % 187.68/187.59 <=> ? [B_g] : hAPP(c_Set_Oimage(T_b,T_a,B_g),V_A_H_2) = V_A_2 ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_UN__equiv__class,axiom, % 187.68/187.59 ! [V_a_2,V_f_2,T_b,V_r_2,V_A_2,T_a] : % 187.68/187.59 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 187.68/187.59 => ( c_Equiv__Relations_Ocongruent(T_a,tc_fun(T_b,tc_HOL_Obool),V_r_2,V_f_2) % 187.68/187.59 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 187.68/187.59 => 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) ) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_SUP2__I,axiom, % 187.68/187.59 ! [T_c,T_b,V_c_2,V_b_2,V_B_2,V_A_2,V_a_2,T_a] : % 187.68/187.59 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 187.68/187.59 => ( hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_c_2)) % 187.68/187.59 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2)) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_Rep__Integ__inject,axiom, % 187.68/187.59 ! [V_y_2,V_x_2] : % 187.68/187.59 ( hAPP(c_Int_ORep__Integ,V_x_2) = hAPP(c_Int_ORep__Integ,V_y_2) % 187.68/187.59 <=> V_x_2 = V_y_2 ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_Rep__Integ__inverse,axiom, % 187.68/187.59 ! [V_x_2] : hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,V_x_2)) = V_x_2 ). % 187.68/187.59 % 187.68/187.59 fof(fact_congruentD,axiom, % 187.68/187.59 ! [V_z_2,V_y_2,V_f_2,V_r_2,T_b,T_a] : % 187.68/187.59 ( c_Equiv__Relations_Ocongruent(T_a,T_b,V_r_2,V_f_2) % 187.68/187.59 => ( 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)) % 187.68/187.59 => hAPP(V_f_2,V_y_2) = hAPP(V_f_2,V_z_2) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_nat__def,axiom, % 187.68/187.59 ! [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)))))) ). % 187.68/187.59 % 187.68/187.59 fof(fact_congruent2__implies__congruent__UN,axiom, % 187.68/187.59 ! [V_a_2,V_f_2,T_c,V_r2_2,V_A2_2,T_b,V_r1_2,V_A1_2,T_a] : % 187.68/187.59 ( c_Equiv__Relations_Oequiv(T_a,V_A1_2,V_r1_2) % 187.68/187.59 => ( c_Equiv__Relations_Oequiv(T_b,V_A2_2,V_r2_2) % 187.68/187.59 => ( c_Equiv__Relations_Ocongruent2(T_a,T_b,tc_fun(T_c,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2) % 187.68/187.59 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A2_2)) % 187.68/187.59 => 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)) ) ) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_UN__equiv__class2,axiom, % 187.68/187.59 ! [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] : % 187.68/187.59 ( c_Equiv__Relations_Oequiv(T_a,V_A1_2,V_r1_2) % 187.68/187.59 => ( c_Equiv__Relations_Oequiv(T_b,V_A2_2,V_r2_2) % 187.68/187.59 => ( c_Equiv__Relations_Ocongruent2(T_a,T_b,tc_fun(T_c,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2) % 187.68/187.59 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a1_2),V_A1_2)) % 187.68/187.59 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a2_2),V_A2_2)) % 187.68/187.59 => 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) ) ) ) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_UN__equiv__class__inject,axiom, % 187.68/187.59 ! [V_Y_2,V_X_2,V_f_2,T_b,V_r_2,V_A_2,T_a] : % 187.68/187.59 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 187.68/187.59 => ( c_Equiv__Relations_Ocongruent(T_a,tc_fun(T_b,tc_HOL_Obool),V_r_2,V_f_2) % 187.68/187.59 => ( 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) % 187.68/187.59 => ( 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))) % 187.68/187.59 => ( 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))) % 187.68/187.59 => ( ! [B_x] : % 187.68/187.59 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 187.68/187.59 => ! [B_y] : % 187.68/187.59 ( hBOOL(hAPP(hAPP(c_member(T_a),B_y),V_A_2)) % 187.68/187.59 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y) % 187.68/187.59 => 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)) ) ) ) % 187.68/187.59 => V_X_2 = V_Y_2 ) ) ) ) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_SUP2__iff,axiom, % 187.68/187.59 ! [V_c_2,V_b_2,V_B_2,V_A_2,T_c,T_b,T_a] : % 187.68/187.59 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2)) % 187.68/187.59 <=> ? [B_x] : % 187.68/187.59 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 187.68/187.59 & hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_c_2)) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_congruent2D,axiom, % 187.68/187.59 ! [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] : % 187.68/187.59 ( c_Equiv__Relations_Ocongruent2(T_a,T_b,T_c,V_r1_2,V_r2_2,V_f_2) % 187.68/187.59 => ( 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)) % 187.68/187.59 => ( 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)) % 187.68/187.59 => hAPP(hAPP(V_f_2,V_y1_2),V_y2_2) = hAPP(hAPP(V_f_2,V_z1_2),V_z2_2) ) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_congruent2__implies__congruent,axiom, % 187.68/187.59 ! [V_a_2,V_f_2,V_r2_2,T_c,T_b,V_r1_2,V_A_2,T_a] : % 187.68/187.59 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r1_2) % 187.68/187.59 => ( c_Equiv__Relations_Ocongruent2(T_a,T_b,T_c,V_r1_2,V_r2_2,V_f_2) % 187.68/187.59 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 187.68/187.59 => c_Equiv__Relations_Ocongruent(T_b,T_c,V_r2_2,hAPP(V_f_2,V_a_2)) ) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_UN__equiv__class__type2,axiom, % 187.68/187.59 ! [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] : % 187.68/187.59 ( c_Equiv__Relations_Oequiv(T_a,V_A1_2,V_r1_2) % 187.68/187.59 => ( c_Equiv__Relations_Oequiv(T_b,V_A2_2,V_r2_2) % 187.68/187.59 => ( c_Equiv__Relations_Ocongruent2(T_a,T_b,tc_fun(T_c,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2) % 187.68/187.59 => ( 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))) % 187.68/187.59 => ( 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))) % 187.68/187.59 => ( ! [B_x1] : % 187.68/187.59 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x1),V_A1_2)) % 187.68/187.59 => ! [B_x2] : % 187.68/187.59 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x2),V_A2_2)) % 187.68/187.59 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(V_f_2,B_x1),B_x2)),V_B_2)) ) ) % 187.68/187.59 => 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)) ) ) ) ) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_UN__equiv__class__type,axiom, % 187.68/187.59 ! [V_B_2,V_X_2,V_f_2,T_b,V_r_2,V_A_2,T_a] : % 187.68/187.59 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 187.68/187.59 => ( c_Equiv__Relations_Ocongruent(T_a,tc_fun(T_b,tc_HOL_Obool),V_r_2,V_f_2) % 187.68/187.59 => ( 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))) % 187.68/187.59 => ( ! [B_x] : % 187.68/187.59 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 187.68/187.59 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_f_2,B_x)),V_B_2)) ) % 187.68/187.59 => 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)) ) ) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_folding__image_Oreindex,axiom, % 187.68/187.59 ! [V_g_2,V_h_2,V_A_2,V_F_2,V_z_2,V_f_2,T_b,T_a] : % 187.68/187.59 ( c_Finite__Set_Ofolding__image(T_a,T_b,V_f_2,V_z_2,V_F_2) % 187.68/187.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.68/187.59 => ( c_Fun_Oinj__on(T_b,T_b,V_h_2,V_A_2) % 187.68/187.59 => 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) ) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_folding__image_Odistrib,axiom, % 187.68/187.59 ! [V_h_2,V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_b,T_a] : % 187.68/187.59 ( c_Finite__Set_Ofolding__image(T_a,T_b,V_f_2,V_z_2,V_F_2) % 187.68/187.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.68/187.59 => 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)) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_folding__image_Oeq__fold,axiom, % 187.68/187.59 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_b,T_a] : % 187.68/187.59 ( c_Finite__Set_Ofolding__image(T_a,T_b,V_f_2,V_z_2,V_F_2) % 187.68/187.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.68/187.59 => 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) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_Id__on__def,axiom, % 187.68/187.59 ! [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)))) ). % 187.68/187.59 % 187.68/187.59 fof(fact_the__inv__into__comp,axiom, % 187.68/187.59 ! [V_x_2,V_A_2,V_g_2,T_c,V_f_2,T_b,T_a] : % 187.68/187.59 ( 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)) % 187.68/187.59 => ( c_Fun_Oinj__on(T_c,T_a,V_g_2,V_A_2) % 187.68/187.59 => ( 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)))) % 187.68/187.59 => 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) ) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_the__inv__into__into,axiom, % 187.68/187.59 ! [V_B_2,V_x_2,V_A_2,V_f_2,T_b,T_a] : % 187.68/187.59 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 187.68/187.59 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2))) % 187.68/187.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 187.68/187.59 => 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)) ) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_Id__on__def_H,axiom, % 187.68/187.59 ! [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)) ). % 187.68/187.59 % 187.68/187.59 fof(fact_Id__on__empty,axiom, % 187.68/187.59 ! [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)) ). % 187.68/187.59 % 187.68/187.59 fof(fact_Image__Id__on,axiom, % 187.68/187.59 ! [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) ). % 187.68/187.59 % 187.68/187.59 fof(fact_the__inv__into__f__f,axiom, % 187.68/187.59 ! [V_x_2,V_A_2,V_f_2,T_b,T_a] : % 187.68/187.59 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 187.68/187.59 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 187.68/187.59 => 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 ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_the__inv__into__f__eq,axiom, % 187.68/187.59 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_b,T_a] : % 187.68/187.59 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 187.68/187.59 => ( hAPP(V_f_2,V_x_2) = V_y_2 % 187.68/187.59 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 187.68/187.59 => hAPP(c_Fun_Othe__inv__into(T_a,T_b,V_A_2,V_f_2),V_y_2) = V_x_2 ) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_the__inv__into__onto,axiom, % 187.68/187.59 ! [V_A_2,V_f_2,T_b,T_a] : % 187.68/187.59 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 187.68/187.59 => 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 ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_inj__on__the__inv__into,axiom, % 187.68/187.59 ! [V_A_2,V_f_2,T_b,T_a] : % 187.68/187.59 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 187.68/187.59 => 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)) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_the__inv__into__def,axiom, % 187.68/187.59 ! [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))) ). % 187.68/187.59 % 187.68/187.59 fof(fact_Id__on__iff,axiom, % 187.68/187.59 ! [V_A_2,V_y_2,V_x_2,T_a] : % 187.68/187.59 ( 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))) % 187.68/187.59 <=> ( V_x_2 = V_y_2 % 187.68/187.59 & hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_Id__on__eqI,axiom, % 187.68/187.59 ! [V_A_2,T_a,V_b_2,V_a_2] : % 187.68/187.59 ( V_a_2 = V_b_2 % 187.68/187.59 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 187.68/187.59 => 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))) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_f__the__inv__into__f,axiom, % 187.68/187.59 ! [V_y_2,V_A_2,V_f_2,T_b,T_a] : % 187.68/187.59 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 187.68/187.59 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2))) % 187.68/187.59 => 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 ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_Id__onE,axiom, % 187.68/187.59 ! [V_A_2,V_c_2,T_a] : % 187.68/187.59 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_c_2),c_Relation_OId__on(T_a,V_A_2))) % 187.68/187.59 => ~ ! [B_x] : % 187.68/187.59 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 187.68/187.59 => V_c_2 != hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_Inf__fin_Ohom__commute,axiom, % 187.68/187.59 ! [V_N_2,V_h_2,T_a] : % 187.68/187.59 ( class_Lattices_Olattice(T_a) % 187.68/187.59 => ( ! [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)) % 187.68/187.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 187.68/187.59 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.59 => 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)) ) ) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_strong__setprod__reindex__cong,axiom, % 187.68/187.59 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_b,T_a,T_c] : % 187.68/187.59 ( class_Groups_Ocomm__monoid__mult(T_c) % 187.68/187.59 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 187.68/187.59 => ( V_B_2 = hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2) % 187.68/187.59 => ( ! [B_x] : % 187.68/187.59 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 187.68/187.59 => 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) ) % 187.68/187.59 => 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) ) ) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_atMost__Int__atLeast,axiom, % 187.68/187.59 ! [V_n_2,T_a] : % 187.68/187.59 ( class_Orderings_Oorder(T_a) % 187.68/187.59 => 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))) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_code__numeral_Osimps_I5_J,axiom, % 187.68/187.59 ! [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) ). % 187.68/187.59 % 187.68/187.59 fof(fact_divmod__int__pdivmod,axiom, % 187.68/187.59 ! [V_l_2,V_k_2] : % 187.68/187.59 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 187.68/187.59 => 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)) ) % 187.68/187.59 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 187.68/187.59 => ( ( V_l_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 187.68/187.59 => 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) ) % 187.68/187.59 & ( V_l_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 187.68/187.59 => 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)))) ) ) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_setsum__abs,axiom, % 187.68/187.59 ! [V_A_2,V_f_2,T_b,T_a] : % 187.68/187.59 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 187.68/187.59 => 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))) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_setsum__abs__ge__zero,axiom, % 187.68/187.59 ! [V_A_2,V_f_2,T_b,T_a] : % 187.68/187.59 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 187.68/187.59 => 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))) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_apsnd__compose,axiom, % 187.68/187.59 ! [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) ). % 187.68/187.59 % 187.68/187.59 fof(fact_abs__setsum__abs,axiom, % 187.68/187.59 ! [V_A_2,V_f_2,T_b,T_a] : % 187.68/187.59 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 187.68/187.59 => 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) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_atLeast__eq__iff,axiom, % 187.68/187.59 ! [V_y_2,V_x_2,T_a] : % 187.68/187.59 ( class_Orderings_Olinorder(T_a) % 187.68/187.59 => ( hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_x_2) = hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_y_2) % 187.68/187.59 <=> V_x_2 = V_y_2 ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_abs__one,axiom, % 187.68/187.59 ! [T_a] : % 187.68/187.59 ( class_Rings_Olinordered__idom(T_a) % 187.68/187.59 => hAPP(c_Groups_Oabs__class_Oabs(T_a),c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(T_a) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_abs__minus__cancel,axiom, % 187.68/187.59 ! [V_a,T_a] : % 187.68/187.59 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 187.68/187.59 => 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) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_power__abs,axiom, % 187.68/187.59 ! [V_n,V_a,T_a] : % 187.68/187.59 ( class_Rings_Olinordered__idom(T_a) % 187.68/187.59 => 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) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_abs__of__nat,axiom, % 187.68/187.59 ! [V_n,T_a] : % 187.68/187.59 ( class_Rings_Olinordered__idom(T_a) % 187.68/187.59 => 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) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_abs__idempotent,axiom, % 187.68/187.59 ! [V_a,T_a] : % 187.68/187.59 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 187.68/187.59 => 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) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_abs__mult__self,axiom, % 187.68/187.59 ! [V_a,T_a] : % 187.68/187.59 ( class_Rings_Olinordered__idom(T_a) % 187.68/187.59 => 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) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_abs__mult,axiom, % 187.68/187.59 ! [V_b,V_a,T_a] : % 187.68/187.59 ( class_Rings_Olinordered__idom(T_a) % 187.68/187.59 => 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)) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_abs__add__abs,axiom, % 187.68/187.59 ! [V_b,V_a,T_a] : % 187.68/187.59 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 187.68/187.59 => 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)) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_abs__zero,axiom, % 187.68/187.59 ! [T_a] : % 187.68/187.59 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 187.68/187.59 => hAPP(c_Groups_Oabs__class_Oabs(T_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_abs__eq__0,axiom, % 187.68/187.59 ! [V_a_2,T_a] : % 187.68/187.59 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 187.68/187.59 => ( hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a_2) = c_Groups_Ozero__class_Ozero(T_a) % 187.68/187.59 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_abs__int__eq,axiom, % 187.68/187.59 ! [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) ). % 187.68/187.59 % 187.68/187.59 fof(fact_abs__divide,axiom, % 187.68/187.59 ! [V_b,V_a,T_a] : % 187.68/187.59 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 187.68/187.59 => 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)) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_abs__setprod,axiom, % 187.68/187.59 ! [V_A_2,V_f_2,T_b,T_a] : % 187.68/187.59 ( class_Fields_Olinordered__field(T_a) % 187.68/187.59 => 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) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_abs__le__D1,axiom, % 187.68/187.59 ! [V_b,V_a,T_a] : % 187.68/187.59 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 187.68/187.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b)) % 187.68/187.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_abs__ge__self,axiom, % 187.68/187.59 ! [V_a,T_a] : % 187.68/187.59 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 187.68/187.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a))) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_apsnd__conv,axiom, % 187.68/187.59 ! [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)) ). % 187.68/187.59 % 187.68/187.59 fof(fact_abs__minus__commute,axiom, % 187.68/187.59 ! [V_b,V_a,T_a] : % 187.68/187.59 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 187.68/187.59 => 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)) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_abs__ge__zero,axiom, % 187.68/187.59 ! [V_a,T_a] : % 187.68/187.59 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 187.68/187.59 => 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))) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_abs__le__zero__iff,axiom, % 187.68/187.59 ! [V_a_2,T_a] : % 187.68/187.59 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 187.68/187.59 => ( 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))) % 187.68/187.59 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_abs__of__nonneg,axiom, % 187.68/187.59 ! [V_a,T_a] : % 187.68/187.59 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 187.68/187.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 187.68/187.59 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_abs__of__pos,axiom, % 187.68/187.59 ! [V_a,T_a] : % 187.68/187.59 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 187.68/187.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 187.68/187.59 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_zero__less__abs__iff,axiom, % 187.68/187.59 ! [V_a_2,T_a] : % 187.68/187.59 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 187.68/187.59 => ( 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))) % 187.68/187.59 <=> V_a_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_abs__not__less__zero,axiom, % 187.68/187.59 ! [V_a,T_a] : % 187.68/187.59 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 187.68/187.59 => ~ 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))) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_abs__triangle__ineq,axiom, % 187.68/187.59 ! [V_b,V_a,T_a] : % 187.68/187.59 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 187.68/187.59 => 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)))) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_abs__mult__less,axiom, % 187.68/187.59 ! [V_d,V_b,V_c,V_a,T_a] : % 187.68/187.59 ( class_Rings_Olinordered__idom(T_a) % 187.68/187.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_c)) % 187.68/187.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)),V_d)) % 187.68/187.59 => 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))) ) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_fst__apsnd,axiom, % 187.68/187.59 ! [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) ). % 187.68/187.59 % 187.68/187.59 fof(fact_abs__triangle__ineq2__sym,axiom, % 187.68/187.59 ! [V_b,V_a,T_a] : % 187.68/187.59 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 187.68/187.59 => 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)))) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_abs__triangle__ineq2,axiom, % 187.68/187.59 ! [V_b,V_a,T_a] : % 187.68/187.59 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 187.68/187.59 => 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)))) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_abs__triangle__ineq3,axiom, % 187.68/187.59 ! [V_b,V_a,T_a] : % 187.68/187.59 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 187.68/187.59 => 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)))) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_abs__ge__minus__self,axiom, % 187.68/187.59 ! [V_a,T_a] : % 187.68/187.59 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 187.68/187.59 => 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))) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_abs__le__iff,axiom, % 187.68/187.59 ! [V_b_2,V_a_2,T_a] : % 187.68/187.59 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 187.68/187.59 => ( 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)) % 187.68/187.59 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) % 187.68/187.59 & 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)) ) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_abs__leI,axiom, % 187.68/187.59 ! [V_b,V_a,T_a] : % 187.68/187.59 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 187.68/187.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 187.68/187.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b)) % 187.68/187.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b)) ) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_abs__le__D2,axiom, % 187.68/187.59 ! [V_b,V_a,T_a] : % 187.68/187.59 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 187.68/187.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b)) % 187.68/187.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b)) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_snd__apsnd,axiom, % 187.68/187.59 ! [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)) ). % 187.68/187.59 % 187.68/187.59 fof(fact_apsnd__eq__conv,axiom, % 187.68/187.59 ! [V_g_2,V_x_2,V_f_2,T_a,T_b,T_c] : % 187.68/187.59 ( 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) % 187.68/187.59 <=> 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)) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_abs__less__iff,axiom, % 187.68/187.59 ! [V_b_2,V_a_2,T_a] : % 187.68/187.59 ( class_Rings_Olinordered__idom(T_a) % 187.68/187.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a_2)),V_b_2)) % 187.68/187.59 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) % 187.68/187.59 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),V_b_2)) ) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_nonzero__abs__divide,axiom, % 187.68/187.59 ! [V_a,V_b,T_a] : % 187.68/187.59 ( class_Fields_Olinordered__field(T_a) % 187.68/187.59 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 187.68/187.59 => 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)) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_abs__power__minus,axiom, % 187.68/187.59 ! [V_n,V_a,T_a] : % 187.68/187.59 ( class_Rings_Olinordered__idom(T_a) % 187.68/187.59 => 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)) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_abs__zmult__eq__1,axiom, % 187.68/187.59 ! [V_n,V_m] : % 187.68/187.59 ( 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) % 187.68/187.59 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_m) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_pdivmod__def,axiom, % 187.68/187.59 ! [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))) ). % 187.68/187.59 % 187.68/187.59 fof(fact_abs__sgn,axiom, % 187.68/187.59 ! [V_k,T_a] : % 187.68/187.59 ( class_Rings_Olinordered__idom(T_a) % 187.68/187.59 => 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)) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_mult__sgn__abs,axiom, % 187.68/187.59 ! [V_x,T_a] : % 187.68/187.59 ( class_Rings_Olinordered__idom(T_a) % 187.68/187.59 => 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 ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_pdivmod__posDivAlg,axiom, % 187.68/187.59 ! [V_k,V_l] : % 187.68/187.59 ( ( V_l = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 187.68/187.59 => 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)) ) % 187.68/187.59 & ( V_l != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 187.68/187.59 => 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)) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_abs__mult__pos,axiom, % 187.68/187.59 ! [V_y,V_x,T_a] : % 187.68/187.59 ( class_Rings_Olinordered__idom(T_a) % 187.68/187.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 187.68/187.59 => 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)) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_abs__eq__mult,axiom, % 187.68/187.59 ! [V_b,V_a,T_a] : % 187.68/187.59 ( class_Rings_Oordered__ring__abs(T_a) % 187.68/187.59 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 187.68/187.59 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) ) % 187.68/187.59 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 187.68/187.59 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) ) ) % 187.68/187.59 => 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)) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_abs__diff__triangle__ineq,axiom, % 187.68/187.59 ! [V_d,V_c,V_b,V_a,T_a] : % 187.68/187.59 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 187.68/187.59 => 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))))) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_abs__triangle__ineq4,axiom, % 187.68/187.59 ! [V_b,V_a,T_a] : % 187.68/187.59 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 187.68/187.59 => 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)))) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_abs__minus__le__zero,axiom, % 187.68/187.59 ! [V_a,T_a] : % 187.68/187.59 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 187.68/187.59 => 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))) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_abs__of__nonpos,axiom, % 187.68/187.59 ! [V_a,T_a] : % 187.68/187.59 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 187.68/187.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 187.68/187.59 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_abs__of__neg,axiom, % 187.68/187.59 ! [V_a,T_a] : % 187.68/187.59 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 187.68/187.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 187.68/187.59 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_abs__if,axiom, % 187.68/187.59 ! [V_a,T_a] : % 187.68/187.59 ( class_Groups_Oabs__if(T_a) % 187.68/187.59 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 187.68/187.59 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) % 187.68/187.59 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 187.68/187.59 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_zero__le__power__abs,axiom, % 187.68/187.59 ! [V_n,V_a,T_a] : % 187.68/187.59 ( class_Rings_Olinordered__idom(T_a) % 187.68/187.59 => 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))) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_abs__div__pos,axiom, % 187.68/187.59 ! [V_x,V_y,T_a] : % 187.68/187.59 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 187.68/187.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 187.68/187.59 => 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)) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_abs__minus__one,axiom, % 187.68/187.59 ! [T_a] : % 187.68/187.59 ( ( class_Int_Onumber__ring(T_a) % 187.68/187.59 & class_Rings_Olinordered__idom(T_a) ) % 187.68/187.59 => 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) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_atLeast__iff,axiom, % 187.68/187.59 ! [V_k_2,V_i_2,T_a] : % 187.68/187.59 ( class_Orderings_Oord(T_a) % 187.68/187.59 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_k_2))) % 187.68/187.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_k_2),V_i_2)) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_zabs__less__one__iff,axiom, % 187.68/187.59 ! [V_z_2] : % 187.68/187.59 ( 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))) % 187.68/187.59 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_zabs__def,axiom, % 187.68/187.59 ! [V_i] : % 187.68/187.59 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 187.68/187.59 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_i) ) % 187.68/187.59 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 187.68/187.59 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i) = V_i ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_nat__abs__mult__distrib,axiom, % 187.68/187.59 ! [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))) ). % 187.68/187.59 % 187.68/187.59 fof(fact_atLeast__subset__iff,axiom, % 187.68/187.59 ! [V_y_2,V_x_2,T_a] : % 187.68/187.59 ( class_Orderings_Oorder(T_a) % 187.68/187.59 => ( 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))) % 187.68/187.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_zero__le__zpower__abs,axiom, % 187.68/187.59 ! [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))) ). % 187.68/187.59 % 187.68/187.59 fof(fact_Compl__lessThan,axiom, % 187.68/187.59 ! [V_k_2,T_a] : % 187.68/187.59 ( class_Orderings_Olinorder(T_a) % 187.68/187.59 => 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) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_Compl__atLeast,axiom, % 187.68/187.59 ! [V_k_2,T_a] : % 187.68/187.59 ( class_Orderings_Olinorder(T_a) % 187.68/187.59 => 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) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_negateSnd__def,axiom, % 187.68/187.59 c_Divides_OnegateSnd = c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)) ). % 187.68/187.59 % 187.68/187.59 fof(fact_abs__number__of,axiom, % 187.68/187.59 ! [V_x,T_a] : % 187.68/187.59 ( ( class_Int_Onumber__ring(T_a) % 187.68/187.59 & class_Rings_Olinordered__idom(T_a) ) % 187.68/187.59 => ( ( 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))) % 187.68/187.59 => 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)) ) % 187.68/187.59 & ( ~ 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))) % 187.68/187.59 => 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) ) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_abs__power__minus__one,axiom, % 187.68/187.59 ! [V_n,T_a] : % 187.68/187.59 ( ( class_Int_Onumber__ring(T_a) % 187.68/187.59 & class_Rings_Olinordered__idom(T_a) ) % 187.68/187.59 => 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) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_zero__less__zpower__abs__iff,axiom, % 187.68/187.59 ! [V_n_2,V_x_2] : % 187.68/187.59 ( 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))) % 187.68/187.59 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 187.68/187.59 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_ivl__disj__un_I14_J,axiom, % 187.68/187.59 ! [V_u_2,V_l_2,T_a] : % 187.68/187.59 ( class_Orderings_Olinorder(T_a) % 187.68/187.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2)) % 187.68/187.59 => 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) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_ivl__disj__int_I8_J,axiom, % 187.68/187.59 ! [V_u_2,V_l_2,T_a] : % 187.68/187.59 ( class_Orderings_Oorder(T_a) % 187.68/187.59 => 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)) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_Int__atLeastAtMostR2,axiom, % 187.68/187.59 ! [V_d_2,V_c_2,V_a_2,T_a] : % 187.68/187.59 ( class_Orderings_Olinorder(T_a) % 187.68/187.59 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_a_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_c_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a_2),V_c_2),V_d_2) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_Int__atLeastAtMostL2,axiom, % 187.68/187.59 ! [V_c_2,V_b_2,V_a_2,T_a] : % 187.68/187.59 ( class_Orderings_Olinorder(T_a) % 187.68/187.59 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_c_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a_2),V_c_2),V_b_2) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_ivl__disj__int_I6_J,axiom, % 187.68/187.59 ! [V_u_2,V_l_2,T_a] : % 187.68/187.59 ( class_Orderings_Oorder(T_a) % 187.68/187.59 => 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)) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_image__uminus__atMost,axiom, % 187.68/187.59 ! [V_x_2,T_a] : % 187.68/187.59 ( class_Groups_Oordered__ab__group__add(T_a) % 187.68/187.59 => 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)) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_image__uminus__atLeast,axiom, % 187.68/187.59 ! [V_x_2,T_a] : % 187.68/187.59 ( class_Groups_Oordered__ab__group__add(T_a) % 187.68/187.59 => 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)) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_power2__abs,axiom, % 187.68/187.59 ! [V_a,T_a] : % 187.68/187.59 ( class_Rings_Olinordered__idom(T_a) % 187.68/187.59 => 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)))) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_abs__power2,axiom, % 187.68/187.59 ! [V_a,T_a] : % 187.68/187.59 ( class_Rings_Olinordered__idom(T_a) % 187.68/187.59 => 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)))) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_atLeast__Suc,axiom, % 187.68/187.59 ! [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)))) ). % 187.68/187.59 % 187.68/187.59 fof(fact_divmod__int__code,axiom, % 187.68/187.59 ! [V_l_2,V_k_2] : % 187.68/187.59 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 187.68/187.59 => 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)) ) % 187.68/187.59 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 187.68/187.59 => ( ( V_l_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 187.68/187.59 => 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) ) % 187.68/187.59 & ( V_l_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 187.68/187.59 => 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)))) ) ) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_code__numeral_Osimps_I4_J,axiom, % 187.68/187.59 ! [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 ). % 187.68/187.59 % 187.68/187.59 fof(fact_decr__lemma,axiom, % 187.68/187.59 ! [V_z,V_x,V_d] : % 187.68/187.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d)) % 187.68/187.59 => 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)) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_incr__lemma,axiom, % 187.68/187.59 ! [V_x,V_z,V_d] : % 187.68/187.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d)) % 187.68/187.59 => 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)))) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_Nitpick_Oint__gcd__def,axiom, % 187.68/187.59 ! [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)))) ). % 187.68/187.59 % 187.68/187.59 fof(fact_ivl__disj__un_I12_J,axiom, % 187.68/187.59 ! [V_u_2,V_l_2,T_a] : % 187.68/187.59 ( class_Orderings_Olinorder(T_a) % 187.68/187.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_l_2),V_u_2)) % 187.68/187.59 => 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) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_Nitpick_Oint__lcm__def,axiom, % 187.68/187.59 ! [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)))) ). % 187.68/187.59 % 187.68/187.59 fof(fact_atLeast__Suc__greaterThan,axiom, % 187.68/187.59 ! [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) ). % 187.68/187.59 % 187.68/187.59 fof(fact_greaterThan__eq__iff,axiom, % 187.68/187.59 ! [V_y_2,V_x_2,T_a] : % 187.68/187.59 ( class_Orderings_Olinorder(T_a) % 187.68/187.59 => ( hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_x_2) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_y_2) % 187.68/187.59 <=> V_x_2 = V_y_2 ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_greaterThan__iff,axiom, % 187.68/187.59 ! [V_k_2,V_i_2,T_a] : % 187.68/187.59 ( class_Orderings_Oord(T_a) % 187.68/187.59 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_k_2))) % 187.68/187.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_k_2),V_i_2)) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_greaterThan__subset__iff,axiom, % 187.68/187.59 ! [V_y_2,V_x_2,T_a] : % 187.68/187.59 ( class_Orderings_Olinorder(T_a) % 187.68/187.59 => ( 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))) % 187.68/187.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_Nitpick_Onat__lcm__def,axiom, % 187.68/187.59 ! [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)) ). % 187.68/187.59 % 187.68/187.59 fof(fact_Compl__atMost,axiom, % 187.68/187.59 ! [V_k_2,T_a] : % 187.68/187.59 ( class_Orderings_Olinorder(T_a) % 187.68/187.59 => 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) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_Compl__greaterThan,axiom, % 187.68/187.59 ! [V_k_2,T_a] : % 187.68/187.59 ( class_Orderings_Olinorder(T_a) % 187.68/187.59 => 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) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_ivl__disj__int_I7_J,axiom, % 187.68/187.59 ! [V_u_2,V_l_2,T_a] : % 187.68/187.59 ( class_Orderings_Oorder(T_a) % 187.68/187.59 => 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)) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_ivl__disj__un_I11_J,axiom, % 187.68/187.59 ! [V_u_2,V_l_2,T_a] : % 187.68/187.59 ( class_Orderings_Olinorder(T_a) % 187.68/187.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2)) % 187.68/187.59 => 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) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_image__uminus__lessThan,axiom, % 187.68/187.59 ! [V_x_2,T_a] : % 187.68/187.59 ( class_Groups_Oordered__ab__group__add(T_a) % 187.68/187.59 => 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)) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_image__uminus__greaterThan,axiom, % 187.68/187.59 ! [V_x_2,T_a] : % 187.68/187.59 ( class_Groups_Oordered__ab__group__add(T_a) % 187.68/187.59 => 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)) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_ivl__disj__int_I5_J,axiom, % 187.68/187.59 ! [V_u_2,V_l_2,T_a] : % 187.68/187.59 ( class_Orderings_Oorder(T_a) % 187.68/187.59 => 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)) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_greaterThan__Suc,axiom, % 187.68/187.59 ! [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)))) ). % 187.68/187.59 % 187.68/187.59 fof(fact_nat__gcd_Osimps,axiom, % 187.68/187.59 ! [V_x,V_y] : % 187.68/187.59 ( ( V_y = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 187.68/187.59 => c_Nitpick_Onat__gcd(V_x,V_y) = V_x ) % 187.68/187.59 & ( V_y != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 187.68/187.59 => 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)) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_ivl__disj__un_I1_J,axiom, % 187.68/187.59 ! [V_l_2,T_a] : % 187.68/187.59 ( class_Orderings_Olinorder(T_a) % 187.68/187.59 => 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) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_ivl__disj__un_I13_J,axiom, % 187.68/187.59 ! [V_u_2,V_l_2,T_a] : % 187.68/187.59 ( class_Orderings_Olinorder(T_a) % 187.68/187.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2)) % 187.68/187.59 => 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) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_nat__gcd_Opsimps,axiom, % 187.68/187.59 ! [V_y_2,V_x_2] : % 187.68/187.59 ( 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))) % 187.68/187.59 => ( ( V_y_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 187.68/187.59 => c_Nitpick_Onat__gcd(V_x_2,V_y_2) = V_x_2 ) % 187.68/187.59 & ( V_y_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 187.68/187.59 => 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)) ) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_apfst__apsnd,axiom, % 187.68/187.59 ! [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))) ). % 187.68/187.59 % 187.68/187.59 fof(fact_apsnd__apfst,axiom, % 187.68/187.59 ! [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))) ). % 187.68/187.59 % 187.68/187.59 fof(fact_apfst__eq__conv,axiom, % 187.68/187.59 ! [V_g_2,V_x_2,V_f_2,T_b,T_a,T_c] : % 187.68/187.59 ( 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) % 187.68/187.59 <=> 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)) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_fst__apfst,axiom, % 187.68/187.59 ! [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)) ). % 187.68/187.59 % 187.68/187.59 fof(fact_apfst__compose,axiom, % 187.68/187.59 ! [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) ). % 187.68/187.59 % 187.68/187.59 fof(fact_apfst__conv,axiom, % 187.68/187.59 ! [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) ). % 187.68/187.59 % 187.68/187.59 fof(fact_snd__apfst,axiom, % 187.68/187.59 ! [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) ). % 187.68/187.59 % 187.68/187.59 fof(fact_apsnd__apfst__commute,axiom, % 187.68/187.59 ! [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)) ). % 187.68/187.59 % 187.68/187.59 fof(fact_nat__gcd_Opinduct,axiom, % 187.68/187.59 ! [V_P_2,V_a1_2,V_a0_2] : % 187.68/187.59 ( 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))) % 187.68/187.59 => ( ! [B_x,B_y] : % 187.68/187.59 ( 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))) % 187.68/187.59 => ( ( B_y != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 187.68/187.59 => hBOOL(hAPP(hAPP(V_P_2,B_y),c_Divides_Odiv__class_Omod(tc_Nat_Onat,B_x,B_y))) ) % 187.68/187.59 => hBOOL(hAPP(hAPP(V_P_2,B_x),B_y)) ) ) % 187.68/187.59 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_compl__unique,axiom, % 187.68/187.59 ! [V_y,V_x,T_a] : % 187.68/187.59 ( class_Lattices_Oboolean__algebra(T_a) % 187.68/187.59 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = c_Orderings_Obot__class_Obot(T_a) % 187.68/187.59 => ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = c_Orderings_Otop__class_Otop(T_a) % 187.68/187.59 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x) = V_y ) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_transfer__nat__int__sum__prod__cong_I1_J,axiom, % 187.68/187.59 ! [V_g_2,V_f_2,V_B_2,V_A_2,T_a] : % 187.68/187.59 ( ( class_Groups_Ocomm__monoid__add(T_a) % 187.68/187.59 & class_Groups_Ocomm__monoid__mult(T_a) ) % 187.68/187.59 => ( V_A_2 = V_B_2 % 187.68/187.59 => ( c_Nat__Transfer_Onat__set(V_B_2) % 187.68/187.59 => ( ! [B_x] : % 187.68/187.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 187.68/187.59 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) % 187.68/187.59 => 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) ) ) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_UNIV__I,axiom, % 187.68/187.59 ! [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)))) ). % 187.68/187.59 % 187.68/187.59 fof(fact_range__composition,axiom, % 187.68/187.59 ! [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)))) ). % 187.68/187.59 % 187.68/187.59 fof(fact_infinite__UNIV__int,axiom, % 187.68/187.59 ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint,tc_HOL_Obool)))) ). % 187.68/187.59 % 187.68/187.59 fof(fact_top__greatest,axiom, % 187.68/187.59 ! [V_x,T_a] : % 187.68/187.59 ( class_Orderings_Otop(T_a) % 187.68/187.59 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Orderings_Otop__class_Otop(T_a))) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_Un__UNIV__left,axiom, % 187.68/187.59 ! [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)) ). % 187.68/187.59 % 187.68/187.59 fof(fact_Un__UNIV__right,axiom, % 187.68/187.59 ! [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)) ). % 187.68/187.59 % 187.68/187.59 fof(fact_iso__tuple__UNIV__I,axiom, % 187.68/187.59 ! [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)))) ). % 187.68/187.59 % 187.68/187.59 fof(fact_UNIV__not__empty,axiom, % 187.68/187.59 ! [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)) ). % 187.68/187.59 % 187.68/187.59 fof(fact_subset__UNIV,axiom, % 187.68/187.59 ! [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)))) ). % 187.68/187.59 % 187.68/187.59 fof(fact_finite__UNIV,axiom, % 187.68/187.59 ! [T_a] : % 187.68/187.59 ( class_Finite__Set_Ofinite(T_a) % 187.68/187.59 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_finite__option__UNIV,axiom, % 187.68/187.59 ! [T_a] : % 187.68/187.59 ( 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)))) % 187.68/187.59 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_finite__Prod__UNIV,axiom, % 187.68/187.59 ! [T_b,T_a] : % 187.68/187.59 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) % 187.68/187.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) % 187.68/187.59 => 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)))) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_finite__fun__UNIVD2,axiom, % 187.68/187.59 ! [T_b,T_a] : % 187.68/187.59 ( 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)))) % 187.68/187.59 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_finite__Plus__UNIV__iff,axiom, % 187.68/187.59 ! [T_b,T_a] : % 187.68/187.59 ( 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)))) % 187.68/187.59 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) % 187.68/187.59 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_UNIV__Plus__UNIV,axiom, % 187.68/187.59 ! [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)) ). % 187.68/187.59 % 187.68/187.59 fof(fact_top__apply,axiom, % 187.68/187.59 ! [V_x_2,T_b,T_a] : % 187.68/187.59 ( class_Orderings_Otop(T_a) % 187.68/187.59 => hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_b,T_a)),V_x_2) = c_Orderings_Otop__class_Otop(T_a) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_Pow__UNIV,axiom, % 187.68/187.59 ! [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)) ). % 187.68/187.59 % 187.68/187.59 fof(fact_card__UNIV__unit,axiom, % 187.68/187.59 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) ). % 187.68/187.59 % 187.68/187.59 fof(fact_infinite__UNIV__nat,axiom, % 187.68/187.59 ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ). % 187.68/187.59 % 187.68/187.59 fof(fact_equiv__intrel,axiom, % 187.68/187.59 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) ). % 187.68/187.59 % 187.68/187.59 fof(fact_Int__UNIV__left,axiom, % 187.68/187.59 ! [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 ). % 187.68/187.59 % 187.68/187.59 fof(fact_Int__UNIV__right,axiom, % 187.68/187.59 ! [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 ). % 187.68/187.59 % 187.68/187.59 fof(fact_inf__top__left,axiom, % 187.68/187.59 ! [V_x,T_a] : % 187.68/187.59 ( class_Lattices_Obounded__lattice__top(T_a) % 187.68/187.59 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Orderings_Otop__class_Otop(T_a)),V_x) = V_x ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_inf__top__right,axiom, % 187.68/187.59 ! [V_x,T_a] : % 187.68/187.59 ( class_Lattices_Obounded__lattice__top(T_a) % 187.68/187.59 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),c_Orderings_Otop__class_Otop(T_a)) = V_x ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_inf__eq__top__iff,axiom, % 187.68/187.59 ! [V_y_2,V_x_2,T_a] : % 187.68/187.59 ( class_Lattices_Obounded__lattice__top(T_a) % 187.68/187.59 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x_2),V_y_2) = c_Orderings_Otop__class_Otop(T_a) % 187.68/187.59 <=> ( V_x_2 = c_Orderings_Otop__class_Otop(T_a) % 187.68/187.59 & V_y_2 = c_Orderings_Otop__class_Otop(T_a) ) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_sup__top__left,axiom, % 187.68/187.59 ! [V_x,T_a] : % 187.68/187.59 ( class_Lattices_Obounded__lattice__top(T_a) % 187.68/187.59 => 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) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_sup__top__right,axiom, % 187.68/187.59 ! [V_x,T_a] : % 187.68/187.59 ( class_Lattices_Obounded__lattice__top(T_a) % 187.68/187.59 => 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) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_inj__int,axiom, % 187.68/187.59 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))) ). % 187.68/187.59 % 187.68/187.59 fof(fact_inj__eq,axiom, % 187.68/187.59 ! [V_y_2,V_x_2,V_f_2,T_b,T_a] : % 187.68/187.59 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 187.68/187.59 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) % 187.68/187.59 <=> V_x_2 = V_y_2 ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_injD,axiom, % 187.68/187.59 ! [V_y_2,V_x_2,V_f_2,T_b,T_a] : % 187.68/187.59 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 187.68/187.59 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) % 187.68/187.59 => V_x_2 = V_y_2 ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_UNIV__option__conv,axiom, % 187.68/187.59 ! [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)))) ). % 187.68/187.59 % 187.68/187.59 fof(fact_UN__lessThan__UNIV,axiom, % 187.68/187.59 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)) ). % 187.68/187.59 % 187.68/187.59 fof(fact_UN__atMost__UNIV,axiom, % 187.68/187.59 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)) ). % 187.68/187.59 % 187.68/187.59 fof(fact_range__eqI,axiom, % 187.68/187.59 ! [T_b,T_a,V_x_2,V_f_2,V_b_2] : % 187.68/187.59 ( V_b_2 = hAPP(V_f_2,V_x_2) % 187.68/187.59 => 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))))) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_rangeI,axiom, % 187.68/187.59 ! [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))))) ). % 187.68/187.59 % 187.68/187.59 fof(fact_UN__atLeast__UNIV,axiom, % 187.68/187.59 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)) ). % 187.68/187.59 % 187.68/187.59 fof(fact_Diff__UNIV,axiom, % 187.68/187.59 ! [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)) ). % 187.68/187.59 % 187.68/187.59 fof(fact_comp__surj,axiom, % 187.68/187.59 ! [V_g_2,T_c,V_f_2,T_a,T_b] : % 187.68/187.59 ( 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)) % 187.68/187.59 => ( 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)) % 187.68/187.59 => 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)) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_card__eq__UNIV__imp__eq__UNIV,axiom, % 187.68/187.59 ! [V_A_2,T_a] : % 187.68/187.59 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) % 187.68/187.59 => ( 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))) % 187.68/187.59 => V_A_2 = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_inj__image__eq__iff,axiom, % 187.68/187.59 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 187.68/187.59 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 187.68/187.59 => ( 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) % 187.68/187.59 <=> V_A_2 = V_B_2 ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_inj__comp,axiom, % 187.68/187.59 ! [V_g_2,T_c,V_f_2,T_b,T_a] : % 187.68/187.59 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 187.68/187.59 => ( c_Fun_Oinj__on(T_c,T_a,V_g_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) % 187.68/187.59 => 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))) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_Compl__empty__eq,axiom, % 187.68/187.59 ! [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)) ). % 187.68/187.59 % 187.68/187.59 fof(fact_Compl__UNIV__eq,axiom, % 187.68/187.59 ! [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)) ). % 187.68/187.59 % 187.68/187.59 fof(fact_finite__compl,axiom, % 187.68/187.59 ! [V_A_2,T_a] : % 187.68/187.59 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2))) % 187.68/187.59 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_Compl__partition,axiom, % 187.68/187.59 ! [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)) ). % 187.68/187.59 % 187.68/187.59 fof(fact_Compl__partition2,axiom, % 187.68/187.59 ! [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)) ). % 187.68/187.59 % 187.68/187.59 fof(fact_Compl__eq__Diff__UNIV,axiom, % 187.68/187.59 ! [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) ). % 187.68/187.59 % 187.68/187.59 fof(fact_SUP__UN__eq,axiom, % 187.68/187.59 ! [V_x_2,V_r_2,T_b,T_a] : % 187.68/187.59 ( 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)) % 187.68/187.59 <=> 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))) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_finite__range__imageI,axiom, % 187.68/187.59 ! [V_f_2,T_c,V_g_2,T_b,T_a] : % 187.68/187.59 ( 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))))) % 187.68/187.59 => 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))))) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_the__inv__f__f,axiom, % 187.68/187.59 ! [V_x_2,V_f_2,T_b,T_a] : % 187.68/187.59 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 187.68/187.59 => 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 ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_finite__fun__UNIVD1,axiom, % 187.68/187.59 ! [T_b,T_a] : % 187.68/187.59 ( 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)))) % 187.68/187.59 => ( 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)) % 187.68/187.59 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_inj__of__nat,axiom, % 187.68/187.59 ! [T_a] : % 187.68/187.59 ( class_Nat_Osemiring__char__0(T_a) % 187.68/187.59 => 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))) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_dom__const,axiom, % 187.68/187.59 ! [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)) ). % 187.68/187.59 % 187.68/187.59 fof(fact_atLeast__0,axiom, % 187.68/187.59 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)) ). % 187.68/187.59 % 187.68/187.59 fof(fact_inj__fun,axiom, % 187.68/187.59 ! [T_c,V_f_2,T_b,T_a] : % 187.68/187.59 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 187.68/187.59 => 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))) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_compl__bot__eq,axiom, % 187.68/187.59 ! [T_a] : % 187.68/187.59 ( class_Lattices_Oboolean__algebra(T_a) % 187.68/187.59 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Orderings_Obot__class_Obot(T_a)) = c_Orderings_Otop__class_Otop(T_a) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_compl__top__eq,axiom, % 187.68/187.59 ! [T_a] : % 187.68/187.59 ( class_Lattices_Oboolean__algebra(T_a) % 187.68/187.59 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Orderings_Otop__class_Otop(T_a)) = c_Orderings_Obot__class_Obot(T_a) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_sup__compl__top,axiom, % 187.68/187.59 ! [V_x,T_a] : % 187.68/187.59 ( class_Lattices_Oboolean__algebra(T_a) % 187.68/187.59 => 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) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_compl__sup__top,axiom, % 187.68/187.59 ! [V_x,T_a] : % 187.68/187.59 ( class_Lattices_Oboolean__algebra(T_a) % 187.68/187.59 => 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) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_inj__image__mem__iff,axiom, % 187.68/187.59 ! [V_A_2,V_a_2,V_f_2,T_b,T_a] : % 187.68/187.59 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 187.68/187.59 => ( 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))) % 187.68/187.59 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_range__ex1__eq,axiom, % 187.68/187.59 ! [V_b_2,V_f_2,T_b,T_a] : % 187.68/187.59 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 187.68/187.59 => ( 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))))) % 187.68/187.59 <=> ? [B_x] : % 187.68/187.59 ( V_b_2 = hAPP(V_f_2,B_x) % 187.68/187.59 & ! [B_y] : % 187.68/187.59 ( V_b_2 = hAPP(V_f_2,B_y) % 187.68/187.59 => B_y = B_x ) ) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_finite__UNIV__surj__inj,axiom, % 187.68/187.59 ! [V_f_2,T_a] : % 187.68/187.59 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) % 187.68/187.59 => ( 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)) % 187.68/187.59 => c_Fun_Oinj__on(T_a,T_a,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_finite__UNIV__inj__surj,axiom, % 187.68/187.59 ! [V_f_2,T_a] : % 187.68/187.59 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) % 187.68/187.59 => ( c_Fun_Oinj__on(T_a,T_a,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 187.68/187.59 => 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)) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_inj__image__subset__iff,axiom, % 187.68/187.59 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 187.68/187.59 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 187.68/187.59 => ( 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))) % 187.68/187.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_image__Int,axiom, % 187.68/187.59 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 187.68/187.59 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 187.68/187.59 => 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)) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_image__set__diff,axiom, % 187.68/187.59 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 187.68/187.59 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 187.68/187.59 => 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)) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_surj__Compl__image__subset,axiom, % 187.68/187.59 ! [V_A_2,V_f_2,T_a,T_b] : % 187.68/187.59 ( 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)) % 187.68/187.59 => 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)))) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_finite__range__updI,axiom, % 187.68/187.59 ! [V_b_2,V_a_2,V_f_2,T_b,T_a] : % 187.68/187.59 ( 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))))) % 187.68/187.59 => 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))))) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_UN__UN__finite__eq,axiom, % 187.68/187.59 ! [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) ). % 187.68/187.59 % 187.68/187.59 fof(fact_inj__singleton,axiom, % 187.68/187.59 ! [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))) ). % 187.68/187.59 % 187.68/187.59 fof(fact_finite__UNIV__card__ge__0,axiom, % 187.68/187.59 ! [T_a] : % 187.68/187.59 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) % 187.68/187.59 => 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))))) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_card__UNIV__bool,axiom, % 187.68/187.59 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))) ). % 187.68/187.59 % 187.68/187.59 fof(fact_inj__image__Compl__subset,axiom, % 187.68/187.59 ! [V_A_2,V_f_2,T_b,T_a] : % 187.68/187.59 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 187.68/187.59 => 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)))) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_greaterThan__0,axiom, % 187.68/187.59 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))) ). % 187.68/187.59 % 187.68/187.59 fof(fact_SUP__UN__eq2,axiom, % 187.68/187.59 ! [V_y_2,V_x_2,V_r_2,T_c,T_b,T_a] : % 187.68/187.59 ( 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)) % 187.68/187.59 <=> 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))) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_UN__finite2__subset,axiom, % 187.68/187.59 ! [V_B_2,V_k_2,V_A_2,T_a] : % 187.68/187.59 ( ! [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))) % 187.68/187.59 => 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))) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_UN__finite2__eq,axiom, % 187.68/187.59 ! [V_B_2,V_k_2,V_A_2,T_a] : % 187.68/187.59 ( ! [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) % 187.68/187.59 => 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) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_UN__finite__subset,axiom, % 187.68/187.59 ! [V_C_2,V_A_2,T_a] : % 187.68/187.59 ( ! [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)) % 187.68/187.59 => 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)) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_top1I,axiom, % 187.68/187.59 ! [V_x_2,T_a] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_x_2)) ). % 187.68/187.59 % 187.68/187.59 fof(fact_Integ__def,axiom, % 187.68/187.59 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) ). % 187.68/187.59 % 187.68/187.59 fof(fact_equivp__equiv,axiom, % 187.68/187.59 ! [V_A_2,T_a] : % 187.68/187.59 ( c_Equiv__Relations_Oequiv(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_A_2) % 187.68/187.59 <=> 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)) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_inj__vimage__singleton,axiom, % 187.68/187.59 ! [V_a_2,V_f_2,T_b,T_a] : % 187.68/187.59 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 187.68/187.59 => 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))))) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_vimageI,axiom, % 187.68/187.59 ! [T_b,V_B_2,T_a,V_b_2,V_a_2,V_f_2] : % 187.68/187.59 ( hAPP(V_f_2,V_a_2) = V_b_2 % 187.68/187.59 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),V_B_2)) % 187.68/187.59 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_a,V_f_2),V_B_2))) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_vimage__UNIV,axiom, % 187.68/187.59 ! [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)) ). % 187.68/187.59 % 187.68/187.59 fof(fact_vimage__UN,axiom, % 187.68/187.59 ! [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)) ). % 187.68/187.59 % 187.68/187.59 fof(fact_vimage__compose,axiom, % 187.68/187.59 ! [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)) ). % 187.68/187.59 % 187.68/187.59 fof(fact_vimage__Un,axiom, % 187.68/187.59 ! [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)) ). % 187.68/187.59 % 187.68/187.59 fof(fact_vimage__eq,axiom, % 187.68/187.59 ! [V_B_2,V_f_2,T_b,V_a_2,T_a] : % 187.68/187.59 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_B_2))) % 187.68/187.59 <=> hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_a_2)),V_B_2)) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_vimageD,axiom, % 187.68/187.59 ! [V_A_2,V_f_2,T_b,V_a_2,T_a] : % 187.68/187.59 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_A_2))) % 187.68/187.59 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_a_2)),V_A_2)) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_vimageI2,axiom, % 187.68/187.59 ! [T_b,V_A_2,V_a_2,V_f_2,T_a] : % 187.68/187.59 ( hBOOL(hAPP(hAPP(c_member(T_a),hAPP(V_f_2,V_a_2)),V_A_2)) % 187.68/187.59 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_a,V_f_2),V_A_2))) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_vimage__empty,axiom, % 187.68/187.59 ! [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)) ). % 187.68/187.59 % 187.68/187.59 fof(fact_vimage__mono,axiom, % 187.68/187.59 ! [V_f_2,T_b,V_B_2,V_A_2,T_a] : % 187.68/187.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 187.68/187.59 => 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))) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_vimage__ident,axiom, % 187.68/187.59 ! [V_Y_2,T_a] : hAPP(c_Set_Ovimage(T_a,T_a,c_COMBI(T_a)),V_Y_2) = V_Y_2 ). % 187.68/187.59 % 187.68/187.59 fof(fact_vimage__code,axiom, % 187.68/187.59 ! [V_x_2,V_A_2,V_f_2,T_b,T_a] : % 187.68/187.59 ( hBOOL(hAPP(hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_A_2),V_x_2)) % 187.68/187.59 <=> hBOOL(hAPP(V_A_2,hAPP(V_f_2,V_x_2))) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_vimage__Compl,axiom, % 187.68/187.59 ! [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)) ). % 187.68/187.59 % 187.68/187.59 fof(fact_equivp__transp,axiom, % 187.68/187.59 ! [V_z_2,V_y_2,V_x_2,V_R_2,T_a] : % 187.68/187.59 ( c_Equiv__Relations_Oequivp(T_a,V_R_2) % 187.68/187.59 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2)) % 187.68/187.59 => ( hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_z_2)) % 187.68/187.59 => hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_z_2)) ) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_equivp__symp,axiom, % 187.68/187.59 ! [V_y_2,V_x_2,V_R_2,T_a] : % 187.68/187.59 ( c_Equiv__Relations_Oequivp(T_a,V_R_2) % 187.68/187.59 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2)) % 187.68/187.59 => hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_x_2)) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_equivp__reflp,axiom, % 187.68/187.59 ! [V_x_2,V_R_2,T_a] : % 187.68/187.59 ( c_Equiv__Relations_Oequivp(T_a,V_R_2) % 187.68/187.59 => hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_x_2)) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_equivp__def,axiom, % 187.68/187.59 ! [V_R_2,T_a] : % 187.68/187.59 ( c_Equiv__Relations_Oequivp(T_a,V_R_2) % 187.68/187.59 <=> ! [B_x,B_y] : % 187.68/187.59 ( hBOOL(hAPP(hAPP(V_R_2,B_x),B_y)) % 187.68/187.59 <=> hAPP(V_R_2,B_x) = hAPP(V_R_2,B_y) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_identity__equivp,axiom, % 187.68/187.59 ! [T_a] : c_Equiv__Relations_Oequivp(T_a,c_fequal) ). % 187.68/187.59 % 187.68/187.59 fof(fact_vimage__Int,axiom, % 187.68/187.59 ! [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)) ). % 187.68/187.59 % 187.68/187.59 fof(fact_vimage__Diff,axiom, % 187.68/187.59 ! [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)) ). % 187.68/187.59 % 187.68/187.59 fof(fact_image__vimage__subset,axiom, % 187.68/187.59 ! [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)) ). % 187.68/187.59 % 187.68/187.59 fof(fact_surj__image__vimage__eq,axiom, % 187.68/187.59 ! [V_A_2,V_f_2,T_a,T_b] : % 187.68/187.59 ( 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)) % 187.68/187.59 => 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 ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_vimage__singleton__eq,axiom, % 187.68/187.59 ! [V_b_2,V_f_2,T_b,V_a_2,T_a] : % 187.68/187.59 ( 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)))))) % 187.68/187.59 <=> hAPP(V_f_2,V_a_2) = V_b_2 ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_vimage__insert,axiom, % 187.68/187.59 ! [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)) ). % 187.68/187.59 % 187.68/187.59 fof(fact_finite__vimageD,axiom, % 187.68/187.59 ! [V_F_2,V_h_2,T_b,T_a] : % 187.68/187.59 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_Ovimage(T_a,T_b,V_h_2),V_F_2))) % 187.68/187.59 => ( 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)) % 187.68/187.59 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_vimage__subsetD,axiom, % 187.68/187.59 ! [V_A_2,V_B_2,V_f_2,T_a,T_b] : % 187.68/187.59 ( 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)) % 187.68/187.59 => ( 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)) % 187.68/187.59 => 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))) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_image__vimage__eq,axiom, % 187.68/187.59 ! [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)))) ). % 187.68/187.59 % 187.68/187.59 fof(fact_finite__vimageI,axiom, % 187.68/187.59 ! [V_h_2,T_b,V_F_2,T_a] : % 187.68/187.59 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) % 187.68/187.59 => ( c_Fun_Oinj__on(T_b,T_a,V_h_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 187.68/187.59 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Ovimage(T_b,T_a,V_h_2),V_F_2))) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_inj__vimage__image__eq,axiom, % 187.68/187.59 ! [V_A_2,V_f_2,T_b,T_a] : % 187.68/187.59 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 187.68/187.59 => 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 ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_vimage__const,axiom, % 187.68/187.59 ! [T_b,V_A_2,V_c_2,T_a] : % 187.68/187.59 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) % 187.68/187.59 => hAPP(c_Set_Ovimage(T_b,T_a,hAPP(c_COMBK(T_a,T_b),V_c_2)),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) % 187.68/187.59 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) % 187.68/187.59 => hAPP(c_Set_Ovimage(T_b,T_a,hAPP(c_COMBK(T_a,T_b),V_c_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_vimage__eq__UN,axiom, % 187.68/187.59 ! [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))))) ). % 187.68/187.59 % 187.68/187.59 fof(fact_Rep__Integ,axiom, % 187.68/187.59 ! [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)) ). % 187.68/187.59 % 187.68/187.59 fof(fact_vimage__subsetI,axiom, % 187.68/187.59 ! [V_A_2,V_B_2,V_f_2,T_b,T_a] : % 187.68/187.59 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 187.68/187.59 => ( 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))) % 187.68/187.59 => 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)) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_vimage__if,axiom, % 187.68/187.59 ! [V_B_2,T_b,V_d_2,V_A_2,V_c_2,T_a] : % 187.68/187.59 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) % 187.68/187.59 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_d_2),V_A_2)) % 187.68/187.59 => hAPP(c_Set_Ovimage(T_b,T_a,hAPP(hAPP(c_COMBC(T_b,T_a,T_a),hAPP(hAPP(c_COMBC(T_b,T_a,tc_fun(T_a,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_a,tc_fun(T_a,T_a)),T_b),c_If(T_a)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))),V_c_2)),V_d_2)),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) % 187.68/187.59 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_d_2),V_A_2)) % 187.68/187.59 => hAPP(c_Set_Ovimage(T_b,T_a,hAPP(hAPP(c_COMBC(T_b,T_a,T_a),hAPP(hAPP(c_COMBC(T_b,T_a,tc_fun(T_a,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_a,tc_fun(T_a,T_a)),T_b),c_If(T_a)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))),V_c_2)),V_d_2)),V_A_2) = V_B_2 ) ) ) % 187.68/187.59 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_c_2),V_A_2)) % 187.68/187.59 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_d_2),V_A_2)) % 187.68/187.59 => hAPP(c_Set_Ovimage(T_b,T_a,hAPP(hAPP(c_COMBC(T_b,T_a,T_a),hAPP(hAPP(c_COMBC(T_b,T_a,tc_fun(T_a,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_a,tc_fun(T_a,T_a)),T_b),c_If(T_a)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))),V_c_2)),V_d_2)),V_A_2) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2) ) % 187.68/187.59 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_d_2),V_A_2)) % 187.68/187.59 => hAPP(c_Set_Ovimage(T_b,T_a,hAPP(hAPP(c_COMBC(T_b,T_a,T_a),hAPP(hAPP(c_COMBC(T_b,T_a,tc_fun(T_a,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_a,tc_fun(T_a,T_a)),T_b),c_If(T_a)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))),V_c_2)),V_d_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_type__definition__Integ,axiom, % 187.68/187.59 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) ). % 187.68/187.59 % 187.68/187.59 fof(fact_accp__acc__eq,axiom, % 187.68/187.59 ! [V_x_2,V_r_2,T_a] : % 187.68/187.59 ( 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)) % 187.68/187.59 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Wellfounded_Oacc(T_a,V_r_2))) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_max__extp_Oequations,axiom, % 187.68/187.59 ! [V_a2_2,V_a1_2,V_R_2,T_a] : % 187.68/187.59 ( c_Wellfounded_Omax__extp(T_a,V_R_2,V_a1_2,V_a2_2) % 187.68/187.59 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_a1_2)) % 187.68/187.59 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_a2_2)) % 187.68/187.59 & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.59 & ! [B_x] : % 187.68/187.59 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_a1_2)) % 187.68/187.59 => ? [B_xa] : % 187.68/187.59 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_a2_2)) % 187.68/187.59 & hBOOL(hAPP(hAPP(V_R_2,B_x),B_xa)) ) ) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_acc__subset,axiom, % 187.68/187.59 ! [V_R2_2,V_R1_2,T_a] : % 187.68/187.59 ( 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)) % 187.68/187.59 => 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))) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_acc__downward,axiom, % 187.68/187.59 ! [V_a_2,V_r_2,V_b_2,T_a] : % 187.68/187.59 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Wellfounded_Oacc(T_a,V_r_2))) % 187.68/187.59 => ( 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)) % 187.68/187.59 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Wellfounded_Oacc(T_a,V_r_2))) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_acc_Osimps,axiom, % 187.68/187.59 ! [V_r_2,V_a_2,T_a] : % 187.68/187.59 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Wellfounded_Oacc(T_a,V_r_2))) % 187.68/187.59 <=> ! [B_x] : % 187.68/187.59 ( 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)) % 187.68/187.59 => hBOOL(hAPP(hAPP(c_member(T_a),B_x),c_Wellfounded_Oacc(T_a,V_r_2))) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_type__definition_OAbs__image,axiom, % 187.68/187.59 ! [V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] : % 187.68/187.59 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2) % 187.68/187.59 => 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)) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_type__definition_ORep__range,axiom, % 187.68/187.59 ! [V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] : % 187.68/187.59 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2) % 187.68/187.59 => 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 ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_type__definition_ORep,axiom, % 187.68/187.59 ! [V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] : % 187.68/187.59 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2) % 187.68/187.59 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_Rep_2,V_x_2)),V_A_2)) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_type__definition_ORep__inverse,axiom, % 187.68/187.59 ! [V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] : % 187.68/187.59 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2) % 187.68/187.59 => hAPP(V_Abs_2,hAPP(V_Rep_2,V_x_2)) = V_x_2 ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_type__definition_ORep__inject,axiom, % 187.68/187.59 ! [V_y_2,V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] : % 187.68/187.59 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2) % 187.68/187.59 => ( hAPP(V_Rep_2,V_x_2) = hAPP(V_Rep_2,V_y_2) % 187.68/187.59 <=> V_x_2 = V_y_2 ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_type__definition_OAbs__inject,axiom, % 187.68/187.59 ! [V_y_2,V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] : % 187.68/187.59 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2) % 187.68/187.59 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 187.68/187.59 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) % 187.68/187.59 => ( hAPP(V_Abs_2,V_x_2) = hAPP(V_Abs_2,V_y_2) % 187.68/187.59 <=> V_x_2 = V_y_2 ) ) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_type__definition_OAbs__inverse,axiom, % 187.68/187.59 ! [V_y_2,V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] : % 187.68/187.59 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2) % 187.68/187.59 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) % 187.68/187.59 => hAPP(V_Rep_2,hAPP(V_Abs_2,V_y_2)) = V_y_2 ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_max__ext_Ointros,axiom, % 187.68/187.59 ! [V_R_2,V_Y_2,V_X_2,T_a] : % 187.68/187.59 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_X_2)) % 187.68/187.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_Y_2)) % 187.68/187.59 => ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.59 => ( ! [B_x] : % 187.68/187.59 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_X_2)) % 187.68/187.59 => ? [B_xa] : % 187.68/187.59 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_Y_2)) % 187.68/187.59 & 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)) ) ) % 187.68/187.59 => 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))) ) ) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_Nitpick_Ozero__frac__def,axiom, % 187.68/187.59 ! [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))) ). % 187.68/187.59 % 187.68/187.59 fof(fact_image__split__eq__Sigma,axiom, % 187.68/187.59 ! [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))) ). % 187.68/187.59 % 187.68/187.59 fof(fact_SigmaI,axiom, % 187.68/187.59 ! [V_B_2,V_b_2,T_b,V_A_2,V_a_2,T_a] : % 187.68/187.59 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 187.68/187.59 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2))) % 187.68/187.59 => 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))) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_Sigma__Diff__distrib2,axiom, % 187.68/187.59 ! [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)) ). % 187.68/187.59 % 187.68/187.59 fof(fact_Times__Diff__distrib1,axiom, % 187.68/187.59 ! [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))) ). % 187.68/187.59 % 187.68/187.59 fof(fact_Sigma__Diff__distrib1,axiom, % 187.68/187.59 ! [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)) ). % 187.68/187.59 % 187.68/187.59 fof(fact_Sigma__empty1,axiom, % 187.68/187.59 ! [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)) ). % 187.68/187.59 % 187.68/187.59 fof(fact_Times__eq__cancel2,axiom, % 187.68/187.59 ! [V_B_2,V_A_2,T_b,V_C_2,V_x_2,T_a] : % 187.68/187.59 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_C_2)) % 187.68/187.59 => ( 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)) % 187.68/187.59 <=> V_A_2 = V_B_2 ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_card__cartesian__product,axiom, % 187.68/187.59 ! [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)) ). % 187.68/187.59 % 187.68/187.59 fof(fact_setsum__cartesian__product,axiom, % 187.68/187.59 ! [V_A_2,V_B_2,V_f_2,T_c,T_b,T_a] : % 187.68/187.59 ( class_Groups_Ocomm__monoid__add(T_a) % 187.68/187.59 => 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))) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_Times__empty,axiom, % 187.68/187.59 ! [V_B_2,V_A_2,T_b,T_a] : % 187.68/187.59 ( 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)) % 187.68/187.59 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.59 | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_Sigma__empty2,axiom, % 187.68/187.59 ! [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)) ). % 187.68/187.59 % 187.68/187.59 fof(fact_Compl__Times__UNIV1,axiom, % 187.68/187.59 ! [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))) ). % 187.68/187.59 % 187.68/187.59 fof(fact_Compl__Times__UNIV2,axiom, % 187.68/187.59 ! [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)))) ). % 187.68/187.59 % 187.68/187.59 fof(fact_setprod__cartesian__product,axiom, % 187.68/187.59 ! [V_A_2,V_B_2,V_f_2,T_c,T_b,T_a] : % 187.68/187.59 ( class_Groups_Ocomm__monoid__mult(T_a) % 187.68/187.59 => 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))) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_Sigma__Un__distrib2,axiom, % 187.68/187.59 ! [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)) ). % 187.68/187.59 % 187.68/187.59 fof(fact_Times__Un__distrib1,axiom, % 187.68/187.59 ! [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))) ). % 187.68/187.59 % 187.68/187.59 fof(fact_Sigma__Un__distrib1,axiom, % 187.68/187.59 ! [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)) ). % 187.68/187.59 % 187.68/187.59 fof(fact_swap__product,axiom, % 187.68/187.59 ! [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)) ). % 187.68/187.59 % 187.68/187.59 fof(fact_finite__cartesian__product,axiom, % 187.68/187.59 ! [V_B_2,T_b,V_A_2,T_a] : % 187.68/187.59 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 187.68/187.59 => 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)))) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_equiv__type,axiom, % 187.68/187.59 ! [V_r_2,V_A_2,T_a] : % 187.68/187.59 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 187.68/187.59 => 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)))) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_Sigma__Int__distrib2,axiom, % 187.68/187.59 ! [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)) ). % 187.68/187.59 % 187.68/187.59 fof(fact_Times__Int__distrib1,axiom, % 187.68/187.59 ! [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))) ). % 187.68/187.59 % 187.68/187.59 fof(fact_Sigma__Int__distrib1,axiom, % 187.68/187.59 ! [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)) ). % 187.68/187.59 % 187.68/187.59 fof(fact_Id__on__subset__Times,axiom, % 187.68/187.59 ! [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)))) ). % 187.68/187.59 % 187.68/187.59 fof(fact_UNIV__Times__UNIV,axiom, % 187.68/187.59 ! [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)) ). % 187.68/187.59 % 187.68/187.59 fof(fact_SigmaE2,axiom, % 187.68/187.59 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_b,T_a] : % 187.68/187.59 ( 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))) % 187.68/187.59 => ~ ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 187.68/187.59 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_SigmaD2,axiom, % 187.68/187.59 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_b,T_a] : % 187.68/187.59 ( 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))) % 187.68/187.59 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2))) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_SigmaD1,axiom, % 187.68/187.59 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_b,T_a] : % 187.68/187.59 ( 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))) % 187.68/187.59 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_mem__Sigma__iff,axiom, % 187.68/187.59 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_b,T_a] : % 187.68/187.59 ( 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))) % 187.68/187.59 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 187.68/187.59 & hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_card__cartesian__product__singleton,axiom, % 187.68/187.59 ! [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) ). % 187.68/187.59 % 187.68/187.59 fof(fact_Times__subset__cancel2,axiom, % 187.68/187.59 ! [V_B_2,V_A_2,T_b,V_C_2,V_x_2,T_a] : % 187.68/187.59 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_C_2)) % 187.68/187.59 => ( 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)))) % 187.68/187.59 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_Image__subset,axiom, % 187.68/187.59 ! [V_C_2,V_B_2,V_A_2,V_r_2,T_b,T_a] : % 187.68/187.59 ( 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)))) % 187.68/187.59 => 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)) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_finite__cartesian__productD1,axiom, % 187.68/187.59 ! [V_B_2,V_A_2,T_b,T_a] : % 187.68/187.59 ( 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)))) % 187.68/187.59 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 187.68/187.59 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_finite__cartesian__productD2,axiom, % 187.68/187.59 ! [V_B_2,V_A_2,T_b,T_a] : % 187.68/187.59 ( 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)))) % 187.68/187.59 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.59 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_fst__image__times,axiom, % 187.68/187.59 ! [V_A_2,T_b,T_a,V_B_2] : % 187.68/187.59 ( ( V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.59 => 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)) ) % 187.68/187.59 & ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.59 => 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 ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_snd__image__times,axiom, % 187.68/187.59 ! [V_B_2,T_b,T_a,V_A_2] : % 187.68/187.59 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.59 => 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)) ) % 187.68/187.59 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.59 => 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 ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_insert__times__insert,axiom, % 187.68/187.59 ! [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)))) ). % 187.68/187.59 % 187.68/187.59 fof(fact_finite__equiv__class,axiom, % 187.68/187.59 ! [V_X_2,V_r_2,V_A_2,T_a] : % 187.68/187.59 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.59 => ( 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)))) % 187.68/187.59 => ( 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))) % 187.68/187.59 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_X_2)) ) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_vimage__Times,axiom, % 187.68/187.59 ! [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)) ). % 187.68/187.59 % 187.68/187.59 fof(fact_UN__Times__distrib,axiom, % 187.68/187.59 ! [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))) ). % 187.68/187.59 % 187.68/187.59 fof(fact_Sigma__def,axiom, % 187.68/187.59 ! [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))))) ). % 187.68/187.59 % 187.68/187.59 fof(fact_finite__quotient,axiom, % 187.68/187.59 ! [V_r_2,V_A_2,T_a] : % 187.68/187.59 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.59 => ( 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)))) % 187.68/187.59 => 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))) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_Nitpick_Oone__frac__def,axiom, % 187.68/187.59 ! [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))) ). % 187.68/187.59 % 187.68/187.59 fof(fact_Nitpick_Onumber__of__frac__def,axiom, % 187.68/187.59 ! [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))) ). % 187.68/187.59 % 187.68/187.59 fof(fact_Nitpick_Ofrac__def,axiom, % 187.68/187.59 ! [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)) ). % 187.68/187.59 % 187.68/187.59 fof(fact_Ex__inj__on__UNION__Sigma,axiom, % 187.68/187.59 ! [V_A_2,V_I_2,T_b,T_a] : % 187.68/187.59 ? [B_f] : % 187.68/187.59 ( 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)) % 187.68/187.59 & 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))) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_setprod__Sigma,axiom, % 187.68/187.59 ! [V_f_2,V_B_2,T_b,V_A_2,T_a,T_c] : % 187.68/187.59 ( class_Groups_Ocomm__monoid__mult(T_c) % 187.68/187.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.59 => ( ! [B_x] : % 187.68/187.59 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 187.68/187.59 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_x))) ) % 187.68/187.59 => 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)) ) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_setsum__Sigma,axiom, % 187.68/187.59 ! [V_f_2,V_B_2,T_b,V_A_2,T_a,T_c] : % 187.68/187.59 ( class_Groups_Ocomm__monoid__add(T_c) % 187.68/187.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.59 => ( ! [B_x] : % 187.68/187.59 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 187.68/187.59 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_x))) ) % 187.68/187.59 => 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)) ) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_fold__image__Sigma,axiom, % 187.68/187.59 ! [V_g_2,V_B_2,T_b,V_A_2,T_a,T_c] : % 187.68/187.59 ( class_Groups_Ocomm__monoid__mult(T_c) % 187.68/187.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.59 => ( ! [B_x] : % 187.68/187.59 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 187.68/187.59 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_x))) ) % 187.68/187.59 => 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)) ) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_card__SigmaI,axiom, % 187.68/187.59 ! [V_B_2,T_b,V_A_2,T_a] : % 187.68/187.59 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.59 => ( ! [B_x] : % 187.68/187.59 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 187.68/187.59 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_x))) ) % 187.68/187.59 => 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) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_finite__SigmaI,axiom, % 187.68/187.59 ! [V_B_2,T_b,V_A_2,T_a] : % 187.68/187.59 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.59 => ( ! [B_a] : % 187.68/187.59 ( hBOOL(hAPP(hAPP(c_member(T_a),B_a),V_A_2)) % 187.68/187.59 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_a))) ) % 187.68/187.59 => 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))) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_SigmaE,axiom, % 187.68/187.59 ! [V_B_2,V_A_2,V_c_2,T_b,T_a] : % 187.68/187.59 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),V_c_2),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),V_B_2))) % 187.68/187.59 => ~ ! [B_x] : % 187.68/187.59 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 187.68/187.59 => ! [B_y] : % 187.68/187.59 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),hAPP(V_B_2,B_x))) % 187.68/187.59 => V_c_2 != hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_x),B_y) ) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_map__pair__surj,axiom, % 187.68/187.59 ! [V_g_2,T_c,T_d,V_f_2,T_a,T_b] : % 187.68/187.59 ( 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)) % 187.68/187.59 => ( 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)) % 187.68/187.59 => 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)) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_map__pair__inj__on,axiom, % 187.68/187.59 ! [V_B_2,V_g_2,T_d,T_c,V_A_2,V_f_2,T_b,T_a] : % 187.68/187.59 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 187.68/187.59 => ( c_Fun_Oinj__on(T_c,T_d,V_g_2,V_B_2) % 187.68/187.59 => 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))) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_map__pair__imageI,axiom, % 187.68/187.59 ! [V_g_2,V_f_2,T_d,T_c,V_R_2,V_b_2,V_a_2,T_b,T_a] : % 187.68/187.59 ( 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)) % 187.68/187.59 => 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))) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_map__pair_Ocompositionality,axiom, % 187.68/187.59 ! [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) ). % 187.68/187.59 % 187.68/187.59 fof(fact_map__pair__compose,axiom, % 187.68/187.59 ! [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)) ). % 187.68/187.59 % 187.68/187.59 fof(fact_map__pair_Ocomp,axiom, % 187.68/187.59 ! [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)) ). % 187.68/187.59 % 187.68/187.59 fof(fact_fst__comp__map__pair,axiom, % 187.68/187.59 ! [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)) ). % 187.68/187.59 % 187.68/187.59 fof(fact_snd__comp__map__pair,axiom, % 187.68/187.59 ! [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)) ). % 187.68/187.59 % 187.68/187.59 fof(fact_map__pair__simp,axiom, % 187.68/187.59 ! [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)) ). % 187.68/187.59 % 187.68/187.59 fof(fact_map__pair__ident,axiom, % 187.68/187.59 ! [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 ). % 187.68/187.59 % 187.68/187.59 fof(fact_fst__map__pair,axiom, % 187.68/187.59 ! [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)) ). % 187.68/187.59 % 187.68/187.59 fof(fact_snd__prod__fun,axiom, % 187.68/187.59 ! [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)) ). % 187.68/187.59 % 187.68/187.59 fof(fact_map__pair__def,axiom, % 187.68/187.59 ! [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)) ). % 187.68/187.59 % 187.68/187.59 fof(fact_map__pair__surj__on,axiom, % 187.68/187.59 ! [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] : % 187.68/187.59 ( hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2) = V_A_H_2 % 187.68/187.59 => ( hAPP(c_Set_Oimage(T_d,T_c,V_g_2),V_B_2) = V_B_H_2 % 187.68/187.59 => 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)) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_prod__fun__imageE,axiom, % 187.68/187.59 ! [V_R_2,V_g_2,V_f_2,T_d,T_c,V_c_2,T_b,T_a] : % 187.68/187.59 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),V_c_2),hAPP(c_Set_Oimage(tc_prod(T_c,T_d),tc_prod(T_a,T_b),c_Product__Type_Omap__pair(T_c,T_a,T_d,T_b,V_f_2,V_g_2)),V_R_2))) % 187.68/187.59 => ~ ! [B_x,B_y] : % 187.68/187.59 ( V_c_2 = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_y)) % 187.68/187.59 => ~ 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)) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_refl__on__def,axiom, % 187.68/187.59 ! [V_r_2,V_A_2,T_a] : % 187.68/187.59 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2) % 187.68/187.59 <=> ( 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)))) % 187.68/187.59 & ! [B_x] : % 187.68/187.59 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 187.68/187.59 => 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)) ) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_nat0__intermed__int__val,axiom, % 187.68/187.59 ! [V_k_2,V_f_2,V_n_2] : % 187.68/187.59 ( ! [B_i] : % 187.68/187.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2)) % 187.68/187.59 => 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))) ) % 187.68/187.59 => ( 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)) % 187.68/187.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2))) % 187.68/187.59 => ? [B_i] : % 187.68/187.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2)) % 187.68/187.59 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_refl__on__Id__on,axiom, % 187.68/187.59 ! [V_A_2,T_a] : c_Relation_Orefl__on(T_a,V_A_2,c_Relation_OId__on(T_a,V_A_2)) ). % 187.68/187.59 % 187.68/187.59 fof(fact_refl__on__empty,axiom, % 187.68/187.59 ! [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))) ). % 187.68/187.59 % 187.68/187.59 fof(fact_refl__on__Un,axiom, % 187.68/187.59 ! [V_s_2,V_B_2,V_r_2,V_A_2,T_a] : % 187.68/187.59 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2) % 187.68/187.59 => ( c_Relation_Orefl__on(T_a,V_B_2,V_s_2) % 187.68/187.59 => 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)) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_refl__on__Int,axiom, % 187.68/187.59 ! [V_s_2,V_B_2,V_r_2,V_A_2,T_a] : % 187.68/187.59 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2) % 187.68/187.59 => ( c_Relation_Orefl__on(T_a,V_B_2,V_s_2) % 187.68/187.59 => 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)) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_refl__onD2,axiom, % 187.68/187.59 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_a] : % 187.68/187.59 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2) % 187.68/187.59 => ( 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)) % 187.68/187.59 => hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_refl__onD1,axiom, % 187.68/187.59 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_a] : % 187.68/187.59 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2) % 187.68/187.59 => ( 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)) % 187.68/187.59 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_refl__onD,axiom, % 187.68/187.59 ! [V_a_2,V_r_2,V_A_2,T_a] : % 187.68/187.59 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2) % 187.68/187.59 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 187.68/187.59 => 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)) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_refl__onI,axiom, % 187.68/187.59 ! [V_A_2,V_r_2,T_a] : % 187.68/187.59 ( 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)))) % 187.68/187.59 => ( ! [B_x] : % 187.68/187.59 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 187.68/187.59 => 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)) ) % 187.68/187.59 => c_Relation_Orefl__on(T_a,V_A_2,V_r_2) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_int__val__lemma,axiom, % 187.68/187.59 ! [V_k_2,V_f_2,V_n_2] : % 187.68/187.59 ( ! [B_i] : % 187.68/187.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2)) % 187.68/187.59 => 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))) ) % 187.68/187.59 => ( 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)) % 187.68/187.59 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2))) % 187.68/187.59 => ? [B_i] : % 187.68/187.59 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2)) % 187.68/187.59 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_setprod__pos__nat,axiom, % 187.68/187.59 ! [V_f_2,V_S_2,T_a] : % 187.68/187.59 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 187.68/187.59 => ( ! [B_x] : % 187.68/187.59 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2)) % 187.68/187.59 => 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))) ) % 187.68/187.59 => 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))) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_folding__one__idem_Ohom__commute,axiom, % 187.68/187.59 ! [V_N_2,V_h_2,V_F_2,V_f_2,T_a] : % 187.68/187.59 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2) % 187.68/187.59 => ( ! [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)) % 187.68/187.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 187.68/187.59 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.59 => 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)) ) ) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_Rep__Integ__induct,axiom, % 187.68/187.59 ! [V_P_2,V_y_2] : % 187.68/187.59 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_y_2),c_Int_OInteg)) % 187.68/187.59 => ( ! [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Int_ORep__Integ,B_x))) % 187.68/187.59 => hBOOL(hAPP(V_P_2,V_y_2)) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_Rep__Integ__cases,axiom, % 187.68/187.59 ! [V_y_2] : % 187.68/187.59 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_y_2),c_Int_OInteg)) % 187.68/187.59 => ~ ! [B_x] : V_y_2 != hAPP(c_Int_ORep__Integ,B_x) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_folding__image__simple_Ounion__inter__neutral,axiom, % 187.68/187.59 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 187.68/187.59 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 187.68/187.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 187.68/187.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 187.68/187.59 => ( ! [B_x] : % 187.68/187.59 ( 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))) % 187.68/187.59 => hAPP(V_g_2,B_x) = V_z_2 ) % 187.68/187.59 => 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)) ) ) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_card__less__Suc2,axiom, % 187.68/187.59 ! [V_i_2,V_M_2] : % 187.68/187.59 ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2)) % 187.68/187.59 => 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))))) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_card__less,axiom, % 187.68/187.59 ! [V_i_2,V_M_2] : % 187.68/187.59 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2)) % 187.68/187.59 => 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) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_CollectI,axiom, % 187.68/187.59 ! [T_a,V_a_2,V_P_2] : % 187.68/187.59 ( hBOOL(hAPP(V_P_2,V_a_2)) % 187.68/187.59 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_OCollect(T_a),V_P_2))) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_finite__Collect__conjI,axiom, % 187.68/187.59 ! [V_Q_2,V_P_2,T_a] : % 187.68/187.59 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_P_2))) % 187.68/187.59 | hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_Q_2))) ) % 187.68/187.59 => 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)))) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_finite__Collect__less__nat,axiom, % 187.68/187.59 ! [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)))) ). % 187.68/187.59 % 187.68/187.59 fof(fact_finite__Collect__le__nat,axiom, % 187.68/187.59 ! [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)))) ). % 187.68/187.59 % 187.68/187.59 fof(fact_SetCompr__Sigma__eq,axiom, % 187.68/187.59 ! [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)) ). % 187.68/187.59 % 187.68/187.59 fof(fact_Collect__split,axiom, % 187.68/187.59 ! [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))) ). % 187.68/187.59 % 187.68/187.59 fof(fact_Collect__neg__eq,axiom, % 187.68/187.59 ! [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)) ). % 187.68/187.59 % 187.68/187.59 fof(fact_vimage__Collect__eq,axiom, % 187.68/187.59 ! [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)) ). % 187.68/187.59 % 187.68/187.59 fof(fact_Collect__conj__eq,axiom, % 187.68/187.59 ! [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)) ). % 187.68/187.59 % 187.68/187.59 fof(fact_Collect__def,axiom, % 187.68/187.59 ! [V_P_2,T_a] : hAPP(c_Set_OCollect(T_a),V_P_2) = V_P_2 ). % 187.68/187.59 % 187.68/187.59 fof(fact_empty__def,axiom, % 187.68/187.59 ! [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)) ). % 187.68/187.59 % 187.68/187.59 fof(fact_empty__Collect__eq,axiom, % 187.68/187.59 ! [V_P_2,T_a] : % 187.68/187.59 ( c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_a),V_P_2) % 187.68/187.59 <=> ! [B_x] : ~ hBOOL(hAPP(V_P_2,B_x)) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_Collect__empty__eq,axiom, % 187.68/187.59 ! [V_P_2,T_a] : % 187.68/187.59 ( hAPP(c_Set_OCollect(T_a),V_P_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.59 <=> ! [B_x] : ~ hBOOL(hAPP(V_P_2,B_x)) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_Collect__disj__eq,axiom, % 187.68/187.59 ! [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)) ). % 187.68/187.59 % 187.68/187.59 fof(fact_insert__Collect,axiom, % 187.68/187.59 ! [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)) ). % 187.68/187.59 % 187.68/187.59 fof(fact_finite__Collect__disjI,axiom, % 187.68/187.59 ! [V_Q_2,V_P_2,T_a] : % 187.68/187.59 ( 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)))) % 187.68/187.59 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_P_2))) % 187.68/187.59 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_Q_2))) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_UNIV__def,axiom, % 187.68/187.59 ! [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)) ). % 187.68/187.59 % 187.68/187.59 fof(fact_Collect__mem__eq,axiom, % 187.68/187.59 ! [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 ). % 187.68/187.59 % 187.68/187.59 fof(fact_mem__Collect__eq,axiom, % 187.68/187.59 ! [V_P_2,V_a_2,T_a] : % 187.68/187.59 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_OCollect(T_a),V_P_2))) % 187.68/187.59 <=> hBOOL(hAPP(V_P_2,V_a_2)) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_CollectD,axiom, % 187.68/187.59 ! [V_P_2,V_a_2,T_a] : % 187.68/187.59 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_OCollect(T_a),V_P_2))) % 187.68/187.59 => hBOOL(hAPP(V_P_2,V_a_2)) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_CollectE,axiom, % 187.68/187.59 ! [V_P_2,V_a_2,T_a] : % 187.68/187.59 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_OCollect(T_a),V_P_2))) % 187.68/187.59 => hBOOL(hAPP(V_P_2,V_a_2)) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_insert__compr,axiom, % 187.68/187.59 ! [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))) ). % 187.68/187.59 % 187.68/187.59 fof(fact_insert__compr__raw,axiom, % 187.68/187.59 ! [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))) ). % 187.68/187.59 % 187.68/187.59 fof(fact_Un__def,axiom, % 187.68/187.59 ! [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))) ). % 187.68/187.59 % 187.68/187.59 fof(fact_Int__Collect,axiom, % 187.68/187.59 ! [V_P_2,V_A_2,V_x_2,T_a] : % 187.68/187.59 ( 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)))) % 187.68/187.59 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 187.68/187.59 & hBOOL(hAPP(V_P_2,V_x_2)) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_Int__def,axiom, % 187.68/187.59 ! [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))) ). % 187.68/187.59 % 187.68/187.59 fof(fact_Collect__conv__if,axiom, % 187.68/187.59 ! [T_a,V_a_2,V_P_2] : % 187.68/187.59 ( ( hBOOL(hAPP(V_P_2,V_a_2)) % 187.68/187.59 => 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))) ) % 187.68/187.59 & ( ~ hBOOL(hAPP(V_P_2,V_a_2)) % 187.68/187.59 => 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)) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_Collect__conv__if2,axiom, % 187.68/187.59 ! [T_a,V_a_2,V_P_2] : % 187.68/187.59 ( ( hBOOL(hAPP(V_P_2,V_a_2)) % 187.68/187.59 => 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))) ) % 187.68/187.59 & ( ~ hBOOL(hAPP(V_P_2,V_a_2)) % 187.68/187.59 => 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)) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_singleton__conv,axiom, % 187.68/187.59 ! [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))) ). % 187.68/187.59 % 187.68/187.59 fof(fact_singleton__conv2,axiom, % 187.68/187.59 ! [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))) ). % 187.68/187.59 % 187.68/187.59 fof(fact_set__diff__eq,axiom, % 187.68/187.59 ! [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)))) ). % 187.68/187.59 % 187.68/187.59 fof(fact_finite__Collect__not,axiom, % 187.68/187.59 ! [V_P_2,T_a] : % 187.68/187.59 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_P_2))) % 187.68/187.59 => ( 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)))) % 187.68/187.59 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_insert__def,axiom, % 187.68/187.59 ! [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) ). % 187.68/187.59 % 187.68/187.59 fof(fact_Compl__eq,axiom, % 187.68/187.59 ! [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))) ). % 187.68/187.59 % 187.68/187.59 fof(fact_vimage__def,axiom, % 187.68/187.59 ! [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)) ). % 187.68/187.59 % 187.68/187.59 fof(fact_Collect__imp__eq,axiom, % 187.68/187.59 ! [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)) ). % 187.68/187.59 % 187.68/187.59 fof(fact_dom__def,axiom, % 187.68/187.59 ! [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)))) ). % 187.68/187.59 % 187.68/187.59 fof(fact_finite__M__bounded__by__nat,axiom, % 187.68/187.59 ! [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))))) ). % 187.68/187.59 % 187.68/187.59 fof(fact_setsum__setsum__restrict,axiom, % 187.68/187.59 ! [V_R_2,V_f_2,V_T_2,T_b,V_S_2,T_a,T_c] : % 187.68/187.59 ( class_Groups_Ocomm__monoid__add(T_c) % 187.68/187.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 187.68/187.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2)) % 187.68/187.59 => 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) ) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_if__image__distrib,axiom, % 187.68/187.59 ! [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))))) ). % 187.68/187.59 % 187.68/187.59 fof(fact_dom__if,axiom, % 187.68/187.59 ! [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)))) ). % 187.68/187.59 % 187.68/187.59 fof(fact_nat__seg__image__imp__finite,axiom, % 187.68/187.59 ! [V_n_2,V_f_2,T_a,V_A_2] : % 187.68/187.59 ( 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))) % 187.68/187.59 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_setsum__restrict__set_H,axiom, % 187.68/187.59 ! [V_B_2,V_f_2,V_A_2,T_a,T_b] : % 187.68/187.59 ( class_Groups_Ocomm__monoid__add(T_b) % 187.68/187.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.59 => 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) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_setsum__image__gen,axiom, % 187.68/187.59 ! [V_f_2,T_c,V_g_2,V_S_2,T_a,T_b] : % 187.68/187.59 ( class_Groups_Ocomm__monoid__add(T_b) % 187.68/187.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 187.68/187.59 => 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)) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_Image__singleton,axiom, % 187.68/187.59 ! [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)) ). % 187.68/187.59 % 187.68/187.59 fof(fact_setsum__cases,axiom, % 187.68/187.59 ! [V_g_2,V_f_2,V_P_2,V_A_2,T_a,T_b] : % 187.68/187.59 ( class_Groups_Ocomm__monoid__add(T_b) % 187.68/187.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.59 => 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))))) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_card__less__Suc,axiom, % 187.68/187.59 ! [V_i_2,V_M_2] : % 187.68/187.59 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2)) % 187.68/187.59 => 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))))) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_dom__override__on,axiom, % 187.68/187.59 ! [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))))) ). % 187.68/187.59 % 187.68/187.59 fof(fact_setsum__multicount,axiom, % 187.68/187.59 ! [V_k_2,V_R_2,V_T_2,T_b,V_S_2,T_a] : % 187.68/187.59 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 187.68/187.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2)) % 187.68/187.59 => ( ! [B_x] : % 187.68/187.59 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_T_2)) % 187.68/187.59 => 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 ) % 187.68/187.59 => 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)) ) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_min__max_Oinf__Sup2__distrib,axiom, % 187.68/187.59 ! [V_B_2,V_A_2,T_a] : % 187.68/187.59 ( class_Orderings_Olinorder(T_a) % 187.68/187.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.59 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 187.68/187.59 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.59 => 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))))))) ) ) ) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_finite__Collect__subsets,axiom, % 187.68/187.59 ! [V_A_2,T_a] : % 187.68/187.59 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.59 => 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)))) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_Pow__Compl,axiom, % 187.68/187.59 ! [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))))) ). % 187.68/187.59 % 187.68/187.59 fof(fact_Pow__def,axiom, % 187.68/187.59 ! [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)) ). % 187.68/187.59 % 187.68/187.59 fof(fact_finite__image__set,axiom, % 187.68/187.59 ! [V_f_2,T_b,V_P_2,T_a] : % 187.68/187.59 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_P_2))) % 187.68/187.59 => 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))))) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_finite__Collect__bounded__ex,axiom, % 187.68/187.59 ! [V_Q_2,T_b,V_P_2,T_a] : % 187.68/187.59 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_P_2))) % 187.68/187.59 => ( 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))))) % 187.68/187.59 <=> ! [B_y] : % 187.68/187.59 ( hBOOL(hAPP(V_P_2,B_y)) % 187.68/187.59 => 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)))) ) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_override__on__apply__notin,axiom, % 187.68/187.59 ! [V_g_2,V_f_2,T_b,V_A_2,V_a_2,T_a] : % 187.68/187.59 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 187.68/187.59 => 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) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_override__on__apply__in,axiom, % 187.68/187.59 ! [V_g_2,V_f_2,T_b,V_A_2,V_a_2,T_a] : % 187.68/187.59 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 187.68/187.59 => 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) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_override__on__emptyset,axiom, % 187.68/187.59 ! [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 ). % 187.68/187.59 % 187.68/187.59 fof(fact_inj__graph,axiom, % 187.68/187.59 ! [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))) ). % 187.68/187.59 % 187.68/187.59 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I4_J,axiom, % 187.68/187.59 ! [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))) ). % 187.68/187.59 % 187.68/187.59 fof(fact_override__on__def,axiom, % 187.68/187.59 ! [V_g_2,V_f_2,T_b,V_A_2,V_a_2,T_a] : % 187.68/187.59 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 187.68/187.59 => 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) ) % 187.68/187.59 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 187.68/187.59 => 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) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_finite__psubset__def,axiom, % 187.68/187.59 ! [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)))) ). % 187.68/187.59 % 187.68/187.59 fof(fact_ran__def,axiom, % 187.68/187.59 ! [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)))) ). % 187.68/187.59 % 187.68/187.59 fof(fact_inv__image__def,axiom, % 187.68/187.59 ! [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))) ). % 187.68/187.59 % 187.68/187.59 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I5_J,axiom, % 187.68/187.59 ! [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)))) ). % 187.68/187.59 % 187.68/187.59 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I5_J,axiom, % 187.68/187.59 ! [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)))) ). % 187.68/187.59 % 187.68/187.59 fof(fact_add__Min__commute,axiom, % 187.68/187.59 ! [V_k_2,V_N_2,T_a] : % 187.68/187.59 ( class_Groups_Olinordered__ab__semigroup__add(T_a) % 187.68/187.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 187.68/187.59 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.59 => 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))))) ) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_add__Max__commute,axiom, % 187.68/187.59 ! [V_k_2,V_N_2,T_a] : % 187.68/187.59 ( class_Groups_Olinordered__ab__semigroup__add(T_a) % 187.68/187.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 187.68/187.59 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.59 => 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))))) ) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_sup__Inf1__distrib,axiom, % 187.68/187.59 ! [V_x_2,V_A_2,T_a] : % 187.68/187.59 ( class_Lattices_Odistrib__lattice(T_a) % 187.68/187.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.59 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.59 => 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))))) ) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_sup__Inf2__distrib,axiom, % 187.68/187.59 ! [V_B_2,V_A_2,T_a] : % 187.68/187.59 ( class_Lattices_Odistrib__lattice(T_a) % 187.68/187.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.59 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 187.68/187.59 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.59 => 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))))))) ) ) ) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_inf__Sup1__distrib,axiom, % 187.68/187.59 ! [V_x_2,V_A_2,T_a] : % 187.68/187.59 ( class_Lattices_Odistrib__lattice(T_a) % 187.68/187.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.59 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.59 => 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))))) ) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_inf__Sup2__distrib,axiom, % 187.68/187.59 ! [V_B_2,V_A_2,T_a] : % 187.68/187.59 ( class_Lattices_Odistrib__lattice(T_a) % 187.68/187.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.59 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 187.68/187.59 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.59 => 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))))))) ) ) ) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_min__max_Osup__Inf1__distrib,axiom, % 187.68/187.59 ! [V_x_2,V_A_2,T_a] : % 187.68/187.59 ( class_Orderings_Olinorder(T_a) % 187.68/187.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.59 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.59 => 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))))) ) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_min__max_Osup__Inf2__distrib,axiom, % 187.68/187.59 ! [V_B_2,V_A_2,T_a] : % 187.68/187.59 ( class_Orderings_Olinorder(T_a) % 187.68/187.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.59 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 187.68/187.59 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.59 => 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))))))) ) ) ) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_min__max_Oinf__Sup1__distrib,axiom, % 187.68/187.59 ! [V_x_2,V_A_2,T_a] : % 187.68/187.59 ( class_Orderings_Olinorder(T_a) % 187.68/187.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.59 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.59 => 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))))) ) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_Nitpick_Oprod__def,axiom, % 187.68/187.59 ! [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)))) ). % 187.68/187.59 % 187.68/187.59 fof(fact_int__ge__less__than__def,axiom, % 187.68/187.59 ! [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)))) ). % 187.68/187.59 % 187.68/187.59 fof(fact_int__ge__less__than2__def,axiom, % 187.68/187.59 ! [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)))) ). % 187.68/187.59 % 187.68/187.59 fof(fact_reflp__def,axiom, % 187.68/187.59 ! [V_r_2,T_a] : % 187.68/187.59 ( c_Predicate_Oreflp(T_a,V_r_2) % 187.68/187.59 <=> 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))) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_setsum__mult__setsum__if__inj,axiom, % 187.68/187.59 ! [V_B_2,V_A_2,V_g_2,V_f_2,T_b,T_a,T_c] : % 187.68/187.59 ( class_Rings_Osemiring__0(T_c) % 187.68/187.59 => ( 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))) % 187.68/187.59 => 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))))))) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_setsum__multicount__gen,axiom, % 187.68/187.59 ! [V_k_2,V_R_2,V_t_2,T_b,V_s_2,T_a] : % 187.68/187.59 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_s_2)) % 187.68/187.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_t_2)) % 187.68/187.59 => ( ! [B_x] : % 187.68/187.59 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_t_2)) % 187.68/187.59 => 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) ) % 187.68/187.59 => 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) ) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_inj__on__id,axiom, % 187.68/187.59 ! [V_A_2,T_a] : c_Fun_Oinj__on(T_a,T_a,c_Fun_Oid(T_a),V_A_2) ). % 187.68/187.59 % 187.68/187.59 fof(fact_of__int__eq__id,axiom, % 187.68/187.59 c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint) ). % 187.68/187.59 % 187.68/187.59 fof(fact_map__pair_Oid,axiom, % 187.68/187.59 ! [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)) ). % 187.68/187.59 % 187.68/187.59 fof(fact_map__pair_Oidentity,axiom, % 187.68/187.59 ! [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)) ). % 187.68/187.59 % 187.68/187.59 fof(fact_apfst__id,axiom, % 187.68/187.59 ! [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)) ). % 187.68/187.59 % 187.68/187.59 fof(fact_id__apply,axiom, % 187.68/187.59 ! [V_x,T_a] : hAPP(c_Fun_Oid(T_a),V_x) = V_x ). % 187.68/187.59 % 187.68/187.59 fof(fact_id__def,axiom, % 187.68/187.59 ! [V_x_1,T_a] : hAPP(c_Fun_Oid(T_a),V_x_1) = V_x_1 ). % 187.68/187.59 % 187.68/187.59 fof(fact_reflpE,axiom, % 187.68/187.59 ! [V_x_2,V_r_2,T_a] : % 187.68/187.59 ( c_Predicate_Oreflp(T_a,V_r_2) % 187.68/187.59 => hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_x_2)) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_apsnd__id,axiom, % 187.68/187.59 ! [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)) ). % 187.68/187.59 % 187.68/187.59 fof(fact_vimage__id,axiom, % 187.68/187.59 ! [V_A_2,T_a] : hAPP(c_Set_Ovimage(T_a,T_a,c_Fun_Oid(T_a)),V_A_2) = V_A_2 ). % 187.68/187.59 % 187.68/187.59 fof(fact_o__eq__id__dest,axiom, % 187.68/187.59 ! [V_v_2,V_c_2,V_b_2,V_a_2,T_a,T_b,T_c] : % 187.68/187.59 ( hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_a_2),V_b_2) = hAPP(c_Fun_Ocomp(T_b,T_b,T_a,c_Fun_Oid(T_b)),V_c_2) % 187.68/187.59 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_c_2,V_v_2) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_o__id,axiom, % 187.68/187.59 ! [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 ). % 187.68/187.59 % 187.68/187.59 fof(fact_id__o,axiom, % 187.68/187.59 ! [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 ). % 187.68/187.59 % 187.68/187.59 fof(fact_image__id,axiom, % 187.68/187.59 ! [V_Y_2,T_a] : hAPP(c_Set_Oimage(T_a,T_a,c_Fun_Oid(T_a)),V_Y_2) = V_Y_2 ). % 187.68/187.59 % 187.68/187.59 fof(fact_surj__id,axiom, % 187.68/187.59 ! [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)) ). % 187.68/187.59 % 187.68/187.59 fof(fact_folding_Oempty,axiom, % 187.68/187.59 ! [V_F_2,V_f_2,T_b,T_a] : % 187.68/187.59 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 187.68/187.59 => hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = c_Fun_Oid(T_b) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_apfst__def,axiom, % 187.68/187.59 ! [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)) ). % 187.68/187.59 % 187.68/187.59 fof(fact_apsnd__def,axiom, % 187.68/187.59 ! [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) ). % 187.68/187.59 % 187.68/187.59 fof(fact_split__Pair,axiom, % 187.68/187.59 ! [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)) ). % 187.68/187.59 % 187.68/187.59 fof(fact_setsum__reindex__id,axiom, % 187.68/187.59 ! [V_B_2,V_f_2,T_a,T_b] : % 187.68/187.59 ( class_Groups_Ocomm__monoid__add(T_b) % 187.68/187.59 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2) % 187.68/187.59 => 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)) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_setprod__reindex__id,axiom, % 187.68/187.59 ! [V_B_2,V_f_2,T_a,T_b] : % 187.68/187.59 ( class_Groups_Ocomm__monoid__mult(T_b) % 187.68/187.59 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2) % 187.68/187.59 => 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)) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_finite__conv__nat__seg__image,axiom, % 187.68/187.59 ! [V_A_2,T_a] : % 187.68/187.59 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.59 <=> ? [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))) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_rel__comp__def,axiom, % 187.68/187.59 ! [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))))) ). % 187.68/187.59 % 187.68/187.59 fof(fact_Range__Collect__split,axiom, % 187.68/187.59 ! [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))) ). % 187.68/187.59 % 187.68/187.59 fof(fact_rel__compI,axiom, % 187.68/187.59 ! [V_s_2,V_c_2,T_c,V_r_2,V_b_2,V_a_2,T_b,T_a] : % 187.68/187.59 ( 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)) % 187.68/187.59 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_b_2),V_c_2)),V_s_2)) % 187.68/187.59 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_c),V_a_2),V_c_2)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_b,T_c),V_r_2),V_s_2))) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_RangeI,axiom, % 187.68/187.59 ! [V_r_2,V_b_2,V_a_2,T_b,T_a] : % 187.68/187.59 ( 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)) % 187.68/187.59 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_ORange(T_a,T_b),V_r_2))) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_rel__comp__UNION__distrib2,axiom, % 187.68/187.59 ! [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)) ). % 187.68/187.59 % 187.68/187.59 fof(fact_rel__comp__UNION__distrib,axiom, % 187.68/187.59 ! [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)) ). % 187.68/187.59 % 187.68/187.59 fof(fact_O__assoc,axiom, % 187.68/187.59 ! [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)) ). % 187.68/187.59 % 187.68/187.59 fof(fact_rel__comp__empty1,axiom, % 187.68/187.59 ! [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)) ). % 187.68/187.59 % 187.68/187.59 fof(fact_rel__comp__empty2,axiom, % 187.68/187.59 ! [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)) ). % 187.68/187.59 % 187.68/187.59 fof(fact_rel__comp__mono,axiom, % 187.68/187.59 ! [V_s_2,V_s_H_2,T_c,V_r_2,V_r_H_2,T_b,T_a] : % 187.68/187.59 ( 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)) % 187.68/187.59 => ( 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)) % 187.68/187.59 => 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))) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_rel__comp__distrib,axiom, % 187.68/187.59 ! [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)) ). % 187.68/187.59 % 187.68/187.59 fof(fact_rel__comp__distrib2,axiom, % 187.68/187.59 ! [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)) ). % 187.68/187.59 % 187.68/187.59 fof(fact_Range__Id__on,axiom, % 187.68/187.59 ! [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 ). % 187.68/187.59 % 187.68/187.59 fof(fact_union__comp__emptyL,axiom, % 187.68/187.59 ! [V_B_2,V_C_2,V_A_2,T_a] : % 187.68/187.59 ( 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)) % 187.68/187.59 => ( 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)) % 187.68/187.59 => 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)) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_union__comp__emptyR,axiom, % 187.68/187.59 ! [V_C_2,V_B_2,V_A_2,T_a] : % 187.68/187.59 ( 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)) % 187.68/187.59 => ( 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)) % 187.68/187.59 => 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)) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_Range__empty__iff,axiom, % 187.68/187.59 ! [V_r_2,T_a,T_b] : % 187.68/187.59 ( hAPP(c_Relation_ORange(T_b,T_a),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.59 <=> V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool)) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_Range__empty,axiom, % 187.68/187.59 ! [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)) ). % 187.68/187.59 % 187.68/187.59 fof(fact_rel__comp__subset__Sigma,axiom, % 187.68/187.59 ! [V_C_2,V_s_2,T_c,V_B_2,V_A_2,V_r_2,T_b,T_a] : % 187.68/187.59 ( 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)))) % 187.68/187.59 => ( 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)))) % 187.68/187.59 => 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)))) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_Range__Un__eq,axiom, % 187.68/187.59 ! [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)) ). % 187.68/187.59 % 187.68/187.59 fof(fact_finite__Range,axiom, % 187.68/187.59 ! [V_r_2,T_b,T_a] : % 187.68/187.59 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_b)),V_r_2)) % 187.68/187.59 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Relation_ORange(T_a,T_b),V_r_2))) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_snd__eq__Range,axiom, % 187.68/187.59 ! [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) ). % 187.68/187.59 % 187.68/187.59 fof(fact_Range__iff,axiom, % 187.68/187.59 ! [V_r_2,T_b,V_a_2,T_a] : % 187.68/187.59 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Relation_ORange(T_b,T_a),V_r_2))) % 187.68/187.59 <=> ? [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)) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_Range__insert,axiom, % 187.68/187.59 ! [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)) ). % 187.68/187.59 % 187.68/187.59 fof(fact_Range__Int__subset,axiom, % 187.68/187.59 ! [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)))) ). % 187.68/187.59 % 187.68/187.59 fof(fact_Range__Diff__subset,axiom, % 187.68/187.59 ! [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)))) ). % 187.68/187.59 % 187.68/187.59 fof(fact_max__ext__compat,axiom, % 187.68/187.59 ! [V_S_2,V_R_2,T_a] : % 187.68/187.59 ( 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)) % 187.68/187.59 => 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))) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_min__ext__compat,axiom, % 187.68/187.59 ! [V_S_2,V_R_2,T_a] : % 187.68/187.59 ( 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)) % 187.68/187.59 => 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))) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_RangeP__Range__eq,axiom, % 187.68/187.59 ! [V_x_2,V_r_2,T_b,T_a] : % 187.68/187.59 ( 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)) % 187.68/187.59 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Relation_ORange(T_a,T_b),V_r_2))) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_RangeE,axiom, % 187.68/187.59 ! [V_r_2,T_b,V_b_2,T_a] : % 187.68/187.59 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(c_Relation_ORange(T_b,T_a),V_r_2))) % 187.68/187.59 => ~ ! [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)) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_pred__comp__rel__comp__eq,axiom, % 187.68/187.59 ! [V_y_2,V_x_2,V_s_2,V_r_2,T_c,T_b,T_a] : % 187.68/187.59 ( 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) % 187.68/187.59 <=> 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))) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_pred__comp_Ointros,axiom, % 187.68/187.59 ! [T_c,T_b,T_a,V_c_2,V_s_2,V_b_2,V_a_2,V_r_2] : % 187.68/187.59 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2)) % 187.68/187.59 => ( hBOOL(hAPP(hAPP(V_s_2,V_b_2),V_c_2)) % 187.68/187.59 => c_Predicate_Opred__comp(T_a,T_b,T_c,V_r_2,V_s_2,V_a_2,V_c_2) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_RangeP_Ointros,axiom, % 187.68/187.59 ! [T_b,T_a,V_b_2,V_a_2,V_r_2] : % 187.68/187.59 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2)) % 187.68/187.59 => hBOOL(hAPP(c_Predicate_ORangeP(T_a,T_b,V_r_2),V_b_2)) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_pred__comp_Oequations,axiom, % 187.68/187.59 ! [V_a3_2,V_a1_2,V_s_2,V_r_2,T_c,T_b,T_a] : % 187.68/187.59 ( c_Predicate_Opred__comp(T_a,T_b,T_c,V_r_2,V_s_2,V_a1_2,V_a3_2) % 187.68/187.59 <=> ? [B_b] : % 187.68/187.59 ( hBOOL(hAPP(hAPP(V_r_2,V_a1_2),B_b)) % 187.68/187.59 & hBOOL(hAPP(hAPP(V_s_2,B_b),V_a3_2)) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_RangeP_Oequations,axiom, % 187.68/187.59 ! [V_a2_2,V_r_2,T_b,T_a] : % 187.68/187.59 ( hBOOL(hAPP(c_Predicate_ORangeP(T_a,T_b,V_r_2),V_a2_2)) % 187.68/187.59 <=> ? [B_a] : hBOOL(hAPP(hAPP(V_r_2,B_a),V_a2_2)) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_reduction__pairI,axiom, % 187.68/187.59 ! [V_S_2,V_R_2,T_a] : % 187.68/187.59 ( c_Wellfounded_Owf(T_a,V_R_2) % 187.68/187.59 => ( 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)) % 187.68/187.59 => 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)) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_Domain__Collect__split,axiom, % 187.68/187.59 ! [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)) ). % 187.68/187.59 % 187.68/187.59 fof(fact_pigeonhole__infinite,axiom, % 187.68/187.59 ! [V_f_2,T_b,V_A_2,T_a] : % 187.68/187.59 ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.59 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2))) % 187.68/187.59 => ? [B_x] : % 187.68/187.59 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 187.68/187.59 & ~ 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)))))) ) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_wf__less__than,axiom, % 187.68/187.59 c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than) ). % 187.68/187.59 % 187.68/187.59 fof(fact_wf__empty,axiom, % 187.68/187.59 ! [T_a] : c_Wellfounded_Owf(T_a,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))) ). % 187.68/187.59 % 187.68/187.59 fof(fact_wf__inv__image,axiom, % 187.68/187.59 ! [V_f_2,T_b,V_r_2,T_a] : % 187.68/187.59 ( c_Wellfounded_Owf(T_a,V_r_2) % 187.68/187.59 => c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Relation_Oinv__image(T_a,T_b),V_r_2),V_f_2)) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_wf__lex__prod,axiom, % 187.68/187.59 ! [V_rb_2,T_b,V_ra_2,T_a] : % 187.68/187.59 ( c_Wellfounded_Owf(T_a,V_ra_2) % 187.68/187.59 => ( c_Wellfounded_Owf(T_b,V_rb_2) % 187.68/187.59 => c_Wellfounded_Owf(tc_prod(T_a,T_b),c_Wellfounded_Olex__prod(T_a,T_b,V_ra_2,V_rb_2)) ) ) ). % 187.68/187.59 % 187.68/187.59 fof(fact_wf__measure,axiom, % 187.68/187.60 ! [V_f_2,T_a] : c_Wellfounded_Owf(T_a,hAPP(c_Wellfounded_Omeasure(T_a),V_f_2)) ). % 187.68/187.60 % 187.68/187.60 fof(fact_DomainI,axiom, % 187.68/187.60 ! [V_r_2,V_b_2,V_a_2,T_b,T_a] : % 187.68/187.60 ( 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)) % 187.68/187.60 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Relation_ODomain(T_a,T_b),V_r_2))) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_wf__comp__self,axiom, % 187.68/187.60 ! [V_R_2,T_a] : % 187.68/187.60 ( c_Wellfounded_Owf(T_a,V_R_2) % 187.68/187.60 <=> c_Wellfounded_Owf(T_a,hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_R_2),V_R_2)) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_wf__subset,axiom, % 187.68/187.60 ! [V_p_2,V_r_2,T_a] : % 187.68/187.60 ( c_Wellfounded_Owf(T_a,V_r_2) % 187.68/187.60 => ( 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)) % 187.68/187.60 => c_Wellfounded_Owf(T_a,V_p_2) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_min__ext__wf,axiom, % 187.68/187.60 ! [V_r_2,T_a] : % 187.68/187.60 ( c_Wellfounded_Owf(T_a,V_r_2) % 187.68/187.60 => c_Wellfounded_Owf(tc_fun(T_a,tc_HOL_Obool),c_Wellfounded_Omin__ext(T_a,V_r_2)) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_wf__irrefl,axiom, % 187.68/187.60 ! [V_a_2,V_r_2,T_a] : % 187.68/187.60 ( c_Wellfounded_Owf(T_a,V_r_2) % 187.68/187.60 => ~ 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)) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_wf__asym,axiom, % 187.68/187.60 ! [V_x_2,V_a_2,V_r_2,T_a] : % 187.68/187.60 ( c_Wellfounded_Owf(T_a,V_r_2) % 187.68/187.60 => ( 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)) % 187.68/187.60 => ~ 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)) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_wf__not__sym,axiom, % 187.68/187.60 ! [V_x_2,V_a_2,V_r_2,T_a] : % 187.68/187.60 ( c_Wellfounded_Owf(T_a,V_r_2) % 187.68/187.60 => ( 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)) % 187.68/187.60 => ~ 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)) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_wf__not__refl,axiom, % 187.68/187.60 ! [V_a_2,V_r_2,T_a] : % 187.68/187.60 ( c_Wellfounded_Owf(T_a,V_r_2) % 187.68/187.60 => ~ 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)) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_wf__mlex,axiom, % 187.68/187.60 ! [V_f_2,V_R_2,T_a] : % 187.68/187.60 ( c_Wellfounded_Owf(T_a,V_R_2) % 187.68/187.60 => c_Wellfounded_Owf(T_a,c_Wellfounded_Omlex__prod(T_a,V_f_2,V_R_2)) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_wf__finite__psubset,axiom, % 187.68/187.60 ! [T_a] : c_Wellfounded_Owf(tc_fun(T_a,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(T_a)) ). % 187.68/187.60 % 187.68/187.60 fof(fact_wf__Int2,axiom, % 187.68/187.60 ! [V_r_H_2,V_r_2,T_a] : % 187.68/187.60 ( c_Wellfounded_Owf(T_a,V_r_2) % 187.68/187.60 => 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)) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_wf__Int1,axiom, % 187.68/187.60 ! [V_r_H_2,V_r_2,T_a] : % 187.68/187.60 ( c_Wellfounded_Owf(T_a,V_r_2) % 187.68/187.60 => 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)) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_max__ext__wf,axiom, % 187.68/187.60 ! [V_r_2,T_a] : % 187.68/187.60 ( c_Wellfounded_Owf(T_a,V_r_2) % 187.68/187.60 => c_Wellfounded_Owf(tc_fun(T_a,tc_HOL_Obool),c_Wellfounded_Omax__ext(T_a,V_r_2)) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_wf__pair__less,axiom, % 187.68/187.60 c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ). % 187.68/187.60 % 187.68/187.60 fof(fact_Domain__Id__on,axiom, % 187.68/187.60 ! [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 ). % 187.68/187.60 % 187.68/187.60 fof(fact_wf__less,axiom, % 187.68/187.60 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)))) ). % 187.68/187.60 % 187.68/187.60 fof(fact_wf__int__ge__less__than,axiom, % 187.68/187.60 ! [V_d_2] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than(V_d_2)) ). % 187.68/187.60 % 187.68/187.60 fof(fact_wf__int__ge__less__than2,axiom, % 187.68/187.60 ! [V_d_2] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than2(V_d_2)) ). % 187.68/187.60 % 187.68/187.60 fof(fact_wf__Un,axiom, % 187.68/187.60 ! [V_s_2,V_r_2,T_a] : % 187.68/187.60 ( c_Wellfounded_Owf(T_a,V_r_2) % 187.68/187.60 => ( c_Wellfounded_Owf(T_a,V_s_2) % 187.68/187.60 => ( 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)) % 187.68/187.60 => 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)) ) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_acc__wfD,axiom, % 187.68/187.60 ! [V_x_2,V_r_2,T_a] : % 187.68/187.60 ( c_Wellfounded_Owf(T_a,V_r_2) % 187.68/187.60 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Wellfounded_Oacc(T_a,V_r_2))) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_wf__acc__iff,axiom, % 187.68/187.60 ! [V_r_2,T_a] : % 187.68/187.60 ( c_Wellfounded_Owf(T_a,V_r_2) % 187.68/187.60 <=> ! [B_x] : hBOOL(hAPP(hAPP(c_member(T_a),B_x),c_Wellfounded_Oacc(T_a,V_r_2))) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_wf__no__loop,axiom, % 187.68/187.60 ! [V_R_2,T_a] : % 187.68/187.60 ( 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)) % 187.68/187.60 => c_Wellfounded_Owf(T_a,V_R_2) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_wf__union__merge,axiom, % 187.68/187.60 ! [V_S_2,V_R_2,T_a] : % 187.68/187.60 ( 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)) % 187.68/187.60 <=> 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)) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_Domain__empty__iff,axiom, % 187.68/187.60 ! [V_r_2,T_b,T_a] : % 187.68/187.60 ( hAPP(c_Relation_ODomain(T_a,T_b),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.60 <=> V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_Domain__empty,axiom, % 187.68/187.60 ! [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)) ). % 187.68/187.60 % 187.68/187.60 fof(fact_Domain__mono,axiom, % 187.68/187.60 ! [V_s_2,V_r_2,T_b,T_a] : % 187.68/187.60 ( 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)) % 187.68/187.60 => 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))) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_Domain__Un__eq,axiom, % 187.68/187.60 ! [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)) ). % 187.68/187.60 % 187.68/187.60 fof(fact_finite__Domain,axiom, % 187.68/187.60 ! [V_r_2,T_b,T_a] : % 187.68/187.60 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_b)),V_r_2)) % 187.68/187.60 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Relation_ODomain(T_a,T_b),V_r_2))) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_fst__eq__Domain,axiom, % 187.68/187.60 ! [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) ). % 187.68/187.60 % 187.68/187.60 fof(fact_wf__iff__no__infinite__down__chain,axiom, % 187.68/187.60 ! [V_r_2,T_a] : % 187.68/187.60 ( c_Wellfounded_Owf(T_a,V_r_2) % 187.68/187.60 <=> ~ ? [B_f] : % 187.68/187.60 ! [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)) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_wfE__pf,axiom, % 187.68/187.60 ! [V_A_2,V_R_2,T_a] : % 187.68/187.60 ( c_Wellfounded_Owf(T_a,V_R_2) % 187.68/187.60 => ( 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))) % 187.68/187.60 => V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_wf__union__compatible,axiom, % 187.68/187.60 ! [V_S_2,V_R_2,T_a] : % 187.68/187.60 ( c_Wellfounded_Owf(T_a,V_R_2) % 187.68/187.60 => ( c_Wellfounded_Owf(T_a,V_S_2) % 187.68/187.60 => ( 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)) % 187.68/187.60 => 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)) ) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_Domain__iff,axiom, % 187.68/187.60 ! [V_r_2,T_b,V_a_2,T_a] : % 187.68/187.60 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Relation_ODomain(T_a,T_b),V_r_2))) % 187.68/187.60 <=> ? [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)) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_wf,axiom, % 187.68/187.60 ! [T_a] : % 187.68/187.60 ( class_Orderings_Owellorder(T_a) % 187.68/187.60 => 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)))) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_Domain__insert,axiom, % 187.68/187.60 ! [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)) ). % 187.68/187.60 % 187.68/187.60 fof(fact_reduction__pair__def,axiom, % 187.68/187.60 ! [V_P_2,T_a] : % 187.68/187.60 ( c_FunDef_Oreduction__pair(T_a,V_P_2) % 187.68/187.60 <=> ( 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)) % 187.68/187.60 & 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))) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_reduction__pair__lemma,axiom, % 187.68/187.60 ! [V_S_2,V_R_2,V_P_2,T_a] : % 187.68/187.60 ( c_FunDef_Oreduction__pair(T_a,V_P_2) % 187.68/187.60 => ( 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))) % 187.68/187.60 => ( 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))) % 187.68/187.60 => ( c_Wellfounded_Owf(T_a,V_S_2) % 187.68/187.60 => 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)) ) ) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_Domain__Int__subset,axiom, % 187.68/187.60 ! [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)))) ). % 187.68/187.60 % 187.68/187.60 fof(fact_Domain__Diff__subset,axiom, % 187.68/187.60 ! [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)))) ). % 187.68/187.60 % 187.68/187.60 fof(fact_Field__def,axiom, % 187.68/187.60 ! [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)) ). % 187.68/187.60 % 187.68/187.60 fof(fact_wf__map__pair__image,axiom, % 187.68/187.60 ! [V_f_2,T_b,V_r_2,T_a] : % 187.68/187.60 ( c_Wellfounded_Owf(T_a,V_r_2) % 187.68/187.60 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 187.68/187.60 => 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)) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_DomainP__Domain__eq,axiom, % 187.68/187.60 ! [V_x_2,V_r_2,T_b,T_a] : % 187.68/187.60 ( 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)) % 187.68/187.60 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_Relation_ODomain(T_a,T_b),V_r_2))) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_wf__lenlex,axiom, % 187.68/187.60 ! [V_r_2,T_a] : % 187.68/187.60 ( c_Wellfounded_Owf(T_a,V_r_2) % 187.68/187.60 => c_Wellfounded_Owf(tc_List_Olist(T_a),c_List_Olenlex(T_a,V_r_2)) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_DomainE,axiom, % 187.68/187.60 ! [V_r_2,T_b,V_a_2,T_a] : % 187.68/187.60 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Relation_ODomain(T_a,T_b),V_r_2))) % 187.68/187.60 => ~ ! [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)) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_DomainP_Ointros,axiom, % 187.68/187.60 ! [T_b,T_a,V_b_2,V_a_2,V_r_2] : % 187.68/187.60 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2)) % 187.68/187.60 => hBOOL(hAPP(c_Predicate_ODomainP(T_a,T_b,V_r_2),V_a_2)) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_DomainP_Oequations,axiom, % 187.68/187.60 ! [V_a1_2,V_r_2,T_b,T_a] : % 187.68/187.60 ( hBOOL(hAPP(c_Predicate_ODomainP(T_a,T_b,V_r_2),V_a1_2)) % 187.68/187.60 <=> ? [B_x1] : hBOOL(hAPP(hAPP(V_r_2,V_a1_2),B_x1)) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_pred__nat__def,axiom, % 187.68/187.60 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))) ). % 187.68/187.60 % 187.68/187.60 fof(fact_wf__lex,axiom, % 187.68/187.60 ! [V_r_2,T_a] : % 187.68/187.60 ( c_Wellfounded_Owf(T_a,V_r_2) % 187.68/187.60 => c_Wellfounded_Owf(tc_List_Olist(T_a),c_List_Olex(T_a,V_r_2)) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_wf__lexn,axiom, % 187.68/187.60 ! [V_n_2,V_r_2,T_a] : % 187.68/187.60 ( c_Wellfounded_Owf(T_a,V_r_2) % 187.68/187.60 => c_Wellfounded_Owf(tc_List_Olist(T_a),hAPP(c_List_Olexn(T_a,V_r_2),V_n_2)) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_lex__def,axiom, % 187.68/187.60 ! [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)) ). % 187.68/187.60 % 187.68/187.60 fof(fact_lexn_Osimps_I1_J,axiom, % 187.68/187.60 ! [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)) ). % 187.68/187.60 % 187.68/187.60 fof(fact_wf__pred__nat,axiom, % 187.68/187.60 c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat) ). % 187.68/187.60 % 187.68/187.60 fof(fact_wf__same__fst,axiom, % 187.68/187.60 ! [T_a,V_R_2,T_b,V_P_2] : % 187.68/187.60 ( ! [B_x] : % 187.68/187.60 ( hBOOL(hAPP(V_P_2,B_x)) % 187.68/187.60 => c_Wellfounded_Owf(T_b,hAPP(V_R_2,B_x)) ) % 187.68/187.60 => c_Wellfounded_Owf(tc_prod(T_a,T_b),c_Recdef_Osame__fst(T_a,T_b,V_P_2,V_R_2)) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_wf__if__measure,axiom, % 187.68/187.60 ! [T_a,V_g_2,V_f_2,V_P_2] : % 187.68/187.60 ( ! [B_x] : % 187.68/187.60 ( hBOOL(hAPP(V_P_2,B_x)) % 187.68/187.60 => 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))) ) % 187.68/187.60 => 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))))) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_wfP__def,axiom, % 187.68/187.60 ! [V_r_2,T_a] : % 187.68/187.60 ( c_Wellfounded_OwfP(T_a,V_r_2) % 187.68/187.60 <=> 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))) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_wfP__empty,axiom, % 187.68/187.60 ! [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))) ). % 187.68/187.60 % 187.68/187.60 fof(fact_wfP__accp__iff,axiom, % 187.68/187.60 ! [V_r_2,T_a] : % 187.68/187.60 ( c_Wellfounded_OwfP(T_a,V_r_2) % 187.68/187.60 <=> ! [B_x1] : hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),B_x1)) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_accp__wfPD,axiom, % 187.68/187.60 ! [V_x_2,V_r_2,T_a] : % 187.68/187.60 ( c_Wellfounded_OwfP(T_a,V_r_2) % 187.68/187.60 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_x_2)) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_wfP__subset,axiom, % 187.68/187.60 ! [V_p_2,V_r_2,T_a] : % 187.68/187.60 ( c_Wellfounded_OwfP(T_a,V_r_2) % 187.68/187.60 => ( 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)) % 187.68/187.60 => c_Wellfounded_OwfP(T_a,V_p_2) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_wf__in__rel,axiom, % 187.68/187.60 ! [V_R_2,T_a] : % 187.68/187.60 ( c_Wellfounded_Owf(T_a,V_R_2) % 187.68/187.60 => c_Wellfounded_OwfP(T_a,c_FunDef_Oin__rel(T_a,T_a,V_R_2)) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_wfP__wf__eq,axiom, % 187.68/187.60 ! [V_r_2,T_a] : % 187.68/187.60 ( 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)) % 187.68/187.60 <=> c_Wellfounded_Owf(T_a,V_r_2) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_wfP__acyclicP,axiom, % 187.68/187.60 ! [V_r_2,T_a] : % 187.68/187.60 ( c_Wellfounded_OwfP(T_a,V_r_2) % 187.68/187.60 => 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))) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_refl__on__def_H,axiom, % 187.68/187.60 ! [V_r_2,V_A_2,T_a] : % 187.68/187.60 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2) % 187.68/187.60 <=> ( ! [B_x] : % 187.68/187.60 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),B_x),V_r_2)) % 187.68/187.60 => 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)) ) % 187.68/187.60 & ! [B_x] : % 187.68/187.60 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 187.68/187.60 => 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)) ) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_Abs__Integ__induct,axiom, % 187.68/187.60 ! [V_x_2,V_P_2] : % 187.68/187.60 ( ! [B_y] : % 187.68/187.60 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),B_y),c_Int_OInteg)) % 187.68/187.60 => hBOOL(hAPP(V_P_2,hAPP(c_Int_OAbs__Integ,B_y))) ) % 187.68/187.60 => hBOOL(hAPP(V_P_2,V_x_2)) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_ball__empty,axiom, % 187.68/187.60 ! [V_P_2,T_a,B_x] : % 187.68/187.60 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) % 187.68/187.60 => hBOOL(hAPP(V_P_2,B_x)) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_wf__acyclic,axiom, % 187.68/187.60 ! [V_r_2,T_a] : % 187.68/187.60 ( c_Wellfounded_Owf(T_a,V_r_2) % 187.68/187.60 => c_Wellfounded_Oacyclic(T_a,V_r_2) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_acyclic__subset,axiom, % 187.68/187.60 ! [V_r_2,V_s_2,T_a] : % 187.68/187.60 ( c_Wellfounded_Oacyclic(T_a,V_s_2) % 187.68/187.60 => ( 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)) % 187.68/187.60 => c_Wellfounded_Oacyclic(T_a,V_r_2) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_ball__UNIV,axiom, % 187.68/187.60 ! [V_P_2,T_a] : % 187.68/187.60 ( ! [B_x] : % 187.68/187.60 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) % 187.68/187.60 => hBOOL(hAPP(V_P_2,B_x)) ) % 187.68/187.60 <=> ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_Powp__def,axiom, % 187.68/187.60 ! [V_B_2,V_A_2,T_a] : % 187.68/187.60 ( hBOOL(hAPP(c_Predicate_OPowp(T_a,V_A_2),V_B_2)) % 187.68/187.60 <=> ! [B_x] : % 187.68/187.60 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_B_2)) % 187.68/187.60 => hBOOL(hAPP(V_A_2,B_x)) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_congruent__def,axiom, % 187.68/187.60 ! [V_f_2,V_r_2,T_b,T_a] : % 187.68/187.60 ( c_Equiv__Relations_Ocongruent(T_a,T_b,V_r_2,V_f_2) % 187.68/187.60 <=> ! [B_x] : % 187.68/187.60 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),B_x),V_r_2)) % 187.68/187.60 => 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)) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_wf__iff__acyclic__if__finite,axiom, % 187.68/187.60 ! [V_r_2,T_a] : % 187.68/187.60 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2)) % 187.68/187.60 => ( c_Wellfounded_Owf(T_a,V_r_2) % 187.68/187.60 <=> c_Wellfounded_Oacyclic(T_a,V_r_2) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_finite__acyclic__wf,axiom, % 187.68/187.60 ! [V_r_2,T_a] : % 187.68/187.60 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2)) % 187.68/187.60 => ( c_Wellfounded_Oacyclic(T_a,V_r_2) % 187.68/187.60 => c_Wellfounded_Owf(T_a,V_r_2) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_Nitpick_Owf_H__def,axiom, % 187.68/187.60 ! [V_r_2,T_a] : % 187.68/187.60 ( c_Nitpick_Owf_H(T_a,V_r_2) % 187.68/187.60 <=> ( c_Wellfounded_Oacyclic(T_a,V_r_2) % 187.68/187.60 & ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2)) % 187.68/187.60 | c_Nitpick_Ounknown(tc_HOL_Obool) ) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_Abs__Integ__cases,axiom, % 187.68/187.60 ! [V_x_2] : % 187.68/187.60 ~ ! [B_y] : % 187.68/187.60 ( V_x_2 = hAPP(c_Int_OAbs__Integ,B_y) % 187.68/187.60 => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),B_y),c_Int_OInteg)) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_finite__UN__I,axiom, % 187.68/187.60 ! [V_B_2,T_b,V_A_2,T_a] : % 187.68/187.60 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.60 => ( ! [B_a] : % 187.68/187.60 ( hBOOL(hAPP(hAPP(c_member(T_a),B_a),V_A_2)) % 187.68/187.60 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_a))) ) % 187.68/187.60 => 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))) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_triples__valid__Suc,axiom, % 187.68/187.60 ! [V_n_2,V_ts_2,T_a] : % 187.68/187.60 ( ! [B_x] : % 187.68/187.60 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_a)),B_x),V_ts_2)) % 187.68/187.60 => c_Hoare__Mirabelle_Otriple__valid(T_a,hAPP(c_Nat_OSuc,V_n_2),B_x) ) % 187.68/187.60 => ! [B_x] : % 187.68/187.60 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_a)),B_x),V_ts_2)) % 187.68/187.60 => c_Hoare__Mirabelle_Otriple__valid(T_a,V_n_2,B_x) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_hoare__valids__def,axiom, % 187.68/187.60 ! [V_ts_2,V_Ga_2,T_a] : % 187.68/187.60 ( c_Hoare__Mirabelle_Ohoare__valids(T_a,V_Ga_2,V_ts_2) % 187.68/187.60 <=> ! [B_n] : % 187.68/187.60 ( ! [B_x] : % 187.68/187.60 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_a)),B_x),V_Ga_2)) % 187.68/187.60 => c_Hoare__Mirabelle_Otriple__valid(T_a,B_n,B_x) ) % 187.68/187.60 => ! [B_x] : % 187.68/187.60 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_a)),B_x),V_ts_2)) % 187.68/187.60 => c_Hoare__Mirabelle_Otriple__valid(T_a,B_n,B_x) ) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_inj__on__diff__nat,axiom, % 187.68/187.60 ! [V_k_2,V_N_2] : % 187.68/187.60 ( ! [B_x] : % 187.68/187.60 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2)) % 187.68/187.60 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),B_x)) ) % 187.68/187.60 => 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) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_wfP__SUP,axiom, % 187.68/187.60 ! [T_a,V_r_2,T_b] : % 187.68/187.60 ( ! [B_i] : c_Wellfounded_OwfP(T_b,hAPP(V_r_2,B_i)) % 187.68/187.60 => ( ! [B_i,B_j] : % 187.68/187.60 ( hAPP(V_r_2,B_i) != hAPP(V_r_2,B_j) % 187.68/187.60 => 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)) ) % 187.68/187.60 => 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)) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_finite__map__freshness,axiom, % 187.68/187.60 ! [V_f_2,T_b,T_a] : % 187.68/187.60 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Map_Odom(T_a,T_b,V_f_2))) % 187.68/187.60 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) % 187.68/187.60 => ? [B_x] : hAPP(V_f_2,B_x) = c_Option_Ooption_ONone(T_b) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_mem__splitE,axiom, % 187.68/187.60 ! [V_p_2,V_c_2,T_c,T_b,V_z_2,T_a] : % 187.68/187.60 ( hBOOL(hAPP(hAPP(c_member(T_a),V_z_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_fun(T_a,tc_HOL_Obool)),V_c_2),V_p_2))) % 187.68/187.60 => ~ ! [B_x,B_y] : % 187.68/187.60 ( V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_y) % 187.68/187.60 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_z_2),hAPP(hAPP(V_c_2,B_x),B_y))) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_mem__splitI2,axiom, % 187.68/187.60 ! [V_c_2,V_z_2,T_c,T_b,T_a,V_p_2] : % 187.68/187.60 ( ! [B_a,B_b] : % 187.68/187.60 ( V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_a),B_b) % 187.68/187.60 => hBOOL(hAPP(hAPP(c_member(T_c),V_z_2),hAPP(hAPP(V_c_2,B_a),B_b))) ) % 187.68/187.60 => hBOOL(hAPP(hAPP(c_member(T_c),V_z_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_fun(T_c,tc_HOL_Obool)),V_c_2),V_p_2))) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_setsum__SucD,axiom, % 187.68/187.60 ! [V_n_2,V_A_2,V_f_2,T_a] : % 187.68/187.60 ( 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) % 187.68/187.60 => ? [B_x] : % 187.68/187.60 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 187.68/187.60 & 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))) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_Eps__split,axiom, % 187.68/187.60 ! [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))) ). % 187.68/187.60 % 187.68/187.60 fof(fact_nat__mod__eq__lemma,axiom, % 187.68/187.60 ! [V_y,V_n,V_x] : % 187.68/187.60 ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_x,V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_y,V_n) % 187.68/187.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y),V_x)) % 187.68/187.60 => ? [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)) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_wfI__pf,axiom, % 187.68/187.60 ! [V_R_2,T_a] : % 187.68/187.60 ( ! [B_A] : % 187.68/187.60 ( 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))) % 187.68/187.60 => B_A = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) % 187.68/187.60 => c_Wellfounded_Owf(T_a,V_R_2) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_tfl__some,axiom, % 187.68/187.60 ! [T_a,B_P] : % 187.68/187.60 ( ? [B_x] : hBOOL(hAPP(B_P,B_x)) % 187.68/187.60 => hBOOL(hAPP(B_P,c_Hilbert__Choice_OEps(T_a,B_P))) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_someI,axiom, % 187.68/187.60 ! [T_a,V_x_2,V_P_2] : % 187.68/187.60 ( hBOOL(hAPP(V_P_2,V_x_2)) % 187.68/187.60 => hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_a,V_P_2))) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_some__sym__eq__trivial,axiom, % 187.68/187.60 ! [V_x_2,T_a] : c_Hilbert__Choice_OEps(T_a,hAPP(c_fequal,V_x_2)) = V_x_2 ). % 187.68/187.60 % 187.68/187.60 fof(fact_some__eq__trivial,axiom, % 187.68/187.60 ! [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 ). % 187.68/187.60 % 187.68/187.60 fof(fact_some__eq__ex,axiom, % 187.68/187.60 ! [T_a,V_P_2] : % 187.68/187.60 ( hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_a,V_P_2))) % 187.68/187.60 <=> ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_someI__ex,axiom, % 187.68/187.60 ! [T_a,V_P_2] : % 187.68/187.60 ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) % 187.68/187.60 => hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_a,V_P_2))) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_exE__some,axiom, % 187.68/187.60 ! [T_a,V_c_2,V_P_2] : % 187.68/187.60 ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) % 187.68/187.60 => ( V_c_2 = c_Hilbert__Choice_OEps(T_a,V_P_2) % 187.68/187.60 => hBOOL(hAPP(V_P_2,V_c_2)) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_Eps__split__eq,axiom, % 187.68/187.60 ! [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) ). % 187.68/187.60 % 187.68/187.60 fof(fact_split__paired__Eps,axiom, % 187.68/187.60 ! [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)))) ). % 187.68/187.60 % 187.68/187.60 fof(fact_LeastM__def,axiom, % 187.68/187.60 ! [V_P_2,V_m_2,T_a,T_b] : % 187.68/187.60 ( class_Orderings_Oord(T_b) % 187.68/187.60 => 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))))) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_GreatestM__def,axiom, % 187.68/187.60 ! [V_P_2,V_m_2,T_a,T_b] : % 187.68/187.60 ( class_Orderings_Oord(T_b) % 187.68/187.60 => 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))))) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_Sigma__mono,axiom, % 187.68/187.60 ! [V_D_2,V_B_2,T_b,V_C_2,V_A_2,T_a] : % 187.68/187.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) % 187.68/187.60 => ( ! [B_x] : % 187.68/187.60 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 187.68/187.60 => 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))) ) % 187.68/187.60 => 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))) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_LeastM__nat__lemma,axiom, % 187.68/187.60 ! [V_m_2,T_a,V_k_2,V_P_2] : % 187.68/187.60 ( hBOOL(hAPP(V_P_2,V_k_2)) % 187.68/187.60 => ( hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OLeastM(T_a,tc_Nat_Onat,V_m_2,V_P_2))) % 187.68/187.60 & ! [B_y] : % 187.68/187.60 ( hBOOL(hAPP(V_P_2,B_y)) % 187.68/187.60 => 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))) ) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_LeastM__nat__le,axiom, % 187.68/187.60 ! [T_a,V_m_2,V_x_2,V_P_2] : % 187.68/187.60 ( hBOOL(hAPP(V_P_2,V_x_2)) % 187.68/187.60 => 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))) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_Greatest__def,axiom, % 187.68/187.60 ! [T_a] : % 187.68/187.60 ( class_Orderings_Oord(T_a) % 187.68/187.60 => c_Hilbert__Choice_OGreatest(T_a) = c_Hilbert__Choice_OGreatestM(T_a,T_a,c_COMBI(T_a)) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_not__acc__down,axiom, % 187.68/187.60 ! [V_R_2,V_x_2,T_a] : % 187.68/187.60 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Wellfounded_Oacc(T_a,V_R_2))) % 187.68/187.60 => ~ ! [B_z] : % 187.68/187.60 ( 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)) % 187.68/187.60 => hBOOL(hAPP(hAPP(c_member(T_a),B_z),c_Wellfounded_Oacc(T_a,V_R_2))) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_acc_OaccI,axiom, % 187.68/187.60 ! [V_r_2,V_x_2,T_a] : % 187.68/187.60 ( ! [B_y] : % 187.68/187.60 ( 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)) % 187.68/187.60 => hBOOL(hAPP(hAPP(c_member(T_a),B_y),c_Wellfounded_Oacc(T_a,V_r_2))) ) % 187.68/187.60 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Wellfounded_Oacc(T_a,V_r_2))) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_LeastM__natI,axiom, % 187.68/187.60 ! [V_m_2,T_a,V_k_2,V_P_2] : % 187.68/187.60 ( hBOOL(hAPP(V_P_2,V_k_2)) % 187.68/187.60 => hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OLeastM(T_a,tc_Nat_Onat,V_m_2,V_P_2))) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_fold__image__1,axiom, % 187.68/187.60 ! [V_f_2,V_S_2,T_a,T_b] : % 187.68/187.60 ( class_Groups_Ocomm__monoid__mult(T_b) % 187.68/187.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 187.68/187.60 => ( ! [B_x] : % 187.68/187.60 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2)) % 187.68/187.60 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_b) ) % 187.68/187.60 => 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) ) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_max__ext_Osimps,axiom, % 187.68/187.60 ! [V_R_2,V_a2_2,V_a1_2,T_a] : % 187.68/187.60 ( 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))) % 187.68/187.60 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_a1_2)) % 187.68/187.60 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_a2_2)) % 187.68/187.60 & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.60 & ! [B_x] : % 187.68/187.60 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_a1_2)) % 187.68/187.60 => ? [B_xa] : % 187.68/187.60 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_a2_2)) % 187.68/187.60 & 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)) ) ) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_mod__induct__0,axiom, % 187.68/187.60 ! [V_i_2,V_P_2,V_p_2] : % 187.68/187.60 ( ! [B_i] : % 187.68/187.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_p_2)) % 187.68/187.60 => ( hBOOL(hAPP(V_P_2,B_i)) % 187.68/187.60 => hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,B_i),V_p_2))) ) ) % 187.68/187.60 => ( hBOOL(hAPP(V_P_2,V_i_2)) % 187.68/187.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),V_p_2)) % 187.68/187.60 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_coinduct__set,axiom, % 187.68/187.60 ! [V_X_2,V_a_2,V_f_2,T_a] : % 187.68/187.60 ( c_Orderings_Oorder__class_Omono(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),V_f_2) % 187.68/187.60 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_X_2)) % 187.68/187.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_X_2),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_X_2),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_a,tc_HOL_Obool),V_f_2))))) % 187.68/187.60 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_a,tc_HOL_Obool),V_f_2))) ) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_def__coinduct__set,axiom, % 187.68/187.60 ! [V_X_2,V_a_2,V_f_2,T_a,V_A_2] : % 187.68/187.60 ( V_A_2 = c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_a,tc_HOL_Obool),V_f_2) % 187.68/187.60 => ( c_Orderings_Oorder__class_Omono(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),V_f_2) % 187.68/187.60 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_X_2)) % 187.68/187.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_X_2),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_X_2),V_A_2)))) % 187.68/187.60 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_fold__image__cong,axiom, % 187.68/187.60 ! [V_z_2,V_h_2,V_g_2,V_A_2,T_a,T_b] : % 187.68/187.60 ( class_Groups_Oab__semigroup__mult(T_b) % 187.68/187.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.60 => ( ! [B_x] : % 187.68/187.60 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 187.68/187.60 => hAPP(V_g_2,B_x) = hAPP(V_h_2,B_x) ) % 187.68/187.60 => 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) ) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_gfp__upperbound,axiom, % 187.68/187.60 ! [V_f_2,V_X_2,T_a] : % 187.68/187.60 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 187.68/187.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_X_2),hAPP(V_f_2,V_X_2))) % 187.68/187.60 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_X_2),c_Inductive_Ocomplete__lattice__class_Ogfp(T_a,V_f_2))) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_gfp__unfold,axiom, % 187.68/187.60 ! [V_f_2,T_a] : % 187.68/187.60 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 187.68/187.60 => ( c_Orderings_Oorder__class_Omono(T_a,T_a,V_f_2) % 187.68/187.60 => c_Inductive_Ocomplete__lattice__class_Ogfp(T_a,V_f_2) = hAPP(V_f_2,c_Inductive_Ocomplete__lattice__class_Ogfp(T_a,V_f_2)) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_def__gfp__unfold,axiom, % 187.68/187.60 ! [V_f_2,V_A_2,T_a] : % 187.68/187.60 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 187.68/187.60 => ( V_A_2 = c_Inductive_Ocomplete__lattice__class_Ogfp(T_a,V_f_2) % 187.68/187.60 => ( c_Orderings_Oorder__class_Omono(T_a,T_a,V_f_2) % 187.68/187.60 => V_A_2 = hAPP(V_f_2,V_A_2) ) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_weak__coinduct,axiom, % 187.68/187.60 ! [V_f_2,V_X_2,V_a_2,T_a] : % 187.68/187.60 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_X_2)) % 187.68/187.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_X_2),hAPP(V_f_2,V_X_2))) % 187.68/187.60 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_a,tc_HOL_Obool),V_f_2))) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_gfp__lemma3,axiom, % 187.68/187.60 ! [V_f_2,T_a] : % 187.68/187.60 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 187.68/187.60 => ( c_Orderings_Oorder__class_Omono(T_a,T_a,V_f_2) % 187.68/187.60 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(V_f_2,c_Inductive_Ocomplete__lattice__class_Ogfp(T_a,V_f_2))),c_Inductive_Ocomplete__lattice__class_Ogfp(T_a,V_f_2))) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_gfp__lemma2,axiom, % 187.68/187.60 ! [V_f_2,T_a] : % 187.68/187.60 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 187.68/187.60 => ( c_Orderings_Oorder__class_Omono(T_a,T_a,V_f_2) % 187.68/187.60 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Inductive_Ocomplete__lattice__class_Ogfp(T_a,V_f_2)),hAPP(V_f_2,c_Inductive_Ocomplete__lattice__class_Ogfp(T_a,V_f_2)))) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_weak__coinduct__image,axiom, % 187.68/187.60 ! [V_f_2,V_g_2,T_b,V_X_2,V_a_2,T_a] : % 187.68/187.60 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_X_2)) % 187.68/187.60 => ( 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_g_2),V_X_2)),hAPP(V_f_2,hAPP(c_Set_Oimage(T_a,T_b,V_g_2),V_X_2)))) % 187.68/187.60 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_g_2,V_a_2)),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_b,tc_HOL_Obool),V_f_2))) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_gfp__fun__UnI2,axiom, % 187.68/187.60 ! [V_X_2,V_a_2,V_f_2,T_a] : % 187.68/187.60 ( c_Orderings_Oorder__class_Omono(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),V_f_2) % 187.68/187.60 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_a,tc_HOL_Obool),V_f_2))) % 187.68/187.60 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_X_2),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_a,tc_HOL_Obool),V_f_2))))) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_coinduct,axiom, % 187.68/187.60 ! [V_X_2,V_f_2,T_a] : % 187.68/187.60 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 187.68/187.60 => ( c_Orderings_Oorder__class_Omono(T_a,T_a,V_f_2) % 187.68/187.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_X_2),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_X_2),c_Inductive_Ocomplete__lattice__class_Ogfp(T_a,V_f_2))))) % 187.68/187.60 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_X_2),c_Inductive_Ocomplete__lattice__class_Ogfp(T_a,V_f_2))) ) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_coinduct__lemma,axiom, % 187.68/187.60 ! [V_f_2,V_X_2,T_a] : % 187.68/187.60 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 187.68/187.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_X_2),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_X_2),c_Inductive_Ocomplete__lattice__class_Ogfp(T_a,V_f_2))))) % 187.68/187.60 => ( c_Orderings_Oorder__class_Omono(T_a,T_a,V_f_2) % 187.68/187.60 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_X_2),c_Inductive_Ocomplete__lattice__class_Ogfp(T_a,V_f_2))),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_X_2),c_Inductive_Ocomplete__lattice__class_Ogfp(T_a,V_f_2))))) ) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_def__coinduct,axiom, % 187.68/187.60 ! [V_X_2,V_f_2,V_A_2,T_a] : % 187.68/187.60 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 187.68/187.60 => ( V_A_2 = c_Inductive_Ocomplete__lattice__class_Ogfp(T_a,V_f_2) % 187.68/187.60 => ( c_Orderings_Oorder__class_Omono(T_a,T_a,V_f_2) % 187.68/187.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_X_2),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_X_2),V_A_2)))) % 187.68/187.60 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_X_2),V_A_2)) ) ) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_coinduct3,axiom, % 187.68/187.60 ! [V_X_2,V_a_2,V_f_2,T_a] : % 187.68/187.60 ( c_Orderings_Oorder__class_Omono(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),V_f_2) % 187.68/187.60 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_X_2)) % 187.68/187.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_X_2),hAPP(V_f_2,c_Inductive_Ocomplete__lattice__class_Olfp(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_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)),tc_fun(T_a,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(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_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)),tc_fun(T_a,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool))),V_f_2)),V_X_2))),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_a,tc_HOL_Obool),V_f_2)))))) % 187.68/187.60 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_a,tc_HOL_Obool),V_f_2))) ) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_def__coinduct3,axiom, % 187.68/187.60 ! [V_X_2,V_a_2,V_f_2,T_a,V_A_2] : % 187.68/187.60 ( V_A_2 = c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_a,tc_HOL_Obool),V_f_2) % 187.68/187.60 => ( c_Orderings_Oorder__class_Omono(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),V_f_2) % 187.68/187.60 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_X_2)) % 187.68/187.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_X_2),hAPP(V_f_2,c_Inductive_Ocomplete__lattice__class_Olfp(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_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)),tc_fun(T_a,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(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_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)),tc_fun(T_a,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool))),V_f_2)),V_X_2))),V_A_2))))) % 187.68/187.60 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_def__Collect__coinduct,axiom, % 187.68/187.60 ! [V_X_2,V_a_2,V_P_2,T_a,V_A_2] : % 187.68/187.60 ( V_A_2 = c_Inductive_Ocomplete__lattice__class_Ogfp(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),tc_fun(T_a,tc_HOL_Obool)),c_Set_OCollect(T_a)),V_P_2)) % 187.68/187.60 => ( c_Orderings_Oorder__class_Omono(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(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),c_Set_OCollect(T_a)),V_P_2)) % 187.68/187.60 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_X_2)) % 187.68/187.60 => ( ! [B_z] : % 187.68/187.60 ( hBOOL(hAPP(hAPP(c_member(T_a),B_z),V_X_2)) % 187.68/187.60 => hBOOL(hAPP(hAPP(V_P_2,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_X_2),V_A_2)),B_z)) ) % 187.68/187.60 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_def__lfp__unfold,axiom, % 187.68/187.60 ! [V_f_2,V_h_2,T_a] : % 187.68/187.60 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 187.68/187.60 => ( V_h_2 = c_Inductive_Ocomplete__lattice__class_Olfp(T_a,V_f_2) % 187.68/187.60 => ( c_Orderings_Oorder__class_Omono(T_a,T_a,V_f_2) % 187.68/187.60 => V_h_2 = hAPP(V_f_2,V_h_2) ) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_lfp__unfold,axiom, % 187.68/187.60 ! [V_f_2,T_a] : % 187.68/187.60 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 187.68/187.60 => ( c_Orderings_Oorder__class_Omono(T_a,T_a,V_f_2) % 187.68/187.60 => c_Inductive_Ocomplete__lattice__class_Olfp(T_a,V_f_2) = hAPP(V_f_2,c_Inductive_Ocomplete__lattice__class_Olfp(T_a,V_f_2)) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_lfp__const,axiom, % 187.68/187.60 ! [V_t_2,T_a] : % 187.68/187.60 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 187.68/187.60 => c_Inductive_Ocomplete__lattice__class_Olfp(T_a,hAPP(c_COMBK(T_a,T_a),V_t_2)) = V_t_2 ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_lfp__lowerbound,axiom, % 187.68/187.60 ! [V_A_2,V_f_2,T_a] : % 187.68/187.60 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 187.68/187.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(V_f_2,V_A_2)),V_A_2)) % 187.68/187.60 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Inductive_Ocomplete__lattice__class_Olfp(T_a,V_f_2)),V_A_2)) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_lfp__lemma3,axiom, % 187.68/187.60 ! [V_f_2,T_a] : % 187.68/187.60 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 187.68/187.60 => ( c_Orderings_Oorder__class_Omono(T_a,T_a,V_f_2) % 187.68/187.60 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Inductive_Ocomplete__lattice__class_Olfp(T_a,V_f_2)),hAPP(V_f_2,c_Inductive_Ocomplete__lattice__class_Olfp(T_a,V_f_2)))) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_lfp__lemma2,axiom, % 187.68/187.60 ! [V_f_2,T_a] : % 187.68/187.60 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 187.68/187.60 => ( c_Orderings_Oorder__class_Omono(T_a,T_a,V_f_2) % 187.68/187.60 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(V_f_2,c_Inductive_Ocomplete__lattice__class_Olfp(T_a,V_f_2))),c_Inductive_Ocomplete__lattice__class_Olfp(T_a,V_f_2))) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_def__lfp__induct,axiom, % 187.68/187.60 ! [V_P_2,V_f_2,V_A_2,T_a] : % 187.68/187.60 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 187.68/187.60 => ( V_A_2 = c_Inductive_Ocomplete__lattice__class_Olfp(T_a,V_f_2) % 187.68/187.60 => ( c_Orderings_Oorder__class_Omono(T_a,T_a,V_f_2) % 187.68/187.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_A_2),V_P_2))),V_P_2)) % 187.68/187.60 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_A_2),V_P_2)) ) ) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_lfp__induct,axiom, % 187.68/187.60 ! [V_P_2,V_f_2,T_a] : % 187.68/187.60 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 187.68/187.60 => ( c_Orderings_Oorder__class_Omono(T_a,T_a,V_f_2) % 187.68/187.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Inductive_Ocomplete__lattice__class_Olfp(T_a,V_f_2)),V_P_2))),V_P_2)) % 187.68/187.60 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Inductive_Ocomplete__lattice__class_Olfp(T_a,V_f_2)),V_P_2)) ) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_coinduct3__lemma,axiom, % 187.68/187.60 ! [V_f_2,V_X_2,T_a] : % 187.68/187.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_X_2),hAPP(V_f_2,c_Inductive_Ocomplete__lattice__class_Olfp(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_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)),tc_fun(T_a,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(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_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)),tc_fun(T_a,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool))),V_f_2)),V_X_2))),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_a,tc_HOL_Obool),V_f_2)))))) % 187.68/187.60 => ( c_Orderings_Oorder__class_Omono(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),V_f_2) % 187.68/187.60 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),c_Inductive_Ocomplete__lattice__class_Olfp(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_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)),tc_fun(T_a,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(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_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)),tc_fun(T_a,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool))),V_f_2)),V_X_2))),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_a,tc_HOL_Obool),V_f_2)))),hAPP(V_f_2,c_Inductive_Ocomplete__lattice__class_Olfp(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_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)),tc_fun(T_a,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(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_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)),tc_fun(T_a,tc_HOL_Obool)),c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool))),V_f_2)),V_X_2))),c_Inductive_Ocomplete__lattice__class_Ogfp(tc_fun(T_a,tc_HOL_Obool),V_f_2)))))) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_def__lfp__induct__set,axiom, % 187.68/187.60 ! [V_P_2,V_a_2,V_f_2,T_a,V_A_2] : % 187.68/187.60 ( V_A_2 = c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(T_a,tc_HOL_Obool),V_f_2) % 187.68/187.60 => ( c_Orderings_Oorder__class_Omono(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),V_f_2) % 187.68/187.60 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 187.68/187.60 => ( ! [B_x] : % 187.68/187.60 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(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))))) % 187.68/187.60 => hBOOL(hAPP(V_P_2,B_x)) ) % 187.68/187.60 => hBOOL(hAPP(V_P_2,V_a_2)) ) ) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_lfp__induct__set,axiom, % 187.68/187.60 ! [V_P_2,V_f_2,V_a_2,T_a] : % 187.68/187.60 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(T_a,tc_HOL_Obool),V_f_2))) % 187.68/187.60 => ( c_Orderings_Oorder__class_Omono(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),V_f_2) % 187.68/187.60 => ( ! [B_x] : % 187.68/187.60 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(T_a,tc_HOL_Obool),V_f_2)),hAPP(c_Set_OCollect(T_a),V_P_2))))) % 187.68/187.60 => hBOOL(hAPP(V_P_2,B_x)) ) % 187.68/187.60 => hBOOL(hAPP(V_P_2,V_a_2)) ) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_lfp__induct2,axiom, % 187.68/187.60 ! [V_P_2,V_f_2,V_b_2,V_a_2,T_b,T_a] : % 187.68/187.60 ( 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)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),V_f_2))) % 187.68/187.60 => ( c_Orderings_Oorder__class_Omono(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),V_f_2) % 187.68/187.60 => ( ! [B_a,B_b] : % 187.68/187.60 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_a),B_b)),hAPP(V_f_2,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)),c_Inductive_Ocomplete__lattice__class_Olfp(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),V_f_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),V_P_2)))))) % 187.68/187.60 => hBOOL(hAPP(hAPP(V_P_2,B_a),B_b)) ) % 187.68/187.60 => hBOOL(hAPP(hAPP(V_P_2,V_a_2),V_b_2)) ) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_Max__eqI,axiom, % 187.68/187.60 ! [V_x_2,V_A_2,T_a] : % 187.68/187.60 ( class_Orderings_Olinorder(T_a) % 187.68/187.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.60 => ( ! [B_y] : % 187.68/187.60 ( hBOOL(hAPP(hAPP(c_member(T_a),B_y),V_A_2)) % 187.68/187.60 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_y),V_x_2)) ) % 187.68/187.60 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 187.68/187.60 => c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2) = V_x_2 ) ) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_Min__eqI,axiom, % 187.68/187.60 ! [V_x_2,V_A_2,T_a] : % 187.68/187.60 ( class_Orderings_Olinorder(T_a) % 187.68/187.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.60 => ( ! [B_y] : % 187.68/187.60 ( hBOOL(hAPP(hAPP(c_member(T_a),B_y),V_A_2)) % 187.68/187.60 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),B_y)) ) % 187.68/187.60 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 187.68/187.60 => c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2) = V_x_2 ) ) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_wf__no__infinite__down__chainE,axiom, % 187.68/187.60 ! [V_f_2,V_r_2,T_a] : % 187.68/187.60 ( c_Wellfounded_Owf(T_a,V_r_2) % 187.68/187.60 => ~ ! [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)) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_setsum__reindex__cong,axiom, % 187.68/187.60 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_b,T_a,T_c] : % 187.68/187.60 ( class_Groups_Ocomm__monoid__add(T_c) % 187.68/187.60 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 187.68/187.60 => ( V_B_2 = hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2) % 187.68/187.60 => ( ! [B_a] : % 187.68/187.60 ( hBOOL(hAPP(hAPP(c_member(T_a),B_a),V_A_2)) % 187.68/187.60 => hAPP(V_g_2,B_a) = hAPP(V_h_2,hAPP(V_f_2,B_a)) ) % 187.68/187.60 => 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) ) ) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_scomp__unfold,axiom, % 187.68/187.60 ! [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))) ). % 187.68/187.60 % 187.68/187.60 fof(fact_Pair__scomp,axiom, % 187.68/187.60 ! [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) ). % 187.68/187.60 % 187.68/187.60 fof(fact_scomp__scomp,axiom, % 187.68/187.60 ! [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)) ). % 187.68/187.60 % 187.68/187.60 fof(fact_scomp__Pair,axiom, % 187.68/187.60 ! [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 ). % 187.68/187.60 % 187.68/187.60 fof(fact_scomp__apply,axiom, % 187.68/187.60 ! [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)) ). % 187.68/187.60 % 187.68/187.60 fof(fact_scomp__def,axiom, % 187.68/187.60 ! [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)) ). % 187.68/187.60 % 187.68/187.60 fof(fact_iterate_Osimps,axiom, % 187.68/187.60 ! [V_x_2,V_f_2,T_a,T_b,V_k_2] : % 187.68/187.60 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 187.68/187.60 => 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) ) % 187.68/187.60 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 187.68/187.60 => 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)) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_setsum__ivl__cong,axiom, % 187.68/187.60 ! [V_g_2,V_f_2,V_d_2,V_b_2,V_c_2,V_a_2,T_a,T_b] : % 187.68/187.60 ( ( class_Groups_Ocomm__monoid__add(T_b) % 187.68/187.60 & class_Orderings_Oord(T_a) ) % 187.68/187.60 => ( V_a_2 = V_c_2 % 187.68/187.60 => ( V_b_2 = V_d_2 % 187.68/187.60 => ( ! [B_x] : % 187.68/187.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c_2),B_x)) % 187.68/187.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),B_x),V_d_2)) % 187.68/187.60 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) ) % 187.68/187.60 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2),V_b_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_c_2),V_d_2)) ) ) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_log_Osimps,axiom, % 187.68/187.60 ! [V_i,V_b] : % 187.68/187.60 ( ( ( 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))) % 187.68/187.60 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),V_b)) ) % 187.68/187.60 => c_Random_Olog(V_b,V_i) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) ) % 187.68/187.60 & ( ~ ( 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))) % 187.68/187.60 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),V_b)) ) % 187.68/187.60 => 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))) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_minus__shift__def,axiom, % 187.68/187.60 ! [V_r,V_l,V_k] : % 187.68/187.60 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l)) % 187.68/187.60 => 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) ) % 187.68/187.60 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l)) % 187.68/187.60 => 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) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_inc__shift__def,axiom, % 187.68/187.60 ! [V_k,V_v] : % 187.68/187.60 ( ( V_v = V_k % 187.68/187.60 => c_Random_Oinc__shift(V_v,V_k) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) ) % 187.68/187.60 & ( V_v != V_k % 187.68/187.60 => 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)) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_range,axiom, % 187.68/187.60 ! [V_s,V_k] : % 187.68/187.60 ( 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)) % 187.68/187.60 => 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)) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_less__eq,axiom, % 187.68/187.60 ! [V_n_2,V_m_2] : % 187.68/187.60 ( 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))) % 187.68/187.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_nat__intermed__int__val,axiom, % 187.68/187.60 ! [V_k_2,V_f_2,V_n_2,V_m_2] : % 187.68/187.60 ( ! [B_i] : % 187.68/187.60 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),B_i)) % 187.68/187.60 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2)) ) % 187.68/187.60 => 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))) ) % 187.68/187.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 187.68/187.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(V_f_2,V_m_2)),V_k_2)) % 187.68/187.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2))) % 187.68/187.60 => ? [B_i] : % 187.68/187.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),B_i)) % 187.68/187.60 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2)) % 187.68/187.60 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_wf__trancl,axiom, % 187.68/187.60 ! [V_r_2,T_a] : % 187.68/187.60 ( c_Wellfounded_Owf(T_a,V_r_2) % 187.68/187.60 => c_Wellfounded_Owf(T_a,c_Transitive__Closure_Otrancl(T_a,V_r_2)) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_less__than__def,axiom, % 187.68/187.60 c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat) ). % 187.68/187.60 % 187.68/187.60 fof(fact_acyclic__def,axiom, % 187.68/187.60 ! [V_r_2,T_a] : % 187.68/187.60 ( c_Wellfounded_Oacyclic(T_a,V_r_2) % 187.68/187.60 <=> ! [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))) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_trancl_Or__into__trancl,axiom, % 187.68/187.60 ! [V_r_2,V_b_2,V_a_2,T_a] : % 187.68/187.60 ( 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)) % 187.68/187.60 => 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))) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_trancl__subset__Field2,axiom, % 187.68/187.60 ! [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))))) ). % 187.68/187.60 % 187.68/187.60 fof(fact_r__into__trancl_H,axiom, % 187.68/187.60 ! [V_r_2,V_p_2,T_a] : % 187.68/187.60 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),V_r_2)) % 187.68/187.60 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_trancl__empty,axiom, % 187.68/187.60 ! [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)) ). % 187.68/187.60 % 187.68/187.60 fof(fact_trancl__domain,axiom, % 187.68/187.60 ! [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) ). % 187.68/187.60 % 187.68/187.60 fof(fact_trancl__range,axiom, % 187.68/187.60 ! [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) ). % 187.68/187.60 % 187.68/187.60 fof(fact_finite__trancl,axiom, % 187.68/187.60 ! [V_r_2,T_a] : % 187.68/187.60 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) % 187.68/187.60 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2)) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_r__r__into__trancl,axiom, % 187.68/187.60 ! [V_c_2,V_R_2,V_b_2,V_a_2,T_a] : % 187.68/187.60 ( 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)) % 187.68/187.60 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_b_2),V_c_2)),V_R_2)) % 187.68/187.60 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_a,V_R_2))) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_trancl__into__trancl2,axiom, % 187.68/187.60 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_a] : % 187.68/187.60 ( 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)) % 187.68/187.60 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_b_2),V_c_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) % 187.68/187.60 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_Transitive__Closure_Otrancl__into__trancl,axiom, % 187.68/187.60 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_a] : % 187.68/187.60 ( 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))) % 187.68/187.60 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_b_2),V_c_2)),V_r_2)) % 187.68/187.60 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_trancl__trans,axiom, % 187.68/187.60 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_a] : % 187.68/187.60 ( 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))) % 187.68/187.60 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_b_2),V_c_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) % 187.68/187.60 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_trancl__mono,axiom, % 187.68/187.60 ! [V_s_2,V_r_2,V_p_2,T_a] : % 187.68/187.60 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Otrancl(T_a,V_r_2))) % 187.68/187.60 => ( 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)) % 187.68/187.60 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Otrancl(T_a,V_s_2))) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_trancl__unfold,axiom, % 187.68/187.60 ! [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)) ). % 187.68/187.60 % 187.68/187.60 fof(fact_trancl__subset__Sigma,axiom, % 187.68/187.60 ! [V_A_2,V_r_2,T_a] : % 187.68/187.60 ( 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)))) % 187.68/187.60 => 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)))) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_trancl__Int__subset,axiom, % 187.68/187.60 ! [V_s_2,V_r_2,T_a] : % 187.68/187.60 ( 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)) % 187.68/187.60 => ( 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)) % 187.68/187.60 => 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)) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_trancl__insert,axiom, % 187.68/187.60 ! [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)))))) ). % 187.68/187.60 % 187.68/187.60 fof(fact_reflcl__set__eq,axiom, % 187.68/187.60 ! [V_y_2,V_x_2,V_r_2,T_a] : % 187.68/187.60 ( 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)) % 187.68/187.60 <=> 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)))) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_r__into__rtrancl,axiom, % 187.68/187.60 ! [V_r_2,V_p_2,T_a] : % 187.68/187.60 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),V_r_2)) % 187.68/187.60 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_rtrancl_Ortrancl__refl,axiom, % 187.68/187.60 ! [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))) ). % 187.68/187.60 % 187.68/187.60 fof(fact_IdI,axiom, % 187.68/187.60 ! [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))) ). % 187.68/187.60 % 187.68/187.60 fof(fact_trancl__into__rtrancl,axiom, % 187.68/187.60 ! [V_r_2,V_b_2,V_a_2,T_a] : % 187.68/187.60 ( 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))) % 187.68/187.60 => 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))) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_rtrancl__trancl__absorb,axiom, % 187.68/187.60 ! [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) ). % 187.68/187.60 % 187.68/187.60 fof(fact_trancl__rtrancl__absorb,axiom, % 187.68/187.60 ! [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) ). % 187.68/187.60 % 187.68/187.60 fof(fact_trancl__reflcl,axiom, % 187.68/187.60 ! [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) ). % 187.68/187.60 % 187.68/187.60 fof(fact_reflcl__trancl,axiom, % 187.68/187.60 ! [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) ). % 187.68/187.60 % 187.68/187.60 fof(fact_trancl__unfold__left,axiom, % 187.68/187.60 ! [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)) ). % 187.68/187.60 % 187.68/187.60 fof(fact_trancl__unfold__right,axiom, % 187.68/187.60 ! [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) ). % 187.68/187.60 % 187.68/187.60 fof(fact_rtrancl__Un__subset,axiom, % 187.68/187.60 ! [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)))) ). % 187.68/187.60 % 187.68/187.60 fof(fact_rtrancl__mono,axiom, % 187.68/187.60 ! [V_s_2,V_r_2,T_a] : % 187.68/187.60 ( 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)) % 187.68/187.60 => 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))) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_rtrancl__subset,axiom, % 187.68/187.60 ! [V_S_2,V_R_2,T_a] : % 187.68/187.60 ( 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)) % 187.68/187.60 => ( 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))) % 187.68/187.60 => c_Transitive__Closure_Ortrancl(T_a,V_S_2) = c_Transitive__Closure_Ortrancl(T_a,V_R_2) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_rtrancl__subset__rtrancl,axiom, % 187.68/187.60 ! [V_s_2,V_r_2,T_a] : % 187.68/187.60 ( 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))) % 187.68/187.60 => 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))) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_Image__closed__trancl,axiom, % 187.68/187.60 ! [V_X_2,V_r_2,T_a] : % 187.68/187.60 ( 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)) % 187.68/187.60 => hAPP(c_Relation_OImage(T_a,T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2)),V_X_2) = V_X_2 ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_rtrancl__Int__subset,axiom, % 187.68/187.60 ! [V_r_2,V_s_2,T_a] : % 187.68/187.60 ( 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)) % 187.68/187.60 => ( 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)) % 187.68/187.60 => 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)) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_rtrancl__empty,axiom, % 187.68/187.60 ! [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) ). % 187.68/187.60 % 187.68/187.60 fof(fact_rtrancl__idemp__self__comp,axiom, % 187.68/187.60 ! [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) ). % 187.68/187.60 % 187.68/187.60 fof(fact_r__comp__rtrancl__eq,axiom, % 187.68/187.60 ! [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) ). % 187.68/187.60 % 187.68/187.60 fof(fact_rtrancl__unfold,axiom, % 187.68/187.60 ! [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)) ). % 187.68/187.60 % 187.68/187.60 fof(fact_in__rtrancl__UnI,axiom, % 187.68/187.60 ! [V_S_2,V_R_2,V_x_2,T_a] : % 187.68/187.60 ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_x_2),c_Transitive__Closure_Ortrancl(T_a,V_R_2))) % 187.68/187.60 | hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_x_2),c_Transitive__Closure_Ortrancl(T_a,V_S_2))) ) % 187.68/187.60 => 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)))) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_rtrancl__reflcl__absorb,axiom, % 187.68/187.60 ! [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) ). % 187.68/187.60 % 187.68/187.60 fof(fact_rtrancl__Un__rtrancl,axiom, % 187.68/187.60 ! [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)) ). % 187.68/187.60 % 187.68/187.60 fof(fact_rtrancl__reflcl,axiom, % 187.68/187.60 ! [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) ). % 187.68/187.60 % 187.68/187.60 fof(fact_refl__rtrancl,axiom, % 187.68/187.60 ! [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)) ). % 187.68/187.60 % 187.68/187.60 fof(fact_rtrancl__r__diff__Id,axiom, % 187.68/187.60 ! [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) ). % 187.68/187.60 % 187.68/187.60 fof(fact_rtrancl__idemp,axiom, % 187.68/187.60 ! [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) ). % 187.68/187.60 % 187.68/187.60 fof(fact_converse__rtrancl__into__rtrancl,axiom, % 187.68/187.60 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_a] : % 187.68/187.60 ( 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)) % 187.68/187.60 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_b_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) % 187.68/187.60 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_rtrancl_Ortrancl__into__rtrancl,axiom, % 187.68/187.60 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_a] : % 187.68/187.60 ( 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))) % 187.68/187.60 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_b_2),V_c_2)),V_r_2)) % 187.68/187.60 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_rtrancl__trans,axiom, % 187.68/187.60 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_a] : % 187.68/187.60 ( 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))) % 187.68/187.60 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_b_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) % 187.68/187.60 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_Range__rtrancl,axiom, % 187.68/187.60 ! [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)) ). % 187.68/187.60 % 187.68/187.60 fof(fact_Domain__rtrancl,axiom, % 187.68/187.60 ! [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)) ). % 187.68/187.60 % 187.68/187.60 fof(fact_Image__Id,axiom, % 187.68/187.60 ! [V_A_2,T_a] : hAPP(c_Relation_OImage(T_a,T_a,c_Relation_OId(T_a)),V_A_2) = V_A_2 ). % 187.68/187.60 % 187.68/187.60 fof(fact_R__O__Id,axiom, % 187.68/187.60 ! [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 ). % 187.68/187.60 % 187.68/187.60 fof(fact_Id__O__R,axiom, % 187.68/187.60 ! [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 ). % 187.68/187.60 % 187.68/187.60 fof(fact_pair__in__Id__conv,axiom, % 187.68/187.60 ! [V_b_2,V_a_2,T_a] : % 187.68/187.60 ( 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))) % 187.68/187.60 <=> V_a_2 = V_b_2 ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_rtrancl__trancl__trancl,axiom, % 187.68/187.60 ! [V_z_2,V_r_2,V_y_2,V_x_2,T_a] : % 187.68/187.60 ( 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))) % 187.68/187.60 => ( 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))) % 187.68/187.60 => 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))) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_trancl__rtrancl__trancl,axiom, % 187.68/187.60 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_a] : % 187.68/187.60 ( 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))) % 187.68/187.60 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_b_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) % 187.68/187.60 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_rtrancl__into__trancl1,axiom, % 187.68/187.60 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_a] : % 187.68/187.60 ( 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))) % 187.68/187.60 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_b_2),V_c_2)),V_r_2)) % 187.68/187.60 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_rtranclD,axiom, % 187.68/187.60 ! [V_R_2,V_b_2,V_a_2,T_a] : % 187.68/187.60 ( 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))) % 187.68/187.60 => ( V_a_2 = V_b_2 % 187.68/187.60 | ( V_a_2 != V_b_2 % 187.68/187.60 & 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))) ) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_rtrancl__into__trancl2,axiom, % 187.68/187.60 ! [V_c_2,V_r_2,V_b_2,V_a_2,T_a] : % 187.68/187.60 ( 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)) % 187.68/187.60 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_b_2),V_c_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) % 187.68/187.60 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_c_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_rtrancl__eq__or__trancl,axiom, % 187.68/187.60 ! [V_R_2,V_y_2,V_x_2,T_a] : % 187.68/187.60 ( 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))) % 187.68/187.60 <=> ( V_x_2 = V_y_2 % 187.68/187.60 | ( V_x_2 != V_y_2 % 187.68/187.60 & 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))) ) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_Domain__Id,axiom, % 187.68/187.60 ! [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)) ). % 187.68/187.60 % 187.68/187.60 fof(fact_Range__Id,axiom, % 187.68/187.60 ! [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)) ). % 187.68/187.60 % 187.68/187.60 fof(fact_refl__Id,axiom, % 187.68/187.60 ! [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)) ). % 187.68/187.60 % 187.68/187.60 fof(fact_pair__leq__def,axiom, % 187.68/187.60 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))) ). % 187.68/187.60 % 187.68/187.60 fof(fact_Not__Domain__rtrancl,axiom, % 187.68/187.60 ! [V_y_2,V_R_2,V_x_2,T_a] : % 187.68/187.60 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_Relation_ODomain(T_a,T_a),V_R_2))) % 187.68/187.60 => ( 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))) % 187.68/187.60 <=> V_x_2 = V_y_2 ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_acc__downwards,axiom, % 187.68/187.60 ! [V_b_2,V_r_2,V_a_2,T_a] : % 187.68/187.60 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Wellfounded_Oacc(T_a,V_r_2))) % 187.68/187.60 => ( 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))) % 187.68/187.60 => hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Wellfounded_Oacc(T_a,V_r_2))) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_acc__downwards__aux,axiom, % 187.68/187.60 ! [V_r_2,V_a_2,V_b_2,T_a] : % 187.68/187.60 ( 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))) % 187.68/187.60 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Wellfounded_Oacc(T_a,V_r_2))) % 187.68/187.60 => hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Wellfounded_Oacc(T_a,V_r_2))) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_wf__insert,axiom, % 187.68/187.60 ! [V_r_2,V_x_2,V_y_2,T_a] : % 187.68/187.60 ( 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)) % 187.68/187.60 <=> ( c_Wellfounded_Owf(T_a,V_r_2) % 187.68/187.60 & ~ 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))) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_acyclic__insert,axiom, % 187.68/187.60 ! [V_r_2,V_x_2,V_y_2,T_a] : % 187.68/187.60 ( 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)) % 187.68/187.60 <=> ( c_Wellfounded_Oacyclic(T_a,V_r_2) % 187.68/187.60 & ~ 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))) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_refl__reflcl,axiom, % 187.68/187.60 ! [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))) ). % 187.68/187.60 % 187.68/187.60 fof(fact_Id__def,axiom, % 187.68/187.60 ! [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))))) ). % 187.68/187.60 % 187.68/187.60 fof(fact_irrefl__diff__Id,axiom, % 187.68/187.60 ! [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))) ). % 187.68/187.60 % 187.68/187.60 fof(fact_pred__nat__trancl__eq__le,axiom, % 187.68/187.60 ! [V_n_2,V_m_2] : % 187.68/187.60 ( 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))) % 187.68/187.60 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_trancl__subset__Sigma__aux,axiom, % 187.68/187.60 ! [V_A_2,V_r_2,V_b_2,V_a_2,T_a] : % 187.68/187.60 ( 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))) % 187.68/187.60 => ( 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)))) % 187.68/187.60 => ( V_a_2 = V_b_2 % 187.68/187.60 | hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_irrefl__tranclI,axiom, % 187.68/187.60 ! [V_x_2,V_r_2,T_a] : % 187.68/187.60 ( 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)) % 187.68/187.60 => ~ 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))) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_sequence__trans,axiom, % 187.68/187.60 ! [V_k_2,V_i_2,V_r_2,V_f_2,T_a] : % 187.68/187.60 ( ! [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))) % 187.68/187.60 => 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))) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_rtrancl__converse,axiom, % 187.68/187.60 ! [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)) ). % 187.68/187.60 % 187.68/187.60 fof(fact_converse__Id,axiom, % 187.68/187.60 ! [T_a] : hAPP(c_Relation_Oconverse(T_a,T_a),c_Relation_OId(T_a)) = c_Relation_OId(T_a) ). % 187.68/187.60 % 187.68/187.60 fof(fact_converse__UNION,axiom, % 187.68/187.60 ! [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)) ). % 187.68/187.60 % 187.68/187.60 fof(fact_converse__rel__comp,axiom, % 187.68/187.60 ! [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)) ). % 187.68/187.60 % 187.68/187.60 fof(fact_converse__Un,axiom, % 187.68/187.60 ! [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)) ). % 187.68/187.60 % 187.68/187.60 fof(fact_converse__iff,axiom, % 187.68/187.60 ! [V_r_2,V_b_2,V_a_2,T_b,T_a] : % 187.68/187.60 ( 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))) % 187.68/187.60 <=> 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)) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_converseI,axiom, % 187.68/187.60 ! [V_r_2,V_b_2,V_a_2,T_b,T_a] : % 187.68/187.60 ( 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)) % 187.68/187.60 => 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))) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_converseD,axiom, % 187.68/187.60 ! [V_r_2,V_b_2,V_a_2,T_b,T_a] : % 187.68/187.60 ( 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))) % 187.68/187.60 => 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)) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_refl__on__converse,axiom, % 187.68/187.60 ! [V_r_2,V_A_2,T_a] : % 187.68/187.60 ( c_Relation_Orefl__on(T_a,V_A_2,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)) % 187.68/187.60 <=> c_Relation_Orefl__on(T_a,V_A_2,V_r_2) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_converse__Int,axiom, % 187.68/187.60 ! [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)) ). % 187.68/187.60 % 187.68/187.60 fof(fact_converse__inv__image,axiom, % 187.68/187.60 ! [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) ). % 187.68/187.60 % 187.68/187.60 fof(fact_converse__converse,axiom, % 187.68/187.60 ! [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 ). % 187.68/187.60 % 187.68/187.60 fof(fact_Field__converse,axiom, % 187.68/187.60 ! [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) ). % 187.68/187.60 % 187.68/187.60 fof(fact_converse__Id__on,axiom, % 187.68/187.60 ! [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) ). % 187.68/187.60 % 187.68/187.60 fof(fact_finite__converse,axiom, % 187.68/187.60 ! [V_r_2,T_b,T_a] : % 187.68/187.60 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_b)),hAPP(c_Relation_Oconverse(T_b,T_a),V_r_2))) % 187.68/187.60 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_a)),V_r_2)) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_acyclic__converse,axiom, % 187.68/187.60 ! [V_r_2,T_a] : % 187.68/187.60 ( c_Wellfounded_Oacyclic(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)) % 187.68/187.60 <=> c_Wellfounded_Oacyclic(T_a,V_r_2) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_trancl__converse,axiom, % 187.68/187.60 ! [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)) ). % 187.68/187.60 % 187.68/187.60 fof(fact_wf__converse__trancl,axiom, % 187.68/187.60 ! [V_r_2,T_a] : % 187.68/187.60 ( c_Wellfounded_Owf(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)) % 187.68/187.60 => c_Wellfounded_Owf(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_equiv__comp__eq,axiom, % 187.68/187.60 ! [V_r_2,V_A_2,T_a] : % 187.68/187.60 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 187.68/187.60 => 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 ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_Range__def,axiom, % 187.68/187.60 ! [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)) ). % 187.68/187.60 % 187.68/187.60 fof(fact_Domain__converse,axiom, % 187.68/187.60 ! [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) ). % 187.68/187.60 % 187.68/187.60 fof(fact_Range__converse,axiom, % 187.68/187.60 ! [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) ). % 187.68/187.60 % 187.68/187.60 fof(fact_rtrancl__converseI,axiom, % 187.68/187.60 ! [V_r_2,V_x_2,V_y_2,T_a] : % 187.68/187.60 ( 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))) % 187.68/187.60 => 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)))) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_rtrancl__converseD,axiom, % 187.68/187.60 ! [V_r_2,V_y_2,V_x_2,T_a] : % 187.68/187.60 ( 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)))) % 187.68/187.60 => 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))) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_trancl__converseI,axiom, % 187.68/187.60 ! [V_r_2,V_y_2,V_x_2,T_a] : % 187.68/187.60 ( 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)))) % 187.68/187.60 => 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)))) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_trancl__converseD,axiom, % 187.68/187.60 ! [V_r_2,V_y_2,V_x_2,T_a] : % 187.68/187.60 ( 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)))) % 187.68/187.60 => 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)))) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_Image__subset__eq,axiom, % 187.68/187.60 ! [V_B_2,V_A_2,V_r_2,T_b,T_a] : % 187.68/187.60 ( 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)) % 187.68/187.60 <=> 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))))) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_refl__on__comp__subset,axiom, % 187.68/187.60 ! [V_r_2,V_A_2,T_a] : % 187.68/187.60 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2) % 187.68/187.60 => 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))) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_comp__equivI,axiom, % 187.68/187.60 ! [V_A_2,V_r_2,T_a] : % 187.68/187.60 ( 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 % 187.68/187.60 => ( hAPP(c_Relation_ODomain(T_a,T_a),V_r_2) = V_A_2 % 187.68/187.60 => c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_finite__acyclic__wf__converse,axiom, % 187.68/187.60 ! [V_r_2,T_a] : % 187.68/187.60 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2)) % 187.68/187.60 => ( c_Wellfounded_Oacyclic(T_a,V_r_2) % 187.68/187.60 => c_Wellfounded_Owf(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_converse__def,axiom, % 187.68/187.60 ! [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))) ). % 187.68/187.60 % 187.68/187.60 fof(fact_total__on__diff__Id,axiom, % 187.68/187.60 ! [V_r_2,V_A_2,T_a] : % 187.68/187.60 ( 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))) % 187.68/187.60 <=> c_Relation_Ototal__on(T_a,V_A_2,V_r_2) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_rtrancl__imp__UN__rel__pow,axiom, % 187.68/187.60 ! [V_R_2,V_p_2,T_a] : % 187.68/187.60 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Ortrancl(T_a,V_R_2))) % 187.68/187.60 => 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)))) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_rel__pow__commute,axiom, % 187.68/187.60 ! [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) ). % 187.68/187.60 % 187.68/187.60 fof(fact_rel__pow__1,axiom, % 187.68/187.60 ! [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 ). % 187.68/187.60 % 187.68/187.60 fof(fact_funpow__mult,axiom, % 187.68/187.60 ! [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) ). % 187.68/187.60 % 187.68/187.60 fof(fact_funpow__swap1,axiom, % 187.68/187.60 ! [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)) ). % 187.68/187.60 % 187.68/187.60 fof(fact_comp__funpow,axiom, % 187.68/187.60 ! [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)) ). % 187.68/187.60 % 187.68/187.60 fof(fact_wf__exp,axiom, % 187.68/187.60 ! [V_R_2,V_n_2,T_a] : % 187.68/187.60 ( 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)) % 187.68/187.60 => c_Wellfounded_Owf(T_a,V_R_2) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_rel__pow__imp__rtrancl,axiom, % 187.68/187.60 ! [V_R_2,V_n_2,V_p_2,T_a] : % 187.68/187.60 ( 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))) % 187.68/187.60 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Ortrancl(T_a,V_R_2))) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_rtrancl__power,axiom, % 187.68/187.60 ! [V_R_2,V_p_2,T_a] : % 187.68/187.60 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Ortrancl(T_a,V_R_2))) % 187.68/187.60 <=> ? [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))) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_relpow_Osimps_I2_J,axiom, % 187.68/187.60 ! [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) ). % 187.68/187.60 % 187.68/187.60 fof(fact_rel__pow__add,axiom, % 187.68/187.60 ! [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)) ). % 187.68/187.60 % 187.68/187.60 fof(fact_relpow_Osimps_I1_J,axiom, % 187.68/187.60 ! [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) ). % 187.68/187.60 % 187.68/187.60 fof(fact_total__on__empty,axiom, % 187.68/187.60 ! [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) ). % 187.68/187.60 % 187.68/187.60 fof(fact_total__on__converse,axiom, % 187.68/187.60 ! [V_r_2,V_A_2,T_a] : % 187.68/187.60 ( c_Relation_Ototal__on(T_a,V_A_2,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)) % 187.68/187.60 <=> c_Relation_Ototal__on(T_a,V_A_2,V_r_2) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_rel__pow__0__I,axiom, % 187.68/187.60 ! [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))) ). % 187.68/187.60 % 187.68/187.60 fof(fact_rel__pow__0__E,axiom, % 187.68/187.60 ! [V_R_2,V_y_2,V_x_2,T_a] : % 187.68/187.60 ( 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))) % 187.68/187.60 => V_x_2 = V_y_2 ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_rel__pow__Suc__I,axiom, % 187.68/187.60 ! [V_z_2,V_R_2,V_n_2,V_y_2,V_x_2,T_a] : % 187.68/187.60 ( 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))) % 187.68/187.60 => ( 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)) % 187.68/187.60 => 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))) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_rel__pow__Suc__I2,axiom, % 187.68/187.60 ! [V_n_2,V_z_2,V_R_2,V_y_2,V_x_2,T_a] : % 187.68/187.60 ( 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)) % 187.68/187.60 => ( 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))) % 187.68/187.60 => 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))) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_funpow_Osimps_I2_J,axiom, % 187.68/187.60 ! [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)) ). % 187.68/187.60 % 187.68/187.60 fof(fact_funpow__add,axiom, % 187.68/187.60 ! [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)) ). % 187.68/187.60 % 187.68/187.60 fof(fact_funpow_Osimps_I1_J,axiom, % 187.68/187.60 ! [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) ). % 187.68/187.60 % 187.68/187.60 fof(fact_trancl__power,axiom, % 187.68/187.60 ! [V_R_2,V_p_2,T_a] : % 187.68/187.60 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Otrancl(T_a,V_R_2))) % 187.68/187.60 <=> ? [B_n] : % 187.68/187.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n)) % 187.68/187.60 & 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))) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_total__on__def,axiom, % 187.68/187.60 ! [V_r_2,V_A_2,T_a] : % 187.68/187.60 ( c_Relation_Ototal__on(T_a,V_A_2,V_r_2) % 187.68/187.60 <=> ! [B_x] : % 187.68/187.60 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 187.68/187.60 => ! [B_xa] : % 187.68/187.60 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_A_2)) % 187.68/187.60 => ( B_x != B_xa % 187.68/187.60 => ( 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)) % 187.68/187.60 | 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)) ) ) ) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_rtrancl__is__UN__rel__pow,axiom, % 187.68/187.60 ! [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)) ). % 187.68/187.60 % 187.68/187.60 fof(fact_funpow__code__def,axiom, % 187.68/187.60 ! [T_a] : c_Nat_Ofunpow(T_a) = c_Nat_Ocompow(T_a,T_a) ). % 187.68/187.60 % 187.68/187.60 fof(fact_rel__pow__E2,axiom, % 187.68/187.60 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_a] : % 187.68/187.60 ( 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))) % 187.68/187.60 => ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 187.68/187.60 => V_x_2 != V_z_2 ) % 187.68/187.60 => ~ ! [B_y,B_m] : % 187.68/187.60 ( V_n_2 = hAPP(c_Nat_OSuc,B_m) % 187.68/187.60 => ( 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)) % 187.68/187.60 => ~ 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))) ) ) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_rel__pow__E,axiom, % 187.68/187.60 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_a] : % 187.68/187.60 ( 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))) % 187.68/187.60 => ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 187.68/187.60 => V_x_2 != V_z_2 ) % 187.68/187.60 => ~ ! [B_y,B_m] : % 187.68/187.60 ( V_n_2 = hAPP(c_Nat_OSuc,B_m) % 187.68/187.60 => ( 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))) % 187.68/187.60 => ~ 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)) ) ) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_acyclicI,axiom, % 187.68/187.60 ! [V_r_2,T_a] : % 187.68/187.60 ( ! [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))) % 187.68/187.60 => c_Wellfounded_Oacyclic(T_a,V_r_2) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_Image__Int__eq,axiom, % 187.68/187.60 ! [V_B_2,V_A_2,V_R_2,T_b,T_a] : % 187.68/187.60 ( c_Relation_Osingle__valued(T_a,T_b,hAPP(c_Relation_Oconverse(T_b,T_a),V_R_2)) % 187.68/187.60 => 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)) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_rtrancl__Un__separatorE,axiom, % 187.68/187.60 ! [V_Q_2,V_P_2,V_b_2,V_a_2,T_a] : % 187.68/187.60 ( 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)))) % 187.68/187.60 => ( ! [B_x] : % 187.68/187.60 ( 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))) % 187.68/187.60 => ! [B_y] : % 187.68/187.60 ( 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)) % 187.68/187.60 => B_x = B_y ) ) % 187.68/187.60 => 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))) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_single__valued__subset,axiom, % 187.68/187.60 ! [V_s_2,V_r_2,T_b,T_a] : % 187.68/187.60 ( 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)) % 187.68/187.60 => ( c_Relation_Osingle__valued(T_a,T_b,V_s_2) % 187.68/187.60 => c_Relation_Osingle__valued(T_a,T_b,V_r_2) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_single__valued__rel__comp,axiom, % 187.68/187.60 ! [V_s_2,T_c,V_r_2,T_b,T_a] : % 187.68/187.60 ( c_Relation_Osingle__valued(T_a,T_b,V_r_2) % 187.68/187.60 => ( c_Relation_Osingle__valued(T_b,T_c,V_s_2) % 187.68/187.60 => 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)) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_single__valued__Id,axiom, % 187.68/187.60 ! [T_a] : c_Relation_Osingle__valued(T_a,T_a,c_Relation_OId(T_a)) ). % 187.68/187.60 % 187.68/187.60 fof(fact_single__valued__Id__on,axiom, % 187.68/187.60 ! [V_A_2,T_a] : c_Relation_Osingle__valued(T_a,T_a,c_Relation_OId__on(T_a,V_A_2)) ). % 187.68/187.60 % 187.68/187.60 fof(fact_single__valued__rel__pow,axiom, % 187.68/187.60 ! [V_n_2,V_R_2,T_a] : % 187.68/187.60 ( c_Relation_Osingle__valued(T_a,T_a,V_R_2) % 187.68/187.60 => 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)) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_single__valuedD,axiom, % 187.68/187.60 ! [V_z_2,V_y_2,V_x_2,V_r_2,T_b,T_a] : % 187.68/187.60 ( c_Relation_Osingle__valued(T_a,T_b,V_r_2) % 187.68/187.60 => ( 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)) % 187.68/187.60 => ( 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)) % 187.68/187.60 => V_y_2 = V_z_2 ) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_single__valued__def,axiom, % 187.68/187.60 ! [V_r_2,T_b,T_a] : % 187.68/187.60 ( c_Relation_Osingle__valued(T_a,T_b,V_r_2) % 187.68/187.60 <=> ! [B_x,B_y] : % 187.68/187.60 ( 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)) % 187.68/187.60 => ! [B_z] : % 187.68/187.60 ( 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)) % 187.68/187.60 => B_y = B_z ) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_single__valued__confluent,axiom, % 187.68/187.60 ! [V_z_2,V_y_2,V_x_2,V_r_2,T_a] : % 187.68/187.60 ( c_Relation_Osingle__valued(T_a,T_a,V_r_2) % 187.68/187.60 => ( 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))) % 187.68/187.60 => ( 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))) % 187.68/187.60 => ( 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))) % 187.68/187.60 | 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))) ) ) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_rtrancl__Un__separator__converseE,axiom, % 187.68/187.60 ! [V_Q_2,V_P_2,V_b_2,V_a_2,T_a] : % 187.68/187.60 ( 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)))) % 187.68/187.60 => ( ! [B_x] : % 187.68/187.60 ( 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))) % 187.68/187.60 => ! [B_y] : % 187.68/187.60 ( 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)) % 187.68/187.60 => B_y = B_x ) ) % 187.68/187.60 => 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))) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_rel__pow__Suc__D2,axiom, % 187.68/187.60 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_a] : % 187.68/187.60 ( 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))) % 187.68/187.60 => ? [B_y] : % 187.68/187.60 ( 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)) % 187.68/187.60 & 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))) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_rel__pow__Suc__E,axiom, % 187.68/187.60 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_a] : % 187.68/187.60 ( 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))) % 187.68/187.60 => ~ ! [B_y] : % 187.68/187.60 ( 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))) % 187.68/187.60 => ~ 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)) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_rel__pow__Suc__E2,axiom, % 187.68/187.60 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_a] : % 187.68/187.60 ( 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))) % 187.68/187.60 => ~ ! [B_y] : % 187.68/187.60 ( 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)) % 187.68/187.60 => ~ 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))) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_tranclD2,axiom, % 187.68/187.60 ! [V_R_2,V_y_2,V_x_2,T_a] : % 187.68/187.60 ( 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))) % 187.68/187.60 => ? [B_z] : % 187.68/187.60 ( 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))) % 187.68/187.60 & 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)) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_tranclD,axiom, % 187.68/187.60 ! [V_R_2,V_y_2,V_x_2,T_a] : % 187.68/187.60 ( 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))) % 187.68/187.60 => ? [B_z] : % 187.68/187.60 ( 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)) % 187.68/187.60 & 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))) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_IdE,axiom, % 187.68/187.60 ! [V_p_2,T_a] : % 187.68/187.60 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Relation_OId(T_a))) % 187.68/187.60 => ~ ! [B_x] : V_p_2 != hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_min__max_OSup__fin_Oeq__fold_H,axiom, % 187.68/187.60 ! [V_x_2,V_A_2,T_a] : % 187.68/187.60 ( class_Orderings_Olinorder(T_a) % 187.68/187.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.60 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 187.68/187.60 => 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) ) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_fold__empty,axiom, % 187.68/187.60 ! [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 ). % 187.68/187.60 % 187.68/187.60 fof(fact_fold__image__def,axiom, % 187.68/187.60 ! [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)) ). % 187.68/187.60 % 187.68/187.60 fof(fact_folding_Oeq__fold,axiom, % 187.68/187.60 ! [V_s_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 187.68/187.60 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 187.68/187.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.60 => 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) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_fold__def,axiom, % 187.68/187.60 ! [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)) ). % 187.68/187.60 % 187.68/187.60 fof(fact_union__fold__insert,axiom, % 187.68/187.60 ! [V_B_2,V_A_2,T_a] : % 187.68/187.60 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.60 => 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) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_fold__sup__insert,axiom, % 187.68/187.60 ! [V_a_2,V_b_2,V_A_2,T_a] : % 187.68/187.60 ( class_Lattices_Osemilattice__sup(T_a) % 187.68/187.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.60 => 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)) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_fold__inf__insert,axiom, % 187.68/187.60 ! [V_a_2,V_b_2,V_A_2,T_a] : % 187.68/187.60 ( class_Lattices_Osemilattice__inf(T_a) % 187.68/187.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.60 => 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)) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_min__max_Ofold__inf__insert,axiom, % 187.68/187.60 ! [V_a_2,V_b_2,V_A_2,T_a] : % 187.68/187.60 ( class_Orderings_Olinorder(T_a) % 187.68/187.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.60 => 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)) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_min__max_Ofold__sup__insert,axiom, % 187.68/187.60 ! [V_a_2,V_b_2,V_A_2,T_a] : % 187.68/187.60 ( class_Orderings_Olinorder(T_a) % 187.68/187.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.60 => 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)) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_fun__left__comm__idem_Ofold__insert__idem,axiom, % 187.68/187.60 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_b,T_a] : % 187.68/187.60 ( c_Finite__Set_Ofun__left__comm__idem(T_a,T_b,V_f_2) % 187.68/187.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.60 => 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)) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_fun__left__comm__idem_Ofold__insert__idem2,axiom, % 187.68/187.60 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_b,T_a] : % 187.68/187.60 ( c_Finite__Set_Ofun__left__comm__idem(T_a,T_b,V_f_2) % 187.68/187.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.60 => 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) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_sup__SUPR__fold__sup,axiom, % 187.68/187.60 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] : % 187.68/187.60 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 187.68/187.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.60 => 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) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_folding__one__idem_Oeq__fold__idem_H,axiom, % 187.68/187.60 ! [V_a_2,V_A_2,V_F_2,V_f_2,T_a] : % 187.68/187.60 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2) % 187.68/187.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.60 => 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) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_sup__le__fold__sup,axiom, % 187.68/187.60 ! [V_b_2,V_a_2,V_A_2,T_a] : % 187.68/187.60 ( class_Lattices_Osemilattice__sup(T_a) % 187.68/187.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.60 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 187.68/187.60 => 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))) ) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_fold__inf__le__inf,axiom, % 187.68/187.60 ! [V_b_2,V_a_2,V_A_2,T_a] : % 187.68/187.60 ( class_Lattices_Osemilattice__inf(T_a) % 187.68/187.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.60 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 187.68/187.60 => 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))) ) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_min__max_Ofold__inf__le__inf,axiom, % 187.68/187.60 ! [V_b_2,V_a_2,V_A_2,T_a] : % 187.68/187.60 ( class_Orderings_Olinorder(T_a) % 187.68/187.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.60 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 187.68/187.60 => 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))) ) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_min__max_Osup__le__fold__sup,axiom, % 187.68/187.60 ! [V_b_2,V_a_2,V_A_2,T_a] : % 187.68/187.60 ( class_Orderings_Olinorder(T_a) % 187.68/187.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.60 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 187.68/187.60 => 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))) ) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_fold1__eq__fold__idem,axiom, % 187.68/187.60 ! [V_a_2,V_A_2,T_a] : % 187.68/187.60 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 187.68/187.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.60 => 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) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_Sup__fin_Oeq__fold__idem_H,axiom, % 187.68/187.60 ! [V_a_2,V_A_2,T_a] : % 187.68/187.60 ( class_Lattices_Olattice(T_a) % 187.68/187.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.60 => 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) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_Inf__fin_Oeq__fold__idem_H,axiom, % 187.68/187.60 ! [V_a_2,V_A_2,T_a] : % 187.68/187.60 ( class_Lattices_Olattice(T_a) % 187.68/187.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.60 => 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) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_Min_Oeq__fold__idem_H,axiom, % 187.68/187.60 ! [V_a_2,V_A_2,T_a] : % 187.68/187.60 ( class_Orderings_Olinorder(T_a) % 187.68/187.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.60 => 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) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_Max_Oeq__fold__idem_H,axiom, % 187.68/187.60 ! [V_a_2,V_A_2,T_a] : % 187.68/187.60 ( class_Orderings_Olinorder(T_a) % 187.68/187.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.60 => 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) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_min__max_OInf__fin_Oeq__fold__idem_H,axiom, % 187.68/187.60 ! [V_a_2,V_A_2,T_a] : % 187.68/187.60 ( class_Orderings_Olinorder(T_a) % 187.68/187.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.60 => 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) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_min__max_OSup__fin_Oeq__fold__idem_H,axiom, % 187.68/187.60 ! [V_a_2,V_A_2,T_a] : % 187.68/187.60 ( class_Orderings_Olinorder(T_a) % 187.68/187.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.60 => 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) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_minus__fold__remove,axiom, % 187.68/187.60 ! [V_B_2,V_A_2,T_a] : % 187.68/187.60 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.60 => 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) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_folding__one_Oeq__fold_H,axiom, % 187.68/187.60 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_a] : % 187.68/187.60 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2) % 187.68/187.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.60 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 187.68/187.60 => 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) ) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_SUPR__fold__sup,axiom, % 187.68/187.60 ! [V_f_2,V_A_2,T_a,T_b] : % 187.68/187.60 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 187.68/187.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.60 => 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) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_fold1__eq__fold,axiom, % 187.68/187.60 ! [V_a_2,V_A_2,T_a] : % 187.68/187.60 ( class_Groups_Oab__semigroup__mult(T_a) % 187.68/187.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.60 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 187.68/187.60 => 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) ) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_Sup__fin_Oeq__fold_H,axiom, % 187.68/187.60 ! [V_x_2,V_A_2,T_a] : % 187.68/187.60 ( class_Lattices_Olattice(T_a) % 187.68/187.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.60 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 187.68/187.60 => 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) ) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_Inf__fin_Oeq__fold_H,axiom, % 187.68/187.60 ! [V_x_2,V_A_2,T_a] : % 187.68/187.60 ( class_Lattices_Olattice(T_a) % 187.68/187.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.60 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 187.68/187.60 => 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) ) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_Min_Oeq__fold_H,axiom, % 187.68/187.60 ! [V_x_2,V_A_2,T_a] : % 187.68/187.60 ( class_Orderings_Olinorder(T_a) % 187.68/187.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.60 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 187.68/187.60 => 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) ) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_Max_Oeq__fold_H,axiom, % 187.68/187.60 ! [V_x_2,V_A_2,T_a] : % 187.68/187.60 ( class_Orderings_Olinorder(T_a) % 187.68/187.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.60 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 187.68/187.60 => 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) ) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_min__max_OInf__fin_Oeq__fold_H,axiom, % 187.68/187.60 ! [V_x_2,V_A_2,T_a] : % 187.68/187.60 ( class_Orderings_Olinorder(T_a) % 187.68/187.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.60 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 187.68/187.60 => 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) ) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_fun__left__comm_Ofold__rec,axiom, % 187.68/187.60 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_b,T_a] : % 187.68/187.60 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 187.68/187.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.60 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 187.68/187.60 => 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)))))) ) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_fun__left__comm_Ofold__insert__remove,axiom, % 187.68/187.60 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_b,T_a] : % 187.68/187.60 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 187.68/187.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.60 => 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)))))) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_fun__left__comm_Ofold__graph__determ,axiom, % 187.68/187.60 ! [V_y_2,V_x_2,V_A_2,V_z_2,V_f_2,T_b,T_a] : % 187.68/187.60 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 187.68/187.60 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),V_x_2)) % 187.68/187.60 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),V_y_2)) % 187.68/187.60 => V_y_2 = V_x_2 ) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_fun__left__comm_Ofun__left__comm__apply,axiom, % 187.68/187.60 ! [V_g_2,T_c,V_f_2,T_b,T_a] : % 187.68/187.60 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 187.68/187.60 => 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)) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_fun__left__comm_Ofun__left__comm,axiom, % 187.68/187.60 ! [V_z_2,V_y_2,V_x_2,V_f_2,T_b,T_a] : % 187.68/187.60 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 187.68/187.60 => 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)) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_fun__left__comm,axiom, % 187.68/187.60 ! [T_a] : % 187.68/187.60 ( class_Groups_Oab__semigroup__mult(T_a) % 187.68/187.60 => c_Finite__Set_Ofun__left__comm(T_a,T_a,c_Groups_Otimes__class_Otimes(T_a)) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_fun__left__comm_Ofun__comp__comm,axiom, % 187.68/187.60 ! [V_y_2,V_x_2,V_f_2,T_b,T_a] : % 187.68/187.60 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 187.68/187.60 => 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)) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_fun__left__comm_Ofold__fun__comm,axiom, % 187.68/187.60 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_b,T_a] : % 187.68/187.60 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 187.68/187.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.60 => 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) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_fun__left__comm_Ofold__equality,axiom, % 187.68/187.60 ! [V_y_2,V_A_2,V_z_2,V_f_2,T_b,T_a] : % 187.68/187.60 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 187.68/187.60 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),V_y_2)) % 187.68/187.60 => hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_z_2),V_A_2) = V_y_2 ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_fun__left__comm_Ofold__graph__fold,axiom, % 187.68/187.60 ! [V_z_2,V_A_2,V_f_2,T_b,T_a] : % 187.68/187.60 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 187.68/187.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.60 => 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))) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_fun__left__comm_Ofold__insert2,axiom, % 187.68/187.60 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_b,T_a] : % 187.68/187.60 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 187.68/187.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.60 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 187.68/187.60 => 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) ) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_fun__left__comm_Ofold__insert,axiom, % 187.68/187.60 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_b,T_a] : % 187.68/187.60 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 187.68/187.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.60 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 187.68/187.60 => 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)) ) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_fun__left__comm_Ofold__graph__insertE__aux,axiom, % 187.68/187.60 ! [V_a_2,V_y_2,V_A_2,V_z_2,V_f_2,T_b,T_a] : % 187.68/187.60 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 187.68/187.60 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),V_y_2)) % 187.68/187.60 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 187.68/187.60 => ? [B_y_H] : % 187.68/187.60 ( V_y_2 = hAPP(hAPP(V_f_2,V_a_2),B_y_H) % 187.68/187.60 & 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)) ) ) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_INFI__fold__inf,axiom, % 187.68/187.60 ! [V_f_2,V_A_2,T_a,T_b] : % 187.68/187.60 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 187.68/187.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.60 => 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) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_INT__D,axiom, % 187.68/187.60 ! [V_a_2,V_B_2,V_A_2,T_b,V_b_2,T_a] : % 187.68/187.60 ( 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))) % 187.68/187.60 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 187.68/187.60 => hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_INT__E,axiom, % 187.68/187.60 ! [V_a_2,V_B_2,V_A_2,T_b,V_b_2,T_a] : % 187.68/187.60 ( 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))) % 187.68/187.60 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(V_B_2,V_a_2))) % 187.68/187.60 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_INF1__E,axiom, % 187.68/187.60 ! [V_a_2,V_b_2,V_B_2,V_A_2,T_b,T_a] : % 187.68/187.60 ( 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)) % 187.68/187.60 => ( ~ hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2)) % 187.68/187.60 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_INF1__D,axiom, % 187.68/187.60 ! [V_a_2,V_b_2,V_B_2,V_A_2,T_b,T_a] : % 187.68/187.60 ( 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)) % 187.68/187.60 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 187.68/187.60 => hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2)) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_INF2__E,axiom, % 187.68/187.60 ! [V_a_2,V_c_2,V_b_2,V_B_2,V_A_2,T_c,T_b,T_a] : % 187.68/187.60 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2)) % 187.68/187.60 => ( ~ hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_c_2)) % 187.68/187.60 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_INF2__D,axiom, % 187.68/187.60 ! [V_a_2,V_c_2,V_b_2,V_B_2,V_A_2,T_c,T_b,T_a] : % 187.68/187.60 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2)) % 187.68/187.60 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 187.68/187.60 => hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_c_2)) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_finite__INT,axiom, % 187.68/187.60 ! [V_A_2,T_b,V_I_2,T_a] : % 187.68/187.60 ( ? [B_x] : % 187.68/187.60 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_I_2)) % 187.68/187.60 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_A_2,B_x))) ) % 187.68/187.60 => 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))) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_Compl__UN,axiom, % 187.68/187.60 ! [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)) ). % 187.68/187.60 % 187.68/187.60 fof(fact_Compl__INT,axiom, % 187.68/187.60 ! [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)) ). % 187.68/187.60 % 187.68/187.60 fof(fact_INT__extend__simps_I9_J,axiom, % 187.68/187.60 ! [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) ). % 187.68/187.60 % 187.68/187.60 fof(fact_INT__simps_I9_J,axiom, % 187.68/187.60 ! [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)) ). % 187.68/187.60 % 187.68/187.60 fof(fact_UN__extend__simps_I7_J,axiom, % 187.68/187.60 ! [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)) ). % 187.68/187.60 % 187.68/187.60 fof(fact_UN__simps_I7_J,axiom, % 187.68/187.60 ! [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)) ). % 187.68/187.60 % 187.68/187.60 fof(fact_Image__INT__subset,axiom, % 187.68/187.60 ! [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)))) ). % 187.68/187.60 % 187.68/187.60 fof(fact_INF__less__iff,axiom, % 187.68/187.60 ! [V_a_2,V_f_2,V_A_2,T_b,T_a] : % 187.68/187.60 ( ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 187.68/187.60 & class_Orderings_Olinorder(T_a) ) % 187.68/187.60 => ( 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)) % 187.68/187.60 <=> ? [B_x] : % 187.68/187.60 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 187.68/187.60 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(V_f_2,B_x)),V_a_2)) ) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_le__INF__iff,axiom, % 187.68/187.60 ! [V_M_2,V_A_2,T_b,V_u_2,T_a] : % 187.68/187.60 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 187.68/187.60 => ( 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))) % 187.68/187.60 <=> ! [B_x] : % 187.68/187.60 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 187.68/187.60 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_u_2),hAPP(V_M_2,B_x))) ) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_INT__subset__iff,axiom, % 187.68/187.60 ! [V_A_2,V_I_2,T_b,V_B_2,T_a] : % 187.68/187.60 ( 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))) % 187.68/187.60 <=> ! [B_x] : % 187.68/187.60 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_I_2)) % 187.68/187.60 => 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))) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_INT__lower,axiom, % 187.68/187.60 ! [V_B_2,T_b,V_A_2,V_a_2,T_a] : % 187.68/187.60 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 187.68/187.60 => 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))) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_INT__extend__simps_I2_J,axiom, % 187.68/187.60 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 187.68/187.60 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.60 => 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 ) % 187.68/187.60 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.60 => 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)) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_INT__extend__simps_I1_J,axiom, % 187.68/187.60 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 187.68/187.60 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.60 => 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 ) % 187.68/187.60 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.60 => 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)) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_INT__constant,axiom, % 187.68/187.60 ! [V_c_2,T_b,T_a,V_A_2] : % 187.68/187.60 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.60 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_c_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) % 187.68/187.60 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.60 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_c_2)) = V_c_2 ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_INT__empty,axiom, % 187.68/187.60 ! [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)) ). % 187.68/187.60 % 187.68/187.60 fof(fact_INF__const,axiom, % 187.68/187.60 ! [V_M_2,T_a,V_A_2,T_b] : % 187.68/187.60 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 187.68/187.60 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.60 => 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 ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_INT__insert,axiom, % 187.68/187.60 ! [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)) ). % 187.68/187.60 % 187.68/187.60 fof(fact_INF__INT__eq,axiom, % 187.68/187.60 ! [V_x_2,V_r_2,T_b,T_a] : % 187.68/187.60 ( 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)) % 187.68/187.60 <=> 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))) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_INT__absorb,axiom, % 187.68/187.60 ! [V_A_2,T_b,V_I_2,V_k_2,T_a] : % 187.68/187.60 ( hBOOL(hAPP(hAPP(c_member(T_a),V_k_2),V_I_2)) % 187.68/187.60 => 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) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_INT__simps_I5_J,axiom, % 187.68/187.60 ! [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)) ). % 187.68/187.60 % 187.68/187.60 fof(fact_INT__extend__simps_I5_J,axiom, % 187.68/187.60 ! [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)) ). % 187.68/187.60 % 187.68/187.60 fof(fact_INT__insert__distrib,axiom, % 187.68/187.60 ! [V_B_2,V_a_2,T_b,V_A_2,V_u_2,T_a] : % 187.68/187.60 ( hBOOL(hAPP(hAPP(c_member(T_a),V_u_2),V_A_2)) % 187.68/187.60 => 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)) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_INT__extend__simps_I10_J,axiom, % 187.68/187.60 ! [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) ). % 187.68/187.60 % 187.68/187.60 fof(fact_INT__simps_I10_J,axiom, % 187.68/187.60 ! [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)) ). % 187.68/187.60 % 187.68/187.60 fof(fact_vimage__INT,axiom, % 187.68/187.60 ! [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)) ). % 187.68/187.60 % 187.68/187.60 fof(fact_INF__commute,axiom, % 187.68/187.60 ! [V_f_2,V_B_2,T_c,V_A_2,T_b,T_a] : % 187.68/187.60 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 187.68/187.60 => 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))) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_INFI__apply,axiom, % 187.68/187.60 ! [V_x_2,V_f_2,V_A_2,T_c,T_b,T_a] : % 187.68/187.60 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 187.68/187.60 => 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)) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_Pow__INT__eq,axiom, % 187.68/187.60 ! [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)) ). % 187.68/187.60 % 187.68/187.60 fof(fact_INT__Int__distrib,axiom, % 187.68/187.60 ! [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)) ). % 187.68/187.60 % 187.68/187.60 fof(fact_INTER__UNIV__conv_I1_J,axiom, % 187.68/187.60 ! [V_B_2,V_A_2,T_b,T_a] : % 187.68/187.60 ( 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) % 187.68/187.60 <=> ! [B_x] : % 187.68/187.60 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 187.68/187.60 => hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_INTER__UNIV__conv_I2_J,axiom, % 187.68/187.60 ! [V_B_2,V_A_2,T_a,T_b] : % 187.68/187.60 ( 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)) % 187.68/187.60 <=> ! [B_x] : % 187.68/187.60 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 187.68/187.60 => hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_INF__INT__eq2,axiom, % 187.68/187.60 ! [V_y_2,V_x_2,V_r_2,T_c,T_b,T_a] : % 187.68/187.60 ( 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)) % 187.68/187.60 <=> 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))) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_INT__iff,axiom, % 187.68/187.60 ! [V_B_2,V_A_2,T_b,V_b_2,T_a] : % 187.68/187.60 ( 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))) % 187.68/187.60 <=> ! [B_x] : % 187.68/187.60 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 187.68/187.60 => hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(V_B_2,B_x))) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_INFI__bool__eq,axiom, % 187.68/187.60 ! [T_a] : c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_HOL_Obool) = c_Set_OBall(T_a) ). % 187.68/187.60 % 187.68/187.60 fof(fact_Collect__ball__eq,axiom, % 187.68/187.60 ! [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))) ). % 187.68/187.60 % 187.68/187.60 fof(fact_INT__Un,axiom, % 187.68/187.60 ! [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)) ). % 187.68/187.60 % 187.68/187.60 fof(fact_converse__INTER,axiom, % 187.68/187.60 ! [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)) ). % 187.68/187.60 % 187.68/187.60 fof(fact_Un__INT__distrib2,axiom, % 187.68/187.60 ! [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))) ). % 187.68/187.60 % 187.68/187.60 fof(fact_INT__extend__simps_I6_J,axiom, % 187.68/187.60 ! [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)) ). % 187.68/187.60 % 187.68/187.60 fof(fact_Un__INT__distrib,axiom, % 187.68/187.60 ! [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)) ). % 187.68/187.60 % 187.68/187.60 fof(fact_INT__extend__simps_I7_J,axiom, % 187.68/187.60 ! [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)) ). % 187.68/187.60 % 187.68/187.60 fof(fact_INT__simps_I6_J,axiom, % 187.68/187.60 ! [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) ). % 187.68/187.60 % 187.68/187.60 fof(fact_INT__simps_I7_J,axiom, % 187.68/187.60 ! [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)) ). % 187.68/187.60 % 187.68/187.60 fof(fact_INF__subset,axiom, % 187.68/187.60 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] : % 187.68/187.60 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 187.68/187.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 187.68/187.60 => 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))) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_INTER__def,axiom, % 187.68/187.60 ! [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)))) ). % 187.68/187.60 % 187.68/187.60 fof(fact_INT__simps_I1_J,axiom, % 187.68/187.60 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 187.68/187.60 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.60 => 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)) ) % 187.68/187.60 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.60 => 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) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_INT__simps_I2_J,axiom, % 187.68/187.60 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 187.68/187.60 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.60 => 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)) ) % 187.68/187.60 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.60 => 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)) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_Collect__all__eq,axiom, % 187.68/187.60 ! [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))) ). % 187.68/187.60 % 187.68/187.60 fof(fact_INT__simps_I3_J,axiom, % 187.68/187.60 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 187.68/187.60 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.60 => 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)) ) % 187.68/187.60 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.60 => 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) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_INT__extend__simps_I3_J,axiom, % 187.68/187.60 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 187.68/187.60 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.60 => 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) ) % 187.68/187.60 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.60 => 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)) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_INT__extend__simps_I4_J,axiom, % 187.68/187.60 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 187.68/187.60 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.60 => 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 ) % 187.68/187.60 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.60 => 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)) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_INF__leI,axiom, % 187.68/187.60 ! [V_M_2,V_A_2,V_i_2,T_a,T_b] : % 187.68/187.60 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 187.68/187.60 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),V_A_2)) % 187.68/187.60 => 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))) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_INT__greaterThan__UNIV,axiom, % 187.68/187.60 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)) ). % 187.68/187.60 % 187.68/187.60 fof(fact_INT__simps_I4_J,axiom, % 187.68/187.60 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 187.68/187.60 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.60 => 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)) ) % 187.68/187.60 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.60 => 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)) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_Image__INT__eq,axiom, % 187.68/187.60 ! [V_B_2,T_c,V_A_2,V_r_2,T_b,T_a] : % 187.68/187.60 ( c_Relation_Osingle__valued(T_a,T_b,hAPP(c_Relation_Oconverse(T_b,T_a),V_r_2)) % 187.68/187.60 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 187.68/187.60 => 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)) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_inf__INFI__fold__inf,axiom, % 187.68/187.60 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] : % 187.68/187.60 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 187.68/187.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.60 => 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) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_Inf__fold__inf,axiom, % 187.68/187.60 ! [V_A_2,T_a] : % 187.68/187.60 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 187.68/187.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.60 => 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) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_Sup__fold__sup,axiom, % 187.68/187.60 ! [V_A_2,T_a] : % 187.68/187.60 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 187.68/187.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.60 => 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) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_finite__Inter,axiom, % 187.68/187.60 ! [V_M_2,T_a] : % 187.68/187.60 ( ? [B_x] : % 187.68/187.60 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_x),V_M_2)) % 187.68/187.60 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),B_x)) ) % 187.68/187.60 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_M_2))) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_UnionI,axiom, % 187.68/187.60 ! [V_A_2,V_C_2,V_X_2,T_a] : % 187.68/187.60 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),V_C_2)) % 187.68/187.60 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),V_X_2)) % 187.68/187.60 => 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))) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_InterE,axiom, % 187.68/187.60 ! [V_X_2,V_C_2,V_A_2,T_a] : % 187.68/187.60 ( 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))) % 187.68/187.60 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),V_C_2)) % 187.68/187.60 => hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),V_X_2)) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_InterD,axiom, % 187.68/187.60 ! [V_X_2,V_C_2,V_A_2,T_a] : % 187.68/187.60 ( 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))) % 187.68/187.60 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),V_C_2)) % 187.68/187.60 => hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),V_X_2)) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_Inter__image__eq,axiom, % 187.68/187.60 ! [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) ). % 187.68/187.60 % 187.68/187.60 fof(fact_INTER__eq__Inter__image,axiom, % 187.68/187.60 ! [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)) ). % 187.68/187.60 % 187.68/187.60 fof(fact_INF2__iff,axiom, % 187.68/187.60 ! [V_c_2,V_b_2,V_B_2,V_A_2,T_c,T_b,T_a] : % 187.68/187.60 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_c_2)) % 187.68/187.60 <=> ! [B_x] : % 187.68/187.60 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 187.68/187.60 => hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_c_2)) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_INF1__iff,axiom, % 187.68/187.60 ! [V_b_2,V_B_2,V_A_2,T_b,T_a] : % 187.68/187.60 ( 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)) % 187.68/187.60 <=> ! [B_x] : % 187.68/187.60 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 187.68/187.60 => hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2)) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_INT__extend__simps_I8_J,axiom, % 187.68/187.60 ! [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) ). % 187.68/187.60 % 187.68/187.60 fof(fact_INT__simps_I8_J,axiom, % 187.68/187.60 ! [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)) ). % 187.68/187.60 % 187.68/187.60 fof(fact_Un__Inter,axiom, % 187.68/187.60 ! [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)) ). % 187.68/187.60 % 187.68/187.60 fof(fact_Union__mono,axiom, % 187.68/187.60 ! [V_B_2,V_A_2,T_a] : % 187.68/187.60 ( 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)) % 187.68/187.60 => 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))) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_Inf__Sup,axiom, % 187.68/187.60 ! [V_A_2,T_a] : % 187.68/187.60 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 187.68/187.60 => 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))))) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_Sup__Inf,axiom, % 187.68/187.60 ! [V_A_2,T_a] : % 187.68/187.60 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 187.68/187.60 => 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)))))) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_Inter__lower,axiom, % 187.68/187.60 ! [V_A_2,V_B_2,T_a] : % 187.68/187.60 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 187.68/187.60 => 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)) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_Union__Pow__eq,axiom, % 187.68/187.60 ! [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 ). % 187.68/187.60 % 187.68/187.60 fof(fact_Field__Union,axiom, % 187.68/187.60 ! [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)) ). % 187.68/187.60 % 187.68/187.60 fof(fact_Union__disjoint,axiom, % 187.68/187.60 ! [V_A_2,V_C_2,T_a] : % 187.68/187.60 ( 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)) % 187.68/187.60 <=> ! [B_x] : % 187.68/187.60 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_x),V_C_2)) % 187.68/187.60 => 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)) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_Union__upper,axiom, % 187.68/187.60 ! [V_A_2,V_B_2,T_a] : % 187.68/187.60 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 187.68/187.60 => 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))) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_le__Inf__iff,axiom, % 187.68/187.60 ! [V_A_2,V_b_2,T_a] : % 187.68/187.60 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 187.68/187.60 => ( 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))) % 187.68/187.60 <=> ! [B_x] : % 187.68/187.60 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 187.68/187.60 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),B_x)) ) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_Sup__le__iff,axiom, % 187.68/187.60 ! [V_b_2,V_A_2,T_a] : % 187.68/187.60 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 187.68/187.60 => ( 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)) % 187.68/187.60 <=> ! [B_x] : % 187.68/187.60 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 187.68/187.60 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_x),V_b_2)) ) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_less__Sup__iff,axiom, % 187.68/187.60 ! [V_S_2,V_a_2,T_a] : % 187.68/187.60 ( ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 187.68/187.60 & class_Orderings_Olinorder(T_a) ) % 187.68/187.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Complete__Lattice_OSup__class_OSup(T_a,V_S_2))) % 187.68/187.60 <=> ? [B_x] : % 187.68/187.60 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2)) % 187.68/187.60 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),B_x)) ) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_Inf__less__iff,axiom, % 187.68/187.60 ! [V_a_2,V_S_2,T_a] : % 187.68/187.60 ( ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 187.68/187.60 & class_Orderings_Olinorder(T_a) ) % 187.68/187.60 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Complete__Lattice_OInf__class_OInf(T_a,V_S_2)),V_a_2)) % 187.68/187.60 <=> ? [B_x] : % 187.68/187.60 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2)) % 187.68/187.60 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),B_x),V_a_2)) ) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_Union__empty,axiom, % 187.68/187.60 ! [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)) ). % 187.68/187.60 % 187.68/187.60 fof(fact_Domain__Union,axiom, % 187.68/187.60 ! [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)) ). % 187.68/187.60 % 187.68/187.60 fof(fact_Range__Union,axiom, % 187.68/187.60 ! [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)) ). % 187.68/187.60 % 187.68/187.60 fof(fact_vimage__Union,axiom, % 187.68/187.60 ! [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)) ). % 187.68/187.60 % 187.68/187.60 fof(fact_Int__Union,axiom, % 187.68/187.60 ! [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)) ). % 187.68/187.60 % 187.68/187.60 fof(fact_Int__Union2,axiom, % 187.68/187.60 ! [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)) ). % 187.68/187.60 % 187.68/187.60 fof(fact_UN__simps_I8_J,axiom, % 187.68/187.60 ! [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)) ). % 187.68/187.60 % 187.68/187.60 fof(fact_UN__extend__simps_I8_J,axiom, % 187.68/187.60 ! [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) ). % 187.68/187.60 % 187.68/187.60 fof(fact_Sigma__Union,axiom, % 187.68/187.60 ! [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)) ). % 187.68/187.60 % 187.68/187.60 fof(fact_image__Union,axiom, % 187.68/187.60 ! [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)) ). % 187.68/187.60 % 187.68/187.60 fof(fact_Union__insert,axiom, % 187.68/187.60 ! [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)) ). % 187.68/187.60 % 187.68/187.60 fof(fact_Union__quotient,axiom, % 187.68/187.60 ! [V_r_2,V_A_2,T_a] : % 187.68/187.60 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 187.68/187.60 => 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 ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_finite__UnionD,axiom, % 187.68/187.60 ! [V_A_2,T_a] : % 187.68/187.60 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_A_2))) % 187.68/187.60 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_a,tc_HOL_Obool)),V_A_2)) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_subset__Pow__Union,axiom, % 187.68/187.60 ! [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)))) ). % 187.68/187.60 % 187.68/187.60 fof(fact_Inter__anti__mono,axiom, % 187.68/187.60 ! [V_A_2,V_B_2,T_a] : % 187.68/187.60 ( 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)) % 187.68/187.60 => 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))) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_Inter__empty,axiom, % 187.68/187.60 ! [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)) ). % 187.68/187.60 % 187.68/187.60 fof(fact_Inter__eq,axiom, % 187.68/187.60 ! [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)))) ). % 187.68/187.60 % 187.68/187.60 fof(fact_Union__UNIV,axiom, % 187.68/187.60 ! [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)) ). % 187.68/187.60 % 187.68/187.60 fof(fact_Union__Un__distrib,axiom, % 187.68/187.60 ! [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)) ). % 187.68/187.60 % 187.68/187.60 fof(fact_Inter__insert,axiom, % 187.68/187.60 ! [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)) ). % 187.68/187.60 % 187.68/187.60 fof(fact_UNION__eq__Union__image,axiom, % 187.68/187.60 ! [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)) ). % 187.68/187.60 % 187.68/187.60 fof(fact_Union__image__eq,axiom, % 187.68/187.60 ! [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) ). % 187.68/187.60 % 187.68/187.60 fof(fact_Sup__upper,axiom, % 187.68/187.60 ! [V_A_2,V_x_2,T_a] : % 187.68/187.60 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 187.68/187.60 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 187.68/187.60 => 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))) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_Inter__UNIV,axiom, % 187.68/187.60 ! [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)) ). % 187.68/187.60 % 187.68/187.60 fof(fact_Inf__lower,axiom, % 187.68/187.60 ! [V_A_2,V_x_2,T_a] : % 187.68/187.60 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 187.68/187.60 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 187.68/187.60 => 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)) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_Sup__empty,axiom, % 187.68/187.60 ! [T_a] : % 187.68/187.60 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 187.68/187.60 => 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) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_Inter__Un__distrib,axiom, % 187.68/187.60 ! [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)) ). % 187.68/187.60 % 187.68/187.60 fof(fact_Sup__singleton,axiom, % 187.68/187.60 ! [V_a_2,T_a] : % 187.68/187.60 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 187.68/187.60 => 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 ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_Sup__insert,axiom, % 187.68/187.60 ! [V_A_2,V_a_2,T_a] : % 187.68/187.60 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 187.68/187.60 => 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)) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_Int__Inter__image,axiom, % 187.68/187.60 ! [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))) ). % 187.68/187.60 % 187.68/187.60 fof(fact_Inf__singleton,axiom, % 187.68/187.60 ! [V_a_2,T_a] : % 187.68/187.60 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 187.68/187.60 => 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 ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_Sup__UNIV,axiom, % 187.68/187.60 ! [T_a] : % 187.68/187.60 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 187.68/187.60 => 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) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_Inf__empty,axiom, % 187.68/187.60 ! [T_a] : % 187.68/187.60 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 187.68/187.60 => 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) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_Inf__UNIV,axiom, % 187.68/187.60 ! [T_a] : % 187.68/187.60 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 187.68/187.60 => 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) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_Inf__insert,axiom, % 187.68/187.60 ! [V_A_2,V_a_2,T_a] : % 187.68/187.60 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 187.68/187.60 => 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)) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_Un__eq__Union,axiom, % 187.68/187.60 ! [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))))) ). % 187.68/187.60 % 187.68/187.60 fof(fact_Un__Union__image,axiom, % 187.68/187.60 ! [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))) ). % 187.68/187.60 % 187.68/187.60 fof(fact_Union__Int__subset,axiom, % 187.68/187.60 ! [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)))) ). % 187.68/187.60 % 187.68/187.60 fof(fact_Int__eq__Inter,axiom, % 187.68/187.60 ! [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))))) ). % 187.68/187.60 % 187.68/187.60 fof(fact_Inter__Un__subset,axiom, % 187.68/187.60 ! [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)))) ). % 187.68/187.60 % 187.68/187.60 fof(fact_Sup__binary,axiom, % 187.68/187.60 ! [V_b_2,V_a_2,T_a] : % 187.68/187.60 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 187.68/187.60 => 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) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_Inf__binary,axiom, % 187.68/187.60 ! [V_b_2,V_a_2,T_a] : % 187.68/187.60 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 187.68/187.60 => 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) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_sup__Sup__fold__sup,axiom, % 187.68/187.60 ! [V_B_2,V_A_2,T_a] : % 187.68/187.60 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 187.68/187.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.60 => 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) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_Sup__fin__Sup,axiom, % 187.68/187.60 ! [V_A_2,T_a] : % 187.68/187.60 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 187.68/187.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.60 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.60 => c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2) = c_Complete__Lattice_OSup__class_OSup(T_a,V_A_2) ) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_inf__Inf__fold__inf,axiom, % 187.68/187.60 ! [V_B_2,V_A_2,T_a] : % 187.68/187.60 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 187.68/187.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.60 => 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) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_Inf__fin__Inf,axiom, % 187.68/187.60 ! [V_A_2,T_a] : % 187.68/187.60 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 187.68/187.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.60 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.60 => c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2) = c_Complete__Lattice_OInf__class_OInf(T_a,V_A_2) ) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_image__INT,axiom, % 187.68/187.60 ! [V_j_2,V_B_2,V_A_2,T_c,V_C_2,V_f_2,T_b,T_a] : % 187.68/187.60 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_C_2) % 187.68/187.60 => ( ! [B_x] : % 187.68/187.60 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 187.68/187.60 => 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)) ) % 187.68/187.60 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_j_2),V_A_2)) % 187.68/187.60 => 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)) ) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_card__partition,axiom, % 187.68/187.60 ! [V_k_2,V_C_2,T_a] : % 187.68/187.60 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_a,tc_HOL_Obool)),V_C_2)) % 187.68/187.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_C_2))) % 187.68/187.60 => ( ! [B_c] : % 187.68/187.60 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_c),V_C_2)) % 187.68/187.60 => hAPP(c_Finite__Set_Ocard(T_a),B_c) = V_k_2 ) % 187.68/187.60 => ( ! [B_c1] : % 187.68/187.60 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_c1),V_C_2)) % 187.68/187.60 => ! [B_c2] : % 187.68/187.60 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_c2),V_C_2)) % 187.68/187.60 => ( B_c1 != B_c2 % 187.68/187.60 => 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)) ) ) ) % 187.68/187.60 => 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)) ) ) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_Inter__def,axiom, % 187.68/187.60 ! [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))) ). % 187.68/187.60 % 187.68/187.60 fof(fact_Union__def,axiom, % 187.68/187.60 ! [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))) ). % 187.68/187.60 % 187.68/187.60 fof(fact_finite__Union,axiom, % 187.68/187.60 ! [V_A_2,T_a] : % 187.68/187.60 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_a,tc_HOL_Obool)),V_A_2)) % 187.68/187.60 => ( ! [B_M] : % 187.68/187.60 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_M),V_A_2)) % 187.68/187.60 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),B_M)) ) % 187.68/187.60 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_A_2))) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_insert__partition,axiom, % 187.68/187.60 ! [V_F_2,V_x_2,T_a] : % 187.68/187.60 ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_x_2),V_F_2)) % 187.68/187.60 => ( ! [B_x] : % 187.68/187.60 ( 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))) % 187.68/187.60 => ! [B_xa] : % 187.68/187.60 ( 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))) % 187.68/187.60 => ( B_x != B_xa % 187.68/187.60 => 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)) ) ) ) % 187.68/187.60 => 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)) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_inj__on__Inter,axiom, % 187.68/187.60 ! [V_f_2,T_b,T_a,V_S_2] : % 187.68/187.60 ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)) % 187.68/187.60 => ( ! [B_A] : % 187.68/187.60 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_A),V_S_2)) % 187.68/187.60 => c_Fun_Oinj__on(T_a,T_b,V_f_2,B_A) ) % 187.68/187.60 => 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)) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_Inter__subset,axiom, % 187.68/187.60 ! [V_B_2,V_A_2,T_a] : % 187.68/187.60 ( ! [B_X] : % 187.68/187.60 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_X),V_A_2)) % 187.68/187.60 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),B_X),V_B_2)) ) % 187.68/187.60 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)) % 187.68/187.60 => 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)) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_inj__on__INTER,axiom, % 187.68/187.60 ! [V_A_2,V_f_2,T_c,T_b,T_a,V_I_2] : % 187.68/187.60 ( V_I_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.60 => ( ! [B_i] : % 187.68/187.60 ( hBOOL(hAPP(hAPP(c_member(T_a),B_i),V_I_2)) % 187.68/187.60 => c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(V_A_2,B_i)) ) % 187.68/187.60 => 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)) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_fun__left__comm_Ofold__graph__insertE,axiom, % 187.68/187.60 ! [V_v_2,V_A_2,V_x_2,V_z_2,V_f_2,T_b,T_a] : % 187.68/187.60 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 187.68/187.60 => ( 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)) % 187.68/187.60 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 187.68/187.60 => ~ ! [B_y] : % 187.68/187.60 ( V_v_2 = hAPP(hAPP(V_f_2,V_x_2),B_y) % 187.68/187.60 => ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),B_y)) ) ) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_min__max_Ofold__sup__le__sup,axiom, % 187.68/187.60 ! [V_c_2,V_b_2,V_A_2,T_a] : % 187.68/187.60 ( class_Orderings_Olinorder(T_a) % 187.68/187.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.60 => ( ! [B_x] : % 187.68/187.60 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 187.68/187.60 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_x),V_b_2)) ) % 187.68/187.60 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omax(T_a)),V_c_2),V_A_2)),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_b_2),V_c_2))) ) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_min__max_Oinf__le__fold__inf,axiom, % 187.68/187.60 ! [V_c_2,V_b_2,V_A_2,T_a] : % 187.68/187.60 ( class_Orderings_Olinorder(T_a) % 187.68/187.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.60 => ( ! [B_x] : % 187.68/187.60 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 187.68/187.60 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),B_x)) ) % 187.68/187.60 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b_2),V_c_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omin(T_a)),V_c_2),V_A_2))) ) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_InterI,axiom, % 187.68/187.60 ! [V_A_2,V_C_2,T_a] : % 187.68/187.60 ( ! [B_X] : % 187.68/187.60 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_X),V_C_2)) % 187.68/187.60 => hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),B_X)) ) % 187.68/187.60 => 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))) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_inf__le__fold__inf,axiom, % 187.68/187.60 ! [V_c_2,V_b_2,V_A_2,T_a] : % 187.68/187.60 ( class_Lattices_Osemilattice__inf(T_a) % 187.68/187.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.60 => ( ! [B_x] : % 187.68/187.60 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 187.68/187.60 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),B_x)) ) % 187.68/187.60 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_b_2),V_c_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a)),V_c_2),V_A_2))) ) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_fold__sup__le__sup,axiom, % 187.68/187.60 ! [V_c_2,V_b_2,V_A_2,T_a] : % 187.68/187.60 ( class_Lattices_Osemilattice__sup(T_a) % 187.68/187.60 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.60 => ( ! [B_x] : % 187.68/187.60 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 187.68/187.60 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_x),V_b_2)) ) % 187.68/187.60 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a)),V_c_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_b_2),V_c_2))) ) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_mod__div__decomp,axiom, % 187.68/187.60 ! [V_b,V_a,T_a] : % 187.68/187.60 ( class_Divides_Osemiring__div(T_a) % 187.68/187.60 => 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)) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_wf__eq__minimal,axiom, % 187.68/187.60 ! [V_r_2,T_a] : % 187.68/187.60 ( c_Wellfounded_Owf(T_a,V_r_2) % 187.68/187.60 <=> ! [B_Q] : % 187.68/187.60 ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_a),B_x),B_Q)) % 187.68/187.60 => ? [B_x] : % 187.68/187.60 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),B_Q)) % 187.68/187.60 & ! [B_y] : % 187.68/187.60 ( 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)) % 187.68/187.60 => ~ hBOOL(hAPP(hAPP(c_member(T_a),B_y),B_Q)) ) ) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_transfer__nat__int__set__cong,axiom, % 187.68/187.60 ! [V_P_H_2,V_P_2] : % 187.68/187.60 ( ! [B_x] : % 187.68/187.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 187.68/187.60 => ( hBOOL(hAPP(V_P_2,B_x)) % 187.68/187.60 <=> hBOOL(hAPP(V_P_H_2,B_x)) ) ) % 187.68/187.60 => 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)) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_Int__Collect__mono,axiom, % 187.68/187.60 ! [V_Q_2,V_P_2,V_B_2,V_A_2,T_a] : % 187.68/187.60 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 187.68/187.60 => ( ! [B_x] : % 187.68/187.60 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 187.68/187.60 => ( hBOOL(hAPP(V_P_2,B_x)) % 187.68/187.60 => hBOOL(hAPP(V_Q_2,B_x)) ) ) % 187.68/187.60 => 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)))) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_UnionE,axiom, % 187.68/187.60 ! [V_C_2,V_A_2,T_a] : % 187.68/187.60 ( 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))) % 187.68/187.60 => ~ ! [B_X] : % 187.68/187.60 ( hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),B_X)) % 187.68/187.60 => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_X),V_C_2)) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_option_Orecs_I2_J,axiom, % 187.68/187.60 ! [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) ). % 187.68/187.60 % 187.68/187.60 fof(fact_option_Orecs_I1_J,axiom, % 187.68/187.60 ! [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 ). % 187.68/187.60 % 187.68/187.60 fof(fact_rel__compE,axiom, % 187.68/187.60 ! [V_s_2,V_r_2,T_c,V_xz_2,T_b,T_a] : % 187.68/187.60 ( 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))) % 187.68/187.60 => ~ ! [B_x,B_y,B_z] : % 187.68/187.60 ( V_xz_2 = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_x),B_z) % 187.68/187.60 => ( 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)) % 187.68/187.60 => ~ 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)) ) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_converseE,axiom, % 187.68/187.60 ! [V_r_2,V_yx_2,T_b,T_a] : % 187.68/187.60 ( 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))) % 187.68/187.60 => ~ ! [B_x,B_y] : % 187.68/187.60 ( V_yx_2 = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_y),B_x) % 187.68/187.60 => ~ 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)) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_Nitpick_Oplus__frac__def,axiom, % 187.68/187.60 ! [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))) ). % 187.68/187.60 % 187.68/187.60 fof(fact_map__add__upd__left,axiom, % 187.68/187.60 ! [V_u1_2,V_e1_2,V_e2_2,T_b,V_m_2,T_a] : % 187.68/187.60 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_m_2),c_Map_Odom(T_a,T_b,V_e2_2))) % 187.68/187.60 => 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)) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_map__add__SomeD,axiom, % 187.68/187.60 ! [V_x_2,V_k_2,V_n_2,V_m_2,T_a,T_b] : % 187.68/187.60 ( 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) % 187.68/187.60 => ( hAPP(V_n_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_x_2) % 187.68/187.60 | ( hAPP(V_n_2,V_k_2) = c_Option_Ooption_ONone(T_a) % 187.68/187.60 & hAPP(V_m_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_x_2) ) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_map__add__Some__iff,axiom, % 187.68/187.60 ! [V_x_2,V_k_2,V_n_2,V_m_2,T_a,T_b] : % 187.68/187.60 ( 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) % 187.68/187.60 <=> ( hAPP(V_n_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_x_2) % 187.68/187.60 | ( hAPP(V_n_2,V_k_2) = c_Option_Ooption_ONone(T_a) % 187.68/187.60 & hAPP(V_m_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_x_2) ) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_map__add__dom__app__simps_I2_J,axiom, % 187.68/187.60 ! [V_l2_2,V_l1_2,T_b,V_m_2,T_a] : % 187.68/187.60 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_m_2),c_Map_Odom(T_a,T_b,V_l1_2))) % 187.68/187.60 => 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) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_map__add__dom__app__simps_I3_J,axiom, % 187.68/187.60 ! [V_l1_2,V_l2_2,T_b,V_m_2,T_a] : % 187.68/187.60 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_m_2),c_Map_Odom(T_a,T_b,V_l2_2))) % 187.68/187.60 => 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) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_map__add__dom__app__simps_I1_J,axiom, % 187.68/187.60 ! [V_l1_2,V_l2_2,T_b,V_m_2,T_a] : % 187.68/187.60 ( hBOOL(hAPP(hAPP(c_member(T_a),V_m_2),c_Map_Odom(T_a,T_b,V_l2_2))) % 187.68/187.60 => 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) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_map__add__find__right,axiom, % 187.68/187.60 ! [V_m_2,T_b,V_xx_2,T_a,V_k_2,V_n_2] : % 187.68/187.60 ( hAPP(V_n_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_xx_2) % 187.68/187.60 => 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) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_map__add__None,axiom, % 187.68/187.60 ! [V_k_2,V_n_2,V_m_2,T_a,T_b] : % 187.68/187.60 ( hAPP(c_Map_Omap__add(T_b,T_a,V_m_2,V_n_2),V_k_2) = c_Option_Ooption_ONone(T_a) % 187.68/187.60 <=> ( hAPP(V_n_2,V_k_2) = c_Option_Ooption_ONone(T_a) % 187.68/187.60 & hAPP(V_m_2,V_k_2) = c_Option_Ooption_ONone(T_a) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_map__add__assoc,axiom, % 187.68/187.60 ! [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) ). % 187.68/187.60 % 187.68/187.60 fof(fact_map__add__def,axiom, % 187.68/187.60 ! [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)) ). % 187.68/187.60 % 187.68/187.60 fof(fact_map__add__empty,axiom, % 187.68/187.60 ! [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 ). % 187.68/187.60 % 187.68/187.60 fof(fact_empty__map__add,axiom, % 187.68/187.60 ! [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 ). % 187.68/187.60 % 187.68/187.60 fof(fact_dom__map__add,axiom, % 187.68/187.60 ! [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)) ). % 187.68/187.60 % 187.68/187.60 fof(fact_map__add__upd,axiom, % 187.68/187.60 ! [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)) ). % 187.68/187.60 % 187.68/187.60 fof(fact_inj__on__map__add__dom,axiom, % 187.68/187.60 ! [V_m_H_2,V_m_2,T_b,T_a] : % 187.68/187.60 ( 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)) % 187.68/187.60 <=> 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)) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_map__add__comm,axiom, % 187.68/187.60 ! [V_m2_2,V_m1_2,T_b,T_a] : % 187.68/187.60 ( 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)) % 187.68/187.60 => 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) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_Nitpick_Otimes__frac__def,axiom, % 187.68/187.60 ! [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))) ). % 187.68/187.60 % 187.68/187.60 fof(fact_Nitpick_Oof__frac__def,axiom, % 187.68/187.60 ! [V_q,T_a,T_b] : % 187.68/187.60 ( ( class_Rings_Oinverse(T_b) % 187.68/187.60 & class_Rings_Oring__1(T_b) ) % 187.68/187.60 => 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))) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_Nitpick_Oinverse__frac__def,axiom, % 187.68/187.60 ! [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)) ). % 187.68/187.60 % 187.68/187.60 fof(fact_Nitpick_Ouminus__frac__def,axiom, % 187.68/187.60 ! [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))) ). % 187.68/187.60 % 187.68/187.60 fof(fact_Nitpick_Oless__frac__def,axiom, % 187.68/187.60 ! [V_r_2,V_q_2,T_a] : % 187.68/187.60 ( c_Nitpick_Oless__frac(T_a,V_q_2,V_r_2) % 187.68/187.60 <=> 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))) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_Nitpick_Oless__eq__frac__def,axiom, % 187.68/187.60 ! [V_r_2,V_q_2,T_a] : % 187.68/187.60 ( c_Nitpick_Oless__eq__frac(T_a,V_q_2,V_r_2) % 187.68/187.60 <=> 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))) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_Nitpick_Odenom__def,axiom, % 187.68/187.60 ! [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)) ). % 187.68/187.60 % 187.68/187.60 fof(fact_Nitpick_Onum__def,axiom, % 187.68/187.60 ! [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)) ). % 187.68/187.60 % 187.68/187.60 fof(fact_,axiom, % 187.68/187.60 ! [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) ). % 187.68/187.60 % 187.68/187.60 fof(fact_map__comp__def,axiom, % 187.68/187.60 ! [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)) ). % 187.68/187.60 % 187.68/187.60 fof(fact_map__comp__simps_I2_J,axiom, % 187.68/187.60 ! [V_m1_2,T_b,T_c,V_k_H_2,T_a,V_k_2,V_m2_2] : % 187.68/187.60 ( hAPP(V_m2_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_k_H_2) % 187.68/187.60 => 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) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_map__comp__Some__iff,axiom, % 187.68/187.60 ! [V_v_2,V_k_2,V_m2_2,V_m1_2,T_c,T_a,T_b] : % 187.68/187.60 ( 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) % 187.68/187.60 <=> ? [B_k_H] : % 187.68/187.60 ( hAPP(V_m2_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),B_k_H) % 187.68/187.60 & hAPP(V_m1_2,B_k_H) = hAPP(c_Option_Ooption_OSome(T_a),V_v_2) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_map__comp__simps_I1_J,axiom, % 187.68/187.60 ! [V_m1_2,T_b,T_c,T_a,V_k_2,V_m2_2] : % 187.68/187.60 ( hAPP(V_m2_2,V_k_2) = c_Option_Ooption_ONone(T_a) % 187.68/187.60 => 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) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_map__comp__empty_I1_J,axiom, % 187.68/187.60 ! [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) ). % 187.68/187.60 % 187.68/187.60 fof(fact_map__comp__empty_I2_J,axiom, % 187.68/187.60 ! [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) ). % 187.68/187.60 % 187.68/187.60 fof(fact_map__comp__None__iff,axiom, % 187.68/187.60 ! [V_k_2,V_m2_2,V_m1_2,T_c,T_a,T_b] : % 187.68/187.60 ( 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) % 187.68/187.60 <=> ( hAPP(V_m2_2,V_k_2) = c_Option_Ooption_ONone(T_b) % 187.68/187.60 | ? [B_k_H] : % 187.68/187.60 ( hAPP(V_m2_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),B_k_H) % 187.68/187.60 & hAPP(V_m1_2,B_k_H) = c_Option_Ooption_ONone(T_a) ) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_full__small__int__def,axiom, % 187.68/187.60 ! [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))) ). % 187.68/187.60 % 187.68/187.60 fof(fact_small_H_Osimps,axiom, % 187.68/187.60 ! [V_f_2,V_i_2,V_d_2] : % 187.68/187.60 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2)) % 187.68/187.60 => c_Smallcheck_Osmall_H(V_f_2,V_d_2,V_i_2) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)) ) % 187.68/187.60 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2)) % 187.68/187.60 => 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)) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_small_H_Opsimps,axiom, % 187.68/187.60 ! [V_i_2,V_d_2,V_f_2] : % 187.68/187.60 ( 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)))) % 187.68/187.60 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2)) % 187.68/187.60 => c_Smallcheck_Osmall_H(V_f_2,V_d_2,V_i_2) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)) ) % 187.68/187.60 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2)) % 187.68/187.60 => 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)) ) ) ) ). % 187.68/187.60 % 187.68/187.60 fof(fact_small__int__def,axiom, % 187.68/187.60 ! [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))) ). % 187.68/187.60 % 187.68/187.60 fof(fact_small__prod__def,axiom, % 187.68/187.60 ! [V_d_2,V_f_2,T_a,T_b] : % 187.68/187.60 ( ( class_Smallcheck_Osmall(T_b) % 187.68/187.60 & class_Smallcheck_Osmall(T_a) ) % 187.68/187.60 => 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) ) ). % 187.68/187.60 % 187.68/187.61 fof(fact_small_H_Opinduct,axiom, % 187.68/187.61 ! [V_P_2,V_a2_2,V_a1_2,V_a0_2] : % 187.68/187.61 ( 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)))) % 187.68/187.61 => ( ! [B_f,B_d,B_i] : % 187.68/187.61 ( 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)))) % 187.68/187.61 => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_d),B_i)) % 187.68/187.61 => ( hAPP(B_f,B_i) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)) % 187.68/187.61 => 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)))) ) ) % 187.68/187.61 => hBOOL(hAPP(hAPP(hAPP(V_P_2,B_f),B_d),B_i)) ) ) % 187.68/187.61 => hBOOL(hAPP(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2),V_a2_2)) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_Option_Omap__def,axiom, % 187.68/187.61 ! [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)) ). % 187.68/187.61 % 187.68/187.61 fof(fact_Option_Omap_Oidentity,axiom, % 187.68/187.61 ! [T_a] : hAPP(c_Option_Omap(T_a,T_a),c_COMBI(T_a)) = c_Fun_Oid(tc_Option_Ooption(T_a)) ). % 187.68/187.61 % 187.68/187.61 fof(fact_Option_Omap_Oid,axiom, % 187.68/187.61 ! [T_a] : hAPP(c_Option_Omap(T_a,T_a),c_Fun_Oid(T_a)) = c_Fun_Oid(tc_Option_Ooption(T_a)) ). % 187.68/187.61 % 187.68/187.61 fof(fact_dom__option__map,axiom, % 187.68/187.61 ! [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) ). % 187.68/187.61 % 187.68/187.61 fof(fact_Option_Omap_Ocomp,axiom, % 187.68/187.61 ! [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)) ). % 187.68/187.61 % 187.68/187.61 fof(fact_Option_Omap_Ocompositionality,axiom, % 187.68/187.61 ! [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) ). % 187.68/187.61 % 187.68/187.61 fof(fact_option__map__comp,axiom, % 187.68/187.61 ! [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) ). % 187.68/187.61 % 187.68/187.61 fof(fact_option__map__o__empty,axiom, % 187.68/187.61 ! [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) ). % 187.68/187.61 % 187.68/187.61 fof(fact_option__map__Some,axiom, % 187.68/187.61 ! [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)) ). % 187.68/187.61 % 187.68/187.61 fof(fact_option__map__eq__Some,axiom, % 187.68/187.61 ! [V_y_2,V_xo_2,V_f_2,T_a,T_b] : % 187.68/187.61 ( 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) % 187.68/187.61 <=> ? [B_z] : % 187.68/187.61 ( V_xo_2 = hAPP(c_Option_Ooption_OSome(T_b),B_z) % 187.68/187.61 & hAPP(V_f_2,B_z) = V_y_2 ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_option__map__None,axiom, % 187.68/187.61 ! [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) ). % 187.68/187.61 % 187.68/187.61 fof(fact_option__map__is__None,axiom, % 187.68/187.61 ! [V_opt_2,V_f_2,T_a,T_b] : % 187.68/187.61 ( hAPP(hAPP(c_Option_Omap(T_b,T_a),V_f_2),V_opt_2) = c_Option_Ooption_ONone(T_a) % 187.68/187.61 <=> V_opt_2 = c_Option_Ooption_ONone(T_b) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_option__map__o__map__upd,axiom, % 187.68/187.61 ! [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))) ). % 187.68/187.61 % 187.68/187.61 fof(fact_finite__range__map__of__map__add,axiom, % 187.68/187.61 ! [V_l_2,V_f_2,T_b,T_a] : % 187.68/187.61 ( 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))))) % 187.68/187.61 => 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))))) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_setprod__pos,axiom, % 187.68/187.61 ! [V_f_2,V_A_2,T_a,T_b] : % 187.68/187.61 ( class_Rings_Olinordered__semidom(T_b) % 187.68/187.61 => ( ! [B_x] : % 187.68/187.61 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 187.68/187.61 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(V_f_2,B_x))) ) % 187.68/187.61 => 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))) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_finite__dom__map__of,axiom, % 187.68/187.61 ! [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)))) ). % 187.68/187.61 % 187.68/187.61 fof(fact_finite__range__map__of,axiom, % 187.68/187.61 ! [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))))) ). % 187.68/187.61 % 187.68/187.61 fof(fact_map__add__map__of__foldr,axiom, % 187.68/187.61 ! [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) ). % 187.68/187.61 % 187.68/187.61 fof(fact_map__of__mapk__SomeI,axiom, % 187.68/187.61 ! [V_x_2,V_k_2,V_t_2,T_c,V_f_2,T_b,T_a] : % 187.68/187.61 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 187.68/187.61 => ( 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) % 187.68/187.61 => 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) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_inj__mapI,axiom, % 187.68/187.61 ! [V_f_2,T_b,T_a] : % 187.68/187.61 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 187.68/187.61 => 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))) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_foldr__map,axiom, % 187.68/187.61 ! [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) ). % 187.68/187.61 % 187.68/187.61 fof(fact_map__map,axiom, % 187.68/187.61 ! [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) ). % 187.68/187.61 % 187.68/187.61 fof(fact_List_Omap_Ocompositionality,axiom, % 187.68/187.61 ! [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) ). % 187.68/187.61 % 187.68/187.61 fof(fact_map__comp__map,axiom, % 187.68/187.61 ! [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)) ). % 187.68/187.61 % 187.68/187.61 fof(fact_List_Omap_Ocomp,axiom, % 187.68/187.61 ! [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)) ). % 187.68/187.61 % 187.68/187.61 fof(fact_List_Omap_Oid,axiom, % 187.68/187.61 ! [T_a] : hAPP(c_List_Omap(T_a,T_a),c_Fun_Oid(T_a)) = c_Fun_Oid(tc_List_Olist(T_a)) ). % 187.68/187.61 % 187.68/187.61 fof(fact_List_Omap_Oidentity,axiom, % 187.68/187.61 ! [T_a] : hAPP(c_List_Omap(T_a,T_a),c_COMBI(T_a)) = c_Fun_Oid(tc_List_Olist(T_a)) ). % 187.68/187.61 % 187.68/187.61 fof(fact_map__ident,axiom, % 187.68/187.61 ! [V_xs_2,T_a] : hAPP(hAPP(c_List_Omap(T_a,T_a),c_COMBI(T_a)),V_xs_2) = V_xs_2 ). % 187.68/187.61 % 187.68/187.61 fof(fact_map__injective,axiom, % 187.68/187.61 ! [V_ys_2,V_xs_2,V_f_2,T_a,T_b] : % 187.68/187.61 ( 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) % 187.68/187.61 => ( c_Fun_Oinj__on(T_b,T_a,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 187.68/187.61 => V_xs_2 = V_ys_2 ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_inj__mapD,axiom, % 187.68/187.61 ! [V_f_2,T_b,T_a] : % 187.68/187.61 ( 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))) % 187.68/187.61 => c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_inj__map__eq__map,axiom, % 187.68/187.61 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_a] : % 187.68/187.61 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 187.68/187.61 => ( 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) % 187.68/187.61 <=> V_xs_2 = V_ys_2 ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_inj__map,axiom, % 187.68/187.61 ! [V_f_2,T_b,T_a] : % 187.68/187.61 ( 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))) % 187.68/187.61 <=> c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_map__of__map,axiom, % 187.68/187.61 ! [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)) ). % 187.68/187.61 % 187.68/187.61 fof(fact_map__of__map__restrict,axiom, % 187.68/187.61 ! [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)) ). % 187.68/187.61 % 187.68/187.61 fof(fact_body__def,axiom, % 187.68/187.61 c_Com_Obody = hAPP(c_Map_Omap__of(tc_Com_Opname,tc_Com_Ocom),c_Com_Obodies) ). % 187.68/187.61 % 187.68/187.61 fof(fact_finite__set,axiom, % 187.68/187.61 ! [V_xs_2,T_a] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_List_Oset(T_a),V_xs_2))) ). % 187.68/187.61 % 187.68/187.61 fof(fact_set__map,axiom, % 187.68/187.61 ! [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)) ). % 187.68/187.61 % 187.68/187.61 fof(fact_map__eq__conv,axiom, % 187.68/187.61 ! [V_g_2,V_xs_2,V_f_2,T_a,T_b] : % 187.68/187.61 ( 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) % 187.68/187.61 <=> ! [B_x] : % 187.68/187.61 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 187.68/187.61 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_infinite__UNIV__listI,axiom, % 187.68/187.61 ! [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)))) ). % 187.68/187.61 % 187.68/187.61 fof(fact_WT__bodies__def,axiom, % 187.68/187.61 ( c_Com_OWT__bodies % 187.68/187.61 <=> ! [B_x] : % 187.68/187.61 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Com_Opname,tc_Com_Ocom)),B_x),hAPP(c_List_Oset(tc_prod(tc_Com_Opname,tc_Com_Ocom)),c_Com_Obodies))) % 187.68/187.61 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(tc_Com_Opname,tc_Com_Ocom,tc_HOL_Obool),hAPP(c_COMBK(tc_fun(tc_Com_Ocom,tc_HOL_Obool),tc_Com_Opname),c_Com_OWT)),B_x)) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_inj__on__map__eq__map,axiom, % 187.68/187.61 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_a] : % 187.68/187.61 ( 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))) % 187.68/187.61 => ( 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) % 187.68/187.61 <=> V_xs_2 = V_ys_2 ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_map__inj__on,axiom, % 187.68/187.61 ! [V_ys_2,V_xs_2,V_f_2,T_a,T_b] : % 187.68/187.61 ( 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) % 187.68/187.61 => ( 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))) % 187.68/187.61 => V_xs_2 = V_ys_2 ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_map__fun__upd,axiom, % 187.68/187.61 ! [V_v_2,V_f_2,T_b,V_xs_2,V_y_2,T_a] : % 187.68/187.61 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 187.68/187.61 => 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) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_inj__on__mapI,axiom, % 187.68/187.61 ! [V_A_2,V_f_2,T_b,T_a] : % 187.68/187.61 ( 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))) % 187.68/187.61 => 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) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_map__of__eq__dom,axiom, % 187.68/187.61 ! [V_ys_2,V_xs_2,T_b,T_a] : % 187.68/187.61 ( hAPP(c_Map_Omap__of(T_a,T_b),V_xs_2) = hAPP(c_Map_Omap__of(T_a,T_b),V_ys_2) % 187.68/187.61 => 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)) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_map__of__SomeD,axiom, % 187.68/187.61 ! [V_y_2,V_k_2,V_xs_2,T_a,T_b] : % 187.68/187.61 ( 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) % 187.68/187.61 => 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))) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_map__of__is__SomeD,axiom, % 187.68/187.61 ! [V_y_2,V_x_2,V_xys_2,T_a,T_b] : % 187.68/187.61 ( 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) % 187.68/187.61 => 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))) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_dom__map__of__conv__image__fst,axiom, % 187.68/187.61 ! [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)) ). % 187.68/187.61 % 187.68/187.61 fof(fact_map__of__eq__None__iff,axiom, % 187.68/187.61 ! [V_x_2,V_xys_2,T_a,T_b] : % 187.68/187.61 ( hAPP(hAPP(c_Map_Omap__of(T_b,T_a),V_xys_2),V_x_2) = c_Option_Ooption_ONone(T_a) % 187.68/187.61 <=> ~ 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)))) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_map__of__map__keys,axiom, % 187.68/187.61 ! [V_m_2,T_b,V_xs_2,T_a] : % 187.68/187.61 ( hAPP(c_List_Oset(T_a),V_xs_2) = c_Map_Odom(T_a,T_b,V_m_2) % 187.68/187.61 => 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 ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_ran__distinct,axiom, % 187.68/187.61 ! [V_al_2,T_b,T_a] : % 187.68/187.61 ( 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))) % 187.68/187.61 => 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)) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_set__map__of__compr,axiom, % 187.68/187.61 ! [V_xs_2,T_b,T_a] : % 187.68/187.61 ( 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))) % 187.68/187.61 => 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)))) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_distinct__map,axiom, % 187.68/187.61 ! [V_xs_2,V_f_2,T_b,T_a] : % 187.68/187.61 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2))) % 187.68/187.61 <=> ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 187.68/187.61 & c_Fun_Oinj__on(T_b,T_a,V_f_2,hAPP(c_List_Oset(T_b),V_xs_2)) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_map__of__inject__set,axiom, % 187.68/187.61 ! [V_ys_2,V_xs_2,T_b,T_a] : % 187.68/187.61 ( 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))) % 187.68/187.61 => ( 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))) % 187.68/187.61 => ( hAPP(c_Map_Omap__of(T_a,T_b),V_xs_2) = hAPP(c_Map_Omap__of(T_a,T_b),V_ys_2) % 187.68/187.61 <=> 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) ) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_Some__eq__map__of__iff,axiom, % 187.68/187.61 ! [V_x_2,V_y_2,V_xys_2,T_b,T_a] : % 187.68/187.61 ( 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))) % 187.68/187.61 => ( 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) % 187.68/187.61 <=> 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))) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_map__of__eq__Some__iff,axiom, % 187.68/187.61 ! [V_y_2,V_x_2,V_xys_2,T_b,T_a] : % 187.68/187.61 ( 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))) % 187.68/187.61 => ( 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) % 187.68/187.61 <=> 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))) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_map__of__is__SomeI,axiom, % 187.68/187.61 ! [V_y_2,V_x_2,V_xys_2,T_b,T_a] : % 187.68/187.61 ( 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))) % 187.68/187.61 => ( 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))) % 187.68/187.61 => 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) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_greaterThanLessThan__upto,axiom, % 187.68/187.61 ! [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)))) ). % 187.68/187.61 % 187.68/187.61 fof(fact_weak__map__of__SomeI,axiom, % 187.68/187.61 ! [V_l_2,V_x_2,V_k_2,T_b,T_a] : % 187.68/187.61 ( 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))) % 187.68/187.61 => ? [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) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_set__upto,axiom, % 187.68/187.61 ! [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) ). % 187.68/187.61 % 187.68/187.61 fof(fact_atLeastAtMost__upto,axiom, % 187.68/187.61 ! [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)) ). % 187.68/187.61 % 187.68/187.61 fof(fact_distinct__upto,axiom, % 187.68/187.61 ! [V_j,V_i] : hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(V_i,V_j))) ). % 187.68/187.61 % 187.68/187.61 fof(fact_atLeastLessThan__upto,axiom, % 187.68/187.61 ! [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)))) ). % 187.68/187.61 % 187.68/187.61 fof(fact_greaterThanAtMost__upto,axiom, % 187.68/187.61 ! [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)) ). % 187.68/187.61 % 187.68/187.61 fof(fact_nat__list__def,axiom, % 187.68/187.61 ! [V_l_2] : % 187.68/187.61 ( c_List_Onat__list(V_l_2) % 187.68/187.61 <=> c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),V_l_2)) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_set__remove1__eq,axiom, % 187.68/187.61 ! [V_x_2,V_xs_2,T_a] : % 187.68/187.61 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 187.68/187.61 => 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)))) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_in__set__remove1,axiom, % 187.68/187.61 ! [V_xs_2,T_a,V_b_2,V_a_2] : % 187.68/187.61 ( V_a_2 != V_b_2 % 187.68/187.61 => ( 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)))) % 187.68/187.61 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_notin__set__remove1,axiom, % 187.68/187.61 ! [V_y_2,V_xs_2,V_x_2,T_a] : % 187.68/187.61 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 187.68/187.61 => ~ 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)))) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_remove1__idem,axiom, % 187.68/187.61 ! [V_xs_2,V_x_2,T_a] : % 187.68/187.61 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 187.68/187.61 => c_List_Oremove1(T_a,V_x_2,V_xs_2) = V_xs_2 ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_remove1__commute,axiom, % 187.68/187.61 ! [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)) ). % 187.68/187.61 % 187.68/187.61 fof(fact_distinct__remove1,axiom, % 187.68/187.61 ! [V_x,V_xs,T_a] : % 187.68/187.61 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 187.68/187.61 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oremove1(T_a,V_x,V_xs))) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_set__remove1__subset,axiom, % 187.68/187.61 ! [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))) ). % 187.68/187.61 % 187.68/187.61 fof(fact_sorted__list__of__set__remove,axiom, % 187.68/187.61 ! [V_x_2,V_A_2,T_a] : % 187.68/187.61 ( class_Orderings_Olinorder(T_a) % 187.68/187.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.61 => 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)) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_map__of__zip__map,axiom, % 187.68/187.61 ! [V_f_2,T_b,V_xs_2,V_x_2,T_a] : % 187.68/187.61 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 187.68/187.61 => 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)) ) % 187.68/187.61 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 187.68/187.61 => 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) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_distinct__zipI1,axiom, % 187.68/187.61 ! [V_ys,T_b,V_xs,T_a] : % 187.68/187.61 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 187.68/187.61 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys))) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_distinct__zipI2,axiom, % 187.68/187.61 ! [V_xs,T_b,V_ys,T_a] : % 187.68/187.61 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_ys)) % 187.68/187.61 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_b,T_a)),hAPP(hAPP(c_List_Ozip(T_b,T_a),V_xs),V_ys))) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_zip__same__conv__map,axiom, % 187.68/187.61 ! [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) ). % 187.68/187.61 % 187.68/187.61 fof(fact_zip__map__fst__snd,axiom, % 187.68/187.61 ! [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 ). % 187.68/187.61 % 187.68/187.61 fof(fact_map__zip__map2,axiom, % 187.68/187.61 ! [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)) ). % 187.68/187.61 % 187.68/187.61 fof(fact_map__zip__map,axiom, % 187.68/187.61 ! [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)) ). % 187.68/187.61 % 187.68/187.61 fof(fact_in__set__zipE,axiom, % 187.68/187.61 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_b,T_a] : % 187.68/187.61 ( 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)))) % 187.68/187.61 => ~ ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 187.68/187.61 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),V_ys_2))) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_set__zip__rightD,axiom, % 187.68/187.61 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_b,T_a] : % 187.68/187.61 ( 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)))) % 187.68/187.61 => hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),V_ys_2))) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_set__zip__leftD,axiom, % 187.68/187.61 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_b,T_a] : % 187.68/187.61 ( 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)))) % 187.68/187.61 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_zip__same,axiom, % 187.68/187.61 ! [V_xs_2,V_b_2,V_a_2,T_a] : % 187.68/187.61 ( 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)))) % 187.68/187.61 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 187.68/187.61 & V_a_2 = V_b_2 ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_zip__map2,axiom, % 187.68/187.61 ! [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)) ). % 187.68/187.61 % 187.68/187.61 fof(fact_zip__map1,axiom, % 187.68/187.61 ! [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)) ). % 187.68/187.61 % 187.68/187.61 fof(fact_zip__map__map,axiom, % 187.68/187.61 ! [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)) ). % 187.68/187.61 % 187.68/187.61 fof(fact_sorted__list__of__set__insert,axiom, % 187.68/187.61 ! [V_x_2,V_A_2,T_a] : % 187.68/187.61 ( class_Orderings_Olinorder(T_a) % 187.68/187.61 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.61 => 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)))))) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_map__of__zip__upd,axiom, % 187.68/187.61 ! [V_z_2,V_y_2,V_x_2,V_zs_2,V_xs_2,T_b,V_ys_2,T_a] : % 187.68/187.61 ( 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) % 187.68/187.61 => ( 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) % 187.68/187.61 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 187.68/187.61 => ( 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)) % 187.68/187.61 => 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)) ) ) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_length__zip,axiom, % 187.68/187.61 ! [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)) ). % 187.68/187.61 % 187.68/187.61 fof(fact_set__insort,axiom, % 187.68/187.61 ! [V_xs_2,V_x_2,V_f_2,T_a,T_b] : % 187.68/187.61 ( class_Orderings_Olinorder(T_b) % 187.68/187.61 => 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)) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_lexn__length,axiom, % 187.68/187.61 ! [V_n_2,V_r_2,V_ys_2,V_xs_2,T_a] : % 187.68/187.61 ( 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))) % 187.68/187.61 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = V_n_2 % 187.68/187.61 & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2) = V_n_2 ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_insort__left__comm,axiom, % 187.68/187.61 ! [V_xs_2,V_y_2,V_x_2,T_a] : % 187.68/187.61 ( class_Orderings_Olinorder(T_a) % 187.68/187.61 => 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)) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_insort__key__left__comm,axiom, % 187.68/187.61 ! [V_xs_2,T_b,V_y_2,V_x_2,V_f_2,T_a] : % 187.68/187.61 ( class_Orderings_Olinorder(T_a) % 187.68/187.61 => ( hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2) % 187.68/187.61 => 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)) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_neq__if__length__neq,axiom, % 187.68/187.61 ! [V_ys,V_xs,T_a] : % 187.68/187.61 ( 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) % 187.68/187.61 => V_xs != V_ys ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_length__insort,axiom, % 187.68/187.61 ! [V_xs_2,V_x_2,V_f_2,T_a,T_b] : % 187.68/187.61 ( class_Orderings_Olinorder(T_b) % 187.68/187.61 => 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)) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_fun__left__comm__insort,axiom, % 187.68/187.61 ! [T_a] : % 187.68/187.61 ( class_Orderings_Olinorder(T_a) % 187.68/187.61 => 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))) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_length__map,axiom, % 187.68/187.61 ! [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) ). % 187.68/187.61 % 187.68/187.61 fof(fact_map__eq__imp__length__eq,axiom, % 187.68/187.61 ! [V_ys_2,V_g_2,T_c,V_xs_2,V_f_2,T_a,T_b] : % 187.68/187.61 ( 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) % 187.68/187.61 => 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) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_remove1__insort,axiom, % 187.68/187.61 ! [V_xs_2,V_x_2,T_a] : % 187.68/187.61 ( class_Orderings_Olinorder(T_a) % 187.68/187.61 => 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 ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_card__length,axiom, % 187.68/187.61 ! [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))) ). % 187.68/187.61 % 187.68/187.61 fof(fact_card__distinct,axiom, % 187.68/187.61 ! [V_xs_2,T_a] : % 187.68/187.61 ( 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) % 187.68/187.61 => hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_distinct__card,axiom, % 187.68/187.61 ! [V_xs_2,T_a] : % 187.68/187.61 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 187.68/187.61 => 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) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_map__of__zip__inject,axiom, % 187.68/187.61 ! [V_zs_2,V_xs_2,T_b,V_ys_2,T_a] : % 187.68/187.61 ( 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) % 187.68/187.61 => ( 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) % 187.68/187.61 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 187.68/187.61 => ( 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)) % 187.68/187.61 => V_ys_2 = V_zs_2 ) ) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_map__fst__zip,axiom, % 187.68/187.61 ! [V_ys_2,T_b,V_xs_2,T_a] : % 187.68/187.61 ( 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) % 187.68/187.61 => 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 ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_map__snd__zip,axiom, % 187.68/187.61 ! [V_ys_2,T_b,V_xs_2,T_a] : % 187.68/187.61 ( 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) % 187.68/187.61 => 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 ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_distinct__insort,axiom, % 187.68/187.61 ! [V_xs_2,V_x_2,V_f_2,T_a,T_b] : % 187.68/187.61 ( class_Orderings_Olinorder(T_b) % 187.68/187.61 => ( 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))) % 187.68/187.61 <=> ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 187.68/187.61 & hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_length__pos__if__in__set,axiom, % 187.68/187.61 ! [V_xs_2,V_x_2,T_a] : % 187.68/187.61 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 187.68/187.61 => 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))) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_zip__eq__conv,axiom, % 187.68/187.61 ! [V_zs_2,V_ys_2,T_b,V_xs_2,T_a] : % 187.68/187.61 ( 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) % 187.68/187.61 => ( hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2) = V_zs_2 % 187.68/187.61 <=> ( 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 % 187.68/187.61 & 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 ) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_lenlex__conv,axiom, % 187.68/187.61 ! [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)))))) ). % 187.68/187.61 % 187.68/187.61 fof(fact_lenlex__def,axiom, % 187.68/187.61 ! [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)))) ). % 187.68/187.61 % 187.68/187.61 fof(fact_finite__lists__length__eq,axiom, % 187.68/187.61 ! [V_n_2,V_A_2,T_a] : % 187.68/187.61 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.61 => 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))))) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_list__eq__iff__zip__eq,axiom, % 187.68/187.61 ! [T_a,V_ys_2,V_xs_2] : % 187.68/187.61 ( V_xs_2 = V_ys_2 % 187.68/187.61 <=> ( 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) % 187.68/187.61 & ! [B_x] : % 187.68/187.61 ( 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)))) % 187.68/187.61 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),c_fequal),B_x)) ) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_map__of__zip__is__None,axiom, % 187.68/187.61 ! [V_x_2,V_ys_2,T_b,V_xs_2,T_a] : % 187.68/187.61 ( 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) % 187.68/187.61 => ( 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) % 187.68/187.61 <=> ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_map__of__zip__is__Some,axiom, % 187.68/187.61 ! [V_x_2,V_ys_2,T_b,V_xs_2,T_a] : % 187.68/187.61 ( 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) % 187.68/187.61 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 187.68/187.61 <=> ? [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) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_length__remove1,axiom, % 187.68/187.61 ! [V_xs_2,V_x_2,T_a] : % 187.68/187.61 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 187.68/187.61 => 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)) ) % 187.68/187.61 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 187.68/187.61 => 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) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_dom__map__of__zip,axiom, % 187.68/187.61 ! [V_ys_2,T_b,V_xs_2,T_a] : % 187.68/187.61 ( 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) % 187.68/187.61 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 187.68/187.61 => 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) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_finite__lists__length__le,axiom, % 187.68/187.61 ! [V_n_2,V_A_2,T_a] : % 187.68/187.61 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.61 => 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))))) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_Nitpick_Ocard_H__def,axiom, % 187.68/187.61 ! [V_A_2,T_a] : % 187.68/187.61 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.61 => 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)))) ) % 187.68/187.61 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.61 => c_Nitpick_Ocard_H(T_a,V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_listrel__iff__zip,axiom, % 187.68/187.61 ! [V_r_2,V_ys_2,V_xs_2,T_a] : % 187.68/187.61 ( 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))) % 187.68/187.61 <=> ( 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) % 187.68/187.61 & ! [B_x] : % 187.68/187.61 ( 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)))) % 187.68/187.61 => 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)) ) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_listrel__rtrancl__refl,axiom, % 187.68/187.61 ! [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)))) ). % 187.68/187.61 % 187.68/187.61 fof(fact_listrel__eq__len,axiom, % 187.68/187.61 ! [V_r_2,V_ys_2,V_xs_2,T_a] : % 187.68/187.61 ( 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))) % 187.68/187.61 => 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) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_listrel__mono,axiom, % 187.68/187.61 ! [V_s_2,V_r_2,T_a] : % 187.68/187.61 ( 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)) % 187.68/187.61 => 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))) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_listrel__rtrancl__trans,axiom, % 187.68/187.61 ! [V_zs_2,V_r_2,V_ys_2,V_xs_2,T_a] : % 187.68/187.61 ( 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)))) % 187.68/187.61 => ( 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)))) % 187.68/187.61 => 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)))) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_listrelp__listrel__eq,axiom, % 187.68/187.61 ! [V_xa_2,V_x_2,V_r_2,T_a] : % 187.68/187.61 ( 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) % 187.68/187.61 <=> 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))) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_lexn_Osimps_I2_J,axiom, % 187.68/187.61 ! [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)))))) ). % 187.68/187.61 % 187.68/187.61 fof(fact_impossible__Cons,axiom, % 187.68/187.61 ! [V_x,V_ys,V_xs,T_a] : % 187.68/187.61 ( 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))) % 187.68/187.61 => V_xs != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_ys) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_set__ConsD,axiom, % 187.68/187.61 ! [V_xs_2,V_x_2,V_y_2,T_a] : % 187.68/187.61 ( 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)))) % 187.68/187.61 => ( V_y_2 = V_x_2 % 187.68/187.61 | hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_zip__Cons__Cons,axiom, % 187.68/187.61 ! [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)) ). % 187.68/187.61 % 187.68/187.61 fof(fact_set__subset__Cons,axiom, % 187.68/187.61 ! [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)))) ). % 187.68/187.61 % 187.68/187.61 fof(fact_List_Oset_Osimps_I2_J,axiom, % 187.68/187.61 ! [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)) ). % 187.68/187.61 % 187.68/187.61 fof(fact_foldr_Osimps_I2_J,axiom, % 187.68/187.61 ! [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)) ). % 187.68/187.61 % 187.68/187.61 fof(fact_listrelp_OCons,axiom, % 187.68/187.61 ! [V_ys_2,V_xs_2,T_a,V_y_2,V_x_2,V_r_2] : % 187.68/187.61 ( hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_y_2)) % 187.68/187.61 => ( c_List_Olistrelp(T_a,V_r_2,V_xs_2,V_ys_2) % 187.68/187.61 => 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)) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_listrelp_Oequations_I2_J,axiom, % 187.68/187.61 ! [V_a4_2,V_a2_2,V_a3_2,V_a1_2,V_r_2,T_a] : % 187.68/187.61 ( 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)) % 187.68/187.61 <=> ( hBOOL(hAPP(hAPP(V_r_2,V_a1_2),V_a2_2)) % 187.68/187.61 & c_List_Olistrelp(T_a,V_r_2,V_a3_2,V_a4_2) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_list_Oinject,axiom, % 187.68/187.61 ! [V_list_H_2,V_a_H_2,V_list_2,V_a_2,T_a] : % 187.68/187.61 ( 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) % 187.68/187.61 <=> ( V_a_2 = V_a_H_2 % 187.68/187.61 & V_list_2 = V_list_H_2 ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_not__Cons__self2,axiom, % 187.68/187.61 ! [V_xs,V_x,T_a] : hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) != V_xs ). % 187.68/187.61 % 187.68/187.61 fof(fact_not__Cons__self,axiom, % 187.68/187.61 ! [V_x,T_a,V_xs] : V_xs != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) ). % 187.68/187.61 % 187.68/187.61 fof(fact_map_Osimps_I2_J,axiom, % 187.68/187.61 ! [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)) ). % 187.68/187.61 % 187.68/187.61 fof(fact_remove1_Osimps_I2_J,axiom, % 187.68/187.61 ! [V_xs,T_a,V_y,V_x] : % 187.68/187.61 ( ( V_x = V_y % 187.68/187.61 => c_List_Oremove1(T_a,V_x,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_xs)) = V_xs ) % 187.68/187.61 & ( V_x != V_y % 187.68/187.61 => 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)) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_insort__key_Osimps_I2_J,axiom, % 187.68/187.61 ! [V_ys_2,T_b,V_y_2,V_x_2,V_f_2,T_a] : % 187.68/187.61 ( class_Orderings_Olinorder(T_a) % 187.68/187.61 => ( ( 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))) % 187.68/187.61 => 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)) ) % 187.68/187.61 & ( ~ 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))) % 187.68/187.61 => 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)) ) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_distinct_Osimps_I2_J,axiom, % 187.68/187.61 ! [V_xs_2,V_x_2,T_a] : % 187.68/187.61 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))) % 187.68/187.61 <=> ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 187.68/187.61 & hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_map__of__Cons__code_I2_J,axiom, % 187.68/187.61 ! [V_ps,V_v,T_c,T_b,V_k,V_l] : % 187.68/187.61 ( ( V_l = V_k % 187.68/187.61 => 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) ) % 187.68/187.61 & ( V_l != V_k % 187.68/187.61 => 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) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_list_Osize_I4_J,axiom, % 187.68/187.61 ! [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))) ). % 187.68/187.61 % 187.68/187.61 fof(fact_listrel_OCons,axiom, % 187.68/187.61 ! [V_ys_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_a] : % 187.68/187.61 ( 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)) % 187.68/187.61 => ( 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))) % 187.68/187.61 => 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))) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_map__of_Osimps_I2_J,axiom, % 187.68/187.61 ! [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))) ). % 187.68/187.61 % 187.68/187.61 fof(fact_Cons__in__lex,axiom, % 187.68/187.61 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,V_x_2,T_a] : % 187.68/187.61 ( 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))) % 187.68/187.61 <=> ( ( 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)) % 187.68/187.61 & 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) ) % 187.68/187.61 | ( V_x_2 = V_y_2 % 187.68/187.61 & 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))) ) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_listrel__Cons,axiom, % 187.68/187.61 ! [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))))) ). % 187.68/187.61 % 187.68/187.61 fof(fact_set__Cons__def,axiom, % 187.68/187.61 ! [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)))))) ). % 187.68/187.61 % 187.68/187.61 fof(fact_listrel__Cons1,axiom, % 187.68/187.61 ! [V_r_2,V_xs_2,V_ys_2,V_y_2,T_a] : % 187.68/187.61 ( 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))) % 187.68/187.61 => ~ ! [B_y,B_ys] : % 187.68/187.61 ( V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_y),B_ys) % 187.68/187.61 => ( 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)) % 187.68/187.61 => ~ 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))) ) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_listrel__Cons2,axiom, % 187.68/187.61 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,T_a] : % 187.68/187.61 ( 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))) % 187.68/187.61 => ~ ! [B_x,B_xs] : % 187.68/187.61 ( V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_x),B_xs) % 187.68/187.61 => ( 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)) % 187.68/187.61 => ~ 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))) ) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_length__sublist,axiom, % 187.68/187.61 ! [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)))) ). % 187.68/187.61 % 187.68/187.61 fof(fact_pick_Osimps,axiom, % 187.68/187.61 ! [V_xs,V_x,T_a,V_i] : % 187.68/187.61 ( ( 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))) % 187.68/187.61 => 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) ) % 187.68/187.61 & ( ~ 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))) % 187.68/187.61 => 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))) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_distinct__sublistI,axiom, % 187.68/187.61 ! [V_I_2,V_xs_2,T_a] : % 187.68/187.61 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 187.68/187.61 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Osublist(T_a,V_xs_2,V_I_2))) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_notin__set__sublistI,axiom, % 187.68/187.61 ! [V_I_2,V_xs_2,V_x_2,T_a] : % 187.68/187.61 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 187.68/187.61 => ~ 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)))) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_in__set__sublistD,axiom, % 187.68/187.61 ! [V_I_2,V_xs_2,V_x_2,T_a] : % 187.68/187.61 ( 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)))) % 187.68/187.61 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_set__sublist__subset,axiom, % 187.68/187.61 ! [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))) ). % 187.68/187.61 % 187.68/187.61 fof(fact_select__weight__cons__zero,axiom, % 187.68/187.61 ! [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) ). % 187.68/187.61 % 187.68/187.61 fof(fact_pick__member,axiom, % 187.68/187.61 ! [V_xs_2,T_a,V_i_2] : % 187.68/187.61 ( 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)))) % 187.68/187.61 => 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)))) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_listsum__simps_I2_J,axiom, % 187.68/187.61 ! [V_xs,V_x,T_a] : % 187.68/187.61 ( class_Groups_Omonoid__add(T_a) % 187.68/187.61 => 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)) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_listsum__0,axiom, % 187.68/187.61 ! [V_xs_2,T_b,T_a] : % 187.68/187.61 ( class_Groups_Omonoid__add(T_a) % 187.68/187.61 => 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) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_listsum__addf,axiom, % 187.68/187.61 ! [V_xs_2,V_g_2,V_f_2,T_b,T_a] : % 187.68/187.61 ( class_Groups_Ocomm__monoid__add(T_a) % 187.68/187.61 => 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))) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_listsum__mult__const,axiom, % 187.68/187.61 ! [V_xs_2,V_c_2,V_f_2,T_b,T_a] : % 187.68/187.61 ( class_Rings_Osemiring__0(T_a) % 187.68/187.61 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),hAPP(hAPP(c_COMBC(T_b,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),c_Groups_Otimes__class_Otimes(T_a)),V_f_2)),V_c_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2))),V_c_2) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_listsum__const__mult,axiom, % 187.68/187.61 ! [V_xs_2,V_f_2,V_c_2,T_b,T_a] : % 187.68/187.61 ( class_Rings_Osemiring__0(T_a) % 187.68/187.61 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),hAPP(hAPP(c_COMBB(T_a,T_a,T_b),hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2)),V_f_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_c_2),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2))) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_listsum__subtractf,axiom, % 187.68/187.61 ! [V_xs_2,V_g_2,V_f_2,T_b,T_a] : % 187.68/187.61 ( class_Groups_Oab__group__add(T_a) % 187.68/187.61 => 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))) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_listsum__abs,axiom, % 187.68/187.61 ! [V_xs_2,T_a] : % 187.68/187.61 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 187.68/187.61 => 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)))) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_uminus__listsum__map,axiom, % 187.68/187.61 ! [V_xs_2,V_f_2,T_b,T_a] : % 187.68/187.61 ( class_Groups_Oab__group__add(T_a) % 187.68/187.61 => 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)) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_select__weight__def,axiom, % 187.68/187.61 ! [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))) ). % 187.68/187.61 % 187.68/187.61 fof(fact_distinct__listsum__conv__Setsum,axiom, % 187.68/187.61 ! [V_xs_2,T_a] : % 187.68/187.61 ( class_Groups_Ocomm__monoid__add(T_a) % 187.68/187.61 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 187.68/187.61 => 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)) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_listsum__distinct__conv__setsum__set,axiom, % 187.68/187.61 ! [V_f_2,V_xs_2,T_a,T_b] : % 187.68/187.61 ( class_Groups_Ocomm__monoid__add(T_b) % 187.68/187.61 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 187.68/187.61 => 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)) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_interv__listsum__conv__setsum__set__int,axiom, % 187.68/187.61 ! [V_l_2,V_k_2,V_f_2,T_a] : % 187.68/187.61 ( class_Groups_Ocomm__monoid__add(T_a) % 187.68/187.61 => 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))) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_setsum__set__upto__conv__listsum__int,axiom, % 187.68/187.61 ! [V_j_2,V_i_2,V_f_2,T_a] : % 187.68/187.61 ( class_Groups_Ocomm__monoid__add(T_a) % 187.68/187.61 => 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))) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_listsum__triv,axiom, % 187.68/187.61 ! [V_xs_2,V_r_2,T_b,T_a] : % 187.68/187.61 ( class_Rings_Osemiring__1(T_a) % 187.68/187.61 => 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) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_listsum__map__remove1,axiom, % 187.68/187.61 ! [V_f_2,V_xs_2,V_x_2,T_a,T_b] : % 187.68/187.61 ( class_Groups_Ocomm__monoid__add(T_b) % 187.68/187.61 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 187.68/187.61 => 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)))) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_select__weight__member,axiom, % 187.68/187.61 ! [V_s_2,V_xs_2,T_a] : % 187.68/187.61 ( 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)))) % 187.68/187.61 => 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)))) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_Nitpick_Osetsum_H__def,axiom, % 187.68/187.61 ! [V_f_2,V_A_2,T_a,T_b] : % 187.68/187.61 ( class_Groups_Ocomm__monoid__add(T_b) % 187.68/187.61 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.61 => 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))))) ) % 187.68/187.61 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.61 => c_Nitpick_Osetsum_H(T_a,T_b,V_f_2,V_A_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_insort__insert__insort__key,axiom, % 187.68/187.61 ! [V_xs_2,T_b,V_x_2,V_f_2,T_a] : % 187.68/187.61 ( class_Orderings_Olinorder(T_a) % 187.68/187.61 => ( ~ 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)))) % 187.68/187.61 => 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) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_listsum__eq__0__nat__iff__nat,axiom, % 187.68/187.61 ! [V_ns_2] : % 187.68/187.61 ( hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),V_ns_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 187.68/187.61 <=> ! [B_x] : % 187.68/187.61 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2))) % 187.68/187.61 => B_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_distinct__insort__insert,axiom, % 187.68/187.61 ! [V_x_2,V_f_2,V_xs_2,T_a,T_b] : % 187.68/187.61 ( class_Orderings_Olinorder(T_b) % 187.68/187.61 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 187.68/187.61 => 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))) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_insort__insert__triv,axiom, % 187.68/187.61 ! [V_xs_2,V_x_2,T_a] : % 187.68/187.61 ( class_Orderings_Olinorder(T_a) % 187.68/187.61 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 187.68/187.61 => c_List_Olinorder__class_Oinsort__insert__key(T_a,T_a,c_COMBI(T_a),V_x_2,V_xs_2) = V_xs_2 ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_set__insort__insert,axiom, % 187.68/187.61 ! [V_xs_2,V_x_2,T_a] : % 187.68/187.61 ( class_Orderings_Olinorder(T_a) % 187.68/187.61 => 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)) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_insort__insert__key__triv,axiom, % 187.68/187.61 ! [V_xs_2,T_b,V_x_2,V_f_2,T_a] : % 187.68/187.61 ( class_Orderings_Olinorder(T_a) % 187.68/187.61 => ( 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)))) % 187.68/187.61 => c_List_Olinorder__class_Oinsort__insert__key(T_b,T_a,V_f_2,V_x_2,V_xs_2) = V_xs_2 ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_insort__insert__insort,axiom, % 187.68/187.61 ! [V_xs_2,V_x_2,T_a] : % 187.68/187.61 ( class_Orderings_Olinorder(T_a) % 187.68/187.61 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 187.68/187.61 => 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) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_lexord__cons__cons,axiom, % 187.68/187.61 ! [V_r_2,V_y_2,V_b_2,V_x_2,V_a_2,T_a] : % 187.68/187.61 ( 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))) % 187.68/187.61 <=> ( 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)) % 187.68/187.61 | ( V_a_2 = V_b_2 % 187.68/187.61 & 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))) ) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_set__zip,axiom, % 187.68/187.61 ! [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)))))) ). % 187.68/187.61 % 187.68/187.61 fof(fact_nth__zip,axiom, % 187.68/187.61 ! [V_ys,T_b,V_xs,T_a,V_i] : % 187.68/187.61 ( 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))) % 187.68/187.61 => ( 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))) % 187.68/187.61 => 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)) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_elem__le__listsum__nat,axiom, % 187.68/187.61 ! [V_ns,V_k] : % 187.68/187.61 ( 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))) % 187.68/187.61 => 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))) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_nth_Osimps,axiom, % 187.68/187.61 ! [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) ). % 187.68/187.61 % 187.68/187.61 fof(fact_nth__Cons__Suc,axiom, % 187.68/187.61 ! [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) ). % 187.68/187.61 % 187.68/187.61 fof(fact_nth__Cons__0,axiom, % 187.68/187.61 ! [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 ). % 187.68/187.61 % 187.68/187.61 fof(fact_list__eq__iff__nth__eq,axiom, % 187.68/187.61 ! [T_a,V_ys_2,V_xs_2] : % 187.68/187.61 ( V_xs_2 = V_ys_2 % 187.68/187.61 <=> ( 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) % 187.68/187.61 & ! [B_i] : % 187.68/187.61 ( 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))) % 187.68/187.61 => hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i) = hAPP(hAPP(c_List_Onth(T_a),V_ys_2),B_i) ) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_all__set__conv__all__nth,axiom, % 187.68/187.61 ! [V_P_2,V_xs_2,T_a] : % 187.68/187.61 ( ! [B_x] : % 187.68/187.61 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 187.68/187.61 => hBOOL(hAPP(V_P_2,B_x)) ) % 187.68/187.61 <=> ! [B_i] : % 187.68/187.61 ( 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))) % 187.68/187.61 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i))) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_nth__map,axiom, % 187.68/187.61 ! [V_f_2,T_b,V_xs_2,T_a,V_n_2] : % 187.68/187.61 ( 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))) % 187.68/187.61 => 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)) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_distinct__conv__nth,axiom, % 187.68/187.61 ! [V_xs_2,T_a] : % 187.68/187.61 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 187.68/187.61 <=> ! [B_i] : % 187.68/187.61 ( 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))) % 187.68/187.61 => ! [B_j] : % 187.68/187.61 ( 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))) % 187.68/187.61 => ( B_i != B_j % 187.68/187.61 => hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i) != hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_j) ) ) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_nth__eq__iff__index__eq,axiom, % 187.68/187.61 ! [V_j_2,V_i_2,V_xs_2,T_a] : % 187.68/187.61 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 187.68/187.61 => ( 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))) % 187.68/187.61 => ( 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))) % 187.68/187.61 => ( 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) % 187.68/187.61 <=> V_i_2 = V_j_2 ) ) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_in__set__conv__nth,axiom, % 187.68/187.61 ! [V_xs_2,V_x_2,T_a] : % 187.68/187.61 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 187.68/187.61 <=> ? [B_i] : % 187.68/187.61 ( 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))) % 187.68/187.61 & hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i) = V_x_2 ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_nth__mem,axiom, % 187.68/187.61 ! [V_xs_2,T_a,V_n_2] : % 187.68/187.61 ( 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))) % 187.68/187.61 => 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))) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_nth__Cons_H,axiom, % 187.68/187.61 ! [V_xs,V_x,T_a,V_n] : % 187.68/187.61 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 187.68/187.61 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),V_n) = V_x ) % 187.68/187.61 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 187.68/187.61 => 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))) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_set__conv__nth,axiom, % 187.68/187.61 ! [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))))) ). % 187.68/187.61 % 187.68/187.61 fof(fact_nth__Cons__number__of,axiom, % 187.68/187.61 ! [V_xs,V_x,T_a,V_v] : % 187.68/187.61 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 187.68/187.61 => 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 ) % 187.68/187.61 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 187.68/187.61 => 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))) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_listsum__setsum__nth,axiom, % 187.68/187.61 ! [V_xs_2,T_a] : % 187.68/187.61 ( class_Groups_Ocomm__monoid__add(T_a) % 187.68/187.61 => 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))) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_set__sublist,axiom, % 187.68/187.61 ! [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))))) ). % 187.68/187.61 % 187.68/187.61 fof(fact_lexord__lex,axiom, % 187.68/187.61 ! [V_r_2,V_y_2,V_x_2,T_a] : % 187.68/187.61 ( 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))) % 187.68/187.61 <=> ( 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))) % 187.68/187.61 & 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) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_listrel__iff__nth,axiom, % 187.68/187.61 ! [V_r_2,V_ys_2,V_xs_2,T_a] : % 187.68/187.61 ( 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))) % 187.68/187.61 <=> ( 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) % 187.68/187.61 & ! [B_n] : % 187.68/187.61 ( 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))) % 187.68/187.61 => 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)) ) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_lexord__take__index__conv,axiom, % 187.68/187.61 ! [V_r_2,V_y_2,V_x_2,T_a] : % 187.68/187.61 ( 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))) % 187.68/187.61 <=> ( ( 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))) % 187.68/187.61 & 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 ) % 187.68/187.61 | ? [B_i] : % 187.68/187.61 ( 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)))) % 187.68/187.61 & hAPP(hAPP(c_List_Otake(T_a),B_i),V_x_2) = hAPP(hAPP(c_List_Otake(T_a),B_i),V_y_2) % 187.68/187.61 & 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)) ) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_pick__same,axiom, % 187.68/187.61 ! [V_xs_2,T_a,V_l_2] : % 187.68/187.61 ( 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))) % 187.68/187.61 => 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) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_in__set__takeD,axiom, % 187.68/187.61 ! [V_xs_2,V_n_2,V_x_2,T_a] : % 187.68/187.61 ( 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)))) % 187.68/187.61 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_nth__take,axiom, % 187.68/187.61 ! [V_xs,T_a,V_n,V_i] : % 187.68/187.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_n)) % 187.68/187.61 => 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) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_set__take__subset,axiom, % 187.68/187.61 ! [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))) ). % 187.68/187.61 % 187.68/187.61 fof(fact_take__all,axiom, % 187.68/187.61 ! [V_n,V_xs,T_a] : % 187.68/187.61 ( 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)) % 187.68/187.61 => hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs) = V_xs ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_distinct__take,axiom, % 187.68/187.61 ! [V_i,V_xs,T_a] : % 187.68/187.61 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 187.68/187.61 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs))) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_take__take,axiom, % 187.68/187.61 ! [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) ). % 187.68/187.61 % 187.68/187.61 fof(fact_times__code__numeral__code,axiom, % 187.68/187.61 ! [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)) ). % 187.68/187.61 % 187.68/187.61 fof(fact_Code__Numeral_Oof__nat__inject,axiom, % 187.68/187.61 ! [V_m_2,V_n_2] : % 187.68/187.61 ( hAPP(c_Code__Numeral_Oof__nat,V_n_2) = hAPP(c_Code__Numeral_Oof__nat,V_m_2) % 187.68/187.61 <=> V_n_2 = V_m_2 ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_Code__Numeral_Oof__nat__code,axiom, % 187.68/187.61 c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral) ). % 187.68/187.61 % 187.68/187.61 fof(fact_zero__code__numeral__def,axiom, % 187.68/187.61 c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ). % 187.68/187.61 % 187.68/187.61 fof(fact_take__zip,axiom, % 187.68/187.61 ! [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)) ). % 187.68/187.61 % 187.68/187.61 fof(fact_length__take,axiom, % 187.68/187.61 ! [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) ). % 187.68/187.61 % 187.68/187.61 fof(fact_take__Suc__Cons,axiom, % 187.68/187.61 ! [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)) ). % 187.68/187.61 % 187.68/187.61 fof(fact_sublist__upt__eq__take,axiom, % 187.68/187.61 ! [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) ). % 187.68/187.61 % 187.68/187.61 fof(fact_take__map,axiom, % 187.68/187.61 ! [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)) ). % 187.68/187.61 % 187.68/187.61 fof(fact_one__code__numeral__def,axiom, % 187.68/187.61 c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ). % 187.68/187.61 % 187.68/187.61 fof(fact_less__code__numeral__code,axiom, % 187.68/187.61 ! [V_m_2,V_n_2] : % 187.68/187.61 ( 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))) % 187.68/187.61 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_code__numeral_Oof__nat__inject,axiom, % 187.68/187.61 ! [V_y_2,V_x_2] : % 187.68/187.61 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_x_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) % 187.68/187.61 => ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) % 187.68/187.61 => ( hAPP(c_Code__Numeral_Oof__nat,V_x_2) = hAPP(c_Code__Numeral_Oof__nat,V_y_2) % 187.68/187.61 <=> V_x_2 = V_y_2 ) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_number__of__code__numeral__def,axiom, % 187.68/187.61 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) ). % 187.68/187.61 % 187.68/187.61 fof(fact_set__take__subset__set__take,axiom, % 187.68/187.61 ! [V_xs_2,T_a,V_n_2,V_m_2] : % 187.68/187.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 187.68/187.61 => 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)))) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_plus__code__numeral__code,axiom, % 187.68/187.61 ! [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)) ). % 187.68/187.61 % 187.68/187.61 fof(fact_less__eq__code__numeral__code,axiom, % 187.68/187.61 ! [V_m_2,V_n_2] : % 187.68/187.61 ( 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))) % 187.68/187.61 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_code__numeral__not__eq__zero,axiom, % 187.68/187.61 ! [V_i_2] : % 187.68/187.61 ( V_i_2 != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 187.68/187.61 <=> 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)) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_listsum__update__nat,axiom, % 187.68/187.61 ! [V_n,V_ns,V_k] : % 187.68/187.61 ( 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))) % 187.68/187.61 => 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)) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_distinct__list__update,axiom, % 187.68/187.61 ! [V_i_2,V_a_2,V_xs_2,T_a] : % 187.68/187.61 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 187.68/187.61 => ( ~ 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)))))) % 187.68/187.61 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),V_i_2),V_a_2))) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_nth__list__update__neq,axiom, % 187.68/187.61 ! [V_x,V_xs,T_a,V_j,V_i] : % 187.68/187.61 ( V_i != V_j % 187.68/187.61 => 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) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_list__update__id,axiom, % 187.68/187.61 ! [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 ). % 187.68/187.61 % 187.68/187.61 fof(fact_list__update__beyond,axiom, % 187.68/187.61 ! [V_x,V_i,V_xs,T_a] : % 187.68/187.61 ( 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)) % 187.68/187.61 => hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x) = V_xs ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_length__list__update,axiom, % 187.68/187.61 ! [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) ). % 187.68/187.61 % 187.68/187.61 fof(fact_map__update,axiom, % 187.68/187.61 ! [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)) ). % 187.68/187.61 % 187.68/187.61 fof(fact_zip__update,axiom, % 187.68/187.61 ! [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)) ). % 187.68/187.61 % 187.68/187.61 fof(fact_update__zip,axiom, % 187.68/187.61 ! [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))) ). % 187.68/187.61 % 187.68/187.61 fof(fact_list__update_Osimps_I2_J,axiom, % 187.68/187.61 ! [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) ). % 187.68/187.61 % 187.68/187.61 fof(fact_list__update__code_I3_J,axiom, % 187.68/187.61 ! [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)) ). % 187.68/187.61 % 187.68/187.61 fof(fact_list__update__code_I2_J,axiom, % 187.68/187.61 ! [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) ). % 187.68/187.61 % 187.68/187.61 fof(fact_list__update__swap,axiom, % 187.68/187.61 ! [V_x_H,V_x,V_xs,T_a,V_i_H,V_i] : % 187.68/187.61 ( V_i != V_i_H % 187.68/187.61 => 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) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_list__update__overwrite,axiom, % 187.68/187.61 ! [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) ). % 187.68/187.61 % 187.68/187.61 fof(fact_set__update__subsetI,axiom, % 187.68/187.61 ! [V_i_2,V_x_2,V_A_2,V_xs_2,T_a] : % 187.68/187.61 ( 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)) % 187.68/187.61 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 187.68/187.61 => 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)) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_set__update__subset__insert,axiom, % 187.68/187.61 ! [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)))) ). % 187.68/187.61 % 187.68/187.61 fof(fact_nth__list__update__eq,axiom, % 187.68/187.61 ! [V_x,V_xs,T_a,V_i] : % 187.68/187.61 ( 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))) % 187.68/187.61 => 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 ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_list__update__same__conv,axiom, % 187.68/187.61 ! [V_x_2,V_xs_2,T_a,V_i_2] : % 187.68/187.61 ( 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))) % 187.68/187.61 => ( hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),V_i_2),V_x_2) = V_xs_2 % 187.68/187.61 <=> hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_i_2) = V_x_2 ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_nth__list__update,axiom, % 187.68/187.61 ! [V_x,V_j,V_xs,T_a,V_i] : % 187.68/187.61 ( 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))) % 187.68/187.61 => ( ( V_i = V_j % 187.68/187.61 => 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 ) % 187.68/187.61 & ( V_i != V_j % 187.68/187.61 => 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) ) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_set__update__memI,axiom, % 187.68/187.61 ! [V_x_2,V_xs_2,T_a,V_n_2] : % 187.68/187.61 ( 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))) % 187.68/187.61 => 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)))) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_map__upd__upds__conv__if,axiom, % 187.68/187.61 ! [V_y_2,V_f_2,V_xs_2,V_ys_2,T_b,V_x_2,T_a] : % 187.68/187.61 ( ( 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)))) % 187.68/187.61 => 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) ) % 187.68/187.61 & ( ~ 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)))) % 187.68/187.61 => 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)) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_select__def,axiom, % 187.68/187.61 ! [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))) ). % 187.68/187.61 % 187.68/187.61 fof(fact_map__upds__apply__nontin,axiom, % 187.68/187.61 ! [V_ys_2,V_f_2,T_b,V_xs_2,V_x_2,T_a] : % 187.68/187.61 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 187.68/187.61 => 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) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_map__add__upds,axiom, % 187.68/187.61 ! [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) ). % 187.68/187.61 % 187.68/187.61 fof(fact_Code__Numeral_Onat__of__inject,axiom, % 187.68/187.61 ! [V_l_2,V_k_2] : % 187.68/187.61 ( hAPP(c_Code__Numeral_Onat__of,V_k_2) = hAPP(c_Code__Numeral_Onat__of,V_l_2) % 187.68/187.61 <=> V_k_2 = V_l_2 ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_code__numeral_Onat__of__inject,axiom, % 187.68/187.61 ! [V_y_2,V_x_2] : % 187.68/187.61 ( hAPP(c_Code__Numeral_Onat__of,V_x_2) = hAPP(c_Code__Numeral_Onat__of,V_y_2) % 187.68/187.61 <=> V_x_2 = V_y_2 ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_nat__of__inverse,axiom, % 187.68/187.61 ! [V_x] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,V_x)) = V_x ). % 187.68/187.61 % 187.68/187.61 fof(fact_of__nat__nat__of,axiom, % 187.68/187.61 ! [V_k] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,V_k)) = V_k ). % 187.68/187.61 % 187.68/187.61 fof(fact_nat__of__of__nat,axiom, % 187.68/187.61 ! [V_n] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,V_n)) = V_n ). % 187.68/187.61 % 187.68/187.61 fof(fact_type__definition__code__numeral,axiom, % 187.68/187.61 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))) ). % 187.68/187.61 % 187.68/187.61 fof(fact_less__code__numeral__def,axiom, % 187.68/187.61 ! [V_m_2,V_n_2] : % 187.68/187.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_n_2),V_m_2)) % 187.68/187.61 <=> 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))) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_nat__of,axiom, % 187.68/187.61 ! [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)))) ). % 187.68/187.61 % 187.68/187.61 fof(fact_nat__of__number,axiom, % 187.68/187.61 ! [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) ). % 187.68/187.61 % 187.68/187.61 fof(fact_int__of__def,axiom, % 187.68/187.61 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) ). % 187.68/187.61 % 187.68/187.61 fof(fact_less__eq__code__numeral__def,axiom, % 187.68/187.61 ! [V_m_2,V_n_2] : % 187.68/187.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_n_2),V_m_2)) % 187.68/187.61 <=> 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))) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_nat__of__code,axiom, % 187.68/187.61 ! [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)) ). % 187.68/187.61 % 187.68/187.61 fof(fact_nat__of__aux__def,axiom, % 187.68/187.61 ! [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) ). % 187.68/187.61 % 187.68/187.61 fof(fact_map__upds__Cons,axiom, % 187.68/187.61 ! [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) ). % 187.68/187.61 % 187.68/187.61 fof(fact_Suc__code__numeral__def,axiom, % 187.68/187.61 ! [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))) ). % 187.68/187.61 % 187.68/187.61 fof(fact_minus__code__numeral__def,axiom, % 187.68/187.61 ! [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))) ). % 187.68/187.61 % 187.68/187.61 fof(fact_of__nat__inverse,axiom, % 187.68/187.61 ! [V_y_2] : % 187.68/187.61 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) % 187.68/187.61 => hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,V_y_2)) = V_y_2 ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_plus__code__numeral__def,axiom, % 187.68/187.61 ! [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))) ). % 187.68/187.61 % 187.68/187.61 fof(fact_div__code__numeral__def,axiom, % 187.68/187.61 ! [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))) ). % 187.68/187.61 % 187.68/187.61 fof(fact_times__code__numeral__def,axiom, % 187.68/187.61 ! [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))) ). % 187.68/187.61 % 187.68/187.61 fof(fact_mod__code__numeral__def,axiom, % 187.68/187.61 ! [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))) ). % 187.68/187.61 % 187.68/187.61 fof(fact_map__upds__list__update2__drop,axiom, % 187.68/187.61 ! [V_y_2,V_m_2,V_ys_2,T_b,V_i_2,V_xs_2,T_a] : % 187.68/187.61 ( 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)) % 187.68/187.61 => ( 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))) % 187.68/187.61 => 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) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_map__upds__twist,axiom, % 187.68/187.61 ! [V_bs_2,V_b_2,V_m_2,T_b,V_as_2,V_a_2,T_a] : % 187.68/187.61 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_List_Oset(T_a),V_as_2))) % 187.68/187.61 => 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)) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_code__numeral__decr,axiom, % 187.68/187.61 ! [V_k] : % 187.68/187.61 ( V_k != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 187.68/187.61 => 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))) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_restrict__map__upds,axiom, % 187.68/187.61 ! [V_m_2,V_D_2,V_ys_2,T_b,V_xs_2,T_a] : % 187.68/187.61 ( 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) % 187.68/187.61 => ( 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)) % 187.68/187.61 => 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) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_dom__map__upds,axiom, % 187.68/187.61 ! [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)) ). % 187.68/187.61 % 187.68/187.61 fof(fact_select__weigth__select,axiom, % 187.68/187.61 ! [T_a,V_xs_2] : % 187.68/187.61 ( V_xs_2 != c_List_Olist_ONil(T_a) % 187.68/187.61 => 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) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_subtract__code__numeral__code,axiom, % 187.68/187.61 ! [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)) ). % 187.68/187.61 % 187.68/187.61 fof(fact_listrel__Nil1,axiom, % 187.68/187.61 ! [V_r_2,V_xs_2,T_a] : % 187.68/187.61 ( 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))) % 187.68/187.61 => V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_listrel__Nil2,axiom, % 187.68/187.61 ! [V_r_2,V_xs_2,T_a] : % 187.68/187.61 ( 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))) % 187.68/187.61 => V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_list__update__code_I1_J,axiom, % 187.68/187.61 ! [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) ). % 187.68/187.61 % 187.68/187.61 fof(fact_list__update_Osimps_I1_J,axiom, % 187.68/187.61 ! [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) ). % 187.68/187.61 % 187.68/187.61 fof(fact_list__update__nonempty,axiom, % 187.68/187.61 ! [V_x_2,V_k_2,V_xs_2,T_a] : % 187.68/187.61 ( hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),V_k_2),V_x_2) = c_List_Olist_ONil(T_a) % 187.68/187.61 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_map__upds__Nil1,axiom, % 187.68/187.61 ! [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 ). % 187.68/187.61 % 187.68/187.61 fof(fact_map__upds__Nil2,axiom, % 187.68/187.61 ! [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 ). % 187.68/187.61 % 187.68/187.61 fof(fact_list_Osize_I3_J,axiom, % 187.68/187.61 ! [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) ). % 187.68/187.61 % 187.68/187.61 fof(fact_length__0__conv,axiom, % 187.68/187.61 ! [V_xs_2,T_a] : % 187.68/187.61 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 187.68/187.61 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_map__is__Nil__conv,axiom, % 187.68/187.61 ! [V_xs_2,V_f_2,T_a,T_b] : % 187.68/187.61 ( hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2) = c_List_Olist_ONil(T_a) % 187.68/187.61 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_map_Osimps_I1_J,axiom, % 187.68/187.61 ! [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) ). % 187.68/187.61 % 187.68/187.61 fof(fact_Nil__is__map__conv,axiom, % 187.68/187.61 ! [V_xs_2,V_f_2,T_b,T_a] : % 187.68/187.61 ( c_List_Olist_ONil(T_a) = hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2) % 187.68/187.61 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_sublist__nil,axiom, % 187.68/187.61 ! [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) ). % 187.68/187.61 % 187.68/187.61 fof(fact_sublist__empty,axiom, % 187.68/187.61 ! [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) ). % 187.68/187.61 % 187.68/187.61 fof(fact_insort__key_Osimps_I1_J,axiom, % 187.68/187.61 ! [V_x_2,V_f_2,T_a,T_b] : % 187.68/187.61 ( class_Orderings_Olinorder(T_b) % 187.68/187.61 => 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)) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_list_Osimps_I2_J,axiom, % 187.68/187.61 ! [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) ). % 187.68/187.61 % 187.68/187.61 fof(fact_list_Osimps_I3_J,axiom, % 187.68/187.61 ! [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) ). % 187.68/187.61 % 187.68/187.61 fof(fact_sorted__list__of__set__empty,axiom, % 187.68/187.61 ! [T_a] : % 187.68/187.61 ( class_Orderings_Olinorder(T_a) % 187.68/187.61 => 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) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_map__of_Osimps_I1_J,axiom, % 187.68/187.61 ! [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) ). % 187.68/187.61 % 187.68/187.61 fof(fact_zip__Nil,axiom, % 187.68/187.61 ! [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)) ). % 187.68/187.61 % 187.68/187.61 fof(fact_zip_Osimps_I1_J,axiom, % 187.68/187.61 ! [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)) ). % 187.68/187.61 % 187.68/187.61 fof(fact_upto__empty,axiom, % 187.68/187.61 ! [V_i,V_j] : % 187.68/187.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j),V_i)) % 187.68/187.61 => c_List_Oupto(V_i,V_j) = c_List_Olist_ONil(tc_Int_Oint) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_foldr_Osimps_I1_J,axiom, % 187.68/187.61 ! [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 ). % 187.68/187.61 % 187.68/187.61 fof(fact_map__of__Cons__code_I1_J,axiom, % 187.68/187.61 ! [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) ). % 187.68/187.61 % 187.68/187.61 fof(fact_remove1_Osimps_I1_J,axiom, % 187.68/187.61 ! [V_x,T_a] : c_List_Oremove1(T_a,V_x,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 187.68/187.61 % 187.68/187.61 fof(fact_distinct_Osimps_I1_J,axiom, % 187.68/187.61 ! [T_a] : hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Olist_ONil(T_a))) ). % 187.68/187.61 % 187.68/187.61 fof(fact_insort__not__Nil,axiom, % 187.68/187.61 ! [V_xs_2,V_a_2,V_f_2,T_a,T_b] : % 187.68/187.61 ( class_Orderings_Olinorder(T_b) % 187.68/187.61 => 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) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_listrelp_Oequations_I1_J,axiom, % 187.68/187.61 ! [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)) ). % 187.68/187.61 % 187.68/187.61 fof(fact_listrelp_ONil,axiom, % 187.68/187.61 ! [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)) ). % 187.68/187.61 % 187.68/187.61 fof(fact_List_Oset_Osimps_I1_J,axiom, % 187.68/187.61 ! [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)) ). % 187.68/187.61 % 187.68/187.61 fof(fact_set__empty2,axiom, % 187.68/187.61 ! [V_xs_2,T_a] : % 187.68/187.61 ( c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = hAPP(c_List_Oset(T_a),V_xs_2) % 187.68/187.61 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_set__empty,axiom, % 187.68/187.61 ! [V_xs_2,T_a] : % 187.68/187.61 ( hAPP(c_List_Oset(T_a),V_xs_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 187.68/187.61 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_listsum__simps_I1_J,axiom, % 187.68/187.61 ! [T_a] : % 187.68/187.61 ( class_Groups_Omonoid__add(T_a) % 187.68/187.61 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),c_List_Olist_ONil(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_take__eq__Nil,axiom, % 187.68/187.61 ! [V_xs_2,V_n_2,T_a] : % 187.68/187.61 ( hAPP(hAPP(c_List_Otake(T_a),V_n_2),V_xs_2) = c_List_Olist_ONil(T_a) % 187.68/187.61 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 187.68/187.61 | V_xs_2 = c_List_Olist_ONil(T_a) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_take__0,axiom, % 187.68/187.61 ! [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) ). % 187.68/187.61 % 187.68/187.61 fof(fact_take__Nil,axiom, % 187.68/187.61 ! [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) ). % 187.68/187.61 % 187.68/187.61 fof(fact_length__greater__0__conv,axiom, % 187.68/187.61 ! [V_xs_2,T_a] : % 187.68/187.61 ( 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))) % 187.68/187.61 <=> V_xs_2 != c_List_Olist_ONil(T_a) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_take__1__Cons,axiom, % 187.68/187.61 ! [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)) ). % 187.68/187.61 % 187.68/187.61 fof(fact_listrel_ONil,axiom, % 187.68/187.61 ! [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))) ). % 187.68/187.61 % 187.68/187.61 fof(fact_lexord__Nil__right,axiom, % 187.68/187.61 ! [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))) ). % 187.68/187.61 % 187.68/187.61 fof(fact_Nil2__notin__lex,axiom, % 187.68/187.61 ! [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))) ). % 187.68/187.61 % 187.68/187.61 fof(fact_Nil__notin__lex,axiom, % 187.68/187.61 ! [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))) ). % 187.68/187.61 % 187.68/187.61 fof(fact_take__Cons,axiom, % 187.68/187.61 ! [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) ). % 187.68/187.61 % 187.68/187.61 fof(fact_upto_Osimps,axiom, % 187.68/187.61 ! [V_j,V_i] : % 187.68/187.61 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j)) % 187.68/187.61 => 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)) ) % 187.68/187.61 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j)) % 187.68/187.61 => c_List_Oupto(V_i,V_j) = c_List_Olist_ONil(tc_Int_Oint) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_sublist__singleton,axiom, % 187.68/187.61 ! [V_x_2,T_a,V_A_2] : % 187.68/187.61 ( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2)) % 187.68/187.61 => 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)) ) % 187.68/187.61 & ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2)) % 187.68/187.61 => 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) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_minus__code__numeral__code,axiom, % 187.68/187.61 ! [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) ). % 187.68/187.61 % 187.68/187.61 fof(fact_subtract__code__numeral__def,axiom, % 187.68/187.61 c_Code__Numeral_Osubtract__code__numeral = c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral) ). % 187.68/187.61 % 187.68/187.61 fof(fact_take__Cons_H,axiom, % 187.68/187.61 ! [V_xs,V_x,T_a,V_n] : % 187.68/187.61 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 187.68/187.61 => 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) ) % 187.68/187.61 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 187.68/187.61 => 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)) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_upto__rec__number__of,axiom, % 187.68/187.61 ! [V_n,V_m] : % 187.68/187.61 ( ( 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))) % 187.68/187.61 => 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))) ) % 187.68/187.61 & ( ~ 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))) % 187.68/187.61 => 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) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_select,axiom, % 187.68/187.61 ! [V_s_2,T_a,V_xs_2] : % 187.68/187.61 ( V_xs_2 != c_List_Olist_ONil(T_a) % 187.68/187.61 => 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))) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_listrel__Nil,axiom, % 187.68/187.61 ! [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))) ). % 187.68/187.61 % 187.68/187.61 fof(fact_set__Cons__sing__Nil,axiom, % 187.68/187.61 ! [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) ). % 187.68/187.61 % 187.68/187.61 fof(fact_take__Cons__number__of,axiom, % 187.68/187.61 ! [V_xs,V_x,T_a,V_v] : % 187.68/187.61 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 187.68/187.61 => 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) ) % 187.68/187.61 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 187.68/187.61 => 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)) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_upto_Opsimps,axiom, % 187.68/187.61 ! [V_j_2,V_i_2] : % 187.68/187.61 ( 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))) % 187.68/187.61 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),V_j_2)) % 187.68/187.61 => 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)) ) % 187.68/187.61 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),V_j_2)) % 187.68/187.61 => c_List_Oupto(V_i_2,V_j_2) = c_List_Olist_ONil(tc_Int_Oint) ) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_anamorph_Osimps,axiom, % 187.68/187.61 ! [V_x_2,V_f_2,T_a,T_b,V_k_2] : % 187.68/187.61 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 187.68/187.61 => 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) ) % 187.68/187.61 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 187.68/187.61 => 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))))),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)) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_listset_Osimps_I1_J,axiom, % 187.68/187.61 ! [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))) ). % 187.68/187.61 % 187.68/187.61 fof(fact_zip__Cons1,axiom, % 187.68/187.61 ! [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) ). % 187.68/187.61 % 187.68/187.61 fof(fact_list_Osimps_I5_J,axiom, % 187.68/187.61 ! [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) ). % 187.68/187.61 % 187.68/187.61 fof(fact_list_Osimps_I4_J,axiom, % 187.68/187.61 ! [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 ). % 187.68/187.61 % 187.68/187.61 fof(fact_listset_Osimps_I2_J,axiom, % 187.68/187.61 ! [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)) ). % 187.68/187.61 % 187.68/187.61 fof(fact_zip__Cons,axiom, % 187.68/187.61 ! [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) ). % 187.68/187.61 % 187.68/187.61 fof(fact_upto_Opinduct,axiom, % 187.68/187.61 ! [V_P_2,V_a1_2,V_a0_2] : % 187.68/187.61 ( 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))) % 187.68/187.61 => ( ! [B_i,B_j] : % 187.68/187.61 ( 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))) % 187.68/187.61 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_i),B_j)) % 187.68/187.61 => 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)) ) % 187.68/187.61 => hBOOL(hAPP(hAPP(V_P_2,B_i),B_j)) ) ) % 187.68/187.61 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_map__upds__append1,axiom, % 187.68/187.61 ! [V_x_2,V_m_2,V_ys_2,T_b,V_xs_2,T_a] : % 187.68/187.61 ( 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))) % 187.68/187.61 => 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)))) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_append__eq__Cons__conv,axiom, % 187.68/187.61 ! [V_xs_2,V_x_2,V_zs_2,V_ys_2,T_a] : % 187.68/187.61 ( 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) % 187.68/187.61 <=> ( ( V_ys_2 = c_List_Olist_ONil(T_a) % 187.68/187.61 & V_zs_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2) ) % 187.68/187.61 | ? [B_ys_H] : % 187.68/187.61 ( V_ys_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),B_ys_H) % 187.68/187.61 & hAPP(hAPP(c_List_Oappend(T_a),B_ys_H),V_zs_2) = V_xs_2 ) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_Cons__eq__append__conv,axiom, % 187.68/187.61 ! [V_zs_2,V_ys_2,V_xs_2,V_x_2,T_a] : % 187.68/187.61 ( 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) % 187.68/187.61 <=> ( ( V_ys_2 = c_List_Olist_ONil(T_a) % 187.68/187.61 & hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2) = V_zs_2 ) % 187.68/187.61 | ? [B_ys_H] : % 187.68/187.61 ( hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),B_ys_H) = V_ys_2 % 187.68/187.61 & V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),B_ys_H),V_zs_2) ) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_append1__eq__conv,axiom, % 187.68/187.61 ! [V_y_2,V_ys_2,V_x_2,V_xs_2,T_a] : % 187.68/187.61 ( 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))) % 187.68/187.61 <=> ( V_xs_2 = V_ys_2 % 187.68/187.61 & V_x_2 = V_y_2 ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_eq__Nil__appendI,axiom, % 187.68/187.61 ! [T_a,V_ys,V_xs] : % 187.68/187.61 ( V_xs = V_ys % 187.68/187.61 => V_xs = hAPP(hAPP(c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_ys) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_append__self__conv2,axiom, % 187.68/187.61 ! [V_ys_2,V_xs_2,T_a] : % 187.68/187.61 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) = V_ys_2 % 187.68/187.61 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_append__self__conv,axiom, % 187.68/187.61 ! [V_ys_2,V_xs_2,T_a] : % 187.68/187.61 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) = V_xs_2 % 187.68/187.61 <=> V_ys_2 = c_List_Olist_ONil(T_a) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_append__is__Nil__conv,axiom, % 187.68/187.61 ! [V_ys_2,V_xs_2,T_a] : % 187.68/187.61 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) = c_List_Olist_ONil(T_a) % 187.68/187.61 <=> ( V_xs_2 = c_List_Olist_ONil(T_a) % 187.68/187.61 & V_ys_2 = c_List_Olist_ONil(T_a) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_self__append__conv2,axiom, % 187.68/187.61 ! [V_xs_2,T_a,V_ys_2] : % 187.68/187.61 ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) % 187.68/187.61 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_self__append__conv,axiom, % 187.68/187.61 ! [V_ys_2,T_a,V_xs_2] : % 187.68/187.61 ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) % 187.68/187.61 <=> V_ys_2 = c_List_Olist_ONil(T_a) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_append__Nil2,axiom, % 187.68/187.61 ! [V_xs,T_a] : hAPP(hAPP(c_List_Oappend(T_a),V_xs),c_List_Olist_ONil(T_a)) = V_xs ). % 187.68/187.61 % 187.68/187.61 fof(fact_Nil__is__append__conv,axiom, % 187.68/187.61 ! [V_ys_2,V_xs_2,T_a] : % 187.68/187.61 ( c_List_Olist_ONil(T_a) = hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) % 187.68/187.61 <=> ( V_xs_2 = c_List_Olist_ONil(T_a) % 187.68/187.61 & V_ys_2 = c_List_Olist_ONil(T_a) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_append__Nil,axiom, % 187.68/187.61 ! [V_ys,T_a] : hAPP(hAPP(c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_ys) = V_ys ). % 187.68/187.61 % 187.68/187.61 fof(fact_listsum__append,axiom, % 187.68/187.61 ! [V_ys,V_xs,T_a] : % 187.68/187.61 ( class_Groups_Omonoid__add(T_a) % 187.68/187.61 => 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)) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_set__append,axiom, % 187.68/187.61 ! [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)) ). % 187.68/187.61 % 187.68/187.61 fof(fact_append__assoc,axiom, % 187.68/187.61 ! [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)) ). % 187.68/187.61 % 187.68/187.61 fof(fact_append__eq__append__conv2,axiom, % 187.68/187.61 ! [V_ts_2,V_zs_2,V_ys_2,V_xs_2,T_a] : % 187.68/187.61 ( 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) % 187.68/187.61 <=> ? [B_us] : % 187.68/187.61 ( ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),V_zs_2),B_us) % 187.68/187.61 & hAPP(hAPP(c_List_Oappend(T_a),B_us),V_ys_2) = V_ts_2 ) % 187.68/187.61 | ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),B_us) = V_zs_2 % 187.68/187.61 & V_ys_2 = hAPP(hAPP(c_List_Oappend(T_a),B_us),V_ts_2) ) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_same__append__eq,axiom, % 187.68/187.61 ! [V_zs_2,V_ys_2,V_xs_2,T_a] : % 187.68/187.61 ( 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) % 187.68/187.61 <=> V_ys_2 = V_zs_2 ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_append__same__eq,axiom, % 187.68/187.61 ! [V_zs_2,V_xs_2,V_ys_2,T_a] : % 187.68/187.61 ( 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) % 187.68/187.61 <=> V_ys_2 = V_zs_2 ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_append__eq__appendI,axiom, % 187.68/187.61 ! [V_us,V_ys,V_zs,V_xs1,V_xs,T_a] : % 187.68/187.61 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_xs1) = V_zs % 187.68/187.61 => ( V_ys = hAPP(hAPP(c_List_Oappend(T_a),V_xs1),V_us) % 187.68/187.61 => hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys) = hAPP(hAPP(c_List_Oappend(T_a),V_zs),V_us) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_map__of__append,axiom, % 187.68/187.61 ! [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)) ). % 187.68/187.61 % 187.68/187.61 fof(fact_foldr__append,axiom, % 187.68/187.61 ! [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)) ). % 187.68/187.61 % 187.68/187.61 fof(fact_map__append,axiom, % 187.68/187.61 ! [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)) ). % 187.68/187.61 % 187.68/187.61 fof(fact_zip__append,axiom, % 187.68/187.61 ! [V_vs,V_ys,V_us,T_b,V_xs,T_a] : % 187.68/187.61 ( 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) % 187.68/187.61 => ( 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) % 187.68/187.61 => 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)) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_length__append,axiom, % 187.68/187.61 ! [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)) ). % 187.68/187.61 % 187.68/187.61 fof(fact_fun__upds__append__drop,axiom, % 187.68/187.61 ! [V_zs_2,V_m_2,V_ys_2,T_b,V_xs_2,T_a] : % 187.68/187.61 ( 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) % 187.68/187.61 => 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) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_fun__upds__append2__drop,axiom, % 187.68/187.61 ! [V_zs_2,V_m_2,V_ys_2,T_b,V_xs_2,T_a] : % 187.68/187.61 ( 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) % 187.68/187.61 => 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) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_append__Cons,axiom, % 187.68/187.61 ! [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)) ). % 187.68/187.61 % 187.68/187.61 fof(fact_Cons__eq__appendI,axiom, % 187.68/187.61 ! [V_zs,V_xs,V_ys,V_xs1,V_x,T_a] : % 187.68/187.61 ( hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs1) = V_ys % 187.68/187.61 => ( V_xs = hAPP(hAPP(c_List_Oappend(T_a),V_xs1),V_zs) % 187.68/187.61 => hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) = hAPP(hAPP(c_List_Oappend(T_a),V_ys),V_zs) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_nth__append__length,axiom, % 187.68/187.61 ! [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 ). % 187.68/187.61 % 187.68/187.61 fof(fact_nth__append__length__plus,axiom, % 187.68/187.61 ! [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) ). % 187.68/187.61 % 187.68/187.61 fof(fact_take__append,axiom, % 187.68/187.61 ! [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)) ). % 187.68/187.61 % 187.68/187.61 fof(fact_list__update__append1,axiom, % 187.68/187.61 ! [V_x,V_ys,V_xs,T_a,V_i] : % 187.68/187.61 ( 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))) % 187.68/187.61 => 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) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_list__update__length,axiom, % 187.68/187.61 ! [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)) ). % 187.68/187.61 % 187.68/187.61 fof(fact_remove1__append,axiom, % 187.68/187.61 ! [V_ys_2,V_xs_2,V_x_2,T_a] : % 187.68/187.61 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 187.68/187.61 => 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) ) % 187.68/187.61 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 187.68/187.61 => 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)) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_lexord__append__leftI,axiom, % 187.68/187.61 ! [V_x_2,V_r_2,V_v_2,V_u_2,T_a] : % 187.68/187.61 ( 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))) % 187.68/187.61 => 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))) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_distinct__append,axiom, % 187.68/187.61 ! [V_ys_2,V_xs_2,T_a] : % 187.68/187.61 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2))) % 187.68/187.61 <=> ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 187.68/187.61 & hBOOL(hAPP(c_List_Odistinct(T_a),V_ys_2)) % 187.68/187.61 & 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)) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_nth__append,axiom, % 187.68/187.61 ! [V_ys,V_xs,T_a,V_n] : % 187.68/187.61 ( ( 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))) % 187.68/187.61 => 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) ) % 187.68/187.61 & ( ~ 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))) % 187.68/187.61 => 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))) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_list__update__append,axiom, % 187.68/187.61 ! [V_x,V_ys,V_xs,T_a,V_n] : % 187.68/187.61 ( ( 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))) % 187.68/187.61 => 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) ) % 187.68/187.61 & ( ~ 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))) % 187.68/187.61 => 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)) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_sublist__append,axiom, % 187.68/187.61 ! [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)))) ). % 187.68/187.61 % 187.68/187.61 fof(fact_lexord__append__left__rightI,axiom, % 187.68/187.61 ! [V_y_2,V_x_2,V_u_2,V_r_2,V_b_2,V_a_2,T_a] : % 187.68/187.61 ( 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)) % 187.68/187.61 => 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))) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_take__Suc__conv__app__nth,axiom, % 187.68/187.61 ! [V_xs,T_a,V_i] : % 187.68/187.61 ( 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))) % 187.68/187.61 => 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))) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_sublist__Cons,axiom, % 187.68/187.61 ! [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)))) ). % 187.68/187.61 % 187.68/187.61 fof(fact_snoc__listrel1__snoc__iff,axiom, % 187.68/187.61 ! [V_r_2,V_y_2,V_ys_2,V_x_2,V_xs_2,T_a] : % 187.68/187.61 ( 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))) % 187.68/187.61 <=> ( ( 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))) % 187.68/187.61 & V_x_2 = V_y_2 ) % 187.68/187.61 | ( V_xs_2 = V_ys_2 % 187.68/187.61 & 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)) ) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_lexord__append__leftD,axiom, % 187.68/187.61 ! [V_r_2,V_v_2,V_u_2,V_x_2,T_a] : % 187.68/187.61 ( 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))) % 187.68/187.61 => ( ! [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)) % 187.68/187.61 => 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))) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_Cons__acc__listrel1I,axiom, % 187.68/187.61 ! [V_xs_2,V_r_2,V_x_2,T_a] : % 187.68/187.61 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Wellfounded_Oacc(T_a,V_r_2))) % 187.68/187.61 => ( 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)))) % 187.68/187.61 => 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)))) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_listrel__rtrancl__eq__rtrancl__listrel1,axiom, % 187.68/187.61 ! [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)) ). % 187.68/187.61 % 187.68/187.61 fof(fact_listrel1__converse,axiom, % 187.68/187.61 ! [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)) ). % 187.68/187.61 % 187.68/187.61 fof(fact_listrel1__rtrancl__subset__rtrancl__listrel1,axiom, % 187.68/187.61 ! [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)))) ). % 187.68/187.61 % 187.68/187.61 fof(fact_listrel1__mono,axiom, % 187.68/187.61 ! [V_s_2,V_r_2,T_a] : % 187.68/187.61 ( 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)) % 187.68/187.61 => 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))) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_listrel__subset__rtrancl__listrel1,axiom, % 187.68/187.61 ! [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)))) ). % 187.68/187.61 % 187.68/187.61 fof(fact_rtrancl__listrel1__ConsI1,axiom, % 187.68/187.61 ! [V_x_2,V_r_2,V_ys_2,V_xs_2,T_a] : % 187.68/187.61 ( 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)))) % 187.68/187.61 => 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)))) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_listrel1I2,axiom, % 187.68/187.61 ! [V_x_2,V_r_2,V_ys_2,V_xs_2,T_a] : % 187.68/187.61 ( 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))) % 187.68/187.61 => 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))) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_rtrancl__listrel1__eq__len,axiom, % 187.68/187.61 ! [V_r_2,V_y_2,V_x_2,T_a] : % 187.68/187.61 ( 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)))) % 187.68/187.61 => 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) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_listrel1__eq__len,axiom, % 187.68/187.61 ! [V_r_2,V_ys_2,V_xs_2,T_a] : % 187.68/187.61 ( 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))) % 187.68/187.61 => 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) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_not__Nil__listrel1,axiom, % 187.68/187.61 ! [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))) ). % 187.68/187.61 % 187.68/187.61 fof(fact_not__listrel1__Nil,axiom, % 187.68/187.61 ! [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))) ). % 187.68/187.61 % 187.68/187.61 fof(fact_append__listrel1I,axiom, % 187.68/187.61 ! [V_vs_2,V_us_2,V_r_2,V_ys_2,V_xs_2,T_a] : % 187.68/187.61 ( ( ( 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))) % 187.68/187.61 & V_us_2 = V_vs_2 ) % 187.68/187.61 | ( V_xs_2 = V_ys_2 % 187.68/187.61 & 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))) ) ) % 187.68/187.61 => 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))) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_in__listrel1__converse,axiom, % 187.68/187.61 ! [V_r_2,V_y_2,V_x_2,T_a] : % 187.68/187.61 ( 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)))) % 187.68/187.61 <=> 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)))) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_rtrancl__listrel1__if__listrel,axiom, % 187.68/187.61 ! [V_r_2,V_ys_2,V_xs_2,T_a] : % 187.68/187.61 ( 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))) % 187.68/187.61 => 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)))) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_listrel__reflcl__if__listrel1,axiom, % 187.68/187.61 ! [V_r_2,V_ys_2,V_xs_2,T_a] : % 187.68/187.61 ( 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))) % 187.68/187.61 => 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)))) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_listrel1I1,axiom, % 187.68/187.61 ! [V_xs_2,V_r_2,V_y_2,V_x_2,T_a] : % 187.68/187.61 ( 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)) % 187.68/187.61 => 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))) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_Cons__listrel1__Cons,axiom, % 187.68/187.61 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,V_x_2,T_a] : % 187.68/187.61 ( 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))) % 187.68/187.61 <=> ( ( 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)) % 187.68/187.61 & V_xs_2 = V_ys_2 ) % 187.68/187.61 | ( V_x_2 = V_y_2 % 187.68/187.61 & 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))) ) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_listrel1__subset__listrel,axiom, % 187.68/187.61 ! [V_r_H_2,V_r_2,T_a] : % 187.68/187.61 ( 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)) % 187.68/187.61 => ( c_Relation_Orefl__on(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_r_H_2) % 187.68/187.61 => 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))) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_listrel1I,axiom, % 187.68/187.61 ! [V_ys_2,V_vs_2,V_us_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_a] : % 187.68/187.61 ( 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)) % 187.68/187.61 => ( 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)) % 187.68/187.61 => ( 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)) % 187.68/187.61 => 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))) ) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_rtrancl__listrel1__ConsI2,axiom, % 187.68/187.61 ! [V_ys_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_a] : % 187.68/187.61 ( 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))) % 187.68/187.61 => ( 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)))) % 187.68/187.61 => 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)))) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_listrel1__iff__update,axiom, % 187.68/187.61 ! [V_r_2,V_ys_2,V_xs_2,T_a] : % 187.68/187.61 ( 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))) % 187.68/187.61 <=> ? [B_y,B_n] : % 187.68/187.61 ( 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)) % 187.68/187.61 & 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))) % 187.68/187.61 & V_ys_2 = hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),B_n),B_y) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_listrel1E,axiom, % 187.68/187.61 ! [V_r_2,V_ys_2,V_xs_2,T_a] : % 187.68/187.61 ( 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))) % 187.68/187.61 => ~ ! [B_x,B_y] : % 187.68/187.61 ( 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)) % 187.68/187.61 => ! [B_us,B_vs] : % 187.68/187.61 ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),B_us),hAPP(hAPP(c_List_Olist_OCons(T_a),B_x),B_vs)) % 187.68/187.61 => V_ys_2 != hAPP(hAPP(c_List_Oappend(T_a),B_us),hAPP(hAPP(c_List_Olist_OCons(T_a),B_y),B_vs)) ) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_rotate1__def,axiom, % 187.68/187.61 ! [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) ). % 187.68/187.61 % 187.68/187.61 fof(fact_upd__conv__take__nth__drop,axiom, % 187.68/187.61 ! [V_a,V_xs,T_a,V_i] : % 187.68/187.61 ( 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))) % 187.68/187.61 => 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))) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_nth__via__drop,axiom, % 187.68/187.61 ! [V_ys,V_y,V_xs,V_n,T_a] : % 187.68/187.61 ( hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_ys) % 187.68/187.61 => hAPP(hAPP(c_List_Onth(T_a),V_xs),V_n) = V_y ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_drop__1__Cons,axiom, % 187.68/187.61 ! [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 ). % 187.68/187.61 % 187.68/187.61 fof(fact_drop__Suc__Cons,axiom, % 187.68/187.61 ! [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) ). % 187.68/187.61 % 187.68/187.61 fof(fact_length__drop,axiom, % 187.68/187.61 ! [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) ). % 187.68/187.61 % 187.68/187.61 fof(fact_length__rotate1,axiom, % 187.68/187.61 ! [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) ). % 187.68/187.61 % 187.68/187.61 fof(fact_drop__map,axiom, % 187.68/187.61 ! [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)) ). % 187.68/187.61 % 187.68/187.61 fof(fact_drop__zip,axiom, % 187.68/187.61 ! [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)) ). % 187.68/187.61 % 187.68/187.61 fof(fact_drop__0,axiom, % 187.68/187.61 ! [V_xs,T_a] : hAPP(hAPP(c_List_Odrop(T_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_xs) = V_xs ). % 187.68/187.61 % 187.68/187.61 fof(fact_drop__drop,axiom, % 187.68/187.61 ! [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) ). % 187.68/187.61 % 187.68/187.61 fof(fact_distinct1__rotate,axiom, % 187.68/187.61 ! [V_xs_2,T_a] : % 187.68/187.61 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Orotate1(T_a),V_xs_2))) % 187.68/187.61 <=> hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_distinct__drop,axiom, % 187.68/187.61 ! [V_i,V_xs,T_a] : % 187.68/187.61 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 187.68/187.61 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_i),V_xs))) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_set__drop__subset,axiom, % 187.68/187.61 ! [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))) ). % 187.68/187.61 % 187.68/187.61 fof(fact_set__rotate1,axiom, % 187.68/187.61 ! [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) ). % 187.68/187.61 % 187.68/187.61 fof(fact_in__set__dropD,axiom, % 187.68/187.61 ! [V_xs_2,V_n_2,V_x_2,T_a] : % 187.68/187.61 ( 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)))) % 187.68/187.61 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_drop__take,axiom, % 187.68/187.61 ! [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)) ). % 187.68/187.61 % 187.68/187.61 fof(fact_take__drop,axiom, % 187.68/187.61 ! [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)) ). % 187.68/187.61 % 187.68/187.61 fof(fact_drop__Nil,axiom, % 187.68/187.61 ! [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) ). % 187.68/187.61 % 187.68/187.61 fof(fact_rotate1__is__Nil__conv,axiom, % 187.68/187.61 ! [V_xs_2,T_a] : % 187.68/187.61 ( hAPP(c_List_Orotate1(T_a),V_xs_2) = c_List_Olist_ONil(T_a) % 187.68/187.61 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_append__take__drop__id,axiom, % 187.68/187.61 ! [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 ). % 187.68/187.61 % 187.68/187.61 fof(fact_set__drop__subset__set__drop,axiom, % 187.68/187.61 ! [V_xs_2,T_a,V_m_2,V_n_2] : % 187.68/187.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) % 187.68/187.61 => 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)))) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_drop__eq__Nil,axiom, % 187.68/187.61 ! [V_xs_2,V_n_2,T_a] : % 187.68/187.61 ( hAPP(hAPP(c_List_Odrop(T_a),V_n_2),V_xs_2) = c_List_Olist_ONil(T_a) % 187.68/187.61 <=> 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)) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_drop__all,axiom, % 187.68/187.61 ! [V_n,V_xs,T_a] : % 187.68/187.61 ( 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)) % 187.68/187.61 => hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs) = c_List_Olist_ONil(T_a) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_drop__append,axiom, % 187.68/187.61 ! [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)) ). % 187.68/187.61 % 187.68/187.61 fof(fact_append__eq__conv__conj,axiom, % 187.68/187.61 ! [V_zs_2,V_ys_2,V_xs_2,T_a] : % 187.68/187.61 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) = V_zs_2 % 187.68/187.61 <=> ( 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) % 187.68/187.61 & 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) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_drop__Cons,axiom, % 187.68/187.61 ! [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) ). % 187.68/187.61 % 187.68/187.61 fof(fact_drop__Cons_H,axiom, % 187.68/187.61 ! [V_xs,V_x,T_a,V_n] : % 187.68/187.61 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 187.68/187.61 => 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) ) % 187.68/187.61 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 187.68/187.61 => 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) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_nth__drop,axiom, % 187.68/187.61 ! [V_xs,T_a,V_i,V_n] : % 187.68/187.61 ( 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))) % 187.68/187.61 => 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)) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_append__eq__append__conv__if,axiom, % 187.68/187.61 ! [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] : % 187.68/187.61 ( 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) % 187.68/187.61 <=> ( ( 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))) % 187.68/187.61 => ( 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) % 187.68/187.61 & 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) ) ) % 187.68/187.61 & ( ~ 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))) % 187.68/187.61 => ( 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 % 187.68/187.61 & 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 ) ) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_nth__drop_H,axiom, % 187.68/187.61 ! [V_xs,T_a,V_i] : % 187.68/187.61 ( 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))) % 187.68/187.61 => 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) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_rotate__simps,axiom, % 187.68/187.61 ! [V_xs,V_x,T_b,T_a] : % 187.68/187.61 ( hAPP(c_List_Orotate1(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) % 187.68/187.61 & 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))) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_drop__Cons__number__of,axiom, % 187.68/187.61 ! [V_xs,V_x,T_a,V_v] : % 187.68/187.61 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 187.68/187.61 => 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) ) % 187.68/187.61 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 187.68/187.61 => 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) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_take__add,axiom, % 187.68/187.61 ! [V_xs,T_a,V_j,V_i] : % 187.68/187.61 ( 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))) % 187.68/187.61 => 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))) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_rotate1__length01,axiom, % 187.68/187.61 ! [V_xs,T_a] : % 187.68/187.61 ( 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))) % 187.68/187.61 => hAPP(c_List_Orotate1(T_a),V_xs) = V_xs ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_zip__append2,axiom, % 187.68/187.61 ! [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)) ). % 187.68/187.61 % 187.68/187.61 fof(fact_zip__append1,axiom, % 187.68/187.61 ! [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))) ). % 187.68/187.61 % 187.68/187.61 fof(fact_id__take__nth__drop,axiom, % 187.68/187.61 ! [V_xs,T_a,V_i] : % 187.68/187.61 ( 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))) % 187.68/187.61 => 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))) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_take__hd__drop,axiom, % 187.68/187.61 ! [V_xs,T_a,V_n] : % 187.68/187.61 ( 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))) % 187.68/187.61 => 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) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_hd__drop__conv__nth,axiom, % 187.68/187.61 ! [V_n,T_a,V_xs] : % 187.68/187.61 ( V_xs != c_List_Olist_ONil(T_a) % 187.68/187.61 => ( 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))) % 187.68/187.61 => 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) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_hd__map,axiom, % 187.68/187.61 ! [V_f_2,T_b,T_a,V_xs_2] : % 187.68/187.61 ( V_xs_2 != c_List_Olist_ONil(T_a) % 187.68/187.61 => 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)) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_hd_Osimps,axiom, % 187.68/187.61 ! [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 ). % 187.68/187.61 % 187.68/187.61 fof(fact_hd__append,axiom, % 187.68/187.61 ! [V_ys,T_a,V_xs] : % 187.68/187.61 ( ( V_xs = c_List_Olist_ONil(T_a) % 187.68/187.61 => 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) ) % 187.68/187.61 & ( V_xs != c_List_Olist_ONil(T_a) % 187.68/187.61 => 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) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_hd__append2,axiom, % 187.68/187.61 ! [V_ys,T_a,V_xs] : % 187.68/187.61 ( V_xs != c_List_Olist_ONil(T_a) % 187.68/187.61 => 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) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_hd__in__set,axiom, % 187.68/187.61 ! [T_a,V_xs_2] : % 187.68/187.61 ( V_xs_2 != c_List_Olist_ONil(T_a) % 187.68/187.61 => 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))) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_hd__conv__nth,axiom, % 187.68/187.61 ! [T_a,V_xs] : % 187.68/187.61 ( V_xs != c_List_Olist_ONil(T_a) % 187.68/187.61 => 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)) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_rotate1__hd__tl,axiom, % 187.68/187.61 ! [T_a,V_xs] : % 187.68/187.61 ( V_xs != c_List_Olist_ONil(T_a) % 187.68/187.61 => 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))) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_hd__rotate__conv__nth,axiom, % 187.68/187.61 ! [V_n,T_a,V_xs] : % 187.68/187.61 ( V_xs != c_List_Olist_ONil(T_a) % 187.68/187.61 => 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))) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_drop__tl,axiom, % 187.68/187.61 ! [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)) ). % 187.68/187.61 % 187.68/187.61 fof(fact_tl__drop,axiom, % 187.68/187.61 ! [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)) ). % 187.68/187.61 % 187.68/187.61 fof(fact_drop__Suc,axiom, % 187.68/187.61 ! [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)) ). % 187.68/187.61 % 187.68/187.61 fof(fact_tl_Osimps_I2_J,axiom, % 187.68/187.61 ! [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 ). % 187.68/187.61 % 187.68/187.61 fof(fact_take__tl,axiom, % 187.68/187.61 ! [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)) ). % 187.68/187.61 % 187.68/187.61 fof(fact_rotate__conv__mod,axiom, % 187.68/187.61 ! [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) ). % 187.68/187.61 % 187.68/187.61 fof(fact_length__rotate,axiom, % 187.68/187.61 ! [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) ). % 187.68/187.61 % 187.68/187.61 fof(fact_rotate__map,axiom, % 187.68/187.61 ! [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)) ). % 187.68/187.61 % 187.68/187.61 fof(fact_map__tl,axiom, % 187.68/187.61 ! [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)) ). % 187.68/187.61 % 187.68/187.61 fof(fact_rotate__rotate,axiom, % 187.68/187.61 ! [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) ). % 187.68/187.61 % 187.68/187.61 fof(fact_distinct__rotate,axiom, % 187.68/187.61 ! [V_xs_2,V_n_2,T_a] : % 187.68/187.61 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Orotate(T_a,V_n_2),V_xs_2))) % 187.68/187.61 <=> hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_distinct__tl,axiom, % 187.68/187.61 ! [V_xs,T_a] : % 187.68/187.61 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 187.68/187.61 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Otl(T_a),V_xs))) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_set__rotate,axiom, % 187.68/187.61 ! [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) ). % 187.68/187.61 % 187.68/187.61 fof(fact_tl_Osimps_I1_J,axiom, % 187.68/187.61 ! [T_a] : hAPP(c_List_Otl(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 187.68/187.61 % 187.68/187.61 fof(fact_rotate__is__Nil__conv,axiom, % 187.68/187.61 ! [V_xs_2,V_n_2,T_a] : % 187.68/187.61 ( hAPP(c_List_Orotate(T_a,V_n_2),V_xs_2) = c_List_Olist_ONil(T_a) % 187.68/187.61 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_tl__append2,axiom, % 187.68/187.61 ! [V_ys,T_a,V_xs] : % 187.68/187.61 ( V_xs != c_List_Olist_ONil(T_a) % 187.68/187.61 => 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) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_rotate1__rotate__swap,axiom, % 187.68/187.61 ! [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)) ). % 187.68/187.61 % 187.68/187.61 fof(fact_rotate__def,axiom, % 187.68/187.61 ! [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)) ). % 187.68/187.61 % 187.68/187.61 fof(fact_rotate__Suc,axiom, % 187.68/187.61 ! [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)) ). % 187.68/187.61 % 187.68/187.61 fof(fact_tl__append,axiom, % 187.68/187.61 ! [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) ). % 187.68/187.61 % 187.68/187.61 fof(fact_rotate0,axiom, % 187.68/187.61 ! [T_a] : c_List_Orotate(T_a,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(T_a)) ). % 187.68/187.61 % 187.68/187.61 fof(fact_rotate__add,axiom, % 187.68/187.61 ! [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)) ). % 187.68/187.61 % 187.68/187.61 fof(fact_rotate__id,axiom, % 187.68/187.61 ! [V_xs,T_a,V_n] : % 187.68/187.61 ( 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) % 187.68/187.61 => hAPP(c_List_Orotate(T_a,V_n),V_xs) = V_xs ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_rotate__length01,axiom, % 187.68/187.61 ! [V_n,V_xs,T_a] : % 187.68/187.61 ( 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))) % 187.68/187.61 => hAPP(c_List_Orotate(T_a,V_n),V_xs) = V_xs ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_length__tl,axiom, % 187.68/187.61 ! [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)) ). % 187.68/187.61 % 187.68/187.61 fof(fact_tl__take,axiom, % 187.68/187.61 ! [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)) ). % 187.68/187.61 % 187.68/187.61 fof(fact_take__Suc,axiom, % 187.68/187.61 ! [V_n,T_a,V_xs] : % 187.68/187.61 ( V_xs != c_List_Olist_ONil(T_a) % 187.68/187.61 => 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))) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_rotate__drop__take,axiom, % 187.68/187.61 ! [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)) ). % 187.68/187.61 % 187.68/187.61 fof(fact_fold1__set,axiom, % 187.68/187.61 ! [V_xs_2,T_a] : % 187.68/187.61 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 187.68/187.61 => ( V_xs_2 != c_List_Olist_ONil(T_a) % 187.68/187.61 => 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)) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_list_Osize_I2_J,axiom, % 187.68/187.61 ! [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))) ). % 187.68/187.61 % 187.68/187.61 fof(fact_foldl__append,axiom, % 187.68/187.61 ! [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) ). % 187.68/187.61 % 187.68/187.61 fof(fact_foldl__Nil,axiom, % 187.68/187.61 ! [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 ). % 187.68/187.61 % 187.68/187.61 fof(fact_list__size__map,axiom, % 187.68/187.61 ! [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) ). % 187.68/187.61 % 187.68/187.61 fof(fact_start__le__sum,axiom, % 187.68/187.61 ! [V_ns_2,V_n_2,V_m_2] : % 187.68/187.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 187.68/187.61 => 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))) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_foldl__assoc,axiom, % 187.68/187.61 ! [V_zs_2,V_y_2,V_x_2,T_a] : % 187.68/187.61 ( class_Groups_Osemigroup__add(T_a) % 187.68/187.61 => 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)) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_foldl__absorb0,axiom, % 187.68/187.61 ! [V_zs_2,V_x_2,T_a] : % 187.68/187.61 ( class_Groups_Omonoid__add(T_a) % 187.68/187.61 => 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) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_foldr__conv__foldl,axiom, % 187.68/187.61 ! [V_a_2,V_xs_2,T_a] : % 187.68/187.61 ( class_Groups_Oab__semigroup__add(T_a) % 187.68/187.61 => 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) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_foldl__map,axiom, % 187.68/187.61 ! [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) ). % 187.68/187.61 % 187.68/187.61 fof(fact_foldl__Cons,axiom, % 187.68/187.61 ! [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) ). % 187.68/187.61 % 187.68/187.61 fof(fact_listsum__foldl,axiom, % 187.68/187.61 ! [T_a] : % 187.68/187.61 ( class_Groups_Omonoid__add(T_a) % 187.68/187.61 => 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)) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_foldl__foldr1__lemma,axiom, % 187.68/187.61 ! [V_xs_2,V_a_2,T_a] : % 187.68/187.61 ( class_Groups_Omonoid__add(T_a) % 187.68/187.61 => 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))) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_foldl__foldr1,axiom, % 187.68/187.61 ! [V_xs_2,T_a] : % 187.68/187.61 ( class_Groups_Omonoid__add(T_a) % 187.68/187.61 => 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)) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_sum__eq__0__conv,axiom, % 187.68/187.61 ! [V_ns_2,V_m_2] : % 187.68/187.61 ( 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) % 187.68/187.61 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 187.68/187.61 & ! [B_x] : % 187.68/187.61 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2))) % 187.68/187.61 => B_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_list_Osize_I1_J,axiom, % 187.68/187.61 ! [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) ). % 187.68/187.61 % 187.68/187.61 fof(fact_fun__left__comm__idem_Ofold__set,axiom, % 187.68/187.61 ! [V_xs_2,V_y_2,V_f_2,T_b,T_a] : % 187.68/187.61 ( c_Finite__Set_Ofun__left__comm__idem(T_a,T_b,V_f_2) % 187.68/187.61 => 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) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_Sup__set__fold,axiom, % 187.68/187.61 ! [V_xs_2,T_a] : % 187.68/187.61 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 187.68/187.61 => 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) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_Inf__set__fold,axiom, % 187.68/187.61 ! [V_xs_2,T_a] : % 187.68/187.61 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 187.68/187.61 => 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) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_Sup__fin__set__fold,axiom, % 187.68/187.61 ! [V_xs_2,V_x_2,T_a] : % 187.68/187.61 ( class_Lattices_Olattice(T_a) % 187.68/187.61 => 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) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_Inf__fin__set__fold,axiom, % 187.68/187.61 ! [V_xs_2,V_x_2,T_a] : % 187.68/187.61 ( class_Lattices_Olattice(T_a) % 187.68/187.61 => 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) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_Min__fin__set__fold,axiom, % 187.68/187.61 ! [V_xs_2,V_x_2,T_a] : % 187.68/187.61 ( class_Orderings_Olinorder(T_a) % 187.68/187.61 => 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) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_Max__fin__set__fold,axiom, % 187.68/187.61 ! [V_xs_2,V_x_2,T_a] : % 187.68/187.61 ( class_Orderings_Olinorder(T_a) % 187.68/187.61 => 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) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_min__max_OInf__fin__set__fold,axiom, % 187.68/187.61 ! [V_xs_2,V_x_2,T_a] : % 187.68/187.61 ( class_Orderings_Olinorder(T_a) % 187.68/187.61 => 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) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_min__max_OSup__fin__set__fold,axiom, % 187.68/187.61 ! [V_xs_2,V_x_2,T_a] : % 187.68/187.61 ( class_Orderings_Olinorder(T_a) % 187.68/187.61 => 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) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_SUPR__set__fold,axiom, % 187.68/187.61 ! [V_f_2,V_xs_2,T_b,T_a] : % 187.68/187.61 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 187.68/187.61 => 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) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_INFI__set__fold,axiom, % 187.68/187.61 ! [V_f_2,V_xs_2,T_b,T_a] : % 187.68/187.61 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 187.68/187.61 => 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) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_list__size__estimation,axiom, % 187.68/187.61 ! [V_f_2,V_y_2,V_xs_2,V_x_2,T_a] : % 187.68/187.61 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 187.68/187.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y_2),hAPP(V_f_2,V_x_2))) % 187.68/187.61 => 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))) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_list__size__estimation_H,axiom, % 187.68/187.61 ! [V_f_2,V_y_2,V_xs_2,V_x_2,T_a] : % 187.68/187.61 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 187.68/187.61 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),hAPP(V_f_2,V_x_2))) % 187.68/187.61 => 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))) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_map__upds__fold__map__upd,axiom, % 187.68/187.61 ! [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)) ). % 187.68/187.61 % 187.68/187.61 fof(fact_elem__le__sum,axiom, % 187.68/187.61 ! [V_ns_2,V_n_2] : % 187.68/187.61 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_n_2),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2))) % 187.68/187.61 => 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))) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_list__size__conv__listsum,axiom, % 187.68/187.61 ! [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)) ). % 187.68/187.61 % 187.68/187.61 fof(fact_listrel__subset,axiom, % 187.68/187.61 ! [V_A_2,V_r_2,T_a] : % 187.68/187.61 ( 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)))) % 187.68/187.61 => 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))))) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_lists__accD,axiom, % 187.68/187.61 ! [V_r_2,V_xs_2,T_a] : % 187.68/187.61 ( 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)))) % 187.68/187.61 => 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)))) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_lists_ONil,axiom, % 187.68/187.61 ! [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))) ). % 187.68/187.61 % 187.68/187.61 fof(fact_lists__mono,axiom, % 187.68/187.61 ! [V_B_2,V_A_2,T_a] : % 187.68/187.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 187.68/187.61 => 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))) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_append__in__lists__conv,axiom, % 187.68/187.61 ! [V_A_2,V_ys_2,V_xs_2,T_a] : % 187.68/187.61 ( 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))) % 187.68/187.61 <=> ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_xs_2),c_List_Olists(T_a,V_A_2))) % 187.68/187.61 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_ys_2),c_List_Olists(T_a,V_A_2))) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_lists__UNIV,axiom, % 187.68/187.61 ! [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)) ). % 187.68/187.61 % 187.68/187.61 fof(fact_equiv__listrel,axiom, % 187.68/187.61 ! [V_r_2,V_A_2,T_a] : % 187.68/187.61 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 187.68/187.61 => 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)) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_listrel__refl__on,axiom, % 187.68/187.61 ! [V_r_2,V_A_2,T_a] : % 187.68/187.61 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2) % 187.68/187.61 => 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)) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_Cons__in__lists__iff,axiom, % 187.68/187.61 ! [V_A_2,V_xs_2,V_x_2,T_a] : % 187.68/187.61 ( 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))) % 187.68/187.61 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 187.68/187.61 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_xs_2),c_List_Olists(T_a,V_A_2))) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_in__lists__conv__set,axiom, % 187.68/187.61 ! [V_A_2,V_xs_2,T_a] : % 187.68/187.61 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_xs_2),c_List_Olists(T_a,V_A_2))) % 187.68/187.61 <=> ! [B_x] : % 187.68/187.61 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 187.68/187.61 => hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_lists__eq__set,axiom, % 187.68/187.61 ! [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)) ). % 187.68/187.61 % 187.68/187.61 fof(fact_lists__empty,axiom, % 187.68/187.61 ! [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))) ). % 187.68/187.61 % 187.68/187.61 fof(fact_lists__accI,axiom, % 187.68/187.61 ! [V_r_2,V_xs_2,T_a] : % 187.68/187.61 ( 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)))) % 187.68/187.61 => 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)))) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_lexord__append__rightI,axiom, % 187.68/187.61 ! [V_r_2,V_x_2,T_a,V_y_2] : % 187.68/187.61 ( ? [B_b,B_z] : V_y_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_b),B_z) % 187.68/187.61 => 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))) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_lexord__Nil__left,axiom, % 187.68/187.61 ! [V_r_2,V_y_2,T_a] : % 187.68/187.61 ( 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))) % 187.68/187.61 <=> ? [B_a,B_x] : V_y_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_a),B_x) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_last__list__update,axiom, % 187.68/187.61 ! [V_x,V_k,T_a,V_xs] : % 187.68/187.61 ( V_xs != c_List_Olist_ONil(T_a) % 187.68/187.61 => ( ( 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)) % 187.68/187.61 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_k),V_x)) = V_x ) % 187.68/187.61 & ( 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)) % 187.68/187.61 => 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) ) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_listsum__mono,axiom, % 187.68/187.61 ! [V_g_2,V_f_2,V_xs_2,T_a,T_b] : % 187.68/187.61 ( ( class_Groups_Omonoid__add(T_b) % 187.68/187.61 & class_Groups_Oordered__ab__semigroup__add(T_b) ) % 187.68/187.61 => ( ! [B_x] : % 187.68/187.61 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 187.68/187.61 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) ) % 187.68/187.61 => 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)))) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_last_Osimps,axiom, % 187.68/187.61 ! [V_x,T_a,V_xs] : % 187.68/187.61 ( ( V_xs = c_List_Olist_ONil(T_a) % 187.68/187.61 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x ) % 187.68/187.61 & ( V_xs != c_List_Olist_ONil(T_a) % 187.68/187.61 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olast(T_a,V_xs) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_last__ConsR,axiom, % 187.68/187.61 ! [V_x,T_a,V_xs] : % 187.68/187.61 ( V_xs != c_List_Olist_ONil(T_a) % 187.68/187.61 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olast(T_a,V_xs) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_last__ConsL,axiom, % 187.68/187.61 ! [V_x,T_a,V_xs] : % 187.68/187.61 ( V_xs = c_List_Olist_ONil(T_a) % 187.68/187.61 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_last__append,axiom, % 187.68/187.61 ! [V_xs,T_a,V_ys] : % 187.68/187.61 ( ( V_ys = c_List_Olist_ONil(T_a) % 187.68/187.61 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_xs) ) % 187.68/187.61 & ( V_ys != c_List_Olist_ONil(T_a) % 187.68/187.61 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_ys) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_last__appendR,axiom, % 187.68/187.61 ! [V_xs,T_a,V_ys] : % 187.68/187.61 ( V_ys != c_List_Olist_ONil(T_a) % 187.68/187.61 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_ys) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_last__appendL,axiom, % 187.68/187.61 ! [V_xs,T_a,V_ys] : % 187.68/187.61 ( V_ys = c_List_Olist_ONil(T_a) % 187.68/187.61 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_xs) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_last__map,axiom, % 187.68/187.61 ! [V_f_2,T_b,T_a,V_xs_2] : % 187.68/187.61 ( V_xs_2 != c_List_Olist_ONil(T_a) % 187.68/187.61 => 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)) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_last__in__set,axiom, % 187.68/187.61 ! [T_a,V_as_2] : % 187.68/187.61 ( V_as_2 != c_List_Olist_ONil(T_a) % 187.68/187.61 => hBOOL(hAPP(hAPP(c_member(T_a),c_List_Olast(T_a,V_as_2)),hAPP(c_List_Oset(T_a),V_as_2))) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_last__snoc,axiom, % 187.68/187.61 ! [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 ). % 187.68/187.61 % 187.68/187.61 fof(fact_last__drop,axiom, % 187.68/187.61 ! [V_xs,T_a,V_n] : % 187.68/187.61 ( 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))) % 187.68/187.61 => c_List_Olast(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = c_List_Olast(T_a,V_xs) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_last__conv__nth,axiom, % 187.68/187.61 ! [T_a,V_xs] : % 187.68/187.61 ( V_xs != c_List_Olist_ONil(T_a) % 187.68/187.61 => 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))) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_New__DSequence_Opos__not__seq__def,axiom, % 187.68/187.61 ! [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))) ). % 187.68/187.61 % 187.68/187.61 fof(fact_lexord__linear,axiom, % 187.68/187.61 ! [V_y_2,V_x_2,V_r_2,T_a] : % 187.68/187.61 ( ! [B_a,B_b] : % 187.68/187.61 ( 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)) % 187.68/187.61 | B_a = B_b % 187.68/187.61 | 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)) ) % 187.68/187.61 => ( 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))) % 187.68/187.61 | V_x_2 = V_y_2 % 187.68/187.61 | 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))) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_lexord__irreflexive,axiom, % 187.68/187.61 ! [V_y_2,V_r_2,T_a] : % 187.68/187.61 ( ! [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)) % 187.68/187.61 => ~ 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))) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_lists_Osimps,axiom, % 187.68/187.61 ! [V_A_2,V_a_2,T_a] : % 187.68/187.61 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_a_2),c_List_Olists(T_a,V_A_2))) % 187.68/187.61 <=> ( V_a_2 = c_List_Olist_ONil(T_a) % 187.68/187.61 | ? [B_a,B_l] : % 187.68/187.61 ( V_a_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_a),B_l) % 187.68/187.61 & hBOOL(hAPP(hAPP(c_member(T_a),B_a),V_A_2)) % 187.68/187.61 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_l),c_List_Olists(T_a,V_A_2))) ) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_list__size__pointwise,axiom, % 187.68/187.61 ! [V_g_2,V_f_2,V_xs_2,T_a] : % 187.68/187.61 ( ! [B_x] : % 187.68/187.61 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 187.68/187.61 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) ) % 187.68/187.61 => 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))) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_butlast__take,axiom, % 187.68/187.61 ! [V_xs,T_a,V_n] : % 187.68/187.61 ( 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))) % 187.68/187.61 => 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) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_map__butlast,axiom, % 187.68/187.61 ! [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)) ). % 187.68/187.61 % 187.68/187.61 fof(fact_butlast__append,axiom, % 187.68/187.61 ! [V_xs,T_a,V_ys] : % 187.68/187.61 ( ( V_ys = c_List_Olist_ONil(T_a) % 187.68/187.61 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Obutlast(T_a,V_xs) ) % 187.68/187.61 & ( V_ys != c_List_Olist_ONil(T_a) % 187.68/187.61 => 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)) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_butlast_Osimps_I1_J,axiom, % 187.68/187.61 ! [T_a] : c_List_Obutlast(T_a,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 187.68/187.61 % 187.68/187.61 fof(fact_distinct__butlast,axiom, % 187.68/187.61 ! [T_a,V_xs] : % 187.68/187.61 ( V_xs != c_List_Olist_ONil(T_a) % 187.68/187.61 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 187.68/187.61 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Obutlast(T_a,V_xs))) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_in__set__butlastD,axiom, % 187.68/187.61 ! [V_xs_2,V_x_2,T_a] : % 187.68/187.61 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_List_Obutlast(T_a,V_xs_2)))) % 187.68/187.61 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_butlast_Osimps_I2_J,axiom, % 187.68/187.61 ! [V_x,T_a,V_xs] : % 187.68/187.61 ( ( V_xs = c_List_Olist_ONil(T_a) % 187.68/187.61 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olist_ONil(T_a) ) % 187.68/187.61 & ( V_xs != c_List_Olist_ONil(T_a) % 187.68/187.61 => 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)) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_butlast__drop,axiom, % 187.68/187.61 ! [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)) ). % 187.68/187.61 % 187.68/187.61 fof(fact_drop__butlast,axiom, % 187.68/187.61 ! [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)) ). % 187.68/187.61 % 187.68/187.61 fof(fact_in__set__butlast__appendI,axiom, % 187.68/187.61 ! [V_ys_2,V_xs_2,V_x_2,T_a] : % 187.68/187.61 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_List_Obutlast(T_a,V_xs_2)))) % 187.68/187.61 | hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_List_Obutlast(T_a,V_ys_2)))) ) % 187.68/187.61 => 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))))) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_butlast__snoc,axiom, % 187.68/187.61 ! [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 ). % 187.68/187.61 % 187.68/187.61 fof(fact_take__butlast,axiom, % 187.68/187.61 ! [V_xs,T_a,V_n] : % 187.68/187.61 ( 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))) % 187.68/187.61 => 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) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_length__butlast,axiom, % 187.68/187.61 ! [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)) ). % 187.68/187.61 % 187.68/187.61 fof(fact_butlast__conv__take,axiom, % 187.68/187.61 ! [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) ). % 187.68/187.61 % 187.68/187.61 fof(fact_butlast__list__update,axiom, % 187.68/187.61 ! [V_x,V_xs,T_a,V_k] : % 187.68/187.61 ( ( 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)) % 187.68/187.61 => 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) ) % 187.68/187.61 & ( 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)) % 187.68/187.61 => 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) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_snoc__eq__iff__butlast,axiom, % 187.68/187.61 ! [V_ys_2,V_x_2,V_xs_2,T_a] : % 187.68/187.61 ( 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 % 187.68/187.61 <=> ( V_ys_2 != c_List_Olist_ONil(T_a) % 187.68/187.61 & c_List_Obutlast(T_a,V_ys_2) = V_xs_2 % 187.68/187.61 & c_List_Olast(T_a,V_ys_2) = V_x_2 ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_append__butlast__last__id,axiom, % 187.68/187.61 ! [T_a,V_xs] : % 187.68/187.61 ( V_xs != c_List_Olist_ONil(T_a) % 187.68/187.61 => 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 ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_nth__take__lemma,axiom, % 187.68/187.61 ! [V_ys,V_xs,T_a,V_k] : % 187.68/187.61 ( 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))) % 187.68/187.61 => ( 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))) % 187.68/187.61 => ( ! [B_i] : % 187.68/187.61 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_k)) % 187.68/187.61 => hAPP(hAPP(c_List_Onth(T_a),V_xs),B_i) = hAPP(hAPP(c_List_Onth(T_a),V_ys),B_i) ) % 187.68/187.61 => hAPP(hAPP(c_List_Otake(T_a),V_k),V_xs) = hAPP(hAPP(c_List_Otake(T_a),V_k),V_ys) ) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_transpose__aux__max,axiom, % 187.68/187.61 ! [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)))) ). % 187.68/187.61 % 187.68/187.61 fof(fact_filter__is__subset,axiom, % 187.68/187.61 ! [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))) ). % 187.68/187.61 % 187.68/187.61 fof(fact_length__filter__le,axiom, % 187.68/187.61 ! [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))) ). % 187.68/187.61 % 187.68/187.61 fof(fact_filter_Osimps_I2_J,axiom, % 187.68/187.61 ! [V_xs_2,T_a,V_x_2,V_P_2] : % 187.68/187.61 ( ( hBOOL(hAPP(V_P_2,V_x_2)) % 187.68/187.61 => 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)) ) % 187.68/187.61 & ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 187.68/187.61 => 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) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_sum__length__filter__compl,axiom, % 187.68/187.61 ! [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) ). % 187.68/187.61 % 187.68/187.61 fof(fact_filter__filter,axiom, % 187.68/187.61 ! [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) ). % 187.68/187.61 % 187.68/187.61 fof(fact_filter__remove1,axiom, % 187.68/187.61 ! [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)) ). % 187.68/187.61 % 187.68/187.61 fof(fact_remove1__filter__not,axiom, % 187.68/187.61 ! [V_xs_2,T_a,V_x_2,V_P_2] : % 187.68/187.61 ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 187.68/187.61 => 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) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_distinct__filter,axiom, % 187.68/187.61 ! [V_P_2,V_xs_2,T_a] : % 187.68/187.61 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 187.68/187.61 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2))) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_filter__insort__triv,axiom, % 187.68/187.61 ! [V_xs_2,V_f_2,T_a,V_x_2,V_P_2,T_b] : % 187.68/187.61 ( class_Orderings_Olinorder(T_b) % 187.68/187.61 => ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 187.68/187.61 => 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) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_filter__id__conv,axiom, % 187.68/187.61 ! [V_xs_2,V_P_2,T_a] : % 187.68/187.61 ( hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2) = V_xs_2 % 187.68/187.61 <=> ! [B_x] : % 187.68/187.61 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 187.68/187.61 => hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_filter__empty__conv,axiom, % 187.68/187.61 ! [V_xs_2,V_P_2,T_a] : % 187.68/187.61 ( hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2) = c_List_Olist_ONil(T_a) % 187.68/187.61 <=> ! [B_x] : % 187.68/187.61 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 187.68/187.61 => ~ hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_filter_Osimps_I1_J,axiom, % 187.68/187.61 ! [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) ). % 187.68/187.61 % 187.68/187.61 fof(fact_filter__append,axiom, % 187.68/187.61 ! [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)) ). % 187.68/187.61 % 187.68/187.61 fof(fact_filter__map,axiom, % 187.68/187.61 ! [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)) ). % 187.68/187.61 % 187.68/187.61 fof(fact_set__filter,axiom, % 187.68/187.61 ! [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)) ). % 187.68/187.61 % 187.68/187.61 fof(fact_length__filter__map,axiom, % 187.68/187.61 ! [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)) ). % 187.68/187.61 % 187.68/187.61 fof(fact_length__filter__less,axiom, % 187.68/187.61 ! [V_P_2,V_xs_2,V_x_2,T_a] : % 187.68/187.61 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 187.68/187.61 => ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 187.68/187.61 => 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))) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_set__minus__filter__out,axiom, % 187.68/187.61 ! [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)) ). % 187.68/187.61 % 187.68/187.61 fof(fact_filter__in__sublist,axiom, % 187.68/187.61 ! [V_s_2,V_xs_2,T_a] : % 187.68/187.61 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 187.68/187.61 => 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) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_length__filter__conv__card,axiom, % 187.68/187.61 ! [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))))) ). % 187.68/187.61 % 187.68/187.61 fof(fact_map__filter__def,axiom, % 187.68/187.61 ! [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)) ). % 187.68/187.61 % 187.68/187.61 fof(fact_transpose__max__length,axiom, % 187.68/187.61 ! [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)) ). % 187.68/187.61 % 187.68/187.61 fof(fact_transpose__map__map,axiom, % 187.68/187.61 ! [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)) ). % 187.68/187.61 % 187.68/187.61 fof(fact_map__filter__simps_I2_J,axiom, % 187.68/187.61 ! [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) ). % 187.68/187.61 % 187.68/187.61 fof(fact_transpose_Osimps_I1_J,axiom, % 187.68/187.61 ! [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)) ). % 187.68/187.61 % 187.68/187.61 fof(fact_transpose__empty,axiom, % 187.68/187.61 ! [V_xs_2,T_a] : % 187.68/187.61 ( c_List_Otranspose(T_a,V_xs_2) = c_List_Olist_ONil(tc_List_Olist(T_a)) % 187.68/187.61 <=> ! [B_x] : % 187.68/187.61 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xs_2))) % 187.68/187.61 => B_x = c_List_Olist_ONil(T_a) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_transpose_Osimps_I2_J,axiom, % 187.68/187.61 ! [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) ). % 187.68/187.61 % 187.68/187.61 fof(fact_map__of__filter__in,axiom, % 187.68/187.61 ! [V_P_2,V_z_2,V_k_2,V_xs_2,T_a,T_b] : % 187.68/187.61 ( 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) % 187.68/187.61 => ( hBOOL(hAPP(hAPP(V_P_2,V_k_2),V_z_2)) % 187.68/187.61 => 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) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_map__filter__simps_I1_J,axiom, % 187.68/187.61 ! [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)) ). % 187.68/187.61 % 187.68/187.61 fof(fact_sublist__shift__lemma__Suc,axiom, % 187.68/187.61 ! [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)))) ). % 187.68/187.61 % 187.68/187.61 fof(fact_pick__drop__zero,axiom, % 187.68/187.61 ! [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) ). % 187.68/187.61 % 187.68/187.61 fof(fact_select__weigth__drop__zero,axiom, % 187.68/187.61 ! [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) ). % 187.68/187.61 % 187.68/187.61 fof(fact_nth__transpose,axiom, % 187.68/187.61 ! [V_xs_2,T_a,V_i_2] : % 187.68/187.61 ( 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)))) % 187.68/187.61 => 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)) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_length__transpose,axiom, % 187.68/187.61 ! [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)) ). % 187.68/187.61 % 187.68/187.61 fof(fact_map__filter__map__filter,axiom, % 187.68/187.61 ! [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) ). % 187.68/187.61 % 187.68/187.61 fof(fact_insort__key__remove1,axiom, % 187.68/187.61 ! [V_f_2,V_xs_2,V_a_2,T_a,T_b] : % 187.68/187.61 ( class_Orderings_Olinorder(T_b) % 187.68/187.61 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 187.68/187.61 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2)) % 187.68/187.61 => ( 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 % 187.68/187.61 => 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 ) ) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_sublist__def,axiom, % 187.68/187.61 ! [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))))) ). % 187.68/187.61 % 187.68/187.61 fof(fact_sorted_ONil,axiom, % 187.68/187.61 ! [T_a] : % 187.68/187.61 ( class_Orderings_Olinorder(T_a) % 187.68/187.61 => c_List_Olinorder__class_Osorted(T_a,c_List_Olist_ONil(T_a)) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_sorted__single,axiom, % 187.68/187.61 ! [V_x,T_a] : % 187.68/187.61 ( class_Orderings_Olinorder(T_a) % 187.68/187.61 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a))) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_sorted__same,axiom, % 187.68/187.61 ! [V_xs_2,V_g_2,T_a] : % 187.68/187.61 ( class_Orderings_Olinorder(T_a) % 187.68/187.61 => 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)) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_sorted__filter,axiom, % 187.68/187.61 ! [V_P_2,V_xs_2,V_f_2,T_b,T_a] : % 187.68/187.61 ( class_Orderings_Olinorder(T_a) % 187.68/187.61 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) % 187.68/187.61 => 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))) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_sorted__map__same,axiom, % 187.68/187.61 ! [V_xs_2,V_g_2,V_f_2,T_b,T_a] : % 187.68/187.61 ( class_Orderings_Olinorder(T_a) % 187.68/187.61 => 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))) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_length__upt,axiom, % 187.68/187.61 ! [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) ). % 187.68/187.61 % 187.68/187.61 fof(fact_sorted__butlast,axiom, % 187.68/187.61 ! [V_xs,T_a] : % 187.68/187.61 ( class_Orderings_Olinorder(T_a) % 187.68/187.61 => ( V_xs != c_List_Olist_ONil(T_a) % 187.68/187.61 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 187.68/187.61 => c_List_Olinorder__class_Osorted(T_a,c_List_Obutlast(T_a,V_xs)) ) ) ) ). % 187.68/187.61 % 187.68/187.61 fof(fact_upt__Suc,axiom, % 187.68/187.62 ! [V_j,V_i] : % 187.68/187.62 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 187.68/187.62 => 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))) ) % 187.68/187.62 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 187.68/187.62 => c_List_Oupt(V_i,hAPP(c_Nat_OSuc,V_j)) = c_List_Olist_ONil(tc_Nat_Onat) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_upt__Suc__append,axiom, % 187.68/187.62 ! [V_j,V_i] : % 187.68/187.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 187.68/187.62 => 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))) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_upt__add__eq__append,axiom, % 187.68/187.62 ! [V_k,V_j,V_i] : % 187.68/187.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 187.68/187.62 => 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))) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_upt__eq__Nil__conv,axiom, % 187.68/187.62 ! [V_j_2,V_i_2] : % 187.68/187.62 ( c_List_Oupt(V_i_2,V_j_2) = c_List_Olist_ONil(tc_Nat_Onat) % 187.68/187.62 <=> ( V_j_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 187.68/187.62 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_upt__conv__Nil,axiom, % 187.68/187.62 ! [V_i,V_j] : % 187.68/187.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_i)) % 187.68/187.62 => c_List_Oupt(V_i,V_j) = c_List_Olist_ONil(tc_Nat_Onat) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_take__upt,axiom, % 187.68/187.62 ! [V_n,V_m,V_i] : % 187.68/187.62 ( 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)) % 187.68/187.62 => 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)) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_sorted__many__eq,axiom, % 187.68/187.62 ! [V_zs_2,V_y_2,V_x_2,T_a] : % 187.68/187.62 ( class_Orderings_Olinorder(T_a) % 187.68/187.62 => ( 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))) % 187.68/187.62 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 187.68/187.62 & c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_zs_2)) ) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_sorted__many,axiom, % 187.68/187.62 ! [V_zs,V_y,V_x,T_a] : % 187.68/187.62 ( class_Orderings_Olinorder(T_a) % 187.68/187.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 187.68/187.62 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_zs)) % 187.68/187.62 => 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))) ) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_sorted__drop,axiom, % 187.68/187.62 ! [V_n,V_xs,T_a] : % 187.68/187.62 ( class_Orderings_Olinorder(T_a) % 187.68/187.62 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 187.68/187.62 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_drop__upt,axiom, % 187.68/187.62 ! [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) ). % 187.68/187.62 % 187.68/187.62 fof(fact_hd__upt,axiom, % 187.68/187.62 ! [V_j,V_i] : % 187.68/187.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 187.68/187.62 => hAPP(c_List_Ohd(tc_Nat_Onat),c_List_Oupt(V_i,V_j)) = V_i ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_upt__rec,axiom, % 187.68/187.62 ! [V_j,V_i] : % 187.68/187.62 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 187.68/187.62 => 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)) ) % 187.68/187.62 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 187.68/187.62 => c_List_Oupt(V_i,V_j) = c_List_Olist_ONil(tc_Nat_Onat) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_upt__conv__Cons,axiom, % 187.68/187.62 ! [V_j,V_i] : % 187.68/187.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 187.68/187.62 => 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)) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_sorted__insort__insert,axiom, % 187.68/187.62 ! [V_x_2,V_xs_2,T_a] : % 187.68/187.62 ( class_Orderings_Olinorder(T_a) % 187.68/187.62 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2) % 187.68/187.62 => 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)) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_sorted__list__of__set__range,axiom, % 187.68/187.62 ! [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) ). % 187.68/187.62 % 187.68/187.62 fof(fact_sorted__upto,axiom, % 187.68/187.62 ! [V_j,V_i] : c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(V_i,V_j)) ). % 187.68/187.62 % 187.68/187.62 fof(fact_sorted__upt,axiom, % 187.68/187.62 ! [V_j,V_i] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Oupt(V_i,V_j)) ). % 187.68/187.62 % 187.68/187.62 fof(fact_sorted__remove1,axiom, % 187.68/187.62 ! [V_a,V_xs,T_a] : % 187.68/187.62 ( class_Orderings_Olinorder(T_a) % 187.68/187.62 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 187.68/187.62 => c_List_Olinorder__class_Osorted(T_a,c_List_Oremove1(T_a,V_a,V_xs)) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_distinct__upt,axiom, % 187.68/187.62 ! [V_j,V_i] : hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),c_List_Oupt(V_i,V_j))) ). % 187.68/187.62 % 187.68/187.62 fof(fact_sorted__insort,axiom, % 187.68/187.62 ! [V_xs_2,V_x_2,T_a] : % 187.68/187.62 ( class_Orderings_Olinorder(T_a) % 187.68/187.62 => ( 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)) % 187.68/187.62 <=> c_List_Olinorder__class_Osorted(T_a,V_xs_2) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_sorted__distinct__set__unique,axiom, % 187.68/187.62 ! [V_ys_2,V_xs_2,T_a] : % 187.68/187.62 ( class_Orderings_Olinorder(T_a) % 187.68/187.62 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2) % 187.68/187.62 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 187.68/187.62 => ( c_List_Olinorder__class_Osorted(T_a,V_ys_2) % 187.68/187.62 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_ys_2)) % 187.68/187.62 => ( hAPP(c_List_Oset(T_a),V_xs_2) = hAPP(c_List_Oset(T_a),V_ys_2) % 187.68/187.62 => V_xs_2 = V_ys_2 ) ) ) ) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_atLeastLessThan__upt,axiom, % 187.68/187.62 ! [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)) ). % 187.68/187.62 % 187.68/187.62 fof(fact_set__upt,axiom, % 187.68/187.62 ! [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) ). % 187.68/187.62 % 187.68/187.62 fof(fact_sorted__take,axiom, % 187.68/187.62 ! [V_n,V_xs,T_a] : % 187.68/187.62 ( class_Orderings_Olinorder(T_a) % 187.68/187.62 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 187.68/187.62 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_sorted_Oequations_I1_J,axiom, % 187.68/187.62 ! [T_a] : % 187.68/187.62 ( class_Orderings_Olinorder(T_a) % 187.68/187.62 => c_List_Olinorder__class_Osorted(T_a,c_List_Olist_ONil(T_a)) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_upt__0,axiom, % 187.68/187.62 ! [V_i] : c_List_Oupt(V_i,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_List_Olist_ONil(tc_Nat_Onat) ). % 187.68/187.62 % 187.68/187.62 fof(fact_sorted__tl,axiom, % 187.68/187.62 ! [V_xs,T_a] : % 187.68/187.62 ( class_Orderings_Olinorder(T_a) % 187.68/187.62 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 187.68/187.62 => c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Otl(T_a),V_xs)) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_map__Suc__upt,axiom, % 187.68/187.62 ! [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)) ). % 187.68/187.62 % 187.68/187.62 fof(fact_sorted__insort__insert__key,axiom, % 187.68/187.62 ! [V_x_2,V_xs_2,V_f_2,T_b,T_a] : % 187.68/187.62 ( class_Orderings_Olinorder(T_a) % 187.68/187.62 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) % 187.68/187.62 => 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))) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_sorted__map__remove1,axiom, % 187.68/187.62 ! [V_x_2,V_xs_2,V_f_2,T_b,T_a] : % 187.68/187.62 ( class_Orderings_Olinorder(T_a) % 187.68/187.62 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) % 187.68/187.62 => 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))) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_sorted__insort__key,axiom, % 187.68/187.62 ! [V_xs_2,V_x_2,V_f_2,T_b,T_a] : % 187.68/187.62 ( class_Orderings_Olinorder(T_a) % 187.68/187.62 => ( 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))) % 187.68/187.62 <=> c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_sorted__Cons,axiom, % 187.68/187.62 ! [V_xs_2,V_x_2,T_a] : % 187.68/187.62 ( class_Orderings_Olinorder(T_a) % 187.68/187.62 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) % 187.68/187.62 <=> ( c_List_Olinorder__class_Osorted(T_a,V_xs_2) % 187.68/187.62 & ! [B_x] : % 187.68/187.62 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 187.68/187.62 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),B_x)) ) ) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_sorted__append,axiom, % 187.68/187.62 ! [V_ys_2,V_xs_2,T_a] : % 187.68/187.62 ( class_Orderings_Olinorder(T_a) % 187.68/187.62 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)) % 187.68/187.62 <=> ( c_List_Olinorder__class_Osorted(T_a,V_xs_2) % 187.68/187.62 & c_List_Olinorder__class_Osorted(T_a,V_ys_2) % 187.68/187.62 & ! [B_x] : % 187.68/187.62 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 187.68/187.62 => ! [B_xa] : % 187.68/187.62 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),hAPP(c_List_Oset(T_a),V_ys_2))) % 187.68/187.62 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_x),B_xa)) ) ) ) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_upt__rec__number__of,axiom, % 187.68/187.62 ! [V_n,V_m] : % 187.68/187.62 ( ( 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))) % 187.68/187.62 => 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))) ) % 187.68/187.62 & ( ~ 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))) % 187.68/187.62 => 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) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_upt__eq__Cons__conv,axiom, % 187.68/187.62 ! [V_xs_2,V_x_2,V_j_2,V_i_2] : % 187.68/187.62 ( c_List_Oupt(V_i_2,V_j_2) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_x_2),V_xs_2) % 187.68/187.62 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),V_j_2)) % 187.68/187.62 & V_i_2 = V_x_2 % 187.68/187.62 & 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 ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_last__upt,axiom, % 187.68/187.62 ! [V_j,V_i] : % 187.68/187.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 187.68/187.62 => 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)) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_filter__insort,axiom, % 187.68/187.62 ! [V_x_2,V_P_2,V_xs_2,V_f_2,T_b,T_a] : % 187.68/187.62 ( class_Orderings_Olinorder(T_a) % 187.68/187.62 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) % 187.68/187.62 => ( hBOOL(hAPP(V_P_2,V_x_2)) % 187.68/187.62 => 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)) ) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_map__nth,axiom, % 187.68/187.62 ! [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 ). % 187.68/187.62 % 187.68/187.62 fof(fact_atLeastAtMost__upt,axiom, % 187.68/187.62 ! [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))) ). % 187.68/187.62 % 187.68/187.62 fof(fact_atLeast__upt,axiom, % 187.68/187.62 ! [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)) ). % 187.68/187.62 % 187.68/187.62 fof(fact_setsum__set__upt__conv__listsum__nat,axiom, % 187.68/187.62 ! [V_n_2,V_m_2,V_f_2,T_a] : % 187.68/187.62 ( class_Groups_Ocomm__monoid__add(T_a) % 187.68/187.62 => 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))) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_interv__listsum__conv__setsum__set__nat,axiom, % 187.68/187.62 ! [V_n_2,V_m_2,V_f_2,T_a] : % 187.68/187.62 ( class_Groups_Ocomm__monoid__add(T_a) % 187.68/187.62 => 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))) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_nth__upt,axiom, % 187.68/187.62 ! [V_j,V_k,V_i] : % 187.68/187.62 ( 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)) % 187.68/187.62 => 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) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_greaterThanAtMost__upt,axiom, % 187.68/187.62 ! [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))) ). % 187.68/187.62 % 187.68/187.62 fof(fact_sorted_Oequations_I2_J,axiom, % 187.68/187.62 ! [V_a1_2,V_a2_2,T_a] : % 187.68/187.62 ( class_Orderings_Olinorder(T_a) % 187.68/187.62 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_a2_2),V_a1_2)) % 187.68/187.62 <=> ( ! [B_x] : % 187.68/187.62 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_a1_2))) % 187.68/187.62 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a2_2),B_x)) ) % 187.68/187.62 & c_List_Olinorder__class_Osorted(T_a,V_a1_2) ) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_greaterThanLessThan__upt,axiom, % 187.68/187.62 ! [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)) ). % 187.68/187.62 % 187.68/187.62 fof(fact_nth__map__upt,axiom, % 187.68/187.62 ! [V_f_2,T_a,V_m_2,V_n_2,V_i_2] : % 187.68/187.62 ( 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))) % 187.68/187.62 => 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)) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_sorted__list__of__set,axiom, % 187.68/187.62 ! [V_A_2,T_a] : % 187.68/187.62 ( class_Orderings_Olinorder(T_a) % 187.68/187.62 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.62 => ( hAPP(c_List_Oset(T_a),c_List_Olinorder__class_Osorted__list__of__set(T_a,V_A_2)) = V_A_2 % 187.68/187.62 & c_List_Olinorder__class_Osorted(T_a,c_List_Olinorder__class_Osorted__list__of__set(T_a,V_A_2)) % 187.68/187.62 & hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Olinorder__class_Osorted__list__of__set(T_a,V_A_2))) ) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_atMost__upto,axiom, % 187.68/187.62 ! [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))) ). % 187.68/187.62 % 187.68/187.62 fof(fact_insort__remove1,axiom, % 187.68/187.62 ! [V_xs_2,V_a_2,T_a] : % 187.68/187.62 ( class_Orderings_Olinorder(T_a) % 187.68/187.62 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 187.68/187.62 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2) % 187.68/187.62 => 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 ) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_sorted__nth__mono,axiom, % 187.68/187.62 ! [V_j,V_i,V_xs,T_a] : % 187.68/187.62 ( class_Orderings_Olinorder(T_a) % 187.68/187.62 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 187.68/187.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 187.68/187.62 => ( 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))) % 187.68/187.62 => 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))) ) ) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_sorted__equals__nth__mono,axiom, % 187.68/187.62 ! [V_xs_2,T_a] : % 187.68/187.62 ( class_Orderings_Olinorder(T_a) % 187.68/187.62 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2) % 187.68/187.62 <=> ! [B_j] : % 187.68/187.62 ( 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))) % 187.68/187.62 => ! [B_i] : % 187.68/187.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_j)) % 187.68/187.62 => 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))) ) ) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_map__sorted__distinct__set__unique,axiom, % 187.68/187.62 ! [V_ys_2,V_xs_2,V_f_2,T_a,T_b] : % 187.68/187.62 ( class_Orderings_Olinorder(T_b) % 187.68/187.62 => ( 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))) % 187.68/187.62 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2)) % 187.68/187.62 => ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2))) % 187.68/187.62 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_ys_2)) % 187.68/187.62 => ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_ys_2))) % 187.68/187.62 => ( hAPP(c_List_Oset(T_a),V_xs_2) = hAPP(c_List_Oset(T_a),V_ys_2) % 187.68/187.62 => V_xs_2 = V_ys_2 ) ) ) ) ) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_sublist__shift__lemma,axiom, % 187.68/187.62 ! [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))))) ). % 187.68/187.62 % 187.68/187.62 fof(fact_transpose__rectangle,axiom, % 187.68/187.62 ! [V_n_2,T_a,V_xs_2] : % 187.68/187.62 ( ( V_xs_2 = c_List_Olist_ONil(tc_List_Olist(T_a)) % 187.68/187.62 => V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 187.68/187.62 => ( ! [B_i] : % 187.68/187.62 ( 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))) % 187.68/187.62 => 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 ) % 187.68/187.62 => 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)) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_transpose_Opsimps_I2_J,axiom, % 187.68/187.62 ! [V_xss_2,T_a] : % 187.68/187.62 ( 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))) % 187.68/187.62 => 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) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_transpose_Opsimps_I1_J,axiom, % 187.68/187.62 ! [T_a] : % 187.68/187.62 ( 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)))) % 187.68/187.62 => c_List_Otranspose(T_a,c_List_Olist_ONil(tc_List_Olist(T_a))) = c_List_Olist_ONil(tc_List_Olist(T_a)) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_transpose__column,axiom, % 187.68/187.62 ! [V_i_2,V_xs_2,T_a] : % 187.68/187.62 ( 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))) % 187.68/187.62 => ( 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))) % 187.68/187.62 => 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) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_transpose__aux__filter__head,axiom, % 187.68/187.62 ! [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)) ). % 187.68/187.62 % 187.68/187.62 fof(fact_inj__on__rev,axiom, % 187.68/187.62 ! [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) ). % 187.68/187.62 % 187.68/187.62 fof(fact_filter__concat,axiom, % 187.68/187.62 ! [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)) ). % 187.68/187.62 % 187.68/187.62 fof(fact_rev__singleton__conv,axiom, % 187.68/187.62 ! [V_x_2,V_xs_2,T_a] : % 187.68/187.62 ( 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)) % 187.68/187.62 <=> V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a)) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_singleton__rev__conv,axiom, % 187.68/187.62 ! [V_xs_2,V_x_2,T_a] : % 187.68/187.62 ( 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) % 187.68/187.62 <=> V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a)) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_Nil__eq__concat__conv,axiom, % 187.68/187.62 ! [V_xss_2,T_a] : % 187.68/187.62 ( c_List_Olist_ONil(T_a) = c_List_Oconcat(T_a,V_xss_2) % 187.68/187.62 <=> ! [B_x] : % 187.68/187.62 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xss_2))) % 187.68/187.62 => B_x = c_List_Olist_ONil(T_a) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_concat__eq__Nil__conv,axiom, % 187.68/187.62 ! [V_xss_2,T_a] : % 187.68/187.62 ( c_List_Oconcat(T_a,V_xss_2) = c_List_Olist_ONil(T_a) % 187.68/187.62 <=> ! [B_x] : % 187.68/187.62 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xss_2))) % 187.68/187.62 => B_x = c_List_Olist_ONil(T_a) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_rev_Osimps_I1_J,axiom, % 187.68/187.62 ! [T_a] : hAPP(c_List_Orev(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 187.68/187.62 % 187.68/187.62 fof(fact_concat_Osimps_I1_J,axiom, % 187.68/187.62 ! [T_a] : c_List_Oconcat(T_a,c_List_Olist_ONil(tc_List_Olist(T_a))) = c_List_Olist_ONil(T_a) ). % 187.68/187.62 % 187.68/187.62 fof(fact_Nil__is__rev__conv,axiom, % 187.68/187.62 ! [V_xs_2,T_a] : % 187.68/187.62 ( c_List_Olist_ONil(T_a) = hAPP(c_List_Orev(T_a),V_xs_2) % 187.68/187.62 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_rev__is__Nil__conv,axiom, % 187.68/187.62 ! [V_xs_2,T_a] : % 187.68/187.62 ( hAPP(c_List_Orev(T_a),V_xs_2) = c_List_Olist_ONil(T_a) % 187.68/187.62 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_concat_Osimps_I2_J,axiom, % 187.68/187.62 ! [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)) ). % 187.68/187.62 % 187.68/187.62 fof(fact_rev__concat,axiom, % 187.68/187.62 ! [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))) ). % 187.68/187.62 % 187.68/187.62 fof(fact_rev__map,axiom, % 187.68/187.62 ! [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)) ). % 187.68/187.62 % 187.68/187.62 fof(fact_map__concat,axiom, % 187.68/187.62 ! [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)) ). % 187.68/187.62 % 187.68/187.62 fof(fact_rev__foldl__cons,axiom, % 187.68/187.62 ! [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) ). % 187.68/187.62 % 187.68/187.62 fof(fact_concat__conv__foldl,axiom, % 187.68/187.62 ! [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) ). % 187.68/187.62 % 187.68/187.62 fof(fact_foldl__conv__concat,axiom, % 187.68/187.62 ! [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)) ). % 187.68/187.62 % 187.68/187.62 fof(fact_rev__append,axiom, % 187.68/187.62 ! [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)) ). % 187.68/187.62 % 187.68/187.62 fof(fact_concat__append,axiom, % 187.68/187.62 ! [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)) ). % 187.68/187.62 % 187.68/187.62 fof(fact_distinct__rev,axiom, % 187.68/187.62 ! [V_xs_2,T_a] : % 187.68/187.62 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Orev(T_a),V_xs_2))) % 187.68/187.62 <=> hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_rev_Osimps_I2_J,axiom, % 187.68/187.62 ! [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))) ). % 187.68/187.62 % 187.68/187.62 fof(fact_rev__eq__Cons__iff,axiom, % 187.68/187.62 ! [V_ys_2,V_y_2,V_xs_2,T_a] : % 187.68/187.62 ( hAPP(c_List_Orev(T_a),V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2) % 187.68/187.62 <=> 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))) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_length__concat,axiom, % 187.68/187.62 ! [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)) ). % 187.68/187.62 % 187.68/187.62 fof(fact_length__rev,axiom, % 187.68/187.62 ! [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) ). % 187.68/187.62 % 187.68/187.62 fof(fact_rev__is__rev__conv,axiom, % 187.68/187.62 ! [V_ys_2,V_xs_2,T_a] : % 187.68/187.62 ( hAPP(c_List_Orev(T_a),V_xs_2) = hAPP(c_List_Orev(T_a),V_ys_2) % 187.68/187.62 <=> V_xs_2 = V_ys_2 ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_rev__swap,axiom, % 187.68/187.62 ! [V_ys_2,V_xs_2,T_a] : % 187.68/187.62 ( hAPP(c_List_Orev(T_a),V_xs_2) = V_ys_2 % 187.68/187.62 <=> V_xs_2 = hAPP(c_List_Orev(T_a),V_ys_2) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_rev__rev__ident,axiom, % 187.68/187.62 ! [V_xs,T_a] : hAPP(c_List_Orev(T_a),hAPP(c_List_Orev(T_a),V_xs)) = V_xs ). % 187.68/187.62 % 187.68/187.62 fof(fact_listsum__rev,axiom, % 187.68/187.62 ! [V_xs,T_a] : % 187.68/187.62 ( class_Groups_Ocomm__monoid__add(T_a) % 187.68/187.62 => 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) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_foldr__foldl,axiom, % 187.68/187.62 ! [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)) ). % 187.68/187.62 % 187.68/187.62 fof(fact_foldl__foldr,axiom, % 187.68/187.62 ! [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) ). % 187.68/187.62 % 187.68/187.62 fof(fact_set__rev,axiom, % 187.68/187.62 ! [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) ). % 187.68/187.62 % 187.68/187.62 fof(fact_zip__rev,axiom, % 187.68/187.62 ! [V_ys,T_b,V_xs,T_a] : % 187.68/187.62 ( 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) % 187.68/187.62 => 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)) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_rev__filter,axiom, % 187.68/187.62 ! [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)) ). % 187.68/187.62 % 187.68/187.62 fof(fact_set__concat,axiom, % 187.68/187.62 ! [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)) ). % 187.68/187.62 % 187.68/187.62 fof(fact_last__rev,axiom, % 187.68/187.62 ! [T_a,V_xs] : % 187.68/187.62 ( V_xs != c_List_Olist_ONil(T_a) % 187.68/187.62 => c_List_Olast(T_a,hAPP(c_List_Orev(T_a),V_xs)) = hAPP(c_List_Ohd(T_a),V_xs) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_hd__rev,axiom, % 187.68/187.62 ! [T_a,V_xs] : % 187.68/187.62 ( V_xs != c_List_Olist_ONil(T_a) % 187.68/187.62 => hAPP(c_List_Ohd(T_a),hAPP(c_List_Orev(T_a),V_xs)) = c_List_Olast(T_a,V_xs) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_sorted__transpose,axiom, % 187.68/187.62 ! [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)))) ). % 187.68/187.62 % 187.68/187.62 fof(fact_rev__take,axiom, % 187.68/187.62 ! [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)) ). % 187.68/187.62 % 187.68/187.62 fof(fact_rev__drop,axiom, % 187.68/187.62 ! [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)) ). % 187.68/187.62 % 187.68/187.62 fof(fact_rotate__rev,axiom, % 187.68/187.62 ! [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)) ). % 187.68/187.62 % 187.68/187.62 fof(fact_transpose_Osimps_I3_J,axiom, % 187.68/187.62 ! [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))))) ). % 187.68/187.62 % 187.68/187.62 fof(fact_rev__nth,axiom, % 187.68/187.62 ! [V_xs,T_a,V_n] : % 187.68/187.62 ( 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))) % 187.68/187.62 => 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))) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_concat__eq__concat__iff,axiom, % 187.68/187.62 ! [V_ys_2,V_xs_2,T_a] : % 187.68/187.62 ( ! [B_x] : % 187.68/187.62 ( 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)))) % 187.68/187.62 => 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)) ) % 187.68/187.62 => ( 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) % 187.68/187.62 => ( c_List_Oconcat(T_a,V_xs_2) = c_List_Oconcat(T_a,V_ys_2) % 187.68/187.62 <=> V_xs_2 = V_ys_2 ) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_concat__injective,axiom, % 187.68/187.62 ! [V_ys_2,V_xs_2,T_a] : % 187.68/187.62 ( c_List_Oconcat(T_a,V_xs_2) = c_List_Oconcat(T_a,V_ys_2) % 187.68/187.62 => ( 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) % 187.68/187.62 => ( ! [B_x] : % 187.68/187.62 ( 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)))) % 187.68/187.62 => 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)) ) % 187.68/187.62 => V_xs_2 = V_ys_2 ) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_rev__update,axiom, % 187.68/187.62 ! [V_y,V_xs,T_a,V_k] : % 187.68/187.62 ( 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))) % 187.68/187.62 => 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) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_concat__map__singleton,axiom, % 187.68/187.62 ! [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) ). % 187.68/187.62 % 187.68/187.62 fof(fact_sorted__rev__nth__mono,axiom, % 187.68/187.62 ! [V_j,V_i,V_xs,T_a] : % 187.68/187.62 ( class_Orderings_Olinorder(T_a) % 187.68/187.62 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Orev(T_a),V_xs)) % 187.68/187.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 187.68/187.62 => ( 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))) % 187.68/187.62 => 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))) ) ) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_foldr__max__sorted,axiom, % 187.68/187.62 ! [V_y_2,V_xs_2,T_a] : % 187.68/187.62 ( class_Orderings_Olinorder(T_a) % 187.68/187.62 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Orev(T_a),V_xs_2)) % 187.68/187.62 => ( ( V_xs_2 = c_List_Olist_ONil(T_a) % 187.68/187.62 => c_List_Ofoldr(T_a,T_a,c_Orderings_Oord__class_Omax(T_a),V_xs_2,V_y_2) = V_y_2 ) % 187.68/187.62 & ( V_xs_2 != c_List_Olist_ONil(T_a) % 187.68/187.62 => 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) ) ) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_transpose_Opsimps_I3_J,axiom, % 187.68/187.62 ! [V_xss_2,V_xs_2,V_x_2,T_a] : % 187.68/187.62 ( 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))) % 187.68/187.62 => 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))))) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_length__transpose__sorted,axiom, % 187.68/187.62 ! [V_xs_2,T_a] : % 187.68/187.62 ( 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))) % 187.68/187.62 => ( ( V_xs_2 = c_List_Olist_ONil(tc_List_Olist(T_a)) % 187.68/187.62 => 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) ) % 187.68/187.62 & ( V_xs_2 != c_List_Olist_ONil(tc_List_Olist(T_a)) % 187.68/187.62 => 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))) ) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_transpose__column__length,axiom, % 187.68/187.62 ! [V_i_2,V_xs_2,T_a] : % 187.68/187.62 ( 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))) % 187.68/187.62 => ( 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))) % 187.68/187.62 => 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)) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_transpose__aux__filter__tail,axiom, % 187.68/187.62 ! [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)) ). % 187.68/187.62 % 187.68/187.62 fof(fact_nth__nth__transpose__sorted,axiom, % 187.68/187.62 ! [V_j_2,V_i_2,V_xs_2,T_a] : % 187.68/187.62 ( 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))) % 187.68/187.62 => ( 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)))) % 187.68/187.62 => ( 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)))) % 187.68/187.62 => 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) ) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_transpose__transpose,axiom, % 187.68/187.62 ! [V_xs_2,T_a] : % 187.68/187.62 ( 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))) % 187.68/187.62 => 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) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_transfer__nat__int__list__functions_I2_J,axiom, % 187.68/187.62 c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oreturn__list(c_List_Olist_ONil(tc_Int_Oint)) ). % 187.68/187.62 % 187.68/187.62 fof(fact_takeWhile__map,axiom, % 187.68/187.62 ! [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)) ). % 187.68/187.62 % 187.68/187.62 fof(fact_zip__takeWhile__fst,axiom, % 187.68/187.62 ! [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)) ). % 187.68/187.62 % 187.68/187.62 fof(fact_zip__takeWhile__snd,axiom, % 187.68/187.62 ! [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)) ). % 187.68/187.62 % 187.68/187.62 fof(fact_takeWhile__eq__all__conv,axiom, % 187.68/187.62 ! [V_xs_2,V_P_2,T_a] : % 187.68/187.62 ( c_List_OtakeWhile(T_a,V_P_2,V_xs_2) = V_xs_2 % 187.68/187.62 <=> ! [B_x] : % 187.68/187.62 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 187.68/187.62 => hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_set__takeWhileD,axiom, % 187.68/187.62 ! [V_xs_2,V_P_2,V_x_2,T_a] : % 187.68/187.62 ( 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)))) % 187.68/187.62 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 187.68/187.62 & hBOOL(hAPP(V_P_2,V_x_2)) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_length__takeWhile__le,axiom, % 187.68/187.62 ! [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))) ). % 187.68/187.62 % 187.68/187.62 fof(fact_takeWhile__eq__take,axiom, % 187.68/187.62 ! [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) ). % 187.68/187.62 % 187.68/187.62 fof(fact_distinct__takeWhile,axiom, % 187.68/187.62 ! [V_P_2,V_xs_2,T_a] : % 187.68/187.62 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 187.68/187.62 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_OtakeWhile(T_a,V_P_2,V_xs_2))) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_takeWhile__tail,axiom, % 187.68/187.62 ! [V_l_2,V_xs_2,T_a,V_x_2,V_P_2] : % 187.68/187.62 ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 187.68/187.62 => 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) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_takeWhile_Osimps_I1_J,axiom, % 187.68/187.62 ! [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) ). % 187.68/187.62 % 187.68/187.62 fof(fact_sorted__takeWhile,axiom, % 187.68/187.62 ! [V_P_2,V_xs_2,T_a] : % 187.68/187.62 ( class_Orderings_Olinorder(T_a) % 187.68/187.62 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2) % 187.68/187.62 => c_List_Olinorder__class_Osorted(T_a,c_List_OtakeWhile(T_a,V_P_2,V_xs_2)) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_takeWhile_Osimps_I2_J,axiom, % 187.68/187.62 ! [V_xs_2,T_a,V_x_2,V_P_2] : % 187.68/187.62 ( ( hBOOL(hAPP(V_P_2,V_x_2)) % 187.68/187.62 => 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)) ) % 187.68/187.62 & ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 187.68/187.62 => 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) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_return__list__def,axiom, % 187.68/187.62 ! [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) ). % 187.68/187.62 % 187.68/187.62 fof(fact_takeWhile__append1,axiom, % 187.68/187.62 ! [V_ys_2,V_P_2,V_xs_2,V_x_2,T_a] : % 187.68/187.62 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 187.68/187.62 => ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 187.68/187.62 => 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) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_nth__length__takeWhile,axiom, % 187.68/187.62 ! [V_xs_2,V_P_2,T_a] : % 187.68/187.62 ( 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))) % 187.68/187.62 => ~ 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))))) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_takeWhile__nth,axiom, % 187.68/187.62 ! [V_xs_2,V_P_2,T_a,V_j_2] : % 187.68/187.62 ( 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)))) % 187.68/187.62 => 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) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_map__upds__def,axiom, % 187.68/187.62 ! [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)))) ). % 187.68/187.62 % 187.68/187.62 fof(fact_takeWhile__not__last,axiom, % 187.68/187.62 ! [T_a,V_xs_2] : % 187.68/187.62 ( V_xs_2 != c_List_Olist_ONil(T_a) % 187.68/187.62 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 187.68/187.62 => 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) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_filter__equals__takeWhile__sorted__rev,axiom, % 187.68/187.62 ! [V_t_2,V_xs_2,V_f_2,T_b,T_a] : % 187.68/187.62 ( class_Orderings_Olinorder(T_a) % 187.68/187.62 => ( 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))) % 187.68/187.62 => 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) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_transfer__nat__int__list__return__embed,axiom, % 187.68/187.62 ! [V_l] : % 187.68/187.62 ( c_List_Onat__list(V_l) % 187.68/187.62 => c_List_Oembed__list(c_List_Oreturn__list(V_l)) = V_l ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_length__remdups__concat,axiom, % 187.68/187.62 ! [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))) ). % 187.68/187.62 % 187.68/187.62 fof(fact_distinct__remdups,axiom, % 187.68/187.62 ! [V_xs,T_a] : hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oremdups(T_a,V_xs))) ). % 187.68/187.62 % 187.68/187.62 fof(fact_length__remdups__leq,axiom, % 187.68/187.62 ! [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))) ). % 187.68/187.62 % 187.68/187.62 fof(fact_remdups__map__remdups,axiom, % 187.68/187.62 ! [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)) ). % 187.68/187.62 % 187.68/187.62 fof(fact_set__remdups,axiom, % 187.68/187.62 ! [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) ). % 187.68/187.62 % 187.68/187.62 fof(fact_sorted__remdups,axiom, % 187.68/187.62 ! [V_l,T_a] : % 187.68/187.62 ( class_Orderings_Olinorder(T_a) % 187.68/187.62 => ( c_List_Olinorder__class_Osorted(T_a,V_l) % 187.68/187.62 => c_List_Olinorder__class_Osorted(T_a,c_List_Oremdups(T_a,V_l)) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_remdups_Osimps_I1_J,axiom, % 187.68/187.62 ! [T_a] : c_List_Oremdups(T_a,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 187.68/187.62 % 187.68/187.62 fof(fact_remdups__eq__nil__right__iff,axiom, % 187.68/187.62 ! [V_x_2,T_a] : % 187.68/187.62 ( c_List_Olist_ONil(T_a) = c_List_Oremdups(T_a,V_x_2) % 187.68/187.62 <=> V_x_2 = c_List_Olist_ONil(T_a) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_remdups__eq__nil__iff,axiom, % 187.68/187.62 ! [V_x_2,T_a] : % 187.68/187.62 ( c_List_Oremdups(T_a,V_x_2) = c_List_Olist_ONil(T_a) % 187.68/187.62 <=> V_x_2 = c_List_Olist_ONil(T_a) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_distinct__remdups__id,axiom, % 187.68/187.62 ! [V_xs,T_a] : % 187.68/187.62 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 187.68/187.62 => c_List_Oremdups(T_a,V_xs) = V_xs ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_remdups__id__iff__distinct,axiom, % 187.68/187.62 ! [V_xs_2,T_a] : % 187.68/187.62 ( c_List_Oremdups(T_a,V_xs_2) = V_xs_2 % 187.68/187.62 <=> hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_remove1__remdups,axiom, % 187.68/187.62 ! [V_x,V_xs,T_a] : % 187.68/187.62 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 187.68/187.62 => 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)) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_length__remdups__eq,axiom, % 187.68/187.62 ! [V_xs_2,T_a] : % 187.68/187.62 ( 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) % 187.68/187.62 <=> c_List_Oremdups(T_a,V_xs_2) = V_xs_2 ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_remdups__remdups,axiom, % 187.68/187.62 ! [V_xs,T_a] : c_List_Oremdups(T_a,c_List_Oremdups(T_a,V_xs)) = c_List_Oremdups(T_a,V_xs) ). % 187.68/187.62 % 187.68/187.62 fof(fact_remdups__filter,axiom, % 187.68/187.62 ! [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)) ). % 187.68/187.62 % 187.68/187.62 fof(fact_embed__list__def,axiom, % 187.68/187.62 ! [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) ). % 187.68/187.62 % 187.68/187.62 fof(fact_remdups_Osimps_I2_J,axiom, % 187.68/187.62 ! [V_xs_2,V_x_2,T_a] : % 187.68/187.62 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 187.68/187.62 => 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) ) % 187.68/187.62 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 187.68/187.62 => 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)) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_length__remdups__card__conv,axiom, % 187.68/187.62 ! [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)) ). % 187.68/187.62 % 187.68/187.62 fof(fact_fun__left__comm_Ofold__set__remdups,axiom, % 187.68/187.62 ! [V_xs_2,V_y_2,V_f_2,T_b,T_a] : % 187.68/187.62 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 187.68/187.62 => 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)) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_transfer__nat__int__list__functions_I1_J,axiom, % 187.68/187.62 ! [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))) ). % 187.68/187.62 % 187.68/187.62 fof(fact_takeWhile__neq__rev,axiom, % 187.68/187.62 ! [V_x_2,V_xs_2,T_a] : % 187.68/187.62 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 187.68/187.62 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 187.68/187.62 => 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))) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_dropWhile__neq__rev,axiom, % 187.68/187.62 ! [V_x_2,V_xs_2,T_a] : % 187.68/187.62 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 187.68/187.62 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 187.68/187.62 => 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))) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_dropWhile__map,axiom, % 187.68/187.62 ! [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)) ). % 187.68/187.62 % 187.68/187.62 fof(fact_takeWhile__dropWhile__id,axiom, % 187.68/187.62 ! [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 ). % 187.68/187.62 % 187.68/187.62 fof(fact_length__dropWhile__le,axiom, % 187.68/187.62 ! [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))) ). % 187.68/187.62 % 187.68/187.62 fof(fact_distinct__dropWhile,axiom, % 187.68/187.62 ! [V_P_2,V_xs_2,T_a] : % 187.68/187.62 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 187.68/187.62 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_OdropWhile(T_a,V_P_2,V_xs_2))) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_hd__dropWhile,axiom, % 187.68/187.62 ! [V_xs_2,V_P_2,T_a] : % 187.68/187.62 ( c_List_OdropWhile(T_a,V_P_2,V_xs_2) != c_List_Olist_ONil(T_a) % 187.68/187.62 => ~ hBOOL(hAPP(V_P_2,hAPP(c_List_Ohd(T_a),c_List_OdropWhile(T_a,V_P_2,V_xs_2)))) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_dropWhile_Osimps_I1_J,axiom, % 187.68/187.62 ! [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) ). % 187.68/187.62 % 187.68/187.62 fof(fact_sorted__dropWhile,axiom, % 187.68/187.62 ! [V_P_2,V_xs_2,T_a] : % 187.68/187.62 ( class_Orderings_Olinorder(T_a) % 187.68/187.62 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2) % 187.68/187.62 => c_List_Olinorder__class_Osorted(T_a,c_List_OdropWhile(T_a,V_P_2,V_xs_2)) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_dropWhile_Osimps_I2_J,axiom, % 187.68/187.62 ! [V_xs_2,T_a,V_x_2,V_P_2] : % 187.68/187.62 ( ( hBOOL(hAPP(V_P_2,V_x_2)) % 187.68/187.62 => 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) ) % 187.68/187.62 & ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 187.68/187.62 => 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) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_dropWhile__eq__Nil__conv,axiom, % 187.68/187.62 ! [V_xs_2,V_P_2,T_a] : % 187.68/187.62 ( c_List_OdropWhile(T_a,V_P_2,V_xs_2) = c_List_Olist_ONil(T_a) % 187.68/187.62 <=> ! [B_x] : % 187.68/187.62 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 187.68/187.62 => hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_dropWhile__append1,axiom, % 187.68/187.62 ! [V_ys_2,V_P_2,V_xs_2,V_x_2,T_a] : % 187.68/187.62 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 187.68/187.62 => ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 187.68/187.62 => 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) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_dropWhile__eq__Cons__conv,axiom, % 187.68/187.62 ! [V_ys_2,V_y_2,V_xs_2,V_P_2,T_a] : % 187.68/187.62 ( 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) % 187.68/187.62 <=> ( 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)) % 187.68/187.62 & ~ hBOOL(hAPP(V_P_2,V_y_2)) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_dropWhile__eq__drop,axiom, % 187.68/187.62 ! [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) ). % 187.68/187.62 % 187.68/187.62 fof(fact_dropWhile__nth,axiom, % 187.68/187.62 ! [V_xs_2,V_P_2,T_a,V_j_2] : % 187.68/187.62 ( 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)))) % 187.68/187.62 => 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)))) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_listsum__map__filter,axiom, % 187.68/187.62 ! [V_f_2,V_P_2,V_xs_2,T_a,T_b] : % 187.68/187.62 ( class_Groups_Omonoid__add(T_b) % 187.68/187.62 => ( ! [B_x] : % 187.68/187.62 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 187.68/187.62 => ( ~ hBOOL(hAPP(V_P_2,B_x)) % 187.68/187.62 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) ) ) % 187.68/187.62 => 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)) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_sorted__nth__monoI,axiom, % 187.68/187.62 ! [V_xs,T_a] : % 187.68/187.62 ( class_Orderings_Olinorder(T_a) % 187.68/187.62 => ( ! [B_i,B_j] : % 187.68/187.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_j)) % 187.68/187.62 => ( 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))) % 187.68/187.62 => 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))) ) ) % 187.68/187.62 => c_List_Olinorder__class_Osorted(T_a,V_xs) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_n__lists_Osimps_I2_J,axiom, % 187.68/187.62 ! [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))) ). % 187.68/187.62 % 187.68/187.62 fof(fact_partition__filter__conv,axiom, % 187.68/187.62 ! [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)) ). % 187.68/187.62 % 187.68/187.62 fof(fact_partition__filter1,axiom, % 187.68/187.62 ! [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) ). % 187.68/187.62 % 187.68/187.62 fof(fact_distinct__n__lists,axiom, % 187.68/187.62 ! [V_n,V_xs,T_a] : % 187.68/187.62 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 187.68/187.62 => hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(T_a)),c_Enum_On__lists(T_a,V_n,V_xs))) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_length__n__lists,axiom, % 187.68/187.62 ! [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) ). % 187.68/187.62 % 187.68/187.62 fof(fact_length__n__lists__elem,axiom, % 187.68/187.62 ! [V_xs_2,V_n_2,V_ys_2,T_a] : % 187.68/187.62 ( 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)))) % 187.68/187.62 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2) = V_n_2 ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_partition__P,axiom, % 187.68/187.62 ! [V_no_2,V_yes_2,V_xs_2,V_P_2,T_a] : % 187.68/187.62 ( 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) % 187.68/187.62 => ( ! [B_x] : % 187.68/187.62 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_yes_2))) % 187.68/187.62 => hBOOL(hAPP(V_P_2,B_x)) ) % 187.68/187.62 & ! [B_x] : % 187.68/187.62 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_no_2))) % 187.68/187.62 => ~ hBOOL(hAPP(V_P_2,B_x)) ) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_partition_Osimps_I1_J,axiom, % 187.68/187.62 ! [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)) ). % 187.68/187.62 % 187.68/187.62 fof(fact_n__lists_Osimps_I1_J,axiom, % 187.68/187.62 ! [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))) ). % 187.68/187.62 % 187.68/187.62 fof(fact_n__lists__Nil,axiom, % 187.68/187.62 ! [T_a,V_n] : % 187.68/187.62 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 187.68/187.62 => 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))) ) % 187.68/187.62 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 187.68/187.62 => c_Enum_On__lists(T_a,V_n,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(tc_List_Olist(T_a)) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_partition_Osimps_I2_J,axiom, % 187.68/187.62 ! [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)) ). % 187.68/187.62 % 187.68/187.62 fof(fact_partition__filter2,axiom, % 187.68/187.62 ! [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) ). % 187.68/187.62 % 187.68/187.62 fof(fact_partition__set,axiom, % 187.68/187.62 ! [V_no_2,V_yes_2,V_xs_2,V_P_2,T_a] : % 187.68/187.62 ( 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) % 187.68/187.62 => 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) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_set__n__lists,axiom, % 187.68/187.62 ! [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)))) ). % 187.68/187.62 % 187.68/187.62 fof(fact_sublists__powset,axiom, % 187.68/187.62 ! [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)) ). % 187.68/187.62 % 187.68/187.62 fof(fact_length__sublists,axiom, % 187.68/187.62 ! [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)) ). % 187.68/187.62 % 187.68/187.62 fof(fact_distinct__set__sublists,axiom, % 187.68/187.62 ! [V_xs_2,T_a] : % 187.68/187.62 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 187.68/187.62 => 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)))) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_sublists_Osimps_I1_J,axiom, % 187.68/187.62 ! [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))) ). % 187.68/187.62 % 187.68/187.62 fof(fact_sublists_Osimps_I2_J,axiom, % 187.68/187.62 ! [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))))) ). % 187.68/187.62 % 187.68/187.62 fof(fact_product_Osimps_I2_J,axiom, % 187.68/187.62 ! [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)) ). % 187.68/187.62 % 187.68/187.62 fof(fact_enum__the__def,axiom, % 187.68/187.62 ! [V_P_2,T_a] : c_Enum_Oenum__the(T_a,V_P_2) = c_HOL_OThe(T_a,V_P_2) ). % 187.68/187.62 % 187.68/187.62 fof(fact_product_Osimps_I1_J,axiom, % 187.68/187.62 ! [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)) ). % 187.68/187.62 % 187.68/187.62 fof(fact_distinct__product,axiom, % 187.68/187.62 ! [V_ys,T_b,V_xs,T_a] : % 187.68/187.62 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 187.68/187.62 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_ys)) % 187.68/187.62 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_a,T_b)),c_Enum_Oproduct(T_a,T_b,V_xs,V_ys))) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_product__list__set,axiom, % 187.68/187.62 ! [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))) ). % 187.68/187.62 % 187.68/187.62 fof(fact_map__of__zip__enum__inject,axiom, % 187.68/187.62 ! [V_ys_2,V_xs_2,T_a,T_b] : % 187.68/187.62 ( ( class_Enum_Oenum(T_b) % 187.68/187.62 & class_Enum_Oenum(T_a) ) % 187.68/187.62 => ( 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)) % 187.68/187.62 => ( 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)) % 187.68/187.62 => ( 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))) % 187.68/187.62 => V_xs_2 = V_ys_2 ) ) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_sort__foldl__insort,axiom, % 187.68/187.62 ! [V_xs_2,T_a] : % 187.68/187.62 ( class_Orderings_Olinorder(T_a) % 187.68/187.62 => 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) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_enum__distinct,axiom, % 187.68/187.62 ! [T_a] : % 187.68/187.62 ( class_Enum_Oenum(T_a) % 187.68/187.62 => hBOOL(hAPP(c_List_Odistinct(T_a),c_Enum_Oenum__class_Oenum(T_a))) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_distinct__sort,axiom, % 187.68/187.62 ! [V_xs_2,V_f_2,T_a,T_b] : % 187.68/187.62 ( class_Orderings_Olinorder(T_b) % 187.68/187.62 => ( hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Olinorder__class_Osort__key(T_a,T_b,V_f_2,V_xs_2))) % 187.68/187.62 <=> hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_enum__option__def,axiom, % 187.68/187.62 ! [T_a] : % 187.68/187.62 ( class_Enum_Oenum(T_a) % 187.68/187.62 => 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))) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_enum__prod__def,axiom, % 187.68/187.62 ! [T_b,T_a] : % 187.68/187.62 ( ( class_Enum_Oenum(T_a) % 187.68/187.62 & class_Enum_Oenum(T_b) ) % 187.68/187.62 => 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)) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_in__enum,axiom, % 187.68/187.62 ! [V_x_2,T_a] : % 187.68/187.62 ( class_Enum_Oenum(T_a) % 187.68/187.62 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_Enum_Oenum__class_Oenum(T_a)))) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_enum__UNIV,axiom, % 187.68/187.62 ! [T_a] : % 187.68/187.62 ( class_Enum_Oenum(T_a) % 187.68/187.62 => 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)) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_UNIV__enum,axiom, % 187.68/187.62 ! [T_a] : % 187.68/187.62 ( class_Enum_Oenum(T_a) % 187.68/187.62 => 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)) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_set__sort,axiom, % 187.68/187.62 ! [V_xs_2,V_f_2,T_a,T_b] : % 187.68/187.62 ( class_Orderings_Olinorder(T_b) % 187.68/187.62 => 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) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_sorted__sort,axiom, % 187.68/187.62 ! [V_xs_2,T_a] : % 187.68/187.62 ( class_Orderings_Olinorder(T_a) % 187.68/187.62 => c_List_Olinorder__class_Osorted(T_a,c_List_Olinorder__class_Osort__key(T_a,T_a,c_COMBI(T_a),V_xs_2)) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_sort__key__simps_I1_J,axiom, % 187.68/187.62 ! [V_f_2,T_a,T_b] : % 187.68/187.62 ( class_Orderings_Olinorder(T_b) % 187.68/187.62 => 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) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_length__sort,axiom, % 187.68/187.62 ! [V_xs_2,V_f_2,T_a,T_b] : % 187.68/187.62 ( class_Orderings_Olinorder(T_b) % 187.68/187.62 => 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) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_filter__sort,axiom, % 187.68/187.62 ! [V_xs_2,V_f_2,V_P_2,T_a,T_b] : % 187.68/187.62 ( class_Orderings_Olinorder(T_b) % 187.68/187.62 => 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)) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_sorted__sort__key,axiom, % 187.68/187.62 ! [V_xs_2,V_f_2,T_b,T_a] : % 187.68/187.62 ( class_Orderings_Olinorder(T_a) % 187.68/187.62 => 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))) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_sort__key__simps_I2_J,axiom, % 187.68/187.62 ! [V_xs_2,V_x_2,V_f_2,T_a,T_b] : % 187.68/187.62 ( class_Orderings_Olinorder(T_b) % 187.68/187.62 => 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)) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_enum__fun__code,axiom, % 187.68/187.62 ! [T_b,T_a] : % 187.68/187.62 ( ( class_Enum_Oenum(T_a) % 187.68/187.62 & class_HOL_Oequal(T_a) % 187.68/187.62 & class_Enum_Oenum(T_b) ) % 187.68/187.62 => 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))) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_enum__fun__def,axiom, % 187.68/187.62 ! [T_b,T_a] : % 187.68/187.62 ( ( class_Enum_Oenum(T_a) % 187.68/187.62 & class_Enum_Oenum(T_b) ) % 187.68/187.62 => 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))) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_sorted__list__of__set__sort__remdups,axiom, % 187.68/187.62 ! [V_xs_2,T_a] : % 187.68/187.62 ( class_Orderings_Olinorder(T_a) % 187.68/187.62 => 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)) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_all__n__lists__def,axiom, % 187.68/187.62 ! [V_n_2,V_P_2,T_a] : % 187.68/187.62 ( class_Enum_Oenum(T_a) % 187.68/187.62 => ( c_Enum_Oall__n__lists(T_a,V_P_2,V_n_2) % 187.68/187.62 <=> ! [B_x] : % 187.68/187.62 ( 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))))) % 187.68/187.62 => hBOOL(hAPP(V_P_2,B_x)) ) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_ex__n__lists__def,axiom, % 187.68/187.62 ! [V_n_2,V_P_2,T_a] : % 187.68/187.62 ( class_Enum_Oenum(T_a) % 187.68/187.62 => ( c_Enum_Oex__n__lists(T_a,V_P_2,V_n_2) % 187.68/187.62 <=> ? [B_x] : % 187.68/187.62 ( 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))))) % 187.68/187.62 & hBOOL(hAPP(V_P_2,B_x)) ) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_enum__ex__fun__code,axiom, % 187.68/187.62 ! [V_P_2,T_a,T_b] : % 187.68/187.62 ( ( class_Enum_Oenum(T_b) % 187.68/187.62 & class_Enum_Oenum(T_a) % 187.68/187.62 & class_HOL_Oequal(T_a) ) % 187.68/187.62 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_fun(T_a,T_b)),V_P_2)) % 187.68/187.62 <=> 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))) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_enum__all__fun__code,axiom, % 187.68/187.62 ! [V_P_2,T_a,T_b] : % 187.68/187.62 ( ( class_Enum_Oenum(T_b) % 187.68/187.62 & class_Enum_Oenum(T_a) % 187.68/187.62 & class_HOL_Oequal(T_a) ) % 187.68/187.62 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_fun(T_a,T_b)),V_P_2)) % 187.68/187.62 <=> 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))) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_enum__all__option__def,axiom, % 187.68/187.62 ! [V_P_2,T_a] : % 187.68/187.62 ( class_Enum_Oenum(T_a) % 187.68/187.62 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_Option_Ooption(T_a)),V_P_2)) % 187.68/187.62 <=> ( hBOOL(hAPP(V_P_2,c_Option_Ooption_ONone(T_a))) % 187.68/187.62 & 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)))) ) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_enum__ex__option__def,axiom, % 187.68/187.62 ! [V_P_2,T_a] : % 187.68/187.62 ( class_Enum_Oenum(T_a) % 187.68/187.62 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_Option_Ooption(T_a)),V_P_2)) % 187.68/187.62 <=> ( hBOOL(hAPP(V_P_2,c_Option_Ooption_ONone(T_a))) % 187.68/187.62 | 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)))) ) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_all__code,axiom, % 187.68/187.62 ! [V_P_2,T_a] : % 187.68/187.62 ( class_Enum_Oenum(T_a) % 187.68/187.62 => ( ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) % 187.68/187.62 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_a),V_P_2)) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_exists__code,axiom, % 187.68/187.62 ! [V_P_2,T_a] : % 187.68/187.62 ( class_Enum_Oenum(T_a) % 187.68/187.62 => ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) % 187.68/187.62 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_a),V_P_2)) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_enum__all,axiom, % 187.68/187.62 ! [V_P_2,T_a] : % 187.68/187.62 ( class_Enum_Oenum(T_a) % 187.68/187.62 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_a),V_P_2)) % 187.68/187.62 <=> ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_enum__ex,axiom, % 187.68/187.62 ! [V_P_2,T_a] : % 187.68/187.62 ( class_Enum_Oenum(T_a) % 187.68/187.62 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_a),V_P_2)) % 187.68/187.62 <=> ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_enum__all__prod__def,axiom, % 187.68/187.62 ! [V_P_2,T_a,T_b] : % 187.68/187.62 ( ( class_Enum_Oenum(T_b) % 187.68/187.62 & class_Enum_Oenum(T_a) ) % 187.68/187.62 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(T_a,T_b)),V_P_2)) % 187.68/187.62 <=> 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))))) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_enum__ex__prod__def,axiom, % 187.68/187.62 ! [V_P_2,T_a,T_b] : % 187.68/187.62 ( ( class_Enum_Oenum(T_b) % 187.68/187.62 & class_Enum_Oenum(T_a) ) % 187.68/187.62 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(T_a,T_b)),V_P_2)) % 187.68/187.62 <=> 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))))) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_order__fun_I1_J,axiom, % 187.68/187.62 ! [V_g_2,V_f_2,T_a,T_b] : % 187.68/187.62 ( ( class_Orderings_Oorder(T_b) % 187.68/187.62 & class_Enum_Oenum(T_a) ) % 187.68/187.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_f_2),V_g_2)) % 187.68/187.62 <=> 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))) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_order__fun_I2_J,axiom, % 187.68/187.62 ! [V_g_2,V_f_2,T_a,T_b] : % 187.68/187.62 ( ( class_Orderings_Oorder(T_b) % 187.68/187.62 & class_Enum_Oenum(T_a) ) % 187.68/187.62 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b)),V_f_2),V_g_2)) % 187.68/187.62 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_f_2),V_g_2)) % 187.68/187.62 & 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)))) ) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_enum__all__fun__def,axiom, % 187.68/187.62 ! [V_P_2,T_a,T_b] : % 187.68/187.62 ( ( class_Enum_Oenum(T_b) % 187.68/187.62 & class_Enum_Oenum(T_a) ) % 187.68/187.62 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_fun(T_a,T_b)),V_P_2)) % 187.68/187.62 <=> 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))) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_enum__ex__fun__def,axiom, % 187.68/187.62 ! [V_P_2,T_a,T_b] : % 187.68/187.62 ( ( class_Enum_Oenum(T_b) % 187.68/187.62 & class_Enum_Oenum(T_a) ) % 187.68/187.62 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_fun(T_a,T_b)),V_P_2)) % 187.68/187.62 <=> 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))) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_map__of__zip__enum__is__Some,axiom, % 187.68/187.62 ! [V_x,V_ys,T_b,T_a] : % 187.68/187.62 ( class_Enum_Oenum(T_a) % 187.68/187.62 => ( 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)) % 187.68/187.62 => ? [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) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_takeWhile__eq__filter,axiom, % 187.68/187.62 ! [V_xs_2,V_P_2,T_a] : % 187.68/187.62 ( ! [B_x] : % 187.68/187.62 ( 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)))) % 187.68/187.62 => ~ hBOOL(hAPP(V_P_2,B_x)) ) % 187.68/187.62 => c_List_OtakeWhile(T_a,V_P_2,V_xs_2) = hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_takeWhile__eq__take__P__nth,axiom, % 187.68/187.62 ! [V_P_2,V_xs_2,T_a,V_n_2] : % 187.68/187.62 ( ! [B_i] : % 187.68/187.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2)) % 187.68/187.62 => ( 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))) % 187.68/187.62 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i))) ) ) % 187.68/187.62 => ( ( 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))) % 187.68/187.62 => ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_n_2))) ) % 187.68/187.62 => c_List_OtakeWhile(T_a,V_P_2,V_xs_2) = hAPP(hAPP(c_List_Otake(T_a),V_n_2),V_xs_2) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_length__takeWhile__less__P__nth,axiom, % 187.68/187.62 ! [V_xs_2,T_a,V_P_2,V_j_2] : % 187.68/187.62 ( ! [B_i] : % 187.68/187.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_j_2)) % 187.68/187.62 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i))) ) % 187.68/187.62 => ( 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))) % 187.68/187.62 => 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)))) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_lists__IntI,axiom, % 187.68/187.62 ! [V_B_2,V_A_2,V_l_2,T_a] : % 187.68/187.62 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_l_2),c_List_Olists(T_a,V_A_2))) % 187.68/187.62 => ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_l_2),c_List_Olists(T_a,V_B_2))) % 187.68/187.62 => 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)) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_lists__Int__eq,axiom, % 187.68/187.62 ! [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))) ). % 187.68/187.62 % 187.68/187.62 fof(fact_listsp_ONil,axiom, % 187.68/187.62 ! [V_A_2,T_a] : hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),c_List_Olist_ONil(T_a))) ). % 187.68/187.62 % 187.68/187.62 fof(fact_listsp__infI,axiom, % 187.68/187.62 ! [V_B_2,V_l_2,V_A_2,T_a] : % 187.68/187.62 ( hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_l_2)) % 187.68/187.62 => ( hBOOL(hAPP(c_List_Olistsp(T_a,V_B_2),V_l_2)) % 187.68/187.62 => 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)) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_listsp__inf__eq,axiom, % 187.68/187.62 ! [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)) ). % 187.68/187.62 % 187.68/187.62 fof(fact_listsp__conj__eq,axiom, % 187.68/187.62 ! [V_x_2,V_B_2,V_A_2,T_a] : % 187.68/187.62 ( 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)) % 187.68/187.62 <=> ( hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_x_2)) % 187.68/187.62 & hBOOL(hAPP(c_List_Olistsp(T_a,V_B_2),V_x_2)) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_listsp_Oequations_I1_J,axiom, % 187.68/187.62 ! [V_A_2,T_a] : hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),c_List_Olist_ONil(T_a))) ). % 187.68/187.62 % 187.68/187.62 fof(fact_in__listsp__conv__set,axiom, % 187.68/187.62 ! [V_xs_2,V_A_2,T_a] : % 187.68/187.62 ( hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_xs_2)) % 187.68/187.62 <=> ! [B_x] : % 187.68/187.62 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 187.68/187.62 => hBOOL(hAPP(V_A_2,B_x)) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_append__in__listsp__conv,axiom, % 187.68/187.62 ! [V_ys_2,V_xs_2,V_A_2,T_a] : % 187.68/187.62 ( hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2))) % 187.68/187.62 <=> ( hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_xs_2)) % 187.68/187.62 & hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_ys_2)) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_listsp_Oequations_I2_J,axiom, % 187.68/187.62 ! [V_a2_2,V_a1_2,V_A_2,T_a] : % 187.68/187.62 ( hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_a1_2),V_a2_2))) % 187.68/187.62 <=> ( hBOOL(hAPP(V_A_2,V_a1_2)) % 187.68/187.62 & hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_a2_2)) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_listsp__mono,axiom, % 187.68/187.62 ! [V_B_2,V_A_2,T_a] : % 187.68/187.62 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 187.68/187.62 => 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))) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_listsp__lists__eq,axiom, % 187.68/187.62 ! [V_x_2,V_A_2,T_a] : % 187.68/187.62 ( 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)) % 187.68/187.62 <=> hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_x_2),c_List_Olists(T_a,V_A_2))) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_list__all2__def,axiom, % 187.68/187.62 ! [V_ys_2,V_xs_2,V_P_2,T_b,T_a] : % 187.68/187.62 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) % 187.68/187.62 <=> ( 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) % 187.68/187.62 & ! [B_x] : % 187.68/187.62 ( 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)))) % 187.68/187.62 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),V_P_2),B_x)) ) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_sorted_Osimps,axiom, % 187.68/187.62 ! [V_a_2,T_a] : % 187.68/187.62 ( class_Orderings_Olinorder(T_a) % 187.68/187.62 => ( c_List_Olinorder__class_Osorted(T_a,V_a_2) % 187.68/187.62 <=> ( V_a_2 = c_List_Olist_ONil(T_a) % 187.68/187.62 | ? [B_xs,B_x] : % 187.68/187.62 ( V_a_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_x),B_xs) % 187.68/187.62 & ! [B_xa] : % 187.68/187.62 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),hAPP(c_List_Oset(T_a),B_xs))) % 187.68/187.62 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_x),B_xa)) ) % 187.68/187.62 & c_List_Olinorder__class_Osorted(T_a,B_xs) ) ) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_list__all2__Cons,axiom, % 187.68/187.62 ! [V_ys_2,V_y_2,V_xs_2,V_x_2,V_P_2,T_b,T_a] : % 187.68/187.62 ( 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)) % 187.68/187.62 <=> ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2)) % 187.68/187.62 & c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_list__all2__map2,axiom, % 187.68/187.62 ! [V_bs_2,V_f_2,T_c,V_as_2,V_P_2,T_b,T_a] : % 187.68/187.62 ( 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)) % 187.68/187.62 <=> 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) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_list__all2__map1,axiom, % 187.68/187.62 ! [V_bs_2,V_as_2,V_f_2,T_c,V_P_2,T_b,T_a] : % 187.68/187.62 ( 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) % 187.68/187.62 <=> 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) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_list__all2__appendI,axiom, % 187.68/187.62 ! [V_d_2,V_c_2,V_b_2,V_a_2,V_P_2,T_b,T_a] : % 187.68/187.62 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_a_2,V_b_2) % 187.68/187.62 => ( c_List_Olist__all2(T_a,T_b,V_P_2,V_c_2,V_d_2) % 187.68/187.62 => c_List_Olist__all2(T_a,T_b,V_P_2,hAPP(hAPP(c_List_Oappend(T_a),V_a_2),V_c_2),hAPP(hAPP(c_List_Oappend(T_b),V_b_2),V_d_2)) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_list__all2__append,axiom, % 187.68/187.62 ! [V_vs_2,V_us_2,V_P_2,V_ys_2,T_b,V_xs_2,T_a] : % 187.68/187.62 ( 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) % 187.68/187.62 => ( 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)) % 187.68/187.62 <=> ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) % 187.68/187.62 & c_List_Olist__all2(T_a,T_b,V_P_2,V_us_2,V_vs_2) ) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_list__all2__rev,axiom, % 187.68/187.62 ! [V_ys_2,V_xs_2,V_P_2,T_b,T_a] : % 187.68/187.62 ( 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)) % 187.68/187.62 <=> c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_list__all2__rev1,axiom, % 187.68/187.62 ! [V_ys_2,V_xs_2,V_P_2,T_b,T_a] : % 187.68/187.62 ( c_List_Olist__all2(T_a,T_b,V_P_2,hAPP(c_List_Orev(T_a),V_xs_2),V_ys_2) % 187.68/187.62 <=> c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,hAPP(c_List_Orev(T_b),V_ys_2)) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_list__all2__update__cong,axiom, % 187.68/187.62 ! [V_y_2,V_x_2,V_ys_2,V_P_2,T_b,V_xs_2,T_a,V_i_2] : % 187.68/187.62 ( 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))) % 187.68/187.62 => ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) % 187.68/187.62 => ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2)) % 187.68/187.62 => 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)) ) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_list__all2__update__cong2,axiom, % 187.68/187.62 ! [V_i_2,V_y_2,V_x_2,V_ys_2,V_xs_2,V_P_2,T_b,T_a] : % 187.68/187.62 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) % 187.68/187.62 => ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2)) % 187.68/187.62 => ( 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))) % 187.68/187.62 => 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)) ) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_list__all2__Nil,axiom, % 187.68/187.62 ! [V_ys_2,V_P_2,T_b,T_a] : % 187.68/187.62 ( c_List_Olist__all2(T_a,T_b,V_P_2,c_List_Olist_ONil(T_a),V_ys_2) % 187.68/187.62 <=> V_ys_2 = c_List_Olist_ONil(T_b) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_list__all2__Nil2,axiom, % 187.68/187.62 ! [V_xs_2,V_P_2,T_b,T_a] : % 187.68/187.62 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,c_List_Olist_ONil(T_b)) % 187.68/187.62 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_list__all2__takeI,axiom, % 187.68/187.62 ! [V_n_2,V_ys_2,V_xs_2,V_P_2,T_b,T_a] : % 187.68/187.62 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) % 187.68/187.62 => 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)) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_list__all2__dropI,axiom, % 187.68/187.62 ! [V_n_2,V_bs_2,V_as_2,V_P_2,T_b,T_a] : % 187.68/187.62 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_as_2,V_bs_2) % 187.68/187.62 => 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)) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_list__all2__nthD2,axiom, % 187.68/187.62 ! [V_p_2,V_ys_2,V_xs_2,V_P_2,T_b,T_a] : % 187.68/187.62 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) % 187.68/187.62 => ( 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))) % 187.68/187.62 => 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))) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_list__all2__nthD,axiom, % 187.68/187.62 ! [V_p_2,V_ys_2,V_xs_2,V_P_2,T_b,T_a] : % 187.68/187.62 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) % 187.68/187.62 => ( 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))) % 187.68/187.62 => 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))) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_list__all2__conv__all__nth,axiom, % 187.68/187.62 ! [V_ys_2,V_xs_2,V_P_2,T_b,T_a] : % 187.68/187.62 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) % 187.68/187.62 <=> ( 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) % 187.68/187.62 & ! [B_i] : % 187.68/187.62 ( 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))) % 187.68/187.62 => 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))) ) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_list__all2__lengthD,axiom, % 187.68/187.62 ! [V_ys_2,V_xs_2,V_P_2,T_b,T_a] : % 187.68/187.62 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) % 187.68/187.62 => 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) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_list__all2__eq,axiom, % 187.68/187.62 ! [T_a,V_ys_2,V_xs_2] : % 187.68/187.62 ( V_xs_2 = V_ys_2 % 187.68/187.62 <=> c_List_Olist__all2(T_a,T_a,c_fequal,V_xs_2,V_ys_2) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_list__all2I,axiom, % 187.68/187.62 ! [V_P_2,V_b_2,V_a_2,T_b,T_a] : % 187.68/187.62 ( ! [B_x] : % 187.68/187.62 ( 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)))) % 187.68/187.62 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),V_P_2),B_x)) ) % 187.68/187.62 => ( 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) % 187.68/187.62 => c_List_Olist__all2(T_a,T_b,V_P_2,V_a_2,V_b_2) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_all__nth__imp__all__set,axiom, % 187.68/187.62 ! [V_x_2,V_P_2,V_xs_2,T_a] : % 187.68/187.62 ( ! [B_i] : % 187.68/187.62 ( 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))) % 187.68/187.62 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i))) ) % 187.68/187.62 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 187.68/187.62 => hBOOL(hAPP(V_P_2,V_x_2)) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_map__removeAll__inj__on,axiom, % 187.68/187.62 ! [V_xs_2,V_x_2,V_f_2,T_b,T_a] : % 187.68/187.62 ( 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))) % 187.68/187.62 => 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)) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_List_Oinsert__def,axiom, % 187.68/187.62 ! [V_xs_2,V_x_2,T_a] : % 187.68/187.62 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 187.68/187.62 => c_List_Oinsert(T_a,V_x_2,V_xs_2) = V_xs_2 ) % 187.68/187.62 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 187.68/187.62 => 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) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_removeAll_Osimps_I2_J,axiom, % 187.68/187.62 ! [V_xs,T_a,V_y,V_x] : % 187.68/187.62 ( ( V_x = V_y % 187.68/187.62 => 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) ) % 187.68/187.62 & ( V_x != V_y % 187.68/187.62 => 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)) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_distinct__removeAll,axiom, % 187.68/187.62 ! [V_x,V_xs,T_a] : % 187.68/187.62 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 187.68/187.62 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_OremoveAll(T_a,V_x),V_xs))) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_distinct__insert,axiom, % 187.68/187.62 ! [V_x,V_xs,T_a] : % 187.68/187.62 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 187.68/187.62 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oinsert(T_a,V_x,V_xs))) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_removeAll__append,axiom, % 187.68/187.62 ! [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)) ). % 187.68/187.62 % 187.68/187.62 fof(fact_removeAll__id,axiom, % 187.68/187.62 ! [V_xs_2,V_x_2,T_a] : % 187.68/187.62 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 187.68/187.62 => hAPP(c_List_OremoveAll(T_a,V_x_2),V_xs_2) = V_xs_2 ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_removeAll_Osimps_I1_J,axiom, % 187.68/187.62 ! [V_x,T_a] : hAPP(c_List_OremoveAll(T_a,V_x),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 187.68/187.62 % 187.68/187.62 fof(fact_removeAll__filter__not,axiom, % 187.68/187.62 ! [V_xs_2,T_a,V_x_2,V_P_2] : % 187.68/187.62 ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 187.68/187.62 => 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) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_removeAll__filter__not__eq,axiom, % 187.68/187.62 ! [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))) ). % 187.68/187.62 % 187.68/187.62 fof(fact_insert__remdups,axiom, % 187.68/187.62 ! [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)) ). % 187.68/187.62 % 187.68/187.62 fof(fact_distinct__remove1__removeAll,axiom, % 187.68/187.62 ! [V_x,V_xs,T_a] : % 187.68/187.62 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 187.68/187.62 => c_List_Oremove1(T_a,V_x,V_xs) = hAPP(c_List_OremoveAll(T_a,V_x),V_xs) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_in__set__insert,axiom, % 187.68/187.62 ! [V_xs_2,V_x_2,T_a] : % 187.68/187.62 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 187.68/187.62 => c_List_Oinsert(T_a,V_x_2,V_xs_2) = V_xs_2 ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_List_Oset__insert,axiom, % 187.68/187.62 ! [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)) ). % 187.68/187.62 % 187.68/187.62 fof(fact_insert__Nil,axiom, % 187.68/187.62 ! [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)) ). % 187.68/187.62 % 187.68/187.62 fof(fact_map__removeAll__inj,axiom, % 187.68/187.62 ! [V_xs_2,V_x_2,V_f_2,T_b,T_a] : % 187.68/187.62 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 187.68/187.62 => 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)) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_set__removeAll,axiom, % 187.68/187.62 ! [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)))) ). % 187.68/187.62 % 187.68/187.62 fof(fact_not__in__set__insert,axiom, % 187.68/187.62 ! [V_xs_2,V_x_2,T_a] : % 187.68/187.62 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 187.68/187.62 => 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) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_concat__map__maps,axiom, % 187.68/187.62 ! [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) ). % 187.68/187.62 % 187.68/187.62 fof(fact_maps__def,axiom, % 187.68/187.62 ! [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)) ). % 187.68/187.62 % 187.68/187.62 fof(fact_maps__simps_I2_J,axiom, % 187.68/187.62 ! [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) ). % 187.68/187.62 % 187.68/187.62 fof(fact_maps__simps_I1_J,axiom, % 187.68/187.62 ! [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)) ). % 187.68/187.62 % 187.68/187.62 fof(fact_distinct__concat,axiom, % 187.68/187.62 ! [V_xs_2,T_a] : % 187.68/187.62 ( hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(T_a)),V_xs_2)) % 187.68/187.62 => ( ! [B_ys] : % 187.68/187.62 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_ys),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xs_2))) % 187.68/187.62 => hBOOL(hAPP(c_List_Odistinct(T_a),B_ys)) ) % 187.68/187.62 => ( ! [B_ys] : % 187.68/187.62 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_ys),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xs_2))) % 187.68/187.62 => ! [B_zs] : % 187.68/187.62 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_zs),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xs_2))) % 187.68/187.62 => ( B_ys != B_zs % 187.68/187.62 => 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)) ) ) ) % 187.68/187.62 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oconcat(T_a,V_xs_2))) ) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_measures__lesseq,axiom, % 187.68/187.62 ! [V_fs_2,T_a,V_y_2,V_x_2,V_f_2] : % 187.68/187.62 ( 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))) % 187.68/187.62 => ( 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))) % 187.68/187.62 => 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)))) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_wf__measures,axiom, % 187.68/187.62 ! [V_fs_2,T_a] : c_Wellfounded_Owf(T_a,c_List_Omeasures(T_a,V_fs_2)) ). % 187.68/187.62 % 187.68/187.62 fof(fact_in__measures_I1_J,axiom, % 187.68/187.62 ! [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))))) ). % 187.68/187.62 % 187.68/187.62 fof(fact_measures__def,axiom, % 187.68/187.62 ! [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)) ). % 187.68/187.62 % 187.68/187.62 fof(fact_in__measures_I2_J,axiom, % 187.68/187.62 ! [V_fs_2,V_f_2,V_y_2,V_x_2,T_a] : % 187.68/187.62 ( 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)))) % 187.68/187.62 <=> ( 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))) % 187.68/187.62 | ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) % 187.68/187.62 & 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))) ) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_measures__less,axiom, % 187.68/187.62 ! [V_fs_2,T_a,V_y_2,V_x_2,V_f_2] : % 187.68/187.62 ( 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))) % 187.68/187.62 => 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)))) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_foldl__apply,axiom, % 187.68/187.62 ! [V_s_2,V_g_2,V_h_2,V_f_2,T_b,T_c,V_xs_2,T_a] : % 187.68/187.62 ( ! [B_x] : % 187.68/187.62 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 187.68/187.62 => 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)) ) % 187.68/187.62 => 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)) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_zip__obtain__same__length,axiom, % 187.68/187.62 ! [V_P_2,V_ys_2,T_b,V_xs_2,T_a] : % 187.68/187.62 ( ( 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)) % 187.68/187.62 => 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)))) ) % 187.68/187.62 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2))) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_map__of__eqI,axiom, % 187.68/187.62 ! [V_ys_2,V_xs_2,T_b,T_a] : % 187.68/187.62 ( 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)) % 187.68/187.62 => ( ! [B_x] : % 187.68/187.62 ( 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)))) % 187.68/187.62 => 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) ) % 187.68/187.62 => hAPP(c_Map_Omap__of(T_a,T_b),V_xs_2) = hAPP(c_Map_Omap__of(T_a,T_b),V_ys_2) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_pos__not__random__dseq__def,axiom, % 187.68/187.62 ! [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)) ). % 187.68/187.62 % 187.68/187.62 fof(fact_dropWhile__append2,axiom, % 187.68/187.62 ! [V_ys_2,V_P_2,V_xs_2,T_a] : % 187.68/187.62 ( ! [B_x] : % 187.68/187.62 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 187.68/187.62 => hBOOL(hAPP(V_P_2,B_x)) ) % 187.68/187.62 => 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) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_list__all2__all__nthI,axiom, % 187.68/187.62 ! [V_P_2,V_b_2,T_b,V_a_2,T_a] : % 187.68/187.62 ( 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) % 187.68/187.62 => ( ! [B_n] : % 187.68/187.62 ( 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))) % 187.68/187.62 => 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))) ) % 187.68/187.62 => c_List_Olist__all2(T_a,T_b,V_P_2,V_a_2,V_b_2) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_finite__sorted__distinct__unique,axiom, % 187.68/187.62 ! [V_A_2,T_a] : % 187.68/187.62 ( class_Orderings_Olinorder(T_a) % 187.68/187.62 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 187.68/187.62 => ? [B_x] : % 187.68/187.62 ( hAPP(c_List_Oset(T_a),B_x) = V_A_2 % 187.68/187.62 & c_List_Olinorder__class_Osorted(T_a,B_x) % 187.68/187.62 & hBOOL(hAPP(c_List_Odistinct(T_a),B_x)) % 187.68/187.62 & ! [B_y] : % 187.68/187.62 ( ( hAPP(c_List_Oset(T_a),B_y) = V_A_2 % 187.68/187.62 & c_List_Olinorder__class_Osorted(T_a,B_y) % 187.68/187.62 & hBOOL(hAPP(c_List_Odistinct(T_a),B_y)) ) % 187.68/187.62 => B_y = B_x ) ) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_takeWhile__append2,axiom, % 187.68/187.62 ! [V_ys_2,V_P_2,V_xs_2,T_a] : % 187.68/187.62 ( ! [B_x] : % 187.68/187.62 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 187.68/187.62 => hBOOL(hAPP(V_P_2,B_x)) ) % 187.68/187.62 => 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)) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_insort__is__Cons,axiom, % 187.68/187.62 ! [V_a_2,V_f_2,V_xs_2,T_a,T_b] : % 187.68/187.62 ( class_Orderings_Olinorder(T_b) % 187.68/187.62 => ( ! [B_x] : % 187.68/187.62 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 187.68/187.62 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,V_a_2)),hAPP(V_f_2,B_x))) ) % 187.68/187.62 => 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) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_Cons__eq__filter__iff,axiom, % 187.68/187.62 ! [V_ys_2,V_P_2,V_xs_2,V_x_2,T_a] : % 187.68/187.62 ( 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) % 187.68/187.62 <=> ? [B_us,B_vs] : % 187.68/187.62 ( 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)) % 187.68/187.62 & ! [B_x] : % 187.68/187.62 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),B_us))) % 187.68/187.62 => ~ hBOOL(hAPP(V_P_2,B_x)) ) % 187.68/187.62 & hBOOL(hAPP(V_P_2,V_x_2)) % 187.68/187.62 & V_xs_2 = hAPP(c_List_Ofilter(T_a,V_P_2),B_vs) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_filter__eq__Cons__iff,axiom, % 187.68/187.62 ! [V_xs_2,V_x_2,V_ys_2,V_P_2,T_a] : % 187.68/187.62 ( 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) % 187.68/187.62 <=> ? [B_us,B_vs] : % 187.68/187.62 ( 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)) % 187.68/187.62 & ! [B_x] : % 187.68/187.62 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),B_us))) % 187.68/187.62 => ~ hBOOL(hAPP(V_P_2,B_x)) ) % 187.68/187.62 & hBOOL(hAPP(V_P_2,V_x_2)) % 187.68/187.62 & V_xs_2 = hAPP(c_List_Ofilter(T_a,V_P_2),B_vs) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_list__ball__nth,axiom, % 187.68/187.62 ! [V_P_2,V_xs_2,T_a,V_n_2] : % 187.68/187.62 ( 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))) % 187.68/187.62 => ( ! [B_x] : % 187.68/187.62 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 187.68/187.62 => hBOOL(hAPP(V_P_2,B_x)) ) % 187.68/187.62 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_n_2))) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_sorted_OCons,axiom, % 187.68/187.62 ! [V_x_2,V_xs_2,T_a] : % 187.68/187.62 ( class_Orderings_Olinorder(T_a) % 187.68/187.62 => ( ! [B_x] : % 187.68/187.62 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 187.68/187.62 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),B_x)) ) % 187.68/187.62 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2) % 187.68/187.62 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) ) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_list__ex__length,axiom, % 187.68/187.62 ! [V_xs_2,V_P_2,T_a] : % 187.68/187.62 ( c_List_Olist__ex(T_a,V_P_2,V_xs_2) % 187.68/187.62 <=> ? [B_n] : % 187.68/187.62 ( 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))) % 187.68/187.62 & hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_n))) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_list__ex__simps_I1_J,axiom, % 187.68/187.62 ! [V_xs_2,V_x_2,V_P_2,T_a] : % 187.68/187.62 ( c_List_Olist__ex(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) % 187.68/187.62 <=> ( hBOOL(hAPP(V_P_2,V_x_2)) % 187.68/187.62 | c_List_Olist__ex(T_a,V_P_2,V_xs_2) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_list__ex__iff,axiom, % 187.68/187.62 ! [V_xs_2,V_P_2,T_a] : % 187.68/187.62 ( c_List_Olist__ex(T_a,V_P_2,V_xs_2) % 187.68/187.62 <=> ? [B_x] : % 187.68/187.62 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 187.68/187.62 & hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_list__ex__rev,axiom, % 187.68/187.62 ! [V_xs_2,V_P_2,T_a] : % 187.68/187.62 ( c_List_Olist__ex(T_a,V_P_2,hAPP(c_List_Orev(T_a),V_xs_2)) % 187.68/187.62 <=> c_List_Olist__ex(T_a,V_P_2,V_xs_2) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_list__ex__append,axiom, % 187.68/187.62 ! [V_ys_2,V_xs_2,V_P_2,T_a] : % 187.68/187.62 ( c_List_Olist__ex(T_a,V_P_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)) % 187.68/187.62 <=> ( c_List_Olist__ex(T_a,V_P_2,V_xs_2) % 187.68/187.62 | c_List_Olist__ex(T_a,V_P_2,V_ys_2) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_list__ex__simps_I2_J,axiom, % 187.68/187.62 ! [V_P_2,T_a] : ~ c_List_Olist__ex(T_a,V_P_2,c_List_Olist_ONil(T_a)) ). % 187.68/187.62 % 187.68/187.62 fof(fact_in__set__conv__decomp__first,axiom, % 187.68/187.62 ! [V_xs_2,V_x_2,T_a] : % 187.68/187.62 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 187.68/187.62 <=> ? [B_ys] : % 187.68/187.62 ( ? [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)) % 187.68/187.62 & ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),B_ys))) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_in__set__conv__decomp__last,axiom, % 187.68/187.62 ! [V_xs_2,V_x_2,T_a] : % 187.68/187.62 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 187.68/187.62 <=> ? [B_ys,B_zs] : % 187.68/187.62 ( 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)) % 187.68/187.62 & ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),B_zs))) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_in__set__conv__decomp,axiom, % 187.68/187.62 ! [V_xs_2,V_x_2,T_a] : % 187.68/187.62 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 187.68/187.62 <=> ? [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)) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_list__all__length,axiom, % 187.68/187.62 ! [V_xs_2,V_P_2,T_a] : % 187.68/187.62 ( c_List_Olist__all(T_a,V_P_2,V_xs_2) % 187.68/187.62 <=> ! [B_n] : % 187.68/187.62 ( 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))) % 187.68/187.62 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_n))) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_list__all__simps_I1_J,axiom, % 187.68/187.62 ! [V_xs_2,V_x_2,V_P_2,T_a] : % 187.68/187.62 ( c_List_Olist__all(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) % 187.68/187.62 <=> ( hBOOL(hAPP(V_P_2,V_x_2)) % 187.68/187.62 & c_List_Olist__all(T_a,V_P_2,V_xs_2) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_list__all__iff,axiom, % 187.68/187.62 ! [V_xs_2,V_P_2,T_a] : % 187.68/187.62 ( c_List_Olist__all(T_a,V_P_2,V_xs_2) % 187.68/187.62 <=> ! [B_x] : % 187.68/187.62 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 187.68/187.62 => hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_list__all__rev,axiom, % 187.68/187.62 ! [V_xs_2,V_P_2,T_a] : % 187.68/187.62 ( c_List_Olist__all(T_a,V_P_2,hAPP(c_List_Orev(T_a),V_xs_2)) % 187.68/187.62 <=> c_List_Olist__all(T_a,V_P_2,V_xs_2) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_Ball__set__list__all,axiom, % 187.68/187.62 ! [V_P_2,V_xs_2,T_a] : % 187.68/187.62 ( ! [B_x] : % 187.68/187.62 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 187.68/187.62 => hBOOL(hAPP(V_P_2,B_x)) ) % 187.68/187.62 <=> c_List_Olist__all(T_a,V_P_2,V_xs_2) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_list__all__append,axiom, % 187.68/187.62 ! [V_ys_2,V_xs_2,V_P_2,T_a] : % 187.68/187.62 ( c_List_Olist__all(T_a,V_P_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)) % 187.68/187.62 <=> ( c_List_Olist__all(T_a,V_P_2,V_xs_2) % 187.68/187.62 & c_List_Olist__all(T_a,V_P_2,V_ys_2) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_list__all__simps_I2_J,axiom, % 187.68/187.62 ! [V_P_2,T_a] : c_List_Olist__all(T_a,V_P_2,c_List_Olist_ONil(T_a)) ). % 187.68/187.62 % 187.68/187.62 fof(fact_list__all__iff__raw,axiom, % 187.68/187.62 ! [V_xs_2,V_P_2,T_a] : % 187.68/187.62 ( c_List_Olist__all(T_a,V_P_2,V_xs_2) % 187.68/187.62 <=> ! [B_x] : % 187.68/187.62 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 187.68/187.62 => hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_list__ex1__simps_I2_J,axiom, % 187.68/187.62 ! [V_xs_2,V_x_2,V_P_2,T_a] : % 187.68/187.62 ( c_List_Olist__ex1(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) % 187.68/187.62 <=> ( ( hBOOL(hAPP(V_P_2,V_x_2)) % 187.68/187.62 => 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) ) % 187.68/187.62 & ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 187.68/187.62 => c_List_Olist__ex1(T_a,V_P_2,V_xs_2) ) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_internal__split__def,axiom, % 187.68/187.62 ! [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) ). % 187.68/187.62 % 187.68/187.62 fof(fact_list__ex1__simps_I1_J,axiom, % 187.68/187.62 ! [V_P_2,T_a] : ~ c_List_Olist__ex1(T_a,V_P_2,c_List_Olist_ONil(T_a)) ). % 187.68/187.62 % 187.68/187.62 fof(fact_exists1__code,axiom, % 187.68/187.62 ! [V_P_2,T_a] : % 187.68/187.62 ( class_Enum_Oenum(T_a) % 187.68/187.62 => ( ? [B_x] : % 187.68/187.62 ( hBOOL(hAPP(V_P_2,B_x)) % 187.68/187.62 & ! [B_y] : % 187.68/187.62 ( hBOOL(hAPP(V_P_2,B_y)) % 187.68/187.62 => B_y = B_x ) ) % 187.68/187.62 <=> c_List_Olist__ex1(T_a,V_P_2,c_Enum_Oenum__class_Oenum(T_a)) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_internal__split__conv,axiom, % 187.68/187.62 ! [V_b_2,V_a_2,V_c_2,T_a,T_c,T_b] : hAPP(hAPP(c_Product__Type_Ointernal__split(T_b,T_c,T_a),V_c_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)) = hAPP(hAPP(V_c_2,V_a_2),V_b_2) ). % 187.68/187.62 % 187.68/187.62 fof(fact_list__ex1__iff,axiom, % 187.68/187.62 ! [V_xs_2,V_P_2,T_a] : % 187.68/187.62 ( c_List_Olist__ex1(T_a,V_P_2,V_xs_2) % 187.68/187.62 <=> ? [B_x] : % 187.68/187.62 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 187.68/187.62 & hBOOL(hAPP(V_P_2,B_x)) % 187.68/187.62 & ! [B_y] : % 187.68/187.62 ( ( hBOOL(hAPP(hAPP(c_member(T_a),B_y),hAPP(c_List_Oset(T_a),V_xs_2))) % 187.68/187.62 & hBOOL(hAPP(V_P_2,B_y)) ) % 187.68/187.62 => B_y = B_x ) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_setprod__nonneg,axiom, % 187.68/187.62 ! [V_f_2,V_A_2,T_a,T_b] : % 187.68/187.62 ( class_Rings_Olinordered__semidom(T_b) % 187.68/187.62 => ( ! [B_x] : % 187.68/187.62 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 187.68/187.62 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(V_f_2,B_x))) ) % 187.68/187.62 => 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))) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_bool_Osize_I1_J,axiom, % 187.68/187.62 c_HOL_Obool_Obool__size(c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 187.68/187.62 % 187.68/187.62 fof(fact_bool_Osize_I2_J,axiom, % 187.68/187.62 c_HOL_Obool_Obool__size(c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 187.68/187.62 % 187.68/187.62 fof(fact_finite__less__ub,axiom, % 187.68/187.62 ! [V_u_2,V_f_2] : % 187.68/187.62 ( ! [B_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_n),hAPP(V_f_2,B_n))) % 187.68/187.62 => 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)))) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_measure__function__int,axiom, % 187.68/187.62 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))) ). % 187.68/187.62 % 187.68/187.62 fof(fact_measure__size,axiom, % 187.68/187.62 ! [T_a] : % 187.68/187.62 ( class_Nat_Osize(T_a) % 187.68/187.62 => c_FunDef_Ois__measure(T_a,c_Nat_Osize__class_Osize(T_a)) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_is__measure_Osimps,axiom, % 187.68/187.62 ! [V_a_2,T_a] : c_FunDef_Ois__measure(T_a,V_a_2) ). % 187.68/187.62 % 187.68/187.62 fof(fact_is__measure_Oequations,axiom, % 187.68/187.62 ! [V_a_2,T_a] : c_FunDef_Ois__measure(T_a,V_a_2) ). % 187.68/187.62 % 187.68/187.62 fof(fact_is__measure_Ointros,axiom, % 187.68/187.62 ! [V_f_2,T_a] : c_FunDef_Ois__measure(T_a,V_f_2) ). % 187.68/187.62 % 187.68/187.62 fof(fact_measure__fst,axiom, % 187.68/187.62 ! [T_b,V_f_2,T_a] : % 187.68/187.62 ( c_FunDef_Ois__measure(T_a,V_f_2) % 187.68/187.62 => 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))) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_measure__snd,axiom, % 187.68/187.62 ! [T_b,V_f_2,T_a] : % 187.68/187.62 ( c_FunDef_Ois__measure(T_a,V_f_2) % 187.68/187.62 => 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))) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_equal__fun__def,axiom, % 187.68/187.62 ! [V_g_2,V_f_2,T_a,T_b] : % 187.68/187.62 ( ( class_HOL_Oequal(T_b) % 187.68/187.62 & class_Enum_Oenum(T_a) ) % 187.68/187.62 => ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_fun(T_a,T_b)),V_f_2),V_g_2)) % 187.68/187.62 <=> ! [B_x] : % 187.68/187.62 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),c_Enum_Oenum__class_Oenum(T_a)))) % 187.68/187.62 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_transfer__morphism__int__nat,axiom, % 187.68/187.62 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)) ). % 187.68/187.62 % 187.68/187.62 fof(fact_equal,axiom, % 187.68/187.62 ! [T_a] : % 187.68/187.62 ( class_HOL_Oequal(T_a) % 187.68/187.62 => c_HOL_Oequal__class_Oequal(T_a) = c_fequal ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_equal__refl,axiom, % 187.68/187.62 ! [V_x,T_a] : % 187.68/187.62 ( class_HOL_Oequal(T_a) % 187.68/187.62 => hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(T_a),V_x),V_x)) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_equal__eq,axiom, % 187.68/187.62 ! [V_y_2,V_x_2,T_a] : % 187.68/187.62 ( class_HOL_Oequal(T_a) % 187.68/187.62 => ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(T_a),V_x_2),V_y_2)) % 187.68/187.62 <=> V_x_2 = V_y_2 ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_eq__equal,axiom, % 187.68/187.62 ! [T_a] : % 187.68/187.62 ( class_HOL_Oequal(T_a) % 187.68/187.62 => c_fequal = c_HOL_Oequal__class_Oequal(T_a) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_bool_Osize_I4_J,axiom, % 187.68/187.62 hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 187.68/187.62 % 187.68/187.62 fof(fact_bool_Osize_I3_J,axiom, % 187.68/187.62 hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 187.68/187.62 % 187.68/187.62 fof(fact_size__code,axiom, % 187.68/187.62 ! [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))))),c_Lazy__Sequence_Oyield(T_a,V_xq_2)) ). % 187.68/187.62 % 187.68/187.62 fof(fact_New__DSequence_Oneg__decr__bind__def,axiom, % 187.68/187.62 ! [V_f_2,V_x_2,T_a,T_b,V_i_2] : % 187.68/187.62 ( ( V_i_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 187.68/187.62 => 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) ) % 187.68/187.62 & ( V_i_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 187.68/187.62 => 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)) ) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_eq__int__code_I5_J,axiom, % 187.68/187.62 ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ). % 187.68/187.62 % 187.68/187.62 fof(fact_eq__int__code_I2_J,axiom, % 187.68/187.62 ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ). % 187.68/187.62 % 187.68/187.62 fof(fact_eq__int__code_I4_J,axiom, % 187.68/187.62 ! [V_k2] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k2))) ). % 187.68/187.62 % 187.68/187.62 fof(fact_eq__int__code_I10_J,axiom, % 187.68/187.62 ! [V_k1] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(V_k1)),c_Int_OPls)) ). % 187.68/187.62 % 187.68/187.62 fof(fact_eq__int__code_I1_J,axiom, % 187.68/187.62 hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ). % 187.68/187.62 % 187.68/187.62 fof(fact_eq__int__code_I16_J,axiom, % 187.68/187.62 ! [V_k2_2,V_k1_2] : % 187.68/187.62 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2))) % 187.68/187.62 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_eq__number__of__int__code,axiom, % 187.68/187.62 ! [V_l_2,V_k_2] : % 187.68/187.62 ( 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))) % 187.68/187.62 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_eq__int__code_I13_J,axiom, % 187.68/187.62 ! [V_k2_2,V_k1_2] : % 187.68/187.62 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2))) % 187.68/187.62 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_eq__int__code_I6_J,axiom, % 187.68/187.62 hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OMin)) ). % 187.68/187.62 % 187.68/187.62 fof(fact_equal__int__def,axiom, % 187.68/187.62 ! [V_l_2,V_k_2] : % 187.68/187.62 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k_2),V_l_2)) % 187.68/187.62 <=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k_2),V_l_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ). % 187.68/187.62 % 187.68/187.62 fof(fact_eq__int__code_I14_J,axiom, % 187.68/187.62 ! [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))) ). % 187.68/187.62 % 187.68/187.62 %----Arity declarations (233) % 187.68/187.62 fof(arity_HOL__Obool__Lattices_Obounded__lattice,axiom, % 187.68/187.62 class_Lattices_Obounded__lattice(tc_HOL_Obool) ). % 187.68/187.62 % 187.68/187.62 fof(arity_fun__Lattices_Obounded__lattice,axiom, % 187.68/187.62 ! [T_2,T_1] : % 187.68/187.62 ( class_Lattices_Obounded__lattice(T_1) % 187.68/187.62 => class_Lattices_Obounded__lattice(tc_fun(T_2,T_1)) ) ). % 187.68/187.62 % 187.68/187.62 fof(arity_fun__Complete__Lattice_Ocomplete__lattice,axiom, % 187.68/187.62 ! [T_2,T_1] : % 187.68/187.62 ( class_Complete__Lattice_Ocomplete__lattice(T_1) % 187.68/187.62 => class_Complete__Lattice_Ocomplete__lattice(tc_fun(T_2,T_1)) ) ). % 187.68/187.62 % 187.68/187.62 fof(arity_fun__Lattices_Obounded__lattice__top,axiom, % 187.68/187.62 ! [T_2,T_1] : % 187.68/187.62 ( class_Lattices_Obounded__lattice(T_1) % 187.68/187.62 => class_Lattices_Obounded__lattice__top(tc_fun(T_2,T_1)) ) ). % 187.68/187.62 % 187.68/187.62 fof(arity_fun__Lattices_Obounded__lattice__bot,axiom, % 187.68/187.62 ! [T_2,T_1] : % 187.68/187.62 ( class_Lattices_Obounded__lattice(T_1) % 187.68/187.62 => class_Lattices_Obounded__lattice__bot(tc_fun(T_2,T_1)) ) ). % 187.68/187.62 % 187.68/187.62 fof(arity_fun__Lattices_Osemilattice__sup,axiom, % 187.68/187.62 ! [T_2,T_1] : % 187.68/187.62 ( class_Lattices_Olattice(T_1) % 187.68/187.62 => class_Lattices_Osemilattice__sup(tc_fun(T_2,T_1)) ) ). % 187.68/187.62 % 187.68/187.62 fof(arity_fun__Lattices_Osemilattice__inf,axiom, % 187.68/187.62 ! [T_2,T_1] : % 187.68/187.62 ( class_Lattices_Olattice(T_1) % 187.68/187.62 => class_Lattices_Osemilattice__inf(tc_fun(T_2,T_1)) ) ). % 187.68/187.62 % 187.68/187.62 fof(arity_fun__Lattices_Odistrib__lattice,axiom, % 187.68/187.62 ! [T_2,T_1] : % 187.68/187.62 ( class_Lattices_Odistrib__lattice(T_1) % 187.68/187.62 => class_Lattices_Odistrib__lattice(tc_fun(T_2,T_1)) ) ). % 187.68/187.62 % 187.68/187.62 fof(arity_fun__Lattices_Oboolean__algebra,axiom, % 187.68/187.62 ! [T_2,T_1] : % 187.68/187.62 ( class_Lattices_Oboolean__algebra(T_1) % 187.68/187.62 => class_Lattices_Oboolean__algebra(tc_fun(T_2,T_1)) ) ). % 187.68/187.62 % 187.68/187.62 fof(arity_fun__Orderings_Opreorder,axiom, % 187.68/187.62 ! [T_2,T_1] : % 187.68/187.62 ( class_Orderings_Opreorder(T_1) % 187.68/187.62 => class_Orderings_Opreorder(tc_fun(T_2,T_1)) ) ). % 187.68/187.62 % 187.68/187.62 fof(arity_fun__Finite__Set_Ofinite,axiom, % 187.68/187.62 ! [T_1,T_2] : % 187.68/187.62 ( ( class_Finite__Set_Ofinite(T_2) % 187.68/187.62 & class_Finite__Set_Ofinite(T_1) ) % 187.68/187.62 => class_Finite__Set_Ofinite(tc_fun(T_2,T_1)) ) ). % 187.68/187.62 % 187.68/187.62 fof(arity_fun__Lattices_Olattice,axiom, % 187.68/187.62 ! [T_2,T_1] : % 187.68/187.62 ( class_Lattices_Olattice(T_1) % 187.68/187.62 => class_Lattices_Olattice(tc_fun(T_2,T_1)) ) ). % 187.68/187.62 % 187.68/187.62 fof(arity_fun__Orderings_Oorder,axiom, % 187.68/187.62 ! [T_2,T_1] : % 187.68/187.62 ( class_Orderings_Oorder(T_1) % 187.68/187.62 => class_Orderings_Oorder(tc_fun(T_2,T_1)) ) ). % 187.68/187.62 % 187.68/187.62 fof(arity_fun__Orderings_Otop,axiom, % 187.68/187.62 ! [T_2,T_1] : % 187.68/187.62 ( class_Orderings_Otop(T_1) % 187.68/187.62 => class_Orderings_Otop(tc_fun(T_2,T_1)) ) ). % 187.68/187.62 % 187.68/187.62 fof(arity_fun__Orderings_Oord,axiom, % 187.68/187.62 ! [T_2,T_1] : % 187.68/187.62 ( class_Orderings_Oord(T_1) % 187.68/187.62 => class_Orderings_Oord(tc_fun(T_2,T_1)) ) ). % 187.68/187.62 % 187.68/187.62 fof(arity_fun__Orderings_Obot,axiom, % 187.68/187.62 ! [T_2,T_1] : % 187.68/187.62 ( class_Orderings_Obot(T_1) % 187.68/187.62 => class_Orderings_Obot(tc_fun(T_2,T_1)) ) ). % 187.68/187.62 % 187.68/187.62 fof(arity_fun__Groups_Ouminus,axiom, % 187.68/187.62 ! [T_2,T_1] : % 187.68/187.62 ( class_Groups_Ouminus(T_1) % 187.68/187.62 => class_Groups_Ouminus(tc_fun(T_2,T_1)) ) ). % 187.68/187.62 % 187.68/187.62 fof(arity_fun__Groups_Ominus,axiom, % 187.68/187.62 ! [T_2,T_1] : % 187.68/187.62 ( class_Groups_Ominus(T_1) % 187.68/187.62 => class_Groups_Ominus(tc_fun(T_2,T_1)) ) ). % 187.68/187.62 % 187.68/187.62 fof(arity_fun__HOL_Oequal,axiom, % 187.68/187.62 ! [T_1,T_2] : % 187.68/187.62 ( ( class_Enum_Oenum(T_2) % 187.68/187.62 & class_HOL_Oequal(T_1) ) % 187.68/187.62 => class_HOL_Oequal(tc_fun(T_2,T_1)) ) ). % 187.68/187.62 % 187.68/187.62 fof(arity_fun__Enum_Oenum,axiom, % 187.68/187.62 ! [T_1,T_2] : % 187.68/187.62 ( ( class_Enum_Oenum(T_2) % 187.68/187.62 & class_Enum_Oenum(T_1) ) % 187.68/187.62 => class_Enum_Oenum(tc_fun(T_2,T_1)) ) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Com__Ocom__HOL_Oequal,axiom, % 187.68/187.62 class_HOL_Oequal(tc_Com_Ocom) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Com__Ocom__Nat_Osize,axiom, % 187.68/187.62 class_Nat_Osize(tc_Com_Ocom) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom, % 187.68/187.62 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add,axiom, % 187.68/187.62 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le,axiom, % 187.68/187.62 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Int__Oint__Rings_Olinordered__comm__semiring__strict,axiom, % 187.68/187.62 class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Int__Oint__Rings_Olinordered__semiring__1__strict,axiom, % 187.68/187.62 class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Int__Oint__Groups_Olinordered__ab__semigroup__add,axiom, % 187.68/187.62 class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Int__Oint__Rings_Olinordered__semiring__strict,axiom, % 187.68/187.62 class_Rings_Olinordered__semiring__strict(tc_Int_Oint) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add,axiom, % 187.68/187.62 class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Int__Oint__Groups_Oordered__ab__group__add__abs,axiom, % 187.68/187.62 class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Int__Oint__Groups_Oordered__comm__monoid__add,axiom, % 187.68/187.62 class_Groups_Oordered__comm__monoid__add(tc_Int_Oint) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Int__Oint__Groups_Olinordered__ab__group__add,axiom, % 187.68/187.62 class_Groups_Olinordered__ab__group__add(tc_Int_Oint) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Int__Oint__Groups_Ocancel__ab__semigroup__add,axiom, % 187.68/187.62 class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Int__Oint__Rings_Oring__1__no__zero__divisors,axiom, % 187.68/187.62 class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Int__Oint__Rings_Oordered__cancel__semiring,axiom, % 187.68/187.62 class_Rings_Oordered__cancel__semiring(tc_Int_Oint) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Int__Oint__Rings_Olinordered__ring__strict,axiom, % 187.68/187.62 class_Rings_Olinordered__ring__strict(tc_Int_Oint) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Int__Oint__Rings_Oring__no__zero__divisors,axiom, % 187.68/187.62 class_Rings_Oring__no__zero__divisors(tc_Int_Oint) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Int__Oint__Rings_Oordered__comm__semiring,axiom, % 187.68/187.62 class_Rings_Oordered__comm__semiring(tc_Int_Oint) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Int__Oint__Rings_Olinordered__semiring__1,axiom, % 187.68/187.62 class_Rings_Olinordered__semiring__1(tc_Int_Oint) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Int__Oint__Groups_Oordered__ab__group__add,axiom, % 187.68/187.62 class_Groups_Oordered__ab__group__add(tc_Int_Oint) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Int__Oint__Groups_Ocancel__semigroup__add,axiom, % 187.68/187.62 class_Groups_Ocancel__semigroup__add(tc_Int_Oint) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Int__Oint__Rings_Olinordered__semiring,axiom, % 187.68/187.62 class_Rings_Olinordered__semiring(tc_Int_Oint) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Int__Oint__Rings_Olinordered__semidom,axiom, % 187.68/187.62 class_Rings_Olinordered__semidom(tc_Int_Oint) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Int__Oint__Lattices_Osemilattice__sup,axiom, % 187.68/187.62 class_Lattices_Osemilattice__sup(tc_Int_Oint) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Int__Oint__Lattices_Osemilattice__inf,axiom, % 187.68/187.62 class_Lattices_Osemilattice__inf(tc_Int_Oint) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Int__Oint__Lattices_Odistrib__lattice,axiom, % 187.68/187.62 class_Lattices_Odistrib__lattice(tc_Int_Oint) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Int__Oint__Groups_Oab__semigroup__mult,axiom, % 187.68/187.62 class_Groups_Oab__semigroup__mult(tc_Int_Oint) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Int__Oint__Groups_Ocomm__monoid__mult,axiom, % 187.68/187.62 class_Groups_Ocomm__monoid__mult(tc_Int_Oint) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Int__Oint__Groups_Oab__semigroup__add,axiom, % 187.68/187.62 class_Groups_Oab__semigroup__add(tc_Int_Oint) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Int__Oint__Rings_Oordered__semiring,axiom, % 187.68/187.62 class_Rings_Oordered__semiring(tc_Int_Oint) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Int__Oint__Rings_Oordered__ring__abs,axiom, % 187.68/187.62 class_Rings_Oordered__ring__abs(tc_Int_Oint) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Int__Oint__Rings_Ono__zero__divisors,axiom, % 187.68/187.62 class_Rings_Ono__zero__divisors(tc_Int_Oint) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Int__Oint__Groups_Ocomm__monoid__add,axiom, % 187.68/187.62 class_Groups_Ocomm__monoid__add(tc_Int_Oint) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Int__Oint__Rings_Olinordered__ring,axiom, % 187.68/187.62 class_Rings_Olinordered__ring(tc_Int_Oint) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Int__Oint__Rings_Olinordered__idom,axiom, % 187.68/187.62 class_Rings_Olinordered__idom(tc_Int_Oint) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Int__Oint__Rings_Ocomm__semiring__1,axiom, % 187.68/187.62 class_Rings_Ocomm__semiring__1(tc_Int_Oint) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Int__Oint__Groups_Osemigroup__add,axiom, % 187.68/187.62 class_Groups_Osemigroup__add(tc_Int_Oint) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Int__Oint__Divides_Osemiring__div,axiom, % 187.68/187.62 class_Divides_Osemiring__div(tc_Int_Oint) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Int__Oint__Rings_Ocomm__semiring,axiom, % 187.68/187.62 class_Rings_Ocomm__semiring(tc_Int_Oint) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Int__Oint__Nat_Osemiring__char__0,axiom, % 187.68/187.62 class_Nat_Osemiring__char__0(tc_Int_Oint) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Int__Oint__Groups_Oab__group__add,axiom, % 187.68/187.62 class_Groups_Oab__group__add(tc_Int_Oint) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Int__Oint__Rings_Ozero__neq__one,axiom, % 187.68/187.62 class_Rings_Ozero__neq__one(tc_Int_Oint) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Int__Oint__Rings_Oordered__ring,axiom, % 187.68/187.62 class_Rings_Oordered__ring(tc_Int_Oint) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Int__Oint__Orderings_Opreorder,axiom, % 187.68/187.62 class_Orderings_Opreorder(tc_Int_Oint) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Int__Oint__Orderings_Olinorder,axiom, % 187.68/187.62 class_Orderings_Olinorder(tc_Int_Oint) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Int__Oint__Groups_Omonoid__mult,axiom, % 187.68/187.62 class_Groups_Omonoid__mult(tc_Int_Oint) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Int__Oint__Rings_Ocomm__ring__1,axiom, % 187.68/187.62 class_Rings_Ocomm__ring__1(tc_Int_Oint) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Int__Oint__Groups_Omonoid__add,axiom, % 187.68/187.62 class_Groups_Omonoid__add(tc_Int_Oint) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Int__Oint__Smallcheck_Osmall,axiom, % 187.68/187.62 class_Smallcheck_Osmall(tc_Int_Oint) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Int__Oint__Rings_Osemiring__1,axiom, % 187.68/187.62 class_Rings_Osemiring__1(tc_Int_Oint) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Int__Oint__Rings_Osemiring__0,axiom, % 187.68/187.62 class_Rings_Osemiring__0(tc_Int_Oint) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Int__Oint__Lattices_Olattice,axiom, % 187.68/187.62 class_Lattices_Olattice(tc_Int_Oint) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Int__Oint__Groups_Ogroup__add,axiom, % 187.68/187.62 class_Groups_Ogroup__add(tc_Int_Oint) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Int__Oint__Divides_Oring__div,axiom, % 187.68/187.62 class_Divides_Oring__div(tc_Int_Oint) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Int__Oint__Rings_Omult__zero,axiom, % 187.68/187.62 class_Rings_Omult__zero(tc_Int_Oint) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Int__Oint__Orderings_Oorder,axiom, % 187.68/187.62 class_Orderings_Oorder(tc_Int_Oint) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Int__Oint__Int_Oring__char__0,axiom, % 187.68/187.62 class_Int_Oring__char__0(tc_Int_Oint) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Int__Oint__Int_Onumber__ring,axiom, % 187.68/187.62 class_Int_Onumber__ring(tc_Int_Oint) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Int__Oint__Rings_Osemiring,axiom, % 187.68/187.62 class_Rings_Osemiring(tc_Int_Oint) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Int__Oint__Orderings_Oord,axiom, % 187.68/187.62 class_Orderings_Oord(tc_Int_Oint) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Int__Oint__Groups_Ouminus,axiom, % 187.68/187.62 class_Groups_Ouminus(tc_Int_Oint) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Int__Oint__Groups_Osgn__if,axiom, % 187.68/187.62 class_Groups_Osgn__if(tc_Int_Oint) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Int__Oint__Groups_Oabs__if,axiom, % 187.68/187.62 class_Groups_Oabs__if(tc_Int_Oint) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Int__Oint__Rings_Oring__1,axiom, % 187.68/187.62 class_Rings_Oring__1(tc_Int_Oint) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Int__Oint__Groups_Ominus,axiom, % 187.68/187.62 class_Groups_Ominus(tc_Int_Oint) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Int__Oint__Power_Opower,axiom, % 187.68/187.62 class_Power_Opower(tc_Int_Oint) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Int__Oint__Groups_Ozero,axiom, % 187.68/187.62 class_Groups_Ozero(tc_Int_Oint) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Int__Oint__Rings_Oring,axiom, % 187.68/187.62 class_Rings_Oring(tc_Int_Oint) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Int__Oint__Rings_Oidom,axiom, % 187.68/187.62 class_Rings_Oidom(tc_Int_Oint) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Int__Oint__Int_Onumber,axiom, % 187.68/187.62 class_Int_Onumber(tc_Int_Oint) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Int__Oint__Groups_Oone,axiom, % 187.68/187.62 class_Groups_Oone(tc_Int_Oint) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Int__Oint__HOL_Oequal,axiom, % 187.68/187.62 class_HOL_Oequal(tc_Int_Oint) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom, % 187.68/187.62 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add,axiom, % 187.68/187.62 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le,axiom, % 187.68/187.62 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict,axiom, % 187.68/187.62 class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Nat__Onat__Groups_Olinordered__ab__semigroup__add,axiom, % 187.68/187.62 class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Nat__Onat__Rings_Olinordered__semiring__strict,axiom, % 187.68/187.62 class_Rings_Olinordered__semiring__strict(tc_Nat_Onat) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add,axiom, % 187.68/187.62 class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Nat__Onat__Groups_Oordered__comm__monoid__add,axiom, % 187.68/187.62 class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add,axiom, % 187.68/187.62 class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Nat__Onat__Rings_Oordered__cancel__semiring,axiom, % 187.68/187.62 class_Rings_Oordered__cancel__semiring(tc_Nat_Onat) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Nat__Onat__Rings_Oordered__comm__semiring,axiom, % 187.68/187.62 class_Rings_Oordered__comm__semiring(tc_Nat_Onat) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Nat__Onat__Groups_Ocancel__semigroup__add,axiom, % 187.68/187.62 class_Groups_Ocancel__semigroup__add(tc_Nat_Onat) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Nat__Onat__Rings_Olinordered__semiring,axiom, % 187.68/187.62 class_Rings_Olinordered__semiring(tc_Nat_Onat) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Nat__Onat__Rings_Olinordered__semidom,axiom, % 187.68/187.62 class_Rings_Olinordered__semidom(tc_Nat_Onat) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Nat__Onat__Lattices_Osemilattice__sup,axiom, % 187.68/187.62 class_Lattices_Osemilattice__sup(tc_Nat_Onat) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Nat__Onat__Lattices_Osemilattice__inf,axiom, % 187.68/187.62 class_Lattices_Osemilattice__inf(tc_Nat_Onat) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Nat__Onat__Lattices_Odistrib__lattice,axiom, % 187.68/187.62 class_Lattices_Odistrib__lattice(tc_Nat_Onat) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Nat__Onat__Groups_Oab__semigroup__mult,axiom, % 187.68/187.62 class_Groups_Oab__semigroup__mult(tc_Nat_Onat) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Nat__Onat__Groups_Ocomm__monoid__mult,axiom, % 187.68/187.62 class_Groups_Ocomm__monoid__mult(tc_Nat_Onat) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Nat__Onat__Groups_Oab__semigroup__add,axiom, % 187.68/187.62 class_Groups_Oab__semigroup__add(tc_Nat_Onat) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Nat__Onat__Rings_Oordered__semiring,axiom, % 187.68/187.62 class_Rings_Oordered__semiring(tc_Nat_Onat) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Nat__Onat__Rings_Ono__zero__divisors,axiom, % 187.68/187.62 class_Rings_Ono__zero__divisors(tc_Nat_Onat) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Nat__Onat__Groups_Ocomm__monoid__add,axiom, % 187.68/187.62 class_Groups_Ocomm__monoid__add(tc_Nat_Onat) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Nat__Onat__Rings_Ocomm__semiring__1,axiom, % 187.68/187.62 class_Rings_Ocomm__semiring__1(tc_Nat_Onat) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Nat__Onat__Groups_Osemigroup__add,axiom, % 187.68/187.62 class_Groups_Osemigroup__add(tc_Nat_Onat) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Nat__Onat__Divides_Osemiring__div,axiom, % 187.68/187.62 class_Divides_Osemiring__div(tc_Nat_Onat) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Nat__Onat__Rings_Ocomm__semiring,axiom, % 187.68/187.62 class_Rings_Ocomm__semiring(tc_Nat_Onat) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Nat__Onat__Orderings_Owellorder,axiom, % 187.68/187.62 class_Orderings_Owellorder(tc_Nat_Onat) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Nat__Onat__Nat_Osemiring__char__0,axiom, % 187.68/187.62 class_Nat_Osemiring__char__0(tc_Nat_Onat) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Nat__Onat__Rings_Ozero__neq__one,axiom, % 187.68/187.62 class_Rings_Ozero__neq__one(tc_Nat_Onat) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Nat__Onat__Orderings_Opreorder,axiom, % 187.68/187.62 class_Orderings_Opreorder(tc_Nat_Onat) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Nat__Onat__Orderings_Olinorder,axiom, % 187.68/187.62 class_Orderings_Olinorder(tc_Nat_Onat) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Nat__Onat__Groups_Omonoid__mult,axiom, % 187.68/187.62 class_Groups_Omonoid__mult(tc_Nat_Onat) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Nat__Onat__Groups_Omonoid__add,axiom, % 187.68/187.62 class_Groups_Omonoid__add(tc_Nat_Onat) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Nat__Onat__Rings_Osemiring__1,axiom, % 187.68/187.62 class_Rings_Osemiring__1(tc_Nat_Onat) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Nat__Onat__Rings_Osemiring__0,axiom, % 187.68/187.62 class_Rings_Osemiring__0(tc_Nat_Onat) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Nat__Onat__Lattices_Olattice,axiom, % 187.68/187.62 class_Lattices_Olattice(tc_Nat_Onat) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Nat__Onat__Rings_Omult__zero,axiom, % 187.68/187.62 class_Rings_Omult__zero(tc_Nat_Onat) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Nat__Onat__Orderings_Oorder,axiom, % 187.68/187.62 class_Orderings_Oorder(tc_Nat_Onat) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Nat__Onat__Rings_Osemiring,axiom, % 187.68/187.62 class_Rings_Osemiring(tc_Nat_Onat) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Nat__Onat__Orderings_Oord,axiom, % 187.68/187.62 class_Orderings_Oord(tc_Nat_Onat) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Nat__Onat__Orderings_Obot,axiom, % 187.68/187.62 class_Orderings_Obot(tc_Nat_Onat) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Nat__Onat__Groups_Ominus,axiom, % 187.68/187.62 class_Groups_Ominus(tc_Nat_Onat) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Nat__Onat__Power_Opower,axiom, % 187.68/187.62 class_Power_Opower(tc_Nat_Onat) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Nat__Onat__Groups_Ozero,axiom, % 187.68/187.62 class_Groups_Ozero(tc_Nat_Onat) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Nat__Onat__Int_Onumber,axiom, % 187.68/187.62 class_Int_Onumber(tc_Nat_Onat) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Nat__Onat__Groups_Oone,axiom, % 187.68/187.62 class_Groups_Oone(tc_Nat_Onat) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Nat__Onat__HOL_Oequal,axiom, % 187.68/187.62 class_HOL_Oequal(tc_Nat_Onat) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Nat__Onat__Nat_Osize,axiom, % 187.68/187.62 class_Nat_Osize(tc_Nat_Onat) ). % 187.68/187.62 % 187.68/187.62 fof(arity_HOL__Obool__Complete__Lattice_Ocomplete__lattice,axiom, % 187.68/187.62 class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool) ). % 187.68/187.62 % 187.68/187.62 fof(arity_HOL__Obool__Lattices_Obounded__lattice__top,axiom, % 187.68/187.62 class_Lattices_Obounded__lattice__top(tc_HOL_Obool) ). % 187.68/187.62 % 187.68/187.62 fof(arity_HOL__Obool__Lattices_Obounded__lattice__bot,axiom, % 187.68/187.62 class_Lattices_Obounded__lattice__bot(tc_HOL_Obool) ). % 187.68/187.62 % 187.68/187.62 fof(arity_HOL__Obool__Lattices_Osemilattice__sup,axiom, % 187.68/187.62 class_Lattices_Osemilattice__sup(tc_HOL_Obool) ). % 187.68/187.62 % 187.68/187.62 fof(arity_HOL__Obool__Lattices_Osemilattice__inf,axiom, % 187.68/187.62 class_Lattices_Osemilattice__inf(tc_HOL_Obool) ). % 187.68/187.62 % 187.68/187.62 fof(arity_HOL__Obool__Lattices_Odistrib__lattice,axiom, % 187.68/187.62 class_Lattices_Odistrib__lattice(tc_HOL_Obool) ). % 187.68/187.62 % 187.68/187.62 fof(arity_HOL__Obool__Lattices_Oboolean__algebra,axiom, % 187.68/187.62 class_Lattices_Oboolean__algebra(tc_HOL_Obool) ). % 187.68/187.62 % 187.68/187.62 fof(arity_HOL__Obool__Orderings_Opreorder,axiom, % 187.68/187.62 class_Orderings_Opreorder(tc_HOL_Obool) ). % 187.68/187.62 % 187.68/187.62 fof(arity_HOL__Obool__Finite__Set_Ofinite,axiom, % 187.68/187.62 class_Finite__Set_Ofinite(tc_HOL_Obool) ). % 187.68/187.62 % 187.68/187.62 fof(arity_HOL__Obool__Lattices_Olattice,axiom, % 187.68/187.62 class_Lattices_Olattice(tc_HOL_Obool) ). % 187.68/187.62 % 187.68/187.62 fof(arity_HOL__Obool__Orderings_Oorder,axiom, % 187.68/187.62 class_Orderings_Oorder(tc_HOL_Obool) ). % 187.68/187.62 % 187.68/187.62 fof(arity_HOL__Obool__Orderings_Otop,axiom, % 187.68/187.62 class_Orderings_Otop(tc_HOL_Obool) ). % 187.68/187.62 % 187.68/187.62 fof(arity_HOL__Obool__Orderings_Oord,axiom, % 187.68/187.62 class_Orderings_Oord(tc_HOL_Obool) ). % 187.68/187.62 % 187.68/187.62 fof(arity_HOL__Obool__Orderings_Obot,axiom, % 187.68/187.62 class_Orderings_Obot(tc_HOL_Obool) ). % 187.68/187.62 % 187.68/187.62 fof(arity_HOL__Obool__Groups_Ouminus,axiom, % 187.68/187.62 class_Groups_Ouminus(tc_HOL_Obool) ). % 187.68/187.62 % 187.68/187.62 fof(arity_HOL__Obool__Groups_Ominus,axiom, % 187.68/187.62 class_Groups_Ominus(tc_HOL_Obool) ). % 187.68/187.62 % 187.68/187.62 fof(arity_HOL__Obool__HOL_Oequal,axiom, % 187.68/187.62 class_HOL_Oequal(tc_HOL_Obool) ). % 187.68/187.62 % 187.68/187.62 fof(arity_HOL__Obool__Enum_Oenum,axiom, % 187.68/187.62 class_Enum_Oenum(tc_HOL_Obool) ). % 187.68/187.62 % 187.68/187.62 fof(arity_HOL__Obool__Nat_Osize,axiom, % 187.68/187.62 class_Nat_Osize(tc_HOL_Obool) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Com__Ostate__HOL_Oequal,axiom, % 187.68/187.62 class_HOL_Oequal(tc_Com_Ostate) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Com__Ostate__Nat_Osize,axiom, % 187.68/187.62 class_Nat_Osize(tc_Com_Ostate) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Com__Ovname__HOL_Oequal,axiom, % 187.68/187.62 class_HOL_Oequal(tc_Com_Ovname) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Com__Ovname__Nat_Osize,axiom, % 187.68/187.62 class_Nat_Osize(tc_Com_Ovname) ). % 187.68/187.62 % 187.68/187.62 fof(arity_List__Olist__HOL_Oequal,axiom, % 187.68/187.62 ! [T_1] : class_HOL_Oequal(tc_List_Olist(T_1)) ). % 187.68/187.62 % 187.68/187.62 fof(arity_List__Olist__Nat_Osize,axiom, % 187.68/187.62 ! [T_1] : class_Nat_Osize(tc_List_Olist(T_1)) ). % 187.68/187.62 % 187.68/187.62 fof(arity_sum__Finite__Set_Ofinite,axiom, % 187.68/187.62 ! [T_1,T_2] : % 187.68/187.62 ( ( class_Finite__Set_Ofinite(T_2) % 187.68/187.62 & class_Finite__Set_Ofinite(T_1) ) % 187.68/187.62 => class_Finite__Set_Ofinite(tc_sum(T_2,T_1)) ) ). % 187.68/187.62 % 187.68/187.62 fof(arity_sum__HOL_Oequal,axiom, % 187.68/187.62 ! [T_1,T_2] : class_HOL_Oequal(tc_sum(T_2,T_1)) ). % 187.68/187.62 % 187.68/187.62 fof(arity_sum__Enum_Oenum,axiom, % 187.68/187.62 ! [T_1,T_2] : % 187.68/187.62 ( ( class_Enum_Oenum(T_2) % 187.68/187.62 & class_Enum_Oenum(T_1) ) % 187.68/187.62 => class_Enum_Oenum(tc_sum(T_2,T_1)) ) ). % 187.68/187.62 % 187.68/187.62 fof(arity_sum__Nat_Osize,axiom, % 187.68/187.62 ! [T_1,T_2] : class_Nat_Osize(tc_sum(T_2,T_1)) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Option__Ooption__Finite__Set_Ofinite,axiom, % 187.68/187.62 ! [T_1] : % 187.68/187.62 ( class_Finite__Set_Ofinite(T_1) % 187.68/187.62 => class_Finite__Set_Ofinite(tc_Option_Ooption(T_1)) ) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Option__Ooption__HOL_Oequal,axiom, % 187.68/187.62 ! [T_1] : class_HOL_Oequal(tc_Option_Ooption(T_1)) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Option__Ooption__Enum_Oenum,axiom, % 187.68/187.62 ! [T_1] : % 187.68/187.62 ( class_Enum_Oenum(T_1) % 187.68/187.62 => class_Enum_Oenum(tc_Option_Ooption(T_1)) ) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Option__Ooption__Nat_Osize,axiom, % 187.68/187.62 ! [T_1] : class_Nat_Osize(tc_Option_Ooption(T_1)) ). % 187.68/187.62 % 187.68/187.62 fof(arity_prod__Finite__Set_Ofinite,axiom, % 187.68/187.62 ! [T_1,T_2] : % 187.68/187.62 ( ( class_Finite__Set_Ofinite(T_2) % 187.68/187.62 & class_Finite__Set_Ofinite(T_1) ) % 187.68/187.62 => class_Finite__Set_Ofinite(tc_prod(T_2,T_1)) ) ). % 187.68/187.62 % 187.68/187.62 fof(arity_prod__Smallcheck_Osmall,axiom, % 187.68/187.62 ! [T_1,T_2] : % 187.68/187.62 ( ( class_Smallcheck_Osmall(T_2) % 187.68/187.62 & class_Smallcheck_Osmall(T_1) ) % 187.68/187.62 => class_Smallcheck_Osmall(tc_prod(T_2,T_1)) ) ). % 187.68/187.62 % 187.68/187.62 fof(arity_prod__HOL_Oequal,axiom, % 187.68/187.62 ! [T_1,T_2] : class_HOL_Oequal(tc_prod(T_2,T_1)) ). % 187.68/187.62 % 187.68/187.62 fof(arity_prod__Enum_Oenum,axiom, % 187.68/187.62 ! [T_1,T_2] : % 187.68/187.62 ( ( class_Enum_Oenum(T_2) % 187.68/187.62 & class_Enum_Oenum(T_1) ) % 187.68/187.62 => class_Enum_Oenum(tc_prod(T_2,T_1)) ) ). % 187.68/187.62 % 187.68/187.62 fof(arity_prod__Nat_Osize,axiom, % 187.68/187.62 ! [T_1,T_2] : class_Nat_Osize(tc_prod(T_2,T_1)) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Product____Type__Ounit__Finite__Set_Ofinite,axiom, % 187.68/187.62 class_Finite__Set_Ofinite(tc_Product__Type_Ounit) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Product____Type__Ounit__Smallcheck_Osmall,axiom, % 187.68/187.62 class_Smallcheck_Osmall(tc_Product__Type_Ounit) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Product____Type__Ounit__HOL_Oequal,axiom, % 187.68/187.62 class_HOL_Oequal(tc_Product__Type_Ounit) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Product____Type__Ounit__Enum_Oenum,axiom, % 187.68/187.62 class_Enum_Oenum(tc_Product__Type_Ounit) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Product____Type__Ounit__Nat_Osize,axiom, % 187.68/187.62 class_Nat_Osize(tc_Product__Type_Ounit) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Code____Evaluation__Oterm__HOL_Oequal,axiom, % 187.68/187.62 class_HOL_Oequal(tc_Code__Evaluation_Oterm) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Code____Evaluation__Oterm__Nat_Osize,axiom, % 187.68/187.62 class_Nat_Osize(tc_Code__Evaluation_Oterm) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Hoare____Mirabelle__Otriple__HOL_Oequal,axiom, % 187.68/187.62 ! [T_1] : class_HOL_Oequal(tc_Hoare__Mirabelle_Otriple(T_1)) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Hoare____Mirabelle__Otriple__Nat_Osize,axiom, % 187.68/187.62 ! [T_1] : class_Nat_Osize(tc_Hoare__Mirabelle_Otriple(T_1)) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__cancel__ab__semigroup__add,axiom, % 187.68/187.62 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add__imp__le,axiom, % 187.68/187.62 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__comm__semiring__strict,axiom, % 187.68/187.62 class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Code____Numeral__Ocode____numeral__Groups_Olinordered__ab__semigroup__add,axiom, % 187.68/187.62 class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring__strict,axiom, % 187.68/187.62 class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add,axiom, % 187.68/187.62 class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__comm__monoid__add,axiom, % 187.68/187.62 class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__ab__semigroup__add,axiom, % 187.68/187.62 class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__cancel__semiring,axiom, % 187.68/187.62 class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__comm__semiring,axiom, % 187.68/187.62 class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__semigroup__add,axiom, % 187.68/187.62 class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring,axiom, % 187.68/187.62 class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semidom,axiom, % 187.68/187.62 class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__mult,axiom, % 187.68/187.62 class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__mult,axiom, % 187.68/187.62 class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__add,axiom, % 187.68/187.62 class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__semiring,axiom, % 187.68/187.62 class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ono__zero__divisors,axiom, % 187.68/187.62 class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__add,axiom, % 187.68/187.62 class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring__1,axiom, % 187.68/187.62 class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Code____Numeral__Ocode____numeral__Groups_Osemigroup__add,axiom, % 187.68/187.62 class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Code____Numeral__Ocode____numeral__Divides_Osemiring__div,axiom, % 187.68/187.62 class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring,axiom, % 187.68/187.62 class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Code____Numeral__Ocode____numeral__Nat_Osemiring__char__0,axiom, % 187.68/187.62 class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ozero__neq__one,axiom, % 187.68/187.62 class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Opreorder,axiom, % 187.68/187.62 class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Olinorder,axiom, % 187.68/187.62 class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__mult,axiom, % 187.68/187.62 class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__add,axiom, % 187.68/187.62 class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__1,axiom, % 187.68/187.62 class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__0,axiom, % 187.68/187.62 class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Code____Numeral__Ocode____numeral__Rings_Omult__zero,axiom, % 187.68/187.62 class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Oorder,axiom, % 187.68/187.62 class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring,axiom, % 187.68/187.62 class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Oord,axiom, % 187.68/187.62 class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ominus,axiom, % 187.68/187.62 class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Code____Numeral__Ocode____numeral__Power_Opower,axiom, % 187.68/187.62 class_Power_Opower(tc_Code__Numeral_Ocode__numeral) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ozero,axiom, % 187.68/187.62 class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Code____Numeral__Ocode____numeral__Int_Onumber,axiom, % 187.68/187.62 class_Int_Onumber(tc_Code__Numeral_Ocode__numeral) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oone,axiom, % 187.68/187.62 class_Groups_Oone(tc_Code__Numeral_Ocode__numeral) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Code____Numeral__Ocode____numeral__HOL_Oequal,axiom, % 187.68/187.62 class_HOL_Oequal(tc_Code__Numeral_Ocode__numeral) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Code____Numeral__Ocode____numeral__Nat_Osize,axiom, % 187.68/187.62 class_Nat_Osize(tc_Code__Numeral_Ocode__numeral) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Lazy____Sequence__Olazy____sequence__HOL_Oequal,axiom, % 187.68/187.62 ! [T_1] : class_HOL_Oequal(tc_Lazy__Sequence_Olazy__sequence(T_1)) ). % 187.68/187.62 % 187.68/187.62 fof(arity_Lazy____Sequence__Olazy____sequence__Nat_Osize,axiom, % 187.68/187.62 ! [T_1] : class_Nat_Osize(tc_Lazy__Sequence_Olazy__sequence(T_1)) ). % 187.68/187.62 % 187.68/187.62 %----Helper facts (20) % 187.68/187.62 fof(help_c__COMBI__1,axiom, % 187.68/187.62 ! [V_P,T_a] : hAPP(c_COMBI(T_a),V_P) = V_P ). % 187.68/187.62 % 187.68/187.62 fof(help_c__COMBK__1,axiom, % 187.68/187.62 ! [V_Q,V_P,T_b,T_a] : hAPP(hAPP(c_COMBK(T_a,T_b),V_P),V_Q) = V_P ). % 187.68/187.62 % 187.68/187.62 fof(help_c__COMBB__1,axiom, % 187.68/187.62 ! [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)) ). % 187.68/187.62 % 187.68/187.62 fof(help_c__COMBC__1,axiom, % 187.68/187.62 ! [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) ). % 187.68/187.62 % 187.68/187.62 fof(help_c__COMBS__1,axiom, % 187.68/187.62 ! [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)) ). % 187.68/187.62 % 187.68/187.62 fof(help_c__fequal__1,axiom, % 187.68/187.62 ! [V_y_2,V_x_2] : % 187.68/187.62 ( ~ hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2)) % 187.68/187.62 | V_x_2 = V_y_2 ) ). % 187.68/187.62 % 187.68/187.62 fof(help_c__fequal__2,axiom, % 187.68/187.62 ! [V_y_2,V_x_2] : % 187.68/187.62 ( V_x_2 != V_y_2 % 187.68/187.62 | hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2)) ) ). % 187.68/187.62 % 187.68/187.62 fof(help_c__fFalse__1,axiom, % 187.68/187.62 ~ hBOOL(c_fFalse) ). % 187.68/187.62 % 187.68/187.62 fof(help_c__fTrue__1,axiom, % 187.68/187.62 hBOOL(c_fTrue) ). % 187.68/187.62 % 187.68/187.62 fof(help_c__fNot__1,axiom, % 187.68/187.62 ! [V_P_2] : % 187.68/187.62 ( ~ hBOOL(hAPP(c_fNot,V_P_2)) % 187.68/187.62 | ~ hBOOL(V_P_2) ) ). % 187.68/187.62 % 187.68/187.62 fof(help_c__fNot__2,axiom, % 187.68/187.62 ! [V_P_2] : % 187.68/187.62 ( ~ ~ hBOOL(V_P_2) % 187.68/187.62 | hBOOL(hAPP(c_fNot,V_P_2)) ) ). % 187.68/187.62 % 187.68/187.62 fof(help_c__fconj__1,axiom, % 187.68/187.62 ! [V_Q_2,V_P_2] : % 187.68/187.62 ( ~ hBOOL(V_P_2) % 187.68/187.62 | ~ hBOOL(V_Q_2) % 187.68/187.62 | hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2)) ) ). % 187.68/187.62 % 187.68/187.62 fof(help_c__fconj__2,axiom, % 187.68/187.62 ! [V_Q_2,V_P_2] : % 187.68/187.62 ( ~ hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2)) % 187.68/187.62 | hBOOL(V_P_2) ) ). % 187.68/187.62 % 187.68/187.62 fof(help_c__fconj__3,axiom, % 187.68/187.62 ! [V_Q_2,V_P_2] : % 187.68/187.62 ( ~ hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2)) % 187.68/187.62 | hBOOL(V_Q_2) ) ). % 187.68/187.62 % 187.68/187.62 fof(help_c__fdisj__1,axiom, % 187.68/187.62 ! [V_Q_2,V_P_2] : % 187.68/187.62 ( ~ hBOOL(V_P_2) % 187.68/187.62 | hBOOL(hAPP(hAPP(c_fdisj,V_P_2),V_Q_2)) ) ). % 187.68/187.62 % 187.68/187.62 fof(help_c__fdisj__2,axiom, % 187.68/187.62 ! [V_P_2,V_Q_2] : % 187.68/187.62 ( ~ hBOOL(V_Q_2) % 187.68/187.62 | hBOOL(hAPP(hAPP(c_fdisj,V_P_2),V_Q_2)) ) ). % 187.68/187.62 % 187.68/187.62 fof(help_c__fdisj__3,axiom, % 187.68/187.62 ! [V_Q_2,V_P_2] : % 187.68/187.62 ( ~ hBOOL(hAPP(hAPP(c_fdisj,V_P_2),V_Q_2)) % 187.68/187.62 | hBOOL(V_P_2) % 187.68/187.62 | hBOOL(V_Q_2) ) ). % 187.68/187.62 % 187.68/187.62 fof(help_c__fimplies__1,axiom, % 187.68/187.62 ! [V_Q_2,V_P_2] : % 187.68/187.62 ( hBOOL(V_P_2) % 187.68/187.62 | hBOOL(hAPP(hAPP(c_fimplies,V_P_2),V_Q_2)) ) ). % 187.68/187.62 % 187.68/187.62 fof(help_c__fimplies__2,axiom, % 187.68/187.62 ! [V_P_2,V_Q_2] : % 187.68/187.62 ( ~ hBOOL(V_Q_2) % 187.68/187.62 | hBOOL(hAPP(hAPP(c_fimplies,V_P_2),V_Q_2)) ) ). % 187.68/187.62 % 187.68/187.62 fof(help_c__fimplies__3,axiom, % 187.68/187.62 ! [V_Q_2,V_P_2] : % 187.68/187.62 ( ~ hBOOL(hAPP(hAPP(c_fimplies,V_P_2),V_Q_2)) % 187.68/187.62 | ~ hBOOL(V_P_2) % 187.68/187.62 | hBOOL(V_Q_2) ) ). % 187.68/187.62 % 187.68/187.62 %----Conjectures (2) % 187.68/187.62 fof(conj_0,hypothesis, % 187.68/187.62 c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,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,v_pn)),c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,v_pn)))),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_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))),c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_pn))))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) ). % 187.68/187.62 % 187.68/187.62 fof(conj_1,conjecture, % 187.68/187.62 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,v_pn)),c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,v_pn)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) ). % 187.68/187.62 % 187.68/187.62 %------------------------------------------------------------------------------ % 187.68/187.62 %------------------------------------------- % 187.68/187.62 % Proof found % 187.68/187.62 % SZS status Theorem for theBenchmark % 187.68/187.62 % SZS output start Proof % 187.68/187.63 %ClaNum:10196(EqnAxiom:2864) % 187.68/187.63 %VarNum:70487(SingletonVarNum:20489) % 187.68/187.63 %MaxLitNum:8 % 187.68/187.63 %MaxfuncDepth:15 % 187.68/187.63 %SharedTerms:1108 % 187.68/187.63 %goalClause: 4527 % 187.68/187.63 %singleGoalClaCount:1 % 187.68/187.63 [2868]P1(a184) % 187.68/187.63 [2869]P2(a859) % 187.68/187.63 [2870]P2(a865) % 187.68/187.63 [2871]P3(a859) % 187.68/187.63 [2872]P3(a868) % 187.68/187.63 [2873]P105(a865) % 187.68/187.63 [2874]P106(a859) % 187.68/187.63 [2875]P106(a865) % 187.68/187.63 [2876]P106(a1) % 187.68/187.63 [2877]P106(a106) % 187.68/187.63 [2878]P107(a859) % 187.68/187.63 [2879]P107(a865) % 187.68/187.63 [2880]P107(a1) % 187.68/187.63 [2881]P107(a106) % 187.68/187.63 [2882]P108(a865) % 187.68/187.63 [2883]P108(a1) % 187.68/187.63 [2884]P108(a106) % 187.68/187.63 [2885]P109(a859) % 187.68/187.63 [2886]P109(a865) % 187.68/187.63 [2887]P109(a1) % 187.68/187.63 [2888]P109(a106) % 187.68/187.63 [2889]P65(a1) % 187.68/187.63 [2890]P66(a859) % 187.68/187.63 [2891]P66(a865) % 187.68/187.63 [2892]P66(a1) % 187.68/187.63 [2893]P66(a106) % 187.68/187.63 [2894]P67(a1) % 187.68/187.63 [2895]P81(a865) % 187.68/187.63 [2896]P81(a1) % 187.68/187.63 [2897]P81(a106) % 187.68/187.63 [2898]P68(a1) % 187.68/187.63 [2899]P78(a865) % 187.68/187.63 [2900]P78(a1) % 187.68/187.63 [2901]P78(a106) % 187.68/187.63 [2902]P111(a865) % 187.68/187.63 [2903]P111(a1) % 187.68/187.63 [2904]P111(a106) % 187.68/187.63 [2905]P124(a865) % 187.68/187.63 [2906]P124(a1) % 187.68/187.63 [2907]P124(a106) % 187.68/187.63 [2908]P69(a865) % 187.68/187.63 [2909]P69(a1) % 187.68/187.63 [2910]P69(a106) % 187.68/187.63 [2911]P70(a865) % 187.68/187.63 [2912]P70(a1) % 187.68/187.63 [2913]P70(a106) % 187.68/187.63 [2914]P71(a865) % 187.68/187.63 [2915]P71(a1) % 187.68/187.63 [2916]P71(a106) % 187.68/187.63 [2917]P82(a865) % 187.68/187.63 [2918]P82(a1) % 187.68/187.63 [2919]P82(a106) % 187.68/187.63 [2920]P83(a865) % 187.68/187.63 [2921]P83(a1) % 187.68/187.63 [2922]P83(a106) % 187.68/187.63 [2923]P74(a865) % 187.68/187.63 [2924]P74(a1) % 187.68/187.63 [2925]P74(a106) % 187.68/187.63 [2926]P79(a865) % 187.68/187.63 [2927]P79(a1) % 187.68/187.63 [2928]P79(a106) % 187.68/187.63 [2929]P76(a1) % 187.68/187.63 [2930]P85(a865) % 187.68/187.63 [2931]P85(a1) % 187.68/187.63 [2932]P85(a106) % 187.68/187.63 [2933]P86(a865) % 187.68/187.63 [2934]P86(a1) % 187.68/187.63 [2935]P86(a106) % 187.68/187.63 [2936]P112(a1) % 187.68/187.63 [2937]P143(a865) % 187.68/187.63 [2938]P143(a1) % 187.68/187.63 [2939]P113(a865) % 187.68/187.63 [2940]P113(a1) % 187.68/187.63 [2941]P113(a106) % 187.68/187.63 [2942]P90(a1) % 187.68/187.63 [2943]P125(a1) % 187.68/187.63 [2944]P94(a859) % 187.68/187.63 [2945]P87(a859) % 187.68/187.63 [2946]P87(a1) % 187.68/187.63 [2947]P114(a1) % 187.68/187.63 [2948]P88(a1) % 187.68/187.63 [2949]P72(a865) % 187.68/187.63 [2950]P72(a1) % 187.68/187.63 [2951]P72(a106) % 187.68/187.63 [2952]P91(a1) % 187.68/187.63 [2953]P92(a865) % 187.68/187.63 [2954]P92(a1) % 187.68/187.63 [2955]P92(a106) % 187.68/187.63 [2956]P126(a1) % 187.68/187.63 [2957]P138(a865) % 187.68/187.63 [2958]P138(a1) % 187.68/187.63 [2959]P138(a106) % 187.68/187.63 [2960]P127(a865) % 187.68/187.63 [2961]P127(a1) % 187.68/187.63 [2962]P127(a106) % 187.68/187.63 [2963]P139(a1) % 187.68/187.63 [2964]P132(a865) % 187.68/187.63 [2965]P132(a1) % 187.68/187.63 [2966]P132(a106) % 187.68/187.63 [2967]P116(a865) % 187.68/187.63 [2968]P116(a1) % 187.68/187.63 [2969]P116(a106) % 187.68/187.63 [2970]P75(a865) % 187.68/187.63 [2971]P75(a1) % 187.68/187.63 [2972]P75(a106) % 187.68/187.63 [2973]P80(a865) % 187.68/187.63 [2974]P80(a1) % 187.68/187.63 [2975]P80(a106) % 187.68/187.63 [2976]P117(a1) % 187.68/187.63 [2977]P133(a865) % 187.68/187.63 [2978]P133(a1) % 187.68/187.63 [2979]P133(a106) % 187.68/187.63 [2980]P134(a1) % 187.68/187.63 [2981]P136(a865) % 187.68/187.63 [2982]P136(a1) % 187.68/187.63 [2983]P136(a106) % 187.68/187.63 [2984]P135(a865) % 187.68/187.63 [2985]P135(a1) % 187.68/187.63 [2986]P135(a106) % 187.68/187.63 [2987]P122(a1) % 187.68/187.63 [2988]P123(a1) % 187.68/187.63 [2989]P128(a865) % 187.68/187.63 [2990]P128(a1) % 187.68/187.63 [2991]P128(a106) % 187.68/187.63 [2992]P120(a865) % 187.68/187.63 [2993]P120(a1) % 187.68/187.63 [2994]P120(a106) % 187.68/187.63 [2995]P140(a1) % 187.68/187.63 [2996]P129(a865) % 187.68/187.63 [2997]P129(a1) % 187.68/187.63 [2998]P129(a106) % 187.68/187.63 [2999]P130(a1) % 187.68/187.63 [3000]P131(a1) % 187.68/187.63 [3001]P96(a865) % 187.68/187.63 [3002]P96(a1) % 187.68/187.63 [3003]P96(a106) % 187.68/187.63 [3004]P141(a865) % 187.68/187.63 [3005]P141(a1) % 187.68/187.63 [3006]P141(a106) % 187.68/187.63 [3007]P115(a865) % 187.68/187.63 [3008]P115(a1) % 187.68/187.63 [3009]P115(a106) % 187.68/187.63 [3010]P142(a865) % 187.68/187.63 [3011]P142(a1) % 187.68/187.63 [3012]P142(a106) % 187.68/187.63 [3013]P4(a865) % 187.68/187.63 [3014]P4(a1) % 187.68/187.63 [3015]P4(a106) % 187.68/187.63 [3016]P5(a1) % 187.68/187.63 [3017]P97(a859) % 187.68/187.63 [3018]P97(a865) % 187.68/187.63 [3019]P97(a1) % 187.68/187.63 [3020]P98(a859) % 187.68/187.63 [3021]P98(a865) % 187.68/187.63 [3022]P98(a1) % 187.68/187.63 [3023]P99(a859) % 187.68/187.63 [3024]P101(a859) % 187.68/187.63 [3025]P101(a865) % 187.68/187.63 [3026]P101(a1) % 187.68/187.63 [3027]P103(a859) % 187.68/187.63 [3028]P103(a865) % 187.68/187.63 [3029]P103(a1) % 187.68/187.63 [3030]P6(a859) % 187.68/187.63 [3031]P84(a1) % 187.68/187.63 [3032]P137(a1) % 187.68/187.63 [3033]P73(a1) % 187.68/187.63 [3034]P110(a859) % 187.68/187.63 [3035]P102(a859) % 187.68/187.63 [3036]P77(a865) % 187.68/187.63 [3037]P77(a1) % 187.68/187.63 [3038]P77(a106) % 187.68/187.63 [3039]P144(a1) % 187.68/187.63 [3040]P144(a868) % 187.68/187.63 [3041]P89(a865) % 187.68/187.63 [3042]P89(a1) % 187.68/187.63 [3043]P89(a106) % 187.68/187.63 [3044]P60(a859) % 187.68/187.63 [3045]P60(a868) % 187.68/187.63 [3046]P93(a859) % 187.68/187.63 [3047]P93(a860) % 187.68/187.63 [3048]P93(a861) % 187.68/187.63 [3049]P93(a865) % 187.68/187.63 [3050]P93(a1) % 187.68/187.63 [3051]P93(a106) % 187.68/187.63 [3052]P93(a868) % 187.68/187.63 [3053]P93(a302) % 187.68/187.63 [3054]P93(a863) % 187.68/187.63 [3055]P104(a859) % 187.68/187.63 [3056]P104(a860) % 187.68/187.63 [3057]P104(a861) % 187.68/187.63 [3058]P104(a865) % 187.68/187.63 [3059]P104(a106) % 187.68/187.63 [3060]P104(a868) % 187.68/187.63 [3061]P104(a302) % 187.68/187.63 [3062]P104(a863) % 187.68/187.63 [3063]P100(a859) % 187.68/187.63 [3083]P40(a865,a227) % 187.68/187.63 [3084]P40(a865,a296) % 187.68/187.63 [3162]P41(a865,a865,a119) % 187.68/187.63 [4414]~E(a104,a84) % 187.68/187.63 [4415]~P1(a226) % 187.68/187.63 [2865]E(f2(a1),a84) % 187.68/187.63 [2866]E(f107(a106),a3) % 187.68/187.63 [2867]E(f22(a106),a23) % 187.68/187.63 [3064]E(f185(a865),f2(a865)) % 187.68/187.63 [3065]E(f32(a24),f2(a865)) % 187.68/187.63 [3066]E(f219(a865),f108(a865)) % 187.68/187.63 [3067]E(f225(a865),f109(a865)) % 187.68/187.63 [3068]E(f110(a1),f35(a1)) % 187.68/187.63 [3069]E(f85(a226),f2(a865)) % 187.68/187.63 [3070]E(f85(a184),f2(a865)) % 187.68/187.63 [3071]P7(f2(a1)) % 187.68/187.63 [3072]P7(f79(a1)) % 187.68/187.63 [3120]P1(f306(a25,a24)) % 187.68/187.63 [3133]P40(f871(a865,a865),a36) % 187.68/187.63 [3478]E(f299(a865,a865,a227,a227),a36) % 187.68/187.63 [4416]~E(f79(a1),f2(a1)) % 187.68/187.63 [3073]E(f118(f2(a865)),f2(a865)) % 187.68/187.63 [3074]E(f4(f2(a106)),f2(a865)) % 187.68/187.63 [3086]E(f306(f80(a1),a84),a84) % 187.68/187.63 [3090]E(f306(a3,f2(a865)),f2(a106)) % 187.68/187.63 [3091]E(f306(a119,f2(a865)),f79(a865)) % 187.68/187.63 [3092]E(f306(a112,f79(a1)),f79(a865)) % 187.68/187.63 [3093]E(f306(a3,f79(a865)),f79(a106)) % 187.68/187.63 [3095]E(f306(f111(a1),a84),f2(a1)) % 187.68/187.63 [3096]E(f306(f111(a106),a84),f2(a106)) % 187.68/187.63 [3097]E(f306(a112,f2(a1)),f2(a865)) % 187.68/187.63 [3098]E(f306(f186(a859),a226),f2(a865)) % 187.68/187.63 [3099]E(f306(f186(a859),a184),f2(a865)) % 187.68/187.63 [3100]E(f306(f186(a860),a24),f2(a865)) % 187.68/187.63 [3101]E(f306(f111(a865),a84),f2(a865)) % 187.68/187.63 [3105]E(f306(f80(a1),f79(a1)),a104) % 187.68/187.63 [3113]E(f306(f186(a106),f2(a106)),f2(a865)) % 187.68/187.63 [3114]E(f306(f80(a1),f2(a1)),f2(a1)) % 187.68/187.63 [3115]E(f306(f107(a1),f2(a865)),f2(a1)) % 187.68/187.63 [3116]E(f306(f107(a1),f79(a865)),f79(a1)) % 187.68/187.63 [3129]E(f306(a112,f79(a1)),f306(a119,f2(a865))) % 187.68/187.63 [3130]E(f306(f169(a862,a860),a27),a28) % 187.68/187.63 [3131]E(f297(f871(a865,a865),a36),a37) % 187.68/187.63 [3132]E(f298(f871(a865,a865),a36),a38) % 187.68/187.63 [3154]E(f306(f229(a865),f2(a865)),f185(f872(a865,a859))) % 187.68/187.63 [3155]E(f306(f230(a865),f2(a865)),f231(f872(a865,a859))) % 187.68/187.63 [3164]P42(f185(f872(a1,a859))) % 187.68/187.63 [3198]E(f306(f306(f22(a106),f2(a106)),f79(a106)),f2(a106)) % 187.68/187.63 [3273]P1(f306(f306(f221(a1),a104),f2(a1))) % 187.68/187.63 [3299]P1(f306(f306(f220(a1),f2(a1)),f79(a1))) % 187.68/187.63 [3300]P1(f306(f306(f221(a1),f2(a1)),f79(a1))) % 187.68/187.63 [3471]P1(f306(f63(a862),f175(a862,a860,a28))) % 187.68/187.63 [3508]E(f306(f306(f263(a865,a865,a865),a296),f282(a865,a296)),a227) % 187.68/187.63 [3544]P43(a1,a865,a112,f306(f220(a1),f2(a1))) % 187.68/187.63 [3548]E(f306(f306(f43(a865,f872(a865,a859)),f231(f872(a865,a859))),f275(a865)),f231(f872(a865,a859))) % 187.68/187.63 [3549]E(f306(f306(f43(a865,f872(a865,a859)),f231(f872(a865,a859))),f229(a865)),f231(f872(a865,a859))) % 187.68/187.63 [3550]E(f306(f306(f43(a865,f872(a865,a859)),f231(f872(a865,a859))),f230(a865)),f231(f872(a865,a859))) % 187.68/187.63 [3551]E(f306(f306(f44(a865,f872(a865,a859)),f231(f872(a865,a859))),f278(a865)),f185(f872(a865,a859))) % 187.68/187.63 [3567]P28(a865,a1,f107(a1),f231(f872(a865,a859))) % 187.68/187.63 [3578]P43(a865,a1,f107(a1),f306(f16(a859,a865),a184)) % 187.68/187.63 [3710]E(f306(f74(a865,a106,a1,a3),a112),f111(a106)) % 187.68/187.63 [3928]P56(a106,a865,a19,a3,f231(f872(a865,a859))) % 187.68/187.63 [3937]P56(a1,f872(f871(a865,a865),a859),a114,a90,a105) % 187.68/187.63 [4195]E(f246(a1,a1,a1,a1,f35(a1),f80(a1)),a52) % 187.68/187.63 [4439]~E(f306(f111(a1),a104),f306(f111(a1),a84)) % 187.68/187.63 [4440]~P1(f306(a190,f2(a1))) % 187.68/187.63 [4441]~P1(f306(a190,f79(a1))) % 187.68/187.63 [4490]~P1(f306(f306(f221(a1),a84),f2(a1))) % 187.68/187.63 [3146]E(f306(f306(f22(a1),a104),a104),a84) % 187.68/187.63 [3161]E(f306(f107(a1),f306(a119,f2(a865))),f79(a1)) % 187.68/187.63 [3223]E(f306(f39(a868),f231(f872(a868,a859))),f79(a865)) % 187.68/187.63 [3244]P1(f306(a190,f306(f111(a1),a104))) % 187.68/187.63 [3246]P1(f306(f306(f220(a1),a104),a84)) % 187.68/187.63 [3248]P1(f306(f306(f221(a1),a104),a84)) % 187.68/187.63 [3249]P1(f306(f306(f92(a1),a84),a84)) % 187.68/187.63 [3250]P1(f306(f306(f92(a1),a104),a104)) % 187.68/187.63 [3310]E(f306(f306(f284(a865),f2(a865)),f185(f872(a865,a859))),f306(f275(a865),f2(a865))) % 187.68/187.63 [3365]P1(f306(f306(f220(a1),f2(a1)),f306(f111(a1),a84))) % 187.68/187.63 [3377]E(f306(f285(a865,a865,a119),f231(f872(a865,a859))),f306(f278(a865),f2(a865))) % 187.68/187.63 [3416]P9(f871(a865,a865),f231(f872(f871(a865,a865),a859)),a116) % 187.68/187.63 [3718]E(f306(f74(a865,a1,a106,f107(a1)),a19),a20) % 187.68/187.63 [3777]P40(a865,f306(f228(f871(a865,a865)),f306(f245(a865,a865,a859),f221(a865)))) % 187.68/187.63 [4479]~P1(f306(a190,f306(f111(a1),a84))) % 187.68/187.63 [4480]~P1(f306(f306(f220(a1),a84),a104)) % 187.68/187.63 [4481]~P1(f306(f306(f221(a1),a84),a84)) % 187.68/187.63 [4482]~P1(f306(f306(f221(a1),a84),a104)) % 187.68/187.63 [4483]~P1(f306(f306(f221(a1),a104),a104)) % 187.68/187.63 [4484]~P1(f306(f306(f92(a1),a84),a104)) % 187.68/187.63 [4485]~P1(f306(f306(f92(a1),a104),a84)) % 187.68/187.63 [4500]~P1(f306(f63(a865),f231(f872(a865,a859)))) % 187.68/187.63 [4501]~P1(f306(f63(a1),f231(f872(a1,a859)))) % 187.68/187.63 [4364]E(f306(f245(a1,a1,a859),f306(f306(f8(f872(a1,a859),f872(a1,a859),a1),f306(f18(a1,a859,a859),f306(f306(f8(a859,f872(a859,a859),a1),a304),f306(f221(a1),f2(a1))))),f306(f306(f7(a1,a1,f872(a1,a859)),f306(f306(f8(f872(a1,f872(a1,a859)),f872(a1,f872(a1,a859)),a1),f7(a1,a1,a859)),f306(f306(f8(f872(a1,a1),f872(a1,f872(a1,a859)),a1),f306(f8(a1,f872(a1,a859),a1),a303)),a203))),f79(a1)))),a199) % 187.68/187.63 [4527]~P27(a861,a874,f306(f306(f284(f864(a861)),f306(f306(f306(f93(a861),a303),f306(a26,a873)),f193(f306(a26,a873)))),f185(f872(f864(a861),a859)))) % 187.68/187.63 [3453]E(f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104),f306(f80(a1),a104)) % 187.68/187.63 [3491]E(f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104),f306(f306(f22(a1),a84),a104)) % 187.68/187.63 [3645]E(f306(f306(f62(f871(a865,a865)),f231(f872(f871(a865,a865),a859))),a116),a105) % 187.68/187.63 [4174]P27(a861,f306(f306(f284(f864(a861)),f306(f306(f306(f93(a861),a303),f306(a26,a873)),f193(f306(a26,a873)))),a874),f306(f306(f284(f864(a861)),f306(f306(f306(f93(a861),a303),f306(f218(a860),f306(a28,a873))),f193(f306(f218(a860),f306(a28,a873))))),f185(f872(f864(a861),a859)))) % 187.68/187.63 [3674]E(f306(f111(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f79(a1)) % 187.68/187.63 [3675]E(f306(f111(a106),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f79(a106)) % 187.68/187.63 [3676]E(f306(f111(a865),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f79(a865)) % 187.68/187.63 [3680]E(f306(f111(a865),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(a119,f2(a865))) % 187.68/187.63 [4058]E(f306(f306(f108(f872(f871(f871(a865,a865),f871(a865,a865)),a859)),a36),f282(f871(a865,a865),f185(f872(f871(f871(a865,a865),f871(a865,a865)),a859)))),a71) % 187.68/187.63 [4128]E(f306(a90,f306(f260(f871(a865,a865),f871(a865,a865),a116),f306(f306(f284(f871(a865,a865)),f306(f306(f236(a865,a865),f2(a865)),f2(a865))),f185(f872(f871(a865,a865),a859))))),f2(a1)) % 187.68/187.63 [4129]E(f306(a90,f306(f260(f871(a865,a865),f871(a865,a865),a116),f306(f306(f284(f871(a865,a865)),f306(f306(f236(a865,a865),f79(a865)),f2(a865))),f185(f872(f871(a865,a865),a859))))),f79(a1)) % 187.68/187.63 [4144]E(f306(f228(f871(a865,a865)),f306(f245(a865,a865,a859),f306(f306(f8(a865,f872(a865,a859),a865),f306(f7(a865,a865,a859),a303)),a119))),a296) % 187.68/187.63 [4114]E(f306(f111(a865),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104))),f306(a119,f306(a119,f2(a865)))) % 187.68/187.63 [4117]E(f306(f111(a865),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104))),f306(f306(f81(a865),f79(a865)),f79(a865))) % 187.68/187.63 [4118]E(f306(f111(a865),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104))),f306(f39(a859),f231(f872(a859,a859)))) % 187.68/187.63 [4181]P7(f306(f111(a1),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)))) % 187.68/187.63 [4253]P29(f872(f871(a865,a865),a859),f306(f306(f236(f872(f871(f872(f871(a865,a865),a859),f872(f871(a865,a865),a859)),a859),f872(f871(f872(f871(a865,a865),a859),f872(f871(a865,a865),a859)),a859)),a37),a72)) % 187.68/187.63 [4254]P29(f872(f871(a865,a865),a859),f306(f306(f236(f872(f871(f872(f871(a865,a865),a859),f872(f871(a865,a865),a859)),a859),f872(f871(f872(f871(a865,a865),a859),f872(f871(a865,a865),a859)),a859)),a38),a70)) % 187.68/187.63 [4293]E(f306(f306(f108(f872(f871(f872(f871(a865,a865),a859),f872(f871(a865,a865),a859)),a859)),f298(f871(a865,a865),a71)),f306(f306(f284(f871(f872(f871(a865,a865),a859),f872(f871(a865,a865),a859))),f306(f306(f236(f872(f871(a865,a865),a859),f872(f871(a865,a865),a859)),f185(f872(f871(a865,a865),a859))),f185(f872(f871(a865,a865),a859)))),f185(f872(f871(f872(f871(a865,a865),a859),f872(f871(a865,a865),a859)),a859)))),a70) % 187.68/187.63 [4294]E(f306(f306(f108(f872(f871(f872(f871(a865,a865),a859),f872(f871(a865,a865),a859)),a859)),f297(f871(a865,a865),a71)),f306(f306(f284(f871(f872(f871(a865,a865),a859),f872(f871(a865,a865),a859))),f306(f306(f236(f872(f871(a865,a865),a859),f872(f871(a865,a865),a859)),f185(f872(f871(a865,a865),a859))),f185(f872(f871(a865,a865),a859)))),f185(f872(f871(f872(f871(a865,a865),a859),f872(f871(a865,a865),a859)),a859)))),a72) % 187.68/187.63 [4183]E(f306(a112,f306(f111(a1),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)))),f306(a119,f306(a119,f2(a865)))) % 187.68/187.63 [4230]E(f306(f107(a1),f306(f111(a865),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)))),f306(f111(a1),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)))) % 187.68/187.63 [4265]P1(f306(f306(f220(a1),f2(a1)),f306(f111(a1),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104))))) % 187.68/187.63 [4266]E(f306(f111(a865),f306(f306(f22(a1),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104))),a104)),f306(a119,f306(a119,f306(a119,f2(a865))))) % 187.68/187.63 [4307]P7(f306(f111(a1),f306(f306(f22(a1),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104))),a104))) % 187.68/187.63 [4335]E(f306(f107(a1),f306(f111(a865),f306(f306(f22(a1),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104))),a104))),f306(f111(a1),f306(f306(f22(a1),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104))),a104))) % 187.68/187.63 [4350]P1(f306(f306(f220(a1),f2(a1)),f306(f111(a1),f306(f306(f22(a1),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104))),a104)))) % 187.68/187.63 [3085]P8(x30851,a303) % 187.68/187.63 [3479]P28(a865,a865,a119,x34791) % 187.68/187.63 [3075]P93(f864(x30751)) % 187.68/187.63 [3076]P93(f869(x30761)) % 187.68/187.63 [3077]P93(f866(x30771)) % 187.68/187.63 [3078]P93(f867(x30781)) % 187.68/187.63 [3079]P104(f864(x30791)) % 187.68/187.63 [3080]P104(f869(x30801)) % 187.68/187.63 [3081]P104(f866(x30811)) % 187.68/187.63 [3082]P104(f867(x30821)) % 187.68/187.63 [3102]P40(a1,f113(x31021)) % 187.68/187.63 [3103]P40(a1,f115(x31031)) % 187.68/187.63 [3151]P40(f872(x31511,a859),f281(x31511)) % 187.68/187.63 [3189]E(f46(a1,x31891,x31891),f2(a1)) % 187.68/187.63 [3241]P18(x32411,f872(x32411,a859),f284(x32411)) % 187.68/187.63 [4418]~E(f306(a26,x44181),a24) % 187.68/187.63 [4420]~E(f306(a119,x44201),x44201) % 187.68/187.63 [4430]~E(f306(a119,x44301),f2(a865)) % 187.68/187.63 [3087]E(f306(f186(a865),x30871),x30871) % 187.68/187.63 [3088]E(f306(f111(a1),x30881),x30881) % 187.68/187.63 [3104]E(f306(a90,f307(x31041)),x31041) % 187.68/187.63 [3117]E(f121(x31171,f120(x31171)),f120(x31171)) % 187.68/187.63 [3118]E(f144(x31181,f120(x31181)),f120(x31181)) % 187.68/187.63 [3121]E(f32(f306(a26,x31211)),f2(a865)) % 187.68/187.63 [3126]E(f306(f160(x31261),f120(x31261)),f120(x31261)) % 187.68/187.63 [3127]E(f306(f163(x31271),f120(x31271)),f120(x31271)) % 187.68/187.63 [3128]E(f306(f161(x31281),f120(x31281)),f120(x31281)) % 187.68/187.63 [3134]E(f306(f111(a1),x31341),f306(f110(a1),x31341)) % 187.68/187.63 [3135]E(f306(a90,f306(a114,x31351)),x31351) % 187.68/187.63 [3137]E(f306(a3,f306(a19,x31371)),x31371) % 187.68/187.63 [3138]E(f306(a19,f306(a3,x31381)),x31381) % 187.68/187.63 [3139]P7(f306(f107(a1),x31391)) % 187.68/187.63 [3144]E(f306(f186(f869(x31441)),f188(x31441)),f2(a865)) % 187.68/187.63 [3145]E(f306(f186(f866(x31451)),f120(x31451)),f2(a865)) % 187.68/187.63 [3150]E(f306(f186(a860),f306(a26,x31501)),f2(a865)) % 187.68/187.63 [3159]E(f213(x31591,f188(x31591)),f185(f872(x31591,a859))) % 187.68/187.63 [3167]E(f306(f306(f22(a865),x31671),f2(a865)),x31671) % 187.68/187.63 [3168]E(f306(f306(f81(a865),x31681),f2(a865)),x31681) % 187.68/187.63 [3169]E(f306(f306(f81(a1),x31691),f2(a1)),x31691) % 187.68/187.63 [3170]E(f306(f306(f82(a865),x31701),f79(a865)),x31701) % 187.68/187.63 [3171]E(f306(f306(f82(a1),x31711),f79(a1)),x31711) % 187.68/187.63 [3172]E(f306(f306(f219(a865),x31721),f2(a865)),x31721) % 187.68/187.63 [3173]E(f306(f306(f82(a865),x31731),f2(a865)),f2(a865)) % 187.68/187.63 [3174]E(f306(f306(f225(a865),x31741),f2(a865)),f2(a865)) % 187.68/187.63 [3175]E(f306(f306(f40(a1),x31751),f2(a1)),f2(a1)) % 187.68/187.63 [3181]E(f306(f164(x31811),f120(x31811)),f185(f872(x31811,a859))) % 187.68/187.63 [3184]P1(f306(f129(x31841),f120(x31841))) % 187.68/187.63 [3190]E(f306(f189(x31901,x31901),f5(x31901)),f35(f869(x31901))) % 187.68/187.63 [3191]E(f306(f189(x31911,x31911),f35(x31911)),f35(f869(x31911))) % 187.68/187.63 [3192]E(f306(f146(x31921,x31921),f5(x31921)),f35(f866(x31921))) % 187.68/187.63 [3193]E(f306(f146(x31931,x31931),f35(x31931)),f35(f866(x31931))) % 187.68/187.63 [3194]E(f46(a1,x31941,f2(a1)),x31941) % 187.68/187.63 [3195]E(f306(f220(a865),f306(a119,x31951)),f306(f221(a865),x31951)) % 187.68/187.63 [3196]E(f306(f229(a865),f306(a119,x31961)),f306(f275(a865),x31961)) % 187.68/187.63 [3197]E(f306(f230(a865),f306(a119,x31971)),f306(f278(a865),x31971)) % 187.68/187.63 [3199]E(f46(a1,f2(a1),x31991),f2(a1)) % 187.68/187.63 [3207]E(f306(f306(f81(a865),x32071),f79(a865)),f306(a119,x32071)) % 187.68/187.63 [3217]E(f306(f276(a865,x32171),f2(a865)),f185(f872(a865,a859))) % 187.68/187.63 [3229]E(f277(a865,f2(a865),x32291),f306(f275(a865),x32291)) % 187.68/187.63 [3276]E(f306(f306(f22(a865),f306(a119,x32761)),f79(a865)),x32761) % 187.68/187.63 [3289]E(f48(f2(a1),x32891),f306(f306(f236(a1,a1),f2(a1)),f2(a1))) % 187.68/187.63 [3340]P1(f306(f306(f221(a865),x33401),f306(a119,x33401))) % 187.68/187.63 [3352]P1(f306(f306(f221(a865),f2(a865)),f306(a119,x33521))) % 187.68/187.63 [3632]E(f306(f306(f22(a106),f306(a3,f306(a119,f306(a19,x36321)))),f79(a106)),x36321) % 187.68/187.63 [3702]P1(f306(f306(f220(a1),f306(f80(a1),f306(f107(a1),x37021))),f2(a1))) % 187.68/187.63 [3847]P1(f306(f306(f221(a1),f306(f80(a1),f306(f107(a1),f306(a119,x38471)))),f2(a1))) % 187.68/187.63 [4446]~E(f231(f872(x44461,a859)),f185(f872(x44461,a859))) % 187.68/187.63 [4493]~P1(f306(f306(f221(a865),x44931),f2(a865))) % 187.68/187.63 [4509]~P1(f306(f306(f221(a1),f306(f107(a1),x45091)),f2(a1))) % 187.68/187.63 [3149]E(f171(x31491,f120(f866(x31491))),f120(f866(x31491))) % 187.68/187.63 [3152]E(f306(f306(f82(a1),a84),x31521),a84) % 187.68/187.63 [3153]E(f306(f306(f81(a1),a84),x31531),x31531) % 187.68/187.63 [3156]E(f306(a112,f306(f107(a1),x31561)),x31561) % 187.68/187.63 [3157]E(f306(f306(f22(a1),x31571),a84),x31571) % 187.68/187.63 [3158]E(f306(f306(f81(a1),x31581),a84),x31581) % 187.68/187.63 [3160]E(f306(f306(f22(a865),x31601),x31601),f2(a865)) % 187.68/187.63 [3165]E(f306(f39(a865),f306(f229(a865),x31651)),x31651) % 187.68/187.63 [3166]E(f306(f80(a1),f306(f80(a1),x31661)),x31661) % 187.68/187.63 [3176]E(f306(f306(f81(a865),f2(a865)),x31761),x31761) % 187.68/187.63 [3177]E(f306(f306(f81(a1),f2(a1)),x31771),x31771) % 187.68/187.63 [3178]E(f306(f306(f82(a865),f79(a865)),x31781),x31781) % 187.68/187.63 [3179]E(f306(f306(f82(a1),f79(a1)),x31791),x31791) % 187.68/187.63 [3180]E(f306(f306(f219(a865),f2(a865)),x31801),x31801) % 187.68/187.63 [3185]E(f306(f306(f22(a865),f2(a865)),x31851),f2(a865)) % 187.68/187.63 [3186]E(f306(f306(f82(a865),f2(a865)),x31861),f2(a865)) % 187.68/187.63 [3187]E(f306(f306(f225(a865),f2(a865)),x31871),f2(a865)) % 187.68/187.63 [3188]E(f306(f306(f40(a1),f2(a1)),x31881),f2(a1)) % 187.68/187.63 [3204]E(f306(f276(a865,f2(a865)),x32041),f306(f229(a865),x32041)) % 187.68/187.63 [3205]E(f306(f306(f82(a1),a104),x32051),f306(f80(a1),x32051)) % 187.68/187.63 [3209]E(f306(a112,f306(f111(a1),x32091)),f306(f111(a865),x32091)) % 187.68/187.63 [3210]E(f306(a19,f306(f111(a106),x32101)),f306(f111(a865),x32101)) % 187.68/187.63 [3211]E(f306(f39(a865),f306(f275(a865),x32111)),f306(a119,x32111)) % 187.68/187.63 [3221]E(f306(f306(f81(a865),f79(a865)),x32211),f306(a119,x32211)) % 187.68/187.63 [3225]E(f306(f110(a1),f306(f107(a1),x32251)),f306(f107(a1),x32251)) % 187.68/187.63 [3226]E(f306(f76(a1),f306(f107(a1),x32261)),f306(f107(a1),x32261)) % 187.68/187.63 [3231]E(f306(f39(x32311),f185(f872(x32311,a859))),f2(a865)) % 187.68/187.63 [3233]E(f306(f306(f40(a865),x32331),f306(a119,f2(a865))),x32331) % 187.68/187.63 [3242]E(f46(a865,x32421,f306(a119,f2(a865))),f2(a865)) % 187.68/187.63 [3243]E(f46(a1,x32431,f306(f111(a1),a104)),f2(a1)) % 187.68/187.63 [3259]E(f306(f306(f40(a1),x32591),f306(f111(a1),a104)),f306(f80(a1),x32591)) % 187.68/187.63 [3263]E(f131(a865,f306(f276(a865,x32631),f2(a865))),f120(a865)) % 187.68/187.63 [3264]E(f306(f306(f81(a1),x32641),f79(a1)),f306(f306(f22(a1),x32641),a104)) % 187.68/187.63 [3265]E(f306(f306(f22(a1),x32651),f79(a1)),f306(f306(f81(a1),x32651),a104)) % 187.68/187.63 [3270]P1(f306(f306(f193(a24),x32701),x32701)) % 187.68/187.63 [3271]P1(f306(f306(f220(a865),x32711),x32711)) % 187.68/187.63 [3272]P1(f306(f306(f220(a1),x32721),x32721)) % 187.68/187.63 [3277]E(f306(f80(a1),f306(f111(a1),x32771)),f306(f111(a1),f306(f80(a1),x32771))) % 187.68/187.63 [3278]P1(f306(f63(a865),f306(f275(a865),x32781))) % 187.68/187.63 [3279]P1(f306(f63(a865),f306(f229(a865),x32791))) % 187.68/187.63 [3287]E(f153(x32871,f231(f872(x32871,a859))),f231(f872(f866(x32871),a859))) % 187.68/187.63 [3292]P1(f306(f306(f220(a865),f2(a865)),x32921)) % 187.68/187.63 [3303]E(f306(f306(f81(a865),f118(x33031)),f306(a119,f2(a865))),f118(f306(a119,x33031))) % 187.68/187.63 [3304]E(f306(f228(x33041),f306(f16(a859,x33041),a226)),f185(f872(x33041,a859))) % 187.68/187.63 [3305]E(f306(f228(x33051),f306(f16(a859,x33051),a184)),f231(f872(x33051,a859))) % 187.68/187.63 [3309]E(f306(f306(f284(a865),x33091),f306(f229(a865),x33091)),f306(f229(a865),f306(a119,x33091))) % 187.68/187.63 [3321]E(f306(f306(f81(a1),f79(a1)),f306(f107(a1),x33211)),f306(f107(a1),f306(a119,x33211))) % 187.68/187.63 [3324]E(f306(f306(f143(f866(x33241)),f120(x33241)),f120(f866(x33241))),f55(x33241,f120(x33241))) % 187.68/187.63 [3343]E(f185(f872(f871(x33431,x33431),a859)),f233(x33431,f185(f872(x33431,a859)))) % 187.68/187.63 [3344]E(f306(f283(x33441),f231(f872(x33441,a859))),f231(f872(f872(x33441,a859),a859))) % 187.68/187.63 [3345]E(f306(f80(f872(x33451,a859)),f185(f872(x33451,a859))),f231(f872(x33451,a859))) % 187.68/187.63 [3346]E(f306(f80(f872(x33461,a859)),f231(f872(x33461,a859))),f185(f872(x33461,a859))) % 187.68/187.63 [3348]P1(f306(f63(x33481),f185(f872(x33481,a859)))) % 187.68/187.63 [3350]E(f306(f276(a865,x33501),f306(a119,x33501)),f306(f306(f284(a865),x33501),f185(f872(a865,a859)))) % 187.68/187.63 [3351]E(f86(f871(a865,a865),f49(x33511,f2(a865))),f306(f306(f236(a865,a865),f2(a865)),x33511)) % 187.68/187.63 [3364]E(f306(f306(f284(a865),f306(a119,x33641)),f306(f275(a865),x33641)),f306(f275(a865),f306(a119,x33641))) % 187.68/187.63 [3368]P40(x33681,f185(f872(f871(x33681,x33681),a859))) % 187.68/187.63 [3371]P1(f306(f306(f220(a1),f2(a1)),f306(f107(a1),x33711))) % 187.68/187.63 [3379]E(f306(f306(f81(a865),f306(f186(a865),x33791)),f306(a119,f2(a865))),f306(f186(a865),f306(a119,x33791))) % 187.68/187.63 [3486]P42(f306(f285(a865,a1,f107(a1)),x34861)) % 187.68/187.63 [3522]P50(x35221,f185(f872(x35221,a859)),f185(f872(f871(x35221,x35221),a859))) % 187.68/187.63 [3541]E(f306(f306(f236(a1,a1),f306(f111(a1),a104)),f306(f306(f22(a1),x35411),f79(a1))),f51(f306(f111(a1),a104),x35411)) % 187.68/187.63 [3590]P59(x35901,f306(f16(f872(x35901,a859),x35901),f306(f16(a859,x35901),a226))) % 187.68/187.63 [3788]P1(f306(f306(f308(f872(f871(a865,a865),a859)),f307(x37881)),a105)) % 187.68/187.63 [3813]P1(f306(f306(f308(f872(f871(a865,a865),a859)),f306(a114,x38131)),a105)) % 187.68/187.63 [3946]P28(x39461,f872(x39461,a859),f306(f306(f7(x39461,f872(x39461,a859),f872(x39461,a859)),f284(x39461)),f185(f872(x39461,a859))),f231(f872(x39461,a859))) % 187.68/187.63 [4443]~E(f306(f306(f81(a1),x44431),x44431),a104) % 187.68/187.63 [4478]~E(f306(a3,f306(a119,f306(a19,x44781))),f2(a106)) % 187.68/187.63 [4486]~P1(f306(a190,f306(f107(a1),x44861))) % 187.68/187.63 [4489]~P1(f306(f306(f221(a865),x44891),x44891)) % 187.68/187.63 [4502]~P1(f306(f306(f220(a865),f306(a119,x45021)),x45021)) % 187.68/187.63 [3294]E(f306(a112,f306(f80(a1),f306(f107(a1),x32941))),f2(a865)) % 187.68/187.63 [3297]E(f306(f306(f81(a1),f306(f80(a1),x32971)),x32971),f2(a1)) % 187.68/187.63 [3302]E(f306(f39(a1),f306(f276(a1,f2(a1)),x33021)),f306(a112,x33021)) % 187.68/187.63 [3314]E(f306(f306(f237(a865),f306(a119,f2(a865))),x33141),f306(a119,f2(a865))) % 187.68/187.63 [3413]E(f306(f259(x34131),f185(f872(f871(x34131,x34131),a859))),f185(f872(x34131,a859))) % 187.68/187.63 [3421]E(f42(f872(x34211,a859),f185(f872(f872(x34211,a859),a859))),f231(f872(x34211,a859))) % 187.68/187.63 [3422]E(f42(f872(x34221,a859),f231(f872(f872(x34221,a859),a859))),f185(f872(x34221,a859))) % 187.68/187.63 [3423]E(f41(f872(x34231,a859),f185(f872(f872(x34231,a859),a859))),f185(f872(x34231,a859))) % 187.68/187.63 [3424]E(f41(f872(x34241,a859),f231(f872(f872(x34241,a859),a859))),f231(f872(x34241,a859))) % 187.68/187.63 [3469]E(f306(f306(f284(f866(x34691)),f120(x34691)),f185(f872(f866(x34691),a859))),f154(x34691,f120(f872(x34691,a859)))) % 187.68/187.63 [3470]E(f306(f306(f284(f866(x34701)),f120(x34701)),f185(f872(f866(x34701),a859))),f153(x34701,f185(f872(x34701,a859)))) % 187.68/187.63 [3507]E(f306(f306(f81(a865),f4(x35071)),f306(a119,f2(a865))),f4(f306(a3,f306(a119,f306(a19,x35071))))) % 187.68/187.63 [3533]E(f306(f39(a1),f306(f285(a865,a1,f107(a1)),x35331)),f306(f39(a865),x35331)) % 187.68/187.63 [3536]P1(f306(f306(f220(a865),x35361),f306(f306(f82(a865),x35361),x35361))) % 187.68/187.63 [3571]E(f306(f285(a1,a865,a112),f277(a1,f2(a1),f306(f107(a1),x35711))),f306(f275(a865),x35711)) % 187.68/187.63 [3585]E(f306(f306(f40(a865),f306(a119,f2(a865))),f306(f111(a865),x35851)),f306(a112,f306(f306(f40(a1),f79(a1)),f306(f111(a1),x35851)))) % 187.68/187.63 [3587]E(f306(f164(a865),f131(a865,f306(f276(a865,f2(a865)),f306(a119,x35871)))),f306(f275(a865),x35871)) % 187.68/187.63 [3588]E(f306(f306(f81(a865),f306(f186(a106),x35881)),f306(a119,f2(a865))),f306(f186(a106),f306(a3,f306(a119,f306(a19,x35881))))) % 187.68/187.63 [3606]E(f306(f285(a1,a865,a112),f306(f285(a865,a1,f107(a1)),x36061)),x36061) % 187.68/187.63 [3637]E(f306(f306(f284(a865),f2(a865)),f306(f285(a865,a865,a119),f306(f229(a865),x36371))),f306(f229(a865),f306(a119,x36371))) % 187.68/187.63 [3644]P54(x36441,x36441,f282(x36441,f185(f872(f871(x36441,x36441),a859)))) % 187.68/187.63 [3650]P1(f306(a190,f306(f80(a1),f306(f107(a1),f306(a119,x36501))))) % 187.68/187.63 [3661]E(f306(f306(f22(f872(a865,a859)),f306(f230(a865),x36611)),f306(f306(f284(a865),x36611),f185(f872(a865,a859)))),f306(f230(a865),f306(a119,x36611))) % 187.68/187.63 [3677]E(f306(f306(f81(a1),f306(f306(f22(a1),a84),x36771)),f306(f306(f22(a1),a84),x36771)),f306(f306(f22(a1),a84),f306(f306(f81(a1),x36771),x36771))) % 187.68/187.63 [3692]E(f306(f306(f284(f872(x36921,a859)),f185(f872(x36921,a859))),f185(f872(f872(x36921,a859),a859))),f306(f283(x36921),f185(f872(x36921,a859)))) % 187.68/187.63 [3719]E(f306(f306(f22(f872(a865,a859)),f306(f278(a865),x37191)),f306(f306(f284(a865),f306(a119,x37191)),f185(f872(a865,a859)))),f306(f278(a865),f306(a119,x37191))) % 187.68/187.63 [3727]E(f306(f306(f284(f869(x37271)),f188(x37271)),f306(f285(x37271,f869(x37271),f214(x37271)),f231(f872(x37271,a859)))),f231(f872(f869(x37271),a859))) % 187.68/187.63 [3825]E(f306(f111(a865),f306(f306(f81(a1),x38251),x38251)),f306(f306(f87(a865,a865),f306(f111(a865),x38251)),f306(f306(f18(a865,a865,a865),f81(a865)),f5(a865)))) % 187.68/187.63 [4204]P18(x42041,f872(x42041,a859),f306(f306(f8(f872(x42041,a859),f872(f872(x42041,a859),f872(x42041,a859)),x42041),f306(f7(f872(x42041,a859),f872(x42041,a859),f872(x42041,a859)),f22(f872(x42041,a859)))),f306(f306(f7(x42041,f872(x42041,a859),f872(x42041,a859)),f284(x42041)),f185(f872(x42041,a859))))) % 187.68/187.63 [4292]E(f306(f228(f871(a1,a1)),f306(f245(a1,a1,a859),f306(f306(f8(f872(a1,a859),f872(a1,a859),a1),f306(f18(a1,a859,a859),f306(f306(f8(a859,f872(a859,a859),a1),a304),f306(f220(a1),x42921)))),f221(a1)))),f115(x42921)) % 187.68/187.63 [4325]E(f306(f228(f871(a1,a1)),f306(f245(a1,a1,a859),f306(f306(f18(a1,f872(a1,a859),f872(a1,a859)),f306(f306(f8(f872(a859,a859),f872(f872(a1,a859),f872(a1,a859)),a1),f8(a859,a859,a1)),f306(f306(f8(a859,f872(a859,a859),a1),a304),f306(f220(a1),x43251)))),f221(a1)))),f113(x43251)) % 187.68/187.63 [4376]E(f306(f228(f871(f872(x43761,a859),f872(x43761,a859))),f306(f245(f872(x43761,a859),f872(x43761,a859),a859),f306(f306(f7(f872(x43761,a859),f872(f872(x43761,a859),a859),f872(f872(x43761,a859),a859)),f306(f306(f8(f872(f872(x43761,a859),f872(a859,a859)),f872(f872(f872(x43761,a859),a859),f872(f872(x43761,a859),a859)),f872(x43761,a859)),f18(f872(x43761,a859),a859,a859)),f306(f306(f8(f872(f872(x43761,a859),a859),f872(f872(x43761,a859),f872(a859,a859)),f872(x43761,a859)),f306(f8(a859,f872(a859,a859),f872(x43761,a859)),a304)),f221(f872(x43761,a859))))),f63(x43761)))),f281(x43761)) % 187.68/187.63 [4506]~P1(f306(f63(f866(x45061)),f231(f872(f866(x45061),a859)))) % 187.68/187.63 [4519]~P1(f306(f306(f220(a1),f2(a1)),f306(f80(a1),f306(f107(a1),f306(a119,x45191))))) % 187.68/187.63 [3447]E(f306(f306(f22(a1),f306(f306(f81(a1),x34471),a104)),a104),x34471) % 187.68/187.63 [3463]E(f306(f164(a865),f131(a865,f306(f276(a865,f2(a865)),x34631))),f306(f229(a865),x34631)) % 187.68/187.63 [3698]E(f306(f306(f81(a1),f306(f306(f81(a1),f79(a1)),x36981)),x36981),f306(f306(f22(a1),f306(f306(f81(a1),x36981),x36981)),a104)) % 187.68/187.63 [3744]E(f306(f261(x37441,x37441),f282(x37441,f185(f872(f871(x37441,x37441),a859)))),f282(x37441,f185(f872(f871(x37441,x37441),a859)))) % 187.68/187.63 [3791]P1(f306(f306(f220(a865),x37911),f306(f306(f82(a865),x37911),f306(f306(f82(a865),x37911),x37911)))) % 187.68/187.63 [4062]P1(f306(f63(a865),f306(f228(a865),f306(f306(f7(a865,a865,a859),f220(a865)),x40621)))) % 187.68/187.63 [4063]P1(f306(f63(a865),f306(f228(a865),f306(f306(f7(a865,a865,a859),f221(a865)),x40631)))) % 187.68/187.63 [4345]E(f306(f228(f871(x43451,x43451)),f306(f306(f8(f872(x43451,a859),a859,f871(x43451,x43451)),f88(x43451)),f306(f306(f7(f871(x43451,x43451),f872(x43451,f871(x43451,x43451)),f872(x43451,a859)),f306(f306(f8(f872(f871(x43451,x43451),a859),f872(f872(x43451,f871(x43451,x43451)),f872(x43451,a859)),f871(x43451,x43451)),f8(f871(x43451,x43451),a859,x43451)),a303)),f306(f306(f18(x43451,x43451,f871(x43451,x43451)),f236(x43451,x43451)),f5(x43451))))),f282(x43451,f185(f872(f871(x43451,x43451),a859)))) % 187.68/187.63 [4508]~E(f306(f306(f22(a1),f306(f306(f81(a1),x45081),x45081)),a104),a84) % 187.68/187.63 [4510]~E(f306(f306(f81(a1),f306(f306(f81(a1),f79(a1)),x45101)),x45101),f2(a1)) % 187.68/187.63 [3836]E(f306(f306(f81(a1),f306(f306(f22(a1),a104),x38361)),f306(f306(f22(a1),a104),x38361)),f306(f306(f22(a1),a104),f306(f306(f22(a1),f306(f306(f81(a1),x38361),x38361)),a104))) % 187.68/187.63 [3954]E(f306(f306(f22(a1),f306(f306(f81(a1),f306(f306(f22(a1),a104),x39541)),f306(f306(f22(a1),a104),x39541))),a104),f306(f306(f22(a1),a104),f306(f306(f81(a1),x39541),x39541))) % 187.68/187.63 [3986]E(f306(f306(f22(a1),f306(f306(f81(a1),f306(f306(f81(a1),x39861),a104)),f306(f306(f81(a1),x39861),a104))),a104),f306(f306(f81(a1),f306(f306(f81(a1),x39861),x39861)),a104)) % 187.68/187.63 [4024]E(f306(f306(f22(a1),f306(f306(f81(a1),f306(f306(f22(a1),a104),x40241)),f306(f306(f22(a1),a104),x40241))),a104),f306(f306(f22(a1),a84),f306(f306(f22(a1),f306(f306(f81(a1),x40241),x40241)),a104))) % 187.68/187.63 [4124]E(f306(a90,f306(f260(f871(a865,a865),f871(a865,a865),a116),f306(f306(f284(f871(a865,a865)),f306(f306(f236(a865,a865),x41241),f2(a865))),f185(f872(f871(a865,a865),a859))))),f306(f107(a1),x41241)) % 187.68/187.63 [4134]E(f306(a90,f306(f260(f871(a865,a865),f871(a865,a865),a116),f306(f306(f284(f871(a865,a865)),f306(f306(f236(a865,a865),f311(x41341)),f408(x41341))),f185(f872(f871(a865,a865),a859))))),x41341) % 187.68/187.63 [4166]E(f306(f228(a1),f306(f306(f18(a1,a859,a859),f306(f306(f8(a859,f872(a859,a859),a1),a304),f306(f220(a1),f2(a1)))),x41661)),f306(f285(a865,a1,f107(a1)),f306(f228(a865),f306(f306(f8(a1,a859,a865),x41661),f107(a1))))) % 187.68/187.63 [4212]P42(f306(f228(a1),f306(f306(f18(a1,a859,a859),f306(f306(f8(a859,f872(a859,a859),a1),a304),f306(f220(a1),f2(a1)))),x42121))) % 187.68/187.63 [4233]P1(f306(f306(f308(f871(f872(f871(a865,a865),a859),f872(f871(a865,a865),a859))),f306(f306(f236(f872(f871(a865,a865),a859),f872(f871(a865,a865),a859)),x42331),f185(f872(f871(a865,a865),a859)))),a72)) % 187.68/187.63 [4239]E(f306(f285(a1,a865,a112),f306(f228(a1),f306(f306(f18(a1,a859,a859),f306(f306(f8(a859,f872(a859,a859),a1),a304),f306(f220(a1),f2(a1)))),f306(f306(f8(a865,a859,a1),x42391),a112)))),f306(f228(a865),x42391)) % 187.68/187.63 [4390]E(f287(a865,f306(f306(f43(f871(a865,a865),f872(a865,a859)),f306(a114,x43901)),f306(f245(a865,a865,f872(a865,a859)),f306(f306(f7(a865,f872(a865,a859),f872(a865,f872(a865,a859))),f306(f306(f8(f872(a865,f872(f872(a865,a859),f872(a865,a859))),f872(f872(a865,a859),f872(a865,f872(a865,a859))),a865),f7(a865,f872(a865,a859),f872(a865,a859))),f306(f306(f8(f872(a865,a865),f872(a865,f872(f872(a865,a859),f872(a865,a859))),a865),f306(f8(a865,f872(f872(a865,a859),f872(a865,a859)),a865),f284(a865))),f22(a865)))),f185(f872(a865,a859)))))),f306(a112,x43901)) % 187.68/187.63 [4521]~P1(f306(f306(f92(a1),a84),f306(f306(f22(a1),f306(f306(f81(a1),x45211),x45211)),a104))) % 187.68/187.63 [3879]E(f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),x38791),x38791)),a104)),a104),f306(f306(f81(a1),x38791),x38791)) % 187.68/187.63 [3929]E(f306(f306(f22(a1),f306(f306(f22(a1),f306(f306(f81(a1),x39291),x39291)),a104)),a104),f306(f306(f81(a1),f306(f306(f22(a1),x39291),a104)),f306(f306(f22(a1),x39291),a104))) % 187.68/187.63 [4142]E(f306(f306(f22(a1),f306(f306(f81(a1),f306(f306(f81(a1),f306(f80(a1),x41421)),a104)),f306(f306(f81(a1),f306(f80(a1),x41421)),a104))),a104),f306(f80(a1),f306(f306(f22(a1),f306(f306(f81(a1),x41421),x41421)),a104))) % 187.68/187.63 [4530]~P1(f306(f306(f92(a1),f306(f306(f22(a1),f306(f306(f81(a1),x45301),x45301)),a104)),a84)) % 187.68/187.63 [4184]E(f306(f306(f81(a865),x41841),f306(f111(a865),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)))),f306(a119,f306(a119,x41841))) % 187.68/187.63 [4185]E(f306(f306(f82(a865),x41851),f306(f111(a865),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)))),f306(f306(f81(a865),x41851),x41851)) % 187.68/187.63 [4186]E(f306(f306(f40(a865),f306(f306(f81(a865),x41861),x41861)),f306(f111(a865),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)))),x41861) % 187.68/187.63 [4268]E(f46(a865,f306(a119,f306(a119,x42681)),f306(f111(a865),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)))),f46(a865,x42681,f306(f111(a865),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104))))) % 187.68/187.63 [4405]E(f306(a90,f306(f306(f43(f871(a865,a865),f872(f871(a865,a865),a859)),f306(a114,x44051)),f306(f245(a865,a865,f872(f871(a865,a865),a859)),f306(f306(f8(f872(a865,f872(f871(a865,a865),a859)),f872(a865,f872(f871(a865,a865),a859)),a865),f306(f8(f872(f871(a865,a865),a859),f872(f871(a865,a865),a859),a865),f260(f871(a865,a865),f871(a865,a865),a116))),f306(f306(f7(a865,f872(f871(a865,a865),a859),f872(a865,f872(f871(a865,a865),a859))),f306(f306(f8(f872(a865,f872(f872(f871(a865,a865),a859),f872(f871(a865,a865),a859))),f872(f872(f871(a865,a865),a859),f872(a865,f872(f871(a865,a865),a859))),a865),f7(a865,f872(f871(a865,a865),a859),f872(f871(a865,a865),a859))),f306(f306(f8(f872(a865,f871(a865,a865)),f872(a865,f872(f872(f871(a865,a865),a859),f872(f871(a865,a865),a859))),a865),f306(f8(f871(a865,a865),f872(f872(f871(a865,a865),a859),f872(f871(a865,a865),a859)),a865),f284(f871(a865,a865)))),f306(f7(a865,a865,f871(a865,a865)),f236(a865,a865))))),f185(f872(f871(a865,a865),a859))))))),f306(f80(a1),x44051)) % 187.68/187.63 [4263]E(f306(f306(f81(a865),f306(f111(a865),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)))),x42631),f306(a119,f306(a119,x42631))) % 187.68/187.63 [4264]E(f306(f306(f82(a865),f306(f111(a865),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)))),x42641),f306(f306(f81(a865),x42641),x42641)) % 187.68/187.63 [4297]E(f306(f306(f40(a865),f306(a119,f306(a119,x42971))),f306(f111(a865),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)))),f306(a119,f306(f306(f40(a865),x42971),f306(f111(a865),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)))))) % 187.68/187.63 [4351]E(f306(f306(f81(a865),f306(f111(a865),f306(f306(f22(a1),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104))),a104))),x43511),f306(a119,f306(a119,f306(a119,x43511)))) % 187.68/187.63 [4412]E(f306(f245(a1,a1,f871(a1,a1)),f306(f306(f18(a1,f872(a1,f871(a1,a1)),f872(a1,f871(a1,a1))),f306(f306(f8(f872(a1,f872(f871(a1,a1),f871(a1,a1))),f872(f872(a1,f871(a1,a1)),f872(a1,f871(a1,a1))),a1),f18(a1,f871(a1,a1),f871(a1,a1))),f306(f306(f8(f872(a1,f871(a1,a1)),f872(a1,f872(f871(a1,a1),f871(a1,a1))),a1),f306(f18(a1,f871(a1,a1),f872(f871(a1,a1),f871(a1,a1))),f306(f306(f8(a859,f872(f871(a1,a1),f872(f871(a1,a1),f871(a1,a1))),a1),f101(f871(a1,a1))),f306(f306(f8(a1,a859,a1),f306(f220(a1),f2(a1))),f306(f306(f7(a1,a1,a1),f22(a1)),x44121))))),f306(f306(f7(a1,f872(a1,a1),f872(a1,f871(a1,a1))),f306(f306(f8(f872(a1,f871(a1,a1)),f872(f872(a1,a1),f872(a1,f871(a1,a1))),a1),f8(a1,f871(a1,a1),a1)),f306(f306(f8(a1,f872(a1,f871(a1,a1)),a1),f236(a1,a1)),f306(f306(f7(a1,a1,a1),f306(f306(f8(a1,f872(a1,a1),a1),f81(a1)),f306(f82(a1),f306(f111(a1),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)))))),f79(a1))))),f306(f306(f7(a1,a1,a1),f22(a1)),x44121))))),f306(f306(f8(a1,f872(a1,f871(a1,a1)),a1),f236(a1,a1)),f306(f82(a1),f306(f111(a1),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104))))))),f45(x44121)) % 187.68/187.63 [3122]P93(f870(x31221,x31222)) % 187.68/187.63 [3123]P93(f871(x31231,x31232)) % 187.68/187.63 [3124]P104(f870(x31241,x31242)) % 187.68/187.63 [3125]P104(f871(x31251,x31252)) % 187.68/187.63 [3142]P17(a1,f170(x31421,x31422)) % 187.68/187.63 [3143]P40(x31431,f145(x31431,x31432)) % 187.68/187.63 [3206]P34(x32061,x32062,f120(x32061)) % 187.68/187.63 [3237]P50(x32371,x32372,f233(x32371,x32372)) % 187.68/187.63 [3238]P54(x32381,x32381,f233(x32381,x32382)) % 187.68/187.63 [3510]P28(x35101,x35101,f5(x35101),x35102) % 187.68/187.63 [3511]P28(x35111,x35111,f35(x35111),x35112) % 187.68/187.63 [3517]P35(x35171,x35172,f120(x35171),f120(x35171)) % 187.68/187.63 [3518]P28(x35181,f869(x35181),f214(x35181),x35182) % 187.68/187.63 [3527]P28(f866(x35271),f866(x35271),f161(x35271),x35272) % 187.68/187.63 [4423]~E(f34(x44231,x44232),a24) % 187.68/187.63 [4424]~E(f33(x44241,x44242),a24) % 187.68/187.63 [4455]~P36(x44551,x44552,f120(x44551)) % 187.68/187.63 [4456]~P38(x44561,x44562,f120(x44561)) % 187.68/187.63 [3106]E(f306(f5(x31061),x31062),x31062) % 187.68/187.63 [3107]E(f306(f228(x31071),x31072),x31072) % 187.68/187.63 [3109]E(f306(f35(x31091),x31092),x31092) % 187.68/187.63 [3140]E(f86(x31401,f306(a303,x31402)),x31402) % 187.68/187.63 [3141]E(f91(x31411,f306(a303,x31412)),x31412) % 187.68/187.63 [3163]E(f306(f128(x31631,x31632),f120(x31631)),f120(x31631)) % 187.68/187.63 [3182]E(f282(x31821,f282(x31821,x31822)),f282(x31821,x31822)) % 187.68/187.63 [3183]E(f144(x31831,f144(x31831,x31832)),f144(x31831,x31832)) % 187.68/187.63 [3202]E(f306(f306(f122(x32021),x32022),f120(x32021)),x32022) % 187.68/187.63 [3212]E(f306(f306(f165(x32121),x32122),f120(x32121)),f120(x32121)) % 187.68/187.63 [3213]E(f306(f306(f130(x32131),x32132),f120(x32131)),f120(x32131)) % 187.68/187.63 [3215]E(f215(x32151,x32152,f188(x32151)),f2(a865)) % 187.68/187.63 [3216]E(f147(x32161,x32162,f120(x32161)),f2(a865)) % 187.68/187.63 [3218]E(f162(x32181,x32182,f120(x32181)),f120(x32181)) % 187.68/187.63 [3219]E(f168(x32191,x32192,f120(x32191)),f120(x32191)) % 187.68/187.63 [3220]E(f166(x32201,f120(x32201),x32202),f120(x32201)) % 187.68/187.63 [3224]E(f306(f164(x32241),f144(x32241,x32242)),f306(f164(x32241),x32242)) % 187.68/187.63 [3227]E(f306(f232(x32271,x32271),f233(x32271,x32272)),x32272) % 187.68/187.63 [3228]E(f306(f234(x32281,x32281),f233(x32281,x32282)),x32282) % 187.68/187.63 [3236]E(f306(f261(x32361,x32361),f233(x32361,x32362)),f233(x32361,x32362)) % 187.68/187.63 [3251]E(f282(f866(x32511),f149(x32511,x32512)),f150(x32511,f282(x32511,x32512))) % 187.68/187.63 [3253]P1(f306(f129(a1),f170(x32531,x32532))) % 187.68/187.63 [3261]E(f306(f232(x32611,x32611),f282(x32611,x32612)),f231(f872(x32611,a859))) % 187.68/187.63 [3262]E(f306(f234(x32621,x32621),f282(x32621,x32622)),f231(f872(x32621,a859))) % 187.68/187.63 [3266]P1(f306(f129(x32661),f144(x32661,x32662))) % 187.68/187.63 [3268]P1(f306(f152(x32681,x32682),f120(x32681))) % 187.68/187.63 [3275]E(f306(f164(a1),f170(x32751,x32752)),f277(a1,x32751,x32752)) % 187.68/187.63 [3290]P55(x32901,f185(f872(x32901,a859)),x32902) % 187.68/187.63 [3295]E(f306(f244(a1,a1),f47(x32951,x32952)),f46(a1,x32951,x32952)) % 187.68/187.63 [3296]E(f306(f276(a865,x32961),f306(a119,x32962)),f277(a865,x32961,x32962)) % 187.68/187.63 [3313]E(f306(f306(f143(x33131),x33132),f120(x33131)),f132(x33131,x33132,f120(x33131))) % 187.68/187.63 [3326]E(f277(a865,f306(a119,x33261),x33262),f279(a865,x33261,x33262)) % 187.68/187.63 [3329]P50(x33291,f231(f872(x33291,a859)),f282(x33291,x33292)) % 187.68/187.63 [3390]E(f306(f306(f22(a865),x33901),f306(a119,x33902)),f306(f39(a865),f280(a865,x33902,x33901))) % 187.68/187.63 [3448]E(f159(x34481,x34482,f120(x34481)),f306(f306(f236(f866(x34481),f866(x34481)),f120(x34481)),f120(x34481))) % 187.68/187.63 [3467]E(f306(f245(x34671,x34672,f871(x34671,x34672)),f236(x34671,x34672)),f35(f871(x34671,x34672))) % 187.68/187.63 [3472]P1(f306(f306(f308(f866(x34721)),f120(x34721)),f153(x34721,x34722))) % 187.68/187.63 [3473]E(f306(f186(f866(x34731)),f121(x34731,x34732)),f306(f306(f22(a865),f306(f186(f866(x34731)),x34732)),f79(a865))) % 187.68/187.63 [3480]P1(f306(f63(a865),f280(a865,x34801,x34802))) % 187.68/187.63 [3481]P1(f306(f63(a865),f279(a865,x34811,x34812))) % 187.68/187.63 [3482]P1(f306(f63(a865),f277(a865,x34821,x34822))) % 187.68/187.63 [3483]P1(f306(f63(a1),f280(a1,x34831,x34832))) % 187.68/187.63 [3484]P1(f306(f63(a1),f279(a1,x34841,x34842))) % 187.68/187.63 [3485]P1(f306(f63(a1),f277(a1,x34851,x34852))) % 187.68/187.63 [3584]E(f306(f285(a865,a865,a119),f277(a865,x35841,x35842)),f277(a865,f306(a119,x35841),f306(a119,x35842))) % 187.68/187.63 [3603]E(f306(f306(f263(x36031,x36031,x36031),f282(x36031,x36032)),f282(x36031,x36032)),f282(x36031,x36032)) % 187.68/187.63 [3635]E(f306(f306(f236(a1,a1),f306(f306(f40(a1),x36351),x36352)),f46(a1,x36351,x36352)),f47(x36351,x36352)) % 187.68/187.63 [3636]E(f306(f306(f236(a106,a106),f306(f306(f40(a106),x36361),x36362)),f46(a106,x36361,x36362)),f21(x36361,x36362)) % 187.68/187.63 [3665]E(f306(f306(f236(a865,a865),f306(f306(f40(a865),x36651),x36652)),f46(a865,x36651,x36652)),f86(f871(a865,a865),f49(x36651,x36652))) % 187.68/187.63 [3715]P1(f306(f306(f221(a865),f306(f306(f22(a865),x37151),x37152)),f306(a119,x37151))) % 187.68/187.63 [3812]E(f306(f306(f81(a1),f306(f306(f82(a1),x38121),f306(f306(f40(a1),x38122),x38121))),f46(a1,x38122,x38121)),x38122) % 187.68/187.63 [3816]E(f306(f306(f43(a865,f872(f871(f866(x38161),f866(x38161)),a859)),f231(f872(a865,a859))),f135(x38161,x38162)),f137(x38161,x38162)) % 187.68/187.63 [4037]P1(f306(f306(f308(f871(f866(x40371),f866(x40371))),f306(f306(f236(f866(x40371),f866(x40371)),f120(x40371)),f120(x40371))),f150(x40371,x40372))) % 187.68/187.63 [4197]E(f246(x41971,x41971,x41972,x41972,f5(x41971),f5(x41972)),f35(f871(x41971,x41972))) % 187.68/187.63 [4199]E(f246(x41991,x41991,x41992,x41992,f35(x41991),f35(x41992)),f35(f871(x41991,x41992))) % 187.68/187.63 [4432]~E(f306(f214(x44321),x44322),f188(x44321)) % 187.68/187.63 [3200]E(f306(f218(x32001),f306(f214(x32001),x32002)),x32002) % 187.68/187.63 [3201]E(f306(f161(x32011),f306(f161(x32011),x32012)),x32012) % 187.68/187.63 [3203]E(f306(f306(f130(x32031),f2(a865)),x32032),x32032) % 187.68/187.63 [3214]E(f306(f306(f165(x32141),f2(a865)),x32142),f120(x32141)) % 187.68/187.63 [3222]E(f306(f306(f122(x32221),f120(x32221)),x32222),x32222) % 187.68/187.63 [3230]E(f306(f186(f869(x32301)),f306(f214(x32301),x32302)),f2(a865)) % 187.68/187.63 [3232]E(f41(f872(x32321,a859),f306(f283(x32321),x32322)),x32322) % 187.68/187.63 [3234]E(f306(f164(x32341),f306(f160(x32341),x32342)),f306(f164(x32341),x32342)) % 187.68/187.63 [3235]E(f306(f164(x32351),f306(f161(x32351),x32352)),f306(f164(x32351),x32352)) % 187.68/187.63 [3240]E(f306(f306(f22(a106),x32401),x32402),f306(f306(a23,x32401),x32402)) % 187.68/187.63 [3255]E(f306(f306(f81(a865),x32551),x32552),f306(f306(f81(a865),x32552),x32551)) % 187.68/187.63 [3256]E(f306(f306(f81(a1),x32561),x32562),f306(f306(f81(a1),x32562),x32561)) % 187.68/187.63 [3257]E(f306(f306(f82(a865),x32571),x32572),f306(f306(f82(a865),x32572),x32571)) % 187.68/187.63 [3258]E(f306(f306(f82(a1),x32581),x32582),f306(f306(f82(a1),x32582),x32581)) % 187.68/187.63 [3282]E(f306(f306(f180(x32821,x32821),f2(a865)),x32822),f35(x32821)) % 187.68/187.63 [3283]E(f306(f186(f866(x32831)),f306(f160(x32831),x32832)),f306(f186(f866(x32831)),x32832)) % 187.68/187.63 [3284]E(f306(f186(f866(x32841)),f306(f161(x32841),x32842)),f306(f186(f866(x32841)),x32842)) % 187.68/187.63 [3285]E(f166(x32851,x32852,f185(f872(a865,a859))),f120(x32851)) % 187.68/187.63 [3286]E(f306(f306(f146(x32861,x32861),f5(x32861)),x32862),x32862) % 187.68/187.63 [3288]E(f306(f235(a1,a1),f47(x32881,x32882)),f306(f306(f40(a1),x32881),x32882)) % 187.68/187.63 [3306]E(f306(f186(f866(x33061)),f144(x33061,x33062)),f306(f39(x33061),f306(f164(x33061),x33062))) % 187.68/187.63 [3307]E(f32(f33(x33071,x33072)),f306(f306(f81(a865),f32(x33072)),f306(a119,f2(a865)))) % 187.68/187.63 [3308]E(f306(f259(x33081),f306(f261(x33081,x33081),x33082)),f306(f259(x33081),x33082)) % 187.68/187.63 [3312]P1(f306(f63(x33121),f306(f164(x33121),x33122))) % 187.68/187.63 [3320]E(f306(f306(f81(a1),x33201),f306(f80(a1),x33202)),f306(f306(f22(a1),x33201),x33202)) % 187.68/187.63 [3328]P27(x33281,x33282,f185(f872(f864(x33281),a859))) % 187.68/187.63 [3330]E(f306(f285(x33301,x33301,f5(x33301)),x33302),x33302) % 187.68/187.63 [3331]E(f306(f285(x33311,x33311,f35(x33311)),x33312),x33312) % 187.68/187.63 [3332]E(f306(f286(x33321,x33321,f5(x33321)),x33322),x33322) % 187.68/187.63 [3333]E(f306(f286(x33331,x33331,f35(x33331)),x33332),x33332) % 187.68/187.63 [3334]P1(f306(f231(f872(x33341,a859)),x33342)) % 187.68/187.63 [3336]E(f306(f39(a865),f306(f276(a865,x33361),x33362)),f306(f306(f22(a865),x33362),x33361)) % 187.68/187.63 [3337]E(f306(f276(a865,f306(a119,x33371)),x33372),f280(a865,x33371,x33372)) % 187.68/187.63 [3349]E(f306(f306(f284(x33491),x33492),f185(f872(x33491,a859))),f306(f228(x33491),f306(a303,x33492))) % 187.68/187.63 [3353]E(f306(f306(f284(x33531),x33532),f185(f872(x33531,a859))),f213(x33531,f306(f214(x33531),x33532))) % 187.68/187.63 [3355]E(f282(x33551,f306(f261(x33551,x33551),x33552)),f306(f261(x33551,x33551),f282(x33551,x33552))) % 187.68/187.63 [3360]E(f306(f306(f81(a865),f306(a119,x33601)),x33602),f306(f306(f81(a865),x33601),f306(a119,x33602))) % 187.68/187.63 [3361]E(f306(f306(f22(a865),f306(a119,x33611)),f306(a119,x33612)),f306(f306(f22(a865),x33611),x33612)) % 187.68/187.63 [3366]E(f56(x33661,f2(a865),x33662),f306(f306(f143(f866(x33661)),f120(x33661)),f120(f866(x33661)))) % 187.68/187.63 [3367]E(f306(f39(a865),f279(a865,x33671,x33672)),f306(f306(f22(a865),x33672),x33671)) % 187.68/187.63 [3376]P40(x33761,f306(f306(f262(a865,x33761),a227),x33762)) % 187.68/187.63 [3378]P17(a865,f131(a865,f306(f276(a865,x33781),x33782))) % 187.68/187.63 [3380]P1(f306(f63(a865),f306(f276(a865,x33801),x33802))) % 187.68/187.63 [3381]P1(f306(f63(a1),f306(f276(a1,x33811),x33812))) % 187.68/187.63 [3383]E(f306(f261(f866(x33831),f866(x33831)),f149(x33831,x33832)),f149(x33831,f306(f261(x33831,x33831),x33832))) % 187.68/187.63 [3384]E(f306(f186(a860),f33(x33841,x33842)),f306(f306(f81(a865),f306(f186(a860),x33842)),f306(a119,f2(a865)))) % 187.68/187.63 [3386]E(f306(f276(a1,x33861),f306(f306(f81(a1),x33862),f79(a1))),f277(a1,x33861,x33862)) % 187.68/187.63 [3389]E(f306(f306(f40(a1),f306(f80(a1),x33891)),f306(f80(a1),x33892)),f306(f306(f40(a1),x33891),x33892)) % 187.68/187.63 [3397]E(f175(x33971,x33972,f306(f16(f869(x33972),x33971),f188(x33972))),f185(f872(x33971,a859))) % 187.68/187.63 [3398]E(f177(x33981,x33982,f306(f16(f869(x33982),x33981),f188(x33982))),f185(f872(x33982,a859))) % 187.68/187.63 [3399]E(f306(f306(f180(f871(x33991,x33991),a859),f79(a865)),x33992),x33992) % 187.68/187.63 [3401]E(f306(f306(f22(f872(x34011,a859)),x34012),f185(f872(x34011,a859))),x34012) % 187.68/187.63 [3402]E(f306(f306(f108(f872(x34021,a859)),x34022),f185(f872(x34021,a859))),x34022) % 187.68/187.63 [3403]E(f306(f306(f109(f872(x34031,a859)),x34032),f231(f872(x34031,a859))),x34032) % 187.68/187.63 [3404]E(f306(f235(a865,a865),f86(f871(a865,a865),f49(x34041,x34042))),f306(f306(f40(a865),x34041),x34042)) % 187.68/187.63 [3411]E(f288(x34111,f306(a20,x34112),f306(f80(a1),f306(a20,x34112))),f306(f306(f291(a1),x34111),x34112)) % 187.68/187.63 [3412]E(f277(a1,f306(f306(f81(a1),x34121),f79(a1)),x34122),f279(a1,x34121,x34122)) % 187.68/187.63 [3417]E(f306(f244(a865,a865),f86(f871(a865,a865),f49(x34171,x34172))),f46(a865,x34171,x34172)) % 187.68/187.63 [3425]E(f289(x34251,f306(a20,x34252),f306(f80(a1),f306(a20,x34252))),f290(a1,x34251,x34252)) % 187.68/187.63 [3428]P1(f306(f306(f308(x34281),x34282),f231(f872(x34281,a859)))) % 187.68/187.63 [3433]E(f306(f306(f22(a865),f306(a119,x34331)),x34332),f306(f39(a865),f277(a865,x34332,x34331))) % 187.68/187.63 [3459]E(f306(f306(f22(f872(x34591,a859)),x34592),f231(f872(x34591,a859))),f185(f872(x34591,a859))) % 187.68/187.63 [3460]E(f306(f306(f108(f872(x34601,a859)),x34602),f231(f872(x34601,a859))),f231(f872(x34601,a859))) % 187.68/187.63 [3461]E(f306(f306(f109(f872(x34611,a859)),x34612),f185(f872(x34611,a859))),f185(f872(x34611,a859))) % 187.68/187.63 [3475]E(f46(a1,f306(f80(a1),x34751),f306(f80(a1),x34752)),f306(f80(a1),f46(a1,x34751,x34752))) % 187.68/187.63 [3476]E(f46(a1,f306(f107(a1),x34761),f306(f107(a1),x34762)),f306(f107(a1),f46(a865,x34761,x34762))) % 187.68/187.63 [3487]E(f306(f186(f866(x34871)),f306(f163(x34871),x34872)),f306(f306(f22(a865),f306(f186(f866(x34871)),x34872)),f79(a865))) % 187.68/187.63 [3512]E(f306(f306(f40(a1),f46(a1,x35121,x35122)),x35122),f2(a1)) % 187.68/187.63 [3520]E(f306(a3,f46(a865,f306(a19,x35201),f306(a19,x35202))),f46(a106,x35201,x35202)) % 187.68/187.63 [3553]E(f306(a3,f306(f306(f22(a865),f306(a19,x35531)),f306(a19,x35532))),f306(f306(f22(a106),x35531),x35532)) % 187.68/187.63 [3554]E(f306(a3,f306(f306(f81(a865),f306(a19,x35541)),f306(a19,x35542))),f306(f306(f81(a106),x35541),x35542)) % 187.68/187.63 [3555]E(f306(a3,f306(f306(f82(a865),f306(a19,x35551)),f306(a19,x35552))),f306(f306(f82(a106),x35551),x35552)) % 187.68/187.63 [3556]E(f306(a3,f306(f306(f40(a865),f306(a19,x35561)),f306(a19,x35562))),f306(f306(f40(a106),x35561),x35562)) % 187.68/187.63 [3565]E(f306(f285(a865,a865,a119),f306(f276(a865,x35651),x35652)),f306(f276(a865,f306(a119,x35651)),f306(a119,x35652))) % 187.68/187.63 [3589]P1(f306(f49(x35891,x35892),f86(f871(a865,a865),f49(x35891,x35892)))) % 187.68/187.63 [3609]E(f306(f306(f81(a865),f306(f306(f81(a865),f32(x36091)),f32(x36092))),f306(a119,f2(a865))),f32(f34(x36091,x36092))) % 187.68/187.63 [3610]E(f46(a865,f306(a119,f46(a865,x36101,x36102)),x36102),f46(a865,f306(a119,x36101),x36102)) % 187.68/187.63 [3624]E(f306(f306(f44(f872(x36241,a859),f872(x36241,a859)),x36242),f5(f872(x36241,a859))),f42(f872(x36241,a859),x36242)) % 187.68/187.63 [3625]E(f306(f306(f43(f872(x36251,a859),f872(x36251,a859)),x36252),f5(f872(x36251,a859))),f41(f872(x36251,a859),x36252)) % 187.68/187.63 [3626]E(f306(f285(f866(x36261),f872(x36261,a859),f164(x36261)),f306(f164(f866(x36261)),f55(x36261,x36262))),f306(f283(x36261),f306(f164(x36261),x36262))) % 187.68/187.63 [3629]P1(f306(f306(f308(f872(x36291,a859)),x36292),f306(f283(x36291),x36292))) % 187.68/187.63 [3634]E(f46(a1,f306(f80(a1),f46(a1,x36341,x36342)),x36342),f46(a1,f306(f80(a1),x36341),x36342)) % 187.68/187.63 [3646]P1(f306(f306(f220(f872(x36461,a859)),x36462),f231(f872(x36461,a859)))) % 187.68/187.63 [3648]E(f306(f306(f263(x36481,x36481,x36481),f282(x36481,x36482)),f282(x36481,f282(x36481,x36482))),f282(x36481,x36482)) % 187.68/187.63 [3649]E(f306(f306(f108(f872(x36491,a859)),f306(f234(x36491,x36491),x36492)),f306(f232(x36491,x36491),x36492)),f306(f259(x36491),x36492)) % 187.68/187.63 [3670]E(f293(x36701,x36702,f231(f872(x36701,a859)),f231(f872(x36702,a859))),f231(f872(f870(x36701,x36702),a859))) % 187.68/187.63 [3720]P1(f306(f306(f220(a865),f46(a865,x37201,x37202)),x37201)) % 187.68/187.63 [3742]P1(f306(f306(f220(a1),f306(f80(a1),f306(f107(a1),x37421))),f306(f107(a1),x37422))) % 187.68/187.63 [3768]P1(f306(f306(f308(f872(x37681,a859)),f185(f872(x37681,a859))),f306(f283(x37681),x37682))) % 187.68/187.63 [3773]E(f282(x37731,f306(f306(f263(x37731,x37731,x37731),x37732),f282(x37731,x37732))),f282(x37731,x37732)) % 187.68/187.63 [3776]E(f306(f306(f263(x37761,x37761,x37761),f282(x37761,x37762)),x37762),f306(f306(f263(x37761,x37761,x37761),x37762),f282(x37761,x37762))) % 187.68/187.63 [3778]E(f306(a112,f306(f306(f81(a1),f306(f306(f22(a1),x37781),x37782)),f79(a1))),f306(f39(a1),f277(a1,x37782,x37781))) % 187.68/187.63 [3792]E(f306(f232(x37921,x37921),f306(f306(f263(x37921,x37921,x37921),x37922),f282(x37921,x37922))),f306(f232(x37921,x37921),x37922)) % 187.68/187.63 [3793]E(f306(f234(x37931,x37931),f306(f306(f263(x37931,x37931,x37931),x37932),f282(x37931,x37932))),f306(f234(x37931,x37931),x37932)) % 187.68/187.63 [3809]E(f306(f306(f81(a865),f306(f306(f81(a865),f306(f186(a860),x38091)),f306(f186(a860),x38092))),f306(a119,f2(a865))),f306(f186(a860),f34(x38091,x38092))) % 187.68/187.63 [3820]P28(a865,a865,f306(f306(f7(a865,a865,a865),f81(a865)),x38201),x38202) % 187.68/187.63 [3822]P17(a865,f306(f161(a865),f306(f306(f146(f866(x38221),a865),f186(f866(x38221))),f171(x38221,x38222)))) % 187.68/187.63 [3867]P1(f306(f306(f221(a1),f306(f80(a1),f306(f107(a1),f306(a119,x38671)))),f306(f107(a1),x38672))) % 187.68/187.63 [3911]E(f306(f134(f866(x39111),x39111,f306(f7(x39111,f866(x39111),f866(x39111)),f143(x39111)),f120(x39111)),x39112),f306(f161(x39111),x39112)) % 187.68/187.63 [3961]P1(f306(f306(f220(f872(f871(f866(x39611),f866(x39611)),a859)),f150(x39611,x39612)),f282(f866(x39611),f149(x39611,x39612)))) % 187.68/187.63 [3990]P1(f306(f49(x39901,x39902),f306(f306(f236(a865,a865),f306(f306(f40(a865),x39901),x39902)),f46(a865,x39901,x39902)))) % 187.68/187.63 [4001]P1(f306(f306(f220(f872(f871(f866(x40011),f866(x40011)),a859)),f149(x40011,f282(x40011,x40012))),f282(f866(x40011),f149(x40011,x40012)))) % 187.68/187.63 [4223]E(f306(f306(f247(f871(a106,a106),a106,f871(a106,a106),f871(x42231,f871(a106,a106))),f251(f306(f158(a106),f306(f306(f146(f871(a106,x42231),a106),f235(a106,x42231)),x42232)))),f306(f306(f8(x42231,f872(f871(a106,a106),f871(x42231,f871(a106,a106))),a106),f236(x42231,f871(a106,a106))),f252(x42231,x42232))),f250(x42231,x42232)) % 187.68/187.63 [4333]E(f306(f216(a865,f871(x43331,f867(x43331)),f2(a865),f306(f245(x43331,f867(x43331),a865),f306(f16(f872(f867(x43331),a865),x43331),f306(f306(f7(f867(x43331),a865,a865),f306(f306(f8(a865,f872(a865,a865),f867(x43331)),f81(a865)),f186(f867(x43331)))),f79(a865))))),f123(x43331,x43332)),f306(f186(f867(x43331)),x43332)) % 187.68/187.63 [4404]E(f306(f245(f872(f871(x44041,x44041),a859),f872(f871(x44041,x44041),a859),f872(f872(x44042,x44041),f871(f872(f871(x44042,x44042),a859),f872(f871(x44042,x44042),a859)))),f306(f306(f7(f872(f871(x44041,x44041),a859),f872(f872(f871(x44041,x44041),a859),f872(f872(x44042,x44041),f872(f871(x44042,x44042),a859))),f872(f872(f871(x44041,x44041),a859),f872(f872(x44042,x44041),f871(f872(f871(x44042,x44042),a859),f872(f871(x44042,x44042),a859))))),f306(f306(f8(f872(f872(f872(x44042,x44041),f872(f871(x44042,x44042),a859)),f872(f872(x44042,x44041),f871(f872(f871(x44042,x44042),a859),f872(f871(x44042,x44042),a859)))),f872(f872(f872(f871(x44041,x44041),a859),f872(f872(x44042,x44041),f872(f871(x44042,x44042),a859))),f872(f872(f871(x44041,x44041),a859),f872(f872(x44042,x44041),f871(f872(f871(x44042,x44042),a859),f872(f871(x44042,x44042),a859))))),f872(f871(x44041,x44041),a859)),f8(f872(f872(x44042,x44041),f872(f871(x44042,x44042),a859)),f872(f872(x44042,x44041),f871(f872(f871(x44042,x44042),a859),f872(f871(x44042,x44042),a859))),f872(f871(x44041,x44041),a859))),f306(f306(f8(f872(f872(x44042,x44041),f872(f872(f871(x44042,x44042),a859),f871(f872(f871(x44042,x44042),a859),f872(f871(x44042,x44042),a859)))),f872(f872(f872(x44042,x44041),f872(f871(x44042,x44042),a859)),f872(f872(x44042,x44041),f871(f872(f871(x44042,x44042),a859),f872(f871(x44042,x44042),a859)))),f872(f871(x44041,x44041),a859)),f18(f872(x44042,x44041),f872(f871(x44042,x44042),a859),f871(f872(f871(x44042,x44042),a859),f872(f871(x44042,x44042),a859)))),f306(f306(f8(f872(f872(x44042,x44041),f872(f871(x44042,x44042),a859)),f872(f872(x44042,x44041),f872(f872(f871(x44042,x44042),a859),f871(f872(f871(x44042,x44042),a859),f872(f871(x44042,x44042),a859)))),f872(f871(x44041,x44041),a859)),f306(f8(f872(f871(x44042,x44042),a859),f872(f872(f871(x44042,x44042),a859),f871(f872(f871(x44042,x44042),a859),f872(f871(x44042,x44042),a859))),f872(x44042,x44041)),f236(f872(f871(x44042,x44042),a859),f872(f871(x44042,x44042),a859)))),f262(x44041,x44042))))),f262(x44041,x44042))),f75(x44041,x44042)) % 187.68/187.63 [4487]~E(f306(f283(x44871),x44872),f185(f872(f872(x44871,a859),a859))) % 187.68/187.63 [4505]~P1(f306(f306(f308(x45051),x45052),f185(f872(x45051,a859)))) % 187.68/187.63 [4514]~P1(f306(f306(f221(f872(x45141,a859)),x45142),f185(f872(x45141,a859)))) % 187.68/187.63 [3339]E(f306(f306(f22(a865),x33391),f306(f306(f81(a865),x33391),x33392)),f2(a865)) % 187.68/187.63 [3341]E(f306(f306(f108(f872(x33411,a859)),x33412),x33412),x33412) % 187.68/187.63 [3342]E(f306(f306(f109(f872(x33421,a859)),x33422),x33422),x33422) % 187.68/187.63 [3369]E(f306(f306(f22(f872(x33691,a859)),x33692),x33692),f185(f872(x33691,a859))) % 187.68/187.63 [3372]E(f306(f135(x33721,x33722),f2(a865)),f185(f872(f871(f866(x33721),f866(x33721)),a859))) % 187.68/187.63 [3373]E(f306(f306(f81(a865),x33731),f306(a119,x33732)),f306(a119,f306(f306(f81(a865),x33731),x33732))) % 187.68/187.63 [3385]E(f194(f306(f107(a1),x33851),f306(f107(a1),x33852)),f306(f107(a1),f306(f306(f22(a865),x33851),x33852))) % 187.68/187.63 [3388]E(f306(f306(f40(a1),f306(f80(a1),x33881)),x33882),f306(f306(f40(a1),x33881),f306(f80(a1),x33882))) % 187.68/187.63 [3392]E(f306(f39(a1),f306(f276(a1,x33921),x33922)),f306(a112,f306(f306(f22(a1),x33922),x33921))) % 187.68/187.63 [3395]E(f306(f306(f81(a865),f306(a119,x33951)),x33952),f306(a119,f306(f306(f81(a865),x33951),x33952))) % 187.68/187.63 [3400]E(f306(f80(f872(x34001,a859)),f306(f80(f872(x34001,a859)),x34002)),x34002) % 187.68/187.63 [3414]E(f171(x34141,f306(f306(f143(f866(x34141)),f120(x34141)),x34142)),f171(x34141,x34142)) % 187.68/187.63 [3418]E(f306(f306(f81(a865),x34181),f306(f306(f82(a865),x34181),x34182)),f306(f306(f82(a865),x34181),f306(a119,x34182))) % 187.68/187.63 [3426]E(f306(f306(a23,f306(a3,x34261)),f306(a3,x34262)),f306(a3,f306(f306(f22(a865),x34261),x34262))) % 187.68/187.63 [3439]E(f306(f306(f82(a1),f306(f80(a1),x34391)),x34392),f306(f80(a1),f306(f306(f82(a1),x34391),x34392))) % 187.68/187.63 [3441]E(f306(f306(f237(a1),f306(f107(a1),x34411)),x34412),f306(f107(a1),f306(f306(f237(a865),x34411),x34412))) % 187.68/187.63 [3442]E(f306(f306(f81(a106),f306(a3,x34421)),f306(a3,x34422)),f306(a3,f306(f306(f81(a865),x34421),x34422))) % 187.68/187.63 [3443]E(f306(f306(f82(a106),f306(a3,x34431)),f306(a3,x34432)),f306(a3,f306(f306(f82(a865),x34431),x34432))) % 187.68/187.63 [3444]E(f306(f306(f225(a865),f306(a119,x34441)),f306(a119,x34442)),f306(a119,f306(f306(f225(a865),x34441),x34442))) % 187.68/187.63 [3445]E(f306(f306(f219(a865),f306(a119,x34451)),f306(a119,x34452)),f306(a119,f306(f306(f219(a865),x34451),x34452))) % 187.68/187.63 [3451]E(f306(f164(a865),f131(a865,f306(f276(a865,x34511),x34512))),f306(f276(a865,x34511),x34512)) % 187.68/187.63 [3452]E(f287(x34521,f306(f306(f284(x34521),x34522),f185(f872(x34521,a859)))),x34522) % 187.68/187.63 [3457]E(f306(f232(x34571,x34572),f185(f872(f871(x34571,x34572),a859))),f185(f872(x34572,a859))) % 187.68/187.63 [3458]E(f306(f234(x34581,x34582),f185(f872(f871(x34581,x34582),a859))),f185(f872(x34581,a859))) % 187.68/187.63 [3462]E(f306(a112,f306(f306(f22(a1),x34621),x34622)),f306(f39(a1),f279(a1,x34622,x34621))) % 187.68/187.63 [3466]E(f306(f306(f81(a865),x34661),f306(f306(f82(a865),x34662),x34661)),f306(f306(f82(a865),f306(a119,x34662)),x34661)) % 187.68/187.63 [3468]E(f306(f306(f62(x34681),f185(f872(x34681,a859))),x34682),f185(f872(f872(x34681,a859),a859))) % 187.68/187.63 [3477]E(f306(f186(f866(a865)),f131(a865,f306(f276(a865,x34771),x34772))),f306(f306(f22(a865),x34772),x34771)) % 187.68/187.63 [3492]E(f306(f306(f108(f872(x34921,a859)),f185(f872(x34921,a859))),x34922),x34922) % 187.68/187.63 [3493]E(f306(f306(f109(f872(x34931,a859)),f231(f872(x34931,a859))),x34932),x34932) % 187.68/187.63 [3494]E(f306(f306(f81(a1),f306(f80(a1),x34941)),f306(f80(a1),x34942)),f306(f80(a1),f306(f306(f81(a1),x34941),x34942))) % 187.68/187.63 [3498]E(f306(f306(f81(a1),f306(f111(a1),x34981)),f306(f111(a1),x34982)),f306(f111(a1),f306(f306(f81(a1),x34981),x34982))) % 187.68/187.63 [3500]E(f306(f306(f81(a1),f306(f107(a1),x35001)),f306(f107(a1),x35002)),f306(f107(a1),f306(f306(f81(a865),x35001),x35002))) % 187.68/187.63 [3501]E(f306(f306(f82(a1),f306(f111(a1),x35011)),f306(f111(a1),x35012)),f306(f111(a1),f306(f306(f82(a1),x35011),x35012))) % 187.68/187.63 [3503]E(f306(f306(f82(a1),f306(f107(a1),x35031)),f306(f107(a1),x35032)),f306(f107(a1),f306(f306(f82(a865),x35031),x35032))) % 187.68/187.63 [3504]E(f306(f306(f40(a1),f306(f107(a1),x35041)),f306(f107(a1),x35042)),f306(f107(a1),f306(f306(f40(a865),x35041),x35042))) % 187.68/187.63 [3521]E(f306(f306(f6(x35211,a865),f306(f16(a865,x35211),f79(a865))),x35212),f306(f39(x35211),x35212)) % 187.68/187.63 [3528]E(f306(f80(a1),f46(a1,f306(f80(a1),x35281),x35282)),f46(a1,x35281,f306(f80(a1),x35282))) % 187.68/187.63 [3530]E(f306(f164(a1),f170(x35301,f306(f306(f22(a1),x35302),f79(a1)))),f306(f276(a1,x35301),x35302)) % 187.68/187.63 [3534]P1(f306(f306(f220(a865),x35341),f306(f306(f81(a865),x35342),x35341))) % 187.68/187.63 [3535]P1(f306(f306(f220(a865),x35351),f306(f306(f81(a865),x35351),x35352))) % 187.68/187.63 [3538]E(f306(f306(f22(f872(x35381,a859)),f185(f872(x35381,a859))),x35382),f185(f872(x35381,a859))) % 187.68/187.63 [3539]E(f306(f306(f108(f872(x35391,a859)),f231(f872(x35391,a859))),x35392),f231(f872(x35391,a859))) % 187.68/187.63 [3540]E(f306(f306(f109(f872(x35401,a859)),f185(f872(x35401,a859))),x35402),f185(f872(x35401,a859))) % 187.68/187.63 [3545]E(f306(f306(f236(a1,a1),x35451),f306(f80(a1),x35452)),f306(a52,f306(f306(f236(a1,a1),x35451),x35452))) % 187.68/187.63 [3546]E(f306(f276(a1,f306(f306(f81(a1),x35461),f79(a1))),x35462),f280(a1,x35461,x35462)) % 187.68/187.63 [3557]E(f306(f306(f82(a865),x35571),f306(f306(f40(a865),x35572),x35571)),f306(f306(f22(a865),x35572),f46(a865,x35572,x35571))) % 187.68/187.63 [3558]E(f306(f306(f82(a1),x35581),f306(f306(f40(a1),x35582),x35581)),f306(f306(f22(a1),x35582),f46(a1,x35582,x35581))) % 187.68/187.63 [3562]E(f306(f164(a1),f170(f306(f306(f81(a1),x35621),f79(a1)),x35622)),f279(a1,x35621,x35622)) % 187.68/187.63 [3566]P1(f306(f306(f220(f872(x35661,a859)),x35662),x35662)) % 187.68/187.63 [3569]E(f306(f306(f108(f872(x35691,a859)),x35692),f306(f80(f872(x35691,a859)),x35692)),f231(f872(x35691,a859))) % 187.68/187.63 [3570]E(f306(f306(f109(f872(x35701,a859)),x35702),f306(f80(f872(x35701,a859)),x35702)),f185(f872(x35701,a859))) % 187.68/187.63 [3576]E(f306(f306(f22(a865),f306(f306(f22(a865),x35761),f79(a865))),x35762),f306(f306(f22(a865),x35761),f306(a119,x35762))) % 187.68/187.63 [3581]E(f306(f306(f22(f872(x35811,a859)),f231(f872(x35811,a859))),x35812),f306(f80(f872(x35811,a859)),x35812)) % 187.68/187.63 [3582]E(f306(f306(f22(a1),f306(f111(a1),x35821)),f306(f111(a1),x35822)),f306(f111(a1),f306(f306(f81(a1),x35821),f306(f80(a1),x35822)))) % 187.68/187.63 [3594]E(f306(f164(a865),f131(a865,f306(f276(a865,x35941),f306(a119,x35942)))),f277(a865,x35941,x35942)) % 187.68/187.63 [3601]P1(f306(f306(f306(f306(a195,a24),x36011),x36012),x36011)) % 187.68/187.63 [3607]E(f306(f186(f866(f866(x36071))),f55(x36071,x36072)),f306(f306(f237(a865),f306(a119,f306(a119,f2(a865)))),f306(f186(f866(x36071)),x36072))) % 187.68/187.63 [3627]E(f306(f306(f180(f871(x36271,x36271),a859),f2(a865)),x36272),f282(x36271,f185(f872(f871(x36271,x36271),a859)))) % 187.68/187.63 [3631]P1(f306(f129(a865),f131(a865,f306(f276(a865,x36311),x36312)))) % 187.68/187.63 [3647]E(f306(f285(a1,a865,a112),f277(a1,f306(f107(a1),x36471),f306(f107(a1),x36472))),f277(a865,x36471,x36472)) % 187.68/187.63 [3657]E(f182(a865,f2(a865),f5(a865),f306(f306(f22(a865),x36571),x36572)),f306(f306(f22(a865),x36571),f306(a119,x36572))) % 187.68/187.63 [3658]E(f306(a112,f306(f306(f22(a1),x36581),f306(f306(f81(a1),x36582),f79(a1)))),f306(f39(a1),f280(a1,x36582,x36581))) % 187.68/187.63 [3693]E(f306(f306(f146(a865,a865),a119),f131(a865,f306(f276(a865,x36931),x36932))),f131(a865,f306(f276(a865,f306(a119,x36931)),f306(a119,x36932)))) % 187.68/187.63 [3700]E(f306(f164(a1),f170(f306(f306(f81(a1),x37001),f79(a1)),f306(f306(f22(a1),x37002),f79(a1)))),f280(a1,x37001,x37002)) % 187.68/187.63 [3711]P1(f306(f306(f220(f872(x37111,a859)),f185(f872(x37111,a859))),x37112)) % 187.68/187.63 [3716]E(f86(x37161,f306(f306(f7(x37161,x37161,a859),a303),x37162)),x37162) % 187.68/187.63 [3717]E(f91(x37171,f306(f306(f7(x37171,x37171,a859),a303),x37172)),x37172) % 187.68/187.63 [3721]E(f306(f164(a865),f131(a865,f306(f276(a865,f306(a119,x37211)),f306(a119,x37212)))),f279(a865,x37211,x37212)) % 187.68/187.63 [3745]E(f306(f306(f243(x37451,x37452),f231(f872(x37451,a859))),f306(f16(f872(x37452,a859),x37451),f231(f872(x37452,a859)))),f231(f872(f871(x37451,x37452),a859))) % 187.68/187.63 [3780]E(f306(f228(x37801),f306(f306(f8(a859,a859,x37801),a301),x37802)),f306(f80(f872(x37801,a859)),f306(f228(x37801),x37802))) % 187.68/187.63 [3783]E(f306(f228(x37831),f306(f306(f7(x37831,x37831,a859),a303),x37832)),f306(f306(f284(x37831),x37832),f185(f872(x37831,a859)))) % 187.68/187.63 [3789]E(f306(f306(f81(a1),f306(f306(f22(a1),x37891),x37892)),f306(f306(f22(a1),x37891),x37892)),f306(f306(f22(a1),f306(f306(f81(a1),x37891),x37891)),f306(f306(f81(a1),x37892),x37892))) % 187.68/187.63 [3790]E(f306(f306(f81(a1),f306(f306(f81(a1),x37901),x37901)),f306(f306(f81(a1),x37902),x37902)),f306(f306(f81(a1),f306(f306(f81(a1),x37901),x37902)),f306(f306(f81(a1),x37901),x37902))) % 187.68/187.63 [3806]P1(f306(f306(f220(a865),f306(f39(x38061),f306(f164(x38061),x38062))),f306(f186(f866(x38061)),x38062))) % 187.68/187.63 [3807]P1(f306(f306(f220(a865),f306(f186(f866(x38071)),f144(x38071,x38072))),f306(f186(f866(x38071)),x38072))) % 187.68/187.63 [3817]E(f306(f228(x38171),f306(f306(f7(x38171,f872(x38171,a859),a859),f308(x38171)),x38172)),x38172) % 187.68/187.63 [3832]E(f306(f306(f165(x38321),f306(f306(f22(a865),f306(f186(f866(x38321)),x38322)),f79(a865))),x38322),f121(x38321,x38322)) % 187.68/187.63 [3854]E(f182(a865,f2(a865),f306(f306(f8(a865,a865,a865),a119),f306(f225(a865),x38541)),x38542),f306(f306(f225(a865),f306(a119,x38541)),x38542)) % 187.68/187.63 [3858]E(f41(f872(x38581,a859),f306(f285(f872(f871(x38581,x38581),a859),f872(x38581,a859),f259(x38581)),x38582)),f306(f259(x38581),f41(f872(f871(x38581,x38581),a859),x38582))) % 187.68/187.63 [3859]E(f182(a865,f306(a119,x38591),f306(f306(f8(a865,a865,a865),a119),f306(f219(a865),x38591)),x38592),f306(f306(f219(a865),f306(a119,x38591)),x38592)) % 187.68/187.63 [3861]E(f306(f306(f236(a1,a1),f306(f306(f40(a1),f306(f76(a1),x38611)),f306(f76(a1),x38612))),f46(a1,f306(f76(a1),x38611),f306(f76(a1),x38612))),f54(x38611,x38612)) % 187.68/187.63 [3882]P1(f306(f306(f220(f872(f872(x38821,a859),a859)),x38822),f306(f283(x38821),f41(f872(x38821,a859),x38822)))) % 187.68/187.63 [3916]E(f306(f306(f43(x39161,f872(x39161,a859)),x39162),f306(f306(f7(x39161,f872(x39161,a859),f872(x39161,a859)),f284(x39161)),f185(f872(x39161,a859)))),x39162) % 187.68/187.63 [3917]E(f306(f306(f263(x39171,x39171,x39171),f306(f261(x39171,x39171),x39172)),f282(x39171,f306(f261(x39171,x39171),x39172))),f306(f261(x39171,x39171),f306(f306(f263(x39171,x39171,x39171),x39172),f282(x39171,x39172)))) % 187.68/187.63 [3981]E(f306(f164(x39811),f306(f134(f866(x39811),f866(x39811),f122(x39811),f120(x39811)),x39812)),f306(f306(f43(f866(x39811),f872(x39811,a859)),f306(f164(f866(x39811)),x39812)),f164(x39811))) % 187.68/187.63 [4013]E(f306(f306(f108(f872(f871(x40131,x40131),a859)),f282(x40131,f185(f872(f871(x40131,x40131),a859)))),f306(f306(f263(x40131,x40131,x40131),f282(x40131,x40132)),x40132)),f282(x40131,x40132)) % 187.68/187.63 [4047]E(f306(f306(f173(x40471,x40471),x40472),x40472),f306(f306(f146(x40471,f871(x40471,x40471)),f306(f306(f18(x40471,x40471,f871(x40471,x40471)),f236(x40471,x40471)),f5(x40471))),x40472)) % 187.68/187.63 [4160]E(f306(f134(a865,f866(x41601),f306(f7(f866(x41601),a865,a865),f306(f306(f8(a865,f872(a865,a865),f866(x41601)),f219(a865)),f186(f866(x41601)))),f2(a865)),f306(f161(f866(x41601)),x41602)),f306(f186(f866(f866(x41601))),f171(x41601,x41602))) % 187.68/187.63 [4238]E(f306(f306(f262(f871(a865,f866(x42381)),f866(x42381)),f299(a865,f866(x42381),a227,f137(x42381,x42382))),f306(f306(f18(f866(x42381),f866(x42381),f871(a865,f866(x42381))),f306(f306(f8(a865,f872(f866(x42381),f871(a865,f866(x42381))),f866(x42381)),f236(a865,f866(x42381))),f186(f866(x42381)))),f5(f866(x42381)))),f138(x42381,x42382)) % 187.68/187.63 [4366]E(f306(f228(x43661),f306(f306(f8(f872(f872(x43661,a859),a859),a859,x43661),f89(f872(x43661,a859))),f306(f306(f8(f872(f872(x43661,a859),a859),f872(f872(x43661,a859),a859),x43661),f306(f18(f872(x43661,a859),a859,a859),f306(f306(f8(a859,f872(a859,a859),f872(x43661,a859)),a309),f306(f306(f7(f872(x43661,a859),f872(f872(x43661,a859),a859),a859),f308(f872(x43661,a859))),x43662)))),f308(x43661)))),f42(f872(x43661,a859),x43662)) % 187.68/187.63 [4515]~P1(f306(f306(f221(a1),f306(f107(a1),x45151)),f306(f80(a1),f306(f107(a1),x45152)))) % 187.68/187.63 [3464]E(f306(f306(f22(a865),f306(f306(f81(a865),x34641),x34642)),x34642),x34641) % 187.68/187.63 [3465]E(f306(f306(f22(a865),f306(f306(f81(a865),x34651),x34652)),x34651),x34652) % 187.68/187.63 [3529]E(f306(f306(f81(a865),f306(f306(f22(a865),x35291),x35292)),x35292),f306(f306(f219(a865),x35291),x35292)) % 187.68/187.63 [3633]E(f306(f306(f82(a865),f306(f306(f40(a865),x36331),x36332)),x36332),f306(f306(f22(a865),x36331),f46(a865,x36331,x36332))) % 187.68/187.63 [3662]E(f306(f164(a865),f131(a865,f306(f276(a865,f306(a119,x36621)),x36622))),f280(a865,x36621,x36622)) % 187.68/187.63 [3669]E(f306(f107(a1),f202(f306(a112,f306(f76(a1),x36691)),f306(a112,f306(f76(a1),x36692)))),f306(f306(a203,x36691),x36692)) % 187.68/187.63 [3671]E(f306(f306(f108(f872(x36711,a859)),f306(f80(f872(x36711,a859)),x36712)),x36712),f231(f872(x36711,a859))) % 187.68/187.63 [3672]E(f306(f306(f109(f872(x36721,a859)),f306(f80(f872(x36721,a859)),x36722)),x36722),f185(f872(x36721,a859))) % 187.68/187.63 [3689]P1(f306(f306(f220(a865),f306(f306(f22(a865),x36891),x36892)),x36891)) % 187.68/187.63 [3690]P1(f306(f306(f220(a865),f306(f306(f40(a865),x36901),x36902)),x36901)) % 187.68/187.63 [3713]P1(f306(f306(f221(a865),x37131),f306(a119,f306(f306(f81(a865),x37132),x37131)))) % 187.68/187.63 [3714]P1(f306(f306(f221(a865),x37141),f306(a119,f306(f306(f81(a865),x37141),x37142)))) % 187.68/187.63 [3731]E(f306(f306(f82(a865),f306(a112,f306(f76(a1),x37311))),f306(a112,f306(f76(a1),x37312))),f306(a112,f306(f76(a1),f306(f306(f82(a1),x37311),x37312)))) % 187.68/187.63 [3741]P1(f306(f306(f220(a1),f2(a1)),f306(f306(f237(a1),f306(f76(a1),x37411)),x37412))) % 187.68/187.63 [3811]E(f306(f260(f866(x38111),f866(x38111),f150(x38111,x38112)),f306(f306(f284(f866(x38111)),f120(x38111)),f185(f872(f866(x38111),a859)))),f306(f306(f284(f866(x38111)),f120(x38111)),f185(f872(f866(x38111),a859)))) % 187.68/187.63 [3830]E(f306(f306(f108(f872(f871(x38301,x38301),a859)),f282(x38301,x38302)),f282(x38301,f185(f872(f871(x38301,x38301),a859)))),f282(x38301,x38302)) % 187.68/187.63 [3844]E(f306(f306(f40(a1),f306(f111(a1),f306(f306(f81(a1),x38441),x38441))),f306(f111(a1),f306(f306(f81(a1),x38442),x38442))),f306(f306(f40(a1),f306(f111(a1),x38441)),f306(f111(a1),x38442))) % 187.68/187.63 [3906]E(f306(f306(f237(a1),x39061),f306(f111(a865),f306(f306(f81(a1),x39062),x39062))),f306(f306(f87(a1,a1),f306(f306(f237(a1),x39061),f306(f111(a865),x39062))),f306(f306(f18(a1,a1,a1),f82(a1)),f5(a1)))) % 187.68/187.63 [3912]E(f306(f228(f872(x39121,a859)),f306(f306(f7(f872(x39121,a859),f872(x39121,a859),a859),f220(f872(x39121,a859))),x39122)),f306(f283(x39121),x39122)) % 187.68/187.63 [3926]E(f306(f306(f146(a1,a865),a112),f306(f306(f122(a1),f306(f306(f146(a865,a1),f107(a1)),x39261)),f306(f306(f146(a865,a1),f107(a1)),x39262))),f306(f306(f122(a865),x39261),x39262)) % 187.68/187.63 [3960]E(f306(f285(a1,a1,f306(f306(f7(a1,a1,a1),f81(a1)),x39601)),f306(f276(a1,f2(a1)),f306(f306(f22(a1),x39602),x39601))),f306(f276(a1,x39601),x39602)) % 187.68/187.63 [3962]P51(x39621,f306(f306(f22(f872(f871(x39621,x39621),a859)),x39622),f282(x39621,f185(f872(f871(x39621,x39621),a859))))) % 187.68/187.63 [3979]E(f306(f186(f866(x39791)),f306(f134(f866(x39791),f866(x39791),f122(x39791),f120(x39791)),x39792)),f306(f158(a865),f306(f306(f146(f866(x39791),a865),f186(f866(x39791))),x39792))) % 187.68/187.63 [3984]P50(x39841,f231(f872(x39841,a859)),f306(f306(f108(f872(f871(x39841,x39841),a859)),x39842),f282(x39841,f185(f872(f871(x39841,x39841),a859))))) % 187.68/187.63 [4027]E(f182(a865,f2(a865),f306(f306(f8(a865,a865,a865),a119),f306(f306(f7(a865,a865,a865),f225(a865)),x40271)),x40272),f306(f306(f225(a865),x40272),f306(a119,x40271))) % 187.68/187.63 [4030]E(f182(a865,f306(a119,x40301),f306(f306(f8(a865,a865,a865),a119),f306(f306(f7(a865,a865,a865),f219(a865)),x40301)),x40302),f306(f306(f219(a865),x40302),f306(a119,x40301))) % 187.68/187.63 [4033]E(f306(f285(x40331,f866(x40331),f306(f306(f7(x40331,f866(x40331),f866(x40331)),f143(x40331)),f120(x40331))),x40332),f167(x40331,x40332,f306(f306(f284(f866(x40331)),f120(x40331)),f185(f872(f866(x40331),a859))))) % 187.68/187.63 [4034]E(f306(f306(f108(f872(f871(x40341,x40341),a859)),f306(f306(f263(x40341,x40341,x40341),x40342),f282(x40341,x40342))),f282(x40341,f185(f872(f871(x40341,x40341),a859)))),f282(x40341,x40342)) % 187.68/187.63 [4042]P1(f306(f306(f220(f872(f871(x40421,x40421),a859)),f233(x40421,x40422)),f306(f306(f243(x40421,x40421),x40422),f306(f16(f872(x40421,a859),x40421),x40422)))) % 187.68/187.63 [4045]E(f306(f285(a1,a865,a112),f306(f306(f108(f872(a1,a859)),f306(f285(a865,a1,f107(a1)),x40451)),f306(f285(a865,a1,f107(a1)),x40452))),f306(f306(f108(f872(a865,a859)),x40451),x40452)) % 187.68/187.63 [4046]E(f306(f285(a1,a865,a112),f306(f306(f109(f872(a1,a859)),f306(f285(a865,a1,f107(a1)),x40461)),f306(f285(a865,a1,f107(a1)),x40462))),f306(f306(f109(f872(a865,a859)),x40461),x40462)) % 187.68/187.63 [4050]E(f306(f228(x40501),f306(f306(f8(a859,a859,x40501),a301),f306(f306(f7(x40501,f872(x40501,a859),a859),f308(x40501)),x40502))),f306(f80(f872(x40501,a859)),x40502)) % 187.68/187.63 [4077]E(f306(f134(f866(x40771),f866(x40771),f122(x40771),f120(x40771)),f306(f306(f146(f866(x40771),f866(x40771)),f161(x40771)),f306(f161(f866(x40771)),x40772))),f306(f161(x40771),f306(f134(f866(x40771),f866(x40771),f122(x40771),f120(x40771)),x40772))) % 187.68/187.63 [4105]E(f306(f306(f43(a865,f872(f871(x41051,x41051),a859)),f231(f872(a865,a859))),f306(f306(f7(a865,f872(f871(x41051,x41051),a859),f872(f871(x41051,x41051),a859)),f180(f871(x41051,x41051),a859)),x41052)),f282(x41051,x41052)) % 187.68/187.63 [4125]E(f86(x41251,f306(f306(f8(f872(x41251,a859),a859,x41251),f306(a303,x41252)),f306(f306(f7(x41251,f872(x41251,a859),f872(x41251,a859)),f284(x41251)),f185(f872(x41251,a859))))),f287(x41251,x41252)) % 187.68/187.63 [4133]E(f306(f186(f866(x41331)),f144(x41331,f306(f134(f866(x41331),f866(x41331),f122(x41331),f120(x41331)),x41332))),f306(f39(x41331),f306(f306(f43(f866(x41331),f872(x41331,a859)),f306(f164(f866(x41331)),x41332)),f164(x41331)))) % 187.68/187.63 [4149]E(f306(f306(f108(f872(f871(x41491,x41491),a859)),x41492),f306(f306(f263(x41491,x41491,x41491),f306(f306(f263(x41491,x41491,x41491),x41492),f282(x41491,x41492))),x41492)),f306(f306(f263(x41491,x41491,x41491),x41492),f282(x41491,x41492))) % 187.68/187.63 [4170]P1(f306(f306(f220(f872(f871(x41701,x41701),a859)),f306(f306(f263(x41701,x41701,x41701),x41702),f282(x41701,x41702))),f306(f306(f243(x41701,x41701),f306(f259(x41701),x41702)),f306(f16(f872(x41701,a859),x41701),f306(f259(x41701),x41702))))) % 187.68/187.63 [4213]E(f306(f228(f866(x42131)),f306(f306(f7(f866(x42131),f872(x42131,a859),a859),f306(f306(f8(f872(x42131,a859),f872(f872(x42131,a859),a859),f866(x42131)),f220(f872(x42131,a859))),f164(x42131))),x42132)),f153(x42131,x42132)) % 187.68/187.63 [4225]E(f306(f148(f866(x42251),x42251,f120(x42251),f306(f306(f8(f866(x42251),f872(f866(x42251),f866(x42251)),x42251),f306(f7(f866(x42251),f866(x42251),f866(x42251)),f122(x42251))),f306(f306(f7(x42251,f866(x42251),f866(x42251)),f143(x42251)),f120(x42251)))),x42252),f306(f160(x42251),x42252)) % 187.68/187.63 [4267]P28(f872(x42671,x42672),f872(f871(x42671,x42672),a859),f306(f306(f8(f872(f871(x42671,x42672),a859),f872(f871(x42671,x42672),a859),f872(x42671,x42672)),f228(f871(x42671,x42672))),f306(f306(f8(f872(x42671,f872(x42672,a859)),f872(f871(x42671,x42672),a859),f872(x42671,x42672)),f245(x42671,x42672,a859)),f306(f8(x42672,f872(x42672,a859),x42671),f306(f7(x42672,x42672,a859),a303)))),f231(f872(f872(x42671,x42672),a859))) % 187.68/187.63 [4272]E(f46(a1,f306(f111(a1),f306(f306(f81(a1),x42721),x42721)),f306(f111(a1),f306(f306(f81(a1),x42722),x42722))),f306(f306(f82(a1),f306(f111(a1),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)))),f46(a1,f306(f111(a1),x42721),f306(f111(a1),x42722)))) % 187.68/187.63 [4314]E(f306(f306(f43(x43141,f872(f871(x43141,x43141),a859)),x43142),f306(f306(f7(x43141,f872(f871(x43141,x43141),a859),f872(f871(x43141,x43141),a859)),f306(f306(f8(f871(x43141,x43141),f872(f872(f871(x43141,x43141),a859),f872(f871(x43141,x43141),a859)),x43141),f284(f871(x43141,x43141))),f306(f306(f18(x43141,x43141,f871(x43141,x43141)),f236(x43141,x43141)),f5(x43141)))),f185(f872(f871(x43141,x43141),a859)))),f233(x43141,x43142)) % 187.68/187.63 [4322]E(f192(x43221,f306(f306(f236(a1,a1),f306(f80(a1),f306(f306(f74(f871(a1,a1),a1,x43221,f235(a1,a1)),f198(x43221)),x43222))),f306(f306(f74(f871(a1,a1),a1,x43221,f244(a1,a1)),f198(x43221)),x43222))),f206(x43221,x43222)) % 187.68/187.63 [4399]E(f306(f228(f872(x43991,a859)),f306(f306(f8(f872(f872(x43991,a859),a859),a859,f872(x43991,a859)),f88(f872(x43991,a859))),f306(f306(f7(f872(x43991,a859),f872(f872(x43991,a859),a859),f872(f872(x43991,a859),a859)),f306(f306(f8(f872(f872(x43991,a859),f872(a859,a859)),f872(f872(f872(x43991,a859),a859),f872(f872(x43991,a859),a859)),f872(x43991,a859)),f18(f872(x43991,a859),a859,a859)),f306(f306(f8(f872(f872(x43991,a859),a859),f872(f872(x43991,a859),f872(a859,a859)),f872(x43991,a859)),f306(f8(a859,f872(a859,a859),f872(x43991,a859)),a304)),f306(f306(f7(f872(x43991,a859),f872(f872(x43991,a859),f872(x43991,a859)),f872(f872(x43991,a859),a859)),f306(f306(f8(f872(f872(x43991,a859),a859),f872(f872(f872(x43991,a859),f872(x43991,a859)),f872(f872(x43991,a859),a859)),f872(x43991,a859)),f8(f872(x43991,a859),a859,f872(x43991,a859))),a303)),f80(f872(x43991,a859)))))),f306(f306(f8(f872(f872(x43991,a859),a859),a859,f872(x43991,a859)),f306(f308(f872(x43991,a859)),x43992)),f283(x43991))))),f306(f283(x43991),f306(f80(f872(x43991,a859)),x43992))) % 187.68/187.63 [4512]~E(f306(f306(f81(a1),x45121),x45121),f306(f306(f22(a1),f306(f306(f81(a1),x45122),x45122)),a104)) % 187.68/187.63 [4517]~P1(f306(f306(f221(a865),f306(f306(f81(a865),x45171),x45172)),x45172)) % 187.68/187.63 [4518]~P1(f306(f306(f221(a865),f306(f306(f81(a865),x45181),x45182)),x45181)) % 187.68/187.63 [3746]E(f306(f306(f22(a865),x37461),f306(f306(f82(a865),f306(f306(f40(a865),x37461),x37462)),x37462)),f46(a865,x37461,x37462)) % 187.68/187.63 [3747]E(f306(f306(f22(a1),x37471),f306(f306(f82(a1),f306(f306(f40(a1),x37471),x37472)),x37472)),f46(a1,x37471,x37472)) % 187.68/187.63 [3781]E(f306(f306(f146(a865,x37811),f306(f157(x37811),x37812)),f131(a865,f306(f276(a865,f2(a865)),f306(f186(f866(x37811)),x37812)))),x37812) % 187.68/187.63 [3840]E(f306(f260(x38401,x38401,f282(x38401,f185(f872(f871(x38401,x38401),a859)))),x38402),x38402) % 187.68/187.63 [3963]E(f282(x39631,f306(f306(f22(f872(f871(x39631,x39631),a859)),x39632),f282(x39631,f185(f872(f871(x39631,x39631),a859))))),f282(x39631,x39632)) % 187.68/187.63 [3964]E(f282(x39641,f306(f306(f108(f872(f871(x39641,x39641),a859)),x39642),f282(x39641,f185(f872(f871(x39641,x39641),a859))))),f282(x39641,x39642)) % 187.68/187.63 [4016]E(f306(f306(f22(a1),f306(f306(f22(a1),f306(f306(f81(a1),x40161),x40161)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),x40162),x40162)),a104)),f306(f306(f81(a1),f306(f306(f22(a1),x40161),x40162)),f306(f306(f22(a1),x40161),x40162))) % 187.68/187.63 [4055]E(f306(f306(f22(a1),f306(f306(f81(a1),f306(f306(f81(a1),x40551),x40552)),f306(f306(f81(a1),x40551),x40552))),a104),f306(f306(f81(a1),f306(f306(f81(a1),x40551),x40551)),f306(f306(f22(a1),f306(f306(f81(a1),x40552),x40552)),a104))) % 187.68/187.63 [4081]E(f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),x40811),x40811)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),x40812),x40812)),a104)),f306(f306(f81(a1),f306(f306(f81(a1),x40811),f306(f306(f22(a1),x40812),a104))),f306(f306(f81(a1),x40811),f306(f306(f22(a1),x40812),a104)))) % 187.68/187.63 [4091]E(f306(f306(f22(a1),f306(f306(f81(a1),f306(f306(f22(a1),x40911),x40912)),f306(f306(f22(a1),x40911),x40912))),a104),f306(f306(f22(a1),f306(f306(f22(a1),f306(f306(f81(a1),x40911),x40911)),a104)),f306(f306(f81(a1),x40912),x40912))) % 187.68/187.63 [4092]E(f306(f306(f22(a1),f306(f306(f81(a1),f306(f306(f81(a1),x40921),x40922)),f306(f306(f81(a1),x40921),x40922))),a104),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),x40921),x40921)),a104)),f306(f306(f81(a1),x40922),x40922))) % 187.68/187.63 [4146]E(f306(f107(a1),f306(f306(f40(a865),f306(f306(f82(a865),f306(a112,f306(f76(a1),x41461))),f306(a112,f306(f76(a1),x41462)))),f202(f306(a112,f306(f76(a1),x41461)),f306(a112,f306(f76(a1),x41462))))),f204(x41461,x41462)) % 187.68/187.63 [4190]E(f306(f306(f247(f871(a106,a106),a106,f871(a106,a106),f871(x41901,f871(a106,a106))),f251(f306(a3,f306(f186(f866(x41901)),x41902)))),f306(f306(f8(x41901,f872(f871(a106,a106),f871(x41901,f871(a106,a106))),a106),f236(x41901,f871(a106,a106))),f306(f306(f8(a865,x41901,a106),f306(f157(x41901),x41902)),a19))),f257(x41901,x41902)) % 187.68/187.63 [4273]E(f306(f134(a865,f866(x42731),f306(f7(f866(x42731),a865,a865),f306(f306(f8(a865,f872(a865,a865),f866(x42731)),f219(a865)),f186(f866(x42731)))),f2(a865)),f306(f161(f866(x42731)),f171(x42731,x42732))),f306(f186(f866(f866(x42731))),f306(f128(f866(x42731),f306(f306(f8(a859,a859,f866(x42731)),a301),f306(f306(f7(f866(x42731),f866(x42731),a859),a303),f120(x42731)))),x42732))) % 187.68/187.63 [4279]E(f306(f306(f43(a865,f872(x42791,a859)),f231(f872(a865,a859))),f306(f306(f7(a865,f872(a865,f872(x42791,a859)),f872(x42791,a859)),f306(f306(f8(f872(a865,a859),f872(f872(a865,f872(x42791,a859)),f872(x42791,a859)),a865),f43(a865,f872(x42791,a859))),f276(a865,f2(a865)))),x42792)),f306(f306(f43(a865,f872(x42791,a859)),f231(f872(a865,a859))),x42792)) % 187.68/187.63 [4298]P1(f306(f63(a865),f306(f228(a865),f306(f306(f18(a865,a859,a859),f306(f306(f8(a859,f872(a859,a859),a865),a304),x42981)),f306(f306(f7(a865,a865,a859),f221(a865)),x42982))))) % 187.68/187.63 [4409]E(f306(f228(f871(f866(x44091),f866(x44091))),f306(f245(f866(x44091),f866(x44091),a859),f306(f306(f18(f866(x44091),f872(f866(x44091),a859),f872(f866(x44091),a859)),f306(f306(f8(f872(f866(x44091),f872(a859,a859)),f872(f872(f866(x44091),a859),f872(f866(x44091),a859)),f866(x44091)),f18(f866(x44091),a859,a859)),f306(f306(f8(f872(f866(x44091),a859),f872(f866(x44091),f872(a859,a859)),f866(x44091)),f306(f8(a859,f872(a859,a859),f866(x44091)),a305)),f306(f306(f7(f866(x44091),f872(f866(x44091),a865),f872(f866(x44091),a859)),f306(f306(f8(f872(a865,a859),f872(f872(f866(x44091),a865),f872(f866(x44091),a859)),f866(x44091)),f8(a865,a859,f866(x44091))),f306(f306(f8(a865,f872(a865,a859),f866(x44091)),f221(a865)),f186(f866(x44091))))),f186(f866(x44091)))))),f306(f306(f18(f866(x44091),f872(f866(x44091),a859),f872(f866(x44091),a859)),f306(f306(f8(f872(f866(x44091),f872(a859,a859)),f872(f872(f866(x44091),a859),f872(f866(x44091),a859)),f866(x44091)),f18(f866(x44091),a859,a859)),f306(f306(f8(f872(f866(x44091),a859),f872(f866(x44091),f872(a859,a859)),f866(x44091)),f306(f8(a859,f872(a859,a859),f866(x44091)),a304)),f306(f306(f7(f866(x44091),f872(f866(x44091),a865),f872(f866(x44091),a859)),f306(f306(f8(f872(a865,a859),f872(f872(f866(x44091),a865),f872(f866(x44091),a859)),f866(x44091)),f8(a865,a859,f866(x44091))),f306(f306(f8(a865,f872(a865,a859),f866(x44091)),a303),f186(f866(x44091))))),f186(f866(x44091)))))),f306(f306(f7(f866(x44091),f872(f871(f866(x44091),f866(x44091)),a859),f872(f866(x44091),a859)),f306(f306(f8(f872(f866(x44091),f872(f872(f871(f866(x44091),f866(x44091)),a859),a859)),f872(f872(f871(f866(x44091),f866(x44091)),a859),f872(f866(x44091),a859)),f866(x44091)),f7(f866(x44091),f872(f871(f866(x44091),f866(x44091)),a859),a859)),f306(f306(f8(f872(f866(x44091),f871(f866(x44091),f866(x44091))),f872(f866(x44091),f872(f872(f871(f866(x44091),f866(x44091)),a859),a859)),f866(x44091)),f306(f8(f871(f866(x44091),f866(x44091)),f872(f872(f871(f866(x44091),f866(x44091)),a859),a859),f866(x44091)),f308(f871(f866(x44091),f866(x44091))))),f236(f866(x44091),f866(x44091))))),f137(x44091,x44092)))))),f138(x44091,x44092)) % 187.68/187.63 [4523]~P1(f306(f306(f92(a1),f306(f306(f81(a1),x45231),x45231)),f306(f306(f22(a1),f306(f306(f81(a1),x45232),x45232)),a104))) % 187.68/187.63 [4084]E(f306(f306(f81(a1),f306(f306(f81(a1),f306(f306(f82(a1),x40841),x40842)),f306(f306(f82(a1),x40841),x40842))),x40842),f306(f306(f82(a1),f306(f306(f22(a1),f306(f306(f81(a1),x40841),x40841)),a104)),x40842)) % 187.68/187.63 [4188]E(f306(a112,f306(a90,f306(f260(f871(a865,a865),f871(a865,a865),a116),f306(f306(f284(f871(a865,a865)),f306(f306(f236(a865,a865),x41881),x41882)),f185(f872(f871(a865,a865),a859)))))),f306(f306(f22(a865),x41881),x41882)) % 187.68/187.63 [4193]E(f306(f306(f263(x41931,x41931,x41931),f306(f306(f108(f872(f871(x41931,x41931),a859)),x41932),f282(x41931,f185(f872(f871(x41931,x41931),a859))))),f282(x41931,f306(f306(f108(f872(f871(x41931,x41931),a859)),x41932),f282(x41931,f185(f872(f871(x41931,x41931),a859)))))),f282(x41931,x41932)) % 187.68/187.63 [4231]E(f252(x42311,f306(f128(f871(a106,x42311),f306(f245(a106,x42311,a859),f306(f306(f8(a859,f872(x42311,a859),a106),f16(a859,x42311)),f306(f221(a106),f2(a106))))),x42312)),f252(x42311,x42312)) % 187.68/187.63 [4232]E(f250(x42321,f306(f128(f871(a106,x42321),f306(f245(a106,x42321,a859),f306(f306(f8(a859,f872(x42321,a859),a106),f16(a859,x42321)),f306(f221(a106),f2(a106))))),x42322)),f250(x42321,x42322)) % 187.68/187.63 [4234]E(f306(f80(a1),f306(a90,f306(f260(f871(a865,a865),f871(a865,a865),a116),f306(f306(f284(f871(a865,a865)),f306(f306(f236(a865,a865),x42341),x42342)),f185(f872(f871(a865,a865),a859)))))),f306(a90,f306(f260(f871(a865,a865),f871(a865,a865),a116),f306(f306(f284(f871(a865,a865)),f306(f306(f236(a865,a865),x42342),x42341)),f185(f872(f871(a865,a865),a859)))))) % 187.68/187.63 [4290]E(f306(f306(f262(f866(a865),x42901),f137(a865,a227)),f306(f306(f7(x42901,f866(f872(x42901,a865)),f866(a865)),f306(f306(f8(f872(f872(x42901,a865),a865),f872(f866(f872(x42901,a865)),f866(a865)),x42901),f146(f872(x42901,a865),a865)),f306(f7(f872(x42901,a865),x42901,a865),f5(f872(x42901,a865))))),x42902)),f145(x42901,x42902)) % 187.68/187.63 [4311]E(f306(f306(f87(a1,a865),f306(f111(a1),f306(f306(f81(a1),x43111),a104))),f306(f306(f18(a1,a865,a865),f306(f306(f7(a1,a865,f872(a865,a865)),f306(f306(f8(a859,f872(a865,f872(a865,a865)),a1),f101(a865)),a190)),f2(a865))),f306(f306(f8(a865,a865,a1),a119),f306(f306(f8(a865,a865,a1),f306(f225(a865),x43112)),a112)))),f306(f306(f225(a865),f306(a119,x43112)),f306(f111(a865),x43111))) % 187.68/187.63 [4312]E(f306(f306(f87(a1,a865),f306(f111(a1),f306(f306(f81(a1),x43121),a104))),f306(f306(f18(a1,a865,a865),f306(f306(f7(a1,a865,f872(a865,a865)),f306(f306(f8(a859,f872(a865,f872(a865,a865)),a1),f101(a865)),a190)),f306(a119,x43122))),f306(f306(f8(a865,a865,a1),a119),f306(f306(f8(a865,a865,a1),f306(f219(a865),x43122)),a112)))),f306(f306(f219(a865),f306(a119,x43122)),f306(f111(a865),x43121))) % 187.68/187.63 [4332]E(f306(f134(f866(x43321),f866(x43321),f122(x43321),f120(x43321)),f306(f306(f146(f866(x43321),f866(x43321)),f148(f866(x43321),x43321,f120(x43321),f306(f306(f8(f866(x43321),f872(f866(x43321),f866(x43321)),x43321),f16(f866(x43321),f866(x43321))),f306(f306(f7(x43321,f866(x43321),f866(x43321)),f143(x43321)),f120(x43321))))),x43322)),f306(f306(f146(f866(x43321),x43321),f133(x43321)),f306(f128(f866(x43321),f306(f306(f8(a859,a859,f866(x43321)),a301),f306(f306(f7(f866(x43321),f866(x43321),a859),a303),f120(x43321)))),x43322))) % 187.68/187.63 [4391]E(f306(f245(a1,a1,a859),f306(f306(f7(a1,f872(a1,a859),f872(a1,a859)),f306(f306(f8(f872(a1,f872(a859,a859)),f872(f872(a1,a859),f872(a1,a859)),a1),f18(a1,a859,a859)),f306(f306(f8(f872(a1,a859),f872(a1,f872(a859,a859)),a1),f306(f8(a859,f872(a859,a859),a1),a304)),f306(f306(f8(f872(a1,a1),f872(a1,a859),a1),f306(f8(a1,a859,a1),f306(a303,x43911))),f306(f306(f8(a1,f872(a1,a1),a1),f81(a1)),f306(f82(a1),x43912)))))),f306(f306(f18(a1,a859,a859),f306(f306(f8(a859,f872(a859,a859),a1),a304),f306(f306(f8(a859,a859,a1),f306(a309,f306(f306(f221(a1),f2(a1)),x43912))),f306(f306(f18(a1,a859,a859),f306(f306(f8(a859,f872(a859,a859),a1),a304),f306(f220(a1),f2(a1)))),f306(f306(f7(a1,a1,a859),f221(a1)),x43912))))),f306(f306(f8(a859,a859,a1),f306(a309,f306(a301,f306(f306(f221(a1),f2(a1)),x43912)))),f306(f306(f18(a1,a859,a859),f306(f306(f8(a859,f872(a859,a859),a1),a304),f306(f221(a1),x43912))),f306(f306(f7(a1,a1,a859),f220(a1)),f2(a1))))))),f50(x43911,x43912)) % 187.68/187.63 [4393]E(f306(f228(x43931),f306(f306(f8(f872(a865,a859),a859,x43931),f88(a865)),f306(f306(f7(x43931,f872(a865,a859),f872(a865,a859)),f306(f306(f8(f872(a865,f872(a859,a859)),f872(f872(a865,a859),f872(a865,a859)),x43931),f18(a865,a859,a859)),f306(f306(f8(f872(a865,a859),f872(a865,f872(a859,a859)),x43931),f306(f8(a859,f872(a859,a859),a865),a304)),f306(f306(f7(x43931,f872(a865,x43931),f872(a865,a859)),f306(f306(f8(f872(x43931,a859),f872(f872(a865,x43931),f872(a865,a859)),x43931),f8(x43931,a859,a865)),a303)),f306(f157(x43931),x43932))))),f306(f306(f7(a865,a865,a859),f221(a865)),f306(f186(f866(x43931)),x43932))))),f306(f164(x43931),x43932)) % 187.68/187.63 [4203]E(f306(f306(f22(a1),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),x42031),a104)),x42032)),f306(f306(f22(a1),f306(f306(f81(a1),x42031),a104)),x42032))),a104),f306(f306(f22(a1),f306(f306(f81(a1),x42031),x42031)),f306(f306(f22(a1),f306(f306(f81(a1),x42032),x42032)),a104))) % 187.68/187.63 [4327]E(f306(f134(f866(f866(x43271)),f866(f866(x43271)),f122(f866(x43271)),f120(f866(x43271))),f306(f306(f146(f866(x43271),f866(f866(x43271))),f148(f866(f866(x43271)),x43271,f120(f866(x43271)),f306(f16(f872(f866(x43271),f866(f866(x43271))),x43271),f306(f306(f7(f866(x43271),f866(f866(x43271)),f866(f866(x43271))),f143(f866(x43271))),f120(f866(x43271)))))),x43272)),f306(f306(f146(f866(x43271),f866(x43271)),f163(x43271)),f306(f128(f866(x43271),f306(f306(f8(a859,a859,f866(x43271)),a301),f306(f306(f7(f866(x43271),f866(x43271),a859),a303),f120(x43271)))),x43272))) % 187.68/187.63 [4338]E(f306(f306(f87(a1,a865),f306(f111(a1),f306(f306(f81(a1),x43381),a104))),f306(f306(f18(a1,a865,a865),f306(f306(f7(a1,a865,f872(a865,a865)),f306(f306(f8(a859,f872(a865,f872(a865,a865)),a1),f101(a865)),a190)),f2(a865))),f306(f306(f8(a865,a865,a1),a119),f306(f306(f7(a1,a865,a865),f306(f306(f8(a865,f872(a865,a865),a1),f225(a865)),a112)),x43382)))),f306(f306(f225(a865),f306(f111(a865),x43381)),f306(a119,x43382))) % 187.68/187.63 [4339]E(f306(f306(f87(a1,a865),f306(f111(a1),f306(f306(f81(a1),x43391),a104))),f306(f306(f18(a1,a865,a865),f306(f306(f7(a1,a865,f872(a865,a865)),f306(f306(f8(a859,f872(a865,f872(a865,a865)),a1),f101(a865)),a190)),f306(a119,x43392))),f306(f306(f8(a865,a865,a1),a119),f306(f306(f7(a1,a865,a865),f306(f306(f8(a865,f872(a865,a865),a1),f219(a865)),a112)),x43392)))),f306(f306(f219(a865),f306(f111(a865),x43391)),f306(a119,x43392))) % 187.68/187.63 [4326]E(f306(f245(x43261,x43261,a859),f306(f306(f18(x43261,a859,f872(x43261,a859)),f306(f306(f8(f872(x43261,f872(a859,a859)),f872(a859,f872(x43261,a859)),x43261),f7(x43261,a859,a859)),f306(f306(f8(f872(x43261,a859),f872(x43261,f872(a859,a859)),x43261),f306(f8(a859,f872(a859,a859),x43261),a304)),a303))),x43262)),f233(x43261,x43262)) % 187.68/187.63 [4371]E(f306(f306(f40(a865),x43711),f306(f306(f81(a865),f306(f111(a865),f306(f306(f22(a1),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104))),a104))),x43712)),f306(f306(f40(a865),x43711),f306(a119,f306(a119,f306(a119,x43712))))) % 187.68/187.63 [4372]E(f46(a865,x43721,f306(f306(f81(a865),f306(f111(a865),f306(f306(f22(a1),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104))),a104))),x43722)),f46(a865,x43721,f306(a119,f306(a119,f306(a119,x43722))))) % 187.68/187.63 [4373]E(f46(a865,f306(f306(f81(a865),f306(f111(a865),f306(f306(f22(a1),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104))),a104))),x43731),x43732),f46(a865,f306(a119,f306(a119,f306(a119,x43731))),x43732)) % 187.68/187.63 [4384]E(f124(f306(x43841,f306(f306(f82(a106),f306(f111(a106),f306(f306(f22(a1),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104))),a104))),x43842))),f306(f196(x43841),x43842)) % 187.68/187.63 [4385]E(f306(f306(f40(a865),f306(f306(f81(a865),f306(f111(a865),f306(f306(f22(a1),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104))),a104))),x43851)),x43852),f306(f306(f40(a865),f306(a119,f306(a119,f306(a119,x43851)))),x43852)) % 187.68/187.63 [4433]~E(f34(x44331,x44332),f306(a26,x44333)) % 187.68/187.63 [4434]~E(f33(x44341,x44342),f306(a26,x44343)) % 187.68/187.63 [4435]~E(f306(a26,x44351),f34(x44352,x44353)) % 187.68/187.63 [4436]~E(f306(a26,x44361),f33(x44362,x44363)) % 187.68/187.63 [4450]~E(f29(x44501,x44502,x44503),a24) % 187.68/187.63 [4451]~E(f31(x44511,x44512,x44513),a24) % 187.68/187.63 [4452]~E(f30(x44521,x44522,x44523),a24) % 187.68/187.63 [3280]E(f306(f306(f189(x32801,x32802),x32803),f188(x32801)),f188(x32802)) % 187.68/187.63 [3281]E(f306(f306(f146(x32811,x32812),x32813),f120(x32811)),f120(x32812)) % 187.68/187.63 [3301]E(f32(f29(x33011,x33012,x33013)),f2(a865)) % 187.68/187.63 [3322]E(f306(f181(x33221,x33222,x33223),f2(a865)),x33222) % 187.68/187.63 [3323]E(f306(f186(a860),f29(x33231,x33232,x33233)),f2(a865)) % 187.68/187.63 [3325]E(f306(f306(f173(x33251,x33252),x33253),f120(x33252)),f120(f871(x33251,x33252))) % 187.68/187.63 [3359]E(f86(x33591,f64(x33591,x33592,x33593)),f306(f65(x33591,x33592),x33593)) % 187.68/187.63 [3410]E(f132(x34101,x34102,f144(x34101,x34103)),f144(x34101,f132(x34101,x34102,x34103))) % 187.68/187.63 [3429]E(f306(f235(f866(x34291),f866(x34291)),f159(x34291,x34292,x34293)),f306(f128(x34291,x34292),x34293)) % 187.68/187.63 [3505]E(f182(x35051,x35052,x35053,f2(a865)),x35052) % 187.68/187.63 [3506]E(f17(x35061,x35062,x35063,f2(a106)),x35062) % 187.68/187.63 [3513]E(f155(x35131,x35132,x35133,f120(x35131)),f120(x35132)) % 187.68/187.63 [3514]E(f156(x35141,x35142,x35143,f120(x35141)),f120(x35142)) % 187.68/187.63 [3519]E(f306(f306(f157(x35191),f306(f306(f143(x35191),x35192),x35193)),f2(a865)),x35192) % 187.68/187.63 [3547]E(f61(x35471,x35472,f120(x35471),x35473),f120(f871(x35471,x35472))) % 187.68/187.63 [3568]P28(x35681,x35682,x35683,f185(f872(x35681,a859))) % 187.68/187.63 [3722]E(f306(f74(x37221,x37222,x37221,x37223),f35(x37221)),x37223) % 187.68/187.63 [3897]P1(f306(f306(f308(f871(x38971,x38971)),f306(f306(f236(x38971,x38971),x38972),x38972)),f282(x38971,x38973))) % 187.68/187.63 [4524]~P1(f306(f306(f308(f871(f866(x45241),f866(x45241))),f306(f306(f236(f866(x45241),f866(x45241)),x45242),f120(x45241))),f137(x45241,x45243))) % 187.68/187.63 [4525]~P1(f306(f306(f308(f871(f866(x45251),f866(x45251))),f306(f306(f236(f866(x45251),f866(x45251)),x45252),f120(x45251))),f139(x45251,x45253))) % 187.68/187.63 [4526]~P1(f306(f306(f308(f871(f866(x45261),f866(x45261))),f306(f306(f236(f866(x45261),f866(x45261)),x45262),f120(x45261))),f149(x45261,x45263))) % 187.68/187.63 [4528]~P1(f306(f306(f308(f871(f866(x45281),f866(x45281))),f306(f306(f236(f866(x45281),f866(x45281)),f120(x45281)),x45282)),f137(x45281,x45283))) % 187.68/187.63 [4529]~P1(f306(f306(f308(f871(f866(x45291),f866(x45291))),f306(f306(f236(f866(x45291),f866(x45291)),f120(x45291)),x45292)),f149(x45291,x45293))) % 187.68/187.63 [3254]E(f306(f306(f191(x32541),x32542),x32543),f192(x32541,f201(x32542,x32543))) % 187.68/187.63 [3311]E(f306(f261(x33111,x33112),f306(f261(x33112,x33111),x33113)),x33113) % 187.68/187.63 [3335]E(f306(f306(f173(x33351,x33352),f120(x33351)),x33353),f120(f871(x33351,x33352))) % 187.68/187.63 [3338]E(f166(x33381,x33382,f306(f229(a865),x33383)),f306(f306(f165(x33381),x33383),x33382)) % 187.68/187.63 [3356]E(f144(x33561,f306(f128(x33561,x33562),x33563)),f306(f128(x33561,x33562),f144(x33561,x33563))) % 187.68/187.63 [3357]E(f306(f232(x33571,x33572),f306(f261(x33572,x33571),x33573)),f306(f234(x33572,x33571),x33573)) % 187.68/187.63 [3358]E(f306(f234(x33581,x33582),f306(f261(x33582,x33581),x33583)),f306(f232(x33582,x33581),x33583)) % 187.68/187.63 [3374]E(f306(f128(x33741,x33742),f306(f161(x33741),x33743)),f306(f161(x33741),f306(f128(x33741,x33742),x33743))) % 187.68/187.63 [3387]E(f306(f306(f130(x33871),x33872),f306(f163(x33871),x33873)),f306(f306(f130(x33871),f306(a119,x33872)),x33873)) % 187.68/187.63 [3405]E(f32(f30(x34051,x34052,x34053)),f306(f306(f81(a865),f32(x34053)),f306(a119,f2(a865)))) % 187.68/187.63 [3406]E(f306(f285(x34061,x34062,x34063),f185(f872(x34061,a859))),f185(f872(x34062,a859))) % 187.68/187.63 [3407]E(f306(f260(x34071,x34072,x34073),f185(f872(x34071,a859))),f185(f872(x34072,a859))) % 187.68/187.63 [3408]E(f306(f286(x34081,x34082,x34083),f185(f872(x34082,a859))),f185(f872(x34081,a859))) % 187.68/187.63 [3409]E(f306(f286(x34091,x34092,x34093),f231(f872(x34092,a859))),f231(f872(x34091,a859))) % 187.68/187.63 [3437]E(f306(f306(f284(x34371),x34372),f306(f164(x34371),x34373)),f306(f164(x34371),f132(x34371,x34372,x34373))) % 187.68/187.63 [3449]E(f215(x34491,x34492,f306(f214(x34491),x34493)),f306(f306(f81(a865),f306(x34492,x34493)),f306(a119,f2(a865)))) % 187.68/187.63 [3523]E(f306(f186(a860),f30(x35231,x35232,x35233)),f306(f306(f81(a865),f306(f186(a860),x35233)),f306(a119,f2(a865)))) % 187.68/187.63 [3524]E(f306(f285(f871(x35241,x35242),x35242,f244(x35241,x35242)),x35243),f306(f232(x35241,x35242),x35243)) % 187.68/187.63 [3525]E(f306(f285(f871(x35251,x35252),x35251,f235(x35251,x35252)),x35253),f306(f234(x35251,x35252),x35253)) % 187.68/187.63 [3593]E(f306(f306(f236(x35931,x35932),f306(f235(x35931,x35932),x35933)),f306(f244(x35931,x35932),x35933)),x35933) % 187.68/187.63 [3602]E(f306(f306(f245(x36021,x36022,x36021),f16(x36021,x36022)),x36023),f306(f235(x36021,x36022),x36023)) % 187.68/187.63 [3622]E(f176(x36221,x36222,x36223,f306(f16(f869(x36222),x36221),f188(x36222))),x36223) % 187.68/187.63 [3623]E(f176(x36231,x36232,f306(f16(f869(x36232),x36231),f188(x36232)),x36233),x36233) % 187.68/187.63 [3678]E(f32(f31(x36781,x36782,x36783)),f306(f306(f81(a865),f306(f306(f81(a865),f32(x36782)),f32(x36783))),f306(a119,f2(a865)))) % 187.68/187.63 [3726]E(f306(f74(x37261,x37261,x37262,f35(x37261)),x37263),x37263) % 187.68/187.63 [3833]E(f306(f186(a860),f31(x38331,x38332,x38333)),f306(f306(f81(a865),f306(f306(f81(a865),f306(f186(a860),x38332)),f306(f186(a860),x38333))),f306(a119,f2(a865)))) % 187.68/187.63 [3907]P1(f306(f306(f220(f872(x39071,a859)),f306(f164(x39071),f306(f128(x39071,x39072),x39073))),f306(f164(x39071),x39073))) % 187.68/187.63 [3951]P1(f306(f306(f220(f872(x39511,a859)),f306(f164(x39511),f306(f306(f165(x39511),x39512),x39513))),f306(f164(x39511),x39513))) % 187.68/187.63 [3952]P1(f306(f306(f220(f872(x39521,a859)),f306(f164(x39521),f306(f306(f130(x39521),x39522),x39523))),f306(f164(x39521),x39523))) % 187.68/187.63 [3956]P1(f306(f306(f220(f872(x39561,a859)),f306(f164(x39561),f162(x39561,x39562,x39563))),f306(f164(x39561),x39563))) % 187.68/187.63 [3957]P1(f306(f306(f220(f872(x39571,a859)),f306(f164(x39571),f166(x39571,x39572,x39573))),f306(f164(x39571),x39572))) % 187.68/187.63 [3977]P28(f871(x39771,x39772),f871(x39772,x39771),f306(f245(x39771,x39772,f871(x39772,x39771)),f306(f7(x39772,x39771,f871(x39772,x39771)),f236(x39772,x39771))),x39773) % 187.68/187.63 [3989]E(f306(f306(f306(f180(f866(x39891),f866(x39891)),f46(a865,x39892,f306(f186(f866(x39891)),x39893))),f160(x39891)),x39893),f306(f306(f306(f180(f866(x39891),f866(x39891)),x39892),f160(x39891)),x39893)) % 187.68/187.63 [4031]P1(f306(f306(f308(f871(f866(x40311),f866(x40311))),f306(f306(f236(f866(x40311),f866(x40311)),x40312),x40312)),f150(x40311,f282(x40311,x40313)))) % 187.68/187.63 [4172]E(f86(f871(x41721,x41722),f306(f306(f18(f871(x41721,x41722),x41722,a859),f306(f306(f8(x41721,f872(x41722,a859),f871(x41721,x41722)),x41723),f235(x41721,x41722))),f244(x41721,x41722))),f86(f871(x41721,x41722),f306(f245(x41721,x41722,a859),x41723))) % 187.68/187.63 [4173]E(f91(f871(x41731,x41732),f306(f306(f18(f871(x41731,x41732),x41732,a859),f306(f306(f8(x41731,f872(x41732,a859),f871(x41731,x41732)),x41733),f235(x41731,x41732))),f244(x41731,x41732))),f91(f871(x41731,x41732),f306(f245(x41731,x41732,a859),x41733))) % 187.68/187.63 [4210]E(f306(f306(f262(f871(a865,x42101),x42101),f299(a865,x42101,a227,x42102)),f306(f306(f18(x42101,x42101,f871(a865,x42101)),f306(f306(f8(a865,f872(x42101,f871(a865,x42101)),x42101),f236(a865,x42101)),x42103)),f5(x42101))),f300(x42101,x42103,x42102)) % 187.68/187.63 [4275]E(f306(f246(x42751,x42751,x42752,x42752,f5(x42751),f5(x42752)),x42753),x42753) % 187.68/187.63 [4349]E(f306(f134(f866(f866(x43491)),f866(f866(x43491)),f122(f866(x43491)),f120(f866(x43491))),f306(f306(f146(f866(x43491),f866(f866(x43491))),f306(f306(f7(f866(x43491),f866(x43491),f866(f866(x43491))),f306(f306(f8(f872(x43491,f866(x43491)),f872(f866(x43491),f866(f866(x43491))),f866(x43491)),f146(x43491,f866(x43491))),f306(f7(x43491,f866(x43491),f866(x43491)),f143(x43491)))),x43492)),f56(x43491,x43493,x43492))),f56(x43491,f306(a119,x43493),x43492)) % 187.68/187.63 [4408]E(f306(f306(f87(a1,x44081),f204(f306(f306(f74(f871(a1,a1),a1,x44081,f244(a1,a1)),f198(x44081)),x44082),f306(f306(f74(f871(a1,a1),a1,x44081,f244(a1,a1)),f198(x44081)),x44083))),f306(f306(f18(a1,a1,x44081),f306(f306(f8(a1,f872(a1,x44081),a1),f191(x44081)),f306(f306(f18(a1,a1,a1),f306(f306(f8(a1,f872(a1,a1),a1),f81(a1)),f306(f306(f8(a1,a1,a1),f306(f82(a1),f306(f306(f74(f871(a1,a1),a1,x44081,f235(a1,a1)),f198(x44081)),x44082))),f306(f306(f7(a1,a1,a1),f40(a1)),f306(f306(f74(f871(a1,a1),a1,x44081,f244(a1,a1)),f198(x44081)),x44082))))),f306(f306(f8(a1,a1,a1),f306(f82(a1),f306(f306(f74(f871(a1,a1),a1,x44081,f235(a1,a1)),f198(x44081)),x44083))),f306(f306(f7(a1,a1,a1),f40(a1)),f306(f306(f74(f871(a1,a1),a1,x44081,f244(a1,a1)),f198(x44081)),x44083)))))),f5(a1))),f209(x44081,x44082,x44083)) % 187.68/187.63 [4445]~E(f306(f306(f143(x44451),x44452),x44453),x44453) % 187.68/187.63 [4454]~E(f306(f306(f143(x44541),x44542),x44543),f120(x44541)) % 187.68/187.63 [4476]~E(f306(f306(f284(x44761),x44762),x44763),f185(f872(x44761,a859))) % 187.68/187.63 [4503]~E(f306(f285(x45031,f872(x45031,a859),x45032),x45033),f306(f283(x45031),x45033)) % 187.68/187.63 [3316]E(f306(f306(f151(x33161,f120(x33161)),x33162),x33163),f120(x33161)) % 187.68/187.63 [3317]E(f306(f133(x33171),f306(f306(f143(x33171),x33172),x33173)),x33172) % 187.68/187.63 [3318]E(f306(f163(x33181),f306(f306(f143(x33181),x33182),x33183)),x33183) % 187.68/187.63 [3362]E(f306(f306(f130(x33621),f79(a865)),f306(f306(f143(x33621),x33622),x33623)),x33623) % 187.68/187.63 [3394]E(f121(x33941,f306(f306(f130(x33941),x33942),x33943)),f306(f306(f130(x33941),x33942),f121(x33941,x33943))) % 187.68/187.63 [3396]E(f306(f306(f151(x33961,x33962),x33963),f306(f306(f157(x33961),x33962),x33963)),x33962) % 187.68/187.63 [3420]E(f306(f306(f284(x34201),x34202),f306(f306(f284(x34201),x34202),x34203)),f306(f306(f284(x34201),x34202),x34203)) % 187.68/187.63 [3431]E(f306(f306(f169(x34311,x34312),f120(f871(x34311,x34312))),x34313),f188(x34312)) % 187.68/187.63 [3434]E(f306(f306(f284(x34341),x34342),f306(f164(x34341),x34343)),f306(f164(x34341),f306(f306(f143(x34341),x34342),x34343))) % 187.68/187.63 [3436]E(f306(f306(f130(x34361),x34362),f306(f163(x34361),x34363)),f306(f163(x34361),f306(f306(f130(x34361),x34362),x34363))) % 187.68/187.63 [3446]E(f306(f306(f165(x34461),f79(a865)),f306(f306(f143(x34461),x34462),x34463)),f306(f306(f143(x34461),x34462),f120(x34461))) % 187.68/187.63 [3490]E(f306(f65(x34901,x34902),f306(f306(f284(x34901),x34903),f185(f872(x34901,a859)))),x34903) % 187.68/187.63 [3531]E(f306(f306(f81(a865),x35311),f306(f306(f81(a865),x35312),x35313)),f306(f306(f81(a865),x35312),f306(f306(f81(a865),x35311),x35313))) % 187.68/187.63 [3532]E(f306(f306(f81(a1),x35321),f306(f306(f81(a1),x35322),x35323)),f306(f306(f81(a1),x35322),f306(f306(f81(a1),x35321),x35323))) % 187.68/187.63 [3537]E(f306(f306(f243(x35371,x35372),f185(f872(x35371,a859))),x35373),f185(f872(f871(x35371,x35372),a859))) % 187.68/187.63 [3560]E(f306(f306(f108(f872(x35601,a859)),x35602),x35603),f306(f306(f108(f872(x35601,a859)),x35603),x35602)) % 187.68/187.63 [3561]E(f306(f306(f109(f872(x35611,a859)),x35612),x35613),f306(f306(f109(f872(x35611,a859)),x35613),x35612)) % 187.68/187.63 [3563]E(f306(f306(f122(x35631),x35632),f306(f306(f143(x35631),x35633),f120(x35631))),f306(f160(x35631),f306(f306(f143(x35631),x35633),x35632))) % 187.68/187.63 [3564]E(f306(f306(f122(x35641),f306(f161(x35641),x35642)),f306(f161(x35641),x35643)),f306(f161(x35641),f306(f306(f122(x35641),x35643),x35642))) % 187.68/187.63 [3572]E(f306(f163(x35721),f306(f306(f165(x35721),f306(a119,x35722)),x35723)),f306(f306(f165(x35721),x35722),f306(f163(x35721),x35723))) % 187.68/187.63 [3579]P1(f306(f306(f308(x35791),x35792),f306(f306(f284(x35791),x35792),x35793))) % 187.68/187.63 [3583]E(f306(f306(f44(x35831,f872(x35832,a859)),f185(f872(x35831,a859))),x35833),f231(f872(x35832,a859))) % 187.68/187.63 [3586]E(f306(f260(x35861,x35861,f233(x35861,x35862)),x35863),f306(f306(f109(f872(x35861,a859)),x35862),x35863)) % 187.68/187.63 [3599]E(f306(f186(f866(x35991)),f306(f306(f143(x35991),x35992),x35993)),f306(f306(f81(a865),f306(f186(f866(x35991)),x35993)),f306(a119,f2(a865)))) % 187.68/187.63 [3604]E(f136(x36041,f306(f306(f122(x36041),x36042),f306(f306(f143(x36041),x36043),f120(x36041)))),x36043) % 187.68/187.63 [3605]E(f121(x36051,f306(f306(f122(x36051),x36052),f306(f306(f143(x36051),x36053),f120(x36051)))),x36052) % 187.68/187.63 [3611]E(f306(f306(f122(x36111),f306(f306(f165(x36111),x36112),x36113)),f306(f306(f130(x36111),x36112),x36113)),x36113) % 187.68/187.63 [3620]E(f306(f306(f22(a865),f306(f306(f81(a865),x36201),x36202)),f306(f306(f81(a865),x36203),x36202)),f306(f306(f22(a865),x36201),x36203)) % 187.68/187.63 [3621]E(f306(f306(f22(a865),f306(f306(f81(a865),x36211),x36212)),f306(f306(f81(a865),x36211),x36213)),f306(f306(f22(a865),x36212),x36213)) % 187.68/187.63 [3628]E(f306(f306(f122(x36281),f306(f161(x36281),x36282)),f306(f306(f143(x36281),x36283),f120(x36281))),f306(f161(x36281),f306(f306(f143(x36281),x36283),x36282))) % 187.68/187.63 [3630]E(f306(f306(f81(a865),f306(f186(f866(x36301)),x36302)),f306(f186(f866(x36301)),x36303)),f306(f186(f866(x36301)),f306(f306(f122(x36301),x36302),x36303))) % 187.68/187.63 [3640]E(f306(f306(f108(f872(x36401,a859)),f306(f164(x36401),x36402)),f306(f164(x36401),x36403)),f306(f164(x36401),f306(f306(f122(x36401),x36402),x36403))) % 187.68/187.63 [3641]E(f46(a865,f306(f306(f82(a865),x36411),x36412),f306(f306(f82(a865),x36411),x36413)),f306(f306(f82(a865),x36411),f46(a865,x36412,x36413))) % 187.68/187.63 [3654]E(f306(f306(f165(x36541),f306(f306(f22(a865),x36542),f79(a865))),f306(f163(x36541),x36543)),f306(f163(x36541),f306(f306(f165(x36541),x36542),x36543))) % 187.68/187.63 [3659]E(f306(f306(f109(f872(x36591,a859)),x36592),f306(f80(f872(x36591,a859)),x36593)),f306(f306(f22(f872(x36591,a859)),x36592),x36593)) % 187.68/187.63 [3660]E(f306(f306(f22(f872(x36601,a859)),x36602),f306(f80(f872(x36601,a859)),x36603)),f306(f306(f109(f872(x36601,a859)),x36602),x36603)) % 187.68/187.63 [3682]E(f306(f306(f243(x36821,x36822),x36823),f306(f16(f872(x36822,a859),x36821),f185(f872(x36822,a859)))),f185(f872(f871(x36821,x36822),a859))) % 187.68/187.63 [3684]E(f306(f306(f22(a865),f306(f306(f82(a865),x36841),x36842)),f306(f306(f82(a865),x36841),x36843)),f306(f306(f82(a865),x36841),f306(f306(f22(a865),x36842),x36843))) % 187.68/187.63 [3685]E(f306(f306(f81(a865),f306(f306(f82(a865),x36851),x36852)),f306(f306(f82(a865),x36851),x36853)),f306(f306(f82(a865),x36851),f306(f306(f81(a865),x36852),x36853))) % 187.68/187.63 [3686]E(f306(f306(f22(a1),f306(f306(f82(a1),x36861),x36862)),f306(f306(f82(a1),x36861),x36863)),f306(f306(f82(a1),x36861),f306(f306(f22(a1),x36862),x36863))) % 187.68/187.63 [3687]E(f306(f306(f81(a1),f306(f306(f82(a1),x36871),x36872)),f306(f306(f82(a1),x36871),x36873)),f306(f306(f82(a1),x36871),f306(f306(f81(a1),x36872),x36873))) % 187.68/187.63 [3688]E(f306(f306(f82(a1),f306(f306(f237(a1),x36881),x36882)),f306(f306(f237(a1),x36881),x36883)),f306(f306(f237(a1),x36881),f306(f306(f81(a865),x36882),x36883))) % 187.68/187.63 [3701]E(f306(f306(f43(x37011,f872(x37012,a859)),x37013),f306(f16(f872(x37012,a859),x37011),f185(f872(x37012,a859)))),f185(f872(x37012,a859))) % 187.68/187.63 [3703]E(f46(a865,f306(f306(f82(a865),x37031),x37032),f306(f306(f82(a865),x37033),x37032)),f306(f306(f82(a865),f46(a865,x37031,x37033)),x37032)) % 187.68/187.63 [3707]E(f46(a1,f306(f306(f22(a1),x37071),f46(a1,x37072,x37073)),x37073),f46(a1,f306(f306(f22(a1),x37071),x37072),x37073)) % 187.68/187.63 [3708]E(f46(a1,f306(f306(f82(a1),x37081),f46(a1,x37082,x37083)),x37083),f46(a1,f306(f306(f82(a1),x37081),x37082),x37083)) % 187.68/187.63 [3709]P1(f306(f306(f220(f872(x37091,a859)),x37092),f306(f306(f284(x37091),x37093),x37092))) % 187.68/187.63 [3712]E(f306(f285(f871(x37121,x37122),x37121,f235(x37121,x37122)),f306(f164(f871(x37121,x37122)),x37123)),f175(x37121,x37122,f306(f169(x37121,x37122),x37123))) % 187.68/187.63 [3760]P1(f306(f63(x37601),f175(x37601,x37602,f306(f169(x37601,x37602),x37603)))) % 187.68/187.63 [3785]E(f306(f306(f44(f872(x37851,a859),f872(x37851,a859)),x37852),f306(f108(f872(x37851,a859)),x37853)),f306(f306(f108(f872(x37851,a859)),x37853),f42(f872(x37851,a859),x37852))) % 187.68/187.63 [3786]E(f306(f306(f43(f872(x37861,a859),f872(x37861,a859)),x37862),f306(f109(f872(x37861,a859)),x37863)),f306(f306(f109(f872(x37861,a859)),x37863),f41(f872(x37861,a859),x37862))) % 187.68/187.63 [3796]E(f306(f164(x37961),f306(f306(f306(f180(f866(x37961),f866(x37961)),x37962),f160(x37961)),x37963)),f306(f164(x37961),x37963)) % 187.68/187.63 [3800]E(f306(f306(f165(x38001),f306(f186(f866(x38001)),f168(x38001,x38002,x38003))),x38003),f168(x38001,x38002,x38003)) % 187.68/187.63 [3801]E(f175(x38011,x38012,f306(f306(f8(x38012,f869(x38012),x38011),f214(x38012)),x38013)),f231(f872(x38011,a859))) % 187.68/187.63 [3805]E(f306(f186(f866(x38051)),f306(f306(f306(f180(f866(x38051),f866(x38051)),x38052),f160(x38051)),x38053)),f306(f186(f866(x38051)),x38053)) % 187.68/187.63 [3808]E(f306(f306(f245(x38081,x38082,x38082),f306(f16(f872(x38082,x38082),x38081),f5(x38082))),x38083),f306(f244(x38081,x38082),x38083)) % 187.68/187.63 [3814]E(f46(a1,f306(f306(f22(a1),f46(a1,x38141,x38142)),x38143),x38142),f46(a1,f306(f306(f22(a1),x38141),x38143),x38142)) % 187.68/187.63 [3815]E(f46(a1,f306(f306(f237(a1),f46(a1,x38151,x38152)),x38153),x38152),f46(a1,f306(f306(f237(a1),x38151),x38153),x38152)) % 187.68/187.63 [3818]E(f306(f306(f43(f872(f871(x38181,x38182),a859),f872(x38182,a859)),x38183),f232(x38181,x38182)),f306(f232(x38181,x38182),f41(f872(f871(x38181,x38182),a859),x38183))) % 187.68/187.63 [3819]E(f306(f306(f43(f872(f871(x38191,x38192),a859),f872(x38191,a859)),x38193),f234(x38191,x38192)),f306(f234(x38191,x38192),f41(f872(f871(x38191,x38192),a859),x38193))) % 187.68/187.63 [3845]E(f306(f74(x38451,x38451,x38451,x38452),f306(f306(f180(x38451,x38451),x38453),x38452)),f306(f306(f180(x38451,x38451),f306(a119,x38453)),x38452)) % 187.68/187.63 [3855]E(f216(f869(x38551),x38552,f188(x38551),f306(f306(f8(x38551,f869(x38551),x38552),f214(x38551)),x38553)),f306(f189(x38552,x38551),x38553)) % 187.68/187.63 [3862]E(f306(f306(f130(x38621),f306(f306(f22(a865),f306(f186(f866(x38621)),x38622)),x38623)),f306(f161(x38621),x38622)),f306(f161(x38621),f306(f306(f165(x38621),x38623),x38622))) % 187.68/187.63 [3863]E(f306(f306(f165(x38631),f306(f306(f22(a865),f306(f186(f866(x38631)),x38632)),x38633)),f306(f161(x38631),x38632)),f306(f161(x38631),f306(f306(f130(x38631),x38633),x38632))) % 187.68/187.63 [3866]E(f306(f306(f81(a865),f306(f158(a865),f306(f306(f146(x38661,a865),x38662),x38663))),f306(f186(f866(x38661)),x38663)),f147(x38661,x38662,x38663)) % 187.68/187.63 [3883]E(f306(f160(x38831),f306(f306(f306(f180(f866(x38831),f866(x38831)),x38832),f160(x38831)),x38833)),f306(f306(f306(f180(f866(x38831),f866(x38831)),f306(a119,x38832)),f160(x38831)),x38833)) % 187.68/187.63 [3898]P1(f306(f306(f220(a865),f306(f186(f866(x38981)),f306(f128(x38981,x38982),x38983))),f306(f186(f866(x38981)),x38983))) % 187.68/187.63 [3915]E(f306(f306(f108(f872(f872(x39151,a859),a859)),f306(f283(x39151),x39152)),f306(f285(f872(x39151,a859),f872(x39151,a859),f306(f284(x39151),x39153)),f306(f283(x39151),x39152))),f306(f283(x39151),f306(f306(f284(x39151),x39153),x39152))) % 187.68/187.63 [3933]P27(x39331,x39332,f306(f306(f284(f864(x39331)),f306(f306(f306(f93(x39331),x39333),a24),x39333)),f185(f872(f864(x39331),a859)))) % 187.68/187.63 [3948]P1(f306(f306(f220(a865),f306(f186(f866(x39481)),f168(x39481,x39482,x39483))),f306(f186(f866(x39481)),x39483))) % 187.68/187.63 [3955]E(f306(f234(x39551,x39552),f306(f228(f871(x39551,x39552)),f306(f245(x39551,x39552,a859),x39553))),f306(f228(x39551),f306(f306(f8(f872(x39552,a859),a859,x39551),f88(x39552)),x39553))) % 187.68/187.63 [3965]E(f306(f285(a865,a865,f306(f306(f7(a865,a865,a865),f81(a865)),x39651)),f277(a865,x39652,x39653)),f277(a865,f306(f306(f81(a865),x39652),x39651),f306(f306(f81(a865),x39653),x39651))) % 187.68/187.63 [3967]P1(f306(f63(f869(x39671)),f306(f285(x39672,f869(x39671),f306(f169(x39672,x39671),x39673)),f231(f872(x39672,a859))))) % 187.68/187.63 [3980]E(f306(f285(a865,a865,f306(f306(f7(a865,a865,a865),f81(a865)),x39801)),f306(f276(a865,x39802),x39803)),f306(f276(a865,f306(f306(f81(a865),x39802),x39801)),f306(f306(f81(a865),x39803),x39801))) % 187.68/187.63 [3998]E(f306(f306(f173(x39981,x39982),f306(f306(f146(f871(x39981,x39982),x39981),f235(x39981,x39982)),x39983)),f306(f306(f146(f871(x39981,x39982),x39982),f244(x39981,x39982)),x39983)),x39983) % 187.68/187.63 [4003]E(f306(f306(f81(a865),f306(f306(f82(a865),x40031),f46(a865,f306(f306(f40(a865),x40032),x40031),x40033))),f46(a865,x40032,x40031)),f46(a865,x40032,f306(f306(f82(a865),x40031),x40033))) % 187.68/187.63 [4017]E(f306(f306(f122(x40171),x40172),f306(f134(f866(x40171),f866(x40171),f122(x40171),f120(x40171)),x40173)),f306(f134(f866(x40171),f866(x40171),f122(x40171),x40172),x40173)) % 187.68/187.63 [4035]P1(f306(f306(f308(f871(x40351,x40351)),f306(f306(f236(x40351,x40351),x40352),x40352)),f306(f306(f180(f871(x40351,x40351),a859),f2(a865)),x40353))) % 187.68/187.63 [4041]E(f306(f228(x40411),f306(f306(f8(f872(x40412,a859),a859,x40411),f88(x40412)),f306(f7(x40412,x40411,a859),x40413))),f306(f232(x40412,x40411),f306(f228(f871(x40412,x40411)),f306(f245(x40412,x40411,a859),x40413)))) % 187.68/187.63 [4059]E(f306(f306(f108(f872(x40591,a859)),f306(f306(f43(a865,f872(x40591,a859)),f277(a865,f79(a865),x40592)),x40593)),f306(x40593,f2(a865))),f306(f306(f43(a865,f872(x40591,a859)),f306(f275(a865),x40592)),x40593)) % 187.68/187.63 [4074]E(f306(f134(f866(x40741),f866(x40741),f122(x40741),f120(x40741)),f306(f306(f146(f866(x40741),f866(x40741)),f128(x40741,x40742)),x40743)),f306(f128(x40741,x40742),f306(f134(f866(x40741),f866(x40741),f122(x40741),f120(x40741)),x40743))) % 187.68/187.63 [4079]E(f306(f244(f866(x40791),f866(x40791)),f159(x40791,x40792,x40793)),f306(f128(x40791,f306(f74(a859,a859,x40791,a301),x40792)),x40793)) % 187.68/187.63 [4096]E(f306(f306(f44(x40961,f872(x40962,a859)),f231(f872(x40961,a859))),f306(f306(f8(f872(x40962,a859),f872(x40962,a859),x40961),f228(x40962)),f306(f7(x40962,x40961,a859),x40963))),f306(f228(x40962),f306(f306(f8(f872(x40961,a859),a859,x40962),f89(x40961)),x40963))) % 187.68/187.63 [4127]E(f306(f306(f81(a1),f306(f306(f81(a1),f306(f306(f82(a1),x41271),f306(f306(f40(a1),x41272),x41271))),f46(a1,x41272,x41271))),x41273),f306(f306(f81(a1),x41272),x41273)) % 187.68/187.63 [4162]E(f306(f306(f81(a1),f306(f306(f81(a1),f306(f306(f82(a1),f306(f306(f40(a1),x41621),x41622)),x41622)),f46(a1,x41621,x41622))),x41623),f306(f306(f81(a1),x41621),x41623)) % 187.68/187.63 [4191]E(f86(f871(x41911,x41912),f306(f245(x41911,x41912,a859),f306(f306(f8(f872(x41912,f871(x41911,x41912)),f872(x41912,a859),x41911),f306(f8(f871(x41911,x41912),a859,x41912),x41913)),f236(x41911,x41912)))),f86(f871(x41911,x41912),x41913)) % 187.68/187.63 [4192]E(f91(f871(x41921,x41922),f306(f245(x41921,x41922,a859),f306(f306(f8(f872(x41922,f871(x41921,x41922)),f872(x41922,a859),x41921),f306(f8(f871(x41921,x41922),a859,x41922),x41923)),f236(x41921,x41922)))),f91(f871(x41921,x41922),x41923)) % 187.68/187.63 [4220]P1(f306(f306(f220(f872(x42201,a859)),f41(f872(x42201,a859),f306(f306(f109(f872(f872(x42201,a859),a859)),x42202),x42203))),f306(f306(f109(f872(x42201,a859)),f41(f872(x42201,a859),x42202)),f41(f872(x42201,a859),x42203)))) % 187.68/187.63 [4221]E(f306(f161(x42211),f306(f306(f306(f180(f866(x42211),f866(x42211)),f306(f306(f22(a865),f306(f186(f866(x42211)),x42212)),f46(a865,x42213,f306(f186(f866(x42211)),x42212)))),f160(x42211)),x42212)),f306(f306(f306(f180(f866(x42211),f866(x42211)),x42213),f160(x42211)),f306(f161(x42211),x42212))) % 187.68/187.63 [4235]E(f306(f228(x42351),f306(f306(f8(a859,a859,x42351),a301),f306(f306(f7(x42351,f869(x42352),a859),f306(f306(f8(f869(x42352),f872(f869(x42352),a859),x42351),a303),x42353)),f188(x42352)))),f175(x42351,x42352,x42353)) % 187.68/187.63 [4260]P1(f306(f306(f220(a865),f306(f186(f866(x42601)),f306(f306(f130(x42601),f306(f186(f866(x42601)),f168(x42601,x42602,x42603))),x42603))),f306(f186(f866(x42601)),x42603))) % 187.68/187.63 [4300]E(f306(f228(x43001),f306(f306(f8(f872(x43002,a859),a859,x43001),f88(x43002)),f306(f306(f8(f869(x43001),f872(x43002,a859),x43001),f306(f7(x43002,f869(x43001),a859),f306(f306(f8(f869(x43001),f872(f869(x43001),a859),x43002),a303),x43003))),f214(x43001)))),f177(x43002,x43001,x43003)) % 187.68/187.63 [4516]~P1(f306(f64(x45161,x45162,f185(f872(x45161,a859))),x45163)) % 187.68/187.63 [4522]~P1(f306(f306(f308(f871(x45221,x45221)),f306(f306(f236(x45221,x45221),x45222),x45223)),f145(x45221,f120(f872(x45221,a865))))) % 187.68/187.63 [3573]E(f306(f186(f866(x35731)),f306(f306(f165(x35731),x35732),x35733)),f306(f306(f225(a865),f306(f186(f866(x35731)),x35733)),x35732)) % 187.68/187.63 [3574]E(f306(f186(f866(x35741)),f306(f306(f130(x35741),x35742),x35743)),f306(f306(f22(a865),f306(f186(f866(x35741)),x35743)),x35742)) % 187.68/187.63 [3598]E(f306(f186(f866(f866(x35981))),f56(x35981,x35982,x35983)),f306(f306(f237(a865),f306(f186(f866(x35981)),x35983)),x35982)) % 187.68/187.63 [3613]E(f306(f306(f40(a865),f306(f306(f40(a865),x36131),x36132)),x36133),f306(f306(f40(a865),x36131),f306(f306(f82(a865),x36132),x36133))) % 187.68/187.63 [3614]E(f306(f306(f22(a865),f306(f306(f22(a865),x36141),x36142)),x36143),f306(f306(f22(a865),x36141),f306(f306(f81(a865),x36142),x36143))) % 187.68/187.63 [3615]E(f306(f306(f81(a865),f306(f306(f81(a865),x36151),x36152)),x36153),f306(f306(f81(a865),x36151),f306(f306(f81(a865),x36152),x36153))) % 187.68/187.63 [3616]E(f306(f306(f81(a1),f306(f306(f81(a1),x36161),x36162)),x36163),f306(f306(f81(a1),x36161),f306(f306(f81(a1),x36162),x36163))) % 187.68/187.63 [3617]E(f306(f306(f82(a865),f306(f306(f82(a865),x36171),x36172)),x36173),f306(f306(f82(a865),x36171),f306(f306(f82(a865),x36172),x36173))) % 187.68/187.63 [3618]E(f306(f306(f82(a1),f306(f306(f82(a1),x36181),x36182)),x36183),f306(f306(f82(a1),x36181),f306(f306(f82(a1),x36182),x36183))) % 187.68/187.63 [3619]E(f306(f306(f237(a1),f306(f306(f237(a1),x36191),x36192)),x36193),f306(f306(f237(a1),x36191),f306(f306(f82(a865),x36192),x36193))) % 187.68/187.63 [3638]E(f154(x36381,f306(f306(f143(f872(x36381,a859)),x36382),x36383)),f167(x36381,x36382,f154(x36381,x36383))) % 187.68/187.63 [3683]E(f306(f306(f22(a865),f306(f306(f22(a865),x36831),x36832)),x36833),f306(f306(f22(a865),f306(f306(f22(a865),x36831),x36833)),x36832)) % 187.68/187.63 [3691]E(f306(f306(f109(f872(x36911,a859)),x36912),f306(f306(f22(f872(x36911,a859)),x36913),x36912)),f185(f872(x36911,a859))) % 187.68/187.63 [3732]E(f42(f872(x37321,a859),f306(f306(f284(f872(x37321,a859)),x37322),x37323)),f306(f306(f109(f872(x37321,a859)),x37322),f42(f872(x37321,a859),x37323))) % 187.68/187.63 [3733]E(f41(f872(x37331,a859),f306(f306(f284(f872(x37331,a859)),x37332),x37333)),f306(f306(f108(f872(x37331,a859)),x37332),f41(f872(x37331,a859),x37333))) % 187.68/187.63 [3735]E(f306(f306(f22(a865),f306(f306(f82(a865),x37351),x37352)),f306(f306(f82(a865),x37353),x37352)),f306(f306(f82(a865),f306(f306(f22(a865),x37351),x37353)),x37352)) % 187.68/187.63 [3736]E(f306(f306(f81(a865),f306(f306(f82(a865),x37361),x37362)),f306(f306(f82(a865),x37363),x37362)),f306(f306(f82(a865),f306(f306(f81(a865),x37361),x37363)),x37362)) % 187.68/187.63 [3737]E(f306(f306(f22(a1),f306(f306(f82(a1),x37371),x37372)),f306(f306(f82(a1),x37373),x37372)),f306(f306(f82(a1),f306(f306(f22(a1),x37371),x37373)),x37372)) % 187.68/187.63 [3738]E(f306(f306(f81(a1),f306(f306(f82(a1),x37381),x37382)),f306(f306(f82(a1),x37383),x37382)),f306(f306(f82(a1),f306(f306(f81(a1),x37381),x37383)),x37382)) % 187.68/187.63 [3740]E(f306(f306(f225(a865),f306(f306(f22(a865),x37401),x37402)),f306(f306(f22(a865),x37403),x37402)),f306(f306(f22(a865),f306(f306(f225(a865),x37401),x37403)),x37402)) % 187.68/187.63 [3763]E(f306(f306(f109(f872(f866(x37631),a859)),f152(x37631,x37632)),f152(x37631,x37633)),f152(x37631,f306(f306(f109(f872(x37631,a859)),x37632),x37633))) % 187.68/187.63 [3765]E(f306(f306(f108(f872(x37651,a859)),x37652),f306(f306(f22(f872(x37651,a859)),x37653),x37652)),f306(f306(f108(f872(x37651,a859)),x37652),x37653)) % 187.68/187.63 [3766]E(f306(f306(f108(f872(x37661,a859)),x37662),f306(f306(f108(f872(x37661,a859)),x37662),x37663)),f306(f306(f108(f872(x37661,a859)),x37662),x37663)) % 187.68/187.63 [3767]E(f306(f306(f109(f872(x37671,a859)),x37672),f306(f306(f109(f872(x37671,a859)),x37672),x37673)),f306(f306(f109(f872(x37671,a859)),x37672),x37673)) % 187.68/187.63 [3779]E(f306(f306(f263(x37791,x37792,x37792),x37793),f282(x37792,f185(f872(f871(x37792,x37792),a859)))),x37793) % 187.68/187.63 [3782]E(f306(f306(f108(f872(x37821,a859)),f306(f306(f284(x37821),x37822),f185(f872(x37821,a859)))),x37823),f306(f306(f284(x37821),x37822),x37823)) % 187.68/187.63 [3799]E(f306(f306(f22(a865),f306(f306(f22(a865),f306(a119,x37991)),x37992)),f306(a119,x37993)),f306(f306(f22(a865),f306(f306(f22(a865),x37991),x37992)),x37993)) % 187.68/187.63 [3827]E(f306(f306(f109(f872(f872(x38271,a859),a859)),f306(f283(x38271),x38272)),f306(f283(x38271),x38273)),f306(f283(x38271),f306(f306(f109(f872(x38271,a859)),x38272),x38273))) % 187.68/187.63 [3831]E(f306(f306(f108(f872(x38311,a859)),f306(f80(f872(x38311,a859)),x38312)),x38313),f306(f80(f872(x38311,a859)),f306(f306(f22(f872(x38311,a859)),x38312),x38313))) % 187.68/187.63 [3842]E(f306(f306(f284(x38421),x38422),f306(f306(f22(f872(x38421,a859)),x38423),f306(f306(f284(x38421),x38422),f185(f872(x38421,a859))))),f306(f306(f284(x38421),x38422),x38423)) % 187.68/187.63 [3852]P1(f306(f306(f220(f872(x38521,a859)),x38522),f306(f306(f108(f872(x38521,a859)),x38523),x38522))) % 187.68/187.63 [3853]P1(f306(f306(f220(f872(x38531,a859)),x38532),f306(f306(f108(f872(x38531,a859)),x38532),x38533))) % 187.68/187.63 [3856]E(f306(f306(f109(f872(x38561,a859)),f306(f80(f872(x38561,a859)),x38562)),f306(f80(f872(x38561,a859)),x38563)),f306(f80(f872(x38561,a859)),f306(f306(f108(f872(x38561,a859)),x38562),x38563))) % 187.68/187.63 [3857]E(f306(f306(f108(f872(x38571,a859)),f306(f80(f872(x38571,a859)),x38572)),f306(f80(f872(x38571,a859)),x38573)),f306(f80(f872(x38571,a859)),f306(f306(f109(f872(x38571,a859)),x38572),x38573))) % 187.68/187.63 [3870]P1(f306(f306(f220(f872(x38701,a859)),f306(f164(x38701),x38702)),f306(f164(x38701),f306(f306(f143(x38701),x38703),x38702)))) % 187.68/187.63 [3880]E(f306(f306(f108(f872(x38801,a859)),f306(f306(f22(f872(x38801,a859)),x38802),x38803)),f306(f306(f109(f872(x38801,a859)),x38802),x38803)),x38802) % 187.68/187.63 [3935]E(f306(f306(f9(x39351,a1),f306(f306(f8(a865,a1,x39351),f107(a1)),x39352)),x39353),f306(f107(a1),f306(f306(f9(x39351,a865),x39352),x39353))) % 187.68/187.63 [3936]E(f306(f306(f6(x39361,a1),f306(f306(f8(a865,a1,x39361),f107(a1)),x39362)),x39363),f306(f107(a1),f306(f306(f6(x39361,a865),x39362),x39363))) % 187.68/187.63 [3982]E(f306(f306(f122(x39821),f168(x39821,x39822,x39823)),f306(f306(f130(x39821),f306(f186(f866(x39821)),f168(x39821,x39822,x39823))),x39823)),x39823) % 187.68/187.63 [3987]E(f306(f80(f872(f871(x39871,x39872),a859)),f306(f306(f243(x39871,x39872),x39873),f306(f16(f872(x39872,a859),x39871),f231(f872(x39872,a859))))),f306(f306(f243(x39871,x39872),f306(f80(f872(x39871,a859)),x39873)),f306(f16(f872(x39872,a859),x39871),f231(f872(x39872,a859))))) % 187.68/187.63 [3988]E(f306(f80(f872(f871(x39881,x39882),a859)),f306(f306(f243(x39881,x39882),f231(f872(x39881,a859))),f306(f16(f872(x39882,a859),x39881),x39883))),f306(f306(f243(x39881,x39882),f231(f872(x39881,a859))),f306(f16(f872(x39882,a859),x39881),f306(f80(f872(x39882,a859)),x39883)))) % 187.68/187.63 [4036]E(f306(f306(f43(f872(x40361,a859),f872(x40361,a859)),x40362),f306(f306(f7(f872(x40361,a859),f872(x40361,a859),f872(x40361,a859)),f109(f872(x40361,a859))),x40363)),f306(f306(f109(f872(x40361,a859)),f41(f872(x40361,a859),x40362)),x40363)) % 187.68/187.63 [4043]E(f306(f134(f866(x40431),f866(x40431),f122(x40431),f120(x40431)),f306(f306(f143(f866(x40431)),x40432),x40433)),f306(f306(f122(x40431),x40432),f306(f134(f866(x40431),f866(x40431),f122(x40431),f120(x40431)),x40433))) % 187.68/187.63 [4065]E(f306(f306(f284(f872(x40651,a859)),f306(f260(x40651,x40651,x40652),f306(f306(f284(x40651),x40653),f185(f872(x40651,a859))))),f185(f872(f872(x40651,a859),a859))),f306(f306(f62(x40651),f306(f306(f284(x40651),x40653),f185(f872(x40651,a859)))),x40652)) % 187.68/187.63 [4075]E(f306(f306(f81(a865),f306(f306(f82(a865),x40751),f306(f306(f40(a865),x40752),x40753))),f306(f306(f40(a865),f306(f306(f82(a865),x40751),f46(a865,x40752,x40753))),x40753)),f306(f306(f40(a865),f306(f306(f82(a865),x40751),x40752)),x40753)) % 187.68/187.63 [4076]E(f306(f306(f81(a1),f306(f306(f82(a1),x40761),f306(f306(f40(a1),x40762),x40763))),f306(f306(f40(a1),f306(f306(f82(a1),x40761),f46(a1,x40762,x40763))),x40763)),f306(f306(f40(a1),f306(f306(f82(a1),x40761),x40762)),x40763)) % 187.68/187.63 [4112]E(f306(f306(f22(f872(x41121,a859)),f306(f164(x41121),x41122)),f306(f306(f284(x41121),x41123),f185(f872(x41121,a859)))),f306(f164(x41121),f306(f128(x41121,f306(f306(f8(a859,a859,x41121),a301),f306(a303,x41123))),x41122))) % 187.68/187.63 [4159]E(f306(f306(f122(x41591),f306(f134(f866(x41591),f866(x41591),f122(x41591),f120(x41591)),x41592)),f306(f134(f866(x41591),f866(x41591),f122(x41591),f120(x41591)),x41593)),f306(f134(f866(x41591),f866(x41591),f122(x41591),f120(x41591)),f306(f306(f122(f866(x41591)),x41592),x41593))) % 187.68/187.63 [4164]E(f306(f306(f236(f866(x41641),f866(x41641)),f306(f128(x41641,x41642),x41643)),f306(f128(x41641,f306(f74(a859,a859,x41641,a301),x41642)),x41643)),f159(x41641,x41642,x41643)) % 187.68/187.63 [4167]E(f306(f306(f81(a865),f306(f306(f81(a865),f306(f306(f40(a865),x41671),x41672)),f306(f306(f40(a865),x41673),x41672))),f306(f306(f40(a865),f306(f306(f81(a865),f46(a865,x41671,x41672)),f46(a865,x41673,x41672))),x41672)),f306(f306(f40(a865),f306(f306(f81(a865),x41671),x41673)),x41672)) % 187.68/187.63 [4168]E(f306(f306(f81(a1),f306(f306(f81(a1),f306(f306(f40(a1),x41681),x41682)),f306(f306(f40(a1),x41683),x41682))),f306(f306(f40(a1),f306(f306(f81(a1),f46(a1,x41681,x41682)),f46(a1,x41683,x41682))),x41682)),f306(f306(f40(a1),f306(f306(f81(a1),x41681),x41683)),x41682)) % 187.68/187.63 [4224]E(f306(f306(f109(f872(f866(x42241),a859)),f306(f306(f7(f866(x42241),f872(f866(x42241),a859),a859),f308(f866(x42241))),f153(x42241,x42242))),f306(f306(f7(f866(x42241),f872(f866(x42241),a859),a859),f308(f866(x42241))),f153(x42241,x42243))),f152(x42241,f306(f306(f109(f872(x42241,a859)),f306(f306(f7(x42241,f872(x42241,a859),a859),f308(x42241)),x42242)),f306(f306(f7(x42241,f872(x42241,a859),a859),f308(x42241)),x42243)))) % 187.68/187.63 [4237]E(f306(f228(x42371),f306(f306(f18(x42371,a859,a859),f306(f306(f8(a859,f872(a859,a859),x42371),a305),f306(f306(f7(x42371,x42371,a859),a303),x42372))),f306(f306(f7(x42371,f872(x42371,a859),a859),f308(x42371)),x42373))),f306(f306(f284(x42371),x42372),x42373)) % 187.68/187.63 [4257]E(f306(f306(f87(f866(f866(x42571)),f866(f866(x42571))),f55(x42571,x42572)),f306(f306(f18(f866(f866(x42571)),f866(f866(x42571)),f866(f866(x42571))),f306(f306(f8(f866(f866(x42571)),f872(f866(f866(x42571)),f866(f866(x42571))),f866(f866(x42571))),f122(f866(x42571))),f306(f146(f866(x42571),f866(x42571)),f306(f143(x42571),x42573)))),f5(f866(f866(x42571))))),f55(x42571,f306(f306(f143(x42571),x42573),x42572))) % 187.68/187.63 [4261]E(f306(f228(x42611),f306(f306(f18(x42611,a859,a859),f306(f306(f8(a859,f872(a859,a859),x42611),a305),f306(f306(f7(x42611,f872(x42611,a859),a859),f308(x42611)),x42612))),f306(f306(f7(x42611,f872(x42611,a859),a859),f308(x42611)),x42613))),f306(f306(f108(f872(x42611,a859)),x42612),x42613)) % 187.68/187.63 [4262]E(f306(f228(x42621),f306(f306(f18(x42621,a859,a859),f306(f306(f8(a859,f872(a859,a859),x42621),a304),f306(f306(f7(x42621,f872(x42621,a859),a859),f308(x42621)),x42622))),f306(f306(f7(x42621,f872(x42621,a859),a859),f308(x42621)),x42623))),f306(f306(f109(f872(x42621,a859)),x42622),x42623)) % 187.68/187.63 [4352]E(f306(f306(f43(x43521,f872(f872(x43521,a859),a859)),x43522),f306(f306(f7(x43521,f872(f872(x43521,a859),a859),f872(f872(x43521,a859),a859)),f306(f306(f8(f872(x43521,a859),f872(f872(f872(x43521,a859),a859),f872(f872(x43521,a859),a859)),x43521),f284(f872(x43521,a859))),f306(f306(f8(f872(x43521,a859),f872(x43521,a859),x43521),f260(x43521,x43521,x43523)),f306(f306(f7(x43521,f872(x43521,a859),f872(x43521,a859)),f284(x43521)),f185(f872(x43521,a859)))))),f185(f872(f872(x43521,a859),a859)))),f306(f306(f62(x43521),x43522),x43523)) % 187.68/187.63 [4354]E(f306(f306(f191(x43541),f306(f306(f82(a1),f306(f306(f74(f871(a1,a1),a1,x43541,f235(a1,a1)),f198(x43541)),x43542)),f306(f306(f74(f871(a1,a1),a1,x43541,f235(a1,a1)),f198(x43541)),x43543))),f306(f306(f82(a1),f306(f306(f74(f871(a1,a1),a1,x43541,f244(a1,a1)),f198(x43541)),x43542)),f306(f306(f74(f871(a1,a1),a1,x43541,f244(a1,a1)),f198(x43541)),x43543))),f207(x43541,x43542,x43543)) % 187.68/187.63 [4357]E(f306(f228(f866(x43571)),f306(f306(f18(f866(x43571),a859,a859),f306(f306(f8(a859,f872(a859,a859),f866(x43571)),a304),f306(f306(f7(f866(x43571),a865,a859),f306(f306(f8(a865,f872(a865,a859),f866(x43571)),a303),f186(f866(x43571)))),x43572))),f306(f306(f7(f866(x43571),f872(x43571,a859),a859),f306(f306(f8(f872(x43571,a859),f872(f872(x43571,a859),a859),f866(x43571)),f220(f872(x43571,a859))),f164(x43571))),f306(f164(x43571),x43573)))),f306(f164(f866(x43571)),f56(x43571,x43572,x43573))) % 187.68/187.63 [3753]E(f46(a865,f306(f306(f81(a865),f306(f306(f82(a865),x37531),x37532)),x37533),x37532),f46(a865,x37533,x37532)) % 187.68/187.63 [3798]E(f131(a865,f306(f276(a865,f306(f306(f81(a865),x37981),x37982)),x37983)),f306(f306(f130(a865),x37982),f131(a865,f306(f276(a865,x37981),x37983)))) % 187.68/187.63 [3841]E(f306(f306(f81(a1),f306(f107(a1),x38411)),f306(f306(f81(a1),f306(f107(a1),x38412)),x38413)),f306(f306(f81(a1),f306(f107(a1),f306(f306(f81(a865),x38411),x38412))),x38413)) % 187.68/187.63 [3848]E(f306(f306(f22(f872(x38481,a859)),f306(f306(f22(f872(x38481,a859)),x38482),x38483)),x38483),f306(f306(f22(f872(x38481,a859)),x38482),x38483)) % 187.68/187.63 [3849]E(f306(f306(f108(f872(x38491,a859)),f306(f306(f22(f872(x38491,a859)),x38492),x38493)),x38493),f306(f306(f108(f872(x38491,a859)),x38492),x38493)) % 187.68/187.63 [3871]E(f306(f306(f263(x38711,x38711,x38712),f282(x38711,f185(f872(f871(x38711,x38711),a859)))),x38713),x38713) % 187.68/187.63 [3877]E(f306(f306(f108(f872(x38771,a859)),f306(f259(x38771),x38772)),f306(f259(x38771),x38773)),f306(f259(x38771),f306(f306(f108(f872(f871(x38771,x38771),a859)),x38772),x38773))) % 187.68/187.63 [3888]E(f250(x38881,f306(f306(f143(f871(a106,x38881)),f306(f306(f236(a106,x38881),f2(a106)),x38882)),x38883)),f250(x38881,x38883)) % 187.68/187.63 [3891]E(f306(f306(f109(f872(x38911,a859)),f42(f872(x38911,a859),x38912)),f42(f872(x38911,a859),x38913)),f42(f872(x38911,a859),f306(f306(f108(f872(f872(x38911,a859),a859)),x38912),x38913))) % 187.68/187.63 [3892]E(f306(f306(f108(f872(x38921,a859)),f41(f872(x38921,a859),x38922)),f41(f872(x38921,a859),x38923)),f41(f872(x38921,a859),f306(f306(f108(f872(f872(x38921,a859),a859)),x38922),x38923))) % 187.68/187.63 [3927]E(f306(f306(f263(x39271,x39271,x39271),f306(f306(f180(f871(x39271,x39271),a859),x39272),x39273)),x39273),f306(f306(f180(f871(x39271,x39271),a859),f306(a119,x39272)),x39273)) % 187.68/187.63 [3973]P1(f306(f306(f220(f872(x39731,a859)),f306(f306(f22(f872(x39731,a859)),x39732),x39733)),x39732)) % 187.68/187.63 [3974]P1(f306(f306(f220(f872(x39741,a859)),f306(f306(f109(f872(x39741,a859)),x39742),x39743)),x39743)) % 187.68/187.63 [3975]P1(f306(f306(f220(f872(x39751,a859)),f306(f306(f109(f872(x39751,a859)),x39752),x39753)),x39752)) % 187.68/187.63 [4000]E(f282(x40001,f306(f306(f108(f872(f871(x40001,x40001),a859)),f282(x40001,x40002)),f282(x40001,x40003))),f282(x40001,f306(f306(f108(f872(f871(x40001,x40001),a859)),x40002),x40003))) % 187.68/187.63 [4004]E(f41(f872(x40041,a859),f306(f306(f284(f872(x40041,a859)),x40042),f306(f306(f284(f872(x40041,a859)),x40043),f185(f872(f872(x40041,a859),a859))))),f306(f306(f108(f872(x40041,a859)),x40042),x40043)) % 187.68/187.63 [4005]E(f42(f872(x40051,a859),f306(f306(f284(f872(x40051,a859)),x40052),f306(f306(f284(f872(x40051,a859)),x40053),f185(f872(f872(x40051,a859),a859))))),f306(f306(f109(f872(x40051,a859)),x40052),x40053)) % 187.68/187.63 [4011]E(f306(f306(f263(x40111,x40111,x40111),f306(f306(f180(f871(x40111,x40111),a859),x40112),x40113)),x40113),f306(f306(f263(x40111,x40111,x40111),x40113),f306(f306(f180(f871(x40111,x40111),a859),x40112),x40113))) % 187.68/187.63 [4080]E(f306(f306(f108(f872(x40801,a859)),f306(f228(x40801),f306(f306(f7(x40801,x40801,a859),a303),x40802))),x40803),f306(f306(f284(x40801),x40802),x40803)) % 187.68/187.63 [4082]E(f306(a112,f306(f306(f9(x40821,a1),f306(f306(f8(a865,a1,x40821),f107(a1)),x40822)),x40823)),f306(f306(f9(x40821,a865),x40822),x40823)) % 187.68/187.63 [4083]E(f306(a112,f306(f306(f6(x40831,a1),f306(f306(f8(a865,a1,x40831),f107(a1)),x40832)),x40833)),f306(f306(f6(x40831,a865),x40832),x40833)) % 187.68/187.63 [4156]E(f306(f148(f866(x41561),x41561,f306(f163(x41561),x41562),f306(f16(f872(f866(x41561),f866(x41561)),x41561),f306(f306(f7(f866(x41561),f866(x41561),f866(x41561)),f122(x41561)),x41562))),x41563),f306(f163(x41561),f306(f306(f122(x41561),x41563),x41562))) % 187.68/187.63 [4187]P1(f306(f306(f220(f872(f872(x41871,a859),a859)),f306(f306(f108(f872(f872(x41871,a859),a859)),f306(f283(x41871),x41872)),f306(f283(x41871),x41873))),f306(f283(x41871),f306(f306(f108(f872(x41871,a859)),x41872),x41873)))) % 187.68/187.63 [4280]E(f306(f228(x42801),f306(f306(f18(x42801,a859,a859),f306(f306(f8(a859,f872(a859,a859),x42801),a304),f306(f306(f7(x42801,f872(x42801,a859),a859),f308(x42801)),x42802))),f306(f306(f8(a859,a859,x42801),a301),f306(f306(f7(x42801,f872(x42801,a859),a859),f308(x42801)),x42803)))),f306(f306(f22(f872(x42801,a859)),x42802),x42803)) % 187.68/187.63 [4301]E(f306(f39(a865),f306(f228(a865),f306(f306(f18(a865,a859,a859),f306(f306(f8(a859,f872(a859,a859),a865),a304),f306(f306(f7(a865,a865,a859),f221(a865)),f306(f186(f866(x43011)),x43012)))),f306(f306(f8(x43011,a859,a865),x43013),f306(f157(x43011),x43012))))),f306(f186(f866(x43011)),f306(f128(x43011,x43013),x43012))) % 187.68/187.63 [4303]E(f306(f186(f866(x43031)),f166(x43031,x43032,x43033)),f306(f39(a865),f306(f228(a865),f306(f306(f18(a865,a859,a859),f306(f306(f8(a859,f872(a859,a859),a865),a304),f306(f306(f7(a865,a865,a859),f221(a865)),f306(f186(f866(x43031)),x43032)))),f306(f306(f7(a865,f872(a865,a859),a859),f308(a865)),x43033))))) % 187.68/187.63 [4396]E(f306(f306(f109(f872(f871(f866(x43961),f866(x43961)),a859)),f306(f285(f871(f871(x43961,f866(x43961)),f871(x43961,f866(x43961))),f871(f866(x43961),f866(x43961)),f246(f871(x43961,f866(x43961)),f866(x43961),f871(x43961,f866(x43961)),f866(x43961),f306(f245(x43961,f866(x43961),f866(x43961)),f143(x43961)),f306(f245(x43961,f866(x43961),f866(x43961)),f143(x43961)))),f299(x43961,f866(x43961),x43962,f306(f135(x43961,x43962),x43963)))),f306(f228(f871(f866(x43961),f866(x43961))),f306(f245(f866(x43961),f866(x43961),a859),f306(f306(f7(f866(x43961),f872(f866(x43961),a859),f872(f866(x43961),a859)),f306(f306(f8(f872(a859,a859),f872(f872(f866(x43961),a859),f872(f866(x43961),a859)),f866(x43961)),f8(a859,a859,f866(x43961))),f306(f306(f8(a859,f872(a859,a859),f866(x43961)),a304),f306(f306(f7(f866(x43961),a865,a859),f306(f306(f8(a865,f872(a865,a859),f866(x43961)),a303),f186(f866(x43961)))),f306(a119,x43963))))),f306(f306(f7(f866(x43961),a865,a859),f306(f306(f8(a865,f872(a865,a859),f866(x43961)),a303),f186(f866(x43961)))),f306(a119,x43963)))))),f306(f135(x43961,x43962),f306(a119,x43963))) % 187.68/187.63 [3893]E(f46(a865,f306(a119,f306(f306(f81(a865),f306(f306(f82(a865),x38931),x38932)),x38933)),x38932),f46(a865,f306(a119,x38933),x38932)) % 187.68/187.63 [4147]E(f306(f228(x41471),f306(f306(f18(x41471,a859,a859),f306(f306(f8(a859,f872(a859,a859),x41471),a304),x41472)),x41473)),f306(f306(f109(f872(x41471,a859)),f306(f228(x41471),x41472)),f306(f228(x41471),x41473))) % 187.68/187.63 [4148]E(f306(f228(x41481),f306(f306(f18(x41481,a859,a859),f306(f306(f8(a859,f872(a859,a859),x41481),a305),x41482)),x41483)),f306(f306(f108(f872(x41481,a859)),f306(f228(x41481),x41482)),f306(f228(x41481),x41483))) % 187.68/187.63 [4150]E(f306(f306(f122(x41501),f306(f306(f130(x41501),f46(a865,x41502,f306(f186(f866(x41501)),x41503))),x41503)),f306(f306(f165(x41501),f46(a865,x41502,f306(f186(f866(x41501)),x41503))),x41503)),f306(f306(f306(f180(f866(x41501),f866(x41501)),x41502),f160(x41501)),x41503)) % 187.68/187.63 [4155]E(f306(f228(x41551),f306(f306(f18(x41551,a859,a859),f306(f306(f8(a859,f872(a859,a859),x41551),a309),x41552)),x41553)),f306(f306(f108(f872(x41551,a859)),f306(f80(f872(x41551,a859)),f306(f228(x41551),x41552))),f306(f228(x41551),x41553))) % 187.68/187.63 [4169]E(f306(f306(f81(a865),f306(f186(f866(x41691)),f306(f128(x41691,x41692),x41693))),f306(f186(f866(x41691)),f306(f128(x41691,f306(f306(f8(a859,a859,x41691),a301),x41692)),x41693))),f306(f186(f866(x41691)),x41693)) % 187.68/187.63 [4194]P1(f306(f306(f220(f872(x41941,a859)),f306(f306(f108(f872(x41941,a859)),f42(f872(x41941,a859),x41942)),f42(f872(x41941,a859),x41943))),f42(f872(x41941,a859),f306(f306(f109(f872(f872(x41941,a859),a859)),x41942),x41943)))) % 187.68/187.63 [4208]E(f306(f164(x42081),f306(f128(x42081,f306(f306(f8(a859,a859,x42081),a301),f306(f306(f7(x42081,x42081,a859),a303),x42082))),x42083)),f306(f306(f22(f872(x42081,a859)),f306(f164(x42081),x42083)),f306(f306(f284(x42081),x42082),f185(f872(x42081,a859))))) % 187.68/187.63 [4217]P1(f306(f306(f220(f872(f871(x42171,x42171),a859)),f306(f306(f108(f872(f871(x42171,x42171),a859)),f282(x42171,x42172)),f282(x42171,x42173))),f282(x42171,f306(f306(f108(f872(f871(x42171,x42171),a859)),x42172),x42173)))) % 187.68/187.63 [4242]E(f306(f306(f82(a865),f306(a119,f306(a119,f2(a865)))),f306(f306(f6(a865,a865),f306(f306(f8(a865,a865,a865),f306(f81(a865),x42421)),f306(f306(f7(a865,a865,a865),f82(a865)),x42422))),f306(f229(a865),x42423))),f306(f306(f82(a865),x42423),f306(f306(f81(a865),x42421),f306(f306(f81(a865),x42421),f306(f306(f82(a865),f306(f306(f22(a865),x42423),f79(a865))),x42422))))) % 187.68/187.63 [4252]E(f306(f228(x42521),f306(f306(f18(x42521,a859,a859),f306(f306(f8(a859,f872(a859,a859),x42521),a304),f306(f306(f7(x42521,f872(x42521,a859),a859),f308(x42521)),f306(f164(x42521),x42522)))),x42523)),f306(f164(x42521),f306(f128(x42521,x42523),x42522))) % 187.68/187.63 [4395]E(f306(f228(x43951),f306(f306(f8(f872(a865,a859),a859,x43951),f88(a865)),f306(f306(f7(x43951,f872(a865,a859),f872(a865,a859)),f306(f306(f8(f872(a865,f872(a859,a859)),f872(f872(a865,a859),f872(a865,a859)),x43951),f18(a865,a859,a859)),f306(f306(f8(f872(a865,a859),f872(a865,f872(a859,a859)),x43951),f306(f8(a859,f872(a859,a859),a865),a304)),f306(f306(f7(x43951,f872(a865,x43951),f872(a865,a859)),f306(f306(f8(f872(x43951,a859),f872(f872(a865,x43951),f872(a865,a859)),x43951),f8(x43951,a859,a865)),a303)),f306(f157(x43951),x43952))))),f306(f306(f18(a865,a859,a859),f306(f306(f8(a859,f872(a859,a859),a865),a304),f306(f306(f7(a865,a865,a859),f221(a865)),f306(f186(f866(x43951)),x43952)))),f306(f306(f7(a865,f872(a865,a859),a859),f308(a865)),x43953))))),f306(f164(x43951),f166(x43951,x43952,x43953))) % 187.68/187.63 [4291]E(f306(f228(x42911),f306(f306(f18(x42911,a859,a859),f306(f306(f8(a859,f872(a859,a859),x42911),a309),f306(f306(f8(a859,a859,x42911),a301),f306(f306(f7(x42911,x42911,a859),a303),x42912)))),x42913)),f306(f306(f284(x42911),x42912),f306(f228(x42911),x42913))) % 187.68/187.63 [4323]E(f306(f306(f146(f871(x43231,a865),x43231),f235(x43231,a865)),f306(f128(f871(x43231,a865),f306(f306(f7(f871(x43231,a865),f872(a865,a859),a859),f306(f306(f8(a865,f872(f872(a865,a859),a859),f871(x43231,a865)),f308(a865)),f244(x43231,a865))),x43232)),f306(f306(f173(x43231,a865),x43233),f131(a865,f306(f276(a865,f2(a865)),f306(f186(f866(x43231)),x43233)))))),f166(x43231,x43233,x43232)) % 187.68/187.63 [4353]E(f306(f306(f82(a1),f306(f111(a1),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)))),f306(f306(f6(a865,a1),f306(f306(f8(a1,a1,a865),f306(f81(a1),x43531)),f306(f306(f7(a865,a1,a1),f306(f306(f8(a1,f872(a1,a1),a865),f82(a1)),f107(a1))),x43532))),f306(f229(a865),x43533))),f306(f306(f82(a1),f306(f107(a1),x43533)),f306(f306(f81(a1),x43531),f306(f306(f81(a1),x43531),f306(f306(f82(a1),f306(f107(a1),f306(f306(f22(a865),x43533),f79(a865)))),x43532))))) % 187.68/187.63 [4389]E(f306(f228(f871(x43891,x43892)),f306(f245(x43891,x43892,a859),f306(f306(f7(x43891,f872(f871(x43892,x43891),a859),f872(x43892,a859)),f306(f306(f8(f872(x43892,f872(f872(f871(x43892,x43891),a859),a859)),f872(f872(f871(x43892,x43891),a859),f872(x43892,a859)),x43891),f7(x43892,f872(f871(x43892,x43891),a859),a859)),f306(f306(f8(f872(x43892,f871(x43892,x43891)),f872(x43892,f872(f872(f871(x43892,x43891),a859),a859)),x43891),f306(f8(f871(x43892,x43891),f872(f872(f871(x43892,x43891),a859),a859),x43892),f308(f871(x43892,x43891)))),f306(f7(x43892,x43891,f871(x43892,x43891)),f236(x43892,x43891))))),x43893))),f306(f261(x43892,x43891),x43893)) % 187.68/187.63 [4410]E(f306(f228(f866(x44101)),f306(f306(f8(f872(x44101,a859),a859,f866(x44101)),f88(x44101)),f306(f306(f8(f872(x44101,f872(f866(x44101),a859)),f872(x44101,a859),f866(x44101)),f306(f8(f872(f866(x44101),a859),a859,x44101),f88(f866(x44101)))),f306(f306(f7(f866(x44101),f872(x44101,f872(f866(x44101),a859)),f872(x44101,f872(f866(x44101),a859))),f306(f306(f8(f872(x44101,f872(f872(f866(x44101),a859),f872(f866(x44101),a859))),f872(f872(x44101,f872(f866(x44101),a859)),f872(x44101,f872(f866(x44101),a859))),f866(x44101)),f18(x44101,f872(f866(x44101),a859),f872(f866(x44101),a859))),f306(f306(f8(f872(x44101,f872(f866(x44101),f872(a859,a859))),f872(x44101,f872(f872(f866(x44101),a859),f872(f866(x44101),a859))),f866(x44101)),f306(f8(f872(f866(x44101),f872(a859,a859)),f872(f872(f866(x44101),a859),f872(f866(x44101),a859)),x44101),f18(f866(x44101),a859,a859))),f306(f306(f8(f872(x44101,f872(f866(x44101),a859)),f872(x44101,f872(f866(x44101),f872(a859,a859))),f866(x44101)),f306(f8(f872(f866(x44101),a859),f872(f866(x44101),f872(a859,a859)),x44101),f306(f8(a859,f872(a859,a859),f866(x44101)),a304))),f306(f306(f7(f866(x44101),f872(x44101,f872(f866(x44101),f866(x44101))),f872(x44101,f872(f866(x44101),a859))),f306(f306(f8(f872(f872(f866(x44101),f866(x44101)),f872(f866(x44101),a859)),f872(f872(x44101,f872(f866(x44101),f866(x44101))),f872(x44101,f872(f866(x44101),a859))),f866(x44101)),f8(f872(f866(x44101),f866(x44101)),f872(f866(x44101),a859),x44101)),f306(f306(f8(f872(f866(x44101),a859),f872(f872(f866(x44101),f866(x44101)),f872(f866(x44101),a859)),f866(x44101)),f8(f866(x44101),a859,f866(x44101))),a303))),f143(x44101)))))),f306(f306(f7(x44101,f872(f866(x44101),a859),f872(f866(x44101),a859)),f306(f306(f8(f872(a859,a859),f872(f872(f866(x44101),a859),f872(f866(x44101),a859)),x44101),f8(a859,a859,f866(x44101))),f306(f306(f8(a859,f872(a859,a859),x44101),a304),f306(f306(f7(x44101,f872(x44101,a859),a859),f308(x44101)),x44102)))),f306(f306(f7(f866(x44101),f872(f866(x44101),a859),a859),f308(f866(x44101))),x44103)))))),f167(x44101,x44102,x44103)) % 187.68/187.63 [4407]E(f306(f306(f87(a1,f871(a1,a1)),f306(f306(f22(a1),x44071),x44072)),f306(f306(f7(a1,f871(a1,a1),f871(a1,a1)),f306(f306(f18(a1,f871(a1,a1),f872(f871(a1,a1),f871(a1,a1))),f306(f306(f8(a859,f872(f871(a1,a1),f872(f871(a1,a1),f871(a1,a1))),a1),f101(f871(a1,a1))),f306(f220(a1),f2(a1)))),f306(f236(a1,a1),f306(f306(f81(a1),f306(f306(f82(a1),f306(f111(a1),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)))),x44073)),f79(a1))))),f306(f306(f236(a1,a1),f306(f306(f82(a1),f306(f111(a1),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)))),x44073)),x44071))),f306(f45(x44072),f306(f306(f236(a1,a1),x44073),x44071))) % 187.68/187.63 [4438]~E(f33(x44381,x44382),f34(x44383,x44384)) % 187.68/187.63 [4457]~E(f306(a26,x44571),f29(x44572,x44573,x44574)) % 187.68/187.63 [4458]~E(f306(a26,x44581),f31(x44582,x44583,x44584)) % 187.68/187.63 [4459]~E(f306(a26,x44591),f30(x44592,x44593,x44594)) % 187.68/187.63 [4460]~E(f29(x44601,x44602,x44603),f306(a26,x44604)) % 187.68/187.63 [4461]~E(f31(x44611,x44612,x44613),f306(a26,x44614)) % 187.68/187.63 [4462]~E(f30(x44621,x44622,x44623),f306(a26,x44624)) % 187.68/187.63 [3456]E(f306(f306(f306(f73(x34561,x34562),x34563),x34564),f306(x34563,x34564)),x34563) % 187.68/187.63 [3515]E(f306(f306(f238(x35151,x35152,x35153),x35154),f2(a865)),x35152) % 187.68/187.63 [3552]E(f182(x35521,x35522,x35523,f306(a119,x35524)),f306(x35523,x35524)) % 187.68/187.63 [3591]E(f162(x35911,x35912,f162(x35911,x35913,x35914)),f162(x35911,x35913,f162(x35911,x35912,x35914))) % 187.68/187.63 [3723]E(f306(f216(x37231,x37232,x37233,x37234),f188(x37232)),x37233) % 187.68/187.63 [3724]E(f306(f148(x37241,x37242,x37243,x37244),f120(x37242)),x37243) % 187.68/187.63 [3725]E(f306(f134(x37251,x37252,x37253,x37254),f120(x37252)),x37254) % 187.68/187.63 [3838]E(f306(f216(f869(x38381),x38382,f188(x38381),f306(f16(f869(x38381),x38382),f188(x38381))),f306(x38383,x38384)),f188(x38381)) % 187.68/187.63 [3881]E(f306(f306(f108(f872(x38811,a859)),f175(x38811,x38812,x38813)),f175(x38811,x38812,x38814)),f175(x38811,x38812,f176(x38811,x38812,x38814,x38813))) % 187.68/187.63 [3913]E(f306(f306(f247(x39131,x39132,x39133,f871(x39132,x39133)),x39134),f236(x39132,x39133)),x39134) % 187.68/187.63 [3922]E(f217(x39221,x39222,x39223,x39224,f188(x39222)),x39223) % 187.68/187.63 [3923]E(f178(x39231,x39232,x39233,x39234,f120(x39232)),x39233) % 187.68/187.63 [3924]E(f178(x39241,x39242,x39243,f120(x39241),x39244),x39243) % 187.68/187.63 [4201]P44(x42011,x42012,x42013,x42014,f185(f872(x42011,a859)),x42014) % 187.68/187.63 [3260]E(f306(f306(f16(x32601,x32602),x32603),x32604),x32603) % 187.68/187.63 [3375]E(f306(f306(f189(x33751,x33752),x33753),f306(f214(x33751),x33754)),f306(f214(x33752),f306(x33753,x33754))) % 187.68/187.63 [3543]E(f162(x35431,x35432,f306(f128(x35431,x35433),x35434)),f306(f128(x35431,x35433),f162(x35431,x35432,x35434))) % 187.68/187.63 [3575]E(f306(f306(f66(x35751,x35752,x35753),x35754),f185(f872(x35751,a859))),x35754) % 187.68/187.63 [3597]E(f306(f306(f157(x35971),f306(f306(f143(x35971),x35972),x35973)),f306(a119,x35974)),f306(f306(f157(x35971),x35973),x35974)) % 187.68/187.63 [3639]P30(x36391,f2(a865),f306(f306(f306(f93(x36391),x36392),f306(a26,x36393)),x36394)) % 187.68/187.63 [3664]E(f306(f306(x36641,x36642),f306(f181(x36643,x36644,x36641),x36642)),f306(f181(x36643,x36644,x36641),f306(a119,x36642))) % 187.68/187.63 [3758]E(f306(f306(f151(x37581,f306(f306(f143(x37581),x37582),x37583)),f2(a865)),x37584),f306(f306(f143(x37581),x37584),x37583)) % 187.68/187.63 [3769]E(f306(f306(f43(f872(x37691,a859),f872(x37692,a859)),x37693),f285(x37691,x37692,x37694)),f306(f285(x37691,x37692,x37694),f41(f872(x37691,a859),x37693))) % 187.68/187.63 [3770]E(f306(f306(f43(f872(x37701,a859),f872(x37702,a859)),x37703),f286(x37702,x37701,x37704)),f306(f286(x37702,x37701,x37704),f41(f872(x37701,a859),x37703))) % 187.68/187.63 [3865]E(f175(x38651,x38652,f179(x38651,x38652,x38653,x38654)),f306(f306(f109(f872(x38651,a859)),f175(x38651,x38652,x38653)),x38654)) % 187.68/187.63 [3887]E(f306(f134(x38871,x38872,f306(f7(x38872,x38871,x38871),x38873),x38874),f306(f161(x38872),f120(x38872))),x38874) % 187.68/187.63 [3934]E(f77(x39341,x39342,x39343,x39344,f185(f872(x39341,a859))),x39343) % 187.68/187.63 [3976]E(f306(f306(f306(f306(f73(x39761,f869(x39762)),f306(f16(f869(x39762),x39761),f188(x39762))),x39763),f188(x39762)),x39764),f188(x39762)) % 187.68/187.63 [4130]E(f306(f245(x41301,x41302,x41303),f306(f306(f8(f872(x41302,f871(x41301,x41302)),f872(x41302,x41303),x41301),f306(f8(f871(x41301,x41302),x41303,x41302),x41304)),f236(x41301,x41302))),x41304) % 187.68/187.63 [3454]E(f306(f244(x34541,x34542),f306(f306(f236(x34541,x34542),x34543),x34544)),x34544) % 187.68/187.63 [3455]E(f306(f235(x34551,x34552),f306(f306(f236(x34551,x34552),x34553),x34554)),x34553) % 187.68/187.63 [3488]E(f306(f186(f866(x34881)),f306(f306(f146(x34882,x34881),x34883),x34884)),f306(f186(f866(x34882)),x34884)) % 187.68/187.63 [3489]E(f306(f186(f866(x34891)),f306(f306(f151(x34891,x34892),x34893),x34894)),f306(f186(f866(x34891)),x34892)) % 187.68/187.63 [3509]E(f306(f306(f130(x35091),f306(a119,x35092)),f306(f306(f143(x35091),x35093),x35094)),f306(f306(f130(x35091),x35092),x35094)) % 187.68/187.63 [3577]E(f306(f306(f284(x35771),x35772),f306(f306(f284(x35771),x35773),x35774)),f306(f306(f284(x35771),x35773),f306(f306(f284(x35771),x35772),x35774))) % 187.68/187.63 [3580]E(f306(f306(f146(x35801,x35802),x35803),f121(x35801,x35804)),f121(x35802,f306(f306(f146(x35801,x35802),x35803),x35804))) % 187.68/187.63 [3595]E(f306(f161(x35951),f306(f306(f146(x35952,x35951),x35953),x35954)),f306(f306(f146(x35952,x35951),x35953),f306(f161(x35952),x35954))) % 187.68/187.63 [3596]E(f306(f306(f146(x35961,x35962),x35963),f306(f163(x35961),x35964)),f306(f163(x35962),f306(f306(f146(x35961,x35962),x35963),x35964))) % 187.68/187.63 [3608]E(f306(f306(f165(x36081),f306(a119,x36082)),f306(f306(f143(x36081),x36083),x36084)),f306(f306(f143(x36081),x36083),f306(f306(f165(x36081),x36082),x36084))) % 187.68/187.63 [3612]E(f306(f164(x36121),f306(f306(f146(x36122,x36121),x36123),x36124)),f306(f285(x36122,x36121,x36123),f306(f164(x36122),x36124))) % 187.68/187.63 [3663]E(f17(x36631,x36632,x36633,f306(a3,f306(a119,f306(a19,x36634)))),f306(x36633,x36634)) % 187.68/187.63 [3666]E(f306(f306(f122(x36661),f306(f128(x36661,x36662),x36663)),f306(f128(x36661,x36662),x36664)),f306(f128(x36661,x36662),f306(f306(f122(x36661),x36663),x36664))) % 187.68/187.63 [3679]E(f144(x36791,f306(f306(f146(x36792,x36791),x36793),f144(x36792,x36794))),f144(x36791,f306(f306(f146(x36792,x36791),x36793),x36794))) % 187.68/187.63 [3694]E(f306(f261(x36941,x36941),f306(f306(f262(x36942,x36941),x36943),x36944)),f306(f306(f262(x36942,x36941),f306(f261(x36942,x36942),x36943)),x36944)) % 187.68/187.63 [3704]E(f306(f306(f263(x37041,x37042,x37043),x37044),f185(f872(f871(x37042,x37043),a859))),f185(f872(f871(x37041,x37043),a859))) % 187.68/187.63 [3705]E(f306(f306(f165(x37051),f306(f306(f22(a865),x37052),x37053)),f306(f306(f130(x37051),x37053),x37054)),f306(f306(f130(x37051),x37053),f306(f306(f165(x37051),x37052),x37054))) % 187.68/187.63 [3750]E(f42(f872(x37501,a859),f306(f285(x37502,f872(x37501,a859),x37503),x37504)),f306(f306(f44(x37502,f872(x37501,a859)),x37504),x37503)) % 187.68/187.63 [3751]E(f41(f872(x37511,a859),f306(f285(x37512,f872(x37511,a859),x37513),x37514)),f306(f306(f43(x37512,f872(x37511,a859)),x37514),x37513)) % 187.68/187.63 [3752]E(f306(f186(f866(f871(x37521,x37522))),f306(f306(f173(x37521,x37522),x37523),x37524)),f306(f306(f225(a865),f306(f186(f866(x37521)),x37523)),f306(f186(f866(x37522)),x37524))) % 187.68/187.63 [3754]E(f306(f286(x37541,x37542,x37543),f306(f80(f872(x37542,a859)),x37544)),f306(f80(f872(x37541,a859)),f306(f286(x37541,x37542,x37543),x37544))) % 187.68/187.63 [3784]E(f306(f179(x37841,x37842,x37843,f185(f872(x37841,a859))),x37844),f188(x37842)) % 187.68/187.63 [3804]E(f306(f286(x38041,x38042,x38043),f306(f228(x38042),x38044)),f306(f228(x38041),f306(f306(f8(x38042,a859,x38041),x38044),x38043))) % 187.68/187.63 [3821]E(f306(f306(f157(x38211),f306(f306(f122(x38211),x38212),f306(f306(f143(x38211),x38213),x38214))),f306(f186(f866(x38211)),x38212)),x38213) % 187.68/187.63 [3826]E(f306(f179(x38261,x38262,f306(f16(f869(x38262),x38261),f188(x38262)),x38263),x38264),f188(x38262)) % 187.68/187.63 [3846]E(f306(f285(x38461,x38462,x38463),f306(f286(x38461,x38462,x38463),x38464)),f306(f306(f109(f872(x38462,a859)),x38464),f306(f285(x38461,x38462,x38463),f231(f872(x38461,a859))))) % 187.68/187.63 [3864]P1(f306(f306(f308(x38641),f306(x38642,x38643)),f306(f285(x38644,x38641,x38642),f231(f872(x38644,a859))))) % 187.68/187.63 [3876]E(f306(f306(f243(x38761,x38762),f306(f164(x38761),x38763)),f306(f16(f872(x38762,a859),x38761),f306(f164(x38762),x38764))),f306(f164(f871(x38761,x38762)),f61(x38761,x38762,x38763,x38764))) % 187.68/187.63 [3890]E(f147(x38901,x38902,f306(f306(f143(x38901),x38903),x38904)),f306(f306(f81(a865),f306(f306(f81(a865),f306(x38902,x38903)),f147(x38901,x38902,x38904))),f306(a119,f2(a865)))) % 187.68/187.63 [3904]E(f182(f866(x39041),f306(f306(f143(x39041),x39042),x39043),f306(f306(f7(a865,f866(x39041),f866(x39041)),f130(x39041)),x39043),x39044),f306(f306(f130(x39041),x39044),f306(f306(f143(x39041),x39042),x39043))) % 187.68/187.63 [3905]P28(x39051,f871(x39052,x39051),f310(x39053,x39054,x39052,x39051),f306(f306(f43(x39052,f872(x39051,a859)),x39054),x39053)) % 187.68/187.63 [3914]E(f306(f306(f22(f872(x39141,a859)),f306(f306(f22(f872(x39141,a859)),x39142),x39143)),f306(f306(f284(x39141),x39144),f185(f872(x39141,a859)))),f306(f306(f22(f872(x39141,a859)),x39142),f306(f306(f284(x39141),x39144),x39143))) % 187.68/187.63 [3925]E(f306(f306(f180(f872(x39251,x39252),f872(x39251,x39252)),x39253),f74(x39252,x39252,x39251,x39254)),f74(x39252,x39252,x39251,f306(f306(f180(x39252,x39252),x39253),x39254))) % 187.68/187.63 [3999]E(f306(f306(f306(f180(f866(x39991),f866(x39991)),x39992),f160(x39991)),f306(f306(f306(f180(f866(x39991),f866(x39991)),x39993),f160(x39991)),x39994)),f306(f306(f306(f180(f866(x39991),f866(x39991)),f306(f306(f81(a865),x39992),x39993)),f160(x39991)),x39994)) % 187.68/187.63 [4085]P1(f306(f306(f220(f872(x40851,a859)),f306(f164(x40851),f306(f306(f151(x40851,x40852),x40853),x40854))),f306(f306(f284(x40851),x40854),f306(f164(x40851),x40852)))) % 187.68/187.63 [4120]E(f306(f306(f43(f872(x41201,a859),f872(f871(x41201,x41202),a859)),x41203),f306(f306(f7(f872(x41201,a859),f872(x41201,f872(x41202,a859)),f872(f871(x41201,x41202),a859)),f243(x41201,x41202)),x41204)),f306(f306(f243(x41201,x41202),f41(f872(x41201,a859),x41203)),x41204)) % 187.68/187.63 [4177]P1(f306(f68(x41771,x41772,x41773,x41774,f185(f872(x41771,a859))),x41774)) % 187.68/187.63 [4219]E(f306(f306(f43(x42191,f872(x42192,a859)),x42193),f306(f306(f7(x42191,f872(x42192,a859),f872(x42192,a859)),f306(f306(f8(x42192,f872(f872(x42192,a859),f872(x42192,a859)),x42191),f284(x42192)),x42194)),f185(f872(x42192,a859)))),f306(f285(x42191,x42192,x42194),x42193)) % 187.68/187.63 [4226]P1(f306(f306(f220(f872(x42261,a859)),f306(f232(x42262,x42261),f306(f306(f109(f872(f871(x42262,x42261),a859)),x42263),x42264))),f306(f306(f109(f872(x42261,a859)),f306(f232(x42262,x42261),x42263)),f306(f232(x42262,x42261),x42264)))) % 187.68/187.63 [4227]P1(f306(f306(f220(f872(x42271,a859)),f306(f234(x42271,x42272),f306(f306(f109(f872(f871(x42271,x42272),a859)),x42273),x42274))),f306(f306(f109(f872(x42271,a859)),f306(f234(x42271,x42272),x42273)),f306(f234(x42271,x42272),x42274)))) % 187.68/187.63 [4289]P1(f306(f306(f220(f872(f871(x42891,x42892),a859)),f306(f285(x42892,f871(x42891,x42892),f310(x42893,x42894,x42891,x42892)),f306(f306(f43(x42891,f872(x42892,a859)),x42894),x42893))),f306(f306(f243(x42891,x42892),x42894),x42893))) % 187.68/187.63 [4329]E(f86(f871(x43291,x43292),f306(f245(x43291,x43292,a859),f306(f306(f7(x43291,f872(x43292,a859),f872(x43292,a859)),f306(f306(f8(f872(a859,a859),f872(f872(x43292,a859),f872(x43292,a859)),x43291),f8(a859,a859,x43292)),f306(f306(f8(a859,f872(a859,a859),x43291),a304),f306(a303,x43293)))),f306(a303,x43294)))),f306(f306(f236(x43291,x43292),x43293),x43294)) % 187.68/187.63 [4330]E(f91(f871(x43301,x43302),f306(f245(x43301,x43302,a859),f306(f306(f7(x43301,f872(x43302,a859),f872(x43302,a859)),f306(f306(f8(f872(a859,a859),f872(f872(x43302,a859),f872(x43302,a859)),x43301),f8(a859,a859,x43302)),f306(f306(f8(a859,f872(a859,a859),x43301),a304),f306(a303,x43303)))),f306(a303,x43304)))),f306(f306(f236(x43301,x43302),x43303),x43304)) % 187.68/187.63 [4397]E(f306(f306(f245(f866(x43971),f866(x43971),f871(f866(x43971),f866(x43971))),f306(f306(f18(f866(x43971),f872(f866(x43971),f871(f866(x43971),f866(x43971))),f872(f866(x43971),f871(f866(x43971),f866(x43971)))),f306(f306(f8(f872(f866(x43971),f872(f871(f866(x43971),f866(x43971)),f871(f866(x43971),f866(x43971)))),f872(f872(f866(x43971),f871(f866(x43971),f866(x43971))),f872(f866(x43971),f871(f866(x43971),f866(x43971)))),f866(x43971)),f18(f866(x43971),f871(f866(x43971),f866(x43971)),f871(f866(x43971),f866(x43971)))),f306(f306(f8(f872(f866(x43971),f871(f866(x43971),f866(x43971))),f872(f866(x43971),f872(f871(f866(x43971),f866(x43971)),f871(f866(x43971),f866(x43971)))),f866(x43971)),f306(f8(f871(f866(x43971),f866(x43971)),f872(f871(f866(x43971),f866(x43971)),f871(f866(x43971),f866(x43971))),f866(x43971)),f306(f101(f871(f866(x43971),f866(x43971))),f306(x43972,x43973)))),f306(f306(f8(f866(x43971),f872(f866(x43971),f871(f866(x43971),f866(x43971))),f866(x43971)),f236(f866(x43971),f866(x43971))),f306(f143(x43971),x43973))))),f306(f306(f7(f866(x43971),f872(f866(x43971),f866(x43971)),f872(f866(x43971),f871(f866(x43971),f866(x43971)))),f306(f306(f8(f872(f866(x43971),f871(f866(x43971),f866(x43971))),f872(f872(f866(x43971),f866(x43971)),f872(f866(x43971),f871(f866(x43971),f866(x43971)))),f866(x43971)),f8(f866(x43971),f871(f866(x43971),f866(x43971)),f866(x43971))),f236(f866(x43971),f866(x43971)))),f306(f143(x43971),x43973)))),f159(x43971,x43972,x43974)),f159(x43971,x43972,f306(f306(f143(x43971),x43973),x43974))) % 187.68/187.63 [4403]E(f306(f134(f872(x44031,f869(x44032)),f871(x44031,x44032),f306(f7(f871(x44031,x44032),f872(x44031,f869(x44032)),f872(x44031,f869(x44032))),f306(f245(x44031,x44032,f872(f872(x44031,f869(x44032)),f872(x44031,f869(x44032)))),f306(f306(f7(x44031,f872(x44032,f869(x44032)),f872(x44032,f872(f872(x44031,f869(x44032)),f872(x44031,f869(x44032))))),f306(f306(f8(f872(f869(x44032),f872(f872(x44031,f869(x44032)),f872(x44031,f869(x44032)))),f872(f872(x44032,f869(x44032)),f872(x44032,f872(f872(x44031,f869(x44032)),f872(x44031,f869(x44032))))),x44031),f8(f869(x44032),f872(f872(x44031,f869(x44032)),f872(x44031,f869(x44032))),x44032)),f306(f306(f8(f872(f872(x44031,f869(x44032)),f872(f869(x44032),f872(x44031,f869(x44032)))),f872(f869(x44032),f872(f872(x44031,f869(x44032)),f872(x44031,f869(x44032)))),x44031),f7(f872(x44031,f869(x44032)),f869(x44032),f872(x44031,f869(x44032)))),f306(f7(f872(x44031,f869(x44032)),x44031,f872(f869(x44032),f872(x44031,f869(x44032)))),f73(x44031,f869(x44032)))))),f214(x44032)))),x44033),f306(f161(f871(x44031,x44032)),x44034)),f176(x44031,x44032,x44033,f306(f169(x44031,x44032),x44034))) % 187.68/187.63 [3526]E(f306(f186(f864(x35261)),f306(f306(f306(f93(x35261),x35262),x35263),x35264)),f2(a865)) % 187.68/187.63 [3642]E(f306(f306(f165(x36421),x36422),f306(f306(f165(x36421),x36423),x36424)),f306(f306(f165(x36421),f306(f306(f225(a865),x36422),x36423)),x36424)) % 187.68/187.63 [3643]E(f306(f306(f130(x36431),x36432),f306(f306(f130(x36431),x36433),x36434)),f306(f306(f130(x36431),f306(f306(f81(a865),x36432),x36433)),x36434)) % 187.68/187.63 [3655]E(f306(f306(f122(x36551),f306(f306(f143(x36551),x36552),x36553)),x36554),f306(f306(f143(x36551),x36552),f306(f306(f122(x36551),x36553),x36554))) % 187.68/187.63 [3656]E(f306(f306(f122(x36561),f306(f306(f122(x36561),x36562),x36563)),x36564),f306(f306(f122(x36561),x36562),f306(f306(f122(x36561),x36563),x36564))) % 187.68/187.63 [3734]E(f306(f306(f157(x37341),f306(f306(f143(x37341),x37342),x37343)),x37344),f182(x37341,x37342,f306(f157(x37341),x37343),x37344)) % 187.68/187.63 [3743]E(f306(f306(f180(x37431,x37431),x37432),f306(f306(f180(x37431,x37431),x37433),x37434)),f306(f306(f180(x37431,x37431),f306(f306(f82(a865),x37433),x37432)),x37434)) % 187.68/187.63 [3772]E(f306(f306(f108(f872(x37721,a859)),x37722),f306(f306(f284(x37721),x37723),x37724)),f306(f306(f284(x37721),x37723),f306(f306(f108(f872(x37721,a859)),x37722),x37724))) % 187.68/187.63 [3787]E(f306(f306(f306(f180(x37871,x37871),x37872),x37873),f306(x37873,x37874)),f306(x37873,f306(f306(f306(f180(x37871,x37871),x37872),x37873),x37874))) % 187.68/187.63 [3794]E(f306(f306(f263(x37941,x37942,x37943),f185(f872(f871(x37941,x37942),a859))),x37944),f185(f872(f871(x37941,x37943),a859))) % 187.68/187.63 [3810]E(f306(f306(f108(f872(x38101,a859)),f306(f306(f284(x38101),x38102),x38103)),x38104),f306(f306(f284(x38101),x38102),f306(f306(f108(f872(x38101,a859)),x38103),x38104))) % 187.68/187.63 [3828]E(f176(x38281,x38282,f306(f169(x38281,x38282),x38283),f306(f169(x38281,x38282),x38284)),f306(f169(x38281,x38282),f306(f306(f122(f871(x38281,x38282)),x38284),x38283))) % 187.68/187.63 [3829]E(f306(f39(f871(x38291,x38292)),f306(f306(f243(x38291,x38292),x38293),f306(f16(f872(x38292,a859),x38291),x38294))),f306(f306(f82(a865),f306(f39(x38291),x38293)),f306(f39(x38292),x38294))) % 187.68/187.63 [3835]E(f306(f306(f109(f872(x38351,a859)),f306(f306(f284(x38351),x38352),x38353)),f306(f306(f284(x38351),x38352),x38354)),f306(f306(f284(x38351),x38352),f306(f306(f109(f872(x38351,a859)),x38353),x38354))) % 187.68/187.63 [3850]E(f306(f306(f108(f872(x38501,a859)),x38502),f306(f306(f108(f872(x38501,a859)),x38503),x38504)),f306(f306(f108(f872(x38501,a859)),x38503),f306(f306(f108(f872(x38501,a859)),x38502),x38504))) % 187.68/187.63 [3851]E(f306(f306(f109(f872(x38511,a859)),x38512),f306(f306(f109(f872(x38511,a859)),x38513),x38514)),f306(f306(f109(f872(x38511,a859)),x38513),f306(f306(f109(f872(x38511,a859)),x38512),x38514))) % 187.68/187.63 [3860]E(f66(x38601,x38602,f306(f306(f8(x38602,f872(x38602,x38602),x38601),x38603),x38604)),f306(f67(x38602,x38601,x38603),x38604)) % 187.68/187.63 [3869]E(f171(x38691,f306(f306(f146(f866(x38692),f866(x38691)),f306(f146(x38692,x38691),x38693)),x38694)),f306(f306(f146(f866(x38692),f866(x38691)),f306(f146(x38692,x38691),x38693)),f171(x38692,x38694))) % 187.68/187.63 [3886]E(f306(f134(f866(x38861),f866(x38861),f122(x38861),f120(x38861)),f306(f306(f146(x38862,f866(x38861)),x38863),x38864)),f156(x38862,x38861,x38863,x38864)) % 187.68/187.63 [3889]E(f179(x38891,x38892,x38893,f306(f80(f872(x38891,a859)),f306(f306(f284(x38891),x38894),f185(f872(x38891,a859))))),f306(f306(f306(f73(x38891,f869(x38892)),x38893),x38894),f188(x38892))) % 187.68/187.63 [3930]E(f306(f306(f306(f73(x39301,f869(x39302)),f306(f169(x39301,x39302),x39303)),f306(f235(x39301,x39302),x39304)),f306(f214(x39302),f306(f244(x39301,x39302),x39304))),f306(f169(x39301,x39302),f306(f306(f143(f871(x39301,x39302)),x39304),x39303))) % 187.68/187.63 [3947]E(f306(f74(x39471,x39471,x39471,f306(f306(f180(x39471,x39471),x39472),x39473)),f306(f306(f180(x39471,x39471),x39474),x39473)),f306(f306(f180(x39471,x39471),f306(f306(f81(a865),x39472),x39474)),x39473)) % 187.68/187.63 [3968]E(f306(f306(f109(f872(x39681,a859)),f306(f306(f22(f872(x39681,a859)),x39682),x39683)),f306(f306(f22(f872(x39681,a859)),x39682),x39684)),f306(f306(f22(f872(x39681,a859)),x39682),f306(f306(f108(f872(x39681,a859)),x39683),x39684))) % 187.68/187.63 [3969]E(f306(f306(f108(f872(x39691,a859)),f306(f306(f22(f872(x39691,a859)),x39692),x39693)),f306(f306(f22(f872(x39691,a859)),x39692),x39694)),f306(f306(f22(f872(x39691,a859)),x39692),f306(f306(f109(f872(x39691,a859)),x39693),x39694))) % 187.68/187.63 [3970]E(f306(f306(f109(f872(x39701,a859)),f306(f306(f108(f872(x39701,a859)),x39702),x39703)),f306(f306(f108(f872(x39701,a859)),x39702),x39704)),f306(f306(f108(f872(x39701,a859)),x39702),f306(f306(f109(f872(x39701,a859)),x39703),x39704))) % 187.68/187.63 [3971]E(f306(f306(f22(f872(x39711,a859)),f306(f306(f109(f872(x39711,a859)),x39712),x39713)),f306(f306(f109(f872(x39711,a859)),x39712),x39714)),f306(f306(f109(f872(x39711,a859)),x39712),f306(f306(f22(f872(x39711,a859)),x39713),x39714))) % 187.68/187.63 [3972]E(f306(f306(f108(f872(x39721,a859)),f306(f306(f109(f872(x39721,a859)),x39722),x39723)),f306(f306(f109(f872(x39721,a859)),x39722),x39724)),f306(f306(f109(f872(x39721,a859)),x39722),f306(f306(f108(f872(x39721,a859)),x39723),x39724))) % 187.68/187.63 [3978]E(f306(f39(f871(x39781,x39782)),f306(f306(f243(x39781,x39782),f306(f306(f284(x39781),x39783),f185(f872(x39781,a859)))),f306(f16(f872(x39782,a859),x39781),x39784))),f306(f39(x39782),x39784)) % 187.68/187.63 [4014]E(f306(f306(f44(x40141,f872(x40142,a859)),x40143),f306(f306(f8(f872(x40142,a859),f872(x40142,a859),x40141),f80(f872(x40142,a859))),x40144)),f306(f80(f872(x40142,a859)),f306(f306(f43(x40141,f872(x40142,a859)),x40143),x40144))) % 187.68/187.63 [4015]E(f306(f306(f43(x40151,f872(x40152,a859)),x40153),f306(f306(f8(f872(x40152,a859),f872(x40152,a859),x40151),f80(f872(x40152,a859))),x40154)),f306(f80(f872(x40152,a859)),f306(f306(f44(x40151,f872(x40152,a859)),x40153),x40154))) % 187.68/187.63 [4029]E(f306(f306(f263(x40291,x40291,x40291),f306(f306(f180(f871(x40291,x40291),a859),x40292),x40293)),f306(f306(f180(f871(x40291,x40291),a859),x40294),x40293)),f306(f306(f180(f871(x40291,x40291),a859),f306(f306(f81(a865),x40292),x40294)),x40293)) % 187.68/187.63 [4060]E(f306(f306(f44(x40601,f872(f872(x40602,a859),a859)),x40603),f306(f306(f8(f872(x40602,a859),f872(f872(x40602,a859),a859),x40601),f283(x40602)),x40604)),f306(f283(x40602),f306(f306(f44(x40601,f872(x40602,a859)),x40603),x40604))) % 187.68/187.63 [4089]E(f306(f306(f43(f872(x40891,a859),f872(x40892,a859)),x40893),f306(f306(f7(f872(x40891,a859),f872(x40891,f872(x40892,a859)),f872(x40892,a859)),f43(x40891,f872(x40892,a859))),x40894)),f306(f306(f43(x40891,f872(x40892,a859)),f41(f872(x40891,a859),x40893)),x40894)) % 187.68/187.63 [4090]E(f306(f306(f44(f872(x40901,a859),f872(x40902,a859)),x40903),f306(f306(f7(f872(x40901,a859),f872(x40901,f872(x40902,a859)),f872(x40902,a859)),f44(x40901,f872(x40902,a859))),x40904)),f306(f306(f44(x40901,f872(x40902,a859)),f41(f872(x40901,a859),x40903)),x40904)) % 187.68/187.63 [4095]E(f306(f306(f146(x40951,x40952),x40953),f306(f134(f866(x40951),f866(x40951),f122(x40951),f120(x40951)),x40954)),f306(f134(f866(x40952),f866(x40952),f122(x40952),f120(x40952)),f306(f306(f146(f866(x40951),f866(x40952)),f306(f146(x40951,x40952),x40953)),x40954))) % 187.68/187.63 [4098]E(f182(f866(x40981),f120(x40981),f306(f306(f8(f866(x40981),f866(x40981),a865),f306(f143(x40981),x40982)),f306(f306(f7(a865,f866(x40981),f866(x40981)),f165(x40981)),x40983)),x40984),f306(f306(f165(x40981),x40984),f306(f306(f143(x40981),x40982),x40983))) % 187.68/187.63 [4140]P1(f306(f306(f220(f872(x41401,a859)),f306(f285(x41402,x41401,x41403),f306(f286(x41402,x41401,x41403),x41404))),x41404)) % 187.68/187.63 [4143]E(f306(f285(f871(x41431,x41432),f871(x41432,x41431),f306(f245(x41431,x41432,f871(x41432,x41431)),f306(f7(x41432,x41431,f871(x41432,x41431)),f236(x41432,x41431)))),f306(f306(f243(x41431,x41432),x41433),f306(f16(f872(x41432,a859),x41431),x41434))),f306(f306(f243(x41432,x41431),x41434),f306(f16(f872(x41431,a859),x41432),x41433))) % 187.68/187.63 [4152]E(f306(f306(f43(x41521,f872(x41522,a859)),x41523),f306(f306(f8(f872(x41521,a859),f872(x41522,a859),x41521),f260(x41521,x41522,x41524)),f306(f306(f7(x41521,f872(x41521,a859),f872(x41521,a859)),f284(x41521)),f185(f872(x41521,a859))))),f306(f260(x41521,x41522,x41524),x41523)) % 187.68/187.63 [4153]E(f306(f306(f43(x41531,f872(x41532,a859)),x41533),f306(f306(f8(f872(x41531,a859),f872(x41532,a859),x41531),f286(x41532,x41531,x41534)),f306(f306(f7(x41531,f872(x41531,a859),f872(x41531,a859)),f284(x41531)),f185(f872(x41531,a859))))),f306(f286(x41532,x41531,x41534),x41533)) % 187.68/187.63 [4241]E(f306(f306(f109(f872(x42411,a859)),f306(f306(f109(f872(x42411,a859)),f306(f306(f108(f872(x42411,a859)),x42412),x42413)),f306(f306(f108(f872(x42411,a859)),x42413),x42414))),f306(f306(f108(f872(x42411,a859)),x42414),x42412)),f306(f306(f108(f872(x42411,a859)),f306(f306(f108(f872(x42411,a859)),f306(f306(f109(f872(x42411,a859)),x42412),x42413)),f306(f306(f109(f872(x42411,a859)),x42413),x42414))),f306(f306(f109(f872(x42411,a859)),x42414),x42412))) % 187.68/187.63 [4302]E(f306(f134(f866(x43021),f866(x43021),f122(x43021),f120(x43021)),f306(f306(f146(x43022,f866(x43021)),f306(f306(f7(x43022,f866(x43021),f866(x43021)),f306(f306(f8(x43021,f872(f866(x43021),f866(x43021)),x43022),f143(x43021)),x43023)),f120(x43021))),x43024)),f306(f306(f146(x43022,x43021),x43023),x43024)) % 187.68/187.63 [4313]E(f306(f306(f87(a1,x43131),f306(f111(a1),f306(f306(f81(a1),x43132),a104))),f306(f306(f18(a1,x43131,x43131),f306(f306(f7(a1,x43131,f872(x43131,x43131)),f306(f306(f8(a859,f872(x43131,f872(x43131,x43131)),a1),f101(x43131)),a190)),x43133)),f306(f306(f8(a865,x43131,a1),x43134),a112))),f182(x43131,x43133,x43134,f306(f111(a865),x43132))) % 187.68/187.63 [4520]~P1(f306(f306(f185(f872(x45201,f872(x45202,a859))),x45203),x45204)) % 187.68/187.63 [3797]E(f306(f306(f157(x37971),f306(f306(f122(x37971),x37972),x37973)),f306(f306(f81(a865),f306(f186(f866(x37971)),x37972)),x37974)),f306(f306(f157(x37971),x37973),x37974)) % 187.68/187.63 [3803]E(f306(f306(f130(x38031),x38032),f306(f306(f165(x38031),f306(f306(f81(a865),x38033),x38032)),x38034)),f306(f306(f165(x38031),x38033),f306(f306(f130(x38031),x38032),x38034))) % 187.68/187.63 [3902]E(f306(f306(f108(f872(x39021,a859)),f306(f232(x39022,x39021),x39023)),f306(f232(x39022,x39021),x39024)),f306(f232(x39022,x39021),f306(f306(f108(f872(f871(x39022,x39021),a859)),x39023),x39024))) % 187.68/187.63 [3903]E(f306(f306(f108(f872(x39031,a859)),f306(f234(x39031,x39032),x39033)),f306(f234(x39031,x39032),x39034)),f306(f234(x39031,x39032),f306(f306(f108(f872(f871(x39031,x39032),a859)),x39033),x39034))) % 187.68/187.63 [3908]E(f306(f306(f22(f872(x39081,a859)),f306(f306(f109(f872(x39081,a859)),x39082),x39083)),x39084),f306(f306(f109(f872(x39081,a859)),x39082),f306(f306(f22(f872(x39081,a859)),x39083),x39084))) % 187.68/187.63 [3909]E(f306(f306(f108(f872(x39091,a859)),f306(f306(f108(f872(x39091,a859)),x39092),x39093)),x39094),f306(f306(f108(f872(x39091,a859)),x39092),f306(f306(f108(f872(x39091,a859)),x39093),x39094))) % 187.68/187.63 [3910]E(f306(f306(f109(f872(x39101,a859)),f306(f306(f109(f872(x39101,a859)),x39102),x39103)),x39104),f306(f306(f109(f872(x39101,a859)),x39102),f306(f306(f109(f872(x39101,a859)),x39103),x39104))) % 187.68/187.63 [3949]E(f306(f306(f108(f872(f871(x39491,x39492),a859)),f306(f261(x39492,x39491),x39493)),f306(f261(x39492,x39491),x39494)),f306(f261(x39492,x39491),f306(f306(f108(f872(f871(x39492,x39491),a859)),x39493),x39494))) % 187.68/187.63 [3950]E(f306(f306(f109(f872(f871(x39501,x39502),a859)),f306(f261(x39502,x39501),x39503)),f306(f261(x39502,x39501),x39504)),f306(f261(x39502,x39501),f306(f306(f109(f872(f871(x39502,x39501),a859)),x39503),x39504))) % 187.68/187.63 [4018]E(f306(f306(f108(f872(x40181,a859)),f306(f306(f22(f872(x40181,a859)),x40182),x40183)),f306(f306(f22(f872(x40181,a859)),x40184),x40183)),f306(f306(f22(f872(x40181,a859)),f306(f306(f108(f872(x40181,a859)),x40182),x40184)),x40183)) % 187.68/187.63 [4019]E(f306(f306(f109(f872(x40191,a859)),f306(f306(f108(f872(x40191,a859)),x40192),x40193)),f306(f306(f108(f872(x40191,a859)),x40194),x40193)),f306(f306(f108(f872(x40191,a859)),f306(f306(f109(f872(x40191,a859)),x40192),x40194)),x40193)) % 187.68/187.63 [4020]E(f306(f306(f22(f872(x40201,a859)),f306(f306(f109(f872(x40201,a859)),x40202),x40203)),f306(f306(f109(f872(x40201,a859)),x40204),x40203)),f306(f306(f109(f872(x40201,a859)),f306(f306(f22(f872(x40201,a859)),x40202),x40204)),x40203)) % 187.68/187.63 [4021]E(f306(f306(f108(f872(x40211,a859)),f306(f306(f109(f872(x40211,a859)),x40212),x40213)),f306(f306(f109(f872(x40211,a859)),x40214),x40213)),f306(f306(f109(f872(x40211,a859)),f306(f306(f108(f872(x40211,a859)),x40212),x40214)),x40213)) % 187.68/187.63 [4022]E(f306(f306(f22(f872(x40221,a859)),f306(f306(f109(f872(x40221,a859)),x40222),x40223)),f306(f306(f109(f872(x40221,a859)),x40224),x40223)),f306(f306(f22(f872(x40221,a859)),f306(f306(f109(f872(x40221,a859)),x40222),x40223)),x40224)) % 187.68/187.63 [4032]E(f306(f306(f22(f872(x40321,a859)),f306(f306(f22(f872(x40321,a859)),x40322),f306(f306(f284(x40321),x40323),f185(f872(x40321,a859))))),x40324),f306(f306(f22(f872(x40321,a859)),x40322),f306(f306(f284(x40321),x40323),x40324))) % 187.68/187.63 [4086]E(f306(f306(f108(f872(x40861,a859)),f306(f306(f284(x40861),x40862),f306(f306(f284(x40861),x40863),f185(f872(x40861,a859))))),f306(f259(x40861),x40864)),f306(f259(x40861),f306(f306(f284(f871(x40861,x40861)),f306(f306(f236(x40861,x40861),x40862),x40863)),x40864))) % 187.68/187.63 [4115]E(f306(f306(f43(a865,f872(x41151,a859)),f306(f275(a865),x41152)),f306(f306(f8(a865,f872(x41151,a859),a865),x41153),f306(f306(f7(a865,a865,a865),f81(a865)),x41154))),f306(f306(f43(a865,f872(x41151,a859)),f277(a865,x41154,f306(f306(f81(a865),x41152),x41154))),x41153)) % 187.68/187.63 [4116]E(f167(x41161,f306(f260(x41161,x41161,x41162),f306(f306(f284(x41161),x41163),f185(f872(x41161,a859)))),f306(f260(f866(x41161),f866(x41161),f150(x41161,x41162)),f306(f306(f284(f866(x41161)),x41164),f185(f872(f866(x41161),a859))))),f306(f260(f866(x41161),f866(x41161),f150(x41161,x41162)),f306(f306(f284(f866(x41161)),f306(f306(f143(x41161),x41163),x41164)),f185(f872(f866(x41161),a859))))) % 187.68/187.63 [4175]E(f306(f169(x41751,x41752),f306(f306(f146(x41751,f871(x41751,x41752)),f306(f306(f18(x41751,x41752,f871(x41751,x41752)),f236(x41751,x41752)),x41753)),x41754)),f179(x41751,x41752,f306(f74(x41752,f869(x41752),x41751,f214(x41752)),x41753),f306(f164(x41751),x41754))) % 187.68/187.63 [4180]E(f306(f228(x41801),f306(f306(f7(x41801,f872(x41802,a859),a859),f306(f306(f8(x41802,f872(f872(x41802,a859),a859),x41801),f308(x41802)),x41803)),x41804)),f306(f286(x41801,x41802,x41803),x41804)) % 187.68/187.63 [4274]E(f306(f228(x42741),f306(f306(f7(x42741,f872(f871(x42742,x42741),a859),a859),f306(f306(f8(f871(x42742,x42741),f872(f872(f871(x42742,x42741),a859),a859),x42741),f308(f871(x42742,x42741))),f306(f236(x42742,x42741),x42743))),x42744)),f306(f260(x42742,x42741,x42744),f306(f306(f284(x42742),x42743),f185(f872(x42742,a859))))) % 187.68/187.63 [4288]E(f306(f306(f146(f871(x42881,a865),x42881),f235(x42881,a865)),f306(f128(f871(x42881,a865),f306(f306(f8(a865,a859,f871(x42881,a865)),x42882),f306(f306(f8(a865,a865,f871(x42881,a865)),a119),f244(x42881,a865)))),f306(f306(f173(x42881,a865),x42883),x42884))),f306(f306(f146(f871(x42881,a865),x42881),f235(x42881,a865)),f306(f128(f871(x42881,a865),f306(f306(f8(a865,a859,f871(x42881,a865)),x42882),f244(x42881,a865))),f306(f306(f173(x42881,a865),x42883),f306(f306(f146(a865,a865),a119),x42884))))) % 187.68/187.63 [4295]P1(f306(f306(f220(f872(f872(x42951,a859),a859)),f306(f306(f43(x42952,f872(f872(x42951,a859),a859)),x42953),f306(f306(f8(f872(x42951,a859),f872(f872(x42951,a859),a859),x42952),f283(x42951)),x42954))),f306(f283(x42951),f306(f306(f43(x42952,f872(x42951,a859)),x42953),x42954)))) % 187.68/187.63 [4337]E(f306(f306(f87(a1,x43371),f306(f111(a1),f306(f306(f81(a1),x43372),a104))),f306(f306(f18(a1,x43371,x43371),f306(f306(f7(a1,x43371,f872(x43371,x43371)),f306(f306(f8(a859,f872(x43371,f872(x43371,x43371)),a1),f101(x43371)),a190)),x43373)),f306(f306(f18(a1,x43371,x43371),f306(f306(f8(a865,f872(x43371,x43371),a1),x43374),a112)),f306(f306(f8(a865,x43371,a1),f181(x43371,x43373,x43374)),a112)))),f306(f181(x43371,x43373,x43374),f306(f111(a865),x43372))) % 187.68/187.63 [4340]E(f306(f306(f146(x43401,x43402),f306(f74(f869(x43402),x43402,x43401,f218(x43402)),x43403)),f306(f128(x43401,f306(f306(f8(a859,a859,x43401),a301),f306(f306(f7(x43401,f869(x43402),a859),f306(f306(f8(f869(x43402),f872(f869(x43402),a859),x43401),a303),x43403)),f188(x43402)))),x43404)),f155(x43401,x43402,x43403,x43404)) % 187.68/187.63 [4363]E(f306(f228(f871(x43631,x43632)),f306(f245(x43631,x43632,a859),f306(f306(f7(x43631,f872(x43632,a859),f872(x43632,a859)),f306(f306(f8(f872(a859,a859),f872(f872(x43632,a859),f872(x43632,a859)),x43631),f8(a859,a859,x43632)),f306(f306(f8(a859,f872(a859,a859),x43631),a304),f306(f306(f7(x43631,f872(x43631,a859),a859),f308(x43631)),x43633)))),f306(f306(f7(x43632,f872(x43632,a859),a859),f308(x43632)),x43634)))),f208(x43631,x43632,x43633,x43634)) % 187.68/187.63 [4392]E(f306(f306(f43(x43921,f872(f871(x43921,x43922),a859)),x43923),f306(f306(f18(x43921,f872(x43922,f872(f871(x43921,x43922),a859)),f872(f871(x43921,x43922),a859)),f306(f306(f8(f872(x43922,a859),f872(f872(x43922,f872(f871(x43921,x43922),a859)),f872(f871(x43921,x43922),a859)),x43921),f43(x43922,f872(f871(x43921,x43922),a859))),x43924)),f306(f306(f7(x43921,f872(f871(x43921,x43922),a859),f872(x43922,f872(f871(x43921,x43922),a859))),f306(f306(f8(f872(x43922,f872(f872(f871(x43921,x43922),a859),f872(f871(x43921,x43922),a859))),f872(f872(f871(x43921,x43922),a859),f872(x43922,f872(f871(x43921,x43922),a859))),x43921),f7(x43922,f872(f871(x43921,x43922),a859),f872(f871(x43921,x43922),a859))),f306(f306(f8(f872(x43922,f871(x43921,x43922)),f872(x43922,f872(f872(f871(x43921,x43922),a859),f872(f871(x43921,x43922),a859))),x43921),f306(f8(f871(x43921,x43922),f872(f872(f871(x43921,x43922),a859),f872(f871(x43921,x43922),a859)),x43922),f284(f871(x43921,x43922)))),f236(x43921,x43922)))),f185(f872(f871(x43921,x43922),a859))))),f306(f306(f243(x43921,x43922),x43923),x43924)) % 187.68/187.63 [3958]E(f306(f306(f122(x39581),f306(f306(f165(x39581),x39582),x39583)),f306(f306(f165(x39581),f306(f306(f22(a865),x39582),f306(f186(f866(x39581)),x39583))),x39584)),f306(f306(f165(x39581),x39582),f306(f306(f122(x39581),x39583),x39584))) % 187.68/187.63 [3959]E(f306(f306(f122(x39591),f306(f306(f130(x39591),x39592),x39593)),f306(f306(f130(x39591),f306(f306(f22(a865),x39592),f306(f186(f866(x39591)),x39593))),x39594)),f306(f306(f130(x39591),x39592),f306(f306(f122(x39591),x39593),x39594))) % 187.68/187.63 [4008]E(f306(f306(f81(a865),f306(f306(f82(a865),x40081),x40082)),f306(f306(f81(a865),f306(f306(f82(a865),x40083),x40082)),x40084)),f306(f306(f81(a865),f306(f306(f82(a865),f306(f306(f81(a865),x40081),x40083)),x40082)),x40084)) % 187.68/187.63 [4205]P1(f306(f306(f220(f872(x42051,a859)),f306(f306(f22(f872(x42051,a859)),f306(f232(x42052,x42051),x42053)),f306(f232(x42052,x42051),x42054))),f306(f232(x42052,x42051),f306(f306(f22(f872(f871(x42052,x42051),a859)),x42053),x42054)))) % 187.68/187.63 [4206]P1(f306(f306(f220(f872(x42061,a859)),f306(f306(f22(f872(x42061,a859)),f306(f234(x42061,x42062),x42063)),f306(f234(x42061,x42062),x42064))),f306(f234(x42061,x42062),f306(f306(f22(f872(f871(x42061,x42062),a859)),x42063),x42064)))) % 187.68/187.63 [4315]E(f306(f306(f81(a1),f306(a90,f306(f260(f871(a865,a865),f871(a865,a865),a116),f306(f306(f284(f871(a865,a865)),f306(f306(f236(a865,a865),x43151),x43152)),f185(f872(f871(a865,a865),a859)))))),f306(a90,f306(f260(f871(a865,a865),f871(a865,a865),a116),f306(f306(f284(f871(a865,a865)),f306(f306(f236(a865,a865),x43153),x43154)),f185(f872(f871(a865,a865),a859)))))),f306(a90,f306(f260(f871(a865,a865),f871(a865,a865),a116),f306(f306(f284(f871(a865,a865)),f306(f306(f236(a865,a865),f306(f306(f81(a865),x43151),x43153)),f306(f306(f81(a865),x43152),x43154))),f185(f872(f871(a865,a865),a859)))))) % 187.68/187.63 [4358]E(f306(f306(f82(a1),f306(a90,f306(f260(f871(a865,a865),f871(a865,a865),a116),f306(f306(f284(f871(a865,a865)),f306(f306(f236(a865,a865),x43581),x43582)),f185(f872(f871(a865,a865),a859)))))),f306(a90,f306(f260(f871(a865,a865),f871(a865,a865),a116),f306(f306(f284(f871(a865,a865)),f306(f306(f236(a865,a865),x43583),x43584)),f185(f872(f871(a865,a865),a859)))))),f306(a90,f306(f260(f871(a865,a865),f871(a865,a865),a116),f306(f306(f284(f871(a865,a865)),f306(f306(f236(a865,a865),f306(f306(f81(a865),f306(f306(f82(a865),x43581),x43583)),f306(f306(f82(a865),x43582),x43584))),f306(f306(f81(a865),f306(f306(f82(a865),x43581),x43584)),f306(f306(f82(a865),x43582),x43583)))),f185(f872(f871(a865,a865),a859)))))) % 187.68/187.63 [4375]E(f306(f228(x43751),f306(f306(f8(f872(x43752,a859),a859,x43751),f89(x43752)),f306(f306(f8(f872(x43752,a859),f872(x43752,a859),x43751),f306(f18(x43752,a859,a859),f306(f306(f8(a859,f872(a859,a859),x43752),a309),f306(f306(f7(x43752,f872(x43752,a859),a859),f308(x43752)),x43753)))),f306(f306(f7(x43751,f872(x43752,f872(x43751,a859)),f872(x43752,a859)),f306(f306(f8(f872(f872(x43751,a859),a859),f872(f872(x43752,f872(x43751,a859)),f872(x43752,a859)),x43751),f8(f872(x43751,a859),a859,x43752)),f308(x43751))),x43754)))),f306(f306(f44(x43752,f872(x43751,a859)),x43753),x43754)) % 187.68/187.63 [4406]E(f306(f306(f263(x44061,x44061,x44061),f306(f306(f284(f871(x44061,x44061)),f306(f306(f236(x44061,x44061),x44062),x44063)),x44064)),f282(x44061,f306(f306(f284(f871(x44061,x44061)),f306(f306(f236(x44061,x44061),x44062),x44063)),x44064))),f306(f306(f108(f872(f871(x44061,x44061),a859)),f306(f306(f263(x44061,x44061,x44061),x44064),f282(x44061,x44064))),f306(f228(f871(x44061,x44061)),f306(f245(x44061,x44061,a859),f306(f306(f7(x44061,f872(x44061,a859),f872(x44061,a859)),f306(f306(f8(f872(a859,a859),f872(f872(x44061,a859),f872(x44061,a859)),x44061),f8(a859,a859,x44061)),f306(f306(f8(a859,f872(a859,a859),x44061),a304),f306(f306(f7(x44061,f872(f871(x44061,x44061),a859),a859),f306(f306(f8(f871(x44061,x44061),f872(f872(f871(x44061,x44061),a859),a859),x44061),f308(f871(x44061,x44061))),f306(f306(f7(x44061,x44061,f871(x44061,x44061)),f236(x44061,x44061)),x44062))),f282(x44061,x44064))))),f306(f306(f7(x44061,f872(f871(x44061,x44061),a859),a859),f306(f306(f8(f871(x44061,x44061),f872(f872(f871(x44061,x44061),a859),a859),x44061),f308(f871(x44061,x44061))),f306(f236(x44061,x44061),x44063))),f282(x44061,x44064))))))) % 187.68/187.63 [4207]E(f306(f128(x42071,f306(f306(f18(x42071,a859,a859),f306(f306(f8(a859,f872(a859,a859),x42071),a304),x42072)),x42073)),x42074),f306(f128(x42071,x42073),f306(f128(x42071,x42072),x42074))) % 187.68/187.63 [4309]E(f306(f306(f122(x43091),f306(f306(f306(f101(f866(x43091)),f306(f306(f308(a865),f2(a865)),x43092)),f306(f306(f143(x43091),x43093),f120(x43091))),f120(x43091))),f166(x43091,x43094,f306(f228(a865),f306(f306(f7(a865,f872(a865,a859),a859),f306(f306(f8(a865,f872(f872(a865,a859),a859),a865),f308(a865)),a119)),x43092)))),f166(x43091,f306(f306(f143(x43091),x43093),x43094),x43092)) % 187.68/187.63 [4401]E(f306(f228(f871(x44011,x44012)),f306(f306(f8(f872(a865,a859),a859,f871(x44011,x44012)),f88(a865)),f306(f306(f7(f871(x44011,x44012),f872(a865,a859),f872(a865,a859)),f306(f306(f8(f872(a865,f872(a859,a859)),f872(f872(a865,a859),f872(a865,a859)),f871(x44011,x44012)),f18(a865,a859,a859)),f306(f306(f8(f872(a865,a859),f872(a865,f872(a859,a859)),f871(x44011,x44012)),f306(f8(a859,f872(a859,a859),a865),a304)),f306(f306(f7(f871(x44011,x44012),f872(a865,f871(x44011,x44012)),f872(a865,a859)),f306(f306(f8(f872(f871(x44011,x44012),a859),f872(f872(a865,f871(x44011,x44012)),f872(a865,a859)),f871(x44011,x44012)),f8(f871(x44011,x44012),a859,a865)),a303)),f306(f306(f18(a865,x44012,f871(x44011,x44012)),f306(f306(f8(x44011,f872(x44012,f871(x44011,x44012)),a865),f236(x44011,x44012)),f306(f157(x44011),x44013))),f306(f157(x44012),x44014)))))),f306(f306(f7(a865,a865,a859),f221(a865)),f306(f306(f225(a865),f306(f186(f866(x44011)),x44013)),f306(f186(f866(x44012)),x44014)))))),f306(f164(f871(x44011,x44012)),f306(f306(f173(x44011,x44012),x44013),x44014))) % 187.68/187.63 [4328]E(f306(f228(f871(x43281,x43282)),f306(f245(x43281,x43282,a859),f306(f306(f7(x43281,f872(x43282,a859),f872(x43282,a859)),f306(f306(f8(f872(a859,a859),f872(f872(x43282,a859),f872(x43282,a859)),x43281),f8(a859,a859,x43282)),f306(f306(f8(a859,f872(a859,a859),x43281),a304),x43283))),x43284))),f306(f306(f243(x43281,x43282),f306(f228(x43281),x43283)),f306(f16(f872(x43282,a859),x43281),f306(f228(x43282),x43284)))) % 187.68/187.63 [4331]E(f306(f228(f871(x43311,x43312)),f306(f245(x43311,x43312,a859),f306(f306(f18(x43311,f872(x43312,a859),f872(x43312,a859)),f306(f306(f8(f872(a859,a859),f872(f872(x43312,a859),f872(x43312,a859)),x43311),f8(a859,a859,x43312)),f306(f306(f8(a859,f872(a859,a859),x43311),a304),x43313))),x43314))),f306(f306(f243(x43311,x43312),f306(f228(x43311),x43313)),f306(f306(f8(f872(x43312,a859),f872(x43312,a859),x43311),f228(x43312)),x43314))) % 187.68/187.63 [4347]E(f306(f228(x43471),f306(f306(f8(f872(x43472,a859),a859,x43471),f89(x43472)),f306(f306(f8(f872(x43472,a859),f872(x43472,a859),x43471),f306(f18(x43472,a859,a859),f306(f306(f8(a859,f872(a859,a859),x43472),a309),f306(f306(f7(x43472,f872(x43472,a859),a859),f308(x43472)),x43473)))),x43474))),f306(f306(f44(x43472,f872(x43471,a859)),x43473),f306(f306(f8(f872(x43471,a859),f872(x43471,a859),x43472),f228(x43471)),f306(f7(x43471,x43472,a859),x43474)))) % 187.68/187.63 [4387]E(f306(f306(f146(f871(x43871,a865),x43871),f235(x43871,a865)),f306(f128(f871(x43871,a865),f306(f306(f7(f871(x43871,a865),f872(a865,a859),a859),f306(f306(f8(a865,f872(f872(a865,a859),a859),f871(x43871,a865)),f308(a865)),f244(x43871,a865))),x43872)),f306(f306(f173(x43871,a865),x43873),f131(a865,f306(f276(a865,x43874),f306(f306(f81(a865),x43874),f306(f186(f866(x43871)),x43873))))))),f306(f306(f146(f871(x43871,a865),x43871),f235(x43871,a865)),f306(f128(f871(x43871,a865),f306(f306(f7(f871(x43871,a865),f872(a865,a859),a859),f306(f306(f8(a865,f872(f872(a865,a859),a859),f871(x43871,a865)),f308(a865)),f306(f306(f7(f871(x43871,a865),a865,a865),f306(f306(f8(a865,f872(a865,a865),f871(x43871,a865)),f81(a865)),f244(x43871,a865))),x43874))),x43872)),f306(f306(f173(x43871,a865),x43873),f131(a865,f306(f276(a865,f2(a865)),f306(f186(f866(x43871)),x43873))))))) % 187.68/187.63 [4388]E(f306(a119,f306(f306(f219(a865),f306(f186(f866(x43881)),x43882)),f306(f134(a865,f866(x43883),f306(f7(f866(x43883),a865,a865),f306(f306(f8(a865,f872(a865,a865),f866(x43883)),f219(a865)),f306(f306(f7(f866(x43883),a865,a865),f306(f306(f8(a865,f872(a865,a865),f866(x43883)),f22(a865)),f186(f866(x43883)))),f306(a119,f2(a865))))),f2(a865)),f306(f161(f866(x43883)),f306(f128(f866(x43883),f306(f306(f8(a859,a859,f866(x43883)),a301),f306(f306(f7(f866(x43883),f866(x43883),a859),a303),f120(x43883)))),x43884))))),f306(f306(f219(a865),f306(a119,f306(f186(f866(x43881)),x43882))),f306(f134(a865,f866(x43883),f306(f7(f866(x43883),a865,a865),f306(f306(f8(a865,f872(a865,a865),f866(x43883)),f219(a865)),f186(f866(x43883)))),f2(a865)),f306(f161(f866(x43883)),x43884)))) % 187.68/187.63 [4346]E(f306(f306(f122(x43461),f166(x43461,x43462,x43463)),f166(x43461,x43464,f306(f228(a865),f306(f306(f7(a865,f872(a865,a859),a859),f306(f306(f8(a865,f872(f872(a865,a859),a859),a865),f308(a865)),f306(f306(f7(a865,a865,a865),f81(a865)),f306(f186(f866(x43461)),x43462)))),x43463)))),f166(x43461,f306(f306(f122(x43461),x43462),x43464),x43463)) % 187.68/187.63 [4394]E(f306(f306(f143(f866(x43941)),f306(f306(f143(x43941),x43942),f306(f134(f866(x43941),f866(x43941),f122(x43941),f120(x43941)),f306(f306(f146(f866(x43941),f866(x43941)),f148(f866(x43941),x43941,f120(x43941),f306(f306(f8(f866(x43941),f872(f866(x43941),f866(x43941)),x43941),f16(f866(x43941),f866(x43941))),f306(f306(f7(x43941,f866(x43941),f866(x43941)),f143(x43941)),f120(x43941))))),x43943)))),f171(x43941,f306(f306(f143(f866(x43941)),x43944),f306(f134(f866(f866(x43941)),f866(f866(x43941)),f122(f866(x43941)),f120(f866(x43941))),f306(f306(f146(f866(x43941),f866(f866(x43941))),f148(f866(f866(x43941)),x43941,f120(f866(x43941)),f306(f16(f872(f866(x43941),f866(f866(x43941))),x43941),f306(f306(f7(f866(x43941),f866(f866(x43941)),f866(f866(x43941))),f143(f866(x43941))),f120(f866(x43941)))))),x43943))))),f171(x43941,f306(f306(f143(f866(x43941)),f306(f306(f143(x43941),x43942),x43944)),x43943))) % 187.68/187.63 [4402]E(f306(f228(f871(x44021,x44021)),f306(f245(x44021,x44021,a859),f306(f306(f7(x44021,f872(f871(x44022,x44022),a859),f872(x44021,a859)),f306(f306(f8(f872(x44021,f872(f872(f871(x44022,x44022),a859),a859)),f872(f872(f871(x44022,x44022),a859),f872(x44021,a859)),x44021),f7(x44021,f872(f871(x44022,x44022),a859),a859)),f306(f306(f8(f872(x44021,f871(x44022,x44022)),f872(x44021,f872(f872(f871(x44022,x44022),a859),a859)),x44021),f306(f8(f871(x44022,x44022),f872(f872(f871(x44022,x44022),a859),a859),x44021),f308(f871(x44022,x44022)))),f306(f306(f7(x44021,f872(x44021,x44022),f872(x44021,f871(x44022,x44022))),f306(f306(f8(f872(x44022,f871(x44022,x44022)),f872(f872(x44021,x44022),f872(x44021,f871(x44022,x44022))),x44021),f8(x44022,f871(x44022,x44022),x44021)),f306(f306(f8(x44022,f872(x44022,f871(x44022,x44022)),x44021),f236(x44022,x44022)),x44023))),x44023)))),x44024))),f306(f306(f262(x44022,x44021),x44024),x44023)) % 187.68/187.63 [4463]~E(f34(x44631,x44632),f29(x44633,x44634,x44635)) % 187.68/187.63 [4464]~E(f34(x44641,x44642),f31(x44643,x44644,x44645)) % 187.68/187.63 [4465]~E(f34(x44651,x44652),f30(x44653,x44654,x44655)) % 187.68/187.63 [4466]~E(f33(x44661,x44662),f29(x44663,x44664,x44665)) % 187.68/187.63 [4467]~E(f33(x44671,x44672),f31(x44673,x44674,x44675)) % 187.68/187.63 [4468]~E(f33(x44681,x44682),f30(x44683,x44684,x44685)) % 187.68/187.63 [4469]~E(f29(x44691,x44692,x44693),f34(x44694,x44695)) % 187.68/187.63 [4470]~E(f29(x44701,x44702,x44703),f33(x44704,x44705)) % 187.68/187.63 [4471]~E(f31(x44711,x44712,x44713),f34(x44714,x44715)) % 187.68/187.63 [4472]~E(f31(x44721,x44722,x44723),f33(x44724,x44725)) % 187.68/187.63 [4473]~E(f30(x44731,x44732,x44733),f34(x44734,x44735)) % 187.68/187.63 [4474]~E(f30(x44741,x44742,x44743),f33(x44744,x44745)) % 187.68/187.63 [3900]E(f306(f176(x39001,x39002,x39003,x39004),x39005),f306(f216(f869(x39002),x39002,f306(x39003,x39005),f214(x39002)),f306(x39004,x39005))) % 187.68/187.63 [3983]E(f176(x39831,x39832,f176(x39831,x39832,x39833,x39834),x39835),f176(x39831,x39832,x39833,f176(x39831,x39832,x39834,x39835))) % 187.68/187.63 [4161]E(f306(f306(f108(f872(x41611,a859)),f306(f164(x41611),f306(f306(f165(x41611),f306(f186(f866(x41612)),x41613)),x41614))),f175(x41611,x41612,x41615)),f175(x41611,x41612,f178(x41611,x41612,x41615,x41614,x41613))) % 187.68/187.63 [3730]E(f306(f306(f245(x37301,x37302,x37303),x37304),x37305),f306(f306(x37304,f306(f235(x37301,x37302),x37305)),f306(f244(x37301,x37302),x37305))) % 187.68/187.63 [3755]E(f306(f216(x37551,x37552,x37553,x37554),f306(f214(x37552),x37555)),f306(x37554,x37555)) % 187.68/187.63 [3764]E(f306(f306(f306(f67(x37641,x37642,x37643),x37644),x37645),f185(f872(x37642,a859))),x37645) % 187.68/187.63 [3931]E(f217(x39311,x39312,x39313,x39314,f306(f214(x39312),x39315)),f306(x39314,x39315)) % 187.68/187.63 [4038]E(f306(f74(f869(x40381),f869(x40382),f869(x40383),f306(f189(x40381,x40382),x40384)),f306(f189(x40383,x40381),x40385)),f306(f189(x40383,x40382),f306(f74(x40381,x40382,x40383,x40384),x40385))) % 187.68/187.63 [4040]E(f306(f74(f866(x40401),f866(x40402),f866(x40403),f306(f146(x40401,x40402),x40404)),f306(f146(x40403,x40401),x40405)),f306(f146(x40403,x40402),f306(f74(x40401,x40402,x40403,x40404),x40405))) % 187.68/187.63 [4119]E(f86(x41191,f68(x41192,x41191,x41193,x41194,x41195)),f306(f306(f66(x41192,x41191,x41193),x41194),x41195)) % 187.68/187.63 [4154]E(f306(f306(f81(a865),f306(f306(f81(a865),f306(x41541,f306(f235(x41542,x41543),x41544))),f306(x41545,f306(f244(x41542,x41543),x41544)))),f306(a119,f2(a865))),f249(x41542,x41543,x41541,x41545,x41544)) % 187.68/187.63 [4342]E(f155(x43421,x43422,f306(f306(f7(x43421,f869(x43422),f869(x43422)),f306(f306(f18(x43421,f869(x43422),f872(f869(x43422),f869(x43422))),f306(f306(f8(a859,f872(f869(x43422),f872(f869(x43422),f869(x43422))),x43421),f101(f869(x43422))),x43423)),f306(f306(f8(x43422,f869(x43422),x43421),f214(x43422)),x43424))),f188(x43422)),x43425),f306(f306(f146(x43421,x43422),x43424),f306(f128(x43421,x43423),x43425))) % 187.68/187.63 [4513]~E(f306(f306(f306(f73(x45131,f869(x45132)),x45133),x45134),f306(f214(x45132),x45135)),f306(f16(f869(x45132),x45131),f188(x45132))) % 187.68/187.63 [3667]E(f306(f306(f165(x36671),x36672),f306(f306(f146(x36673,x36671),x36674),x36675)),f306(f306(f146(x36673,x36671),x36674),f306(f306(f165(x36673),x36672),x36675))) % 187.68/187.63 [3668]E(f306(f306(f130(x36681),x36682),f306(f306(f146(x36683,x36681),x36684),x36685)),f306(f306(f146(x36683,x36681),x36684),f306(f306(f130(x36683),x36682),x36685))) % 187.68/187.63 [3699]E(f306(f306(f146(x36991,x36992),x36993),f306(f306(f143(x36991),x36994),x36995)),f306(f306(f143(x36992),f306(x36993,x36994)),f306(f306(f146(x36991,x36992),x36993),x36995))) % 187.68/187.63 [3759]E(f306(f285(x37591,x37592,x37593),f306(f306(f284(x37591),x37594),x37595)),f306(f306(f284(x37592),f306(x37593,x37594)),f306(f285(x37591,x37592,x37593),x37595))) % 187.68/187.63 [3823]E(f306(f306(f173(x38231,x38232),f306(f306(f165(x38231),x38233),x38234)),f306(f306(f165(x38232),x38233),x38235)),f306(f306(f165(f871(x38231,x38232)),x38233),f306(f306(f173(x38231,x38232),x38234),x38235))) % 187.68/187.63 [3824]E(f306(f306(f173(x38241,x38242),f306(f306(f130(x38241),x38243),x38244)),f306(f306(f130(x38242),x38243),x38245)),f306(f306(f130(f871(x38241,x38242)),x38243),f306(f306(f173(x38241,x38242),x38244),x38245))) % 187.68/187.63 [3834]E(f306(f306(f151(x38341,f306(f306(f143(x38341),x38342),x38343)),f306(a119,x38344)),x38345),f306(f306(f143(x38341),x38342),f306(f306(f151(x38341,x38343),x38344),x38345))) % 187.68/187.63 [3837]E(f306(f216(f869(x38371),x38372,f188(x38371),x38373),f306(f306(f16(f869(x38372),x38374),f188(x38372)),x38375)),f188(x38371)) % 187.68/187.63 [3839]E(f306(f306(f122(x38391),f306(f306(f146(x38392,x38391),x38393),x38394)),f306(f306(f146(x38392,x38391),x38393),x38395)),f306(f306(f146(x38392,x38391),x38393),f306(f306(f122(x38392),x38394),x38395))) % 187.68/187.63 [3843]E(f306(f306(x38431,x38432),f306(f306(f238(x38433,x38434,x38431),x38432),x38435)),f306(f306(f238(x38433,x38434,x38431),x38432),f306(a119,x38435))) % 187.68/187.63 [3872]E(f156(x38721,x38722,x38723,f306(f306(f143(x38721),x38724),x38725)),f306(f306(f122(x38722),f306(x38723,x38724)),f156(x38721,x38722,x38723,x38725))) % 187.68/187.63 [3884]E(f306(f306(f263(x38841,x38842,x38843),f306(f261(x38842,x38841),x38844)),f306(f261(x38843,x38842),x38845)),f306(f261(x38843,x38841),f306(f306(f263(x38843,x38842,x38841),x38845),x38844))) % 187.68/187.63 [3918]E(f306(f306(f306(f180(f866(x39181),f866(x39181)),x39182),f160(x39181)),f306(f306(f146(x39183,x39181),x39184),x39185)),f306(f306(f146(x39183,x39181),x39184),f306(f306(f306(f180(f866(x39183),f866(x39183)),x39182),f160(x39183)),x39185))) % 187.68/187.63 [3919]E(f306(f306(f247(x39191,x39192,x39191,x39193),f306(f236(x39192,x39191),x39194)),x39195),f306(x39195,x39194)) % 187.68/187.63 [3945]E(f147(x39451,x39452,f306(f306(f146(x39453,x39451),x39454),x39455)),f147(x39453,f306(f74(x39451,a865,x39453,x39452),x39454),x39455)) % 187.68/187.63 [4006]E(f306(f306(f74(f869(x40061),f869(x40062),x40063,f306(f189(x40061,x40062),x40064)),f306(f16(f869(x40061),x40063),f188(x40061))),x40065),f188(x40062)) % 187.68/187.63 [4007]E(f168(f871(x40071,x40072),f306(f74(x40072,a859,f871(x40071,x40072),x40073),f244(x40071,x40072)),f306(f306(f173(x40071,x40072),x40074),x40075)),f306(f306(f173(x40071,x40072),x40074),f168(x40072,x40073,x40075))) % 187.68/187.63 [4012]E(f306(f285(x40121,x40122,f306(f306(f8(x40123,x40122,x40121),x40124),x40125)),f231(f872(x40121,a859))),f306(f285(x40123,x40122,x40124),f306(f285(x40121,x40123,x40125),f231(f872(x40121,a859))))) % 187.68/187.63 [4025]E(f168(f871(x40251,x40252),f306(f74(x40251,a859,f871(x40251,x40252),x40253),f235(x40251,x40252)),f306(f306(f173(x40251,x40252),x40254),x40255)),f306(f306(f173(x40251,x40252),f168(x40251,x40253,x40254)),x40255)) % 187.68/187.63 [4044]E(f306(f306(f108(f872(x40441,a859)),f306(f286(x40441,x40442,x40443),f306(f306(f284(x40442),x40444),f185(f872(x40442,a859))))),f306(f286(x40441,x40442,x40443),x40445)),f306(f286(x40441,x40442,x40443),f306(f306(f284(x40442),x40444),x40445))) % 187.68/187.63 [4103]E(f306(f306(f122(f871(x41031,x41032)),f306(f306(f146(x41032,f871(x41031,x41032)),f306(f236(x41031,x41032),x41033)),x41034)),f61(x41031,x41032,x41035,x41034)),f61(x41031,x41032,f306(f306(f143(x41031),x41033),x41035),x41034)) % 187.68/187.63 [4104]E(f306(f306(f146(x41041,x41042),x41043),f168(x41041,f306(f74(x41042,a859,x41041,x41044),x41043),x41045)),f168(x41042,x41044,f306(f306(f146(x41041,x41042),x41043),x41045))) % 187.68/187.63 [4110]E(f306(f134(x41101,x41102,f306(f7(x41102,x41101,x41101),f306(f7(x41101,x41102,x41101),x41103)),x41104),f306(f161(x41102),f306(f161(x41102),x41105))),f306(f134(x41101,x41102,x41103,x41104),x41105)) % 187.68/187.63 [4111]E(f306(f306(f306(f73(x41111,f869(x41112)),f179(x41111,x41112,x41113,x41114)),x41115),f306(x41113,x41115)),f179(x41111,x41112,x41113,f306(f306(f284(x41111),x41115),x41114))) % 187.68/187.63 [4178]E(f306(f216(f866(x41781),x41781,f155(x41782,x41781,x41783,x41784),f306(f306(f7(x41781,f866(x41781),f866(x41781)),f143(x41781)),f155(x41782,x41781,x41783,x41784))),f306(x41783,x41785)),f155(x41782,x41781,x41783,f306(f306(f143(x41782),x41785),x41784))) % 187.68/187.63 [4215]P1(f306(f306(f220(f872(x42151,a859)),f306(f285(x42152,x42151,x42153),f306(f306(f109(f872(x42152,a859)),x42154),x42155))),f306(f306(f109(f872(x42151,a859)),f306(f285(x42152,x42151,x42153),x42154)),f306(f285(x42152,x42151,x42153),x42155)))) % 187.68/187.63 [4216]P1(f306(f306(f220(f872(x42161,a859)),f306(f260(x42162,x42161,x42163),f306(f306(f109(f872(x42162,a859)),x42164),x42165))),f306(f306(f109(f872(x42161,a859)),f306(f260(x42162,x42161,x42163),x42164)),f306(f260(x42162,x42161,x42163),x42165)))) % 187.68/187.63 [4316]E(f306(f244(x43161,x43162),f306(f246(x43163,x43161,x43162,x43162,x43164,f35(x43162)),x43165)),f306(f244(x43163,x43162),x43165)) % 187.68/187.63 [4317]E(f306(f235(x43171,x43172),f306(f246(x43171,x43171,x43173,x43172,f35(x43171),x43174),x43175)),f306(f235(x43171,x43173),x43175)) % 187.68/187.63 [4398]E(f306(f134(f872(x43981,f869(x43982)),f871(x43981,x43982),f306(f306(f8(f872(x43981,f872(x43982,f872(x43981,f869(x43982)))),f872(f871(x43981,x43982),f872(x43981,f869(x43982))),f872(x43981,f869(x43982))),f245(x43981,x43982,f872(x43981,f869(x43982)))),f306(f306(f7(f872(x43981,f869(x43982)),f872(x43982,f869(x43982)),f872(x43981,f872(x43982,f872(x43981,f869(x43982))))),f306(f306(f8(f872(x43981,f872(f872(x43982,f869(x43982)),f872(x43982,f872(x43981,f869(x43982))))),f872(f872(x43982,f869(x43982)),f872(x43981,f872(x43982,f872(x43981,f869(x43982))))),f872(x43981,f869(x43982))),f7(x43981,f872(x43982,f869(x43982)),f872(x43982,f872(x43981,f869(x43982))))),f306(f306(f8(f872(x43981,f872(f869(x43982),f872(x43981,f869(x43982)))),f872(x43981,f872(f872(x43982,f869(x43982)),f872(x43982,f872(x43981,f869(x43982))))),f872(x43981,f869(x43982))),f306(f8(f872(f869(x43982),f872(x43981,f869(x43982))),f872(f872(x43982,f869(x43982)),f872(x43982,f872(x43981,f869(x43982)))),x43981),f8(f869(x43982),f872(x43981,f869(x43982)),x43982))),f73(x43981,f869(x43982))))),f214(x43982))),x43983),f306(f306(f173(x43981,x43982),x43984),x43985)),f178(x43981,x43982,x43983,x43984,x43985)) % 187.68/187.63 [4400]P27(x44001,x44002,f306(f306(f284(f864(x44001)),f306(f306(f306(f93(x44001),f306(f306(f7(x44001,f872(a861,a859),f872(a861,a859)),f306(f306(f8(f872(a861,f872(a859,a859)),f872(f872(a861,a859),f872(a861,a859)),x44001),f18(a861,a859,a859)),f306(f306(f8(f872(a861,a859),f872(a861,f872(a859,a859)),x44001),f306(f8(a859,f872(a859,a859),a861),a304)),x44003))),f306(f306(f8(a859,a859,a861),a301),x44004))),f33(x44004,x44005)),x44003)),f185(f872(f864(x44001),a859)))) % 187.68/187.63 [3559]E(f98(x35591,x35592,f306(f306(f306(f93(x35591),x35593),x35594),x35595)),f2(a865)) % 187.68/187.63 [3651]E(f306(f306(f306(f306(f73(x36511,x36512),x36513),x36514),x36515),x36514),x36515) % 187.68/187.63 [3873]E(f306(f306(f43(x38731,f872(x38732,a859)),f306(f306(f284(x38731),x38733),x38734)),x38735),f306(f306(f108(f872(x38732,a859)),f306(x38735,x38733)),f306(f306(f43(x38731,f872(x38732,a859)),x38734),x38735))) % 187.68/187.63 [3874]E(f306(f306(f44(x38741,f872(x38742,a859)),f306(f306(f284(x38741),x38743),x38744)),x38745),f306(f306(f109(f872(x38742,a859)),f306(x38745,x38743)),f306(f306(f44(x38741,f872(x38742,a859)),x38744),x38745))) % 187.68/187.63 [3938]E(f306(f306(f108(f872(x39381,a859)),f306(f285(x39382,x39381,x39383),x39384)),f306(f285(x39382,x39381,x39383),x39385)),f306(f285(x39382,x39381,x39383),f306(f306(f108(f872(x39382,a859)),x39384),x39385))) % 187.68/187.63 [3939]E(f306(f306(f108(f872(x39391,a859)),f306(f260(x39392,x39391,x39393),x39394)),f306(f260(x39392,x39391,x39393),x39395)),f306(f260(x39392,x39391,x39393),f306(f306(f108(f872(x39392,a859)),x39394),x39395))) % 187.68/187.63 [3940]E(f306(f306(f22(f872(x39401,a859)),f306(f286(x39401,x39402,x39403),x39404)),f306(f286(x39401,x39402,x39403),x39405)),f306(f286(x39401,x39402,x39403),f306(f306(f22(f872(x39402,a859)),x39404),x39405))) % 187.68/187.63 [3941]E(f306(f306(f108(f872(x39411,a859)),f306(f286(x39411,x39412,x39413),x39414)),f306(f286(x39411,x39412,x39413),x39415)),f306(f286(x39411,x39412,x39413),f306(f306(f108(f872(x39412,a859)),x39414),x39415))) % 187.68/187.63 [3942]E(f306(f306(f109(f872(x39421,a859)),f306(f286(x39421,x39422,x39423),x39424)),f306(f286(x39421,x39422,x39423),x39425)),f306(f286(x39421,x39422,x39423),f306(f306(f109(f872(x39422,a859)),x39424),x39425))) % 187.68/187.63 [3944]E(f179(x39441,x39442,f179(x39441,x39442,x39443,x39444),x39445),f179(x39441,x39442,x39443,f306(f306(f109(f872(x39441,a859)),x39444),x39445))) % 187.68/187.63 [4002]E(f306(f306(f151(x40021,f306(f306(f122(x40021),x40022),f306(f306(f143(x40021),x40023),x40024))),f306(f186(f866(x40021)),x40022)),x40025),f306(f306(f122(x40021),x40022),f306(f306(f143(x40021),x40025),x40024))) % 187.68/187.63 [4010]E(f306(f306(f44(x40101,f872(x40102,a859)),x40103),f306(f306(f8(f872(x40102,a859),f872(x40102,a859),x40101),f306(f284(x40102),x40104)),x40105)),f306(f306(f284(x40102),x40104),f306(f306(f44(x40101,f872(x40102,a859)),x40103),x40105))) % 187.68/187.63 [4078]E(f179(x40781,x40782,f306(f306(f306(f73(x40781,f869(x40782)),x40783),x40784),f306(f214(x40782),x40785)),f306(f80(f872(x40781,a859)),f306(f306(f284(x40781),x40784),f185(f872(x40781,a859))))),f179(x40781,x40782,x40783,f306(f80(f872(x40781,a859)),f306(f306(f284(x40781),x40784),f185(f872(x40781,a859)))))) % 187.68/187.63 [4165]E(f306(f306(f146(x41651,x41652),x41653),f306(f128(x41651,f306(f74(x41652,a859,x41651,x41654),x41653)),x41655)),f306(f128(x41652,x41654),f306(f306(f146(x41651,x41652),x41653),x41655))) % 187.68/187.63 [4171]E(f306(f186(f866(x41711)),f306(f128(x41711,x41712),f306(f306(f146(x41713,x41711),x41714),x41715))),f306(f186(f866(x41713)),f306(f128(x41713,f306(f74(x41711,a859,x41713,x41712),x41714)),x41715))) % 187.68/187.63 [4308]E(f306(f306(f108(f872(x43081,a859)),f306(f306(f22(f872(x43081,a859)),f175(x43081,x43082,x43083)),f306(f228(x43081),f306(f306(f7(x43081,f872(x43081,a859),a859),f308(x43081)),f306(f306(f22(f872(x43081,a859)),x43084),f175(x43081,x43082,x43085)))))),f306(f228(x43081),f306(f306(f7(x43081,f872(x43081,a859),a859),f308(x43081)),f306(f306(f109(f872(x43081,a859)),x43084),f175(x43081,x43082,x43085))))),f175(x43081,x43082,f77(x43081,f869(x43082),x43083,x43085,x43084))) % 187.68/187.63 [4379]E(f306(f148(f866(f871(x43791,x43792)),x43792,f120(f871(x43791,x43792)),f306(f306(f7(x43792,f872(f866(x43792),f866(f871(x43791,x43792))),f872(f866(x43792),f866(f871(x43791,x43792)))),f306(f306(f8(f872(f866(f871(x43791,x43792)),f866(f871(x43791,x43792))),f872(f872(f866(x43792),f866(f871(x43791,x43792))),f872(f866(x43792),f866(f871(x43791,x43792)))),x43792),f8(f866(f871(x43791,x43792)),f866(f871(x43791,x43792)),f866(x43792))),f306(f306(f8(f871(x43791,x43792),f872(f866(f871(x43791,x43792)),f866(f871(x43791,x43792))),x43792),f143(f871(x43791,x43792))),f306(f236(x43791,x43792),x43793)))),f306(f173(x43791,x43792),x43794))),x43795),f306(f306(f173(x43791,x43792),f306(f306(f143(x43791),x43793),x43794)),x43795)) % 187.68/187.63 [3868]E(f306(f306(f151(x38681,f306(f306(f151(x38681,x38682),x38683),x38684)),x38683),x38685),f306(f306(f151(x38681,x38682),x38683),x38685)) % 187.68/187.63 [3920]E(f306(f232(x39201,x39202),f306(f306(f284(f871(x39201,x39202)),f306(f306(f236(x39201,x39202),x39203),x39204)),x39205)),f306(f306(f284(x39202),x39204),f306(f232(x39201,x39202),x39205))) % 187.68/187.63 [3921]E(f306(f234(x39211,x39212),f306(f306(f284(f871(x39211,x39212)),f306(f306(f236(x39211,x39212),x39213),x39214)),x39215)),f306(f306(f284(x39211),x39213),f306(f234(x39211,x39212),x39215))) % 187.68/187.63 [3995]E(f306(f306(f22(f872(f871(x39951,x39952),a859)),f306(f306(f243(x39951,x39952),x39953),x39954)),f306(f306(f243(x39951,x39952),x39955),x39954)),f306(f306(f243(x39951,x39952),f306(f306(f22(f872(x39951,a859)),x39953),x39955)),x39954)) % 187.68/187.63 [3996]E(f306(f306(f108(f872(f871(x39961,x39962),a859)),f306(f306(f243(x39961,x39962),x39963),x39964)),f306(f306(f243(x39961,x39962),x39965),x39964)),f306(f306(f243(x39961,x39962),f306(f306(f108(f872(x39961,a859)),x39963),x39965)),x39964)) % 187.68/187.63 [3997]E(f306(f306(f109(f872(f871(x39971,x39972),a859)),f306(f306(f243(x39971,x39972),x39973),x39974)),f306(f306(f243(x39971,x39972),x39975),x39974)),f306(f306(f243(x39971,x39972),f306(f306(f109(f872(x39971,a859)),x39973),x39975)),x39974)) % 187.68/187.63 [4056]E(f306(f306(f108(f872(x40561,a859)),f306(f306(f43(x40562,f872(x40561,a859)),x40563),x40564)),f306(f306(f43(x40562,f872(x40561,a859)),x40565),x40564)),f306(f306(f43(x40562,f872(x40561,a859)),f306(f306(f108(f872(x40562,a859)),x40563),x40565)),x40564)) % 187.68/187.63 [4057]E(f306(f306(f109(f872(x40571,a859)),f306(f306(f44(x40572,f872(x40571,a859)),x40573),x40574)),f306(f306(f44(x40572,f872(x40571,a859)),x40575),x40574)),f306(f306(f44(x40572,f872(x40571,a859)),f306(f306(f108(f872(x40572,a859)),x40573),x40575)),x40574)) % 187.68/187.63 [4071]E(f306(f306(f43(x40711,f872(x40712,a859)),x40713),f306(f306(f8(f872(x40712,a859),f872(x40712,a859),x40711),f306(f22(f872(x40712,a859)),x40714)),x40715)),f306(f306(f22(f872(x40712,a859)),x40714),f306(f306(f44(x40711,f872(x40712,a859)),x40713),x40715))) % 187.68/187.63 [4072]E(f306(f306(f43(x40721,f872(x40722,a859)),x40723),f306(f306(f8(f872(x40722,a859),f872(x40722,a859),x40721),f306(f109(f872(x40722,a859)),x40724)),x40725)),f306(f306(f109(f872(x40722,a859)),x40724),f306(f306(f43(x40721,f872(x40722,a859)),x40723),x40725))) % 187.68/187.63 [4073]E(f306(f306(f44(x40731,f872(x40732,a859)),x40733),f306(f306(f8(f872(x40732,a859),f872(x40732,a859),x40731),f306(f108(f872(x40732,a859)),x40734)),x40735)),f306(f306(f108(f872(x40732,a859)),x40734),f306(f306(f44(x40731,f872(x40732,a859)),x40733),x40735))) % 187.68/187.63 [4109]E(f176(x41091,x41092,x41093,f306(f169(x41091,x41092),f306(f161(f871(x41091,x41092)),f306(f306(f173(x41091,x41092),x41094),x41095)))),f178(x41091,x41092,x41093,x41094,x41095)) % 187.68/187.63 [4131]E(f182(f866(x41311),f306(f306(f143(x41311),x41312),x41313),f306(f306(f8(f866(x41311),f866(x41311),a865),f306(f143(x41311),x41314)),f306(f306(f7(a865,x41311,f866(x41311)),f151(x41311,x41313)),x41312)),x41315),f306(f306(f151(x41311,f306(f306(f143(x41311),x41314),x41313)),x41315),x41312)) % 187.68/187.63 [4135]E(f306(f306(f43(x41351,f872(f871(x41352,x41353),a859)),x41354),f306(f306(f8(f872(f871(x41353,x41352),a859),f872(f871(x41352,x41353),a859),x41351),f261(x41353,x41352)),x41355)),f306(f261(x41353,x41352),f306(f306(f43(x41351,f872(f871(x41353,x41352),a859)),x41354),x41355))) % 187.68/187.63 [4136]E(f306(f306(f44(x41361,f872(f871(x41362,x41363),a859)),x41364),f306(f306(f8(f872(f871(x41363,x41362),a859),f872(f871(x41362,x41363),a859),x41361),f261(x41363,x41362)),x41365)),f306(f261(x41363,x41362),f306(f306(f44(x41361,f872(f871(x41363,x41362),a859)),x41364),x41365))) % 187.68/187.63 [4189]E(f175(x41891,x41892,f306(f306(f18(x41891,f869(x41893),f869(x41892)),f306(f306(f8(f872(x41893,x41892),f872(f869(x41893),f869(x41892)),x41891),f189(x41893,x41892)),x41894)),x41895)),f175(x41891,x41893,x41895)) % 187.68/187.63 [4240]P1(f306(f306(f220(f872(x42401,a859)),f306(f306(f22(f872(x42401,a859)),f306(f285(x42402,x42401,x42403),x42404)),f306(f285(x42402,x42401,x42403),x42405))),f306(f285(x42402,x42401,x42403),f306(f306(f22(f872(x42402,a859)),x42404),x42405)))) % 187.68/187.63 [4383]E(f306(f148(f866(f871(x43831,x43832)),x43831,f120(f871(x43831,x43832)),f306(f306(f7(x43831,f872(f866(x43831),f866(f871(x43831,x43832))),f872(f866(x43831),f866(f871(x43831,x43832)))),f306(f306(f8(f872(f866(f871(x43831,x43832)),f866(f871(x43831,x43832))),f872(f872(f866(x43831),f866(f871(x43831,x43832))),f872(f866(x43831),f866(f871(x43831,x43832)))),x43831),f8(f866(f871(x43831,x43832)),f866(f871(x43831,x43832)),f866(x43831))),f306(f306(f8(f871(x43831,x43832),f872(f866(f871(x43831,x43832)),f866(f871(x43831,x43832))),x43831),f143(f871(x43831,x43832))),f306(f306(f7(x43831,x43832,f871(x43831,x43832)),f236(x43831,x43832)),x43833)))),f306(f306(f7(f866(x43831),f866(x43832),f866(f871(x43831,x43832))),f173(x43831,x43832)),x43834))),x43835),f306(f306(f173(x43831,x43832),x43835),f306(f306(f143(x43832),x43833),x43834))) % 187.68/187.63 [4097]E(f306(f306(f108(f872(x40971,a859)),f306(f260(x40972,x40971,x40973),x40974)),f306(f260(x40972,x40971,x40975),x40974)),f306(f260(x40972,x40971,f306(f306(f108(f872(f871(x40972,x40971),a859)),x40973),x40975)),x40974)) % 187.68/187.63 [4138]E(f306(f306(f122(f871(x41381,x41382)),f306(f306(f173(x41381,x41382),x41383),f306(f306(f165(x41382),f306(f186(f866(x41381)),x41383)),x41384))),f306(f306(f173(x41381,x41382),x41385),f306(f306(f130(x41382),f306(f186(f866(x41381)),x41383)),x41384))),f306(f306(f173(x41381,x41382),f306(f306(f122(x41381),x41383),x41385)),x41384)) % 187.68/187.63 [4243]E(f306(f306(f243(x42431,x42432),x42433),f306(f306(f18(x42431,f872(x42432,a859),f872(x42432,a859)),f306(f306(f8(f872(x42432,a859),f872(f872(x42432,a859),f872(x42432,a859)),x42431),f22(f872(x42432,a859))),x42434)),x42435)),f306(f306(f22(f872(f871(x42431,x42432),a859)),f306(f306(f243(x42431,x42432),x42433),x42434)),f306(f306(f243(x42431,x42432),x42433),x42435))) % 187.68/187.63 [4244]E(f306(f306(f243(x42441,x42442),x42443),f306(f306(f18(x42441,f872(x42442,a859),f872(x42442,a859)),f306(f306(f8(f872(x42442,a859),f872(f872(x42442,a859),f872(x42442,a859)),x42441),f108(f872(x42442,a859))),x42444)),x42445)),f306(f306(f108(f872(f871(x42441,x42442),a859)),f306(f306(f243(x42441,x42442),x42443),x42444)),f306(f306(f243(x42441,x42442),x42443),x42445))) % 187.68/187.63 [4245]E(f306(f306(f243(x42451,x42452),x42453),f306(f306(f18(x42451,f872(x42452,a859),f872(x42452,a859)),f306(f306(f8(f872(x42452,a859),f872(f872(x42452,a859),f872(x42452,a859)),x42451),f109(f872(x42452,a859))),x42454)),x42455)),f306(f306(f109(f872(f871(x42451,x42452),a859)),f306(f306(f243(x42451,x42452),x42453),x42454)),f306(f306(f243(x42451,x42452),x42453),x42455))) % 187.68/187.63 [4249]E(f306(f306(f43(x42491,f872(x42492,a859)),x42493),f306(f306(f7(x42491,f872(x42492,a859),f872(x42492,a859)),f306(f306(f8(f872(x42492,a859),f872(f872(x42492,a859),f872(x42492,a859)),x42491),f22(f872(x42492,a859))),x42494)),x42495)),f306(f306(f22(f872(x42492,a859)),f306(f306(f43(x42491,f872(x42492,a859)),x42493),x42494)),x42495)) % 187.68/187.63 [4250]E(f306(f306(f43(x42501,f872(x42502,a859)),x42503),f306(f306(f7(x42501,f872(x42502,a859),f872(x42502,a859)),f306(f306(f8(f872(x42502,a859),f872(f872(x42502,a859),f872(x42502,a859)),x42501),f109(f872(x42502,a859))),x42504)),x42505)),f306(f306(f109(f872(x42502,a859)),f306(f306(f43(x42501,f872(x42502,a859)),x42503),x42504)),x42505)) % 187.68/187.63 [4251]E(f306(f306(f44(x42511,f872(x42512,a859)),x42513),f306(f306(f7(x42511,f872(x42512,a859),f872(x42512,a859)),f306(f306(f8(f872(x42512,a859),f872(f872(x42512,a859),f872(x42512,a859)),x42511),f108(f872(x42512,a859))),x42514)),x42515)),f306(f306(f108(f872(x42512,a859)),f306(f306(f44(x42511,f872(x42512,a859)),x42513),x42514)),x42515)) % 187.68/187.63 [4255]E(f306(f306(f43(x42551,f872(x42552,a859)),x42553),f306(f306(f18(x42551,f872(x42552,a859),f872(x42552,a859)),f306(f306(f8(f872(x42552,a859),f872(f872(x42552,a859),f872(x42552,a859)),x42551),f108(f872(x42552,a859))),x42554)),x42555)),f306(f306(f108(f872(x42552,a859)),f306(f306(f43(x42551,f872(x42552,a859)),x42553),x42554)),f306(f306(f43(x42551,f872(x42552,a859)),x42553),x42555))) % 187.68/187.63 [4256]E(f306(f306(f44(x42561,f872(x42562,a859)),x42563),f306(f306(f18(x42561,f872(x42562,a859),f872(x42562,a859)),f306(f306(f8(f872(x42562,a859),f872(f872(x42562,a859),f872(x42562,a859)),x42561),f109(f872(x42562,a859))),x42564)),x42565)),f306(f306(f109(f872(x42562,a859)),f306(f306(f44(x42561,f872(x42562,a859)),x42563),x42564)),f306(f306(f44(x42561,f872(x42562,a859)),x42563),x42565))) % 187.68/187.63 [4270]E(f306(f306(f43(x42701,f872(x42702,a859)),x42703),f306(f306(f18(x42701,f872(x42702,a859),f872(x42702,a859)),f306(f306(f8(f872(x42702,a859),f872(f872(x42702,a859),f872(x42702,a859)),x42701),f108(f872(x42702,a859))),x42704)),x42705)),f306(f306(f108(f872(x42702,a859)),f41(f872(x42702,a859),f306(f285(x42701,f872(x42702,a859),x42704),x42703))),f41(f872(x42702,a859),f306(f285(x42701,f872(x42702,a859),x42705),x42703)))) % 187.68/187.63 [4271]E(f306(f306(f44(x42711,f872(x42712,a859)),x42713),f306(f306(f18(x42711,f872(x42712,a859),f872(x42712,a859)),f306(f306(f8(f872(x42712,a859),f872(f872(x42712,a859),f872(x42712,a859)),x42711),f109(f872(x42712,a859))),x42714)),x42715)),f306(f306(f109(f872(x42712,a859)),f42(f872(x42712,a859),f306(f285(x42711,f872(x42712,a859),x42714),x42713))),f42(f872(x42712,a859),f306(f285(x42711,f872(x42712,a859),x42715),x42713)))) % 187.68/187.63 [4304]E(f306(f306(f130(x43041),f306(f186(f866(x43041)),f168(x43041,x43042,f306(f306(f146(x43043,x43041),x43044),x43045)))),f306(f306(f146(x43043,x43041),x43044),x43045)),f306(f306(f146(x43043,x43041),x43044),f306(f306(f130(x43043),f306(f186(f866(x43043)),f168(x43043,f306(f74(x43041,a859,x43043,x43042),x43044),x43045))),x43045))) % 187.68/187.63 [4179]E(f306(f306(f122(f871(x41791,x41792)),f306(f306(f173(x41791,x41792),f306(f306(f165(x41791),f306(f186(f866(x41792)),x41793)),x41794)),x41793)),f306(f306(f173(x41791,x41792),f306(f306(f130(x41791),f306(f186(f866(x41792)),x41793)),x41794)),x41795)),f306(f306(f173(x41791,x41792),x41794),f306(f306(f122(x41792),x41793),x41795))) % 187.68/187.63 [4296]E(f86(x42961,f306(f306(f18(x42961,a859,a859),f306(f306(f8(a859,f872(a859,a859),x42961),a304),f306(f306(f7(x42961,f872(x42961,a859),a859),f308(x42961)),x42962))),f306(f306(f7(x42961,x42963,a859),f306(f306(f8(x42963,f872(x42963,a859),x42961),a303),x42964)),x42965))),f306(f78(x42961,x42963,x42962,x42964),x42965)) % 187.68/187.63 [4348]E(f306(f306(f87(a1,x43481),f306(f111(a1),f306(f306(f81(a1),x43482),a104))),f306(f306(f18(a1,x43481,x43481),f306(f306(f7(a1,x43481,f872(x43481,x43481)),f306(f306(f8(a859,f872(x43481,f872(x43481,x43481)),a1),f101(x43481)),a190)),f182(x43481,x43483,x43484,x43485))),f306(f306(f8(a865,x43481,a1),x43484),f306(f306(f7(a1,a865,a865),f306(f306(f8(a865,f872(a865,a865),a1),f81(a865)),a112)),x43485)))),f182(x43481,x43483,x43484,f306(f306(f81(a865),f306(f111(a865),x43482)),x43485))) % 187.68/187.63 [4380]E(f306(f169(x43801,x43802),f306(f306(f146(f871(x43801,x43803),f871(x43801,x43802)),f306(f245(x43801,x43803,f871(x43801,x43802)),f306(f306(f7(x43801,f872(x43803,x43802),f872(x43803,f871(x43801,x43802))),f306(f306(f8(f872(x43802,f871(x43801,x43802)),f872(f872(x43803,x43802),f872(x43803,f871(x43801,x43802))),x43801),f8(x43802,f871(x43801,x43802),x43803)),f236(x43801,x43802))),x43804))),x43805)),f306(f74(f869(x43803),f869(x43802),x43801,f306(f189(x43803,x43802),x43804)),f306(f169(x43801,x43803),x43805))) % 187.68/187.63 [4341]E(f175(x43411,x43412,f306(f306(f18(x43411,f869(x43412),f869(x43412)),f306(f306(f18(x43411,f869(x43412),f872(f869(x43412),f869(x43412))),f306(f306(f8(a859,f872(f869(x43412),f872(f869(x43412),f869(x43412))),x43411),f101(f869(x43412))),x43413)),x43414)),x43415)),f306(f306(f108(f872(x43411,a859)),f306(f306(f109(f872(x43411,a859)),f175(x43411,x43412,x43414)),f306(f228(x43411),x43413))),f306(f306(f109(f872(x43411,a859)),f175(x43411,x43412,x43415)),f306(f228(x43411),f306(f306(f8(a859,a859,x43411),a301),x43413))))) % 187.68/187.63 [4378]E(f306(f306(f87(a1,x43781),f306(f111(a1),f306(f306(f81(a1),x43782),a104))),f306(f306(f18(a1,x43781,x43781),f306(f306(f7(a1,x43781,f872(x43781,x43781)),f306(f306(f8(a859,f872(x43781,f872(x43781,x43781)),a1),f101(x43781)),a190)),f306(f181(x43781,x43783,x43784),x43785))),f306(f306(f18(a1,x43781,x43781),f306(f306(f8(a865,f872(x43781,x43781),a1),x43784),f306(f306(f7(a1,a865,a865),f306(f306(f8(a865,f872(a865,a865),a1),f81(a865)),a112)),x43785))),f306(f306(f8(a865,x43781,a1),f181(x43781,x43783,x43784)),f306(f306(f7(a1,a865,a865),f306(f306(f8(a865,f872(a865,a865),a1),f81(a865)),a112)),x43785))))),f306(f181(x43781,x43783,x43784),f306(f306(f81(a865),f306(f111(a865),x43782)),x43785))) % 187.68/187.63 [4411]E(f306(f228(f871(x44111,x44112)),f306(f245(x44111,x44112,a859),f306(f306(f8(f872(x44112,f872(x44113,a859)),f872(x44112,a859),x44111),f306(f8(f872(x44113,a859),a859,x44112),f88(x44113))),f306(f306(f7(x44111,f872(x44112,f872(x44113,a859)),f872(x44112,f872(x44113,a859))),f306(f306(f8(f872(f872(x44113,a859),f872(x44113,a859)),f872(f872(x44112,f872(x44113,a859)),f872(x44112,f872(x44113,a859))),x44111),f8(f872(x44113,a859),f872(x44113,a859),x44112)),f306(f306(f8(f872(x44113,f872(a859,a859)),f872(f872(x44113,a859),f872(x44113,a859)),x44111),f18(x44113,a859,a859)),f306(f306(f8(f872(x44113,a859),f872(x44113,f872(a859,a859)),x44111),f306(f8(a859,f872(a859,a859),x44113),a304)),f306(f306(f7(x44111,f872(f871(x44111,x44113),a859),f872(x44113,a859)),f306(f306(f8(f872(x44113,f872(f872(f871(x44111,x44113),a859),a859)),f872(f872(f871(x44111,x44113),a859),f872(x44113,a859)),x44111),f7(x44113,f872(f871(x44111,x44113),a859),a859)),f306(f306(f8(f872(x44113,f871(x44111,x44113)),f872(x44113,f872(f872(f871(x44111,x44113),a859),a859)),x44111),f306(f8(f871(x44111,x44113),f872(f872(f871(x44111,x44113),a859),a859),x44113),f308(f871(x44111,x44113)))),f236(x44111,x44113)))),x44114))))),f306(f306(f7(x44112,f872(f871(x44113,x44112),a859),f872(x44113,a859)),f306(f306(f8(f872(x44113,f872(f872(f871(x44113,x44112),a859),a859)),f872(f872(f871(x44113,x44112),a859),f872(x44113,a859)),x44112),f7(x44113,f872(f871(x44113,x44112),a859),a859)),f306(f306(f8(f872(x44113,f871(x44113,x44112)),f872(x44113,f872(f872(f871(x44113,x44112),a859),a859)),x44112),f306(f8(f871(x44113,x44112),f872(f872(f871(x44113,x44112),a859),a859),x44113),f308(f871(x44113,x44112)))),f306(f7(x44113,x44112,f871(x44113,x44112)),f236(x44113,x44112))))),x44115))))),f306(f306(f263(x44111,x44113,x44112),x44114),x44115)) % 187.68/187.63 [4495]~E(f31(x44951,x44952,x44953),f29(x44954,x44955,x44956)) % 187.68/187.63 [4498]~E(f30(x44981,x44982,x44983),f29(x44984,x44985,x44986)) % 187.68/187.63 [4499]~E(f30(x44991,x44992,x44993),f31(x44994,x44995,x44996)) % 187.68/187.63 [4163]E(f178(x41631,x41632,f176(x41631,x41632,x41633,x41634),x41635,x41636),f176(x41631,x41632,x41633,f178(x41631,x41632,x41634,x41635,x41636))) % 187.68/187.63 [4286]E(f306(f74(f871(x42861,x42862),x42862,f871(x42863,x42864),f244(x42861,x42862)),f246(x42863,x42861,x42864,x42862,x42865,x42866)),f306(f74(x42864,x42862,f871(x42863,x42864),x42866),f244(x42863,x42864))) % 187.68/187.63 [4287]E(f306(f74(f871(x42871,x42872),x42871,f871(x42873,x42874),f235(x42871,x42872)),f246(x42873,x42871,x42874,x42872,x42875,x42876)),f306(f74(x42873,x42871,f871(x42873,x42874),x42875),f235(x42873,x42874))) % 187.68/187.63 [3895]E(f306(f306(f74(x38951,x38952,x38953,x38954),x38955),x38956),f306(x38954,f306(x38955,x38956))) % 187.68/187.63 [3697]E(f306(f306(f245(x36971,x36972,x36973),x36974),f306(f306(f236(x36971,x36972),x36975),x36976)),f306(f306(x36974,x36975),x36976)) % 187.68/187.63 [3756]E(f306(f306(f306(f8(x37561,x37562,x37563),x37564),x37565),x37566),f306(x37564,f306(x37565,x37566))) % 187.68/187.63 [3757]E(f306(f306(f306(f7(x37571,x37572,x37573),x37574),x37575),x37576),f306(f306(x37574,x37576),x37575)) % 187.68/187.63 [3774]E(f306(f306(f306(f18(x37741,x37742,x37743),x37744),x37745),x37746),f306(f306(x37744,x37746),f306(x37745,x37746))) % 187.68/187.63 [3795]E(f306(f148(x37951,x37952,x37953,x37954),f306(f306(f143(x37952),x37955),x37956)),f306(f306(x37954,x37955),x37956)) % 187.68/187.63 [3899]E(f306(f306(f143(f871(x38991,x38992)),f306(f306(f236(x38991,x38992),x38993),x38994)),f306(f306(f173(x38991,x38992),x38995),x38996)),f306(f306(f173(x38991,x38992),f306(f306(f143(x38991),x38993),x38995)),f306(f306(f143(x38992),x38994),x38996))) % 187.68/187.63 [3901]E(f306(f306(f146(x39011,x39012),x39013),f306(f306(f151(x39011,x39014),x39015),x39016)),f306(f306(f151(x39012,f306(f306(f146(x39011,x39012),x39013),x39014)),x39015),f306(x39013,x39016))) % 187.68/187.63 [3943]E(f306(f134(x39431,x39432,x39433,x39434),f306(f306(f143(x39432),x39435),x39436)),f306(f134(x39431,x39432,x39433,f306(f306(x39433,x39434),x39435)),x39436)) % 187.68/187.63 [3966]E(f248(x39661,x39662,x39663,x39664,f306(f306(f236(x39661,x39662),x39665),x39666)),f306(f306(x39664,x39665),x39666)) % 187.68/187.63 [4049]E(f306(f306(f43(x40491,f872(x40492,a859)),x40493),f306(f74(x40494,f872(x40492,a859),x40491,x40495),x40496)),f306(f306(f43(x40494,f872(x40492,a859)),f306(f285(x40491,x40494,x40496),x40493)),x40495)) % 187.68/187.63 [4100]E(f306(f306(f189(x41001,x41002),x41003),f306(f306(f189(x41004,x41001),x41005),x41006)),f306(f306(f189(x41004,x41002),f306(f74(x41001,x41002,x41004,x41003),x41005)),x41006)) % 187.68/187.63 [4102]E(f306(f306(f146(x41021,x41022),x41023),f306(f306(f146(x41024,x41021),x41025),x41026)),f306(f306(f146(x41024,x41022),f306(f74(x41021,x41022,x41024,x41023),x41025)),x41026)) % 187.68/187.63 [4107]E(f306(f285(x41071,x41072,f306(f74(x41073,x41072,x41071,x41074),x41075)),x41076),f306(f285(x41073,x41072,x41074),f306(f285(x41071,x41073,x41075),x41076))) % 187.68/187.63 [4108]E(f306(f286(x41081,x41082,f306(f74(x41083,x41082,x41081,x41084),x41085)),x41086),f306(f286(x41081,x41083,x41085),f306(f286(x41083,x41082,x41084),x41086))) % 187.68/187.63 [4137]E(f176(x41371,x41372,x41373,f306(f306(f306(f73(x41371,f869(x41372)),x41374),x41375),f306(f214(x41372),x41376))),f306(f306(f306(f73(x41371,f869(x41372)),f176(x41371,x41372,x41373,x41374)),x41375),f306(f214(x41372),x41376))) % 187.68/187.63 [4139]E(f306(f134(x41391,x41392,x41393,f306(f134(x41391,x41392,x41393,x41394),x41395)),x41396),f306(f134(x41391,x41392,x41393,x41394),f306(f306(f122(x41392),x41395),x41396))) % 187.68/187.63 [4276]E(f306(f246(x42761,x42761,x42762,x42763,f35(x42761),x42764),f306(f306(f236(x42761,x42762),x42765),x42766)),f306(f306(f236(x42761,x42763),x42765),f306(x42764,x42766))) % 187.68/187.63 [4277]E(f306(f246(x42771,x42772,x42773,x42773,x42774,f35(x42773)),f306(f306(f236(x42771,x42773),x42775),x42776)),f306(f306(f236(x42772,x42773),f306(x42774,x42775)),x42776)) % 187.68/187.63 [4365]E(f306(f306(f146(f871(x43651,x43652),f871(x43651,x43653)),f306(f245(x43651,x43652,f871(x43651,x43653)),f306(f306(f7(x43651,f872(x43652,x43653),f872(x43652,f871(x43651,x43653))),f306(f306(f8(f872(x43653,f871(x43651,x43653)),f872(f872(x43652,x43653),f872(x43652,f871(x43651,x43653))),x43651),f8(x43653,f871(x43651,x43653),x43652)),f236(x43651,x43653))),x43654))),f306(f306(f173(x43651,x43652),x43655),x43656)),f306(f306(f173(x43651,x43653),x43655),f306(f306(f146(x43652,x43653),x43654),x43656))) % 187.68/187.63 [3761]E(f99(x37611,x37612,x37613,f306(f306(f306(f93(x37611),x37614),x37615),x37616)),f306(f306(f306(x37613,x37614),x37615),x37616)) % 187.68/187.63 [3762]E(f100(x37621,x37622,x37623,f306(f306(f306(f93(x37621),x37624),x37625),x37626)),f306(f306(f306(x37623,x37624),x37625),x37626)) % 187.68/187.63 [3953]E(f306(f306(f74(x39531,x39532,x39533,f306(f16(x39532,x39531),x39534)),x39535),x39536),x39534) % 187.68/187.63 [3985]E(f306(f285(x39851,x39852,x39853),f306(f285(x39854,x39851,x39855),x39856)),f306(f285(x39854,x39852,f306(f306(f8(x39851,x39852,x39854),x39853),x39855)),x39856)) % 187.68/187.63 [3991]E(f306(f306(f43(x39911,f872(x39912,a859)),f306(f285(x39913,x39911,x39914),x39915)),x39916),f306(f306(f43(x39913,f872(x39912,a859)),x39915),f306(f306(f8(x39911,f872(x39912,a859),x39913),x39916),x39914))) % 187.68/187.63 [3992]E(f306(f306(f44(x39921,f872(x39922,a859)),f306(f285(x39923,x39921,x39924),x39925)),x39926),f306(f306(f44(x39923,f872(x39922,a859)),x39925),f306(f306(f8(x39921,f872(x39922,a859),x39923),x39926),x39924))) % 187.68/187.63 [3993]E(f306(f306(f43(x39931,f872(x39932,a859)),x39933),f306(f306(f8(x39934,f872(x39932,a859),x39931),x39935),x39936)),f306(f306(f43(x39934,f872(x39932,a859)),f306(f285(x39931,x39934,x39936),x39933)),x39935)) % 187.68/187.63 [3994]E(f306(f306(f44(x39941,f872(x39942,a859)),x39943),f306(f306(f8(x39944,f872(x39942,a859),x39941),x39945),x39946)),f306(f306(f44(x39944,f872(x39942,a859)),f306(f285(x39941,x39944,x39946),x39943)),x39945)) % 187.68/187.63 [4051]E(f306(f306(f43(x40511,f872(x40512,a859)),x40513),f306(f306(f8(f872(x40514,a859),f872(x40512,a859),x40511),f285(x40514,x40512,x40515)),x40516)),f306(f285(x40514,x40512,x40515),f306(f306(f43(x40511,f872(x40514,a859)),x40513),x40516))) % 187.68/187.63 [4052]E(f306(f306(f43(x40521,f872(x40522,a859)),x40523),f306(f306(f8(f872(x40524,a859),f872(x40522,a859),x40521),f260(x40524,x40522,x40525)),x40526)),f306(f260(x40524,x40522,x40525),f306(f306(f43(x40521,f872(x40524,a859)),x40523),x40526))) % 187.68/187.63 [4053]E(f306(f306(f43(x40531,f872(x40532,a859)),x40533),f306(f306(f8(f872(x40534,a859),f872(x40532,a859),x40531),f286(x40532,x40534,x40535)),x40536)),f306(f286(x40532,x40534,x40535),f306(f306(f43(x40531,f872(x40534,a859)),x40533),x40536))) % 187.68/187.63 [4054]E(f306(f306(f44(x40541,f872(x40542,a859)),x40543),f306(f306(f8(f872(x40544,a859),f872(x40542,a859),x40541),f286(x40542,x40544,x40545)),x40546)),f306(f286(x40542,x40544,x40545),f306(f306(f44(x40541,f872(x40544,a859)),x40543),x40546))) % 187.68/187.63 [4145]E(f306(f134(x41451,x41452,f306(f7(x41452,x41451,x41451),x41453),x41454),f306(f161(x41452),f306(f306(f143(x41452),x41455),x41456))),f306(f306(x41453,x41455),f306(f134(x41451,x41452,f306(f7(x41452,x41451,x41451),x41453),x41454),f306(f161(x41452),x41456)))) % 187.68/187.63 [4202]E(f306(f306(f18(f871(x42021,x42022),x42022,x42023),f306(f306(f8(x42024,f872(x42022,x42023),f871(x42021,x42022)),x42025),f306(f306(f8(x42021,x42024,f871(x42021,x42022)),x42026),f235(x42021,x42022)))),f244(x42021,x42022)),f306(f245(x42021,x42022,x42023),f306(f306(f8(x42024,f872(x42022,x42023),x42021),x42025),x42026))) % 187.68/187.63 [4209]E(f306(f134(x42091,x42092,f306(f7(x42092,x42091,x42091),x42093),f306(f134(x42091,x42092,f306(f7(x42092,x42091,x42091),x42093),x42094),f306(f161(x42092),x42095))),f306(f161(x42092),x42096)),f306(f134(x42091,x42092,f306(f7(x42092,x42091,x42091),x42093),x42094),f306(f161(x42092),f306(f306(f122(x42092),x42096),x42095)))) % 187.68/187.63 [4211]E(f306(f306(f146(f871(x42111,x42112),f871(x42113,x42112)),f306(f245(x42111,x42112,f871(x42113,x42112)),f306(f306(f8(x42113,f872(x42112,f871(x42113,x42112)),x42111),f236(x42113,x42112)),x42114))),f306(f306(f173(x42111,x42112),x42115),x42116)),f306(f306(f173(x42113,x42112),f306(f306(f146(x42111,x42113),x42114),x42115)),x42116)) % 187.68/187.63 [4259]P1(f306(f306(f220(f872(x42591,a859)),f306(f260(x42592,x42591,x42593),f306(f306(f44(x42594,f872(x42592,a859)),x42595),x42596))),f306(f306(f44(x42594,f872(x42591,a859)),x42595),f306(f306(f8(f872(x42592,a859),f872(x42591,a859),x42594),f260(x42592,x42591,x42593)),x42596)))) % 187.68/187.63 [4064]E(f306(f306(f173(x40641,x40642),f306(f306(f151(x40641,x40643),x40644),f306(f235(x40641,x40642),x40645))),f306(f306(f151(x40642,x40646),x40644),f306(f244(x40641,x40642),x40645))),f306(f306(f151(f871(x40641,x40642),f306(f306(f173(x40641,x40642),x40643),x40646)),x40644),x40645)) % 187.68/187.63 [4126]E(f306(f306(f108(f872(f871(x41261,x41262),a859)),f306(f306(f263(x41261,x41263,x41262),x41264),x41265)),f306(f306(f263(x41261,x41263,x41262),x41264),x41266)),f306(f306(f263(x41261,x41263,x41262),x41264),f306(f306(f108(f872(f871(x41263,x41262),a859)),x41265),x41266))) % 187.68/187.63 [4222]E(f306(f306(f284(f871(x42221,x42222)),f306(f306(f236(x42221,x42222),x42223),x42224)),f306(f306(f108(f872(f871(x42221,x42222),a859)),f306(f306(f243(x42221,x42222),x42225),f306(f16(f872(x42222,a859),x42221),f306(f306(f284(x42222),x42224),x42226)))),f306(f306(f243(x42221,x42222),f306(f306(f284(x42221),x42223),x42225)),f306(f16(f872(x42222,a859),x42221),x42226)))),f306(f306(f243(x42221,x42222),f306(f306(f284(x42221),x42223),x42225)),f306(f16(f872(x42222,a859),x42221),f306(f306(f284(x42222),x42224),x42226)))) % 187.68/187.63 [4299]E(f306(f306(f109(f872(x42991,a859)),f306(f286(x42991,x42992,f306(f74(f871(x42992,x42993),x42992,x42991,f235(x42992,x42993)),x42994)),x42995)),f306(f286(x42991,x42993,f306(f74(f871(x42992,x42993),x42993,x42991,f244(x42992,x42993)),x42994)),x42996)),f306(f286(x42991,f871(x42992,x42993),x42994),f306(f306(f243(x42992,x42993),x42995),f306(f16(f872(x42993,a859),x42992),x42996)))) % 187.68/187.63 [4048]E(f306(f306(f306(f73(x40481,x40482),f306(f306(f306(f73(x40481,x40482),x40483),x40484),x40485)),x40484),x40486),f306(f306(f306(f73(x40481,x40482),x40483),x40484),x40486)) % 187.68/187.63 [4151]E(f306(f306(f108(f872(f871(x41511,x41512),a859)),f306(f306(f263(x41511,x41513,x41512),x41514),x41515)),f306(f306(f263(x41511,x41513,x41512),x41516),x41515)),f306(f306(f263(x41511,x41513,x41512),f306(f306(f108(f872(f871(x41511,x41513),a859)),x41514),x41516)),x41515)) % 187.68/187.63 [4284]E(f306(f306(f43(x42841,f872(x42842,a859)),x42843),f306(f306(f7(x42841,f872(x42844,f872(x42842,a859)),f872(x42842,a859)),f306(f306(f8(f872(x42844,a859),f872(f872(x42844,f872(x42842,a859)),f872(x42842,a859)),x42841),f43(x42844,f872(x42842,a859))),x42845)),x42846)),f306(f306(f43(x42844,f872(x42842,a859)),f306(f306(f43(x42841,f872(x42844,a859)),x42843),x42845)),x42846)) % 187.68/187.63 [4285]E(f306(f306(f44(x42851,f872(x42852,a859)),x42853),f306(f306(f7(x42851,f872(x42854,f872(x42852,a859)),f872(x42852,a859)),f306(f306(f8(f872(x42854,a859),f872(f872(x42854,f872(x42852,a859)),f872(x42852,a859)),x42851),f44(x42854,f872(x42852,a859))),x42855)),x42856)),f306(f306(f44(x42854,f872(x42852,a859)),f306(f306(f43(x42851,f872(x42854,a859)),x42853),x42855)),x42856)) % 187.68/187.63 [4336]E(f306(f245(x43361,x43362,f871(x43363,x43364)),f306(f306(f7(x43361,f872(x43362,x43364),f872(x43362,f871(x43363,x43364))),f306(f306(f8(f872(x43364,f871(x43363,x43364)),f872(f872(x43362,x43364),f872(x43362,f871(x43363,x43364))),x43361),f8(x43364,f871(x43363,x43364),x43362)),f306(f306(f8(x43363,f872(x43364,f871(x43363,x43364)),x43361),f236(x43363,x43364)),x43365))),x43366)),f246(x43361,x43363,x43362,x43364,x43365,x43366)) % 187.68/187.63 [4258]E(f306(f306(f306(f73(x42581,f869(x42582)),f179(x42581,x42582,x42583,f306(f306(f22(f872(x42581,a859)),x42584),f306(f306(f284(x42581),x42585),f185(f872(x42581,a859)))))),x42585),x42586),f306(f306(f306(f73(x42581,f869(x42582)),f179(x42581,x42582,x42583,x42584)),x42585),x42586)) % 187.68/187.63 [4361]E(f306(f285(x43611,x43612,f306(f306(f18(x43611,x43612,x43612),f306(f306(f18(x43611,x43612,f872(x43612,x43612)),f306(f306(f8(a859,f872(x43612,f872(x43612,x43612)),x43611),f101(x43612)),x43613)),x43614)),x43615)),x43616),f306(f306(f108(f872(x43612,a859)),f306(f285(x43611,x43612,x43614),f306(f306(f109(f872(x43611,a859)),x43616),f306(f228(x43611),x43613)))),f306(f285(x43611,x43612,x43615),f306(f306(f109(f872(x43611,a859)),x43616),f306(f228(x43611),f306(f306(f8(a859,a859,x43611),a301),x43613)))))) % 187.68/187.63 [4370]E(f306(f285(x43701,f871(x43702,x43703),f306(f306(f18(x43701,x43703,f871(x43702,x43703)),f306(f306(f8(x43702,f872(x43703,f871(x43702,x43703)),x43701),f236(x43702,x43703)),x43704)),x43705)),x43706),f306(f306(f243(x43702,x43703),f306(f285(x43701,x43702,x43704),x43706)),f306(f306(f8(f872(x43701,a859),f872(x43703,a859),x43702),f285(x43701,x43703,x43705)),f306(f306(f7(x43702,f872(x43701,a859),f872(x43701,a859)),f306(f306(f8(f872(x43701,a859),f872(f872(x43701,a859),f872(x43701,a859)),x43702),f109(f872(x43701,a859))),f306(f306(f8(f872(x43702,a859),f872(x43701,a859),x43702),f286(x43701,x43702,x43704)),f306(f306(f7(x43702,f872(x43702,a859),f872(x43702,a859)),f284(x43702)),f185(f872(x43702,a859)))))),x43706)))) % 187.68/187.63 [4318]E(f306(f244(x43181,x43182),f306(f246(x43183,x43181,x43184,x43182,x43185,x43186),x43187)),f306(x43186,f306(f244(x43183,x43184),x43187))) % 187.68/187.63 [4319]E(f306(f235(x43191,x43192),f306(f246(x43193,x43191,x43194,x43192,x43195,x43196),x43197)),f306(x43195,f306(f235(x43193,x43194),x43197))) % 187.68/187.63 [4026]E(f306(f306(f173(x40261,x40262),f306(f306(f151(x40261,x40263),x40264),x40265)),f306(f306(f151(x40262,x40266),x40264),x40267)),f306(f306(f151(f871(x40261,x40262),f306(f306(f173(x40261,x40262),x40263),x40266)),x40264),f306(f306(f236(x40261,x40262),x40265),x40267))) % 187.68/187.63 [4094]E(f306(f306(f306(f247(x40941,x40942,x40943,x40944),x40945),x40946),x40947),f306(f306(f245(x40942,x40943,x40944),x40946),f306(x40945,x40947))) % 187.68/187.63 [4106]E(f306(f306(f306(f247(x41061,x41062,x41063,x41064),x41065),x41066),x41067),f306(f306(x41066,f306(f235(x41062,x41063),f306(x41065,x41067))),f306(f244(x41062,x41063),f306(x41065,x41067)))) % 187.68/187.64 [4141]E(f178(x41411,x41412,f306(f306(f306(f73(x41411,f869(x41412)),x41413),x41414),f306(f214(x41412),x41415)),x41416,x41417),f178(x41411,x41412,x41413,f306(f306(f143(x41411),x41414),x41416),f306(f306(f143(x41412),x41415),x41417))) % 187.68/187.64 [4157]E(f306(f74(x41571,x41572,x41573,x41574),f306(f74(x41575,x41571,x41573,x41576),x41577)),f306(f74(x41575,x41572,x41573,f306(f74(x41571,x41572,x41575,x41574),x41576)),x41577)) % 187.68/187.64 [4218]E(f306(f74(f869(x42181),f869(x42182),x42183,f306(f189(x42181,x42182),x42184)),f306(f306(f306(f73(x42183,f869(x42181)),x42185),x42186),f306(f214(x42181),x42187))),f306(f306(f306(f73(x42183,f869(x42182)),f306(f74(f869(x42181),f869(x42182),x42183,f306(f189(x42181,x42182),x42184)),x42185)),x42186),f306(f214(x42182),f306(x42184,x42187)))) % 187.68/187.64 [4343]E(f306(f246(x43431,x43432,x43433,x43433,x43434,f35(x43433)),f306(f246(x43431,x43431,x43435,x43433,f35(x43431),x43436),x43437)),f306(f306(f236(x43432,x43433),f306(x43434,f306(f235(x43431,x43435),x43437))),f306(x43436,f306(f244(x43431,x43435),x43437)))) % 187.68/187.64 [4344]E(f306(f246(x43441,x43441,x43442,x43443,f35(x43441),x43444),f306(f246(x43445,x43441,x43442,x43442,x43446,f35(x43442)),x43447)),f306(f306(f236(x43441,x43443),f306(x43446,f306(f235(x43445,x43442),x43447))),f306(x43444,f306(f244(x43445,x43442),x43447)))) % 187.68/187.64 [4359]E(f306(f246(x43591,x43592,x43593,x43593,x43594,f35(x43593)),f306(f246(x43595,x43591,x43593,x43593,x43596,f35(x43593)),x43597)),f306(f246(x43595,x43592,x43593,x43593,f306(f74(x43591,x43592,x43595,x43594),x43596),f35(x43593)),x43597)) % 187.68/187.64 [4360]E(f306(f246(x43601,x43601,x43602,x43603,f35(x43601),x43604),f306(f246(x43601,x43601,x43605,x43602,f35(x43601),x43606),x43607)),f306(f246(x43601,x43601,x43605,x43603,f35(x43601),f306(f74(x43602,x43603,x43605,x43604),x43606)),x43607)) % 187.68/187.64 [4367]E(f306(f246(x43671,x43672,x43673,x43673,x43674,f35(x43673)),f306(f246(x43671,x43671,x43675,x43673,f35(x43671),x43676),x43677)),f306(f246(x43672,x43672,x43675,x43673,f35(x43672),x43676),f306(f246(x43671,x43672,x43675,x43675,x43674,f35(x43675)),x43677))) % 187.68/187.64 [4061]E(f306(f306(f263(x40611,x40612,x40613),f306(f306(f263(x40611,x40614,x40612),x40615),x40616)),x40617),f306(f306(f263(x40611,x40614,x40613),x40615),f306(f306(f263(x40614,x40612,x40613),x40616),x40617))) % 187.68/187.64 [4132]E(f306(f306(f245(x41321,x41322,x41323),f306(f74(x41324,f872(x41322,x41323),x41321,x41325),x41326)),x41327),f306(f306(x41325,f306(x41326,f306(f235(x41321,x41322),x41327))),f306(f244(x41321,x41322),x41327))) % 187.68/187.64 [4182]E(f306(f74(x41821,x41822,x41823,x41824),f306(f306(f306(f73(x41823,x41821),x41825),x41826),x41827)),f306(f306(f306(f73(x41823,x41822),f306(f74(x41821,x41822,x41823,x41824),x41825)),x41826),f306(x41824,x41827))) % 187.68/187.64 [4214]E(f306(f134(x42141,x42142,f306(f7(x42142,x42141,x42141),x42143),x42144),f306(f161(x42142),f306(f306(f146(x42145,x42142),x42146),x42147))),f306(f134(x42141,x42145,f306(f7(x42145,x42141,x42141),f306(f74(x42142,f872(x42141,x42141),x42145,x42143),x42146)),x42144),f306(f161(x42145),x42147))) % 187.68/187.64 [4158]E(f306(f306(f43(x41581,f872(f871(x41582,x41583),a859)),x41584),f306(f306(f8(f872(f871(x41585,x41583),a859),f872(f871(x41582,x41583),a859),x41581),f306(f263(x41582,x41585,x41583),x41586)),x41587)),f306(f306(f263(x41582,x41585,x41583),x41586),f306(f306(f43(x41581,f872(f871(x41585,x41583),a859)),x41584),x41587))) % 187.68/187.64 [4305]E(f306(f306(f43(x43051,f872(f871(x43052,x43053),a859)),x43054),f306(f306(f7(x43051,f872(f871(x43055,x43053),a859),f872(f871(x43052,x43053),a859)),f306(f306(f8(f872(f871(x43052,x43055),a859),f872(f872(f871(x43055,x43053),a859),f872(f871(x43052,x43053),a859)),x43051),f263(x43052,x43055,x43053)),x43056)),x43057)),f306(f306(f263(x43052,x43055,x43053),f306(f306(f43(x43051,f872(f871(x43052,x43055),a859)),x43054),x43056)),x43057)) % 187.68/187.64 [4306]E(f306(f134(x43061,x43062,f306(f306(f7(x43061,f872(x43062,x43063),f872(x43062,x43061)),f306(f306(f8(f872(x43063,x43061),f872(f872(x43062,x43063),f872(x43062,x43061)),x43061),f8(x43063,x43061,x43062)),x43064)),x43065),x43066),x43067),f306(f134(x43061,x43063,x43064,x43066),f306(f306(f146(x43062,x43063),x43065),x43067))) % 187.68/187.64 [4368]E(f306(f306(f44(x43681,f872(x43682,a859)),x43683),f306(f306(f8(f872(x43684,f872(x43682,a859)),f872(x43682,a859),x43681),f306(f44(x43684,f872(x43682,a859)),x43685)),f306(f306(f7(x43681,f872(x43684,f872(x43682,a859)),f872(x43684,f872(x43682,a859))),f306(f306(f8(f872(f872(x43682,a859),f872(x43682,a859)),f872(f872(x43684,f872(x43682,a859)),f872(x43684,f872(x43682,a859))),x43681),f8(f872(x43682,a859),f872(x43682,a859),x43684)),f306(f306(f8(f872(x43682,a859),f872(f872(x43682,a859),f872(x43682,a859)),x43681),f108(f872(x43682,a859))),x43686))),x43687))),f306(f306(f108(f872(x43682,a859)),f306(f306(f44(x43681,f872(x43682,a859)),x43683),x43686)),f306(f306(f44(x43684,f872(x43682,a859)),x43685),x43687))) % 187.68/187.64 [4369]E(f306(f306(f43(x43691,f872(x43692,a859)),x43693),f306(f306(f8(f872(x43694,f872(x43692,a859)),f872(x43692,a859),x43691),f306(f43(x43694,f872(x43692,a859)),x43695)),f306(f306(f7(x43691,f872(x43694,f872(x43692,a859)),f872(x43694,f872(x43692,a859))),f306(f306(f8(f872(f872(x43692,a859),f872(x43692,a859)),f872(f872(x43694,f872(x43692,a859)),f872(x43694,f872(x43692,a859))),x43691),f8(f872(x43692,a859),f872(x43692,a859),x43694)),f306(f306(f8(f872(x43692,a859),f872(f872(x43692,a859),f872(x43692,a859)),x43691),f109(f872(x43692,a859))),x43696))),x43697))),f306(f306(f109(f872(x43692,a859)),f306(f306(f43(x43691,f872(x43692,a859)),x43693),x43696)),f306(f306(f43(x43694,f872(x43692,a859)),x43695),x43697))) % 187.68/187.64 [4278]E(f306(f246(x42781,x42782,x42783,x42784,x42785,x42786),f306(f306(f236(x42781,x42783),x42787),x42788)),f306(f306(f236(x42782,x42784),f306(x42785,x42787)),f306(x42786,x42788))) % 187.68/187.64 [4377]E(f306(f306(f146(f871(x43771,x43772),f871(x43773,x43774)),f306(f245(x43771,x43772,f871(x43773,x43774)),f306(f306(f7(x43771,f872(x43772,x43774),f872(x43772,f871(x43773,x43774))),f306(f306(f8(f872(x43774,f871(x43773,x43774)),f872(f872(x43772,x43774),f872(x43772,f871(x43773,x43774))),x43771),f8(x43774,f871(x43773,x43774),x43772)),f306(f306(f8(x43773,f872(x43774,f871(x43773,x43774)),x43771),f236(x43773,x43774)),x43775))),x43776))),f306(f306(f173(x43771,x43772),x43777),x43778)),f306(f306(f173(x43773,x43774),f306(f306(f146(x43771,x43773),x43775),x43777)),f306(f306(f146(x43772,x43774),x43776),x43778))) % 187.68/187.64 [4381]E(f306(f306(f146(f871(x43811,x43812),x43813),f306(f245(x43811,x43812,x43813),f306(f306(f8(f872(x43812,f871(x43811,x43814)),f872(x43812,x43813),x43811),f306(f8(f871(x43811,x43814),x43813,x43812),x43815)),f306(f306(f7(x43811,f872(x43812,x43814),f872(x43812,f871(x43811,x43814))),f306(f306(f8(f872(x43814,f871(x43811,x43814)),f872(f872(x43812,x43814),f872(x43812,f871(x43811,x43814))),x43811),f8(x43814,f871(x43811,x43814),x43812)),f236(x43811,x43814))),x43816)))),f306(f306(f173(x43811,x43812),x43817),x43818)),f306(f306(f146(f871(x43811,x43814),x43813),x43815),f306(f306(f173(x43811,x43814),x43817),f306(f306(f146(x43812,x43814),x43816),x43818)))) % 187.68/187.64 [4310]E(f306(f306(f146(f871(x43101,x43102),x43103),f306(f245(x43101,x43102,x43103),f306(f306(f8(f872(x43102,f871(x43104,x43102)),f872(x43102,x43103),x43101),f306(f8(f871(x43104,x43102),x43103,x43102),x43105)),f306(f306(f8(x43104,f872(x43102,f871(x43104,x43102)),x43101),f236(x43104,x43102)),x43106)))),f306(f306(f173(x43101,x43102),x43107),x43108)),f306(f306(f146(f871(x43104,x43102),x43103),x43105),f306(f306(f173(x43104,x43102),f306(f306(f146(x43101,x43104),x43106),x43107)),x43108))) % 187.68/187.64 [4269]E(f306(f306(f245(x42691,x42692,x42693),f306(f306(f8(f872(x42692,f871(x42694,x42695)),f872(x42692,x42693),x42691),f306(f8(f871(x42694,x42695),x42693,x42692),f306(f245(x42694,x42695,x42693),x42696))),x42697)),x42698),f306(f306(f245(x42694,x42695,x42693),x42696),f306(f306(f245(x42691,x42692,f871(x42694,x42695)),x42697),x42698))) % 187.68/187.64 [4382]E(f306(f306(f43(f871(x43821,x43822),f872(f871(x43823,x43824),a859)),f306(f306(f243(x43821,x43822),x43825),f306(f16(f872(x43822,a859),x43821),x43826))),f306(f245(x43821,x43822,f872(f871(x43823,x43824),a859)),f306(f306(f7(x43821,f872(x43822,f872(x43823,f872(x43824,a859))),f872(x43822,f872(f871(x43823,x43824),a859))),f306(f306(f8(f872(f872(x43823,f872(x43824,a859)),f872(f871(x43823,x43824),a859)),f872(f872(x43822,f872(x43823,f872(x43824,a859))),f872(x43822,f872(f871(x43823,x43824),a859))),x43821),f8(f872(x43823,f872(x43824,a859)),f872(f871(x43823,x43824),a859),x43822)),f306(f306(f8(f872(x43823,a859),f872(f872(x43823,f872(x43824,a859)),f872(f871(x43823,x43824),a859)),x43821),f243(x43823,x43824)),x43827))),f306(f306(f8(f872(x43824,a859),f872(x43823,f872(x43824,a859)),x43822),f16(f872(x43824,a859),x43823)),x43828)))),f306(f306(f243(x43823,x43824),f306(f306(f43(x43821,f872(x43823,a859)),x43825),x43827)),f306(f16(f872(x43824,a859),x43823),f306(f306(f43(x43822,f872(x43824,a859)),x43826),x43828)))) % 187.68/187.64 [4324]E(f306(f306(f247(x43241,x43242,x43243,x43244),f306(f306(f247(x43241,x43245,x43246,f871(x43242,x43243)),x43247),x43248)),x43249),f306(f306(f247(x43241,x43245,x43246,x43244),x43247),f306(f306(f7(x43245,f872(x43242,f872(x43243,x43244)),f872(x43246,x43244)),f306(f306(f8(f872(x43246,f871(x43242,x43243)),f872(f872(x43242,f872(x43243,x43244)),f872(x43246,x43244)),x43245),f247(x43246,x43242,x43243,x43244)),x43248)),x43249))) % 187.68/187.64 [4356]E(f306(f74(f871(x43561,x43562),f871(x43563,x43564),f871(x43565,x43566),f246(x43561,x43563,x43562,x43564,x43567,x43568)),f246(x43565,x43561,x43566,x43562,x43569,x435610)),f246(x43565,x43563,x43566,x43564,f306(f74(x43561,x43563,x43565,x43567),x43569),f306(f74(x43562,x43564,x43566,x43568),x435610))) % 187.68/187.64 [4362]E(f306(f246(x43621,x43622,x43623,x43624,x43625,x43626),f306(f246(x43627,x43621,x43628,x43623,x43629,x436210),x436211)),f306(f246(x43627,x43622,x43628,x43624,f306(f74(x43621,x43622,x43627,x43625),x43629),f306(f74(x43623,x43624,x43628,x43626),x436210)),x436211)) % 187.68/187.64 [6427]P10(a5000)+P1(f306(f306(f308(f871(a862,a860)),a665),f306(f164(f871(a862,a860)),a27))) % 187.68/187.64 [8431]P10(a5000)+~P1(f306(f306(f245(a862,a860,a859),f306(f16(f872(a860,a859),a862),a25)),a665)) % 187.68/187.64 [4532]~P93(x45321)+E(f92(x45321),a303) % 187.68/187.64 [4533]~P3(x45331)+P3(f869(x45331)) % 187.68/187.64 [4534]~P60(x45341)+P60(f869(x45341)) % 187.68/187.64 [4537]~P124(x45371)+~E(f79(x45371),f2(x45371)) % 187.68/187.64 [4539]~E(x45391,f2(a106))+E(f306(a20,x45391),f2(a1)) % 187.68/187.64 [4540]~E(x45401,f2(a1))+E(f83(a1,x45401),f2(a1)) % 187.68/187.64 [4546]~P141(x45461)+P33(x45461,f2(x45461)) % 187.68/187.64 [4548]~P108(x45481)+P17(x45481,f120(x45481)) % 187.68/187.64 [4557]P1(x45571)+P1(f306(a301,x45571)) % 187.68/187.64 [4600]~P141(x46001)+~P33(x46001,f79(x46001)) % 187.68/187.64 [4646]~P1(x46461)+~P1(f306(a301,x46461)) % 187.68/187.64 [4669]E(f306(a112,x46691),f2(a865))+~P1(f306(a190,x46691)) % 187.68/187.64 [4733]~P95(x47331)+P18(x47331,x47331,f82(x47331)) % 187.68/187.64 [4734]~P108(x47341)+P18(x47341,x47341,f225(x47341)) % 187.68/187.64 [4735]~P108(x47351)+P18(x47351,x47351,f219(x47351)) % 187.68/187.64 [4736]~P97(x47361)+P18(x47361,x47361,f108(x47361)) % 187.68/187.64 [4737]~P103(x47371)+P18(x47371,x47371,f109(x47371)) % 187.68/187.64 [4738]~P72(x47381)+P19(x47381,x47381,f82(x47381)) % 187.68/187.64 [4543]~E(x45431,f2(a865))+E(f306(f107(a1),x45431),f2(a1)) % 187.68/187.64 [4550]~P91(x45501)+E(f306(f111(x45501),a84),f2(x45501)) % 187.68/187.64 [4553]~E(f546(x45531),f2(a865))+E(f306(f158(a865),x45531),f2(a865)) % 187.68/187.64 [4554]~P107(x45541)+E(f222(x45541,f220(x45541)),f225(x45541)) % 187.68/187.64 [4555]~P107(x45551)+E(f223(x45551,f220(x45551)),f219(x45551)) % 187.68/187.64 [4556]~P88(x45561)+E(f83(x45561,f2(x45561)),f2(x45561)) % 187.68/187.64 [4565]~P141(x45651)+E(f306(f107(x45651),f2(a865)),f2(x45651)) % 187.68/187.64 [4566]~P141(x45661)+E(f306(f107(x45661),f79(a865)),f79(x45661)) % 187.68/187.64 [4567]~P125(x45671)+E(f306(f110(x45671),f2(a1)),f2(x45671)) % 187.68/187.64 [4568]~P125(x45681)+E(f306(f110(x45681),f79(a1)),f79(x45681)) % 187.68/187.64 [4569]E(x45691,f2(a865))+~E(f306(f107(a1),x45691),f2(a1)) % 187.68/187.64 [4594]~P94(x45941)+E(f306(f80(x45941),f185(x45941)),f231(x45941)) % 187.68/187.64 [4595]~P67(x45951)+E(f306(f80(x45951),f2(x45951)),f2(x45951)) % 187.68/187.64 [4596]~P94(x45961)+E(f306(f80(x45961),f231(x45961)),f185(x45961)) % 187.68/187.64 [4597]~P84(x45971)+E(f306(f76(x45971),f2(x45971)),f2(x45971)) % 187.68/187.64 [4598]~P112(x45981)+E(f306(f76(x45981),f79(x45981)),f79(x45981)) % 187.68/187.64 [4599]~P79(x45991)+E(f306(f158(x45991),f120(x45991)),f2(x45991)) % 187.68/187.64 [4620]~P39(x46201)+P42(f306(f164(a1),x46201)) % 187.68/187.64 [4651]~P91(x46511)+E(f306(f80(x46511),f79(x46511)),f306(f111(x46511),a104)) % 187.68/187.64 [4668]~P91(x46681)+P33(x46681,f306(f111(x46681),a84)) % 187.68/187.64 [4685]~P60(x46851)+E(f306(f164(x46851),f57(x46851)),f231(f872(x46851,a859))) % 187.68/187.64 [4695]P39(x46951)+~P42(f306(f164(a1),x46951)) % 187.68/187.64 [4696]~P60(x46961)+P1(f306(f129(x46961),f57(x46961))) % 187.68/187.64 [4739]E(f306(f107(a1),f306(a112,x47391)),x47391)+P1(f306(a190,x47391)) % 187.68/187.64 [4756]~P107(x47561)+E(f94(x47561,x47561,f5(x47561)),f95(x47561)) % 187.68/187.64 [4809]~P115(x48091)+E(f238(x48091,f79(x48091),f82(x48091)),f237(x48091)) % 187.68/187.64 [4839]~P91(x48391)+~P33(x48391,f306(f111(x48391),a104)) % 187.68/187.64 [4850]E(f306(a28,x48501),f188(a860))+P1(f306(a25,f306(a26,x48501))) % 187.68/187.64 [4981]E(f306(f76(a1),x49811),x49811)+P1(f306(f306(f221(a1),x49811),f2(a1))) % 187.68/187.64 [5002]~E(f306(a112,x50021),f2(a865))+P1(f306(f306(f220(a1),x50021),f2(a1))) % 187.68/187.64 [5066]~P1(f306(a190,x50661))+P1(f306(f306(f221(a1),x50661),f2(a1))) % 187.68/187.64 [5108]~P125(x51081)+P1(f306(f306(f308(x51081),f2(x51081)),f117(x51081))) % 187.68/187.64 [5109]~P141(x51091)+P1(f306(f306(f308(x51091),f2(x51091)),f183(x51091))) % 187.68/187.64 [5110]~P125(x51101)+P1(f306(f306(f308(x51101),f79(x51101)),f117(x51101))) % 187.68/187.64 [5111]~P141(x51111)+P1(f306(f306(f308(x51111),f79(x51111)),f183(x51111))) % 187.68/187.64 [5112]~P111(x51121)+P1(f306(f306(f220(x51121),f2(x51121)),f79(x51121))) % 187.68/187.64 [5113]~P111(x51131)+P1(f306(f306(f221(x51131),f2(x51131)),f79(x51131))) % 187.68/187.64 [5116]E(f306(f214(a860),f769(x51161)),f306(a28,x51161))+~P1(f306(a25,f306(a26,x51161))) % 187.68/187.64 [5117]E(f306(f214(a860),f814(x51171)),f306(a28,x51171))+~P1(f306(a25,f306(a26,x51171))) % 187.68/187.64 [5172]E(x51721,f2(a865))+~P1(f306(f306(f220(a865),x51721),f2(a865))) % 187.68/187.64 [5216]E(f306(a112,x52161),f2(a865))+~P1(f306(f306(f220(a1),x52161),f2(a1))) % 187.68/187.64 [5277]P1(f306(a190,x52771))+~P1(f306(f306(f221(a1),x52771),f2(a1))) % 187.68/187.64 [5282]~P108(x52821)+P19(x52821,f866(x52821),f140(x52821,x52821,f5(x52821))) % 187.68/187.64 [5300]P42(x53001)+~P1(f306(f306(f220(a1),f2(a1)),f312(x53001))) % 187.68/187.64 [5306]E(f306(f76(a1),x53061),f306(f80(a1),x53061))+~P1(f306(f306(f221(a1),x53061),f2(a1))) % 187.68/187.64 [5480]~P111(x54801)+~P1(f306(f306(f220(x54801),f79(x54801)),f2(x54801))) % 187.68/187.64 [5481]~P111(x54811)+~P1(f306(f306(f221(x54811),f79(x54811)),f2(x54811))) % 187.68/187.64 [5491]~E(x54911,f2(a865))+P1(f306(f306(f220(a1),f306(f107(a1),x54911)),f2(a1))) % 187.68/187.64 [5492]~E(x54921,f2(a1))+P1(f306(f306(f221(a1),f306(f76(a1),x54921)),f79(a1))) % 187.68/187.64 [5611]~P79(x56111)+E(f134(x56111,x56111,f81(x56111),f2(x56111)),f158(x56111)) % 187.68/187.64 [5783]~P96(x57831)+P28(a865,x57831,f107(x57831),f231(f872(a865,a859))) % 187.68/187.64 [5983]E(x59831,f2(a865))+~P1(f306(f306(f220(a1),f306(f107(a1),x59831)),f2(a1))) % 187.68/187.64 [5984]E(x59841,f2(a1))+~P1(f306(f306(f221(a1),f306(f76(a1),x59841)),f79(a1))) % 187.68/187.64 [6783]~P1(f306(f306(f221(a1),x67831),f2(a1)))+P1(f306(f306(f221(a1),f306(f306(f81(a1),x67831),x67831)),f2(a1))) % 187.68/187.64 [7329]P1(f306(f306(f221(a1),x73291),f2(a1)))+~P1(f306(f306(f221(a1),f306(f306(f81(a1),x73291),x73291)),f2(a1))) % 187.68/187.64 [7882]E(x78821,f306(a3,f2(a865)))+P1(f306(f306(f221(a865),f306(f306(f22(a865),f306(a19,x78821)),f306(a119,f2(a865)))),f306(a19,x78821))) % 187.68/187.64 [8655]~P1(f306(f306(f221(a1),x86551),f2(a1)))+P1(f306(f306(f221(a1),f306(f306(f22(a1),f306(f306(f81(a1),x86551),x86551)),a104)),f2(a1))) % 187.68/187.64 [8742]~P1(f306(f306(f221(a1),x87421),f2(a1)))+P1(f306(f306(f221(a1),f306(f306(f81(a1),f306(f306(f81(a1),f79(a1)),x87421)),x87421)),f2(a1))) % 187.68/187.64 [9067]P1(f306(f306(f221(a1),x90671),f2(a1)))+~P1(f306(f306(f221(a1),f306(f306(f22(a1),f306(f306(f81(a1),x90671),x90671)),a104)),f2(a1))) % 187.68/187.64 [9132]P1(f306(f306(f221(a1),x91321),f2(a1)))+~P1(f306(f306(f221(a1),f306(f306(f81(a1),f306(f306(f81(a1),f79(a1)),x91321)),x91321)),f2(a1))) % 187.68/187.64 [4639]~E(a84,x46391)+E(f306(f306(f81(a1),x46391),x46391),a84) % 187.68/187.64 [4640]~E(x46401,a84)+E(f306(f306(f81(a1),x46401),x46401),a84) % 187.68/187.64 [4654]E(x46541,f2(a1))+E(f306(f306(f40(a1),x46541),x46541),f79(a1)) % 187.68/187.64 [4785]E(x47851,a84)+~E(f306(f306(f81(a1),x47851),x47851),a84) % 187.68/187.64 [4786]E(a84,x47861)+~E(f306(f306(f81(a1),x47861),x47861),a84) % 187.68/187.64 [4799]~P6(x47991)+E(f42(x47991,f185(f872(x47991,a859))),f231(x47991)) % 187.68/187.64 [4800]~P6(x48001)+E(f42(x48001,f231(f872(x48001,a859))),f185(x48001)) % 187.68/187.64 [4801]~P6(x48011)+E(f41(x48011,f185(f872(x48011,a859))),f185(x48011)) % 187.68/187.64 [4802]~P6(x48021)+E(f41(x48021,f231(f872(x48021,a859))),f231(x48021)) % 187.68/187.64 [4803]~P108(x48031)+E(f131(x48031,f185(f872(x48031,a859))),f120(x48031)) % 187.68/187.64 [4940]E(x49401,f2(a865))+P1(f306(f306(f221(a865),f2(a865)),x49401)) % 187.68/187.64 [4959]~P7(x49591)+P1(f306(f306(f220(a1),f2(a1)),x49591)) % 187.68/187.64 [4993]~E(f306(f111(a865),x49931),f2(a865))+P1(f306(f306(f220(a1),x49931),a84)) % 187.68/187.64 [4998]P42(x49981)+P1(f306(f306(f308(a1),f312(x49981)),x49981)) % 187.68/187.64 [4999]E(x49991,f306(a3,f2(a865)))+P1(f306(f306(f220(a106),f79(a106)),x49991)) % 187.68/187.64 [5038]P1(f306(a190,x50381))+P1(f306(f306(f220(a1),f2(a1)),x50381)) % 187.68/187.64 [5090]E(f306(f107(a1),f306(a112,x50901)),f2(a1))+P1(f306(f306(f220(a1),f2(a1)),x50901)) % 187.68/187.64 [5158]E(f306(f107(a1),f306(f111(a865),x51581)),f306(f111(a1),x51581))+P1(f306(a190,f306(f111(a1),x51581))) % 187.68/187.64 [5178]E(f306(f111(a865),x51781),f2(a865))+~P1(f306(a190,f306(f111(a1),x51781))) % 187.68/187.64 [5179]E(f306(f111(a865),x51791),f2(a865))+~P1(f306(f306(f220(a1),x51791),a84)) % 187.68/187.64 [5213]P7(x52131)+~P1(f306(f306(f220(a1),f2(a1)),x52131)) % 187.68/187.64 [5285]E(f306(a119,f689(x52851)),x52851)+~P1(f306(f306(f221(a865),f2(a865)),x52851)) % 187.68/187.64 [5294]E(f306(a119,f306(f111(a865),x52941)),f79(a865))+~P1(f306(a190,f306(f111(a1),x52941))) % 187.68/187.64 [5302]E(f306(f107(a1),f833(x53021)),x53021)+~P1(f306(f306(f221(a1),f2(a1)),x53021)) % 187.68/187.64 [5310]~E(x53101,f306(a3,f2(a865)))+~P1(f306(f306(f220(a106),f79(a106)),x53101)) % 187.68/187.64 [5317]E(f306(f107(a1),f306(f111(a865),x53171)),f2(a1))+~P1(f306(a190,f306(f111(a1),x53171))) % 187.68/187.64 [5343]E(f306(f158(a865),x53431),f2(a865))+P1(f306(f306(f308(a865),f546(x53431)),f306(f164(a865),x53431))) % 187.68/187.64 [5364]E(f306(f107(a1),f306(a112,x53641)),x53641)+~P1(f306(f306(f220(a1),f2(a1)),x53641)) % 187.68/187.64 [5373]~P1(f306(a190,x53731))+~P1(f306(f306(f220(a1),f2(a1)),x53731)) % 187.68/187.64 [5473]E(f306(f306(f81(a865),f79(a865)),f306(f111(a865),x54731)),f79(a865))+~P1(f306(f306(f221(a1),x54731),a84)) % 187.68/187.64 [5531]E(x55311,f2(a865))+~P1(f306(f306(f221(a865),x55311),f306(a119,f2(a865)))) % 187.68/187.64 [5569]E(f306(f306(f22(a865),f306(f111(a865),x55691)),f79(a865)),f2(a865))+~P1(f306(f306(f220(a1),x55691),a84)) % 187.68/187.64 [5570]E(f306(f306(f81(a865),f306(f111(a865),x55701)),f79(a865)),f79(a865))+~P1(f306(f306(f221(a1),x55701),a84)) % 187.68/187.64 [5580]~P42(x55801)+E(f306(f39(a865),f306(f285(a1,a865,a112),x55801)),f306(f39(a1),x55801)) % 187.68/187.64 [5612]~P108(x56121)+E(f222(x56121,f306(f7(x56121,x56121,a859),f220(x56121))),f219(x56121)) % 187.68/187.64 [5613]~P108(x56131)+E(f223(x56131,f306(f7(x56131,x56131,a859),f220(x56131))),f225(x56131)) % 187.68/187.64 [5623]E(f46(a865,f306(a119,f2(a865)),f306(f111(a865),x56231)),f306(a119,f2(a865)))+~P1(f306(a190,f306(f111(a1),x56231))) % 187.68/187.64 [5632]~P1(f306(f306(f221(a1),f2(a1)),x56321))+P1(f306(f306(f220(a1),f79(a1)),x56321)) % 187.68/187.64 [5633]P1(f306(f306(f221(a1),f2(a1)),x56331))+~P1(f306(f306(f220(a1),f79(a1)),x56331)) % 187.68/187.64 [5644]E(f306(a119,f306(f306(f22(a865),x56441),f79(a865))),x56441)+~P1(f306(f306(f221(a865),f2(a865)),x56441)) % 187.68/187.64 [5701]P1(f306(f306(f221(a865),f2(a865)),f833(x57011)))+~P1(f306(f306(f221(a1),f2(a1)),x57011)) % 187.68/187.64 [5760]E(f46(a1,f306(f111(a1),a104),x57601),f306(f306(f22(a1),x57601),f79(a1)))+~P1(f306(f306(f221(a1),f2(a1)),x57601)) % 187.68/187.64 [5795]~P1(f306(f306(f221(a1),a84),x57951))+P1(f306(f306(f221(a865),f2(a865)),f306(f111(a865),x57951))) % 187.68/187.64 [5845]P1(f306(f306(f221(a865),f2(a865)),f306(a112,x58451)))+~P1(f306(f306(f221(a1),f2(a1)),x58451)) % 187.68/187.64 [5897]~P1(f306(f306(f221(a865),f2(a865)),x58971))+P1(f306(f306(f221(a1),f2(a1)),f306(f107(a1),x58971))) % 187.68/187.64 [5935]~P1(f306(f306(f221(a865),f2(a865)),f306(a112,x59351)))+P1(f306(f306(f221(a1),f2(a1)),x59351)) % 187.68/187.64 [5952]~P42(x59521)+E(f306(f285(a865,a1,f107(a1)),f306(f285(a1,a865,a112),x59521)),x59521) % 187.68/187.64 [5964]P1(f306(f306(f221(a1),a84),x59641))+~P1(f306(f306(f221(a865),f2(a865)),f306(f111(a865),x59641))) % 187.68/187.64 [6012]~P60(x60121)+E(f306(f306(f143(f869(x60121)),f188(x60121)),f306(f306(f146(x60121,f869(x60121)),f214(x60121)),f57(x60121))),f57(f869(x60121))) % 187.68/187.64 [6023]P1(f306(f306(f221(a865),f2(a865)),x60231))+~P1(f306(f306(f221(a1),f2(a1)),f306(f107(a1),x60231))) % 187.68/187.64 [6136]E(f306(f285(a865,a1,f107(a1)),f306(f229(a865),f306(a112,x61361))),f306(f276(a1,f2(a1)),x61361))+~P1(f306(f306(f220(a1),f2(a1)),x61361)) % 187.68/187.64 [6151]~P111(x61511)+P1(f306(f306(f221(x61511),f2(x61511)),f306(f306(f81(x61511),f79(x61511)),f79(x61511)))) % 187.68/187.64 [6202]P1(f306(f306(f221(a865),f306(a119,f2(a865))),f306(a112,x62021)))+~P1(f306(f306(f221(a1),f79(a1)),x62021)) % 187.68/187.64 [6298]E(x62981,f2(a1))+P1(f306(f50(f2(a1),x62981),f306(f306(f236(a1,a1),f2(a1)),f2(a1)))) % 187.68/187.64 [6466]~P1(f306(f306(f221(a865),f306(a119,f2(a865))),f306(a112,x64661)))+P1(f306(f306(f221(a1),f79(a1)),x64661)) % 187.68/187.64 [6893]~P105(x68931)+P40(x68931,f306(f228(f871(x68931,x68931)),f306(f245(x68931,x68931,a859),f221(x68931)))) % 187.68/187.64 [5518]E(f306(f111(a865),f306(f306(f22(a1),x55181),a104)),f306(a119,f306(f111(a865),x55181)))+P1(f306(a190,f306(f111(a1),x55181))) % 187.68/187.64 [5534]~P39(x55341)+E(f306(f306(f146(a865,a1),f107(a1)),f306(f306(f146(a1,a865),a112),x55341)),x55341) % 187.68/187.64 [5650]E(f306(f80(a1),f306(f107(a1),f306(a119,f834(x56501)))),x56501)+~P1(f306(f306(f221(a1),x56501),f2(a1))) % 187.68/187.64 [5660]E(f306(f306(f81(a865),f79(a865)),f306(f111(a865),x56601)),f306(f111(a865),f306(f306(f22(a1),x56601),a104)))+P1(f306(f306(f221(a1),x56601),a84)) % 187.68/187.64 [5703]E(f306(f306(f40(a1),f306(f111(a1),a104)),x57031),f306(f111(a1),a104))+~P1(f306(f306(f221(a1),f2(a1)),x57031)) % 187.68/187.64 [5791]E(f306(f306(f22(a865),f306(f111(a865),x57911)),f79(a865)),f306(f111(a865),f306(f306(f81(a1),x57911),a104)))+P1(f306(f306(f220(a1),x57911),a84)) % 187.68/187.64 [5792]E(f306(f306(f81(a865),f306(f111(a865),x57921)),f79(a865)),f306(f111(a865),f306(f306(f22(a1),x57921),a104)))+P1(f306(f306(f221(a1),x57921),a84)) % 187.68/187.64 [5833]E(f306(a112,f306(f306(f81(a1),f79(a1)),x58331)),f306(a119,f306(a112,x58331)))+~P1(f306(f306(f220(a1),f2(a1)),x58331)) % 187.68/187.64 [5869]E(f306(a119,f306(f306(f22(a865),x58691),f306(a119,f2(a865)))),x58691)+~P1(f306(f306(f221(a865),f2(a865)),x58691)) % 187.68/187.64 [6082]E(f46(a865,f306(a119,f2(a865)),f306(f111(a865),x60821)),f306(a112,f46(a1,f79(a1),f306(f111(a1),x60821))))+P1(f306(a190,f306(f111(a1),x60821))) % 187.68/187.64 [6127]~P1(f306(f306(f220(a1),a84),x61271))+P1(f306(f306(f220(a1),a84),f306(f306(f81(a1),x61271),x61271))) % 187.68/187.64 [6128]~P1(f306(f306(f221(a1),a104),x61281))+P1(f306(f306(f220(a1),a104),f306(f306(f81(a1),x61281),x61281))) % 187.68/187.64 [6129]~P1(f306(f306(f221(a1),a84),x61291))+P1(f306(f306(f221(a1),a84),f306(f306(f81(a1),x61291),x61291))) % 187.68/187.64 [6130]~P1(f306(f306(f221(a1),a104),x61301))+P1(f306(f306(f221(a1),a104),f306(f306(f81(a1),x61301),x61301))) % 187.68/187.64 [6311]~P1(f306(f63(x63111),f231(f872(x63111,a859))))+P1(f306(f63(f869(x63111)),f231(f872(f869(x63111),a859)))) % 187.68/187.64 [6399]~P1(f306(f306(f220(a1),f2(a1)),x63991))+P1(f306(f306(f221(a1),f2(a1)),f306(f306(f81(a1),f79(a1)),x63991))) % 187.68/187.64 [6406]E(f306(f235(a1,a1),f48(f79(a1),f306(f111(a1),x64061))),f306(f306(f40(a1),f79(a1)),f306(f111(a1),x64061)))+~P1(f306(f306(f220(a1),f2(a1)),f306(f111(a1),x64061))) % 187.68/187.64 [6426]E(f306(f244(a1,a1),f48(f79(a1),f306(f111(a1),x64261))),f46(a1,f79(a1),f306(f111(a1),x64261)))+~P1(f306(f306(f220(a1),f2(a1)),f306(f111(a1),x64261))) % 187.68/187.64 [6438]P1(f306(f63(x64381),f231(f872(x64381,a859))))+~P1(f306(f63(f869(x64381)),f231(f872(f869(x64381),a859)))) % 187.68/187.64 [6467]P1(f306(f306(f220(a1),a84),x64671))+~P1(f306(f306(f220(a1),a84),f306(f306(f81(a1),x64671),x64671))) % 187.68/187.64 [6468]P1(f306(f306(f221(a1),a84),x64681))+~P1(f306(f306(f221(a1),a84),f306(f306(f81(a1),x64681),x64681))) % 187.68/187.64 [6469]P1(f306(f306(f221(a1),a104),x64691))+~P1(f306(f306(f220(a1),a104),f306(f306(f81(a1),x64691),x64691))) % 187.68/187.64 [6470]P1(f306(f306(f221(a1),a104),x64701))+~P1(f306(f306(f221(a1),a104),f306(f306(f81(a1),x64701),x64701))) % 187.68/187.64 [6787]~P1(f306(f63(x67871),f231(f872(x67871,a859))))+P1(f306(f306(f221(a865),f2(a865)),f306(f39(x67871),f231(f872(x67871,a859))))) % 187.68/187.64 [7371]P1(f306(f63(a865),x73711))+~P1(f306(f63(a1),f306(f285(a865,a1,f107(a1)),x73711))) % 187.68/187.64 [5448]~E(a104,x54481)+E(f306(f306(f22(a1),f306(f306(f81(a1),x54481),x54481)),a104),a104) % 187.68/187.64 [5449]~E(x54491,a104)+E(f306(f306(f22(a1),f306(f306(f81(a1),x54491),x54491)),a104),a104) % 187.68/187.64 [5957]E(x59571,a104)+~E(f306(f306(f22(a1),f306(f306(f81(a1),x59571),x59571)),a104),a104) % 187.68/187.64 [5958]E(a104,x59581)+~E(f306(f306(f22(a1),f306(f306(f81(a1),x59581),x59581)),a104),a104) % 187.68/187.64 [6368]~E(f306(f111(a865),x63681),f2(a865))+P1(f306(a190,f306(f111(a1),f306(f306(f81(a1),x63681),a104)))) % 187.68/187.64 [6715]~P1(f306(a190,f306(f111(a1),x67151)))+P1(f306(a190,f306(f111(a1),f306(f306(f81(a1),x67151),x67151)))) % 187.68/187.64 [6716]~P1(f306(f306(f220(a1),x67161),a84))+P1(f306(f306(f220(a1),f306(f306(f81(a1),x67161),x67161)),a84)) % 187.68/187.64 [6717]~P1(f306(f306(f220(a1),x67171),a104))+P1(f306(f306(f220(a1),f306(f306(f81(a1),x67171),x67171)),a104)) % 187.68/187.64 [6718]~P1(f306(f306(f221(a1),x67181),a84))+P1(f306(f306(f221(a1),f306(f306(f81(a1),x67181),x67181)),a84)) % 187.68/187.64 [6719]~P1(f306(f306(f220(a1),x67191),a104))+P1(f306(f306(f221(a1),f306(f306(f81(a1),x67191),x67191)),a104)) % 187.68/187.64 [7040]E(f306(f111(a865),x70401),f2(a865))+~P1(f306(a190,f306(f111(a1),f306(f306(f81(a1),x70401),a104)))) % 187.68/187.64 [7279]~P1(f306(f306(f220(a1),f2(a1)),f306(f111(a1),x72791)))+P1(f306(f306(f220(a1),f2(a1)),f306(f111(a1),f306(f306(f81(a1),x72791),x72791)))) % 187.68/187.64 [7280]P1(f306(a190,f306(f111(a1),x72801)))+~P1(f306(a190,f306(f111(a1),f306(f306(f81(a1),x72801),x72801)))) % 187.68/187.64 [7281]P1(f306(f306(f220(a1),x72811),a84))+~P1(f306(f306(f220(a1),f306(f306(f81(a1),x72811),x72811)),a84)) % 187.68/187.64 [7282]P1(f306(f306(f220(a1),x72821),a104))+~P1(f306(f306(f220(a1),f306(f306(f81(a1),x72821),x72821)),a104)) % 187.68/187.64 [7283]P1(f306(f306(f220(a1),x72831),a104))+~P1(f306(f306(f221(a1),f306(f306(f81(a1),x72831),x72831)),a104)) % 187.68/187.64 [7284]P1(f306(f306(f221(a1),x72841),a84))+~P1(f306(f306(f221(a1),f306(f306(f81(a1),x72841),x72841)),a84)) % 187.68/187.64 [7650]E(f306(a114,f493(x76501)),x76501)+~P1(f306(f306(f308(f872(f871(a865,a865),a859)),x76501),a105)) % 187.68/187.64 [6283]~P91(x62831)+E(f306(f111(x62831),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f79(x62831)) % 187.68/187.64 [6766]~P1(f306(a190,f306(f111(a1),x67661)))+E(f306(f111(a865),f306(f306(f22(a1),f306(f306(f81(a1),x67661),x67661)),a104)),f2(a865)) % 187.68/187.64 [7827]~P1(f306(f306(f221(a1),f306(f111(a1),x78271)),f2(a1)))+E(f306(f235(a1,a1),f306(a52,f51(f306(f80(a1),f79(a1)),f306(f80(a1),f306(f111(a1),x78271))))),f306(f306(f40(a1),f79(a1)),f306(f111(a1),x78271))) % 187.68/187.64 [7840]~P1(f306(f306(f221(a1),f306(f111(a1),x78401)),f2(a1)))+E(f306(f244(a1,a1),f306(a52,f51(f306(f80(a1),f79(a1)),f306(f80(a1),f306(f111(a1),x78401))))),f46(a1,f79(a1),f306(f111(a1),x78401))) % 187.68/187.64 [7889]~P1(f306(f306(f220(a1),a84),x78891))+P1(f306(f306(f220(a1),a84),f306(f306(f22(a1),f306(f306(f81(a1),x78891),x78891)),a104))) % 187.68/187.64 [7890]~P1(f306(f306(f220(a1),a104),x78901))+P1(f306(f306(f220(a1),a104),f306(f306(f22(a1),f306(f306(f81(a1),x78901),x78901)),a104))) % 187.68/187.64 [7891]~P1(f306(f306(f220(a1),a84),x78911))+P1(f306(f306(f221(a1),a84),f306(f306(f22(a1),f306(f306(f81(a1),x78911),x78911)),a104))) % 187.68/187.64 [7892]~P1(f306(f306(f221(a1),a104),x78921))+P1(f306(f306(f221(a1),a104),f306(f306(f22(a1),f306(f306(f81(a1),x78921),x78921)),a104))) % 187.68/187.64 [8202]~P91(x82021)+~P33(x82021,f306(f111(x82021),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104))) % 187.68/187.64 [8382]P1(f306(f306(f220(a1),a84),x83821))+~P1(f306(f306(f220(a1),a84),f306(f306(f22(a1),f306(f306(f81(a1),x83821),x83821)),a104))) % 187.68/187.64 [8383]P1(f306(f306(f220(a1),a84),x83831))+~P1(f306(f306(f221(a1),a84),f306(f306(f22(a1),f306(f306(f81(a1),x83831),x83831)),a104))) % 187.68/187.64 [8384]P1(f306(f306(f220(a1),a104),x83841))+~P1(f306(f306(f220(a1),a104),f306(f306(f22(a1),f306(f306(f81(a1),x83841),x83841)),a104))) % 187.68/187.64 [8385]P1(f306(f306(f221(a1),a104),x83851))+~P1(f306(f306(f221(a1),a104),f306(f306(f22(a1),f306(f306(f81(a1),x83851),x83851)),a104))) % 187.68/187.64 [8699]E(f306(f111(a865),f306(f306(f22(a1),f306(f306(f81(a1),x86991),x86991)),a104)),f306(f306(f87(a865,a865),f306(f111(a865),x86991)),f306(f306(f8(a865,a865,a865),a119),f306(f306(f18(a865,a865,a865),f81(a865)),f5(a865)))))+P1(f306(a190,f306(f111(a1),x86991))) % 187.68/187.64 [9556]E(x95561,f185(f872(f871(a865,a865),a859)))+P1(f306(f306(f308(f871(f872(f871(a865,a865),a859),f872(f871(a865,a865),a859))),f306(f306(f236(f872(f871(a865,a865),a859),f872(f871(a865,a865),a859)),x95561),f185(f872(f871(a865,a865),a859)))),a37)) % 187.68/187.64 [8632]~P1(f306(a190,f306(f111(a1),x86321)))+P1(f306(a190,f306(f111(a1),f306(f306(f22(a1),f306(f306(f81(a1),x86321),x86321)),a104)))) % 187.68/187.64 [8633]~P1(f306(f306(f221(a1),x86331),a84))+P1(f306(f306(f220(a1),f306(f306(f22(a1),f306(f306(f81(a1),x86331),x86331)),a104)),a84)) % 187.68/187.64 [8634]~P1(f306(f306(f220(a1),x86341),a104))+P1(f306(f306(f220(a1),f306(f306(f22(a1),f306(f306(f81(a1),x86341),x86341)),a104)),a104)) % 187.68/187.64 [8635]~P1(f306(f306(f221(a1),x86351),a84))+P1(f306(f306(f221(a1),f306(f306(f22(a1),f306(f306(f81(a1),x86351),x86351)),a104)),a84)) % 187.68/187.64 [8636]~P1(f306(f306(f221(a1),x86361),a104))+P1(f306(f306(f221(a1),f306(f306(f22(a1),f306(f306(f81(a1),x86361),x86361)),a104)),a104)) % 187.68/187.64 [8735]~P1(f306(f306(f220(a1),f2(a1)),f306(f111(a1),x87351)))+P1(f306(f306(f220(a1),f2(a1)),f306(f111(a1),f306(f306(f22(a1),f306(f306(f81(a1),x87351),x87351)),a104)))) % 187.68/187.64 [8895]~P91(x88951)+E(f306(f306(f81(x88951),f79(x88951)),f79(x88951)),f306(f111(x88951),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)))) % 187.68/187.64 [9052]P1(f306(a190,f306(f111(a1),x90521)))+~P1(f306(a190,f306(f111(a1),f306(f306(f22(a1),f306(f306(f81(a1),x90521),x90521)),a104)))) % 187.68/187.64 [9053]P1(f306(f306(f220(a1),x90531),a104))+~P1(f306(f306(f220(a1),f306(f306(f22(a1),f306(f306(f81(a1),x90531),x90531)),a104)),a104)) % 187.68/187.64 [9054]P1(f306(f306(f221(a1),x90541),a84))+~P1(f306(f306(f220(a1),f306(f306(f22(a1),f306(f306(f81(a1),x90541),x90541)),a104)),a84)) % 187.68/187.64 [9055]P1(f306(f306(f221(a1),x90551),a84))+~P1(f306(f306(f221(a1),f306(f306(f22(a1),f306(f306(f81(a1),x90551),x90551)),a104)),a84)) % 187.68/187.64 [9056]P1(f306(f306(f221(a1),x90561),a104))+~P1(f306(f306(f221(a1),f306(f306(f22(a1),f306(f306(f81(a1),x90561),x90561)),a104)),a104)) % 187.68/187.64 [9602]~P1(f306(f63(f871(a865,a865)),x96021))+P1(f306(f306(f308(f871(f872(f871(a865,a865),a859),f872(f871(a865,a865),a859))),f306(f306(f236(f872(f871(a865,a865),a859),f872(f871(a865,a865),a859)),f185(f872(f871(a865,a865),a859))),x96021)),a70)) % 187.68/187.64 [9385]~P141(x93851)+E(f306(f306(f237(x93851),f2(x93851)),f306(f111(a865),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)))),f2(x93851)) % 187.68/187.64 [9386]~P141(x93861)+E(f306(f306(f237(x93861),f79(x93861)),f306(f111(a865),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)))),f79(x93861)) % 187.68/187.64 [9830]~P1(f306(f306(f221(a865),f79(a865)),x98301))+P1(f306(f306(f221(a865),f2(a865)),f306(f306(f40(a865),x98301),f306(f111(a865),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)))))) % 187.68/187.64 [9842]~P1(f306(f306(f221(a865),f2(a865)),x98421))+P1(f306(f306(f221(a865),f2(a865)),f306(f306(f40(a865),f306(f306(f81(a865),x98421),f79(a865))),f306(f111(a865),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)))))) % 187.68/187.64 [9883]~E(f46(a865,x98831,f306(f111(a865),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)))),f79(a865))+P1(f306(f306(f221(a865),f2(a865)),f46(a865,x98831,f306(f111(a865),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)))))) % 187.68/187.64 [9904]E(f46(a865,x99041,f306(f111(a865),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)))),f79(a865))+~P1(f306(f306(f221(a865),f2(a865)),f46(a865,x99041,f306(f111(a865),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)))))) % 187.68/187.64 [4573]~P40(x45731,x45732)+P57(x45731,x45732) % 187.68/187.64 [4574]~P45(x45741,x45742)+P57(x45741,x45742) % 187.68/187.64 [4535]~E(x45351,x45352)+E(f253(x45351,x45352),f79(a106)) % 187.68/187.64 [4538]E(f202(x45381,x45382),x45381)+~E(x45382,f2(a865)) % 187.68/187.64 [4545]~E(x45452,f120(x45451))+E(f144(x45451,x45452),f120(x45451)) % 187.68/187.64 [4564]~E(f144(x45642,x45641),f120(x45642))+E(x45641,f120(x45642)) % 187.68/187.64 [4578]~P2(x45782)+P2(f872(x45781,x45782)) % 187.68/187.64 [4579]~P106(x45792)+P106(f872(x45791,x45792)) % 187.68/187.64 [4580]~P107(x45802)+P107(f872(x45801,x45802)) % 187.68/187.64 [4581]~P109(x45812)+P109(f872(x45811,x45812)) % 187.68/187.64 [4582]~P66(x45822)+P66(f872(x45821,x45822)) % 187.68/187.64 [4583]~P94(x45832)+P94(f872(x45831,x45832)) % 187.68/187.64 [4584]~P87(x45842)+P87(f872(x45841,x45842)) % 187.68/187.64 [4585]~P98(x45852)+P97(f872(x45851,x45852)) % 187.68/187.64 [4586]~P98(x45862)+P98(f872(x45861,x45862)) % 187.68/187.64 [4587]~P100(x45872)+P99(f872(x45871,x45872)) % 187.68/187.64 [4588]~P101(x45882)+P101(f872(x45881,x45882)) % 187.68/187.64 [4589]~P98(x45892)+P103(f872(x45891,x45892)) % 187.68/187.64 [4590]~P6(x45902)+P6(f872(x45901,x45902)) % 187.68/187.64 [4591]~P110(x45912)+P110(f872(x45911,x45912)) % 187.68/187.64 [4592]~P100(x45922)+P102(f872(x45921,x45922)) % 187.68/187.64 [4593]~P100(x45932)+P100(f872(x45931,x45932)) % 187.68/187.64 [4605]E(x46051,x46052)+~E(f306(a26,x46051),f306(a26,x46052)) % 187.68/187.64 [4607]E(x46071,x46072)+~E(f306(a119,x46071),f306(a119,x46072)) % 187.68/187.64 [4608]E(x46081,x46082)+~E(f306(a114,x46081),f306(a114,x46082)) % 187.68/187.64 [4609]E(x46091,x46092)+~E(f306(a3,x46091),f306(a3,x46092)) % 187.68/187.64 [4611]E(x46111,x46112)+~E(f306(a19,x46111),f306(a19,x46112)) % 187.68/187.64 [4712]~P4(x47121)+E(f46(x47121,x47122,x47122),f2(x47121)) % 187.68/187.64 [4746]~P40(x47461,x47462)+P40(f866(x47461),f138(x47461,x47462)) % 187.68/187.64 [4747]~P40(x47471,x47472)+P40(f866(x47471),f137(x47471,x47472)) % 187.68/187.64 [4844]~P40(x48441,x48442)+P40(f872(x48441,a859),f297(x48441,x48442)) % 187.68/187.64 [4845]~P40(x48451,x48452)+P40(f872(x48451,a859),f298(x48451,x48452)) % 187.68/187.64 [4965]~P7(x49651)+P42(f277(a1,x49651,x49652)) % 187.68/187.64 [5069]~P40(x50691,x50692)+P59(x50691,f69(x50691,x50691,x50692)) % 187.68/187.64 [5574]~P65(x55741)+P28(x55741,x55741,f80(x55741),x55742) % 187.68/187.64 [4559]~E(x45592,f120(x45591))+E(f306(f160(x45591),x45592),f120(x45591)) % 187.68/187.64 [4560]~E(x45602,f120(x45601))+E(f306(f161(x45601),x45602),f120(x45601)) % 187.68/187.64 [4615]E(x46151,f306(a112,x46152))+~E(f306(f107(a1),x46151),x46152) % 187.68/187.64 [4618]E(x46181,f120(x46182))+~E(f306(f160(x46182),x46181),f120(x46182)) % 187.68/187.64 [4619]E(x46191,f120(x46192))+~E(f306(f161(x46192),x46191),f120(x46192)) % 187.68/187.64 [4636]~P91(x46361)+E(f306(f111(x46361),x46362),f306(f110(x46361),x46362)) % 187.68/187.64 [4643]~E(x46432,f188(x46431))+E(f213(x46431,x46432),f185(f872(x46431,a859))) % 187.68/187.64 [4645]~P3(x46451)+P1(f306(f63(x46451),x46452)) % 187.68/187.64 [4652]E(x46521,f188(x46522))+E(f306(f214(x46522),f681(x46522,x46521)),x46521) % 187.68/187.64 [4653]E(x46531,f188(x46532))+E(f306(f214(x46532),f812(x46532,x46531)),x46531) % 187.68/187.64 [4655]~E(f682(x46552,x46551),f120(x46551))+E(f171(x46551,x46552),f120(f866(x46551))) % 187.68/187.64 [4664]~E(x46642,f120(x46641))+E(f306(f164(x46641),x46642),f185(f872(x46641,a859))) % 187.68/187.64 [4665]~E(x46652,f120(x46651))+E(f185(f872(x46651,a859)),f306(f164(x46651),x46652)) % 187.68/187.64 [4667]E(x46671,x46672)+~E(f306(f107(a1),x46671),f306(f107(a1),x46672)) % 187.68/187.64 [4670]E(f200(x46701,x46702),f2(a865))+P1(f306(f63(x46701),x46702)) % 187.68/187.64 [4690]~P112(x46901)+E(f83(x46901,f83(x46901,x46902)),f83(x46901,x46902)) % 187.68/187.64 [4703]~P113(x47031)+E(f306(f306(f237(x47031),x47032),f79(a865)),x47032) % 187.68/187.64 [4704]~P80(x47041)+E(f306(f306(f237(x47041),x47042),f79(a865)),x47042) % 187.68/187.64 [4706]E(x47061,x47062)+E(f253(x47061,x47062),f306(f306(f81(a106),x47062),f79(a106))) % 187.68/187.64 [4709]E(f306(f39(x47091),x47092),f2(a865))+P1(f306(f63(x47091),x47092)) % 187.68/187.64 [4713]~E(f144(x47131,x47132),x47132)+P1(f306(f129(x47131),x47132)) % 187.68/187.64 [4716]~P67(x47161)+E(f306(f306(f22(x47161),x47162),f2(x47161)),x47162) % 187.68/187.64 [4717]~P74(x47171)+E(f306(f306(f81(x47171),x47172),f2(x47171)),x47172) % 187.68/187.64 [4718]~P79(x47181)+E(f306(f306(f81(x47181),x47182),f2(x47181)),x47182) % 187.68/187.64 [4719]~P113(x47191)+E(f306(f306(f81(x47191),x47192),f2(x47191)),x47192) % 187.68/187.64 [4720]~P113(x47201)+E(f306(f306(f82(x47201),x47202),f79(x47201)),x47202) % 187.68/187.64 [4721]~P75(x47211)+E(f306(f306(f82(x47211),x47212),f79(x47211)),x47212) % 187.68/187.64 [4722]~P80(x47221)+E(f306(f306(f82(x47221),x47222),f79(x47221)),x47222) % 187.68/187.64 [4723]~P4(x47231)+E(f306(f306(f40(x47231),x47232),f79(x47231)),x47232) % 187.68/187.64 [4724]~P118(x47241)+E(f306(f306(f264(x47241),x47242),f79(x47241)),x47242) % 187.68/187.64 [4725]~P99(x47251)+E(f306(f306(f108(x47251),x47252),f185(x47251)),x47252) % 187.68/187.64 [4726]~P102(x47261)+E(f306(f306(f109(x47261),x47262),f231(x47261)),x47262) % 187.68/187.64 [4727]~P113(x47271)+E(f306(f306(f237(x47271),x47272),f2(a865)),f79(x47271)) % 187.68/187.64 [4728]~P115(x47281)+E(f306(f306(f237(x47281),x47282),f2(a865)),f79(x47281)) % 187.68/187.64 [4729]~E(x47292,f185(f872(x47291,a859)))+E(f306(f39(x47291),x47292),f2(a865)) % 187.68/187.64 [4740]~P4(x47401)+E(f46(x47401,x47402,f2(x47401)),x47402) % 187.68/187.64 [4748]~P113(x47481)+E(f306(f306(f82(x47481),x47482),f2(x47481)),f2(x47481)) % 187.68/187.64 [4749]~P127(x47491)+E(f306(f306(f82(x47491),x47492),f2(x47491)),f2(x47491)) % 187.68/187.64 [4750]~P4(x47501)+E(f306(f306(f40(x47501),x47502),f2(x47501)),f2(x47501)) % 187.68/187.64 [4751]~P119(x47511)+E(f306(f306(f264(x47511),x47512),f2(x47511)),f2(x47511)) % 187.68/187.64 [4752]~P102(x47521)+E(f306(f306(f108(x47521),x47522),f231(x47521)),f231(x47521)) % 187.68/187.64 [4753]~P99(x47531)+E(f306(f306(f109(x47531),x47532),f185(x47531)),f185(x47531)) % 187.68/187.64 [4754]E(x47541,f188(x47542))+~E(f213(x47542,x47541),f185(f872(x47542,a859))) % 187.68/187.64 [4757]~P4(x47571)+E(f46(x47571,x47572,f79(x47571)),f2(x47571)) % 187.68/187.64 [4758]~P4(x47581)+E(f46(x47581,f2(x47581),x47582),f2(x47581)) % 187.68/187.64 [4787]E(x47871,f2(a865))+E(f56(x47872,x47871,f120(x47872)),f120(f866(x47872))) % 187.68/187.64 [4811]P40(x48111,x48112)+~E(f547(x48112,x48111),f185(f872(x48111,a859))) % 187.68/187.64 [4812]E(x48121,f120(x48122))+~E(f306(f164(x48122),x48121),f185(f872(x48122,a859))) % 187.68/187.64 [4813]E(x48131,f120(x48132))+~E(f185(f872(x48132,a859)),f306(f164(x48132),x48131)) % 187.68/187.64 [4816]~E(x48161,x48162)+P1(f306(f306(a303,x48161),x48162)) % 187.68/187.64 [4826]P1(x48261)+P1(f306(f306(a309,x48261),x48262)) % 187.68/187.64 [4827]E(x48271,f120(x48272))+E(f306(f306(f157(x48272),x48271),f2(a865)),f306(f133(x48272),x48271)) % 187.68/187.64 [4830]E(f144(x48301,x48302),x48302)+~P1(f306(f129(x48301),x48302)) % 187.68/187.64 [4835]~P1(x48352)+P1(f306(f306(a309,x48351),x48352)) % 187.68/187.64 [4836]~P1(x48362)+P1(f306(f306(a305,x48361),x48362)) % 187.68/187.64 [4837]~P1(x48371)+P1(f306(f306(a305,x48371),x48372)) % 187.68/187.64 [4847]~E(x48472,f185(f872(x48471,a859)))+P1(f306(f63(x48471),x48472)) % 187.68/187.64 [4848]~E(f683(x48482,x48481),f687(x48482,x48481))+P1(f306(f129(x48481),x48482)) % 187.68/187.64 [4856]E(f306(f228(x48561),x48562),f185(f872(x48561,a859)))+P1(f306(x48562,f491(x48562))) % 187.68/187.64 [4857]E(f185(f872(x48571,a859)),f306(f228(x48571),x48572))+P1(f306(x48572,f492(x48572))) % 187.68/187.64 [4922]~P112(x49221)+E(f306(f306(f82(x49221),x49222),f83(x49221,x49222)),f306(f76(x49221),x49222)) % 187.68/187.64 [4933]~E(x49331,f2(a1))+E(f47(x49331,x49332),f306(f306(f236(a1,a1),f2(a1)),f2(a1))) % 187.68/187.64 [4964]~P57(x49641,x49642)+P57(x49641,f306(f261(x49641,x49641),x49642)) % 187.68/187.64 [4982]~E(f306(a28,x49821),f306(f214(a860),x49822))+P1(f306(a25,f306(a26,x49821))) % 187.68/187.64 [4987]E(x49871,x49872)+~P1(f306(f306(a303,x49871),x49872)) % 187.68/187.64 [4991]~P1(f306(a25,x49912))+P1(f306(a25,f33(x49911,x49912))) % 187.68/187.64 [5000]P1(x50001)+~P1(f306(f306(a304,x50002),x50001)) % 187.68/187.64 [5001]P1(x50011)+~P1(f306(f306(a304,x50011),x50012)) % 187.68/187.64 [5005]~P110(x50051)+P1(f306(f306(f220(x50051),x50052),f231(x50051))) % 187.68/187.64 [5009]E(x50091,x50092)+~E(f306(x50091,f409(x50092,x50091)),f306(x50092,f409(x50092,x50091))) % 187.68/187.64 [5040]E(x50401,f2(a865))+E(f202(x50401,f46(a865,x50402,x50401)),f202(x50402,x50401)) % 187.68/187.64 [5045]~P108(x50451)+P17(x50451,f306(f306(f143(x50451),x50452),f120(x50451))) % 187.68/187.64 [5049]E(x50491,f2(a1))+P1(f306(f50(x50492,x50491),f47(x50492,x50491))) % 187.68/187.64 [5067]~E(x50671,x50672)+P1(f306(f306(f221(a865),x50671),f306(a119,x50672))) % 187.68/187.64 [5077]~E(x50771,f2(a865))+P1(f306(f306(f221(a865),x50771),f306(a119,x50772))) % 187.68/187.64 [5089]P1(f306(x50891,x50892))+P1(f306(f306(f220(a1),f2(a1)),f827(x50891))) % 187.68/187.64 [5126]P1(f306(a25,x51261))+~P1(f306(a25,f33(x51262,x51261))) % 187.68/187.64 [5128]P1(f306(a25,x51281))+~P1(f306(a25,f34(x51282,x51281))) % 187.68/187.64 [5130]P1(f306(a25,x51301))+~P1(f306(a25,f34(x51301,x51302))) % 187.68/187.64 [5162]P57(x51621,x51622)+~P57(x51621,f306(f261(x51621,x51621),x51622)) % 187.68/187.64 [5165]~E(f46(a865,x51652,x51651),f2(a865))+E(f306(f306(f82(a865),x51651),f830(x51651,x51652)),x51652) % 187.68/187.64 [5166]~E(f46(a1,x51662,x51661),f2(a1))+E(f306(f306(f82(a1),x51661),f831(x51661,x51662)),x51662) % 187.68/187.64 [5192]~P1(f306(x51921,x51922))+P1(f306(f306(f220(a1),f2(a1)),f813(x51921))) % 187.68/187.64 [5204]E(f306(f306(f22(a865),f306(a112,x52041)),f306(a112,x52042)),f306(a112,x52041))+~P1(f306(a190,x52042)) % 187.68/187.64 [5234]E(f254(x52341,x52342),f79(a106))+~P1(f306(f306(f220(a106),x52341),f79(a106))) % 187.68/187.64 [5329]E(f306(f306(f157(x53291),x53292),f683(x53292,x53291)),f306(f306(f157(x53291),x53292),f687(x53292,x53291)))+P1(f306(f129(x53291),x53292)) % 187.68/187.64 [5374]~P1(f306(x53741,f91(x53742,x53741)))+P1(f306(x53741,f567(x53742,x53741))) % 187.68/187.64 [5437]P59(x54371,x54372)+~P1(f306(f294(x54371,x54372),f517(x54372,x54371))) % 187.68/187.64 [5581]~E(f306(a119,f46(a865,x55811,x55812)),x55812)+E(f46(a865,f306(a119,x55811),x55812),f2(a865)) % 187.68/187.64 [5639]P40(x56391,x56392)+P1(f306(f306(f308(x56391),f607(x56392,x56391)),f608(x56392,x56391))) % 187.68/187.64 [5646]~P91(x56461)+P1(f306(f306(f308(x56461),f306(f111(x56461),x56462)),f117(x56461))) % 187.68/187.64 [5647]~P125(x56471)+P1(f306(f306(f308(x56471),f306(f107(x56471),x56472)),f117(x56471))) % 187.68/187.64 [5648]~P141(x56481)+P1(f306(f306(f308(x56481),f306(f107(x56481),x56482)),f183(x56481))) % 187.68/187.64 [5649]~P125(x56491)+P1(f306(f306(f308(x56491),f306(f110(x56491),x56492)),f117(x56491))) % 187.68/187.64 [5794]E(f306(a119,f46(a865,x57941,x57942)),x57942)+E(f46(a865,f306(a119,x57941),x57942),f306(a119,f46(a865,x57941,x57942))) % 187.68/187.64 [6214]P40(x62141,x62142)+~P1(f306(f306(f308(x62141),f518(x62142,x62141)),f295(x62141,x62142))) % 187.68/187.64 [6249]~P111(x62491)+~P1(f306(f306(f221(x62491),f306(f107(x62491),x62492)),f2(x62491))) % 187.68/187.64 [6250]~P84(x62501)+~P1(f306(f306(f221(x62501),f306(f76(x62501),x62502)),f2(x62501))) % 187.68/187.64 [6341]P1(f306(f306(f221(a1),x63411),f46(a1,x63412,x63411)))+~P1(f306(f306(f221(a1),x63411),f2(a1))) % 187.68/187.64 [6440]E(f306(f306(f284(a865),f306(a119,x64401)),f277(a865,x64402,x64401)),f277(a865,x64402,f306(a119,x64401)))+~P1(f306(f306(f220(a865),x64402),f306(a119,x64401))) % 187.68/187.64 [6524]~P108(x65241)+P17(x65241,f142(x65241,x65241,f5(x65241),x65242)) % 187.68/187.64 [6659]E(f306(f160(x66591),x66592),x66592)+~P1(f306(f306(f220(a865),f306(f186(f866(x66591)),x66592)),f79(a865))) % 187.68/187.64 [6679]~P84(x66791)+P1(f306(f306(f220(x66791),f306(f80(x66791),f306(f76(x66791),x66792))),f2(x66791))) % 187.68/187.64 [6712]~P40(x67121,x67122)+P40(x67121,f306(f306(f263(x67121,x67121,x67121),x67122),f282(x67121,x67122))) % 187.68/187.64 [6931]~P1(f306(f306(f221(a1),x69312),f2(a1)))+P1(f306(f306(f220(a1),f46(a1,x69311,x69312)),f2(a1))) % 187.68/187.64 [7326]~P141(x73261)+E(f187(x73261,f306(f306(f7(x73261,x73261,x73261),f81(x73261)),f79(x73261)),x73262,f2(x73261)),f306(f107(x73261),x73262)) % 187.68/187.64 [7354]~P123(x73541)+~P1(f306(f306(f221(x73541),f306(f306(f82(x73541),x73542),x73542)),f2(x73541))) % 187.68/187.64 [9996]~P112(x99961)+~P1(f306(f306(f221(x99961),f306(f306(f237(x99961),x99962),f306(f111(a865),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104))))),f2(x99961))) % 187.68/187.64 [4616]~E(x46162,f120(x46161))+E(f306(f186(f866(x46161)),x46162),f2(a865)) % 187.68/187.64 [4656]~E(x46561,f2(a865))+E(f306(f306(f81(a865),x46561),x46562),x46562) % 187.68/187.64 [4657]~E(x46572,f2(a865))+E(f306(f306(f82(a865),x46571),x46572),f2(a865)) % 187.68/187.64 [4659]~E(x46591,f2(a865))+E(f306(f306(f82(a865),x46591),x46592),f2(a865)) % 187.68/187.64 [4660]~E(x46602,f2(a865))+E(f306(f306(f237(a865),x46601),x46602),f79(a865)) % 187.68/187.64 [4661]~E(x46612,f2(a1))+E(f306(f306(f40(a1),x46611),x46612),f2(a1)) % 187.68/187.64 [4671]E(x46711,f120(x46712))+~E(f306(f186(f866(x46712)),x46711),f2(a865)) % 187.68/187.64 [4673]~P95(x46731)+E(f306(f306(f82(x46731),x46732),x46732),x46732) % 187.68/187.64 [4675]~P108(x46751)+E(f306(f306(f225(x46751),x46752),x46752),x46752) % 187.68/187.64 [4677]~P108(x46771)+E(f306(f306(f219(x46771),x46772),x46772),x46772) % 187.68/187.64 [4679]~P97(x46791)+E(f306(f306(f108(x46791),x46792),x46792),x46792) % 187.68/187.64 [4680]~P98(x46801)+E(f306(f306(f108(x46801),x46802),x46802),x46802) % 187.68/187.64 [4681]~P98(x46811)+E(f306(f306(f109(x46811),x46812),x46812),x46812) % 187.68/187.64 [4683]~P103(x46831)+E(f306(f306(f109(x46831),x46832),x46832),x46832) % 187.68/187.64 [4702]~P67(x47021)+E(f306(f306(f22(x47021),x47022),x47022),f2(x47021)) % 187.68/187.64 [4714]~P67(x47141)+E(f306(f80(x47141),f306(f80(x47141),x47142)),x47142) % 187.68/187.64 [4715]~P94(x47151)+E(f306(f80(x47151),f306(f80(x47151),x47152)),x47152) % 187.68/187.64 [4732]~E(x47322,f2(a865))+E(f306(f306(f237(a865),x47321),x47322),f306(a119,f2(a865))) % 187.68/187.64 [4766]~P74(x47661)+E(f306(f306(f81(x47661),f2(x47661)),x47662),x47662) % 187.68/187.64 [4767]~P79(x47671)+E(f306(f306(f81(x47671),f2(x47671)),x47672),x47672) % 187.68/187.64 [4768]~P113(x47681)+E(f306(f306(f81(x47681),f2(x47681)),x47682),x47682) % 187.68/187.64 [4769]~P113(x47691)+E(f306(f306(f82(x47691),f79(x47691)),x47692),x47692) % 187.68/187.64 [4770]~P75(x47701)+E(f306(f306(f82(x47701),f79(x47701)),x47702),x47702) % 187.68/187.64 [4771]~P80(x47711)+E(f306(f306(f82(x47711),f79(x47711)),x47712),x47712) % 187.68/187.64 [4772]~P99(x47721)+E(f306(f306(f108(x47721),f185(x47721)),x47722),x47722) % 187.68/187.64 [4773]~P102(x47731)+E(f306(f306(f109(x47731),f231(x47731)),x47732),x47732) % 187.68/187.64 [4792]~P113(x47921)+E(f306(f306(f82(x47921),f2(x47921)),x47922),f2(x47921)) % 187.68/187.64 [4793]~P127(x47931)+E(f306(f306(f82(x47931),f2(x47931)),x47932),f2(x47931)) % 187.68/187.64 [4794]~P80(x47941)+E(f306(f306(f237(x47941),f79(x47941)),x47942),f79(x47941)) % 187.68/187.64 [4795]~P4(x47951)+E(f306(f306(f40(x47951),f2(x47951)),x47952),f2(x47951)) % 187.68/187.64 [4796]~P118(x47961)+E(f306(f306(f264(x47961),f2(x47961)),x47962),f2(x47961)) % 187.68/187.64 [4797]~P102(x47971)+E(f306(f306(f108(x47971),f231(x47971)),x47972),f231(x47971)) % 187.68/187.64 [4798]~P99(x47981)+E(f306(f306(f109(x47981),f185(x47981)),x47982),f185(x47981)) % 187.68/187.64 [4806]E(x48061,f120(x48062))+E(f136(x48062,f306(f161(x48062),x48061)),f306(f133(x48062),x48061)) % 187.68/187.64 [4807]E(x48071,f120(x48072))+E(f306(f133(x48072),f306(f161(x48072),x48071)),f136(x48072,x48071)) % 187.68/187.64 [4808]E(x48081,f2(a865))+~E(f306(f306(f81(a865),x48082),x48081),x48082) % 187.68/187.64 [4814]~P91(x48141)+E(f306(f110(x48141),f306(f111(a1),x48142)),f306(f111(x48141),x48142)) % 187.68/187.64 [4815]~P125(x48151)+E(f306(f110(x48151),f306(f107(a1),x48152)),f306(f107(x48151),x48152)) % 187.68/187.64 [4822]E(x48221,f2(a865))+~E(f306(f306(f81(a865),x48222),x48221),f2(a865)) % 187.68/187.64 [4823]E(x48231,f2(a865))+~E(f306(f306(f81(a865),x48231),x48232),f2(a865)) % 187.68/187.64 [4824]E(x48241,f79(a865))+~E(f306(f306(f82(a865),x48242),x48241),f79(a865)) % 187.68/187.64 [4825]E(x48251,f79(a865))+~E(f306(f306(f82(a865),x48251),x48252),f79(a865)) % 187.68/187.64 [4840]~P84(x48401)+E(f306(f76(x48401),f306(f80(x48401),x48402)),f306(f76(x48401),x48402)) % 187.68/187.64 [4841]~P112(x48411)+E(f306(f76(x48411),f306(f107(x48411),x48412)),f306(f107(x48411),x48412)) % 187.68/187.64 [4842]~P84(x48421)+E(f306(f76(x48421),f306(f76(x48421),x48422)),f306(f76(x48421),x48422)) % 187.68/187.64 [4843]~P74(x48431)+E(f306(f158(x48431),f306(f161(x48431),x48432)),f306(f158(x48431),x48432)) % 187.68/187.64 [4849]~E(x48491,f306(a119,f2(a865)))+E(f306(f306(f237(a865),x48491),x48492),f306(a119,f2(a865))) % 187.68/187.64 [4859]~P67(x48591)+E(f306(f306(f22(x48591),f2(x48591)),x48592),f306(f80(x48591),x48592)) % 187.68/187.64 [4860]~E(x48602,f2(a865))+E(f131(a865,f306(f276(a865,x48601),x48602)),f120(a865)) % 187.68/187.64 [4869]~P91(x48691)+E(f306(f306(f81(x48691),x48692),f306(f111(x48691),a84)),x48692) % 187.68/187.64 [4870]E(x48701,f2(a1))+E(f48(f306(f76(a1),x48702),f306(f76(a1),x48701)),f54(x48702,x48701)) % 187.68/187.64 [4884]~E(x48841,x48842)+P1(f306(f306(f220(a865),x48841),x48842)) % 187.68/187.64 [4891]~E(x48911,f2(a106))+E(f306(f306(f81(a865),f306(a19,x48911)),x48912),x48912) % 187.68/187.64 [4893]~P6(x48931)+E(f102(x48931,f306(f16(x48931,x48931),x48932)),x48932) % 187.68/187.64 [4902]~P7(x49021)+P7(f306(f306(f237(a1),x49021),x49022)) % 187.68/187.64 [4903]~P67(x49031)+E(f306(f306(f81(x49031),x49032),f306(f80(x49031),x49032)),f2(x49031)) % 187.68/187.64 [4904]~P94(x49041)+E(f306(f306(f108(x49041),x49042),f306(f80(x49041),x49042)),f231(x49041)) % 187.68/187.64 [4905]~P94(x49051)+E(f306(f306(f109(x49051),x49052),f306(f80(x49051),x49052)),f185(x49051)) % 187.68/187.64 [4930]E(x49301,f2(a865))+~E(f306(f80(a1),f306(f107(a1),x49302)),f306(f107(a1),x49301)) % 187.68/187.64 [4931]E(x49311,f2(a865))+~E(f306(f80(a1),f306(f107(a1),x49311)),f306(f107(a1),x49312)) % 187.68/187.64 [4941]E(f194(x49411,x49412),f2(a1))+P1(f306(f306(f220(a1),x49412),x49411)) % 187.68/187.64 [4942]E(f170(x49421,x49422),f120(a1))+P1(f306(f306(f220(a1),x49421),x49422)) % 187.68/187.64 [4955]E(x49551,f306(a119,f2(a865)))+~E(f306(f306(f82(a865),x49552),x49551),f306(a119,f2(a865))) % 187.68/187.64 [4956]E(x49561,f306(a119,f2(a865)))+~E(f306(f306(f82(a865),x49561),x49562),f306(a119,f2(a865))) % 187.68/187.64 [4957]~P106(x49571)+P1(f306(f306(f220(x49571),x49572),x49572)) % 187.68/187.64 [4958]~P93(x49581)+P1(f306(f306(f92(x49581),x49582),x49582)) % 187.68/187.64 [4961]~P91(x49611)+E(f306(f306(f82(x49611),x49612),f306(f111(x49611),a104)),f306(f80(x49611),x49612)) % 187.68/187.64 [4979]~P91(x49791)+E(f306(f80(x49791),f306(f111(x49791),x49792)),f306(f111(x49791),f306(f80(a1),x49792))) % 187.68/187.64 [4980]~P125(x49801)+E(f306(f80(x49801),f306(f110(x49801),x49802)),f306(f110(x49801),f306(f80(a1),x49802))) % 187.68/187.64 [5010]~E(x50101,f306(a119,x50102))+P1(f306(f306(f221(a865),f2(a865)),x50101)) % 187.68/187.64 [5027]~P108(x50271)+E(f306(f80(f872(x50271,a859)),f306(f275(x50271),x50272)),f306(f278(x50271),x50272)) % 187.68/187.64 [5028]~P108(x50281)+E(f306(f80(f872(x50281,a859)),f306(f229(x50281),x50282)),f306(f230(x50281),x50282)) % 187.68/187.64 [5029]~P108(x50291)+E(f306(f80(f872(x50291,a859)),f306(f230(x50291),x50292)),f306(f229(x50291),x50292)) % 187.68/187.64 [5030]~P108(x50301)+E(f306(f80(f872(x50301,a859)),f306(f278(x50301),x50302)),f306(f275(x50301),x50302)) % 187.68/187.64 [5039]~E(f306(f107(a1),x50392),x50391)+P1(f306(f306(f220(a1),f2(a1)),x50391)) % 187.68/187.64 [5048]~E(x50482,f2(a1))+E(f54(x50481,x50482),f306(f306(f236(a1,a1),f2(a1)),f306(f76(a1),x50481))) % 187.68/187.64 [5050]~P2(x50501)+P1(f306(f306(f220(x50501),f185(x50501)),x50502)) % 187.68/187.64 [5082]E(x50821,x50822)+~E(f306(f306(f81(a1),x50821),x50821),f306(f306(f81(a1),x50822),x50822)) % 187.68/187.64 [5088]~P1(f306(x50881,x50882))+P1(f306(x50881,f306(a112,f813(x50881)))) % 187.68/187.64 [5114]~P112(x51141)+E(f306(f306(f82(x51141),f83(x51141,x51142)),f306(f76(x51141),x51142)),x51142) % 187.68/187.64 [5115]E(x51151,x51152)+~P1(f306(f306(f193(a24),x51151),x51152)) % 187.68/187.64 [5124]~E(x51242,f2(a865))+E(f86(f871(a865,a865),f49(x51241,x51242)),f306(f306(f236(a865,a865),f2(a865)),x51241)) % 187.68/187.64 [5135]~E(x51351,x51352)+~P1(f306(f306(f221(a865),x51351),x51352)) % 187.68/187.64 [5136]~E(x51361,x51362)+~P1(f306(f306(f221(a1),x51361),x51362)) % 187.68/187.64 [5139]~P141(x51391)+E(f306(f306(f81(x51391),f79(x51391)),f306(f107(x51391),x51392)),f306(f107(x51391),f306(a119,x51392))) % 187.68/187.64 [5143]~E(x51431,f2(a865))+~P1(f306(f306(f221(a865),x51432),x51431)) % 187.68/187.64 [5159]E(f144(x51591,x51592),x51592)+~E(f306(f186(f866(x51591)),f144(x51591,x51592)),f306(f186(f866(x51591)),x51592)) % 187.68/187.64 [5160]E(f306(f39(x51601),f306(f164(x51601),x51602)),f306(f186(f866(x51601)),x51602))+~P1(f306(f129(x51601),x51602)) % 187.68/187.64 [5170]~P1(f306(x51701,f817(x51701)))+P1(f306(x51701,f306(f107(a1),x51702))) % 187.68/187.64 [5181]E(f254(x51811,x51812),f79(a106))+~P1(f306(f306(f221(a106),x51812),x51811)) % 187.68/187.64 [5182]E(f170(x51821,x51822),f120(a1))+~P1(f306(f306(f221(a1),x51822),x51821)) % 187.68/187.64 [5185]~P109(x51851)+E(f277(x51851,x51852,x51852),f306(f306(f284(x51851),x51852),f185(f872(x51851,a859)))) % 187.68/187.64 [5207]~E(f306(f306(f22(a865),x52071),x52072),f2(a865))+P1(f306(f306(f220(a865),x52071),x52072)) % 187.68/187.64 [5208]~E(f306(f306(f22(a1),x52081),x52082),f2(a1))+P1(f306(f306(f92(a1),x52081),x52082)) % 187.68/187.64 [5231]~E(x52312,f2(a865))+E(f56(x52311,x52312,f120(x52311)),f306(f306(f143(f866(x52311)),f120(x52311)),f120(f866(x52311)))) % 187.68/187.64 [5235]~P106(x52351)+~P1(f306(f306(f221(x52351),x52352),x52352)) % 187.68/187.64 [5238]~E(f46(a1,x52381,x52382),f2(a1))+E(f46(a1,x52381,f306(f80(a1),x52382)),f2(a1)) % 187.68/187.64 [5240]~E(f46(a1,x52401,x52402),f2(a1))+E(f46(a1,f306(f80(a1),x52401),x52402),f2(a1)) % 187.68/187.64 [5248]E(f306(f276(a865,x52481),f306(a119,x52482)),f185(f872(a865,a859)))+P1(f306(f306(f220(a865),x52481),x52482)) % 187.68/187.64 [5268]E(f131(a865,f306(f276(a865,x52681),x52682)),f120(a865))+P1(f306(f306(f221(a865),x52681),x52682)) % 187.68/187.64 [5273]~E(f306(f39(x52731),f306(f164(x52731),x52732)),f306(f186(f866(x52731)),x52732))+P1(f306(f129(x52731),x52732)) % 187.68/187.64 [5278]~P1(f306(f129(x52781),x52782))+P1(f306(f129(x52781),f306(f160(x52781),x52782))) % 187.68/187.64 [5279]~P1(f306(f129(x52791),x52792))+P1(f306(f129(x52791),f306(f163(x52791),x52792))) % 187.68/187.64 [5280]~P1(f306(f129(x52801),x52802))+P1(f306(f129(x52801),f306(f161(x52801),x52802))) % 187.68/187.64 [5287]P1(f306(x52871,x52872))+~P1(f306(x52871,f306(a112,f827(x52871)))) % 187.68/187.64 [5288]P1(f306(f306(f220(a865),x52882),x52881))+P1(f306(f306(f220(a865),x52881),x52882)) % 187.68/187.64 [5289]P1(f306(f306(f220(a1),x52892),x52891))+P1(f306(f306(f220(a1),x52891),x52892)) % 187.68/187.64 [5292]~P84(x52921)+P1(f306(f306(f220(x52921),x52922),f306(f76(x52921),x52922))) % 187.68/187.64 [5295]P1(f306(x52951,f818(x52951)))+~P1(f306(x52951,f306(f107(a1),x52952))) % 187.68/187.64 [5321]E(f306(f306(f22(a865),x53211),x53212),f2(a865))+~P1(f306(f306(f220(a865),x53211),x53212)) % 187.68/187.64 [5322]E(f306(f306(f22(a1),x53221),x53222),f2(a1))+~P1(f306(f306(f92(a1),x53221),x53222)) % 187.68/187.64 [5323]E(f306(f306(f40(a865),x53231),x53232),f2(a865))+~P1(f306(f306(f221(a865),x53231),x53232)) % 187.68/187.64 [5341]E(f46(a865,x53411,x53412),x53411)+~P1(f306(f306(f221(a865),x53411),x53412)) % 187.68/187.64 [5350]E(f46(a1,x53501,f306(f80(a1),x53502)),f265(x53501,x53502))+P1(f306(f306(f220(a1),f2(a1)),x53502)) % 187.68/187.64 [5362]E(f306(f306(f22(a1),x53621),x53622),f194(x53621,x53622))+~P1(f306(f306(f220(a1),x53622),x53621)) % 187.68/187.64 [5381]P1(f306(f306(f220(a1),f2(a1)),f817(x53811)))+P1(f306(x53811,f306(f107(a1),x53812))) % 187.68/187.64 [5393]~P60(x53931)+P1(f306(f306(f308(x53931),x53932),f306(f164(x53931),f57(x53931)))) % 187.68/187.64 [5395]~P111(x53951)+P1(f306(f306(f220(x53951),f2(x53951)),f306(f107(x53951),x53952))) % 187.68/187.64 [5396]~P84(x53961)+P1(f306(f306(f220(x53961),f2(x53961)),f306(f76(x53961),x53962))) % 187.68/187.64 [5423]E(f306(f306(f81(a865),x54231),f710(x54232,x54231)),x54232)+~P1(f306(f306(f220(a865),x54231),x54232)) % 187.68/187.64 [5438]E(f277(a1,x54381,x54382),f185(f872(a1,a859)))+~P1(f306(f306(f221(a1),x54382),x54381)) % 187.68/187.64 [5441]~P112(x54411)+E(f306(f306(f82(x54411),f306(f76(x54411),x54412)),f306(f76(x54411),x54412)),f306(f306(f82(x54411),x54412),x54412)) % 187.68/187.64 [5447]E(f131(a865,f306(f276(a865,x54471),f306(a119,x54472))),f120(a865))+P1(f306(f306(f220(a865),x54471),x54472)) % 187.68/187.64 [5451]E(f306(f306(f40(a1),x54511),x54512),f266(x54511,x54512))+~P1(f306(f306(f220(a1),f2(a1)),x54512)) % 187.68/187.64 [5471]P1(f306(f129(x54711),x54712))+~P1(f306(f129(x54711),f306(f160(x54711),x54712))) % 187.68/187.64 [5472]P1(f306(f129(x54721),x54722))+~P1(f306(f129(x54721),f306(f161(x54721),x54722))) % 187.68/187.64 [5493]P1(f306(f63(a865),x54931))+P1(f306(f306(f308(a865),f313(x54931,x54932)),x54931)) % 187.68/187.64 [5494]P1(f306(f63(a865),x54941))+P1(f306(f306(f308(a865),f361(x54941,x54942)),x54941)) % 187.68/187.64 [5495]P1(f306(f306(f221(a865),x54952),f306(a119,x54951)))+P1(f306(f306(f221(a865),x54951),x54952)) % 187.68/187.64 [5496]E(f46(a1,x54961,x54962),f265(x54961,x54962))+~P1(f306(f306(f220(a1),f2(a1)),x54962)) % 187.68/187.64 [5499]E(f131(a865,f306(f276(a865,x54991),x54992)),f120(a865))+~P1(f306(f306(f220(a865),x54992),x54991)) % 187.68/187.64 [5500]~P65(x55001)+E(f306(f285(x55001,x55001,f80(x55001)),f306(f275(x55001),x55002)),f306(f230(x55001),f306(f80(x55001),x55002))) % 187.68/187.64 [5501]~P65(x55011)+E(f306(f285(x55011,x55011,f80(x55011)),f306(f229(x55011),x55012)),f306(f278(x55011),f306(f80(x55011),x55012))) % 187.68/187.64 [5502]~P65(x55021)+E(f306(f285(x55021,x55021,f80(x55021)),f306(f230(x55021),x55022)),f306(f275(x55021),f306(f80(x55021),x55022))) % 187.68/187.64 [5503]~P65(x55031)+E(f306(f285(x55031,x55031,f80(x55031)),f306(f278(x55031),x55032)),f306(f229(x55031),f306(f80(x55031),x55032))) % 187.68/187.64 [5514]E(x55141,f185(f872(x55142,a859)))+P1(f306(f306(f308(x55142),f542(x55141,x55142)),x55141)) % 187.68/187.64 [5515]E(x55151,f185(f872(x55152,a859)))+P1(f306(f306(f308(x55152),f548(x55151,x55152)),x55151)) % 187.68/187.64 [5526]~P1(f306(f306(f221(a865),x55261),x55262))+P1(f306(f306(f220(a865),x55261),x55262)) % 187.68/187.64 [5527]~P1(f306(f306(f221(a1),x55271),x55272))+P1(f306(f306(f220(a1),x55271),x55272)) % 187.68/187.64 [5543]E(f48(x55431,x55432),f306(f306(f236(a1,a1),f2(a1)),x55431))+~P1(f306(f306(f221(a1),x55431),x55432)) % 187.68/187.64 [5544]E(f201(f306(f80(a1),x55441),f306(f80(a1),x55442)),f201(x55441,x55442))+~P1(f306(f306(f221(a1),x55442),f2(a1))) % 187.68/187.64 [5555]E(x55551,x55552)+~E(f306(a3,f306(a119,f306(a19,x55551))),f306(a3,f306(a119,f306(a19,x55552)))) % 187.68/187.64 [5560]E(f48(x55601,x55602),f306(f306(f236(a1,a1),f2(a1)),x55601))+~P1(f306(f306(f220(a1),x55602),f2(a1))) % 187.68/187.64 [5587]E(f46(a865,f306(f111(a865),x55871),f306(f111(a865),x55872)),f2(a865))+~P1(f306(a190,f306(f111(a1),x55871))) % 187.68/187.64 [5603]P1(f306(f306(f220(a1),f2(a1)),f818(x56031)))+~P1(f306(x56031,f306(f107(a1),x56032))) % 187.68/187.64 [5637]P42(f277(a1,x56371,x56372))+~P1(f306(f306(f220(a1),f2(a1)),x56371)) % 187.68/187.64 [5642]~P1(f306(f63(x56421),x56422))+P1(f306(f63(f872(x56421,a859)),f306(f283(x56421),x56422))) % 187.68/187.64 [5655]E(f306(f306(f81(a1),x56551),f306(f107(a1),f821(x56552,x56551))),x56552)+~P1(f306(f306(f220(a1),x56551),x56552)) % 187.68/187.64 [5663]P1(f306(f306(f220(a865),x56631),x56632))+P1(f306(f306(f220(a865),f306(a119,x56632)),x56631)) % 187.68/187.64 [5707]E(f306(f306(f40(a865),f306(f111(a865),x57071)),f306(f111(a865),x57072)),f2(a865))+~P1(f306(a190,f306(f111(a1),x57071))) % 187.68/187.64 [5708]E(f306(f306(f82(a865),f306(f111(a865),x57081)),f306(f111(a865),x57082)),f2(a865))+~P1(f306(f306(f221(a1),x57081),a84)) % 187.68/187.64 [5710]P1(f306(f306(f220(a865),x57101),f306(a119,x57102)))+~P1(f306(f306(f220(a865),x57101),x57102)) % 187.68/187.64 [5712]P1(f306(f306(f221(a865),x57121),f306(a119,x57122)))+~P1(f306(f306(f220(a865),x57121),x57122)) % 187.68/187.64 [5714]P1(f306(f306(f221(a865),x57141),f306(a119,x57142)))+~P1(f306(f306(f221(a865),x57141),x57142)) % 187.68/187.64 [5717]~E(x57171,x57172)+P1(f306(f306(f221(a1),x57171),f306(f306(f81(a1),x57172),f79(a1)))) % 187.68/187.64 [5720]E(f46(a1,x57201,x57202),f2(a1))+E(f306(f306(f22(a1),x57202),f46(a1,x57201,x57202)),f46(a1,f306(f80(a1),x57201),x57202)) % 187.68/187.64 [5729]E(x57291,f120(x57292))+P1(f306(f306(f308(x57292),f136(x57292,x57291)),f306(f164(x57292),x57291))) % 187.68/187.64 [5741]E(f86(f871(a865,a865),f49(x57411,x57412)),f306(f306(f236(a865,a865),f2(a865)),x57411))+~P1(f306(f306(f221(a865),x57411),x57412)) % 187.68/187.64 [5774]E(f306(f306(f22(a865),f306(f111(a865),x57741)),f306(f111(a865),x57742)),f306(f111(a865),x57741))+~P1(f306(f306(f221(a1),x57742),a84)) % 187.68/187.64 [5775]E(f306(f306(f81(a865),f306(f111(a865),x57751)),f306(f111(a865),x57752)),f306(f111(a865),x57752))+~P1(f306(f306(f221(a1),x57751),a84)) % 187.68/187.64 [5780]E(f306(a119,f306(f306(f81(a865),x57801),f732(x57802,x57801))),x57802)+~P1(f306(f306(f221(a865),x57801),x57802)) % 187.68/187.64 [5804]P1(f306(x58041,x58042))+~P1(f306(x58041,f306(a90,f539(x58042,x58041)))) % 187.68/187.64 [5812]~P1(f306(f306(f221(a865),x58121),f306(a119,x58122)))+P1(f306(f306(f220(a865),x58121),x58122)) % 187.68/187.64 [5858]E(f306(f306(f284(a865),x58581),f306(f276(a865,x58582),x58581)),f306(f276(a865,x58582),f306(a119,x58581)))+~P1(f306(f306(f220(a865),x58582),x58581)) % 187.68/187.64 [5862]E(x58621,f120(x58622))+E(f306(f306(f122(x58622),f121(x58622,x58621)),f306(f306(f143(x58622),f136(x58622,x58621)),f120(x58622))),x58621) % 187.68/187.64 [5876]P1(f306(f63(x58761),x58762))+~P1(f306(f306(f221(a865),f2(a865)),f306(f39(x58761),x58762))) % 187.68/187.64 [5878]~E(x58781,f185(f872(x58782,a859)))+~P1(f306(f306(f221(a865),f2(a865)),f306(f39(x58782),x58781))) % 187.68/187.64 [5890]~P1(f306(f306(f221(a865),x58901),x58902))+P1(f306(f306(f220(a865),f306(a119,x58901)),x58902)) % 187.68/187.64 [5898]~P108(x58981)+E(f142(x58981,x58981,f5(x58981),f144(x58981,x58982)),f131(x58981,f306(f164(x58981),x58982))) % 187.68/187.64 [5901]E(x59011,f120(x59012))+P1(f306(f306(f308(x59012),f306(f133(x59012),x59011)),f306(f164(x59012),x59011))) % 187.68/187.64 [5907]~P111(x59071)+P1(f306(f306(f221(x59071),x59072),f306(f306(f81(x59071),x59072),f79(x59071)))) % 187.68/187.64 [5909]~P84(x59091)+P1(f306(f306(f220(x59091),f306(f80(x59091),x59092)),f306(f76(x59091),x59092))) % 187.68/187.64 [5944]P1(f306(f63(a865),x59441))+~P1(f306(f306(f220(a865),f313(x59441,x59442)),x59442)) % 187.68/187.64 [5945]P1(f306(f63(a865),x59451))+~P1(f306(f306(f221(a865),f361(x59451,x59452)),x59452)) % 187.68/187.64 [5949]~P1(f306(f63(f871(x59491,x59491)),x59492))+P1(f306(f63(x59491),f306(f259(x59491),x59492))) % 187.68/187.64 [6004]~P1(f306(f306(f221(a865),x60042),f306(a119,x60041)))+~P1(f306(f306(f221(a865),x60041),x60042)) % 187.68/187.64 [6005]~P109(x60051)+E(f306(f306(f109(f872(x60051,a859)),f306(f275(x60051),x60052)),f306(f230(x60051),x60052)),f306(f306(f284(x60051),x60052),f185(f872(x60051,a859)))) % 187.68/187.64 [6018]P1(f306(f63(x60181),x60182))+~P1(f306(f63(f872(x60181,a859)),f306(f283(x60181),x60182))) % 187.68/187.64 [6042]P1(f306(f306(f220(a865),f306(a119,x60421)),f306(a119,x60422)))+~P1(f306(f306(f220(a865),x60421),x60422)) % 187.68/187.64 [6043]P1(f306(f306(f220(a865),f306(a19,x60431)),f306(a19,x60432)))+~P1(f306(f306(f220(a106),x60431),x60432)) % 187.68/187.64 [6044]P1(f306(f306(f220(a106),f306(a3,x60441)),f306(a3,x60442)))+~P1(f306(f306(f220(a865),x60441),x60442)) % 187.68/187.64 [6046]P1(f306(f306(f221(a865),f306(a119,x60461)),f306(a119,x60462)))+~P1(f306(f306(f221(a865),x60461),x60462)) % 187.68/187.64 [6047]P1(f306(f306(f221(a865),f306(a19,x60471)),f306(a19,x60472)))+~P1(f306(f306(f221(a106),x60471),x60472)) % 187.68/187.64 [6048]P1(f306(f306(f221(a106),f306(a3,x60481)),f306(a3,x60482)))+~P1(f306(f306(f221(a865),x60481),x60482)) % 187.68/187.64 [6051]E(x60511,x60512)+~E(f306(f285(a865,a1,f107(a1)),x60511),f306(f285(a865,a1,f107(a1)),x60512)) % 187.68/187.64 [6067]P1(f306(f306(f220(a865),x60671),x60672))+~P1(f306(f306(f220(a865),f306(a119,x60671)),x60672)) % 187.68/187.64 [6070]P1(f306(f306(f221(a865),x60701),x60702))+~P1(f306(f306(f220(a865),f306(a119,x60701)),x60702)) % 187.68/187.64 [6071]P1(f306(f306(f221(a865),x60711),x60712))+~P1(f306(f306(f221(a865),f306(a119,x60711)),x60712)) % 187.68/187.64 [6085]E(f46(a1,x60851,x60852),f2(a1))+E(f306(f306(f22(a1),f46(a1,x60851,x60852)),x60852),f46(a1,x60851,f306(f80(a1),x60852))) % 187.68/187.64 [6154]E(f306(f39(f872(x61541,a859)),f306(f283(x61541),x61542)),f306(f306(f237(a865),f306(a119,f306(a119,f2(a865)))),f306(f39(x61541),x61542)))+~P1(f306(f63(x61541),x61542)) % 187.68/187.64 [6157]E(x61571,f120(x61572))+E(f306(f306(f157(x61572),x61571),f306(f306(f22(a865),f306(f186(f866(x61572)),x61571)),f79(a865))),f136(x61572,x61571)) % 187.68/187.64 [6182]E(x61821,f120(x61822))+E(f306(f306(f122(x61822),f306(f163(x61822),x61821)),f306(f306(f143(x61822),f306(f133(x61822),x61821)),f120(x61822))),f306(f160(x61822),x61821)) % 187.68/187.64 [6211]~P1(f306(f63(x62111),f41(f872(x62111,a859),x62112)))+P1(f306(f63(f872(x62111,a859)),x62112)) % 187.68/187.64 [6234]P1(f306(f306(f220(a865),f306(f111(a865),x62341)),f306(f111(a865),x62342)))+~P1(f306(f306(f220(a1),x62341),a84)) % 187.68/187.64 [6251]~P1(f306(f306(f221(a1),x62511),x62512))+P1(f306(f306(f220(a1),x62511),f306(f306(f22(a1),x62512),f79(a1)))) % 187.68/187.64 [6252]~P1(f306(f306(f220(a1),x62521),x62522))+P1(f306(f306(f221(a1),x62521),f306(f306(f81(a1),x62522),f79(a1)))) % 187.68/187.64 [6253]~P1(f306(f306(f221(a1),x62531),x62532))+P1(f306(f306(f221(a1),x62531),f306(f306(f81(a1),x62532),f79(a1)))) % 187.68/187.64 [6255]~P1(f306(f306(f220(a1),x62551),x62552))+P1(f306(f306(f220(a865),f306(f111(a865),x62551)),f306(f111(a865),x62552))) % 187.68/187.64 [6256]~P1(f306(f306(f220(a1),x62561),x62562))+P1(f306(f306(f220(a1),f306(f111(a1),x62561)),f306(f111(a1),x62562))) % 187.68/187.64 [6258]~P1(f306(f306(f220(a865),x62581),x62582))+P1(f306(f306(f220(a1),f306(f107(a1),x62581)),f306(f107(a1),x62582))) % 187.68/187.64 [6259]~P1(f306(f306(f221(a1),x62591),x62592))+P1(f306(f306(f221(a1),f306(f111(a1),x62591)),f306(f111(a1),x62592))) % 187.68/187.64 [6261]~P1(f306(f306(f221(a865),x62611),x62612))+P1(f306(f306(f221(a1),f306(f107(a1),x62611)),f306(f107(a1),x62612))) % 187.68/187.64 [6262]~P1(f306(f306(f92(a1),x62621),x62622))+P1(f306(f306(f92(a1),f306(f111(a1),x62621)),f306(f111(a1),x62622))) % 187.68/187.64 [6280]~P1(f306(f306(f220(a865),x62801),x62802))+~P1(f306(f306(f220(a865),f306(a119,x62802)),x62801)) % 187.68/187.64 [6325]~P1(f306(f306(f220(a865),f306(a119,x63251)),f306(a119,x63252)))+P1(f306(f306(f220(a865),x63251),x63252)) % 187.68/187.64 [6326]~P1(f306(f306(f220(a106),f306(a3,x63261)),f306(a3,x63262)))+P1(f306(f306(f220(a865),x63261),x63262)) % 187.68/187.64 [6327]~P1(f306(f306(f220(a865),f306(a19,x63271)),f306(a19,x63272)))+P1(f306(f306(f220(a106),x63271),x63272)) % 187.68/187.64 [6329]~P1(f306(f306(f221(a865),f306(a119,x63291)),f306(a119,x63292)))+P1(f306(f306(f221(a865),x63291),x63292)) % 187.68/187.64 [6330]~P1(f306(f306(f221(a106),f306(a3,x63301)),f306(a3,x63302)))+P1(f306(f306(f221(a865),x63301),x63302)) % 187.68/187.64 [6331]~P1(f306(f306(f221(a865),f306(a112,x63311)),f306(a112,x63312)))+P1(f306(f306(f221(a1),x63311),x63312)) % 187.68/187.64 [6332]~P1(f306(f306(f221(a865),f306(a19,x63321)),f306(a19,x63322)))+P1(f306(f306(f221(a106),x63321),x63322)) % 187.68/187.64 [6374]~P1(f306(f306(f221(a865),f306(a112,x63742)),f306(a112,x63741)))+P1(f306(f306(f221(a1),f2(a1)),x63741)) % 187.68/187.64 [6405]P1(f306(f306(f220(a1),f2(a1)),f46(a1,x64051,x64052)))+~P1(f306(f306(f221(a1),f2(a1)),x64052)) % 187.68/187.64 [6561]P40(x65611,x65612)+~E(f306(f306(f263(x65611,x65611,x65611),x65612),x65612),f185(f872(f871(x65611,x65611),a859))) % 187.68/187.64 [6573]~P40(x65731,x65732)+P40(x65731,f306(f306(f263(x65731,x65731,x65731),x65732),x65732)) % 187.68/187.64 [6585]P1(f306(f306(f220(a1),x65851),x65852))+~P1(f306(f306(f221(a1),x65851),f306(f306(f81(a1),x65852),f79(a1)))) % 187.68/187.64 [6586]P1(f306(f306(f221(a1),x65861),x65862))+~P1(f306(f306(f220(a1),x65861),f306(f306(f22(a1),x65862),f79(a1)))) % 187.68/187.64 [6589]P1(f306(f306(f220(a865),x65891),x65892))+~P1(f306(f306(f220(a1),f306(f107(a1),x65891)),f306(f107(a1),x65892))) % 187.68/187.64 [6590]P1(f306(f306(f220(a1),x65901),x65902))+~P1(f306(f306(f220(a1),f306(f111(a1),x65901)),f306(f111(a1),x65902))) % 187.68/187.64 [6592]P1(f306(f306(f221(a865),x65921),x65922))+~P1(f306(f306(f221(a1),f306(f107(a1),x65921)),f306(f107(a1),x65922))) % 187.68/187.64 [6593]P1(f306(f306(f221(a1),x65931),x65932))+~P1(f306(f306(f221(a865),f306(f111(a865),x65931)),f306(f111(a865),x65932))) % 187.68/187.64 [6594]P1(f306(f306(f221(a1),x65941),x65942))+~P1(f306(f306(f221(a1),f306(f111(a1),x65941)),f306(f111(a1),x65942))) % 187.68/187.64 [6595]P1(f306(f306(f92(a1),x65951),x65952))+~P1(f306(f306(f92(a1),f306(f111(a1),x65951)),f306(f111(a1),x65952))) % 187.68/187.64 [6692]~E(f733(x66922,x66921),f120(x66921))+E(f306(f134(f866(x66921),f866(x66921),f122(x66921),f120(x66921)),x66922),f120(x66921)) % 187.68/187.64 [6693]~E(f736(x66932,x66931),f120(x66931))+E(f306(f134(f866(x66931),f866(x66931),f122(x66931),f120(x66931)),x66932),f120(x66931)) % 187.68/187.64 [6700]~P6(x67001)+E(f306(f134(x67001,x67001,f109(x67001),f231(x67001)),x67002),f42(x67001,f306(f164(x67001),x67002))) % 187.68/187.64 [6701]~P6(x67011)+E(f306(f134(x67011,x67011,f108(x67011),f185(x67011)),x67012),f41(x67011,f306(f164(x67011),x67012))) % 187.68/187.64 [6713]E(x67131,f2(a106))+E(f306(f306(f81(a865),f306(a19,f306(f306(f22(a106),x67131),f79(a106)))),f306(a119,x67132)),f306(f306(f81(a865),f306(a19,x67131)),x67132)) % 187.68/187.64 [6762]P1(f306(f306(f221(a1),f306(f306(f22(a1),x67621),x67622)),f2(a1)))+~P1(f306(f306(f221(a1),x67621),x67622)) % 187.68/187.64 [6789]~P108(x67891)+E(f306(f306(f108(f872(x67891,a859)),f306(f306(f284(x67891),x67892),f185(f872(x67891,a859)))),f306(f278(x67891),x67892)),f306(f230(x67891),x67892)) % 187.68/187.64 [6862]~P59(x68621,x68622)+P40(x68621,f306(f228(f871(x68621,x68621)),f306(f245(x68621,x68621,a859),x68622))) % 187.68/187.64 [6863]~P59(x68631,x68632)+P57(x68631,f306(f228(f871(x68631,x68631)),f306(f245(x68631,x68631,a859),x68632))) % 187.68/187.64 [6864]E(x68641,f185(f872(x68642,a859)))+~P1(f306(f306(f220(f872(x68642,a859)),x68641),f185(f872(x68642,a859)))) % 187.68/187.64 [6947]~P1(f306(f306(f221(a865),f2(a865)),x69472))+P1(f306(f306(f220(a865),f46(a865,x69471,x69472)),x69472)) % 187.68/187.64 [6948]~P1(f306(f306(f220(a1),f2(a1)),x69481))+P1(f306(f306(f220(a1),f46(a1,x69481,x69482)),x69481)) % 187.68/187.64 [6949]~P1(f306(f306(f221(a865),f2(a865)),x69492))+P1(f306(f306(f221(a865),f46(a865,x69491,x69492)),x69492)) % 187.68/187.64 [6951]~P1(f306(f306(f221(a1),f2(a1)),x69512))+P1(f306(f306(f221(a1),f46(a1,x69511,x69512)),x69512)) % 187.68/187.64 [7029]~P109(x70291)+E(f306(f306(f22(f872(x70291,a859)),f306(f306(f284(x70291),x70292),f185(f872(x70291,a859)))),f306(f229(x70291),x70292)),f306(f306(f284(x70291),x70292),f185(f872(x70291,a859)))) % 187.68/187.64 [7102]~P52(x71021,x71022)+P50(x71021,f231(f872(x71021,a859)),f306(f228(f871(x71021,x71021)),f306(f245(x71021,x71021,a859),x71022))) % 187.68/187.64 [7103]P1(f306(x71031,x71032))+P1(f306(f306(f308(f872(f871(a865,a865),a859)),f539(x71032,x71031)),a105)) % 187.68/187.64 [7148]E(f306(f306(f122(a865),f131(a865,f306(f276(a865,x71481),x71482))),f306(f306(f143(a865),x71482),f120(a865))),f131(a865,f306(f276(a865,x71481),f306(a119,x71482))))+~P1(f306(f306(f220(a865),x71481),x71482)) % 187.68/187.64 [7288]E(x72881,f2(a865))+~E(f306(f134(a865,a865,f81(a865),x72881),x72882),f2(a865)) % 187.68/187.64 [7316]~P1(f306(f306(f221(a1),f306(f306(f22(a1),x73161),x73162)),f2(a1)))+P1(f306(f306(f221(a1),x73161),x73162)) % 187.68/187.64 [7345]P40(x73451,x73452)+~P40(x73451,f306(f306(f263(x73451,x73451,x73451),x73452),x73452)) % 187.68/187.64 [7374]~P1(f306(f306(f220(a865),f306(a119,x73741)),x73742))+P1(f182(a859,a226,f306(f220(a865),x73741),x73742)) % 187.68/187.64 [7529]P28(a865,a865,f306(f306(f7(a865,a865,a865),f22(a865)),x75291),x75292)+P1(f306(f306(f308(a865),f554(x75291,x75292)),x75292)) % 187.68/187.64 [7585]E(f306(f306(f306(f67(a865,x75851,f81(a865)),f306(f16(a865,x75851),f79(a865))),f2(a865)),x75852),f306(f39(x75851),x75852))+~P1(f306(f63(x75851),x75852)) % 187.68/187.64 [7628]P28(a865,a865,f306(f306(f7(a865,a865,a865),f22(a865)),x76281),x76282)+~P1(f306(f306(f220(a865),x76281),f554(x76281,x76282))) % 187.68/187.64 [7686]P40(x76861,x76862)+P1(f306(f306(f220(f872(x76861,a859)),f547(x76862,x76861)),f306(f260(x76861,x76861,x76862),f547(x76862,x76861)))) % 187.68/187.64 [7691]P59(x76911,x76912)+~P40(x76911,f306(f228(f871(x76911,x76911)),f306(f245(x76911,x76911,a859),x76912))) % 187.68/187.64 [7760]P1(f306(f306(f220(a865),f306(a119,x77601)),x77602))+~P1(f182(a859,a226,f306(f220(a865),x77601),x77602)) % 187.68/187.64 [7815]P1(f306(f306(f308(f871(a865,a865)),f306(f306(f236(a865,a865),x78151),x78152)),f282(a865,a296)))+~P1(f306(f306(f220(a865),x78151),x78152)) % 187.68/187.64 [7912]P52(x79121,x79122)+~P50(x79121,f231(f872(x79121,a859)),f306(f228(f871(x79121,x79121)),f306(f245(x79121,x79121,a859),x79122))) % 187.68/187.64 [7972]~P1(f306(f129(x79721),x79722))+P1(f306(f129(f872(x79721,a859)),f306(f306(f146(f866(x79721),f872(x79721,a859)),f164(x79721)),f55(x79721,x79722)))) % 187.68/187.64 [8179]~P40(x81791,f306(f261(x81791,x81791),x81792))+P40(x81791,f306(f261(x81791,x81791),f306(f306(f263(x81791,x81791,x81791),x81792),f282(x81791,x81792)))) % 187.68/187.64 [8301]P1(f306(f63(f871(x83011,x83011)),f306(f306(f263(x83011,x83011,x83011),x83012),f282(x83011,x83012))))+~P1(f306(f63(f871(x83011,x83011)),x83012)) % 187.68/187.64 [8332]E(x83321,f2(a1))+P1(f306(f50(x83322,x83321),f306(f306(f236(a1,a1),f306(f306(f40(a1),x83322),x83321)),f46(a1,x83322,x83321)))) % 187.68/187.64 [8343]~P1(f306(f306(f308(f871(a865,a865)),f306(f306(f236(a865,a865),x83431),x83432)),f282(a865,a296)))+P1(f306(f306(f220(a865),x83431),x83432)) % 187.68/187.64 [8362]~P79(x83621)+E(f306(f134(x83621,x83621,f306(f7(x83621,x83621,x83621),f81(x83621)),f2(x83621)),f306(f161(x83621),x83622)),f306(f134(x83621,x83621,f81(x83621),f2(x83621)),x83622)) % 187.68/187.64 [8541]~P108(x85411)+E(f306(f134(f866(x85411),x85411,f306(f7(x85411,f866(x85411),f866(x85411)),f140(x85411,x85411,f5(x85411))),f120(x85411)),x85412),f142(x85411,x85411,f5(x85411),x85412)) % 187.68/187.64 [8654]P1(f306(f306(f308(f871(a865,a865)),f306(f306(f236(a865,a865),x86541),x86542)),f306(f306(f263(a865,a865,a865),a296),f282(a865,a296))))+~P1(f306(f306(f221(a865),x86541),x86542)) % 187.68/187.64 [8697]~P1(f306(f63(f871(x86971,x86971)),f306(f306(f263(x86971,x86971,x86971),x86972),f282(x86971,x86972))))+P1(f306(f63(f871(x86971,x86971)),x86972)) % 187.68/187.64 [8953]P57(x89531,x89532)+P1(f306(f306(f308(f871(x89531,x89531)),f306(f306(f236(x89531,x89531),f593(x89532,x89531)),f593(x89532,x89531))),f306(f306(f263(x89531,x89531,x89531),x89532),f282(x89531,x89532)))) % 187.68/187.64 [8954]P57(x89541,x89542)+P1(f306(f306(f308(f871(x89541,x89541)),f306(f306(f236(x89541,x89541),f601(x89542,x89541)),f601(x89542,x89541))),f306(f306(f263(x89541,x89541,x89541),x89542),f282(x89541,x89542)))) % 187.68/187.64 [9070]~P1(f306(f306(f308(f871(a865,a865)),f306(f306(f236(a865,a865),x90701),x90702)),f306(f306(f263(a865,a865,a865),a296),f282(a865,a296))))+P1(f306(f306(f221(a865),x90701),x90702)) % 187.68/187.64 [5023]~P91(x50231)+E(f306(f306(f81(x50231),f306(f111(x50231),a84)),x50232),x50232) % 187.68/187.64 [5055]~P67(x50551)+E(f306(f306(f81(x50551),f306(f80(x50551),x50552)),x50552),f2(x50551)) % 187.68/187.64 [5056]~P68(x50561)+E(f306(f306(f81(x50561),f306(f80(x50561),x50562)),x50562),f2(x50561)) % 187.68/187.64 [5057]~P94(x50571)+E(f306(f306(f108(x50571),f306(f80(x50571),x50572)),x50572),f231(x50571)) % 187.68/187.64 [5058]~P94(x50581)+E(f306(f306(f109(x50581),f306(f80(x50581),x50582)),x50582),f185(x50581)) % 187.68/187.64 [5092]~P91(x50921)+E(f306(f306(f82(x50921),f306(f111(x50921),a104)),x50922),f306(f80(x50921),x50922)) % 187.68/187.64 [5262]~P114(x52621)+E(f306(f306(f82(x52621),f306(f80(x52621),f79(x52621))),x52622),f306(f80(x52621),x52622)) % 187.68/187.64 [5305]E(f306(f76(a1),x53051),f79(a1))+~E(f306(f76(a1),f306(f306(f82(a1),x53051),x53052)),f79(a1)) % 187.68/187.64 [5398]~P91(x53981)+E(f306(f306(f81(x53981),f79(x53981)),f306(f111(x53981),x53982)),f306(f111(x53981),f306(f306(f22(a1),x53982),a104))) % 187.68/187.64 [5452]~P108(x54521)+E(f14(x54521,f306(f306(f284(x54521),x54522),f185(f872(x54521,a859)))),x54522) % 187.68/187.64 [5453]~P108(x54531)+E(f15(x54531,f306(f306(f284(x54531),x54532),f185(f872(x54531,a859)))),x54532) % 187.68/187.64 [5454]~P98(x54541)+E(f13(x54541,f306(f306(f284(x54541),x54542),f185(f872(x54541,a859)))),x54542) % 187.68/187.64 [5455]~P98(x54551)+E(f10(x54551,f306(f306(f284(x54551),x54552),f185(f872(x54551,a859)))),x54552) % 187.68/187.64 [5456]~P6(x54561)+E(f42(x54561,f306(f306(f284(x54561),x54562),f185(f872(x54561,a859)))),x54562) % 187.68/187.64 [5457]~P6(x54571)+E(f41(x54571,f306(f306(f284(x54571),x54572),f185(f872(x54571,a859)))),x54572) % 187.68/187.64 [5479]E(f306(f306(f81(a865),x54791),f306(f306(f22(a865),x54792),x54791)),x54792)+P1(f306(f306(f221(a865),x54792),x54791)) % 187.68/187.64 [5509]E(x55091,f120(x55092))+P1(f306(f306(f221(a865),f2(a865)),f306(f186(f866(x55092)),x55091))) % 187.68/187.64 [5634]~P108(x56341)+E(f11(x56341,f225(x56341),f306(f306(f284(x56341),x56342),f185(f872(x56341,a859)))),x56342) % 187.68/187.64 [5635]~P108(x56351)+E(f12(x56351,f219(x56351),f306(f306(f284(x56351),x56352),f185(f872(x56351,a859)))),x56352) % 187.68/187.64 [5697]E(f306(f306(f22(a865),x56971),f306(f306(f22(a865),x56971),x56972)),x56972)+~P1(f306(f306(f220(a865),x56972),x56971)) % 187.68/187.64 [5698]E(f306(f306(f81(a865),x56981),f306(f306(f22(a865),x56982),x56981)),x56982)+~P1(f306(f306(f220(a865),x56981),x56982)) % 187.68/187.64 [5719]E(f46(a865,f306(f306(f22(a865),x57191),x57192),x57192),f46(a865,x57191,x57192))+P1(f306(f306(f221(a865),x57191),x57192)) % 187.68/187.64 [5730]E(f306(f80(a1),f306(f306(f40(a1),x57301),f306(f80(a1),x57302))),f266(x57301,x57302))+P1(f306(f306(f220(a1),f2(a1)),x57302)) % 187.68/187.64 [5732]~E(x57322,f2(a865))+P1(f306(f306(f221(a865),f2(a865)),f306(f306(f237(a865),x57321),x57322))) % 187.68/187.64 [5784]~P91(x57841)+E(f306(f306(f81(x57841),f306(f80(x57841),f79(x57841))),f306(f111(x57841),x57842)),f306(f111(x57841),f306(f306(f81(a1),x57842),a104))) % 187.68/187.64 [5785]E(f306(f306(f237(a865),f306(f111(a865),x57851)),x57852),f306(f306(f237(a865),f2(a865)),x57852))+~P1(f306(a190,f306(f111(a1),x57851))) % 187.68/187.64 [5882]E(f306(f133(a865),f131(a865,f306(f276(a865,x58821),x58822))),x58821)+~P1(f306(f306(f221(a865),x58821),x58822)) % 187.68/187.64 [5902]E(f306(f306(f82(a865),f306(f111(a865),x59021)),f306(f111(a865),x59022)),f306(f111(a865),f306(f306(f82(a1),x59021),x59022)))+P1(f306(f306(f221(a1),x59021),a84)) % 187.68/187.64 [5908]~P123(x59081)+P1(f306(f306(f220(x59081),f2(x59081)),f306(f306(f82(x59081),x59082),x59082))) % 187.68/187.64 [5920]E(f306(f306(f22(a865),f306(a119,x59201)),x59202),f306(a119,f306(f306(f22(a865),x59201),x59202)))+~P1(f306(f306(f220(a865),x59202),x59201)) % 187.68/187.64 [5923]E(f46(a865,f306(f306(f22(a865),x59231),x59232),x59232),f46(a865,x59231,x59232))+~P1(f306(f306(f220(a865),x59232),x59231)) % 187.68/187.64 [5979]E(f306(f306(f237(a865),f306(a112,x59791)),x59792),f306(a112,f306(f306(f237(a1),x59791),x59792)))+~P1(f306(f306(f220(a1),f2(a1)),x59791)) % 187.68/187.64 [5995]P1(f306(f129(x59951),x59952))+P1(f306(f306(f221(a865),f683(x59952,x59951)),f306(f186(f866(x59951)),x59952))) % 187.68/187.64 [5996]P1(f306(f129(x59961),x59962))+P1(f306(f306(f221(a865),f687(x59962,x59961)),f306(f186(f866(x59961)),x59962))) % 187.68/187.64 [6011]~E(x60111,f120(x60112))+~P1(f306(f306(f221(a865),f2(a865)),f306(f186(f866(x60112)),x60111))) % 187.68/187.64 [6025]E(f136(a865,f131(a865,f306(f276(a865,x60251),x60252))),f306(f306(f22(a865),x60252),f79(a865)))+~P1(f306(f306(f221(a865),x60251),x60252)) % 187.68/187.64 [6028]E(f306(f306(f81(a1),x60281),f306(f107(a1),f306(a119,f823(x60282,x60281)))),x60282)+~P1(f306(f306(f221(a1),x60281),x60282)) % 187.68/187.64 [6035]E(x60351,f2(a865))+E(f306(f306(f82(a865),x60352),f306(f306(f237(a865),x60352),f306(f306(f22(a865),x60351),f79(a865)))),f306(f306(f237(a865),x60352),x60351)) % 187.68/187.64 [6061]E(f306(f306(f82(a865),f306(a112,x60611)),f306(a112,x60612)),f306(a112,f306(f306(f82(a1),x60611),x60612)))+~P1(f306(f306(f220(a1),f2(a1)),x60611)) % 187.68/187.64 [6062]E(f306(f306(f40(a865),f306(a112,x60621)),f306(a112,x60622)),f306(a112,f306(f306(f40(a1),x60621),x60622)))+~P1(f306(f306(f220(a1),f2(a1)),x60621)) % 187.68/187.64 [6075]~P113(x60751)+E(f306(f306(f81(x60751),x60752),x60752),f306(f306(f82(x60751),f306(f306(f81(x60751),f79(x60751)),f79(x60751))),x60752)) % 187.68/187.64 [6092]E(f306(f306(f22(a1),f306(f107(a1),x60921)),f306(f107(a1),x60922)),f306(f107(a1),f306(f306(f22(a865),x60921),x60922)))+~P1(f306(f306(f220(a865),x60922),x60921)) % 187.68/187.64 [6094]E(f306(f306(f236(a1,a1),f306(f111(a1),a104)),f306(f306(f81(a1),x60941),x60942)),f51(x60941,x60942))+~P1(f306(f306(f220(a1),x60942),f2(a1))) % 187.68/187.64 [6133]E(f171(x61331,x61332),f120(f866(x61331)))+P1(f306(f306(f308(f866(x61331)),f682(x61332,x61331)),f306(f164(f866(x61331)),x61332))) % 187.68/187.64 [6217]E(f306(f306(f143(a1),x62171),f170(f306(f306(f81(a1),x62171),f79(a1)),x62172)),f170(x62171,x62172))+~P1(f306(f306(f220(a1),x62171),x62172)) % 187.68/187.64 [6254]~P1(f306(f306(f221(a865),x62542),x62541))+P1(f306(f306(f221(a865),f2(a865)),f306(f306(f22(a865),x62541),x62542))) % 187.68/187.64 [6285]~P1(f306(f306(f221(a865),x62851),f306(a112,x62852)))+P1(f306(f306(f221(a1),f306(f107(a1),x62851)),x62852)) % 187.68/187.64 [6317]~P108(x63171)+E(f306(f306(f108(f872(x63171,a859)),f306(f229(x63171),x63172)),f306(f306(f284(x63171),x63172),f185(f872(x63171,a859)))),f306(f275(x63171),x63172)) % 187.68/187.64 [6318]~P1(f306(f306(f220(a1),f2(a1)),x63181))+P1(f306(f306(f220(a1),f2(a1)),f306(f306(f237(a1),x63181),x63182))) % 187.68/187.64 [6321]~P1(f306(f306(f221(a865),f2(a865)),x63211))+P1(f306(f306(f221(a865),f2(a865)),f306(f306(f237(a865),x63211),x63212))) % 187.68/187.64 [6350]~E(f306(x63501,f2(a865)),f2(a865))+E(f306(f306(f6(a865,a865),x63501),f277(a865,f306(a119,f2(a865)),x63502)),f306(f306(f6(a865,a865),x63501),f277(a865,f2(a865),x63502))) % 187.68/187.64 [6413]~P91(x64131)+E(f306(f306(f82(x64131),f306(f306(f81(x64131),f79(x64131)),f79(x64131))),f306(f111(x64131),x64132)),f306(f111(x64131),f306(f306(f81(a1),x64132),x64132))) % 187.68/187.64 [6429]E(f306(f306(f284(a1),x64291),f277(a1,f306(f306(f81(a1),x64291),f79(a1)),x64292)),f277(a1,x64291,x64292))+P1(f306(f306(f221(a1),x64292),x64291)) % 187.68/187.64 [6430]P1(f306(f306(f221(a865),x64301),f306(a112,x64302)))+~P1(f306(f306(f221(a1),f306(f107(a1),x64301)),x64302)) % 187.68/187.64 [6528]E(f306(a112,f306(f306(f40(a1),f306(f111(a1),x65281)),f306(f111(a1),x65282))),f306(f306(f40(a865),f306(f111(a865),x65281)),f306(f111(a865),x65282)))+P1(f306(a190,f306(f111(a1),x65281))) % 187.68/187.64 [6587]P1(f306(f306(f221(a865),x65871),x65872))+~P1(f306(f306(f221(a865),f2(a865)),f306(f306(f22(a865),x65872),x65871))) % 187.68/187.64 [6633]P1(f306(f306(f221(a865),f2(a865)),x66331))+~P1(f306(f306(f221(a865),f2(a865)),f306(f306(f82(a865),x66332),x66331))) % 187.68/187.64 [6634]P1(f306(f306(f221(a865),f2(a865)),x66341))+~P1(f306(f306(f221(a865),f2(a865)),f306(f306(f82(a865),x66341),x66342))) % 187.68/187.64 [6653]~P1(f306(f306(f220(a1),x66531),f2(a1)))+E(f306(f306(f82(a865),f306(a112,f306(f80(a1),x66531))),f306(a112,f306(f80(a1),x66532))),f306(a112,f306(f306(f82(a1),x66531),x66532))) % 187.68/187.64 [6711]~E(x67112,f185(f872(x67111,a859)))+P1(f306(f306(f220(f872(x67111,a859)),x67112),f306(f80(f872(x67111,a859)),x67112))) % 187.68/187.64 [6773]~P91(x67731)+E(f306(f306(f81(x67731),f306(f306(f81(x67731),f2(x67731)),f306(f111(x67731),x67732))),f306(f111(x67731),x67732)),f306(f111(x67731),f306(f306(f81(a1),x67732),x67732))) % 187.68/187.64 [6829]~P1(f306(f306(f221(a1),x68291),x68292))+P1(f306(f306(f220(a1),f306(f306(f81(a1),x68291),f79(a1))),x68292)) % 187.68/187.64 [6894]E(x68941,f2(a865))+~P1(f306(f306(f220(a1),f306(f107(a1),x68942)),f306(f80(a1),f306(f107(a1),x68941)))) % 187.68/187.64 [6895]E(x68951,f2(a865))+~P1(f306(f306(f220(a1),f306(f107(a1),x68951)),f306(f80(a1),f306(f107(a1),x68952)))) % 187.68/187.64 [7000]E(f306(f306(f236(a1,a1),f306(f111(a1),a104)),f306(f306(f81(a1),x70001),x70002)),f51(x70001,x70002))+~P1(f306(f306(f220(a1),f2(a1)),f306(f306(f81(a1),x70001),x70002))) % 187.68/187.64 [7042]~P29(x70421,x70422)+P40(x70421,f306(f235(f872(f871(x70421,x70421),a859),f872(f871(x70421,x70421),a859)),x70422)) % 187.68/187.64 [7060]~P1(f306(f306(f220(a865),f306(a119,f2(a865))),x70601))+P1(f306(f306(f220(a865),f306(a119,f2(a865))),f306(f306(f237(a865),x70601),x70602))) % 187.68/187.64 [7230]~P1(f306(f306(f220(a1),x72301),x72302))+P1(f306(f306(f220(a1),f306(f306(f81(a1),x72301),x72301)),f306(f306(f81(a1),x72302),x72302))) % 187.68/187.64 [7235]~P1(f306(f306(f221(a1),x72351),x72352))+P1(f306(f306(f221(a1),f306(f306(f81(a1),x72351),x72351)),f306(f306(f81(a1),x72352),x72352))) % 187.68/187.64 [7236]~P1(f306(f306(f92(a1),x72361),x72362))+P1(f306(f306(f92(a1),f306(f306(f81(a1),x72361),x72361)),f306(f306(f81(a1),x72362),x72362))) % 187.68/187.64 [7290]~P1(f306(f306(f221(a865),f2(a865)),x72901))+P1(f306(f306(f221(a865),f306(f306(f22(a865),x72901),f306(a119,x72902))),x72901)) % 187.68/187.64 [7327]P1(f306(f306(f220(a865),f306(a119,f2(a865))),x73271))+~P1(f306(f306(f220(a865),f306(a119,f2(a865))),f306(f306(f82(a865),x73272),x73271))) % 187.68/187.64 [7328]P1(f306(f306(f220(a865),f306(a119,f2(a865))),x73281))+~P1(f306(f306(f220(a865),f306(a119,f2(a865))),f306(f306(f82(a865),x73281),x73282))) % 187.68/187.64 [7332]P1(f306(f306(f220(a865),f306(f306(f157(a865),x73321),x73322)),f306(f158(a865),x73321)))+~P1(f306(f306(f221(a865),x73322),f306(f186(f866(a865)),x73321))) % 187.68/187.64 [7373]P1(f306(f306(f221(a1),x73731),x73732))+~P1(f306(f306(f220(a1),f306(f306(f81(a1),x73731),f79(a1))),x73732)) % 187.68/187.64 [7418]P1(f306(f63(x74181),f231(f872(x74181,a859))))+~P1(f306(f63(f872(x74182,x74181)),f231(f872(f872(x74182,x74181),a859)))) % 187.68/187.64 [7419]P1(f306(f63(x74191),f231(f872(x74191,a859))))+~P1(f306(f63(f870(x74192,x74191)),f231(f872(f870(x74192,x74191),a859)))) % 187.68/187.64 [7420]P1(f306(f63(x74201),f231(f872(x74201,a859))))+~P1(f306(f63(f870(x74201,x74202)),f231(f872(f870(x74201,x74202),a859)))) % 187.68/187.64 [7459]E(x74591,f185(f872(x74592,a859)))+~P1(f306(f306(f220(f872(x74592,a859)),x74591),f306(f80(f872(x74592,a859)),x74591))) % 187.68/187.64 [7595]E(f306(f134(f866(x75951),f866(x75951),f122(x75951),f120(x75951)),x75952),f120(x75951))+P1(f306(f306(f308(f866(x75951)),f733(x75952,x75951)),f306(f164(f866(x75951)),x75952))) % 187.68/187.64 [7596]E(f306(f134(f866(x75961),f866(x75961),f122(x75961),f120(x75961)),x75962),f120(x75961))+P1(f306(f306(f308(f866(x75961)),f736(x75962,x75961)),f306(f164(f866(x75961)),x75962))) % 187.68/187.64 [7832]P1(f306(f306(f220(a1),x78321),x78322))+~P1(f306(f306(f220(a1),f306(f306(f81(a1),x78321),x78321)),f306(f306(f81(a1),x78322),x78322))) % 187.68/187.64 [7837]P1(f306(f306(f221(a1),x78371),x78372))+~P1(f306(f306(f221(a1),f306(f306(f81(a1),x78371),x78371)),f306(f306(f81(a1),x78372),x78372))) % 187.68/187.64 [7838]P1(f306(f306(f92(a1),x78381),x78382))+~P1(f306(f306(f92(a1),f306(f306(f81(a1),x78381),x78381)),f306(f306(f81(a1),x78382),x78382))) % 187.68/187.64 [7932]~P113(x79321)+E(f306(f306(f82(x79321),f306(f306(f81(x79321),f79(x79321)),f79(x79321))),f306(f306(f6(a865,x79321),f107(x79321)),f277(a865,f79(a865),x79322))),f306(f306(f82(x79321),f306(f107(x79321),x79322)),f306(f306(f81(x79321),f306(f107(x79321),x79322)),f79(x79321)))) % 187.68/187.64 [7988]P1(f306(f306(f308(a865),x79881),x79882))+~P1(f306(f306(f308(a1),f306(f107(a1),x79881)),f306(f285(a865,a1,f107(a1)),x79882))) % 187.68/187.64 [8150]~P1(f306(f63(x81501),x81502))+E(f306(f285(a865,x81501,f524(x81502,x81501)),f306(f228(a865),f306(f306(f7(a865,a865,a859),f221(a865)),f525(x81502,x81501)))),x81502) % 187.68/187.64 [8440]P51(x84401,x84402)+P1(f306(f306(f308(f871(x84401,x84401)),f306(f306(f236(x84401,x84401),f337(x84402,x84401)),f337(x84402,x84401))),x84402)) % 187.68/187.64 [8582]~P91(x85821)+E(f306(f306(f22(x85821),f79(x85821)),f306(f111(x85821),x85822)),f306(f111(x85821),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f80(a1),x85822)))) % 187.68/187.64 [8694]~P1(f306(f306(f221(f872(a865,a859)),x86941),x86942))+P1(f306(f306(f221(f872(a1,a859)),f306(f285(a865,a1,f107(a1)),x86941)),f306(f285(a865,a1,f107(a1)),x86942))) % 187.68/187.64 [8723]~P1(f306(f306(f221(a1),x87231),x87232))+P1(f306(f306(f220(a1),f306(f306(f22(a1),f306(f306(f81(a1),x87231),x87231)),a104)),f306(f306(f81(a1),x87232),x87232))) % 187.68/187.64 [8725]~P1(f306(f306(f221(a1),x87251),x87252))+P1(f306(f306(f221(a1),f306(f306(f22(a1),f306(f306(f81(a1),x87251),x87251)),a104)),f306(f306(f81(a1),x87252),x87252))) % 187.68/187.64 [8795]~P1(f306(f306(f308(a865),x87951),f306(f164(a865),x87952)))+P1(f306(f306(f220(a865),x87951),f306(f134(a865,a865,f81(a865),f2(a865)),x87952))) % 187.68/187.64 [8889]P47(x88891,x88892)+~P1(f306(f306(f308(f871(x88891,x88891)),f306(f306(f236(x88891,x88891),f322(x88892,x88891)),f322(x88892,x88891))),x88892)) % 187.68/187.64 [9037]~P1(f306(f306(f220(f872(a1,a859)),f306(f285(a865,a1,f107(a1)),x90371)),f306(f285(a865,a1,f107(a1)),x90372)))+P1(f306(f306(f220(f872(a865,a859)),x90371),x90372)) % 187.68/187.64 [9038]~P1(f306(f306(f221(f872(a1,a859)),f306(f285(a865,a1,f107(a1)),x90381)),f306(f285(a865,a1,f107(a1)),x90382)))+P1(f306(f306(f221(f872(a865,a859)),x90381),x90382)) % 187.68/187.64 [9119]P1(f306(f306(f221(a1),x91191),x91192))+~P1(f306(f306(f220(a1),f306(f306(f22(a1),f306(f306(f81(a1),x91191),x91191)),a104)),f306(f306(f81(a1),x91192),x91192))) % 187.68/187.64 [9121]P1(f306(f306(f221(a1),x91211),x91212))+~P1(f306(f306(f221(a1),f306(f306(f22(a1),f306(f306(f81(a1),x91211),x91211)),a104)),f306(f306(f81(a1),x91212),x91212))) % 187.68/187.64 [10038]~P1(f306(f63(x100381),x100382))+E(f306(f186(f866(x100381)),f91(f866(x100381),f306(f306(f18(f866(x100381),a859,a859),f306(f306(f8(a859,f872(a859,a859),f866(x100381)),a304),f306(f306(f7(f866(x100381),f872(x100381,a859),a859),f306(f306(f8(f872(x100381,a859),f872(f872(x100381,a859),a859),f866(x100381)),a303),f164(x100381))),x100382))),f129(x100381)))),f200(x100381,x100382)) % 187.68/187.64 [10180]~P27(a861,x101801,f306(f306(f284(f864(a861)),f306(f306(f306(f93(a861),a303),x101802),f193(x101802))),f185(f872(f864(a861),a859))))+P27(a861,x101801,f306(f306(f284(f864(a861)),f306(f306(f306(f93(a861),f306(f306(f8(f872(a861,f872(a861,a859)),f872(a861,a859),a861),f306(f8(f872(a861,a859),a859,a861),f89(a861))),f306(f306(f8(f872(a861,a859),f872(a861,f872(a861,a859)),a861),f306(f7(a861,f872(a861,a859),f872(a861,a859)),f306(f306(f8(f872(a861,f872(a859,a859)),f872(f872(a861,a859),f872(a861,a859)),a861),f18(a861,a859,a859)),f306(f306(f8(f872(a861,a859),f872(a861,f872(a859,a859)),a861),f306(f8(a859,f872(a859,a859),a861),a309)),f193(x101802))))),a303))),x101802),a303)),f185(f872(f864(a861),a859)))) % 187.68/187.64 [6024]E(f306(f306(f81(a865),f306(f306(f22(a865),x60241),x60242)),x60242),x60241)+~P1(f306(f306(f220(a865),x60242),x60241)) % 187.68/187.64 [6088]E(f306(f306(f40(a865),f306(f306(f82(a865),x60881),x60882)),x60882),x60881)+~P1(f306(f306(f221(a865),f2(a865)),x60882)) % 187.68/187.64 [6089]E(f306(f306(f40(a865),f306(f306(f82(a865),x60891),x60892)),x60891),x60892)+~P1(f306(f306(f221(a865),f2(a865)),x60891)) % 187.68/187.64 [6093]~P74(x60931)+E(f306(f306(f6(a865,x60931),f306(f157(x60931),x60932)),f306(f276(a865,f2(a865)),f306(f186(f866(x60931)),x60932))),f306(f158(x60931),x60932)) % 187.68/187.64 [6209]E(f46(a865,f306(a119,f306(f306(f82(a865),x62091),x62092)),x62091),f79(a865))+~P1(f306(f306(f221(a865),f79(a865)),x62091)) % 187.68/187.64 [6215]E(f306(a119,f306(f306(f81(a865),f306(f111(a865),x62151)),x62152)),f306(f306(f81(a865),f79(a865)),x62152))+~P1(f306(a190,f306(f111(a1),x62151))) % 187.68/187.64 [6243]E(f306(a112,f306(f306(f237(a1),f306(f111(a1),x62431)),x62432)),f306(f306(f237(a865),f306(f111(a865),x62431)),x62432))+P1(f306(a190,f306(f111(a1),x62431))) % 187.68/187.64 [6482]E(f306(f306(f22(a865),x64821),f306(f111(a865),f306(f306(f81(a1),x64822),a104))),f306(f306(f22(a865),f306(a119,x64821)),f306(f111(a865),x64822)))+~P1(f306(f306(f221(a1),a84),x64822)) % 187.68/187.64 [6560]E(x65601,f2(a865))+E(f306(a119,f306(f306(f81(a865),f306(f306(f22(a865),x65601),f79(a865))),x65602)),f306(f306(f81(a865),x65601),x65602)) % 187.68/187.64 [6601]E(x66011,f2(a1))+P1(f306(f306(f221(a1),f2(a1)),f306(f306(f237(a1),f306(f76(a1),x66011)),x66012))) % 187.68/187.64 [6617]~E(x66172,f2(a865))+P1(f306(f306(f221(a1),f2(a1)),f306(f306(f237(a1),f306(f76(a1),x66171)),x66172))) % 187.68/187.64 [6657]E(x66571,f2(a865))+E(f306(f306(f81(a865),x66572),f306(f306(f82(a865),f306(f306(f22(a865),x66571),f79(a865))),x66572)),f306(f306(f82(a865),x66571),x66572)) % 187.68/187.64 [6705]~P1(f306(f306(f220(a1),x67051),x67052))+P1(f306(f306(f221(a1),f306(f306(f81(a1),x67051),a104)),x67052)) % 187.68/187.64 [6832]E(f306(f306(f143(a865),x68321),f131(a865,f306(f276(a865,f306(a119,x68321)),x68322))),f131(a865,f306(f276(a865,x68321),x68322)))+~P1(f306(f306(f221(a865),x68321),x68322)) % 187.68/187.64 [7033]E(x70331,x70332)+~E(f306(f306(f22(a1),f306(f306(f81(a1),x70331),x70331)),a104),f306(f306(f22(a1),f306(f306(f81(a1),x70332),x70332)),a104)) % 187.68/187.64 [7036]E(x70361,f120(x70362))+E(f250(x70362,f306(f306(f146(x70362,f871(a106,x70362)),f306(f236(a106,x70362),f79(a106))),x70361)),f257(x70362,x70361)) % 187.68/187.64 [7260]P1(f306(f306(f220(a1),x72601),x72602))+~P1(f306(f306(f221(a1),f306(f306(f81(a1),x72601),a104)),x72602)) % 187.68/187.64 [7737]~P1(f306(f306(f221(a865),x77371),x77372))+P1(f306(f306(f308(f871(a865,a865)),f306(f306(f236(a865,a865),x77371),x77372)),a227)) % 187.68/187.64 [7960]~P1(f306(f306(f221(a106),f2(a106)),x79601))+P1(f306(f306(f221(a106),f306(f235(a106,f871(a106,a106)),f306(f251(x79601),x79602))),x79601)) % 187.68/187.64 [8279]~P84(x82791)+P1(f306(f306(f220(x82791),f306(f76(x82791),f306(f158(x82791),x82792))),f306(f158(x82791),f306(f306(f146(x82791,x82791),f76(x82791)),x82792)))) % 187.68/187.64 [8303]P1(f306(f306(f221(a865),x83031),x83032))+~P1(f306(f306(f308(f871(a865,a865)),f306(f306(f236(a865,a865),x83031),x83032)),a227)) % 187.68/187.64 [8465]E(f306(f306(f236(x84651,x84651),f614(x84652,x84651)),f614(x84652,x84651)),x84652)+~P1(f306(f306(f308(f871(x84651,x84651)),x84652),f282(x84651,f185(f872(f871(x84651,x84651),a859))))) % 187.68/187.64 [8506]E(f306(f276(a865,x85061),f306(f306(f81(a865),x85061),f306(f39(a865),x85062))),x85062)+~P1(f306(f306(f220(f872(a865,a859)),x85062),f306(f276(a865,x85061),f306(f306(f81(a865),x85061),f306(f39(a865),x85062))))) % 187.68/187.64 [8835]E(f306(f306(f40(a1),f306(f111(a1),f306(f306(f22(a1),f306(f306(f81(a1),x88351),x88351)),a104))),f306(f111(a1),f306(f306(f81(a1),x88352),x88352))),f306(f306(f40(a1),f306(f111(a1),x88351)),f306(f111(a1),x88352)))+~P1(f306(f306(f220(a1),f2(a1)),f306(f111(a1),x88352))) % 187.68/187.64 [8964]E(f168(f866(x89641),f306(f306(f8(a859,a859,f866(x89641)),a301),f306(f306(f7(f866(x89641),f866(x89641),a859),a303),f120(x89641))),x89642),f171(x89641,f171(x89641,x89642)))+~P17(a865,f306(f161(a865),f306(f306(f146(f866(x89641),a865),f186(f866(x89641))),x89642))) % 187.68/187.64 [8967]E(f306(f306(f40(a1),f306(f111(a1),f306(f306(f22(a1),f306(f306(f81(a1),x89671),x89671)),a104))),f306(f111(a1),f306(f306(f81(a1),x89672),x89672))),f306(f306(f40(a1),f306(f306(f81(a1),f306(f111(a1),x89671)),f79(a1))),f306(f111(a1),x89672)))+P1(f306(f306(f220(a1),f2(a1)),f306(f111(a1),x89672))) % 187.68/187.64 [9809]P1(f306(a190,x98092))+E(f306(f306(f87(a1,a865),f306(f306(f22(a1),x98091),x98092)),f306(f306(f18(a1,a865,a865),f306(f306(f7(a1,a865,f872(a865,a865)),f306(f306(f8(a859,f872(a865,f872(a865,a865)),a1),f101(a865)),a190)),f2(a865))),a112)),f306(f306(f22(a865),f306(a112,x98091)),f306(a112,x98092))) % 187.68/187.64 [9817]E(f306(f306(f87(a1,a865),f306(f111(a1),f306(f306(f81(a1),x98171),f306(f80(a1),x98172)))),f306(f306(f18(a1,a865,a865),f306(f306(f7(a1,a865,f872(a865,a865)),f306(f306(f8(a859,f872(a865,f872(a865,a865)),a1),f101(a865)),a190)),f2(a865))),a112)),f306(f306(f22(a865),f306(f111(a865),x98171)),f306(f111(a865),x98172)))+P1(f306(f306(f221(a1),x98172),a84)) % 187.68/187.64 [9818]~P29(x98181,x98182)+P1(f306(f306(f220(f872(f871(x98181,x98181),a859)),f306(f306(f263(x98181,x98181,x98181),f306(f235(f872(f871(x98181,x98181),a859),f872(f871(x98181,x98181),a859)),x98182)),f306(f244(f872(f871(x98181,x98181),a859),f872(f871(x98181,x98181),a859)),x98182))),f306(f235(f872(f871(x98181,x98181),a859),f872(f871(x98181,x98181),a859)),x98182))) % 187.68/187.64 [9884]~E(f306(f39(a865),f306(f228(a865),f306(f306(f18(a865,a859,a859),f306(f306(f8(a859,f872(a859,a859),a865),a304),f306(f306(f7(a865,f872(a865,a859),a859),f308(a865)),x98841))),f306(f306(f7(a865,a865,a859),f221(a865)),f306(a119,x98842))))),f2(a865))+~P1(f306(f306(f308(a865),f2(a865)),x98841)) % 187.68/187.64 [9942]E(f46(a1,f306(f111(a1),f306(f306(f22(a1),f306(f306(f81(a1),x99421),x99421)),a104)),f306(f111(a1),f306(f306(f81(a1),x99422),x99422))),f306(f306(f81(a1),f306(f306(f82(a1),f306(f111(a1),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)))),f46(a1,f306(f111(a1),x99421),f306(f111(a1),x99422)))),f79(a1)))+~P1(f306(f306(f220(a1),f2(a1)),f306(f111(a1),x99422))) % 187.68/187.64 [9951]E(f46(a1,f306(f111(a1),f306(f306(f22(a1),f306(f306(f81(a1),x99511),x99511)),a104)),f306(f111(a1),f306(f306(f81(a1),x99512),x99512))),f306(f306(f22(a1),f306(f306(f82(a1),f306(f111(a1),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)))),f46(a1,f306(f306(f81(a1),f306(f111(a1),x99511)),f79(a1)),f306(f111(a1),x99512)))),f79(a1)))+P1(f306(f306(f220(a1),f2(a1)),f306(f111(a1),x99512))) % 187.68/187.64 [10005]~P6(x100051)+E(f41(x100051,f306(f228(x100051),f306(f306(f8(f872(x100051,a859),a859,x100051),f89(x100051)),f306(f306(f8(f872(x100051,a859),f872(x100051,a859),x100051),f306(f18(x100051,a859,a859),f306(f306(f8(a859,f872(a859,a859),x100051),a309),f306(f306(f7(x100051,f872(x100051,a859),a859),f308(x100051)),x100052)))),f220(x100051))))),f42(x100051,x100052)) % 187.68/187.64 [10031]~P40(x100311,x100312)+P59(x100311,f306(f306(f7(x100311,f872(f871(x100311,x100311),a859),f872(x100311,a859)),f306(f306(f8(f872(x100311,f872(f872(f871(x100311,x100311),a859),a859)),f872(f872(f871(x100311,x100311),a859),f872(x100311,a859)),x100311),f7(x100311,f872(f871(x100311,x100311),a859),a859)),f306(f306(f8(f872(x100311,f871(x100311,x100311)),f872(x100311,f872(f872(f871(x100311,x100311),a859),a859)),x100311),f306(f8(f871(x100311,x100311),f872(f872(f871(x100311,x100311),a859),a859),x100311),f308(f871(x100311,x100311)))),f236(x100311,x100311)))),x100312)) % 187.68/187.64 [10032]~P9(x100321,f231(f872(x100321,a859)),x100322)+P8(x100321,f306(f306(f7(x100321,f872(f871(x100321,x100321),a859),f872(x100321,a859)),f306(f306(f8(f872(x100321,f872(f872(f871(x100321,x100321),a859),a859)),f872(f872(f871(x100321,x100321),a859),f872(x100321,a859)),x100321),f7(x100321,f872(f871(x100321,x100321),a859),a859)),f306(f306(f8(f872(x100321,f871(x100321,x100321)),f872(x100321,f872(f872(f871(x100321,x100321),a859),a859)),x100321),f306(f8(f871(x100321,x100321),f872(f872(f871(x100321,x100321),a859),a859),x100321),f308(f871(x100321,x100321)))),f236(x100321,x100321)))),x100322)) % 187.68/187.64 [10070]P40(x100701,x100702)+~P59(x100701,f306(f306(f7(x100701,f872(f871(x100701,x100701),a859),f872(x100701,a859)),f306(f306(f8(f872(x100701,f872(f872(f871(x100701,x100701),a859),a859)),f872(f872(f871(x100701,x100701),a859),f872(x100701,a859)),x100701),f7(x100701,f872(f871(x100701,x100701),a859),a859)),f306(f306(f8(f872(x100701,f871(x100701,x100701)),f872(x100701,f872(f872(f871(x100701,x100701),a859),a859)),x100701),f306(f8(f871(x100701,x100701),f872(f872(f871(x100701,x100701),a859),a859),x100701),f308(f871(x100701,x100701)))),f236(x100701,x100701)))),x100702)) % 187.68/187.64 [10071]P9(x100711,f231(f872(x100711,a859)),x100712)+~P8(x100711,f306(f306(f7(x100711,f872(f871(x100711,x100711),a859),f872(x100711,a859)),f306(f306(f8(f872(x100711,f872(f872(f871(x100711,x100711),a859),a859)),f872(f872(f871(x100711,x100711),a859),f872(x100711,a859)),x100711),f7(x100711,f872(f871(x100711,x100711),a859),a859)),f306(f306(f8(f872(x100711,f871(x100711,x100711)),f872(x100711,f872(f872(f871(x100711,x100711),a859),a859)),x100711),f306(f8(f871(x100711,x100711),f872(f872(f871(x100711,x100711),a859),a859),x100711),f308(f871(x100711,x100711)))),f236(x100711,x100711)))),x100712)) % 187.68/187.64 [7211]E(f306(f306(f81(a865),f306(f111(a865),f306(f306(f22(a1),x72111),a104))),x72112),f306(a119,f306(f306(f81(a865),f306(f111(a865),x72111)),x72112)))+P1(f306(a190,f306(f111(a1),x72111))) % 187.68/187.64 [7654]~P91(x76541)+E(f306(f306(f81(x76541),f306(f306(f81(x76541),f79(x76541)),f306(f111(x76541),x76542))),f306(f111(x76541),x76542)),f306(f111(x76541),f306(f306(f22(a1),f306(f306(f81(a1),x76542),x76542)),a104))) % 187.68/187.64 [8305]~P1(f306(f306(f220(a1),x83051),x83052))+P1(f306(f306(f220(a1),f306(f306(f81(a1),x83051),x83051)),f306(f306(f22(a1),f306(f306(f81(a1),x83052),x83052)),a104))) % 187.68/187.64 [8307]~P1(f306(f306(f220(a1),x83071),x83072))+P1(f306(f306(f221(a1),f306(f306(f81(a1),x83071),x83071)),f306(f306(f22(a1),f306(f306(f81(a1),x83072),x83072)),a104))) % 187.68/187.64 [8727]P1(f306(f306(f220(a1),x87271),x87272))+~P1(f306(f306(f220(a1),f306(f306(f81(a1),x87271),x87271)),f306(f306(f22(a1),f306(f306(f81(a1),x87272),x87272)),a104))) % 187.68/187.64 [8729]P1(f306(f306(f220(a1),x87291),x87292))+~P1(f306(f306(f221(a1),f306(f306(f81(a1),x87291),x87291)),f306(f306(f22(a1),f306(f306(f81(a1),x87292),x87292)),a104))) % 187.68/187.64 [9025]~P1(f306(f306(f220(a1),x90251),x90252))+P1(f306(f306(f220(a1),f306(f306(f22(a1),f306(f306(f81(a1),x90251),x90251)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),x90252),x90252)),a104))) % 187.68/187.64 [9027]~P1(f306(f306(f221(a1),x90271),x90272))+P1(f306(f306(f221(a1),f306(f306(f22(a1),f306(f306(f81(a1),x90271),x90271)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),x90272),x90272)),a104))) % 187.68/187.64 [9028]~P1(f306(f306(f92(a1),x90281),x90282))+P1(f306(f306(f92(a1),f306(f306(f22(a1),f306(f306(f81(a1),x90281),x90281)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),x90282),x90282)),a104))) % 187.68/187.64 [9296]P1(f306(f306(f220(a1),x92961),x92962))+~P1(f306(f306(f220(a1),f306(f306(f22(a1),f306(f306(f81(a1),x92961),x92961)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),x92962),x92962)),a104))) % 187.68/187.64 [9298]P1(f306(f306(f221(a1),x92981),x92982))+~P1(f306(f306(f221(a1),f306(f306(f22(a1),f306(f306(f81(a1),x92981),x92981)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),x92982),x92982)),a104))) % 187.68/187.64 [9299]P1(f306(f306(f92(a1),x92991),x92992))+~P1(f306(f306(f92(a1),f306(f306(f22(a1),f306(f306(f81(a1),x92991),x92991)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),x92992),x92992)),a104))) % 187.68/187.64 [9331]~P1(f306(f63(x93311),x93312))+P1(f306(f63(f872(x93311,a859)),f306(f228(f872(x93311,a859)),f306(f306(f7(f872(x93311,a859),f872(x93311,a859),a859),f220(f872(x93311,a859))),x93312)))) % 187.68/187.64 [9380]~E(f306(f260(f871(a865,a865),f871(a865,a865),a116),f306(f306(f284(f871(a865,a865)),x93801),f185(f872(f871(a865,a865),a859)))),f306(f260(f871(a865,a865),f871(a865,a865),a116),f306(f306(f284(f871(a865,a865)),x93802),f185(f872(f871(a865,a865),a859)))))+P1(f306(f306(f308(f871(f871(a865,a865),f871(a865,a865))),f306(f306(f236(f871(a865,a865),f871(a865,a865)),x93801),x93802)),a116)) % 187.68/187.64 [9465]E(f306(f260(f871(a865,a865),f871(a865,a865),a116),f306(f306(f284(f871(a865,a865)),x94651),f185(f872(f871(a865,a865),a859)))),f306(f260(f871(a865,a865),f871(a865,a865),a116),f306(f306(f284(f871(a865,a865)),x94652),f185(f872(f871(a865,a865),a859)))))+~P1(f306(f306(f308(f871(f871(a865,a865),f871(a865,a865))),f306(f306(f236(f871(a865,a865),f871(a865,a865)),x94651),x94652)),a116)) % 187.68/187.64 [9503]P1(f306(f306(f220(a1),f2(a1)),f656(x95031,x95032)))+E(f306(f228(a1),f306(f306(f18(a1,a859,a859),f306(f306(f8(a859,f872(a859,a859),a1),a304),f306(f220(a1),f2(a1)))),x95031)),f306(f228(a1),f306(f306(f18(a1,a859,a859),f306(f306(f8(a859,f872(a859,a859),a1),a304),f306(f220(a1),f2(a1)))),x95032))) % 187.68/187.64 [10016]~P6(x100161)+E(f42(x100161,f306(f228(x100161),f306(f306(f8(f872(x100161,a859),a859,x100161),f89(x100161)),f306(f306(f8(f872(x100161,a859),f872(x100161,a859),x100161),f306(f18(x100161,a859,a859),f306(f306(f8(a859,f872(a859,a859),x100161),a309),f306(f306(f7(x100161,f872(x100161,a859),a859),f308(x100161)),x100162)))),f306(f7(x100161,x100161,a859),f220(x100161)))))),f41(x100161,x100162)) % 187.68/187.64 [10037]P1(f306(f306(f308(a865),f2(a865)),x100371))+E(f306(f39(a865),f306(f228(a865),f306(f306(f18(a865,a859,a859),f306(f306(f8(a859,f872(a859,a859),a865),a304),f306(f306(f7(a865,f872(a865,a859),a859),f306(f306(f8(a865,f872(f872(a865,a859),a859),a865),f308(a865)),a119)),x100371))),f306(f306(f7(a865,a865,a859),f221(a865)),x100372)))),f306(f39(a865),f306(f228(a865),f306(f306(f18(a865,a859,a859),f306(f306(f8(a859,f872(a859,a859),a865),a304),f306(f306(f7(a865,f872(a865,a859),a859),f308(a865)),x100371))),f306(f306(f7(a865,a865,a859),f221(a865)),f306(a119,x100372)))))) % 187.68/187.64 [7523]~P91(x75231)+E(f306(f306(f82(x75231),x75232),f306(f111(x75231),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104))),x75232) % 187.68/187.64 [7785]~P91(x77851)+E(f306(f306(f81(x77851),f306(f111(x77851),x77852)),f79(x77851)),f306(f111(x77851),f306(f306(f81(a1),x77852),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)))) % 187.68/187.64 [7930]P1(f306(f306(f220(a1),f2(a1)),f306(f111(a1),x79302)))+E(f306(f306(f237(a1),x79301),f306(f111(a865),f306(f306(f22(a1),f306(f306(f81(a1),x79302),x79302)),a104))),f79(a1)) % 187.68/187.64 [9357]~P1(f306(f306(f220(a1),f2(a1)),f306(f111(a1),x93572)))+E(f306(f306(f237(a1),x93571),f306(f111(a865),f306(f306(f22(a1),f306(f306(f81(a1),x93572),x93572)),a104))),f306(f306(f87(a1,a1),f306(f306(f237(a1),x93571),f306(f111(a865),x93572))),f306(f306(f18(a1,a1,a1),f306(f306(f8(a1,f872(a1,a1),a1),f82(a1)),f306(f82(a1),x93571))),f5(a1)))) % 187.68/187.64 [9725]~P1(f306(f306(f220(a865),f804(x97252,x97251)),f306(x97251,f804(x97252,x97251))))+P1(f306(f63(a865),f306(f228(a865),f306(f306(f7(a865,a865,a859),f306(f306(f8(a865,f872(a865,a859),a865),f220(a865)),x97251)),x97252)))) % 187.68/187.64 [9874]~P1(f306(f306(f220(a865),f306(f111(a865),x98741)),f306(a119,x98742)))+P1(f306(f306(f87(a1,a859),f306(f111(a1),f306(f306(f81(a1),x98741),a104))),f306(f306(f18(a1,a859,a859),f306(f306(f8(a859,f872(a859,a859),a1),a309),f306(f306(f8(a859,a859,a1),a301),a190))),f306(f306(f7(a1,a865,a859),f306(f306(f8(a865,f872(a865,a859),a1),f220(a865)),a112)),x98742)))) % 187.68/187.64 [9875]~P1(f306(f306(f221(a865),f306(f111(a865),x98751)),f306(a119,x98752)))+P1(f306(f306(f87(a1,a859),f306(f111(a1),f306(f306(f81(a1),x98751),a104))),f306(f306(f18(a1,a859,a859),f306(f306(f8(a859,f872(a859,a859),a1),a309),f306(f306(f8(a859,a859,a1),a301),a190))),f306(f306(f7(a1,a865,a859),f306(f306(f8(a865,f872(a865,a859),a1),f221(a865)),a112)),x98752)))) % 187.68/187.64 [9926]P1(f306(f306(f220(a865),f306(f111(a865),x99261)),f306(a119,x99262)))+~P1(f306(f306(f87(a1,a859),f306(f111(a1),f306(f306(f81(a1),x99261),a104))),f306(f306(f18(a1,a859,a859),f306(f306(f8(a859,f872(a859,a859),a1),a309),f306(f306(f8(a859,a859,a1),a301),a190))),f306(f306(f7(a1,a865,a859),f306(f306(f8(a865,f872(a865,a859),a1),f220(a865)),a112)),x99262)))) % 187.68/187.64 [9927]P1(f306(f306(f221(a865),f306(f111(a865),x99271)),f306(a119,x99272)))+~P1(f306(f306(f87(a1,a859),f306(f111(a1),f306(f306(f81(a1),x99271),a104))),f306(f306(f18(a1,a859,a859),f306(f306(f8(a859,f872(a859,a859),a1),a309),f306(f306(f8(a859,a859,a1),a301),a190))),f306(f306(f7(a1,a865,a859),f306(f306(f8(a865,f872(a865,a859),a1),f221(a865)),a112)),x99272)))) % 187.68/187.64 [9957]~P1(f306(f306(f220(a865),f306(a119,x99572)),f306(f111(a865),x99571)))+P1(f306(f306(f87(a1,a859),f306(f111(a1),f306(f306(f81(a1),x99571),a104))),f306(f306(f18(a1,a859,a859),f306(f306(f8(a859,f872(a859,a859),a1),a304),f306(f306(f8(a859,a859,a1),a301),a190))),f306(f306(f18(a1,a859,a859),f306(f306(f8(a859,f872(a859,a859),a1),a309),f306(f306(f8(a859,a859,a1),a301),a190))),f306(f306(f8(a865,a859,a1),f306(f220(a865),x99572)),a112))))) % 187.68/187.64 [9958]~P1(f306(f306(f221(a865),f306(a119,x99582)),f306(f111(a865),x99581)))+P1(f306(f306(f87(a1,a859),f306(f111(a1),f306(f306(f81(a1),x99581),a104))),f306(f306(f18(a1,a859,a859),f306(f306(f8(a859,f872(a859,a859),a1),a304),f306(f306(f8(a859,a859,a1),a301),a190))),f306(f306(f18(a1,a859,a859),f306(f306(f8(a859,f872(a859,a859),a1),a309),f306(f306(f8(a859,a859,a1),a301),a190))),f306(f306(f8(a865,a859,a1),f306(f221(a865),x99582)),a112))))) % 187.68/187.64 [10003]P1(f306(f306(f220(a865),f306(a119,x100031)),f306(f111(a865),x100032)))+~P1(f306(f306(f87(a1,a859),f306(f111(a1),f306(f306(f81(a1),x100032),a104))),f306(f306(f18(a1,a859,a859),f306(f306(f8(a859,f872(a859,a859),a1),a304),f306(f306(f8(a859,a859,a1),a301),a190))),f306(f306(f18(a1,a859,a859),f306(f306(f8(a859,f872(a859,a859),a1),a309),f306(f306(f8(a859,a859,a1),a301),a190))),f306(f306(f8(a865,a859,a1),f306(f220(a865),x100031)),a112))))) % 187.68/187.64 [10004]P1(f306(f306(f221(a865),f306(a119,x100041)),f306(f111(a865),x100042)))+~P1(f306(f306(f87(a1,a859),f306(f111(a1),f306(f306(f81(a1),x100042),a104))),f306(f306(f18(a1,a859,a859),f306(f306(f8(a859,f872(a859,a859),a1),a304),f306(f306(f8(a859,a859,a1),a301),a190))),f306(f306(f18(a1,a859,a859),f306(f306(f8(a859,f872(a859,a859),a1),a309),f306(f306(f8(a859,a859,a1),a301),a190))),f306(f306(f8(a865,a859,a1),f306(f221(a865),x100041)),a112))))) % 187.68/187.64 [10078]~P1(f306(f306(f308(a865),f2(a865)),x100781))+E(f306(a119,f306(f39(a865),f306(f228(a865),f306(f306(f18(a865,a859,a859),f306(f306(f8(a859,f872(a859,a859),a865),a304),f306(f306(f7(a865,f872(a865,a859),a859),f306(f306(f8(a865,f872(f872(a865,a859),a859),a865),f308(a865)),a119)),x100781))),f306(f306(f7(a865,a865,a859),f221(a865)),x100782))))),f306(f39(a865),f306(f228(a865),f306(f306(f18(a865,a859,a859),f306(f306(f8(a859,f872(a859,a859),a865),a304),f306(f306(f7(a865,f872(a865,a859),a859),f308(a865)),x100781))),f306(f306(f7(a865,a865,a859),f221(a865)),f306(a119,x100782)))))) % 187.68/187.64 [8490]~P91(x84901)+E(f306(f306(f82(x84901),f306(f111(x84901),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104))),x84902),x84902) % 187.68/187.64 [8550]~P91(x85501)+E(f306(f306(f81(x85501),f79(x85501)),f306(f111(x85501),x85502)),f306(f111(x85501),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),x85502))) % 187.68/187.64 [8608]~P91(x86081)+E(f306(f306(f22(x86081),f306(f111(x86081),x86082)),f79(x86081)),f306(f111(x86081),f306(f306(f81(a1),x86082),f306(f80(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104))))) % 187.68/187.64 [8745]~P1(f306(f306(f221(a865),f306(f111(a865),a84)),x87452))+E(f306(f306(f22(a865),x87451),f306(f306(f22(a865),x87452),f306(f111(a865),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)))),f306(f306(f22(a865),f306(a119,x87451)),x87452)) % 187.68/187.64 [9396]~P113(x93961)+E(f306(f306(f82(x93961),x93962),x93962),f306(f306(f237(x93961),x93962),f306(f111(a865),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104))))) % 187.68/187.64 [9397]~P80(x93971)+E(f306(f306(f237(x93971),x93972),f306(f111(a865),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)))),f306(f306(f82(x93971),x93972),x93972)) % 187.68/187.64 [9399]~P91(x93991)+E(f306(f306(f82(x93991),x93992),f306(f111(x93991),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)))),f306(f306(f81(x93991),x93992),x93992)) % 187.68/187.64 [9641]~P125(x96411)+E(f306(f306(f237(x96411),f306(f80(x96411),x96412)),f306(f111(a865),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)))),f306(f306(f237(x96411),x96412),f306(f111(a865),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104))))) % 187.68/187.64 [9642]~P112(x96421)+E(f306(f306(f237(x96421),f306(f76(x96421),x96422)),f306(f111(a865),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)))),f306(f306(f237(x96421),x96422),f306(f111(a865),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104))))) % 187.68/187.64 [9638]~P91(x96381)+E(f306(f306(f82(x96381),f306(f111(x96381),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)))),x96382),f306(f306(f81(x96381),x96382),x96382)) % 187.68/187.64 [9766]~P112(x97661)+E(f306(f76(x97661),f306(f306(f237(x97661),x97662),f306(f111(a865),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104))))),f306(f306(f237(x97661),x97662),f306(f111(a865),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104))))) % 187.68/187.64 [9827]~P112(x98271)+P1(f306(f306(f220(x98271),f2(x98271)),f306(f306(f237(x98271),x98272),f306(f111(a865),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)))))) % 187.68/187.64 [9994]~E(f306(a119,x99942),f306(f111(a865),x99941))+P1(f306(f306(f87(a1,a859),f306(f111(a1),f306(f306(f81(a1),x99941),a104))),f306(f306(f18(a1,a859,a859),f306(f306(f8(a859,f872(a859,a859),a1),a304),f306(f306(f8(a859,a859,a1),a301),a190))),f306(f306(f18(a1,a859,a859),f306(f306(f8(a859,f872(a859,a859),a1),a309),f306(f306(f8(a859,a859,a1),a301),a190))),f306(f306(f7(a1,a865,a859),f306(f306(f8(a865,f872(a865,a859),a1),a303),a112)),x99942))))) % 187.68/187.64 [9995]~E(f306(f111(a865),x99951),f306(a119,x99952))+P1(f306(f306(f87(a1,a859),f306(f111(a1),f306(f306(f81(a1),x99951),a104))),f306(f306(f18(a1,a859,a859),f306(f306(f8(a859,f872(a859,a859),a1),a304),f306(f306(f8(a859,a859,a1),a301),a190))),f306(f306(f18(a1,a859,a859),f306(f306(f8(a859,f872(a859,a859),a1),a309),f306(f306(f8(a859,a859,a1),a301),a190))),f306(f306(f7(a1,a865,a859),f306(f306(f8(a865,f872(a865,a859),a1),a303),a112)),x99952))))) % 187.68/187.64 [10040]E(f306(a119,x100401),f306(f111(a865),x100402))+~P1(f306(f306(f87(a1,a859),f306(f111(a1),f306(f306(f81(a1),x100402),a104))),f306(f306(f18(a1,a859,a859),f306(f306(f8(a859,f872(a859,a859),a1),a304),f306(f306(f8(a859,a859,a1),a301),a190))),f306(f306(f18(a1,a859,a859),f306(f306(f8(a859,f872(a859,a859),a1),a309),f306(f306(f8(a859,a859,a1),a301),a190))),f306(f306(f7(a1,a865,a859),f306(f306(f8(a865,f872(a865,a859),a1),a303),a112)),x100401))))) % 187.68/187.64 [10041]E(f306(f111(a865),x100411),f306(a119,x100412))+~P1(f306(f306(f87(a1,a859),f306(f111(a1),f306(f306(f81(a1),x100411),a104))),f306(f306(f18(a1,a859,a859),f306(f306(f8(a859,f872(a859,a859),a1),a304),f306(f306(f8(a859,a859,a1),a301),a190))),f306(f306(f18(a1,a859,a859),f306(f306(f8(a859,f872(a859,a859),a1),a309),f306(f306(f8(a859,a859,a1),a301),a190))),f306(f306(f7(a1,a865,a859),f306(f306(f8(a865,f872(a865,a859),a1),a303),a112)),x100412))))) % 187.68/187.64 [9823]~P91(x98231)+E(f306(f306(f237(x98231),f306(f111(x98231),a104)),f306(f306(f82(a865),f306(f111(a865),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)))),x98232)),f79(x98231)) % 187.68/187.64 [9824]~P125(x98241)+E(f306(f306(f237(x98241),f306(f80(x98241),f79(x98241))),f306(f306(f82(a865),f306(f111(a865),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)))),x98242)),f79(x98241)) % 187.68/187.64 [9829]~P80(x98291)+E(f306(f306(f237(x98291),x98292),f306(f111(a865),f306(f306(f22(a1),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104))),a104))),f306(f306(f82(x98291),f306(f306(f82(x98291),x98292),x98292)),x98292)) % 187.68/187.64 [10019]~P1(f306(f306(f220(a1),f2(a1)),x100192))+E(f46(a1,f306(f306(f81(a1),f79(a1)),f306(f306(f82(a1),f306(f111(a1),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)))),x100191)),f306(f306(f82(a1),f306(f111(a1),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)))),x100192)),f306(f306(f81(a1),f79(a1)),f306(f306(f82(a1),f306(f111(a1),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)))),f46(a1,x100191,x100192)))) % 187.68/187.64 [10043]~P1(f306(f306(f220(a1),f2(a1)),x100432))+E(f306(f306(f40(a1),f306(f306(f81(a1),f79(a1)),f306(f306(f82(a1),f306(f111(a1),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)))),x100431))),f306(f306(f82(a1),f306(f111(a1),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)))),x100432)),f306(f306(f40(a1),x100431),x100432)) % 187.68/187.64 [10045]~P1(f306(f306(f220(a1),x100452),f2(a1)))+E(f306(f306(f40(a1),f306(f306(f81(a1),f79(a1)),f306(f306(f82(a1),f306(f111(a1),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)))),x100451))),f306(f306(f82(a1),f306(f111(a1),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)))),x100452)),f306(f306(f40(a1),f306(f306(f81(a1),x100451),f79(a1))),x100452)) % 187.68/187.64 [10046]~P1(f306(f306(f220(a1),x100462),f2(a1)))+E(f46(a1,f306(f306(f81(a1),f79(a1)),f306(f306(f82(a1),f306(f111(a1),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)))),x100461)),f306(f306(f82(a1),f306(f111(a1),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)))),x100462)),f306(f306(f22(a1),f306(f306(f82(a1),f306(f111(a1),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)))),f46(a1,f306(f306(f81(a1),x100461),f79(a1)),x100462))),f79(a1))) % 187.68/187.64 [9917]~P91(x99171)+E(f306(f306(f237(x99171),f306(f111(x99171),a104)),f306(a119,f306(f306(f82(a865),f306(f111(a865),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)))),x99172))),f306(f111(x99171),a104)) % 187.68/187.64 [9919]~P125(x99191)+E(f306(f306(f237(x99191),f306(f80(x99191),f79(x99191))),f306(a119,f306(f306(f82(a865),f306(f111(a865),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)))),x99192))),f306(f80(x99191),f79(x99191))) % 187.68/187.64 [5063]~P27(x50631,x50632,x50633)+P31(x50631,x50632,x50633) % 187.68/187.64 [8003]~E(x80032,x80033)+P37(x80031,x80031,a303,x80032,x80033) % 187.68/187.64 [8563]E(x85631,x85632)+~P37(x85633,x85633,a303,x85631,x85632) % 187.68/187.64 [5068]~P40(x50681,x50683)+P40(x50681,f300(x50681,x50682,x50683)) % 187.68/187.64 [5243]P30(x52431,x52432,x52433)+~P30(x52431,f306(a119,x52432),x52433) % 187.68/187.64 [5330]~P9(x53301,x53302,x53303)+P9(f866(x53301),f153(x53301,x53302),f150(x53301,x53303)) % 187.68/187.64 [5331]~P50(x53311,x53312,x53313)+P50(f866(x53311),f153(x53311,x53312),f150(x53311,x53313)) % 187.68/187.64 [5443]P55(x54431,x54432,x54433)+~E(f568(x54433,x54432,x54431),f569(x54433,x54432,x54431)) % 187.68/187.64 [5444]P54(x54441,x54442,x54443)+~E(f596(x54443,x54442,x54441),f597(x54443,x54442,x54441)) % 187.68/187.64 [6388]P31(x63881,x63882,x63883)+~P30(x63881,f549(x63883,x63882,x63881),f553(x63883,x63882,x63881)) % 187.68/187.64 [4613]~E(x46131,f188(x46132))+~E(x46131,f306(f214(x46132),x46133)) % 187.68/187.64 [4662]~E(f306(f161(x46622),x46621),x46623)+E(x46621,f306(f161(x46622),x46623)) % 187.68/187.64 [4663]~E(x46632,f306(f161(x46631),x46633))+E(f306(f161(x46631),x46632),x46633) % 187.68/187.64 [4710]E(x47101,x47102)+~E(f306(f214(x47103),x47101),f306(f214(x47103),x47102)) % 187.68/187.64 [4711]E(x47111,x47112)+~E(f306(f161(x47113),x47111),f306(f161(x47113),x47112)) % 187.68/187.64 [4918]~P8(x49183,x49181)+P1(f306(f306(x49181,x49182),x49182)) % 187.68/187.64 [4919]~P52(x49193,x49191)+P1(f306(f306(x49191,x49192),x49192)) % 187.68/187.64 [4921]~P59(x49211,x49212)+P1(f306(f294(x49211,x49212),x49213)) % 187.68/187.64 [4983]~P40(x49831,x49832)+P40(f866(x49831),f306(f135(x49831,x49832),x49833)) % 187.68/187.64 [4988]~P1(f306(x49882,x49883))+~E(f306(f228(x49881),x49882),f185(f872(x49881,a859))) % 187.68/187.64 [4989]~P1(f306(x49892,x49893))+~E(f185(f872(x49891,a859)),f306(f228(x49891),x49892)) % 187.68/187.64 [5020]~P1(f306(x50201,x50203))+P1(f306(x50201,f91(x50202,x50201))) % 187.68/187.64 [5151]~E(x51512,x51513)+P1(f306(f306(f308(x51511),x51512),f306(a303,x51513))) % 187.68/187.64 [5163]P1(f306(x51631,x51632))+~P1(f306(x51631,f516(x51631,x51633))) % 187.68/187.64 [5209]E(f306(f161(x52091),x52092),f306(f306(f143(x52091),x52093),f120(x52091)))+~E(x52092,f306(f306(f143(x52091),x52093),f120(x52091))) % 187.68/187.64 [5210]~E(x52103,f306(f306(f143(x52101),x52102),f120(x52101)))+E(f306(f306(f143(x52101),x52102),f120(x52101)),f306(f161(x52101),x52103)) % 187.68/187.64 [5236]~E(x52363,f306(f16(f869(x52362),x52361),f188(x52362)))+E(f175(x52361,x52362,x52363),f185(f872(x52361,a859))) % 187.68/187.64 [5257]~P36(x52571,x52572,x52573)+P36(x52571,x52572,f306(f161(x52571),x52573)) % 187.68/187.64 [5258]~P34(x52581,x52582,x52583)+P34(x52581,x52582,f306(f161(x52581),x52583)) % 187.68/187.64 [5261]E(f306(f39(x52611),f566(x52612,x52613,x52611)),x52612)+~E(f306(f39(x52611),x52613),f306(a119,x52612)) % 187.68/187.64 [5267]~P40(x52671,x52673)+P1(f306(f306(f308(x52671),x52672),f295(x52671,x52673))) % 187.68/187.64 [5270]~E(f306(f161(x52702),x52701),f306(f306(f143(x52702),x52703),f120(x52702)))+E(x52701,f306(f306(f143(x52702),x52703),f120(x52702))) % 187.68/187.64 [5271]~E(f306(f306(f143(x52712),x52713),f120(x52712)),f306(f161(x52712),x52711))+E(x52711,f306(f306(f143(x52712),x52713),f120(x52712))) % 187.68/187.64 [5286]E(x52861,f306(f16(f869(x52862),x52863),f188(x52862)))+~E(f175(x52863,x52862,x52861),f185(f872(x52863,a859))) % 187.68/187.64 [5293]E(f86(f871(a865,a865),f49(x52931,x52932)),x52933)+~P1(f306(f49(x52931,x52932),x52933)) % 187.68/187.64 [5301]~E(x53013,f306(f214(x53011),x53012))+P1(f306(f306(f308(x53011),x53012),f213(x53011,x53013))) % 187.68/187.64 [5334]P36(x53341,x53342,x53343)+~P36(x53341,x53342,f306(f161(x53341),x53343)) % 187.68/187.64 [5335]P34(x53351,x53352,x53353)+~P34(x53351,x53352,f306(f161(x53351),x53353)) % 187.68/187.64 [5397]~E(x53972,f120(x53971))+P1(f306(f306(f308(f866(x53971)),x53972),f153(x53971,x53973))) % 187.68/187.64 [5404]~P50(x54041,x54042,x54043)+P50(x54041,x54042,f306(f261(x54041,x54041),x54043)) % 187.68/187.64 [5405]~P55(x54051,x54052,x54053)+P55(x54051,x54052,f306(f261(x54051,x54051),x54053)) % 187.68/187.64 [5424]~P4(x54241)+E(f46(x54241,f46(x54241,x54242,x54243),x54243),f46(x54241,x54242,x54243)) % 187.68/187.64 [5520]E(x55201,x55202)+~P1(f306(f306(f308(x55203),x55201),f306(a303,x55202))) % 187.68/187.64 [5565]~P141(x55651)+E(f187(x55651,x55652,f2(a865),x55653),x55653) % 187.68/187.64 [5585]P50(x55851,x55852,x55853)+~P50(x55851,x55852,f306(f261(x55851,x55851),x55853)) % 187.68/187.64 [5586]P55(x55861,x55862,x55863)+~P55(x55861,x55862,f306(f261(x55861,x55861),x55863)) % 187.68/187.64 [5590]~P108(x55902)+E(f142(x55901,x55902,x55903,f120(x55901)),f120(x55901)) % 187.68/187.64 [5604]E(f162(x56041,x56042,f144(x56041,x56043)),f144(x56041,f162(x56041,x56042,x56043)))+~P1(f306(f129(x56041),x56043)) % 187.68/187.64 [5610]E(x56101,f306(f214(x56102),x56103))+~P1(f306(f306(f308(x56102),x56103),f213(x56102,x56101))) % 187.68/187.64 [5695]~P1(f306(a25,x56953))+P1(f306(a25,f30(x56951,x56952,x56953))) % 187.68/187.64 [5706]E(f306(f128(x57061,x57062),x57063),f120(x57061))+P1(f306(x57062,f721(x57063,x57062,x57061))) % 187.68/187.64 [5850]~P1(f306(f129(x58501),x58503))+P1(f306(f129(x58501),f162(x58501,x58502,x58503))) % 187.68/187.64 [5851]~P1(f306(f129(x58511),x58512))+P1(f306(f129(x58511),f166(x58511,x58512,x58513))) % 187.68/187.64 [5852]~P1(f306(f129(x58521),x58523))+P1(f306(f129(x58521),f168(x58521,x58522,x58523))) % 187.68/187.64 [5853]~P1(f306(f129(x58531),x58533))+P1(f306(f129(x58531),f132(x58531,x58532,x58533))) % 187.68/187.64 [5854]~P145(x58541,x58542,x58543)+P1(f306(x58541,f46(a1,x58542,x58543))) % 187.68/187.64 [5873]~P36(x58733,x58731,x58732)+P1(f306(x58731,f772(x58732,x58731,x58733))) % 187.68/187.64 [5874]~P38(x58743,x58741,x58742)+P1(f306(x58741,f796(x58742,x58741,x58743))) % 187.68/187.64 [5896]E(f306(f128(x58961,x58962),x58963),f168(x58961,x58962,x58963))+P1(f306(x58962,f747(x58963,x58962,x58961))) % 187.68/187.64 [5940]~P1(f306(f129(x59401),x59403))+P1(f306(f129(f866(x59401)),f56(x59401,x59402,x59403))) % 187.68/187.64 [5962]P1(f306(a25,f29(x59621,x59622,x59623)))+~P1(f306(a25,f306(a26,x59622))) % 187.68/187.64 [5974]~P109(x59741)+E(f306(f306(f109(f872(x59741,a859)),f306(f275(x59741),x59742)),f280(x59741,x59742,x59743)),f185(f872(x59741,a859))) % 187.68/187.64 [5975]~P109(x59751)+E(f306(f306(f109(f872(x59751,a859)),f306(f275(x59751),x59752)),f279(x59751,x59752,x59753)),f185(f872(x59751,a859))) % 187.68/187.64 [5976]~P109(x59761)+E(f306(f306(f109(f872(x59761,a859)),f306(f229(x59761),x59762)),f277(x59761,x59762,x59763)),f185(f872(x59761,a859))) % 187.68/187.64 [6122]P1(f306(a25,x61221))+~P1(f306(a25,f30(x61222,x61223,x61221))) % 187.68/187.64 [6124]P1(f306(a25,x61241))+~P1(f306(a25,f31(x61242,x61243,x61241))) % 187.68/187.64 [6126]P1(f306(a25,x61261))+~P1(f306(a25,f31(x61262,x61261,x61263))) % 187.68/187.64 [6205]E(f306(f128(x62051,x62052),x62053),x62053)+~P1(f306(x62052,f711(x62053,x62052,x62051))) % 187.68/187.64 [6207]E(f306(f306(f284(x62071),f653(x62072,x62073,x62071)),f566(x62072,x62073,x62071)),x62073)+~E(f306(f39(x62071),x62073),f306(a119,x62072)) % 187.68/187.64 [6223]P145(x62231,x62232,x62233)+~P1(f306(x62231,f46(a1,x62232,x62233))) % 187.68/187.64 [6270]P34(x62701,x62702,x62703)+~P1(f306(x62702,f785(x62703,x62702,x62701))) % 187.68/187.64 [6271]P34(x62711,x62712,x62713)+~P1(f306(x62712,f794(x62712,x62713,x62711))) % 187.68/187.64 [6272]P34(x62721,x62722,x62723)+~P1(f306(x62722,f795(x62723,x62722,x62721))) % 187.68/187.64 [6274]E(f168(x62741,x62742,x62743),x62743)+~P1(f306(x62742,f735(x62743,x62742,x62741))) % 187.68/187.64 [6313]~P1(f306(a25,f29(x63132,x63131,x63133)))+P1(f306(a25,f306(a26,x63131))) % 187.68/187.64 [6357]~P1(f306(x63572,f544(x63573,x63572,x63571)))+P1(f306(f240(x63571,x63572),x63573)) % 187.68/187.64 [6358]~P1(f306(x63582,f750(x63583,x63582,x63581)))+P1(f306(f152(x63581,x63582),x63583)) % 187.68/187.64 [6602]~P1(f306(f294(x66021,x66022),f319(x66023,x66022,x66021)))+P1(f306(f294(x66021,x66022),x66023)) % 187.68/187.64 [6603]~P1(f306(f294(x66031,x66032),f325(x66033,x66032,x66031)))+P1(f306(f294(x66031,x66032),x66033)) % 187.68/187.64 [7212]~P4(x72121)+E(f306(f306(f81(x72121),f306(f306(f82(x72121),x72122),f306(f306(f40(x72121),x72123),x72122))),f46(x72121,x72123,x72122)),x72123) % 187.68/187.64 [7678]E(f306(f306(f236(x76781,x76781),f466(x76782,x76783,x76781)),f466(x76782,x76783,x76781)),x76783)+~P1(f306(f306(f308(f871(x76781,x76781)),x76783),f233(x76781,x76782))) % 187.68/187.64 [7793]~P1(f306(f306(f308(x77931),f488(x77933,x77932,x77931)),f295(x77931,x77933)))+P1(f306(f306(f308(x77931),x77932),f295(x77931,x77933))) % 187.68/187.64 [7794]~P1(f306(f306(f308(x77941),f571(x77943,x77942,x77941)),f295(x77941,x77943)))+P1(f306(f306(f308(x77941),x77942),f295(x77941,x77943))) % 187.68/187.64 [7795]~P1(f306(f306(f308(x77951),f573(x77953,x77952,x77951)),f295(x77951,x77953)))+P1(f306(f306(f308(x77951),x77952),f295(x77951,x77953))) % 187.68/187.64 [7984]~P4(x79841)+E(f306(f306(f81(x79841),f306(f306(f82(x79841),f306(f306(f40(x79841),x79842),x79843)),x79843)),f46(x79841,x79842,x79843)),x79842) % 187.68/187.64 [8030]~E(f306(f39(x80301),x80302),f306(a119,x80303))+~P1(f306(f306(f308(x80301),f653(x80303,x80302,x80301)),f566(x80303,x80302,x80301))) % 187.68/187.64 [8656]P1(f306(f306(f220(f872(f871(x86561,x86561),a859)),f282(x86561,x86562)),f282(x86561,x86563)))+~P1(f306(f306(f220(f872(f871(x86561,x86561),a859)),x86562),f282(x86561,x86563))) % 187.68/187.64 [8933]E(x89331,f120(x89332))+~P1(f306(f306(f308(f871(f866(x89332),f866(x89332))),f306(f306(f236(f866(x89332),f866(x89332)),x89331),f120(x89332))),f150(x89332,x89333))) % 187.68/187.64 [8958]E(x89581,f120(x89582))+~P1(f306(f306(f308(f871(f866(x89582),f866(x89582))),f306(f306(f236(f866(x89582),f866(x89582)),f120(x89582)),x89581)),f150(x89582,x89583))) % 187.68/187.64 [9081]E(f306(f306(f143(x90811),f709(x90812,x90813,x90811)),f713(x90812,x90813,x90811)),x90813)+~P1(f306(f306(f308(f871(f866(x90811),f866(x90811))),f306(f306(f236(f866(x90811),f866(x90811)),f120(x90811)),x90813)),f139(x90811,x90812))) % 187.68/187.64 [9324]~P123(x93241)+~P1(f306(f306(f221(x93241),f306(f306(f81(x93241),f306(f306(f82(x93241),x93242),x93242)),f306(f306(f82(x93241),x93243),x93243))),f2(x93241))) % 187.68/187.64 [9375]P1(f306(f63(x93751),x93752))+~P1(f306(f306(f308(f871(f872(x93751,a859),f872(x93751,a859))),f306(f306(f236(f872(x93751,a859),f872(x93751,a859)),x93753),x93752)),f281(x93751))) % 187.68/187.64 [9664]~P48(x96641,x96642,x96643)+P1(f306(f306(f220(a1),f306(f306(f74(f871(a1,a1),a1,x96641,f235(a1,a1)),f198(x96641)),f209(x96641,x96642,f206(x96641,x96643)))),f2(a1))) % 187.68/187.64 [9665]~P49(x96651,x96652,x96653)+P1(f306(f306(f221(a1),f306(f306(f74(f871(a1,a1),a1,x96651,f235(a1,a1)),f198(x96651)),f209(x96651,x96652,f206(x96651,x96653)))),f2(a1))) % 187.68/187.64 [9794]P49(x97941,x97942,x97943)+~P1(f306(f306(f221(a1),f306(f306(f74(f871(a1,a1),a1,x97941,f235(a1,a1)),f198(x97941)),f209(x97941,x97942,f206(x97941,x97943)))),f2(a1))) % 187.68/187.64 [9795]P48(x97951,x97952,x97953)+~P1(f306(f306(f220(a1),f306(f306(f74(f871(a1,a1),a1,x97951,f235(a1,a1)),f198(x97951)),f209(x97951,x97952,f206(x97951,x97953)))),f2(a1))) % 187.68/187.64 [10126]~P112(x101261)+~P1(f306(f306(f221(x101261),f306(f306(f81(x101261),f306(f306(f237(x101261),x101262),f306(f111(a865),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104))))),f306(f306(f237(x101261),x101263),f306(f111(a865),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)))))),f2(x101261))) % 187.68/187.64 [4693]~E(x46933,f120(x46931))+E(f306(f306(f122(x46931),x46932),x46933),x46932) % 187.68/187.64 [4694]~E(x46942,f120(x46941))+E(f306(f306(f122(x46941),x46942),x46943),x46943) % 187.68/187.64 [4701]~E(x47012,f2(a865))+E(f306(f306(f165(x47011),x47012),x47013),f120(x47011)) % 187.68/187.64 [4705]~E(x47053,f120(x47051))+E(f306(f306(f165(x47051),x47052),x47053),f120(x47051)) % 187.68/187.64 [4745]~E(x47451,x47453)+E(x47451,f306(f306(f122(x47452),f120(x47452)),x47453)) % 187.68/187.64 [4833]~P2(x48332)+E(f306(f185(f872(x48331,x48332)),x48333),f185(x48332)) % 187.68/187.64 [4834]~P110(x48342)+E(f306(f231(f872(x48341,x48342)),x48343),f231(x48342)) % 187.68/187.64 [4854]E(x48541,f120(x48542))+~E(f306(f306(f122(x48542),x48543),x48541),x48543) % 187.68/187.64 [4855]E(x48551,f120(x48552))+~E(f306(f306(f122(x48552),x48551),x48553),x48553) % 187.68/187.64 [4863]E(x48631,f120(x48632))+~E(f306(f306(f122(x48632),x48633),x48631),f120(x48632)) % 187.68/187.64 [4864]E(x48641,f120(x48642))+~E(f306(f306(f122(x48642),x48641),x48643),f120(x48642)) % 187.68/187.64 [4887]~E(x48872,f2(a865))+E(f306(f306(f82(a865),x48871),x48872),f306(f306(f82(a865),x48873),x48872)) % 187.68/187.64 [4889]~E(x48891,f2(a865))+E(f306(f306(f82(a865),x48891),x48892),f306(f306(f82(a865),x48891),x48893)) % 187.68/187.64 [4943]~P113(x49431)+E(f306(f306(f81(x49431),x49432),x49433),f306(f306(f81(x49431),x49433),x49432)) % 187.68/187.64 [4944]~P113(x49441)+E(f306(f306(f82(x49441),x49442),x49443),f306(f306(f82(x49441),x49443),x49442)) % 187.68/187.64 [4946]~P108(x49461)+E(f306(f306(f225(x49461),x49462),x49463),f306(f306(f225(x49461),x49463),x49462)) % 187.68/187.64 [4948]~P108(x49481)+E(f306(f306(f219(x49481),x49482),x49483),f306(f306(f219(x49481),x49483),x49482)) % 187.68/187.64 [4950]~P97(x49501)+E(f306(f306(f108(x49501),x49502),x49503),f306(f306(f108(x49501),x49503),x49502)) % 187.68/187.64 [4951]~P98(x49511)+E(f306(f306(f108(x49511),x49512),x49513),f306(f306(f108(x49511),x49513),x49512)) % 187.68/187.64 [4952]~P98(x49521)+E(f306(f306(f109(x49521),x49522),x49523),f306(f306(f109(x49521),x49523),x49522)) % 187.68/187.64 [4954]~P103(x49541)+E(f306(f306(f109(x49541),x49542),x49543),f306(f306(f109(x49541),x49543),x49542)) % 187.68/187.64 [5015]E(f46(a865,x50151,x50152),f2(a865))+~E(x50151,f306(f306(f82(a865),x50152),x50153)) % 187.68/187.64 [5016]E(f46(a1,x50161,x50162),f2(a1))+~E(x50161,f306(f306(f82(a1),x50162),x50163)) % 187.68/187.64 [5080]E(x50801,x50802)+~E(f306(f306(f81(a865),x50803),x50801),f306(f306(f81(a865),x50803),x50802)) % 187.68/187.64 [5081]E(x50811,x50812)+~E(f306(f306(f81(a865),x50811),x50813),f306(f306(f81(a865),x50812),x50813)) % 187.68/187.64 [5093]~P67(x50931)+E(f306(f306(f81(x50931),x50932),f306(f80(x50931),x50933)),f306(f306(f22(x50931),x50932),x50933)) % 187.68/187.64 [5094]~P68(x50941)+E(f306(f306(f81(x50941),x50942),f306(f80(x50941),x50943)),f306(f306(f22(x50941),x50942),x50943)) % 187.68/187.64 [5095]~P114(x50951)+E(f306(f306(f81(x50951),x50952),f306(f80(x50951),x50953)),f306(f306(f22(x50951),x50952),x50953)) % 187.68/187.64 [5096]~P94(x50961)+E(f306(f306(f109(x50961),x50962),f306(f80(x50961),x50963)),f306(f306(f22(x50961),x50962),x50963)) % 187.68/187.64 [5097]~P67(x50971)+E(f306(f306(f22(x50971),x50972),f306(f80(x50971),x50973)),f306(f306(f81(x50971),x50972),x50973)) % 187.68/187.64 [5144]~P1(f306(x51443,x51442))+P1(f306(f306(f308(x51441),x51442),x51443)) % 187.68/187.64 [5146]~P75(x51462)+E(f306(f306(f9(x51461,x51462),x51463),f185(f872(x51461,a859))),f79(x51462)) % 187.68/187.64 [5148]~P74(x51482)+E(f306(f306(f6(x51481,x51482),x51483),f185(f872(x51481,a859))),f2(x51482)) % 187.68/187.64 [5197]~E(x51972,f306(f306(f81(a865),x51971),x51973))+P1(f306(f306(f220(a865),x51971),x51972)) % 187.68/187.64 [5200]~E(x52002,f185(f872(x52001,a859)))+E(f306(f306(f62(x52001),x52002),x52003),f185(f872(f872(x52001,a859),a859))) % 187.68/187.64 [5201]~E(x52012,f185(f872(x52011,a859)))+E(f185(f872(f872(x52011,a859),a859)),f306(f306(f62(x52011),x52012),x52013)) % 187.68/187.64 [5275]~E(f306(f232(x52752,x52753),x52751),f185(f872(x52753,a859)))+E(x52751,f185(f872(f871(x52752,x52753),a859))) % 187.68/187.64 [5276]~E(f306(f234(x52762,x52763),x52761),f185(f872(x52762,a859)))+E(x52761,f185(f872(f871(x52762,x52763),a859))) % 187.68/187.64 [5307]E(f306(f232(x53071,x53072),x53073),f185(f872(x53072,a859)))+~E(x53073,f185(f872(f871(x53071,x53072),a859))) % 187.68/187.64 [5308]E(f306(f234(x53081,x53082),x53083),f185(f872(x53081,a859)))+~E(x53083,f185(f872(f871(x53081,x53082),a859))) % 187.68/187.64 [5312]E(f256(x53121,x53122,x53123),f306(f306(f22(a106),x53122),x53123))+P1(f306(f306(f221(a106),x53122),x53123)) % 187.68/187.64 [5328]P1(f306(x53281,x53282))+~P1(f306(f306(f308(x53283),x53282),x53281)) % 187.68/187.64 [5367]E(x53671,x53672)+~E(f306(f80(f872(x53673,a859)),x53671),f306(f80(f872(x53673,a859)),x53672)) % 187.68/187.64 [5372]E(f288(x53721,x53722,x53723),f188(f866(a302)))+~P1(f306(f306(f221(a1),x53722),x53723)) % 187.68/187.64 [5377]~E(x53771,f185(f872(x53772,a859)))+~P1(f306(f306(f308(x53772),x53773),x53771)) % 187.68/187.64 [5406]~E(x54062,f306(f306(f81(a1),x54061),f306(f107(a1),x54063)))+P1(f306(f306(f220(a1),x54061),x54062)) % 187.68/187.64 [5422]E(f306(f306(f284(x54221),x54222),x54223),x54223)+~P1(f306(f306(f308(x54221),x54222),x54223)) % 187.68/187.64 [5433]E(x54331,f185(f872(x54332,a859)))+~E(f306(f306(f62(x54332),x54331),x54333),f185(f872(f872(x54332,a859),a859))) % 187.68/187.64 [5434]E(x54341,f185(f872(x54342,a859)))+~E(f185(f872(f872(x54342,a859),a859)),f306(f306(f62(x54342),x54341),x54343)) % 187.68/187.64 [5440]~P126(x54401)+E(f306(f306(f82(x54401),f306(f80(x54401),x54402)),f306(f80(x54401),x54403)),f306(f306(f82(x54401),x54402),x54403)) % 187.68/187.64 [5442]~P61(x54421)+E(f306(f306(f264(x54421),f306(f80(x54421),x54422)),f306(f80(x54421),x54423)),f306(f306(f264(x54421),x54422),x54423)) % 187.68/187.64 [5475]~P1(f306(x54753,x54752))+P1(f306(f306(f308(x54751),x54752),f306(f228(x54751),x54753))) % 187.68/187.64 [5513]E(f162(x55131,x55132,x55133),x55133)+P1(f306(f306(f308(x55131),x55132),f306(f164(x55131),x55133))) % 187.68/187.64 [5594]~P1(f306(f129(x55941),x55943))+P1(f306(f129(x55941),f306(f128(x55941,x55942),x55943))) % 187.68/187.64 [5640]~P4(x56401)+E(f306(f306(f40(x56401),f46(x56401,x56402,x56403)),x56403),f2(x56401)) % 187.68/187.64 [5659]E(f166(x56591,f306(f306(f143(x56591),x56592),f120(x56591)),x56593),f120(x56591))+P1(f306(f306(f308(a865),f2(a865)),x56593)) % 187.68/187.64 [5716]E(f306(f306(f143(x57161),x57162),x57163),f132(x57161,x57162,x57163))+P1(f306(f306(f308(x57161),x57162),f306(f164(x57161),x57163))) % 187.68/187.64 [5725]E(x57251,x57252)+~E(f306(f306(f82(a865),f306(a119,x57253)),x57251),f306(f306(f82(a865),f306(a119,x57253)),x57252)) % 187.68/187.64 [5726]~E(x57262,f306(f306(f81(a1),x57261),f306(f107(a1),f306(a119,x57263))))+P1(f306(f306(f221(a1),x57261),x57262)) % 187.68/187.64 [5832]~E(x58323,f120(x58321))+E(f306(f306(f306(f180(f866(x58321),f866(x58321)),x58322),f160(x58321)),x58323),f120(x58321)) % 187.68/187.64 [5836]P1(f306(x58361,x58362))+~P1(f306(f306(f308(x58363),x58362),f306(f228(x58363),x58361))) % 187.68/187.64 [5868]E(x58681,x58682)+~E(f306(f306(f284(x58683),x58681),f185(f872(x58683,a859))),f306(f306(f284(x58683),x58682),f185(f872(x58683,a859)))) % 187.68/187.64 [5879]~P109(x58791)+E(f306(f306(f109(f872(x58791,a859)),f306(f229(x58791),x58792)),f306(f276(x58791,x58792),x58793)),f185(f872(x58791,a859))) % 187.68/187.64 [5922]E(f132(x59221,x59222,x59223),x59223)+~P1(f306(f306(f308(x59221),x59222),f306(f164(x59221),x59223))) % 187.68/187.64 [5948]~P65(x59481)+E(f306(f285(x59481,x59481,f80(x59481)),f306(f276(x59481,x59482),x59483)),f279(x59481,f306(f80(x59481),x59483),f306(f80(x59481),x59482))) % 187.68/187.64 [5956]E(f306(f186(f866(x59561)),f162(x59561,x59562,x59563)),f306(f186(f866(x59561)),x59563))+P1(f306(f306(f308(x59561),x59562),f306(f164(x59561),x59563))) % 187.68/187.64 [6010]~P109(x60101)+E(f306(f306(f109(f872(x60101,a859)),f306(f276(x60101,x60102),x60103)),f306(f230(x60101),x60103)),f185(f872(x60101,a859))) % 187.68/187.64 [6033]~P65(x60331)+E(f306(f285(x60331,x60331,f80(x60331)),f280(x60331,x60332,x60333)),f280(x60331,f306(f80(x60331),x60333),f306(f80(x60331),x60332))) % 187.68/187.64 [6034]~P65(x60341)+E(f306(f285(x60341,x60341,f80(x60341)),f277(x60341,x60342,x60343)),f277(x60341,f306(f80(x60341),x60343),f306(f80(x60341),x60342))) % 187.68/187.64 [6090]E(f166(x60901,f306(f306(f143(x60901),x60902),f120(x60901)),x60903),f306(f306(f143(x60901),x60902),f120(x60901)))+~P1(f306(f306(f308(a865),f2(a865)),x60903)) % 187.68/187.64 [6097]~P65(x60971)+E(f306(f285(x60971,x60971,f80(x60971)),f279(x60971,x60972,x60973)),f306(f276(x60971,f306(f80(x60971),x60973)),f306(f80(x60971),x60972))) % 187.68/187.64 [6117]~P5(x61171)+E(f46(x61171,f306(f80(x61171),f46(x61171,x61172,x61173)),x61173),f46(x61171,f306(f80(x61171),x61172),x61173)) % 187.68/187.64 [6220]~P1(f306(f63(f871(x62202,x62201)),x62203))+P1(f306(f63(x62201),f306(f232(x62202,x62201),x62203))) % 187.68/187.64 [6221]~P1(f306(f63(f871(x62211,x62212)),x62213))+P1(f306(f63(x62211),f306(f234(x62211,x62212),x62213))) % 187.68/187.64 [6227]~P109(x62271)+E(f306(f306(f109(f872(x62271,a859)),f280(x62271,x62272,x62273)),f306(f230(x62271),x62273)),f185(f872(x62271,a859))) % 187.68/187.64 [6228]~P109(x62281)+E(f306(f306(f109(f872(x62281,a859)),f279(x62281,x62282,x62283)),f306(f278(x62281),x62283)),f185(f872(x62281,a859))) % 187.68/187.64 [6229]~P109(x62291)+E(f306(f306(f109(f872(x62291,a859)),f277(x62291,x62292,x62293)),f306(f278(x62291),x62293)),f185(f872(x62291,a859))) % 187.68/187.64 [6296]E(f306(f306(f157(x62961),x62962),f691(x62962,x62963,x62961)),x62963)+~P1(f306(f306(f308(x62961),x62963),f306(f164(x62961),x62962))) % 187.68/187.64 [6439]E(x64391,f120(x64392))+~E(f306(f306(f306(f180(f866(x64392),f866(x64392)),x64393),f160(x64392)),x64391),f120(x64392)) % 187.68/187.64 [6539]~P1(f306(f63(f871(x65392,x65391)),x65393))+P1(f306(f63(f871(x65391,x65392)),f306(f261(x65392,x65391),x65393))) % 187.68/187.64 [6694]P55(x66941,x66942,x66943)+P1(f306(f306(f308(x66941),f569(x66943,x66942,x66941)),x66942)) % 187.68/187.64 [6695]P55(x66951,x66952,x66953)+P1(f306(f306(f308(x66951),f568(x66953,x66952,x66951)),x66952)) % 187.68/187.64 [6707]P1(f306(f294(x67071,x67072),x67073))+P1(f306(f306(x67072,f319(x67073,x67072,x67071)),x67073)) % 187.68/187.64 [6708]P1(f306(f294(x67081,x67082),x67083))+P1(f306(f306(x67082,f325(x67083,x67082,x67081)),x67083)) % 187.68/187.64 [6738]E(f306(f186(f866(x67381)),f162(x67381,x67382,x67383)),f306(f306(f22(a865),f306(f186(f866(x67381)),x67383)),f79(a865)))+~P1(f306(f306(f308(x67381),x67382),f306(f164(x67381),x67383))) % 187.68/187.64 [6778]P1(f306(f240(x67781,x67782),x67783))+P1(f306(f306(f308(x67781),f544(x67783,x67782,x67781)),x67783)) % 187.68/187.64 [6788]~P1(f306(f63(f871(x67882,x67881)),f306(f261(x67881,x67882),x67883)))+P1(f306(f63(f871(x67881,x67882)),x67883)) % 187.68/187.64 [6844]~P1(f306(f306(f308(x68441),x68442),f306(f164(x68441),f121(x68441,x68443))))+P1(f306(f306(f308(x68441),x68442),f306(f164(x68441),x68443))) % 187.68/187.64 [6849]P31(x68491,x68492,x68493)+P1(f306(f306(f308(f864(x68491)),f553(x68493,x68492,x68491)),x68493)) % 187.68/187.64 [6877]E(f306(f128(x68771,x68772),x68773),x68773)+P1(f306(f306(f308(x68771),f711(x68773,x68772,x68771)),f306(f164(x68771),x68773))) % 187.68/187.64 [6892]E(f306(f128(x68921,x68922),x68923),f120(x68921))+P1(f306(f306(f308(x68921),f721(x68923,x68922,x68921)),f306(f164(x68921),x68923))) % 187.68/187.64 [6915]P34(x69151,x69152,x69153)+P1(f306(f306(f308(x69151),f785(x69153,x69152,x69151)),f306(f164(x69151),x69153))) % 187.68/187.64 [6916]P34(x69161,x69162,x69163)+P1(f306(f306(f308(x69161),f795(x69163,x69162,x69161)),f306(f164(x69161),x69163))) % 187.68/187.64 [6917]P34(x69171,x69172,x69173)+P1(f306(f306(f308(x69171),f794(x69172,x69173,x69171)),f306(f164(x69171),x69173))) % 187.68/187.64 [6920]E(f168(x69201,x69202,x69203),x69203)+P1(f306(f306(f308(x69201),f735(x69203,x69202,x69201)),f306(f164(x69201),x69203))) % 187.68/187.64 [7001]P1(f306(f152(x70011,x70012),x70013))+P1(f306(f306(f308(x70011),f750(x70013,x70012,x70011)),f306(f164(x70011),x70013))) % 187.68/187.64 [7010]~P36(x70101,x70103,x70102)+P1(f306(f306(f308(x70101),f772(x70102,x70103,x70101)),f306(f164(x70101),x70102))) % 187.68/187.64 [7011]~P38(x70111,x70113,x70112)+P1(f306(f306(f308(x70111),f796(x70112,x70113,x70111)),f306(f164(x70111),x70112))) % 187.68/187.64 [7046]P1(f306(f306(f308(x70461),x70462),f655(x70463,x70462,x70461)))+~P1(f306(f306(f308(x70461),x70462),f41(f872(x70461,a859),x70463))) % 187.68/187.64 [7047]~P74(x70471)+E(f306(f306(f81(x70471),f306(f306(f6(a865,x70471),x70472),f306(f229(a865),x70473))),f306(x70472,x70473)),f306(f306(f6(a865,x70471),x70472),f306(f229(a865),f306(a119,x70473)))) % 187.68/187.64 [7136]~P36(x71362,x71361,x71363)+P1(f306(x71361,f306(f306(f157(x71362),x71363),f784(x71363,x71361,x71362)))) % 187.68/187.64 [7149]~P1(f306(f306(f308(x71491),x71492),f646(x71492,x71493,x71491)))+P1(f306(f306(f308(x71491),x71492),f42(f872(x71491,a859),x71493))) % 187.68/187.64 [7179]~P74(x71791)+E(f306(f306(f81(x71791),f306(f306(f6(a865,x71791),x71792),f306(f275(a865),x71793))),f306(x71792,f306(a119,x71793))),f306(f306(f6(a865,x71791),x71792),f306(f275(a865),f306(a119,x71793)))) % 187.68/187.64 [7313]P1(f306(f306(f308(f866(x73131)),x73132),f153(x73131,x73133)))+P1(f306(f306(f308(x73131),f708(x73133,x73132,x73131)),f306(f164(x73131),x73132))) % 187.68/187.64 [7330]~P1(f306(f306(f308(f866(x73301)),x73302),f153(x73301,f295(x73301,x73303))))+P1(f306(f306(f308(f866(x73301)),x73302),f295(f866(x73301),f149(x73301,x73303)))) % 187.68/187.64 [7355]~P1(f306(f306(f308(f866(x73551)),x73552),f295(f866(x73551),f149(x73551,x73553))))+P1(f306(f306(f308(f866(x73551)),x73552),f153(x73551,f295(x73551,x73553)))) % 187.68/187.64 [7391]E(f306(f306(f306(f180(f866(x73911),f866(x73911)),x73912),f160(x73911)),x73913),x73913)+~P1(f306(f306(f220(a865),f306(f186(f866(x73911)),x73913)),f79(a865))) % 187.68/187.64 [7427]E(f306(f306(f122(x74271),f787(x74272,x74273,x74271)),f306(f306(f143(x74271),x74273),f793(x74272,x74273,x74271))),x74272)+~P1(f306(f306(f308(x74271),x74273),f306(f164(x74271),x74272))) % 187.68/187.64 [7428]E(f306(f306(f122(x74281),f788(x74282,x74283,x74281)),f306(f306(f143(x74281),x74283),f789(x74282,x74283,x74281))),x74282)+~P1(f306(f306(f308(x74281),x74283),f306(f164(x74281),x74282))) % 187.68/187.64 [7429]E(f306(f306(f122(x74291),f790(x74292,x74293,x74291)),f306(f306(f143(x74291),x74293),f791(x74292,x74293,x74291))),x74292)+~P1(f306(f306(f308(x74291),x74293),f306(f164(x74291),x74292))) % 187.68/187.64 [7450]~P28(x74501,x74502,x74503,f231(f872(x74501,a859)))+P28(f866(x74501),f866(x74502),f306(f146(x74501,x74502),x74503),f231(f872(f866(x74501),a859))) % 187.68/187.64 [7598]E(x75981,f306(f306(f81(a865),f306(f306(f82(a865),f306(f235(a865,a865),x75982)),x75983)),f306(f244(a865,a865),x75982)))+~P1(f306(f49(x75981,x75983),x75982)) % 187.68/187.64 [7606]P28(x76061,x76062,x76063,f231(f872(x76061,a859)))+~P28(f866(x76061),f866(x76062),f306(f146(x76061,x76062),x76063),f231(f872(f866(x76061),a859))) % 187.68/187.64 [7645]~P1(f306(f306(f193(x76451),x76452),x76453))+P1(f306(f306(f306(f306(a195,x76451),x76452),f382(x76453,x76452,x76451)),x76453)) % 187.68/187.64 [7649]P1(f306(f306(f308(f872(x76491,a859)),f646(x76492,x76493,x76491)),x76493))+P1(f306(f306(f308(x76491),x76492),f42(f872(x76491,a859),x76493))) % 187.68/187.64 [7741]P1(f306(f306(f308(f866(x77411)),x77412),f153(x77411,x77413)))+~P1(f306(f306(f308(x77411),f708(x77413,x77412,x77411)),x77413)) % 187.68/187.64 [7842]P34(x78421,x78422,x78423)+~P1(f306(x78422,f306(f306(f157(x78421),x78423),f786(x78423,x78422,x78421)))) % 187.68/187.64 [7867]E(x78671,x78672)+~E(f306(f306(f7(x78673,f872(x78673,a859),a859),f308(x78673)),x78671),f306(f306(f7(x78673,f872(x78673,a859),a859),f308(x78673)),x78672)) % 187.68/187.64 [7873]~P1(f306(f306(f308(f871(x78731,x78731)),x78733),f233(x78731,x78732)))+P1(f306(f306(f308(x78731),f466(x78732,x78733,x78731)),x78732)) % 187.68/187.64 [7875]~P1(f306(f306(f308(x78751),x78753),f41(f872(x78751,a859),x78752)))+P1(f306(f306(f308(f872(x78751,a859)),f655(x78752,x78753,x78751)),x78752)) % 187.68/187.64 [8058]~P1(f306(f306(f308(x80581),x80582),f306(f164(x80581),f788(x80583,x80582,x80581))))+~P1(f306(f306(f308(x80581),x80582),f306(f164(x80581),x80583))) % 187.68/187.64 [8059]~P1(f306(f306(f308(x80591),x80592),f306(f164(x80591),f791(x80593,x80592,x80591))))+~P1(f306(f306(f308(x80591),x80592),f306(f164(x80591),x80593))) % 187.68/187.64 [8149]E(f306(f216(f869(f866(a302)),f866(a302),f288(x81491,x81492,f306(f306(f81(a1),x81493),f79(a1))),f214(f866(a302))),f306(x81491,x81493)),f288(x81491,x81492,x81493))+P1(f306(f306(f221(a1),x81492),x81493)) % 187.68/187.64 [8251]E(x82511,f120(x82512))+P1(f306(f306(f308(x82512),f306(f235(x82512,f871(a106,a106)),f306(f257(x82512,x82511),x82513))),f306(f164(x82512),x82511))) % 187.68/187.64 [8349]~P69(x83491)+E(f306(f134(x83491,x83491,f306(f7(x83491,x83491,x83491),f81(x83491)),x83492),f306(f161(x83491),x83493)),f306(f134(x83491,x83491,f81(x83491),x83492),x83493)) % 187.68/187.64 [8841]~P108(x88411)+E(f306(f164(x88411),f141(x88411,x88411,f5(x88411),x88412,x88413)),f306(f306(f284(x88411),x88412),f306(f164(x88411),x88413))) % 187.68/187.64 [8852]P1(f306(f306(f221(a865),f2(a865)),f595(x88521,x88522,x88523)))+~P1(f306(f306(f308(f871(x88523,x88523)),x88522),f306(f306(f263(x88523,x88523,x88523),x88521),f282(x88523,x88521)))) % 187.68/187.64 [9144]~P57(x91441,x91442)+~P1(f306(f306(f308(f871(x91441,x91441)),f306(f306(f236(x91441,x91441),x91443),x91443)),f306(f306(f263(x91441,x91441,x91441),x91442),f282(x91441,x91442)))) % 187.68/187.64 [9279]~E(f306(f306(f109(f872(f871(x92791,x92791),a859)),f306(f261(x92791,x92791),x92792)),f282(x92791,x92792)),f185(f872(f871(x92791,x92791),a859)))+~P1(f306(f306(f308(f871(x92791,x92791)),f306(f306(f236(x92791,x92791),x92793),x92793)),f306(f306(f263(x92791,x92791,x92791),x92792),f282(x92791,x92792)))) % 187.68/187.64 [9460]~P1(f306(f63(x94601),x94602))+P1(f306(f306(f220(a865),f306(f39(x94601),f306(f306(f22(f872(x94601,a859)),x94602),f306(f306(f284(x94601),x94603),f185(f872(x94601,a859)))))),f306(f39(x94601),x94602))) % 187.68/187.64 [5004]~E(x50043,f120(x50041))+E(f136(x50041,f306(f306(f143(x50041),x50042),x50043)),x50042) % 187.68/187.64 [5012]~E(x50123,f120(x50121))+E(f121(x50121,f306(f306(f143(x50121),x50122),x50123)),f120(x50121)) % 187.68/187.64 [5042]E(x50421,f120(x50422))+E(f136(x50422,f306(f306(f143(x50422),x50423),x50421)),f136(x50422,x50421)) % 187.68/187.64 [5044]E(x50441,f120(x50442))+E(f136(x50442,f306(f306(f122(x50442),x50443),x50441)),f136(x50442,x50441)) % 187.68/187.64 [5052]~E(x50523,f120(x50521))+E(f136(x50521,f306(f306(f122(x50521),x50522),x50523)),f136(x50521,x50522)) % 187.68/187.64 [5053]~E(x50533,f120(x50531))+E(f121(x50531,f306(f306(f122(x50531),x50532),x50533)),f121(x50531,x50532)) % 187.68/187.64 [5087]E(x50871,f120(x50872))+E(f306(f133(x50872),f306(f306(f122(x50872),x50871),x50873)),f306(f133(x50872),x50871)) % 187.68/187.64 [5118]~E(x51182,f120(x51181))+E(f306(f133(x51181),f306(f306(f122(x51181),x51182),x51183)),f306(f133(x51181),x51183)) % 187.68/187.64 [5173]~P108(x51731)+E(f306(f306(f225(x51731),x51732),f306(f306(f219(x51731),x51732),x51733)),x51732) % 187.68/187.64 [5174]~P108(x51741)+E(f306(f306(f219(x51741),x51742),f306(f306(f225(x51741),x51742),x51743)),x51742) % 187.68/187.64 [5175]~P98(x51751)+E(f306(f306(f108(x51751),x51752),f306(f306(f109(x51751),x51752),x51753)),x51752) % 187.68/187.64 [5176]~P98(x51761)+E(f306(f306(f109(x51761),x51762),f306(f306(f108(x51761),x51762),x51763)),x51762) % 187.68/187.64 [5195]~P4(x51951)+E(f46(x51951,f306(f306(f82(x51951),x51952),x51953),x51953),f2(x51951)) % 187.68/187.64 [5196]~P4(x51961)+E(f46(x51961,f306(f306(f82(x51961),x51962),x51963),x51962),f2(x51961)) % 187.68/187.64 [5269]~P68(x52691)+E(f306(f80(x52691),f306(f306(f22(x52691),x52692),x52693)),f306(f306(f22(x52691),x52693),x52692)) % 187.68/187.64 [5332]E(x53321,f120(x53322))+E(f121(x53322,f306(f306(f143(x53322),x53323),x53321)),f306(f306(f143(x53322),x53323),f121(x53322,x53321))) % 187.68/187.64 [5333]E(x53331,f120(x53332))+E(f121(x53332,f306(f306(f122(x53332),x53333),x53331)),f306(f306(f122(x53332),x53333),f121(x53332,x53331))) % 187.68/187.64 [5336]~P6(x53361)+E(f42(x53361,f306(f306(f284(x53361),x53362),x53363)),f306(f306(f109(x53361),x53362),f42(x53361,x53363))) % 187.68/187.64 [5337]~P6(x53371)+E(f41(x53371,f306(f306(f284(x53371),x53372),x53373)),f306(f306(f108(x53371),x53372),f41(x53371,x53373))) % 187.68/187.64 [5382]~P95(x53821)+E(f306(f306(f82(x53821),x53822),f306(f306(f82(x53821),x53822),x53823)),f306(f306(f82(x53821),x53822),x53823)) % 187.68/187.64 [5384]~P108(x53841)+E(f306(f306(f225(x53841),x53842),f306(f306(f225(x53841),x53842),x53843)),f306(f306(f225(x53841),x53842),x53843)) % 187.68/187.64 [5386]~P108(x53861)+E(f306(f306(f219(x53861),x53862),f306(f306(f219(x53861),x53862),x53863)),f306(f306(f219(x53861),x53862),x53863)) % 187.68/187.64 [5388]~P97(x53881)+E(f306(f306(f108(x53881),x53882),f306(f306(f108(x53881),x53882),x53883)),f306(f306(f108(x53881),x53882),x53883)) % 187.68/187.64 [5389]~P98(x53891)+E(f306(f306(f108(x53891),x53892),f306(f306(f108(x53891),x53892),x53893)),f306(f306(f108(x53891),x53892),x53893)) % 187.68/187.64 [5390]~P98(x53901)+E(f306(f306(f109(x53901),x53902),f306(f306(f109(x53901),x53902),x53903)),f306(f306(f109(x53901),x53902),x53903)) % 187.68/187.64 [5392]~P103(x53921)+E(f306(f306(f109(x53921),x53922),f306(f306(f109(x53921),x53922),x53923)),f306(f306(f109(x53921),x53922),x53923)) % 187.68/187.64 [5400]~P4(x54001)+E(f46(x54001,f306(f306(f81(x54001),x54002),x54003),x54003),f46(x54001,x54002,x54003)) % 187.68/187.64 [5401]~P4(x54011)+E(f46(x54011,f306(f306(f81(x54011),x54012),x54013),x54012),f46(x54011,x54013,x54012)) % 187.68/187.64 [5407]~P126(x54071)+E(f306(f306(f82(x54071),x54072),f306(f80(x54071),x54073)),f306(f80(x54071),f306(f306(f82(x54071),x54072),x54073))) % 187.68/187.64 [5408]~P61(x54081)+E(f306(f306(f264(x54081),x54082),f306(f80(x54081),x54083)),f306(f80(x54081),f306(f306(f264(x54081),x54082),x54083))) % 187.68/187.64 [5409]~P79(x54091)+E(f306(f306(f81(x54091),x54092),f306(f158(x54091),x54093)),f306(f158(x54091),f306(f306(f143(x54091),x54092),x54093))) % 187.68/187.64 [5439]~P126(x54391)+E(f306(f306(f82(x54391),f306(f80(x54391),x54392)),x54393),f306(f306(f82(x54391),x54392),f306(f80(x54391),x54393))) % 187.68/187.64 [5446]~P9(x54461,x54462,x54463)+E(f41(f872(x54461,a859),f306(f306(f62(x54461),x54462),x54463)),x54462) % 187.68/187.64 [5505]~P115(x55051)+E(f306(f306(f82(x55051),x55052),f306(f306(f237(x55051),x55052),x55053)),f306(f306(f237(x55051),x55052),f306(a119,x55053))) % 187.68/187.64 [5506]~P113(x55061)+E(f306(f306(f82(x55061),x55062),f306(f306(f237(x55061),x55062),x55063)),f306(f306(f237(x55061),x55062),f306(a119,x55063))) % 187.68/187.64 [5516]~P67(x55161)+E(f306(f306(f81(x55161),f306(f80(x55161),x55162)),f306(f306(f81(x55161),x55162),x55163)),x55163) % 187.68/187.64 [5539]~P141(x55391)+E(f306(f306(f237(x55391),f306(f107(x55391),x55392)),x55393),f306(f107(x55391),f306(f306(f237(a865),x55392),x55393))) % 187.68/187.64 [5540]~P125(x55401)+E(f306(f306(f237(x55401),f306(f110(x55401),x55402)),x55403),f306(f110(x55401),f306(f306(f237(a1),x55402),x55403))) % 187.68/187.64 [5545]~P84(x55451)+E(f306(f76(x55451),f306(f306(f22(x55451),x55452),x55453)),f306(f76(x55451),f306(f306(f22(x55451),x55453),x55452))) % 187.68/187.64 [5547]~P112(x55471)+E(f306(f306(f82(x55471),f83(x55471,x55472)),f83(x55471,x55473)),f83(x55471,f306(f306(f82(x55471),x55472),x55473))) % 187.68/187.64 [5551]E(x55511,f120(x55512))+E(f306(f306(f122(x55512),f306(f163(x55512),x55511)),x55513),f306(f163(x55512),f306(f306(f122(x55512),x55511),x55513))) % 187.68/187.64 [5556]~E(x55562,f306(a119,f306(f306(f81(a865),x55561),x55563)))+P1(f306(f306(f221(a865),x55561),x55562)) % 187.68/187.64 [5557]~P126(x55571)+E(f306(f306(f82(x55571),f306(f80(x55571),x55572)),x55573),f306(f80(x55571),f306(f306(f82(x55571),x55572),x55573))) % 187.68/187.64 [5558]~P118(x55581)+E(f306(f306(f264(x55581),f306(f80(x55581),x55582)),x55583),f306(f80(x55581),f306(f306(f264(x55581),x55582),x55583))) % 187.68/187.64 [5559]~P112(x55591)+E(f306(f306(f237(x55591),f306(f76(x55591),x55592)),x55593),f306(f76(x55591),f306(f306(f237(x55591),x55592),x55593))) % 187.68/187.64 [5658]E(f424(x56581,x56582,x56583),f436(x56581,x56582,x56583))+E(f306(f306(f109(f872(x56583,a859)),x56582),x56581),f185(f872(x56583,a859))) % 187.68/187.64 [5672]~P75(x56722)+E(f306(f306(f9(x56721,x56722),f306(f16(x56722,x56721),f79(x56722))),x56723),f79(x56722)) % 187.68/187.64 [5673]~P74(x56732)+E(f306(f306(f6(x56731,x56732),f306(f16(x56732,x56731),f2(x56732))),x56733),f2(x56732)) % 187.68/187.64 [5675]~P91(x56751)+E(f306(f306(f22(x56751),f306(f111(x56751),x56752)),f306(f111(x56751),x56753)),f306(f111(x56751),f306(f306(f22(a1),x56752),x56753))) % 187.68/187.64 [5678]~P141(x56781)+E(f306(f306(f81(x56781),f306(f107(x56781),x56782)),f306(f107(x56781),x56783)),f306(f107(x56781),f306(f306(f81(a865),x56782),x56783))) % 187.68/187.64 [5679]~P141(x56791)+E(f306(f306(f82(x56791),f306(f107(x56791),x56792)),f306(f107(x56791),x56793)),f306(f107(x56791),f306(f306(f82(a865),x56792),x56793))) % 187.68/187.64 [5680]~P125(x56801)+E(f306(f306(f22(x56801),f306(f110(x56801),x56802)),f306(f110(x56801),x56803)),f306(f110(x56801),f306(f306(f22(a1),x56802),x56803))) % 187.68/187.64 [5681]~P125(x56811)+E(f306(f306(f81(x56811),f306(f110(x56811),x56812)),f306(f110(x56811),x56813)),f306(f110(x56811),f306(f306(f81(a1),x56812),x56813))) % 187.68/187.64 [5682]~P125(x56821)+E(f306(f306(f82(x56821),f306(f110(x56821),x56822)),f306(f110(x56821),x56823)),f306(f110(x56821),f306(f306(f82(a1),x56822),x56823))) % 187.68/187.64 [5683]~P91(x56831)+E(f306(f306(f81(x56831),f306(f111(x56831),x56832)),f306(f111(x56831),x56833)),f306(f111(x56831),f306(f306(f81(a1),x56832),x56833))) % 187.68/187.64 [5684]~P91(x56841)+E(f306(f306(f82(x56841),f306(f111(x56841),x56842)),f306(f111(x56841),x56843)),f306(f111(x56841),f306(f306(f82(a1),x56842),x56843))) % 187.68/187.64 [5733]~E(x57333,x57332)+P1(f306(f306(f220(f872(x57331,a859)),x57332),x57333)) % 187.68/187.64 [5739]~E(x57392,x57393)+P1(f306(f306(f220(f872(x57391,a859)),x57392),x57393)) % 187.68/187.64 [5744]~P67(x57441)+E(f306(f306(f81(x57441),f306(f80(x57441),x57442)),f306(f80(x57441),x57443)),f306(f80(x57441),f306(f306(f81(x57441),x57443),x57442))) % 187.68/187.64 [5745]~P68(x57451)+E(f306(f306(f81(x57451),f306(f80(x57451),x57452)),f306(f80(x57451),x57453)),f306(f80(x57451),f306(f306(f81(x57451),x57452),x57453))) % 187.68/187.64 [5746]~P76(x57461)+E(f306(f306(f219(x57461),f306(f80(x57461),x57462)),f306(f80(x57461),x57463)),f306(f80(x57461),f306(f306(f225(x57461),x57462),x57463))) % 187.68/187.64 [5747]~P76(x57471)+E(f306(f306(f225(x57471),f306(f80(x57471),x57472)),f306(f80(x57471),x57473)),f306(f80(x57471),f306(f306(f219(x57471),x57472),x57473))) % 187.68/187.64 [5748]~P94(x57481)+E(f306(f306(f109(x57481),f306(f80(x57481),x57482)),f306(f80(x57481),x57483)),f306(f80(x57481),f306(f306(f108(x57481),x57482),x57483))) % 187.68/187.64 [5749]~P94(x57491)+E(f306(f306(f108(x57491),f306(f80(x57491),x57492)),f306(f80(x57491),x57493)),f306(f80(x57491),f306(f306(f109(x57491),x57492),x57493))) % 187.68/187.64 [5750]~P112(x57501)+E(f306(f306(f82(x57501),f306(f76(x57501),x57502)),f306(f76(x57501),x57503)),f306(f76(x57501),f306(f306(f82(x57501),x57502),x57503))) % 187.68/187.64 [5751]~P63(x57511)+E(f306(f306(f264(x57511),f306(f76(x57511),x57512)),f306(f76(x57511),x57513)),f306(f76(x57511),f306(f306(f264(x57511),x57512),x57513))) % 187.68/187.64 [5752]~P79(x57521)+E(f306(f306(f81(x57521),f306(f158(x57521),x57522)),f306(f158(x57521),x57523)),f306(f158(x57521),f306(f306(f122(x57521),x57522),x57523))) % 187.68/187.64 [5753]E(x57531,f185(f872(x57532,a859)))+~E(f306(f306(f108(f872(x57532,a859)),x57533),x57531),f185(f872(x57532,a859))) % 187.68/187.64 [5754]E(x57541,f185(f872(x57542,a859)))+~E(f306(f306(f108(f872(x57542,a859)),x57541),x57543),f185(f872(x57542,a859))) % 187.68/187.64 [5755]~P146(x57551,x57552,x57553)+P1(f306(x57551,f306(f306(f40(a1),x57552),x57553))) % 187.68/187.64 [5806]~P1(f306(f63(x58061),x58063))+P1(f306(f63(x58061),f306(f306(f284(x58061),x58062),x58063))) % 187.68/187.64 [5807]~P1(f306(f129(x58071),x58073))+P1(f306(f129(x58071),f306(f306(f165(x58071),x58072),x58073))) % 187.68/187.64 [5808]~P1(f306(f129(x58081),x58083))+P1(f306(f129(x58081),f306(f306(f130(x58081),x58082),x58083))) % 187.68/187.64 [5837]~P108(x58371)+P1(f306(f306(f220(x58371),x58372),f306(f306(f219(x58371),x58373),x58372))) % 187.68/187.64 [5838]~P108(x58381)+P1(f306(f306(f220(x58381),x58382),f306(f306(f219(x58381),x58382),x58383))) % 187.68/187.64 [5839]~P97(x58391)+P1(f306(f306(f220(x58391),x58392),f306(f306(f108(x58391),x58393),x58392))) % 187.68/187.64 [5840]~P98(x58401)+P1(f306(f306(f220(x58401),x58402),f306(f306(f108(x58401),x58403),x58402))) % 187.68/187.64 [5841]~P97(x58411)+P1(f306(f306(f220(x58411),x58412),f306(f306(f108(x58411),x58412),x58413))) % 187.68/187.64 [5842]~P98(x58421)+P1(f306(f306(f220(x58421),x58422),f306(f306(f108(x58421),x58422),x58423))) % 187.68/187.64 [5856]~E(x58561,f2(a865))+E(f306(f306(f40(a865),f306(f306(f82(a865),x58561),x58562)),f306(f306(f82(a865),x58561),x58563)),f2(a865)) % 187.68/187.64 [5925]P1(f306(x59251,x59252))+P1(f306(f306(f193(f33(x59251,x59253)),x59252),x59252)) % 187.68/187.64 [5942]~P91(x59421)+E(f306(f306(f22(x59421),f306(f111(x59421),x59422)),f306(f111(x59421),x59423)),f306(f111(x59421),f306(f306(f81(a1),x59422),f306(f80(a1),x59423)))) % 187.68/187.64 [5997]E(x59971,f2(a865))+E(f306(f306(f40(a865),f306(f306(f82(a865),x59971),x59972)),f306(f306(f82(a865),x59971),x59973)),f306(f306(f40(a865),x59972),x59973)) % 187.68/187.64 [6031]E(f144(x60311,f306(f306(f143(x60311),x60312),x60313)),f306(f306(f143(x60311),x60312),f144(x60311,x60313)))+P1(f306(f306(f308(x60311),x60312),f306(f164(x60311),x60313))) % 187.68/187.64 [6065]P146(x60651,x60652,x60653)+~P1(f306(x60651,f306(f306(f40(a1),x60652),x60653))) % 187.68/187.64 [6138]E(x61381,f120(x61382))+E(f306(f306(f143(x61382),f306(f133(x61382),x61381)),f306(f306(f165(x61382),x61383),f306(f163(x61382),x61381))),f306(f306(f165(x61382),f306(a119,x61383)),x61381)) % 187.68/187.64 [6144]E(f306(f306(f22(f872(x61441,a859)),x61442),x61443),x61442)+~E(f306(f306(f109(f872(x61441,a859)),x61442),x61443),f185(f872(x61441,a859))) % 187.68/187.64 [6158]E(f144(x61581,f306(f306(f143(x61581),x61582),x61583)),f144(x61581,x61583))+~P1(f306(f306(f308(x61581),x61582),f306(f164(x61581),x61583))) % 187.68/187.64 [6190]~P1(f306(f306(f220(a865),x61901),x61903))+P1(f306(f306(f220(a865),x61901),f306(f306(f81(a865),x61902),x61903))) % 187.68/187.64 [6192]~P1(f306(f306(f220(a865),x61921),x61922))+P1(f306(f306(f220(a865),x61921),f306(f306(f81(a865),x61922),x61923))) % 187.68/187.64 [6194]~P1(f306(f306(f221(a865),x61941),x61943))+P1(f306(f306(f221(a865),x61941),f306(f306(f81(a865),x61942),x61943))) % 187.68/187.64 [6196]~P1(f306(f306(f221(a865),x61961),x61962))+P1(f306(f306(f221(a865),x61961),f306(f306(f81(a865),x61962),x61963))) % 187.68/187.64 [6235]P1(f306(f63(x62351),x62352))+~P1(f306(f63(x62351),f306(f306(f284(x62351),x62353),x62352))) % 187.68/187.64 [6236]P1(f306(f129(x62361),x62362))+~P1(f306(f129(x62361),f306(f306(f143(x62361),x62363),x62362))) % 187.68/187.64 [6237]P1(f306(f129(x62371),x62372))+~P1(f306(f129(x62371),f306(f306(f122(x62371),x62373),x62372))) % 187.68/187.64 [6238]P1(f306(f129(x62381),x62382))+~P1(f306(f129(x62381),f306(f306(f122(x62381),x62382),x62383))) % 187.68/187.64 [6284]~P113(x62841)+E(f306(f306(f81(x62841),x62842),f306(f306(f82(x62841),x62843),x62842)),f306(f306(f82(x62841),f306(f306(f81(x62841),x62843),f79(x62841))),x62842)) % 187.68/187.64 [6333]~E(x63331,x63332)+~P1(f306(f306(f221(f872(x63333,a859)),x63331),x63332)) % 187.68/187.64 [6379]P1(f306(f306(f308(x63791),x63792),x63793))+P1(f306(f306(f308(x63791),x63792),f306(f80(f872(x63791,a859)),x63793))) % 187.68/187.64 [6385]E(f136(x63851,f306(f306(f130(x63851),x63852),x63853)),f136(x63851,x63853))+~P1(f306(f306(f221(a865),x63852),f306(f186(f866(x63851)),x63853))) % 187.68/187.64 [6386]E(f306(f306(f165(x63861),x63862),f121(x63861,x63863)),f306(f306(f165(x63861),x63862),x63863))+~P1(f306(f306(f221(a865),x63862),f306(f186(f866(x63861)),x63863))) % 187.68/187.64 [6441]E(f306(f306(f306(f180(f866(x64411),f866(x64411)),x64412),f160(x64411)),x64413),x64413)+~E(f46(a865,x64412,f306(f186(f866(x64411)),x64413)),f2(a865)) % 187.68/187.64 [6448]~P9(x64481,x64483,x64482)+E(f306(f306(f263(x64481,x64481,x64481),f306(f261(x64481,x64481),x64482)),x64482),x64482) % 187.68/187.64 [6487]~E(f306(f306(f108(f872(x64871,a859)),x64872),x64873),x64873)+P1(f306(f306(f220(f872(x64871,a859)),x64872),x64873)) % 187.68/187.64 [6492]~P54(x64921,x64921,x64923)+P54(x64921,x64921,f306(f306(f180(f871(x64921,x64921),a859),x64922),x64923)) % 187.68/187.64 [6494]~P1(f306(f306(f308(x64941),x64943),f306(f164(x64941),x64942)))+P1(f306(f306(f221(a865),f2(a865)),f306(f186(f866(x64941)),x64942))) % 187.68/187.64 [6520]~P84(x65201)+E(f306(f76(x65201),f306(f306(f81(x65201),f306(f76(x65201),x65202)),f306(f76(x65201),x65203))),f306(f306(f81(x65201),f306(f76(x65201),x65202)),f306(f76(x65201),x65203))) % 187.68/187.64 [6531]E(f306(f306(f40(a865),f306(f306(f82(a865),x65311),x65312)),f306(f306(f82(a865),x65311),x65313)),f306(f306(f40(a865),x65312),x65313))+~P1(f306(f306(f221(a865),f2(a865)),x65311)) % 187.68/187.64 [6580]E(x65801,x65802)+~P1(f306(f306(f306(f306(a195,a24),x65801),x65803),x65802)) % 187.68/187.64 [6673]~P1(f306(f63(x66731),x66733))+E(f306(f306(f66(x66731,f872(x66731,a859),f284(x66731)),x66732),x66733),f306(f306(f108(f872(x66731,a859)),x66733),x66732)) % 187.68/187.64 [6731]E(f306(f306(f108(f872(x67311,a859)),x67312),x67313),x67312)+~P1(f306(f306(f220(f872(x67311,a859)),x67313),x67312)) % 187.68/187.64 [6733]E(f306(f306(f108(f872(x67331,a859)),x67332),x67333),x67333)+~P1(f306(f306(f220(f872(x67331,a859)),x67332),x67333)) % 187.68/187.64 [6734]E(f306(f306(f109(f872(x67341,a859)),x67342),x67343),x67343)+~P1(f306(f306(f220(f872(x67341,a859)),x67343),x67342)) % 187.68/187.64 [6735]E(f306(f306(f109(f872(x67351,a859)),x67352),x67353),x67352)+~P1(f306(f306(f220(f872(x67351,a859)),x67352),x67353)) % 187.68/187.64 [6786]~P1(f306(f129(x67861),x67862))+E(f306(f306(f22(f872(x67861,a859)),f306(f164(x67861),x67862)),f306(f306(f284(x67861),x67863),f185(f872(x67861,a859)))),f306(f164(x67861),f162(x67861,x67863,x67862))) % 187.68/187.64 [6839]P40(x68391,x68392)+~P40(x68391,f306(f306(f180(f871(x68391,x68391),a859),x68393),x68392)) % 187.68/187.64 [6903]P1(f306(f50(x69031,x69032),f306(a52,x69033)))+~P1(f306(f50(f306(f80(a1),x69031),f306(f80(a1),x69032)),x69033)) % 187.68/187.64 [6908]E(f306(f306(f22(f872(x69081,a859)),f306(f306(f284(x69081),x69082),x69083)),f306(f306(f284(x69081),x69082),f185(f872(x69081,a859)))),x69083)+P1(f306(f306(f308(x69081),x69082),x69083)) % 187.68/187.64 [6929]E(f306(f306(f109(f872(x69291,a859)),f306(f164(x69291),x69292)),f306(f164(x69291),x69293)),f185(f872(x69291,a859)))+~P1(f306(f129(x69291),f306(f306(f122(x69291),x69292),x69293))) % 187.68/187.64 [6945]~P1(f306(f306(f308(x69451),x69452),f306(f164(x69451),x69453)))+~P1(f306(f129(x69451),f306(f306(f143(x69451),x69452),x69453))) % 187.68/187.64 [7017]P34(x70171,x70172,x70173)+P1(f306(f306(f221(a865),f786(x70173,x70172,x70171)),f306(f186(f866(x70171)),x70173))) % 187.68/187.64 [7027]E(f306(f306(f109(f872(x70271,a859)),x70272),x70273),f185(f872(x70271,a859)))+P1(f306(f306(f308(x70271),f424(x70273,x70272,x70271)),x70272)) % 187.68/187.64 [7028]E(f306(f306(f109(f872(x70281,a859)),x70282),x70283),f185(f872(x70281,a859)))+P1(f306(f306(f308(x70281),f436(x70283,x70282,x70281)),x70283)) % 187.68/187.64 [7032]E(f121(x70321,f306(f306(f165(x70321),x70322),x70323)),f306(f306(f165(x70321),f306(f306(f22(a865),x70322),f79(a865))),x70323))+~P1(f306(f306(f220(a865),x70322),f306(f186(f866(x70321)),x70323))) % 187.68/187.64 [7091]~P36(x70913,x70912,x70911)+P1(f306(f306(f221(a865),f784(x70911,x70912,x70913)),f306(f186(f866(x70913)),x70911))) % 187.68/187.64 [7109]P1(f306(f306(f221(a865),f2(a865)),x71091))+P1(f306(f306(f220(a865),f306(f306(f82(a865),x71092),x71091)),f306(f306(f82(a865),x71093),x71091))) % 187.68/187.64 [7110]P1(f306(f306(f221(a865),f2(a865)),x71101))+P1(f306(f306(f220(a865),f306(f306(f82(a865),x71101),x71102)),f306(f306(f82(a865),x71101),x71103))) % 187.68/187.64 [7113]~P1(f306(f306(f308(x71131),x71132),x71133))+~P1(f306(f306(f308(x71131),x71132),f306(f80(f872(x71131,a859)),x71133))) % 187.68/187.64 [7120]~P1(f306(f306(f221(f872(x71201,a859)),x71202),x71203))+P1(f306(f306(f220(f872(x71201,a859)),x71202),x71203)) % 187.68/187.64 [7219]~P1(f306(f306(f220(a865),x72193),x72192))+P1(f306(f306(f220(a865),f306(f306(f22(a865),x72191),x72192)),f306(f306(f22(a865),x72191),x72193))) % 187.68/187.64 [7220]~P1(f306(f306(f220(a865),x72201),x72203))+P1(f306(f306(f220(a865),f306(f306(f22(a865),x72201),x72202)),f306(f306(f22(a865),x72203),x72202))) % 187.68/187.64 [7221]~P1(f306(f306(f220(a865),x72212),x72213))+P1(f306(f306(f220(a865),f306(f306(f81(a865),x72211),x72212)),f306(f306(f81(a865),x72211),x72213))) % 187.68/187.64 [7222]~P1(f306(f306(f220(a865),x72221),x72223))+P1(f306(f306(f220(a865),f306(f306(f81(a865),x72221),x72222)),f306(f306(f81(a865),x72223),x72222))) % 187.68/187.64 [7224]~P1(f306(f306(f220(a865),x72242),x72243))+P1(f306(f306(f220(a865),f306(f306(f82(a865),x72241),x72242)),f306(f306(f82(a865),x72241),x72243))) % 187.68/187.64 [7226]~P1(f306(f306(f220(a865),x72261),x72263))+P1(f306(f306(f220(a865),f306(f306(f82(a865),x72261),x72262)),f306(f306(f82(a865),x72263),x72262))) % 187.68/187.64 [7227]~P1(f306(f306(f220(a865),x72271),x72273))+P1(f306(f306(f220(a865),f306(f306(f40(a865),x72271),x72272)),f306(f306(f40(a865),x72273),x72272))) % 187.68/187.64 [7228]~P1(f306(f306(f220(a1),x72282),x72283))+P1(f306(f306(f220(a1),f306(f306(f81(a1),x72281),x72282)),f306(f306(f81(a1),x72281),x72283))) % 187.68/187.64 [7231]~P1(f306(f306(f221(a865),x72312),x72313))+P1(f306(f306(f221(a865),f306(f306(f81(a865),x72311),x72312)),f306(f306(f81(a865),x72311),x72313))) % 187.68/187.64 [7232]~P1(f306(f306(f221(a865),x72321),x72323))+P1(f306(f306(f221(a865),f306(f306(f81(a865),x72321),x72322)),f306(f306(f81(a865),x72323),x72322))) % 187.68/187.64 [7233]~P1(f306(f306(f221(a1),x72331),x72333))+P1(f306(f306(f221(a1),f306(f306(f81(a1),x72331),x72332)),f306(f306(f81(a1),x72333),x72332))) % 187.68/187.64 [7312]E(x73121,x73122)+~P1(f306(f306(f308(x73123),x73121),f306(f306(f284(x73123),x73122),f185(f872(x73123,a859))))) % 187.68/187.64 [7314]~E(f306(f306(f109(f872(x73141,a859)),x73142),x73143),f185(f872(x73141,a859)))+P1(f306(f306(f220(f872(x73141,a859)),x73142),f306(f80(f872(x73141,a859)),x73143))) % 187.68/187.64 [7322]P1(f306(f306(f308(f872(x73221,a859)),x73222),f306(f283(x73221),x73223)))+~P1(f306(f306(f220(f872(x73221,a859)),x73222),x73223)) % 187.68/187.64 [7375]E(f306(f306(f143(x73751),f306(f306(f157(x73751),x73752),x73753)),f306(f306(f130(x73751),f306(a119,x73753)),x73752)),f306(f306(f130(x73751),x73753),x73752))+~P1(f306(f306(f221(a865),x73753),f306(f186(f866(x73751)),x73752))) % 187.68/187.64 [7402]P1(f306(f306(f308(f871(x74021,x74021)),x74022),f282(x74021,x74023)))+~P1(f306(f306(f308(f871(x74021,x74021)),x74022),x74023)) % 187.68/187.64 [7413]~P1(f306(f306(f308(f872(x74131,a859)),x74132),f306(f283(x74131),x74133)))+P1(f306(f306(f220(f872(x74131,a859)),x74132),x74133)) % 187.68/187.64 [7456]P1(f306(f306(f220(f872(x74561,a859)),x74562),f41(f872(x74561,a859),x74563)))+~P1(f306(f306(f308(f872(x74561,a859)),x74562),x74563)) % 187.68/187.64 [7481]~P125(x74811)+E(f306(f306(f82(x74811),f306(f306(f237(x74811),f306(f80(x74811),f79(x74811))),x74812)),f306(f306(f237(x74811),x74813),x74812)),f306(f306(f237(x74811),f306(f80(x74811),x74813)),x74812)) % 187.68/187.64 [7502]E(f306(f306(f157(x75021),x75022),f306(f306(f22(a865),f306(f186(f866(x75021)),x75022)),f306(a119,x75023))),f306(f306(f157(x75021),f306(f161(x75021),x75022)),x75023))+~P1(f306(f306(f221(a865),x75023),f306(f186(f866(x75021)),x75022))) % 187.68/187.64 [7519]~E(f306(f306(f109(f872(x75191,a859)),f612(x75193,x75192,x75191)),x75193),f185(f872(x75191,a859)))+E(f306(f306(f109(f872(x75191,a859)),f41(f872(x75191,a859),x75192)),x75193),f185(f872(x75191,a859))) % 187.68/187.64 [7580]~P1(f306(f306(f308(x75803),x75802),f306(f164(x75803),x75801)))+P1(f306(f306(f221(a865),f691(x75801,x75802,x75803)),f306(f186(f866(x75803)),x75801))) % 187.68/187.64 [7588]P1(f306(f306(f308(x75881),f306(f306(f157(x75881),x75882),x75883)),f306(f164(x75881),x75882)))+~P1(f306(f306(f221(a865),x75883),f306(f186(f866(x75881)),x75882))) % 187.68/187.64 [7689]~P1(f306(x76892,f739(x76893,x76892,x76891)))+E(f306(f306(f130(x76891),f306(f186(f866(x76891)),f168(x76891,x76892,x76893))),x76893),f120(x76891)) % 187.68/187.64 [7699]P1(f306(f306(f220(f872(f866(x76991),a859)),f153(x76991,x76992)),f153(x76991,x76993)))+~P1(f306(f306(f220(f872(x76991,a859)),x76992),x76993)) % 187.68/187.64 [7700]P1(f306(f306(f220(f872(f866(x77001),a859)),f152(x77001,x77002)),f152(x77001,x77003)))+~P1(f306(f306(f220(f872(x77001,a859)),x77002),x77003)) % 187.68/187.64 [7728]E(f306(f306(f109(f872(x77281,a859)),f41(f872(x77281,a859),x77282)),x77283),f185(f872(x77281,a859)))+P1(f306(f306(f308(f872(x77281,a859)),f612(x77283,x77282,x77281)),x77282)) % 187.68/187.64 [7731]~P1(f306(f306(f308(f872(x77311,a859)),x77313),x77312))+P1(f306(f306(f220(f872(x77311,a859)),f42(f872(x77311,a859),x77312)),x77313)) % 187.68/187.64 [7733]E(f306(f306(f109(f872(x77331,a859)),x77332),x77333),f185(f872(x77331,a859)))+~P1(f306(f306(f220(f872(x77331,a859)),x77332),f306(f80(f872(x77331,a859)),x77333))) % 187.68/187.64 [7781]E(f306(f306(f22(a865),f306(f306(f81(a865),f306(f158(a865),x77811)),x77812)),f306(f306(f157(a865),x77811),x77813)),f306(f158(a865),f306(f306(f151(a865,x77811),x77813),x77812)))+~P1(f306(f306(f221(a865),x77813),f306(f186(f866(a865)),x77811))) % 187.68/187.64 [7830]P1(f306(f306(f220(a865),x78301),x78302))+~P1(f306(f306(f220(a865),f306(f306(f81(a865),x78303),x78301)),f306(f306(f81(a865),x78303),x78302))) % 187.68/187.64 [7833]P1(f306(f306(f221(a865),x78331),x78332))+~P1(f306(f306(f221(a865),f306(f306(f81(a865),x78333),x78331)),f306(f306(f81(a865),x78333),x78332))) % 187.68/187.64 [7834]P1(f306(f306(f221(a865),x78341),x78342))+~P1(f306(f306(f221(a865),f306(f306(f82(a865),x78343),x78341)),f306(f306(f82(a865),x78343),x78342))) % 187.68/187.64 [7835]P1(f306(f306(f221(a865),x78351),x78352))+~P1(f306(f306(f221(a865),f306(f306(f82(a865),x78351),x78353)),f306(f306(f82(a865),x78352),x78353))) % 187.68/187.64 [7865]P1(f306(f306(f221(a865),f2(a865)),x78651))+~P1(f306(f306(f221(a865),f306(f306(f82(a865),x78652),x78651)),f306(f306(f82(a865),x78653),x78651))) % 187.68/187.64 [7866]P1(f306(f306(f221(a865),f2(a865)),x78661))+~P1(f306(f306(f221(a865),f306(f306(f82(a865),x78661),x78662)),f306(f306(f82(a865),x78661),x78663))) % 187.68/187.64 [7939]E(f239(x79391,x79392,x79393),x79392)+~P1(f306(f306(f220(f872(x79391,a859)),x79393),f306(f306(f284(x79391),x79392),f185(f872(x79391,a859))))) % 187.68/187.64 [7997]~P1(f306(f129(x79971),x79973))+E(f306(f128(x79971,f306(f306(f8(a859,a859,x79971),a301),f306(a303,x79972))),x79973),f162(x79971,x79972,x79973)) % 187.68/187.64 [8021]E(f306(f306(f130(x80211),f306(f186(f866(x80211)),f168(x80211,x80212,x80213))),x80213),f120(x80211))+P1(f306(f306(f308(x80211),f739(x80213,x80212,x80211)),f306(f164(x80211),x80213))) % 187.68/187.64 [8025]E(f306(f306(f122(x80251),f306(f306(f165(x80251),x80252),x80253)),f306(f306(f143(x80251),f306(f306(f157(x80251),x80253),x80252)),f120(x80251))),f306(f306(f165(x80251),f306(a119,x80252)),x80253))+~P1(f306(f306(f221(a865),x80252),f306(f186(f866(x80251)),x80253))) % 187.68/187.64 [8087]E(f306(f128(x80871,f306(f306(f8(a859,a859,x80871),a301),f306(a303,x80872))),x80873),x80873)+P1(f306(f306(f308(x80871),x80872),f306(f164(x80871),x80873))) % 187.68/187.64 [8095]P1(f306(f306(f220(f872(f872(x80951,a859),a859)),f240(x80951,x80952)),f240(x80951,x80953)))+~P1(f306(f306(f220(f872(x80951,a859)),x80952),x80953)) % 187.68/187.64 [8140]~P1(f306(f129(x81401),x81403))+P1(f306(f129(x81401),f306(f306(f306(f180(f866(x81401),f866(x81401)),x81402),f160(x81401)),x81403))) % 187.68/187.64 [8146]~P1(f306(f306(f221(a865),x81462),x81463))+P1(f306(f306(f221(a865),f306(f306(f82(a865),f306(a119,x81461)),x81462)),f306(f306(f82(a865),f306(a119,x81461)),x81463))) % 187.68/187.64 [8168]P1(f306(f306(f220(f872(f872(x81681,a859),a859)),f306(f283(x81681),x81682)),f306(f283(x81681),x81683)))+~P1(f306(f306(f220(f872(x81681,a859)),x81682),x81683)) % 187.68/187.64 [8331]~P1(f306(f306(f220(f872(x83311,a859)),x83313),x83312))+P1(f306(f306(f220(f872(x83311,a859)),f306(f80(f872(x83311,a859)),x83312)),f306(f80(f872(x83311,a859)),x83313))) % 187.68/187.64 [8365]E(f306(f285(a865,a865,f306(f306(f7(a865,a865,a865),f22(a865)),x83651)),f306(f276(a865,x83652),x83653)),f306(f276(a865,f306(f306(f22(a865),x83652),x83651)),f306(f306(f22(a865),x83653),x83651)))+~P1(f306(f306(f221(a865),x83651),x83653)) % 187.68/187.64 [8390]~P79(x83901)+E(f306(f306(f81(x83901),x83902),f306(f134(x83901,x83901,f81(x83901),f2(x83901)),x83903)),f306(f134(x83901,x83901,f81(x83901),x83902),x83903)) % 187.68/187.64 [8477]~P84(x84771)+P1(f306(f306(f220(x84771),f306(f76(x84771),f306(f306(f22(x84771),x84772),x84773))),f306(f306(f81(x84771),f306(f76(x84771),x84772)),f306(f76(x84771),x84773)))) % 187.68/187.64 [8478]~P84(x84781)+P1(f306(f306(f220(x84781),f306(f76(x84781),f306(f306(f81(x84781),x84782),x84783))),f306(f306(f81(x84781),f306(f76(x84781),x84782)),f306(f76(x84781),x84783)))) % 187.68/187.64 [8488]E(f306(f306(f81(a1),f306(f306(f82(a1),x84881),f46(a1,f306(f306(f40(a1),x84882),x84881),x84883))),f46(a1,x84882,x84881)),f46(a1,x84882,f306(f306(f82(a1),x84881),x84883)))+~P1(f306(f306(f221(a1),f2(a1)),x84883)) % 187.68/187.64 [8494]E(f306(f306(f122(x84941),f306(f306(f165(x84941),x84942),x84943)),f306(f306(f143(x84941),f306(f133(x84941),f306(f306(f130(x84941),x84942),x84943))),f120(x84941))),f306(f306(f165(x84941),f306(a119,x84942)),x84943))+~P1(f306(f306(f221(a865),x84942),f306(f186(f866(x84941)),x84943))) % 187.68/187.64 [8513]E(f306(f252(x85131,f306(f306(f146(x85131,f871(a106,x85131)),f306(f236(a106,x85131),f79(a106))),x85132)),f306(a3,x85133)),f306(f306(f157(x85131),x85132),x85133))+~P1(f306(f306(f221(a865),x85133),f306(f186(f866(x85131)),x85132))) % 187.68/187.64 [8579]P1(f306(f306(f308(f871(x85791,x85791)),x85792),f306(f306(f263(x85791,x85791,x85791),x85793),f282(x85791,x85793))))+~P1(f306(f306(f308(f871(x85791,x85791)),x85792),x85793)) % 187.68/187.64 [8598]P1(f306(f306(f220(a865),x85981),x85982))+~P1(f306(f306(f220(a865),f306(f306(f82(a865),f306(a119,x85983)),x85981)),f306(f306(f82(a865),f306(a119,x85983)),x85982))) % 187.68/187.64 [8613]P1(f306(f306(f220(f872(x86131,a859)),x86132),x86133))+~P1(f306(f306(f220(f872(x86131,a859)),f306(f80(f872(x86131,a859)),x86133)),f306(f80(f872(x86131,a859)),x86132))) % 187.68/187.64 [8631]P1(f306(f129(x86311),x86312))+~P1(f306(f129(x86311),f306(f306(f306(f180(f866(x86311),f866(x86311)),x86313),f160(x86311)),x86312))) % 187.68/187.64 [8689]E(f306(f285(f871(x86891,x86892),x86892,f244(x86891,x86892)),f306(f164(f871(x86891,x86892)),x86893)),f177(x86891,x86892,f306(f169(x86891,x86892),x86893)))+~P1(f306(f129(x86891),f306(f306(f146(f871(x86891,x86892),x86891),f235(x86891,x86892)),x86893))) % 187.68/187.64 [8698]E(f306(f260(x86981,x86981,f282(x86981,x86982)),x86983),x86983)+~P1(f306(f306(f220(f872(x86981,a859)),f306(f260(x86981,x86981,x86982),x86983)),x86983)) % 187.68/187.64 [8741]~P108(x87411)+P17(x87411,f306(f128(x87411,f306(f306(f7(x87411,x87411,a859),a303),f306(x87412,x87413))),x87413)) % 187.68/187.64 [8747]~P1(f306(f306(f220(a865),x87471),x87472))+P1(f306(f306(f220(a865),x87471),f306(f134(a865,a865,f81(a865),x87472),x87473))) % 187.68/187.64 [8825]~P1(f306(f306(f308(f871(x88251,x88251)),x88252),f282(x88251,x88253)))+P1(f306(f306(f308(f871(x88251,x88251)),x88252),f306(f306(f180(f871(x88251,x88251),a859),f592(x88253,x88252,x88251)),x88253))) % 187.68/187.64 [8918]~P79(x89181)+E(f306(f306(f81(x89181),x89182),f306(f134(x89181,x89181,f306(f7(x89181,x89181,x89181),f81(x89181)),f2(x89181)),f306(f161(x89181),x89183))),f306(f134(x89181,x89181,f81(x89181),x89182),x89183)) % 187.68/187.64 [9190]P54(x91901,x91902,x91903)+P1(f306(f306(f308(f871(x91901,x91902)),f306(f306(f236(x91901,x91902),f604(x91903,x91902,x91901)),f597(x91903,x91902,x91901))),x91903)) % 187.68/187.64 [9191]P54(x91911,x91912,x91913)+P1(f306(f306(f308(f871(x91911,x91912)),f306(f306(f236(x91911,x91912),f604(x91913,x91912,x91911)),f596(x91913,x91912,x91911))),x91913)) % 187.68/187.64 [9264]~P1(f306(f306(f308(f871(x92641,x92641)),x92642),f306(f306(f263(x92641,x92641,x92641),x92643),f282(x92641,x92643))))+P1(f306(f306(f308(f871(x92641,x92641)),x92642),f306(f306(f180(f871(x92641,x92641),a859),f595(x92643,x92642,x92641)),x92643))) % 187.68/187.64 [9265]~P1(f306(x92651,f306(f306(f157(x92652),x92653),f306(f186(f866(x92652)),f168(x92652,x92651,x92653)))))+~P1(f306(f306(f221(a865),f306(f186(f866(x92652)),f168(x92652,x92651,x92653))),f306(f186(f866(x92652)),x92653))) % 187.68/187.64 [9354]~P1(f306(f306(f220(f872(x93541,a859)),x93542),x93543))+P1(f306(f306(f220(f872(x93541,a859)),f306(f306(f7(x93541,f872(x93541,a859),a859),f308(x93541)),x93542)),f306(f306(f7(x93541,f872(x93541,a859),a859),f308(x93541)),x93543))) % 187.68/187.64 [9409]~P1(f306(f306(f308(f871(f872(x94091,a859),f872(x94091,a859))),f306(f306(f236(f872(x94091,a859),f872(x94091,a859)),x94092),x94093)),f281(x94091)))+P1(f306(f306(f221(f872(x94091,a859)),x94092),x94093)) % 187.68/187.64 [9434]P55(x94341,x94342,x94343)+~P1(f306(f306(f308(f871(x94341,x94341)),f306(f306(f236(x94341,x94341),f569(x94343,x94342,x94341)),f568(x94343,x94342,x94341))),x94343)) % 187.68/187.64 [9435]P55(x94351,x94352,x94353)+~P1(f306(f306(f308(f871(x94351,x94351)),f306(f306(f236(x94351,x94351),f568(x94353,x94352,x94351)),f569(x94353,x94352,x94351))),x94353)) % 187.68/187.64 [9471]~P1(f306(f306(f308(f871(f866(x94711),f866(x94711))),f306(f306(f236(f866(x94711),f866(x94711)),x94712),x94712)),f139(x94711,x94713)))+P1(f306(f306(f308(f871(x94711,x94711)),f306(f306(f236(x94711,x94711),f717(x94712,x94713,x94711)),f717(x94712,x94713,x94711))),x94713)) % 187.68/187.64 [9524]P1(f306(f306(f220(f872(x95241,a859)),x95242),x95243))+~P1(f306(f306(f220(f872(x95241,a859)),f306(f306(f7(x95241,f872(x95241,a859),a859),f308(x95241)),x95242)),f306(f306(f7(x95241,f872(x95241,a859),a859),f308(x95241)),x95243))) % 187.68/187.64 [9606]E(f306(f306(f22(a865),f306(f306(f6(a865,a865),x96061),f306(f229(a865),x96062))),f306(f306(f6(a865,a865),x96063),f306(f229(a865),x96062))),f306(f306(f6(a865,a865),f306(f306(f18(a865,a865,a865),f306(f306(f8(a865,f872(a865,a865),a865),f22(a865)),x96061)),x96063)),f306(f229(a865),x96062)))+~P1(f306(f306(f220(a865),f306(x96063,f427(x96062,x96061,x96063))),f306(x96061,f427(x96062,x96061,x96063)))) % 187.68/187.64 [9911]E(f306(f228(f871(x99111,x99112)),f306(f245(x99111,x99112,a859),f306(f306(f7(x99111,f872(x99112,f869(x99112)),f872(x99112,a859)),f306(f306(f8(f872(f869(x99112),a859),f872(f872(x99112,f869(x99112)),f872(x99112,a859)),x99111),f8(f869(x99112),a859,x99112)),f306(f306(f8(f869(x99112),f872(f869(x99112),a859),x99111),a303),f306(f169(x99111,x99112),x99113)))),f214(x99112)))),f306(f164(f871(x99111,x99112)),x99113))+~P1(f306(f129(x99111),f306(f306(f146(f871(x99111,x99112),x99111),f235(x99111,x99112)),x99113))) % 187.68/187.64 [5591]~P67(x55911)+E(f306(f306(f22(x55911),f306(f306(f81(x55911),x55912),x55913)),x55913),x55912) % 187.68/187.64 [5592]~P67(x55921)+E(f306(f306(f81(x55921),f306(f306(f22(x55921),x55922),x55923)),x55923),x55922) % 187.68/187.64 [5814]~P67(x58141)+E(f306(f306(f81(x58141),x58142),f306(f306(f81(x58141),f306(f80(x58141),x58142)),x58143)),x58143) % 187.68/187.64 [5899]~P80(x58991)+E(f306(f306(f82(x58991),f306(f306(f237(x58991),x58992),x58993)),x58992),f306(f306(f237(x58991),x58992),f306(a119,x58993))) % 187.68/187.64 [5900]~P113(x59001)+E(f306(f306(f82(x59001),f306(f306(f237(x59001),x59002),x59003)),x59002),f306(f306(f237(x59001),x59002),f306(a119,x59003))) % 187.68/187.64 [6114]~P112(x61141)+E(f306(f76(x61141),f306(f306(f237(x61141),f306(f80(x61141),x61142)),x61143)),f306(f76(x61141),f306(f306(f237(x61141),x61142),x61143))) % 187.68/187.64 [6166]~P80(x61661)+E(f306(f306(f82(x61661),f306(f306(f237(x61661),x61662),x61663)),x61662),f306(f306(f82(x61661),x61662),f306(f306(f237(x61661),x61662),x61663))) % 187.68/187.64 [6226]E(f306(f306(f22(a106),f306(f306(f81(a106),x62261),x62262)),x62263),f256(x62261,x62262,x62263))+~P1(f306(f306(f221(a106),x62262),x62263)) % 187.68/187.64 [6247]~E(f306(f306(f130(x62471),x62473),x62472),f120(x62471))+P1(f306(f306(f220(a865),f306(f186(f866(x62471)),x62472)),x62473)) % 187.68/187.64 [6384]E(f306(f306(f82(a865),f306(f111(a865),x63841)),f306(f306(f82(a865),f306(f111(a865),x63842)),x63843)),f2(a865))+~P1(f306(f306(f221(a1),x63841),a84)) % 187.68/187.64 [6400]~P61(x64001)+E(f306(f306(f237(x64001),f306(f306(f264(x64001),f79(x64001)),x64002)),x64003),f306(f306(f264(x64001),f79(x64001)),f306(f306(f237(x64001),x64002),x64003))) % 187.68/187.64 [6476]E(f306(f306(f22(a865),f306(f306(f81(a865),x64761),x64762)),x64763),f306(f306(f22(a865),x64761),f306(f306(f22(a865),x64763),x64762)))+~P1(f306(f306(f220(a865),x64762),x64763)) % 187.68/187.64 [6478]E(f306(f306(f22(a865),f306(f306(f81(a865),x64781),x64782)),x64783),f306(f306(f81(a865),x64781),f306(f306(f22(a865),x64782),x64783)))+~P1(f306(f306(f220(a865),x64783),x64782)) % 187.68/187.64 [6511]~P108(x65111)+P1(f306(f306(f220(x65111),f306(f306(f225(x65111),x65112),x65113)),x65113)) % 187.68/187.64 [6512]~P108(x65121)+P1(f306(f306(f220(x65121),f306(f306(f225(x65121),x65122),x65123)),x65122)) % 187.68/187.64 [6513]~P98(x65131)+P1(f306(f306(f220(x65131),f306(f306(f109(x65131),x65132),x65133)),x65133)) % 187.68/187.64 [6514]~P103(x65141)+P1(f306(f306(f220(x65141),f306(f306(f109(x65141),x65142),x65143)),x65143)) % 187.68/187.64 [6515]~P98(x65151)+P1(f306(f306(f220(x65151),f306(f306(f109(x65151),x65152),x65153)),x65152)) % 187.68/187.64 [6516]~P103(x65161)+P1(f306(f306(f220(x65161),f306(f306(f109(x65161),x65162),x65163)),x65162)) % 187.68/187.64 [6530]E(f306(f306(f40(a1),f306(f306(f40(a1),x65301),x65302)),x65303),f306(f306(f40(a1),x65301),f306(f306(f82(a1),x65302),x65303)))+~P1(f306(f306(f221(a1),f2(a1)),x65303)) % 187.68/187.64 [6583]~P113(x65831)+E(f306(f306(f81(x65831),f306(f306(f82(x65831),x65832),x65833)),x65833),f306(f306(f82(x65831),f306(f306(f81(x65831),x65832),f79(x65831))),x65833)) % 187.68/187.64 [6584]~P91(x65841)+E(f306(f306(f82(x65841),f306(f80(x65841),f306(f111(x65841),x65842))),x65843),f306(f306(f82(x65841),f306(f111(x65841),f306(f80(a1),x65842))),x65843)) % 187.68/187.64 [6660]~P79(x66601)+E(f306(f158(x66601),f306(f306(f146(x66602,x66601),f306(f16(x66601,x66602),f2(x66601))),x66603)),f2(x66601)) % 187.68/187.64 [6676]E(f306(f306(f81(a865),f306(f111(a865),x66761)),f306(f306(f81(a865),f306(f111(a865),x66762)),x66763)),f306(f306(f81(a865),f306(f111(a865),x66762)),x66763))+~P1(f306(a190,f306(f111(a1),x66761))) % 187.68/187.64 [6690]~P6(x66901)+E(f42(x66901,f306(f306(f284(x66901),x66902),f306(f306(f284(x66901),x66903),f185(f872(x66901,a859))))),f306(f306(f109(x66901),x66902),x66903)) % 187.68/187.64 [6691]~P6(x66911)+E(f41(x66911,f306(f306(f284(x66911),x66912),f306(f306(f284(x66911),x66913),f185(f872(x66911,a859))))),f306(f306(f108(x66911),x66912),x66913)) % 187.68/187.64 [6714]E(f306(f306(f165(x67141),x67142),x67143),x67143)+~P1(f306(f306(f220(a865),f306(f186(f866(x67141)),x67143)),x67142)) % 187.68/187.64 [6726]E(f306(f306(f130(x67261),x67262),x67263),f120(x67261))+~P1(f306(f306(f220(a865),f306(f186(f866(x67261)),x67263)),x67262)) % 187.68/187.64 [6737]E(f306(f306(f81(a865),f306(f306(f22(a865),x67371),x67372)),x67373),f306(f306(f22(a865),f306(f306(f81(a865),x67371),x67373)),x67372))+~P1(f306(f306(f220(a865),x67372),x67371)) % 187.68/187.64 [6751]~P1(f306(f306(f221(a865),x67511),x67513))+P1(f306(f306(f221(a865),f306(f306(f22(a865),x67511),x67512)),x67513)) % 187.68/187.64 [6779]~P108(x67791)+E(f162(x67791,x67792,f306(f306(f140(x67791,x67791,f5(x67791)),x67792),x67793)),x67793) % 187.68/187.64 [6865]E(f306(f306(f22(a865),f306(f306(f81(a865),x68651),x68652)),f306(a119,x68653)),f306(f306(f22(a865),x68651),f306(a119,f306(f306(f22(a865),x68653),x68652))))+~P1(f306(f306(f220(a865),x68652),x68653)) % 187.68/187.64 [6866]~P112(x68661)+P1(f306(f306(f220(x68661),f2(x68661)),f306(f306(f237(x68661),f306(f76(x68661),x68662)),x68663))) % 187.68/187.64 [6913]P27(x69131,x69132,x69133)+~P1(f306(f306(f220(f872(f864(x69131),a859)),x69133),x69132)) % 187.68/187.64 [6956]~P1(f306(f63(x69561),x69562))+P1(f306(f63(x69561),f306(f306(f22(f872(x69561,a859)),x69562),x69563))) % 187.68/187.64 [6957]~P1(f306(f63(x69571),x69573))+P1(f306(f63(x69571),f306(f306(f109(f872(x69571,a859)),x69572),x69573))) % 187.68/187.64 [6958]~P1(f306(f63(x69581),x69582))+P1(f306(f63(x69581),f306(f306(f109(f872(x69581,a859)),x69582),x69583))) % 187.68/187.64 [7099]~P40(x70991,x70993)+P40(x70991,f306(f306(f109(f872(f871(x70991,x70991),a859)),x70992),x70993)) % 187.68/187.64 [7100]~P40(x71001,x71002)+P40(x71001,f306(f306(f109(f872(f871(x71001,x71001),a859)),x71002),x71003)) % 187.68/187.64 [7215]~P108(x72151)+E(f14(x72151,f306(f164(x72151),f306(f306(f143(x72151),x72152),x72153))),f306(f134(x72151,x72151,f225(x72151),x72152),x72153)) % 187.68/187.64 [7216]~P108(x72161)+E(f15(x72161,f306(f164(x72161),f306(f306(f143(x72161),x72162),x72163))),f306(f134(x72161,x72161,f219(x72161),x72162),x72163)) % 187.68/187.64 [7217]~P98(x72171)+E(f13(x72171,f306(f164(x72171),f306(f306(f143(x72171),x72172),x72173))),f306(f134(x72171,x72171,f108(x72171),x72172),x72173)) % 187.68/187.64 [7218]~P98(x72181)+E(f10(x72181,f306(f164(x72181),f306(f306(f143(x72181),x72182),x72183))),f306(f134(x72181,x72181,f109(x72181),x72182),x72183)) % 187.68/187.64 [7278]~P1(f306(f63(x72781),x72782))+P1(f306(f306(f220(a865),f306(f39(x72781),x72782)),f306(f39(x72781),f306(f306(f284(x72781),x72783),x72782)))) % 187.68/187.64 [7285]E(f306(f306(f108(f872(a865,a859)),f306(f276(a865,x72851),x72852)),f306(f276(a865,x72852),f306(f306(f81(a865),x72852),x72853))),f306(f276(a865,x72851),f306(f306(f81(a865),x72852),x72853)))+~P1(f306(f306(f220(a865),x72851),x72852)) % 187.68/187.64 [7295]P1(f306(f306(f220(a865),x72951),x72952))+~P1(f306(f306(f220(a865),f306(f306(f81(a865),x72953),x72951)),x72952)) % 187.68/187.64 [7296]P1(f306(f306(f220(a865),x72961),x72962))+~P1(f306(f306(f220(a865),f306(f306(f81(a865),x72961),x72963)),x72962)) % 187.68/187.64 [7297]P1(f306(f306(f221(a865),x72971),x72972))+~P1(f306(f306(f221(a865),f306(f306(f81(a865),x72971),x72973)),x72972)) % 187.68/187.64 [7339]~P108(x73391)+E(f11(x73391,f225(x73391),f306(f164(x73391),f306(f306(f143(x73391),x73392),x73393))),f306(f134(x73391,x73391,f225(x73391),x73392),x73393)) % 187.68/187.64 [7340]~P108(x73401)+E(f12(x73401,f219(x73401),f306(f164(x73401),f306(f306(f143(x73401),x73402),x73403))),f306(f134(x73401,x73401,f219(x73401),x73402),x73403)) % 187.68/187.64 [7344]~E(x73442,f185(f872(f871(x73441,x73441),a859)))+P1(f306(f306(f220(f872(f871(x73441,x73441),a859)),x73442),x73443)) % 187.68/187.64 [7451]E(f306(f306(f108(f872(x74511,a859)),x74512),f306(f306(f22(f872(x74511,a859)),x74513),x74512)),x74513)+~P1(f306(f306(f220(f872(x74511,a859)),x74512),x74513)) % 187.68/187.64 [7452]~P1(f306(f306(f220(a865),x74521),f306(f306(f81(a865),x74523),x74522)))+P1(f306(f306(f220(a865),f306(f306(f22(a865),x74521),x74522)),x74523)) % 187.68/187.64 [7453]~P1(f306(f306(f221(a865),x74531),f306(f306(f22(a865),x74533),x74532)))+P1(f306(f306(f221(a865),f306(f306(f81(a865),x74531),x74532)),x74533)) % 187.68/187.64 [7509]E(x75091,f120(x75092))+E(f306(f133(x75092),f306(f306(f306(f180(f866(x75092),f866(x75092)),x75093),f160(x75092)),x75091)),f306(f306(f157(x75092),x75091),f46(a865,x75093,f306(f186(f866(x75092)),x75091)))) % 187.68/187.64 [7518]E(f306(f306(f284(x75181),x75182),f306(f306(f22(f872(x75181,a859)),x75183),f306(f306(f284(x75181),x75182),f185(f872(x75181,a859))))),x75183)+~P1(f306(f306(f308(x75181),x75182),x75183)) % 187.68/187.64 [7680]P1(f306(f306(f220(a865),x76801),f306(f306(f81(a865),x76802),x76803)))+~P1(f306(f306(f220(a865),f306(f306(f22(a865),x76801),x76803)),x76802)) % 187.68/187.64 [7681]P1(f306(f306(f221(a865),x76811),f306(f306(f22(a865),x76812),x76813)))+~P1(f306(f306(f221(a865),f306(f306(f81(a865),x76811),x76813)),x76812)) % 187.68/187.64 [7703]P1(f306(f63(x77031),x77032))+~P1(f306(f63(x77031),f306(f306(f108(f872(x77031,a859)),x77033),x77032))) % 187.68/187.64 [7704]P1(f306(f63(x77041),x77042))+~P1(f306(f63(x77041),f306(f306(f108(f872(x77041,a859)),x77042),x77043))) % 187.68/187.64 [7779]~P47(x77791,x77793)+P1(f306(f306(f308(f871(x77791,x77791)),f306(f306(f236(x77791,x77791),x77792),x77792)),x77793)) % 187.68/187.64 [7913]E(f306(f306(f157(a865),f131(a865,f306(f276(a865,x79131),x79132))),x79133),f306(f306(f81(a865),x79131),x79133))+~P1(f306(f306(f221(a865),f306(f306(f81(a865),x79131),x79133)),x79132)) % 187.68/187.64 [7981]~P1(f306(f306(f193(f306(a26,x79811)),x79812),x79813))+P1(f306(f306(f193(f306(f218(a860),f306(a28,x79811))),x79812),x79813)) % 187.68/187.64 [7986]E(f306(f306(f165(a865),x79861),f131(a865,f306(f276(a865,x79862),x79863))),f131(a865,f306(f276(a865,x79862),f306(f306(f81(a865),x79862),x79861))))+~P1(f306(f306(f220(a865),f306(f306(f81(a865),x79862),x79861)),x79863)) % 187.68/187.64 [8040]~P91(x80401)+E(f306(f306(f237(x80401),x80402),f306(f111(a865),f306(f306(f81(a1),x80403),x80403))),f306(f306(f87(x80401,x80401),f306(f306(f237(x80401),x80402),f306(f111(a865),x80403))),f306(f306(f18(x80401,x80401,x80401),f82(x80401)),f5(x80401)))) % 187.68/187.64 [8250]P1(f306(f306(f193(f306(a26,x82501)),x82502),x82503))+~P1(f306(f306(f193(f306(f218(a860),f306(a28,x82501))),x82502),x82503)) % 187.68/187.64 [8311]E(f306(f306(f122(x83111),f306(f306(f165(x83111),x83112),x83113)),f306(f306(f143(x83111),f306(f306(f157(x83111),x83113),x83112)),f306(f306(f130(x83111),f306(a119,x83112)),x83113))),x83113)+~P1(f306(f306(f221(a865),x83112),f306(f186(f866(x83111)),x83113))) % 187.68/187.64 [8318]P1(f306(f306(f220(f872(x83181,a859)),f294(x83181,x83182)),f294(x83181,x83183)))+~P1(f306(f306(f220(f872(x83181,f872(x83181,a859))),x83183),x83182)) % 187.68/187.64 [8320]~P55(x83201,x83202,x83203)+P55(x83201,x83202,f306(f306(f22(f872(f871(x83201,x83201),a859)),x83203),f282(x83201,f185(f872(f871(x83201,x83201),a859))))) % 187.68/187.64 [8337]P1(f306(f306(f220(f872(x83371,a859)),f295(x83371,x83372)),f295(x83371,x83373)))+~P1(f306(f306(f220(f872(f871(x83371,x83371),a859)),x83373),x83372)) % 187.68/187.64 [8344]~P123(x83441)+P1(f306(f306(f220(x83441),f2(x83441)),f306(f306(f81(x83441),f306(f306(f82(x83441),x83442),x83442)),f306(f306(f82(x83441),x83443),x83443)))) % 187.68/187.64 [8379]P1(f306(f306(f220(f872(x83791,a859)),f306(f259(x83791),x83792)),f306(f259(x83791),x83793)))+~P1(f306(f306(f220(f872(f871(x83791,x83791),a859)),x83792),x83793)) % 187.68/187.64 [8413]~P51(x84131,x84132)+~P1(f306(f306(f308(f871(x84131,x84131)),f306(f306(f236(x84131,x84131),x84133),x84133)),x84132)) % 187.68/187.64 [8415]~P40(x84151,x84152)+~P1(f306(f306(f308(f871(x84151,x84151)),f306(f306(f236(x84151,x84151),x84153),x84153)),x84152)) % 187.68/187.64 [8479]P1(f306(f306(f220(f872(x84791,a859)),f42(f872(x84791,a859),x84792)),f42(f872(x84791,a859),x84793)))+~P1(f306(f306(f220(f872(f872(x84791,a859),a859)),x84793),x84792)) % 187.68/187.64 [8480]P1(f306(f306(f220(f872(x84801,a859)),f41(f872(x84801,a859),x84802)),f41(f872(x84801,a859),x84803)))+~P1(f306(f306(f220(f872(f872(x84801,a859),a859)),x84802),x84803)) % 187.68/187.64 [8532]~P9(x85321,x85323,x85322)+P1(f306(f306(f220(f872(f871(x85321,x85321),a859)),x85322),f306(f306(f243(x85321,x85321),x85323),f306(f16(f872(x85321,a859),x85321),x85323)))) % 187.68/187.64 [8533]~P50(x85331,x85333,x85332)+P1(f306(f306(f220(f872(f871(x85331,x85331),a859)),x85332),f306(f306(f243(x85331,x85331),x85333),f306(f16(f872(x85331,a859),x85331),x85333)))) % 187.68/187.64 [8580]~P84(x85801)+P1(f306(f306(f220(x85801),f306(f306(f22(x85801),f306(f76(x85801),x85802)),f306(f76(x85801),x85803))),f306(f76(x85801),f306(f306(f22(x85801),x85803),x85802)))) % 187.68/187.64 [8581]~P84(x85811)+P1(f306(f306(f220(x85811),f306(f306(f22(x85811),f306(f76(x85811),x85812)),f306(f76(x85811),x85813))),f306(f76(x85811),f306(f306(f22(x85811),x85812),x85813)))) % 187.68/187.64 [8611]P1(f306(f306(f220(f872(f871(x86111,x86111),a859)),f282(x86111,x86112)),f282(x86111,x86113)))+~P1(f306(f306(f220(f872(f871(x86111,x86111),a859)),x86112),x86113)) % 187.68/187.64 [8764]P55(x87641,x87642,x87643)+~P55(x87641,x87642,f306(f306(f22(f872(f871(x87641,x87641),a859)),x87643),f282(x87641,f185(f872(f871(x87641,x87641),a859))))) % 187.68/187.64 [8783]P1(f306(f306(f220(f872(f871(f866(x87831),f866(x87831)),a859)),f150(x87831,x87832)),f150(x87831,x87833)))+~P1(f306(f306(f220(f872(f871(x87831,x87831),a859)),x87832),x87833)) % 187.68/187.64 [8784]P1(f306(f306(f220(f872(f871(f866(x87841),f866(x87841)),a859)),f149(x87841,x87842)),f149(x87841,x87843)))+~P1(f306(f306(f220(f872(f871(x87841,x87841),a859)),x87842),x87843)) % 187.68/187.64 [8803]~P50(x88031,x88033,x88032)+P1(f306(f306(f220(f872(f871(x88031,x88031),a859)),x88032),f306(f306(f263(x88031,x88031,x88031),f306(f261(x88031,x88031),x88032)),x88032))) % 187.68/187.64 [8853]~P1(f306(f129(x88531),x88532))+E(f306(f128(x88531,f306(f306(f7(x88531,f872(x88531,a859),a859),f308(x88531)),f306(f164(x88531),f166(x88531,x88532,x88533)))),x88532),f166(x88531,x88532,x88533)) % 187.68/187.64 [8916]E(x89161,x89162)+~P1(f306(f306(f308(f871(x89163,x89163)),f306(f306(f236(x89163,x89163),x89161),x89162)),f282(x89163,f185(f872(f871(x89163,x89163),a859))))) % 187.68/187.64 [9003]P1(f306(f306(f308(x90031),x90032),f295(x90031,x90033)))+P1(f306(f306(f308(f871(x90031,x90031)),f306(f306(f236(x90031,x90031),f488(x90033,x90032,x90031)),x90032)),x90033)) % 187.68/187.64 [9004]P1(f306(f306(f308(x90041),x90042),f295(x90041,x90043)))+P1(f306(f306(f308(f871(x90041,x90041)),f306(f306(f236(x90041,x90041),f571(x90043,x90042,x90041)),x90042)),x90043)) % 187.68/187.64 [9005]P1(f306(f306(f308(x90051),x90052),f295(x90051,x90053)))+P1(f306(f306(f308(f871(x90051,x90051)),f306(f306(f236(x90051,x90051),f573(x90053,x90052,x90051)),x90052)),x90053)) % 187.68/187.64 [9090]~P1(f306(f306(f308(f866(x90901)),x90903),f153(x90901,x90902)))+P1(f306(f152(x90901,f306(f306(f7(x90901,f872(x90901,a859),a859),f308(x90901)),x90902)),x90903)) % 187.68/187.64 [9113]P1(f306(x91133,x91132))+E(f306(f228(x91131),f306(f306(f18(x91131,a859,a859),f306(f306(f8(a859,f872(a859,a859),x91131),a304),f306(a303,x91132))),x91133)),f185(f872(x91131,a859))) % 187.68/187.64 [9134]~P84(x91341)+P1(f306(f306(f220(x91341),f306(f76(x91341),f306(f306(f22(x91341),f306(f76(x91341),x91342)),f306(f76(x91341),x91343)))),f306(f76(x91341),f306(f306(f22(x91341),x91342),x91343)))) % 187.68/187.64 [9149]~P1(f306(x91493,x91492))+E(f306(f228(x91491),f306(f306(f18(x91491,a859,a859),f306(f306(f8(a859,f872(a859,a859),x91491),a304),f306(a303,x91492))),x91493)),f306(f306(f284(x91491),x91492),f185(f872(x91491,a859)))) % 187.68/187.64 [9156]~P1(f306(f306(f308(f872(x91561,a859)),x91563),f306(f283(x91561),x91562)))+P1(f306(f240(x91561,f306(f306(f7(x91561,f872(x91561,a859),a859),f308(x91561)),x91562)),x91563)) % 187.68/187.64 [9189]P40(x91891,x91892)+P1(f306(f306(f308(f871(x91891,x91891)),f306(f306(f236(x91891,x91891),f306(f531(x91892,x91891),f306(a119,x91893))),f306(f531(x91892,x91891),x91893))),x91892)) % 187.68/187.64 [9333]P1(f306(f306(f308(f866(x93331)),x93332),f153(x93331,x93333)))+~P1(f306(f152(x93331,f306(f306(f7(x93331,f872(x93331,a859),a859),f308(x93331)),x93333)),x93332)) % 187.68/187.64 [9346]P1(f306(f306(f308(f872(x93461,a859)),x93462),f306(f283(x93461),x93463)))+~P1(f306(f240(x93461,f306(f306(f7(x93461,f872(x93461,a859),a859),f308(x93461)),x93463)),x93462)) % 187.68/187.64 [9405]P1(f306(f306(f308(x94051),f306(f252(x94051,x94052),x94053)),f306(f164(x94051),f306(f306(f146(f871(a106,x94051),x94051),f244(a106,x94051)),x94052))))+~P1(f306(f306(f221(a106),x94053),f306(f158(a106),f306(f306(f146(f871(a106,x94051),a106),f235(a106,x94051)),x94052)))) % 187.68/187.64 [9453]P1(f306(f306(f220(f872(f871(f866(x94531),f866(x94531)),a859)),f150(x94531,x94532)),f306(f306(f243(f866(x94531),f866(x94531)),f153(x94531,x94533)),f306(f16(f872(f866(x94531),a859),f866(x94531)),f153(x94531,x94533)))))+~P1(f306(f306(f220(f872(f871(x94531,x94531),a859)),x94532),f306(f306(f243(x94531,x94531),x94533),f306(f16(f872(x94531,a859),x94531),x94533)))) % 187.68/187.64 [9474]P1(f306(f306(f308(x94741),f306(f235(x94741,f871(a106,a106)),f306(f250(x94741,x94742),x94743))),f306(f164(x94741),f306(f306(f146(f871(a106,x94741),x94741),f244(a106,x94741)),x94742))))+~P1(f306(f306(f221(a106),f2(a106)),f306(f158(a106),f306(f306(f146(f871(a106,x94741),a106),f235(a106,x94741)),x94742)))) % 187.68/187.64 [9493]~P1(f306(f306(f220(f872(f871(x94931,x94931),a859)),x94932),f306(f306(f243(x94931,x94931),x94933),f306(f16(f872(x94931,a859),x94931),x94933))))+P1(f306(f306(f220(f872(f871(x94931,x94931),a859)),f306(f306(f263(x94931,x94931,x94931),x94932),f282(x94931,x94932))),f306(f306(f243(x94931,x94931),x94933),f306(f16(f872(x94931,a859),x94931),x94933)))) % 187.68/187.64 [9797]~P40(x97971,x97972)+~P1(f306(f306(f308(f871(x97971,x97971)),f306(f306(f236(x97971,x97971),f306(x97973,f306(a119,f532(x97972,x97971,x97973)))),f306(x97973,f532(x97972,x97971,x97973)))),x97972)) % 187.68/187.64 [9798]~P40(x97981,x97982)+~P1(f306(f306(f308(f871(x97981,x97981)),f306(f306(f236(x97981,x97981),f306(x97983,f306(a119,f587(x97983,x97982,x97981)))),f306(x97983,f587(x97983,x97982,x97981)))),x97982)) % 187.68/187.64 [10055]P1(f306(f306(f220(f872(f871(f872(x100551,a859),f872(x100551,a859)),a859)),f306(f306(f263(f872(x100551,a859),f872(x100551,a859),f872(x100551,a859)),f297(x100551,x100552)),f306(f306(f108(f872(f871(f872(x100551,a859),f872(x100551,a859)),a859)),f297(x100551,x100553)),f306(f306(f284(f871(f872(x100551,a859),f872(x100551,a859))),f306(f306(f236(f872(x100551,a859),f872(x100551,a859)),f185(f872(x100551,a859))),f185(f872(x100551,a859)))),f185(f872(f871(f872(x100551,a859),f872(x100551,a859)),a859)))))),f297(x100551,x100552)))+~P1(f306(f306(f220(f872(f871(x100551,x100551),a859)),f306(f306(f263(x100551,x100551,x100551),x100552),x100553)),x100552)) % 187.68/187.64 [10056]P1(f306(f306(f220(f872(f871(f872(x100561,a859),f872(x100561,a859)),a859)),f306(f306(f263(f872(x100561,a859),f872(x100561,a859),f872(x100561,a859)),f298(x100561,x100562)),f306(f306(f108(f872(f871(f872(x100561,a859),f872(x100561,a859)),a859)),f298(x100561,x100563)),f306(f306(f284(f871(f872(x100561,a859),f872(x100561,a859))),f306(f306(f236(f872(x100561,a859),f872(x100561,a859)),f185(f872(x100561,a859))),f185(f872(x100561,a859)))),f185(f872(f871(f872(x100561,a859),f872(x100561,a859)),a859)))))),f298(x100561,x100562)))+~P1(f306(f306(f220(f872(f871(x100561,x100561),a859)),f306(f306(f263(x100561,x100561,x100561),x100562),x100563)),x100562)) % 187.68/187.64 [7214]~P1(f306(f306(f220(a865),x72142),x72141))+E(f306(f306(f22(a865),f306(a119,f306(f306(f22(a865),x72141),x72142))),x72143),f306(f306(f22(a865),f306(a119,x72141)),f306(f306(f81(a865),x72142),x72143))) % 187.68/187.64 [7253]~P4(x72531)+E(f306(f306(f81(x72531),f46(x72531,x72532,x72533)),f306(f306(f82(x72531),f306(f306(f40(x72531),x72532),x72533)),x72533)),x72532) % 187.68/187.64 [7457]E(f306(f306(f82(a865),f306(f111(a865),x74571)),f306(f306(f82(a865),f306(f111(a865),x74572)),x74573)),f306(f306(f82(a865),f306(f111(a865),f306(f306(f82(a1),x74571),x74572))),x74573))+P1(f306(f306(f221(a1),x74571),a84)) % 187.68/187.64 [7922]~P1(f306(f306(f220(a865),x79223),x79222))+P1(f306(f306(f220(a865),x79221),f306(f306(f22(a865),f306(f306(f81(a865),x79222),x79221)),x79223))) % 187.68/187.64 [8130]~P1(f306(f306(f220(a865),x81301),x81302))+E(f306(f306(f122(a865),f131(a865,f306(f276(a865,x81301),x81302))),f131(a865,f306(f276(a865,x81302),f306(f306(f81(a865),x81302),x81303)))),f131(a865,f306(f276(a865,x81301),f306(f306(f81(a865),x81302),x81303)))) % 187.68/187.64 [8387]~P1(f306(f63(x83871),x83872))+E(f306(a119,f306(f39(x83871),f306(f306(f22(f872(x83871,a859)),x83872),f306(f306(f284(x83871),x83873),f185(f872(x83871,a859)))))),f306(f39(x83871),f306(f306(f284(x83871),x83873),x83872))) % 187.68/187.64 [8437]~P1(f306(f63(x84371),x84372))+E(f306(f306(f81(a865),f79(a865)),f306(f39(x84371),f306(f306(f22(f872(x84371,a859)),x84372),f306(f306(f284(x84371),x84373),f185(f872(x84371,a859)))))),f306(f39(x84371),f306(f306(f284(x84371),x84373),x84372))) % 187.68/187.64 [8620]E(f306(f306(f22(a865),f306(f39(x86201),x86202)),f306(f39(x86201),f306(f306(f109(f872(x86201,a859)),x86202),x86203))),f306(f39(x86201),f306(f306(f22(f872(x86201,a859)),x86202),x86203)))+~P1(f306(f63(x86201),f306(f306(f109(f872(x86201,a859)),x86202),x86203))) % 187.68/187.64 [8849]~P7(f306(x88492,f367(x88492,x88493,x88491)))+E(f306(f107(a1),f306(f306(f9(x88491,a865),f306(f306(f8(a1,a865,x88491),a112),x88492)),x88493)),f306(f306(f9(x88491,a1),x88492),x88493)) % 187.68/187.64 [8850]~P7(f306(x88502,f417(x88502,x88503,x88501)))+E(f306(f107(a1),f306(f306(f6(x88501,a865),f306(f306(f8(a1,a865,x88501),a112),x88502)),x88503)),f306(f306(f6(x88501,a1),x88502),x88503)) % 187.68/187.64 [8898]~P1(f306(f63(x88981),x88983))+P1(f306(f306(f220(a865),f306(f306(f22(a865),f306(f39(x88981),x88982)),f306(f39(x88981),x88983))),f306(f39(x88981),f306(f306(f22(f872(x88981,a859)),x88982),x88983)))) % 187.68/187.64 [8925]P1(f306(f306(f308(x89251),f367(x89252,x89253,x89251)),x89253))+E(f306(f107(a1),f306(f306(f9(x89251,a865),f306(f306(f8(a1,a865,x89251),a112),x89252)),x89253)),f306(f306(f9(x89251,a1),x89252),x89253)) % 187.68/187.64 [8926]P1(f306(f306(f308(x89261),f417(x89262,x89263,x89261)),x89263))+E(f306(f107(a1),f306(f306(f6(x89261,a865),f306(f306(f8(a1,a865,x89261),a112),x89262)),x89263)),f306(f306(f6(x89261,a1),x89262),x89263)) % 187.68/187.64 [8995]E(f86(x89951,f306(f306(f7(x89951,f872(x89951,a859),a859),f308(x89951)),f306(f306(f22(f872(x89951,a859)),x89952),f306(f306(f284(x89951),x89953),f185(f872(x89951,a859)))))),f239(x89951,x89953,x89952))+P1(f306(f306(f220(f872(x89951,a859)),x89952),f306(f306(f284(x89951),x89953),f185(f872(x89951,a859))))) % 187.68/187.64 [9347]E(f306(f306(f146(f866(x93471),x93471),f306(f306(f7(f866(x93471),a865,x93471),f157(x93471)),x93472)),f306(f128(f866(x93471),f306(f306(f8(a865,a859,f866(x93471)),f306(f221(a865),x93472)),f186(f866(x93471)))),x93473)),f306(f306(f157(f866(x93471)),f171(x93471,x93473)),x93472))+~P1(f306(f306(f221(a865),x93472),f306(f186(f866(f866(x93471))),f171(x93471,x93473)))) % 187.68/187.64 [9422]E(f306(f128(x94221,x94222),x94223),f168(x94221,x94222,x94223))+P1(f306(f306(f308(x94221),f747(x94223,x94222,x94221)),f306(f164(x94221),f306(f306(f130(x94221),f306(f186(f866(x94221)),f168(x94221,x94222,x94223))),x94223)))) % 187.68/187.64 [9565]E(f306(f306(f130(x95651),f306(f186(f866(x95651)),f168(x95651,x95652,x95653))),x95653),f120(x95651))+~P1(f306(x95652,f306(f133(x95651),f306(f306(f130(x95651),f306(f186(f866(x95651)),f168(x95651,x95652,x95653))),x95653)))) % 187.68/187.64 [9657]~P1(f306(f306(f308(f871(x96571,x96571)),x96572),f282(x96571,x96573)))+P1(f306(f306(f308(f871(x96571,x96571)),x96572),f306(f306(f43(a865,f872(f871(x96571,x96571),a859)),f231(f872(a865,a859))),f306(f306(f7(a865,f872(f871(x96571,x96571),a859),f872(f871(x96571,x96571),a859)),f180(f871(x96571,x96571),a859)),x96573)))) % 187.68/187.64 [9714]~P1(f306(f306(f220(f872(x97141,a859)),f306(f306(f43(a865,f872(x97141,a859)),f306(f276(a865,f2(a865)),f482(x97143,x97142,x97141))),x97142)),x97143))+P1(f306(f306(f220(f872(x97141,a859)),f306(f306(f43(a865,f872(x97141,a859)),f231(f872(a865,a859))),x97142)),x97143)) % 187.68/187.64 [9774]~P1(f306(f306(f221(a1),f2(a1)),x97743))+P1(f306(f306(f221(a1),x97741),f306(f306(f81(a1),x97742),f306(f306(f82(a1),f306(f306(f81(a1),f306(f76(a1),f306(f306(f22(a1),x97742),x97741))),f79(a1))),x97743)))) % 187.68/187.64 [9784]~P40(x97841,f306(f306(f108(f872(f871(x97841,x97841),a859)),x97842),x97843))+P40(x97841,f306(f306(f108(f872(f871(x97841,x97841),a859)),f306(f306(f108(f872(f871(x97841,x97841),a859)),f306(f306(f263(x97841,x97841,x97841),x97842),x97842)),f306(f306(f263(x97841,x97841,x97841),x97843),x97842))),x97843)) % 187.68/187.64 [9865]P40(x98651,f306(f306(f108(f872(f871(x98651,x98651),a859)),x98652),x98653))+~P40(x98651,f306(f306(f108(f872(f871(x98651,x98651),a859)),f306(f306(f108(f872(f871(x98651,x98651),a859)),f306(f306(f263(x98651,x98651,x98651),x98652),x98652)),f306(f306(f263(x98651,x98651,x98651),x98653),x98652))),x98653)) % 187.68/187.64 [9426]~P125(x94261)+E(f306(f110(x94261),f306(a90,f306(f260(f871(a865,a865),f871(a865,a865),a116),f306(f306(f284(f871(a865,a865)),f306(f306(f236(a865,a865),x94262),x94263)),f185(f872(f871(a865,a865),a859)))))),f306(f306(f22(x94261),f306(f107(x94261),x94262)),f306(f107(x94261),x94263))) % 187.68/187.64 [9511]P1(f306(x95113,x95112))+E(f306(f228(x95111),f306(f306(f18(x95111,a859,a859),f306(f306(f8(a859,f872(a859,a859),x95111),a304),f306(f306(f7(x95111,x95111,a859),a303),x95112))),x95113)),f185(f872(x95111,a859))) % 187.68/187.64 [9513]~P1(f306(x95133,x95132))+E(f306(f228(x95131),f306(f306(f18(x95131,a859,a859),f306(f306(f8(a859,f872(a859,a859),x95131),a304),f306(f306(f7(x95131,x95131,a859),a303),x95132))),x95133)),f306(f306(f284(x95131),x95132),f185(f872(x95131,a859)))) % 187.68/187.64 [9857]~P1(f306(f63(x98571),x98573))+E(f306(f306(f66(x98571,f872(x98571,a859),f306(f306(f8(f872(x98571,a859),f872(f872(x98571,a859),f872(x98571,a859)),x98571),f306(f7(f872(x98571,a859),f872(x98571,a859),f872(x98571,a859)),f22(f872(x98571,a859)))),f306(f306(f7(x98571,f872(x98571,a859),f872(x98571,a859)),f284(x98571)),f185(f872(x98571,a859))))),x98572),x98573),f306(f306(f22(f872(x98571,a859)),x98572),x98573)) % 187.68/187.64 [9891]~P1(f306(f306(f221(a1),f2(a1)),x98913))+P1(f306(f306(f221(a1),f306(f306(f22(a1),x98911),f306(f306(f82(a1),f306(f306(f81(a1),f306(f76(a1),f306(f306(f22(a1),x98911),x98912))),f79(a1))),x98913))),x98912)) % 187.68/187.64 [10122]~P1(f306(f306(f308(x101221),x101223),f295(x101221,x101222)))+P1(f306(f294(x101221,f306(f306(f7(x101221,f872(f871(x101221,x101221),a859),f872(x101221,a859)),f306(f306(f8(f872(x101221,f872(f872(f871(x101221,x101221),a859),a859)),f872(f872(f871(x101221,x101221),a859),f872(x101221,a859)),x101221),f7(x101221,f872(f871(x101221,x101221),a859),a859)),f306(f306(f8(f872(x101221,f871(x101221,x101221)),f872(x101221,f872(f872(f871(x101221,x101221),a859),a859)),x101221),f306(f8(f871(x101221,x101221),f872(f872(f871(x101221,x101221),a859),a859),x101221),f308(f871(x101221,x101221)))),f236(x101221,x101221)))),x101222)),x101223)) % 187.68/187.64 [10135]P1(f306(f306(f308(x101351),x101352),f295(x101351,x101353)))+~P1(f306(f294(x101351,f306(f306(f7(x101351,f872(f871(x101351,x101351),a859),f872(x101351,a859)),f306(f306(f8(f872(x101351,f872(f872(f871(x101351,x101351),a859),a859)),f872(f872(f871(x101351,x101351),a859),f872(x101351,a859)),x101351),f7(x101351,f872(f871(x101351,x101351),a859),a859)),f306(f306(f8(f872(x101351,f871(x101351,x101351)),f872(x101351,f872(f872(f871(x101351,x101351),a859),a859)),x101351),f306(f8(f871(x101351,x101351),f872(f872(f871(x101351,x101351),a859),a859),x101351),f308(f871(x101351,x101351)))),f236(x101351,x101351)))),x101353)),x101352)) % 187.68/187.64 [9712]~P1(f306(f63(x97121),f306(f228(x97121),x97123)))+P1(f306(f63(x97121),f306(f228(x97121),f306(f306(f18(x97121,a859,a859),f306(f306(f8(a859,f872(a859,a859),x97121),a304),x97122)),x97123)))) % 187.68/187.64 [9713]~P1(f306(f63(x97131),f306(f228(x97131),x97132)))+P1(f306(f63(x97131),f306(f228(x97131),f306(f306(f18(x97131,a859,a859),f306(f306(f8(a859,f872(a859,a859),x97131),a304),x97132)),x97133)))) % 187.68/187.64 [9815]P1(f306(f63(x98151),f306(f228(x98151),x98152)))+~P1(f306(f63(x98151),f306(f228(x98151),f306(f306(f18(x98151,a859,a859),f306(f306(f8(a859,f872(a859,a859),x98151),a305),x98153)),x98152)))) % 187.68/187.64 [9816]P1(f306(f63(x98161),f306(f228(x98161),x98162)))+~P1(f306(f63(x98161),f306(f228(x98161),f306(f306(f18(x98161,a859,a859),f306(f306(f8(a859,f872(a859,a859),x98161),a305),x98162)),x98163)))) % 187.68/187.64 [10105]~P1(f306(f63(x101051),x101052))+P1(f306(f63(f866(x101051)),f306(f228(f866(x101051)),f306(f306(f18(f866(x101051),a859,a859),f306(f306(f8(a859,f872(a859,a859),f866(x101051)),a304),f306(f306(f7(f866(x101051),f872(x101051,a859),a859),f306(f306(f8(f872(x101051,a859),f872(f872(x101051,a859),a859),f866(x101051)),f220(f872(x101051,a859))),f164(x101051))),x101052))),f306(f306(f7(f866(x101051),a865,a859),f306(f306(f8(a865,f872(a865,a859),f866(x101051)),a303),f186(f866(x101051)))),x101053))))) % 187.68/187.64 [10106]~P1(f306(f63(x101061),x101062))+P1(f306(f63(f866(x101061)),f306(f228(f866(x101061)),f306(f306(f18(f866(x101061),a859,a859),f306(f306(f8(a859,f872(a859,a859),f866(x101061)),a304),f306(f306(f7(f866(x101061),f872(x101061,a859),a859),f306(f306(f8(f872(x101061,a859),f872(f872(x101061,a859),a859),f866(x101061)),f220(f872(x101061,a859))),f164(x101061))),x101062))),f306(f306(f7(f866(x101061),a865,a859),f306(f306(f8(a865,f872(a865,a859),f866(x101061)),f220(a865)),f186(f866(x101061)))),x101063))))) % 187.68/187.64 [9831]~P113(x98311)+E(f306(f306(f237(x98311),x98312),f306(f306(f82(a865),f306(f111(a865),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)))),x98313)),f306(f306(f82(x98311),f306(f306(f237(x98311),x98312),x98313)),f306(f306(f237(x98311),x98312),x98313))) % 187.68/187.64 [9870]~P80(x98701)+E(f306(f306(f237(x98701),f306(f306(f237(x98701),x98702),x98703)),f306(f111(a865),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)))),f306(f306(f237(x98701),x98702),f306(f306(f82(a865),f306(f111(a865),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)))),x98703))) % 187.68/187.64 [9918]~P125(x99181)+E(f306(f306(f237(x99181),f306(f80(x99181),x99182)),f306(f306(f82(a865),f306(f111(a865),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)))),x99183)),f306(f306(f237(x99181),x99182),f306(f306(f82(a865),f306(f111(a865),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)))),x99183))) % 187.68/187.64 [10062]~P112(x100621)+P1(f306(f306(f220(x100621),f2(x100621)),f306(f306(f81(x100621),f306(f306(f237(x100621),x100622),f306(f111(a865),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104))))),f306(f306(f237(x100621),x100623),f306(f111(a865),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104))))))) % 187.68/187.64 [9928]~P113(x99281)+E(f306(f306(f237(x99281),x99282),f306(a119,f306(f306(f82(a865),f306(f111(a865),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)))),x99283))),f306(f306(f82(x99281),x99282),f306(f306(f82(x99281),f306(f306(f237(x99281),x99282),x99283)),f306(f306(f237(x99281),x99282),x99283)))) % 187.68/187.64 [9979]~P80(x99791)+E(f306(f306(f82(x99791),x99792),f306(f306(f237(x99791),f306(f306(f237(x99791),x99792),x99793)),f306(f111(a865),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104))))),f306(f306(f237(x99791),x99792),f306(a119,f306(f306(f82(a865),f306(f111(a865),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)))),x99793)))) % 187.68/187.64 [10018]~P112(x100181)+P1(f306(f306(f220(x100181),f2(x100181)),f306(f306(f237(x100181),x100182),f306(f306(f82(a865),f306(f111(a865),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)))),x100183)))) % 187.68/187.64 [10085]~P91(x100851)+E(f306(f306(f22(x100851),f306(f306(f81(x100851),f306(f306(f237(x100851),x100852),f306(f111(a865),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104))))),f306(f306(f237(x100851),x100853),f306(f111(a865),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)))))),f306(f306(f82(x100851),f306(f306(f82(x100851),f306(f111(x100851),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)))),x100852)),x100853)),f306(f306(f237(x100851),f306(f306(f22(x100851),x100852),x100853)),f306(f111(a865),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104))))) % 187.68/187.64 [10086]~P91(x100861)+E(f306(f306(f81(x100861),f306(f306(f81(x100861),f306(f306(f237(x100861),x100862),f306(f111(a865),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104))))),f306(f306(f237(x100861),x100863),f306(f111(a865),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)))))),f306(f306(f82(x100861),f306(f306(f82(x100861),f306(f111(x100861),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)))),x100862)),x100863)),f306(f306(f237(x100861),f306(f306(f81(x100861),x100862),x100863)),f306(f111(a865),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104))))) % 187.68/187.64 [10189]~P30(x101891,x101892,x101893)+P1(f100(x101891,a859,f306(f306(f8(f872(a860,f872(f872(x101891,f872(a861,a859)),f872(x101891,a859))),f872(a860,f872(f872(x101891,f872(a861,a859)),a859)),f872(x101891,f872(a861,a859))),f306(f8(f872(f872(x101891,f872(a861,a859)),f872(x101891,a859)),f872(f872(x101891,f872(a861,a859)),a859),a860),f306(f8(f872(x101891,a859),a859,f872(x101891,f872(a861,a859))),f89(x101891)))),f306(f306(f8(f872(a860,f872(f872(x101891,f872(a861,a859)),f872(x101891,f872(a861,a859)))),f872(a860,f872(f872(x101891,f872(a861,a859)),f872(x101891,a859))),f872(x101891,f872(a861,a859))),f306(f8(f872(f872(x101891,f872(a861,a859)),f872(x101891,f872(a861,a859))),f872(f872(x101891,f872(a861,a859)),f872(x101891,a859)),a860),f306(f8(f872(x101891,f872(a861,a859)),f872(x101891,a859),f872(x101891,f872(a861,a859))),f306(f8(f872(a861,a859),a859,x101891),f89(a861))))),f306(f306(f7(f872(x101891,f872(a861,a859)),f872(a860,f872(f872(x101891,f872(a861,a859)),f872(x101891,f872(a861,a859)))),f872(a860,f872(f872(x101891,f872(a861,a859)),f872(x101891,f872(a861,a859))))),f306(f306(f8(f872(f872(f872(x101891,f872(a861,a859)),f872(x101891,f872(a861,a859))),f872(f872(x101891,f872(a861,a859)),f872(x101891,f872(a861,a859)))),f872(f872(a860,f872(f872(x101891,f872(a861,a859)),f872(x101891,f872(a861,a859)))),f872(a860,f872(f872(x101891,f872(a861,a859)),f872(x101891,f872(a861,a859))))),f872(x101891,f872(a861,a859))),f8(f872(f872(x101891,f872(a861,a859)),f872(x101891,f872(a861,a859))),f872(f872(x101891,f872(a861,a859)),f872(x101891,f872(a861,a859))),a860)),f306(f306(f8(f872(f872(x101891,f872(a861,a859)),f872(x101891,f872(a861,a859))),f872(f872(f872(x101891,f872(a861,a859)),f872(x101891,f872(a861,a859))),f872(f872(x101891,f872(a861,a859)),f872(x101891,f872(a861,a859)))),f872(x101891,f872(a861,a859))),f8(f872(x101891,f872(a861,a859)),f872(x101891,f872(a861,a859)),f872(x101891,f872(a861,a859)))),f306(f306(f8(f872(x101891,f872(f872(a861,a859),f872(a861,a859))),f872(f872(x101891,f872(a861,a859)),f872(x101891,f872(a861,a859))),f872(x101891,f872(a861,a859))),f18(x101891,f872(a861,a859),f872(a861,a859))),f306(f306(f8(f872(x101891,f872(a861,f872(a859,a859))),f872(x101891,f872(f872(a861,a859),f872(a861,a859))),f872(x101891,f872(a861,a859))),f306(f8(f872(a861,f872(a859,a859)),f872(f872(a861,a859),f872(a861,a859)),x101891),f18(a861,a859,a859))),f306(f8(f872(a861,a859),f872(a861,f872(a859,a859)),x101891),f306(f8(a859,f872(a859,a859),a861),a309))))))),f306(f306(f8(f872(f872(x101891,f872(a861,a859)),f872(x101891,f872(a861,f872(a861,a859)))),f872(f872(x101891,f872(a861,a859)),f872(x101891,f872(a861,a859))),a860),f306(f8(f872(x101891,f872(a861,f872(a861,a859))),f872(x101891,f872(a861,a859)),f872(x101891,f872(a861,a859))),f306(f8(f872(a861,f872(a861,a859)),f872(a861,a859),x101891),f306(f8(f872(a861,a859),a859,a861),f89(a861))))),f306(f306(f8(f872(f872(a861,a859),f872(a861,f872(a861,a859))),f872(f872(x101891,f872(a861,a859)),f872(x101891,f872(a861,f872(a861,a859)))),a860),f8(f872(a861,a859),f872(a861,f872(a861,a859)),x101891)),f306(f306(f8(f872(a861,f872(f872(a861,a859),f872(a861,a859))),f872(f872(a861,a859),f872(a861,f872(a861,a859))),a860),f7(a861,f872(a861,a859),f872(a861,a859))),f306(f306(f8(f872(a861,f872(a861,f872(a859,a859))),f872(a861,f872(f872(a861,a859),f872(a861,a859))),a860),f306(f8(f872(a861,f872(a859,a859)),f872(f872(a861,a859),f872(a861,a859)),a861),f18(a861,a859,a859))),f306(f306(f8(f872(a861,f872(a861,a859)),f872(a861,f872(a861,f872(a859,a859))),a860),f306(f8(f872(a861,a859),f872(a861,f872(a859,a859)),a861),f306(f8(a859,f872(a859,a859),a861),a309))),f306(f306(f7(a860,a865,f872(a861,f872(a861,a859))),f306(f306(f8(f872(a861,f872(a865,f872(a861,a859))),f872(a865,f872(a861,f872(a861,a859))),a860),f7(a861,a865,f872(a861,a859))),a195)),x101892))))))))),x101893)) % 187.68/187.64 [10191]P30(x101911,x101912,x101913)+~P1(f100(x101911,a859,f306(f306(f8(f872(a860,f872(f872(x101911,f872(a861,a859)),f872(x101911,a859))),f872(a860,f872(f872(x101911,f872(a861,a859)),a859)),f872(x101911,f872(a861,a859))),f306(f8(f872(f872(x101911,f872(a861,a859)),f872(x101911,a859)),f872(f872(x101911,f872(a861,a859)),a859),a860),f306(f8(f872(x101911,a859),a859,f872(x101911,f872(a861,a859))),f89(x101911)))),f306(f306(f8(f872(a860,f872(f872(x101911,f872(a861,a859)),f872(x101911,f872(a861,a859)))),f872(a860,f872(f872(x101911,f872(a861,a859)),f872(x101911,a859))),f872(x101911,f872(a861,a859))),f306(f8(f872(f872(x101911,f872(a861,a859)),f872(x101911,f872(a861,a859))),f872(f872(x101911,f872(a861,a859)),f872(x101911,a859)),a860),f306(f8(f872(x101911,f872(a861,a859)),f872(x101911,a859),f872(x101911,f872(a861,a859))),f306(f8(f872(a861,a859),a859,x101911),f89(a861))))),f306(f306(f7(f872(x101911,f872(a861,a859)),f872(a860,f872(f872(x101911,f872(a861,a859)),f872(x101911,f872(a861,a859)))),f872(a860,f872(f872(x101911,f872(a861,a859)),f872(x101911,f872(a861,a859))))),f306(f306(f8(f872(f872(f872(x101911,f872(a861,a859)),f872(x101911,f872(a861,a859))),f872(f872(x101911,f872(a861,a859)),f872(x101911,f872(a861,a859)))),f872(f872(a860,f872(f872(x101911,f872(a861,a859)),f872(x101911,f872(a861,a859)))),f872(a860,f872(f872(x101911,f872(a861,a859)),f872(x101911,f872(a861,a859))))),f872(x101911,f872(a861,a859))),f8(f872(f872(x101911,f872(a861,a859)),f872(x101911,f872(a861,a859))),f872(f872(x101911,f872(a861,a859)),f872(x101911,f872(a861,a859))),a860)),f306(f306(f8(f872(f872(x101911,f872(a861,a859)),f872(x101911,f872(a861,a859))),f872(f872(f872(x101911,f872(a861,a859)),f872(x101911,f872(a861,a859))),f872(f872(x101911,f872(a861,a859)),f872(x101911,f872(a861,a859)))),f872(x101911,f872(a861,a859))),f8(f872(x101911,f872(a861,a859)),f872(x101911,f872(a861,a859)),f872(x101911,f872(a861,a859)))),f306(f306(f8(f872(x101911,f872(f872(a861,a859),f872(a861,a859))),f872(f872(x101911,f872(a861,a859)),f872(x101911,f872(a861,a859))),f872(x101911,f872(a861,a859))),f18(x101911,f872(a861,a859),f872(a861,a859))),f306(f306(f8(f872(x101911,f872(a861,f872(a859,a859))),f872(x101911,f872(f872(a861,a859),f872(a861,a859))),f872(x101911,f872(a861,a859))),f306(f8(f872(a861,f872(a859,a859)),f872(f872(a861,a859),f872(a861,a859)),x101911),f18(a861,a859,a859))),f306(f8(f872(a861,a859),f872(a861,f872(a859,a859)),x101911),f306(f8(a859,f872(a859,a859),a861),a309))))))),f306(f306(f8(f872(f872(x101911,f872(a861,a859)),f872(x101911,f872(a861,f872(a861,a859)))),f872(f872(x101911,f872(a861,a859)),f872(x101911,f872(a861,a859))),a860),f306(f8(f872(x101911,f872(a861,f872(a861,a859))),f872(x101911,f872(a861,a859)),f872(x101911,f872(a861,a859))),f306(f8(f872(a861,f872(a861,a859)),f872(a861,a859),x101911),f306(f8(f872(a861,a859),a859,a861),f89(a861))))),f306(f306(f8(f872(f872(a861,a859),f872(a861,f872(a861,a859))),f872(f872(x101911,f872(a861,a859)),f872(x101911,f872(a861,f872(a861,a859)))),a860),f8(f872(a861,a859),f872(a861,f872(a861,a859)),x101911)),f306(f306(f8(f872(a861,f872(f872(a861,a859),f872(a861,a859))),f872(f872(a861,a859),f872(a861,f872(a861,a859))),a860),f7(a861,f872(a861,a859),f872(a861,a859))),f306(f306(f8(f872(a861,f872(a861,f872(a859,a859))),f872(a861,f872(f872(a861,a859),f872(a861,a859))),a860),f306(f8(f872(a861,f872(a859,a859)),f872(f872(a861,a859),f872(a861,a859)),a861),f18(a861,a859,a859))),f306(f306(f8(f872(a861,f872(a861,a859)),f872(a861,f872(a861,f872(a859,a859))),a860),f306(f8(f872(a861,a859),f872(a861,f872(a859,a859)),a861),f306(f8(a859,f872(a859,a859),a861),a309))),f306(f306(f7(a860,a865,f872(a861,f872(a861,a859))),f306(f306(f8(f872(a861,f872(a865,f872(a861,a859))),f872(a865,f872(a861,f872(a861,a859))),a860),f7(a861,a865,f872(a861,a859))),a195)),x101912))))))))),x101913)) % 187.68/187.64 [4632]E(x46321,x46322)+~E(f34(x46323,x46321),f34(x46324,x46322)) % 187.68/187.64 [4633]E(x46331,x46332)+~E(f34(x46331,x46333),f34(x46332,x46334)) % 187.68/187.64 [4634]E(x46341,x46342)+~E(f33(x46343,x46341),f33(x46344,x46342)) % 187.68/187.64 [4635]E(x46351,x46352)+~E(f33(x46351,x46353),f33(x46352,x46354)) % 187.68/187.64 [7722]P28(x77221,x77222,x77223,x77224)+~E(f439(x77224,x77223,x77222,x77221),f453(x77224,x77223,x77222,x77221)) % 187.68/187.64 [8019]P37(x80191,x80192,x80193,x80194,f120(x80192))+~E(x80194,f120(x80191)) % 187.68/187.64 [8020]P37(x80201,x80202,x80203,f120(x80201),x80204)+~E(x80204,f120(x80202)) % 187.68/187.64 [8235]~P28(x82351,f869(x82352),x82354,f175(x82351,x82352,x82354))+P28(x82351,f869(x82352),f176(x82351,x82352,x82353,x82354),f175(x82351,x82352,x82354)) % 187.68/187.64 [8453]~P28(x84531,f869(x84532),f176(x84531,x84532,x84534,x84533),f175(x84531,x84532,x84533))+P28(x84531,f869(x84532),x84533,f175(x84531,x84532,x84533)) % 187.68/187.64 [8570]~P37(x85702,x85703,x85704,x85701,f120(x85703))+E(x85701,f120(x85702)) % 187.68/187.64 [8571]~P37(x85713,x85712,x85714,f120(x85713),x85711)+E(x85711,f120(x85712)) % 187.68/187.64 [5008]~P20(x50083,x50081,x50084)+E(f306(f306(x50081,x50082),x50082),x50082) % 187.68/187.64 [5304]~E(x53044,f185(f872(x53041,a859)))+E(f306(f285(x53041,x53042,x53043),x53044),f185(f872(x53042,a859))) % 187.68/187.64 [5572]~E(f306(f285(x55722,x55723,x55724),x55721),f185(f872(x55723,a859)))+E(x55721,f185(f872(x55722,a859))) % 187.68/187.64 [5857]~P108(x58572)+E(f306(f306(f140(x58571,x58572,x58573),x58574),f120(x58571)),f306(f306(f143(x58571),x58574),f120(x58571))) % 187.68/187.64 [5895]E(f306(x58951,x58952),f188(x58953))+P1(f306(f306(f308(x58954),x58952),f175(x58954,x58953,x58951))) % 187.68/187.64 [6219]~E(x62191,f185(f872(x62192,a859)))+~P1(f306(f64(x62192,x62193,x62191),x62194)) % 187.68/187.64 [6241]~P58(x62411,x62413,x62414,x62412)+P1(f306(f63(x62411),x62412)) % 187.68/187.64 [6242]~P58(x62421,x62423,x62422,x62424)+P1(f306(f63(x62421),x62422)) % 187.68/187.64 [6248]~P58(x62482,x62483,x62484,x62481)+~E(x62481,f185(f872(x62482,a859))) % 187.68/187.64 [6279]~P109(x62791)+E(f306(f306(f109(f872(x62791,a859)),f306(f276(x62791,x62792),x62793)),f277(x62791,x62793,x62794)),f185(f872(x62791,a859))) % 187.68/187.64 [6307]~P1(f306(f306(x63073,x63074),x63072))+P1(f306(f306(f308(x63071),x63072),f267(x63071,x63073,x63074))) % 187.68/187.64 [6308]~P1(f306(f306(x63083,x63084),x63082))+P1(f306(f306(f308(x63081),x63082),f268(x63081,x63083,x63084))) % 187.68/187.64 [6309]~P1(f306(f306(x63093,x63092),x63094))+P1(f306(f306(f308(x63091),x63092),f269(x63091,x63093,x63094))) % 187.68/187.64 [6310]~P1(f306(f306(x63103,x63102),x63104))+P1(f306(f306(f308(x63101),x63102),f272(x63101,x63103,x63104))) % 187.68/187.64 [6452]~P109(x64521)+E(f306(f306(f109(f872(x64521,a859)),f280(x64521,x64522,x64523)),f277(x64521,x64523,x64524)),f185(f872(x64521,a859))) % 187.68/187.64 [6453]~P109(x64531)+E(f306(f306(f109(f872(x64531,a859)),f279(x64531,x64532,x64533)),f280(x64531,x64533,x64534)),f185(f872(x64531,a859))) % 187.68/187.64 [6454]~P109(x64541)+E(f306(f306(f109(f872(x64541,a859)),f279(x64541,x64542,x64543)),f279(x64541,x64543,x64544)),f185(f872(x64541,a859))) % 187.68/187.64 [6455]~P109(x64551)+E(f306(f306(f109(f872(x64551,a859)),f277(x64551,x64552,x64553)),f280(x64551,x64553,x64554)),f185(f872(x64551,a859))) % 187.68/187.64 [6456]~P109(x64561)+E(f306(f306(f109(f872(x64561,a859)),f277(x64561,x64562,x64563)),f279(x64561,x64563,x64564)),f185(f872(x64561,a859))) % 187.68/187.64 [6490]P1(f306(f306(x64901,x64902),f530(x64902,x64901)))+~P1(f306(f241(x64903,x64904,x64901),x64902)) % 187.68/187.64 [6540]~E(f306(x65401,x65402),f188(x65403))+~P1(f306(f306(f308(x65404),x65402),f175(x65404,x65403,x65401))) % 187.68/187.64 [6569]~P108(x65692)+E(f306(f164(x65691),f142(x65691,x65692,x65693,x65694)),f306(f164(x65691),x65694)) % 187.68/187.64 [6622]~P141(x66221)+E(f187(x66221,x66222,f306(a119,x66223),x66224),f187(x66221,x66222,x66223,f306(x66222,x66224))) % 187.68/187.64 [6685]~P1(f306(f306(f308(x66854),x66853),f267(x66854,x66851,x66852)))+P1(f306(f306(x66851,x66852),x66853)) % 187.68/187.64 [6686]~P1(f306(f306(f308(x66864),x66863),f268(x66864,x66861,x66862)))+P1(f306(f306(x66861,x66862),x66863)) % 187.68/187.64 [6687]~P1(f306(f306(f308(x66874),x66872),f269(x66874,x66871,x66873)))+P1(f306(f306(x66871,x66872),x66873)) % 187.68/187.64 [6688]~P1(f306(f306(f308(x66884),x66882),f272(x66884,x66881,x66883)))+P1(f306(f306(x66881,x66882),x66883)) % 187.68/187.64 [6764]E(f306(f39(f870(x67641,x67642)),f293(x67641,x67642,x67643,x67644)),f2(a865))+P1(f306(f63(x67642),x67644)) % 187.68/187.64 [6765]E(f306(f39(f870(x67651,x67652)),f293(x67651,x67652,x67653,x67654)),f2(a865))+P1(f306(f63(x67651),x67653)) % 187.68/187.64 [6965]~P18(x69654,x69651,x69652)+E(f306(f74(x69651,x69651,x69651,f306(x69652,x69653)),f306(x69652,x69653)),f306(x69652,x69653)) % 187.68/187.64 [7759]~P1(f306(x77591,x77594))+P1(f306(x77591,f97(x77592,a865,x77593,x77591))) % 187.68/187.64 [7843]~E(x78432,x78433)+P1(f306(f306(f308(f871(x78431,x78431)),f306(f306(f236(x78431,x78431),x78432),x78433)),f282(x78431,x78434))) % 187.68/187.64 [7872]~P28(x78721,x78722,x78723,f231(f872(x78721,a859)))+E(f306(f78(x78721,x78722,f231(f872(x78721,a859)),x78723),f306(x78723,x78724)),x78724) % 187.68/187.64 [7964]~P1(f306(f306(f308(f866(x79641)),f306(f306(f143(x79641),x79644),x79642)),f153(x79641,x79643)))+P1(f306(f306(f308(f866(x79641)),x79642),f153(x79641,x79643))) % 187.68/187.64 [7965]~P1(f306(f306(f308(f866(x79651)),f306(f306(f122(x79651),x79654),x79652)),f153(x79651,x79653)))+P1(f306(f306(f308(f866(x79651)),x79652),f153(x79651,x79653))) % 187.68/187.64 [7966]~P1(f306(f306(f308(f866(x79661)),f306(f306(f122(x79661),x79662),x79664)),f153(x79661,x79663)))+P1(f306(f306(f308(f866(x79661)),x79662),f153(x79661,x79663))) % 187.68/187.64 [7982]~P108(x79821)+P17(x79821,f306(f306(f146(x79822,x79821),x79823),f142(x79822,x79821,x79823,x79824))) % 187.68/187.64 [8081]P28(x80814,x80813,x80811,x80812)+E(f306(x80811,f439(x80812,x80811,x80813,x80814)),f306(x80811,f453(x80812,x80811,x80813,x80814))) % 187.68/187.64 [8094]E(f176(x80941,x80942,x80943,x80944),f176(x80941,x80942,x80944,x80943))+~E(f306(f306(f109(f872(x80941,a859)),f175(x80941,x80942,x80943)),f175(x80941,x80942,x80944)),f185(f872(x80941,a859))) % 187.68/187.64 [8198]~P28(x81982,x81981,x81984,x81983)+P28(x81981,x81982,f78(x81982,x81981,x81983,x81984),f306(f285(x81982,x81981,x81984),x81983)) % 187.68/187.64 [8335]P40(f871(x83352,x83354),f258(x83352,x83354,x83351,x83353))+P1(f306(x83351,f537(x83352,x83353,x83354,x83351))) % 187.68/187.64 [8460]E(x84601,x84602)+~P1(f306(f306(f308(f871(x84603,x84603)),f306(f306(f236(x84603,x84603),x84601),x84602)),f233(x84603,x84604))) % 187.68/187.64 [8524]~P1(f306(f63(f870(x85243,x85241)),f293(x85243,x85241,x85244,x85242)))+P1(f306(f63(x85241),x85242)) % 187.68/187.64 [8525]~P1(f306(f63(f870(x85251,x85253)),f293(x85251,x85253,x85252,x85254)))+P1(f306(f63(x85251),x85252)) % 187.68/187.64 [8701]P40(f871(x87011,x87012),f258(x87011,x87012,x87013,x87014))+~P40(x87012,f306(x87014,f537(x87011,x87014,x87012,x87013))) % 187.68/187.64 [9269]E(f306(f306(f151(x92691,x92692),f701(x92693,x92694,x92692,x92691)),f702(x92693,x92694,x92692,x92691)),x92694)+~P1(f306(f306(f308(f871(f866(x92691),f866(x92691))),f306(f306(f236(f866(x92691),f866(x92691)),x92692),x92694)),f149(x92691,x92693))) % 187.68/187.64 [9270]~P1(f306(x92703,x92704))+P1(f306(f306(f220(a865),f306(x92701,f97(x92702,a865,x92701,x92703))),f306(x92701,x92704))) % 187.68/187.64 [9276]~P1(f306(f306(f308(f871(f866(x92761),f866(x92761))),f306(f306(f236(f866(x92761),f866(x92761)),x92762),x92763)),f137(x92761,x92764)))+P1(f306(f306(f308(f871(f866(x92761),f866(x92761))),f306(f306(f236(f866(x92761),f866(x92761)),x92762),x92763)),f139(x92761,x92764))) % 187.68/187.64 [9383]P1(f306(f63(x93831),x93832))+~P1(f306(f306(f308(f871(f872(x93831,a859),f872(x93831,a859))),f306(f306(f236(f872(x93831,a859),f872(x93831,a859)),x93833),x93832)),f298(x93831,x93834))) % 187.68/187.64 [9384]P1(f306(f63(x93841),x93842))+~P1(f306(f306(f308(f871(f872(x93841,a859),f872(x93841,a859))),f306(f306(f236(f872(x93841,a859),f872(x93841,a859)),x93842),x93843)),f298(x93841,x93844))) % 187.68/187.64 [9387]~E(x93871,f185(f872(x93872,a859)))+~P1(f306(f306(f308(f871(f872(x93872,a859),f872(x93872,a859))),f306(f306(f236(f872(x93872,a859),f872(x93872,a859)),x93873),x93871)),f298(x93872,x93874))) % 187.68/187.64 [10030]P15(x100301,x100302,x100303,x100304)+~P1(f306(f306(f245(x100301,x100301,a859),f306(f306(f7(x100301,f872(x100301,x100302),f872(x100301,a859)),f306(f306(f8(f872(x100302,a859),f872(f872(x100301,x100302),f872(x100301,a859)),x100301),f8(x100302,a859,x100301)),f306(f306(f8(x100302,f872(x100302,a859),x100301),a303),x100304))),x100304)),f545(x100304,x100303,x100302,x100301))) % 187.68/187.64 [4909]~E(x49094,f188(x49091))+E(f306(f306(f189(x49091,x49092),x49093),x49094),f188(x49092)) % 187.68/187.64 [4910]~E(x49104,f120(x49101))+E(f306(f306(f146(x49101,x49102),x49103),x49104),f120(x49102)) % 187.68/187.64 [4911]~E(x49112,f120(x49111))+E(f306(f306(f151(x49111,x49112),x49113),x49114),f120(x49111)) % 187.68/187.64 [5153]E(x51531,f188(x51532))+~E(f306(f306(f189(x51532,x51533),x51534),x51531),f188(x51533)) % 187.68/187.64 [5154]E(x51541,f120(x51542))+~E(f306(f306(f146(x51542,x51543),x51544),x51541),f120(x51543)) % 187.68/187.64 [5155]E(x51551,f120(x51552))+~E(f306(f306(f151(x51552,x51551),x51553),x51554),f120(x51552)) % 187.68/187.64 [5187]E(x51871,x51872)+~E(f306(f306(f122(x51873),x51874),x51871),f306(f306(f122(x51873),x51874),x51872)) % 187.68/187.64 [5188]E(x51881,x51882)+~E(f306(f306(f122(x51883),x51881),x51884),f306(f306(f122(x51883),x51882),x51884)) % 187.68/187.64 [5342]P1(f306(x53423,x53422))+E(f162(x53421,x53422,f306(f128(x53421,x53423),x53424)),f306(f128(x53421,x53423),x53424)) % 187.68/187.64 [5345]~P1(f306(x53452,x53453))+P36(x53451,x53452,f306(f306(f143(x53451),x53453),x53454)) % 187.68/187.64 [5354]E(x53541,x53542)+~E(f131(a865,f306(f276(a865,x53541),x53543)),f306(f306(f143(a865),x53542),x53544)) % 187.68/187.64 [5402]~P29(x54022,x54023)+P29(x54021,f306(f306(f75(x54022,x54021),x54023),x54024)) % 187.68/187.64 [5403]~P40(x54032,x54033)+P40(x54031,f306(f306(f262(x54032,x54031),x54033),x54034)) % 187.68/187.64 [5528]~P36(x55281,x55282,x55284)+P36(x55281,x55282,f306(f306(f143(x55281),x55283),x55284)) % 187.68/187.64 [5529]~P36(x55291,x55292,x55294)+P36(x55291,x55292,f306(f306(f122(x55291),x55293),x55294)) % 187.68/187.64 [5530]~P36(x55301,x55302,x55303)+P36(x55301,x55302,f306(f306(f122(x55301),x55303),x55304)) % 187.68/187.64 [5616]~E(x56161,f120(x56162))+~E(f306(f306(f122(x56162),x56163),f306(f306(f143(x56162),x56164),f120(x56162))),x56161) % 187.68/187.64 [5641]~P34(x56413,x56411,f306(f306(f143(x56413),x56412),x56414))+P1(f306(x56411,x56412)) % 187.68/187.64 [5651]E(f136(x56511,x56512),x56513)+~E(f306(f306(f122(x56511),x56514),f306(f306(f143(x56511),x56513),f120(x56511))),x56512) % 187.68/187.64 [5652]E(f121(x56521,x56522),x56523)+~E(f306(f306(f122(x56521),x56523),f306(f306(f143(x56521),x56524),f120(x56521))),x56522) % 187.68/187.64 [5761]~E(f131(a865,f306(f276(a865,x57611),x57612)),f306(f306(f143(a865),x57613),x57614))+P1(f306(f306(f221(a865),x57611),x57612)) % 187.68/187.64 [5769]P34(x57691,x57692,x57693)+~P34(x57691,x57692,f306(f306(f143(x57691),x57694),x57693)) % 187.68/187.64 [5770]P34(x57701,x57702,x57703)+~P34(x57701,x57702,f306(f306(f122(x57701),x57704),x57703)) % 187.68/187.64 [5771]P34(x57711,x57712,x57713)+~P34(x57711,x57712,f306(f306(f122(x57711),x57713),x57714)) % 187.68/187.64 [5965]E(x59651,f306(f306(f122(x59652),f306(f161(x59652),x59653)),f306(f306(f143(x59652),x59654),f120(x59652))))+~E(f306(f161(x59652),x59651),f306(f306(f143(x59652),x59654),x59653)) % 187.68/187.64 [6140]~P109(x61401)+E(f306(f306(f109(f872(x61401,a859)),f306(f276(x61401,x61402),x61403)),f306(f276(x61401,x61403),x61404)),f185(f872(x61401,a859))) % 187.68/187.64 [6177]~P74(x61771)+E(f306(f158(x61771),f306(f306(f146(a1,x61771),x61772),f170(x61773,x61774))),f306(f306(f6(a1,x61771),x61772),f306(f164(a1),f170(x61773,x61774)))) % 187.68/187.64 [6178]~P74(x61781)+E(f306(f306(f6(a1,x61781),x61782),f306(f164(a1),f170(x61783,x61784))),f306(f158(x61781),f306(f306(f146(a1,x61781),x61782),f170(x61783,x61784)))) % 187.68/187.64 [6322]~E(x63222,f306(f306(f122(x63221),f306(f161(x63221),x63224)),f306(f306(f143(x63221),x63223),f120(x63221))))+E(f306(f161(x63221),x63222),f306(f306(f143(x63221),x63223),x63224)) % 187.68/187.64 [6339]~P22(x63392,x63393,x63394,x63391)+E(f306(x63391,f185(f872(x63392,a859))),f35(x63393)) % 187.68/187.64 [6365]~P109(x63651)+E(f306(f306(f109(f872(x63651,a859)),f280(x63651,x63652,x63653)),f306(f276(x63651,x63653),x63654)),f185(f872(x63651,a859))) % 187.68/187.64 [6570]E(x65701,f185(f872(x65702,a859)))+~E(f293(x65703,x65702,x65704,x65701),f185(f872(f870(x65703,x65702),a859))) % 187.68/187.64 [6571]E(x65711,f185(f872(x65712,a859)))+~E(f293(x65712,x65713,x65711,x65714),f185(f872(f870(x65712,x65713),a859))) % 187.68/187.64 [6644]~P108(x66442)+E(f306(f186(f866(x66441)),f142(x66441,x66442,x66443,x66444)),f306(f186(f866(x66441)),x66444)) % 187.68/187.64 [6656]~P1(f306(f242(x66563,x66564,x66561),x66562))+P1(f306(f306(x66561,f523(x66562,x66561)),x66562)) % 187.68/187.64 [6696]~P1(f306(f63(x66962),x66964))+P1(f306(f63(x66961),f306(f285(x66962,x66961,x66963),x66964))) % 187.68/187.64 [6925]~P28(x69252,x69251,x69253,x69254)+E(f306(f39(x69251),f306(f285(x69252,x69251,x69253),x69254)),f306(f39(x69252),x69254)) % 187.68/187.64 [6944]E(f306(f285(x69441,x69442,x69443),f306(f286(x69441,x69442,x69443),x69444)),x69444)+~E(f306(f285(x69441,x69442,x69443),f231(f872(x69441,a859))),f231(f872(x69442,a859))) % 187.68/187.64 [7353]~P28(x73531,x73532,x73533,f231(f872(x73531,a859)))+E(f306(f286(x73531,x73532,x73533),f306(f285(x73531,x73532,x73533),x73534)),x73534) % 187.68/187.64 [7683]P1(f306(x76831,x76832))+~P1(f306(f306(f308(x76833),x76832),f306(f164(x76833),f168(x76833,x76831,x76834)))) % 187.68/187.64 [7790]~P1(f306(f306(f308(f866(x77901)),f306(f306(f143(x77901),x77902),x77904)),f153(x77901,x77903)))+P1(f306(f306(f308(x77901),x77902),x77903)) % 187.68/187.64 [7918]~P1(f306(f306(f308(x79181),x79182),f306(f164(x79181),f162(x79181,x79184,x79183))))+P1(f306(f306(f308(x79181),x79182),f306(f164(x79181),x79183))) % 187.68/187.64 [7920]~P1(f306(f306(f308(x79201),x79202),f306(f164(x79201),f166(x79201,x79203,x79204))))+P1(f306(f306(f308(x79201),x79202),f306(f164(x79201),x79203))) % 187.68/187.64 [7921]~P1(f306(f306(f308(x79211),x79212),f306(f164(x79211),f168(x79211,x79214,x79213))))+P1(f306(f306(f308(x79211),x79212),f306(f164(x79211),x79213))) % 187.68/187.64 [7931]E(f306(f186(f866(x79311)),x79312),x79313)+~P1(f306(f306(f308(f866(x79311)),x79312),f306(f164(f866(x79311)),f56(x79311,x79313,x79314)))) % 187.68/187.64 [8031]P1(f306(x80313,x80312))+E(f306(f128(x80311,f306(f306(f8(a859,a859,x80311),a301),f306(a303,x80312))),f306(f128(x80311,x80313),x80314)),f306(f128(x80311,x80313),x80314)) % 187.68/187.64 [8147]E(f306(f306(f157(x81471),f168(x81471,x81472,x81473)),x81474),f306(f306(f157(x81471),x81473),x81474))+~P1(f306(f306(f221(a865),x81474),f306(f186(f866(x81471)),f168(x81471,x81472,x81473)))) % 187.68/187.64 [8233]~P74(x82331)+E(f306(f306(f6(a865,x82331),f306(f306(f8(a865,x82331,a865),x82332),a119)),f306(f276(a865,x82333),x82334)),f306(f306(f6(a865,x82331),x82332),f306(f276(a865,f306(a119,x82333)),f306(a119,x82334)))) % 187.68/187.64 [8242]~P74(x82421)+E(f306(f306(f6(a865,x82421),f306(f306(f8(a865,x82421,a865),x82422),a119)),f277(a865,x82423,x82424)),f306(f306(f6(a865,x82421),x82422),f277(a865,f306(a119,x82423),f306(a119,x82424)))) % 187.68/187.64 [8373]~P28(x83731,x83733,x83734,f231(f872(x83731,a859)))+P28(x83731,f872(x83732,x83733),f306(f306(f8(x83733,f872(x83732,x83733),x83731),f16(x83733,x83732)),x83734),f231(f872(x83731,a859))) % 187.68/187.64 [8468]~P28(x84682,x84681,x84684,x84683)+E(f306(f285(x84681,x84682,f78(x84682,x84681,x84683,x84684)),f306(f285(x84682,x84681,x84684),x84683)),x84683) % 187.68/187.64 [8526]~P1(f306(f306(f308(f871(x85261,x85261)),f306(f306(f236(x85261,x85261),x85262),x85264)),f233(x85261,x85263)))+P1(f306(f306(f308(x85261),x85262),x85263)) % 187.68/187.64 [8616]E(f306(f306(f306(f73(x86161,f869(x86162)),f306(f16(f869(x86162),x86161),f188(x86162))),x86163),f306(f214(x86162),f811(x86163,x86164,x86162,x86161))),x86164)+~E(f175(x86161,x86162,x86164),f306(f306(f284(x86161),x86163),f185(f872(x86161,a859)))) % 187.68/187.64 [8737]~E(f306(f306(f6(x87371,a865),x87374),x87373),f306(a119,x87372))+P1(f306(f306(f308(x87371),f560(x87372,x87373,x87374,x87371)),x87373)) % 187.68/187.64 [8756]~E(f306(f306(f6(x87564,a865),x87561),x87563),f306(a119,x87562))+P1(f306(f306(f221(a865),f2(a865)),f306(x87561,f560(x87562,x87563,x87561,x87564)))) % 187.68/187.64 [8767]~P1(f306(f63(x87672),x87674))+P1(f306(f306(f220(a865),f306(f39(x87671),f306(f285(x87672,x87671,x87673),x87674))),f306(f39(x87672),x87674))) % 187.68/187.64 [8768]E(f306(f306(f236(x87681,x87682),f658(x87683,x87684,x87682,x87681)),f659(x87683,x87684,x87682,x87681)),x87684)+~P1(f306(f306(f308(f871(x87681,x87682)),x87684),f306(f261(x87682,x87681),x87683))) % 187.68/187.64 [8777]P28(x87771,x87772,x87773,x87774)+P1(f306(f306(f308(x87771),f439(x87774,x87773,x87772,x87771)),x87774)) % 187.68/187.64 [8778]P28(x87781,x87782,x87783,x87784)+P1(f306(f306(f308(x87781),f453(x87784,x87783,x87782,x87781)),x87784)) % 187.68/187.64 [8840]P15(x88401,x88402,x88403,x88404)+P1(f306(f306(f308(f871(x88401,x88401)),f545(x88404,x88403,x88402,x88401)),x88403)) % 187.68/187.64 [8902]P1(f306(x89021,x89022))+~P1(f306(x89021,f306(f306(f236(x89023,x89024),f323(x89024,x89023,x89021)),f324(x89024,x89023,x89021)))) % 187.68/187.64 [8919]E(f306(f186(f866(x89191)),x89192),f306(f186(f866(x89191)),x89193))+~P1(f306(f306(f308(f871(f866(x89191),f866(x89191))),f306(f306(f236(f866(x89191),f866(x89191)),x89192),x89193)),f137(x89191,x89194))) % 187.68/187.64 [8922]E(f306(f186(f866(x89221)),x89222),f306(f186(f866(x89221)),x89223))+~P1(f306(f306(f308(f871(f866(x89221),f866(x89221))),f306(f306(f236(f866(x89221),f866(x89221)),x89222),x89223)),f150(x89221,x89224))) % 187.68/187.64 [8923]E(f306(f186(f866(x89231)),x89232),f306(f186(f866(x89231)),x89233))+~P1(f306(f306(f308(f871(f866(x89231),f866(x89231))),f306(f306(f236(f866(x89231),f866(x89231)),x89232),x89233)),f149(x89231,x89234))) % 187.68/187.64 [8999]P1(f306(f306(f220(a865),f147(x89991,x89992,x89993)),f147(x89991,x89994,x89993)))+P1(f306(f306(f308(x89991),f720(x89994,x89992,x89993,x89991)),f306(f164(x89991),x89993))) % 187.68/187.64 [9002]E(f306(f186(f866(x90021)),x90022),f306(f186(f866(x90021)),x90023))+~P1(f306(f306(f308(f871(f866(x90021),f866(x90021))),f306(f306(f236(f866(x90021),f866(x90021)),x90022),x90023)),f282(f866(x90021),f149(x90021,x90024)))) % 187.68/187.64 [9240]~P28(x92401,x92402,x92403,x92404)+~P1(f306(f306(f221(a865),f306(f39(x92402),f306(f285(x92401,x92402,x92403),x92404))),f306(f39(x92401),x92404))) % 187.68/187.64 [9287]~P1(f306(f306(f308(f871(f866(x92871),f866(x92871))),f306(f306(f236(f866(x92871),f866(x92871)),x92872),x92873)),f149(x92871,x92874)))+P1(f306(f306(f308(f871(f866(x92871),f866(x92871))),f306(f306(f236(f866(x92871),f866(x92871)),x92872),x92873)),f150(x92871,f282(x92871,x92874)))) % 187.68/187.64 [9291]~P1(f306(f306(f308(f871(f866(x92911),f866(x92911))),f306(f306(f236(f866(x92911),f866(x92911)),x92912),x92913)),f150(x92911,x92914)))+P1(f306(f306(f308(f871(f866(x92911),f866(x92911))),f306(f306(f236(f866(x92911),f866(x92911)),x92912),x92913)),f282(f866(x92911),f149(x92911,x92914)))) % 187.68/187.64 [9308]P1(f306(f306(f308(f871(x93081,x93081)),f306(f306(f236(x93081,x93081),x93082),x93083)),f282(x93081,x93084)))+~P1(f306(f306(f308(f871(x93081,x93081)),f306(f306(f236(x93081,x93081),x93082),x93083)),f306(f306(f263(x93081,x93081,x93081),x93084),f282(x93081,x93084)))) % 187.68/187.64 [9494]E(f306(f306(f122(x94941),f704(x94942,x94943,x94944,x94941)),f306(f306(f143(x94941),f705(x94942,x94943,x94944,x94941)),f707(x94942,x94943,x94944,x94941))),x94944)+~P1(f306(f306(f308(f871(f866(x94941),f866(x94941))),f306(f306(f236(f866(x94941),f866(x94941)),x94944),x94943)),f149(x94941,x94942))) % 187.68/187.64 [9495]E(f306(f306(f122(x94951),f704(x94952,x94953,x94954,x94951)),f306(f306(f143(x94951),f706(x94952,x94953,x94954,x94951)),f707(x94952,x94953,x94954,x94951))),x94953)+~P1(f306(f306(f308(f871(f866(x94951),f866(x94951))),f306(f306(f236(f866(x94951),f866(x94951)),x94954),x94953)),f149(x94951,x94952))) % 187.68/187.64 [9572]P1(f306(f306(f308(f871(x95721,x95721)),f306(f306(f236(x95721,x95721),x95722),f619(x95723,x95724,x95722,x95721))),f282(x95721,x95723)))+~P1(f306(f306(f308(f871(x95721,x95721)),f306(f306(f236(x95721,x95721),x95722),x95724)),f306(f306(f263(x95721,x95721,x95721),x95723),f282(x95721,x95723)))) % 187.68/187.64 [9639]P1(f306(f306(f220(a865),f147(x96391,x96392,x96393)),f147(x96391,x96394,x96393)))+~P1(f306(f306(f221(a865),f306(x96392,f720(x96394,x96392,x96393,x96391))),f306(x96394,f720(x96394,x96392,x96393,x96391)))) % 187.68/187.64 [9708]P1(f306(f306(f308(f871(x97081,x97081)),f306(f306(f236(x97081,x97081),f618(x97082,x97083,x97084,x97081)),x97083)),f282(x97081,x97082)))+~P1(f306(f306(f308(f871(x97081,x97081)),f306(f306(f236(x97081,x97081),x97084),x97083)),f306(f306(f263(x97081,x97081,x97081),x97082),f282(x97081,x97082)))) % 187.68/187.64 [5169]~E(x51692,x51693)+E(f162(x51691,x51692,f306(f306(f143(x51691),x51693),x51694)),x51694) % 187.68/187.64 [5296]P1(f306(x52962,x52963))+E(f168(x52961,x52962,f306(f306(f143(x52961),x52963),x52964)),f120(x52961)) % 187.68/187.64 [5366]~P87(x53662)+E(f306(f306(f80(f872(x53661,x53662)),x53663),x53664),f306(f80(x53662),f306(x53663,x53664))) % 187.68/187.64 [5378]~E(x53782,f2(a865))+E(f306(f306(f130(x53781),x53782),f306(f306(f143(x53781),x53783),x53784)),f306(f306(f143(x53781),x53783),x53784)) % 187.68/187.64 [5379]P1(f306(x53792,x53793))+E(f306(f128(x53791,x53792),f306(f306(f143(x53791),x53793),x53794)),f306(f128(x53791,x53792),x53794)) % 187.68/187.64 [5511]~E(x55112,x55114)+P1(f306(f306(f306(f284(x55111),x55112),x55113),x55114)) % 187.68/187.64 [5519]E(x55191,f120(x55192))+E(f136(x55193,f306(f306(f146(x55192,x55193),x55194),x55191)),f306(x55194,f136(x55192,x55191))) % 187.68/187.64 [5533]~E(x55331,f65(x55332,x55334))+E(f306(x55331,f306(f306(f284(x55332),x55333),f185(f872(x55332,a859)))),x55333) % 187.68/187.64 [5567]E(x55671,f120(x55672))+E(f306(f133(x55673),f306(f306(f146(x55672,x55673),x55674),x55671)),f306(x55674,f306(f133(x55672),x55671))) % 187.68/187.64 [5670]~P1(f306(x56703,x56704))+P1(f306(f306(f306(f284(x56701),x56702),x56703),x56704)) % 187.68/187.64 [5787]~P21(x57872,x57874,x57871)+E(f306(x57871,f306(f306(f284(x57872),x57873),f185(f872(x57872,a859)))),x57873) % 187.68/187.64 [5811]~E(x58112,x58113)+P1(f306(f306(f308(x58111),x58112),f306(f306(f284(x58111),x58113),x58114))) % 187.68/187.64 [5815]~P113(x58151)+E(f306(f306(f81(x58151),x58152),f306(f306(f81(x58151),x58153),x58154)),f306(f306(f81(x58151),x58153),f306(f306(f81(x58151),x58152),x58154))) % 187.68/187.64 [5816]~P113(x58161)+E(f306(f306(f82(x58161),x58162),f306(f306(f82(x58161),x58163),x58164)),f306(f306(f82(x58161),x58163),f306(f306(f82(x58161),x58162),x58164))) % 187.68/187.64 [5818]~P108(x58181)+E(f306(f306(f225(x58181),x58182),f306(f306(f225(x58181),x58183),x58184)),f306(f306(f225(x58181),x58183),f306(f306(f225(x58181),x58182),x58184))) % 187.68/187.64 [5820]~P108(x58201)+E(f306(f306(f219(x58201),x58202),f306(f306(f219(x58201),x58203),x58204)),f306(f306(f219(x58201),x58203),f306(f306(f219(x58201),x58202),x58204))) % 187.68/187.64 [5822]~P97(x58221)+E(f306(f306(f108(x58221),x58222),f306(f306(f108(x58221),x58223),x58224)),f306(f306(f108(x58221),x58223),f306(f306(f108(x58221),x58222),x58224))) % 187.68/187.64 [5823]~P98(x58231)+E(f306(f306(f108(x58231),x58232),f306(f306(f108(x58231),x58233),x58234)),f306(f306(f108(x58231),x58233),f306(f306(f108(x58231),x58232),x58234))) % 187.68/187.64 [5824]~P98(x58241)+E(f306(f306(f109(x58241),x58242),f306(f306(f109(x58241),x58243),x58244)),f306(f306(f109(x58241),x58243),f306(f306(f109(x58241),x58242),x58244))) % 187.68/187.64 [5826]~P103(x58261)+E(f306(f306(f109(x58261),x58262),f306(f306(f109(x58261),x58263),x58264)),f306(f306(f109(x58261),x58263),f306(f306(f109(x58261),x58262),x58264))) % 187.68/187.64 [5831]E(x58311,x58312)+E(f162(x58313,x58311,f306(f306(f143(x58313),x58312),x58314)),f306(f306(f143(x58313),x58312),f162(x58313,x58311,x58314))) % 187.68/187.64 [5844]~P1(f306(x58442,x58443))+E(f306(f128(x58441,x58442),f306(f306(f143(x58441),x58443),x58444)),f306(f306(f143(x58441),x58443),f306(f128(x58441,x58442),x58444))) % 187.68/187.64 [5985]~P1(f306(x59852,x59853))+E(f168(x59851,x59852,f306(f306(f143(x59851),x59853),x59854)),f306(f306(f143(x59851),x59853),f168(x59851,x59852,x59854))) % 187.68/187.64 [6036]P27(x60361,x60362,x60363)+~P27(x60361,x60362,f306(f306(f284(f864(x60361)),x60364),x60363)) % 187.68/187.64 [6049]E(x60491,f185(f872(x60492,a859)))+E(f306(f306(f43(x60492,f872(x60493,a859)),x60491),f306(f16(f872(x60493,a859),x60492),x60494)),x60494) % 187.68/187.64 [6050]E(x60501,f185(f872(x60502,a859)))+E(f306(f306(f44(x60502,f872(x60503,a859)),x60501),f306(f16(f872(x60503,a859),x60502),x60504)),x60504) % 187.68/187.64 [6059]~E(x60594,f185(f872(x60592,a859)))+E(f306(f306(f243(x60591,x60592),x60593),f306(f16(f872(x60592,a859),x60591),x60594)),f185(f872(f871(x60591,x60592),a859))) % 187.68/187.64 [6060]~E(x60603,f185(f872(x60601,a859)))+E(f306(f306(f243(x60601,x60602),x60603),f306(f16(f872(x60602,a859),x60601),x60604)),f185(f872(f871(x60601,x60602),a859))) % 187.68/187.64 [6105]E(x61051,f2(a865))+E(f306(f306(f130(x61052),x61051),f306(f306(f143(x61052),x61053),x61054)),f306(f306(f130(x61052),f306(f306(f22(a865),x61051),f79(a865))),x61054)) % 187.68/187.64 [6134]E(x61341,f185(f872(x61342,a859)))+E(f306(f285(x61342,x61343,f306(f16(x61343,x61342),x61344)),x61341),f306(f306(f284(x61343),x61344),f185(f872(x61343,a859)))) % 187.68/187.64 [6137]E(f306(f286(x61371,x61372,f306(f16(x61372,x61371),x61373)),x61374),f185(f872(x61371,a859)))+P1(f306(f306(f308(x61372),x61373),x61374)) % 187.68/187.64 [6203]~E(x62033,f185(f872(x62031,a859)))+E(f306(f306(f43(x62031,f872(x62032,a859)),x62033),f306(f16(f872(x62032,a859),x62031),x62034)),f185(f872(x62032,a859))) % 187.68/187.64 [6204]~E(x62043,f185(f872(x62041,a859)))+E(f306(f306(f44(x62041,f872(x62042,a859)),x62043),f306(f16(f872(x62042,a859),x62041),x62044)),f231(f872(x62042,a859))) % 187.68/187.64 [6206]~P4(x62061)+E(f46(x62061,f306(f306(f82(x62061),x62062),x62063),f306(f306(f82(x62061),x62062),x62064)),f306(f306(f82(x62061),x62062),f46(x62061,x62063,x62064))) % 187.68/187.64 [6375]E(f306(f286(x63751,x63752,f306(f16(x63752,x63751),x63753)),x63754),f231(f872(x63751,a859)))+~P1(f306(f306(f308(x63752),x63753),x63754)) % 187.68/187.64 [6398]~P1(f306(f306(f308(x63981),x63982),x63984))+P1(f306(f306(f308(x63981),x63982),f306(f306(f284(x63981),x63983),x63984))) % 187.68/187.64 [6403]P1(f306(x64031,x64032))+~P1(f306(f152(x64033,x64031),f306(f306(f143(x64033),x64032),x64034))) % 187.68/187.64 [6412]~E(x64123,f306(f306(f22(a865),f306(f186(f866(x64121)),x64122)),f79(a865)))+E(f121(x64121,f306(f306(f151(x64121,x64122),x64123),x64124)),f121(x64121,x64122)) % 187.68/187.64 [6431]~P108(x64311)+E(f306(f306(f109(f872(x64311,a859)),f306(f275(x64311),x64312)),f277(x64311,x64313,x64314)),f277(x64311,x64313,f306(f306(f225(x64311),x64312),x64314))) % 187.68/187.64 [6432]~P108(x64321)+E(f306(f306(f109(f872(x64321,a859)),f306(f230(x64321),x64322)),f277(x64321,x64323,x64324)),f277(x64321,f306(f306(f219(x64321),x64322),x64323),x64324)) % 187.68/187.64 [6447]E(f306(f306(f109(f872(x64471,a859)),x64472),f306(f306(f284(x64471),x64473),x64474)),f306(f306(f109(f872(x64471,a859)),x64472),x64474))+P1(f306(f306(f308(x64471),x64473),x64472)) % 187.68/187.64 [6459]E(f162(x64591,x64592,f306(f306(f122(x64591),x64593),x64594)),f306(f306(f122(x64591),x64593),f162(x64591,x64592,x64594)))+P1(f306(f306(f308(x64591),x64592),f306(f164(x64591),x64593))) % 187.68/187.64 [6463]~P80(x64631)+E(f306(f306(f82(x64631),f306(f306(f237(x64631),x64632),x64633)),f306(f306(f237(x64631),x64632),x64634)),f306(f306(f237(x64631),x64632),f306(f306(f81(a865),x64633),x64634))) % 187.68/187.64 [6464]~P113(x64641)+E(f306(f306(f82(x64641),f306(f306(f237(x64641),x64642),x64643)),f306(f306(f237(x64641),x64642),x64644)),f306(f306(f237(x64641),x64642),f306(f306(f81(a865),x64643),x64644))) % 187.68/187.64 [6497]~P113(x64971)+E(f306(f306(f81(x64971),f306(f306(f82(x64971),x64972),x64973)),f306(f306(f82(x64971),x64972),x64974)),f306(f306(f82(x64971),x64972),f306(f306(f81(x64971),x64973),x64974))) % 187.68/187.64 [6498]~P108(x64981)+E(f306(f306(f219(x64981),f306(f306(f225(x64981),x64982),x64983)),f306(f306(f225(x64981),x64982),x64984)),f306(f306(f225(x64981),x64982),f306(f306(f219(x64981),x64983),x64984))) % 187.68/187.64 [6499]~P108(x64991)+E(f306(f306(f225(x64991),f306(f306(f219(x64991),x64992),x64993)),f306(f306(f219(x64991),x64992),x64994)),f306(f306(f219(x64991),x64992),f306(f306(f225(x64991),x64993),x64994))) % 187.68/187.64 [6500]~P101(x65001)+E(f306(f306(f109(x65001),f306(f306(f108(x65001),x65002),x65003)),f306(f306(f108(x65001),x65002),x65004)),f306(f306(f108(x65001),x65002),f306(f306(f109(x65001),x65003),x65004))) % 187.68/187.64 [6501]~P101(x65011)+E(f306(f306(f108(x65011),f306(f306(f109(x65011),x65012),x65013)),f306(f306(f109(x65011),x65012),x65014)),f306(f306(f109(x65011),x65012),f306(f306(f108(x65011),x65013),x65014))) % 187.68/187.64 [6534]~P4(x65341)+E(f46(x65341,f306(f306(f82(x65341),x65342),x65343),f306(f306(f82(x65341),x65344),x65343)),f306(f306(f82(x65341),f46(x65341,x65342,x65344)),x65343)) % 187.68/187.64 [6537]~E(f306(f186(f866(x65371)),x65373),f306(f186(f866(x65372)),x65374))+E(f306(f306(f146(f871(x65371,x65372),x65372),f244(x65371,x65372)),f306(f306(f173(x65371,x65372),x65373),x65374)),x65374) % 187.68/187.64 [6538]~E(f306(f186(f866(x65381)),x65383),f306(f186(f866(x65382)),x65384))+E(f306(f306(f146(f871(x65381,x65382),x65381),f235(x65381,x65382)),f306(f306(f173(x65381,x65382),x65383),x65384)),x65383) % 187.68/187.64 [6544]P1(f306(f152(x65441,x65442),x65443))+~P1(f306(f152(x65441,x65442),f306(f306(f143(x65441),x65444),x65443))) % 187.68/187.64 [6545]P1(f306(f152(x65451,x65452),x65453))+~P1(f306(f152(x65451,x65452),f306(f306(f122(x65451),x65454),x65453))) % 187.68/187.64 [6546]P1(f306(f152(x65461,x65462),x65463))+~P1(f306(f152(x65461,x65462),f306(f306(f122(x65461),x65463),x65464))) % 187.68/187.64 [6551]~P5(x65511)+E(f46(x65511,f306(f306(f22(x65511),x65512),f46(x65511,x65513,x65514)),x65514),f46(x65511,f306(f306(f22(x65511),x65512),x65513),x65514)) % 187.68/187.64 [6553]~P4(x65531)+E(f46(x65531,f306(f306(f82(x65531),x65532),f46(x65531,x65533,x65534)),x65534),f46(x65531,f306(f306(f82(x65531),x65532),x65533),x65534)) % 187.68/187.64 [6554]~P4(x65541)+E(f46(x65541,f306(f306(f81(x65541),x65542),f46(x65541,x65543,x65544)),x65544),f46(x65541,f306(f306(f81(x65541),x65542),x65543),x65544)) % 187.68/187.64 [6636]~P108(x66361)+E(f306(f306(f109(f872(x66361,a859)),f277(x66361,x66362,x66363)),f306(f275(x66361),x66364)),f277(x66361,x66362,f306(f306(f225(x66361),x66363),x66364))) % 187.68/187.64 [6637]~P108(x66371)+E(f306(f306(f109(f872(x66371,a859)),f277(x66371,x66372,x66373)),f306(f230(x66371),x66374)),f277(x66371,f306(f306(f219(x66371),x66372),x66374),x66373)) % 187.68/187.64 [6640]~E(f306(f186(f866(x66401)),x66403),f306(f186(f866(x66402)),x66404))+E(f306(f306(f173(x66401,x66402),f306(f161(x66401),x66403)),f306(f161(x66402),x66404)),f306(f161(f871(x66401,x66402)),f306(f306(f173(x66401,x66402),x66403),x66404))) % 187.68/187.64 [6652]E(x66521,f306(f306(f22(a865),f306(f186(f866(x66522)),x66523)),f79(a865)))+E(f121(x66522,f306(f306(f151(x66522,x66523),x66521),x66524)),f306(f306(f151(x66522,f121(x66522,x66523)),x66521),x66524)) % 187.68/187.64 [6667]~P1(f306(f129(x66672),x66674))+P1(f306(f129(f871(x66671,x66672)),f306(f306(f173(x66671,x66672),x66673),x66674))) % 187.68/187.64 [6668]~P1(f306(f129(x66681),x66683))+P1(f306(f129(f871(x66681,x66682)),f306(f306(f173(x66681,x66682),x66683),x66684))) % 187.68/187.64 [6928]E(f306(f306(f40(a865),x69281),x69282),x69283)+~P1(f306(f49(x69281,x69282),f306(f306(f236(a865,a865),x69283),x69284))) % 187.68/187.64 [6952]E(f46(a865,x69521,x69522),x69523)+~P1(f306(f49(x69521,x69522),f306(f306(f236(a865,a865),x69524),x69523))) % 187.68/187.64 [6955]P1(f306(f129(x69551),x69552))+~P1(f306(f129(x69553),f306(f306(f146(x69551,x69553),x69554),x69552))) % 187.68/187.64 [6963]~P27(x69631,x69632,f306(f306(f284(f864(x69631)),x69633),x69634))+P27(x69631,x69632,f306(f306(f284(f864(x69631)),x69633),f185(f872(f864(x69631),a859)))) % 187.68/187.64 [6969]P1(f306(f306(f193(x69691),x69692),x69693))+~P1(f306(f306(f306(f306(a195,x69691),x69692),x69694),x69693)) % 187.68/187.64 [7041]E(f162(x70411,x70412,f306(f306(f122(x70411),x70413),x70414)),f306(f306(f122(x70411),f162(x70411,x70412,x70413)),x70414))+~P1(f306(f306(f308(x70411),x70412),f306(f164(x70411),x70413))) % 187.68/187.64 [7131]~P5(x71311)+E(f46(x71311,f306(f306(f22(x71311),f46(x71311,x71312,x71313)),x71314),x71313),f46(x71311,f306(f306(f22(x71311),x71312),x71314),x71313)) % 187.68/187.64 [7134]~P4(x71341)+E(f46(x71341,f306(f306(f81(x71341),f46(x71341,x71342,x71343)),x71344),x71343),f46(x71341,f306(f306(f81(x71341),x71342),x71344),x71343)) % 187.68/187.64 [7135]~P4(x71351)+E(f46(x71351,f306(f306(f82(x71351),f46(x71351,x71352,x71353)),x71354),x71353),f46(x71351,f306(f306(f82(x71351),x71352),x71354),x71353)) % 187.68/187.64 [7324]~E(x73241,f306(f306(f143(x73242),x73243),x73244))+~P1(f306(f306(f220(a865),f306(f186(f866(x73242)),x73241)),f306(f186(f866(x73242)),x73244))) % 187.68/187.64 [7399]~E(f306(f169(x73991,x73992),x73993),f306(f169(x73991,x73992),x73994))+E(f306(f285(f871(x73991,x73992),x73991,f235(x73991,x73992)),f306(f164(f871(x73991,x73992)),x73993)),f306(f285(f871(x73991,x73992),x73991,f235(x73991,x73992)),f306(f164(f871(x73991,x73992)),x73994))) % 187.68/187.64 [7530]P28(x75301,x75302,x75303,f306(f164(x75301),x75304))+~P1(f306(f129(x75302),f306(f306(f146(x75301,x75302),x75303),x75304))) % 187.68/187.64 [7604]~P1(f306(f306(f220(f872(x76041,a859)),x76042),x76044))+P1(f306(f306(f220(f872(x76041,a859)),x76042),f306(f306(f284(x76041),x76043),x76044))) % 187.68/187.64 [7638]~P5(x76381)+E(f46(x76381,f306(f306(f22(x76381),f46(x76381,x76382,x76383)),f46(x76381,x76384,x76383)),x76383),f46(x76381,f306(f306(f22(x76381),x76382),x76384),x76383)) % 187.68/187.64 [7639]~P4(x76391)+E(f46(x76391,f306(f306(f81(x76391),f46(x76391,x76392,x76393)),f46(x76391,x76394,x76393)),x76393),f46(x76391,f306(f306(f81(x76391),x76392),x76394),x76393)) % 187.68/187.64 [7640]~P4(x76401)+E(f46(x76401,f306(f306(f82(x76401),f46(x76401,x76402,x76403)),f46(x76401,x76404,x76403)),x76403),f46(x76401,f306(f306(f82(x76401),x76402),x76404),x76403)) % 187.68/187.64 [7738]P1(f306(f306(f306(f306(a195,x77381),x77382),f306(a119,x77383)),x77384))+~P1(f306(f306(f306(f306(a195,x77381),x77382),x77383),x77384)) % 187.68/187.64 [7745]~E(f306(x77454,f454(x77454,x77453,x77451,x77452)),f185(f872(x77452,a859)))+E(f306(f306(f43(x77451,f872(x77452,a859)),x77453),x77454),f185(f872(x77452,a859))) % 187.68/187.64 [7746]~E(f306(x77464,f613(x77464,x77463,x77461,x77462)),f231(f872(x77462,a859)))+E(f306(f306(f44(x77461,f872(x77462,a859)),x77463),x77464),f231(f872(x77462,a859))) % 187.68/187.64 [7747]~E(f306(x77474,f463(x77474,x77473,x77472,x77471)),f185(f872(x77472,a859)))+E(f306(f306(f43(x77471,f872(x77472,a859)),x77473),x77474),f185(f872(x77472,a859))) % 187.68/187.64 [7748]~E(f306(x77484,f628(x77484,x77483,x77482,x77481)),f231(f872(x77482,a859)))+E(f306(f306(f44(x77481,f872(x77482,a859)),x77483),x77484),f231(f872(x77482,a859))) % 187.68/187.64 [8148]P1(f306(x81481,x81482))+~P1(f306(f306(f308(x81483),x81482),f306(f306(f109(f872(x81483,a859)),x81484),f306(f228(x81483),x81481)))) % 187.68/187.64 [8187]~P1(f306(f306(f220(f872(x81871,a859)),x81873),x81874))+P1(f306(f306(f220(f872(x81871,a859)),f306(f306(f284(x81871),x81872),x81873)),f306(f306(f284(x81871),x81872),x81874))) % 187.68/187.64 [8356]P1(f306(f306(f193(x83561),x83562),f326(x83563,x83562,x83564,x83561)))+~P1(f306(f306(f193(f34(x83561,x83564)),x83562),x83563)) % 187.68/187.64 [8357]P1(f306(f306(f193(x83571),x83572),f343(x83573,x83572,x83574,x83571)))+~P1(f306(f306(f193(f34(x83571,x83574)),x83572),x83573)) % 187.68/187.64 [8366]P1(f306(x83662,x83663))+E(f306(f306(f130(x83661),f306(f186(f866(x83661)),f168(x83661,x83662,f306(f306(f143(x83661),x83663),x83664)))),f306(f306(f143(x83661),x83663),x83664)),f306(f306(f143(x83661),x83663),x83664)) % 187.68/187.64 [8482]~P1(f306(f306(f221(a865),f306(x84824,x84822)),f306(x84824,x84823)))+P1(f306(f306(f308(f871(x84821,x84821)),f306(f306(f236(x84821,x84821),x84822),x84823)),f306(f306(f262(a865,x84821),a227),x84824))) % 187.68/187.64 [8573]~P1(f306(x85732,f774(x85734,x85732,x85733,x85731)))+E(f168(x85731,x85732,f306(f306(f122(x85731),x85733),x85734)),f306(f306(f122(x85731),x85733),f168(x85731,x85732,x85734))) % 187.68/187.64 [8641]P28(f866(x86411),f866(x86412),f306(f146(x86411,x86412),x86413),x86414)+~P28(x86411,x86412,x86413,f41(f872(x86411,a859),f306(f285(f866(x86411),f872(x86411,a859),f164(x86411)),x86414))) % 187.68/187.64 [8708]~P1(f306(x87082,x87083))+E(f306(f306(f130(x87081),f306(f186(f866(x87081)),f168(x87081,x87082,f306(f306(f143(x87081),x87083),x87084)))),f306(f306(f143(x87081),x87083),x87084)),f306(f306(f130(x87081),f306(f186(f866(x87081)),f168(x87081,x87082,x87084))),x87084)) % 187.68/187.64 [8748]~E(x87482,x87483)+E(f306(f128(x87481,f306(f306(f8(a859,a859,x87481),a301),f306(a303,x87482))),f306(f306(f143(x87481),x87483),x87484)),f306(f128(x87481,f306(f306(f8(a859,a859,x87481),a301),f306(a303,x87482))),x87484)) % 187.68/187.64 [8757]E(f306(f306(f43(x87571,f872(x87572,a859)),x87573),x87574),f185(f872(x87572,a859)))+P1(f306(f306(f308(x87571),f454(x87574,x87573,x87571,x87572)),x87573)) % 187.68/187.64 [8758]E(f306(f306(f44(x87581,f872(x87582,a859)),x87583),x87584),f231(f872(x87582,a859)))+P1(f306(f306(f308(x87581),f613(x87584,x87583,x87581,x87582)),x87583)) % 187.68/187.64 [8759]E(f306(f306(f43(x87591,f872(x87592,a859)),x87593),x87594),f185(f872(x87592,a859)))+P1(f306(f306(f308(x87591),f463(x87594,x87593,x87592,x87591)),x87593)) % 187.68/187.64 [8760]E(f306(f306(f44(x87601,f872(x87602,a859)),x87603),x87604),f231(f872(x87602,a859)))+P1(f306(f306(f308(x87601),f628(x87604,x87603,x87602,x87601)),x87603)) % 187.68/187.64 [8797]P1(f306(f306(f221(a865),f306(x87971,x87972)),f306(x87971,x87973)))+~P1(f306(f306(f308(f871(x87974,x87974)),f306(f306(f236(x87974,x87974),x87972),x87973)),f306(f306(f262(a865,x87974),a227),x87971))) % 187.68/187.64 [8819]E(f168(x88191,x88192,f306(f306(f122(x88191),x88193),x88194)),f306(f306(f122(x88191),x88193),f168(x88191,x88192,x88194)))+P1(f306(f306(f308(x88191),f774(x88194,x88192,x88193,x88191)),f306(f164(x88191),x88193))) % 187.68/187.64 [8856]P1(f306(f306(f193(x88561),f326(x88562,x88563,x88561,x88564)),x88562))+~P1(f306(f306(f193(f34(x88564,x88561)),x88563),x88562)) % 187.68/187.64 [8857]P1(f306(f306(f193(x88571),f343(x88572,x88573,x88571,x88574)),x88572))+~P1(f306(f306(f193(f34(x88574,x88571)),x88573),x88572)) % 187.68/187.64 [8988]P1(f306(f306(f308(x89881),f441(x89882,x89883,x89884,x89881)),x89883))+~P1(f306(f306(f308(f872(x89881,a859)),x89884),f306(f306(f62(x89881),x89883),x89882))) % 187.68/187.64 [8991]E(x89911,x89912)+~P1(f306(f306(f308(f871(x89913,x89913)),f306(f306(f236(x89913,x89913),x89911),x89912)),f306(f306(f180(f871(x89913,x89913),a859),f2(a865)),x89914))) % 187.68/187.64 [9069]E(f306(f260(x90691,x90691,x90692),f306(f306(f284(x90691),f441(x90692,x90693,x90694,x90691)),f185(f872(x90691,a859)))),x90694)+~P1(f306(f306(f308(f872(x90691,a859)),x90694),f306(f306(f62(x90691),x90693),x90692))) % 187.68/187.64 [9074]~P1(f306(f306(f308(f871(x90741,x90741)),f306(f306(f236(x90741,x90741),x90743),x90742)),f282(x90741,x90744)))+P1(f306(f306(f308(f871(x90741,x90741)),f306(f306(f236(x90741,x90741),x90742),x90743)),f282(x90741,f306(f261(x90741,x90741),x90744)))) % 187.68/187.64 [9086]~P4(x90861)+E(f306(f306(f81(x90861),f306(f306(f81(x90861),f306(f306(f82(x90861),x90862),f306(f306(f40(x90861),x90863),x90862))),f46(x90861,x90863,x90862))),x90864),f306(f306(f81(x90861),x90863),x90864)) % 187.68/187.64 [9098]~P1(f306(f306(f308(x90981),x90983),x90984))+P1(f306(f306(f308(f872(x90981,a859)),f306(f260(x90981,x90981,x90982),f306(f306(f284(x90981),x90983),f185(f872(x90981,a859))))),f306(f306(f62(x90981),x90984),x90982))) % 187.68/187.64 [9109]P1(f306(f306(f308(f871(x91091,x91091)),f306(f306(f236(x91091,x91091),x91092),x91093)),f282(x91091,x91094)))+~P1(f306(f306(f308(f871(x91091,x91091)),f306(f306(f236(x91091,x91091),x91093),x91092)),f282(x91091,f306(f261(x91091,x91091),x91094)))) % 187.68/187.64 [9202]E(f306(f306(f151(x92021,f306(f161(x92021),x92022)),f306(f306(f22(a865),f306(f306(f22(a865),f306(f186(f866(x92021)),x92022)),x92023)),f79(a865))),x92024),f306(f161(x92021),f306(f306(f151(x92021,x92022),x92023),x92024)))+~P1(f306(f306(f221(a865),x92023),f306(f186(f866(x92021)),x92022))) % 187.68/187.64 [9206]~P1(f306(x92062,f767(x92064,x92062,x92063,x92061)))+E(f306(f306(f130(x92061),f306(f186(f866(x92061)),f168(x92061,x92062,f306(f306(f122(x92061),x92063),x92064)))),f306(f306(f122(x92061),x92063),x92064)),f306(f306(f130(x92061),f306(f186(f866(x92061)),f168(x92061,x92062,x92064))),x92064)) % 187.68/187.64 [9246]~P28(x92462,x92461,x92463,f231(f872(x92462,a859)))+P1(f306(f306(f220(f872(x92461,a859)),f306(f285(x92462,x92461,x92463),f306(f80(f872(x92462,a859)),x92464))),f306(f80(f872(x92461,a859)),f306(f285(x92462,x92461,x92463),x92464)))) % 187.68/187.64 [9260]~P6(x92601)+E(f306(f134(x92601,x92602,f306(f7(x92602,x92601,x92601),f306(f306(f8(x92601,f872(x92601,x92601),x92602),f108(x92601)),x92603)),f185(x92601)),x92604),f306(f306(f43(x92602,x92601),f306(f164(x92602),x92604)),x92603)) % 187.68/187.64 [9261]~P6(x92611)+E(f306(f134(x92611,x92612,f306(f7(x92612,x92611,x92611),f306(f306(f8(x92611,f872(x92611,x92611),x92612),f109(x92611)),x92613)),f231(x92611)),x92614),f306(f306(f44(x92612,x92611),f306(f164(x92612),x92614)),x92613)) % 187.68/187.64 [9273]E(f306(f306(f130(x92731),f306(f186(f866(x92731)),f168(x92731,x92732,f306(f306(f122(x92731),x92733),x92734)))),f306(f306(f122(x92731),x92733),x92734)),f306(f306(f130(x92731),f306(f186(f866(x92731)),f168(x92731,x92732,x92734))),x92734))+P1(f306(f306(f308(x92731),f767(x92734,x92732,x92733,x92731)),f306(f164(x92731),x92733))) % 187.68/187.64 [9341]~P1(f306(f306(f308(f871(f866(x93414),f866(x93414))),f306(f306(f236(f866(x93414),f866(x93414)),x93413),x93412)),f149(x93414,x93411)))+P1(f306(f306(f221(a865),f701(x93411,x93412,x93413,x93414)),f306(f186(f866(x93414)),x93413))) % 187.68/187.64 [9342]~P4(x93421)+E(f306(f306(f81(x93421),f306(f306(f81(x93421),f306(f306(f82(x93421),f306(f306(f40(x93421),x93422),x93423)),x93423)),f46(x93421,x93422,x93423))),x93424),f306(f306(f81(x93421),x93422),x93424)) % 187.68/187.64 [9371]~P1(f306(f306(f308(f871(f866(x93711),f866(x93711))),f306(f306(f236(f866(x93711),f866(x93711)),x93712),x93713)),f306(f261(f866(x93711),f866(x93711)),f149(x93711,x93714))))+P1(f306(f306(f308(f871(f866(x93711),f866(x93711))),f306(f306(f236(f866(x93711),f866(x93711)),x93712),x93713)),f149(x93711,f306(f261(x93711,x93711),x93714)))) % 187.68/187.64 [9372]P1(f306(f306(f308(f871(f866(x93721),f866(x93721))),f306(f306(f236(f866(x93721),f866(x93721)),x93722),x93723)),f306(f261(f866(x93721),f866(x93721)),f149(x93721,x93724))))+~P1(f306(f306(f308(f871(f866(x93721),f866(x93721))),f306(f306(f236(f866(x93721),f866(x93721)),x93722),x93723)),f149(x93721,f306(f261(x93721,x93721),x93724)))) % 187.68/187.64 [9407]~P1(f306(f306(f308(x94071),x94073),f306(f234(x94071,x94072),x94074)))+P1(f306(f306(f308(f871(x94071,x94072)),f306(f306(f236(x94071,x94072),x94073),f533(x94074,x94072,x94073,x94071))),x94074)) % 187.68/187.64 [9408]~P1(f306(f306(f308(x94081),x94083),f306(f234(x94081,x94082),x94084)))+P1(f306(f306(f308(f871(x94081,x94082)),f306(f306(f236(x94081,x94082),x94083),f536(x94084,x94082,x94083,x94081))),x94084)) % 187.68/187.64 [9519]~P1(f306(f63(f869(x95191)),f306(f285(x95192,f869(x95191),x95193),f231(f872(x95192,a859)))))+P1(f306(f63(f869(x95191)),f306(f285(x95192,f869(x95191),f176(x95192,x95191,x95193,f306(f169(x95192,x95191),x95194))),f231(f872(x95192,a859))))) % 187.68/187.64 [9567]~P1(f306(f306(f308(f871(x95671,x95671)),f306(f306(f236(x95671,x95671),x95672),x95674)),f306(f306(f263(x95671,x95671,x95671),x95673),f282(x95671,x95673))))+P1(f306(f306(f308(f871(x95671,x95671)),f306(f306(f236(x95671,x95671),x95672),f618(x95673,x95674,x95672,x95671))),x95673)) % 187.68/187.64 [9737]~P1(f306(f306(f308(f871(x97372,x97371)),x97374),f306(f261(x97371,x97372),x97373)))+P1(f306(f306(f308(f871(x97371,x97372)),f306(f306(f236(x97371,x97372),f659(x97373,x97374,x97371,x97372)),f658(x97373,x97374,x97371,x97372))),x97373)) % 187.68/187.64 [9765]~P1(f306(f306(f308(f871(f866(x97651),f866(x97651))),f306(f306(f236(f866(x97651),f866(x97651)),x97654),x97653)),f149(x97651,x97652)))+P1(f306(f306(f308(f871(x97651,x97651)),f306(f306(f236(x97651,x97651),f705(x97652,x97653,x97654,x97651)),f706(x97652,x97653,x97654,x97651))),x97652)) % 187.68/187.64 [9859]~P1(f306(f306(f308(f871(f866(x98591),f866(x98591))),f306(f306(f236(f866(x98591),f866(x98591)),x98592),x98594)),f149(x98591,x98593)))+P1(f306(f306(f308(f871(x98591,x98591)),f306(f306(f236(x98591,x98591),f306(f306(f157(x98591),x98592),f701(x98593,x98594,x98592,x98591))),f702(x98593,x98594,x98592,x98591))),x98593)) % 187.68/187.64 [9881]~P1(f306(f63(x98812),x98814))+E(f306(f306(f306(f67(f872(x98811,a859),x98812,f108(f872(x98811,a859))),f306(f306(f7(x98812,f872(x98811,a859),f872(x98811,a859)),f306(f306(f8(x98811,f872(f872(x98811,a859),f872(x98811,a859)),x98812),f284(x98811)),x98813)),f185(f872(x98811,a859)))),f185(f872(x98811,a859))),x98814),f306(f285(x98812,x98811,x98813),x98814)) % 187.68/187.64 [9980]~P28(x99801,x99802,x99803,f231(f872(x99801,a859)))+P1(f306(f306(f220(f872(x99801,a859)),f306(f286(x99801,x99802,x99803),f306(f306(f284(x99802),x99804),f185(f872(x99802,a859))))),f306(f306(f284(x99801),f86(x99801,f306(f306(f7(x99801,x99802,a859),f306(f306(f8(x99802,f872(x99802,a859),x99801),a303),x99803)),x99804))),f185(f872(x99801,a859))))) % 187.68/187.64 [5576]~E(f306(f306(f122(x55761),x55762),x55764),x55763)+E(f306(f306(f165(x55761),f306(f186(f866(x55761)),x55762)),x55763),x55762) % 187.68/187.64 [5577]~E(f306(f306(f122(x55772),x55773),x55771),x55774)+E(x55771,f306(f306(f130(x55772),f306(f186(f866(x55772)),x55773)),x55774)) % 187.68/187.64 [5588]~E(x55884,f2(a865))+E(f306(f306(f157(x55881),f306(f306(f143(x55881),x55882),x55883)),x55884),x55882) % 187.68/187.64 [6118]~P113(x61181)+E(f306(f306(f237(x61181),f306(f306(f237(x61181),x61182),x61183)),x61184),f306(f306(f237(x61181),x61182),f306(f306(f82(a865),x61183),x61184))) % 187.68/187.64 [6119]~P80(x61191)+E(f306(f306(f237(x61191),f306(f306(f237(x61191),x61192),x61193)),x61194),f306(f306(f237(x61191),x61192),f306(f306(f82(a865),x61193),x61194))) % 187.68/187.64 [6135]E(x61351,f2(a865))+E(f306(f306(f157(x61352),f306(f306(f143(x61352),x61353),x61354)),x61351),f306(f306(f157(x61352),x61354),f306(f306(f22(a865),x61351),f79(a865)))) % 187.68/187.64 [6161]~P118(x61611)+E(f306(f306(f264(x61611),f306(f306(f82(x61611),x61612),x61613)),x61614),f306(f306(f82(x61611),x61612),f306(f306(f264(x61611),x61613),x61614))) % 187.68/187.64 [6162]~P69(x61621)+E(f306(f306(f81(x61621),f306(f306(f81(x61621),x61622),x61623)),x61624),f306(f306(f81(x61621),x61622),f306(f306(f81(x61621),x61623),x61624))) % 187.68/187.64 [6163]~P113(x61631)+E(f306(f306(f81(x61631),f306(f306(f81(x61631),x61632),x61633)),x61634),f306(f306(f81(x61631),x61632),f306(f306(f81(x61631),x61633),x61634))) % 187.68/187.64 [6164]~P113(x61641)+E(f306(f306(f82(x61641),f306(f306(f82(x61641),x61642),x61643)),x61644),f306(f306(f82(x61641),x61642),f306(f306(f82(x61641),x61643),x61644))) % 187.68/187.64 [6165]~P72(x61651)+E(f306(f306(f82(x61651),f306(f306(f82(x61651),x61652),x61653)),x61654),f306(f306(f82(x61651),x61652),f306(f306(f82(x61651),x61653),x61654))) % 187.68/187.64 [6168]~P108(x61681)+E(f306(f306(f225(x61681),f306(f306(f225(x61681),x61682),x61683)),x61684),f306(f306(f225(x61681),x61682),f306(f306(f225(x61681),x61683),x61684))) % 187.68/187.64 [6170]~P108(x61701)+E(f306(f306(f219(x61701),f306(f306(f219(x61701),x61702),x61703)),x61704),f306(f306(f219(x61701),x61702),f306(f306(f219(x61701),x61703),x61704))) % 187.68/187.64 [6172]~P97(x61721)+E(f306(f306(f108(x61721),f306(f306(f108(x61721),x61722),x61723)),x61724),f306(f306(f108(x61721),x61722),f306(f306(f108(x61721),x61723),x61724))) % 187.68/187.64 [6173]~P98(x61731)+E(f306(f306(f108(x61731),f306(f306(f108(x61731),x61732),x61733)),x61734),f306(f306(f108(x61731),x61732),f306(f306(f108(x61731),x61733),x61734))) % 187.68/187.64 [6174]~P98(x61741)+E(f306(f306(f109(x61741),f306(f306(f109(x61741),x61742),x61743)),x61744),f306(f306(f109(x61741),x61742),f306(f306(f109(x61741),x61743),x61744))) % 187.68/187.64 [6176]~P103(x61761)+E(f306(f306(f109(x61761),f306(f306(f109(x61761),x61762),x61763)),x61764),f306(f306(f109(x61761),x61762),f306(f306(f109(x61761),x61763),x61764))) % 187.68/187.64 [6187]~P4(x61871)+E(f46(x61871,f306(f306(f81(x61871),x61872),f306(f306(f82(x61871),x61873),x61874)),x61874),f46(x61871,x61872,x61874)) % 187.68/187.64 [6188]~P4(x61881)+E(f46(x61881,f306(f306(f81(x61881),x61882),f306(f306(f82(x61881),x61883),x61884)),x61883),f46(x61881,x61882,x61883)) % 187.68/187.64 [6323]E(f306(f306(f157(x63231),f306(f306(f165(x63231),x63232),x63233)),x63234),f306(f306(f157(x63231),x63233),x63234))+~P1(f306(f306(f221(a865),x63234),x63232)) % 187.68/187.64 [6495]~P113(x64951)+E(f306(f306(f81(x64951),f306(f306(f81(x64951),x64952),x64953)),x64954),f306(f306(f81(x64951),f306(f306(f81(x64951),x64952),x64954)),x64953)) % 187.68/187.64 [6496]~P113(x64961)+E(f306(f306(f82(x64961),f306(f306(f82(x64961),x64962),x64963)),x64964),f306(f306(f82(x64961),f306(f306(f82(x64961),x64962),x64964)),x64963)) % 187.68/187.64 [6557]~P141(x65572)+E(f306(f306(f6(x65571,x65572),f306(f16(x65572,x65571),x65573)),x65574),f306(f306(f82(x65572),f306(f107(x65572),f306(f39(x65571),x65574))),x65573)) % 187.68/187.64 [6729]E(f306(f306(f109(f872(x67291,a859)),f306(f306(f284(x67291),x67292),x67293)),x67294),f306(f306(f109(f872(x67291,a859)),x67293),x67294))+P1(f306(f306(f308(x67291),x67292),x67294)) % 187.68/187.64 [6798]~P65(x67981)+E(f306(f306(f225(x67981),f306(f306(f22(x67981),x67982),x67983)),f306(f306(f22(x67981),x67984),x67983)),f306(f306(f22(x67981),f306(f306(f225(x67981),x67982),x67984)),x67983)) % 187.68/187.64 [6799]~P65(x67991)+E(f306(f306(f219(x67991),f306(f306(f22(x67991),x67992),x67993)),f306(f306(f22(x67991),x67994),x67993)),f306(f306(f22(x67991),f306(f306(f219(x67991),x67992),x67994)),x67993)) % 187.68/187.64 [6800]~P82(x68001)+E(f306(f306(f225(x68001),f306(f306(f81(x68001),x68002),x68003)),f306(f306(f81(x68001),x68004),x68003)),f306(f306(f81(x68001),f306(f306(f225(x68001),x68002),x68004)),x68003)) % 187.68/187.64 [6801]~P82(x68011)+E(f306(f306(f219(x68011),f306(f306(f81(x68011),x68012),x68013)),f306(f306(f81(x68011),x68014),x68013)),f306(f306(f81(x68011),f306(f306(f219(x68011),x68012),x68014)),x68013)) % 187.68/187.64 [6803]~P116(x68031)+E(f306(f306(f81(x68031),f306(f306(f82(x68031),x68032),x68033)),f306(f306(f82(x68031),x68034),x68033)),f306(f306(f82(x68031),f306(f306(f81(x68031),x68032),x68034)),x68033)) % 187.68/187.64 [6804]~P108(x68041)+E(f306(f306(f219(x68041),f306(f306(f225(x68041),x68042),x68043)),f306(f306(f225(x68041),x68044),x68043)),f306(f306(f225(x68041),f306(f306(f219(x68041),x68042),x68044)),x68043)) % 187.68/187.64 [6805]~P108(x68051)+E(f306(f306(f225(x68051),f306(f306(f219(x68051),x68052),x68053)),f306(f306(f219(x68051),x68054),x68053)),f306(f306(f219(x68051),f306(f306(f225(x68051),x68052),x68054)),x68053)) % 187.68/187.64 [6806]~P113(x68061)+E(f306(f306(f82(x68061),f306(f306(f237(x68061),x68062),x68063)),f306(f306(f237(x68061),x68064),x68063)),f306(f306(f237(x68061),f306(f306(f82(x68061),x68062),x68064)),x68063)) % 187.68/187.64 [6807]~P75(x68071)+E(f306(f306(f82(x68071),f306(f306(f237(x68071),x68072),x68073)),f306(f306(f237(x68071),x68074),x68073)),f306(f306(f237(x68071),f306(f306(f82(x68071),x68072),x68074)),x68073)) % 187.68/187.64 [6808]~P61(x68081)+E(f306(f306(f264(x68081),f306(f306(f237(x68081),x68082),x68083)),f306(f306(f237(x68081),x68084),x68083)),f306(f306(f237(x68081),f306(f306(f264(x68081),x68082),x68084)),x68083)) % 187.68/187.64 [6809]~P118(x68091)+E(f306(f306(f22(x68091),f306(f306(f264(x68091),x68092),x68093)),f306(f306(f264(x68091),x68094),x68093)),f306(f306(f264(x68091),f306(f306(f22(x68091),x68092),x68094)),x68093)) % 187.68/187.64 [6810]~P118(x68101)+E(f306(f306(f81(x68101),f306(f306(f264(x68101),x68102),x68103)),f306(f306(f264(x68101),x68104),x68103)),f306(f306(f264(x68101),f306(f306(f81(x68101),x68102),x68104)),x68103)) % 187.68/187.64 [6811]~P101(x68111)+E(f306(f306(f109(x68111),f306(f306(f108(x68111),x68112),x68113)),f306(f306(f108(x68111),x68114),x68113)),f306(f306(f108(x68111),f306(f306(f109(x68111),x68112),x68114)),x68113)) % 187.68/187.64 [6812]~P101(x68121)+E(f306(f306(f108(x68121),f306(f306(f109(x68121),x68122),x68123)),f306(f306(f109(x68121),x68124),x68123)),f306(f306(f109(x68121),f306(f306(f108(x68121),x68122),x68124)),x68123)) % 187.68/187.64 [6813]~P113(x68131)+E(f306(f306(f81(x68131),f306(f306(f82(x68131),x68132),x68133)),f306(f306(f82(x68131),x68134),x68133)),f306(f306(f82(x68131),f306(f306(f81(x68131),x68132),x68134)),x68133)) % 187.68/187.64 [6845]E(f306(f306(f151(x68451,x68452),x68453),x68454),x68452)+~P1(f306(f306(f220(a865),f306(f186(f866(x68451)),x68452)),x68453)) % 187.68/187.64 [6868]~P1(f306(x68683,x68684))+P1(f306(f306(f306(f108(f872(x68681,a859)),x68682),x68683),x68684)) % 187.68/187.64 [6870]~P1(f306(x68702,x68704))+P1(f306(f306(f306(f108(f872(x68701,a859)),x68702),x68703),x68704)) % 187.68/187.64 [6891]E(f306(f306(f157(x68911),f306(f306(f122(x68911),x68912),x68913)),x68914),f306(f306(f157(x68911),x68912),x68914))+~P1(f306(f306(f221(a865),x68914),f306(f186(f866(x68911)),x68912))) % 187.68/187.64 [6901]E(f306(f306(f22(f872(x69011,a859)),f306(f306(f284(x69011),x69012),x69013)),x69014),f306(f306(f22(f872(x69011,a859)),x69013),x69014))+~P1(f306(f306(f308(x69011),x69012),x69014)) % 187.68/187.64 [6942]~E(f131(a865,f306(f276(a865,x69421),x69422)),f306(f306(f143(a865),x69424),x69423))+E(f131(a865,f306(f276(a865,f306(f306(f81(a865),x69421),f79(a865))),x69422)),x69423) % 187.68/187.64 [7015]E(x70151,f2(a865))+E(f306(f306(f143(x70152),x70153),f306(f306(f165(x70152),f306(f306(f22(a865),x70151),f79(a865))),x70154)),f306(f306(f165(x70152),x70151),f306(f306(f143(x70152),x70153),x70154))) % 187.68/187.64 [7115]E(f306(f306(f157(x71151),x71152),f306(f306(f22(a865),x71153),f306(f186(f866(x71151)),x71154))),f306(f306(f157(x71151),f306(f306(f122(x71151),x71154),x71152)),x71153))+P1(f306(f306(f221(a865),x71153),f306(f186(f866(x71151)),x71154))) % 187.68/187.64 [7145]E(f306(f306(f109(f872(x71451,a859)),x71452),f306(f306(f284(x71451),x71453),x71454)),f306(f306(f284(x71451),x71453),f306(f306(f109(f872(x71451,a859)),x71452),x71454)))+~P1(f306(f306(f308(x71451),x71453),x71452)) % 187.68/187.64 [7180]E(f306(f306(f157(x71801),f306(f306(f151(x71801,x71802),x71803),x71804)),x71803),x71804)+~P1(f306(f306(f221(a865),x71803),f306(f186(f866(x71801)),x71802))) % 187.68/187.64 [7201]E(x72011,f185(f872(x72012,a859)))+E(f306(f285(f871(x72013,x72012),x72013,f235(x72013,x72012)),f306(f306(f243(x72013,x72012),x72014),f306(f16(f872(x72012,a859),x72013),x72011))),x72014) % 187.68/187.64 [7202]E(x72021,f185(f872(x72022,a859)))+E(f306(f285(f871(x72022,x72023),x72023,f244(x72022,x72023)),f306(f306(f243(x72022,x72023),x72021),f306(f16(f872(x72023,a859),x72022),x72024))),x72024) % 187.68/187.64 [7269]E(f306(f306(f22(f872(x72691,a859)),f306(f306(f284(x72691),x72692),x72693)),x72694),f306(f306(f284(x72691),x72692),f306(f306(f22(f872(x72691,a859)),x72693),x72694)))+P1(f306(f306(f308(x72691),x72692),x72694)) % 187.68/187.64 [7300]P1(f306(x73001,x73002))+P1(f306(f306(f306(f306(a195,f33(x73001,x73003)),x73002),x73004),x73002)) % 187.68/187.64 [7307]~E(x73074,f185(f872(x73072,a859)))+E(f306(f285(f871(x73071,x73072),x73071,f235(x73071,x73072)),f306(f306(f243(x73071,x73072),x73073),f306(f16(f872(x73072,a859),x73071),x73074))),f185(f872(x73071,a859))) % 187.68/187.64 [7308]~E(x73083,f185(f872(x73081,a859)))+E(f306(f285(f871(x73081,x73082),x73082,f244(x73081,x73082)),f306(f306(f243(x73081,x73082),x73083),f306(f16(f872(x73082,a859),x73081),x73084))),f185(f872(x73082,a859))) % 187.68/187.64 [7364]~P1(f306(f306(f308(x73641),x73642),x73644))+P1(f306(f306(f308(x73641),x73642),f306(f306(f108(f872(x73641,a859)),x73643),x73644))) % 187.68/187.64 [7367]~P1(f306(f306(f308(x73671),x73672),x73673))+P1(f306(f306(f308(x73671),x73672),f306(f306(f108(f872(x73671,a859)),x73673),x73674))) % 187.68/187.64 [7386]E(f306(f306(f109(f872(x73861,a859)),f306(f306(f284(x73861),x73862),x73863)),x73864),f306(f306(f284(x73861),x73862),f306(f306(f109(f872(x73861,a859)),x73863),x73864)))+~P1(f306(f306(f308(x73861),x73862),x73864)) % 187.68/187.64 [7661]P1(f306(x76611,x76612))+~P1(f306(f306(f306(f109(f872(x76613,a859)),x76614),x76611),x76612)) % 187.68/187.64 [7662]P1(f306(x76621,x76622))+~P1(f306(f306(f306(f109(f872(x76623,a859)),x76621),x76624),x76622)) % 187.68/187.64 [7665]E(f306(f306(f6(x76651,a865),x76652),f306(f306(f22(f872(x76651,a859)),x76653),f306(f306(f284(x76651),x76654),f185(f872(x76651,a859))))),f306(f306(f6(x76651,a865),x76652),x76653))+P1(f306(f306(f308(x76651),x76654),x76653)) % 187.68/187.64 [7671]~P74(x76711)+E(f306(f158(x76711),f306(f306(f146(a865,x76711),x76712),f131(a865,f306(f276(a865,x76713),x76714)))),f306(f306(f6(a865,x76711),x76712),f306(f164(a865),f131(a865,f306(f276(a865,x76713),x76714))))) % 187.68/187.64 [7672]~P74(x76721)+E(f306(f306(f6(a865,x76721),x76722),f306(f164(a865),f131(a865,f306(f276(a865,x76723),x76724)))),f306(f158(x76721),f306(f306(f146(a865,x76721),x76722),f131(a865,f306(f276(a865,x76723),x76724))))) % 187.68/187.64 [7783]~E(x77833,x77834)+P1(f306(f64(x77831,x77832,f306(f306(f284(x77831),x77833),f185(f872(x77831,a859)))),x77834)) % 187.68/187.64 [7880]P1(f306(f306(f308(x78801),x78802),f306(f164(x78801),x78803)))+~P1(f306(f306(f308(x78801),x78802),f306(f164(x78801),f306(f306(f165(x78801),x78804),x78803)))) % 187.68/187.64 [7881]P1(f306(f306(f308(x78811),x78812),f306(f164(x78811),x78813)))+~P1(f306(f306(f308(x78811),x78812),f306(f164(x78811),f306(f306(f130(x78811),x78814),x78813)))) % 187.68/187.64 [7954]P1(f306(f306(f308(x79541),x79542),x79543))+~P1(f306(f306(f308(x79541),x79542),f306(f306(f22(f872(x79541,a859)),x79543),x79544))) % 187.68/187.64 [7956]P1(f306(f306(f308(x79561),x79562),x79563))+~P1(f306(f306(f308(x79561),x79562),f306(f306(f109(f872(x79561,a859)),x79564),x79563))) % 187.68/187.64 [7959]P1(f306(f306(f308(x79591),x79592),x79593))+~P1(f306(f306(f308(x79591),x79592),f306(f306(f109(f872(x79591,a859)),x79593),x79594))) % 187.68/187.64 [7977]E(f306(f306(f122(x79771),f306(f306(f165(x79771),x79772),x79773)),f306(f306(f143(x79771),x79774),f306(f306(f130(x79771),f306(a119,x79772)),x79773))),f306(f306(f151(x79771,x79773),x79772),x79774))+~P1(f306(f306(f221(a865),x79772),f306(f186(f866(x79771)),x79773))) % 187.68/187.64 [8002]P1(f306(f306(f308(x80021),x80022),x80023))+~P1(f306(f306(f220(f872(x80021,a859)),f306(f306(f284(x80021),x80022),x80024)),x80023)) % 187.68/187.64 [8036]~P1(f306(f306(f308(x80361),x80362),x80363))+~P1(f306(f306(f308(x80361),x80362),f306(f306(f22(f872(x80361,a859)),x80364),x80363))) % 187.68/187.64 [8069]~P1(f306(f306(f221(a865),x80694),f306(f186(f866(x80691)),x80693)))+P1(f306(f306(f308(x80691),x80692),f306(f164(x80691),f306(f306(f151(x80691,x80693),x80694),x80692)))) % 187.68/187.64 [8125]E(f306(f306(f157(x81251),f306(f306(f130(x81251),x81252),x81253)),x81254),f306(f306(f157(x81251),x81253),f306(f306(f81(a865),x81252),x81254)))+~P1(f306(f306(f220(a865),f306(f306(f81(a865),x81252),x81254)),f306(f186(f866(x81251)),x81253))) % 187.68/187.64 [8135]~P141(x81352)+E(f306(f306(f6(x81351,x81352),f306(f306(f8(a865,x81352,x81351),f107(x81352)),x81353)),x81354),f306(f107(x81352),f306(f306(f6(x81351,a865),x81353),x81354))) % 187.68/187.64 [8136]~P125(x81362)+E(f306(f306(f6(x81361,x81362),f306(f306(f8(a1,x81362,x81361),f110(x81362)),x81363)),x81364),f306(f110(x81362),f306(f306(f6(x81361,a1),x81363),x81364))) % 187.68/187.64 [8189]~P64(x81892)+E(f306(f306(f9(x81891,x81892),f306(f306(f8(x81892,x81892,x81891),f76(x81892)),x81893)),x81894),f306(f76(x81892),f306(f306(f9(x81891,x81892),x81893),x81894))) % 187.68/187.64 [8190]~P68(x81902)+E(f306(f306(f6(x81901,x81902),f306(f306(f8(x81902,x81902,x81901),f80(x81902)),x81903)),x81904),f306(f80(x81902),f306(f306(f6(x81901,x81902),x81903),x81904))) % 187.68/187.64 [8192]E(f306(f306(f6(x81921,a865),x81922),f306(f306(f22(f872(x81921,a859)),x81923),f306(f306(f284(x81921),x81924),f185(f872(x81921,a859))))),f306(f306(f22(a865),f306(f306(f6(x81921,a865),x81922),x81923)),f306(x81922,x81924)))+~P1(f306(f306(f308(x81921),x81924),x81923)) % 187.68/187.64 [8212]P1(f306(f306(f220(f872(x82121,a859)),x82122),x82123))+~P1(f306(f306(f220(f872(x82121,a859)),f306(f306(f284(x82121),x82124),x82122)),x82123)) % 187.68/187.64 [8421]E(f306(a119,f467(x84211,x84212,x84213,x84214)),x84212)+~P1(f306(f306(f306(f306(a195,f306(a26,x84214)),x84213),x84212),x84211)) % 187.68/187.64 [8423]E(f306(f306(f169(x84231,x84232),x84233),x84234),f188(x84232))+P1(f306(f306(f308(x84231),x84234),f306(f285(f871(x84231,x84232),x84231,f235(x84231,x84232)),f306(f164(f871(x84231,x84232)),x84233)))) % 187.68/187.64 [8424]P40(x84241,x84242)+~P40(x84241,f306(f306(f284(f871(x84241,x84241)),f306(f306(f236(x84241,x84241),x84243),x84244)),x84242)) % 187.68/187.64 [8425]P57(x84251,x84252)+~P57(x84251,f306(f306(f284(f871(x84251,x84251)),f306(f306(f236(x84251,x84251),x84253),x84254)),x84252)) % 187.68/187.64 [8434]~P108(x84341)+E(f306(f306(f140(x84341,x84341,f5(x84341)),x84342),f306(f306(f140(x84341,x84341,f5(x84341)),x84343),x84344)),f306(f306(f140(x84341,x84341,f5(x84341)),x84343),f306(f306(f140(x84341,x84341,f5(x84341)),x84342),x84344))) % 187.68/187.64 [8444]E(x84441,x84442)+~P1(f306(f64(x84443,x84444,f306(f306(f284(x84443),x84441),f185(f872(x84443,a859)))),x84442)) % 187.68/187.64 [8456]E(f306(f306(f122(x84561),f306(f306(f165(x84561),x84562),x84563)),f306(f306(f165(x84561),x84564),f306(f306(f130(x84561),x84562),x84563))),f306(f306(f165(x84561),f306(f306(f81(a865),x84562),x84564)),x84563))+~P1(f306(f306(f220(a865),f306(f306(f81(a865),x84562),x84564)),f306(f186(f866(x84561)),x84563))) % 187.68/187.64 [8496]P1(f306(f63(x84961),x84962))+~E(x84962,f306(f285(a865,x84961,x84963),f306(f228(a865),f306(f306(f7(a865,a865,a859),f221(a865)),x84964)))) % 187.68/187.64 [8516]~P89(x85161)+E(f306(f134(x85161,x85161,f81(x85161),f306(f306(f81(x85161),x85162),x85163)),x85164),f306(f306(f81(x85161),x85162),f306(f134(x85161,x85161,f81(x85161),x85163),x85164))) % 187.68/187.64 [8551]P1(f306(f306(f220(f872(x85511,a859)),f306(f234(x85511,x85512),x85513)),f306(f234(x85511,x85512),x85514)))+~P1(f306(f306(f220(f872(f871(x85511,x85512),a859)),x85513),x85514)) % 187.68/187.64 [8564]~P1(f306(f306(f220(a865),x85642),x85644))+P1(f306(f306(f220(f872(x85641,a859)),f306(f164(x85641),f306(f306(f165(x85641),x85642),x85643))),f306(f164(x85641),f306(f306(f165(x85641),x85644),x85643)))) % 187.68/187.64 [8565]~P1(f306(f306(f220(a865),x85654),x85652))+P1(f306(f306(f220(f872(x85651,a859)),f306(f164(x85651),f306(f306(f130(x85651),x85652),x85653))),f306(f164(x85651),f306(f306(f130(x85651),x85654),x85653)))) % 187.68/187.64 [8618]~P1(f306(f63(x86181),f306(f306(f22(f872(x86181,a859)),x86182),x86184)))+P1(f306(f63(x86181),f306(f306(f22(f872(x86181,a859)),x86182),f306(f306(f284(x86181),x86183),x86184)))) % 187.68/187.64 [8652]P1(f306(f306(f308(f871(x86521,x86521)),x86522),f282(x86521,x86523)))+~P1(f306(f306(f308(f871(x86521,x86521)),x86522),f306(f306(f180(f871(x86521,x86521),a859),x86524),x86523))) % 187.68/187.64 [8730]~P1(f306(f63(x87301),f306(f306(f22(f872(x87301,a859)),x87302),f306(f306(f284(x87301),x87304),x87303))))+P1(f306(f63(x87301),f306(f306(f22(f872(x87301,a859)),x87302),x87303))) % 187.68/187.64 [8879]~E(f306(f306(f169(x88791,x88792),x88793),x88794),f188(x88792))+~P1(f306(f306(f308(x88791),x88794),f306(f285(f871(x88791,x88792),x88791,f235(x88791,x88792)),f306(f164(f871(x88791,x88792)),x88793)))) % 187.68/187.64 [8946]~P108(x89461)+P1(f306(f306(f220(x89461),f306(f306(f219(x89461),x89462),f306(f306(f225(x89461),x89463),x89464))),f306(f306(f225(x89461),f306(f306(f219(x89461),x89462),x89463)),f306(f306(f219(x89461),x89462),x89464)))) % 187.68/187.64 [8947]~P98(x89471)+P1(f306(f306(f220(x89471),f306(f306(f108(x89471),x89472),f306(f306(f109(x89471),x89473),x89474))),f306(f306(f109(x89471),f306(f306(f108(x89471),x89472),x89473)),f306(f306(f108(x89471),x89472),x89474)))) % 187.68/187.64 [9093]E(x90931,x90932)+~P1(f306(f306(f308(f871(x90933,x90933)),f306(f306(f236(x90933,x90933),x90931),x90932)),f306(f164(f871(x90933,x90933)),f306(f306(f173(x90933,x90933),x90934),x90934)))) % 187.68/187.64 [9127]~P1(f306(f306(f308(f871(x91271,x91271)),f306(f306(f236(x91271,x91271),x91273),x91272)),f282(x91271,x91274)))+~P40(x91271,f306(f306(f284(f871(x91271,x91271)),f306(f306(f236(x91271,x91271),x91272),x91273)),x91274)) % 187.68/187.64 [9128]~P1(f306(f306(f308(f871(x91281,x91281)),f306(f306(f236(x91281,x91281),x91283),x91282)),f282(x91281,x91284)))+~P57(x91281,f306(f306(f284(f871(x91281,x91281)),f306(f306(f236(x91281,x91281),x91282),x91283)),x91284)) % 187.68/187.64 [9133]E(x91331,x91332)+E(f306(f128(x91333,f306(f306(f8(a859,a859,x91333),a301),f306(a303,x91331))),f306(f306(f143(x91333),x91332),x91334)),f306(f306(f143(x91333),x91332),f306(f128(x91333,f306(f306(f8(a859,a859,x91333),a301),f306(a303,x91331))),x91334))) % 187.68/187.64 [9178]~P108(x91781)+P1(f306(f306(f220(x91781),f306(f306(f219(x91781),f306(f306(f225(x91781),x91782),x91783)),f306(f306(f225(x91781),x91782),x91784))),f306(f306(f225(x91781),x91782),f306(f306(f219(x91781),x91783),x91784)))) % 187.68/187.64 [9179]~P98(x91791)+P1(f306(f306(f220(x91791),f306(f306(f108(x91791),f306(f306(f109(x91791),x91792),x91793)),f306(f306(f109(x91791),x91792),x91794))),f306(f306(f109(x91791),x91792),f306(f306(f108(x91791),x91793),x91794)))) % 187.68/187.64 [9255]~E(f306(f285(x92552,x92551,x92553),f231(f872(x92552,a859))),f231(f872(x92551,a859)))+P1(f306(f306(f220(f872(x92551,a859)),f306(f80(f872(x92551,a859)),f306(f285(x92552,x92551,x92553),x92554))),f306(f285(x92552,x92551,x92553),f306(f80(f872(x92552,a859)),x92554)))) % 187.68/187.64 [9334]P1(f306(f306(f306(f306(a195,f306(f218(a860),f306(a28,x93341))),x93342),f467(x93343,x93344,x93342,x93341)),x93343))+~P1(f306(f306(f306(f306(a195,f306(a26,x93341)),x93342),x93344),x93343)) % 187.68/187.64 [9581]P1(f306(f306(f308(f871(x95811,x95811)),f306(f306(f236(x95811,x95811),x95812),x95813)),f306(f261(x95811,x95811),f306(f306(f263(x95811,x95811,x95811),x95814),f282(x95811,x95814)))))+~P1(f306(f306(f308(f871(x95811,x95811)),f306(f306(f236(x95811,x95811),x95812),x95813)),f306(f306(f263(x95811,x95811,x95811),f306(f261(x95811,x95811),x95814)),f282(x95811,f306(f261(x95811,x95811),x95814))))) % 187.68/187.64 [9582]~P1(f306(f306(f308(f871(x95821,x95821)),f306(f306(f236(x95821,x95821),x95822),x95823)),f306(f261(x95821,x95821),f306(f306(f263(x95821,x95821,x95821),x95824),f282(x95821,x95824)))))+P1(f306(f306(f308(f871(x95821,x95821)),f306(f306(f236(x95821,x95821),x95822),x95823)),f306(f306(f263(x95821,x95821,x95821),f306(f261(x95821,x95821),x95824)),f282(x95821,f306(f261(x95821,x95821),x95824))))) % 187.68/187.64 [9603]~P1(f306(f306(f308(x96032),x96034),f306(f232(x96031,x96032),x96033)))+P1(f306(f306(f308(f871(x96031,x96032)),f306(f306(f236(x96031,x96032),f526(x96033,x96031,x96034,x96032)),x96034)),x96033)) % 187.68/187.64 [9604]~P1(f306(f306(f308(x96042),x96044),f306(f232(x96041,x96042),x96043)))+P1(f306(f306(f308(f871(x96041,x96042)),f306(f306(f236(x96041,x96042),f527(x96043,x96041,x96044,x96042)),x96044)),x96043)) % 187.68/187.64 [9627]~P1(f306(f306(f308(x96271),x96274),f306(f306(f108(f872(x96271,a859)),x96272),x96273)))+P1(f306(f306(f306(f108(f872(x96271,a859)),f306(f306(f7(x96271,f872(x96271,a859),a859),f308(x96271)),x96272)),f306(f306(f7(x96271,f872(x96271,a859),a859),f308(x96271)),x96273)),x96274)) % 187.68/187.64 [9628]~P1(f306(f306(f308(x96281),x96284),f306(f306(f109(f872(x96281,a859)),x96282),x96283)))+P1(f306(f306(f306(f109(f872(x96281,a859)),f306(f306(f7(x96281,f872(x96281,a859),a859),f308(x96281)),x96282)),f306(f306(f7(x96281,f872(x96281,a859),a859),f308(x96281)),x96283)),x96284)) % 187.68/187.64 [9706]~P1(f306(f306(f308(f871(x97061,x97061)),f306(f306(f236(x97061,x97061),x97064),x97063)),f306(f306(f263(x97061,x97061,x97061),x97062),f282(x97061,x97062))))+P1(f306(f306(f308(f871(x97061,x97061)),f306(f306(f236(x97061,x97061),f619(x97062,x97063,x97064,x97061)),x97063)),x97062)) % 187.68/187.64 [9753]P1(f306(f306(f308(x97531),x97532),f306(f306(f108(f872(x97531,a859)),x97533),x97534)))+~P1(f306(f306(f306(f108(f872(x97531,a859)),f306(f306(f7(x97531,f872(x97531,a859),a859),f308(x97531)),x97533)),f306(f306(f7(x97531,f872(x97531,a859),a859),f308(x97531)),x97534)),x97532)) % 187.68/187.64 [9754]P1(f306(f306(f308(x97541),x97542),f306(f306(f109(f872(x97541,a859)),x97543),x97544)))+~P1(f306(f306(f306(f109(f872(x97541,a859)),f306(f306(f7(x97541,f872(x97541,a859),a859),f308(x97541)),x97543)),f306(f306(f7(x97541,f872(x97541,a859),a859),f308(x97541)),x97544)),x97542)) % 187.68/187.64 [10035]P35(x100351,f306(f306(f7(x100351,f872(f871(x100351,x100351),a859),f872(x100351,a859)),f306(f306(f8(f872(x100351,f872(f872(f871(x100351,x100351),a859),a859)),f872(f872(f871(x100351,x100351),a859),f872(x100351,a859)),x100351),f7(x100351,f872(f871(x100351,x100351),a859),a859)),f306(f306(f8(f872(x100351,f871(x100351,x100351)),f872(x100351,f872(f872(f871(x100351,x100351),a859),a859)),x100351),f306(f8(f871(x100351,x100351),f872(f872(f871(x100351,x100351),a859),a859),x100351),f308(f871(x100351,x100351)))),f236(x100351,x100351)))),x100352),x100353,x100354)+~P1(f306(f306(f308(f871(f866(x100351),f866(x100351))),f306(f306(f236(f866(x100351),f866(x100351)),x100353),x100354)),f150(x100351,x100352))) % 187.68/187.64 [10039]P58(x100391,f306(f306(f7(x100391,f872(f871(x100391,x100391),a859),f872(x100391,a859)),f306(f306(f8(f872(x100391,f872(f872(f871(x100391,x100391),a859),a859)),f872(f872(f871(x100391,x100391),a859),f872(x100391,a859)),x100391),f7(x100391,f872(f871(x100391,x100391),a859),a859)),f306(f306(f8(f872(x100391,f871(x100391,x100391)),f872(x100391,f872(f872(f871(x100391,x100391),a859),a859)),x100391),f306(f8(f871(x100391,x100391),f872(f872(f871(x100391,x100391),a859),a859),x100391),f308(f871(x100391,x100391)))),f236(x100391,x100391)))),x100392),x100393,x100394)+~P1(f306(f306(f308(f871(f872(x100391,a859),f872(x100391,a859))),f306(f306(f236(f872(x100391,a859),f872(x100391,a859)),x100393),x100394)),f298(x100391,x100392))) % 187.68/187.64 [10069]E(x100691,x100692)+~E(f306(f306(f7(x100693,f872(f871(x100693,x100694),a859),f872(x100694,a859)),f306(f306(f8(f872(x100694,f872(f872(f871(x100693,x100694),a859),a859)),f872(f872(f871(x100693,x100694),a859),f872(x100694,a859)),x100693),f7(x100694,f872(f871(x100693,x100694),a859),a859)),f306(f306(f8(f872(x100694,f871(x100693,x100694)),f872(x100694,f872(f872(f871(x100693,x100694),a859),a859)),x100693),f306(f8(f871(x100693,x100694),f872(f872(f871(x100693,x100694),a859),a859),x100694),f308(f871(x100693,x100694)))),f236(x100693,x100694)))),x100691),f306(f306(f7(x100693,f872(f871(x100693,x100694),a859),f872(x100694,a859)),f306(f306(f8(f872(x100694,f872(f872(f871(x100693,x100694),a859),a859)),f872(f872(f871(x100693,x100694),a859),f872(x100694,a859)),x100693),f7(x100694,f872(f871(x100693,x100694),a859),a859)),f306(f306(f8(f872(x100694,f871(x100693,x100694)),f872(x100694,f872(f872(f871(x100693,x100694),a859),a859)),x100693),f306(f8(f871(x100693,x100694),f872(f872(f871(x100693,x100694),a859),a859),x100694),f308(f871(x100693,x100694)))),f236(x100693,x100694)))),x100692)) % 187.68/187.64 [10073]~P35(x100731,f306(f306(f7(x100731,f872(f871(x100731,x100731),a859),f872(x100731,a859)),f306(f306(f8(f872(x100731,f872(f872(f871(x100731,x100731),a859),a859)),f872(f872(f871(x100731,x100731),a859),f872(x100731,a859)),x100731),f7(x100731,f872(f871(x100731,x100731),a859),a859)),f306(f306(f8(f872(x100731,f871(x100731,x100731)),f872(x100731,f872(f872(f871(x100731,x100731),a859),a859)),x100731),f306(f8(f871(x100731,x100731),f872(f872(f871(x100731,x100731),a859),a859),x100731),f308(f871(x100731,x100731)))),f236(x100731,x100731)))),x100734),x100732,x100733)+P1(f306(f306(f308(f871(f866(x100731),f866(x100731))),f306(f306(f236(f866(x100731),f866(x100731)),x100732),x100733)),f150(x100731,x100734))) % 187.68/187.64 [10074]~P58(x100741,f306(f306(f7(x100741,f872(f871(x100741,x100741),a859),f872(x100741,a859)),f306(f306(f8(f872(x100741,f872(f872(f871(x100741,x100741),a859),a859)),f872(f872(f871(x100741,x100741),a859),f872(x100741,a859)),x100741),f7(x100741,f872(f871(x100741,x100741),a859),a859)),f306(f306(f8(f872(x100741,f871(x100741,x100741)),f872(x100741,f872(f872(f871(x100741,x100741),a859),a859)),x100741),f306(f8(f871(x100741,x100741),f872(f872(f871(x100741,x100741),a859),a859),x100741),f308(f871(x100741,x100741)))),f236(x100741,x100741)))),x100744),x100742,x100743)+P1(f306(f306(f308(f871(f872(x100741,a859),f872(x100741,a859))),f306(f306(f236(f872(x100741,a859),f872(x100741,a859)),x100742),x100743)),f298(x100741,x100744))) % 187.68/187.64 [7438]~P91(x74381)+E(f306(f306(f81(x74381),f306(f111(x74381),x74382)),f306(f306(f22(x74381),f306(f111(x74381),x74383)),x74384)),f306(f306(f22(x74381),f306(f111(x74381),f306(f306(f81(a1),x74382),x74383))),x74384)) % 187.68/187.64 [7439]~P91(x74391)+E(f306(f306(f81(x74391),f306(f111(x74391),x74392)),f306(f306(f81(x74391),f306(f111(x74391),x74393)),x74394)),f306(f306(f81(x74391),f306(f111(x74391),f306(f306(f81(a1),x74392),x74393))),x74394)) % 187.68/187.64 [7440]~P91(x74401)+E(f306(f306(f82(x74401),f306(f111(x74401),x74402)),f306(f306(f82(x74401),f306(f111(x74401),x74403)),x74404)),f306(f306(f82(x74401),f306(f111(x74401),f306(f306(f82(a1),x74402),x74403))),x74404)) % 187.68/187.64 [7482]~P141(x74821)+E(f306(f158(x74821),f306(f306(f146(x74822,x74821),f306(f16(x74821,x74822),x74823)),x74824)),f306(f306(f82(x74821),f306(f107(x74821),f306(f186(f866(x74822)),x74824))),x74823)) % 187.68/187.64 [7716]E(f306(f252(x77161,f306(f306(f143(f871(a106,x77161)),x77162),x77163)),x77164),f306(f244(a106,x77161),x77162))+~P1(f306(f306(f221(a106),x77164),f306(f235(a106,x77161),x77162))) % 187.68/187.64 [7761]~P91(x77611)+E(f306(f306(f81(x77611),f306(f111(x77611),x77612)),f306(f306(f22(x77611),x77613),f306(f111(x77611),x77614))),f306(f306(f81(x77611),f306(f111(x77611),f306(f306(f81(a1),x77612),f306(f80(a1),x77614)))),x77613)) % 187.68/187.64 [7893]E(f306(f252(x78931,x78932),f306(f306(f22(a106),x78933),f306(f235(a106,x78931),x78934))),f306(f252(x78931,f306(f306(f143(f871(a106,x78931)),x78934),x78932)),x78933))+P1(f306(f306(f221(a106),x78933),f306(f235(a106,x78931),x78934))) % 187.68/187.64 [8339]~P1(f306(f306(f308(x83391),x83392),f306(f164(x83391),f121(x83391,x83394))))+P1(f306(f306(f308(x83391),x83392),f306(f164(x83391),f121(x83391,f306(f306(f122(x83391),x83393),x83394))))) % 187.68/187.64 [8340]~P1(f306(f306(f308(x83401),x83402),f306(f164(x83401),f121(x83401,x83403))))+P1(f306(f306(f308(x83401),x83402),f306(f164(x83401),f121(x83401,f306(f306(f122(x83401),x83403),x83404))))) % 187.68/187.64 [8361]E(f306(f306(f108(f872(x83611,a859)),f306(f306(f109(f872(x83611,a859)),x83612),x83613)),x83614),f306(f306(f109(f872(x83611,a859)),x83612),f306(f306(f108(f872(x83611,a859)),x83613),x83614)))+~P1(f306(f306(f220(f872(x83611,a859)),x83614),x83612)) % 187.68/187.64 [8665]~E(f306(f306(f108(f872(x86651,a859)),f306(f306(f109(f872(x86651,a859)),x86653),x86654)),x86652),f306(f306(f109(f872(x86651,a859)),x86653),f306(f306(f108(f872(x86651,a859)),x86654),x86652)))+P1(f306(f306(f220(f872(x86651,a859)),x86652),x86653)) % 187.68/187.64 [8952]~P1(f306(f306(f220(f872(x89521,a859)),x89522),f306(f306(f108(f872(x89521,a859)),x89523),x89524)))+P1(f306(f306(f220(f872(x89521,a859)),f306(f306(f22(f872(x89521,a859)),x89522),x89523)),x89524)) % 187.68/187.64 [9012]~P1(f306(f306(f306(f306(a195,f306(a26,x90121)),x90122),f306(a119,x90123)),x90124))+P1(f306(f306(f306(f306(a195,f306(f218(a860),f306(a28,x90121))),x90122),x90123),x90124)) % 187.68/187.64 [9071]P1(f306(f306(f220(f872(x90711,a859)),x90712),f306(f306(f108(f872(x90711,a859)),x90713),x90714)))+~P1(f306(f306(f220(f872(x90711,a859)),f306(f306(f22(f872(x90711,a859)),x90712),x90713)),x90714)) % 187.68/187.64 [9126]P1(f306(f306(f306(f306(a195,f306(a26,x91261)),x91262),f306(a119,x91263)),x91264))+~P1(f306(f306(f306(f306(a195,f306(f218(a860),f306(a28,x91261))),x91262),x91263),x91264)) % 187.68/187.64 [9159]~P84(x91591)+E(f306(f76(x91591),f306(f306(f6(x91592,x91591),f306(f306(f8(x91591,x91591,x91592),f76(x91591)),x91593)),x91594)),f306(f306(f6(x91592,x91591),f306(f306(f8(x91591,x91591,x91592),f76(x91591)),x91593)),x91594)) % 187.68/187.64 [9332]~P84(x93321)+P1(f306(f306(f220(x93321),f2(x93321)),f306(f306(f6(x93322,x93321),f306(f306(f8(x93321,x93321,x93322),f76(x93321)),x93323)),x93324))) % 187.68/187.64 [9337]~P68(x93371)+E(f306(f158(x93371),f306(f306(f146(x93372,x93371),f306(f74(x93371,x93371,x93372,f80(x93371)),x93373)),x93374)),f306(f80(x93371),f306(f158(x93371),f306(f306(f146(x93372,x93371),x93373),x93374)))) % 187.68/187.64 [9473]~P84(x94731)+P1(f306(f306(f220(x94731),f306(f76(x94731),f306(f306(f6(x94732,x94731),x94733),x94734))),f306(f306(f6(x94732,x94731),f306(f306(f8(x94731,x94731,x94732),f76(x94731)),x94733)),x94734))) % 187.68/187.64 [9505]~E(f306(f306(f81(a865),x95051),x95054),f306(f306(f81(a865),x95053),x95052))+P1(f306(f306(f308(f871(f871(a865,a865),f871(a865,a865))),f306(f306(f236(f871(a865,a865),f871(a865,a865)),f306(f306(f236(a865,a865),x95051),x95052)),f306(f306(f236(a865,a865),x95053),x95054))),a116)) % 187.68/187.64 [9506]~P1(f306(f306(f221(a865),x95061),x95063))+P1(f306(f306(f308(f871(f871(a865,a865),f871(a865,a865))),f306(f306(f236(f871(a865,a865),f871(a865,a865)),f306(f306(f236(a865,a865),x95061),x95062)),f306(f306(f236(a865,a865),x95063),x95064))),a36)) % 187.68/187.64 [9507]~P1(f306(f306(f221(a865),x95071),x95073))+P1(f306(f306(f308(f871(f871(a865,a865),f871(a865,a865))),f306(f306(f236(f871(a865,a865),f871(a865,a865)),f306(f306(f236(a865,a865),x95071),x95072)),f306(f306(f236(a865,a865),x95073),x95074))),a71)) % 187.68/187.64 [9653]E(f306(f306(f81(a865),x96531),x96532),f306(f306(f81(a865),x96533),x96534))+~P1(f306(f306(f308(f871(f871(a865,a865),f871(a865,a865))),f306(f306(f236(f871(a865,a865),f871(a865,a865)),f306(f306(f236(a865,a865),x96531),x96534)),f306(f306(f236(a865,a865),x96533),x96532))),a116)) % 187.68/187.64 [9679]E(f306(f306(f157(x96791),f306(f306(f130(x96791),f306(f186(f866(x96791)),f168(x96791,x96792,x96793))),x96793)),x96794),f306(f306(f157(x96791),x96793),f306(f306(f81(a865),x96794),f306(f186(f866(x96791)),f168(x96791,x96792,x96793)))))+~P1(f306(f306(f221(a865),x96794),f306(f186(f866(x96791)),f306(f306(f130(x96791),f306(f186(f866(x96791)),f168(x96791,x96792,x96793))),x96793)))) % 187.68/187.64 [9697]~P1(f306(f306(f308(x96972),x96974),f306(f306(f43(x96971,f872(x96972,a859)),f231(f872(x96971,a859))),x96973)))+P1(f306(f306(f306(f43(x96971,f872(x96972,a859)),f231(f872(x96971,a859))),f306(f306(f8(f872(x96972,a859),f872(x96972,a859),x96971),f306(f7(x96972,f872(x96972,a859),a859),f308(x96972))),x96973)),x96974)) % 187.68/187.64 [9698]~P1(f306(f306(f308(x96982),x96984),f306(f306(f44(x96981,f872(x96982,a859)),f231(f872(x96981,a859))),x96983)))+P1(f306(f306(f306(f44(x96981,f872(x96982,a859)),f231(f872(x96981,a859))),f306(f306(f8(f872(x96982,a859),f872(x96982,a859),x96981),f306(f7(x96982,f872(x96982,a859),a859),f308(x96982))),x96983)),x96984)) % 187.68/187.64 [9780]~P1(f306(f50(x97801,x97802),f306(f306(f236(a1,a1),x97804),x97803)))+P1(f306(f50(f306(f80(a1),x97801),x97802),f306(f306(f236(a1,a1),f306(f306(f306(f101(a1),f306(f306(a303,x97803),f2(a1))),f306(f80(a1),x97804)),f306(f306(f22(a1),f306(f80(a1),x97804)),f79(a1)))),f306(f306(f306(f101(a1),f306(f306(a303,x97803),f2(a1))),f2(a1)),f306(f306(f22(a1),x97802),x97803))))) % 187.68/187.64 [9789]P1(f306(f306(f308(x97891),x97892),f306(f306(f43(x97893,f872(x97891,a859)),f231(f872(x97893,a859))),x97894)))+~P1(f306(f306(f306(f43(x97893,f872(x97891,a859)),f231(f872(x97893,a859))),f306(f306(f8(f872(x97891,a859),f872(x97891,a859),x97893),f306(f7(x97891,f872(x97891,a859),a859),f308(x97891))),x97894)),x97892)) % 187.68/187.64 [9790]P1(f306(f306(f308(x97901),x97902),f306(f306(f44(x97903,f872(x97901,a859)),f231(f872(x97903,a859))),x97904)))+~P1(f306(f306(f306(f44(x97903,f872(x97901,a859)),f231(f872(x97903,a859))),f306(f306(f8(f872(x97901,a859),f872(x97901,a859),x97903),f306(f7(x97901,f872(x97901,a859),a859),f308(x97901))),x97904)),x97902)) % 187.68/187.64 [9801]E(f306(f306(f43(a865,f872(x98011,a859)),f231(f872(a865,a859))),x98012),f306(f306(f43(a865,f872(x98011,a859)),f231(f872(a865,a859))),x98013))+~E(f306(f306(f43(a865,f872(x98011,a859)),f306(f276(a865,f2(a865)),f483(x98012,x98014,x98013,x98011))),x98013),f306(f306(f43(a865,f872(x98011,a859)),f306(f276(a865,f2(a865)),f306(f306(f81(a865),f483(x98012,x98014,x98013,x98011)),x98014))),x98012)) % 187.68/187.64 [10133]~P1(f306(f306(f220(f872(f871(x101331,x101332),a859)),x101333),x101334))+P1(f306(f306(f220(f872(x101331,f872(x101332,a859))),f306(f306(f7(x101331,f872(f871(x101331,x101332),a859),f872(x101332,a859)),f306(f306(f8(f872(x101332,f872(f872(f871(x101331,x101332),a859),a859)),f872(f872(f871(x101331,x101332),a859),f872(x101332,a859)),x101331),f7(x101332,f872(f871(x101331,x101332),a859),a859)),f306(f306(f8(f872(x101332,f871(x101331,x101332)),f872(x101332,f872(f872(f871(x101331,x101332),a859),a859)),x101331),f306(f8(f871(x101331,x101332),f872(f872(f871(x101331,x101332),a859),a859),x101332),f308(f871(x101331,x101332)))),f236(x101331,x101332)))),x101333)),f306(f306(f7(x101331,f872(f871(x101331,x101332),a859),f872(x101332,a859)),f306(f306(f8(f872(x101332,f872(f872(f871(x101331,x101332),a859),a859)),f872(f872(f871(x101331,x101332),a859),f872(x101332,a859)),x101331),f7(x101332,f872(f871(x101331,x101332),a859),a859)),f306(f306(f8(f872(x101332,f871(x101331,x101332)),f872(x101332,f872(f872(f871(x101331,x101332),a859),a859)),x101331),f306(f8(f871(x101331,x101332),f872(f872(f871(x101331,x101332),a859),a859),x101332),f308(f871(x101331,x101332)))),f236(x101331,x101332)))),x101334))) % 187.68/187.64 [10149]P1(f306(f306(f220(f872(f871(x101491,x101492),a859)),x101493),x101494))+~P1(f306(f306(f220(f872(x101491,f872(x101492,a859))),f306(f306(f7(x101491,f872(f871(x101491,x101492),a859),f872(x101492,a859)),f306(f306(f8(f872(x101492,f872(f872(f871(x101491,x101492),a859),a859)),f872(f872(f871(x101491,x101492),a859),f872(x101492,a859)),x101491),f7(x101492,f872(f871(x101491,x101492),a859),a859)),f306(f306(f8(f872(x101492,f871(x101491,x101492)),f872(x101492,f872(f872(f871(x101491,x101492),a859),a859)),x101491),f306(f8(f871(x101491,x101492),f872(f872(f871(x101491,x101492),a859),a859),x101492),f308(f871(x101491,x101492)))),f236(x101491,x101492)))),x101493)),f306(f306(f7(x101491,f872(f871(x101491,x101492),a859),f872(x101492,a859)),f306(f306(f8(f872(x101492,f872(f872(f871(x101491,x101492),a859),a859)),f872(f872(f871(x101491,x101492),a859),f872(x101492,a859)),x101491),f7(x101492,f872(f871(x101491,x101492),a859),a859)),f306(f306(f8(f872(x101492,f871(x101491,x101492)),f872(x101492,f872(f872(f871(x101491,x101492),a859),a859)),x101491),f306(f8(f871(x101491,x101492),f872(f872(f871(x101491,x101492),a859),a859),x101492),f308(f871(x101491,x101492)))),f236(x101491,x101492)))),x101494))) % 187.68/187.64 [9209]~P1(f306(f306(f308(f871(x92091,x92091)),x92092),f282(x92091,x92094)))+P1(f306(f306(f308(f871(x92091,x92091)),x92092),f282(x92091,f306(f306(f108(f872(f871(x92091,x92091),a859)),x92093),x92094)))) % 187.68/187.64 [9210]~P1(f306(f306(f308(f871(x92101,x92101)),x92102),f282(x92101,x92103)))+P1(f306(f306(f308(f871(x92101,x92101)),x92102),f282(x92101,f306(f306(f108(f872(f871(x92101,x92101),a859)),x92103),x92104)))) % 187.68/187.64 [9573]~E(f306(f164(x95731),x95734),f175(x95731,x95732,x95733))+E(f306(f169(x95731,x95732),f306(f306(f146(x95731,f871(x95731,x95732)),f306(f306(f18(x95731,x95732,f871(x95731,x95732)),f236(x95731,x95732)),f306(f306(f8(f869(x95732),x95732,x95731),f218(x95732)),x95733))),x95734)),x95733) % 187.68/187.64 [9897]~P1(f306(f306(f220(a865),f306(f306(f81(a865),x98971),x98974)),f306(f306(f81(a865),x98973),x98972)))+P1(f306(f306(f220(a1),f306(a90,f306(f260(f871(a865,a865),f871(a865,a865),a116),f306(f306(f284(f871(a865,a865)),f306(f306(f236(a865,a865),x98971),x98972)),f185(f872(f871(a865,a865),a859)))))),f306(a90,f306(f260(f871(a865,a865),f871(a865,a865),a116),f306(f306(f284(f871(a865,a865)),f306(f306(f236(a865,a865),x98973),x98974)),f185(f872(f871(a865,a865),a859))))))) % 187.68/187.64 [9898]~P1(f306(f306(f221(a865),f306(f306(f81(a865),x98981),x98984)),f306(f306(f81(a865),x98983),x98982)))+P1(f306(f306(f221(a1),f306(a90,f306(f260(f871(a865,a865),f871(a865,a865),a116),f306(f306(f284(f871(a865,a865)),f306(f306(f236(a865,a865),x98981),x98982)),f185(f872(f871(a865,a865),a859)))))),f306(a90,f306(f260(f871(a865,a865),f871(a865,a865),a116),f306(f306(f284(f871(a865,a865)),f306(f306(f236(a865,a865),x98983),x98984)),f185(f872(f871(a865,a865),a859))))))) % 187.68/187.64 [9977]P1(f306(f306(f220(a865),f306(f306(f81(a865),x99771),x99772)),f306(f306(f81(a865),x99773),x99774)))+~P1(f306(f306(f220(a1),f306(a90,f306(f260(f871(a865,a865),f871(a865,a865),a116),f306(f306(f284(f871(a865,a865)),f306(f306(f236(a865,a865),x99771),x99774)),f185(f872(f871(a865,a865),a859)))))),f306(a90,f306(f260(f871(a865,a865),f871(a865,a865),a116),f306(f306(f284(f871(a865,a865)),f306(f306(f236(a865,a865),x99773),x99772)),f185(f872(f871(a865,a865),a859))))))) % 187.68/187.64 [9978]P1(f306(f306(f221(a865),f306(f306(f81(a865),x99781),x99782)),f306(f306(f81(a865),x99783),x99784)))+~P1(f306(f306(f221(a1),f306(a90,f306(f260(f871(a865,a865),f871(a865,a865),a116),f306(f306(f284(f871(a865,a865)),f306(f306(f236(a865,a865),x99781),x99784)),f185(f872(f871(a865,a865),a859)))))),f306(a90,f306(f260(f871(a865,a865),f871(a865,a865),a116),f306(f306(f284(f871(a865,a865)),f306(f306(f236(a865,a865),x99783),x99782)),f185(f872(f871(a865,a865),a859))))))) % 187.68/187.64 [10020]P1(f306(f306(f220(f872(x100201,a859)),f306(f306(f43(a865,f872(x100201,a859)),f231(f872(a865,a859))),x100202)),f306(f306(f43(a865,f872(x100201,a859)),f231(f872(a865,a859))),x100203)))+~P1(f306(f306(f220(f872(x100201,a859)),f306(f306(f43(a865,f872(x100201,a859)),f306(f276(a865,f2(a865)),f484(x100203,x100204,x100202,x100201))),x100202)),f306(f306(f43(a865,f872(x100201,a859)),f306(f276(a865,f2(a865)),f306(f306(f81(a865),f484(x100203,x100204,x100202,x100201)),x100204))),x100203))) % 187.68/187.64 [10123]~P1(f306(f306(f308(x101232),x101234),f306(f232(x101231,x101232),x101233)))+P1(f306(f242(x101231,x101232,f306(f306(f7(x101231,f872(f871(x101231,x101232),a859),f872(x101232,a859)),f306(f306(f8(f872(x101232,f872(f872(f871(x101231,x101232),a859),a859)),f872(f872(f871(x101231,x101232),a859),f872(x101232,a859)),x101231),f7(x101232,f872(f871(x101231,x101232),a859),a859)),f306(f306(f8(f872(x101232,f871(x101231,x101232)),f872(x101232,f872(f872(f871(x101231,x101232),a859),a859)),x101231),f306(f8(f871(x101231,x101232),f872(f872(f871(x101231,x101232),a859),a859),x101232),f308(f871(x101231,x101232)))),f236(x101231,x101232)))),x101233)),x101234)) % 187.68/187.64 [10124]~P1(f306(f306(f308(x101241),x101244),f306(f234(x101241,x101242),x101243)))+P1(f306(f241(x101241,x101242,f306(f306(f7(x101241,f872(f871(x101241,x101242),a859),f872(x101242,a859)),f306(f306(f8(f872(x101242,f872(f872(f871(x101241,x101242),a859),a859)),f872(f872(f871(x101241,x101242),a859),f872(x101242,a859)),x101241),f7(x101242,f872(f871(x101241,x101242),a859),a859)),f306(f306(f8(f872(x101242,f871(x101241,x101242)),f872(x101242,f872(f872(f871(x101241,x101242),a859),a859)),x101241),f306(f8(f871(x101241,x101242),f872(f872(f871(x101241,x101242),a859),a859),x101242),f308(f871(x101241,x101242)))),f236(x101241,x101242)))),x101243)),x101244)) % 187.68/187.64 [10136]P1(f306(f306(f308(x101361),x101362),f306(f232(x101363,x101361),x101364)))+~P1(f306(f242(x101363,x101361,f306(f306(f7(x101363,f872(f871(x101363,x101361),a859),f872(x101361,a859)),f306(f306(f8(f872(x101361,f872(f872(f871(x101363,x101361),a859),a859)),f872(f872(f871(x101363,x101361),a859),f872(x101361,a859)),x101363),f7(x101361,f872(f871(x101363,x101361),a859),a859)),f306(f306(f8(f872(x101361,f871(x101363,x101361)),f872(x101361,f872(f872(f871(x101363,x101361),a859),a859)),x101363),f306(f8(f871(x101363,x101361),f872(f872(f871(x101363,x101361),a859),a859),x101361),f308(f871(x101363,x101361)))),f236(x101363,x101361)))),x101364)),x101362)) % 187.68/187.64 [10137]P1(f306(f306(f308(x101371),x101372),f306(f234(x101371,x101373),x101374)))+~P1(f306(f241(x101371,x101373,f306(f306(f7(x101371,f872(f871(x101371,x101373),a859),f872(x101373,a859)),f306(f306(f8(f872(x101373,f872(f872(f871(x101371,x101373),a859),a859)),f872(f872(f871(x101371,x101373),a859),f872(x101373,a859)),x101371),f7(x101373,f872(f871(x101371,x101373),a859),a859)),f306(f306(f8(f872(x101373,f871(x101371,x101373)),f872(x101373,f872(f872(f871(x101371,x101373),a859),a859)),x101371),f306(f8(f871(x101371,x101373),f872(f872(f871(x101371,x101373),a859),a859),x101373),f308(f871(x101371,x101373)))),f236(x101371,x101373)))),x101374)),x101372)) % 187.68/187.64 [9811]P1(f306(f152(x98111,x98112),x98113))+~P1(f306(f152(x98111,f306(f306(f18(x98111,a859,a859),f306(f306(f8(a859,f872(a859,a859),x98111),a304),x98114)),x98112)),x98113)) % 187.68/187.64 [9812]P1(f306(f152(x98121,x98122),x98123))+~P1(f306(f152(x98121,f306(f306(f18(x98121,a859,a859),f306(f306(f8(a859,f872(a859,a859),x98121),a304),x98122)),x98124)),x98123)) % 187.68/187.64 [9899]~P113(x98991)+E(f306(f306(f82(x98991),f306(f306(f81(x98991),f79(x98991)),f79(x98991))),f306(f306(f6(a865,x98991),f306(f306(f8(x98991,x98991,a865),f306(f81(x98991),x98992)),f306(f306(f7(a865,x98991,x98991),f306(f306(f8(x98991,f872(x98991,x98991),a865),f82(x98991)),f107(x98991))),x98993))),f306(f229(a865),x98994))),f306(f306(f82(x98991),f306(f107(x98991),x98994)),f306(f306(f81(x98991),x98992),f306(f306(f81(x98991),x98992),f306(f306(f82(x98991),f306(f107(x98991),f306(f306(f22(a865),x98994),f79(a865)))),x98993))))) % 187.68/187.64 [10042]P1(f306(x100421,f538(x100422,x100423,x100424,x100421)))+P40(x100422,f306(f228(f871(x100422,x100422)),f306(f245(x100422,x100422,a859),f306(f306(f8(f872(x100422,a859),f872(x100422,a859),x100422),f306(f18(x100422,a859,a859),f306(f306(f8(a859,f872(a859,a859),x100422),a304),x100421))),f306(f306(f7(x100422,f872(x100422,x100422),f872(x100422,a859)),f306(f306(f8(f872(x100422,a859),f872(f872(x100422,x100422),f872(x100422,a859)),x100422),f8(x100422,a859,x100422)),a303)),x100423))))) % 187.68/187.64 [10057]~P1(f306(f306(f221(a865),f306(x100574,f306(x100573,f538(x100571,x100573,x100574,x100572)))),f306(x100574,f538(x100571,x100573,x100574,x100572))))+P40(x100571,f306(f228(f871(x100571,x100571)),f306(f245(x100571,x100571,a859),f306(f306(f8(f872(x100571,a859),f872(x100571,a859),x100571),f306(f18(x100571,a859,a859),f306(f306(f8(a859,f872(a859,a859),x100571),a304),x100572))),f306(f306(f7(x100571,f872(x100571,x100571),f872(x100571,a859)),f306(f306(f8(f872(x100571,a859),f872(f872(x100571,x100571),f872(x100571,a859)),x100571),f8(x100571,a859,x100571)),a303)),x100573))))) % 187.68/187.64 [10163]~P1(f306(f306(f308(f871(x101631,x101631)),f306(f306(f236(x101631,x101631),x101633),x101634)),f306(f306(f108(f872(f871(x101631,x101631),a859)),x101632),f282(x101631,f185(f872(f871(x101631,x101631),a859))))))+P1(f306(f306(f306(f306(f108(f872(x101631,f872(x101631,a859))),f306(f306(f7(x101631,f872(f871(x101631,x101631),a859),f872(x101631,a859)),f306(f306(f8(f872(x101631,f872(f872(f871(x101631,x101631),a859),a859)),f872(f872(f871(x101631,x101631),a859),f872(x101631,a859)),x101631),f7(x101631,f872(f871(x101631,x101631),a859),a859)),f306(f306(f8(f872(x101631,f871(x101631,x101631)),f872(x101631,f872(f872(f871(x101631,x101631),a859),a859)),x101631),f306(f8(f871(x101631,x101631),f872(f872(f871(x101631,x101631),a859),a859),x101631),f308(f871(x101631,x101631)))),f236(x101631,x101631)))),x101632)),a303),x101633),x101634)) % 187.68/187.64 [10173]P1(f306(f306(f308(f871(x101731,x101731)),f306(f306(f236(x101731,x101731),x101732),x101733)),f306(f306(f108(f872(f871(x101731,x101731),a859)),x101734),f282(x101731,f185(f872(f871(x101731,x101731),a859))))))+~P1(f306(f306(f306(f306(f108(f872(x101731,f872(x101731,a859))),f306(f306(f7(x101731,f872(f871(x101731,x101731),a859),f872(x101731,a859)),f306(f306(f8(f872(x101731,f872(f872(f871(x101731,x101731),a859),a859)),f872(f872(f871(x101731,x101731),a859),f872(x101731,a859)),x101731),f7(x101731,f872(f871(x101731,x101731),a859),a859)),f306(f306(f8(f872(x101731,f871(x101731,x101731)),f872(x101731,f872(f872(f871(x101731,x101731),a859),a859)),x101731),f306(f8(f871(x101731,x101731),f872(f872(f871(x101731,x101731),a859),a859),x101731),f308(f871(x101731,x101731)))),f236(x101731,x101731)))),x101734)),a303),x101732),x101733)) % 187.68/187.64 [10028]~P107(x100283)+E(f91(x100281,f306(f306(f18(x100281,a859,a859),f306(f306(f8(a859,f872(a859,a859),x100281),a304),x100282)),f306(f306(f8(f872(x100281,a859),a859,x100281),f89(x100281)),f306(f306(f8(f872(x100281,a859),f872(x100281,a859),x100281),f306(f18(x100281,a859,a859),f306(f306(f8(a859,f872(a859,a859),x100281),a309),x100282))),f306(f306(f8(x100283,f872(x100281,a859),x100281),f306(f7(x100281,x100283,a859),f306(f306(f8(x100283,f872(x100283,a859),x100281),f220(x100283)),x100284))),x100284))))),f306(f94(x100281,x100283,x100284),x100282)) % 187.68/187.64 [10072]~P107(x100723)+E(f91(x100721,f306(f306(f18(x100721,a859,a859),f306(f306(f8(a859,f872(a859,a859),x100721),a304),x100722)),f306(f306(f8(f872(x100721,a859),a859,x100721),f89(x100721)),f306(f306(f8(f872(x100721,a859),f872(x100721,a859),x100721),f306(f18(x100721,a859,a859),f306(f306(f8(a859,f872(a859,a859),x100721),a309),x100722))),f306(f306(f7(x100721,f872(x100721,x100723),f872(x100721,a859)),f306(f306(f8(f872(x100723,a859),f872(f872(x100721,x100723),f872(x100721,a859)),x100721),f8(x100723,a859,x100721)),f306(f306(f8(x100723,f872(x100723,a859),x100721),f220(x100723)),x100724))),x100724))))),f97(x100721,x100723,x100724,x100722)) % 187.68/187.64 [10120]E(f306(f306(f143(f866(x101201)),f306(f306(f143(x101201),x101202),f306(f134(f866(x101201),f866(x101201),f122(x101201),f120(x101201)),f306(f306(f146(f866(x101201),f866(x101201)),f148(f866(x101201),x101201,f120(x101201),f306(f306(f8(f866(x101201),f872(f866(x101201),f866(x101201)),x101201),f16(f866(x101201),f866(x101201))),f306(f306(f7(x101201,f866(x101201),f866(x101201)),f143(x101201)),f120(x101201))))),x101203)))),f171(x101201,f306(f306(f143(f866(x101201)),x101204),f306(f134(f866(f866(x101201)),f866(f866(x101201)),f122(f866(x101201)),f120(f866(x101201))),f306(f306(f146(f866(x101201),f866(f866(x101201))),f148(f866(f866(x101201)),x101201,f120(f866(x101201)),f306(f16(f872(f866(x101201),f866(f866(x101201))),x101201),f306(f306(f7(f866(x101201),f866(f866(x101201)),f866(f866(x101201))),f143(f866(x101201))),f120(f866(x101201)))))),x101203))))),f171(x101201,f306(f306(f143(f866(x101201)),f306(f306(f143(x101201),x101202),x101204)),x101203)))+~P1(f306(f294(f866(f866(x101201)),f172(x101201)),f306(f306(f143(f866(x101201)),f306(f306(f143(x101201),x101202),x101204)),x101203))) % 187.68/187.64 [10162]~P1(f306(f63(x101622),f306(f228(x101622),x101624)))+P1(f306(f63(x101621),f306(f228(x101621),f306(f306(f8(f872(x101622,a859),a859,x101621),f88(x101622)),f306(f306(f7(x101621,f872(x101622,a859),f872(x101622,a859)),f306(f306(f8(f872(x101622,f872(a859,a859)),f872(f872(x101622,a859),f872(x101622,a859)),x101621),f18(x101622,a859,a859)),f306(f306(f8(f872(x101622,a859),f872(x101622,f872(a859,a859)),x101621),f306(f8(a859,f872(a859,a859),x101622),a304)),f306(f306(f7(x101621,f872(x101622,x101621),f872(x101622,a859)),f306(f306(f8(f872(x101621,a859),f872(f872(x101622,x101621),f872(x101622,a859)),x101621),f8(x101621,a859,x101622)),a303)),x101623)))),x101624))))) % 187.68/187.64 [8008]E(f197(x80081,x80082,x80083,x80084,x80085),f127(x80082))+~E(x80085,f2(a106)) % 187.68/187.64 [5602]E(f306(f306(f284(x56021),x56022),f175(x56021,x56023,x56024)),f175(x56021,x56023,x56024))+~E(f306(x56024,x56022),f306(f214(x56023),x56025)) % 187.68/187.64 [6015]P1(f306(f242(x60151,x60152,x60153),x60154))+~P1(f306(f306(x60153,x60155),x60154)) % 187.68/187.64 [6017]P1(f306(f241(x60171,x60172,x60173),x60174))+~P1(f306(f306(x60173,x60174),x60175)) % 187.68/187.64 [6020]~E(f306(x60204,x60202),f306(f214(x60203),x60205))+P1(f306(f306(f308(x60201),x60202),f175(x60201,x60203,x60204))) % 187.68/187.64 [6021]~E(f306(x60214,x60215),f306(f214(x60211),x60212))+P1(f306(f306(f308(x60211),x60212),f177(x60213,x60211,x60214))) % 187.68/187.64 [6624]~E(x66243,f2(a106))+E(f306(f255(x66241,x66242,x66243,x66244),x66245),f306(f236(x66241,x66242),x66245)) % 187.68/187.64 [6699]~E(f306(x66994,x66995),f188(x66992))+E(f306(f216(f869(x66991),x66992,f188(x66991),x66993),f306(x66994,x66995)),f188(x66991)) % 187.68/187.64 [7319]E(f306(x73191,x73192),f188(x73193))+~E(f306(f176(x73194,x73193,x73195,x73191),x73192),f188(x73193)) % 187.68/187.64 [7320]E(f306(x73201,x73202),f188(x73203))+~E(f306(f176(x73204,x73203,x73201,x73205),x73202),f188(x73203)) % 187.68/187.64 [7356]E(f306(f176(x73561,x73562,x73563,x73564),x73565),f306(x73563,x73565))+P1(f306(f306(f308(x73561),x73565),f175(x73561,x73562,x73564))) % 187.68/187.64 [7357]E(f306(f176(x73571,x73572,x73573,x73574),x73575),f306(x73574,x73575))+P1(f306(f306(f308(x73571),x73575),f175(x73571,x73572,x73573))) % 187.68/187.64 [7676]~P23(x76764,x76761,x76762,x76765)+E(f306(f74(x76761,x76761,x76761,f306(x76762,x76763)),f306(x76762,x76763)),f306(x76762,x76763)) % 187.68/187.64 [7720]E(f306(f176(x77201,x77202,x77203,x77204),x77205),f306(x77204,x77205))+~P1(f306(f306(f308(x77201),x77205),f175(x77201,x77202,x77204))) % 187.68/187.64 [8070]~P19(x80705,x80701,x80702)+E(f306(f74(x80701,x80701,x80701,f306(x80702,x80703)),f306(x80702,x80704)),f306(f74(x80701,x80701,x80701,f306(x80702,x80704)),f306(x80702,x80703))) % 187.68/187.64 [8402]P1(f306(f306(f308(f871(x84021,x84021)),f306(f306(f236(x84021,x84021),x84022),x84023)),f300(x84021,x84024,x84025)))+~P1(f306(f306(f221(a865),f306(x84024,x84022)),f306(x84024,x84023))) % 187.68/187.64 [8502]~P1(f306(f306(f308(x85024),x85023),f273(x85024,x85021,x85022,x85025)))+P1(f306(f306(x85021,x85022),x85023)) % 187.68/187.64 [8503]~P1(f306(f306(f308(x85034),x85033),f270(x85034,x85031,x85032,x85035)))+P1(f306(f306(x85031,x85032),x85033)) % 187.68/187.64 [8504]~P1(f306(f306(f308(x85044),x85042),f273(x85044,x85041,x85045,x85043)))+P1(f306(f306(x85041,x85042),x85043)) % 187.68/187.64 [8505]~P1(f306(f306(f308(x85054),x85052),f270(x85054,x85051,x85055,x85053)))+P1(f306(f306(x85051,x85052),x85053)) % 187.68/187.64 [8642]~P56(x86422,x86421,x86425,x86423,x86424)+E(f306(f285(x86421,x86422,x86423),x86424),f231(f872(x86422,a859))) % 187.68/187.64 [9082]~P37(x90821,x90822,x90823,x90824,x90825)+P37(x90821,x90822,x90823,f306(f161(x90821),x90824),f306(f161(x90822),x90825)) % 187.68/187.64 [9084]~P37(x90841,x90842,x90843,f306(f161(x90841),x90844),x90845)+P37(x90841,x90842,x90843,x90844,f306(f161(x90842),x90845)) % 187.68/187.64 [9085]~P37(x90851,x90852,x90853,x90854,f306(f161(x90852),x90855))+P37(x90851,x90852,x90853,f306(f161(x90851),x90854),x90855) % 187.68/187.64 [9091]P37(x90911,x90912,x90913,x90914,x90915)+~P37(x90911,x90912,x90913,f306(f161(x90911),x90914),f306(f161(x90912),x90915)) % 187.68/187.64 [9496]P1(f306(f306(f308(f871(f866(x94961),f866(x94961))),f306(f306(f236(f866(x94961),f866(x94961)),f306(f306(f143(x94961),x94962),x94963)),f306(f306(f143(x94961),x94962),x94964))),f149(x94961,x94965)))+~P1(f306(f306(f308(f871(f866(x94961),f866(x94961))),f306(f306(f236(f866(x94961),f866(x94961)),x94963),x94964)),f149(x94961,x94965))) % 187.68/187.65 [9497]P1(f306(f306(f308(f871(f866(x94971),f866(x94971))),f306(f306(f236(f866(x94971),f866(x94971)),f306(f306(f122(x94971),x94972),x94973)),f306(f306(f122(x94971),x94972),x94974))),f139(x94971,x94975)))+~P1(f306(f306(f308(f871(f866(x94971),f866(x94971))),f306(f306(f236(f866(x94971),f866(x94971)),x94973),x94974)),f139(x94971,x94975))) % 187.68/187.65 [9686]E(f306(f306(f143(x96861),f677(x96862,x96863,x96864,x96865,x96861)),f680(x96862,x96863,x96864,x96865,x96861)),x96865)+~P1(f306(f306(f308(f871(f866(x96861),f866(x96861))),f306(f306(f236(f866(x96861),f866(x96861)),x96865),f306(f306(f143(x96861),x96864),x96863))),f150(x96861,x96862))) % 187.68/187.65 [9709]E(f306(f306(f143(x97091),f678(x97092,x97093,x97094,x97095,x97091)),f679(x97092,x97093,x97094,x97095,x97091)),x97093)+~P1(f306(f306(f308(f871(f866(x97091),f866(x97091))),f306(f306(f236(f866(x97091),f866(x97091)),f306(f306(f143(x97091),x97095),x97094)),x97093)),f150(x97091,x97092))) % 187.68/187.65 [9871]~P1(f306(f306(f308(f871(f866(x98711),f866(x98711))),f306(f306(f236(f866(x98711),f866(x98711)),f306(f306(f143(x98711),x98715),x98712)),x98714)),f150(x98711,x98713)))+P1(f306(f306(f308(f871(f866(x98711),f866(x98711))),f306(f306(f236(f866(x98711),f866(x98711)),x98712),f679(x98713,x98714,x98712,x98715,x98711))),f150(x98711,x98713))) % 187.68/187.65 [9943]~P1(f306(f306(f308(f871(f866(x99431),f866(x99431))),f306(f306(f236(f866(x99431),f866(x99431)),x99435),f306(f306(f143(x99431),x99434),x99433))),f150(x99431,x99432)))+P1(f306(f306(f308(f871(f866(x99431),f866(x99431))),f306(f306(f236(f866(x99431),f866(x99431)),f680(x99432,x99433,x99434,x99435,x99431)),x99433)),f150(x99431,x99432))) % 187.68/187.65 [10114]P1(f306(f306(f308(f871(x101141,x101141)),f306(f306(f236(x101141,x101141),f306(x101142,f306(f306(f81(a865),x101143),x101144))),f306(x101142,x101143))),f282(x101141,x101145)))+~P1(f306(f306(f308(f871(x101141,x101141)),f306(f306(f236(x101141,x101141),f306(x101142,f306(a119,f594(x101144,x101143,x101145,x101142,x101141)))),f306(x101142,f594(x101144,x101143,x101145,x101142,x101141)))),f282(x101141,x101145))) % 187.68/187.65 [10139]E(x101391,f2(a106))+E(f306(f216(f871(f866(x101392),x101393),f871(x101392,x101393),f306(f306(f236(f866(x101392),x101393),f120(x101392)),x101394),f306(f245(x101392,x101393,f871(f866(x101392),x101393)),f306(f306(f7(x101392,f872(x101393,f871(f866(x101392),x101393)),f872(x101393,f871(f866(x101392),x101393))),f306(f306(f8(f872(f871(f866(x101392),x101393),f871(f866(x101392),x101393)),f872(f872(x101393,f871(f866(x101392),x101393)),f872(x101393,f871(f866(x101392),x101393))),x101392),f8(f871(f866(x101392),x101393),f871(f866(x101392),x101393),x101393)),f306(f306(f8(f872(f866(x101392),f872(x101393,f871(f866(x101392),x101393))),f872(f871(f866(x101392),x101393),f871(f866(x101392),x101393)),x101392),f245(f866(x101392),x101393,f871(f866(x101392),x101393))),f306(f306(f8(f872(f866(x101392),f866(x101392)),f872(f866(x101392),f872(x101393,f871(f866(x101392),x101393))),x101392),f306(f8(f866(x101392),f872(x101393,f871(f866(x101392),x101393)),f866(x101392)),f236(f866(x101392),x101393))),f143(x101392))))),f125(x101393,x101392,x101395,f306(f306(f22(a106),x101391),f79(a106)))))),f306(x101395,x101394)),f306(f125(x101393,x101392,x101395,x101391),x101394)) % 187.68/187.65 [5189]E(x51891,x51892)+~E(f306(f306(f143(x51893),x51894),x51891),f306(f306(f143(x51893),x51895),x51892)) % 187.68/187.65 [5190]E(x51901,x51902)+~E(f306(f306(f143(x51903),x51901),x51904),f306(f306(f143(x51903),x51902),x51905)) % 187.68/187.65 [5241]P1(f306(x52411,x52412))+~E(f306(f128(x52413,x52411),x52414),f306(f306(f143(x52413),x52412),x52415)) % 187.68/187.65 [5242]P1(f306(x52421,x52422))+~E(f306(f306(f143(x52423),x52422),x52424),f306(f128(x52423,x52421),x52425)) % 187.68/187.65 [5399]~E(f306(f306(f130(x53991),x53993),x53992),f306(f306(f143(x53991),x53994),x53995))+E(f306(f306(f157(x53991),x53992),x53993),x53994) % 187.68/187.65 [5532]~P18(x55324,x55325,x55321)+E(f306(f306(x55321,x55322),f306(f306(x55321,x55322),x55323)),f306(f306(x55321,x55322),x55323)) % 187.68/187.65 [6143]~P108(x61432)+~E(f306(f306(f140(x61431,x61432,x61433),x61434),x61435),f120(x61431)) % 187.68/187.65 [6522]E(x65221,x65222)+~E(f306(f306(f122(x65223),x65224),f306(f306(f143(x65223),x65221),f120(x65223))),f306(f306(f122(x65223),x65225),f306(f306(f143(x65223),x65222),f120(x65223)))) % 187.68/187.65 [6523]E(x65231,x65232)+~E(f306(f306(f122(x65233),x65231),f306(f306(f143(x65233),x65234),f120(x65233))),f306(f306(f122(x65233),x65232),f306(f306(f143(x65233),x65235),f120(x65233)))) % 187.68/187.65 [6781]E(f306(f179(x67811,x67812,x67813,x67814),x67815),f188(x67812))+P1(f306(f306(f308(x67811),x67815),x67814)) % 187.68/187.65 [6843]E(f306(f306(f284(x68431),f306(x68432,x68433)),f306(f285(x68434,x68431,x68432),x68435)),f306(f285(x68434,x68431,x68432),x68435))+~P1(f306(f306(f308(x68434),x68433),x68435)) % 187.68/187.65 [6850]~P1(f306(x68504,f306(x68503,x68505)))+P1(f306(f306(f286(x68501,x68502,x68503),x68504),x68505)) % 187.68/187.65 [6854]~E(x68544,f2(a106))+E(f306(f125(x68541,x68542,x68543,x68544),x68545),f306(f306(f236(f866(x68542),x68541),f120(x68542)),x68545)) % 187.68/187.65 [6946]~E(f306(f285(x69461,x69462,x69463),x69464),x69465)+E(f306(f285(f872(x69461,a859),f872(x69462,a859),f285(x69461,x69462,x69463)),f306(f283(x69461),x69464)),f306(f283(x69462),x69465)) % 187.68/187.65 [6978]E(f306(f179(x69781,x69782,x69783,x69784),x69785),f306(x69783,x69785))+~P1(f306(f306(f308(x69781),x69785),x69784)) % 187.68/187.65 [7277]P28(x72771,x72772,x72773,x72774)+~P28(x72771,x72772,x72773,f306(f306(f284(x72771),x72775),x72774)) % 187.68/187.65 [7346]P1(f306(x73461,x73462))+~P1(f306(f306(f96(x73463,x73464,x73461),x73465),x73462)) % 187.68/187.65 [7390]~P1(f306(f306(f308(x73904),x73903),x73905))+P1(f306(f306(f308(x73901),f306(x73902,x73903)),f306(f285(x73904,x73901,x73902),x73905))) % 187.68/187.65 [7414]~P108(x74142)+E(f142(x74141,x74142,x74143,f306(f128(x74141,x74144),x74145)),f306(f128(x74141,x74144),f142(x74141,x74142,x74143,x74145))) % 187.68/187.65 [7447]P1(f306(x74471,f306(x74472,x74473)))+~P1(f306(f306(f286(x74474,x74475,x74472),x74471),x74473)) % 187.68/187.65 [7448]P1(f306(f306(x74481,x74482),x74483))+~P1(f306(f306(f96(x74484,x74481,x74485),x74482),x74483)) % 187.68/187.65 [7511]~P1(f306(f306(f308(x75113),f306(x75114,x75112)),x75115))+P1(f306(f306(f308(x75111),x75112),f306(f286(x75111,x75113,x75114),x75115))) % 187.68/187.65 [7907]~P1(f306(f306(f308(x79075),x79073),f306(f286(x79075,x79071,x79072),x79074)))+P1(f306(f306(f308(x79071),f306(x79072,x79073)),x79074)) % 187.68/187.65 [8137]~E(x81373,f306(f306(f306(f73(x81371,f869(x81372)),f306(f16(f869(x81372),x81371),f188(x81372))),x81374),f306(f214(x81372),x81375)))+E(f175(x81371,x81372,x81373),f306(f306(f284(x81371),x81374),f185(f872(x81371,a859)))) % 187.68/187.65 [8217]~P19(x82172,x82171,x82173)+E(f306(f134(x82171,x82172,f306(f7(x82172,x82171,x82171),x82173),x82174),f144(x82172,x82175)),f306(f306(f66(x82172,x82171,x82173),x82174),f306(f164(x82172),x82175))) % 187.68/187.65 [8236]E(f306(x82361,f336(x82362,x82361,x82363,x82364)),x82364)+~P1(f306(f306(f308(x82365),x82364),f306(f285(x82363,x82365,x82361),x82362))) % 187.68/187.65 [8549]~E(x85492,f306(f306(f143(x85491),x85494),x85495))+P1(f306(f306(f308(f871(f866(x85491),f866(x85491))),f306(f306(f236(f866(x85491),f866(x85491)),f120(x85491)),x85492)),f139(x85491,x85493))) % 187.68/187.65 [8602]~P37(x86021,x86023,x86025,x86022,x86024)+E(f306(f186(f866(x86021)),x86022),f306(f186(f866(x86023)),x86024)) % 187.68/187.65 [8612]P1(f306(f306(f220(f872(x86121,a859)),f306(f306(f44(x86122,f872(x86121,a859)),x86123),x86124)),f306(x86124,x86125)))+~P1(f306(f306(f308(x86122),x86125),x86123)) % 187.68/187.65 [8658]~P56(x86581,x86582,x86583,x86585,x86584)+E(f306(f285(x86581,x86582,x86583),f231(f872(x86581,a859))),x86584) % 187.68/187.65 [8865]E(f306(f306(f306(f73(x88651,f869(x88652)),f179(x88651,x88652,x88653,x88654)),x88655),f188(x88652)),f179(x88651,x88652,x88653,x88654))+P1(f306(f306(f308(x88651),x88655),x88654)) % 187.68/187.65 [8870]E(f306(f128(x88701,x88702),f776(x88703,x88704,x88705,x88702,x88701)),x88703)+~E(f306(f128(x88701,x88702),x88705),f306(f306(f143(x88701),x88704),x88703)) % 187.68/187.65 [8871]E(f306(f128(x88711,x88712),f777(x88713,x88712,x88714,x88715,x88711)),x88714)+~E(f306(f306(f143(x88711),x88715),x88714),f306(f128(x88711,x88712),x88713)) % 187.68/187.65 [8872]E(f306(x88721,f667(x88722,x88723,x88721,x88724,x88725)),x88722)+~E(f306(f306(f189(x88725,x88724),x88721),x88723),f306(f214(x88724),x88722)) % 187.68/187.65 [8876]E(f306(f214(x88761),f667(x88762,x88763,x88764,x88765,x88761)),x88763)+~E(f306(f306(f189(x88761,x88765),x88764),x88763),f306(f214(x88765),x88762)) % 187.68/187.65 [8975]E(f306(f186(f866(x89751)),x89752),x89753)+~P1(f306(f306(f308(f871(f866(x89751),f866(x89751))),f306(f306(f236(f866(x89751),f866(x89751)),x89754),x89752)),f306(f135(x89751,x89755),x89753))) % 187.68/187.65 [8976]E(f306(f186(f866(x89761)),x89762),x89763)+~P1(f306(f306(f308(f871(f866(x89761),f866(x89761))),f306(f306(f236(f866(x89761),f866(x89761)),x89762),x89764)),f306(f135(x89761,x89765),x89763))) % 187.68/187.65 [9043]P1(f306(f306(f308(x90431),f336(x90432,x90433,x90431,x90434)),x90432))+~P1(f306(f306(f308(x90435),x90434),f306(f285(x90431,x90435,x90433),x90432))) % 187.68/187.65 [9205]~P41(f872(x92053,a859),f872(x92051,a859),x92052)+P1(f306(f306(f220(f872(x92051,a859)),f306(x92052,f306(f306(f109(f872(x92053,a859)),x92054),x92055))),f306(f306(f109(f872(x92051,a859)),f306(x92052,x92054)),f306(x92052,x92055)))) % 187.68/187.65 [9207]E(f306(f285(x92071,x92072,x92073),f348(x92074,x92073,x92071,x92075,x92072)),x92075)+~P1(f306(f306(f220(f872(x92072,a859)),x92075),f306(f285(x92071,x92072,x92073),x92074))) % 187.68/187.65 [9464]E(f306(x94641,f815(x94642,x94641,x94643,x94644,x94645)),f306(f214(x94645),x94644))+~P1(f306(f306(f308(x94645),x94644),f177(x94643,x94645,f179(x94643,x94645,x94641,x94642)))) % 187.68/187.65 [9512]P1(f306(f306(f308(f871(f866(x95121),f866(x95121))),f306(f306(f236(f866(x95121),f866(x95121)),f306(f306(f143(x95121),x95122),x95123)),f306(f306(f143(x95121),x95122),x95124))),f282(f866(x95121),f149(x95121,x95125))))+~P1(f306(f306(f308(f871(f866(x95121),f866(x95121))),f306(f306(f236(f866(x95121),f866(x95121)),x95123),x95124)),f282(f866(x95121),f149(x95121,x95125)))) % 187.68/187.65 [9543]~E(f306(x95433,f671(x95435,x95434,x95433,x95432,x95431)),f306(x95435,f671(x95435,x95434,x95433,x95432,x95431)))+E(f306(f306(f146(x95431,x95432),x95433),x95434),f306(f306(f146(x95431,x95432),x95435),x95434)) % 187.68/187.65 [9620]~E(f306(f128(x96201,x96205),x96204),f306(f306(f143(x96201),x96203),x96202))+E(f306(f306(f122(x96201),f781(x96202,x96203,x96204,x96205,x96201)),f306(f306(f143(x96201),x96203),f776(x96202,x96203,x96204,x96205,x96201))),x96204) % 187.68/187.65 [9621]~E(f306(f306(f143(x96211),x96215),x96214),f306(f128(x96211,x96213),x96212))+E(f306(f306(f122(x96211),f778(x96212,x96213,x96214,x96215,x96211)),f306(f306(f143(x96211),x96215),f777(x96212,x96213,x96214,x96215,x96211))),x96212) % 187.68/187.65 [9623]E(f306(f306(f146(x96231,x96232),x96233),x96234),f306(f306(f146(x96231,x96232),x96235),x96234))+P1(f306(f306(f308(x96231),f671(x96233,x96234,x96235,x96232,x96231)),f306(f164(x96231),x96234))) % 187.68/187.65 [9654]~P1(f306(f306(f308(x96545),x96544),f306(f260(x96541,x96545,x96543),x96542)))+P1(f306(f306(f308(x96541),f407(x96542,x96543,x96541,x96544,x96545)),x96542)) % 187.68/187.65 [9655]~P1(f306(f306(f308(x96555),x96554),f306(f260(x96551,x96555,x96553),x96552)))+P1(f306(f306(f308(x96551),f431(x96552,x96553,x96551,x96554,x96555)),x96552)) % 187.68/187.65 [9680]~P1(f306(f306(f220(f872(x96805,a859)),x96804),f306(f285(x96801,x96805,x96803),x96802)))+P1(f306(f306(f220(f872(x96801,a859)),f348(x96802,x96803,x96801,x96804,x96805)),x96802)) % 187.68/187.65 [9733]~P1(f306(f306(f308(x97335),x97334),f177(x97331,x97335,f179(x97331,x97335,x97333,x97332))))+P1(f306(f306(f308(x97331),f815(x97332,x97333,x97331,x97334,x97335)),x97332)) % 187.68/187.65 [5412]~E(f306(x54123,x54124),x54125)+E(f306(f306(f306(f73(x54121,x54122),x54123),x54124),x54125),x54123) % 187.68/187.65 [5855]E(f306(x58551,x58552),x58553)+~E(f306(f306(f306(f73(x58554,x58555),x58551),x58552),x58553),x58551) % 187.68/187.65 [5953]E(x59531,x59532)+~E(f306(f244(x59533,x59534),f306(f306(f236(x59533,x59534),x59535),x59531)),x59532) % 187.68/187.65 [5954]E(x59541,x59542)+~E(f306(f235(x59543,x59544),f306(f306(f236(x59543,x59544),x59541),x59545)),x59542) % 187.68/187.65 [6218]~E(x62183,f306(f306(f122(x62181),x62184),f306(f306(f143(x62181),x62182),x62185)))+P1(f306(f306(f308(x62181),x62182),f306(f164(x62181),x62183))) % 187.68/187.65 [6610]E(f306(f285(x66101,x66102,f306(f16(x66102,x66101),x66103)),x66104),f306(f306(f284(x66102),x66103),f185(f872(x66102,a859))))+~P1(f306(f306(f308(x66101),x66105),x66104)) % 187.68/187.65 [6684]E(f306(f306(f108(f872(x66841,a859)),f306(f164(x66841),x66842)),f306(f164(x66841),x66843)),f306(f164(x66841),x66844))+~E(f159(x66841,x66845,x66844),f306(f306(f236(f866(x66841),f866(x66841)),x66842),x66843)) % 187.68/187.65 [6785]~P108(x67852)+E(f306(f186(f866(x67851)),f306(f306(f140(x67851,x67852,x67853),x67854),x67855)),f306(a119,f306(f186(f866(x67851)),x67855))) % 187.68/187.65 [6797]~P108(x67972)+E(f306(f164(x67971),f306(f306(f140(x67971,x67972,x67973),x67974),x67975)),f306(f306(f284(x67971),x67974),f306(f164(x67971),x67975))) % 187.68/187.65 [7069]~P113(x70691)+E(f306(f306(f81(x70691),f306(f306(f81(x70691),x70692),x70693)),f306(f306(f81(x70691),x70694),x70695)),f306(f306(f81(x70691),f306(f306(f81(x70691),x70692),x70694)),f306(f306(f81(x70691),x70693),x70695))) % 187.68/187.65 [7070]~P113(x70701)+E(f306(f306(f82(x70701),f306(f306(f82(x70701),x70702),x70703)),f306(f306(f82(x70701),x70704),x70705)),f306(f306(f82(x70701),f306(f306(f82(x70701),x70702),x70704)),f306(f306(f82(x70701),x70703),x70705))) % 187.68/187.65 [7071]~P61(x70711)+E(f306(f306(f264(x70711),f306(f306(f82(x70711),x70712),x70713)),f306(f306(f82(x70711),x70714),x70715)),f306(f306(f82(x70711),f306(f306(f264(x70711),x70712),x70714)),f306(f306(f264(x70711),x70713),x70715))) % 187.68/187.65 [7085]~P108(x70851)+E(f280(x70851,f306(f306(f219(x70851),x70852),x70853),f306(f306(f225(x70851),x70854),x70855)),f306(f306(f109(f872(x70851,a859)),f280(x70851,x70852,x70854)),f280(x70851,x70853,x70855))) % 187.68/187.65 [7086]~P108(x70861)+E(f279(x70861,f306(f306(f219(x70861),x70862),x70863),f306(f306(f225(x70861),x70864),x70865)),f306(f306(f109(f872(x70861,a859)),f279(x70861,x70862,x70864)),f279(x70861,x70863,x70865))) % 187.68/187.65 [7087]~P108(x70871)+E(f277(x70871,f306(f306(f219(x70871),x70872),x70873),f306(f306(f225(x70871),x70874),x70875)),f306(f306(f109(f872(x70871,a859)),f277(x70871,x70872,x70874)),f277(x70871,x70873,x70875))) % 187.68/187.65 [7088]~P108(x70881)+E(f306(f306(f109(f872(x70881,a859)),f306(f276(x70881,x70882),x70883)),f306(f276(x70881,x70884),x70885)),f306(f276(x70881,f306(f306(f219(x70881),x70882),x70884)),f306(f306(f225(x70881),x70883),x70885))) % 187.68/187.65 [7203]~P1(f306(x72031,f320(x72033,x72032,x72031)))+P1(f306(x72031,f306(f306(f236(x72032,x72033),x72034),x72035))) % 187.68/187.65 [7289]~E(f306(x72893,x72894),f188(x72892))+E(f177(x72891,x72892,f306(f306(f306(f73(x72891,f869(x72892)),x72893),x72894),f306(f214(x72892),x72895))),f306(f306(f284(x72892),x72895),f177(x72891,x72892,x72893))) % 187.68/187.65 [7310]~E(x73102,f306(x73104,x73105))+P1(f306(f306(f308(x73101),x73102),f306(f285(x73103,x73101,x73104),f231(f872(x73103,a859))))) % 187.68/187.65 [7368]~E(f306(x73683,x73684),f188(x73682))+E(f306(f306(f22(f872(x73681,a859)),f175(x73681,x73682,x73683)),f306(f306(f284(x73681),x73684),x73685)),f306(f306(f22(f872(x73681,a859)),f175(x73681,x73682,x73683)),x73685)) % 187.68/187.65 [7387]~P18(x73873,x73872,x73874)+P18(x73871,x73872,f306(f306(f8(x73873,f872(x73872,x73872),x73871),x73874),x73875)) % 187.68/187.65 [7388]~P19(x73883,x73882,x73884)+P19(x73881,x73882,f306(f306(f8(x73883,f872(x73882,x73882),x73881),x73884),x73885)) % 187.68/187.65 [7527]~P28(x75271,x75272,x75273,x75274)+P28(x75271,x75272,x75273,f306(f306(f22(f872(x75271,a859)),x75274),x75275)) % 187.68/187.65 [7685]~P1(f306(f306(x76853,x76854),x76855))+P1(f306(f306(f245(x76851,x76852,a859),x76853),f306(f306(f236(x76851,x76852),x76854),x76855))) % 187.68/187.65 [7796]~P1(f306(x77962,x77964))+~E(f306(f306(f130(x77961),f306(f186(f866(x77961)),f168(x77961,x77962,x77963))),x77963),f306(f306(f143(x77961),x77964),x77965)) % 187.68/187.65 [7816]P28(x78161,x78162,x78163,x78164)+~P28(x78161,x78162,x78163,f306(f306(f108(f872(x78161,a859)),x78165),x78164)) % 187.68/187.65 [7817]P28(x78171,x78172,x78173,x78174)+~P28(x78171,x78172,x78173,f306(f306(f108(f872(x78171,a859)),x78174),x78175)) % 187.68/187.65 [7864]~P108(x78642)+E(f306(f306(f140(x78641,x78642,x78643),x78644),f142(x78641,x78642,x78643,x78645)),f142(x78641,x78642,x78643,f306(f306(f143(x78641),x78644),x78645))) % 187.68/187.65 [8029]~P30(x80291,f306(a119,x80292),f306(f306(f306(f93(x80291),x80293),f306(a26,x80294)),x80295))+P30(x80291,x80292,f306(f306(f306(f93(x80291),x80293),f306(f218(a860),f306(a28,x80294))),x80295)) % 187.68/187.65 [8164]P30(x81641,f306(a119,x81642),f306(f306(f306(f93(x81641),x81643),f306(a26,x81644)),x81645))+~P30(x81641,x81642,f306(f306(f306(f93(x81641),x81643),f306(f218(a860),f306(a28,x81644))),x81645)) % 187.68/187.65 [8193]~P18(x81932,x81931,x81933)+E(f306(f134(x81931,x81932,f306(f7(x81932,x81931,x81931),x81933),x81934),x81935),f306(f306(f66(x81932,x81931,x81933),x81934),f306(f164(x81932),x81935))) % 187.68/187.65 [8222]~E(f306(f306(f130(x82221),f306(f186(f866(x82221)),f168(x82221,x82222,x82223))),x82223),f306(f306(f143(x82221),x82224),x82225))+E(f306(f306(f122(x82221),f168(x82221,x82222,x82223)),f306(f306(f143(x82221),x82224),x82225)),x82223) % 187.68/187.65 [8246]P1(f306(f306(x82461,x82462),x82463))+~P1(f306(f306(f245(x82464,x82465,a859),x82461),f306(f306(f236(x82464,x82465),x82462),x82463))) % 187.68/187.65 [8310]~E(f306(f306(f169(x83101,x83102),x83105),x83103),f306(f214(x83102),x83104))+P1(f306(f306(f308(f871(x83101,x83102)),f306(f306(f236(x83101,x83102),x83103),x83104)),f306(f164(f871(x83101,x83102)),x83105))) % 187.68/187.65 [8714]P1(f306(f306(f220(f872(x87141,a859)),f306(f285(x87142,x87141,x87143),x87144)),f306(f285(x87142,x87141,x87143),x87145)))+~P1(f306(f306(f220(f872(x87142,a859)),x87144),x87145)) % 187.68/187.65 [8715]P1(f306(f306(f220(f872(x87151,a859)),f306(f286(x87151,x87152,x87153),x87154)),f306(f286(x87151,x87152,x87153),x87155)))+~P1(f306(f306(f220(f872(x87152,a859)),x87154),x87155)) % 187.68/187.65 [8790]E(x87901,f2(a106))+E(f306(f306(f247(x87902,x87903,x87902,f871(x87903,x87902)),f306(x87904,x87905)),f255(x87903,x87902,f306(f306(f22(a106),x87901),f79(a106)),x87904)),f306(f255(x87903,x87902,x87901,x87904),x87905)) % 187.68/187.65 [9114]P30(x91141,x91142,f306(f306(f306(f93(x91141),x91143),x91144),x91145))+P1(f306(f306(x91143,f434(x91145,x91144,x91143,x91142)),f445(x91145,x91144,x91143,x91142))) % 187.68/187.65 [9318]E(f306(f214(x93181),f673(x93182,x93183,x93184,x93181,x93185)),f306(f306(f169(x93185,x93181),x93182),x93184))+~P1(f306(f306(f308(f871(x93185,x93181)),f306(f306(f236(x93185,x93181),x93184),x93183)),f306(f164(f871(x93185,x93181)),x93182))) % 187.68/187.65 [9364]P30(x93641,x93642,f306(f306(f306(f93(x93641),x93643),x93644),x93645))+~P1(f306(f306(x93645,f434(x93645,x93644,x93643,x93642)),f456(x93645,x93644,x93643,x93642))) % 187.68/187.65 [9424]P30(x94241,x94242,f306(f306(f306(f93(x94241),x94243),x94244),x94245))+P1(f306(f306(f306(f306(a195,x94244),f445(x94245,x94244,x94243,x94242)),x94242),f456(x94245,x94244,x94243,x94242))) % 187.68/187.65 [9427]~P27(x94271,x94272,f306(f306(f284(f864(x94271)),f306(f306(f306(f93(x94271),x94273),f306(f218(a860),f306(a28,x94274))),x94275)),f185(f872(f864(x94271),a859))))+P27(x94271,x94272,f306(f306(f284(f864(x94271)),f306(f306(f306(f93(x94271),x94273),f306(a26,x94274)),x94275)),f185(f872(f864(x94271),a859)))) % 187.68/187.65 [9455]~P1(f306(f63(x94553),f306(f285(x94552,x94553,x94555),f231(f872(x94552,a859)))))+P1(f306(f63(x94551),f306(f285(x94552,x94551,f306(f306(f8(x94553,x94551,x94552),x94554),x94555)),f231(f872(x94552,a859))))) % 187.68/187.65 [9477]P1(f306(f306(f220(f872(f872(x94771,a859),a859)),f306(f285(f872(x94772,a859),f872(x94771,a859),f285(x94772,x94771,x94773)),f306(f283(x94772),x94774))),f306(f283(x94771),x94775)))+~P1(f306(f306(f220(f872(x94771,a859)),f306(f285(x94772,x94771,x94773),x94774)),x94775)) % 187.68/187.65 [9491]~P1(f306(f63(f869(x94911)),f306(f285(x94912,f869(x94911),x94913),f231(f872(x94912,a859)))))+P1(f306(f63(f869(x94911)),f306(f285(x94912,f869(x94911),f306(f306(f306(f73(x94912,f869(x94911)),x94913),x94914),f306(f214(x94911),x94915))),f231(f872(x94912,a859))))) % 187.68/187.65 [9552]E(x95521,x95522)+~P1(f306(f68(x95523,x95524,x95525,x95521,f185(f872(x95523,a859))),x95522)) % 187.68/187.65 [9568]E(f306(f306(f236(x95681,x95682),f504(x95683,x95684,x95685,x95682,x95681)),f505(x95683,x95684,x95685,x95682,x95681)),x95685)+~P1(f306(f306(f308(f871(x95681,x95682)),x95685),f306(f306(f243(x95681,x95682),x95684),x95683))) % 187.68/187.65 [9659]P1(f306(f306(f308(x96591),f504(x96592,x96593,x96594,x96595,x96591)),x96593))+~P1(f306(f306(f308(f871(x96591,x96595)),x96594),f306(f306(f243(x96591,x96595),x96593),x96592))) % 187.68/187.65 [9770]P27(x97705,x97704,f306(f306(f284(f864(x97705)),f306(f306(f306(f93(x97705),x97701),x97703),x97702)),f185(f872(f864(x97705),a859))))+P1(f306(f306(x97701,f339(x97702,x97703,x97704,x97705,x97701)),f352(x97702,x97703,x97704,x97705,x97701))) % 187.68/187.65 [9819]P1(f306(f306(f308(x98191),f505(x98192,x98193,x98194,x98191,x98195)),f306(x98192,f504(x98192,x98193,x98194,x98191,x98195))))+~P1(f306(f306(f308(f871(x98195,x98191)),x98194),f306(f306(f243(x98195,x98191),x98193),x98192))) % 187.68/187.65 [9847]P1(f306(f306(f308(f871(x98471,x98471)),f306(f306(f236(x98471,x98471),x98472),f620(x98473,x98474,x98475,x98472,x98471))),x98473))+~P1(f306(f306(f308(f871(x98471,x98471)),f306(f306(f236(x98471,x98471),x98472),x98475)),f306(f306(f180(f871(x98471,x98471),a859),f306(a119,x98474)),x98473))) % 187.68/187.65 [9848]P1(f306(f306(f308(f871(x98481,x98481)),f306(f306(f236(x98481,x98481),x98482),f621(x98483,x98484,x98485,x98482,x98481))),x98483))+~P1(f306(f306(f308(f871(x98481,x98481)),f306(f306(f236(x98481,x98481),x98482),x98485)),f306(f306(f180(f871(x98481,x98481),a859),f306(a119,x98484)),x98483))) % 187.68/187.65 [9866]~P1(f306(f306(f308(f871(f866(x98661),f866(x98661))),f306(f306(f236(f866(x98661),f866(x98661)),f306(f306(f143(x98661),x98662),x98665)),x98664)),f150(x98661,x98663)))+P1(f306(f306(f308(f871(x98661,x98661)),f306(f306(f236(x98661,x98661),x98662),f678(x98663,x98664,x98665,x98662,x98661))),x98663)) % 187.68/187.65 [9868]~P27(x98681,x98682,f306(f306(f284(f864(x98681)),f306(f306(f306(f93(x98681),f96(x98681,x98683,x98684)),x98685),x98683)),f185(f872(f864(x98681),a859))))+P27(x98681,x98682,f306(f306(f284(f864(x98681)),f306(f306(f306(f93(x98681),x98683),f33(x98684,x98685)),f96(x98681,x98683,f306(f74(a859,a859,a861,a301),x98684)))),f185(f872(f864(x98681),a859)))) % 187.68/187.65 [9869]~P31(x98691,x98692,f306(f306(f284(f864(x98691)),f306(f306(f306(f93(x98691),f96(x98691,x98693,x98694)),x98695),x98693)),f185(f872(f864(x98691),a859))))+P31(x98691,x98692,f306(f306(f284(f864(x98691)),f306(f306(f306(f93(x98691),x98693),f33(x98694,x98695)),f96(x98691,x98693,f306(f74(a859,a859,a861,a301),x98694)))),f185(f872(f864(x98691),a859)))) % 187.68/187.65 [10140]P27(x101401,x101402,f306(f306(f284(f864(x101401)),f306(f306(f306(f93(x101401),x101403),x101404),x101405)),f185(f872(f864(x101401),a859))))+~P27(x101401,x101402,f306(f306(f284(f864(x101401)),f306(f306(f306(f93(x101401),f306(f16(f872(a861,a859),x101401),f306(f306(f7(a861,a861,a859),a303),f352(x101405,x101404,x101402,x101401,x101403)))),x101404),f306(f16(f872(a861,a859),x101401),f306(x101405,f339(x101405,x101404,x101402,x101401,x101403))))),f185(f872(f864(x101401),a859)))) % 187.68/187.65 [6293]P1(f306(x62932,x62934))+E(f168(x62931,x62932,f306(f306(f122(x62931),x62933),f306(f306(f143(x62931),x62934),x62935))),f168(x62931,x62932,x62933)) % 187.68/187.65 [6344]~P66(x63442)+E(f306(f306(f306(f22(f872(x63441,x63442)),x63443),x63444),x63445),f306(f306(f22(x63442),f306(x63443,x63445)),f306(x63444,x63445))) % 187.68/187.65 [6346]~P98(x63462)+E(f306(f306(f306(f108(f872(x63461,x63462)),x63463),x63464),x63465),f306(f306(f108(x63462),f306(x63463,x63465)),f306(x63464,x63465))) % 187.68/187.65 [6348]~P98(x63482)+E(f306(f306(f306(f109(f872(x63481,x63482)),x63483),x63484),x63485),f306(f306(f109(x63482),f306(x63483,x63485)),f306(x63484,x63485))) % 187.68/187.65 [6366]E(x63661,x63662)+E(f306(f306(f157(x63663),f306(f306(f151(x63663,x63664),x63661),x63665)),x63662),f306(f306(f157(x63663),x63664),x63662)) % 187.68/187.65 [6630]~E(x66304,f185(f872(x66303,a859)))+E(f306(f306(f22(f872(x66301,a859)),x66302),f306(f306(f43(x66303,f872(x66301,a859)),x66304),x66305)),x66302) % 187.68/187.65 [6631]~E(x66314,f185(f872(x66313,a859)))+E(f306(f306(f108(f872(x66311,a859)),x66312),f306(f306(f43(x66313,f872(x66311,a859)),x66314),x66315)),x66312) % 187.68/187.65 [6632]~E(x66324,f185(f872(x66323,a859)))+E(f306(f306(f109(f872(x66321,a859)),x66322),f306(f306(f44(x66323,f872(x66321,a859)),x66324),x66325)),x66322) % 187.68/187.65 [6648]~E(x66484,f185(f872(x66483,a859)))+E(f306(f306(f284(x66481),x66482),f306(f306(f43(x66483,f872(x66481,a859)),x66484),x66485)),f306(f306(f284(x66481),x66482),f185(f872(x66481,a859)))) % 187.68/187.65 [7436]E(f306(f306(f157(x74361),f306(f306(f146(x74362,x74361),x74363),x74364)),x74365),f306(x74363,f306(f306(f157(x74362),x74364),x74365)))+~P1(f306(f306(f221(a865),x74365),f306(f186(f866(x74362)),x74364))) % 187.68/187.65 [7499]E(f306(f306(f108(f872(x74991,a859)),f306(x74992,x74993)),f306(f306(f43(x74994,f872(x74991,a859)),x74995),x74992)),f306(f306(f43(x74994,f872(x74991,a859)),x74995),x74992))+~P1(f306(f306(f308(x74994),x74993),x74995)) % 187.68/187.65 [7500]E(f306(f306(f109(f872(x75001,a859)),f306(x75002,x75003)),f306(f306(f44(x75004,f872(x75001,a859)),x75005),x75002)),f306(f306(f44(x75004,f872(x75001,a859)),x75005),x75002))+~P1(f306(f306(f308(x75004),x75003),x75005)) % 187.68/187.65 [8109]~E(x81093,f185(f872(x81091,a859)))+E(f306(f306(f43(x81091,f872(x81092,a859)),x81093),f306(f306(f8(f872(x81092,a859),f872(x81092,a859),x81091),f306(f284(x81092),x81094)),x81095)),f185(f872(x81092,a859))) % 187.68/187.65 [8115]~P1(f306(f306(f308(x81154),x81153),x81155))+P1(f306(f306(f220(f872(x81151,a859)),f306(x81152,x81153)),f306(f306(f43(x81154,f872(x81151,a859)),x81155),x81152))) % 187.68/187.65 [8245]~E(f306(x82454,x82452),x82455)+P1(f306(f306(f308(x82451),x82452),f306(f286(x82451,x82453,x82454),f306(f306(f284(x82453),x82455),f185(f872(x82453,a859)))))) % 187.68/187.65 [8292]~P54(x82921,x82922,f306(f261(x82922,x82921),x82923))+E(f306(f306(f109(f872(x82921,a859)),f306(f260(x82922,x82921,x82923),x82924)),f306(f260(x82922,x82921,x82923),x82925)),f306(f260(x82922,x82921,x82923),f306(f306(f109(f872(x82922,a859)),x82924),x82925))) % 187.68/187.65 [8412]E(x84121,f185(f872(x84122,a859)))+E(f306(f306(f43(x84122,f872(x84123,a859)),x84121),f306(f306(f8(f872(x84123,a859),f872(x84123,a859),x84122),f306(f284(x84123),x84124)),x84125)),f306(f306(f284(x84123),x84124),f306(f306(f43(x84122,f872(x84123,a859)),x84121),x84125))) % 187.68/187.65 [8469]~P28(x84692,x84691,x84693,f231(f872(x84692,a859)))+E(f306(f306(f22(f872(x84691,a859)),f306(f285(x84692,x84691,x84693),x84694)),f306(f285(x84692,x84691,x84693),x84695)),f306(f285(x84692,x84691,x84693),f306(f306(f22(f872(x84692,a859)),x84694),x84695))) % 187.68/187.65 [8470]~P28(x84702,x84701,x84703,f231(f872(x84702,a859)))+E(f306(f306(f109(f872(x84701,a859)),f306(f285(x84702,x84701,x84703),x84704)),f306(f285(x84702,x84701,x84703),x84705)),f306(f285(x84702,x84701,x84703),f306(f306(f109(f872(x84702,a859)),x84704),x84705))) % 187.68/187.65 [8535]~P1(f306(f306(f69(x85351,x85352,x85355),x85353),x85354))+P1(f306(f306(f308(f871(x85351,x85352)),f306(f306(f236(x85351,x85352),x85353),x85354)),x85355)) % 187.68/187.65 [8567]P1(f306(f306(f308(x85671),x85672),f306(f232(x85673,x85671),x85674)))+~P1(f306(f306(f308(f871(x85673,x85671)),f306(f306(f236(x85673,x85671),x85675),x85672)),x85674)) % 187.68/187.65 [8569]P1(f306(f306(f308(x85691),x85692),f306(f234(x85691,x85693),x85694)))+~P1(f306(f306(f308(f871(x85691,x85693)),f306(f306(f236(x85691,x85693),x85692),x85695)),x85694)) % 187.68/187.65 [8700]P1(f306(f306(f69(x87001,x87002,x87003),x87004),x87005))+~P1(f306(f306(f308(f871(x87001,x87002)),f306(f306(f236(x87001,x87002),x87004),x87005)),x87003)) % 187.68/187.65 [8736]E(f306(x87361,x87362),x87363)+~P1(f306(f306(f308(x87364),x87362),f306(f286(x87364,x87365,x87361),f306(f306(f284(x87365),x87363),f185(f872(x87365,a859)))))) % 187.68/187.65 [8972]P1(f306(f306(f308(f871(x89721,x89722)),f306(f306(f236(x89721,x89722),x89723),x89724)),f306(f261(x89722,x89721),x89725)))+~P1(f306(f306(f308(f871(x89722,x89721)),f306(f306(f236(x89722,x89721),x89724),x89723)),x89725)) % 187.68/187.65 [8990]~P1(f306(f306(x89901,x89905),x89904))+P1(f306(f306(x89901,f306(f244(x89902,x89903),f306(f306(f236(x89902,x89903),x89904),x89905))),f306(f235(x89902,x89903),f306(f306(f236(x89902,x89903),x89904),x89905)))) % 187.68/187.65 [9020]~P1(f306(f306(f308(f871(x90202,x90201)),f306(f306(f236(x90202,x90201),x90204),x90203)),f306(f261(x90201,x90202),x90205)))+P1(f306(f306(f308(f871(x90201,x90202)),f306(f306(f236(x90201,x90202),x90203),x90204)),x90205)) % 187.68/187.65 [9050]~P1(f306(f306(f308(f871(x90503,x90501)),f306(f306(f236(x90503,x90501),x90505),x90502)),x90504))+P1(f306(f306(f308(x90501),x90502),f306(f260(x90503,x90501,x90504),f306(f306(f284(x90503),x90505),f185(f872(x90503,a859)))))) % 187.68/187.65 [9096]P1(f306(f306(f308(f871(x90961,x90962)),f306(f306(f236(x90961,x90962),x90963),x90964)),x90965))+~P1(f306(f306(f308(x90962),x90964),f306(f260(x90961,x90962,x90965),f306(f306(f284(x90961),x90963),f185(f872(x90961,a859)))))) % 187.68/187.65 [9117]E(f306(f306(f306(f73(x91171,f869(x91172)),f179(x91171,x91172,x91173,x91174)),x91175),f188(x91172)),f179(x91171,x91172,x91173,f306(f306(f22(f872(x91171,a859)),x91174),f306(f306(f284(x91171),x91175),f185(f872(x91171,a859))))))+~P1(f306(f306(f308(x91171),x91175),x91174)) % 187.68/187.65 [9186]~P74(x91861)+E(f306(f306(f6(a865,x91861),x91862),f277(a865,f306(f306(f81(a865),x91863),x91864),f306(f306(f81(a865),x91865),x91864))),f306(f306(f6(a865,x91861),f306(f306(f8(a865,x91861,a865),x91862),f306(f306(f7(a865,a865,a865),f81(a865)),x91864))),f277(a865,x91863,x91865))) % 187.68/187.65 [9211]~P74(x92111)+E(f306(f306(f6(a865,x92111),x92112),f306(f276(a865,f306(f306(f81(a865),x92113),x92114)),f306(f306(f81(a865),x92115),x92114))),f306(f306(f6(a865,x92111),f306(f306(f8(a865,x92111,a865),x92112),f306(f306(f7(a865,a865,a865),f81(a865)),x92114))),f306(f276(a865,x92113),x92115))) % 187.68/187.65 [9266]~P28(x92661,x92662,x92663,f231(f872(x92661,a859)))+E(f306(f306(f146(x92661,x92662),x92663),f306(f128(x92661,f306(f306(f8(a859,a859,x92661),a301),f306(a303,x92664))),x92665)),f306(f128(x92662,f306(f306(f8(a859,a859,x92662),a301),f306(a303,f306(x92663,x92664)))),f306(f306(f146(x92661,x92662),x92663),x92665))) % 187.68/187.65 [9284]~P28(x92841,x92842,x92843,f306(f306(f284(x92841),x92844),f306(f164(x92841),x92845)))+E(f306(f306(f146(x92841,x92842),x92843),f306(f128(x92841,f306(f306(f8(a859,a859,x92841),a301),f306(a303,x92844))),x92845)),f306(f128(x92842,f306(f306(f8(a859,a859,x92842),a301),f306(a303,f306(x92843,x92844)))),f306(f306(f146(x92841,x92842),x92843),x92845))) % 187.68/187.65 [9442]P1(f306(f306(f308(f871(f866(x94421),f866(x94421))),f306(f306(f236(f866(x94421),f866(x94421)),f306(f306(f143(x94421),x94422),x94423)),f306(f306(f143(x94421),x94424),x94423))),f149(x94421,x94425)))+~P1(f306(f306(f308(f871(x94421,x94421)),f306(f306(f236(x94421,x94421),x94422),x94424)),x94425)) % 187.68/187.65 [9478]P1(f306(f306(f306(f306(a195,x94781),x94782),x94783),f401(x94784,x94783,x94782,x94785,x94781)))+~P1(f306(f306(f306(f306(a195,f34(x94781,x94785)),x94782),x94783),x94784)) % 187.68/187.65 [9479]P1(f306(f306(f306(f306(a195,x94791),x94792),x94793),f503(x94794,x94793,x94792,x94795,x94791)))+~P1(f306(f306(f306(f306(a195,f34(x94791,x94795)),x94792),x94793),x94794)) % 187.68/187.65 [9550]P27(x95501,x95502,f306(f306(f284(f864(x95501)),f306(f306(f306(f93(x95501),x95503),f306(a26,x95504)),x95505)),f185(f872(f864(x95501),a859))))+~P27(x95501,f306(f306(f284(f864(x95501)),f306(f306(f306(f93(x95501),x95503),f306(a26,x95504)),x95505)),x95502),f306(f306(f284(f864(x95501)),f306(f306(f306(f93(x95501),x95503),f306(f218(a860),f306(a28,x95504))),x95505)),f185(f872(f864(x95501),a859)))) % 187.68/187.65 [9563]E(f306(f306(f284(x95631),f780(x95632,x95633,x95634,x95635,x95631)),f792(x95632,x95633,x95634,x95635,x95631)),f306(f306(f284(x95631),x95634),x95633))+~P1(f306(f64(x95631,x95635,f306(f306(f284(x95631),x95634),x95633)),x95632)) % 187.68/187.65 [9564]E(f306(f306(f284(x95641),f803(x95642,x95643,x95644,x95645,x95641)),f810(x95642,x95643,x95644,x95645,x95641)),f306(f306(f284(x95641),x95644),x95643))+~P1(f306(f64(x95641,x95645,f306(f306(f284(x95641),x95644),x95643)),x95642)) % 187.68/187.65 [9644]P1(f306(f306(f308(x96441),f629(x96442,x96443,x96444,x96445,x96441)),x96444))+P1(f306(f306(f306(f44(x96441,f872(x96445,a859)),x96444),x96443),x96442)) % 187.68/187.65 [9649]P1(f306(f306(f308(x96491),f630(x96492,x96493,x96491,x96494,x96495)),x96493))+P1(f306(f306(f308(x96495),x96494),f306(f306(f44(x96491,f872(x96495,a859)),x96493),x96492))) % 187.68/187.65 [9658]P1(f306(f306(f308(x96581),f627(x96582,x96583,x96581,x96584,x96585)),x96583))+P1(f306(f306(f220(f872(x96585,a859)),x96584),f306(f306(f44(x96581,f872(x96585,a859)),x96583),x96582))) % 187.68/187.65 [9660]P1(f306(f306(x96601,f452(x96602,x96601,x96603,x96604,x96605)),x96602))+~P1(f306(f306(f306(f43(x96605,f872(x96604,a859)),x96603),x96601),x96602)) % 187.68/187.65 [9663]P1(f306(f306(f308(x96631),f452(x96632,x96633,x96634,x96635,x96631)),x96634))+~P1(f306(f306(f306(f43(x96631,f872(x96635,a859)),x96634),x96633),x96632)) % 187.68/187.65 [9673]P1(f306(f306(f308(x96731),f462(x96732,x96733,x96731,x96734,x96735)),x96733))+~P1(f306(f306(f308(x96735),x96734),f306(f306(f43(x96731,f872(x96735,a859)),x96733),x96732))) % 187.68/187.65 [9678]P1(f306(f306(f308(x96781),x96782),f306(x96783,f462(x96783,x96784,x96785,x96782,x96781))))+~P1(f306(f306(f308(x96781),x96782),f306(f306(f43(x96785,f872(x96781,a859)),x96784),x96783))) % 187.68/187.65 [9775]~P1(f306(f306(x97754,f629(x97755,x97754,x97753,x97752,x97751)),x97755))+P1(f306(f306(f306(f44(x97751,f872(x97752,a859)),x97753),x97754),x97755)) % 187.68/187.65 [9778]~P1(f306(f306(f308(x97781),x97782),f306(x97785,f630(x97785,x97784,x97783,x97782,x97781))))+P1(f306(f306(f308(x97781),x97782),f306(f306(f44(x97783,f872(x97781,a859)),x97784),x97785))) % 187.68/187.65 [9781]~P1(f306(f306(f220(f872(x97811,a859)),x97812),f306(x97815,f627(x97815,x97814,x97813,x97812,x97811))))+P1(f306(f306(f220(f872(x97811,a859)),x97812),f306(f306(f44(x97813,f872(x97811,a859)),x97814),x97815))) % 187.68/187.65 [9825]P1(f306(f306(f306(f306(a195,x98251),f401(x98252,x98253,x98254,x98251,x98255)),x98253),x98252))+~P1(f306(f306(f306(f306(a195,f34(x98255,x98251)),x98254),x98253),x98252)) % 187.68/187.65 [9826]P1(f306(f306(f306(f306(a195,x98261),f503(x98262,x98263,x98264,x98261,x98265)),x98263),x98262))+~P1(f306(f306(f306(f306(a195,f34(x98265,x98261)),x98264),x98263),x98262)) % 187.68/187.65 [9851]~P1(f306(f306(f308(x98511),f780(x98515,x98514,x98513,x98512,x98511)),f792(x98515,x98514,x98513,x98512,x98511)))+~P1(f306(f64(x98511,x98512,f306(f306(f284(x98511),x98513),x98514)),x98515)) % 187.68/187.65 [9852]~P1(f306(f306(f308(x98521),f803(x98525,x98524,x98523,x98522,x98521)),f810(x98525,x98524,x98523,x98522,x98521)))+~P1(f306(f64(x98521,x98522,f306(f306(f284(x98521),x98523),x98524)),x98525)) % 187.68/187.65 [9853]~P1(f306(f306(f308(f871(x98531,x98531)),f306(f306(f236(x98531,x98531),x98532),x98535)),f306(f306(f180(f871(x98531,x98531),a859),f306(a119,x98534)),x98533)))+P1(f306(f306(f308(f871(x98531,x98531)),f306(f306(f236(x98531,x98531),x98532),f622(x98533,x98534,x98535,x98532,x98531))),f306(f306(f180(f871(x98531,x98531),a859),x98534),x98533))) % 187.68/187.65 [9860]P1(f306(f68(x98601,x98601,x98602,f780(x98603,x98604,x98605,x98602,x98601),f792(x98603,x98604,x98605,x98602,x98601)),x98603))+~P1(f306(f64(x98601,x98602,f306(f306(f284(x98601),x98605),x98604)),x98603)) % 187.68/187.65 [9861]P1(f306(f68(x98611,x98611,x98612,f803(x98613,x98614,x98615,x98612,x98611),f810(x98613,x98614,x98615,x98612,x98611)),x98613))+~P1(f306(f64(x98611,x98612,f306(f306(f284(x98611),x98615),x98614)),x98613)) % 187.68/187.65 [9873]~P108(x98731)+P17(x98731,f306(f306(f146(x98732,x98731),x98733),f306(f128(x98732,f306(f306(f7(x98732,x98731,a859),f306(f306(f8(x98731,f872(x98731,a859),x98732),a303),x98733)),f306(x98734,x98735))),x98735))) % 187.68/187.65 [9915]~P1(f306(f306(f308(x99152),x99155),f306(f260(x99151,x99152,x99154),x99153)))+P1(f306(f306(f308(f871(x99151,x99152)),f306(f306(f236(x99151,x99152),f407(x99153,x99154,x99151,x99155,x99152)),x99155)),x99154)) % 187.68/187.65 [9916]~P1(f306(f306(f308(x99162),x99165),f306(f260(x99161,x99162,x99164),x99163)))+P1(f306(f306(f308(f871(x99161,x99162)),f306(f306(f236(x99161,x99162),f431(x99163,x99164,x99161,x99165,x99162)),x99165)),x99164)) % 187.68/187.65 [9936]~P1(f306(f306(f308(f871(x99361,x99361)),f306(f306(f236(x99361,x99361),x99365),x99364)),f306(f306(f180(f871(x99361,x99361),a859),f306(a119,x99363)),x99362)))+P1(f306(f306(f308(f871(x99361,x99361)),f306(f306(f236(x99361,x99361),f622(x99362,x99363,x99364,x99365,x99361)),x99364)),x99362)) % 187.68/187.65 [9939]~P1(f306(f306(f308(f871(x99391,x99391)),f306(f306(f236(x99391,x99391),x99395),x99394)),f306(f306(f180(f871(x99391,x99391),a859),f306(a119,x99393)),x99392)))+P1(f306(f306(f308(f871(x99391,x99391)),f306(f306(f236(x99391,x99391),f620(x99392,x99393,x99394,x99395,x99391)),x99394)),f306(f306(f180(f871(x99391,x99391),a859),x99393),x99392))) % 187.68/187.65 [9940]~P1(f306(f306(f308(f871(x99401,x99401)),f306(f306(f236(x99401,x99401),x99405),x99404)),f306(f306(f180(f871(x99401,x99401),a859),f306(a119,x99403)),x99402)))+P1(f306(f306(f308(f871(x99401,x99401)),f306(f306(f236(x99401,x99401),f621(x99402,x99403,x99404,x99405,x99401)),x99404)),f306(f306(f180(f871(x99401,x99401),a859),x99403),x99402))) % 187.68/187.65 [9941]~P1(f306(f306(f308(f871(f866(x99411),f866(x99411))),f306(f306(f236(f866(x99411),f866(x99411)),x99415),f306(f306(f143(x99411),x99414),x99413))),f150(x99411,x99412)))+P1(f306(f306(f308(f871(x99411,x99411)),f306(f306(f236(x99411,x99411),f677(x99412,x99413,x99414,x99415,x99411)),x99414)),x99412)) % 187.68/187.65 [7031]E(x70311,f188(x70312))+E(f175(x70313,x70312,f306(f306(f306(f73(x70313,f869(x70312)),x70314),x70315),x70311)),f306(f306(f284(x70313),x70315),f175(x70313,x70312,x70314))) % 187.68/187.65 [7520]~E(x75203,f185(f872(x75202,a859)))+E(f306(f306(f108(f872(x75201,a859)),f306(f306(f43(x75202,f872(x75201,a859)),x75203),x75204)),x75205),x75205) % 187.68/187.65 [7521]~E(x75213,f185(f872(x75212,a859)))+E(f306(f306(f109(f872(x75211,a859)),f306(f306(f44(x75212,f872(x75211,a859)),x75213),x75214)),x75215),x75215) % 187.68/187.65 [7879]~E(x78795,f188(x78792))+E(f175(x78791,x78792,f306(f306(f306(f73(x78791,f869(x78792)),x78793),x78794),x78795)),f306(f306(f22(f872(x78791,a859)),f175(x78791,x78792,x78793)),f306(f306(f284(x78791),x78794),f185(f872(x78791,a859))))) % 187.68/187.65 [7948]~E(x79483,f185(f872(x79482,a859)))+E(f306(f306(f22(f872(x79481,a859)),f306(f306(f44(x79482,f872(x79481,a859)),x79483),x79484)),x79485),f306(f306(f22(f872(x79481,a859)),f231(f872(x79481,a859))),x79485)) % 187.68/187.65 [8080]E(f306(f306(f151(x80801,f306(f306(f122(x80801),x80802),x80803)),x80804),x80805),f306(f306(f122(x80801),f306(f306(f151(x80801,x80802),x80804),x80805)),x80803))+~P1(f306(f306(f221(a865),x80804),f306(f186(f866(x80801)),x80802))) % 187.68/187.65 [8197]P1(f306(f306(f308(x81971),x81975),f306(f164(x81971),x81973)))+E(f306(f306(f169(x81971,x81972),f306(f306(f173(x81971,x81972),x81973),f306(f306(f146(x81971,x81972),x81974),x81973))),x81975),f188(x81972)) % 187.68/187.65 [8319]~P1(f306(f306(f308(x83191),x83195),f306(f164(x83191),x83193)))+E(f306(f306(f169(x83191,x83192),f306(f306(f173(x83191,x83192),x83193),f306(f306(f146(x83191,x83192),x83194),x83193))),x83195),f306(f214(x83192),f306(x83194,x83195))) % 187.68/187.65 [8360]E(f306(f306(f157(x83601),f306(f306(f146(a865,x83601),x83602),f131(a865,f306(f276(a865,x83603),x83604)))),x83605),f306(x83602,f306(f306(f81(a865),x83603),x83605)))+~P1(f306(f306(f221(a865),x83605),f306(f306(f22(a865),x83604),x83603))) % 187.68/187.65 [8399]~E(x83993,f185(f872(x83991,a859)))+E(f306(f306(f43(x83991,f872(x83992,a859)),x83993),f306(f306(f8(f872(x83992,a859),f872(x83992,a859),x83991),f306(f108(f872(x83992,a859)),x83994)),x83995)),f185(f872(x83992,a859))) % 187.68/187.65 [8400]~E(x84003,f185(f872(x84001,a859)))+E(f306(f306(f44(x84001,f872(x84002,a859)),x84003),f306(f306(f8(f872(x84002,a859),f872(x84002,a859),x84001),f306(f22(f872(x84002,a859)),x84004)),x84005)),f231(f872(x84002,a859))) % 187.68/187.65 [8401]~E(x84013,f185(f872(x84011,a859)))+E(f306(f306(f44(x84011,f872(x84012,a859)),x84013),f306(f306(f8(f872(x84012,a859),f872(x84012,a859),x84011),f306(f109(f872(x84012,a859)),x84014)),x84015)),f231(f872(x84012,a859))) % 187.68/187.65 [8406]~P142(x84062)+E(f306(f306(f6(x84061,x84062),f306(f306(f8(x84062,x84062,x84061),f306(f82(x84062),x84063)),x84064)),x84065),f306(f306(f82(x84062),x84063),f306(f306(f6(x84061,x84062),x84064),x84065))) % 187.68/187.65 [8685]E(x86851,f185(f872(x86852,a859)))+E(f306(f306(f43(x86852,f872(x86853,a859)),x86851),f306(f306(f8(f872(x86853,a859),f872(x86853,a859),x86852),f306(f108(f872(x86853,a859)),x86854)),x86855)),f306(f306(f108(f872(x86853,a859)),x86854),f306(f306(f43(x86852,f872(x86853,a859)),x86851),x86855))) % 187.68/187.65 [8686]E(x86861,f185(f872(x86862,a859)))+E(f306(f306(f44(x86862,f872(x86863,a859)),x86861),f306(f306(f8(f872(x86863,a859),f872(x86863,a859),x86862),f306(f22(f872(x86863,a859)),x86864)),x86865)),f306(f306(f22(f872(x86863,a859)),x86864),f306(f306(f43(x86862,f872(x86863,a859)),x86861),x86865))) % 187.68/187.65 [8687]E(x86871,f185(f872(x86872,a859)))+E(f306(f306(f44(x86872,f872(x86873,a859)),x86871),f306(f306(f8(f872(x86873,a859),f872(x86873,a859),x86872),f306(f109(f872(x86873,a859)),x86874)),x86875)),f306(f306(f109(f872(x86873,a859)),x86874),f306(f306(f44(x86872,f872(x86873,a859)),x86871),x86875))) % 187.68/187.65 [8770]E(x87701,f2(a106))+E(f126(x87702,x87703,f306(x87704,f306(f306(f22(a106),x87701),f79(a106))),f306(f306(f7(x87702,a106,f867(f869(x87703))),x87705),x87701)),f197(x87702,x87703,x87704,x87705,x87701)) % 187.68/187.65 [8884]~P1(f306(f306(f221(a865),f306(x88844,x88842)),f306(x88844,x88843)))+P1(f306(f306(f308(f871(x88841,x88841)),f306(f306(f236(x88841,x88841),x88842),x88843)),f145(x88841,f306(f306(f143(f872(x88841,a865)),x88844),x88845)))) % 187.68/187.65 [9137]~P41(f872(x91375,a859),f872(x91371,a859),x91372)+P1(f306(f306(f220(f872(x91371,a859)),f306(f306(f108(f872(x91371,a859)),f306(x91372,x91373)),f306(x91372,x91374))),f306(x91372,f306(f306(f108(f872(x91375,a859)),x91373),x91374)))) % 187.68/187.65 [9153]~P28(x91532,x91531,x91533,f306(f306(f108(f872(x91532,a859)),x91534),x91535))+E(f306(f306(f109(f872(x91531,a859)),f306(f285(x91532,x91531,x91533),f306(f306(f22(f872(x91532,a859)),x91534),x91535))),f306(f285(x91532,x91531,x91533),f306(f306(f22(f872(x91532,a859)),x91535),x91534))),f185(f872(x91531,a859))) % 187.68/187.65 [9438]~P1(f306(f306(f220(f872(x94383,a859)),f306(f260(x94381,x94383,x94384),x94382)),x94385))+P1(f306(f306(f220(f872(x94381,a859)),x94382),f306(f80(f872(x94381,a859)),f306(f260(x94383,x94381,f306(f261(x94381,x94383),x94384)),f306(f80(f872(x94383,a859)),x94385))))) % 187.68/187.65 [9463]~P28(x94631,x94632,x94633,f306(f306(f284(x94631),x94634),x94635))+~P1(f306(f306(f308(x94632),f306(x94633,x94634)),f306(f285(x94631,x94632,x94633),f306(f306(f22(f872(x94631,a859)),x94635),f306(f306(f284(x94631),x94634),f185(f872(x94631,a859))))))) % 187.68/187.65 [9516]P1(f306(f306(f220(f872(x95161,a859)),f306(f260(x95162,x95161,x95163),x95164)),x95165))+~P1(f306(f306(f220(f872(x95162,a859)),x95164),f306(f80(f872(x95162,a859)),f306(f260(x95161,x95162,f306(f261(x95162,x95161),x95163)),f306(f80(f872(x95161,a859)),x95165))))) % 187.68/187.65 [9591]~P84(x95911)+P1(f306(f306(f220(x95911),f306(f76(x95911),f306(f306(f22(x95911),f306(f306(f81(x95911),x95912),x95913)),f306(f306(f81(x95911),x95914),x95915)))),f306(f306(f81(x95911),f306(f76(x95911),f306(f306(f22(x95911),x95912),x95914))),f306(f76(x95911),f306(f306(f22(x95911),x95913),x95915))))) % 187.68/187.65 [9693]P1(f306(f306(f308(x96931),f465(x96932,x96933,x96934,x96931,x96935)),x96934))+P1(f306(f306(f220(f872(x96935,a859)),f306(f306(f43(x96931,f872(x96935,a859)),x96934),x96933)),x96932)) % 187.68/187.65 [9893]~P1(f306(f306(f220(f872(x98931,a859)),f306(x98934,f465(x98935,x98934,x98933,x98932,x98931))),x98935))+P1(f306(f306(f220(f872(x98931,a859)),f306(f306(f43(x98932,f872(x98931,a859)),x98933),x98934)),x98935)) % 187.68/187.65 [8515]E(f306(f306(f122(x85151),x85152),f306(f306(f151(x85151,x85153),f306(f306(f22(a865),x85154),f306(f186(f866(x85151)),x85152))),x85155)),f306(f306(f151(x85151,f306(f306(f122(x85151),x85152),x85153)),x85154),x85155))+P1(f306(f306(f221(a865),x85154),f306(f186(f866(x85151)),x85152))) % 187.68/187.65 [8543]~P138(x85431)+E(f306(f306(f81(x85431),f306(f306(f82(x85431),x85432),x85433)),f306(f306(f81(x85431),f306(f306(f82(x85431),x85434),x85433)),x85435)),f306(f306(f81(x85431),f306(f306(f82(x85431),f306(f306(f81(x85431),x85432),x85434)),x85433)),x85435)) % 187.68/187.65 [9106]~P142(x91061)+E(f306(f158(x91061),f306(f306(f146(x91062,x91061),f306(f306(f8(x91061,x91061,x91062),f306(f82(x91061),x91063)),x91064)),x91065)),f306(f306(f82(x91061),x91063),f306(f158(x91061),f306(f306(f146(x91062,x91061),x91064),x91065)))) % 187.68/187.65 [9283]E(f306(f186(f866(x92831)),f306(f306(f165(x92831),f306(f306(f225(a865),f306(f186(f866(x92831)),x92832)),f306(f186(f866(x92833)),x92834))),x92832)),f306(f186(f866(x92833)),f306(f306(f165(x92833),f306(f306(f225(a865),f306(f186(f866(x92831)),x92832)),f306(f186(f866(x92833)),x92834))),x92834)))+P1(f306(x92835,f306(f306(f173(x92831,x92833),x92832),x92834))) % 187.68/187.65 [9527]~P142(x95272)+E(f306(f306(f6(x95271,x95272),f306(f306(f7(x95271,x95272,x95272),f306(f306(f8(x95272,f872(x95272,x95272),x95271),f82(x95272)),x95273)),x95274)),x95275),f306(f306(f82(x95272),f306(f306(f6(x95271,x95272),x95273),x95275)),x95274)) % 187.68/187.65 [9528]~P62(x95282)+E(f306(f306(f6(x95281,x95282),f306(f306(f7(x95281,x95282,x95282),f306(f306(f8(x95282,f872(x95282,x95282),x95281),f264(x95282)),x95283)),x95284)),x95285),f306(f306(f264(x95282),f306(f306(f6(x95281,x95282),x95283),x95285)),x95284)) % 187.68/187.65 [9535]~P75(x95352)+E(f306(f306(f9(x95351,x95352),f306(f306(f18(x95351,x95352,x95352),f306(f306(f8(x95352,f872(x95352,x95352),x95351),f82(x95352)),x95353)),x95354)),x95355),f306(f306(f82(x95352),f306(f306(f9(x95351,x95352),x95353),x95355)),f306(f306(f9(x95351,x95352),x95354),x95355))) % 187.68/187.65 [9536]~P68(x95362)+E(f306(f306(f6(x95361,x95362),f306(f306(f18(x95361,x95362,x95362),f306(f306(f8(x95362,f872(x95362,x95362),x95361),f22(x95362)),x95363)),x95364)),x95365),f306(f306(f22(x95362),f306(f306(f6(x95361,x95362),x95363),x95365)),f306(f306(f6(x95361,x95362),x95364),x95365))) % 187.68/187.65 [9537]~P74(x95372)+E(f306(f306(f6(x95371,x95372),f306(f306(f18(x95371,x95372,x95372),f306(f306(f8(x95372,f872(x95372,x95372),x95371),f81(x95372)),x95373)),x95374)),x95375),f306(f306(f81(x95372),f306(f306(f6(x95371,x95372),x95373),x95375)),f306(f306(f6(x95371,x95372),x95374),x95375))) % 187.68/187.65 [9576]~E(x95763,f185(f872(x95761,a859)))+E(f306(f306(f43(x95761,f872(x95762,a859)),x95763),f306(f306(f7(x95761,f872(x95762,a859),f872(x95762,a859)),f306(f306(f8(f872(x95762,a859),f872(f872(x95762,a859),f872(x95762,a859)),x95761),f108(f872(x95762,a859))),x95764)),x95765)),f185(f872(x95762,a859))) % 187.68/187.65 [9577]~E(x95773,f185(f872(x95771,a859)))+E(f306(f306(f44(x95771,f872(x95772,a859)),x95773),f306(f306(f7(x95771,f872(x95772,a859),f872(x95772,a859)),f306(f306(f8(f872(x95772,a859),f872(f872(x95772,a859),f872(x95772,a859)),x95771),f22(f872(x95772,a859))),x95774)),x95775)),f231(f872(x95772,a859))) % 187.68/187.65 [9578]~E(x95783,f185(f872(x95781,a859)))+E(f306(f306(f44(x95781,f872(x95782,a859)),x95783),f306(f306(f7(x95781,f872(x95782,a859),f872(x95782,a859)),f306(f306(f8(f872(x95782,a859),f872(f872(x95782,a859),f872(x95782,a859)),x95781),f109(f872(x95782,a859))),x95784)),x95785)),f231(f872(x95782,a859))) % 187.68/187.65 [9599]E(x95991,f185(f872(x95992,a859)))+E(f306(f306(f43(x95992,f872(x95993,a859)),x95991),f306(f306(f7(x95992,f872(x95993,a859),f872(x95993,a859)),f306(f306(f8(f872(x95993,a859),f872(f872(x95993,a859),f872(x95993,a859)),x95992),f108(f872(x95993,a859))),x95994)),x95995)),f306(f306(f108(f872(x95993,a859)),f306(f306(f43(x95992,f872(x95993,a859)),x95991),x95994)),x95995)) % 187.68/187.65 [9600]E(x96001,f185(f872(x96002,a859)))+E(f306(f306(f44(x96002,f872(x96003,a859)),x96001),f306(f306(f7(x96002,f872(x96003,a859),f872(x96003,a859)),f306(f306(f8(f872(x96003,a859),f872(f872(x96003,a859),f872(x96003,a859)),x96002),f22(f872(x96003,a859))),x96004)),x96005)),f306(f306(f22(f872(x96003,a859)),f306(f306(f44(x96002,f872(x96003,a859)),x96001),x96004)),x96005)) % 187.68/187.65 [9601]E(x96011,f185(f872(x96012,a859)))+E(f306(f306(f44(x96012,f872(x96013,a859)),x96011),f306(f306(f7(x96012,f872(x96013,a859),f872(x96013,a859)),f306(f306(f8(f872(x96013,a859),f872(f872(x96013,a859),f872(x96013,a859)),x96012),f109(f872(x96013,a859))),x96014)),x96015)),f306(f306(f109(f872(x96013,a859)),f306(f306(f44(x96012,f872(x96013,a859)),x96011),x96014)),x96015)) % 187.68/187.65 [9160]~P1(f306(f306(f220(a865),x91601),x91604))+E(f306(f306(f22(a865),f306(f306(f81(a865),f306(f306(f82(a865),x91601),x91602)),x91603)),f306(f306(f81(a865),f306(f306(f82(a865),x91604),x91602)),x91605)),f306(f306(f22(a865),x91603),f306(f306(f81(a865),f306(f306(f82(a865),f306(f306(f22(a865),x91604),x91601)),x91602)),x91605))) % 187.68/187.65 [9756]~P142(x97561)+E(f306(f158(x97561),f306(f306(f146(x97562,x97561),f306(f306(f7(x97562,x97561,x97561),f306(f306(f8(x97561,f872(x97561,x97561),x97562),f82(x97561)),x97563)),x97564)),x97565)),f306(f306(f82(x97561),f306(f158(x97561),f306(f306(f146(x97562,x97561),x97563),x97565))),x97564)) % 187.68/187.65 [9762]~P68(x97621)+E(f306(f158(x97621),f306(f306(f146(x97622,x97621),f306(f306(f18(x97622,x97621,x97621),f306(f306(f8(x97621,f872(x97621,x97621),x97622),f22(x97621)),x97623)),x97624)),x97625)),f306(f306(f22(x97621),f306(f158(x97621),f306(f306(f146(x97622,x97621),x97623),x97625))),f306(f158(x97621),f306(f306(f146(x97622,x97621),x97624),x97625)))) % 187.68/187.65 [9763]~P74(x97631)+E(f306(f158(x97631),f306(f306(f146(x97632,x97631),f306(f306(f18(x97632,x97631,x97631),f306(f306(f8(x97631,f872(x97631,x97631),x97632),f81(x97631)),x97633)),x97634)),x97635)),f306(f306(f81(x97631),f306(f158(x97631),f306(f306(f146(x97632,x97631),x97633),x97635))),f306(f158(x97631),f306(f306(f146(x97632,x97631),x97634),x97635)))) % 187.68/187.65 [9906]P1(f306(x99061,f306(f306(f173(x99062,x99063),x99064),x99065)))+~P1(f306(x99061,f306(f306(f173(x99062,x99063),f306(f306(f165(x99062),f306(f306(f225(a865),f306(f186(f866(x99062)),x99064)),f306(f186(f866(x99063)),x99065))),x99064)),f306(f306(f165(x99063),f306(f306(f225(a865),f306(f186(f866(x99062)),x99064)),f306(f186(f866(x99063)),x99065))),x99065)))) % 187.68/187.65 [9406]~P1(f306(f306(f220(a865),x94064),x94061))+E(f306(f306(f22(a865),f306(f306(f81(a865),f306(f306(f82(a865),x94061),x94062)),x94063)),f306(f306(f81(a865),f306(f306(f82(a865),x94064),x94062)),x94065)),f306(f306(f22(a865),f306(f306(f81(a865),f306(f306(f82(a865),f306(f306(f22(a865),x94061),x94064)),x94062)),x94063)),x94065)) % 187.68/187.65 [10166]P27(x101661,x101662,f306(f285(a862,f864(x101661),f306(f306(f18(a862,f872(x101661,f872(a861,a859)),f864(x101661)),f306(f306(f18(a862,a860,f872(f872(x101661,f872(a861,a859)),f864(x101661))),f306(f306(f8(f872(x101661,f872(a861,a859)),f872(a860,f872(f872(x101661,f872(a861,a859)),f864(x101661))),a862),f93(x101661)),x101663)),a26)),x101664)),x101665))+~P27(x101661,f306(f306(f108(f872(f864(x101661),a859)),x101662),f306(f285(a862,f864(x101661),f306(f306(f18(a862,f872(x101661,f872(a861,a859)),f864(x101661)),f306(f306(f18(a862,a860,f872(f872(x101661,f872(a861,a859)),f864(x101661))),f306(f306(f8(f872(x101661,f872(a861,a859)),f872(a860,f872(f872(x101661,f872(a861,a859)),f864(x101661))),a862),f93(x101661)),x101663)),a26)),x101664)),x101665)),f306(f285(a862,f864(x101661),f306(f306(f18(a862,f872(x101661,f872(a861,a859)),f864(x101661)),f306(f306(f18(a862,a860,f872(f872(x101661,f872(a861,a859)),f864(x101661))),f306(f306(f8(f872(x101661,f872(a861,a859)),f872(a860,f872(f872(x101661,f872(a861,a859)),f864(x101661))),a862),f93(x101661)),x101663)),f306(f306(f8(f869(a860),a860,a862),f218(a860)),a28))),x101664)),x101665)) % 187.68/187.65 [10167]P31(x101671,x101672,f306(f285(a862,f864(x101671),f306(f306(f18(a862,f872(x101671,f872(a861,a859)),f864(x101671)),f306(f306(f18(a862,a860,f872(f872(x101671,f872(a861,a859)),f864(x101671))),f306(f306(f8(f872(x101671,f872(a861,a859)),f872(a860,f872(f872(x101671,f872(a861,a859)),f864(x101671))),a862),f93(x101671)),x101673)),a26)),x101674)),x101675))+~P31(x101671,f306(f306(f108(f872(f864(x101671),a859)),x101672),f306(f285(a862,f864(x101671),f306(f306(f18(a862,f872(x101671,f872(a861,a859)),f864(x101671)),f306(f306(f18(a862,a860,f872(f872(x101671,f872(a861,a859)),f864(x101671))),f306(f306(f8(f872(x101671,f872(a861,a859)),f872(a860,f872(f872(x101671,f872(a861,a859)),f864(x101671))),a862),f93(x101671)),x101673)),a26)),x101674)),x101675)),f306(f285(a862,f864(x101671),f306(f306(f18(a862,f872(x101671,f872(a861,a859)),f864(x101671)),f306(f306(f18(a862,a860,f872(f872(x101671,f872(a861,a859)),f864(x101671))),f306(f306(f8(f872(x101671,f872(a861,a859)),f872(a860,f872(f872(x101671,f872(a861,a859)),f864(x101671))),a862),f93(x101671)),x101673)),f306(f306(f8(f869(a860),a860,a862),f218(a860)),a28))),x101674)),x101675)) % 187.68/187.65 [5217]E(x52171,x52172)+~E(f29(x52173,x52174,x52171),f29(x52175,x52176,x52172)) % 187.68/187.65 [5218]E(x52181,x52182)+~E(f29(x52183,x52181,x52184),f29(x52185,x52182,x52186)) % 187.68/187.65 [5219]E(x52191,x52192)+~E(f29(x52191,x52193,x52194),f29(x52192,x52195,x52196)) % 187.68/187.65 [5220]E(x52201,x52202)+~E(f31(x52203,x52204,x52201),f31(x52205,x52206,x52202)) % 187.68/187.65 [5221]E(x52211,x52212)+~E(f31(x52213,x52211,x52214),f31(x52215,x52212,x52216)) % 187.68/187.65 [5222]E(x52221,x52222)+~E(f31(x52221,x52223,x52224),f31(x52222,x52225,x52226)) % 187.68/187.65 [5223]E(x52231,x52232)+~E(f30(x52233,x52234,x52231),f30(x52235,x52236,x52232)) % 187.68/187.65 [5224]E(x52241,x52242)+~E(f30(x52243,x52241,x52244),f30(x52245,x52242,x52246)) % 187.68/187.65 [5225]E(x52251,x52252)+~E(f30(x52251,x52253,x52254),f30(x52252,x52255,x52256)) % 187.68/187.65 [6675]E(f306(f176(x66751,x66752,x66753,x66754),x66755),f306(f214(x66752),x66756))+~E(f306(x66754,x66755),f306(f214(x66752),x66756)) % 187.68/187.65 [6817]E(f306(f216(f869(x68171),x68172,f188(x68171),x68173),f306(x68174,x68175)),f306(x68173,x68176))+~E(f306(x68174,x68175),f306(f214(x68172),x68176)) % 187.68/187.65 [8342]~P22(x83425,x83421,x83422,x83426)+E(f306(f74(x83421,x83421,x83421,f306(x83422,x83423)),f306(x83422,x83424)),f306(f74(x83421,x83421,x83421,f306(x83422,x83424)),f306(x83422,x83423))) % 187.68/187.65 [8584]~P56(x85844,x85845,x85842,x85841,x85846)+E(f306(x85841,f306(x85842,x85843)),x85843) % 187.68/187.65 [8734]P28(x87341,x87342,x87343,x87344)+~P28(x87341,x87345,f306(f74(x87342,x87345,x87341,x87346),x87343),x87344) % 187.68/187.65 [8818]~P28(x88184,x88182,f306(f74(x88181,x88182,x88184,x88183),x88185),x88186)+P28(x88181,x88182,x88183,f306(f285(x88184,x88181,x88185),x88186)) % 187.68/187.65 [9538]P1(f306(f63(x95381),x95382))+~P1(f306(f68(x95381,x95383,x95384,x95385,x95382),x95386)) % 187.68/187.65 [9546]~P1(f306(f306(f308(x95464),x95463),f274(x95464,x95465,x95461,x95462,x95466)))+P1(f306(f306(x95461,x95462),x95463)) % 187.68/187.65 [9547]~P1(f306(f306(f308(x95474),x95473),f271(x95474,x95471,x95475,x95472,x95476)))+P1(f306(f306(x95471,x95472),x95473)) % 187.68/187.65 [9548]~P1(f306(f306(f308(x95484),x95482),f274(x95484,x95481,x95485,x95486,x95483)))+P1(f306(f306(x95481,x95482),x95483)) % 187.68/187.65 [9549]~P1(f306(f306(f308(x95494),x95492),f271(x95494,x95495,x95491,x95496,x95493)))+P1(f306(f306(x95491,x95492),x95493)) % 187.68/187.65 [5722]E(x57221,x57222)+~E(f306(f306(f236(x57223,x57224),x57225),x57221),f306(f306(f236(x57223,x57224),x57226),x57222)) % 187.68/187.65 [5724]E(x57241,x57242)+~E(f306(f306(f236(x57243,x57244),x57241),x57245),f306(f306(f236(x57243,x57244),x57242),x57246)) % 187.68/187.65 [5849]~P19(x58495,x58496,x58491)+E(f306(f306(x58491,x58492),f306(f306(x58491,x58493),x58494)),f306(f306(x58491,x58493),f306(f306(x58491,x58492),x58494))) % 187.68/187.65 [7271]~P35(x72714,x72711,f306(f306(f143(x72714),x72712),x72715),f306(f306(f143(x72714),x72713),x72716))+P1(f306(f306(x72711,x72712),x72713)) % 187.68/187.65 [7635]P35(x76351,x76352,x76353,x76354)+~P35(x76351,x76352,f306(f306(f143(x76351),x76355),x76353),f306(f306(f143(x76351),x76356),x76354)) % 187.68/187.65 [8676]~P56(x86765,x86761,x86762,x86766,x86764)+P1(f306(f306(f308(x86761),f306(x86762,x86763)),x86764)) % 187.68/187.65 [8846]E(f306(f77(x88461,x88462,x88463,x88464,x88465),x88466),f306(x88463,x88466))+P1(f306(f306(f308(x88461),x88466),x88465)) % 187.68/187.65 [8868]~E(x88683,f306(f306(f143(x88681),x88685),x88686))+P1(f306(f306(f308(f871(f866(x88681),f866(x88681))),f306(f306(f236(f866(x88681),f866(x88681)),x88682),f306(f306(f122(x88681),x88682),x88683))),f139(x88681,x88684))) % 187.68/187.65 [8875]E(f306(f77(x88751,x88752,x88753,x88754,x88755),x88756),f306(x88754,x88756))+~P1(f306(f306(f308(x88751),x88756),x88755)) % 187.68/187.65 [8880]E(f306(f178(x88801,x88802,x88803,x88804,x88805),x88806),f306(x88803,x88806))+P1(f306(f306(f308(x88801),x88806),f306(f164(x88801),x88804))) % 187.68/187.65 [9110]~P37(x91101,x91102,x91103,x91105,x91106)+P37(x91101,x91102,x91103,f306(f306(f165(x91101),x91104),x91105),f306(f306(f165(x91102),x91104),x91106)) % 187.68/187.65 [9111]~P37(x91111,x91112,x91113,x91115,x91116)+P37(x91111,x91112,x91113,f306(f306(f130(x91111),x91114),x91115),f306(f306(f130(x91112),x91114),x91116)) % 187.68/187.65 [9611]~P26(x96114,x96112,x96115,x96113,x96116,x96111)+E(f306(x96111,f185(f872(x96112,a859))),x96113) % 187.68/187.65 [9854]~E(f306(x98544,f306(f235(x98541,x98543),x98545)),f306(x98546,f306(f235(x98541,x98543),x98545)))+E(f306(f246(x98541,x98542,x98543,x98543,x98544,f35(x98543)),x98545),f306(f246(x98541,x98542,x98543,x98543,x98546,f35(x98543)),x98545)) % 187.68/187.65 [9855]~E(f306(x98554,f306(f244(x98551,x98552),x98555)),f306(x98556,f306(f244(x98551,x98552),x98555)))+E(f306(f246(x98551,x98551,x98552,x98553,f35(x98551),x98554),x98555),f306(f246(x98551,x98551,x98552,x98553,f35(x98551),x98556),x98555)) % 187.68/187.65 [9902]~E(f306(f246(x99022,x99026,x99023,x99023,x99021,f35(x99023)),x99024),f306(f246(x99022,x99026,x99023,x99023,x99025,f35(x99023)),x99024))+E(f306(x99021,f306(f235(x99022,x99023),x99024)),f306(x99025,f306(f235(x99022,x99023),x99024))) % 187.68/187.65 [9903]~E(f306(f246(x99032,x99032,x99033,x99036,f35(x99032),x99031),x99034),f306(f246(x99032,x99032,x99033,x99036,f35(x99032),x99035),x99034))+E(f306(x99031,f306(f244(x99032,x99033),x99034)),f306(x99035,f306(f244(x99032,x99033),x99034))) % 187.68/187.65 [8773]P1(f306(f306(f308(x87731),x87732),x87733))+~P1(f306(f306(f308(f871(x87731,x87734)),f306(f306(f236(x87731,x87734),x87732),x87735)),f306(f306(f243(x87731,x87734),x87733),x87736))) % 187.68/187.65 [8787]P1(f306(f306(f308(x87871),x87872),f306(x87873,x87874)))+~P1(f306(f306(f308(f871(x87875,x87871)),f306(f306(f236(x87875,x87871),x87874),x87872)),f306(f306(f243(x87875,x87871),x87876),x87873))) % 187.68/187.65 [8877]~E(f306(f186(f866(x88771)),x88774),f306(f186(f866(x88772)),x88775))+E(f178(x88771,x88772,x88773,x88774,f306(f306(f122(x88772),x88775),x88776)),f178(x88771,x88772,x88773,x88774,x88775)) % 187.68/187.65 [8878]~E(f306(f186(f866(x88781)),x88784),f306(f186(f866(x88782)),x88786))+E(f178(x88781,x88782,x88783,f306(f306(f122(x88781),x88784),x88785),x88786),f178(x88781,x88782,x88783,x88784,x88786)) % 187.68/187.65 [9131]P1(f306(f306(f308(x91311),x91314),f175(x91311,x91312,x91316)))+E(f176(x91311,x91312,f306(f306(f306(f73(x91311,f869(x91312)),x91313),x91314),f306(f214(x91312),x91315)),x91316),f306(f306(f306(f73(x91311,f869(x91312)),f176(x91311,x91312,x91313,x91316)),x91314),f306(f214(x91312),x91315))) % 187.68/187.65 [9233]P1(f306(f306(f308(f871(x92331,x92331)),f306(f306(f236(x92331,x92331),f306(x92332,x92333)),f306(x92332,x92334))),x92335))+~P1(f306(f306(f308(f871(x92336,x92336)),f306(f306(f236(x92336,x92336),x92333),x92334)),f306(f306(f262(x92331,x92336),x92335),x92332))) % 187.68/187.65 [9253]~P1(f306(f306(f308(f871(x92534,x92534)),f306(f306(f236(x92534,x92534),f306(x92536,x92532)),f306(x92536,x92533))),x92535))+P1(f306(f306(f308(f871(x92531,x92531)),f306(f306(f236(x92531,x92531),x92532),x92533)),f306(f306(f262(x92534,x92531),x92535),x92536))) % 187.68/187.65 [9905]E(f306(f306(f236(x99051,x99052),f660(x99053,x99054,x99055,x99056,x99052,x99051)),f661(x99053,x99054,x99055,x99056,x99052,x99051)),x99056)+~P1(f306(f306(f308(f871(x99051,x99052)),x99056),f306(f306(f263(x99051,x99055,x99052),x99054),x99053))) % 187.68/187.65 [10110]~P1(f306(f306(f308(f871(x101101,x101106)),x101105),f306(f306(f263(x101101,x101102,x101106),x101104),x101103)))+P1(f306(f306(f308(f871(x101101,x101102)),f306(f306(f236(x101101,x101102),f660(x101103,x101104,x101102,x101105,x101106,x101101)),f662(x101103,x101104,x101102,x101105,x101106,x101101))),x101104)) % 187.68/187.65 [10111]~P1(f306(f306(f308(f871(x101116,x101112)),x101115),f306(f306(f263(x101116,x101111,x101112),x101114),x101113)))+P1(f306(f306(f308(f871(x101111,x101112)),f306(f306(f236(x101111,x101112),f662(x101113,x101114,x101111,x101115,x101112,x101116)),f661(x101113,x101114,x101111,x101115,x101112,x101116))),x101113)) % 187.68/187.65 [6132]~E(x61326,x61324)+E(f306(f306(f306(f306(f73(x61321,x61322),x61323),x61324),x61325),x61326),x61325) % 187.68/187.65 [6181]E(x61811,x61812)+E(f306(f306(f306(f306(f73(x61813,x61814),x61815),x61812),x61816),x61811),f306(x61815,x61811)) % 187.68/187.65 [7705]~P6(x77052)+E(f306(f306(f43(x77051,x77052),x77053),f306(f306(f7(x77051,x77054,x77052),x77055),x77056)),f306(f306(f306(f43(x77051,f872(x77054,x77052)),x77053),x77055),x77056)) % 187.68/187.65 [7706]~P6(x77062)+E(f306(f306(f44(x77061,x77062),x77063),f306(f306(f7(x77061,x77064,x77062),x77065),x77066)),f306(f306(f306(f44(x77061,f872(x77064,x77062)),x77063),x77065),x77066)) % 187.68/187.65 [8497]E(f306(f306(f43(x84971,f872(x84972,a859)),x84973),f306(f306(f8(f872(x84972,a859),f872(x84972,a859),x84971),f306(f284(x84972),x84974)),x84975)),f306(f306(f284(x84972),x84974),f306(f306(f43(x84971,f872(x84972,a859)),x84973),x84975)))+~P1(f306(f306(f308(x84971),x84976),x84973)) % 187.68/187.65 [8931]~P6(x89312)+E(f306(f306(f43(x89311,x89312),x89313),f306(f306(f8(f872(x89314,x89312),x89312,x89311),f306(f43(x89314,x89312),x89315)),f306(f7(x89314,x89311,x89312),x89316))),f306(f306(f43(x89314,x89312),x89315),f306(f306(f8(f872(x89311,x89312),x89312,x89314),f306(f43(x89311,x89312),x89313)),x89316))) % 187.68/187.65 [8932]~P6(x89322)+E(f306(f306(f44(x89321,x89322),x89323),f306(f306(f8(f872(x89324,x89322),x89322,x89321),f306(f44(x89324,x89322),x89325)),f306(f7(x89324,x89321,x89322),x89326))),f306(f306(f44(x89324,x89322),x89325),f306(f306(f8(f872(x89321,x89322),x89322,x89324),f306(f44(x89321,x89322),x89323)),x89326))) % 187.68/187.65 [9141]P1(f306(f306(f308(x91411),x91412),f306(f164(x91411),x91413)))+~P1(f306(f306(f308(f871(x91414,x91411)),f306(f306(f236(x91414,x91411),x91415),x91412)),f306(f164(f871(x91414,x91411)),f306(f306(f173(x91414,x91411),x91416),x91413)))) % 187.68/187.65 [9142]P1(f306(f306(f308(x91421),x91422),f306(f164(x91421),x91423)))+~P1(f306(f306(f308(f871(x91421,x91424)),f306(f306(f236(x91421,x91424),x91422),x91425)),f306(f164(f871(x91421,x91424)),f306(f306(f173(x91421,x91424),x91423),x91426)))) % 187.68/187.65 [9247]P1(f306(f306(f220(f872(x92471,a859)),f306(f260(x92472,x92471,x92473),x92474)),x92475))+~P1(f306(f306(f220(f872(f871(x92472,x92471),a859)),x92473),f306(f306(f243(x92472,x92471),x92476),f306(f16(f872(x92471,a859),x92472),x92475)))) % 187.68/187.65 [9441]P1(f306(f306(f308(f871(f866(x94411),f866(x94411))),f306(f306(f236(f866(x94411),f866(x94411)),f306(f306(f143(x94411),x94412),x94413)),f306(f306(f143(x94411),x94414),x94415))),f139(x94411,x94416)))+~P1(f306(f306(f308(f871(x94411,x94411)),f306(f306(f236(x94411,x94411),x94412),x94414)),x94416)) % 187.68/187.65 [9901]E(f306(f306(f236(x99011,x99012),f561(x99013,x99014,x99015,x99012,x99011,x99016)),f564(x99013,x99014,x99015,x99012,x99011,x99016)),x99016)+P1(f306(f306(f308(x99015),x99014),f306(f306(f245(x99011,x99012,f872(x99015,a859)),x99013),x99016))) % 187.68/187.65 [9907]E(f306(f306(f236(x99071,x99072),f562(x99073,x99074,x99072,x99071,x99075,x99076)),f563(x99073,x99074,x99072,x99071,x99075,x99076)),x99073)+~P1(f306(f306(f308(x99076),x99075),f306(f306(f245(x99071,x99072,f872(x99076,a859)),x99074),x99073))) % 187.68/187.65 [10068]P1(f306(f306(f308(x100681),x100682),f306(f306(x100683,f562(x100684,x100683,x100685,x100686,x100682,x100681)),f563(x100684,x100683,x100685,x100686,x100682,x100681))))+~P1(f306(f306(f308(x100681),x100682),f306(f306(f245(x100686,x100685,f872(x100681,a859)),x100683),x100684))) % 187.68/187.65 [10088]~P1(f306(f306(f308(x100881),x100882),f306(f306(x100885,f561(x100885,x100882,x100881,x100884,x100883,x100886)),f564(x100885,x100882,x100881,x100884,x100883,x100886))))+P1(f306(f306(f308(x100881),x100882),f306(f306(f245(x100883,x100884,f872(x100881,a859)),x100885),x100886))) % 187.68/187.65 [7825]P1(f306(f306(f308(x78251),x78254),x78256))+E(f179(x78251,x78252,f306(f306(f306(f73(x78251,f869(x78252)),x78253),x78254),x78255),x78256),f179(x78251,x78252,x78253,x78256)) % 187.68/187.65 [7902]P1(f306(f306(f308(x79021),x79024),x79026))+E(f306(f285(x79021,x79022,f306(f306(f306(f73(x79021,x79022),x79023),x79024),x79025)),x79026),f306(f285(x79021,x79022,x79023),x79026)) % 187.68/187.65 [7929]P1(f306(f306(f308(x79291),x79294),f306(f164(x79291),x79296)))+E(f306(f306(f146(x79291,x79292),f306(f306(f306(f73(x79291,x79292),x79293),x79294),x79295)),x79296),f306(f306(f146(x79291,x79292),x79293),x79296)) % 187.68/187.65 [8389]E(x83891,x83892)+E(f306(f306(f151(x83893,f306(f306(f151(x83893,x83894),x83891),x83895)),x83892),x83896),f306(f306(f151(x83893,f306(f306(f151(x83893,x83894),x83892),x83896)),x83891),x83895)) % 187.68/187.65 [8937]~P1(f306(f306(f308(x89373),x89376),x89375))+E(f306(f306(f284(x89371),x89372),f306(f285(x89373,x89371,x89374),f306(f306(f22(f872(x89373,a859)),x89375),f306(f306(f284(x89373),x89376),f185(f872(x89373,a859)))))),f306(f285(x89373,x89371,f306(f306(f306(f73(x89373,x89371),x89374),x89376),x89372)),x89375)) % 187.68/187.65 [9717]E(f178(x97171,x97172,x97173,f306(f306(f122(x97171),x97174),f306(f306(f143(x97171),x97175),f120(x97171))),x97176),f306(f306(f306(f73(x97171,f869(x97172)),f178(x97171,x97172,x97173,x97174,x97176)),x97175),f306(f214(x97172),f306(f306(f157(x97172),x97176),f306(f186(f866(x97171)),x97174)))))+~P1(f306(f306(f221(a865),f306(f186(f866(x97171)),x97174)),f306(f186(f866(x97172)),x97176))) % 187.68/187.65 [8716]~E(x87163,x87166)+E(f306(f306(f169(x87161,x87162),f306(f306(f143(f871(x87161,x87162)),f306(f306(f236(x87161,x87162),x87163),x87164)),x87165)),x87166),f306(f214(x87162),x87164)) % 187.68/187.65 [8743]E(x87431,x87432)+E(f306(f306(f169(x87433,x87434),f306(f306(f143(f871(x87433,x87434)),f306(f306(f236(x87433,x87434),x87431),x87435)),x87436)),x87432),f306(f306(f169(x87433,x87434),x87436),x87432)) % 187.68/187.65 [9014]~P1(f306(f306(x90144,x90145),x90146))+P1(f306(f306(f306(f306(f108(f872(x90141,f872(x90142,a859))),x90143),x90144),x90145),x90146)) % 187.68/187.65 [9016]~P1(f306(f306(x90163,x90165),x90166))+P1(f306(f306(f306(f306(f108(f872(x90161,f872(x90162,a859))),x90163),x90164),x90165),x90166)) % 187.68/187.65 [9305]P1(f306(f306(x93051,x93052),x93053))+~P1(f306(f306(f306(f306(f109(f872(x93054,f872(x93055,a859))),x93056),x93051),x93052),x93053)) % 187.68/187.65 [9306]P1(f306(f306(x93061,x93062),x93063))+~P1(f306(f306(f306(f306(f109(f872(x93064,f872(x93065,a859))),x93061),x93066),x93062),x93063)) % 187.68/187.65 [9741]~P75(x97412)+E(f306(f306(f9(x97411,x97412),f306(f306(f7(x97411,f872(x97413,a859),x97412),f306(f306(f8(f872(x97413,x97412),f872(f872(x97413,a859),x97412),x97411),f9(x97413,x97412)),x97414)),x97415)),x97416),f306(f306(f9(f871(x97411,x97413),x97412),f306(f245(x97411,x97413,x97412),x97414)),f306(f306(f243(x97411,x97413),x97416),f306(f16(f872(x97413,a859),x97411),x97415)))) % 187.68/187.65 [9742]~P74(x97422)+E(f306(f306(f6(x97421,x97422),f306(f306(f7(x97421,f872(x97423,a859),x97422),f306(f306(f8(f872(x97423,x97422),f872(f872(x97423,a859),x97422),x97421),f6(x97423,x97422)),x97424)),x97425)),x97426),f306(f306(f6(f871(x97421,x97423),x97422),f306(f245(x97421,x97423,x97422),x97424)),f306(f306(f243(x97421,x97423),x97426),f306(f16(f872(x97423,a859),x97421),x97425)))) % 187.68/187.65 [9882]~P74(x98822)+E(f306(f306(f6(x98821,x98822),f306(f306(f7(x98821,f872(x98823,a859),x98822),f306(f306(f8(f872(x98823,x98822),f872(f872(x98823,a859),x98822),x98821),f6(x98823,x98822)),f306(f7(x98823,x98821,x98822),x98824))),x98825)),x98826),f306(f306(f6(x98823,x98822),f306(f306(f7(x98823,f872(x98821,a859),x98822),f306(f306(f8(f872(x98821,x98822),f872(f872(x98821,a859),x98822),x98823),f6(x98821,x98822)),x98824)),x98826)),x98825)) % 187.68/187.65 [9580]~P1(f306(f306(f308(x95801),x95805),x95804))+E(f306(f306(f306(f73(x95801,f869(x95802)),f179(x95801,x95802,x95803,f306(f306(f22(f872(x95801,a859)),x95804),f306(f306(f284(x95801),x95805),f185(f872(x95801,a859)))))),x95805),x95806),f179(x95801,x95802,f306(f306(f306(f73(x95801,f869(x95802)),x95803),x95805),x95806),x95804)) % 187.68/187.65 [10170]~P1(f306(f306(f308(f871(x101701,x101702)),f306(f306(f236(x101701,x101702),x101705),x101706)),f306(f306(f108(f872(f871(x101701,x101702),a859)),x101703),x101704)))+P1(f306(f306(f306(f306(f108(f872(x101701,f872(x101702,a859))),f306(f306(f7(x101701,f872(f871(x101701,x101702),a859),f872(x101702,a859)),f306(f306(f8(f872(x101702,f872(f872(f871(x101701,x101702),a859),a859)),f872(f872(f871(x101701,x101702),a859),f872(x101702,a859)),x101701),f7(x101702,f872(f871(x101701,x101702),a859),a859)),f306(f306(f8(f872(x101702,f871(x101701,x101702)),f872(x101702,f872(f872(f871(x101701,x101702),a859),a859)),x101701),f306(f8(f871(x101701,x101702),f872(f872(f871(x101701,x101702),a859),a859),x101702),f308(f871(x101701,x101702)))),f236(x101701,x101702)))),x101703)),f306(f306(f7(x101701,f872(f871(x101701,x101702),a859),f872(x101702,a859)),f306(f306(f8(f872(x101702,f872(f872(f871(x101701,x101702),a859),a859)),f872(f872(f871(x101701,x101702),a859),f872(x101702,a859)),x101701),f7(x101702,f872(f871(x101701,x101702),a859),a859)),f306(f306(f8(f872(x101702,f871(x101701,x101702)),f872(x101702,f872(f872(f871(x101701,x101702),a859),a859)),x101701),f306(f8(f871(x101701,x101702),f872(f872(f871(x101701,x101702),a859),a859),x101702),f308(f871(x101701,x101702)))),f236(x101701,x101702)))),x101704)),x101705),x101706)) % 187.68/187.65 [10171]~P1(f306(f306(f308(f871(x101711,x101712)),f306(f306(f236(x101711,x101712),x101715),x101716)),f306(f306(f109(f872(f871(x101711,x101712),a859)),x101713),x101714)))+P1(f306(f306(f306(f306(f109(f872(x101711,f872(x101712,a859))),f306(f306(f7(x101711,f872(f871(x101711,x101712),a859),f872(x101712,a859)),f306(f306(f8(f872(x101712,f872(f872(f871(x101711,x101712),a859),a859)),f872(f872(f871(x101711,x101712),a859),f872(x101712,a859)),x101711),f7(x101712,f872(f871(x101711,x101712),a859),a859)),f306(f306(f8(f872(x101712,f871(x101711,x101712)),f872(x101712,f872(f872(f871(x101711,x101712),a859),a859)),x101711),f306(f8(f871(x101711,x101712),f872(f872(f871(x101711,x101712),a859),a859),x101712),f308(f871(x101711,x101712)))),f236(x101711,x101712)))),x101713)),f306(f306(f7(x101711,f872(f871(x101711,x101712),a859),f872(x101712,a859)),f306(f306(f8(f872(x101712,f872(f872(f871(x101711,x101712),a859),a859)),f872(f872(f871(x101711,x101712),a859),f872(x101712,a859)),x101711),f7(x101712,f872(f871(x101711,x101712),a859),a859)),f306(f306(f8(f872(x101712,f871(x101711,x101712)),f872(x101712,f872(f872(f871(x101711,x101712),a859),a859)),x101711),f306(f8(f871(x101711,x101712),f872(f872(f871(x101711,x101712),a859),a859),x101712),f308(f871(x101711,x101712)))),f236(x101711,x101712)))),x101714)),x101715),x101716)) % 187.68/187.65 [10177]P1(f306(f306(f308(f871(x101771,x101772)),f306(f306(f236(x101771,x101772),x101773),x101774)),f306(f306(f108(f872(f871(x101771,x101772),a859)),x101775),x101776)))+~P1(f306(f306(f306(f306(f108(f872(x101771,f872(x101772,a859))),f306(f306(f7(x101771,f872(f871(x101771,x101772),a859),f872(x101772,a859)),f306(f306(f8(f872(x101772,f872(f872(f871(x101771,x101772),a859),a859)),f872(f872(f871(x101771,x101772),a859),f872(x101772,a859)),x101771),f7(x101772,f872(f871(x101771,x101772),a859),a859)),f306(f306(f8(f872(x101772,f871(x101771,x101772)),f872(x101772,f872(f872(f871(x101771,x101772),a859),a859)),x101771),f306(f8(f871(x101771,x101772),f872(f872(f871(x101771,x101772),a859),a859),x101772),f308(f871(x101771,x101772)))),f236(x101771,x101772)))),x101775)),f306(f306(f7(x101771,f872(f871(x101771,x101772),a859),f872(x101772,a859)),f306(f306(f8(f872(x101772,f872(f872(f871(x101771,x101772),a859),a859)),f872(f872(f871(x101771,x101772),a859),f872(x101772,a859)),x101771),f7(x101772,f872(f871(x101771,x101772),a859),a859)),f306(f306(f8(f872(x101772,f871(x101771,x101772)),f872(x101772,f872(f872(f871(x101771,x101772),a859),a859)),x101771),f306(f8(f871(x101771,x101772),f872(f872(f871(x101771,x101772),a859),a859),x101772),f308(f871(x101771,x101772)))),f236(x101771,x101772)))),x101776)),x101773),x101774)) % 187.68/187.65 [10178]P1(f306(f306(f308(f871(x101781,x101782)),f306(f306(f236(x101781,x101782),x101783),x101784)),f306(f306(f109(f872(f871(x101781,x101782),a859)),x101785),x101786)))+~P1(f306(f306(f306(f306(f109(f872(x101781,f872(x101782,a859))),f306(f306(f7(x101781,f872(f871(x101781,x101782),a859),f872(x101782,a859)),f306(f306(f8(f872(x101782,f872(f872(f871(x101781,x101782),a859),a859)),f872(f872(f871(x101781,x101782),a859),f872(x101782,a859)),x101781),f7(x101782,f872(f871(x101781,x101782),a859),a859)),f306(f306(f8(f872(x101782,f871(x101781,x101782)),f872(x101782,f872(f872(f871(x101781,x101782),a859),a859)),x101781),f306(f8(f871(x101781,x101782),f872(f872(f871(x101781,x101782),a859),a859),x101782),f308(f871(x101781,x101782)))),f236(x101781,x101782)))),x101785)),f306(f306(f7(x101781,f872(f871(x101781,x101782),a859),f872(x101782,a859)),f306(f306(f8(f872(x101782,f872(f872(f871(x101781,x101782),a859),a859)),f872(f872(f871(x101781,x101782),a859),f872(x101782,a859)),x101781),f7(x101782,f872(f871(x101781,x101782),a859),a859)),f306(f306(f8(f872(x101782,f871(x101781,x101782)),f872(x101782,f872(f872(f871(x101781,x101782),a859),a859)),x101781),f306(f8(f871(x101781,x101782),f872(f872(f871(x101781,x101782),a859),a859),x101782),f308(f871(x101781,x101782)))),f236(x101781,x101782)))),x101786)),x101783),x101784)) % 187.68/187.65 [10164]~P1(f306(f306(f308(f871(x101642,x101643)),f306(f306(f236(x101642,x101643),x101645),x101646)),f306(f306(f43(x101641,f872(f871(x101642,x101643),a859)),f231(f872(x101641,a859))),x101644)))+P1(f306(f306(f306(f306(f43(x101641,f872(x101642,f872(x101643,a859))),f231(f872(x101641,a859))),f306(f306(f8(f872(f871(x101642,x101643),a859),f872(x101642,f872(x101643,a859)),x101641),f306(f7(x101642,f872(f871(x101642,x101643),a859),f872(x101643,a859)),f306(f306(f8(f872(x101643,f872(f872(f871(x101642,x101643),a859),a859)),f872(f872(f871(x101642,x101643),a859),f872(x101643,a859)),x101642),f7(x101643,f872(f871(x101642,x101643),a859),a859)),f306(f306(f8(f872(x101643,f871(x101642,x101643)),f872(x101643,f872(f872(f871(x101642,x101643),a859),a859)),x101642),f306(f8(f871(x101642,x101643),f872(f872(f871(x101642,x101643),a859),a859),x101643),f308(f871(x101642,x101643)))),f236(x101642,x101643))))),x101644)),x101645),x101646)) % 187.68/187.65 [10165]~P1(f306(f306(f308(f871(x101652,x101653)),f306(f306(f236(x101652,x101653),x101655),x101656)),f306(f306(f44(x101651,f872(f871(x101652,x101653),a859)),f231(f872(x101651,a859))),x101654)))+P1(f306(f306(f306(f306(f44(x101651,f872(x101652,f872(x101653,a859))),f231(f872(x101651,a859))),f306(f306(f8(f872(f871(x101652,x101653),a859),f872(x101652,f872(x101653,a859)),x101651),f306(f7(x101652,f872(f871(x101652,x101653),a859),f872(x101653,a859)),f306(f306(f8(f872(x101653,f872(f872(f871(x101652,x101653),a859),a859)),f872(f872(f871(x101652,x101653),a859),f872(x101653,a859)),x101652),f7(x101653,f872(f871(x101652,x101653),a859),a859)),f306(f306(f8(f872(x101653,f871(x101652,x101653)),f872(x101653,f872(f872(f871(x101652,x101653),a859),a859)),x101652),f306(f8(f871(x101652,x101653),f872(f872(f871(x101652,x101653),a859),a859),x101653),f308(f871(x101652,x101653)))),f236(x101652,x101653))))),x101654)),x101655),x101656)) % 187.68/187.65 [10174]P1(f306(f306(f308(f871(x101741,x101742)),f306(f306(f236(x101741,x101742),x101743),x101744)),f306(f306(f43(x101745,f872(f871(x101741,x101742),a859)),f231(f872(x101745,a859))),x101746)))+~P1(f306(f306(f306(f306(f43(x101745,f872(x101741,f872(x101742,a859))),f231(f872(x101745,a859))),f306(f306(f8(f872(f871(x101741,x101742),a859),f872(x101741,f872(x101742,a859)),x101745),f306(f7(x101741,f872(f871(x101741,x101742),a859),f872(x101742,a859)),f306(f306(f8(f872(x101742,f872(f872(f871(x101741,x101742),a859),a859)),f872(f872(f871(x101741,x101742),a859),f872(x101742,a859)),x101741),f7(x101742,f872(f871(x101741,x101742),a859),a859)),f306(f306(f8(f872(x101742,f871(x101741,x101742)),f872(x101742,f872(f872(f871(x101741,x101742),a859),a859)),x101741),f306(f8(f871(x101741,x101742),f872(f872(f871(x101741,x101742),a859),a859),x101742),f308(f871(x101741,x101742)))),f236(x101741,x101742))))),x101746)),x101743),x101744)) % 187.68/187.65 [10175]P1(f306(f306(f308(f871(x101751,x101752)),f306(f306(f236(x101751,x101752),x101753),x101754)),f306(f306(f44(x101755,f872(f871(x101751,x101752),a859)),f231(f872(x101755,a859))),x101756)))+~P1(f306(f306(f306(f306(f44(x101755,f872(x101751,f872(x101752,a859))),f231(f872(x101755,a859))),f306(f306(f8(f872(f871(x101751,x101752),a859),f872(x101751,f872(x101752,a859)),x101755),f306(f7(x101751,f872(f871(x101751,x101752),a859),f872(x101752,a859)),f306(f306(f8(f872(x101752,f872(f872(f871(x101751,x101752),a859),a859)),f872(f872(f871(x101751,x101752),a859),f872(x101752,a859)),x101751),f7(x101752,f872(f871(x101751,x101752),a859),a859)),f306(f306(f8(f872(x101752,f871(x101751,x101752)),f872(x101752,f872(f872(f871(x101751,x101752),a859),a859)),x101751),f306(f8(f871(x101751,x101752),f872(f872(f871(x101751,x101752),a859),a859),x101752),f308(f871(x101751,x101752)))),f236(x101751,x101752))))),x101756)),x101753),x101754)) % 187.68/187.65 [7383]E(f306(x73831,f306(x73832,x73833)),f306(x73834,x73833))+~E(f306(f74(x73835,x73836,x73837,x73831),x73832),x73834) % 187.68/187.65 [9610]~P25(x96103,x96104,x96101,x96105,x96106,x96107)+E(f306(f306(x96101,x96102),x96102),x96102) % 187.68/187.65 [9964]~P53(x99645,x99646,x99647,x99641,x99644,x99642,x99643)+P1(f306(f306(x99641,x99642),f528(x99643,x99642,x99644,x99641))) % 187.68/187.65 [9983]~E(f306(f216(f869(x99837),x99831,f188(x99837),x99835),f306(x99834,x99833)),f306(f214(x99837),x99832))+E(f306(f214(x99831),f664(x99832,x99833,x99834,x99835,x99836,x99837,x99831)),f306(x99834,x99833)) % 187.68/187.65 [9984]~E(f306(f216(f869(x99846),x99847,f188(x99846),x99841),f306(x99844,x99843)),f306(f214(x99846),x99842))+E(f306(x99841,f664(x99842,x99843,x99844,x99841,x99845,x99846,x99847)),f306(f214(x99846),x99842)) % 187.68/187.65 [5955]~E(f306(f306(f146(x59551,x59555),x59556),x59552),f306(f306(f146(x59553,x59555),x59557),x59554))+E(f306(f186(f866(x59551)),x59552),f306(f186(f866(x59553)),x59554)) % 187.68/187.65 [7458]E(x74581,x74582)+~E(f306(f306(f306(f73(x74583,f869(x74584)),x74585),x74586),f306(f214(x74584),x74581)),f306(f306(f306(f73(x74583,f869(x74584)),x74587),x74586),f306(f214(x74584),x74582))) % 187.68/187.65 [8430]E(f306(x84301,f306(x84302,x84303)),f306(x84304,x84303))+~E(f306(f74(x84305,x84306,x84307,x84301),x84302),f306(f74(x84306,x84306,x84307,f35(x84306)),x84304)) % 187.68/187.65 [8761]~P37(x87614,x87615,x87611,f306(f306(f143(x87614),x87612),x87616),f306(f306(f143(x87615),x87613),x87617))+P1(f306(f306(x87611,x87612),x87613)) % 187.68/187.65 [9148]P37(x91481,x91482,x91483,x91484,x91485)+~P37(x91481,x91482,x91483,f306(f306(f143(x91481),x91486),x91484),f306(f306(f143(x91482),x91487),x91485)) % 187.68/187.65 [9969]~P53(x99695,x99696,x99697,x99694,x99691,x99693,x99692)+P1(f306(f306(x99691,f528(x99692,x99693,x99691,x99694)),x99692)) % 187.68/187.65 [6000]E(x60001,x60002)+~E(f306(f306(f306(f93(x60003),x60004),x60005),x60001),f306(f306(f306(f93(x60003),x60006),x60007),x60002)) % 187.68/187.65 [6001]E(x60011,x60012)+~E(f306(f306(f306(f93(x60013),x60014),x60011),x60015),f306(f306(f306(f93(x60013),x60016),x60012),x60017)) % 187.68/187.65 [6002]E(x60021,x60022)+~E(f306(f306(f306(f93(x60023),x60021),x60024),x60025),f306(f306(f306(f93(x60023),x60022),x60026),x60027)) % 187.68/187.65 [8882]~P23(x88826,x88821,x88823,x88827)+E(f306(f74(x88821,x88821,x88822,f306(x88823,x88824)),f306(f74(x88821,x88821,x88822,f306(x88823,x88824)),x88825)),f306(f74(x88821,x88821,x88822,f306(x88823,x88824)),x88825)) % 187.68/187.65 [9256]~P37(x92563,x92562,x92564,f306(f306(f146(x92561,x92563),x92565),x92566),x92567)+P37(x92561,x92562,f306(f306(f8(x92563,f872(x92562,a859),x92561),x92564),x92565),x92566,x92567) % 187.68/187.65 [9280]P37(x92801,x92802,x92803,f306(f306(f146(x92804,x92801),x92805),x92806),x92807)+~P37(x92804,x92802,f306(f306(f8(x92801,f872(x92802,a859),x92804),x92803),x92805),x92806,x92807) % 187.68/187.65 [9696]E(f178(x96961,x96962,f306(f306(f306(f73(x96961,f869(x96962)),x96963),x96964),f306(f214(x96962),x96965)),x96966,x96967),f306(f306(f306(f73(x96961,f869(x96962)),f178(x96961,x96962,x96963,x96966,x96967)),x96964),f306(f214(x96962),x96965)))+P1(f306(f306(f308(x96961),x96964),f306(f164(x96961),x96966))) % 187.68/187.65 [8881]~P1(f306(f306(f308(x88811),x88812),f306(f306(x88815,x88816),x88817)))+P1(f306(f306(f308(x88811),x88812),f306(f306(f245(x88813,x88814,f872(x88811,a859)),x88815),f306(f306(f236(x88813,x88814),x88816),x88817)))) % 187.68/187.65 [9174]P1(f306(f306(f306(x91741,x91742),x91743),x91744))+~P1(f306(f306(f306(f245(x91745,x91746,f872(x91747,a859)),x91741),f306(f306(f236(x91745,x91746),x91742),x91743)),x91744)) % 187.68/187.65 [9319]P1(f306(f306(f308(x93191),f306(f306(x93192,x93193),x93194)),f306(f285(f871(x93195,x93196),x93191,f306(f245(x93195,x93196,x93191),x93192)),x93197)))+~P1(f306(f306(f308(f871(x93195,x93196)),f306(f306(f236(x93195,x93196),x93193),x93194)),x93197)) % 187.68/187.65 [9656]P1(f306(f306(f308(f871(f866(x96561),f866(x96561))),f306(f306(f236(f866(x96561),f866(x96561)),f306(f306(f122(x96561),x96562),f306(f306(f143(x96561),x96563),x96564))),f306(f306(f122(x96561),x96562),f306(f306(f143(x96561),x96565),x96566)))),f139(x96561,x96567)))+~P1(f306(f306(f308(f871(x96561,x96561)),f306(f306(f236(x96561,x96561),x96563),x96565)),x96567)) % 187.68/187.65 [9719]~P37(x97191,x97193,x97194,x97196,f306(f306(f146(x97192,x97193),x97195),x97197))+P37(x97191,x97192,f306(f306(f7(x97191,f872(x97192,x97193),f872(x97192,a859)),f306(f306(f8(f872(x97193,a859),f872(f872(x97192,x97193),f872(x97192,a859)),x97191),f8(x97193,a859,x97192)),x97194)),x97195),x97196,x97197) % 187.68/187.65 [9802]P37(x98021,x98022,x98023,x98024,f306(f306(f146(x98025,x98022),x98026),x98027))+~P37(x98021,x98025,f306(f306(f7(x98021,f872(x98025,x98022),f872(x98025,a859)),f306(f306(f8(f872(x98022,a859),f872(f872(x98025,x98022),f872(x98025,a859)),x98021),f8(x98022,a859,x98025)),x98023)),x98026),x98024,x98027) % 187.68/187.65 [10087]P53(x100871,x100872,x100873,f306(f306(f7(x100871,f872(f871(x100871,x100872),a859),f872(x100872,a859)),f306(f306(f8(f872(x100872,f872(f872(f871(x100871,x100872),a859),a859)),f872(f872(f871(x100871,x100872),a859),f872(x100872,a859)),x100871),f7(x100872,f872(f871(x100871,x100872),a859),a859)),f306(f306(f8(f872(x100872,f871(x100871,x100872)),f872(x100872,f872(f872(f871(x100871,x100872),a859),a859)),x100871),f306(f8(f871(x100871,x100872),f872(f872(f871(x100871,x100872),a859),a859),x100872),f308(f871(x100871,x100872)))),f236(x100871,x100872)))),x100874),f306(f306(f7(x100872,f872(f871(x100872,x100873),a859),f872(x100873,a859)),f306(f306(f8(f872(x100873,f872(f872(f871(x100872,x100873),a859),a859)),f872(f872(f871(x100872,x100873),a859),f872(x100873,a859)),x100872),f7(x100873,f872(f871(x100872,x100873),a859),a859)),f306(f306(f8(f872(x100873,f871(x100872,x100873)),f872(x100873,f872(f872(f871(x100872,x100873),a859),a859)),x100872),f306(f8(f871(x100872,x100873),f872(f872(f871(x100872,x100873),a859),a859),x100873),f308(f871(x100872,x100873)))),f236(x100872,x100873)))),x100875),x100876,x100877)+~P1(f306(f306(f308(f871(x100871,x100873)),f306(f306(f236(x100871,x100873),x100876),x100877)),f306(f306(f263(x100871,x100872,x100873),x100874),x100875))) % 187.68/187.65 [10119]~P53(x101191,x101195,x101192,f306(f306(f7(x101191,f872(f871(x101191,x101195),a859),f872(x101195,a859)),f306(f306(f8(f872(x101195,f872(f872(f871(x101191,x101195),a859),a859)),f872(f872(f871(x101191,x101195),a859),f872(x101195,a859)),x101191),f7(x101195,f872(f871(x101191,x101195),a859),a859)),f306(f306(f8(f872(x101195,f871(x101191,x101195)),f872(x101195,f872(f872(f871(x101191,x101195),a859),a859)),x101191),f306(f8(f871(x101191,x101195),f872(f872(f871(x101191,x101195),a859),a859),x101195),f308(f871(x101191,x101195)))),f236(x101191,x101195)))),x101196),f306(f306(f7(x101195,f872(f871(x101195,x101192),a859),f872(x101192,a859)),f306(f306(f8(f872(x101192,f872(f872(f871(x101195,x101192),a859),a859)),f872(f872(f871(x101195,x101192),a859),f872(x101192,a859)),x101195),f7(x101192,f872(f871(x101195,x101192),a859),a859)),f306(f306(f8(f872(x101192,f871(x101195,x101192)),f872(x101192,f872(f872(f871(x101195,x101192),a859),a859)),x101195),f306(f8(f871(x101195,x101192),f872(f872(f871(x101195,x101192),a859),a859),x101192),f308(f871(x101195,x101192)))),f236(x101195,x101192)))),x101197),x101193,x101194)+P1(f306(f306(f308(f871(x101191,x101192)),f306(f306(f236(x101191,x101192),x101193),x101194)),f306(f306(f263(x101191,x101195,x101192),x101196),x101197))) % 187.68/187.65 [9166]E(x91661,x91662)+E(f306(f306(f306(f73(x91663,x91664),f306(f306(f306(f73(x91663,x91664),x91665),x91661),x91666)),x91662),x91667),f306(f306(f306(f73(x91663,x91664),f306(f306(f306(f73(x91663,x91664),x91665),x91662),x91667)),x91661),x91666)) % 187.68/187.65 [9415]E(f178(x94151,x94152,f306(f306(f306(f73(x94151,f869(x94152)),x94153),x94154),f306(f214(x94152),x94155)),x94156,x94157),f178(x94151,x94152,x94153,x94156,x94157))+~P1(f306(f306(f308(x94151),x94154),f306(f164(x94151),f306(f306(f165(x94151),f306(f186(f866(x94152)),x94157)),x94156)))) % 187.68/187.65 [9730]E(f178(x97301,x97302,f306(f306(f306(f73(x97301,f869(x97302)),x97303),x97304),f306(f214(x97302),x97305)),x97306,x97307),f306(f306(f306(f73(x97301,f869(x97302)),f178(x97301,x97302,x97303,x97306,x97307)),x97304),f306(f214(x97302),x97305)))+P1(f306(f306(f308(x97301),x97304),f306(f164(x97301),f306(f306(f165(x97301),f306(f186(f866(x97302)),x97307)),x97306)))) % 187.68/187.65 [10099]P1(f306(f306(f308(x100991),f631(x100992,x100993,x100994,x100995,x100996,x100997,x100991)),x100995))+P1(f306(f306(f306(f306(f44(x100991,f872(x100997,f872(x100996,a859))),x100995),x100994),x100993),x100992)) % 187.68/187.65 [10100]P1(f306(f306(f308(x101001),f471(x101002,x101003,x101004,x101005,x101006,x101007,x101001)),x101005))+~P1(f306(f306(f306(f306(f43(x101001,f872(x101007,f872(x101006,a859))),x101005),x101004),x101003),x101002)) % 187.68/187.65 [10129]P1(f306(f306(f306(x101291,f471(x101292,x101293,x101291,x101294,x101295,x101296,x101297)),x101293),x101292))+~P1(f306(f306(f306(f306(f43(x101297,f872(x101296,f872(x101295,a859))),x101294),x101291),x101293),x101292)) % 187.68/187.65 [10147]~P1(f306(f306(f306(x101475,f631(x101477,x101476,x101475,x101474,x101473,x101472,x101471)),x101476),x101477))+P1(f306(f306(f306(f306(f44(x101471,f872(x101472,f872(x101473,a859))),x101474),x101475),x101476),x101477)) % 187.68/187.65 [10109]~P142(x101092)+E(f306(f306(f6(x101091,x101092),f306(f306(f7(x101091,f872(x101093,a859),x101092),f306(f306(f8(f872(x101093,x101092),f872(f872(x101093,a859),x101092),x101091),f6(x101093,x101092)),f306(f306(f7(x101091,f872(x101093,x101092),f872(x101093,x101092)),f306(f306(f8(f872(x101092,x101092),f872(f872(x101093,x101092),f872(x101093,x101092)),x101091),f8(x101092,x101092,x101093)),f306(f306(f8(x101092,f872(x101092,x101092),x101091),f82(x101092)),x101094))),x101095))),x101096)),x101097),f306(f306(f82(x101092),f306(f306(f6(x101091,x101092),x101094),x101097)),f306(f306(f6(x101093,x101092),x101095),x101096))) % 187.68/187.65 [9208]~P22(x92087,x92081,x92083,x92088)+E(f306(f74(x92081,x92081,x92082,f306(x92083,x92084)),f306(f74(x92081,x92081,x92082,f306(x92083,x92085)),x92086)),f306(f74(x92081,x92081,x92082,f306(x92083,x92085)),f306(f74(x92081,x92081,x92082,f306(x92083,x92084)),x92086))) % 187.68/187.65 [10168]E(f306(f306(f236(x101681,x101682),f306(x101683,f506(x101684,x101685,x101683,x101686,x101687,x101688,x101682,x101681))),f306(x101685,f507(x101684,x101685,x101683,x101686,x101687,x101688,x101682,x101681))),x101688)+~P1(f306(f306(f308(f871(x101681,x101682)),x101688),f306(f285(f871(x101687,x101686),f871(x101681,x101682),f246(x101687,x101681,x101686,x101682,x101683,x101685)),x101684))) % 187.68/187.65 [10184]~P1(f306(f306(f308(f871(x101848,x101847)),x101846),f306(f285(f871(x101841,x101842),f871(x101848,x101847),f246(x101841,x101848,x101842,x101847,x101845,x101844)),x101843)))+P1(f306(f306(f308(f871(x101841,x101842)),f306(f306(f236(x101841,x101842),f506(x101843,x101844,x101845,x101842,x101841,x101846,x101847,x101848)),f507(x101843,x101844,x101845,x101842,x101841,x101846,x101847,x101848))),x101843)) % 187.68/187.65 [9645]P1(f306(f306(f308(f871(f871(x96451,x96452),f871(x96451,x96452))),f306(f306(f236(f871(x96451,x96452),f871(x96451,x96452)),f306(f306(f236(x96451,x96452),x96453),x96454)),f306(f306(f236(x96451,x96452),x96455),x96456))),f299(x96451,x96452,x96457,x96458)))+~P1(f306(f306(f308(f871(x96451,x96451)),f306(f306(f236(x96451,x96451),x96453),x96455)),x96457)) % 187.68/187.65 [10158]E(f306(f134(x101581,x101582,f306(f7(x101582,x101581,x101581),x101583),f306(x101584,x101585)),x101586),f306(x101584,f306(f134(x101587,x101582,f306(f7(x101582,x101587,x101587),x101588),x101585),x101586)))+P1(f306(f306(f308(x101582),f765(x101585,x101588,x101584,x101583,x101587,x101581,x101586,x101582)),f306(f164(x101582),x101586))) % 187.68/187.65 [10176]~E(f306(f74(x101761,x101761,x101767,f306(x101763,f765(x101765,x101768,x101764,x101763,x101767,x101761,x101766,x101762))),x101764),f306(f74(x101767,x101761,x101767,x101764),f306(x101768,f765(x101765,x101768,x101764,x101763,x101767,x101761,x101766,x101762))))+E(f306(f134(x101761,x101762,f306(f7(x101762,x101761,x101761),x101763),f306(x101764,x101765)),x101766),f306(x101764,f306(f134(x101767,x101762,f306(f7(x101762,x101767,x101767),x101768),x101765),x101766))) % 187.68/187.65 [8436]E(f306(x84361,f306(x84362,x84363)),f306(x84364,f306(x84365,x84363)))+~E(f306(f74(x84366,x84367,x84368,x84361),x84362),f306(f74(x84369,x84367,x84368,x84364),x84365)) % 187.68/187.65 [10036]P1(f306(f306(f308(f871(x100361,x100362)),f306(f306(f236(x100361,x100362),f306(x100363,x100364)),f306(x100365,x100366))),f306(f285(f871(x100367,x100368),f871(x100361,x100362),f246(x100367,x100361,x100368,x100362,x100363,x100365)),x100369)))+~P1(f306(f306(f308(f871(x100367,x100368)),f306(f306(f236(x100367,x100368),x100364),x100366)),x100369)) % 187.68/187.65 [8709]~E(f306(x87094,f306(x87095,x87096)),f306(x87099,f306(x870910,x870911)))+E(f306(f306(f74(x87091,x87092,x87093,x87094),x87095),x87096),f306(f306(f74(x87097,x87092,x87098,x87099),x870910),x870911)) % 187.68/187.65 [4541]~P108(x45411)+~P97(x45411)+E(f219(x45411),f108(x45411)) % 187.68/187.65 [4542]~P108(x45421)+~P103(x45421)+E(f225(x45421),f109(x45421)) % 187.68/187.65 [4784]~P112(x47841)+~P91(x47841)+E(f306(f76(x47841),f306(f111(x47841),a104)),f79(x47841)) % 187.68/187.65 [5065]E(x50651,f2(a1))+E(f83(a1,x50651),f306(f80(a1),f79(a1)))+P1(f306(f306(f221(a1),f2(a1)),x50651)) % 187.68/187.65 [5281]E(x52811,f2(a1))+E(f83(a1,x52811),f79(a1))+~P1(f306(f306(f221(a1),f2(a1)),x52811)) % 187.68/187.65 [7275]~P42(x72751)+P1(f306(f63(a1),x72751))+~P1(f306(f63(a865),f306(f285(a1,a865,a112),x72751))) % 187.68/187.65 [8540]~P10(a5000)+~P1(f306(f306(f308(f871(a862,a860)),x85401),f306(f164(f871(a862,a860)),a27)))+P1(f306(f306(f245(a862,a860,a859),f306(f16(f872(a860,a859),a862),a25)),x85401)) % 187.68/187.65 [9609]E(x96091,f185(f872(f871(a865,a865),a859)))+~P1(f306(f63(f871(a865,a865)),x96091))+P1(f306(f306(f308(f871(f872(f871(a865,a865),a859),f872(f871(a865,a865),a859))),f306(f306(f236(f872(f871(a865,a865),a859),f872(f871(a865,a865),a859)),f185(f872(f871(a865,a865),a859))),x96091)),a38)) % 187.68/187.65 [9779]E(x97791,f2(a865))+E(x97791,f306(a119,f2(a865)))+~P1(f306(f306(f221(a865),x97791),f306(f111(a865),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104))))) % 187.68/187.65 [10065]E(x100651,f2(a106))+E(f306(f306(f81(a1),f306(f306(f82(a1),f306(f111(a1),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)))),f306(a20,f306(f306(f40(a106),x100651),f306(f111(a106),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104))))))),f79(a1)),f306(a20,x100651))+E(f46(a106,x100651,f306(f111(a106),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)))),f2(a106)) % 187.68/187.65 [9912]E(x99121,f2(a106))+~E(f46(a106,x99121,f306(f111(a106),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)))),f2(a106))+E(f306(f306(f82(a1),f306(f111(a1),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)))),f306(a20,f306(f306(f40(a106),x99121),f306(f111(a106),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)))))),f306(a20,x99121)) % 187.68/187.65 [4614]~P57(x46141,x46142)+P45(x46141,x46142)+~P46(a859) % 187.68/187.65 [4551]~P141(x45511)+P33(x45511,x45512)+~E(x45512,f2(x45511)) % 187.68/187.65 [4552]~P108(x45521)+P17(x45521,x45522)+~E(x45522,f120(x45521)) % 187.68/187.65 [4561]~P112(x45611)+~E(x45612,f2(x45611))+E(f83(x45611,x45612),f2(x45611)) % 187.68/187.65 [4562]~P88(x45621)+~E(x45622,f2(x45621))+E(f83(x45621,x45622),f2(x45621)) % 187.68/187.65 [4570]~P141(x45702)+~P33(x45702,x45701)+E(x45701,f2(x45702)) % 187.68/187.65 [4604]~P112(x46042)+~E(f83(x46042,x46041),f2(x46042))+E(x46041,f2(x46042)) % 187.68/187.65 [4621]~P3(x46212)+~P3(x46211)+P3(f872(x46211,x46212)) % 187.68/187.65 [4622]~P3(x46222)+~P3(x46221)+P3(f870(x46221,x46222)) % 187.68/187.65 [4623]~P3(x46232)+~P3(x46231)+P3(f871(x46231,x46232)) % 187.68/187.65 [4624]~P7(x46242)+~P7(x46241)+P7(f194(x46241,x46242)) % 187.68/187.65 [4625]~P144(x46252)+~P144(x46251)+P144(f871(x46251,x46252)) % 187.68/187.65 [4626]~P60(x46262)+~P60(x46261)+P60(f872(x46261,x46262)) % 187.68/187.65 [4627]~P60(x46272)+~P60(x46271)+P60(f870(x46271,x46272)) % 187.68/187.65 [4628]~P60(x46282)+~P60(x46281)+P60(f871(x46281,x46282)) % 187.68/187.65 [4629]~P60(x46291)+~P93(x46292)+P93(f872(x46291,x46292)) % 187.68/187.65 [4755]~P108(x47551)+~P17(x47551,x47552)+P17(x47551,f144(x47551,x47552)) % 187.68/187.65 [4994]~P7(x49942)+~P7(x49941)+P7(f46(a1,x49941,x49942)) % 187.68/187.65 [4572]~P76(x45721)+~E(x45722,f2(x45721))+E(f306(f80(x45721),x45722),x45722) % 187.68/187.65 [4576]~P90(x45761)+~E(x45762,f2(a1))+E(f306(f110(x45761),x45762),f2(x45761)) % 187.68/187.65 [4577]~P125(x45771)+~E(x45772,f2(a1))+E(f306(f110(x45771),x45772),f2(x45771)) % 187.68/187.65 [4601]~P67(x46011)+~E(f2(x46011),x46012)+E(f306(f80(x46011),x46012),f2(x46011)) % 187.68/187.65 [4602]~P67(x46021)+~E(x46022,f2(x46021))+E(f306(f80(x46021),x46022),f2(x46021)) % 187.68/187.65 [4603]~P84(x46031)+~E(x46032,f2(x46031))+E(f306(f76(x46031),x46032),f2(x46031)) % 187.68/187.65 [4631]~P76(x46312)+E(x46311,f2(x46312))+~E(f306(f80(x46312),x46311),x46311) % 187.68/187.65 [4637]E(x46371,f306(a112,x46372))+~E(x46371,f2(a865))+~E(x46372,f306(f107(a1),x46371)) % 187.68/187.65 [4638]E(f306(a112,x46381),x46382)+~E(x46382,f2(a865))+~E(x46381,f306(f107(a1),x46382)) % 187.68/187.65 [4642]~P90(x46422)+E(x46421,f2(a1))+~E(f306(f110(x46422),x46421),f2(x46422)) % 187.68/187.65 [4647]~P67(x46472)+E(x46471,f2(x46472))+~E(f306(f80(x46472),x46471),f2(x46472)) % 187.68/187.65 [4648]~P84(x46482)+E(x46481,f2(x46482))+~E(f306(f76(x46482),x46481),f2(x46482)) % 187.68/187.65 [4649]~P67(x46491)+E(f2(x46491),x46492)+~E(f306(f80(x46491),x46492),f2(x46491)) % 187.68/187.65 [4789]~P10(a5000)+~E(f306(a28,x47892),f306(f214(a860),x47891))+P1(f306(a25,x47891)) % 187.68/187.65 [4831]~P108(x48311)+~P17(x48311,x48312)+P17(x48311,f306(f163(x48311),x48312)) % 187.68/187.65 [4858]~P1(x48582)+~P1(x48581)+P1(f306(f306(a304,x48581),x48582)) % 187.68/187.65 [4890]~E(f79(a865),f2(a865))+E(f306(f39(x48901),x48902),f2(a865))+~P1(f306(f63(x48901),x48902)) % 187.68/187.65 [4924]~P115(x49241)+~P142(x49241)+E(f306(f306(f237(x49241),f2(x49241)),f306(a119,x49242)),f2(x49241)) % 187.68/187.65 [4962]~P108(x49621)+P17(x49621,f131(x49621,x49622))+~P1(f306(f63(x49621),x49622)) % 187.68/187.65 [4963]~P108(x49631)+P17(x49631,f755(x49632,x49631))+~P1(f306(f63(x49631),x49632)) % 187.68/187.65 [4984]~P108(x49841)+E(f306(f164(x49841),f131(x49841,x49842)),x49842)+~P1(f306(f63(x49841),x49842)) % 187.68/187.65 [4985]~P108(x49851)+E(f306(f164(x49851),f755(x49852,x49851)),x49852)+~P1(f306(f63(x49851),x49852)) % 187.68/187.65 [5014]P1(x50141)+P1(x50142)+~P1(f306(f306(a305,x50142),x50141)) % 187.68/187.65 [5026]E(x50261,f185(f872(x50262,a859)))+~E(f306(f39(x50262),x50261),f2(a865))+~P1(f306(f63(x50262),x50261)) % 187.68/187.65 [5031]P1(x50311)+~P1(x50312)+~P1(f306(f306(a309,x50312),x50311)) % 187.68/187.65 [5083]~P73(x50831)+E(f306(f76(x50831),x50832),x50832)+P1(f306(f306(f221(x50831),x50832),f2(x50831))) % 187.68/187.65 [5084]~P6(x50842)+~P41(x50842,x50842,x50841)+E(f306(x50841,f103(x50842,x50841)),f103(x50842,x50841)) % 187.68/187.65 [5085]~P6(x50852)+~P41(x50852,x50852,x50851)+E(f306(x50851,f102(x50852,x50851)),f102(x50852,x50851)) % 187.68/187.65 [5156]~P60(x51562)+~P1(f306(f59(x51562),x51561))+P1(f306(x51561,f723(x51561,x51562))) % 187.68/187.65 [5157]~P60(x51572)+~P1(f306(f59(x51572),x51571))+P1(f306(x51571,f745(x51571,x51572))) % 187.68/187.65 [5184]~P1(f306(a25,x51842))+~P1(f306(a25,x51841))+P1(f306(a25,f34(x51841,x51842))) % 187.68/187.65 [5193]E(x51931,f120(x51932))+P1(f306(f129(x51932),f121(x51932,x51931)))+~P1(f306(f129(x51932),x51931)) % 187.68/187.65 [5198]~P108(x51981)+~P1(f306(f63(x51981),x51982))+P1(f306(f129(x51981),f131(x51981,x51982))) % 187.68/187.65 [5199]~P108(x51991)+~P1(f306(f63(x51991),x51992))+P1(f306(f129(x51991),f755(x51992,x51991))) % 187.68/187.65 [5205]~P125(x52051)+E(f306(f107(x52051),f306(a112,x52052)),f306(f110(x52051),x52052))+P1(f306(f306(f221(a1),x52052),f2(a1))) % 187.68/187.65 [5233]P8(x52332,x52331)+E(f306(x52331,f422(x52331)),f306(x52331,f485(x52331)))+P1(f306(f306(x52331,f422(x52331)),f485(x52331))) % 187.68/187.65 [5247]E(f306(f107(a1),f832(x52471,x52472)),x52471)+P1(f306(x52472,f306(a112,x52471)))+~P1(f306(x52472,f2(a865))) % 187.68/187.65 [5259]~P60(x52591)+~P1(f306(x52592,f724(x52592,x52591)))+P1(f306(f60(x52591),x52592)) % 187.68/187.65 [5260]~P60(x52601)+~P1(f306(x52602,f746(x52602,x52601)))+P1(f306(f60(x52601),x52602)) % 187.68/187.65 [5274]~P60(x52742)+~P38(x52742,x52741,f57(x52742))+P1(f306(x52741,f770(x52741,x52742))) % 187.68/187.65 [5290]~P112(x52901)+~E(f83(x52901,x52902),f306(f80(x52901),f79(x52901)))+P1(f306(f306(f221(x52901),x52902),f2(x52901))) % 187.68/187.65 [5291]E(x52911,f185(f872(x52912,a859)))+P1(f306(f63(x52912),f423(x52911,x52912)))+~P1(f306(f63(x52912),x52911)) % 187.68/187.65 [5368]~E(x53682,f2(a1))+E(f201(x53681,x53682),f306(f306(f236(a1,a1),f2(a1)),f79(a1)))+P1(f306(f306(f221(a1),x53682),f2(a1))) % 187.68/187.65 [5369]~E(x53691,f2(a1))+E(f201(x53691,x53692),f306(f306(f236(a1,a1),f2(a1)),f79(a1)))+P1(f306(f306(f221(a1),x53692),f2(a1))) % 187.68/187.65 [5421]E(f306(f107(a1),f832(x54211,x54212)),x54211)+P1(f306(x54212,f306(a112,x54211)))+P1(f306(f306(f221(a1),x54211),f2(a1))) % 187.68/187.65 [5445]E(f306(f306(f284(x54452),f486(x54451,x54452)),f423(x54451,x54452)),x54451)+E(x54451,f185(f872(x54452,a859)))+~P1(f306(f63(x54452),x54451)) % 187.68/187.65 [5485]~P112(x54851)+E(f83(x54851,x54852),f306(f80(x54851),f79(x54851)))+~P1(f306(f306(f221(x54851),x54852),f2(x54851))) % 187.68/187.65 [5486]~P84(x54861)+E(f306(f76(x54861),x54862),f306(f80(x54861),x54862))+~P1(f306(f306(f220(x54861),x54862),f2(x54861))) % 187.68/187.65 [5487]~P84(x54871)+E(f306(f76(x54871),x54872),f306(f80(x54871),x54872))+~P1(f306(f306(f221(x54871),x54872),f2(x54871))) % 187.68/187.65 [5488]~P73(x54881)+E(f306(f76(x54881),x54882),f306(f80(x54881),x54882))+~P1(f306(f306(f221(x54881),x54882),f2(x54881))) % 187.68/187.65 [5582]~P1(f306(x55821,f832(x55822,x55821)))+P1(f306(x55821,f306(a112,x55822)))+~P1(f306(x55821,f2(a865))) % 187.68/187.65 [5589]E(x55891,f2(a865))+E(f306(a119,f690(x55892,x55891)),x55891)+~P1(f306(f306(f221(a865),x55891),f306(a119,x55892))) % 187.68/187.65 [5593]P8(x55931,x55932)+~E(f306(x55932,f422(x55932)),f306(x55932,f485(x55932)))+~P1(f306(f306(x55932,f422(x55932)),f485(x55932))) % 187.68/187.65 [5614]~P108(x56141)+P17(x56141,x56142)+P1(f306(f306(f220(a865),f725(x56142,x56141)),f726(x56142,x56141))) % 187.68/187.65 [5615]~P108(x56151)+P17(x56151,x56152)+P1(f306(f306(f220(a865),f731(x56152,x56151)),f741(x56152,x56151))) % 187.68/187.65 [5702]~P84(x57021)+~E(x57022,f2(x57021))+P1(f306(f306(f220(x57021),f306(f76(x57021),x57022)),f2(x57021))) % 187.68/187.65 [5781]~P60(x57812)+~P60(x57811)+E(f61(x57811,x57812,f57(x57811),f57(x57812)),f57(f871(x57811,x57812))) % 187.68/187.65 [5786]~P1(f306(x57861,f832(x57862,x57861)))+P1(f306(x57861,f306(a112,x57862)))+P1(f306(f306(f221(a1),x57862),f2(a1))) % 187.68/187.65 [5809]~P1(f306(x58091,f306(a112,x58092)))+P1(f306(x58091,f2(a865)))+~P1(f306(f306(f221(a1),x58092),f2(a1))) % 187.68/187.65 [6153]~P112(x61531)+~P1(f306(f306(f221(x61531),x61532),f2(x61531)))+P1(f306(f306(f221(x61531),f83(x61531,x61532)),f2(x61531))) % 187.68/187.65 [6267]~P112(x62671)+P1(f306(f306(f220(x62671),f306(f110(x62671),x62672)),f2(x62671)))+~P1(f306(f306(f220(a1),x62672),f2(a1))) % 187.68/187.65 [6268]~P112(x62681)+P1(f306(f306(f221(x62681),f306(f110(x62681),x62682)),f2(x62681)))+~P1(f306(f306(f221(a1),x62682),f2(a1))) % 187.68/187.65 [6275]~P84(x62752)+E(x62751,f2(x62752))+~P1(f306(f306(f220(x62752),f306(f76(x62752),x62751)),f2(x62752))) % 187.68/187.65 [6355]~P125(x63551)+~P1(f306(f306(f308(x63551),x63552),f117(x63551)))+P1(f306(f306(f308(x63551),f306(f80(x63551),x63552)),f117(x63551))) % 187.68/187.65 [6387]~P112(x63871)+~P1(f306(f306(f221(x63871),f83(x63871,x63872)),f2(x63871)))+P1(f306(f306(f221(x63871),x63872),f2(x63871))) % 187.68/187.65 [6555]~P112(x65552)+~P1(f306(f306(f220(x65552),f306(f110(x65552),x65551)),f2(x65552)))+P1(f306(f306(f220(a1),x65551),f2(a1))) % 187.68/187.65 [6556]~P112(x65562)+~P1(f306(f306(f221(x65562),f306(f110(x65562),x65561)),f2(x65562)))+P1(f306(f306(f221(a1),x65561),f2(a1))) % 187.68/187.65 [6642]~P6(x66421)+~P41(x66421,x66421,x66422)+P1(f306(f306(f220(x66421),f306(x66422,f103(x66421,x66422))),f103(x66421,x66422))) % 187.68/187.65 [6643]~P6(x66431)+~P41(x66431,x66431,x66432)+P1(f306(f306(f220(x66431),f306(x66432,f102(x66431,x66432))),f102(x66431,x66432))) % 187.68/187.65 [7062]~P76(x70621)+~P1(f306(f306(f220(x70621),x70622),f2(x70621)))+P1(f306(f306(f220(x70621),f306(f306(f81(x70621),x70622),x70622)),f2(x70621))) % 187.68/187.65 [7063]~P76(x70631)+~P1(f306(f306(f221(x70631),x70632),f2(x70631)))+P1(f306(f306(f221(x70631),f306(f306(f81(x70631),x70632),x70632)),f2(x70631))) % 187.68/187.65 [7064]~P112(x70641)+~P1(f306(f306(f221(x70641),x70642),f2(x70641)))+P1(f306(f306(f221(x70641),f306(f306(f81(x70641),x70642),x70642)),f2(x70641))) % 187.68/187.65 [7629]~P76(x76291)+~P1(f306(f306(f220(x76291),f306(f306(f81(x76291),x76292),x76292)),f2(x76291)))+P1(f306(f306(f220(x76291),x76292),f2(x76291))) % 187.68/187.65 [7630]~P76(x76301)+~P1(f306(f306(f221(x76301),f306(f306(f81(x76301),x76302),x76302)),f2(x76301)))+P1(f306(f306(f221(x76301),x76302),f2(x76301))) % 187.68/187.65 [7631]~P112(x76311)+~P1(f306(f306(f221(x76311),f306(f306(f81(x76311),x76312),x76312)),f2(x76311)))+P1(f306(f306(f221(x76311),x76312),f2(x76311))) % 187.68/187.65 [4687]~E(x46872,f2(a865))+~E(x46871,f2(a865))+E(f306(f306(f81(a865),x46871),x46872),f2(a865)) % 187.68/187.65 [4688]~E(x46882,f79(a865))+~E(x46881,f79(a865))+E(f306(f306(f82(a865),x46881),x46882),f79(a865)) % 187.68/187.65 [4689]~E(x46892,f79(a1))+~E(x46891,f79(a1))+E(f306(f306(f82(a1),x46891),x46892),f79(a1)) % 187.68/187.65 [4741]~P4(x47412)+E(x47411,f2(x47412))+E(f306(f306(f40(x47412),x47411),x47411),f79(x47412)) % 187.68/187.65 [4742]~P118(x47422)+E(x47421,f2(x47422))+E(f306(f306(f264(x47422),x47421),x47421),f79(x47422)) % 187.68/187.65 [4743]~P119(x47432)+E(x47431,f2(x47432))+E(f306(f306(f264(x47432),x47431),x47431),f79(x47432)) % 187.68/187.65 [4760]~P76(x47601)+~E(x47602,f2(x47601))+E(f306(f306(f81(x47601),x47602),x47602),f2(x47601)) % 187.68/187.65 [4763]~P140(x47631)+~E(x47632,f79(x47631))+E(f306(f306(f82(x47631),x47632),x47632),f79(x47631)) % 187.68/187.65 [4764]~P119(x47641)+~E(x47642,f2(x47641))+E(f306(f306(f264(x47641),x47642),x47642),f2(x47641)) % 187.68/187.65 [4810]~E(x48102,f2(a865))+~E(x48101,f2(a865))+E(f306(f80(a1),f306(f107(a1),x48101)),f306(f107(a1),x48102)) % 187.68/187.65 [4828]E(x48281,f79(a865))+E(x48282,f2(a865))+~E(f306(f306(f82(a865),x48282),x48281),x48282) % 187.68/187.65 [4838]E(x48381,f2(a865))+E(x48382,f2(a865))+~E(f306(f306(f82(a865),x48382),x48381),f2(a865)) % 187.68/187.65 [4867]~E(x48672,f2(a865))+~E(x48671,f306(a119,f2(a865)))+E(f306(f306(f81(a865),x48671),x48672),f306(a119,f2(a865))) % 187.68/187.65 [4868]~E(x48681,f2(a865))+~E(x48682,f306(a119,f2(a865)))+E(f306(f306(f81(a865),x48681),x48682),f306(a119,f2(a865))) % 187.68/187.65 [4873]E(x48731,f79(a1))+E(x48732,f306(f111(a1),a104))+~E(f306(f306(f82(a1),x48731),x48732),f79(a1)) % 187.68/187.65 [4874]E(x48741,f79(a1))+E(x48742,f306(f111(a1),a104))+~E(f306(f306(f82(a1),x48742),x48741),f79(a1)) % 187.68/187.65 [4875]E(x48751,f79(a1))+E(x48751,f306(f111(a1),a104))+~E(f306(f306(f82(a1),x48752),x48751),f79(a1)) % 187.68/187.65 [4877]E(x48771,f79(a1))+E(x48771,f306(f111(a1),a104))+~E(f306(f306(f82(a1),x48771),x48772),f79(a1)) % 187.68/187.65 [4895]~P76(x48952)+E(x48951,f2(x48952))+~E(f306(f306(f81(x48952),x48951),x48951),f2(x48952)) % 187.68/187.65 [4901]~E(x49011,f306(f111(a1),a104))+~E(x49012,f306(f111(a1),a104))+E(f306(f306(f82(a1),x49011),x49012),f79(a1)) % 187.68/187.65 [4913]E(x49131,f2(a865))+E(x49132,f2(a865))+~E(f306(f306(f81(a865),x49132),x49131),f306(a119,f2(a865))) % 187.68/187.65 [4923]~P91(x49231)+~P61(x49231)+E(f306(f306(f264(x49231),x49232),f306(f111(x49231),a84)),f2(x49231)) % 187.68/187.65 [4929]~P140(x49291)+~E(x49292,f306(f80(x49291),f79(x49291)))+E(f306(f306(f82(x49291),x49292),x49292),f79(x49291)) % 187.68/187.65 [4934]~P7(x49342)+~P7(x49341)+P7(f306(f306(f81(a1),x49341),x49342)) % 187.68/187.65 [4935]~P7(x49352)+~P7(x49351)+P7(f306(f306(f82(a1),x49351),x49352)) % 187.68/187.65 [4936]~P7(x49362)+~P7(x49361)+P7(f306(f306(f40(a1),x49361),x49362)) % 187.68/187.65 [4938]~E(x49382,f2(a1))+E(x49381,f2(a1))+E(f47(x49381,x49382),f306(f306(f236(a1,a1),f2(a1)),x49381)) % 187.68/187.65 [4960]~E(x49602,f306(a119,f2(a865)))+~E(x49601,f306(a119,f2(a865)))+E(f306(f306(f82(a865),x49601),x49602),f306(a119,f2(a865))) % 187.68/187.65 [4975]E(x49751,f2(a865))+E(x49752,f306(a119,f2(a865)))+~E(f306(f306(f237(a865),x49752),x49751),f306(a119,f2(a865))) % 187.68/187.65 [4976]E(x49761,f2(a865))+E(x49761,f306(a119,f2(a865)))+~E(f306(f306(f81(a865),x49762),x49761),f306(a119,f2(a865))) % 187.68/187.65 [4977]E(x49771,f2(a865))+E(x49771,f306(a119,f2(a865)))+~E(f306(f306(f81(a865),x49771),x49772),f306(a119,f2(a865))) % 187.68/187.65 [4986]~P91(x49861)+~P61(x49861)+E(f306(f306(f264(x49861),x49862),f306(f111(x49861),a104)),f306(f80(x49861),x49862)) % 187.68/187.65 [5006]E(x50061,f306(a112,x50062))+~E(x50061,f2(a865))+P1(f306(f306(f220(a1),f2(a1)),x50062)) % 187.68/187.65 [5007]E(f306(a112,x50071),x50072)+~E(x50072,f2(a865))+P1(f306(f306(f220(a1),f2(a1)),x50071)) % 187.68/187.65 [5022]E(x50221,f306(a119,f2(a865)))+E(x50222,f306(a119,f2(a865)))+~E(f306(f306(f81(a865),x50221),x50222),f306(a119,f2(a865))) % 187.68/187.65 [5032]~E(x50321,f306(a112,x50322))+E(x50321,f2(a865))+P1(f306(f306(f220(a1),f2(a1)),x50322)) % 187.68/187.65 [5033]~E(f306(a112,x50332),x50331)+E(x50331,f2(a865))+P1(f306(f306(f220(a1),f2(a1)),x50332)) % 187.68/187.65 [5059]~P108(x50591)+E(f306(f65(x50591,f225(x50591)),x50592),f14(x50591,x50592))+~P1(f306(f63(x50591),x50592)) % 187.68/187.65 [5060]~P108(x50601)+E(f306(f65(x50601,f219(x50601)),x50602),f15(x50601,x50602))+~P1(f306(f63(x50601),x50602)) % 187.68/187.65 [5061]~P98(x50611)+E(f306(f65(x50611,f108(x50611)),x50612),f13(x50611,x50612))+~P1(f306(f63(x50611),x50612)) % 187.68/187.65 [5062]~P98(x50621)+E(f306(f65(x50621,f109(x50621)),x50622),f10(x50621,x50622))+~P1(f306(f63(x50621),x50622)) % 187.68/187.65 [5064]~P60(x50641)+~P1(f306(x50642,f188(x50641)))+P1(f306(f59(f869(x50641)),x50642)) % 187.68/187.65 [5149]~P60(x51492)+P1(f306(x51491,f188(x51492)))+~P1(f306(f60(f869(x51492)),x51491)) % 187.68/187.65 [5150]E(x51501,x51502)+~E(f306(f306(f22(a865),x51502),x51501),f2(a865))+~E(f306(f306(f22(a865),x51501),x51502),f2(a865)) % 187.68/187.65 [5164]P7(x51641)+~P42(x51642)+~P1(f306(f306(f308(a1),x51641),x51642)) % 187.68/187.65 [5194]~P112(x51941)+~E(f83(x51941,x51942),f79(x51941))+P1(f306(f306(f221(x51941),f2(x51941)),x51942)) % 187.68/187.65 [5206]~P91(x52061)+E(f306(f107(x52061),f306(f111(a865),x52062)),f306(f111(x52061),x52062))+P1(f306(a190,f306(f111(a1),x52062))) % 187.68/187.65 [5212]~P45(x52121,x52122)+P46(a859)+P1(f306(f63(f871(x52121,x52121)),x52122)) % 187.68/187.65 [5283]~P108(x52831)+E(f306(f65(x52831,f225(x52831)),x52832),f11(x52831,f225(x52831),x52832))+~P1(f306(f63(x52831),x52832)) % 187.68/187.65 [5284]~P108(x52841)+E(f306(f65(x52841,f219(x52841)),x52842),f12(x52841,f219(x52841),x52842))+~P1(f306(f63(x52841),x52842)) % 187.68/187.65 [5298]E(x52981,x52982)+P1(f306(f306(f221(a865),x52982),x52981))+P1(f306(f306(f221(a865),x52981),x52982)) % 187.68/187.65 [5299]E(x52991,x52992)+P1(f306(f306(f221(a1),x52992),x52991))+P1(f306(f306(f221(a1),x52991),x52992)) % 187.68/187.65 [5355]~P91(x53551)+E(f306(f107(x53551),f306(f111(a865),x53552)),f2(x53551))+~P1(f306(a190,f306(f111(a1),x53552))) % 187.68/187.65 [5358]~E(x53582,f306(a112,x53581))+E(x53581,f306(f107(a1),x53582))+~P1(f306(f306(f220(a1),f2(a1)),x53581)) % 187.68/187.65 [5359]~E(f306(a112,x53591),x53592)+E(x53591,f306(f107(a1),x53592))+~P1(f306(f306(f220(a1),f2(a1)),x53591)) % 187.68/187.65 [5360]~E(x53601,f306(a112,x53602))+E(f306(f107(a1),x53601),x53602)+~P1(f306(f306(f220(a1),f2(a1)),x53602)) % 187.68/187.65 [5370]E(x53701,f306(a112,x53702))+~E(x53702,f306(f107(a1),x53701))+~P1(f306(f306(f220(a1),f2(a1)),x53702)) % 187.68/187.65 [5371]E(f306(a112,x53711),x53712)+~E(x53711,f306(f107(a1),x53712))+~P1(f306(f306(f220(a1),f2(a1)),x53711)) % 187.68/187.65 [5410]~P84(x54102)+E(x54101,f2(x54102))+P1(f306(f306(f221(x54102),f2(x54102)),f306(f76(x54102),x54101))) % 187.68/187.65 [5478]~P112(x54781)+E(f83(x54781,x54782),f79(x54781))+~P1(f306(f306(f221(x54781),f2(x54781)),x54782)) % 187.68/187.65 [5482]~P91(x54821)+E(f306(f107(x54821),f306(f111(a865),x54822)),f2(x54821))+P1(f306(f306(f220(a1),f2(a1)),f306(f111(a1),x54822))) % 187.68/187.65 [5489]~P84(x54891)+E(f306(f76(x54891),x54892),x54892)+~P1(f306(f306(f220(x54891),f2(x54891)),x54892)) % 187.68/187.65 [5490]~P84(x54901)+E(f306(f76(x54901),x54902),x54902)+~P1(f306(f306(f221(x54901),f2(x54901)),x54902)) % 187.68/187.65 [5497]E(x54971,f2(a865))+~E(f131(a865,f306(f276(a865,x54972),x54971)),f120(a865))+P1(f306(f306(f220(a865),x54971),x54972)) % 187.68/187.65 [5507]~P74(x55071)+E(f306(f306(f6(x55071,x55071),f5(x55071)),f306(f164(x55071),x55072)),f306(f158(x55071),x55072))+~P1(f306(f129(x55071),x55072)) % 187.68/187.65 [5510]~P125(x55101)+E(f306(f107(x55101),f306(a112,x55102)),f306(f110(x55101),x55102))+~P1(f306(f306(f220(a1),f2(a1)),x55102)) % 187.68/187.65 [5537]E(x55371,x55372)+P1(f306(f306(f221(a865),x55371),x55372))+~P1(f306(f306(f220(a865),x55371),x55372)) % 187.68/187.65 [5538]E(x55381,x55382)+P1(f306(f306(f221(a1),x55381),x55382))+~P1(f306(f306(f220(a1),x55381),x55382)) % 187.68/187.65 [5541]E(x55411,f79(a1))+~E(f306(f306(f82(a1),x55412),x55411),f79(a1))+~P1(f306(f306(f221(a1),f2(a1)),x55412)) % 187.68/187.65 [5542]E(x55421,f79(a1))+~E(f306(f306(f82(a1),x55421),x55422),f79(a1))+~P1(f306(f306(f221(a1),f2(a1)),x55421)) % 187.68/187.65 [5579]~P42(x55792)+P1(f306(f306(f220(a1),f2(a1)),x55791))+~P1(f306(f306(f308(a1),x55791),x55792)) % 187.68/187.65 [5599]~P57(x55991,x55992)+P40(x55991,x55992)+~P1(f306(f63(f871(x55991,x55991)),x55992)) % 187.68/187.65 [5601]~P57(x56011,x56012)+P45(x56011,x56012)+~P1(f306(f63(f871(x56011,x56011)),x56012)) % 187.68/187.65 [5645]E(x56451,f185(f872(x56452,a859)))+~P1(f306(f63(x56452),x56451))+P1(f306(f306(f221(a865),f2(a865)),f306(f39(x56452),x56451))) % 187.68/187.65 [5671]~P1(f306(x56711,x56712))+P1(f306(x56711,f2(a865)))+P1(f306(f306(f221(a865),f757(x56712,x56711)),x56712)) % 187.68/187.65 [5696]E(x56961,f2(a865))+~E(f306(f158(a865),x56962),f2(a865))+~P1(f306(f306(f308(a865),x56961),f306(f164(a865),x56962))) % 187.68/187.65 [5762]E(x57621,x57622)+~P1(f306(f306(f220(a865),x57622),x57621))+~P1(f306(f306(f220(a865),x57621),x57622)) % 187.68/187.65 [5763]E(x57631,x57632)+~P1(f306(f306(f220(a1),x57632),x57631))+~P1(f306(f306(f220(a1),x57631),x57632)) % 187.68/187.65 [5764]E(f306(f39(x57641),x57642),f2(a865))+~P1(f306(f63(x57641),x57642))+P1(f306(f306(f308(x57641),f819(x57642,x57641)),x57642)) % 187.68/187.65 [5773]E(f51(x57731,x57732),f47(x57731,x57732))+P1(f306(f306(f220(a1),f2(a1)),x57731))+~P1(f306(f306(f221(a1),f2(a1)),x57732)) % 187.68/187.65 [5798]~P1(f306(x57981,f828(x57981)))+P1(f306(x57981,f306(a112,x57982)))+~P1(f306(f306(f220(a1),f2(a1)),x57982)) % 187.68/187.65 [5800]P1(f306(f306(f220(a865),x58001),f314(x58002)))+~P1(f306(f63(a865),x58002))+~P1(f306(f306(f308(a865),x58001),x58002)) % 187.68/187.65 [5801]P1(f306(f306(f221(a865),x58011),f362(x58012)))+~P1(f306(f63(a865),x58012))+~P1(f306(f306(f308(a865),x58011),x58012)) % 187.68/187.65 [5830]E(x58301,x58302)+~P1(f306(f306(f221(a865),x58301),f306(a119,x58302)))+P1(f306(f306(f221(a865),x58301),x58302)) % 187.68/187.65 [5864]E(x58641,f306(a119,x58642))+~P1(f306(f306(f220(a865),x58641),f306(a119,x58642)))+P1(f306(f306(f220(a865),x58641),x58642)) % 187.68/187.65 [5877]P1(f306(x58771,f829(x58771)))+~P1(f306(x58771,f306(a112,x58772)))+~P1(f306(f306(f220(a1),f2(a1)),x58772)) % 187.68/187.65 [5891]~P1(f306(x58911,x58912))+~P1(f306(f306(f220(a1),f2(a1)),x58912))+P1(f306(x58911,f306(f107(a1),f820(x58911)))) % 187.68/187.65 [5906]~P84(x59062)+~E(x59061,f2(x59062))+~P1(f306(f306(f221(x59062),f2(x59062)),f306(f76(x59062),x59061))) % 187.68/187.65 [5933]~P57(x59331,x59332)+P40(x59331,f306(f261(x59331,x59331),x59332))+~P1(f306(f63(f871(x59331,x59331)),x59332)) % 187.68/187.65 [5943]~P91(x59431)+E(f306(f107(x59431),f306(f111(a865),x59432)),f306(f111(x59431),x59432))+~P1(f306(f306(f220(a1),f2(a1)),f306(f111(a1),x59432))) % 187.68/187.65 [5947]E(f306(a119,x59471),x59472)+~P1(f306(f306(f221(a865),x59471),x59472))+P1(f306(f306(f221(a865),f306(a119,x59471)),x59472)) % 187.68/187.65 [5960]E(f306(f306(f40(a1),x59601),x59602),f2(a1))+~P1(f306(f306(f220(a1),x59601),f2(a1)))+~P1(f306(f306(f221(a1),x59602),x59601)) % 187.68/187.65 [5973]E(f46(a1,x59731,x59732),x59731)+~P1(f306(f306(f220(a1),x59731),f2(a1)))+~P1(f306(f306(f221(a1),x59732),x59731)) % 187.68/187.65 [5986]E(f48(x59861,x59862),f47(x59861,x59862))+~P1(f306(f306(f220(a1),f2(a1)),x59861))+~P1(f306(f306(f220(a1),f2(a1)),x59862)) % 187.68/187.65 [5994]E(f306(f306(f40(a1),x59941),x59942),f2(a1))+~P1(f306(f306(f220(a1),f2(a1)),x59941))+~P1(f306(f306(f221(a1),x59941),x59942)) % 187.68/187.65 [6006]E(f46(a865,f306(f111(a865),x60061),f306(f111(a865),x60062)),f306(f111(a865),x60061))+P1(f306(a190,f306(f111(a1),x60061)))+~P1(f306(a190,f306(f111(a1),x60062))) % 187.68/187.65 [6008]E(f46(a1,x60081,x60082),x60081)+~P1(f306(f306(f220(a1),f2(a1)),x60081))+~P1(f306(f306(f221(a1),x60081),x60082)) % 187.68/187.65 [6009]E(x60091,x60092)+~P1(f306(f306(f221(a865),x60091),f306(a119,x60092)))+~P1(f306(f306(f220(a865),x60092),x60091)) % 187.68/187.65 [6026]~P76(x60261)+~P1(f306(f306(f220(x60261),x60262),f2(x60261)))+P1(f306(f306(f220(x60261),x60262),f306(f80(x60261),x60262))) % 187.68/187.65 [6027]~P112(x60271)+~P1(f306(f306(f221(x60271),x60272),f2(x60271)))+P1(f306(f306(f221(x60271),x60272),f306(f80(x60271),x60272))) % 187.68/187.65 [6037]~P6(x60371)+E(f306(f306(f66(x60371,x60371,f109(x60371)),f231(x60371)),x60372),f42(x60371,x60372))+~P1(f306(f63(x60371),x60372)) % 187.68/187.65 [6038]~P6(x60381)+E(f306(f306(f66(x60381,x60381,f108(x60381)),f185(x60381)),x60382),f41(x60381,x60382))+~P1(f306(f63(x60381),x60382)) % 187.68/187.65 [6052]~P112(x60521)+~P1(f306(f306(f220(a1),f2(a1)),x60522))+P1(f306(f306(f220(x60521),f2(x60521)),f306(f110(x60521),x60522))) % 187.68/187.65 [6053]~P111(x60531)+~P1(f306(f306(f221(a865),f2(a865)),x60532))+P1(f306(f306(f221(x60531),f2(x60531)),f306(f107(x60531),x60532))) % 187.68/187.65 [6054]~P112(x60541)+~P1(f306(f306(f221(a1),f2(a1)),x60542))+P1(f306(f306(f221(x60541),f2(x60541)),f306(f110(x60541),x60542))) % 187.68/187.65 [6057]~P7(x60572)+~P7(x60571)+E(f306(f285(a865,a1,f107(a1)),f277(a865,f306(a112,x60571),f306(a112,x60572))),f277(a1,x60571,x60572)) % 187.68/187.65 [6063]P1(f306(x60631,x60632))+~P1(f306(f306(f220(a1),f2(a1)),x60632))+~P1(f306(x60631,f306(f107(a1),f822(x60631)))) % 187.68/187.65 [6087]E(f306(f306(f81(a865),f306(f111(a865),x60871)),f306(f111(a865),x60872)),f306(f111(a865),x60871))+P1(f306(f306(f221(a1),x60871),a84))+~P1(f306(f306(f221(a1),x60872),a84)) % 187.68/187.65 [6091]~P112(x60911)+P1(f306(f306(f221(x60911),f2(x60911)),f83(x60911,x60912)))+~P1(f306(f306(f221(x60911),f2(x60911)),x60912)) % 187.68/187.65 [6102]~P65(x61021)+~P1(f306(f306(f220(x61021),x61022),f2(x61021)))+P1(f306(f306(f220(x61021),f2(x61021)),f306(f80(x61021),x61022))) % 187.68/187.65 [6103]~P65(x61031)+~P1(f306(f306(f221(x61031),x61032),f2(x61031)))+P1(f306(f306(f221(x61031),f2(x61031)),f306(f80(x61031),x61032))) % 187.68/187.65 [6106]E(x61061,f231(f872(x61062,a859)))+~E(f306(f39(x61062),x61061),f306(f39(x61062),f231(f872(x61062,a859))))+~P1(f306(f63(x61062),f231(f872(x61062,a859)))) % 187.68/187.65 [6145]~P76(x61451)+P1(f306(f306(f220(x61451),x61452),f2(x61451)))+~P1(f306(f306(f220(x61451),x61452),f306(f80(x61451),x61452))) % 187.68/187.65 [6146]~P112(x61461)+P1(f306(f306(f221(x61461),x61462),f2(x61461)))+~P1(f306(f306(f221(x61461),x61462),f306(f80(x61461),x61462))) % 187.68/187.65 [6155]~P91(x61551)+P1(f306(f306(f308(x61551),f306(f111(x61551),x61552)),f183(x61551)))+~P1(f306(f306(f220(a1),a84),x61552)) % 187.68/187.65 [6186]E(x61861,f2(a865))+~P1(f306(f306(f221(a865),x61861),f306(a119,x61862)))+P1(f306(f306(f221(a865),f690(x61862,x61861)),x61862)) % 187.68/187.65 [6208]~P112(x62081)+~P1(f306(f306(f221(x62081),f2(x62081)),f83(x62081,x62082)))+P1(f306(f306(f221(x62081),f2(x62081)),x62082)) % 187.68/187.65 [6210]~E(f306(f111(a865),x62102),f306(f111(a865),x62101))+P1(f306(f306(f220(a1),f306(f111(a1),x62101)),f2(a1)))+~P1(f306(a190,f306(f111(a1),x62102))) % 187.68/187.65 [6240]E(f306(f235(a1,a1),f51(x62401,x62402)),f306(f306(f40(a1),x62401),x62402))+~P1(f306(f306(f221(a1),x62401),f2(a1)))+~P1(f306(f306(f221(a1),f2(a1)),x62402)) % 187.68/187.65 [6273]E(f306(f244(a1,a1),f51(x62731,x62732)),f46(a1,x62731,x62732))+~P1(f306(f306(f221(a1),x62731),f2(a1)))+~P1(f306(f306(f221(a1),f2(a1)),x62732)) % 187.68/187.65 [6276]~P112(x62762)+~P1(f306(f306(f220(x62762),f2(x62762)),f306(f110(x62762),x62761)))+P1(f306(f306(f220(a1),f2(a1)),x62761)) % 187.68/187.65 [6277]~P111(x62772)+~P1(f306(f306(f221(x62772),f2(x62772)),f306(f107(x62772),x62771)))+P1(f306(f306(f221(a865),f2(a865)),x62771)) % 187.68/187.65 [6278]~P112(x62782)+~P1(f306(f306(f221(x62782),f2(x62782)),f306(f110(x62782),x62781)))+P1(f306(f306(f221(a1),f2(a1)),x62781)) % 187.68/187.65 [6281]E(f306(f235(a1,a1),f48(x62811,x62812)),f306(f306(f40(a1),x62811),x62812))+~P1(f306(f306(f220(a1),f2(a1)),x62812))+~P1(f306(f306(f221(a1),f2(a1)),x62811)) % 187.68/187.65 [6297]E(f306(f244(a1,a1),f48(x62971,x62972)),f46(a1,x62971,x62972))+~P1(f306(f306(f220(a1),f2(a1)),x62972))+~P1(f306(f306(f221(a1),f2(a1)),x62971)) % 187.68/187.65 [6314]~P65(x63141)+P1(f306(f306(f220(x63141),x63142),f2(x63141)))+~P1(f306(f306(f220(x63141),f2(x63141)),f306(f80(x63141),x63142))) % 187.68/187.65 [6315]~P65(x63151)+P1(f306(f306(f221(x63151),x63152),f2(x63151)))+~P1(f306(f306(f221(x63151),f2(x63151)),f306(f80(x63151),x63152))) % 187.68/187.65 [6337]~P6(x63371)+~P41(x63371,x63371,x63372)+P1(f306(f306(f220(x63371),f103(x63371,x63372)),f306(x63372,f103(x63371,x63372)))) % 187.68/187.65 [6338]~P6(x63381)+~P41(x63381,x63381,x63382)+P1(f306(f306(f220(x63381),f102(x63381,x63382)),f306(x63382,f102(x63381,x63382)))) % 187.68/187.65 [6342]P1(f306(f50(x63421,x63422),f51(x63421,x63422)))+~P1(f306(f306(f221(a1),x63421),f2(a1)))+~P1(f306(f306(f221(a1),f2(a1)),x63422)) % 187.68/187.65 [6367]P1(f306(f50(x63671,x63672),f48(x63671,x63672)))+~P1(f306(f306(f220(a1),f2(a1)),x63671))+~P1(f306(f306(f221(a1),f2(a1)),x63672)) % 187.68/187.65 [6410]~P65(x64101)+P1(f306(f306(f220(x64101),f306(f80(x64101),x64102)),f2(x64101)))+~P1(f306(f306(f220(x64101),f2(x64101)),x64102)) % 187.68/187.65 [6411]~P65(x64111)+P1(f306(f306(f221(x64111),f306(f80(x64111),x64112)),f2(x64111)))+~P1(f306(f306(f221(x64111),f2(x64111)),x64112)) % 187.68/187.65 [6428]E(f306(f306(f22(a865),f306(a112,x64281)),f306(a112,x64282)),f306(a112,f194(x64281,x64282)))+~P1(f306(f306(f220(a1),f2(a1)),x64282))+~P1(f306(f306(f220(a1),f2(a1)),x64281)) % 187.68/187.65 [6445]P1(f306(f306(f220(a1),f2(a1)),f194(x64451,x64452)))+~P1(f306(f306(f220(a1),f2(a1)),x64452))+~P1(f306(f306(f220(a1),f2(a1)),x64451)) % 187.68/187.65 [6481]~P1(f306(x64811,x64812))+P1(f306(x64811,f2(a865)))+P1(f306(x64811,f306(f306(f81(a865),f757(x64812,x64811)),f79(a865)))) % 187.68/187.65 [6562]E(f306(f111(a865),x65621),f306(f111(a865),x65622))+~P1(f306(f306(f220(a1),f306(f111(a1),x65622)),f2(a1)))+~P1(f306(a190,f306(f111(a1),x65621))) % 187.68/187.65 [6572]~E(x65721,f2(a865))+~E(f700(x65722,x65721),f2(a865))+E(f306(f134(a865,a865,f81(a865),x65721),x65722),f2(a865)) % 187.68/187.65 [6598]~P1(f306(f63(x65981),f609(x65982,x65981)))+~P1(f306(f63(f872(x65981,a859)),x65982))+P1(f306(f63(x65981),f41(f872(x65981,a859),x65982))) % 187.68/187.65 [6604]E(x66041,x66042)+P1(f306(f306(f221(a1),x66041),x66042))+~P1(f306(f306(f221(a1),x66041),f306(f306(f81(a1),x66042),f79(a1)))) % 187.68/187.65 [6605]P1(f306(f306(f220(a865),f306(a112,x66051)),f306(a112,x66052)))+~P1(f306(f306(f220(a1),f2(a1)),x66052))+~P1(f306(f306(f220(a1),x66051),x66052)) % 187.68/187.65 [6606]P1(f306(f306(f220(a865),f306(a112,x66061)),f306(a112,x66062)))+~P1(f306(f306(f221(a1),f2(a1)),x66061))+~P1(f306(f306(f220(a1),x66061),x66062)) % 187.68/187.65 [6608]P1(f306(f306(f221(a865),f306(a112,x66081)),f306(a112,x66082)))+~P1(f306(f306(f220(a1),f2(a1)),x66081))+~P1(f306(f306(f221(a1),x66081),x66082)) % 187.68/187.65 [6609]P1(f306(f306(f221(a865),f306(a112,x66091)),f306(a112,x66092)))+~P1(f306(f306(f221(a1),f2(a1)),x66092))+~P1(f306(f306(f221(a1),x66091),x66092)) % 187.68/187.65 [6621]E(f46(a865,f306(a112,x66211),f306(a112,x66212)),f306(a112,f46(a1,x66211,x66212)))+~P1(f306(f306(f220(a1),f2(a1)),x66212))+~P1(f306(f306(f220(a1),f2(a1)),x66211)) % 187.68/187.65 [6646]~P65(x66461)+~P1(f306(f306(f220(x66461),f306(f80(x66461),x66462)),f2(x66461)))+P1(f306(f306(f220(x66461),f2(x66461)),x66462)) % 187.68/187.65 [6647]~P65(x66471)+~P1(f306(f306(f221(x66471),f306(f80(x66471),x66472)),f2(x66471)))+P1(f306(f306(f221(x66471),f2(x66471)),x66472)) % 187.68/187.65 [6662]~P1(f306(f306(f221(a1),a84),x66622))+~P1(f306(f306(f221(a1),x66621),x66622))+P1(f306(f306(f221(a865),f306(f111(a865),x66621)),f306(f111(a865),x66622))) % 187.68/187.65 [6752]~P1(f306(f306(f220(a1),f2(a1)),x67521))+P1(f306(f306(f221(a865),f306(a112,x67521)),x67522))+~P1(f306(f306(f221(a1),x67521),f306(f107(a1),x67522))) % 187.68/187.65 [6769]E(x67691,f2(a1))+E(f46(a1,x67692,x67691),f2(a1))+E(f306(f306(f22(a1),f306(f80(a1),f306(f306(f40(a1),x67692),x67691))),f79(a1)),f306(f306(f40(a1),x67692),f306(f80(a1),x67691))) % 187.68/187.65 [6784]~P1(f306(f306(f220(a1),f2(a1)),x67841))+~P1(f306(f306(f221(a865),f306(a112,x67841)),x67842))+P1(f306(f306(f221(a1),x67841),f306(f107(a1),x67842))) % 187.68/187.65 [6819]~P1(f306(f306(f220(a865),f306(a112,x68191)),f306(a112,x68192)))+~P1(f306(f306(f220(a1),f2(a1)),x68192))+P1(f306(f306(f220(a1),x68191),x68192)) % 187.68/187.65 [6820]~P1(f306(f306(f220(a865),f306(a112,x68201)),f306(a112,x68202)))+~P1(f306(f306(f221(a1),f2(a1)),x68201))+P1(f306(f306(f220(a1),x68201),x68202)) % 187.68/187.65 [6848]P1(f306(f306(f220(a1),x68481),x68482))+~P1(f306(f306(f220(a865),f306(f111(a865),x68481)),f306(f111(a865),x68482)))+P1(f306(f306(f220(a1),x68481),a84)) % 187.68/187.65 [6873]P1(f306(f306(f220(a1),f2(a1)),f46(a1,x68731,x68732)))+~P1(f306(f306(f220(a1),f2(a1)),x68732))+~P1(f306(f306(f220(a1),f2(a1)),x68731)) % 187.68/187.65 [6973]P1(f306(f306(f221(a1),a84),x69731))+~P1(f306(f306(f221(a1),x69732),x69731))+~P1(f306(f306(f221(a865),f306(f111(a865),x69732)),f306(f111(a865),x69731))) % 187.68/187.65 [7024]E(f306(f306(f236(a1,a1),f306(f306(f40(a1),x70241),x70242)),f46(a1,x70241,x70242)),f51(x70241,x70242))+~P1(f306(f306(f221(a1),x70241),f2(a1)))+~P1(f306(f306(f221(a1),f2(a1)),x70242)) % 187.68/187.65 [7045]E(f306(f306(f236(a1,a1),f306(f306(f40(a1),x70451),x70452)),f46(a1,x70451,x70452)),f48(x70451,x70452))+~P1(f306(f306(f220(a1),f2(a1)),x70452))+~P1(f306(f306(f220(a1),f2(a1)),x70451)) % 187.68/187.65 [7096]~P95(x70962)+E(x70961,f120(x70962))+E(f306(f134(x70962,x70962,f82(x70962),f306(f133(x70962),x70961)),f306(f163(x70962),x70961)),f306(f65(x70962,f82(x70962)),f306(f164(x70962),x70961))) % 187.68/187.65 [7208]~E(x72081,f2(a865))+E(f306(f134(a865,a865,f81(a865),x72081),x72082),f2(a865))+P1(f306(f306(f308(a865),f700(x72082,x72081)),f306(f164(a865),x72082))) % 187.68/187.65 [7255]~P1(f306(f306(f220(a1),x72551),f2(a1)))+P1(f306(f306(f220(a1),f306(f306(f40(a1),x72551),x72552)),f2(a1)))+~P1(f306(f306(f221(a1),f2(a1)),x72552)) % 187.68/187.65 [7256]~P1(f306(f306(f221(a1),x72562),f2(a1)))+P1(f306(f306(f220(a1),f306(f306(f40(a1),x72561),x72562)),f2(a1)))+~P1(f306(f306(f220(a1),f2(a1)),x72561)) % 187.68/187.65 [7257]~P1(f306(f306(f221(a1),x72572),f2(a1)))+P1(f306(f306(f221(a1),f306(f306(f40(a1),x72571),x72572)),f2(a1)))+~P1(f306(f306(f221(a1),f2(a1)),x72571)) % 187.68/187.65 [7259]~P1(f306(f306(f221(a1),x72591),f2(a1)))+P1(f306(f306(f221(a1),f306(f306(f40(a1),x72591),x72592)),f2(a1)))+~P1(f306(f306(f221(a1),f2(a1)),x72592)) % 187.68/187.65 [7265]P1(f306(f306(f308(f872(x72651,a859)),f609(x72652,x72651)),x72652))+~P1(f306(f63(f872(x72651,a859)),x72652))+P1(f306(f63(x72651),f41(f872(x72651,a859),x72652))) % 187.68/187.65 [7361]P28(x73611,x73611,x73612,f231(f872(x73611,a859)))+~E(f306(f285(x73611,x73611,x73612),f231(f872(x73611,a859))),f231(f872(x73611,a859)))+~P1(f306(f63(x73611),f231(f872(x73611,a859)))) % 187.68/187.65 [7486]~P28(x74861,x74861,x74862,f231(f872(x74861,a859)))+E(f306(f285(x74861,x74861,x74862),f231(f872(x74861,a859))),f231(f872(x74861,a859)))+~P1(f306(f63(x74861),f231(f872(x74861,a859)))) % 187.68/187.65 [7622]E(f306(f306(f40(a1),x76221),x76222),f306(f111(a1),a104))+~P1(f306(f306(f220(a1),f306(f306(f81(a1),x76221),x76222)),f2(a1)))+~P1(f306(f306(f221(a1),f2(a1)),x76221)) % 187.68/187.65 [7682]~P1(f306(f306(f221(a1),x76822),f2(a1)))+~P1(f306(f306(f221(a1),f306(f306(f40(a1),x76821),x76822)),f2(a1)))+P1(f306(f306(f221(a1),f2(a1)),x76821)) % 187.68/187.65 [7687]E(f306(f306(f81(a1),x76871),x76872),f46(a1,x76871,x76872))+~P1(f306(f306(f220(a1),f306(f306(f81(a1),x76871),x76872)),f2(a1)))+~P1(f306(f306(f221(a1),f2(a1)),x76871)) % 187.68/187.65 [7690]P1(f306(f306(f221(a1),x76901),f2(a1)))+~P1(f306(f306(f221(a1),f306(f306(f40(a1),x76901),x76902)),f2(a1)))+~P1(f306(f306(f221(a1),f2(a1)),x76902)) % 187.68/187.65 [8083]~P60(x80831)+~P1(f306(f60(f869(x80831)),x80832))+P1(f306(f60(x80831),f306(f306(f8(f869(x80831),a859,x80831),x80832),f214(x80831)))) % 187.68/187.65 [8394]~P108(x83941)+P17(x83941,x83942)+~P1(f306(f306(f220(x83941),f306(f306(f157(x83941),x83942),f725(x83942,x83941))),f306(f306(f157(x83941),x83942),f726(x83942,x83941)))) % 187.68/187.65 [8395]~P108(x83951)+P17(x83951,x83952)+~P1(f306(f306(f220(x83951),f306(f306(f157(x83951),x83952),f731(x83952,x83951))),f306(f306(f157(x83951),x83952),f741(x83952,x83951)))) % 187.68/187.65 [8554]~P60(x85541)+P1(f306(f59(f869(x85541)),x85542))+~P1(f306(f59(x85541),f306(f306(f8(f869(x85541),a859,x85541),x85542),f214(x85541)))) % 187.68/187.65 [9727]~P60(x97271)+~P60(x97272)+E(f306(f306(f146(f866(x97271),f872(x97272,x97271)),f306(f306(f8(f872(x97272,f869(x97271)),f872(x97272,x97271),f866(x97271)),f74(f869(x97271),x97271,x97272,f218(x97271))),f306(f306(f8(f866(f871(x97272,x97271)),f872(x97272,f869(x97271)),f866(x97271)),f169(x97272,x97271)),f306(f173(x97272,x97271),f57(x97272))))),f56(x97271,f306(f186(f866(x97272)),f57(x97272)),f57(x97271))),f57(f872(x97272,x97271))) % 187.68/187.65 [5638]E(x56381,f2(a1))+~E(f46(a1,x56382,x56381),f2(a1))+E(f306(f306(f40(a1),x56382),f306(f80(a1),x56381)),f306(f80(a1),f306(f306(f40(a1),x56382),x56381))) % 187.68/187.65 [5656]~P42(x56562)+~P42(x56561)+P42(f306(f306(f108(f872(a1,a859)),x56561),x56562)) % 187.68/187.65 [5657]~P42(x56572)+~P42(x56571)+P42(f306(f306(f109(f872(a1,a859)),x56571),x56572)) % 187.68/187.65 [5674]~P91(x56741)+~P61(x56741)+E(f306(f80(x56741),f306(f306(f264(x56741),f79(x56741)),x56742)),f306(f306(f264(x56741),f306(f111(x56741),a104)),x56742)) % 187.68/187.65 [5790]E(x57901,f2(a1))+~E(f46(a1,x57902,x57901),f2(a1))+E(f306(f306(f40(a1),f306(f80(a1),x57902)),x57901),f306(f80(a1),f306(f306(f40(a1),x57902),x57901))) % 187.68/187.65 [5927]~P108(x59271)+P17(x59271,x59272)+P1(f306(f306(f221(a865),f726(x59272,x59271)),f306(f186(f866(x59271)),x59272))) % 187.68/187.65 [5928]~P108(x59281)+P17(x59281,x59282)+P1(f306(f306(f221(a865),f741(x59282,x59281)),f306(f186(f866(x59281)),x59282))) % 187.68/187.65 [6083]~P91(x60831)+~E(f306(f111(x60831),x60832),f2(x60831))+P33(x60831,f306(f111(x60831),f306(f306(f81(a1),x60832),f306(f80(a1),a84)))) % 187.68/187.65 [6084]~P91(x60841)+~E(f306(f111(x60841),x60842),f2(x60841))+P33(x60841,f306(f111(x60841),f306(f306(f81(a1),a84),f306(f80(a1),x60842)))) % 187.68/187.65 [6086]E(f306(a52,f48(f306(f80(a1),x60861),f306(f80(a1),x60862))),f47(x60861,x60862))+P1(f306(f306(f220(a1),f2(a1)),x60861))+P1(f306(f306(f221(a1),f2(a1)),x60862)) % 187.68/187.65 [6216]~E(x62162,f2(a865))+~E(x62161,f2(a865))+P1(f306(f306(f220(a1),f306(f107(a1),x62161)),f306(f80(a1),f306(f107(a1),x62162)))) % 187.68/187.65 [6244]E(f306(f306(f81(a865),f306(f111(a865),x62441)),f306(f111(a865),x62442)),f306(f111(a865),f306(f306(f81(a1),x62441),x62442)))+P1(f306(f306(f221(a1),x62441),a84))+P1(f306(f306(f221(a1),x62442),a84)) % 187.68/187.65 [6376]~P76(x63761)+~P1(f306(f306(f220(x63761),f2(x63761)),x63762))+P1(f306(f306(f220(x63761),f306(f80(x63761),x63762)),x63762)) % 187.68/187.65 [6377]~P76(x63771)+~P1(f306(f306(f221(x63771),f2(x63771)),x63772))+P1(f306(f306(f221(x63771),f306(f80(x63771),x63772)),x63772)) % 187.68/187.65 [6548]E(f306(f306(f22(a865),f306(a112,x65481)),f306(a112,x65482)),f306(a112,f306(f306(f22(a1),x65481),x65482)))+~P1(f306(f306(f220(a1),f2(a1)),x65482))+~P1(f306(f306(f220(a1),x65482),x65481)) % 187.68/187.65 [6581]E(f306(a112,f46(a1,f306(f111(a1),x65811),f306(f111(a1),x65812))),f46(a865,f306(f111(a865),x65811),f306(f111(a865),x65812)))+P1(f306(a190,f306(f111(a1),x65811)))+P1(f306(a190,f306(f111(a1),x65812))) % 187.68/187.65 [6599]~P76(x65991)+P1(f306(f306(f220(x65991),f2(x65991)),x65992))+~P1(f306(f306(f220(x65991),f306(f80(x65991),x65992)),x65992)) % 187.68/187.65 [6600]~P76(x66001)+P1(f306(f306(f221(x66001),f2(x66001)),x66002))+~P1(f306(f306(f221(x66001),f306(f80(x66001),x66002)),x66002)) % 187.68/187.65 [6612]~P76(x66121)+~P1(f306(f306(f220(x66121),f2(x66121)),x66122))+P1(f306(f306(f220(x66121),f2(x66121)),f306(f306(f81(x66121),x66122),x66122))) % 187.68/187.65 [6615]~P76(x66151)+~P1(f306(f306(f221(x66151),f2(x66151)),x66152))+P1(f306(f306(f221(x66151),f2(x66151)),f306(f306(f81(x66151),x66152),x66152))) % 187.68/187.65 [6627]E(f306(f306(f81(a865),f306(a112,x66271)),f306(a112,x66272)),f306(a112,f306(f306(f81(a1),x66271),x66272)))+~P1(f306(f306(f220(a1),f2(a1)),x66272))+~P1(f306(f306(f220(a1),f2(a1)),x66271)) % 187.68/187.65 [6639]E(x66391,f2(a865))+P1(f306(f306(f221(a865),f2(a865)),x66392))+~P1(f306(f306(f221(a865),f2(a865)),f306(f306(f237(a865),x66392),x66391))) % 187.68/187.65 [6671]~P91(x66711)+E(f306(f111(x66711),x66712),f2(x66711))+~P33(x66711,f306(f111(x66711),f306(f306(f81(a1),a84),f306(f80(a1),x66712)))) % 187.68/187.65 [6672]~P91(x66721)+E(f306(f111(x66721),x66722),f2(x66721))+~P33(x66721,f306(f111(x66721),f306(f306(f81(a1),x66722),f306(f80(a1),a84)))) % 187.68/187.65 [6730]~P1(f306(f63(x67301),x67302))+~P1(f306(f63(x67301),f231(f872(x67301,a859))))+P1(f306(f63(x67301),f306(f80(f872(x67301,a859)),x67302))) % 187.68/187.65 [6753]~P1(f306(f306(f221(a1),f2(a1)),x67532))+~P1(f306(f306(f220(a1),x67532),x67531))+P1(f306(f306(f221(a1),f2(a1)),f306(f306(f40(a1),x67531),x67532))) % 187.68/187.65 [6754]~P1(f306(f306(f220(a1),x67541),f2(a1)))+~P1(f306(f306(f221(a1),x67542),f2(a1)))+P1(f306(f306(f220(a1),f2(a1)),f306(f306(f40(a1),x67541),x67542))) % 187.68/187.65 [6792]~P1(f306(f306(f220(a1),f2(a1)),x67922))+~P1(f306(f306(f220(a1),f2(a1)),x67921))+P1(f306(f306(f220(a1),f2(a1)),f306(f306(f81(a1),x67921),x67922))) % 187.68/187.65 [6793]~P1(f306(f306(f220(a1),f2(a1)),x67932))+~P1(f306(f306(f220(a1),f2(a1)),x67931))+P1(f306(f306(f220(a1),f2(a1)),f306(f306(f82(a1),x67931),x67932))) % 187.68/187.65 [6794]~P1(f306(f306(f220(a1),f2(a1)),x67942))+~P1(f306(f306(f220(a1),f2(a1)),x67941))+P1(f306(f306(f220(a1),f2(a1)),f306(f306(f40(a1),x67941),x67942))) % 187.68/187.65 [6795]~P1(f306(f306(f220(a1),f2(a1)),x67951))+~P1(f306(f306(f221(a1),f2(a1)),x67952))+P1(f306(f306(f220(a1),f2(a1)),f306(f306(f40(a1),x67951),x67952))) % 187.68/187.65 [6796]~P1(f306(f306(f221(a865),f2(a865)),x67962))+~P1(f306(f306(f221(a865),f2(a865)),x67961))+P1(f306(f306(f221(a865),f2(a865)),f306(f306(f82(a865),x67961),x67962))) % 187.68/187.65 [6859]E(x68591,f2(a1))+E(f46(a1,x68592,x68591),f2(a1))+E(f306(f306(f22(a1),f306(f80(a1),f306(f306(f40(a1),x68592),x68591))),f79(a1)),f306(f306(f40(a1),f306(f80(a1),x68592)),x68591)) % 187.68/187.65 [6914]P1(f306(f306(f221(a865),f2(a865)),x69141))+P1(f306(f306(f221(a865),f2(a865)),x69142))+~P1(f306(f306(f221(a865),f2(a865)),f306(f306(f81(a865),x69142),x69141))) % 187.68/187.65 [6918]~P76(x69181)+P1(f306(f306(f220(x69181),f2(x69181)),x69182))+~P1(f306(f306(f220(x69181),f2(x69181)),f306(f306(f81(x69181),x69182),x69182))) % 187.68/187.65 [6919]~P76(x69191)+P1(f306(f306(f221(x69191),f2(x69191)),x69192))+~P1(f306(f306(f221(x69191),f2(x69191)),f306(f306(f81(x69191),x69192),x69192))) % 187.68/187.65 [6974]~P1(f306(f63(x69741),x69742))+P1(f306(f63(x69741),f231(f872(x69741,a859))))+~P1(f306(f63(x69741),f306(f80(f872(x69741,a859)),x69742))) % 187.68/187.65 [7037]P1(f306(f306(f220(a1),x70371),f2(a1)))+~P1(f306(f306(f221(a1),x70372),f2(a1)))+~P1(f306(f306(f220(a1),f2(a1)),f306(f306(f40(a1),x70371),x70372))) % 187.68/187.65 [7043]~P1(f306(f306(f221(a1),f2(a1)),x70431))+P1(f306(f306(f220(a1),x70431),x70432))+~P1(f306(f306(f221(a1),f2(a1)),f306(f306(f40(a1),x70432),x70431))) % 187.68/187.65 [7044]~P1(f306(f306(f220(a1),f2(a1)),x70442))+P1(f306(f306(f220(a1),x70441),x70442))+~P1(f306(f306(f221(a1),f2(a1)),f306(f306(f40(a1),x70442),x70441))) % 187.68/187.65 [7073]P1(f306(f306(f220(a1),f2(a1)),x70731))+~P1(f306(f306(f221(a1),f2(a1)),x70732))+~P1(f306(f306(f220(a1),f2(a1)),f306(f306(f40(a1),x70731),x70732))) % 187.68/187.65 [7074]P1(f306(f306(f221(a1),f2(a1)),x70741))+~P1(f306(f306(f220(a1),f2(a1)),x70742))+~P1(f306(f306(f221(a1),f2(a1)),f306(f306(f40(a1),x70742),x70741))) % 187.68/187.65 [7516]~P1(f306(f63(x75162),f231(f872(x75162,a859))))+~P1(f306(f63(x75161),f231(f872(x75161,a859))))+P1(f306(f63(f870(x75161,x75162)),f231(f872(f870(x75161,x75162),a859)))) % 187.68/187.65 [7517]~P1(f306(f63(x75172),f231(f872(x75172,a859))))+~P1(f306(f63(x75171),f231(f872(x75171,a859))))+P1(f306(f63(f871(x75171,x75172)),f231(f872(f871(x75171,x75172),a859)))) % 187.68/187.65 [7586]~P1(f306(f306(f221(a865),f306(a119,f2(a865))),x75861))+~P1(f306(f306(f221(a865),f306(a119,f2(a865))),x75862))+P1(f306(f306(f221(a865),x75861),f306(f306(f82(a865),x75862),x75861))) % 187.68/187.65 [7587]~P1(f306(f306(f221(a865),f306(a119,f2(a865))),x75871))+~P1(f306(f306(f221(a865),f306(a119,f2(a865))),x75872))+P1(f306(f306(f221(a865),x75871),f306(f306(f82(a865),x75871),x75872))) % 187.68/187.65 [7621]E(f306(f39(x76211),f231(f872(x76211,a859))),f306(a119,f2(a865)))+P1(f306(f63(x76212),f231(f872(x76212,a859))))+~P1(f306(f63(f872(x76212,x76211)),f231(f872(f872(x76212,x76211),a859)))) % 187.68/187.65 [7749]~P1(f306(f306(f220(a865),f306(a119,f2(a865))),x77491))+~P1(f306(f306(f220(a865),f306(a119,f2(a865))),x77492))+P1(f306(f306(f220(a865),f306(a119,f2(a865))),f306(f306(f82(a865),x77491),x77492))) % 187.68/187.65 [7750]~P1(f306(f306(f221(a865),f306(a119,f2(a865))),x77502))+~P1(f306(f306(f221(a865),f306(a119,f2(a865))),x77501))+P1(f306(f306(f221(a865),f306(a119,f2(a865))),f306(f306(f82(a865),x77501),x77502))) % 187.68/187.65 [8098]~P109(x80981)+P41(a865,x80981,x80982)+~P1(f306(f306(f220(x80981),f306(x80982,f366(x80982,x80981))),f306(x80982,f306(a119,f366(x80982,x80981))))) % 187.68/187.65 [8447]E(x84471,f120(x84472))+~P1(f306(f129(x84472),x84471))+E(f168(x84472,f306(f306(f8(a859,a859,x84472),a301),f306(f306(f7(x84472,x84472,a859),a303),f136(x84472,x84471))),x84471),f121(x84472,x84471)) % 187.68/187.65 [8545]~P42(x85452)+~P42(x85451)+E(f306(f285(a865,a1,f107(a1)),f306(f306(f108(f872(a865,a859)),f306(f285(a1,a865,a112),x85451)),f306(f285(a1,a865,a112),x85452))),f306(f306(f108(f872(a1,a859)),x85451),x85452)) % 187.68/187.65 [8546]~P42(x85462)+~P42(x85461)+E(f306(f285(a865,a1,f107(a1)),f306(f306(f109(f872(a865,a859)),f306(f285(a1,a865,a112),x85461)),f306(f285(a1,a865,a112),x85462))),f306(f306(f109(f872(a1,a859)),x85461),x85462)) % 187.68/187.65 [9201]~P91(x92011)+~E(f306(f111(x92011),x92012),f79(x92011))+P33(x92011,f306(f111(x92011),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f80(a1),x92012)))) % 187.68/187.65 [9439]~P91(x94391)+E(f306(f111(x94391),x94392),f79(x94391))+~P33(x94391,f306(f111(x94391),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f80(a1),x94392)))) % 187.68/187.65 [10181]E(x101811,f2(a1))+E(x101812,f2(a1))+E(f306(f246(a1,a1,a1,a1,f35(a1),f306(f82(a1),f83(a1,x101812))),f306(f306(f306(f101(f871(a1,a1)),f306(f306(a303,f83(a1,x101811)),f83(a1,x101812))),f54(x101811,x101812)),f306(f306(f245(a1,a1,f871(a1,a1)),f306(f306(f18(a1,f872(a1,f871(a1,a1)),f872(a1,f871(a1,a1))),f306(f306(f8(f872(a1,f872(f871(a1,a1),f871(a1,a1))),f872(f872(a1,f871(a1,a1)),f872(a1,f871(a1,a1))),a1),f18(a1,f871(a1,a1),f871(a1,a1))),f306(f306(f8(f871(a1,a1),f872(a1,f872(f871(a1,a1),f871(a1,a1))),a1),f306(f7(a1,f871(a1,a1),f872(f871(a1,a1),f871(a1,a1))),f306(f306(f8(a859,f872(f871(a1,a1),f872(f871(a1,a1),f871(a1,a1))),a1),f101(f871(a1,a1))),f306(f306(f7(a1,a1,a859),a303),f2(a1))))),f306(f306(f7(a1,a1,f871(a1,a1)),f306(f306(f8(a1,f872(a1,f871(a1,a1)),a1),f236(a1,a1)),f80(a1))),f2(a1))))),f306(f306(f7(a1,f872(a1,a1),f872(a1,f871(a1,a1))),f306(f306(f8(f872(a1,f871(a1,a1)),f872(f872(a1,a1),f872(a1,f871(a1,a1))),a1),f8(a1,f871(a1,a1),a1)),f306(f306(f8(a1,f872(a1,f871(a1,a1)),a1),f236(a1,a1)),f306(f306(f7(a1,a1,a1),f306(f306(f8(a1,f872(a1,a1),a1),f22(a1)),f80(a1))),f79(a1))))),f306(f22(a1),f306(f76(a1),x101812))))),f54(x101811,x101812)))),f47(x101811,x101812)) % 187.68/187.65 [10182]E(x101821,f2(a1))+E(x101822,f2(a1))+E(f306(f246(a1,a1,a1,a1,f35(a1),f306(f82(a1),f83(a1,x101822))),f306(f306(f306(f101(f871(a1,a1)),f306(f306(a305,f306(f306(a304,f306(f306(f221(a1),f2(a1)),x101822)),f306(f306(f220(a1),f2(a1)),x101821))),f306(f306(a304,f306(f306(f221(a1),x101822),f2(a1))),f306(f306(f221(a1),x101821),f2(a1))))),f54(x101821,x101822)),f306(f306(f245(a1,a1,f871(a1,a1)),f306(f306(f18(a1,f872(a1,f871(a1,a1)),f872(a1,f871(a1,a1))),f306(f306(f8(f872(a1,f872(f871(a1,a1),f871(a1,a1))),f872(f872(a1,f871(a1,a1)),f872(a1,f871(a1,a1))),a1),f18(a1,f871(a1,a1),f871(a1,a1))),f306(f306(f8(f871(a1,a1),f872(a1,f872(f871(a1,a1),f871(a1,a1))),a1),f306(f7(a1,f871(a1,a1),f872(f871(a1,a1),f871(a1,a1))),f306(f306(f8(a859,f872(f871(a1,a1),f872(f871(a1,a1),f871(a1,a1))),a1),f101(f871(a1,a1))),f306(f306(f7(a1,a1,a859),a303),f2(a1))))),f306(f306(f7(a1,a1,f871(a1,a1)),f306(f306(f8(a1,f872(a1,f871(a1,a1)),a1),f236(a1,a1)),f80(a1))),f2(a1))))),f306(f306(f7(a1,f872(a1,a1),f872(a1,f871(a1,a1))),f306(f306(f8(f872(a1,f871(a1,a1)),f872(f872(a1,a1),f872(a1,f871(a1,a1))),a1),f8(a1,f871(a1,a1),a1)),f306(f306(f8(a1,f872(a1,f871(a1,a1)),a1),f236(a1,a1)),f306(f306(f7(a1,a1,a1),f306(f306(f8(a1,f872(a1,a1),a1),f22(a1)),f80(a1))),f79(a1))))),f306(f22(a1),f306(f76(a1),x101822))))),f54(x101821,x101822)))),f47(x101821,x101822)) % 187.68/187.65 [10183]~P32(a5000)+P27(a861,x101831,f306(f306(f284(f864(a861)),f306(f306(f306(f93(a861),a303),x101832),f193(x101832))),f185(f872(f864(a861),a859))))+~P27(a861,x101831,f306(f306(f284(f864(a861)),f306(f306(f306(f93(a861),f306(f306(f8(f872(a861,f872(a861,a859)),f872(a861,a859),a861),f306(f8(f872(a861,a859),a859,a861),f89(a861))),f306(f306(f8(f872(a861,a859),f872(a861,f872(a861,a859)),a861),f306(f7(a861,f872(a861,a859),f872(a861,a859)),f306(f306(f8(f872(a861,f872(a859,a859)),f872(f872(a861,a859),f872(a861,a859)),a861),f18(a861,a859,a859)),f306(f306(f8(f872(a861,a859),f872(a861,f872(a859,a859)),a861),f306(f8(a859,f872(a859,a859),a861),a309)),f193(x101832))))),a303))),x101832),a303)),f185(f872(f864(a861),a859)))) % 187.68/187.65 [5664]~P112(x56641)+~P91(x56641)+E(f306(f76(x56641),f306(f306(f237(x56641),f306(f111(x56641),a104)),x56642)),f79(x56641)) % 187.68/187.65 [6156]~P125(x61561)+~P1(f306(f306(f221(a1),x61562),f2(a1)))+E(f306(f80(x61561),f306(f107(x61561),f306(a112,f306(f80(a1),x61562)))),f306(f110(x61561),x61562)) % 187.68/187.65 [6360]P1(f306(f306(f220(a106),x63601),f79(a106)))+E(f306(f306(f81(a106),f79(a106)),f254(x63601,f306(f306(f40(a106),x63602),x63601))),f254(x63601,x63602))+P1(f306(f306(f221(a106),x63602),x63601)) % 187.68/187.65 [6959]~P90(x69591)+~P1(f306(f306(f308(x69591),x69592),f117(x69591)))+~E(f306(f306(f81(x69591),f306(f306(f81(x69591),f79(x69591)),x69592)),x69592),f2(x69591)) % 187.68/187.65 [7075]~P1(f306(f306(f220(a1),x70752),f2(a1)))+~P1(f306(f306(f221(a1),x70751),f2(a1)))+E(f306(f235(a1,a1),f306(a52,f48(f306(f80(a1),x70751),f306(f80(a1),x70752)))),f306(f306(f40(a1),x70751),x70752)) % 187.68/187.65 [7092]~P1(f306(f306(f220(a1),x70922),f2(a1)))+~P1(f306(f306(f221(a1),x70921),f2(a1)))+E(f306(f244(a1,a1),f306(a52,f48(f306(f80(a1),x70921),f306(f80(a1),x70922)))),f46(a1,x70921,x70922)) % 187.68/187.65 [7098]~P1(f306(f306(f221(a1),x70982),f2(a1)))+E(f306(f235(a1,a1),f306(a52,f51(f306(f80(a1),x70981),f306(f80(a1),x70982)))),f306(f306(f40(a1),x70981),x70982))+~P1(f306(f306(f221(a1),f2(a1)),x70981)) % 187.68/187.65 [7116]~P1(f306(f306(f221(a1),x71162),f2(a1)))+E(f306(f244(a1,a1),f306(a52,f51(f306(f80(a1),x71161),f306(f80(a1),x71162)))),f46(a1,x71161,x71162))+~P1(f306(f306(f221(a1),f2(a1)),x71161)) % 187.68/187.65 [7169]E(f306(f306(f40(a1),f306(f306(f237(a1),x71691),x71692)),x71691),f306(f306(f237(a1),x71691),f306(f306(f22(a865),x71692),f306(a119,f2(a865)))))+~P1(f306(f306(f221(a865),f2(a865)),x71692))+~P1(f306(f306(f221(a1),f2(a1)),x71691)) % 187.68/187.65 [7262]~P1(f306(f306(f221(a865),f2(a865)),x72621))+~P1(f306(f306(f221(a865),f2(a865)),x72622))+P1(f306(f306(f221(a865),f306(f306(f22(a865),x72621),x72622)),x72621)) % 187.68/187.65 [7263]~P1(f306(f306(f221(a865),f2(a865)),x72631))+~P1(f306(f306(f221(a865),f79(a865)),x72632))+P1(f306(f306(f221(a865),f306(f306(f40(a865),x72631),x72632)),x72631)) % 187.68/187.65 [7264]~P1(f306(f306(f221(a1),f2(a1)),x72641))+~P1(f306(f306(f221(a1),f79(a1)),x72642))+P1(f306(f306(f221(a1),f306(f306(f40(a1),x72641),x72642)),x72641)) % 187.68/187.65 [7411]E(x74111,f2(a865))+~E(x74112,f2(a1))+~P1(f306(f306(f221(a1),f2(a1)),f306(f306(f237(a1),f306(f76(a1),x74112)),x74111))) % 187.68/187.65 [7780]~P1(f306(x77801,x77802))+P1(f306(x77801,f2(a865)))+E(f306(a119,f224(a865,f306(f306(f8(a865,a859,a865),x77801),a119))),f224(a865,x77801)) % 187.68/187.65 [7828]~E(x78282,f120(f866(x78281)))+E(f306(f186(f866(f866(x78281))),f171(x78281,x78282)),f2(a865))+~P17(a865,f306(f161(a865),f306(f306(f146(f866(x78281),a865),f186(f866(x78281))),x78282))) % 187.68/187.65 [8082]P1(f306(x80821,x80822))+~P1(f306(x80821,f306(a114,f511(x80821,x80822))))+~P1(f306(f306(f308(f872(f871(a865,a865),a859)),x80822),a105)) % 187.68/187.65 [8102]E(x81021,f120(f866(x81022)))+E(f306(f186(f866(x81022)),f306(f306(f157(f866(x81022)),x81021),f2(a865))),f306(f186(f866(f866(x81022))),f171(x81022,x81021)))+~P17(a865,f306(f161(a865),f306(f306(f146(f866(x81022),a865),f186(f866(x81022))),x81021))) % 187.68/187.65 [8806]~P1(f306(f63(x88061),f306(f228(x88061),x88062)))+~P1(f306(f63(x88061),f231(f872(x88061,a859))))+P1(f306(f63(x88061),f306(f228(x88061),f306(f306(f8(a859,a859,x88061),a301),x88062)))) % 187.68/187.65 [8869]E(f306(f306(f236(a865,a865),f306(a119,f306(f306(f40(a865),f306(f306(f22(a865),x88691),x88692)),x88692))),f46(a865,f306(f306(f22(a865),x88691),x88692),x88692)),f86(f871(a865,a865),f49(x88691,x88692)))+~P1(f306(f306(f221(a865),f2(a865)),x88692))+~P1(f306(f306(f220(a865),x88692),x88691)) % 187.68/187.65 [9164]~P1(f306(f63(x91641),f306(f228(x91641),x91642)))+P1(f306(f63(x91641),f231(f872(x91641,a859))))+~P1(f306(f63(x91641),f306(f228(x91641),f306(f306(f8(a859,a859,x91641),a301),x91642)))) % 187.68/187.65 [9895]P29(x98951,x98952)+~P40(x98951,f306(f235(f872(f871(x98951,x98951),a859),f872(f871(x98951,x98951),a859)),x98952))+~P1(f306(f306(f220(f872(f871(x98951,x98951),a859)),f306(f306(f263(x98951,x98951,x98951),f306(f235(f872(f871(x98951,x98951),a859),f872(f871(x98951,x98951),a859)),x98952)),f306(f244(f872(f871(x98951,x98951),a859),f872(f871(x98951,x98951),a859)),x98952))),f306(f235(f872(f871(x98951,x98951),a859),f872(f871(x98951,x98951),a859)),x98952))) % 187.68/187.65 [7195]~P1(f306(f306(f221(a865),f2(a865)),x71952))+P1(f306(f306(f221(a865),x71951),x71952))+E(f306(a119,f306(f306(f40(a865),f306(f306(f22(a865),x71951),x71952)),x71952)),f306(f306(f40(a865),x71951),x71952)) % 187.68/187.65 [7331]~P1(f306(f306(f221(a865),f2(a865)),x73312))+~P1(f306(f306(f220(a865),x73312),x73311))+E(f306(a119,f306(f306(f40(a865),f306(f306(f22(a865),x73311),x73312)),x73312)),f306(f306(f40(a865),x73311),x73312)) % 187.68/187.65 [8312]~P91(x83121)+~P90(x83121)+~P33(x83121,f306(f111(x83121),f306(f306(f22(a1),f306(f306(f81(a1),x83122),x83122)),a104))) % 187.68/187.65 [9068]E(x90681,f2(a865))+E(f306(f306(f245(a865,a865,f871(a865,a865)),f306(f306(f8(a865,f872(a865,f871(a865,a865)),a865),f236(a865,a865)),a119)),f86(f871(a865,a865),f49(f306(f306(f22(a865),x90682),x90681),x90681))),f86(f871(a865,a865),f49(x90682,x90681)))+P1(f306(f306(f221(a865),x90682),x90681)) % 187.68/187.65 [9504]P1(f306(x95042,f656(x95042,x95041)))+P1(f306(x95041,f656(x95042,x95041)))+E(f306(f228(a1),f306(f306(f18(a1,a859,a859),f306(f306(f8(a859,f872(a859,a859),a1),a304),f306(f220(a1),f2(a1)))),x95041)),f306(f228(a1),f306(f306(f18(a1,a859,a859),f306(f306(f8(a859,f872(a859,a859),a1),a304),f306(f220(a1),f2(a1)))),x95042))) % 187.68/187.65 [9508]~P1(f306(x95082,f656(x95082,x95081)))+~P1(f306(x95081,f656(x95082,x95081)))+E(f306(f228(a1),f306(f306(f18(a1,a859,a859),f306(f306(f8(a859,f872(a859,a859),a1),a304),f306(f220(a1),f2(a1)))),x95081)),f306(f228(a1),f306(f306(f18(a1,a859,a859),f306(f306(f8(a859,f872(a859,a859),a1),a304),f306(f220(a1),f2(a1)))),x95082))) % 187.68/187.65 [7544]~P91(x75441)+~P62(x75441)+E(f306(f306(f264(x75441),x75442),f306(f111(x75441),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104))),x75442) % 187.68/187.65 [9200]~P91(x92001)+~E(f306(f111(x92001),x92002),f79(x92001))+P33(x92001,f306(f111(x92001),f306(f306(f81(a1),x92002),f306(f80(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104))))) % 187.68/187.65 [9381]~P140(x93811)+~E(x93812,f2(x93811))+E(f306(f306(f237(x93811),x93812),f306(f111(a865),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)))),f2(x93811)) % 187.68/187.65 [9382]~P140(x93821)+~E(x93822,f79(x93821))+E(f306(f306(f237(x93821),x93822),f306(f111(a865),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)))),f79(x93821)) % 187.68/187.65 [9395]~P140(x93951)+~E(x93952,f306(f80(x93951),f79(x93951)))+E(f306(f306(f237(x93951),x93952),f306(f111(a865),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)))),f79(x93951)) % 187.68/187.65 [9440]~P91(x94401)+E(f306(f111(x94401),x94402),f79(x94401))+~P33(x94401,f306(f111(x94401),f306(f306(f81(a1),x94402),f306(f80(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104))))) % 187.68/187.65 [9828]~P112(x98282)+E(x98281,f2(x98282))+P1(f306(f306(f221(x98282),f2(x98282)),f306(f306(f237(x98282),x98281),f306(f111(a865),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)))))) % 187.68/187.65 [9894]~P112(x98942)+~E(x98941,f2(x98942))+~P1(f306(f306(f221(x98942),f2(x98942)),f306(f306(f237(x98942),x98941),f306(f111(a865),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)))))) % 187.68/187.65 [9920]P1(f306(f306(f220(a1),x99201),f2(a1)))+P1(f306(f306(f221(a1),x99202),x99201))+E(f306(f45(x99201),f48(x99202,f306(f306(f82(a1),f306(f111(a1),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)))),x99201))),f48(x99202,x99201)) % 187.68/187.65 [9921]~P1(f306(f306(f221(a1),f2(a1)),x99211))+P1(f306(f306(f221(a1),x99212),x99211))+E(f306(f45(x99211),f48(x99212,f306(f306(f82(a1),f306(f111(a1),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)))),x99211))),f48(x99212,x99211)) % 187.68/187.65 [9922]P1(f306(f306(f220(a1),x99221),f2(a1)))+P1(f306(f306(f220(a1),f2(a1)),f306(f306(f81(a1),x99222),x99221)))+E(f306(f45(x99221),f51(x99222,f306(f306(f82(a1),f306(f111(a1),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)))),x99221))),f51(x99222,x99221)) % 187.68/187.65 [9923]~P1(f306(f306(f221(a1),f2(a1)),x99231))+P1(f306(f306(f220(a1),f2(a1)),f306(f306(f81(a1),x99232),x99231)))+E(f306(f45(x99231),f51(x99232,f306(f306(f82(a1),f306(f111(a1),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)))),x99231))),f51(x99232,x99231)) % 187.68/187.65 [9924]~P141(x99241)+~P1(f306(f306(f220(a1),f2(a1)),x99242))+E(f306(f107(x99241),f306(a112,f306(f306(f82(a1),f306(f111(a1),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)))),x99242))),f306(f306(f81(x99241),f306(f107(x99241),f306(a112,x99242))),f306(f107(x99241),f306(a112,x99242)))) % 187.68/187.65 [4995]~P145(x49951,x49952,x49953)+~E(x49953,f2(a1))+P1(f306(x49951,x49952)) % 187.68/187.65 [5122]~P108(x51221)+~P17(x51221,x51223)+P17(x51221,f162(x51221,x51222,x51223)) % 187.68/187.65 [5123]~P108(x51231)+~P17(x51231,x51233)+P17(x51231,f168(x51231,x51232,x51233)) % 187.68/187.65 [4698]~P67(x46982)+~E(x46983,f306(f80(x46982),x46981))+E(x46981,f306(f80(x46982),x46983)) % 187.68/187.65 [4700]~P67(x47001)+~E(f306(f80(x47001),x47003),x47002)+E(f306(f80(x47001),x47002),x47003) % 187.68/187.65 [4774]~P67(x47743)+E(x47741,x47742)+~E(f306(f80(x47743),x47741),f306(f80(x47743),x47742)) % 187.68/187.65 [4775]~P94(x47753)+E(x47751,x47752)+~E(f306(f80(x47753),x47751),f306(f80(x47753),x47752)) % 187.68/187.65 [4776]~P96(x47763)+E(x47761,x47762)+~E(f306(f107(x47763),x47761),f306(f107(x47763),x47762)) % 187.68/187.65 [4777]~P90(x47773)+E(x47771,x47772)+~E(f306(f110(x47773),x47771),f306(f110(x47773),x47772)) % 187.68/187.65 [4778]~P108(x47783)+E(x47781,x47782)+~E(f306(f275(x47783),x47781),f306(f275(x47783),x47782)) % 187.68/187.65 [4779]~P108(x47793)+E(x47791,x47792)+~E(f306(f229(x47793),x47791),f306(f229(x47793),x47792)) % 187.68/187.65 [4780]~P108(x47803)+E(x47801,x47802)+~E(f306(f230(x47803),x47801),f306(f230(x47803),x47802)) % 187.68/187.65 [4781]~P108(x47813)+E(x47811,x47812)+~E(f306(f278(x47813),x47811),f306(f278(x47813),x47812)) % 187.68/187.65 [4881]~P60(x48811)+~P1(f306(x48812,x48813))+P1(f306(f59(x48811),x48812)) % 187.68/187.65 [4915]~P60(x49153)+P1(f306(x49151,x49152))+~P1(f306(f60(x49153),x49151)) % 187.68/187.65 [5013]~P146(x50131,x50133,x50132)+~E(x50132,f2(a1))+P1(f306(x50131,f2(a1))) % 187.68/187.65 [5047]~P105(x50472)+~P1(f306(x50471,x50473))+P1(f306(x50471,f224(x50472,x50471))) % 187.68/187.65 [5054]~E(x50541,f2(a865))+E(f566(x50541,x50542,x50543),f185(f872(x50543,a859)))+~E(f306(f39(x50543),x50542),f306(a119,x50541)) % 187.68/187.65 [5211]~E(x52112,f2(a865))+E(f306(f235(a865,a865),x52111),f2(a865))+~P1(f306(f49(x52113,x52112),x52111)) % 187.68/187.65 [5256]P1(f306(x52561,x52562))+~E(x52563,f306(f107(a1),x52562))+~P1(f306(x52561,f306(a112,x52563))) % 187.68/187.65 [5728]~E(x57283,f2(a865))+~P1(f306(x57281,x57282))+P1(f306(x57281,f46(a865,x57282,x57283))) % 187.68/187.65 [5782]~P105(x57821)+~P1(f306(x57822,x57823))+~P1(f306(f306(f221(x57821),x57823),f224(x57821,x57822))) % 187.68/187.65 [5860]~P1(f306(a25,x58603))+~P1(f306(a25,x58602))+P1(f306(a25,f31(x58601,x58602,x58603))) % 187.68/187.65 [5892]~P60(x58923)+~P13(x58923,x58921,x58922)+P1(f306(x58921,f742(x58922,x58921,x58923))) % 187.68/187.65 [6139]~E(x61393,f2(a865))+P1(f306(x61391,x61392))+~P1(f306(x61391,f46(a865,x61392,x61393))) % 187.68/187.65 [6150]~P6(x61501)+~P1(f306(f306(f220(x61501),x61502),f306(x61503,x61502)))+P1(f306(f306(f220(x61501),x61502),f103(x61501,x61503))) % 187.68/187.65 [6288]~P60(x62881)+P14(x62881,x62882,x62883)+~P1(f306(x62882,f743(x62883,x62882,x62881))) % 187.68/187.65 [6625]E(x66251,f185(f872(x66252,a859)))+~P1(f306(f63(x66252),x66251))+P1(f306(f64(x66252,x66253,x66251),f519(x66253,x66251,x66252))) % 187.68/187.65 [6818]E(x68181,f2(a865))+~P1(f306(x68182,f317(x68181,x68183,x68182)))+P1(f306(x68182,f46(a865,x68183,x68181))) % 187.68/187.65 [6924]~P6(x69241)+~P1(f306(f306(f220(x69241),x69242),f611(x69243,x69242,x69241)))+P1(f306(f306(f220(x69241),x69242),f42(x69241,x69243))) % 187.68/187.65 [6926]~P1(f306(x69261,x69262))+~P1(f306(x69261,f317(x69263,x69262,x69261)))+P1(f306(x69261,f46(a865,x69262,x69263))) % 187.68/187.65 [7030]E(x70301,f120(x70302))+E(f306(f306(f143(x70302),f712(x70303,x70301,x70302)),f718(x70303,x70301,x70302)),x70301)+~P1(f306(f306(f308(f866(x70302)),x70301),f153(x70302,x70303))) % 187.68/187.65 [7061]~P125(x70611)+~P1(f306(f306(f308(x70611),x70612),f117(x70611)))+P1(f306(f306(f308(x70611),f306(f306(f237(x70611),x70612),x70613)),f117(x70611))) % 187.68/187.65 [7380]P40(x73801,x73802)+~P1(f306(f306(f308(x73801),x73803),f608(x73802,x73801)))+P1(f306(f306(f308(x73801),f654(x73802,x73801,x73803)),f608(x73802,x73801))) % 187.68/187.65 [7648]E(x76481,f120(x76482))+~P1(f306(f306(f308(f866(x76482)),x76481),f153(x76482,x76483)))+P1(f306(f306(f308(f866(x76482)),f718(x76483,x76481,x76482)),f153(x76482,x76483))) % 187.68/187.65 [7701]E(x77011,f2(a865))+E(f306(f306(f81(a865),f306(f306(f82(a865),x77011),f857(x77011,x77012,x77013))),f317(x77011,x77012,x77013)),x77012)+P1(f306(x77013,f46(a865,x77012,x77011))) % 187.68/187.65 [7744]~P1(f306(x77443,x77442))+E(f306(f306(f81(a865),f306(f306(f82(a865),x77441),f857(x77441,x77442,x77443))),f317(x77441,x77442,x77443)),x77442)+P1(f306(x77443,f46(a865,x77442,x77441))) % 187.68/187.65 [7885]P1(f306(f306(f221(a1),x78851),f851(x78852,x78853,x78851)))+P1(f306(f306(x78853,f306(f306(f40(a1),x78852),x78851)),f46(a1,x78852,x78851)))+~P1(f306(f306(f221(a1),x78851),f2(a1))) % 187.68/187.65 [8163]P1(f306(f306(x81632,f306(f306(f40(a1),x81631),x81633)),f46(a1,x81631,x81633)))+~P1(f306(f306(f221(a1),x81633),f2(a1)))+P1(f306(f306(f220(a1),f851(x81631,x81632,x81633)),f2(a1))) % 187.68/187.65 [8345]E(f306(f306(f81(a1),f306(f306(f82(a1),x83451),f852(x83452,x83453,x83451))),f851(x83452,x83453,x83451)),x83452)+P1(f306(f306(x83453,f306(f306(f40(a1),x83452),x83451)),f46(a1,x83452,x83451)))+~P1(f306(f306(f221(a1),x83451),f2(a1))) % 187.68/187.65 [8591]~P1(f306(f306(x85911,f852(x85912,x85911,x85913)),f851(x85912,x85911,x85913)))+P1(f306(f306(x85911,f306(f306(f40(a1),x85912),x85913)),f46(a1,x85912,x85913)))+~P1(f306(f306(f221(a1),x85913),f2(a1))) % 187.68/187.65 [8816]~P108(x88161)+~P17(x88161,x88163)+P17(x88161,f141(x88161,x88161,f5(x88161),x88162,x88163)) % 187.68/187.65 [9329]~P122(x93292)+E(x93291,f2(x93292))+~P1(f306(f306(f220(x93292),f306(f306(f81(x93292),f306(f306(f82(x93292),x93293),x93293)),f306(f306(f82(x93292),x93291),x93291))),f2(x93292))) % 187.68/187.65 [9330]~P122(x93302)+E(x93301,f2(x93302))+~P1(f306(f306(f220(x93302),f306(f306(f81(x93302),f306(f306(f82(x93302),x93301),x93301)),f306(f306(f82(x93302),x93303),x93303))),f2(x93302))) % 187.68/187.65 [10117]~P112(x101171)+~P1(f306(f306(f221(x101171),x101172),f2(x101171)))+P1(f306(f306(f221(x101171),f306(f306(f237(x101171),x101172),f306(a119,f306(f306(f82(a865),f306(f111(a865),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)))),x101173)))),f2(x101171))) % 187.68/187.65 [10127]~P112(x101272)+E(x101271,f2(x101272))+~P1(f306(f306(f220(x101272),f306(f306(f81(x101272),f306(f306(f237(x101272),x101273),f306(f111(a865),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104))))),f306(f306(f237(x101272),x101271),f306(f111(a865),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)))))),f2(x101272))) % 187.68/187.65 [10128]~P112(x101282)+E(x101281,f2(x101282))+~P1(f306(f306(f220(x101282),f306(f306(f81(x101282),f306(f306(f237(x101282),x101281),f306(f111(a865),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104))))),f306(f306(f237(x101282),x101283),f306(f111(a865),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)))))),f2(x101282))) % 187.68/187.65 [4730]~E(x47302,x47303)+~P67(x47301)+E(f306(f306(f22(x47301),x47302),x47303),f2(x47301)) % 187.68/187.65 [4731]~E(x47312,x47313)+~P68(x47311)+E(f306(f306(f22(x47311),x47312),x47313),f2(x47311)) % 187.68/187.65 [4744]~P143(x47441)+~E(x47443,f2(x47441))+E(f306(f306(f81(x47441),x47442),x47443),x47442) % 187.68/187.65 [4761]~P139(x47611)+~E(x47613,f2(x47611))+E(f306(f306(f82(x47611),x47612),x47613),f2(x47611)) % 187.68/187.65 [4762]~P139(x47621)+~E(x47622,f2(x47621))+E(f306(f306(f82(x47621),x47622),x47623),f2(x47621)) % 187.68/187.65 [4783]~E(x47833,f120(x47831))+~E(x47832,f120(x47831))+E(f306(f306(f122(x47831),x47832),x47833),f120(x47831)) % 187.68/187.65 [4871]~P143(x48712)+E(x48711,f2(x48712))+~E(f306(f306(f81(x48712),x48713),x48711),x48713) % 187.68/187.65 [4872]~P67(x48721)+~E(x48722,f306(f80(x48721),x48723))+E(f306(f306(f81(x48721),x48722),x48723),f2(x48721)) % 187.68/187.65 [4879]E(x48791,f120(x48792))+E(x48793,f2(a865))+~E(f306(f306(f165(x48792),x48793),x48791),f120(x48792)) % 187.68/187.65 [4885]~P67(x48853)+E(x48851,x48852)+~E(f306(f306(f22(x48853),x48851),x48852),f2(x48853)) % 187.68/187.65 [4886]~P68(x48863)+E(x48861,x48862)+~E(f306(f306(f22(x48863),x48861),x48862),f2(x48863)) % 187.68/187.65 [4896]~P140(x48962)+E(x48961,f2(x48962))+~E(f306(f306(f237(x48962),x48961),x48963),f2(x48962)) % 187.68/187.65 [4897]~P99(x48972)+E(x48971,f185(x48972))+~E(f306(f306(f108(x48972),x48973),x48971),f185(x48972)) % 187.68/187.65 [4898]~P99(x48982)+E(x48981,f185(x48982))+~E(f306(f306(f108(x48982),x48981),x48983),f185(x48982)) % 187.68/187.65 [4899]~P102(x48992)+E(x48991,f231(x48992))+~E(f306(f306(f109(x48992),x48993),x48991),f231(x48992)) % 187.68/187.65 [4900]~P102(x49002)+E(x49001,f231(x49002))+~E(f306(f306(f109(x49002),x49001),x49003),f231(x49002)) % 187.68/187.65 [4966]~P67(x49662)+E(x49661,f306(f80(x49662),x49663))+~E(f306(f306(f81(x49662),x49661),x49663),f2(x49662)) % 187.68/187.65 [4967]~P67(x49671)+E(f306(f80(x49671),x49672),x49673)+~E(f306(f306(f81(x49671),x49672),x49673),f2(x49671)) % 187.68/187.65 [4969]~E(x49692,x49693)+~P106(x49691)+P1(f306(f306(f220(x49691),x49692),x49693)) % 187.68/187.65 [4971]~E(x49712,x49713)+~P109(x49711)+P1(f306(f306(f220(x49711),x49712),x49713)) % 187.68/187.65 [4972]~E(x49722,x49723)+~P93(x49721)+P1(f306(f306(f92(x49721),x49722),x49723)) % 187.68/187.65 [5070]~P117(x50701)+~E(x50702,f306(f80(x50701),x50703))+E(f306(f306(f82(x50701),x50702),x50702),f306(f306(f82(x50701),x50703),x50703)) % 187.68/187.65 [5078]~P108(x50781)+~P17(x50781,x50783)+P17(x50781,f306(f306(f165(x50781),x50782),x50783)) % 187.68/187.65 [5079]~P108(x50791)+~P17(x50791,x50793)+P17(x50791,f306(f306(f130(x50791),x50792),x50793)) % 187.68/187.65 [5120]E(x51201,x51202)+E(x51203,f2(a865))+~E(f306(f306(f82(a865),x51203),x51201),f306(f306(f82(a865),x51203),x51202)) % 187.68/187.65 [5121]E(x51211,x51212)+E(x51213,f2(a865))+~E(f306(f306(f82(a865),x51211),x51213),f306(f306(f82(a865),x51212),x51213)) % 187.68/187.65 [5202]~E(x52022,x52023)+~P109(x52021)+E(f277(x52021,x52022,x52023),f306(f306(f284(x52021),x52022),f185(f872(x52021,a859)))) % 187.68/187.65 [5244]E(x52441,x52442)+~P93(x52443)+~P1(f306(f306(f92(x52443),x52441),x52442)) % 187.68/187.65 [5254]~E(x52541,x52542)+~P108(x52543)+~P1(f306(f306(f221(x52543),x52541),x52542)) % 187.68/187.65 [5255]~E(x52551,x52552)+~P109(x52553)+~P1(f306(f306(f221(x52553),x52551),x52552)) % 187.68/187.65 [5265]~P109(x52651)+E(f306(f276(x52651,x52652),x52653),f185(f872(x52651,a859)))+P1(f306(f306(f221(x52651),x52652),x52653)) % 187.68/187.65 [5313]~P109(x53131)+E(f279(x53131,x53132,x53133),f185(f872(x53131,a859)))+P1(f306(f306(f221(x53131),x53132),x53133)) % 187.68/187.65 [5314]~P109(x53141)+E(f277(x53141,x53142,x53143),f185(f872(x53141,a859)))+P1(f306(f306(f220(x53141),x53142),x53143)) % 187.68/187.65 [5315]~P109(x53151)+E(f185(f872(x53151,a859)),f279(x53151,x53152,x53153))+P1(f306(f306(f221(x53151),x53152),x53153)) % 187.68/187.65 [5316]~P109(x53161)+E(f185(f872(x53161,a859)),f277(x53161,x53162,x53163))+P1(f306(f306(f220(x53161),x53162),x53163)) % 187.68/187.65 [5324]~P108(x53241)+~E(f306(f306(f225(x53241),x53242),x53243),x53242)+P1(f306(f306(f220(x53241),x53242),x53243)) % 187.68/187.65 [5325]~P108(x53251)+~E(f306(f306(f219(x53251),x53252),x53253),x53253)+P1(f306(f306(f220(x53251),x53252),x53253)) % 187.68/187.65 [5326]~P97(x53261)+~E(f306(f306(f108(x53261),x53262),x53263),x53263)+P1(f306(f306(f220(x53261),x53262),x53263)) % 187.68/187.65 [5327]~P103(x53271)+~E(f306(f306(f109(x53271),x53272),x53273),x53272)+P1(f306(f306(f220(x53271),x53272),x53273)) % 187.68/187.65 [5347]~P108(x53471)+P17(x53471,x53472)+~P17(x53471,f306(f306(f143(x53471),x53473),x53472)) % 187.68/187.65 [5348]~P108(x53481)+P17(x53481,x53482)+~P17(x53481,f306(f306(f122(x53481),x53483),x53482)) % 187.68/187.65 [5349]~P108(x53491)+P17(x53491,x53492)+~P17(x53491,f306(f306(f122(x53491),x53492),x53493)) % 187.68/187.65 [5414]~P108(x54141)+P1(f306(f306(f220(x54141),x54143),x54142))+P1(f306(f306(f220(x54141),x54142),x54143)) % 187.68/187.65 [5419]~P108(x54191)+P1(f306(f306(f221(x54191),x54193),x54192))+P1(f306(f306(f220(x54191),x54192),x54193)) % 187.68/187.65 [5458]~P108(x54581)+E(f306(f306(f225(x54581),x54582),x54583),x54583)+~P1(f306(f306(f220(x54581),x54583),x54582)) % 187.68/187.65 [5460]~P108(x54601)+E(f306(f306(f225(x54601),x54602),x54603),x54602)+~P1(f306(f306(f220(x54601),x54602),x54603)) % 187.68/187.65 [5461]~P108(x54611)+E(f306(f306(f219(x54611),x54612),x54613),x54612)+~P1(f306(f306(f220(x54611),x54613),x54612)) % 187.68/187.65 [5463]~P108(x54631)+E(f306(f306(f219(x54631),x54632),x54633),x54633)+~P1(f306(f306(f220(x54631),x54632),x54633)) % 187.68/187.65 [5464]~P97(x54641)+E(f306(f306(f108(x54641),x54642),x54643),x54642)+~P1(f306(f306(f220(x54641),x54643),x54642)) % 187.68/187.65 [5466]~P97(x54661)+E(f306(f306(f108(x54661),x54662),x54663),x54663)+~P1(f306(f306(f220(x54661),x54662),x54663)) % 187.68/187.65 [5467]~P103(x54671)+E(f306(f306(f109(x54671),x54672),x54673),x54673)+~P1(f306(f306(f220(x54671),x54673),x54672)) % 187.68/187.65 [5469]~P103(x54691)+E(f306(f306(f109(x54691),x54692),x54693),x54692)+~P1(f306(f306(f220(x54691),x54692),x54693)) % 187.68/187.65 [5476]~P118(x54762)+E(x54761,f2(x54762))+E(f306(f306(f264(x54762),f306(f80(x54762),x54763)),f306(f80(x54762),x54761)),f306(f306(f264(x54762),x54763),x54761)) % 187.68/187.65 [5521]~P109(x55211)+E(f306(f276(x55211,x55212),x55213),f185(f872(x55211,a859)))+~P1(f306(f306(f220(x55211),x55213),x55212)) % 187.68/187.65 [5552]~P109(x55521)+E(f280(x55521,x55522,x55523),f185(f872(x55521,a859)))+~P1(f306(f306(f220(x55521),x55523),x55522)) % 187.68/187.65 [5553]~P109(x55531)+E(f279(x55531,x55532,x55533),f185(f872(x55531,a859)))+~P1(f306(f306(f220(x55531),x55533),x55532)) % 187.68/187.65 [5554]~P109(x55541)+E(f277(x55541,x55542,x55543),f185(f872(x55541,a859)))+~P1(f306(f306(f221(x55541),x55543),x55542)) % 187.68/187.65 [5595]~P105(x55951)+~P1(f306(x55952,x55953))+P1(f306(f306(f220(x55951),f224(x55951,x55952)),x55953)) % 187.68/187.65 [5606]~E(f306(f306(f22(a865),x56061),x56063),x56062)+E(x56061,f306(f306(f81(a865),x56062),x56063))+~P1(f306(f306(f220(a865),x56063),x56061)) % 187.68/187.65 [5607]~E(x56071,f306(f306(f81(a865),x56073),x56072))+E(f306(f306(f22(a865),x56071),x56072),x56073)+~P1(f306(f306(f220(a865),x56072),x56071)) % 187.68/187.65 [5653]~P1(f306(x56531,x56533))+P1(f306(x56531,f363(x56531,x56532)))+~P1(f306(f306(f220(a865),x56533),x56532)) % 187.68/187.65 [5654]~P1(f306(x56541,x56543))+P1(f306(x56541,f380(x56541,x56542)))+~P1(f306(f306(f221(a865),x56543),x56542)) % 187.68/187.65 [5662]~P109(x56621)+~E(f306(f276(x56621,x56622),x56623),f185(f872(x56621,a859)))+~P1(f306(f306(f221(x56621),x56622),x56623)) % 187.68/187.65 [5666]~P106(x56661)+~P1(f306(f306(f221(x56661),x56662),x56663))+P1(f306(f306(f220(x56661),x56662),x56663)) % 187.68/187.65 [5668]~P109(x56681)+~P1(f306(f306(f221(x56681),x56682),x56683))+P1(f306(f306(f220(x56681),x56682),x56683)) % 187.68/187.65 [5776]~P109(x57761)+~E(f279(x57761,x57762,x57763),f185(f872(x57761,a859)))+~P1(f306(f306(f221(x57761),x57762),x57763)) % 187.68/187.65 [5777]~P109(x57771)+~E(f277(x57771,x57772,x57773),f185(f872(x57771,a859)))+~P1(f306(f306(f220(x57771),x57772),x57773)) % 187.68/187.65 [5778]~P109(x57781)+~E(f185(f872(x57781,a859)),f279(x57781,x57782,x57783))+~P1(f306(f306(f221(x57781),x57782),x57783)) % 187.68/187.65 [5779]~P109(x57791)+~E(f185(f872(x57791,a859)),f277(x57791,x57792,x57793))+~P1(f306(f306(f220(x57791),x57792),x57793)) % 187.68/187.65 [5788]P1(f306(x57881,x57882))+~P1(f306(x57881,f364(x57881,x57883)))+~P1(f306(f306(f220(a865),x57882),x57883)) % 187.68/187.65 [5789]P1(f306(x57891,x57892))+~P1(f306(x57891,f404(x57891,x57893)))+~P1(f306(f306(f221(a865),x57892),x57893)) % 187.68/187.65 [5797]~E(x57971,f306(a119,x57973))+P1(f306(f306(f221(a865),x57971),f306(a119,x57972)))+~P1(f306(f306(f221(a865),x57973),x57972)) % 187.68/187.65 [5813]E(x58131,x58132)+~E(f306(f306(f82(a865),x58133),x58131),f306(f306(f82(a865),x58133),x58132))+~P1(f306(f306(f221(a865),f2(a865)),x58133)) % 187.68/187.65 [5871]E(f306(x58711,f410(x58711,x58712,x58713)),f79(a865))+~E(f306(f306(f6(x58713,a865),x58711),x58712),f79(a865))+~P1(f306(f63(x58713),x58712)) % 187.68/187.65 [5883]~P6(x58831)+P1(f306(f306(f220(x58831),x58832),f41(x58831,x58833)))+~P1(f306(f306(f308(x58831),x58832),x58833)) % 187.68/187.65 [5910]~P106(x59101)+~P1(f306(f306(f221(x59101),x59103),x59102))+~P1(f306(f306(f220(x59101),x59102),x59103)) % 187.68/187.65 [5914]~P106(x59141)+~P1(f306(f306(f221(x59141),x59143),x59142))+~P1(f306(f306(f221(x59141),x59142),x59143)) % 187.68/187.65 [5917]~P108(x59171)+~P1(f306(f306(f221(x59171),x59173),x59172))+~P1(f306(f306(f220(x59171),x59172),x59173)) % 187.68/187.65 [5918]~P108(x59181)+~P1(f306(f306(f221(x59181),x59183),x59182))+~P1(f306(f306(f221(x59181),x59182),x59183)) % 187.68/187.65 [5919]~P109(x59191)+~P1(f306(f306(f221(x59191),x59193),x59192))+~P1(f306(f306(f221(x59191),x59192),x59193)) % 187.68/187.65 [5950]~E(f306(x59502,f315(x59502,x59503,x59501)),f79(a865))+E(f306(f306(f9(x59501,a865),x59502),x59503),f79(a865))+~P1(f306(f63(x59501),x59503)) % 187.68/187.65 [5951]~E(f306(x59512,f411(x59512,x59513,x59511)),f2(a865))+E(f306(f306(f6(x59511,a865),x59512),x59513),f2(a865))+~P1(f306(f63(x59511),x59513)) % 187.68/187.65 [5966]~P107(x59661)+~P1(f306(f306(f220(x59661),x59663),x59662))+P1(f306(f306(f308(x59661),x59662),f306(f230(x59661),x59663))) % 187.68/187.65 [5967]~P107(x59671)+~P1(f306(f306(f221(x59671),x59673),x59672))+P1(f306(f306(f308(x59671),x59672),f306(f278(x59671),x59673))) % 187.68/187.65 [5968]~P107(x59681)+~P1(f306(f306(f220(x59681),x59682),x59683))+P1(f306(f306(f308(x59681),x59682),f306(f275(x59681),x59683))) % 187.68/187.65 [5969]~P107(x59691)+~P1(f306(f306(f221(x59691),x59692),x59693))+P1(f306(f306(f308(x59691),x59692),f306(f229(x59691),x59693))) % 187.68/187.65 [5981]E(f306(x59811,f413(x59811,x59812,x59813)),f306(a119,f2(a865)))+~E(f306(f306(f6(x59813,a865),x59811),x59812),f306(a119,f2(a865)))+~P1(f306(f63(x59813),x59812)) % 187.68/187.65 [6064]~P6(x60641)+~P1(f306(f306(f308(x60641),x60643),x60642))+P1(f306(f306(f220(x60641),f42(x60641,x60642)),x60643)) % 187.68/187.65 [6080]~P1(f306(f306(f220(a865),x60801),x60803))+P1(f306(f306(f220(a865),x60801),x60802))+~P1(f306(f306(f220(a865),x60803),x60802)) % 187.68/187.65 [6081]~P1(f306(f306(f220(a1),x60811),x60813))+P1(f306(f306(f220(a1),x60811),x60812))+~P1(f306(f306(f220(a1),x60813),x60812)) % 187.68/187.65 [6098]~P107(x60981)+~P1(f306(f306(f308(x60981),x60983),f306(f230(x60981),x60982)))+P1(f306(f306(f220(x60981),x60982),x60983)) % 187.68/187.65 [6099]~P107(x60991)+~P1(f306(f306(f308(x60991),x60992),f306(f275(x60991),x60993)))+P1(f306(f306(f220(x60991),x60992),x60993)) % 187.68/187.65 [6100]~P107(x61001)+~P1(f306(f306(f308(x61001),x61003),f306(f278(x61001),x61002)))+P1(f306(f306(f221(x61001),x61002),x61003)) % 187.68/187.65 [6101]~P107(x61011)+~P1(f306(f306(f308(x61011),x61012),f306(f229(x61011),x61013)))+P1(f306(f306(f221(x61011),x61012),x61013)) % 187.68/187.65 [6222]P1(f306(x62221,x62222))+~P1(f306(x62221,f543(x62221)))+~P1(f306(f306(f308(x62223),x62222),f231(f872(x62223,a859)))) % 187.68/187.65 [6287]~P109(x62871)+~P41(a865,x62871,x62872)+P1(f306(f306(f220(x62871),f306(x62872,x62873)),f306(x62872,f306(a119,x62873)))) % 187.68/187.65 [6324]~P63(x63241)+P1(f306(f306(f221(x63241),f2(x63241)),f425(x63243,x63242,x63241)))+P1(f306(f306(f220(x63241),x63242),x63243)) % 187.68/187.65 [6393]~P65(x63931)+~P1(f306(f306(f220(x63931),x63933),f306(f80(x63931),x63932)))+P1(f306(f306(f220(x63931),x63932),f306(f80(x63931),x63933))) % 187.68/187.65 [6395]~P65(x63951)+~P1(f306(f306(f221(x63951),x63953),f306(f80(x63951),x63952)))+P1(f306(f306(f221(x63951),x63952),f306(f80(x63951),x63953))) % 187.68/187.65 [6407]~P1(f306(f306(f221(a865),x64071),x64073))+~P1(f306(f306(f221(a865),x64073),x64072))+P1(f306(f306(f221(a865),f306(a119,x64071)),x64072)) % 187.68/187.65 [6433]~P111(x64331)+P1(f306(f306(f220(x64331),f306(f107(x64331),x64332)),f306(f107(x64331),x64333)))+~P1(f306(f306(f220(a865),x64332),x64333)) % 187.68/187.65 [6434]~P112(x64341)+P1(f306(f306(f220(x64341),f306(f110(x64341),x64342)),f306(f110(x64341),x64343)))+~P1(f306(f306(f220(a1),x64342),x64343)) % 187.68/187.65 [6436]~P112(x64361)+P1(f306(f306(f221(x64361),f306(f110(x64361),x64362)),f306(f110(x64361),x64363)))+~P1(f306(f306(f221(a1),x64362),x64363)) % 187.68/187.65 [6437]~P111(x64371)+P1(f306(f306(f221(x64371),f306(f107(x64371),x64372)),f306(f107(x64371),x64373)))+~P1(f306(f306(f221(a865),x64372),x64373)) % 187.68/187.65 [6443]~P108(x64431)+E(f306(f306(f108(f872(x64431,a859)),f306(f229(x64431),x64432)),f306(f276(x64431,x64432),x64433)),f306(f229(x64431),x64433))+~P1(f306(f306(f220(x64431),x64432),x64433)) % 187.68/187.65 [6472]~P65(x64721)+~P1(f306(f306(f220(x64721),x64723),x64722))+P1(f306(f306(f220(x64721),f306(f80(x64721),x64722)),f306(f80(x64721),x64723))) % 187.68/187.65 [6474]~P94(x64741)+~P1(f306(f306(f220(x64741),x64743),x64742))+P1(f306(f306(f220(x64741),f306(f80(x64741),x64742)),f306(f80(x64741),x64743))) % 187.68/187.65 [6475]~P65(x64751)+~P1(f306(f306(f221(x64751),x64753),x64752))+P1(f306(f306(f221(x64751),f306(f80(x64751),x64752)),f306(f80(x64751),x64753))) % 187.68/187.65 [6505]~P108(x65051)+E(f306(f306(f108(f872(x65051,a859)),f306(f275(x65051),x65052)),f280(x65051,x65052,x65053)),f306(f229(x65051),x65053))+~P1(f306(f306(f221(x65051),x65052),x65053)) % 187.68/187.65 [6506]~P108(x65061)+E(f306(f306(f108(f872(x65061,a859)),f306(f275(x65061),x65062)),f279(x65061,x65062,x65063)),f306(f275(x65061),x65063))+~P1(f306(f306(f220(x65061),x65062),x65063)) % 187.68/187.65 [6507]~P108(x65071)+E(f306(f306(f108(f872(x65071,a859)),f306(f229(x65071),x65072)),f277(x65071,x65072,x65073)),f306(f275(x65071),x65073))+~P1(f306(f306(f220(x65071),x65072),x65073)) % 187.68/187.65 [6543]~P108(x65431)+E(f306(f306(f108(f872(x65431,a859)),f306(f276(x65431,x65432),x65433)),f306(f230(x65431),x65433)),f306(f230(x65431),x65432))+~P1(f306(f306(f220(x65431),x65432),x65433)) % 187.68/187.65 [6611]~P6(x66111)+~P1(f306(f306(f220(x66111),f306(x66112,x66113)),x66113))+P1(f306(f306(f220(x66111),f102(x66111,x66112)),x66113)) % 187.68/187.65 [6702]~P108(x67021)+E(f306(f306(f108(f872(x67021,a859)),f280(x67021,x67022,x67023)),f306(f230(x67021),x67023)),f306(f278(x67021),x67022))+~P1(f306(f306(f221(x67021),x67022),x67023)) % 187.68/187.65 [6703]~P108(x67031)+E(f306(f306(f108(f872(x67031,a859)),f279(x67031,x67032,x67033)),f306(f278(x67031),x67033)),f306(f278(x67031),x67032))+~P1(f306(f306(f220(x67031),x67032),x67033)) % 187.68/187.65 [6704]~P108(x67041)+E(f306(f306(f108(f872(x67041,a859)),f277(x67041,x67042,x67043)),f306(f278(x67041),x67043)),f306(f230(x67041),x67042))+~P1(f306(f306(f220(x67041),x67042),x67043)) % 187.68/187.65 [6721]P1(f306(x67211,x67212))+~P1(f306(f306(f220(a865),x67212),x67213))+P1(f306(f306(f308(a865),f364(x67211,x67213)),f277(a865,f2(a865),x67213))) % 187.68/187.65 [6755]E(x67551,x67552)+~E(f306(f306(f157(x67553),x67551),f684(x67553,x67552,x67551)),f306(f306(f157(x67553),x67552),f684(x67553,x67552,x67551)))+~E(f306(f186(f866(x67553)),x67551),f306(f186(f866(x67553)),x67552)) % 187.68/187.65 [6760]~E(x67603,f306(f306(f40(a865),x67601),x67602))+~P1(f306(f306(f221(a865),f2(a865)),x67602))+P1(f306(f306(f221(a865),x67601),f306(f306(f82(a865),x67602),f306(a119,x67603)))) % 187.68/187.65 [6777]~P1(f306(x67771,x67773))+~P1(f306(f306(f220(a865),x67773),x67772))+P1(f306(f306(f308(a865),f363(x67771,x67772)),f277(a865,f2(a865),x67772))) % 187.68/187.65 [6815]~P1(f306(x68151,x68153))+P1(f306(x68151,f381(x68151,x68152)))+~P1(f306(f306(f308(a865),x68153),f277(a865,f2(a865),x68152))) % 187.68/187.65 [6834]~P111(x68343)+~P1(f306(f306(f220(x68343),f306(f107(x68343),x68341)),f306(f107(x68343),x68342)))+P1(f306(f306(f220(a865),x68341),x68342)) % 187.68/187.65 [6835]~P112(x68353)+~P1(f306(f306(f220(x68353),f306(f110(x68353),x68351)),f306(f110(x68353),x68352)))+P1(f306(f306(f220(a1),x68351),x68352)) % 187.68/187.65 [6837]~P111(x68373)+~P1(f306(f306(f221(x68373),f306(f107(x68373),x68371)),f306(f107(x68373),x68372)))+P1(f306(f306(f221(a865),x68371),x68372)) % 187.68/187.65 [6838]~P112(x68383)+~P1(f306(f306(f221(x68383),f306(f110(x68383),x68381)),f306(f110(x68383),x68382)))+P1(f306(f306(f221(a1),x68381),x68382)) % 187.68/187.65 [6852]~P111(x68521)+~P1(f306(f306(f221(x68521),f79(x68521)),x68522))+P1(f306(f306(f221(x68521),f79(x68521)),f306(f306(f237(x68521),x68522),f306(a119,x68523)))) % 187.68/187.65 [6855]~P65(x68551)+~P1(f306(f306(f220(x68551),f306(f80(x68551),x68553)),f306(f80(x68551),x68552)))+P1(f306(f306(f220(x68551),x68552),x68553)) % 187.68/187.65 [6856]~P94(x68561)+~P1(f306(f306(f220(x68561),f306(f80(x68561),x68563)),f306(f80(x68561),x68562)))+P1(f306(f306(f220(x68561),x68562),x68563)) % 187.68/187.65 [6857]~P65(x68571)+~P1(f306(f306(f221(x68571),f306(f80(x68571),x68573)),f306(f80(x68571),x68572)))+P1(f306(f306(f221(x68571),x68572),x68573)) % 187.68/187.65 [6883]P1(f306(x68831,x68832))+~P1(f306(x68831,f365(x68831,x68833)))+~P1(f306(f306(f308(a865),x68832),f277(a865,f2(a865),x68833))) % 187.68/187.65 [6902]~P63(x69021)+P1(f306(f306(f221(x69021),f425(x69023,x69022,x69021)),f79(x69021)))+P1(f306(f306(f220(x69021),x69022),x69023)) % 187.68/187.65 [6921]~E(f46(a865,x69213,x69212),f46(a865,x69211,x69212))+E(f306(f306(f81(a865),x69211),f306(f306(f82(a865),x69212),f555(x69211,x69212,x69213))),x69213)+~P1(f306(f306(f220(a865),x69211),x69213)) % 187.68/187.65 [6940]E(f306(x69401,f556(x69401,x69402,x69403)),f188(x69402))+~P1(f306(f63(x69403),f175(x69403,x69402,x69401)))+P1(f306(f63(x69403),f231(f872(x69403,a859)))) % 187.68/187.65 [6981]E(f306(f306(f9(x69811,a865),x69812),x69813),f79(a865))+~P1(f306(f63(x69811),x69813))+P1(f306(f306(f308(x69811),f315(x69812,x69813,x69811)),x69813)) % 187.68/187.65 [6982]E(f306(f306(f6(x69821,a865),x69822),x69823),f2(a865))+~P1(f306(f63(x69821),x69823))+P1(f306(f306(f308(x69821),f411(x69822,x69823,x69821)),x69823)) % 187.68/187.65 [7004]~P109(x70041)+~P1(f306(f306(f220(x70041),x70042),x70043))+P1(f306(f306(f220(f872(x70041,a859)),f306(f275(x70041),x70042)),f306(f275(x70041),x70043))) % 187.68/187.65 [7005]~P108(x70051)+~P1(f306(f306(f220(x70051),x70052),x70053))+P1(f306(f306(f220(f872(x70051,a859)),f306(f229(x70051),x70052)),f306(f229(x70051),x70053))) % 187.68/187.65 [7006]~P109(x70061)+~P1(f306(f306(f220(x70061),x70063),x70062))+P1(f306(f306(f220(f872(x70061,a859)),f306(f230(x70061),x70062)),f306(f230(x70061),x70063))) % 187.68/187.65 [7007]~P108(x70071)+~P1(f306(f306(f220(x70071),x70073),x70072))+P1(f306(f306(f220(f872(x70071,a859)),f306(f278(x70071),x70072)),f306(f278(x70071),x70073))) % 187.68/187.65 [7008]~P108(x70081)+~P1(f306(f306(f221(x70081),x70082),x70083))+P1(f306(f306(f221(f872(x70081,a859)),f306(f229(x70081),x70082)),f306(f229(x70081),x70083))) % 187.68/187.65 [7016]~P6(x70161)+P1(f306(f306(f220(x70161),x70162),f42(x70161,x70163)))+P1(f306(f306(f308(x70161),f611(x70163,x70162,x70161)),x70163)) % 187.68/187.65 [7022]~P65(x70221)+P1(f306(f306(f220(x70221),f306(f306(f22(x70221),x70222),x70223)),f2(x70221)))+~P1(f306(f306(f220(x70221),x70222),x70223)) % 187.68/187.65 [7023]~P65(x70231)+P1(f306(f306(f221(x70231),f306(f306(f22(x70231),x70232),x70233)),f2(x70231)))+~P1(f306(f306(f221(x70231),x70232),x70233)) % 187.68/187.65 [7065]P1(f306(x70651,x70652))+P1(f306(f306(f220(a865),f365(x70651,x70653)),x70653))+~P1(f306(f306(f308(a865),x70652),f277(a865,f2(a865),x70653))) % 187.68/187.65 [7105]~E(f306(f306(f6(x71051,a865),x71052),x71053),f79(a865))+~P1(f306(f63(x71051),x71053))+P1(f306(f306(f308(x71051),f410(x71052,x71053,x71051)),x71053)) % 187.68/187.65 [7106]~P1(f306(x71061,x71063))+P1(f306(f306(f220(a865),f381(x71061,x71062)),x71062))+~P1(f306(f306(f308(a865),x71063),f277(a865,f2(a865),x71062))) % 187.68/187.65 [7146]~P6(x71461)+P1(f306(f306(f308(x71461),f632(x71463,x71462,x71461)),x71462))+P1(f306(f306(f220(x71461),f41(x71461,x71462)),x71463)) % 187.68/187.65 [7177]~E(f306(f306(f6(x71771,a865),x71772),x71773),f306(a119,f2(a865)))+~P1(f306(f63(x71771),x71773))+P1(f306(f306(f308(x71771),f413(x71772,x71773,x71771)),x71773)) % 187.68/187.65 [7188]E(x71881,f2(a865))+P1(f306(x71882,f46(a865,x71883,x71881)))+P1(f306(f306(f221(a865),f317(x71881,x71883,x71882)),x71881)) % 187.68/187.65 [7292]~P1(f306(x72921,x72922))+P1(f306(x72921,f46(a865,x72922,x72923)))+P1(f306(f306(f221(a865),f317(x72923,x72922,x72921)),x72923)) % 187.68/187.65 [7415]E(x74151,f120(x74152))+~P1(f306(f306(f308(f866(x74152)),x74151),f153(x74152,x74153)))+P1(f306(f306(f308(x74152),f712(x74153,x74151,x74152)),x74153)) % 187.68/187.65 [7437]~P108(x74371)+E(f306(f306(f108(f872(x74371,a859)),f306(f306(f284(x74371),x74372),f185(f872(x74371,a859)))),f280(x74371,x74372,x74373)),f306(f276(x74371,x74372),x74373))+~P1(f306(f306(f221(x74371),x74372),x74373)) % 187.68/187.65 [7460]~P108(x74601)+E(f306(f306(f108(f872(x74601,a859)),f306(f306(f284(x74601),x74602),f185(f872(x74601,a859)))),f279(x74601,x74602,x74603)),f277(x74601,x74602,x74603))+~P1(f306(f306(f220(x74601),x74602),x74603)) % 187.68/187.65 [7566]~P108(x75661)+P1(f306(f306(f220(x75661),x75662),x75663))+~P1(f306(f306(f220(f872(x75661,a859)),f306(f278(x75661),x75663)),f306(f278(x75661),x75662))) % 187.68/187.65 [7567]~P109(x75671)+P1(f306(f306(f220(x75671),x75672),x75673))+~P1(f306(f306(f220(f872(x75671,a859)),f306(f230(x75671),x75673)),f306(f230(x75671),x75672))) % 187.68/187.65 [7568]~P108(x75681)+P1(f306(f306(f220(x75681),x75682),x75683))+~P1(f306(f306(f220(f872(x75681,a859)),f306(f229(x75681),x75682)),f306(f229(x75681),x75683))) % 187.68/187.65 [7569]~P109(x75691)+P1(f306(f306(f220(x75691),x75692),x75693))+~P1(f306(f306(f220(f872(x75691,a859)),f306(f275(x75691),x75692)),f306(f275(x75691),x75693))) % 187.68/187.65 [7570]~P108(x75701)+P1(f306(f306(f221(x75701),x75702),x75703))+~P1(f306(f306(f221(f872(x75701,a859)),f306(f229(x75701),x75702)),f306(f229(x75701),x75703))) % 187.68/187.65 [7593]~P65(x75931)+~P1(f306(f306(f220(x75931),f306(f306(f22(x75931),x75932),x75933)),f2(x75931)))+P1(f306(f306(f220(x75931),x75932),x75933)) % 187.68/187.65 [7594]~P65(x75941)+~P1(f306(f306(f221(x75941),f306(f306(f22(x75941),x75942),x75943)),f2(x75941)))+P1(f306(f306(f221(x75941),x75942),x75943)) % 187.68/187.65 [7751]E(x77511,f2(a865))+~E(f306(f134(a865,a865,f81(a865),x77512),x77513),f2(a865))+~P1(f306(f306(f308(a865),x77511),f306(f164(a865),x77513))) % 187.68/187.65 [7755]~P6(x77551)+~P1(f306(f306(f220(x77551),f632(x77553,x77552,x77551)),x77553))+P1(f306(f306(f220(x77551),f41(x77551,x77552)),x77553)) % 187.68/187.65 [7910]P1(f306(f306(f220(a1),f2(a1)),f853(x79101,x79102,x79103)))+P1(f306(f306(x79102,f306(f306(f40(a1),x79101),x79103)),f46(a1,x79101,x79103)))+~P1(f306(f306(f221(a1),f2(a1)),x79103)) % 187.68/187.65 [8004]E(x80041,x80042)+~E(f306(f186(f866(x80043)),x80041),f306(f186(f866(x80043)),x80042))+~P1(f306(f306(f245(x80043,x80043,a859),a303),f672(x80043,x80041,x80042))) % 187.68/187.65 [8073]~P40(x80732,x80733)+E(x80731,f185(f872(x80732,a859)))+~P1(f306(f306(f220(f872(x80732,a859)),x80731),f306(f260(x80732,x80732,x80733),x80731))) % 187.68/187.65 [8144]P50(x81441,x81442,x81443)+P1(f306(f306(f308(x81441),f540(x81443,x81442,x81441)),x81442))+P1(f306(f306(f308(f871(x81441,x81441)),f541(x81443,x81442,x81441)),x81443)) % 187.68/187.65 [8167]P1(f306(f306(x81672,f306(f306(f40(a1),x81671),x81673)),f46(a1,x81671,x81673)))+~P1(f306(f306(f221(a1),f2(a1)),x81673))+P1(f306(f306(f221(a1),f853(x81671,x81672,x81673)),x81673)) % 187.68/187.65 [8191]E(f306(f285(a865,a865,f306(f306(f7(a865,a865,a865),f22(a865)),x81911)),f306(f276(a865,x81912),x81913)),f185(f872(a865,a859)))+P1(f306(f306(f221(a865),x81911),x81913))+P1(f306(f306(f221(a865),x81912),x81913)) % 187.68/187.65 [8298]E(f306(f285(a865,a865,f306(f306(f7(a865,a865,a865),f22(a865)),x82981)),f306(f276(a865,x82982),x82983)),f306(f306(f284(a865),f2(a865)),f185(f872(a865,a859))))+P1(f306(f306(f221(a865),x82981),x82983))+~P1(f306(f306(f221(a865),x82982),x82983)) % 187.68/187.65 [8315]~P108(x83151)+E(f141(x83151,x83151,f5(x83151),x83152,x83153),x83153)+~P1(f306(f306(f308(x83151),x83152),f306(f164(x83151),x83153))) % 187.68/187.65 [8329]P28(x83291,x83291,x83292,x83293)+~P1(f306(f63(x83291),x83293))+~P1(f306(f306(f220(f872(x83291,a859)),x83293),f306(f285(x83291,x83291,x83292),x83293))) % 187.68/187.65 [8353]E(f306(f306(f81(a1),f306(f306(f82(a1),x83531),f854(x83532,x83533,x83531))),f853(x83532,x83533,x83531)),x83532)+P1(f306(f306(x83533,f306(f306(f40(a1),x83532),x83531)),f46(a1,x83532,x83531)))+~P1(f306(f306(f221(a1),f2(a1)),x83531)) % 187.68/187.65 [8597]~P1(f306(f306(x85971,f854(x85972,x85971,x85973)),f853(x85972,x85971,x85973)))+P1(f306(f306(x85971,f306(f306(f40(a1),x85972),x85973)),f46(a1,x85972,x85973)))+~P1(f306(f306(f221(a1),f2(a1)),x85973)) % 187.68/187.65 [9469]~P1(f306(f63(x94691),x94692))+~P1(f306(f306(f308(x94691),x94693),x94692))+P1(f306(f306(f221(a865),f306(f39(x94691),f306(f306(f22(f872(x94691,a859)),x94692),f306(f306(f284(x94691),x94693),f185(f872(x94691,a859)))))),f306(f39(x94691),x94692))) % 187.68/187.65 [10075]P50(x100751,x100752,x100753)+~P1(f306(f306(f245(x100751,x100751,a859),f306(f306(f7(x100751,f872(x100751,a859),f872(x100751,a859)),f306(f306(f8(f872(a859,a859),f872(f872(x100751,a859),f872(x100751,a859)),x100751),f8(a859,a859,x100751)),f306(f306(f8(a859,f872(a859,a859),x100751),a304),f306(f306(f7(x100751,f872(x100751,a859),a859),f308(x100751)),x100752)))),f306(f306(f7(x100751,f872(x100751,a859),a859),f308(x100751)),x100752))),f541(x100753,x100752,x100751)))+P1(f306(f306(f308(x100751),f540(x100753,x100752,x100751)),x100752)) % 187.68/187.65 [5436]~P118(x54362)+E(x54361,f2(x54362))+E(f306(f306(f264(x54362),x54363),f306(f80(x54362),x54361)),f306(f80(x54362),f306(f306(f264(x54362),x54363),x54361))) % 187.68/187.65 [5568]~E(x55683,f185(f872(x55681,a859)))+~E(x55682,f185(f872(x55681,a859)))+E(f306(f306(f108(f872(x55681,a859)),x55682),x55683),f185(f872(x55681,a859))) % 187.68/187.65 [5627]~E(x56273,f2(a865))+~P1(f306(x56271,f2(a865)))+P1(f306(x56271,f306(f306(f40(a865),x56272),x56273))) % 187.68/187.65 [5768]~P64(x57682)+E(x57681,f2(x57682))+E(f306(f306(f264(x57682),f306(f76(x57682),x57683)),f306(f76(x57682),x57681)),f306(f76(x57682),f306(f306(f264(x57682),x57683),x57681))) % 187.68/187.65 [5937]~P1(f306(f63(x59371),x59373))+E(f306(f39(x59371),f306(f306(f284(x59371),x59372),x59373)),f306(a119,f306(f39(x59371),x59373)))+P1(f306(f306(f308(x59371),x59372),x59373)) % 187.68/187.65 [6013]~E(x60132,f2(a865))+P1(f306(x60131,f2(a865)))+~P1(f306(x60131,f306(f306(f40(a865),x60133),x60132))) % 187.68/187.65 [6032]~P1(f306(f63(x60321),x60323))+E(f306(f39(x60321),f306(f306(f284(x60321),x60322),x60323)),f306(f39(x60321),x60323))+~P1(f306(f306(f308(x60321),x60322),x60323)) % 187.68/187.65 [6066]~P1(f306(f63(x60661),x60663))+E(f306(f39(x60661),f306(f306(f284(x60661),x60662),x60663)),f306(f306(f81(a865),f79(a865)),f306(f39(x60661),x60663)))+P1(f306(f306(f308(x60661),x60662),x60663)) % 187.68/187.65 [6184]E(f306(f306(f81(a865),x61841),f744(x61841,x61842,x61843)),x61842)+~P1(f306(x61843,f2(a865)))+P1(f306(x61843,f306(f306(f22(a865),x61842),x61841))) % 187.68/187.65 [6185]E(f306(f306(f81(a865),x61851),f749(x61851,x61852,x61853)),x61852)+~P1(f306(x61853,f2(a865)))+P1(f306(x61853,f306(f306(f22(a865),x61852),x61851))) % 187.68/187.65 [6232]~P6(x62321)+~P1(f306(f63(x62321),x62323))+E(f306(f306(f66(x62321,x62321,f108(x62321)),x62322),x62323),f306(f306(f108(x62321),x62322),f41(x62321,x62323))) % 187.68/187.65 [6233]~P6(x62331)+~P1(f306(f63(x62331),x62333))+E(f306(f306(f66(x62331,x62331,f109(x62331)),x62332),x62333),f306(f306(f109(x62331),x62332),f42(x62331,x62333))) % 187.68/187.65 [6239]~P91(x62391)+~E(f306(f111(x62391),x62392),f306(f111(x62391),x62393))+P33(x62391,f306(f111(x62391),f306(f306(f81(a1),x62392),f306(f80(a1),x62393)))) % 187.68/187.65 [6246]~P125(x62461)+E(f306(f306(f22(x62461),f306(f107(x62461),x62462)),f306(f107(x62461),x62463)),f306(f107(x62461),f306(f306(f22(a865),x62462),x62463)))+~P1(f306(f306(f220(a865),x62463),x62462)) % 187.68/187.65 [6334]E(f306(f306(f81(a865),x63341),f744(x63341,x63342,x63343)),x63342)+P1(f306(f306(f221(a865),x63342),x63341))+P1(f306(x63343,f306(f306(f22(a865),x63342),x63341))) % 187.68/187.65 [6335]E(f306(f306(f81(a865),x63351),f749(x63351,x63352,x63353)),x63352)+P1(f306(f306(f221(a865),x63352),x63351))+P1(f306(x63353,f306(f306(f22(a865),x63352),x63351))) % 187.68/187.65 [6352]~P112(x63521)+E(f306(f306(f82(x63521),f306(f76(x63521),x63522)),x63523),f306(f76(x63521),f306(f306(f82(x63521),x63522),x63523)))+~P1(f306(f306(f220(x63521),f2(x63521)),x63523)) % 187.68/187.65 [6353]~P63(x63531)+E(f306(f306(f264(x63531),f306(f76(x63531),x63532)),x63533),f306(f76(x63531),f306(f306(f264(x63531),x63532),x63533)))+~P1(f306(f306(f221(x63531),f2(x63531)),x63533)) % 187.68/187.65 [6361]~P108(x63611)+~P1(f306(f63(x63611),x63613))+E(f306(f306(f66(x63611,x63611,f225(x63611)),x63612),x63613),f14(x63611,f306(f306(f284(x63611),x63612),x63613))) % 187.68/187.65 [6362]~P108(x63621)+~P1(f306(f63(x63621),x63623))+E(f306(f306(f66(x63621,x63621,f219(x63621)),x63622),x63623),f15(x63621,f306(f306(f284(x63621),x63622),x63623))) % 187.68/187.65 [6363]~P98(x63631)+~P1(f306(f63(x63631),x63633))+E(f306(f306(f66(x63631,x63631,f108(x63631)),x63632),x63633),f13(x63631,f306(f306(f284(x63631),x63632),x63633))) % 187.68/187.65 [6364]~P98(x63641)+~P1(f306(f63(x63641),x63643))+E(f306(f306(f66(x63641,x63641,f109(x63641)),x63642),x63643),f10(x63641,f306(f306(f284(x63641),x63642),x63643))) % 187.68/187.65 [6409]E(x64091,f120(x64092))+~E(f171(x64092,x64093),f120(f866(x64092)))+~P1(f306(f306(f308(f866(x64092)),x64091),f306(f164(f866(x64092)),x64093))) % 187.68/187.65 [6451]~P1(f306(f129(x64511),x64513))+P1(f306(f306(f308(x64511),x64512),f306(f164(x64511),x64513)))+P1(f306(f129(x64511),f306(f306(f143(x64511),x64512),x64513))) % 187.68/187.65 [6462]~P95(x64621)+~P1(f306(f63(x64621),x64623))+E(f306(f65(x64621,f82(x64621)),f306(f306(f284(x64621),x64622),x64623)),f306(f306(f66(x64621,x64621,f82(x64621)),x64622),x64623)) % 187.68/187.65 [6483]~P108(x64831)+~P1(f306(f63(x64831),x64833))+E(f11(x64831,f225(x64831),f306(f306(f284(x64831),x64832),x64833)),f306(f306(f66(x64831,x64831,f225(x64831)),x64832),x64833)) % 187.68/187.65 [6484]~P108(x64841)+~P1(f306(f63(x64841),x64843))+E(f12(x64841,f219(x64841),f306(f306(f284(x64841),x64842),x64843)),f306(f306(f66(x64841,x64841,f219(x64841)),x64842),x64843)) % 187.68/187.65 [6486]P1(f306(x64861,f2(a865)))+~P1(f306(f306(f221(a865),x64862),x64863))+~P1(f306(x64861,f306(f306(f22(a865),x64862),x64863))) % 187.68/187.65 [6503]~P84(x65031)+P1(f306(f306(f220(x65031),x65032),x65033))+~P1(f306(f306(f220(x65031),f306(f76(x65031),x65032)),x65033)) % 187.68/187.65 [6504]~P112(x65041)+P1(f306(f306(f221(x65041),x65042),x65043))+~P1(f306(f306(f221(x65041),f306(f76(x65041),x65042)),x65043)) % 187.68/187.65 [6521]E(x65211,f120(x65212))+E(f306(f133(x65212),f306(f306(f130(x65212),x65213),x65211)),f306(f306(f157(x65212),x65211),x65213))+~P1(f306(f306(f221(a865),x65213),f306(f186(f866(x65212)),x65211))) % 187.68/187.65 [6574]~P1(f306(x65741,x65743))+P1(f306(x65741,f405(x65741,x65742)))+~P1(f306(f306(f308(a865),x65743),f306(f276(a865,f2(a865)),x65742))) % 187.68/187.65 [6596]P1(f306(x65961,x65962))+~P1(f306(f306(f221(a865),x65962),x65963))+P1(f306(f306(f308(a865),f404(x65961,x65963)),f306(f276(a865,f2(a865)),x65963))) % 187.68/187.65 [6613]~P111(x66131)+~P1(f306(f306(f220(x66131),f2(x66131)),x66132))+P1(f306(f306(f220(x66131),f2(x66131)),f306(f306(f237(x66131),x66132),x66133))) % 187.68/187.65 [6614]~P111(x66141)+~P1(f306(f306(f220(x66141),f79(x66141)),x66142))+P1(f306(f306(f220(x66141),f79(x66141)),f306(f306(f237(x66141),x66142),x66143))) % 187.68/187.65 [6616]~P111(x66161)+~P1(f306(f306(f221(x66161),f2(x66161)),x66162))+P1(f306(f306(f221(x66161),f2(x66161)),f306(f306(f237(x66161),x66162),x66163))) % 187.68/187.65 [6641]~P1(f306(x66411,x66413))+~P1(f306(f306(f221(a865),x66413),x66412))+P1(f306(f306(f308(a865),f380(x66411,x66412)),f306(f276(a865,f2(a865)),x66412))) % 187.68/187.65 [6650]P1(f306(f63(x66501),x66502))+~P1(f306(f63(x66501),x66503))+~P1(f306(f306(f220(f872(x66501,a859)),x66502),x66503)) % 187.68/187.65 [6658]P1(f306(x66581,x66582))+~P1(f306(x66581,f406(x66581,x66583)))+~P1(f306(f306(f308(a865),x66582),f306(f276(a865,f2(a865)),x66583))) % 187.68/187.65 [6669]E(x66691,f2(a865))+P1(f306(x66692,f316(x66691,x66693,x66692)))+~P1(f306(x66692,f306(f306(f40(a865),x66693),x66691))) % 187.68/187.65 [6677]~P122(x66772)+E(x66771,f2(x66772))+~E(f306(f306(f81(x66772),f306(f306(f82(x66772),x66773),x66773)),f306(f306(f82(x66772),x66771),x66771)),f2(x66772)) % 187.68/187.65 [6678]~P122(x66782)+E(x66781,f2(x66782))+~E(f306(f306(f81(x66782),f306(f306(f82(x66782),x66781),x66781)),f306(f306(f82(x66782),x66783),x66783)),f2(x66782)) % 187.68/187.65 [6722]E(x67221,f2(a865))+~P1(f306(x67222,f855(x67221,x67223,x67222)))+P1(f306(x67222,f306(f306(f40(a865),x67223),x67221))) % 187.68/187.65 [6727]~P108(x67271)+~P17(x67271,x67273)+P17(x67271,f306(f306(f140(x67271,x67271,f5(x67271)),x67272),x67273)) % 187.68/187.65 [6770]P1(f306(x67701,f316(x67702,x67703,x67701)))+P1(f306(x67701,f2(a865)))+~P1(f306(x67701,f306(f306(f40(a865),x67703),x67702))) % 187.68/187.65 [6776]~P91(x67761)+E(f306(f111(x67761),x67762),f306(f111(x67761),x67763))+~P33(x67761,f306(f111(x67761),f306(f306(f81(a1),x67762),f306(f80(a1),x67763)))) % 187.68/187.65 [6841]E(x68411,f2(a1))+E(x68412,f2(a1))+~P1(f306(f50(x68412,x68412),f306(f306(f236(a1,a1),x68413),x68411))) % 187.68/187.65 [6842]E(x68421,f79(a1))+E(x68422,f2(a1))+~P1(f306(f50(x68422,x68422),f306(f306(f236(a1,a1),x68421),x68423))) % 187.68/187.65 [6853]P1(f306(x68531,x68532))+P1(f306(f306(f221(a865),f406(x68531,x68533)),x68533))+~P1(f306(f306(f308(a865),x68532),f306(f276(a865,f2(a865)),x68533))) % 187.68/187.65 [6878]~P1(f306(x68781,f744(x68783,x68782,x68781)))+~P1(f306(x68781,f2(a865)))+P1(f306(x68781,f306(f306(f22(a865),x68782),x68783))) % 187.68/187.65 [6879]~P1(f306(x68791,f749(x68793,x68792,x68791)))+~P1(f306(x68791,f2(a865)))+P1(f306(x68791,f306(f306(f22(a865),x68792),x68793))) % 187.68/187.65 [6880]~P1(f306(x68801,f855(x68803,x68802,x68801)))+~P1(f306(x68801,f2(a865)))+P1(f306(x68801,f306(f306(f40(a865),x68802),x68803))) % 187.68/187.65 [6898]~P1(f306(x68981,x68983))+P1(f306(f306(f221(a865),f405(x68981,x68982)),x68982))+~P1(f306(f306(f308(a865),x68983),f306(f276(a865,f2(a865)),x68982))) % 187.68/187.65 [6899]E(f306(f306(f22(a865),f306(f306(f22(a865),x68991),x68992)),f306(f306(f22(a865),x68993),x68992)),f306(f306(f22(a865),x68991),x68993))+~P1(f306(f306(f220(a865),x68992),x68991))+~P1(f306(f306(f220(a865),x68992),x68993)) % 187.68/187.65 [6934]~P65(x69341)+~P1(f306(f306(f220(x69341),f306(f80(x69341),x69343)),x69342))+P1(f306(f306(f220(x69341),f306(f80(x69341),x69342)),x69343)) % 187.68/187.65 [6936]~P84(x69361)+~P1(f306(f306(f220(x69361),f306(f76(x69361),x69362)),x69363))+P1(f306(f306(f220(x69361),f306(f80(x69361),x69362)),x69363)) % 187.68/187.65 [6938]~P65(x69381)+~P1(f306(f306(f221(x69381),f306(f80(x69381),x69383)),x69382))+P1(f306(f306(f221(x69381),f306(f80(x69381),x69382)),x69383)) % 187.68/187.65 [6939]~P112(x69391)+~P1(f306(f306(f221(x69391),f306(f76(x69391),x69392)),x69393))+P1(f306(f306(f221(x69391),f306(f80(x69391),x69392)),x69393)) % 187.68/187.65 [6975]~P1(f306(x69753,f744(x69752,x69751,x69753)))+P1(f306(f306(f221(a865),x69751),x69752))+P1(f306(x69753,f306(f306(f22(a865),x69751),x69752))) % 187.68/187.65 [6976]~P1(f306(x69763,f749(x69762,x69761,x69763)))+P1(f306(f306(f221(a865),x69761),x69762))+P1(f306(x69763,f306(f306(f22(a865),x69761),x69762))) % 187.68/187.65 [7026]~E(f640(x70263,x70262,x70261),f641(x70263,x70262,x70261))+E(f306(f306(f109(f872(x70261,a859)),x70262),f41(f872(x70261,a859),x70263)),f185(f872(x70261,a859)))+P1(f306(f306(f308(f872(x70261,a859)),x70262),x70263)) % 187.68/187.65 [7035]~P1(f306(f63(x70351),x70353))+P1(f306(f63(x70351),f42(f872(x70351,a859),x70352)))+~P1(f306(f306(f308(f872(x70351,a859)),x70353),x70352)) % 187.68/187.65 [7094]~P108(x70941)+E(f306(f306(f108(f872(x70941,a859)),f306(f276(x70941,x70942),x70943)),f306(f306(f284(x70941),x70943),f185(f872(x70941,a859)))),f277(x70941,x70942,x70943))+~P1(f306(f306(f220(x70941),x70942),x70943)) % 187.68/187.65 [7095]E(x70951,f2(a865))+P1(f306(f306(f221(a865),f856(x70951,x70953,x70952)),x70951))+P1(f306(x70952,f306(f306(f40(a865),x70953),x70951))) % 187.68/187.65 [7130]E(x71301,x71302)+~P1(f306(f306(f220(f872(x71303,a859)),x71301),x71302))+P1(f306(f306(f221(f872(x71303,a859)),x71301),x71302)) % 187.68/187.65 [7143]E(x71431,x71432)+~E(f306(f186(f866(x71433)),x71431),f306(f186(f866(x71433)),x71432))+P1(f306(f306(f221(a865),f684(x71433,x71431,x71432)),f306(f186(f866(x71433)),x71432))) % 187.68/187.65 [7189]P9(x71891,x71892,x71893)+~E(f306(f234(x71891,x71891),x71893),x71892)+~E(f306(f306(f263(x71891,x71891,x71891),f306(f261(x71891,x71891),x71893)),x71893),x71893) % 187.68/187.65 [7261]~P1(f306(x72611,f2(a865)))+P1(f306(f306(f221(a865),f856(x72613,x72612,x72611)),x72613))+P1(f306(x72611,f306(f306(f40(a865),x72612),x72613))) % 187.68/187.65 [7270]~P108(x72701)+E(f306(f306(f108(f872(x72701,a859)),f280(x72701,x72702,x72703)),f306(f306(f284(x72701),x72703),f185(f872(x72701,a859)))),f279(x72701,x72702,x72703))+~P1(f306(f306(f221(x72701),x72702),x72703)) % 187.68/187.65 [7369]~P1(f306(f63(x73691),x73693))+P1(f306(f306(f220(a865),f306(f39(x73691),x73692)),f306(f39(x73691),x73693)))+~P1(f306(f306(f220(f872(x73691,a859)),x73692),x73693)) % 187.68/187.65 [7370]~P1(f306(f63(x73701),x73703))+P1(f306(f306(f221(a865),f306(f39(x73701),x73702)),f306(f39(x73701),x73703)))+~P1(f306(f306(f221(f872(x73701,a859)),x73702),x73703)) % 187.68/187.65 [7408]~P1(f306(x74083,x74082))+P1(f306(f306(f193(x74081),x74082),f416(x74082,x74081,x74083)))+~P1(f306(f306(f193(f33(x74083,x74081)),x74082),x74082)) % 187.68/187.65 [7504]E(x75041,x75042)+~P1(f306(f306(f220(f872(x75043,a859)),x75042),x75041))+~P1(f306(f306(f220(f872(x75043,a859)),x75041),x75042)) % 187.68/187.65 [7507]~P108(x75071)+P17(x75071,x75072)+~P17(x75071,f306(f306(f140(x75071,x75071,f5(x75071)),x75073),x75072)) % 187.68/187.65 [7575]~P1(f306(f306(f221(a865),x75753),x75752))+~P1(f306(f306(f221(a865),x75753),x75751))+P1(f306(f306(f221(a865),f306(f306(f22(a865),x75751),x75752)),f306(f306(f22(a865),x75751),x75753))) % 187.68/187.65 [7576]~P1(f306(f306(f220(a865),x75762),x75761))+~P1(f306(f306(f221(a865),x75761),x75763))+P1(f306(f306(f221(a865),f306(f306(f22(a865),x75761),x75762)),f306(f306(f22(a865),x75763),x75762))) % 187.68/187.65 [7591]~P1(f306(f306(f221(a1),x75912),f2(a1)))+~P1(f306(f306(f220(a1),x75913),x75911))+P1(f306(f306(f220(a1),f306(f306(f40(a1),x75911),x75912)),f306(f306(f40(a1),x75913),x75912))) % 187.68/187.65 [7609]~P1(f306(f306(f221(a865),f2(a865)),x76093))+~P1(f306(f306(f220(a865),x76093),x76092))+P1(f306(f306(f220(a865),f306(f306(f40(a865),x76091),x76092)),f306(f306(f40(a865),x76091),x76093))) % 187.68/187.65 [7610]~P1(f306(f306(f221(a1),f2(a1)),x76102))+~P1(f306(f306(f220(a1),x76101),x76103))+P1(f306(f306(f220(a1),f306(f306(f40(a1),x76101),x76102)),f306(f306(f40(a1),x76103),x76102))) % 187.68/187.65 [7614]~P1(f306(f306(f221(a865),f2(a865)),x76142))+~P1(f306(f306(f221(a865),x76141),x76143))+P1(f306(f306(f221(a865),f306(f306(f82(a865),x76141),x76142)),f306(f306(f82(a865),x76143),x76142))) % 187.68/187.65 [7615]~P1(f306(f306(f221(a865),f2(a865)),x76151))+~P1(f306(f306(f221(a865),x76152),x76153))+P1(f306(f306(f221(a865),f306(f306(f82(a865),x76151),x76152)),f306(f306(f82(a865),x76151),x76153))) % 187.68/187.65 [7616]~P1(f306(f306(f221(a1),f2(a1)),x76161))+~P1(f306(f306(f221(a1),x76162),x76163))+P1(f306(f306(f221(a1),f306(f306(f82(a1),x76161),x76162)),f306(f306(f82(a1),x76161),x76163))) % 187.68/187.65 [7666]E(x76661,f2(a865))+E(f306(f306(f81(a865),f306(f306(f82(a865),x76661),f855(x76661,x76662,x76663))),f856(x76661,x76662,x76663)),x76662)+P1(f306(x76663,f306(f306(f40(a865),x76662),x76661))) % 187.68/187.65 [7725]E(f306(f306(f81(a865),f306(f306(f82(a865),x77251),f855(x77251,x77252,x77253))),f856(x77251,x77252,x77253)),x77252)+~P1(f306(x77253,f2(a865)))+P1(f306(x77253,f306(f306(f40(a865),x77252),x77251))) % 187.68/187.65 [7742]~P1(f306(f63(x77421),x77423))+P1(f306(f306(f308(x77421),f321(x77422,x77423,x77421)),x77423))+P1(f306(f306(f221(a865),f2(a865)),f306(f306(f9(x77421,a865),x77422),x77423))) % 187.68/187.65 [7743]~P1(f306(f63(x77431),x77433))+P1(f306(f306(f308(x77431),f494(x77432,x77433,x77431)),x77433))+P1(f306(f306(f221(a865),f2(a865)),f306(f306(f9(x77431,a865),x77432),x77433))) % 187.68/187.65 [8038]E(x80381,f185(f872(x80382,a859)))+E(x80381,f306(f306(f284(x80382),x80383),f185(f872(x80382,a859))))+~P1(f306(f306(f220(f872(x80382,a859)),x80381),f306(f306(f284(x80382),x80383),f185(f872(x80382,a859))))) % 187.68/187.65 [8056]~P60(x80561)+P14(x80561,x80562,x80563)+P1(f306(f306(f308(f866(x80561)),f743(x80563,x80562,x80561)),f306(f164(f866(x80561)),f56(x80561,x80563,f57(x80561))))) % 187.68/187.65 [8075]~P1(f306(f306(f221(a865),f2(a865)),x80753))+P1(f306(f306(f220(a865),x80751),x80752))+~P1(f306(f306(f220(a865),f306(f306(f82(a865),x80753),x80751)),f306(f306(f82(a865),x80753),x80752))) % 187.68/187.65 [8076]~P1(f306(f306(f221(a865),f2(a865)),x80763))+P1(f306(f306(f220(a865),x80761),x80762))+~P1(f306(f306(f220(a865),f306(f306(f82(a865),x80761),x80763)),f306(f306(f82(a865),x80762),x80763))) % 187.68/187.65 [8078]~P1(f306(f306(f221(a865),f2(a865)),x80783))+P1(f306(f306(f221(a865),x80781),x80782))+~P1(f306(f306(f221(a865),f306(f306(f237(a865),x80783),x80781)),f306(f306(f237(a865),x80783),x80782))) % 187.68/187.65 [8105]~P60(x81051)+~P13(x81051,x81053,x81052)+P1(f306(f306(f308(f866(x81051)),f742(x81052,x81053,x81051)),f306(f164(f866(x81051)),f56(x81051,x81052,f57(x81051))))) % 187.68/187.65 [8113]~P1(f306(x81131,x81133))+P1(f306(f306(f193(f33(x81131,x81132)),f416(x81133,x81132,x81131)),x81133))+~P1(f306(f306(f193(f33(x81131,x81132)),x81133),x81133)) % 187.68/187.65 [8122]~E(f306(f306(f109(f872(x81221,a859)),f641(x81223,x81222,x81221)),f640(x81223,x81222,x81221)),f185(f872(x81221,a859)))+E(f306(f306(f109(f872(x81221,a859)),x81222),f41(f872(x81221,a859),x81223)),f185(f872(x81221,a859)))+P1(f306(f306(f308(f872(x81221,a859)),x81222),x81223)) % 187.68/187.65 [8139]E(x81391,f120(x81392))+~E(f306(f134(f866(x81392),f866(x81392),f122(x81392),f120(x81392)),x81393),f120(x81392))+~P1(f306(f306(f308(f866(x81392)),x81391),f306(f164(f866(x81392)),x81393))) % 187.68/187.65 [8196]E(x81961,f185(f872(f872(x81962,a859),a859)))+P1(f306(f306(f308(f872(x81962,a859)),f642(x81963,x81961,x81962)),x81961))+P1(f306(f306(f220(f872(x81962,a859)),f42(f872(x81962,a859),x81961)),x81963)) % 187.68/187.65 [8203]~P74(x82031)+~P75(x82031)+E(f306(f306(f9(a1,x82031),f306(f306(f8(a865,x82031,a1),x82032),a112)),f306(f285(a865,a1,f107(a1)),x82033)),f306(f306(f9(a865,x82031),x82032),x82033)) % 187.68/187.65 [8204]~P74(x82041)+~P75(x82041)+E(f306(f306(f6(a1,x82041),f306(f306(f8(a865,x82041,a1),x82042),a112)),f306(f285(a865,a1,f107(a1)),x82043)),f306(f306(f6(a865,x82041),x82042),x82043)) % 187.68/187.65 [8243]~P1(f306(f63(x82431),x82433))+~P1(f306(f306(f221(a865),f2(a865)),f306(x82432,f321(x82432,x82433,x82431))))+P1(f306(f306(f221(a865),f2(a865)),f306(f306(f9(x82431,a865),x82432),x82433))) % 187.68/187.65 [8244]~P1(f306(f63(x82441),x82443))+~P1(f306(f306(f221(a865),f2(a865)),f306(x82442,f494(x82442,x82443,x82441))))+P1(f306(f306(f221(a865),f2(a865)),f306(f306(f9(x82441,a865),x82442),x82443))) % 187.68/187.65 [8280]~P62(x82802)+E(x82801,f79(x82802))+E(f306(f306(f264(x82802),f306(f306(f22(x82802),f306(f306(f237(x82802),x82801),x82803)),f79(x82802))),f306(f306(f22(x82802),x82801),f79(x82802))),f306(f306(f6(a865,x82802),f306(f237(x82802),x82801)),f306(f276(a865,f2(a865)),x82803))) % 187.68/187.65 [8338]E(x83381,f2(a865))+~P1(f306(x83383,f306(f306(f40(a865),x83382),x83381)))+P1(f306(f306(f221(a865),x83382),f306(f306(f82(a865),x83381),f306(a119,f316(x83381,x83382,x83383))))) % 187.68/187.65 [8358]P1(f306(x83581,f2(a865)))+~P1(f306(x83581,f306(f306(f40(a865),x83582),x83583)))+P1(f306(f306(f221(a865),x83582),f306(f306(f82(a865),x83583),f306(a119,f316(x83583,x83582,x83581))))) % 187.68/187.65 [8396]E(x83961,f2(a865))+~P1(f306(x83963,f306(f306(f40(a865),x83962),x83961)))+P1(f306(f306(f220(a865),f306(f306(f82(a865),x83961),f316(x83961,x83962,x83963))),x83962)) % 187.68/187.65 [8438]P1(f306(x84381,f2(a865)))+~P1(f306(x84381,f306(f306(f40(a865),x84383),x84382)))+P1(f306(f306(f220(a865),f306(f306(f82(a865),x84382),f316(x84382,x84383,x84381))),x84383)) % 187.68/187.65 [8441]~P108(x84411)+E(f306(f306(f140(x84411,x84411,f5(x84411)),x84412),x84413),f141(x84411,x84411,f5(x84411),x84412,x84413))+P1(f306(f306(f308(x84411),x84412),f306(f164(x84411),x84413))) % 187.68/187.65 [8481]~E(f306(x84813,f557(x84812,x84813,x84811)),f306(x84813,f559(x84812,x84813,x84811)))+~P59(x84811,f306(x84813,f558(x84812,x84813,x84811)))+P59(x84811,f306(f306(f43(x84812,f872(x84811,f872(x84811,a859))),f231(f872(x84812,a859))),x84813)) % 187.68/187.65 [8489]E(x84891,f185(f872(f872(x84892,a859),a859)))+~P1(f306(f306(f220(f872(x84892,a859)),f642(x84893,x84891,x84892)),x84893))+P1(f306(f306(f220(f872(x84892,a859)),f42(f872(x84892,a859),x84891)),x84893)) % 187.68/187.65 [8548]~P64(x85481)+~P1(f306(f306(f221(x85481),x85482),x85483))+P1(f306(f306(f221(x85481),x85482),f306(f306(f264(x85481),f306(f306(f81(x85481),x85482),x85483)),f306(f306(f81(x85481),f79(x85481)),f79(x85481))))) % 187.68/187.65 [8603]~P1(f306(f306(x86031,f328(x86031,x86033,x86032)),f329(x86031,x86033,x86032)))+P1(f306(f306(x86031,x86032),x86033))+~P1(f306(f294(f871(a1,a1),a53),f306(f306(f236(a1,a1),x86032),x86033))) % 187.68/187.65 [8604]~P1(f306(f306(x86041,f330(x86041,x86043,x86042)),f331(x86041,x86043,x86042)))+P1(f306(f306(x86041,x86042),x86043))+~P1(f306(f294(f871(a1,a1),a58),f306(f306(f236(a1,a1),x86042),x86043))) % 187.68/187.65 [8605]~P1(f306(f306(x86051,f332(x86051,x86053,x86052)),f333(x86051,x86053,x86052)))+P1(f306(f306(x86051,x86052),x86053))+~P1(f306(f294(f871(a1,a1),a210),f306(f306(f236(a1,a1),x86052),x86053))) % 187.68/187.65 [8606]~P1(f306(f306(x86061,f474(x86061,x86063,x86062)),f478(x86061,x86063,x86062)))+P1(f306(f306(x86061,x86062),x86063))+~P1(f306(f294(f871(a865,a865),a205),f306(f306(f236(a865,a865),x86062),x86063))) % 187.68/187.65 [8607]~P1(f306(f306(x86071,f692(x86071,x86073,x86072)),f695(x86071,x86073,x86072)))+P1(f306(f306(x86071,x86072),x86073))+~P1(f306(f294(f871(a1,a1),a174),f306(f306(f236(a1,a1),x86072),x86073))) % 187.68/187.65 [8859]P1(f306(f306(x88591,x88592),x88593))+P1(f306(f294(f871(a865,a865),a205),f306(f306(f236(a865,a865),f474(x88591,x88593,x88592)),f478(x88591,x88593,x88592))))+~P1(f306(f294(f871(a865,a865),a205),f306(f306(f236(a865,a865),x88592),x88593))) % 187.68/187.65 [8860]P1(f306(f306(x88601,x88602),x88603))+P1(f306(f294(f871(a1,a1),a53),f306(f306(f236(a1,a1),f328(x88601,x88603,x88602)),f329(x88601,x88603,x88602))))+~P1(f306(f294(f871(a1,a1),a53),f306(f306(f236(a1,a1),x88602),x88603))) % 187.68/187.65 [8861]P1(f306(f306(x88611,x88612),x88613))+P1(f306(f294(f871(a1,a1),a58),f306(f306(f236(a1,a1),f330(x88611,x88613,x88612)),f331(x88611,x88613,x88612))))+~P1(f306(f294(f871(a1,a1),a58),f306(f306(f236(a1,a1),x88612),x88613))) % 187.68/187.65 [8862]P1(f306(f306(x88621,x88622),x88623))+P1(f306(f294(f871(a1,a1),a210),f306(f306(f236(a1,a1),f332(x88621,x88623,x88622)),f333(x88621,x88623,x88622))))+~P1(f306(f294(f871(a1,a1),a210),f306(f306(f236(a1,a1),x88622),x88623))) % 187.68/187.65 [8863]P1(f306(f306(x88631,x88632),x88633))+P1(f306(f294(f871(a1,a1),a174),f306(f306(f236(a1,a1),f692(x88631,x88633,x88632)),f695(x88631,x88633,x88632))))+~P1(f306(f294(f871(a1,a1),a174),f306(f306(f236(a1,a1),x88632),x88633))) % 187.68/187.65 [9212]~P1(f306(f63(x92121),x92123))+P1(f306(f306(f308(f871(f872(x92121,a859),f872(x92121,a859))),f306(f306(f236(f872(x92121,a859),f872(x92121,a859)),x92122),x92123)),f281(x92121)))+~P1(f306(f306(f221(f872(x92121,a859)),x92122),x92123)) % 187.68/187.65 [9285]~P59(x92851,f306(x92853,f558(x92852,x92853,x92851)))+P59(x92851,f306(f306(f43(x92852,f872(x92851,f872(x92851,a859))),f231(f872(x92852,a859))),x92853))+~E(f306(f306(f109(f872(x92851,a859)),f241(x92851,x92851,f306(x92853,f557(x92852,x92853,x92851)))),f242(x92851,x92851,f306(x92853,f559(x92852,x92853,x92851)))),f185(f872(x92851,a859))) % 187.68/187.65 [9356]~P31(a861,f185(f872(f864(a861),a859)),f306(f306(f284(f864(a861)),f306(f306(f306(f93(a861),x93561),x93562),x93563)),f185(f872(f864(a861),a859))))+~P27(a861,f185(f872(f864(a861),a859)),f306(f306(f284(f864(a861)),f306(f306(f306(f93(a861),a303),x93562),f193(x93562))),f185(f872(f864(a861),a859))))+P27(a861,f185(f872(f864(a861),a859)),f306(f306(f284(f864(a861)),f306(f306(f306(f93(a861),x93561),x93562),x93563)),f185(f872(f864(a861),a859)))) % 187.68/187.65 [9485]P50(x94851,x94852,x94853)+P1(f306(f306(f308(f871(x94851,x94851)),f541(x94853,x94852,x94851)),x94853))+~P1(f306(f306(f308(f871(x94851,x94851)),f306(f306(f236(x94851,x94851),f540(x94853,x94852,x94851)),f540(x94853,x94852,x94851))),x94853)) % 187.68/187.65 [10076]P50(x100761,x100762,x100763)+~P1(f306(f306(f245(x100761,x100761,a859),f306(f306(f7(x100761,f872(x100761,a859),f872(x100761,a859)),f306(f306(f8(f872(a859,a859),f872(f872(x100761,a859),f872(x100761,a859)),x100761),f8(a859,a859,x100761)),f306(f306(f8(a859,f872(a859,a859),x100761),a304),f306(f306(f7(x100761,f872(x100761,a859),a859),f308(x100761)),x100762)))),f306(f306(f7(x100761,f872(x100761,a859),a859),f308(x100761)),x100762))),f541(x100763,x100762,x100761)))+~P1(f306(f306(f308(f871(x100761,x100761)),f306(f306(f236(x100761,x100761),f540(x100763,x100762,x100761)),f540(x100763,x100762,x100761))),x100763)) % 187.68/187.65 [5608]~P4(x56082)+E(x56081,f2(x56082))+E(f306(f306(f40(x56082),f306(f306(f82(x56082),x56083),x56081)),x56081),x56083) % 187.68/187.65 [5609]~P4(x56092)+E(x56091,f2(x56092))+E(f306(f306(f40(x56092),f306(f306(f82(x56092),x56091),x56093)),x56091),x56093) % 187.68/187.65 [6408]~P74(x64081)+~E(f306(x64082,f2(a865)),f2(x64081))+E(f306(f306(f6(a865,x64081),x64082),f306(f276(a865,f306(a119,f2(a865))),x64083)),f306(f306(f6(a865,x64081),x64082),f306(f276(a865,f2(a865)),x64083))) % 187.68/187.65 [6535]~P4(x65352)+E(x65351,f2(x65352))+E(f306(f306(f40(x65352),f306(f306(f81(x65352),x65353),x65351)),x65351),f306(f306(f81(x65352),f306(f306(f40(x65352),x65353),x65351)),f79(x65352))) % 187.68/187.65 [6536]~P4(x65362)+E(x65361,f2(x65362))+E(f306(f306(f40(x65362),f306(f306(f81(x65362),x65361),x65363)),x65361),f306(f306(f81(x65362),f306(f306(f40(x65362),x65363),x65361)),f79(x65362))) % 187.68/187.65 [6758]~P1(f306(x67583,f2(a1)))+P1(f306(f306(f220(a865),x67581),x67582))+P1(f306(x67583,f306(f107(a1),f306(f306(f22(a865),x67582),x67581)))) % 187.68/187.65 [6860]P1(f306(f306(f221(a865),x68602),x68601))+P1(f306(f306(f220(a865),x68601),x68602))+P1(f306(x68603,f306(f107(a1),f306(f306(f22(a865),x68602),x68601)))) % 187.68/187.65 [6932]E(f306(f306(f81(a865),f306(f111(a865),x69321)),f306(f306(f81(a865),f306(f111(a865),x69322)),x69323)),f306(f306(f81(a865),f306(f111(a865),x69321)),x69323))+P1(f306(a190,f306(f111(a1),x69321)))+~P1(f306(a190,f306(f111(a1),x69322))) % 187.68/187.65 [7013]~E(x70132,f306(f306(f40(a865),x70133),x70131))+~P1(f306(f306(f221(a865),f2(a865)),x70131))+P1(f306(f306(f220(a865),f306(f306(f82(a865),x70131),x70132)),x70133)) % 187.68/187.65 [7128]~P1(f306(f63(x71281),x71283))+~P1(f306(f63(x71281),x71282))+P1(f306(f63(x71281),f306(f306(f108(f872(x71281,a859)),x71282),x71283))) % 187.68/187.65 [7421]~P108(x74211)+~P1(f306(f63(x74211),x74212))+E(f131(x74211,f306(f306(f22(f872(x74211,a859)),x74212),f306(f306(f284(x74211),x74213),f185(f872(x74211,a859))))),f162(x74211,x74213,f131(x74211,x74212))) % 187.68/187.65 [7484]P1(f306(x74841,f2(a1)))+~P1(f306(f306(f221(a865),x74842),x74843))+~P1(f306(x74841,f306(f107(a1),f306(f306(f22(a865),x74842),x74843)))) % 187.68/187.65 [7501]~P1(f306(f63(x75011),x75012))+E(f306(f39(x75011),f306(f306(f22(f872(x75011,a859)),x75012),f306(f306(f284(x75011),x75013),f185(f872(x75011,a859))))),f306(f39(x75011),x75012))+P1(f306(f306(f308(x75011),x75013),x75012)) % 187.68/187.65 [7632]~P111(x76321)+~P1(f306(f306(f221(x76321),f79(x76321)),x76322))+P1(f306(f306(f221(x76321),f79(x76321)),f306(f306(f82(x76321),x76322),f306(f306(f237(x76321),x76322),x76323)))) % 187.68/187.65 [7677]~P1(f306(f63(x76771),x76773))+E(f306(f306(f22(a865),f306(f39(x76771),x76772)),f306(f39(x76771),x76773)),f306(f39(x76771),f306(f306(f22(f872(x76771,a859)),x76772),x76773)))+~P1(f306(f306(f220(f872(x76771,a859)),x76773),x76772)) % 187.68/187.65 [7734]~P1(f306(f306(f220(a865),x77342),x77343))+~P1(f306(f306(f220(a865),x77341),f306(f306(f22(a865),x77343),x77342)))+P1(f306(f306(f220(a865),f306(f306(f81(a865),x77341),x77342)),x77343)) % 187.68/187.65 [7786]P1(f306(f63(x77861),x77862))+~P1(f306(f63(x77861),x77863))+~P1(f306(f63(x77861),f306(f306(f22(f872(x77861,a859)),x77862),x77863))) % 187.68/187.65 [7792]~P1(f306(f63(x77921),x77922))+E(f306(f39(x77921),f306(f306(f22(f872(x77921,a859)),x77922),f306(f306(f284(x77921),x77923),f185(f872(x77921,a859))))),f306(f306(f22(a865),f306(f39(x77921),x77922)),f79(a865)))+~P1(f306(f306(f308(x77921),x77923),x77922)) % 187.68/187.65 [7868]P59(x78681,x78682)+~P59(x78681,x78683)+~P1(f306(f306(f220(f872(x78681,f872(x78681,a859))),x78682),x78683)) % 187.68/187.65 [7909]~P1(f306(f306(f220(a865),x79093),x79092))+P1(f306(f306(f220(a865),x79091),f306(f306(f22(a865),x79092),x79093)))+~P1(f306(f306(f220(a865),f306(f306(f81(a865),x79091),x79093)),x79092)) % 187.68/187.65 [7927]P40(x79271,x79272)+~P40(x79271,x79273)+~P1(f306(f306(f220(f872(f871(x79271,x79271),a859)),x79272),x79273)) % 187.68/187.65 [7928]P57(x79281,x79282)+~P57(x79281,x79283)+~P1(f306(f306(f220(f872(f871(x79281,x79281),a859)),x79282),x79283)) % 187.68/187.65 [8174]~P111(x81741)+~P1(f306(f306(f221(x81741),f79(x81741)),x81742))+P1(f306(f306(f221(x81741),f306(f306(f237(x81741),x81742),x81743)),f306(f306(f82(x81741),x81742),f306(f306(f237(x81741),x81742),x81743)))) % 187.68/187.65 [8263]~P1(f306(x82631,f2(a1)))+~P1(f306(x82631,f306(f306(f22(a1),f306(f107(a1),x82632)),f306(f107(a1),x82633))))+P1(f306(x82631,f306(f107(a1),f306(f306(f22(a865),x82632),x82633)))) % 187.68/187.65 [8276]~P1(f306(f306(f220(a865),x82763),x82762))+P1(f306(x82761,f306(f306(f22(a1),f306(f107(a1),x82762)),f306(f107(a1),x82763))))+~P1(f306(x82761,f306(f107(a1),f306(f306(f22(a865),x82762),x82763)))) % 187.68/187.65 [8295]P1(f306(f306(f221(a865),x82951),x82952))+~P1(f306(x82953,f306(f306(f22(a1),f306(f107(a1),x82951)),f306(f107(a1),x82952))))+P1(f306(x82953,f306(f107(a1),f306(f306(f22(a865),x82951),x82952)))) % 187.68/187.65 [8350]~P122(x83502)+E(x83501,f2(x83502))+P1(f306(f306(f221(x83502),f2(x83502)),f306(f306(f81(x83502),f306(f306(f82(x83502),x83503),x83503)),f306(f306(f82(x83502),x83501),x83501)))) % 187.68/187.65 [8351]~P122(x83512)+E(x83511,f2(x83512))+P1(f306(f306(f221(x83512),f2(x83512)),f306(f306(f81(x83512),f306(f306(f82(x83512),x83511),x83511)),f306(f306(f82(x83512),x83513),x83513)))) % 187.68/187.65 [8461]~P1(f306(f306(f221(a865),f2(a865)),x84611))+~P1(f306(f306(f221(a1),x84612),x84613))+P1(f306(f306(f221(a1),f306(f306(f82(a1),f306(f107(a1),x84611)),x84612)),f306(f306(f82(a1),f306(f107(a1),x84611)),x84613))) % 187.68/187.65 [8517]E(f306(f306(f109(f872(x85171,a859)),x85172),f41(f872(x85171,a859),x85173)),f185(f872(x85171,a859)))+P1(f306(f306(f308(f872(x85171,a859)),x85172),x85173))+P1(f306(f306(f308(f872(x85171,a859)),f641(x85173,x85172,x85171)),f306(f306(f284(f872(x85171,a859)),x85172),x85173))) % 187.68/187.65 [8518]E(f306(f306(f109(f872(x85181,a859)),x85182),f41(f872(x85181,a859),x85183)),f185(f872(x85181,a859)))+P1(f306(f306(f308(f872(x85181,a859)),x85182),x85183))+P1(f306(f306(f308(f872(x85181,a859)),f640(x85183,x85182,x85181)),f306(f306(f284(f872(x85181,a859)),x85182),x85183))) % 187.68/187.65 [8547]E(x85471,x85472)+~E(f306(f186(f866(x85473)),x85471),f306(f186(f866(x85473)),x85472))+P1(f306(f306(f308(f871(x85473,x85473)),f672(x85473,x85471,x85472)),f306(f164(f871(x85473,x85473)),f306(f306(f173(x85473,x85473),x85472),x85471)))) % 187.68/187.65 [8776]E(f282(x87761,x87762),f282(x87761,x87763))+~P1(f306(f306(f220(f872(f871(x87761,x87761),a859)),x87763),f282(x87761,x87762)))+~P1(f306(f306(f220(f872(f871(x87761,x87761),a859)),x87762),x87763)) % 187.68/187.65 [8837]~P50(x88371,f231(f872(x88371,a859)),x88373)+P1(f306(f306(f220(f872(f871(f866(x88371),f866(x88371)),a859)),f149(x88371,x88372)),f150(x88371,x88373)))+~P1(f306(f306(f220(f872(f871(x88371,x88371),a859)),x88372),x88373)) % 187.68/187.65 [9045]P40(x90451,x90452)+~P1(f306(f306(f308(x90451),x90453),f608(x90452,x90451)))+P1(f306(f306(f308(f871(x90451,x90451)),f306(f306(f236(x90451,x90451),f654(x90452,x90451,x90453)),x90453)),x90452)) % 187.68/187.65 [9078]~P1(f306(f63(x90781),x90782))+P1(f306(f63(f872(x90781,a859)),f306(f306(f62(x90781),x90782),x90783)))+~P1(f306(f306(f220(f872(f871(x90781,x90781),a859)),x90783),f306(f306(f243(x90781,x90781),x90782),f306(f16(f872(x90781,a859),x90781),x90782)))) % 187.68/187.65 [9115]P50(x91151,x91152,x91153)+P1(f306(f306(f308(x91151),f502(x91153,x91152,x91151)),x91152))+~P1(f306(f306(f220(f872(f871(x91151,x91151),a859)),x91153),f306(f306(f243(x91151,x91151),x91152),f306(f16(f872(x91151,a859),x91151),x91152)))) % 187.68/187.65 [9116]P50(x91161,x91162,x91163)+P1(f306(f306(f308(x91161),f510(x91162,x91163,x91161)),x91162))+~P1(f306(f306(f220(f872(f871(x91161,x91161),a859)),x91163),f306(f306(f243(x91161,x91161),x91162),f306(f16(f872(x91161,a859),x91161),x91162)))) % 187.68/187.65 [9152]~P64(x91521)+~P1(f306(f306(f221(x91521),x91522),x91523))+P1(f306(f306(f221(x91521),f306(f306(f264(x91521),f306(f306(f81(x91521),x91522),x91523)),f306(f306(f81(x91521),f79(x91521)),f79(x91521)))),x91523)) % 187.68/187.65 [9181]~P63(x91811)+P1(f306(f306(f220(x91811),x91812),x91813))+~P1(f306(f306(f220(x91811),f306(f306(f82(x91811),f425(x91813,x91812,x91811)),x91812)),x91813)) % 187.68/187.65 [9320]E(f306(f186(f866(f866(x93201))),f306(f128(f866(x93201),f306(f306(f8(a865,a859,f866(x93201)),f306(f221(a865),x93202)),f186(f866(x93201)))),f171(x93201,x93203))),f306(f186(f866(x93201)),f306(f306(f157(f866(x93201)),x93203),x93202)))+~P17(a865,f306(f161(a865),f306(f306(f146(f866(x93201),a865),f186(f866(x93201))),x93203)))+~P1(f306(f306(f221(a865),x93202),f306(f186(f866(f866(x93201))),x93203))) % 187.68/187.65 [9430]~P40(x94301,x94302)+P29(x94301,f306(f306(f236(f872(f871(x94301,x94301),a859),f872(f871(x94301,x94301),a859)),x94302),x94303))+~P1(f306(f306(f220(f872(f871(x94301,x94301),a859)),f306(f306(f263(x94301,x94301,x94301),x94302),x94303)),x94302)) % 187.68/187.65 [9437]E(f306(f306(f146(f866(x94371),x94371),f306(f306(f7(f866(x94371),a865,x94371),f157(x94371)),x94372)),f306(f128(f866(x94371),f306(f306(f8(a865,a859,f866(x94371)),f306(f221(a865),x94372)),f186(f866(x94371)))),f171(x94371,x94373))),f306(f306(f157(f866(x94371)),x94373),x94372))+~P17(a865,f306(f161(a865),f306(f306(f146(f866(x94371),a865),f186(f866(x94371))),x94373)))+~P1(f306(f306(f221(a865),x94372),f306(f186(f866(f866(x94371))),x94373))) % 187.68/187.65 [9574]P50(x95741,x95742,x95743)+~P1(f306(f306(f308(f871(x95741,x95741)),f306(f306(f236(x95741,x95741),f502(x95743,x95742,x95741)),f502(x95743,x95742,x95741))),x95743))+~P1(f306(f306(f220(f872(f871(x95741,x95741),a859)),x95743),f306(f306(f243(x95741,x95741),x95742),f306(f16(f872(x95741,a859),x95741),x95742)))) % 187.68/187.65 [9575]P50(x95751,x95752,x95753)+~P1(f306(f306(f308(f871(x95751,x95751)),f306(f306(f236(x95751,x95751),f510(x95752,x95753,x95751)),f510(x95752,x95753,x95751))),x95753))+~P1(f306(f306(f220(f872(f871(x95751,x95751),a859)),x95753),f306(f306(f243(x95751,x95751),x95752),f306(f16(f872(x95751,a859),x95751),x95752)))) % 187.68/187.65 [9752]~P125(x97521)+~P121(x97521)+E(f306(f306(f264(x97521),f306(f110(x97521),f306(f306(f74(f871(a1,a1),a1,x97522,f235(a1,a1)),f198(x97522)),x97523))),f306(f110(x97521),f306(f306(f74(f871(a1,a1),a1,x97522,f244(a1,a1)),f198(x97522)),x97523))),f211(x97522,x97521,x97523)) % 187.68/187.65 [9952]~E(x99523,f2(a865))+~E(f306(f186(f866(x99521)),f306(f306(f157(f866(x99521)),x99522),f734(x99523,x99521,x99522))),x99523)+E(f306(f306(f146(a865,f866(x99521)),f306(f306(f7(a865,f866(a865),f866(x99521)),f306(f306(f8(f872(a865,x99521),f872(f866(a865),f866(x99521)),a865),f146(a865,x99521)),f306(f7(a865,a865,x99521),f306(f306(f8(f866(x99521),f872(a865,x99521),a865),f157(x99521)),f306(f157(f866(x99521)),x99522))))),f131(a865,f306(f276(a865,f2(a865)),f306(f186(f866(f866(x99521))),x99522))))),f131(a865,f306(f276(a865,f2(a865)),x99523))),f171(x99521,x99522)) % 187.68/187.65 [9953]E(x99531,f120(f866(x99532)))+~E(f306(f186(f866(x99532)),f306(f306(f157(f866(x99532)),x99531),f734(x99533,x99532,x99531))),x99533)+E(f306(f306(f146(a865,f866(x99532)),f306(f306(f7(a865,f866(a865),f866(x99532)),f306(f306(f8(f872(a865,x99532),f872(f866(a865),f866(x99532)),a865),f146(a865,x99532)),f306(f7(a865,a865,x99532),f306(f306(f8(f866(x99532),f872(a865,x99532),a865),f157(x99532)),f306(f157(f866(x99532)),x99531))))),f131(a865,f306(f276(a865,f2(a865)),f306(f186(f866(f866(x99532))),x99531))))),f131(a865,f306(f276(a865,f2(a865)),x99533))),f171(x99532,x99531)) % 187.68/187.65 [9954]~E(x99543,f2(a865))+E(f306(f306(f146(a865,f866(x99541)),f306(f306(f7(a865,f866(a865),f866(x99541)),f306(f306(f8(f872(a865,x99541),f872(f866(a865),f866(x99541)),a865),f146(a865,x99541)),f306(f7(a865,a865,x99541),f306(f306(f8(f866(x99541),f872(a865,x99541),a865),f157(x99541)),f306(f157(f866(x99541)),x99542))))),f131(a865,f306(f276(a865,f2(a865)),f306(f186(f866(f866(x99541))),x99542))))),f131(a865,f306(f276(a865,f2(a865)),x99543))),f171(x99541,x99542))+P1(f306(f306(f221(a865),f734(x99543,x99541,x99542)),f306(f186(f866(f866(x99541))),x99542))) % 187.68/187.65 [9955]E(x99551,f120(f866(x99552)))+E(f306(f306(f146(a865,f866(x99552)),f306(f306(f7(a865,f866(a865),f866(x99552)),f306(f306(f8(f872(a865,x99552),f872(f866(a865),f866(x99552)),a865),f146(a865,x99552)),f306(f7(a865,a865,x99552),f306(f306(f8(f866(x99552),f872(a865,x99552),a865),f157(x99552)),f306(f157(f866(x99552)),x99551))))),f131(a865,f306(f276(a865,f2(a865)),f306(f186(f866(f866(x99552))),x99551))))),f131(a865,f306(f276(a865,f2(a865)),x99553))),f171(x99552,x99551))+P1(f306(f306(f221(a865),f734(x99553,x99552,x99551)),f306(f186(f866(f866(x99552))),x99551))) % 187.68/187.65 [7674]E(f306(f306(f81(a865),f306(f111(a865),x76741)),f306(f306(f81(a865),f306(f111(a865),x76742)),x76743)),f306(f306(f81(a865),f306(f111(a865),f306(f306(f81(a1),x76741),x76742))),x76743))+P1(f306(a190,f306(f111(a1),x76741)))+P1(f306(a190,f306(f111(a1),x76742))) % 187.68/187.65 [8452]~P1(f306(f63(x84521),x84522))+~P1(f306(f306(f308(x84521),x84523),x84522))+E(f306(a119,f306(f39(x84521),f306(f306(f22(f872(x84521,a859)),x84522),f306(f306(f284(x84521),x84523),f185(f872(x84521,a859)))))),f306(f39(x84521),x84522)) % 187.68/187.65 [8471]~P1(f306(f63(x84711),x84712))+~P1(f306(f306(f308(x84711),x84713),x84712))+E(f306(f306(f81(a865),f79(a865)),f306(f39(x84711),f306(f306(f22(f872(x84711,a859)),x84712),f306(f306(f284(x84711),x84713),f185(f872(x84711,a859)))))),f306(f39(x84711),x84712)) % 187.68/187.65 [8556]~P108(x85561)+~P1(f306(f63(x85561),x85563))+E(f306(f306(f140(x85561,x85561,f5(x85561)),x85562),f131(x85561,f306(f306(f22(f872(x85561,a859)),x85563),f306(f306(f284(x85561),x85562),f185(f872(x85561,a859)))))),f131(x85561,f306(f306(f284(x85561),x85562),x85563))) % 187.68/187.65 [8705]~P1(f306(f63(x87051),x87053))+~P1(f306(f63(x87051),x87052))+E(f306(f306(f81(a865),f306(f39(x87051),f306(f306(f108(f872(x87051,a859)),x87052),x87053))),f306(f39(x87051),f306(f306(f109(f872(x87051,a859)),x87052),x87053))),f306(f306(f81(a865),f306(f39(x87051),x87052)),f306(f39(x87051),x87053))) % 187.68/187.65 [9900]~P28(x99001,f872(f872(x99001,a859),a859),f306(f306(f7(x99001,f872(f871(x99001,x99001),a859),f872(f872(x99001,a859),a859)),f306(f306(f8(f872(x99001,a859),f872(f872(f871(x99001,x99001),a859),f872(f872(x99001,a859),a859)),x99001),f62(x99001)),f306(f306(f7(x99001,f872(x99001,a859),f872(x99001,a859)),f284(x99001)),f185(f872(x99001,a859))))),x99003),x99002)+~P1(f306(f63(x99001),x99002))+E(f306(f39(f872(x99001,a859)),f306(f306(f62(x99001),x99002),x99003)),f306(f39(x99001),x99002)) % 187.68/187.65 [10172]~P41(f872(x101721,a859),f872(x101721,a859),x101722)+~P1(f306(f306(f220(f872(x101721,a859)),x101723),f306(x101722,f102(f872(x101721,a859),f306(f306(f7(f872(x101721,a859),f872(x101721,a859),f872(x101721,a859)),f306(f306(f8(f872(x101721,a859),f872(f872(x101721,a859),f872(x101721,a859)),f872(x101721,a859)),f108(f872(x101721,a859))),f306(f306(f7(f872(x101721,a859),f872(x101721,a859),f872(x101721,a859)),f306(f306(f8(f872(x101721,a859),f872(f872(x101721,a859),f872(x101721,a859)),f872(x101721,a859)),f108(f872(x101721,a859))),x101722)),x101723))),f103(f872(x101721,a859),x101722))))))+P1(f306(f306(f220(f872(x101721,a859)),f102(f872(x101721,a859),f306(f306(f7(f872(x101721,a859),f872(x101721,a859),f872(x101721,a859)),f306(f306(f8(f872(x101721,a859),f872(f872(x101721,a859),f872(x101721,a859)),f872(x101721,a859)),f108(f872(x101721,a859))),f306(f306(f7(f872(x101721,a859),f872(x101721,a859),f872(x101721,a859)),f306(f306(f8(f872(x101721,a859),f872(f872(x101721,a859),f872(x101721,a859)),f872(x101721,a859)),f108(f872(x101721,a859))),x101722)),x101723))),f103(f872(x101721,a859),x101722)))),f306(x101722,f102(f872(x101721,a859),f306(f306(f7(f872(x101721,a859),f872(x101721,a859),f872(x101721,a859)),f306(f306(f8(f872(x101721,a859),f872(f872(x101721,a859),f872(x101721,a859)),f872(x101721,a859)),f108(f872(x101721,a859))),f306(f306(f7(f872(x101721,a859),f872(x101721,a859),f872(x101721,a859)),f306(f306(f8(f872(x101721,a859),f872(f872(x101721,a859),f872(x101721,a859)),f872(x101721,a859)),f108(f872(x101721,a859))),x101722)),x101723))),f103(f872(x101721,a859),x101722)))))) % 187.68/187.65 [7943]~P91(x79431)+P1(f306(f306(f220(a1),f2(a1)),f306(f111(a1),x79433)))+E(f306(f306(f237(x79431),x79432),f306(f111(a865),f306(f306(f22(a1),f306(f306(f81(a1),x79433),x79433)),a104))),f79(x79431)) % 187.68/187.65 [9413]~P91(x94131)+~P1(f306(f306(f220(a1),f2(a1)),f306(f111(a1),x94133)))+E(f306(f306(f237(x94131),x94132),f306(f111(a865),f306(f306(f22(a1),f306(f306(f81(a1),x94133),x94133)),a104))),f306(f306(f87(x94131,x94131),f306(f306(f237(x94131),x94132),f306(f111(a865),x94133))),f306(f306(f18(x94131,x94131,x94131),f306(f306(f8(x94131,f872(x94131,x94131),x94131),f82(x94131)),f306(f82(x94131),x94132))),f5(x94131)))) % 187.68/187.65 [9808]~P1(f306(f129(x98081),x98083))+~P1(f306(f306(f308(x98081),x98082),f306(f164(x98081),x98083)))+E(f306(f306(f130(x98081),f306(f186(f866(x98081)),f168(x98081,f306(f306(f8(a859,a859,x98081),a301),f306(f306(f7(x98081,x98081,a859),a303),x98082)),f306(f161(x98081),x98083)))),f306(f161(x98081),x98083)),f306(f306(f143(x98081),x98082),f306(f161(x98081),f168(x98081,f306(f306(f8(a859,a859,x98081),a301),f306(f306(f7(x98081,x98081,a859),a303),x98082)),x98083)))) % 187.68/187.65 [9879]P1(f306(f306(f220(f872(f871(x98791,x98791),a859)),f282(x98791,x98792)),x98793))+~P1(f306(f306(f220(f872(f871(x98791,x98791),a859)),f282(x98791,f185(f872(f871(x98791,x98791),a859)))),x98793))+~P1(f306(f306(f220(f872(f871(x98791,x98791),a859)),f306(f306(f263(x98791,x98791,x98791),f306(f306(f109(f872(f871(x98791,x98791),a859)),f282(x98791,x98792)),x98793)),x98792)),x98793)) % 187.68/187.65 [9721]~P1(f306(f63(x97211),f306(f228(x97211),x97213)))+~P1(f306(f63(x97211),f306(f228(x97211),x97212)))+P1(f306(f63(x97211),f306(f228(x97211),f306(f306(f18(x97211,a859,a859),f306(f306(f8(a859,f872(a859,a859),x97211),a305),x97212)),x97213)))) % 187.68/187.65 [10017]P1(f306(f306(f220(f872(f871(x100171,x100171),a859)),f306(f306(f263(x100171,x100171,x100171),x100172),f282(x100171,x100172))),x100173))+~P1(f306(f306(f220(f872(f871(x100171,x100171),a859)),x100172),x100173))+~P1(f306(f306(f220(f872(f871(x100171,x100171),a859)),f306(f306(f263(x100171,x100171,x100171),f306(f306(f109(f872(f871(x100171,x100171),a859)),f306(f306(f263(x100171,x100171,x100171),x100172),f282(x100171,x100172))),x100173)),x100172)),x100173)) % 187.68/187.65 [9970]~P112(x99702)+E(x99701,f2(x99702))+~E(f306(f306(f81(x99702),f306(f306(f237(x99702),x99703),f306(f111(a865),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104))))),f306(f306(f237(x99702),x99701),f306(f111(a865),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104))))),f2(x99702)) % 187.68/187.65 [9971]~P112(x99712)+E(x99711,f2(x99712))+~E(f306(f306(f81(x99712),f306(f306(f237(x99712),x99711),f306(f111(a865),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104))))),f306(f306(f237(x99712),x99713),f306(f111(a865),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104))))),f2(x99712)) % 187.68/187.65 [9976]~P1(f306(f129(x99761),x99763))+~P1(f306(f306(f308(x99761),x99762),f306(f164(x99761),x99763)))+E(f306(f161(x99761),f306(f163(x99761),f306(f306(f130(x99761),f306(f186(f866(x99761)),f168(x99761,f306(f306(f8(a859,a859,x99761),a301),f306(f306(f7(x99761,x99761,a859),a303),x99762)),x99763))),x99763))),f168(x99761,f306(f306(f8(a859,a859,x99761),a301),f306(f306(f7(x99761,x99761,a859),a303),x99762)),f306(f161(x99761),x99763))) % 187.68/187.65 [10063]~P112(x100632)+E(x100631,f2(x100632))+P1(f306(f306(f221(x100632),f2(x100632)),f306(f306(f81(x100632),f306(f306(f237(x100632),x100633),f306(f111(a865),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104))))),f306(f306(f237(x100632),x100631),f306(f111(a865),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104))))))) % 187.68/187.65 [10064]~P112(x100642)+E(x100641,f2(x100642))+P1(f306(f306(f221(x100642),f2(x100642)),f306(f306(f81(x100642),f306(f306(f237(x100642),x100641),f306(f111(a865),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104))))),f306(f306(f237(x100642),x100643),f306(f111(a865),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104))))))) % 187.68/187.65 [10107]~P112(x101071)+P1(f306(f306(f220(x101071),f2(x101071)),x101072))+~P1(f306(f306(f220(x101071),f2(x101071)),f306(f306(f237(x101071),x101072),f306(a119,f306(f306(f82(a865),f306(f111(a865),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)))),x101073))))) % 187.68/187.65 [5450]~P27(x54501,x54504,x54503)+P27(x54501,x54502,x54503)+~P27(x54501,x54502,x54504) % 187.68/187.65 [4906]~E(x49062,f91(x49063,x49061))+P1(f306(x49061,x49062))+~P1(f306(x49061,x49064)) % 187.68/187.65 [6670]~P40(x66702,x66704)+~P40(x66701,x66703)+P40(f871(x66701,x66702),f299(x66701,x66702,x66703,x66704)) % 187.68/187.65 [5091]~P8(x50914,x50911)+~E(f306(x50911,x50912),f306(x50911,x50913))+P1(f306(f306(x50911,x50912),x50913)) % 187.68/187.65 [5263]~P8(x52634,x52631)+E(f306(x52631,x52632),f306(x52631,x52633))+~P1(f306(f306(x52631,x52632),x52633)) % 187.68/187.65 [5356]~P21(x53563,x53564,x53561)+E(f306(x53561,x53562),f306(f65(x53563,x53564),x53562))+~P1(f306(f63(x53563),x53562)) % 187.68/187.65 [5357]~P11(x53573,x53574,x53571)+E(f306(x53571,x53572),f306(f65(x53573,x53574),x53572))+~P1(f306(f63(x53573),x53572)) % 187.68/187.65 [5483]~P8(x54834,x54831)+~P1(f306(f306(x54831,x54833),x54832))+P1(f306(f306(x54831,x54832),x54833)) % 187.68/187.65 [5550]E(x55501,x55502)+~E(f306(f235(x55503,x55504),x55501),f306(f235(x55503,x55504),x55502))+~E(f306(f244(x55503,x55504),x55501),f306(f244(x55503,x55504),x55502)) % 187.68/187.65 [5575]E(x55751,x55752)+~P1(f306(f49(x55753,x55754),x55752))+~P1(f306(f49(x55753,x55754),x55751)) % 187.68/187.65 [5767]~P74(x57672)+E(f212(x57671,x57672,x57673,x57674),f2(x57672))+P1(f306(f63(x57671),x57674)) % 187.68/187.65 [5905]~P1(f306(f294(x59051,x59052),x59054))+P1(f306(f294(x59051,x59052),x59053))+~P1(f306(f306(x59052,x59053),x59054)) % 187.68/187.65 [7863]~P108(x78632)+~P1(f306(f129(x78631),x78634))+P1(f306(f129(x78631),f142(x78631,x78632,x78633,x78634))) % 187.68/187.65 [8092]~P1(f306(f63(x80922),x80924))+~P1(f306(f63(x80921),x80923))+P1(f306(f63(f870(x80921,x80922)),f293(x80921,x80922,x80923,x80924))) % 187.68/187.65 [8093]~P1(f306(f129(x80932),x80934))+~P1(f306(f129(x80931),x80933))+P1(f306(f129(f871(x80931,x80932)),f61(x80931,x80932,x80933,x80934))) % 187.68/187.65 [8097]P1(f306(f306(f308(f866(x80971)),f306(f306(f122(x80971),x80972),x80973)),f153(x80971,x80974)))+~P1(f306(f306(f308(f866(x80971)),x80973),f153(x80971,x80974)))+~P1(f306(f306(f308(f866(x80971)),x80972),f153(x80971,x80974))) % 187.68/187.65 [8429]~P108(x84293)+~P1(f306(f129(x84291),f142(x84291,x84293,x84294,x84292)))+P1(f306(f129(x84291),x84292)) % 187.68/187.65 [8696]~P1(f306(f306(f308(f871(x86961,x86961)),f306(f306(f236(x86961,x86961),x86962),x86964)),f282(x86961,x86963)))+P1(f306(f306(f308(x86961),x86962),f295(x86961,x86963)))+~P1(f306(f306(f308(x86961),x86964),f295(x86961,x86963))) % 187.68/187.65 [5073]~P75(x50732)+E(f306(f306(f9(x50731,x50732),x50733),x50734),f79(x50732))+P1(f306(f63(x50731),x50734)) % 187.68/187.65 [5076]~P74(x50762)+E(f306(f306(f6(x50761,x50762),x50763),x50764),f2(x50762))+P1(f306(f63(x50761),x50764)) % 187.68/187.65 [5227]~P70(x52273)+E(x52271,x52272)+~E(f306(f306(f81(x52273),x52274),x52271),f306(f306(f81(x52273),x52274),x52272)) % 187.68/187.65 [5228]~P71(x52283)+E(x52281,x52282)+~E(f306(f306(f81(x52283),x52284),x52281),f306(f306(f81(x52283),x52284),x52282)) % 187.68/187.65 [5230]~P70(x52303)+E(x52301,x52302)+~E(f306(f306(f81(x52303),x52301),x52304),f306(f306(f81(x52303),x52302),x52304)) % 187.68/187.65 [5309]~E(x53092,f306(f306(f284(x53091),x53093),x53094))+~P1(f306(f63(x53091),x53094))+P1(f306(f63(x53091),x53092)) % 187.68/187.65 [5352]~P6(x53523)+E(x53521,f185(f872(x53522,a859)))+E(f306(f306(f43(x53522,x53523),x53521),f306(f16(x53523,x53522),x53524)),x53524) % 187.68/187.65 [5353]~P6(x53533)+E(x53531,f185(f872(x53532,a859)))+E(f306(f306(f44(x53532,x53533),x53531),f306(f16(x53533,x53532),x53534)),x53534) % 187.68/187.65 [5563]~P109(x55633)+E(x55631,x55632)+~E(f277(x55633,x55634,x55631),f306(f306(f284(x55633),x55632),f185(f872(x55633,a859)))) % 187.68/187.65 [5564]~P109(x55643)+E(x55641,x55642)+~E(f277(x55643,x55641,x55642),f306(f306(f284(x55643),x55644),f185(f872(x55643,a859)))) % 187.68/187.65 [5625]~P38(x56253,x56251,x56254)+P38(x56253,x56251,f306(f306(f143(x56253),x56252),x56254))+P1(f306(x56251,x56252)) % 187.68/187.65 [5727]~P34(x57271,x57272,x57274)+~P1(f306(x57272,x57273))+P34(x57271,x57272,f306(f306(f143(x57271),x57273),x57274)) % 187.68/187.65 [5861]P1(f306(x58611,x58612))+~P1(f306(f240(x58613,x58611),x58614))+~P1(f306(f306(f308(x58613),x58612),x58614)) % 187.68/187.65 [5870]~P34(x58701,x58702,x58704)+~P34(x58701,x58702,x58703)+P34(x58701,x58702,f306(f306(f122(x58701),x58703),x58704)) % 187.68/187.65 [5880]P36(x58801,x58802,x58803)+~P36(x58801,x58802,f306(f306(f143(x58801),x58804),x58803))+P1(f306(x58802,x58804)) % 187.68/187.65 [5881]P38(x58811,x58812,x58813)+~P38(x58811,x58812,f306(f306(f143(x58811),x58814),x58813))+P1(f306(x58812,x58814)) % 187.68/187.65 [5894]E(x58941,x58942)+~P1(f306(f306(f193(x58943),x58944),x58942))+~P1(f306(f306(f193(x58943),x58944),x58941)) % 187.68/187.65 [5963]P36(x59631,x59632,x59633)+P36(x59631,x59632,x59634)+~P36(x59631,x59632,f306(f306(f122(x59631),x59634),x59633)) % 187.68/187.65 [5982]~P74(x59821)+E(f306(f306(f6(a865,x59821),x59822),f306(f276(a865,x59823),f306(a119,x59824))),f2(x59821))+~P1(f306(f306(f221(a865),x59824),x59823)) % 187.68/187.65 [5987]~P5(x59871)+~E(f46(x59871,x59872,x59873),f46(x59871,x59874,x59873))+E(f46(x59871,f306(f80(x59871),x59872),x59873),f46(x59871,f306(f80(x59871),x59874),x59873)) % 187.68/187.65 [6055]P1(f306(x60551,x60552))+~E(f306(f128(x60553,x60551),x60554),x60554)+~P1(f306(f306(f308(x60553),x60552),f306(f164(x60553),x60554))) % 187.68/187.65 [6073]~E(f306(f306(f81(a865),x60733),x60732),f306(f306(f81(a865),x60731),x60734))+~P1(f306(f306(f221(a865),x60733),x60734))+P1(f306(f306(f221(a865),x60731),x60732)) % 187.68/187.65 [6077]P36(x60771,x60772,x60773)+~P1(f306(x60772,x60774))+~P1(f306(f306(f308(x60771),x60774),f306(f164(x60771),x60773))) % 187.68/187.65 [6113]~P34(x61133,x61131,x61134)+P1(f306(x61131,x61132))+~P1(f306(f306(f308(x61133),x61132),f306(f164(x61133),x61134))) % 187.68/187.65 [6115]~E(f306(f128(x61151,x61152),x61153),f120(x61151))+~P1(f306(x61152,x61154))+~P1(f306(f306(f308(x61151),x61154),f306(f164(x61151),x61153))) % 187.68/187.65 [6116]~E(f168(x61163,x61161,x61164),x61164)+P1(f306(x61161,x61162))+~P1(f306(f306(f308(x61163),x61162),f306(f164(x61163),x61164))) % 187.68/187.65 [6149]~E(x61494,f185(f872(x61492,a859)))+~E(x61493,f185(f872(x61491,a859)))+E(f293(x61491,x61492,x61493,x61494),f185(f872(f870(x61491,x61492),a859))) % 187.68/187.65 [6295]P1(f306(x62951,x62952))+~P1(f306(f152(x62953,x62951),x62954))+~P1(f306(f306(f308(x62953),x62952),f306(f164(x62953),x62954))) % 187.68/187.65 [6564]~P74(x65641)+E(f306(f306(f6(a865,x65641),x65642),f277(a865,x65643,f306(a119,x65644))),f2(x65641))+~P1(f306(f306(f221(a865),f306(a119,x65644)),x65643)) % 187.68/187.65 [6709]~P108(x67091)+E(f306(f306(f22(f872(x67091,a859)),f306(f276(x67091,x67092),x67093)),f306(f276(x67091,x67092),x67094)),f306(f276(x67091,x67094),x67093))+~P1(f306(f306(f220(x67091),x67092),x67094)) % 187.68/187.65 [7059]~P1(f306(f306(f308(f866(x70591)),x70594),f153(x70591,x70593)))+P1(f306(f306(f308(x70591),x70592),x70593))+~P1(f306(f306(f308(x70591),x70592),f306(f164(x70591),x70594))) % 187.68/187.65 [7066]~P40(x70661,x70662)+P1(f306(f306(f308(x70661),f645(x70662,x70661,x70663)),x70663))+~P1(f306(f306(f308(x70661),x70664),x70663)) % 187.68/187.65 [7122]~P75(x71221)+E(f306(f306(f306(f67(x71221,x71222,f82(x71221)),x71223),f79(x71221)),x71224),f306(f306(f9(x71222,x71221),x71223),x71224))+~P1(f306(f63(x71222),x71224)) % 187.68/187.65 [7124]~P74(x71241)+E(f306(f306(f306(f67(x71241,x71242,f81(x71241)),x71243),f2(x71241)),x71244),f306(f306(f6(x71242,x71241),x71243),x71244))+~P1(f306(f63(x71242),x71244)) % 187.68/187.65 [7152]P28(x71521,x71522,x71523,x71524)+~E(f306(f39(x71522),f306(f285(x71521,x71522,x71523),x71524)),f306(f39(x71521),x71524))+~P1(f306(f63(x71521),x71524)) % 187.68/187.65 [7337]~P74(x73371)+E(f306(f306(f81(x73371),f306(x73372,x73373)),f306(f306(f6(a865,x73371),x73372),f279(a865,x73373,x73374))),f306(f306(f6(a865,x73371),x73372),f277(a865,x73373,x73374)))+~P1(f306(f306(f220(a865),x73373),x73374)) % 187.68/187.65 [7347]~P75(x73471)+~P28(x73472,x73471,x73473,x73474)+E(f306(f306(f9(x73471,x73471),f35(x73471)),f306(f285(x73472,x73471,x73473),x73474)),f306(f306(f9(x73472,x73471),x73473),x73474)) % 187.68/187.65 [7348]~P74(x73481)+~P28(x73482,x73481,x73483,x73484)+E(f306(f306(f6(x73481,x73481),f35(x73481)),f306(f285(x73482,x73481,x73483),x73484)),f306(f306(f6(x73482,x73481),x73483),x73484)) % 187.68/187.65 [7401]E(f306(f39(f870(x74011,x74012)),f293(x74011,x74012,x74013,x74014)),f306(f306(f81(a865),f306(f39(x74011),x74013)),f306(f39(x74012),x74014)))+~P1(f306(f63(x74012),x74014))+~P1(f306(f63(x74011),x74013)) % 187.68/187.65 [7485]E(x74851,x74852)+P1(f306(f306(f308(x74853),x74851),f306(f164(x74853),f162(x74853,x74852,x74854))))+~P1(f306(f306(f308(x74853),x74851),f306(f164(x74853),x74854))) % 187.68/187.65 [7625]~P1(f306(f306(f220(f872(x76251,a859)),x76254),f306(x76253,x76254)))+~P1(f306(f306(f308(x76251),x76252),x76254))+P1(f306(f306(f308(x76251),x76252),f103(f872(x76251,a859),x76253))) % 187.68/187.65 [7710]~P74(x77101)+E(f306(f306(f81(x77101),f306(f306(f6(a865,x77101),x77102),f306(f276(a865,x77103),x77104))),f306(x77102,x77104)),f306(f306(f6(a865,x77101),x77102),f306(f276(a865,x77103),f306(a119,x77104))))+P1(f306(f306(f221(a865),x77104),x77103)) % 187.68/187.65 [7763]~P28(x77631,x77632,x77633,f231(f872(x77631,a859)))+~P1(f306(f63(x77632),x77634))+P1(f306(f63(x77631),f306(f286(x77631,x77632,x77633),x77634))) % 187.68/187.65 [7876]P1(f306(f306(f308(f866(x78761)),f306(f306(f143(x78761),x78762),x78763)),f153(x78761,x78764)))+~P1(f306(f306(f308(f866(x78761)),x78763),f153(x78761,x78764)))+~P1(f306(f306(f308(x78761),x78762),x78764)) % 187.68/187.65 [7967]~E(f306(f285(x79673,x79671,x79674),f231(f872(x79673,a859))),f231(f872(x79671,a859)))+P1(f306(f63(x79671),x79672))+~P1(f306(f63(x79673),f306(f286(x79673,x79671,x79674),x79672))) % 187.68/187.65 [8064]~P28(x80641,x80643,x80644,x80642)+P1(f306(f63(x80641),x80642))+~P1(f306(f63(x80643),f306(f285(x80641,x80643,x80644),x80642))) % 187.68/187.65 [8085]~E(x80852,x80853)+P1(f306(f306(f308(f871(x80851,x80851)),f306(f306(f236(x80851,x80851),x80852),x80853)),f233(x80851,x80854)))+~P1(f306(f306(f308(x80851),x80852),x80854)) % 187.68/187.65 [8124]~P74(x81241)+E(f306(f306(f81(x81241),f306(f306(f6(a865,x81241),x81242),f277(a865,x81243,x81244))),f306(x81242,f306(a119,x81244))),f306(f306(f6(a865,x81241),x81242),f277(a865,x81243,f306(a119,x81244))))+P1(f306(f306(f221(a865),f306(a119,x81244)),x81243)) % 187.68/187.65 [8188]P1(f306(x81881,x81882))+~P1(f306(x81881,f306(f306(f157(x81883),x81884),f686(x81881,x81884,x81883))))+~P1(f306(f306(f308(x81883),x81882),f306(f164(x81883),x81884))) % 187.68/187.65 [8328]~P1(f306(f306(f308(x83281),x83282),f295(x83281,x83284)))+P1(f306(f306(f308(f866(x83281)),f306(f306(f143(x83281),x83282),x83283)),f295(f866(x83281),f149(x83281,x83284))))+~P1(f306(f306(f308(f866(x83281)),x83283),f295(f866(x83281),f149(x83281,x83284)))) % 187.68/187.65 [8341]~P28(x83412,x83413,x83414,f643(x83414,x83413,x83412,x83411))+P28(x83412,x83413,x83414,f42(f872(x83412,a859),x83411))+E(x83411,f185(f872(f872(x83412,a859),a859))) % 187.68/187.65 [8617]E(x86171,x86172)+~P1(f306(f306(f308(f871(x86173,x86173)),f306(f306(f236(x86173,x86173),x86171),x86172)),f282(x86173,x86174)))+P1(f306(f306(f308(x86173),x86171),f306(f234(x86173,x86173),x86174))) % 187.68/187.65 [8897]P28(x88972,x88973,x88974,f42(f872(x88972,a859),x88971))+E(x88971,f185(f872(f872(x88972,a859),a859)))+P1(f306(f306(f308(f872(x88972,a859)),f643(x88974,x88973,x88972,x88971)),x88971)) % 187.68/187.65 [9036]P1(f306(f63(x90361),x90362))+~P1(f306(f63(x90364),f306(f285(x90361,x90364,x90363),x90362)))+P1(f306(f306(f308(x90361),f529(x90363,x90364,x90362,x90361)),x90362)) % 187.68/187.65 [9129]~P6(x91292)+E(f306(f306(f66(x91291,x91292,f306(f306(f8(x91292,f872(x91292,x91292),x91291),f108(x91292)),x91293)),f185(x91292)),x91294),f306(f306(f43(x91291,x91292),x91294),x91293))+~P1(f306(f63(x91291),x91294)) % 187.68/187.65 [9130]~P6(x91302)+E(f306(f306(f66(x91301,x91302,f306(f306(f8(x91302,f872(x91302,x91302),x91301),f109(x91302)),x91303)),f231(x91302)),x91304),f306(f306(f44(x91301,x91302),x91304),x91303))+~P1(f306(f63(x91301),x91304)) % 187.68/187.65 [9215]P1(f306(x92151,x92152))+~P1(f306(x92151,f306(f306(f157(x92153),x92154),f759(x92152,x92151,x92154,x92153))))+~P1(f306(f306(f308(x92153),x92152),f306(f164(x92153),x92154))) % 187.68/187.65 [9236]E(x92361,x92362)+~P1(f306(f306(f308(f871(x92363,x92363)),f306(f306(f236(x92363,x92363),x92361),x92362)),f282(x92363,x92364)))+P1(f306(f306(f308(f871(x92363,x92363)),f306(f306(f236(x92363,x92363),x92361),x92362)),f306(f306(f263(x92363,x92363,x92363),x92364),f282(x92363,x92364)))) % 187.68/187.65 [9286]~E(f306(f186(f866(x92861)),x92862),f306(f186(f866(x92861)),x92863))+~P1(f306(f306(f308(f871(f866(x92861),f866(x92861))),f306(f306(f236(f866(x92861),f866(x92861)),x92862),x92863)),f139(x92861,x92864)))+P1(f306(f306(f308(f871(f866(x92861),f866(x92861))),f306(f306(f236(f866(x92861),f866(x92861)),x92862),x92863)),f137(x92861,x92864))) % 187.68/187.65 [9520]P34(x95201,f306(f306(f18(x95201,a859,a859),f306(f306(f8(a859,f872(a859,a859),x95201),a305),f306(f306(f8(a859,a859,x95201),a301),x95202))),f306(a303,x95203)),x95204)+~P1(f306(x95202,x95203))+~P38(x95201,x95202,f306(f306(f143(x95201),x95203),x95204)) % 187.68/187.65 [9681]~P34(x96811,f306(f306(f18(x96811,a859,a859),f306(f306(f8(a859,f872(a859,a859),x96811),a305),f306(f306(f8(a859,a859,x96811),a301),x96812))),f306(a303,x96813)),x96814)+~P1(f306(x96812,x96813))+P38(x96811,x96812,f306(f306(f143(x96811),x96813),x96814)) % 187.68/187.65 [9685]~P38(x96851,x96852,x96854)+~P34(x96851,f306(f306(f18(x96851,a859,a859),f306(f306(f8(a859,f872(a859,a859),x96851),a305),f306(f306(f8(a859,a859,x96851),a301),x96852))),f306(a303,x96853)),x96854)+P38(x96851,x96852,f306(f306(f143(x96851),x96853),x96854)) % 187.68/187.65 [9724]~P68(x97241)+E(f306(f306(f6(a865,x97241),f306(f306(f18(a865,x97241,x97241),f306(f306(f8(x97241,f872(x97241,x97241),a865),f22(x97241)),x97242)),f306(f306(f8(a865,x97241,a865),x97242),f306(f306(f7(a865,a865,a865),f81(a865)),f79(a865))))),f277(a865,x97243,x97244)),f2(x97241))+P1(f306(f306(f220(a865),x97243),x97244)) % 187.68/187.65 [9968]~P40(x99682,x99684)+~P28(x99682,x99681,x99683,f231(f872(x99682,a859)))+P40(x99681,f306(f285(f871(x99682,x99682),f871(x99681,x99681),f246(x99682,x99681,x99682,x99681,x99683,x99683)),x99684)) % 187.68/187.65 [10138]~E(f306(f186(f866(x101381)),x101383),f306(f186(f866(x101381)),x101382))+P1(f306(f306(f308(f871(f866(x101381),f866(x101381))),f306(f306(f236(f866(x101381),f866(x101381)),x101382),x101383)),f150(x101381,x101384)))+~P1(f306(f306(f245(x101381,x101381,a859),f306(f306(f7(x101381,f872(f871(x101381,x101381),a859),f872(x101381,a859)),f306(f306(f8(f872(x101381,f872(f872(f871(x101381,x101381),a859),a859)),f872(f872(f871(x101381,x101381),a859),f872(x101381,a859)),x101381),f7(x101381,f872(f871(x101381,x101381),a859),a859)),f306(f306(f8(f872(x101381,f871(x101381,x101381)),f872(x101381,f872(f872(f871(x101381,x101381),a859),a859)),x101381),f306(f8(f871(x101381,x101381),f872(f872(f871(x101381,x101381),a859),a859),x101381),f308(f871(x101381,x101381)))),f236(x101381,x101381)))),x101384)),f675(x101384,x101383,x101382,x101381))) % 187.68/187.65 [5946]~E(x59464,x59462)+P1(f306(x59461,x59462))+P1(f306(f306(f193(f33(x59461,x59463)),x59462),x59464)) % 187.68/187.65 [6039]~P4(x60391)+~E(x60392,f2(x60391))+E(f306(f306(f40(x60391),f306(f306(f82(x60391),x60392),x60393)),f306(f306(f82(x60391),x60392),x60394)),f2(x60391)) % 187.68/187.65 [6076]E(x60761,f120(x60762))+E(x60763,f306(f306(f22(a865),f306(f186(f866(x60762)),x60761)),f79(a865)))+E(f136(x60762,f306(f306(f151(x60762,x60761),x60763),x60764)),f136(x60762,x60761)) % 187.68/187.65 [6104]E(x61041,x61042)+P1(f306(x61043,x61042))+~P1(f306(f306(f306(f284(x61044),x61041),x61043),x61042)) % 187.68/187.65 [6120]~P74(x61201)+~P1(f306(f129(x61202),x61204))+E(f306(f158(x61201),f306(f306(f146(x61202,x61201),x61203),x61204)),f306(f306(f6(x61202,x61201),x61203),f306(f164(x61202),x61204))) % 187.68/187.65 [6142]~P75(x61422)+~P1(f306(f63(x61421),x61424))+E(f306(f306(f9(x61421,x61422),f306(f16(x61422,x61421),x61423)),x61424),f306(f306(f237(x61422),x61423),f306(f39(x61421),x61424))) % 187.68/187.65 [6197]~P4(x61972)+E(x61971,f2(x61972))+E(f306(f306(f40(x61972),f306(f306(f82(x61972),x61973),x61971)),f306(f306(f82(x61972),x61974),x61971)),f306(f306(f40(x61972),x61973),x61974)) % 187.68/187.65 [6199]~P61(x61992)+E(x61991,f2(x61992))+E(f306(f306(f264(x61992),f306(f306(f82(x61992),x61993),x61991)),f306(f306(f82(x61992),x61994),x61991)),f306(f306(f264(x61992),x61993),x61994)) % 187.68/187.65 [6200]~P61(x62002)+E(x62001,f2(x62002))+E(f306(f306(f264(x62002),f306(f306(f82(x62002),x62001),x62003)),f306(f306(f82(x62002),x62001),x62004)),f306(f306(f264(x62002),x62003),x62004)) % 187.68/187.65 [6201]~P4(x62012)+E(x62011,f2(x62012))+E(f306(f306(f40(x62012),f306(f306(f82(x62012),x62011),x62013)),f306(f306(f82(x62012),x62011),x62014)),f306(f306(f40(x62012),x62013),x62014)) % 187.68/187.65 [6264]P1(f306(x62641,x62642))+~E(x62643,f306(f306(f81(a865),x62644),x62642))+~P1(f306(x62641,f306(f306(f22(a865),x62643),x62644))) % 187.68/187.65 [6349]P31(x63491,x63492,x63493)+P30(x63491,f549(x63493,x63492,x63491),x63494)+~P1(f306(f306(f308(f864(x63491)),x63494),x63492)) % 187.68/187.65 [6351]~P1(f306(x63512,x63513))+~P1(f306(f152(x63511,x63512),x63514))+P1(f306(f152(x63511,x63512),f306(f306(f143(x63511),x63513),x63514))) % 187.68/187.65 [6391]E(x63911,f120(x63912))+~E(x63913,f306(f306(f22(a865),f306(f186(f866(x63912)),x63911)),f79(a865)))+E(f136(x63912,f306(f306(f151(x63912,x63911),x63913),x63914)),x63914) % 187.68/187.65 [6415]~P108(x64151)+~P1(f306(f306(f220(x64151),x64152),x64154))+P1(f306(f306(f220(x64151),x64152),f306(f306(f219(x64151),x64153),x64154))) % 187.68/187.65 [6417]~P108(x64171)+~P1(f306(f306(f220(x64171),x64172),x64173))+P1(f306(f306(f220(x64171),x64172),f306(f306(f219(x64171),x64173),x64174))) % 187.68/187.65 [6418]~P97(x64181)+~P1(f306(f306(f220(x64181),x64182),x64184))+P1(f306(f306(f220(x64181),x64182),f306(f306(f108(x64181),x64183),x64184))) % 187.68/187.65 [6419]~P97(x64191)+~P1(f306(f306(f220(x64191),x64192),x64193))+P1(f306(f306(f220(x64191),x64192),f306(f306(f108(x64191),x64193),x64194))) % 187.68/187.65 [6421]~P108(x64211)+~P1(f306(f306(f221(x64211),x64212),x64214))+P1(f306(f306(f221(x64211),x64212),f306(f306(f219(x64211),x64213),x64214))) % 187.68/187.65 [6423]~P108(x64231)+~P1(f306(f306(f221(x64231),x64232),x64233))+P1(f306(f306(f221(x64231),x64232),f306(f306(f219(x64231),x64233),x64234))) % 187.68/187.65 [6424]~P97(x64241)+~P1(f306(f306(f221(x64241),x64242),x64244))+P1(f306(f306(f221(x64241),x64242),f306(f306(f108(x64241),x64243),x64244))) % 187.68/187.65 [6425]~P97(x64251)+~P1(f306(f306(f221(x64251),x64252),x64253))+P1(f306(f306(f221(x64251),x64252),f306(f306(f108(x64251),x64253),x64254))) % 187.68/187.65 [6508]~E(f306(f306(f157(x65081),x65082),x65083),x65084)+E(f306(f306(f151(x65081,x65082),x65083),x65084),x65082)+~P1(f306(f306(f221(a865),x65083),f306(f186(f866(x65081)),x65082))) % 187.68/187.65 [6525]E(x65251,x65252)+P1(f306(x65253,x65251))+~P1(f306(f306(f193(f33(x65253,x65254)),x65251),x65252)) % 187.68/187.65 [6550]P1(f306(x65501,x65502))+~P1(f306(x65503,x65502))+~P1(f306(f306(f220(f872(x65504,a859)),x65503),x65501)) % 187.68/187.65 [6582]~E(f306(f306(f151(x65821,x65822),x65823),x65824),x65822)+E(f306(f306(f157(x65821),x65822),x65823),x65824)+~P1(f306(f306(f221(a865),x65823),f306(f186(f866(x65821)),x65822))) % 187.68/187.65 [6597]~P1(f306(f152(x65971,x65972),x65974))+~P1(f306(f152(x65971,x65972),x65973))+P1(f306(f152(x65971,x65972),f306(f306(f122(x65971),x65973),x65974))) % 187.68/187.65 [6697]P30(x66971,x66972,x66973)+~P30(x66971,f306(a119,x66972),f550(x66972,x66974,x66971))+~P1(f306(f306(f308(f864(x66971)),x66973),x66974)) % 187.68/187.65 [6706]E(x67061,f185(f872(x67062,a859)))+E(x67063,f185(f872(x67064,a859)))+~E(f306(f306(f243(x67064,x67062),x67063),f306(f16(f872(x67062,a859),x67064),x67061)),f185(f872(f871(x67064,x67062),a859))) % 187.68/187.65 [6724]E(x67241,x67242)+P1(f306(f306(f308(x67243),x67241),x67244))+~P1(f306(f306(f308(x67243),x67241),f306(f306(f284(x67243),x67242),x67244))) % 187.68/187.65 [6741]~P108(x67411)+P1(f306(f306(f220(x67411),x67412),x67413))+~P1(f306(f306(f220(x67411),x67412),f306(f306(f225(x67411),x67414),x67413))) % 187.68/187.65 [6743]~P108(x67431)+P1(f306(f306(f220(x67431),x67432),x67433))+~P1(f306(f306(f220(x67431),x67432),f306(f306(f225(x67431),x67433),x67434))) % 187.68/187.65 [6745]~P103(x67451)+P1(f306(f306(f220(x67451),x67452),x67453))+~P1(f306(f306(f220(x67451),x67452),f306(f306(f109(x67451),x67454),x67453))) % 187.68/187.65 [6747]~P103(x67471)+P1(f306(f306(f220(x67471),x67472),x67473))+~P1(f306(f306(f220(x67471),x67472),f306(f306(f109(x67471),x67473),x67474))) % 187.68/187.65 [6748]~P108(x67481)+P1(f306(f306(f221(x67481),x67482),x67483))+~P1(f306(f306(f221(x67481),x67482),f306(f306(f225(x67481),x67484),x67483))) % 187.68/187.65 [6749]~P108(x67491)+P1(f306(f306(f221(x67491),x67492),x67493))+~P1(f306(f306(f221(x67491),x67492),f306(f306(f225(x67491),x67493),x67494))) % 187.68/187.65 [6771]~E(f306(f306(f157(x67711),x67713),x67714),x67712)+P1(f306(f306(f308(x67711),x67712),f306(f164(x67711),x67713)))+~P1(f306(f306(f221(a865),x67714),f306(f186(f866(x67711)),x67713))) % 187.68/187.65 [6782]~P108(x67821)+~P17(x67821,f306(f306(f143(x67821),x67822),f306(f306(f143(x67821),x67823),x67824)))+P1(f306(f306(f220(x67821),x67822),x67823)) % 187.68/187.65 [6922]~P34(x69222,x69221,x69223)+P1(f306(x69221,f306(f306(f157(x69222),x69223),x69224)))+~P1(f306(f306(f221(a865),x69224),f306(f186(f866(x69222)),x69223))) % 187.68/187.65 [6941]E(x69411,f2(a1))+E(f306(f306(f40(a1),x69412),x69411),x69413)+~P1(f306(f50(x69412,x69411),f306(f306(f236(a1,a1),x69413),x69414))) % 187.68/187.65 [6962]E(f46(a1,x69622,x69621),x69623)+E(x69621,f2(a1))+~P1(f306(f50(x69622,x69621),f306(f306(f236(a1,a1),x69624),x69623))) % 187.68/187.65 [7083]P1(f306(f306(f308(x70831),x70832),x70833))+~P1(f306(f306(f308(x70831),x70832),x70834))+~P1(f306(f306(f221(f872(x70831,a859)),x70834),x70833)) % 187.68/187.65 [7084]P1(f306(f306(f308(x70841),x70842),x70843))+~P1(f306(f306(f308(x70841),x70842),x70844))+~P1(f306(f306(f220(f872(x70841,a859)),x70844),x70843)) % 187.68/187.65 [7192]P36(x71921,x71922,x71923)+~P1(f306(x71922,f306(f306(f157(x71921),x71923),x71924)))+~P1(f306(f306(f221(a865),x71924),f306(f186(f866(x71921)),x71923))) % 187.68/187.65 [7302]~P107(x73022)+~P1(f306(f306(f221(f872(x73021,x73022)),x73023),x73024))+P1(f306(f306(f220(f872(x73021,x73022)),x73023),x73024)) % 187.68/187.65 [7389]~P27(x73891,x73892,x73894)+P27(x73891,x73892,f306(f306(f284(f864(x73891)),x73893),x73894))+~P27(x73891,x73892,f306(f306(f284(f864(x73891)),x73893),f185(f872(f864(x73891),a859)))) % 187.68/187.65 [7434]~P1(f306(f306(f308(x74341),x74342),x74344))+P1(f306(f306(f308(x74341),x74342),f41(f872(x74341,a859),x74343)))+~P1(f306(f306(f308(f872(x74341,a859)),x74344),x74343)) % 187.68/187.65 [7446]P30(x74461,x74462,x74463)+P1(f306(f306(f308(f864(x74461)),f550(x74462,x74464,x74461)),x74464))+~P1(f306(f306(f308(f864(x74461)),x74463),x74464)) % 187.68/187.65 [7463]~P82(x74631)+~P1(f306(f306(f220(x74631),x74633),x74634))+P1(f306(f306(f220(x74631),f306(f306(f81(x74631),x74632),x74633)),f306(f306(f81(x74631),x74632),x74634))) % 187.68/187.65 [7464]~P83(x74641)+~P1(f306(f306(f220(x74641),x74643),x74644))+P1(f306(f306(f220(x74641),f306(f306(f81(x74641),x74642),x74643)),f306(f306(f81(x74641),x74642),x74644))) % 187.68/187.65 [7465]~P82(x74651)+~P1(f306(f306(f220(x74651),x74652),x74654))+P1(f306(f306(f220(x74651),f306(f306(f81(x74651),x74652),x74653)),f306(f306(f81(x74651),x74654),x74653))) % 187.68/187.65 [7466]~P83(x74661)+~P1(f306(f306(f220(x74661),x74662),x74664))+P1(f306(f306(f220(x74661),f306(f306(f81(x74661),x74662),x74663)),f306(f306(f81(x74661),x74664),x74663))) % 187.68/187.65 [7467]~P82(x74671)+~P1(f306(f306(f221(x74671),x74673),x74674))+P1(f306(f306(f221(x74671),f306(f306(f81(x74671),x74672),x74673)),f306(f306(f81(x74671),x74672),x74674))) % 187.68/187.65 [7468]~P85(x74681)+~P1(f306(f306(f221(x74681),x74683),x74684))+P1(f306(f306(f221(x74681),f306(f306(f81(x74681),x74682),x74683)),f306(f306(f81(x74681),x74682),x74684))) % 187.68/187.65 [7469]~P82(x74691)+~P1(f306(f306(f221(x74691),x74692),x74694))+P1(f306(f306(f221(x74691),f306(f306(f81(x74691),x74692),x74693)),f306(f306(f81(x74691),x74694),x74693))) % 187.68/187.65 [7470]~P85(x74701)+~P1(f306(f306(f221(x74701),x74702),x74704))+P1(f306(f306(f221(x74701),f306(f306(f81(x74701),x74702),x74703)),f306(f306(f81(x74701),x74704),x74703))) % 187.68/187.65 [7479]~P92(x74791)+~P126(x74791)+E(f306(f306(f22(x74791),f306(f306(f82(x74791),x74792),f306(f111(x74791),x74793))),f306(f306(f82(x74791),x74794),f306(f111(x74791),x74793))),f306(f306(f82(x74791),f306(f306(f22(x74791),x74792),x74794)),f306(f111(x74791),x74793))) % 187.68/187.65 [7480]~P92(x74801)+~P138(x74801)+E(f306(f306(f81(x74801),f306(f306(f82(x74801),x74802),f306(f111(x74801),x74803))),f306(f306(f82(x74801),x74804),f306(f111(x74801),x74803))),f306(f306(f82(x74801),f306(f306(f81(x74801),x74802),x74804)),f306(f111(x74801),x74803))) % 187.68/187.65 [7515]~P74(x75151)+E(f306(f306(f81(x75151),f306(x75152,x75153)),f306(f306(f6(a865,x75151),x75152),f277(a865,f306(a119,x75153),x75154))),f306(f306(f6(a865,x75151),x75152),f277(a865,x75153,x75154)))+~P1(f306(f306(f220(a865),x75153),x75154)) % 187.68/187.65 [7526]~P28(x75262,x75261,x75263,f306(f164(x75262),x75264))+~P1(f306(f129(x75262),x75264))+P1(f306(f129(x75261),f306(f306(f146(x75262,x75261),x75263),x75264))) % 187.68/187.65 [7573]~P1(f306(f306(f220(a865),x75732),x75734))+~P1(f306(f306(f220(a865),x75731),x75733))+P1(f306(f306(f220(a865),f306(f306(f81(a865),x75731),x75732)),f306(f306(f81(a865),x75733),x75734))) % 187.68/187.65 [7574]~P1(f306(f306(f220(a865),x75742),x75744))+~P1(f306(f306(f220(a865),x75741),x75743))+P1(f306(f306(f220(a865),f306(f306(f82(a865),x75741),x75742)),f306(f306(f82(a865),x75743),x75744))) % 187.68/187.65 [7577]~P1(f306(f306(f221(a865),x75772),x75774))+~P1(f306(f306(f221(a865),x75771),x75773))+P1(f306(f306(f221(a865),f306(f306(f81(a865),x75771),x75772)),f306(f306(f81(a865),x75773),x75774))) % 187.68/187.65 [7578]~P1(f306(f306(f220(a1),x75782),x75784))+~P1(f306(f306(f221(a1),x75781),x75783))+P1(f306(f306(f221(a1),f306(f306(f81(a1),x75781),x75782)),f306(f306(f81(a1),x75783),x75784))) % 187.68/187.65 [7627]P1(f306(f306(f308(x76271),x76272),x76273))+~P1(f306(f306(f308(x76271),x76272),f42(f872(x76271,a859),x76274)))+~P1(f306(f306(f308(f872(x76271,a859)),x76273),x76274)) % 187.68/187.65 [7642]~P1(f306(x76421,f685(x76421,x76423,x76422)))+P1(f306(x76421,f306(f306(f157(x76422),x76423),x76424)))+~P1(f306(f306(f221(a865),x76424),f306(f186(f866(x76422)),x76423))) % 187.68/187.65 [7647]P1(f306(x76471,x76472))+~P1(f306(f306(f308(x76474),x76472),f306(f164(x76474),x76473)))+P1(f306(f306(f221(a865),f686(x76471,x76473,x76474)),f306(f186(f866(x76474)),x76473))) % 187.68/187.65 [7667]~P1(f306(f306(f193(x76672),x76673),x76674))+~P1(f306(f306(f193(f33(x76671,x76672)),x76674),x76673))+P1(f306(f306(f193(f33(x76671,x76672)),x76673),x76673)) % 187.68/187.65 [7696]~P107(x76961)+~P1(f306(f306(f221(f872(x76962,x76961)),x76964),x76963))+~P1(f306(f306(f220(f872(x76962,x76961)),x76963),x76964)) % 187.68/187.65 [7740]~P1(f306(x77404,x77402))+~P1(f306(f306(f308(x77401),x77402),x77403))+P1(f306(f306(f308(x77401),x77402),f306(f306(f109(f872(x77401,a859)),x77403),f306(f228(x77401),x77404)))) % 187.68/187.65 [7886]~P1(f306(f306(f308(x78861),x78863),x78864))+~P1(f306(f306(f221(f872(x78861,a859)),x78862),x78864))+P1(f306(f306(f221(f872(x78861,a859)),x78862),f306(f306(f284(x78861),x78863),x78864))) % 187.68/187.65 [7888]E(f306(f306(f109(f872(x78881,a859)),x78882),x78883),f185(f872(x78881,a859)))+~E(f306(f306(f109(f872(x78881,a859)),f41(f872(x78881,a859),x78884)),x78883),f185(f872(x78881,a859)))+~P1(f306(f306(f308(f872(x78881,a859)),x78882),x78884)) % 187.68/187.65 [7963]P1(f306(f306(f308(x79631),x79632),x79633))+~P1(f306(f306(f220(f872(x79631,a859)),x79633),f306(f306(f284(x79631),x79632),x79634)))+P1(f306(f306(f220(f872(x79631,a859)),x79633),x79634)) % 187.68/187.65 [7985]P1(f306(f306(f308(x79852),f685(x79851,x79853,x79852)),f306(f164(x79852),x79853)))+P1(f306(x79851,f306(f306(f157(x79852),x79853),x79854)))+~P1(f306(f306(f221(a865),x79854),f306(f186(f866(x79852)),x79853))) % 187.68/187.65 [7993]~P1(f306(f306(f220(f872(x79931,a859)),x79932),x79934))+P1(f306(f306(f220(f872(x79931,a859)),x79932),x79933))+~P1(f306(f306(f220(f872(x79931,a859)),x79934),x79933)) % 187.68/187.65 [7994]~P1(f306(f306(f221(f872(x79941,a859)),x79942),x79944))+~P1(f306(f306(f220(f872(x79941,a859)),x79944),x79943))+P1(f306(f306(f221(f872(x79941,a859)),x79942),x79943)) % 187.68/187.65 [7995]~P1(f306(f306(f220(f872(x79951,a859)),x79952),x79954))+~P1(f306(f306(f221(f872(x79951,a859)),x79954),x79953))+P1(f306(f306(f221(f872(x79951,a859)),x79952),x79953)) % 187.68/187.65 [7996]~P1(f306(f306(f221(f872(x79961,a859)),x79962),x79964))+P1(f306(f306(f221(f872(x79961,a859)),x79962),x79963))+~P1(f306(f306(f221(f872(x79961,a859)),x79964),x79963)) % 187.68/187.65 [8037]~P1(f306(f306(f308(x80371),x80374),x80373))+~P1(f306(f306(f221(f872(x80371,a859)),x80372),f306(f306(f284(x80371),x80374),x80373)))+P1(f306(f306(f221(f872(x80371,a859)),x80372),x80373)) % 187.68/187.65 [8049]~P82(x80491)+P1(f306(f306(f220(x80491),x80492),x80493))+~P1(f306(f306(f220(x80491),f306(f306(f81(x80491),x80494),x80492)),f306(f306(f81(x80491),x80494),x80493))) % 187.68/187.65 [8051]~P82(x80511)+P1(f306(f306(f220(x80511),x80512),x80513))+~P1(f306(f306(f220(x80511),f306(f306(f81(x80511),x80512),x80514)),f306(f306(f81(x80511),x80513),x80514))) % 187.68/187.65 [8053]~P82(x80531)+P1(f306(f306(f221(x80531),x80532),x80533))+~P1(f306(f306(f221(x80531),f306(f306(f81(x80531),x80534),x80532)),f306(f306(f81(x80531),x80534),x80533))) % 187.68/187.65 [8055]~P82(x80551)+P1(f306(f306(f221(x80551),x80552),x80553))+~P1(f306(f306(f221(x80551),f306(f306(f81(x80551),x80552),x80554)),f306(f306(f81(x80551),x80553),x80554))) % 187.68/187.65 [8104]P1(f306(x81041,x81042))+~E(f306(f306(f130(x81043),f306(f186(f866(x81043)),f168(x81043,x81041,x81044))),x81044),f120(x81043))+~P1(f306(f306(f308(x81043),x81042),f306(f164(x81043),x81044))) % 187.68/187.65 [8230]P1(f306(x82301,x82302))+~P1(f306(f306(f308(x82303),x82302),f306(f164(x82303),x82304)))+P1(f306(f306(f221(a865),f306(f186(f866(x82303)),f306(f128(x82303,x82301),x82304))),f306(f186(f866(x82303)),x82304))) % 187.68/187.65 [8359]E(x83591,x83592)+P1(f306(f306(f193(x83593),x83591),f412(x83592,x83591,x83593,x83594)))+~P1(f306(f306(f193(f33(x83594,x83593)),x83591),x83592)) % 187.68/187.65 [8386]~P1(f306(x83864,x83862))+P1(f306(f306(f193(x83861),x83862),f412(x83863,x83862,x83861,x83864)))+~P1(f306(f306(f193(f33(x83864,x83861)),x83862),x83863)) % 187.68/187.65 [8707]~P1(f306(x87071,f775(x87071,x87073,x87072,x87074)))+P1(f306(x87071,f306(f306(f157(x87072),x87073),x87074)))+~P1(f306(f306(f221(a865),x87074),f306(f186(f866(x87072)),x87073))) % 187.68/187.65 [8731]~P28(x87314,x87313,x87311,f231(f872(x87314,a859)))+E(f306(x87311,f479(x87312,x87311,x87313,x87314)),x87312)+~P1(f306(f306(f308(x87313),x87312),f306(f285(x87314,x87313,x87311),f231(f872(x87314,a859))))) % 187.68/187.65 [8796]E(f168(x87961,x87962,x87963),f306(f306(f165(x87961),x87964),x87963))+P1(f306(f306(f221(a865),f751(x87962,x87963,x87961,x87964)),x87964))+P1(f306(f306(f221(a865),x87964),f306(f186(f866(x87961)),x87963))) % 187.68/187.65 [8799]E(f168(x87991,x87992,x87993),f306(f306(f165(x87991),x87994),x87993))+P1(f306(f306(f221(a865),f751(x87992,x87993,x87991,x87994)),x87994))+P1(f306(x87992,f306(f306(f157(x87991),x87993),x87994))) % 187.68/187.65 [8829]P1(f306(x88291,x88292))+~P1(f306(f306(f308(x88294),x88292),f306(f164(x88294),x88293)))+P1(f306(f306(f221(a865),f759(x88292,x88291,x88293,x88294)),f306(f186(f866(x88294)),x88293))) % 187.68/187.65 [8832]E(f168(x88321,x88322,x88323),f306(f306(f165(x88321),x88324),x88323))+P1(f306(f306(f221(a865),x88324),f306(f186(f866(x88321)),x88323)))+P1(f306(f306(f221(a865),f751(x88322,x88323,x88321,x88324)),f306(f186(f866(x88321)),x88323))) % 187.68/187.65 [8839]E(f168(x88391,x88392,x88393),f306(f306(f165(x88391),x88394),x88393))+P1(f306(x88392,f306(f306(f157(x88391),x88393),x88394)))+P1(f306(f306(f221(a865),f751(x88392,x88393,x88391,x88394)),f306(f186(f866(x88391)),x88393))) % 187.68/187.65 [8866]~P111(x88664)+P1(f306(f306(f308(x88661),f666(x88662,x88663,x88661,x88664)),x88663))+P1(f306(f306(f221(x88664),f2(x88664)),f306(f306(f9(x88661,x88664),x88662),x88663))) % 187.68/187.65 [8867]~P111(x88674)+P1(f306(f306(f308(x88671),f802(x88672,x88673,x88671,x88674)),x88673))+P1(f306(f306(f220(x88674),f2(x88674)),f306(f306(f9(x88671,x88674),x88672),x88673))) % 187.68/187.65 [8899]~P1(f306(f63(x88991),x88994))+P1(f306(f306(f308(x88991),f497(x88992,x88993,x88994,x88991)),x88994))+P1(f306(f63(f871(x88991,x88993)),f306(f306(f243(x88991,x88993),x88994),x88992))) % 187.68/187.65 [8934]P1(f306(f306(f308(x89342),f775(x89341,x89343,x89342,x89344)),f306(f164(x89342),x89343)))+P1(f306(x89341,f306(f306(f157(x89342),x89343),x89344)))+~P1(f306(f306(f221(a865),x89344),f306(f186(f866(x89342)),x89343))) % 187.68/187.65 [8949]E(x89491,x89492)+P1(f306(f306(f193(f33(x89493,x89494)),f412(x89491,x89492,x89494,x89493)),x89491))+~P1(f306(f306(f193(f33(x89493,x89494)),x89492),x89491)) % 187.68/187.65 [8970]~P1(f306(x89701,x89704))+P1(f306(f306(f193(f33(x89701,x89702)),f412(x89703,x89704,x89702,x89701)),x89703))+~P1(f306(f306(f193(f33(x89701,x89702)),x89704),x89703)) % 187.68/187.65 [9064]P1(f306(f306(f220(a865),x90644),f306(f186(f866(x90642)),f168(x90642,x90643,x90641))))+P1(f306(f306(f221(a865),f752(x90641,x90642,x90643,x90644)),x90644))+~P1(f306(f306(f220(a865),x90644),f306(f186(f866(x90642)),x90641))) % 187.68/187.65 [9171]~E(f306(f306(f169(x91711,x91712),x91713),f766(x91714,x91713,x91712,x91711)),f306(f306(f169(x91711,x91712),x91714),f766(x91714,x91713,x91712,x91711)))+E(f306(f169(x91711,x91712),x91713),f306(f169(x91711,x91712),x91714))+~E(f306(f164(x91711),f306(f306(f146(f871(x91711,x91712),x91711),f235(x91711,x91712)),x91713)),f306(f164(x91711),f306(f306(f146(f871(x91711,x91712),x91711),f235(x91711,x91712)),x91714))) % 187.68/187.65 [9218]E(f168(x92181,x92182,x92183),f306(f306(f165(x92181),x92184),x92183))+~P1(f306(x92182,f306(f306(f157(x92181),x92183),f751(x92182,x92183,x92181,x92184))))+P1(f306(f306(f221(a865),x92184),f306(f186(f866(x92181)),x92183))) % 187.68/187.65 [9223]E(f168(x92231,x92232,x92233),f306(f306(f165(x92231),x92234),x92233))+~P1(f306(x92232,f306(f306(f157(x92231),x92233),f751(x92232,x92233,x92231,x92234))))+P1(f306(x92232,f306(f306(f157(x92231),x92233),x92234))) % 187.68/187.65 [9230]~P1(f306(f63(x92301),x92303))+~P1(f306(f63(x92302),f306(x92304,f497(x92304,x92302,x92303,x92301))))+P1(f306(f63(f871(x92301,x92302)),f306(f306(f243(x92301,x92302),x92303),x92304))) % 187.68/187.65 [9238]~P111(x92381)+~P1(f306(f306(f220(x92381),f2(x92381)),f306(x92383,f802(x92383,x92384,x92382,x92381))))+P1(f306(f306(f220(x92381),f2(x92381)),f306(f306(f9(x92382,x92381),x92383),x92384))) % 187.68/187.65 [9239]~P111(x92391)+~P1(f306(f306(f221(x92391),f2(x92391)),f306(x92393,f666(x92393,x92394,x92392,x92391))))+P1(f306(f306(f221(x92391),f2(x92391)),f306(f306(f9(x92392,x92391),x92393),x92394))) % 187.68/187.65 [9245]~E(f306(f186(f866(x92454)),x92452),f306(f186(f866(x92454)),x92453))+P1(f306(f306(f308(f871(f866(x92454),f866(x92454))),f306(f306(f236(f866(x92454),f866(x92454)),x92453),x92452)),f150(x92454,x92451)))+P1(f306(f306(f221(a865),f693(x92451,x92452,x92453,x92454)),f306(f186(f866(x92454)),x92453))) % 187.68/187.65 [9300]~P1(f306(x93003,f306(f306(f157(x93002),x93004),f752(x93004,x93002,x93003,x93001))))+P1(f306(f306(f220(a865),x93001),f306(f186(f866(x93002)),f168(x93002,x93003,x93004))))+~P1(f306(f306(f220(a865),x93001),f306(f186(f866(x93002)),x93004))) % 187.68/187.65 [9378]E(f306(f306(f165(x93781),f694(x93782,x93783,x93784,x93781)),x93783),f306(f306(f165(x93781),f694(x93782,x93783,x93784,x93781)),x93784))+~P1(f306(f306(f308(f871(f866(x93781),f866(x93781))),f306(f306(f236(f866(x93781),f866(x93781)),x93784),x93783)),f139(x93781,x93782)))+P1(f306(f306(f221(a865),f306(f186(f866(x93781)),x93784)),f306(f186(f866(x93781)),x93783))) % 187.68/187.65 [9433]~P1(f306(f306(f221(a865),f2(a865)),x94333))+~P1(f306(f306(f221(a865),x94334),x94331))+P1(f306(f306(f221(a865),f306(f306(f81(a865),f306(f306(f82(a865),x94331),f46(a865,x94332,x94333))),x94334)),f306(f306(f82(a865),x94331),x94333))) % 187.68/187.65 [9625]~P107(x96252)+~P1(f306(f306(f220(x96252),f306(x96253,f534(x96254,x96253,x96251,x96252))),f306(x96254,f534(x96254,x96253,x96251,x96252))))+P1(f306(f306(f220(f872(x96251,x96252)),x96253),x96254)) % 187.68/187.65 [9731]~P68(x97311)+E(f306(f306(f6(a865,x97311),f306(f306(f18(a865,x97311,x97311),f306(f306(f8(x97311,f872(x97311,x97311),a865),f22(x97311)),x97312)),f306(f306(f8(a865,x97311,a865),x97312),f306(f306(f7(a865,a865,a865),f81(a865)),f79(a865))))),f277(a865,x97313,x97314)),f306(f306(f22(x97311),f306(x97312,x97313)),f306(x97312,f306(f306(f81(a865),x97314),f79(a865)))))+~P1(f306(f306(f220(a865),x97313),x97314)) % 187.68/187.65 [6775]E(f306(f306(f122(x67751),x67752),x67753),x67754)+~E(x67753,f306(f306(f130(x67751),f306(f186(f866(x67751)),x67752)),x67754))+~E(f306(f306(f165(x67751),f306(f186(f866(x67751)),x67752)),x67754),x67752) % 187.68/187.65 [6830]~P62(x68302)+E(x68301,f2(x68302))+E(f306(f306(f264(x68302),f306(f306(f237(x68302),x68303),x68304)),f306(f306(f237(x68302),x68301),x68304)),f306(f306(f237(x68302),f306(f306(f264(x68302),x68303),x68301)),x68304)) % 187.68/187.65 [6964]~E(f306(f186(f866(x69641)),x69643),f306(f186(f866(x69642)),x69644))+~P1(f306(f129(x69641),x69643))+E(f175(x69641,x69642,f306(f169(x69641,x69642),f306(f306(f173(x69641,x69642),x69643),x69644))),f306(f164(x69641),x69643)) % 187.68/187.65 [6984]~P108(x69841)+~P1(f306(f306(f220(x69841),x69843),x69844))+P1(f306(f306(f220(x69841),f306(f306(f225(x69841),x69842),x69843)),x69844)) % 187.68/187.65 [6986]~P108(x69861)+~P1(f306(f306(f220(x69861),x69862),x69864))+P1(f306(f306(f220(x69861),f306(f306(f225(x69861),x69862),x69863)),x69864)) % 187.68/187.65 [6987]~P103(x69871)+~P1(f306(f306(f220(x69871),x69873),x69874))+P1(f306(f306(f220(x69871),f306(f306(f109(x69871),x69872),x69873)),x69874)) % 187.68/187.65 [6988]~P103(x69881)+~P1(f306(f306(f220(x69881),x69882),x69884))+P1(f306(f306(f220(x69881),f306(f306(f109(x69881),x69882),x69883)),x69884)) % 187.68/187.65 [6990]~P108(x69901)+~P1(f306(f306(f221(x69901),x69903),x69904))+P1(f306(f306(f221(x69901),f306(f306(f225(x69901),x69902),x69903)),x69904)) % 187.68/187.65 [6992]~P108(x69921)+~P1(f306(f306(f221(x69921),x69922),x69924))+P1(f306(f306(f221(x69921),f306(f306(f225(x69921),x69922),x69923)),x69924)) % 187.68/187.65 [6993]~P103(x69931)+~P1(f306(f306(f221(x69931),x69933),x69934))+P1(f306(f306(f221(x69931),f306(f306(f109(x69931),x69932),x69933)),x69934)) % 187.68/187.65 [6994]~P103(x69941)+~P1(f306(f306(f221(x69941),x69942),x69944))+P1(f306(f306(f221(x69941),f306(f306(f109(x69941),x69942),x69943)),x69944)) % 187.68/187.65 [7014]~P1(f306(x70143,x70144))+~P1(f306(x70142,x70144))+P1(f306(f306(f306(f109(f872(x70141,a859)),x70142),x70143),x70144)) % 187.68/187.65 [7138]P27(x71381,x71382,x71383)+~P27(x71381,x71384,x71383)+~P1(f306(f306(f220(f872(f864(x71381),a859)),x71384),x71382)) % 187.68/187.65 [7139]P27(x71391,x71392,x71393)+~P27(x71391,x71392,x71394)+~P1(f306(f306(f220(f872(f864(x71391),a859)),x71393),x71394)) % 187.68/187.65 [7505]~P74(x75051)+E(f306(f306(f81(x75051),f306(x75052,x75053)),f306(f306(f6(a865,x75051),x75052),f306(f276(a865,f306(a119,x75053)),x75054))),f306(f306(f6(a865,x75051),x75052),f306(f276(a865,x75053),x75054)))+~P1(f306(f306(f221(a865),x75053),x75054)) % 187.68/187.65 [7534]~P108(x75341)+P1(f306(f306(f220(x75341),x75342),x75343))+~P1(f306(f306(f220(x75341),f306(f306(f219(x75341),x75344),x75342)),x75343)) % 187.68/187.65 [7536]~P108(x75361)+P1(f306(f306(f220(x75361),x75362),x75363))+~P1(f306(f306(f220(x75361),f306(f306(f219(x75361),x75362),x75364)),x75363)) % 187.68/187.65 [7538]~P97(x75381)+P1(f306(f306(f220(x75381),x75382),x75383))+~P1(f306(f306(f220(x75381),f306(f306(f108(x75381),x75384),x75382)),x75383)) % 187.68/187.65 [7540]~P97(x75401)+P1(f306(f306(f220(x75401),x75402),x75403))+~P1(f306(f306(f220(x75401),f306(f306(f108(x75401),x75402),x75404)),x75403)) % 187.68/187.65 [7541]~P108(x75411)+P1(f306(f306(f221(x75411),x75412),x75413))+~P1(f306(f306(f221(x75411),f306(f306(f219(x75411),x75414),x75412)),x75413)) % 187.68/187.65 [7542]~P108(x75421)+P1(f306(f306(f221(x75421),x75422),x75423))+~P1(f306(f306(f221(x75421),f306(f306(f219(x75421),x75422),x75424)),x75423)) % 187.68/187.65 [7618]~P1(f306(f306(f308(x76181),x76182),x76184))+P1(f306(f306(f308(x76181),x76182),x76183))+P1(f306(f306(f308(x76181),x76182),f306(f306(f22(f872(x76181,a859)),x76184),x76183))) % 187.68/187.65 [7702]P1(f306(x77021,x77022))+P1(f306(x77023,x77022))+~P1(f306(f306(f306(f108(f872(x77024,a859)),x77023),x77021),x77022)) % 187.68/187.65 [7712]~P1(f306(f306(f308(x77121),x77122),x77124))+~P1(f306(f306(f308(x77121),x77122),x77123))+P1(f306(f306(f308(x77121),x77122),f306(f306(f109(f872(x77121,a859)),x77123),x77124))) % 187.68/187.65 [7764]~P108(x77641)+~P1(f306(f63(x77641),x77644))+E(f306(f306(f66(x77641,x77641,f225(x77641)),x77642),f306(f306(f284(x77641),x77643),x77644)),f306(f306(f225(x77641),x77643),f306(f306(f66(x77641,x77641,f225(x77641)),x77642),x77644))) % 187.68/187.65 [7765]~P108(x77651)+~P1(f306(f63(x77651),x77654))+E(f306(f306(f66(x77651,x77651,f219(x77651)),x77652),f306(f306(f284(x77651),x77653),x77654)),f306(f306(f219(x77651),x77653),f306(f306(f66(x77651,x77651,f219(x77651)),x77652),x77654))) % 187.68/187.65 [7766]~P97(x77661)+~P1(f306(f63(x77661),x77664))+E(f306(f306(f66(x77661,x77661,f108(x77661)),x77662),f306(f306(f284(x77661),x77663),x77664)),f306(f306(f108(x77661),x77663),f306(f306(f66(x77661,x77661,f108(x77661)),x77662),x77664))) % 187.68/187.65 [7767]~P103(x77671)+~P1(f306(f63(x77671),x77674))+E(f306(f306(f66(x77671,x77671,f109(x77671)),x77672),f306(f306(f284(x77671),x77673),x77674)),f306(f306(f109(x77671),x77673),f306(f306(f66(x77671,x77671,f109(x77671)),x77672),x77674))) % 187.68/187.65 [7768]~P92(x77681)+~P126(x77681)+E(f306(f306(f22(x77681),f306(f306(f82(x77681),f306(f111(x77681),x77682)),x77683)),f306(f306(f82(x77681),f306(f111(x77681),x77682)),x77684)),f306(f306(f82(x77681),f306(f111(x77681),x77682)),f306(f306(f22(x77681),x77683),x77684))) % 187.68/187.65 [7769]~P92(x77691)+~P138(x77691)+E(f306(f306(f81(x77691),f306(f306(f82(x77691),f306(f111(x77691),x77692)),x77693)),f306(f306(f82(x77691),f306(f111(x77691),x77692)),x77694)),f306(f306(f82(x77691),f306(f111(x77691),x77692)),f306(f306(f81(x77691),x77693),x77694))) % 187.68/187.65 [7883]E(x78831,x78832)+P1(f306(f306(f308(x78833),x78831),f306(f164(x78833),x78834)))+~P1(f306(f306(f308(x78833),x78831),f306(f164(x78833),f306(f306(f143(x78833),x78832),x78834)))) % 187.68/187.65 [7908]~P60(x79081)+~E(f306(f186(f866(x79082)),x79083),f306(f186(f866(x79081)),f57(x79081)))+E(f306(f306(f169(x79081,x79082),f306(f306(f173(x79081,x79082),f57(x79081)),x79083)),x79084),f306(f214(x79082),f748(x79084,x79083,x79082,x79081))) % 187.68/187.65 [8062]P54(x80621,x80622,x80623)+~P54(x80621,x80622,x80624)+~P1(f306(f306(f220(f872(f871(x80621,x80622),a859)),x80623),x80624)) % 187.68/187.65 [8107]P1(f306(f306(f308(x81071),x81072),x81073))+P1(f306(f306(f308(x81071),x81072),x81074))+~P1(f306(f306(f308(x81071),x81072),f306(f306(f108(f872(x81071,a859)),x81074),x81073))) % 187.68/187.65 [8118]~P50(x81181,x81184,x81183)+~P1(f306(f306(f308(x81181),x81182),x81184))+P1(f306(f306(f308(f871(x81181,x81181)),f306(f306(f236(x81181,x81181),x81182),x81182)),x81183)) % 187.68/187.65 [8133]~P1(f306(f63(x81332),x81334))+~P1(f306(f63(x81331),x81333))+P1(f306(f63(f871(x81331,x81332)),f306(f306(f243(x81331,x81332),x81333),f306(f16(f872(x81332,a859),x81331),x81334)))) % 187.68/187.65 [8134]~P1(f306(f306(f308(x81341),x81342),x81344))+~P1(f306(f306(f220(f872(x81341,a859)),x81343),x81344))+P1(f306(f306(f220(f872(x81341,a859)),f306(f306(f284(x81341),x81342),x81343)),x81344)) % 187.68/187.65 [8142]~P75(x81422)+~P141(x81422)+E(f306(f306(f9(x81421,x81422),f306(f306(f8(a865,x81422,x81421),f107(x81422)),x81423)),x81424),f306(f107(x81422),f306(f306(f9(x81421,a865),x81423),x81424))) % 187.68/187.65 [8143]~P125(x81432)+~P75(x81432)+E(f306(f306(f9(x81431,x81432),f306(f306(f8(a1,x81432,x81431),f110(x81432)),x81433)),x81434),f306(f110(x81432),f306(f306(f9(x81431,a1),x81433),x81434))) % 187.68/187.65 [8169]E(f306(f306(f22(f872(x81691,a859)),x81692),f306(f306(f22(f872(x81691,a859)),x81693),x81694)),x81694)+~P1(f306(f306(f220(f872(x81691,a859)),x81692),x81693))+~P1(f306(f306(f220(f872(x81691,a859)),x81694),x81692)) % 187.68/187.65 [8264]~P1(f306(f63(x82641),x82644))+E(f306(f306(f22(a865),f306(f306(f6(x82641,a865),x82642),x82643)),f306(f306(f6(x82641,a865),x82642),x82644)),f306(f306(f6(x82641,a865),x82642),f306(f306(f22(f872(x82641,a859)),x82643),x82644)))+~P1(f306(f306(f220(f872(x82641,a859)),x82644),x82643)) % 187.68/187.65 [8422]~P9(x84221,x84224,x84223)+~P1(f306(f306(f308(x84221),x84222),x84224))+P1(f306(f306(f308(x84221),x84222),f306(f260(x84221,x84221,x84223),f306(f306(f284(x84221),x84222),f185(f872(x84221,a859)))))) % 187.68/187.65 [8487]~P1(f306(f306(f220(f872(x84871,a859)),x84872),x84873))+~P1(f306(f306(f220(f872(x84871,a859)),x84872),x84874))+P1(f306(f306(f220(f872(x84871,a859)),x84872),f306(f306(f109(f872(x84871,a859)),x84873),x84874))) % 187.68/187.65 [8585]E(x85851,f185(f872(x85852,a859)))+P1(f306(f63(x85853),x85854))+~P1(f306(f63(f871(x85853,x85852)),f306(f306(f243(x85853,x85852),x85854),f306(f16(f872(x85852,a859),x85853),x85851)))) % 187.68/187.65 [8586]E(x85861,f185(f872(x85862,a859)))+P1(f306(f63(x85863),x85864))+~P1(f306(f63(f871(x85862,x85863)),f306(f306(f243(x85862,x85863),x85861),f306(f16(f872(x85863,a859),x85862),x85864)))) % 187.68/187.65 [8650]P1(f306(f306(f308(x86501),x86502),f295(x86501,x86503)))+~P1(f306(f306(f308(x86501),x86504),f295(x86501,x86503)))+~P1(f306(f306(f308(f871(x86501,x86501)),f306(f306(f236(x86501,x86501),x86502),x86504)),x86503)) % 187.68/187.65 [8702]~P40(x87021,x87024)+P1(f306(f306(f308(f871(x87021,x87021)),f306(f306(f236(x87021,x87021),x87023),x87022)),f282(x87021,x87024)))+P40(x87021,f306(f306(f284(f871(x87021,x87021)),f306(f306(f236(x87021,x87021),x87022),x87023)),x87024)) % 187.68/187.65 [8703]~P57(x87031,x87034)+P1(f306(f306(f308(f871(x87031,x87031)),f306(f306(f236(x87031,x87031),x87033),x87032)),f282(x87031,x87034)))+P57(x87031,f306(f306(f284(f871(x87031,x87031)),f306(f306(f236(x87031,x87031),x87032),x87033)),x87034)) % 187.68/187.65 [8781]~E(x87812,x87813)+~P1(f306(f306(f308(x87811),x87812),f306(f164(x87811),x87814)))+P1(f306(f306(f308(f871(x87811,x87811)),f306(f306(f236(x87811,x87811),x87812),x87813)),f306(f164(f871(x87811,x87811)),f306(f306(f173(x87811,x87811),x87814),x87814)))) % 187.68/187.65 [8804]~P41(f872(x88041,a859),f872(x88041,a859),x88043)+~P1(f306(f306(f308(x88041),x88042),f103(f872(x88041,a859),x88043)))+P1(f306(f306(f308(x88041),x88042),f306(x88043,f306(f306(f108(f872(x88041,a859)),x88044),f103(f872(x88041,a859),x88043))))) % 187.68/187.65 [8864]~E(x88643,x88644)+P1(f306(f306(f245(x88641,x88641,a859),a303),x88642))+~P1(f306(f306(f308(f871(x88641,x88641)),x88642),f306(f164(f871(x88641,x88641)),f306(f306(f173(x88641,x88641),x88643),x88644)))) % 187.68/187.65 [8890]~P1(f306(x88904,x88902))+P1(f306(f306(f306(f306(a195,x88901),x88902),x88903),f379(x88903,x88902,x88901,x88904)))+~P1(f306(f306(f306(f306(a195,f33(x88904,x88901)),x88902),x88903),x88902)) % 187.68/187.65 [8917]P1(f306(f306(f308(f871(f866(x89171),f866(x89171))),f306(f306(f236(f866(x89171),f866(x89171)),x89172),x89173)),f139(x89171,x89174)))+~E(f306(f306(f165(x89171),f306(f186(f866(x89171)),x89172)),x89173),x89172)+~P1(f306(f306(f221(a865),f306(f186(f866(x89171)),x89172)),f306(f186(f866(x89171)),x89173))) % 187.68/187.65 [9017]~P1(f306(f63(x90171),x90174))+P1(f306(f306(f308(x90171),f444(x90172,x90173,x90174,x90171)),x90174))+P1(f306(f63(x90173),f306(f306(f43(x90171,f872(x90173,a859)),x90174),x90172))) % 187.68/187.65 [9018]~P1(f306(f63(x90181),x90184))+P1(f306(f306(f308(x90181),f551(x90182,x90183,x90184,x90181)),x90184))+P1(f306(f63(x90183),f306(f306(f43(x90181,f872(x90183,a859)),x90184),x90182))) % 187.68/187.65 [9100]P1(f306(f306(f308(f871(x91001,x91001)),x91002),f306(f306(f263(x91001,x91001,x91001),x91003),f282(x91001,x91003))))+~P1(f306(f306(f221(a865),f2(a865)),x91004))+~P1(f306(f306(f308(f871(x91001,x91001)),x91002),f306(f306(f180(f871(x91001,x91001),a859),x91004),x91003))) % 187.68/187.65 [9108]~P40(x91081,x91082)+~P1(f306(f306(f308(f871(x91081,x91081)),f306(f306(f236(x91081,x91081),x91084),x91083)),x91082))+~P1(f306(f306(f308(f871(x91081,x91081)),f306(f306(f236(x91081,x91081),x91083),x91084)),x91082)) % 187.68/187.65 [9237]~P1(f306(f63(x92371),x92374))+E(f306(f306(f6(x92371,a865),f306(f306(f8(f872(x92372,a859),a865,x92371),f39(x92372)),x92373)),x92374),f306(f39(f871(x92371,x92372)),f306(f306(f243(x92371,x92372),x92374),x92373)))+P1(f306(f306(f308(x92371),f498(x92373,x92372,x92374,x92371)),x92374)) % 187.68/187.65 [9241]~P1(f306(f129(x92411),x92412))+P1(f306(f129(x92411),f306(f306(f151(x92411,x92412),x92413),x92414)))+P1(f306(f306(f308(x92411),x92414),f306(f306(f22(f872(x92411,a859)),f306(f164(x92411),x92412)),f306(f306(f284(x92411),f306(f306(f157(x92411),x92412),x92413)),f185(f872(x92411,a859)))))) % 187.68/187.65 [9258]~P1(f306(f63(x92582),x92583))+~P1(f306(f63(x92581),f306(x92584,f444(x92584,x92581,x92583,x92582))))+P1(f306(f63(x92581),f306(f306(f43(x92582,f872(x92581,a859)),x92583),x92584))) % 187.68/187.65 [9259]~P1(f306(f63(x92592),x92593))+~P1(f306(f63(x92591),f306(x92594,f551(x92594,x92591,x92593,x92592))))+P1(f306(f63(x92591),f306(f306(f43(x92592,f872(x92591,a859)),x92593),x92594))) % 187.68/187.65 [9338]~P1(f306(f306(f308(f871(x93381,x93381)),x93382),f306(f306(f263(x93381,x93381,x93381),x93384),f282(x93381,x93384))))+P1(f306(f306(f308(f871(x93381,x93381)),x93382),f306(f306(f263(x93381,x93381,x93381),x93383),f282(x93381,x93383))))+~P1(f306(f306(f220(f872(f871(x93381,x93381),a859)),x93384),x93383)) % 187.68/187.65 [9345]E(f306(f306(f165(x93451),f694(x93454,x93453,x93452,x93451)),x93453),f306(f306(f165(x93451),f694(x93454,x93453,x93452,x93451)),x93452))+~P1(f306(f306(f308(f871(f866(x93451),f866(x93451))),f306(f306(f236(f866(x93451),f866(x93451)),x93452),x93453)),f139(x93451,x93454)))+E(f306(f306(f165(x93451),f306(f186(f866(x93451)),x93452)),x93453),x93452) % 187.68/187.65 [9363]~P1(f306(f63(x93631),x93634))+E(f306(f306(f6(x93631,a865),f306(f306(f8(f872(x93632,a859),a865,x93631),f39(x93632)),x93633)),x93634),f306(f39(f871(x93631,x93632)),f306(f306(f243(x93631,x93632),x93634),x93633)))+~P1(f306(f63(x93632),f306(x93633,f498(x93633,x93632,x93634,x93631)))) % 187.68/187.65 [9367]~E(f306(f186(f866(x93671)),x93673),f306(f186(f866(x93671)),x93672))+P1(f306(f306(f308(f871(f866(x93671),f866(x93671))),f306(f306(f236(f866(x93671),f866(x93671)),x93672),x93673)),f150(x93671,x93674)))+P1(f306(f306(f308(f871(x93671,x93671)),f675(x93674,x93673,x93672,x93671)),f306(f164(f871(x93671,x93671)),f306(f306(f173(x93671,x93671),x93672),x93673)))) % 187.68/187.65 [9445]~P1(f306(f306(f308(f871(f866(x94451),f866(x94451))),f306(f306(f236(f866(x94451),f866(x94451)),x94452),x94453)),f139(x94451,x94454)))+E(f306(f306(f165(x94451),f306(f186(f866(x94451)),x94452)),x94453),x94452)+P1(f306(f306(f221(a865),f694(x94454,x94453,x94452,x94451)),f306(f306(f225(a865),f306(f186(f866(x94451)),x94452)),f306(f186(f866(x94451)),x94453)))) % 187.68/187.65 [9446]E(f306(f169(x94461,x94462),x94463),f306(f169(x94461,x94462),x94464))+~E(f306(f164(x94461),f306(f306(f146(f871(x94461,x94462),x94461),f235(x94461,x94462)),x94463)),f306(f164(x94461),f306(f306(f146(f871(x94461,x94462),x94461),f235(x94461,x94462)),x94464)))+P1(f306(f306(f308(x94461),f766(x94463,x94464,x94462,x94461)),f306(f164(x94461),f306(f306(f146(f871(x94461,x94462),x94461),f235(x94461,x94462)),x94464)))) % 187.68/187.65 [9462]~P1(f306(x94621,x94624))+P1(f306(f306(f306(f306(a195,f33(x94621,x94622)),f379(x94623,x94624,x94622,x94621)),x94623),x94624))+~P1(f306(f306(f306(f306(a195,f33(x94621,x94622)),x94624),x94623),x94624)) % 187.68/187.65 [9467]~P1(f306(f306(f308(f871(f866(x94671),f866(x94671))),f306(f306(f236(f866(x94671),f866(x94671)),x94672),x94673)),f139(x94671,x94674)))+P1(f306(f306(f221(a865),f306(f186(f866(x94671)),x94672)),f306(f186(f866(x94671)),x94673)))+P1(f306(f306(f221(a865),f694(x94674,x94673,x94672,x94671)),f306(f306(f225(a865),f306(f186(f866(x94671)),x94672)),f306(f186(f866(x94671)),x94673)))) % 187.68/187.65 [9769]~P1(f306(f306(f306(x97691,f668(x97691,x97694,x97693,x97692)),f669(x97691,x97694,x97693,x97692)),f670(x97691,x97694,x97693,x97692)))+P1(f306(f306(f306(x97691,x97692),x97693),x97694))+~P1(f306(f294(f871(f872(a1,f869(f866(a302))),f871(a1,a1)),a292),f306(f306(f236(f872(a1,f869(f866(a302))),f871(a1,a1)),x97692),f306(f306(f236(a1,a1),x97693),x97694)))) % 187.68/187.65 [9846]P1(f306(f306(f306(x98461,x98462),x98463),x98464))+P1(f306(f294(f871(f872(a1,f869(f866(a302))),f871(a1,a1)),a292),f306(f306(f236(f872(a1,f869(f866(a302))),f871(a1,a1)),f668(x98461,x98464,x98463,x98462)),f306(f306(f236(a1,a1),f669(x98461,x98464,x98463,x98462)),f670(x98461,x98464,x98463,x98462)))))+~P1(f306(f294(f871(f872(a1,f869(f866(a302))),f871(a1,a1)),a292),f306(f306(f236(f872(a1,f869(f866(a302))),f871(a1,a1)),x98462),f306(f306(f236(a1,a1),x98463),x98464)))) % 187.68/187.65 [9885]~P1(f306(f306(f308(f871(f866(x98851),f866(x98851))),f306(f306(f236(f866(x98851),f866(x98851)),x98852),x98853)),f139(x98851,x98854)))+E(f306(f306(f165(x98851),f306(f186(f866(x98851)),x98852)),x98853),x98852)+P1(f306(f306(f308(f871(x98851,x98851)),f306(f306(f236(x98851,x98851),f306(f306(f157(x98851),x98852),f694(x98854,x98853,x98852,x98851))),f306(f306(f157(x98851),x98853),f694(x98854,x98853,x98852,x98851)))),x98854)) % 187.68/187.65 [9888]~P1(f306(f306(f308(f871(f866(x98881),f866(x98881))),f306(f306(f236(f866(x98881),f866(x98881)),x98882),x98883)),f139(x98881,x98884)))+P1(f306(f306(f221(a865),f306(f186(f866(x98881)),x98882)),f306(f186(f866(x98881)),x98883)))+P1(f306(f306(f308(f871(x98881,x98881)),f306(f306(f236(x98881,x98881),f306(f306(f157(x98881),x98882),f694(x98884,x98883,x98882,x98881))),f306(f306(f157(x98881),x98883),f694(x98884,x98883,x98882,x98881)))),x98884)) % 187.68/187.65 [9945]~E(f306(f186(f866(x99451)),x99452),f306(f186(f866(x99451)),x99453))+P1(f306(f306(f308(f871(f866(x99451),f866(x99451))),f306(f306(f236(f866(x99451),f866(x99451)),x99452),x99453)),f150(x99451,x99454)))+~P1(f306(f306(f308(f871(x99451,x99451)),f306(f306(f236(x99451,x99451),f306(f306(f157(x99451),x99452),f693(x99454,x99453,x99452,x99451))),f306(f306(f157(x99451),x99453),f693(x99454,x99453,x99452,x99451)))),x99454)) % 187.68/187.65 [10084]~P74(x100841)+~P1(f306(f63(x100842),x100844))+E(f306(f158(x100841),f306(f306(f146(x100842,x100841),x100843),f91(f866(x100842),f306(f306(f18(f866(x100842),a859,a859),f306(f306(f8(a859,f872(a859,a859),f866(x100842)),a304),f306(f306(f7(f866(x100842),f872(x100842,a859),a859),f306(f306(f8(f872(x100842,a859),f872(f872(x100842,a859),a859),f866(x100842)),a303),f164(x100842))),x100844))),f129(x100842))))),f212(x100842,x100841,x100843,x100844)) % 187.68/187.65 [7349]~P61(x73492)+E(x73491,f2(x73492))+E(f306(f306(f264(x73492),f306(f306(f81(x73492),x73493),f306(f306(f82(x73492),x73494),x73491))),x73491),f306(f306(f81(x73492),x73494),f306(f306(f264(x73492),x73493),x73491))) % 187.68/187.65 [7350]~P4(x73502)+E(x73501,f2(x73502))+E(f306(f306(f40(x73502),f306(f306(f81(x73502),x73503),f306(f306(f82(x73502),x73504),x73501))),x73501),f306(f306(f81(x73502),x73504),f306(f306(f40(x73502),x73503),x73501))) % 187.68/187.65 [7351]~P4(x73512)+E(x73511,f2(x73512))+E(f306(f306(f40(x73512),f306(f306(f81(x73512),x73513),f306(f306(f82(x73512),x73511),x73514))),x73511),f306(f306(f81(x73512),x73514),f306(f306(f40(x73512),x73513),x73511))) % 187.68/187.65 [7581]~P62(x75812)+E(x75811,f2(x75812))+E(f306(f306(f264(x75812),f306(f306(f22(x75812),x75813),f306(f306(f82(x75812),x75811),x75814))),x75811),f306(f306(f22(x75812),f306(f306(f264(x75812),x75813),x75811)),x75814)) % 187.68/187.65 [7582]~P61(x75822)+E(x75821,f2(x75822))+E(f306(f306(f264(x75822),f306(f306(f81(x75822),x75823),f306(f306(f82(x75822),x75824),x75821))),x75821),f306(f306(f81(x75822),f306(f306(f264(x75822),x75823),x75821)),x75824)) % 187.68/187.65 [7583]~P62(x75832)+E(x75831,f2(x75832))+E(f306(f306(f264(x75832),f306(f306(f81(x75832),x75833),f306(f306(f82(x75832),x75831),x75834))),x75831),f306(f306(f81(x75832),f306(f306(f264(x75832),x75833),x75831)),x75834)) % 187.68/187.65 [8293]~P1(f306(f152(x82931,x82933),x82934))+~P1(f306(f152(x82931,x82932),x82934))+P1(f306(f152(x82931,f306(f306(f109(f872(x82931,a859)),x82932),x82933)),x82934)) % 187.68/187.65 [8664]~E(f306(f306(f263(x86641,x86641,x86641),x86642),x86644),f185(f872(f871(x86641,x86641),a859)))+~E(f306(f306(f263(x86641,x86641,x86641),x86642),x86643),f185(f872(f871(x86641,x86641),a859)))+E(f306(f306(f263(x86641,x86641,x86641),x86642),f306(f306(f108(f872(f871(x86641,x86641),a859)),x86643),x86644)),f185(f872(f871(x86641,x86641),a859))) % 187.68/187.65 [8782]~P1(f306(f306(f220(f872(x87821,a859)),x87823),x87824))+~P1(f306(f306(f220(f872(x87821,a859)),x87822),x87824))+P1(f306(f306(f220(f872(x87821,a859)),f306(f306(f108(f872(x87821,a859)),x87822),x87823)),x87824)) % 187.68/187.65 [9165]~P1(f306(f63(x91651),x91654))+~P1(f306(f63(x91651),x91653))+E(f306(f306(f22(a865),f306(f306(f81(a865),f306(f306(f6(x91651,a865),x91652),x91653)),f306(f306(f6(x91651,a865),x91652),x91654))),f306(f306(f6(x91651,a865),x91652),f306(f306(f109(f872(x91651,a859)),x91653),x91654))),f306(f306(f6(x91651,a865),x91652),f306(f306(f108(f872(x91651,a859)),x91653),x91654))) % 187.68/187.65 [9254]~P1(f306(f306(f308(x92541),x92543),x92542))+~P1(f306(f306(f220(f872(x92541,a859)),x92542),f306(f306(f284(x92541),x92543),x92544)))+P1(f306(f306(f220(f872(x92541,a859)),f306(f306(f22(f872(x92541,a859)),x92542),f306(f306(f284(x92541),x92543),f185(f872(x92541,a859))))),x92544)) % 187.68/187.65 [9417]~P1(f306(f306(f308(x94171),x94173),x94172))+P1(f306(f306(f220(f872(x94171,a859)),x94172),f306(f306(f284(x94171),x94173),x94174)))+~P1(f306(f306(f220(f872(x94171,a859)),f306(f306(f22(f872(x94171,a859)),x94172),f306(f306(f284(x94171),x94173),f185(f872(x94171,a859))))),x94174)) % 187.68/187.65 [9509]~P1(f306(f306(f220(a865),x95091),x95093))+~P1(f306(f306(f221(a865),x95092),x95094))+P1(f306(f306(f308(f871(f871(a865,a865),f871(a865,a865))),f306(f306(f236(f871(a865,a865),f871(a865,a865)),f306(f306(f236(a865,a865),x95091),x95092)),f306(f306(f236(a865,a865),x95093),x95094))),a36)) % 187.68/187.65 [9510]~P1(f306(f306(f220(a865),x95102),x95104))+~P1(f306(f306(f220(a865),x95101),x95103))+P1(f306(f306(f308(f871(f871(a865,a865),f871(a865,a865))),f306(f306(f236(f871(a865,a865),f871(a865,a865)),f306(f306(f236(a865,a865),x95101),x95102)),f306(f306(f236(a865,a865),x95103),x95104))),a71)) % 187.68/187.65 [9806]~P1(f306(f306(f308(f866(x98061)),x98064),f153(x98061,x98063)))+~P1(f306(f306(f308(f866(x98061)),x98064),f153(x98061,x98062)))+P1(f306(f152(x98061,f306(f306(f109(f872(x98061,a859)),f306(f306(f7(x98061,f872(x98061,a859),a859),f308(x98061)),x98062)),f306(f306(f7(x98061,f872(x98061,a859),a859),f308(x98061)),x98063))),x98064)) % 187.68/187.65 [9910]~P28(x99101,f872(f872(x99101,a859),a859),f306(f306(f7(x99101,f872(f871(x99101,x99101),a859),f872(f872(x99101,a859),a859)),f306(f306(f8(f872(x99101,a859),f872(f872(f871(x99101,x99101),a859),f872(f872(x99101,a859),a859)),x99101),f62(x99101)),f306(f306(f7(x99101,f872(x99101,a859),f872(x99101,a859)),f284(x99101)),f185(f872(x99101,a859))))),x99103),x99102)+~P1(f306(f306(f308(x99101),x99104),x99102))+E(f306(f306(f22(f872(f872(x99101,a859),a859)),f306(f306(f62(x99101),x99102),x99103)),f306(f306(f62(x99101),f306(f306(f284(x99101),x99104),f185(f872(x99101,a859)))),x99103)),f306(f306(f62(x99101),f306(f306(f22(f872(x99101,a859)),x99102),f306(f306(f284(x99101),x99104),f185(f872(x99101,a859))))),x99103)) % 187.68/187.65 [10047]~P50(x100471,x100472,x100474)+~P1(f306(f306(f308(f871(x100471,x100471)),x100473),x100474))+P1(f306(f306(f245(x100471,x100471,a859),f306(f306(f7(x100471,f872(x100471,a859),f872(x100471,a859)),f306(f306(f8(f872(a859,a859),f872(f872(x100471,a859),f872(x100471,a859)),x100471),f8(a859,a859,x100471)),f306(f306(f8(a859,f872(a859,a859),x100471),a304),f306(f306(f7(x100471,f872(x100471,a859),a859),f308(x100471)),x100472)))),f306(f306(f7(x100471,f872(x100471,a859),a859),f308(x100471)),x100472))),x100473)) % 187.68/187.65 [10060]P1(f306(f63(x100601),x100602))+~P1(f306(f63(x100603),f306(f285(x100601,x100603,x100604),x100602)))+~P1(f306(f63(x100601),f306(f228(x100601),f306(f306(f18(x100601,a859,a859),f306(f306(f8(a859,f872(a859,a859),x100601),a304),f306(f306(f7(x100601,f872(x100601,a859),a859),f308(x100601)),x100602))),f306(f306(f7(x100601,x100603,a859),f306(f306(f8(x100603,f872(x100603,a859),x100601),a303),x100604)),f306(x100604,f529(x100604,x100603,x100602,x100601))))))) % 187.68/187.65 [8044]~P62(x80442)+E(x80441,f2(x80442))+E(f306(f306(f264(x80442),f306(f306(f22(x80442),f306(f306(f82(x80442),x80441),x80443)),x80444)),x80441),f306(f306(f22(x80442),x80443),f306(f306(f264(x80442),x80444),x80441))) % 187.68/187.65 [8045]~P62(x80452)+E(x80451,f2(x80452))+E(f306(f306(f264(x80452),f306(f306(f81(x80452),f306(f306(f82(x80452),x80451),x80453)),x80454)),x80451),f306(f306(f81(x80452),x80453),f306(f306(f264(x80452),x80454),x80451))) % 187.68/187.65 [8948]~E(f306(f306(f263(x89481,x89481,x89481),x89483),x89484),f185(f872(f871(x89481,x89481),a859)))+~E(f306(f306(f263(x89481,x89481,x89481),x89482),x89484),f185(f872(f871(x89481,x89481),a859)))+E(f306(f306(f263(x89481,x89481,x89481),f306(f306(f108(f872(f871(x89481,x89481),a859)),x89482),x89483)),x89484),f185(f872(f871(x89481,x89481),a859))) % 187.68/187.65 [9989]~P144(x99891)+~P144(x99892)+E(f306(f306(f291(x99891),f306(f306(f7(x99891,a106,f869(f866(a302))),f306(f306(f8(f872(x99892,f869(f866(a302))),f872(a106,f869(f866(a302))),x99891),f291(x99892)),f306(f306(f8(f872(x99892,f871(x99891,x99892)),f872(x99892,f869(f866(a302))),x99891),f306(f8(f871(x99891,x99892),f869(f866(a302)),x99892),x99893)),f236(x99891,x99892)))),x99894)),x99894),f306(f306(f291(f871(x99891,x99892)),x99893),x99894)) % 187.68/187.65 [9715]~P1(f306(f152(x97151,x97153),x97154))+~P1(f306(f152(x97151,x97152),x97154))+P1(f306(f152(x97151,f306(f306(f18(x97151,a859,a859),f306(f306(f8(a859,f872(a859,a859),x97151),a304),x97152)),x97153)),x97154)) % 187.68/187.65 [9981]P1(f306(x99811,f520(x99812,x99813,x99811,x99814)))+~P1(f306(f63(x99814),f306(f228(x99814),x99811)))+P1(f306(f63(x99813),f306(f228(x99813),f306(f306(f8(f872(x99814,a859),a859,x99813),f88(x99814)),f306(f306(f8(f872(x99814,a859),f872(x99814,a859),x99813),f306(f18(x99814,a859,a859),f306(f306(f8(a859,f872(a859,a859),x99814),a304),x99811))),x99812))))) % 187.68/187.65 [10002]~P1(f306(f63(x100022),f306(f228(x100022),x100023)))+~P1(f306(f63(x100021),f306(f228(x100021),f306(f306(f7(x100021,x100022,a859),x100024),f520(x100024,x100021,x100023,x100022)))))+P1(f306(f63(x100021),f306(f228(x100021),f306(f306(f8(f872(x100022,a859),a859,x100021),f88(x100022)),f306(f306(f8(f872(x100022,a859),f872(x100022,a859),x100021),f306(f18(x100022,a859,a859),f306(f306(f8(a859,f872(a859,a859),x100022),a304),x100023))),x100024))))) % 187.68/187.65 [6489]E(x64891,x64892)+~E(f306(x64893,x64891),f306(x64893,x64892))+~P28(x64894,x64895,x64893,f231(f872(x64894,a859))) % 187.68/187.65 [6654]~E(f306(x66543,x66545),f188(x66542))+~E(f306(x66544,x66545),f188(x66542))+E(f306(f176(x66541,x66542,x66543,x66544),x66545),f188(x66542)) % 187.68/187.65 [7384]E(x73841,x73842)+~P28(x73843,x73844,x73845,f231(f872(x73843,a859)))+~E(f306(f285(x73843,x73844,x73845),x73841),f306(f285(x73843,x73844,x73845),x73842)) % 187.68/187.65 [7636]P28(x76362,x76363,f438(x76364,x76363,x76362,x76361),x76361)+~E(f306(f285(x76363,x76362,x76365),x76364),x76361)+E(x76361,f185(f872(x76362,a859))) % 187.68/187.65 [8180]~P1(f306(f306(x81803,x81802),x81805))+~P1(f306(f306(x81803,x81804),x81802))+P1(f306(f306(f308(x81801),x81802),f273(x81801,x81803,x81804,x81805))) % 187.68/187.65 [8181]~P1(f306(f306(x81813,x81812),x81815))+~P1(f306(f306(x81813,x81814),x81812))+P1(f306(f306(f308(x81811),x81812),f270(x81811,x81813,x81814,x81815))) % 187.68/187.65 [8740]~P28(x87401,x87403,x87405,f231(f872(x87401,a859)))+~P28(x87403,x87402,x87404,f231(f872(x87403,a859)))+P28(x87401,x87402,f306(f74(x87403,x87402,x87401,x87404),x87405),f231(f872(x87401,a859))) % 187.68/187.65 [9314]P1(f306(f306(f308(f871(x93141,x93141)),f306(f306(f236(x93141,x93141),x93142),x93143)),f282(x93141,x93144)))+~P1(f306(f306(f308(f871(x93141,x93141)),f306(f306(f236(x93141,x93141),x93142),x93145)),f282(x93141,x93144)))+~P1(f306(f306(f308(f871(x93141,x93141)),f306(f306(f236(x93141,x93141),x93145),x93143)),f282(x93141,x93144))) % 187.68/187.65 [9352]~P108(x93522)+~P1(f306(f129(x93521),x93525))+P1(f306(f129(x93521),f141(x93521,x93522,x93523,x93524,x93525))) % 187.68/187.65 [5318]~E(x53182,f120(x53181))+E(f306(f306(f122(x53181),x53182),x53183),f306(f306(f143(x53181),x53184),x53185))+~E(x53183,f306(f306(f143(x53181),x53184),x53185)) % 187.68/187.65 [5319]~E(x53192,f120(x53191))+E(f306(f306(f122(x53191),x53192),x53193),f306(f306(f143(x53191),x53194),x53195))+~E(f306(f306(f143(x53191),x53194),x53195),x53193) % 187.68/187.65 [6449]~E(f306(f186(f866(x64491)),x64495),f306(f186(f866(x64492)),x64494))+E(f306(f306(f146(f871(x64491,x64492),x64492),f244(x64491,x64492)),x64493),x64494)+~E(f306(f306(f173(x64491,x64492),x64495),x64494),x64493) % 187.68/187.65 [6450]~E(f306(f186(f866(x64501)),x64504),f306(f186(f866(x64502)),x64505))+E(f306(f306(f146(f871(x64501,x64502),x64501),f235(x64501,x64502)),x64503),x64504)+~E(f306(f306(f173(x64501,x64502),x64504),x64505),x64503) % 187.68/187.65 [6923]~P108(x69231)+~P17(x69231,f306(f306(f146(x69232,x69231),x69233),x69235))+P17(x69231,f306(f306(f146(x69232,x69231),x69233),f306(f128(x69232,x69234),x69235))) % 187.68/187.65 [6970]~P1(f306(x69703,x69705))+~P1(f306(f306(x69702,x69704),x69705))+P1(f306(f306(f96(x69701,x69702,x69703),x69704),x69705)) % 187.68/187.65 [7067]~P108(x70671)+P17(x70671,f306(f306(f146(x70672,x70671),x70673),f162(x70672,x70674,x70675)))+~P17(x70671,f306(f306(f146(x70672,x70671),x70673),x70675)) % 187.68/187.65 [7090]~P54(x70903,x70902,x70905)+~P54(x70901,x70903,x70904)+P54(x70901,x70902,f306(f306(f263(x70901,x70903,x70902),x70904),x70905)) % 187.68/187.65 [7182]E(x71821,x71822)+~P28(x71823,x71824,x71825,f231(f872(x71823,a859)))+~E(f306(f306(f146(x71823,x71824),x71825),x71821),f306(f306(f146(x71823,x71824),x71825),x71822)) % 187.68/187.65 [7335]~P1(f306(f306(f220(a865),x73351),f306(x73353,x73355)))+P1(f306(f306(f220(a865),x73351),f147(x73352,x73353,x73354)))+~P1(f306(f306(f308(x73352),x73355),f306(f164(x73352),x73354))) % 187.68/187.65 [7336]~P1(f306(f306(f221(a865),x73361),f306(x73363,x73365)))+P1(f306(f306(f221(a865),x73361),f147(x73362,x73363,x73364)))+~P1(f306(f306(f308(x73362),x73365),f306(f164(x73362),x73364))) % 187.68/187.65 [7739]~P109(x77391)+P1(f306(f306(f220(f872(x77391,a859)),f277(x77391,x77392,x77393)),f277(x77391,x77394,x77395)))+P1(f306(f306(f220(x77391),x77392),x77393)) % 187.68/187.65 [7762]~P6(x77621)+P1(f306(f306(f220(x77621),f306(f306(f44(x77622,x77621),x77623),x77624)),f306(x77624,x77625)))+~P1(f306(f306(f308(x77622),x77625),x77623)) % 187.68/187.65 [7829]~P28(x78291,x78292,x78294,x78293)+E(f306(f78(x78291,x78292,x78293,x78294),f306(x78294,x78295)),x78295)+~P1(f306(f306(f308(x78291),x78295),x78293)) % 187.68/187.65 [8032]~P1(f306(x80321,x80325))+P1(f306(x80321,f327(x80321,x80322,x80323,x80324)))+~P1(f306(f306(f308(x80324),x80325),x80323)) % 187.68/187.65 [8033]~P1(f306(x80331,x80335))+P1(f306(x80331,f327(x80331,x80332,x80333,x80334)))+~P1(f306(f306(f308(x80334),x80335),x80332)) % 187.68/187.65 [8131]P1(f306(f63(x81311),x81312))+~P1(f306(f63(x81313),x81314))+~P1(f306(f306(f220(f872(x81311,a859)),x81312),f306(f285(x81313,x81311,x81315),x81314))) % 187.68/187.65 [8297]E(x82971,x82972)+~P28(x82973,x82974,x82975,f306(f306(f108(f872(x82973,a859)),f306(f164(x82973),x82971)),f306(f164(x82973),x82972)))+~E(f306(f306(f146(x82973,x82974),x82975),x82971),f306(f306(f146(x82973,x82974),x82975),x82972)) % 187.68/187.65 [8352]~P109(x83521)+~P1(f306(f306(f221(f872(x83521,a859)),f277(x83521,x83524,x83525)),f277(x83521,x83522,x83523)))+P1(f306(f306(f220(x83521),x83522),x83523)) % 187.68/187.65 [8420]~P28(x84201,x84204,x84205,f231(f872(x84201,a859)))+~P1(f306(f306(f308(x84204),f306(x84205,x84202)),f306(f285(x84201,x84204,x84205),x84203)))+P1(f306(f306(f308(x84201),x84202),x84203)) % 187.68/187.65 [8500]P1(f306(x85001,x85002))+~P1(f306(x85001,f338(x85001,x85003,x85004,x85005)))+~P1(f306(f306(f308(x85005),x85002),x85004)) % 187.68/187.65 [8501]P1(f306(x85011,x85012))+~P1(f306(x85011,f338(x85011,x85013,x85014,x85015)))+~P1(f306(f306(f308(x85015),x85012),x85013)) % 187.68/187.65 [8779]~P28(x87792,x87793,x87791,x87794)+E(f306(x87791,f306(f78(x87792,x87793,x87794,x87791),x87795)),x87795)+~P1(f306(f306(f308(x87793),x87795),f306(f285(x87792,x87793,x87791),x87794))) % 187.68/187.65 [8885]E(x88851,f120(x88852))+E(f306(f306(f143(x88852),x88853),f696(x88854,x88853,x88855,x88851,x88852)),x88851)+~E(f306(f306(f122(x88852),x88851),x88855),f306(f306(f143(x88852),x88853),x88854)) % 187.68/187.65 [8886]E(x88861,f120(x88862))+E(f306(f306(f143(x88862),x88863),f697(x88864,x88861,x88865,x88863,x88862)),x88861)+~E(f306(f306(f122(x88862),x88861),x88864),f306(f306(f143(x88862),x88863),x88865)) % 187.68/187.65 [8903]E(f306(f306(f143(x89032),x89033),f696(x89034,x89033,x89031,x89035,x89032)),x89035)+~E(f306(f306(f122(x89032),x89035),x89031),f306(f306(f143(x89032),x89033),x89034))+E(x89031,f306(f306(f143(x89032),x89033),x89034)) % 187.68/187.65 [8904]E(f306(f306(f143(x89041),x89042),f697(x89044,x89045,x89043,x89042,x89041)),x89045)+~E(f306(f306(f122(x89041),x89045),x89044),f306(f306(f143(x89041),x89042),x89043))+E(f306(f306(f143(x89041),x89042),x89043),x89044) % 187.68/187.65 [8987]~E(f306(f285(x89873,x89872,x89874),f231(f872(x89873,a859))),f231(f872(x89872,a859)))+~E(f306(f285(x89871,x89873,x89875),f231(f872(x89871,a859))),f231(f872(x89873,a859)))+E(f306(f285(x89871,x89872,f306(f74(x89873,x89872,x89871,x89874),x89875)),f231(f872(x89871,a859))),f231(f872(x89872,a859))) % 187.68/187.65 [9360]E(x93601,f120(x93602))+~E(f306(f306(f122(x93602),x93601),x93603),f306(f306(f143(x93602),x93605),x93604))+E(f306(f306(f122(x93602),f697(x93603,x93601,x93604,x93605,x93602)),x93603),x93604) % 187.68/187.65 [9361]E(x93611,f120(x93612))+~E(f306(f306(f122(x93612),x93611),x93615),f306(f306(f143(x93612),x93614),x93613))+E(f306(f306(f122(x93612),f696(x93613,x93614,x93615,x93611,x93612)),x93615),x93613) % 187.68/187.65 [9368]E(f306(f306(f122(x93682),f696(x93684,x93683,x93681,x93685,x93682)),x93681),x93684)+~E(f306(f306(f122(x93682),x93685),x93681),f306(f306(f143(x93682),x93683),x93684))+E(x93681,f306(f306(f143(x93682),x93683),x93684)) % 187.68/187.65 [9369]~E(f306(f306(f122(x93691),x93695),x93694),f306(f306(f143(x93691),x93692),x93693))+E(f306(f306(f122(x93691),f697(x93694,x93695,x93693,x93692,x93691)),x93694),x93693)+E(f306(f306(f143(x93691),x93692),x93693),x93694) % 187.68/187.65 [9370]E(f306(f306(f122(x93701),x93705),f699(x93703,x93702,x93704,x93705,x93701)),x93702)+E(f306(f306(f122(x93701),x93702),f698(x93703,x93702,x93704,x93705,x93701)),x93705)+~E(f306(f306(f122(x93701),x93705),x93704),f306(f306(f122(x93701),x93702),x93703)) % 187.68/187.65 [9403]~P108(x94031)+P17(x94031,f306(f306(f146(x94032,x94031),x94033),f141(x94032,x94031,x94033,x94034,x94035)))+~P17(x94031,f306(f306(f146(x94032,x94031),x94033),x94035)) % 187.68/187.65 [9414]~P58(x94145,x94141,x94144,x94143)+P1(f306(f306(x94141,x94142),f487(x94143,x94144,x94141,x94145,x94142)))+~P1(f306(f306(f308(x94145),x94142),x94144)) % 187.68/187.65 [9521]~P1(f306(f306(f308(f871(x95211,x95211)),f306(f306(f236(x95211,x95211),x95215),x95213)),f282(x95211,x95214)))+P1(f306(f306(f308(f871(x95211,x95211)),f306(f306(f236(x95211,x95211),x95212),x95213)),f306(f306(f263(x95211,x95211,x95211),x95214),f282(x95211,x95214))))+~P1(f306(f306(f308(f871(x95211,x95211)),f306(f306(f236(x95211,x95211),x95212),x95215)),f306(f306(f263(x95211,x95211,x95211),x95214),f282(x95211,x95214)))) % 187.68/187.65 [9522]~P1(f306(f306(f308(f871(x95221,x95221)),f306(f306(f236(x95221,x95221),x95222),x95225)),f282(x95221,x95224)))+P1(f306(f306(f308(f871(x95221,x95221)),f306(f306(f236(x95221,x95221),x95222),x95223)),f306(f306(f263(x95221,x95221,x95221),x95224),f282(x95221,x95224))))+~P1(f306(f306(f308(f871(x95221,x95221)),f306(f306(f236(x95221,x95221),x95225),x95223)),f306(f306(f263(x95221,x95221,x95221),x95224),f282(x95221,x95224)))) % 187.68/187.65 [9525]P1(f306(f306(f308(f871(f866(x95251),f866(x95251))),f306(f306(f236(f866(x95251),f866(x95251)),x95252),x95253)),f150(x95251,f282(x95251,x95254))))+~P1(f306(f306(f308(f871(f866(x95251),f866(x95251))),f306(f306(f236(f866(x95251),f866(x95251)),x95252),x95255)),f150(x95251,f282(x95251,x95254))))+~P1(f306(f306(f308(f871(f866(x95251),f866(x95251))),f306(f306(f236(f866(x95251),f866(x95251)),x95255),x95253)),f150(x95251,f282(x95251,x95254)))) % 187.68/187.65 [9529]E(f306(f306(f122(x95291),x95292),f698(x95293,x95292,x95294,x95295,x95291)),x95295)+E(f306(f306(f122(x95291),f699(x95293,x95292,x95294,x95295,x95291)),x95293),x95294)+~E(f306(f306(f122(x95291),x95292),x95293),f306(f306(f122(x95291),x95295),x95294)) % 187.68/187.65 [9530]E(f306(f306(f122(x95301),x95302),f699(x95303,x95304,x95305,x95302,x95301)),x95304)+E(f306(f306(f122(x95301),f698(x95303,x95304,x95305,x95302,x95301)),x95305),x95303)+~E(f306(f306(f122(x95301),x95302),x95305),f306(f306(f122(x95301),x95304),x95303)) % 187.68/187.65 [9585]P1(f306(f306(f308(f871(x95851,x95851)),f306(f306(f236(x95851,x95851),x95852),x95853)),f306(f306(f263(x95851,x95851,x95851),x95854),f282(x95851,x95854))))+~P1(f306(f306(f308(f871(x95851,x95851)),f306(f306(f236(x95851,x95851),x95852),x95855)),f306(f306(f263(x95851,x95851,x95851),x95854),f282(x95851,x95854))))+~P1(f306(f306(f308(f871(x95851,x95851)),f306(f306(f236(x95851,x95851),x95855),x95853)),f306(f306(f263(x95851,x95851,x95851),x95854),f282(x95851,x95854)))) % 187.68/187.65 [9612]P37(x96121,x96122,x96123,x96124,x96125)+~E(f306(f186(f866(x96121)),x96124),f306(f186(f866(x96122)),x96125))+~P1(f306(f306(f245(x96121,x96122,a859),x96123),f753(x96125,x96124,x96123,x96122,x96121))) % 187.68/187.65 [9613]P37(x96131,x96132,x96133,x96134,x96135)+~E(f306(f186(f866(x96131)),x96134),f306(f186(f866(x96132)),x96135))+~P1(f306(f306(f245(x96131,x96132,a859),x96133),f760(x96133,x96135,x96134,x96132,x96131))) % 187.68/187.65 [9618]E(f306(f306(f122(x96181),f698(x96182,x96183,x96184,x96185,x96181)),x96184),x96182)+~E(f306(f306(f122(x96181),x96183),x96182),f306(f306(f122(x96181),x96185),x96184))+E(f306(f306(f122(x96181),f699(x96182,x96183,x96184,x96185,x96181)),x96182),x96184) % 187.68/187.65 [9631]~P108(x96312)+E(f306(f306(f140(x96311,x96312,x96313),x96314),x96315),f306(f306(f143(x96311),x96314),x96315))+P1(f306(f306(f308(x96311),f779(x96314,x96313,x96315,x96311,x96312)),f306(f164(x96311),x96315))) % 187.68/187.65 [9636]~P58(x96361,x96364,x96363,x96362)+~P1(f306(f306(f308(x96361),x96365),x96363))+P1(f306(f306(f308(x96361),f487(x96362,x96363,x96364,x96361,x96365)),x96362)) % 187.68/187.65 [9760]~P1(f306(f306(f308(f871(f872(x97601,a859),f872(x97601,a859))),f306(f306(f236(f872(x97601,a859),f872(x97601,a859)),x97604),x97603)),f298(x97601,x97602)))+~P1(f306(f306(f308(x97601),x97605),x97604))+P1(f306(f306(f308(x97601),f576(x97602,x97603,x97604,x97601,x97605)),x97603)) % 187.68/187.65 [9772]~P108(x97722)+E(f306(f306(f140(x97721,x97722,x97723),x97724),x97725),f306(f306(f143(x97721),x97724),x97725))+~P1(f306(f306(f220(x97722),f306(x97723,x97724)),f306(x97723,f779(x97724,x97723,x97725,x97721,x97722)))) % 187.68/187.65 [9962]P37(x99621,x99622,x99623,x99624,x99625)+~E(f306(f186(f866(x99621)),x99624),f306(f186(f866(x99622)),x99625))+~P1(f306(f306(x99623,f306(f306(f157(x99621),x99624),f761(x99625,x99624,x99623,x99622,x99621))),f306(f306(f157(x99622),x99625),f761(x99625,x99624,x99623,x99622,x99621)))) % 187.68/187.65 [9963]P37(x99631,x99632,x99633,x99634,x99635)+~E(f306(f186(f866(x99631)),x99634),f306(f186(f866(x99632)),x99635))+~P1(f306(f306(x99633,f306(f306(f157(x99631),x99634),f768(x99633,x99635,x99632,x99634,x99631))),f306(f306(f157(x99632),x99635),f768(x99633,x99635,x99632,x99634,x99631)))) % 187.68/187.65 [6517]~P20(x65172,x65175,x65171)+~P1(f306(f63(x65172),x65174))+E(f306(x65171,f306(f306(f284(x65172),x65173),x65174)),f306(f306(f66(x65172,x65172,x65175),x65173),x65174)) % 187.68/187.65 [6518]~E(x65183,x65184)+~E(x65182,x65185)+E(f306(f306(f284(x65181),x65182),f306(f306(f284(x65181),x65183),f185(f872(x65181,a859)))),f306(f306(f284(x65181),x65184),f306(f306(f284(x65181),x65185),f185(f872(x65181,a859))))) % 187.68/187.65 [6529]P1(f306(x65292,x65295))+E(f168(x65291,x65292,f306(f306(f122(x65291),x65293),x65294)),f168(x65291,x65292,x65293))+~P1(f306(f306(f308(x65291),x65295),f306(f164(x65291),x65293))) % 187.68/187.65 [6567]E(f306(x65671,x65672),f185(f872(x65673,a859)))+~E(f306(f306(f43(x65674,f872(x65673,a859)),x65675),x65671),f185(f872(x65673,a859)))+~P1(f306(f306(f308(x65674),x65672),x65675)) % 187.68/187.65 [6568]E(f306(x65681,x65682),f231(f872(x65683,a859)))+~E(f306(f306(f44(x65684,f872(x65683,a859)),x65685),x65681),f231(f872(x65683,a859)))+~P1(f306(f306(f308(x65684),x65682),x65685)) % 187.68/187.65 [6872]~P1(f306(f306(f193(x68721),x68723),x68725))+~P1(f306(f306(f193(x68722),x68725),x68724))+P1(f306(f306(f193(f34(x68721,x68722)),x68723),x68724)) % 187.68/187.65 [7077]~E(x70772,x70774)+~P143(x70771)+E(f306(f306(f81(x70771),f306(f306(f82(x70771),x70772),x70773)),f306(f306(f82(x70771),x70774),x70775)),f306(f306(f81(x70771),f306(f306(f82(x70771),x70772),x70775)),f306(f306(f82(x70771),x70774),x70773))) % 187.68/187.65 [7137]~P6(x71371)+~P1(f306(f306(f308(x71374),x71373),x71375))+P1(f306(f306(f220(x71371),f306(x71372,x71373)),f306(f306(f43(x71374,x71371),x71375),x71372))) % 187.68/187.65 [7187]~P107(x71871)+P1(f306(f306(f220(x71871),f306(x71872,x71873)),f306(x71874,x71873)))+~P1(f306(f306(f220(f872(x71875,x71871)),x71872),x71874)) % 187.68/187.65 [7303]E(x73031,x73032)+E(x73033,x73031)+~E(f306(f306(f284(x73034),x73031),f306(f306(f284(x73034),x73035),f185(f872(x73034,a859)))),f306(f306(f284(x73034),x73032),f306(f306(f284(x73034),x73033),f185(f872(x73034,a859))))) % 187.68/187.65 [7304]E(x73041,x73042)+E(x73043,x73041)+~E(f306(f306(f284(x73044),x73043),f306(f306(f284(x73044),x73042),f185(f872(x73044,a859)))),f306(f306(f284(x73044),x73045),f306(f306(f284(x73044),x73041),f185(f872(x73044,a859))))) % 187.68/187.65 [7305]E(x73051,x73052)+E(x73051,x73053)+~E(f306(f306(f284(x73054),x73053),f306(f306(f284(x73054),x73052),f185(f872(x73054,a859)))),f306(f306(f284(x73054),x73055),f306(f306(f284(x73054),x73051),f185(f872(x73054,a859))))) % 187.68/187.65 [7306]E(x73061,x73062)+E(x73061,x73063)+~E(f306(f306(f284(x73064),x73061),f306(f306(f284(x73064),x73065),f185(f872(x73064,a859)))),f306(f306(f284(x73064),x73062),f306(f306(f284(x73064),x73063),f185(f872(x73064,a859))))) % 187.68/187.65 [7839]P28(x78391,x78392,x78393,x78394)+~P28(x78391,x78392,x78393,x78395)+~P1(f306(f306(f220(f872(x78391,a859)),x78394),x78395)) % 187.68/187.65 [7846]~P1(f306(f306(f220(a865),x78465),x78463))+~P1(f306(f306(f306(f306(a195,x78461),x78462),x78465),x78464))+P1(f306(f306(f306(f306(a195,x78461),x78462),x78463),x78464)) % 187.68/187.65 [7942]P1(f306(x79421,x79422))+~P1(f306(f306(f193(x79424),x79422),x79425))+P1(f306(f306(f193(f31(x79421,x79423,x79424)),x79422),x79425)) % 187.68/187.65 [7970]~P1(f306(x79701,x79704))+~P1(f306(f306(f193(x79702),x79704),x79705))+P1(f306(f306(f193(f31(x79701,x79702,x79703)),x79704),x79705)) % 187.68/187.65 [8022]E(x80221,x80222)+~E(f306(f285(x80223,x80224,x80225),x80221),f306(f285(x80223,x80224,x80225),x80222))+~P28(x80223,x80224,x80225,f306(f306(f108(f872(x80223,a859)),x80221),x80222)) % 187.68/187.65 [8096]P1(f306(x80962,x80964))+E(f306(f306(f130(x80961),f306(f186(f866(x80961)),f168(x80961,x80962,x80963))),x80963),f306(f306(f143(x80961),x80964),x80965))+~E(f306(f306(f122(x80961),f168(x80961,x80962,x80963)),f306(f306(f143(x80961),x80964),x80965)),x80963) % 187.68/187.65 [8128]~P28(x81281,x81282,x81283,x81285)+~P28(x81281,x81282,x81283,x81284)+P28(x81281,x81282,x81283,f306(f306(f109(f872(x81281,a859)),x81284),x81285)) % 187.68/187.65 [8237]~P74(x82371)+E(f306(f306(f81(x82371),f306(x82372,x82373)),f306(f158(x82371),f306(f306(f146(x82374,x82371),x82372),f162(x82374,x82373,x82375)))),f306(f158(x82371),f306(f306(f146(x82374,x82371),x82372),x82375)))+~P1(f306(f306(f308(x82374),x82373),f306(f164(x82374),x82375))) % 187.68/187.65 [8327]~P108(x83271)+~P17(x83271,f306(f306(f146(x83272,x83271),x83273),x83275))+P17(x83271,f306(f306(f146(x83272,x83271),x83273),f306(f306(f140(x83272,x83271,x83273),x83274),x83275))) % 187.68/187.65 [8405]P1(f306(x84051,x84052))+P1(f306(f306(f193(x84053),x84052),x84054))+~P1(f306(f306(f193(f31(x84051,x84055,x84053)),x84052),x84054)) % 187.68/187.65 [8416]~P6(x84161)+P1(f306(f306(f220(x84161),f306(f306(f43(x84162,x84161),x84163),x84164)),f306(f306(f43(x84162,x84161),x84165),x84164)))+~P1(f306(f306(f220(f872(x84162,a859)),x84163),x84165)) % 187.68/187.65 [8417]~P6(x84171)+P1(f306(f306(f220(x84171),f306(f306(f44(x84172,x84171),x84173),x84174)),f306(f306(f44(x84172,x84171),x84175),x84174)))+~P1(f306(f306(f220(f872(x84172,a859)),x84175),x84173)) % 187.68/187.65 [8428]~P1(f306(x84284,x84282))+P1(f306(f306(f193(x84281),x84282),x84283))+~P1(f306(f306(f193(f31(x84284,x84281,x84285)),x84282),x84283)) % 187.68/187.65 [8454]~P108(x84543)+P1(f306(f129(x84541),x84542))+~P1(f306(f129(x84541),f306(f306(f140(x84541,x84543,x84544),x84545),x84542))) % 187.68/187.65 [8464]P1(f306(f306(f193(x84641),x84642),x84643))+P1(f306(f306(f193(x84644),x84642),x84643))+~P1(f306(f306(f193(f31(x84645,x84641,x84644)),x84642),x84643)) % 187.68/187.65 [8596]~P108(x85961)+~P1(f306(f306(f308(x85962),x85963),f306(f164(x85962),x85964)))+~P1(f306(f129(x85962),f306(f306(f140(x85962,x85961,x85965),x85963),x85964))) % 187.68/187.65 [8674]~P108(x86741)+P17(x86741,f306(f306(f146(x86742,x86741),x86743),x86744))+~P17(x86741,f306(f306(f146(x86742,x86741),x86743),f306(f306(f140(x86742,x86741,x86743),x86745),x86744))) % 187.68/187.65 [8766]~P108(x87662)+E(f306(f306(f140(x87661,x87662,x87663),x87664),x87665),f141(x87661,x87662,x87663,x87664,x87665))+P1(f306(f306(f308(x87662),f306(x87663,x87664)),f306(f285(x87661,x87662,x87663),f306(f164(x87661),x87665)))) % 187.68/187.65 [8842]~P108(x88422)+E(f141(x88421,x88422,x88423,x88424,x88425),x88425)+~P1(f306(f306(f308(x88422),f306(x88423,x88424)),f306(f285(x88421,x88422,x88423),f306(f164(x88421),x88425)))) % 187.68/187.65 [8858]~P28(x88582,x88581,x88583,x88585)+P1(f306(f306(f221(f872(x88581,a859)),f306(f285(x88582,x88581,x88583),x88584)),f306(f285(x88582,x88581,x88583),x88585)))+~P1(f306(f306(f221(f872(x88582,a859)),x88584),x88585)) % 187.68/187.65 [9029]~P28(x90291,x90292,x90293,f231(f872(x90291,a859)))+~P1(f306(f306(f220(f872(x90292,a859)),x90294),f306(f285(x90291,x90292,x90293),x90295)))+P1(f306(f306(f220(f872(x90291,a859)),f306(f286(x90291,x90292,x90293),x90294)),x90295)) % 187.68/187.65 [9049]~E(f306(f285(x90493,x90491,x90494),f231(f872(x90493,a859))),f231(f872(x90491,a859)))+P1(f306(f306(f220(f872(x90491,a859)),x90492),f306(f285(x90493,x90491,x90494),x90495)))+~P1(f306(f306(f220(f872(x90493,a859)),f306(f286(x90493,x90491,x90494),x90492)),x90495)) % 187.68/187.65 [9072]~E(f306(f214(x90722),x90724),f306(f306(f169(x90721,x90722),x90725),x90723))+~P1(f306(f129(x90721),f306(f306(f146(f871(x90721,x90722),x90721),f235(x90721,x90722)),x90725)))+P1(f306(f306(f308(f871(x90721,x90722)),f306(f306(f236(x90721,x90722),x90723),x90724)),f306(f164(f871(x90721,x90722)),x90725))) % 187.68/187.65 [9157]~P28(x91571,x91574,x91575,f231(f872(x91571,a859)))+~P1(f306(f306(f220(f872(x91574,a859)),f306(f285(x91571,x91574,x91575),x91572)),f306(f285(x91571,x91574,x91575),x91573)))+P1(f306(f306(f220(f872(x91571,a859)),x91572),x91573)) % 187.68/187.65 [9224]E(f306(f214(x92241),x92242),f306(f306(f169(x92243,x92241),x92244),x92245))+~P1(f306(f129(x92243),f306(f306(f146(f871(x92243,x92241),x92243),f235(x92243,x92241)),x92244)))+~P1(f306(f306(f308(f871(x92243,x92241)),f306(f306(f236(x92243,x92241),x92245),x92242)),f306(f164(f871(x92243,x92241)),x92244))) % 187.68/187.65 [9226]E(f306(f306(f169(x92261,x92262),x92263),x92264),f306(f214(x92262),x92265))+~P1(f306(f129(x92261),f306(f306(f146(f871(x92261,x92262),x92261),f235(x92261,x92262)),x92263)))+~P1(f306(f306(f308(f871(x92261,x92262)),f306(f306(f236(x92261,x92262),x92264),x92265)),f306(f164(f871(x92261,x92262)),x92263))) % 187.68/187.65 [9282]~P79(x92821)+~E(f306(x92823,f740(x92823,x92824,x92825,x92822,x92821)),f2(x92821))+E(f306(f158(x92821),f306(f306(f146(x92822,x92821),x92823),f306(f128(x92822,x92824),x92825))),f306(f158(x92821),f306(f306(f146(x92822,x92821),x92823),x92825))) % 187.68/187.65 [9461]~P19(x94611,x94612,x94613)+~P1(f306(f63(x94611),x94615))+P1(f306(f68(x94611,x94612,x94613,x94614,x94615),f306(f306(f66(x94611,x94612,x94613),x94614),x94615))) % 187.68/187.65 [9542]P1(f306(x95421,f657(x95422,x95421,x95423,x95424,x95425)))+~P1(f306(f306(f220(f872(x95425,a859)),x95424),x95423))+P1(f306(f306(f220(f872(x95425,a859)),f306(f306(f109(f872(x95425,a859)),x95424),f306(f228(x95425),x95421))),f306(f306(f109(f872(x95425,a859)),x95423),f306(f228(x95425),x95422)))) % 187.68/187.65 [9557]~P79(x95571)+~P1(f306(x95574,f740(x95573,x95574,x95575,x95572,x95571)))+E(f306(f158(x95571),f306(f306(f146(x95572,x95571),x95573),f306(f128(x95572,x95574),x95575))),f306(f158(x95571),f306(f306(f146(x95572,x95571),x95573),x95575))) % 187.68/187.65 [9634]~P6(x96345)+P1(f306(f306(f308(x96341),f624(x96342,x96343,x96341,x96344,x96345)),x96343))+P1(f306(f306(f220(x96345),x96344),f306(f306(f44(x96341,x96345),x96343),x96342))) % 187.68/187.65 [9637]~P79(x96371)+E(f306(f158(x96371),f306(f306(f146(x96372,x96371),x96373),f306(f128(x96372,x96374),x96375))),f306(f158(x96371),f306(f306(f146(x96372,x96371),x96373),x96375)))+P1(f306(f306(f308(x96372),f740(x96373,x96374,x96375,x96372,x96371)),f306(f164(x96372),x96375))) % 187.68/187.65 [9647]~P1(f306(x96475,f657(x96475,x96473,x96474,x96472,x96471)))+~P1(f306(f306(f220(f872(x96471,a859)),x96472),x96474))+P1(f306(f306(f220(f872(x96471,a859)),f306(f306(f109(f872(x96471,a859)),x96472),f306(f228(x96471),x96473))),f306(f306(f109(f872(x96471,a859)),x96474),f306(f228(x96471),x96475)))) % 187.68/187.65 [9682]P37(x96821,x96822,x96823,x96824,x96825)+~E(f306(f186(f866(x96822)),x96825),f306(f186(f866(x96821)),x96824))+P1(f306(f306(f221(a865),f761(x96825,x96824,x96823,x96822,x96821)),f306(f186(f866(x96821)),x96824))) % 187.68/187.65 [9683]P37(x96831,x96832,x96833,x96834,x96835)+~E(f306(f186(f866(x96832)),x96835),f306(f186(f866(x96831)),x96834))+P1(f306(f306(f221(a865),f768(x96833,x96835,x96832,x96834,x96831)),f306(f186(f866(x96831)),x96834))) % 187.68/187.65 [9718]P1(f306(f306(f308(x97181),f657(x97182,x97183,x97184,x97185,x97181)),x97185))+~P1(f306(f306(f220(f872(x97181,a859)),x97185),x97184))+P1(f306(f306(f220(f872(x97181,a859)),f306(f306(f109(f872(x97181,a859)),x97185),f306(f228(x97181),x97183))),f306(f306(f109(f872(x97181,a859)),x97184),f306(f228(x97181),x97182)))) % 187.68/187.65 [9773]~P6(x97731)+~P1(f306(f306(f220(x97731),x97732),f306(x97735,f624(x97735,x97734,x97733,x97732,x97731))))+P1(f306(f306(f220(x97731),x97732),f306(f306(f44(x97733,x97731),x97734),x97735))) % 187.68/187.65 [9804]~P75(x98041)+~P1(f306(f63(x98042),x98045))+E(f306(f306(f306(f67(x98041,x98042,f82(x98041)),f306(f306(f18(x98042,x98041,x98041),f306(f306(f8(x98041,f872(x98041,x98041),x98042),f82(x98041)),x98043)),x98044)),f79(x98041)),x98045),f306(f306(f82(x98041),f306(f306(f306(f67(x98041,x98042,f82(x98041)),x98043),f79(x98041)),x98045)),f306(f306(f306(f67(x98041,x98042,f82(x98041)),x98044),f79(x98041)),x98045))) % 187.68/187.65 [9867]~P1(f306(f306(f308(f871(f872(x98671,a859),f872(x98671,a859))),f306(f306(f236(f872(x98671,a859),f872(x98671,a859)),x98675),x98674)),f298(x98671,x98673)))+~P1(f306(f306(f308(x98671),x98672),x98675))+P1(f306(f306(f308(f871(x98671,x98671)),f306(f306(f236(x98671,x98671),x98672),f576(x98673,x98674,x98675,x98671,x98672))),x98673)) % 187.68/187.65 [9999]~P1(f306(f306(f308(f871(f866(x99991),f866(x99991))),f306(f306(f236(f866(x99991),f866(x99991)),f306(f306(f122(x99991),x99995),x99992)),f306(f306(f122(x99991),x99995),x99993))),f139(x99991,x99994)))+P1(f306(f306(f308(f871(f866(x99991),f866(x99991))),f306(f306(f236(f866(x99991),f866(x99991)),x99992),x99993)),f139(x99991,x99994)))+P1(f306(f306(f308(f871(x99991,x99991)),f306(f306(f236(x99991,x99991),f703(x99994,x99993,x99992,x99995,x99991)),f703(x99994,x99993,x99992,x99995,x99991))),x99994)) % 187.68/187.65 [7117]~E(f306(f186(f866(x71171)),x71173),f306(f186(f866(x71172)),x71174))+E(f306(f306(f169(x71171,x71172),f306(f306(f173(x71171,x71172),x71173),x71174)),x71175),f188(x71172))+P1(f306(f306(f308(x71171),x71175),f306(f164(x71171),x71173))) % 187.68/187.65 [7190]~E(x71903,x71905)+E(f306(f306(f157(x71901),f306(f306(f151(x71901,x71902),x71903),x71904)),x71905),x71904)+~P1(f306(f306(f221(a865),x71903),f306(f186(f866(x71901)),x71902))) % 187.68/187.65 [7298]~E(f306(f306(f122(x72981),x72982),x72984),f306(f306(f122(x72981),x72983),x72985))+E(f306(f306(f165(x72981),f306(f186(f866(x72981)),x72982)),x72983),x72982)+P1(f306(f306(f220(a865),f306(f186(f866(x72981)),x72983)),f306(f186(f866(x72981)),x72982))) % 187.68/187.65 [7315]~E(x73155,x73152)+P1(f306(x73151,x73152))+P1(f306(f306(f306(f306(a195,f33(x73151,x73153)),x73152),x73154),x73155)) % 187.68/187.65 [7800]~E(f306(f306(f122(x78001),x78002),x78004),f306(f306(f122(x78001),x78003),x78005))+E(f306(f306(f165(x78001),f306(f186(f866(x78001)),x78002)),x78003),x78002)+~P1(f306(f306(f220(a865),f306(f186(f866(x78001)),x78002)),f306(f186(f866(x78001)),x78003))) % 187.68/187.65 [7824]~P1(f306(f63(x78241),f306(x78244,x78245)))+~P1(f306(f306(f308(x78242),x78245),x78243))+P1(f306(f63(x78241),f306(f306(f44(x78242,f872(x78241,a859)),x78243),x78244))) % 187.68/187.65 [7877]~E(f306(f186(f866(x78771)),x78772),f306(f186(f866(x78773)),x78774))+~E(f306(f306(f169(x78771,x78773),f306(f306(f173(x78771,x78773),x78772),x78774)),x78775),f188(x78773))+~P1(f306(f306(f308(x78771),x78775),f306(f164(x78771),x78772))) % 187.68/187.65 [8006]~P50(x80061,x80063,x80065)+~P50(x80061,x80062,x80064)+P50(x80061,f306(f306(f108(f872(x80061,a859)),x80062),x80063),f306(f306(f108(f872(f871(x80061,x80061),a859)),x80064),x80065)) % 187.68/187.65 [8007]~P50(x80071,x80073,x80075)+~P50(x80071,x80072,x80074)+P50(x80071,f306(f306(f109(f872(x80071,a859)),x80072),x80073),f306(f306(f109(f872(f871(x80071,x80071),a859)),x80074),x80075)) % 187.68/187.65 [8090]E(x80901,x80902)+P1(f306(x80903,x80901))+~P1(f306(f306(f306(f306(a195,f33(x80903,x80904)),x80901),x80905),x80902)) % 187.68/187.65 [8367]E(f306(f306(f236(x83671,x83672),f306(f306(f157(x83671),x83673),x83674)),f306(f306(f157(x83672),x83675),x83674)),f306(f306(f157(f871(x83671,x83672)),f306(f306(f173(x83671,x83672),x83673),x83675)),x83674))+~P1(f306(f306(f221(a865),x83674),f306(f186(f866(x83671)),x83673)))+~P1(f306(f306(f221(a865),x83674),f306(f186(f866(x83672)),x83675))) % 187.68/187.65 [8528]~P50(x85281,x85283,x85284)+P1(f306(f306(f308(x85281),x85282),x85283))+~P1(f306(f306(f308(f871(x85281,x85281)),f306(f306(f236(x85281,x85281),x85285),x85282)),x85284)) % 187.68/187.65 [8529]~P50(x85291,x85293,x85294)+P1(f306(f306(f308(x85291),x85292),x85293))+~P1(f306(f306(f308(f871(x85291,x85291)),f306(f306(f236(x85291,x85291),x85292),x85295)),x85294)) % 187.68/187.65 [8530]~P9(x85301,x85303,x85304)+P1(f306(f306(f308(x85301),x85302),x85303))+~P1(f306(f306(f308(f871(x85301,x85301)),f306(f306(f236(x85301,x85301),x85305),x85302)),x85304)) % 187.68/187.65 [8531]~P9(x85311,x85313,x85314)+P1(f306(f306(f308(x85311),x85312),x85313))+~P1(f306(f306(f308(f871(x85311,x85311)),f306(f306(f236(x85311,x85311),x85312),x85315)),x85314)) % 187.68/187.65 [8789]~P9(x87891,x87895,x87892)+E(f306(f260(x87891,x87891,x87892),f306(f306(f284(x87891),x87893),f185(f872(x87891,a859)))),f306(f260(x87891,x87891,x87892),f306(f306(f284(x87891),x87894),f185(f872(x87891,a859)))))+~P1(f306(f306(f308(f871(x87891,x87891)),f306(f306(f236(x87891,x87891),x87893),x87894)),x87892)) % 187.68/187.65 [8873]~P1(f306(f306(f306(f306(a195,x88732),x88733),x88734),x88735))+~P1(f306(f306(f306(f306(a195,f33(x88731,x88732)),x88735),x88734),x88733))+P1(f306(f306(f306(f306(a195,f33(x88731,x88732)),x88733),x88734),x88733)) % 187.68/187.65 [8984]P1(f306(x89841,x89842))+~P1(f306(f306(f308(x89843),x89842),x89845))+P1(f306(f306(f308(x89843),f338(x89841,x89844,x89845,x89843)),f306(f306(f108(f872(x89843,a859)),x89845),x89844))) % 187.68/187.65 [8985]P1(f306(x89851,x89852))+~P1(f306(f306(f308(x89853),x89852),x89854))+P1(f306(f306(f308(x89853),f338(x89851,x89854,x89855,x89853)),f306(f306(f108(f872(x89853,a859)),x89855),x89854))) % 187.68/187.65 [8993]~P1(f306(x89932,x89935))+~P1(f306(f306(f308(x89931),x89935),x89934))+P1(f306(f306(f308(x89931),f327(x89932,x89933,x89934,x89931)),f306(f306(f108(f872(x89931,a859)),x89934),x89933))) % 187.68/187.65 [8994]~P1(f306(x89942,x89945))+~P1(f306(f306(f308(x89941),x89945),x89943))+P1(f306(f306(f308(x89941),f327(x89942,x89943,x89944,x89941)),f306(f306(f108(f872(x89941,a859)),x89944),x89943))) % 187.68/187.65 [9009]~P1(f306(f306(f220(f872(x90091,a859)),x90095),x90093))+~P1(f306(f306(f220(f872(x90091,a859)),x90092),x90094))+P1(f306(f306(f220(f872(x90091,a859)),f306(f306(f22(f872(x90091,a859)),x90092),x90093)),f306(f306(f22(f872(x90091,a859)),x90094),x90095))) % 187.68/187.65 [9010]~P1(f306(f306(f220(f872(x90101,a859)),x90103),x90105))+~P1(f306(f306(f220(f872(x90101,a859)),x90102),x90104))+P1(f306(f306(f220(f872(x90101,a859)),f306(f306(f108(f872(x90101,a859)),x90102),x90103)),f306(f306(f108(f872(x90101,a859)),x90104),x90105))) % 187.68/187.65 [9011]~P1(f306(f306(f220(f872(x90111,a859)),x90113),x90115))+~P1(f306(f306(f220(f872(x90111,a859)),x90112),x90114))+P1(f306(f306(f220(f872(x90111,a859)),f306(f306(f109(f872(x90111,a859)),x90112),x90113)),f306(f306(f109(f872(x90111,a859)),x90114),x90115))) % 187.68/187.65 [9099]~E(f306(f186(f866(x90991)),x90993),f306(f186(f866(x90992)),x90994))+E(f306(f306(f169(x90991,x90992),f306(f306(f173(x90991,x90992),x90993),x90994)),x90995),f306(f214(x90992),f674(x90995,x90994,x90992,x90993,x90991)))+~P1(f306(f306(f308(x90991),x90995),f306(f164(x90991),x90993))) % 187.68/187.65 [9103]P1(f306(f306(f308(f871(x91031,x91031)),f306(f306(f236(x91031,x91031),x91032),x91033)),f300(x91031,x91034,x91035)))+~P1(f306(f306(f220(a865),f306(x91034,x91032)),f306(x91034,x91033)))+~P1(f306(f306(f308(f871(x91031,x91031)),f306(f306(f236(x91031,x91031),x91032),x91033)),x91035)) % 187.68/187.65 [9292]P1(f306(f306(f308(f871(x92921,x92921)),f306(f306(f236(x92921,x92921),x92922),x92923)),f282(x92921,x92924)))+~P1(f306(f306(f308(f871(x92921,x92921)),f306(f306(f236(x92921,x92921),x92922),x92925)),f282(x92921,x92924)))+~P1(f306(f306(f308(f871(x92921,x92921)),f306(f306(f236(x92921,x92921),x92925),x92923)),x92924)) % 187.68/187.65 [9293]P1(f306(f306(f308(f871(x92931,x92931)),f306(f306(f236(x92931,x92931),x92932),x92933)),f282(x92931,x92934)))+~P1(f306(f306(f308(f871(x92931,x92931)),f306(f306(f236(x92931,x92931),x92935),x92933)),f282(x92931,x92934)))+~P1(f306(f306(f308(f871(x92931,x92931)),f306(f306(f236(x92931,x92931),x92932),x92935)),x92934)) % 187.68/187.65 [9391]E(x93911,x93912)+E(f306(a119,f599(x93913,x93914,x93911,x93912,x93915)),x93914)+~P1(f306(f306(f308(f871(x93915,x93915)),f306(f306(f236(x93915,x93915),x93912),x93911)),f306(f306(f180(f871(x93915,x93915),a859),x93914),x93913))) % 187.68/187.65 [9392]E(x93921,x93922)+E(f306(a119,f602(x93923,x93924,x93921,x93922,x93925)),x93924)+~P1(f306(f306(f308(f871(x93925,x93925)),f306(f306(f236(x93925,x93925),x93922),x93921)),f306(f306(f180(f871(x93925,x93925),a859),x93924),x93923))) % 187.68/187.65 [9393]E(x93931,f2(a865))+E(f306(a119,f599(x93932,x93931,x93933,x93934,x93935)),x93931)+~P1(f306(f306(f308(f871(x93935,x93935)),f306(f306(f236(x93935,x93935),x93934),x93933)),f306(f306(f180(f871(x93935,x93935),a859),x93931),x93932))) % 187.68/187.65 [9394]E(x93941,f2(a865))+E(f306(a119,f602(x93942,x93941,x93943,x93944,x93945)),x93941)+~P1(f306(f306(f308(f871(x93945,x93945)),f306(f306(f236(x93945,x93945),x93944),x93943)),f306(f306(f180(f871(x93945,x93945),a859),x93941),x93942))) % 187.68/187.65 [9411]P1(f306(f306(f308(f871(x94111,x94111)),f306(f306(f236(x94111,x94111),x94112),x94113)),f306(f306(f263(x94111,x94111,x94111),x94114),f282(x94111,x94114))))+~P1(f306(f306(f308(f871(x94111,x94111)),f306(f306(f236(x94111,x94111),x94112),x94115)),x94114))+~P1(f306(f306(f308(f871(x94111,x94111)),f306(f306(f236(x94111,x94111),x94115),x94113)),x94114)) % 187.68/187.65 [9418]~P1(f306(f306(f308(f871(x94181,x94181)),f306(f306(f236(x94181,x94181),x94182),x94185)),f282(x94181,x94184)))+P1(f306(f306(f308(f871(x94181,x94181)),f306(f306(f236(x94181,x94181),x94182),x94183)),f306(f306(f263(x94181,x94181,x94181),x94184),f282(x94181,x94184))))+~P1(f306(f306(f308(f871(x94181,x94181)),f306(f306(f236(x94181,x94181),x94185),x94183)),x94184)) % 187.68/187.65 [9457]~P9(x94571,x94575,x94572)+~P1(f306(f306(f308(f871(x94571,x94571)),f306(f306(f236(x94571,x94571),x94573),x94574)),x94572))+P1(f306(f306(f220(f872(x94571,a859)),f306(f260(x94571,x94571,x94572),f306(f306(f284(x94571),x94573),f185(f872(x94571,a859))))),f306(f260(x94571,x94571,x94572),f306(f306(f284(x94571),x94574),f185(f872(x94571,a859)))))) % 187.68/187.65 [9480]E(x94801,x94802)+P1(f306(f306(f306(f306(a195,x94803),x94801),x94804),f369(x94802,x94804,x94801,x94803,x94805)))+~P1(f306(f306(f306(f306(a195,f33(x94805,x94803)),x94801),x94804),x94802)) % 187.68/187.65 [9484]~P1(f306(x94845,x94842))+P1(f306(f306(f306(f306(a195,x94841),x94842),x94843),f369(x94844,x94843,x94842,x94841,x94845)))+~P1(f306(f306(f306(f306(a195,f33(x94845,x94841)),x94842),x94843),x94844)) % 187.68/187.65 [9514]P1(f306(f306(f308(f871(x95141,x95141)),f306(f306(f236(x95141,x95141),x95142),x95143)),f306(f306(f263(x95141,x95141,x95141),x95144),f282(x95141,x95144))))+~P1(f306(f306(f308(f871(x95141,x95141)),f306(f306(f236(x95141,x95141),x95142),x95145)),f306(f306(f263(x95141,x95141,x95141),x95144),f282(x95141,x95144))))+~P1(f306(f306(f308(f871(x95141,x95141)),f306(f306(f236(x95141,x95141),x95145),x95143)),x95144)) % 187.68/187.65 [9515]P1(f306(f306(f308(f871(x95151,x95151)),f306(f306(f236(x95151,x95151),x95152),x95153)),f306(f306(f263(x95151,x95151,x95151),x95154),f282(x95151,x95154))))+~P1(f306(f306(f308(f871(x95151,x95151)),f306(f306(f236(x95151,x95151),x95155),x95153)),f306(f306(f263(x95151,x95151,x95151),x95154),f282(x95151,x95154))))+~P1(f306(f306(f308(f871(x95151,x95151)),f306(f306(f236(x95151,x95151),x95152),x95155)),x95154)) % 187.68/187.65 [9566]~P1(f306(f68(x95661,x95661,x95664,x95662,x95663),x95665))+P1(f306(f306(f308(x95661),x95662),x95663))+P1(f306(f64(x95661,x95664,f306(f306(f284(x95661),x95662),x95663)),x95665)) % 187.68/187.65 [9605]~E(f306(f285(x96053,x96052,x96055),x96054),x96051)+E(x96051,f185(f872(x96052,a859)))+P1(f306(f306(f220(f872(x96053,a859)),f306(f285(x96052,x96053,f438(x96054,x96053,x96052,x96051)),x96051)),x96054)) % 187.68/187.65 [9650]~P6(x96505)+P1(f306(f306(f308(x96501),f461(x96502,x96503,x96504,x96501,x96505)),x96504))+P1(f306(f306(f220(x96505),f306(f306(f43(x96501,x96505),x96504),x96503)),x96502)) % 187.68/187.65 [9703]P37(x97031,x97032,x97033,x97034,x97035)+~E(f306(f186(f866(x97031)),x97034),f306(f186(f866(x97032)),x97035))+P1(f306(f306(f308(f871(x97031,x97032)),f753(x97035,x97034,x97033,x97032,x97031)),f306(f164(f871(x97031,x97032)),f306(f306(f173(x97031,x97032),x97034),x97035)))) % 187.68/187.65 [9704]P37(x97041,x97042,x97043,x97044,x97045)+~E(f306(f186(f866(x97041)),x97044),f306(f186(f866(x97042)),x97045))+P1(f306(f306(f308(f871(x97041,x97042)),f760(x97043,x97045,x97044,x97042,x97041)),f306(f164(f871(x97041,x97042)),f306(f306(f173(x97041,x97042),x97044),x97045)))) % 187.68/187.65 [9835]E(x98351,x98352)+P1(f306(f306(f306(f306(a195,f33(x98353,x98354)),f369(x98351,x98355,x98352,x98354,x98353)),x98355),x98351))+~P1(f306(f306(f306(f306(a195,f33(x98353,x98354)),x98352),x98355),x98351)) % 187.68/187.65 [9837]~P1(f306(x98371,x98375))+P1(f306(f306(f306(f306(a195,f33(x98371,x98372)),f369(x98373,x98374,x98375,x98372,x98371)),x98374),x98373))+~P1(f306(f306(f306(f306(a195,f33(x98371,x98372)),x98375),x98374),x98373)) % 187.68/187.65 [9844]E(x98441,x98442)+P1(f306(f306(f308(f871(x98443,x98443)),f306(f306(f236(x98443,x98443),x98441),f600(x98444,x98445,x98442,x98441,x98443))),x98444))+~P1(f306(f306(f308(f871(x98443,x98443)),f306(f306(f236(x98443,x98443),x98441),x98442)),f306(f306(f180(f871(x98443,x98443),a859),x98445),x98444))) % 187.68/187.65 [9845]E(x98451,f2(a865))+P1(f306(f306(f308(f871(x98452,x98452)),f306(f306(f236(x98452,x98452),x98453),f600(x98454,x98451,x98455,x98453,x98452))),x98454))+~P1(f306(f306(f308(f871(x98452,x98452)),f306(f306(f236(x98452,x98452),x98453),x98455)),f306(f306(f180(f871(x98452,x98452),a859),x98451),x98454))) % 187.68/187.65 [9890]~P6(x98901)+~P1(f306(f306(f220(x98901),f306(x98904,f461(x98905,x98904,x98903,x98902,x98901))),x98905))+P1(f306(f306(f220(x98901),f306(f306(f43(x98902,x98901),x98903),x98904)),x98905)) % 187.68/187.65 [9932]E(x99321,x99322)+P1(f306(f306(f308(f871(x99323,x99323)),f306(f306(f236(x99323,x99323),f603(x99324,x99325,x99321,x99322,x99323)),x99321)),x99324))+~P1(f306(f306(f308(f871(x99323,x99323)),f306(f306(f236(x99323,x99323),x99322),x99321)),f306(f306(f180(f871(x99323,x99323),a859),x99325),x99324))) % 187.68/187.65 [9933]E(x99331,f2(a865))+P1(f306(f306(f308(f871(x99332,x99332)),f306(f306(f236(x99332,x99332),f603(x99333,x99331,x99334,x99335,x99332)),x99334)),x99333))+~P1(f306(f306(f308(f871(x99332,x99332)),f306(f306(f236(x99332,x99332),x99335),x99334)),f306(f306(f180(f871(x99332,x99332),a859),x99331),x99333))) % 187.68/187.65 [9937]E(x99371,x99372)+P1(f306(f306(f308(f871(x99373,x99373)),f306(f306(f236(x99373,x99373),x99371),f603(x99374,x99375,x99372,x99371,x99373))),f306(f306(f180(f871(x99373,x99373),a859),f602(x99374,x99375,x99372,x99371,x99373)),x99374)))+~P1(f306(f306(f308(f871(x99373,x99373)),f306(f306(f236(x99373,x99373),x99371),x99372)),f306(f306(f180(f871(x99373,x99373),a859),x99375),x99374))) % 187.68/187.65 [9938]E(x99381,f2(a865))+P1(f306(f306(f308(f871(x99382,x99382)),f306(f306(f236(x99382,x99382),x99383),f603(x99384,x99381,x99385,x99383,x99382))),f306(f306(f180(f871(x99382,x99382),a859),f602(x99384,x99381,x99385,x99383,x99382)),x99384)))+~P1(f306(f306(f308(f871(x99382,x99382)),f306(f306(f236(x99382,x99382),x99383),x99385)),f306(f306(f180(f871(x99382,x99382),a859),x99381),x99384))) % 187.68/187.65 [9990]E(x99901,x99902)+P1(f306(f306(f308(f871(x99903,x99903)),f306(f306(f236(x99903,x99903),f600(x99904,x99905,x99901,x99902,x99903)),x99901)),f306(f306(f180(f871(x99903,x99903),a859),f599(x99904,x99905,x99901,x99902,x99903)),x99904)))+~P1(f306(f306(f308(f871(x99903,x99903)),f306(f306(f236(x99903,x99903),x99902),x99901)),f306(f306(f180(f871(x99903,x99903),a859),x99905),x99904))) % 187.68/187.65 [9991]E(x99911,f2(a865))+P1(f306(f306(f308(f871(x99912,x99912)),f306(f306(f236(x99912,x99912),f600(x99913,x99911,x99914,x99915,x99912)),x99914)),f306(f306(f180(f871(x99912,x99912),a859),f599(x99913,x99911,x99914,x99915,x99912)),x99913)))+~P1(f306(f306(f308(f871(x99912,x99912)),f306(f306(f236(x99912,x99912),x99915),x99914)),f306(f306(f180(f871(x99912,x99912),a859),x99911),x99913))) % 187.68/187.65 [10025]~P74(x100252)+~P1(f306(f63(x100251),x100255))+E(f306(f306(f6(x100251,x100252),f306(f306(f7(x100251,x100252,x100252),f306(f306(f18(x100251,x100252,f872(x100252,x100252)),f306(f306(f8(a859,f872(x100252,f872(x100252,x100252)),x100251),f101(x100252)),f306(f306(f7(x100251,f872(x100251,a859),a859),f308(x100251)),x100253))),x100254)),f2(x100252))),x100255),f306(f306(f6(x100251,x100252),x100254),f306(f306(f109(f872(x100251,a859)),x100255),x100253))) % 187.68/187.65 [8593]~P75(x85931)+~P1(f306(f63(x85934),x85935))+E(f306(f306(f82(x85931),f306(x85932,x85933)),f306(f306(f9(x85934,x85931),x85932),f306(f306(f22(f872(x85934,a859)),x85935),f306(f306(f284(x85934),x85933),f185(f872(x85934,a859)))))),f306(f306(f9(x85934,x85931),x85932),f306(f306(f284(x85934),x85933),x85935))) % 187.68/187.65 [8594]~P74(x85941)+~P1(f306(f63(x85944),x85945))+E(f306(f306(f81(x85941),f306(x85942,x85943)),f306(f306(f6(x85944,x85941),x85942),f306(f306(f22(f872(x85944,a859)),x85945),f306(f306(f284(x85944),x85943),f185(f872(x85944,a859)))))),f306(f306(f6(x85944,x85941),x85942),f306(f306(f284(x85944),x85943),x85945))) % 187.68/187.65 [8912]~P108(x89122)+~P17(x89122,f306(f161(x89122),f306(f306(f146(x89121,x89122),x89124),x89125)))+E(f306(f128(x89121,f306(f306(f8(x89122,a859,x89121),f306(f221(x89122),x89123)),x89124)),x89125),f168(x89121,f306(f306(f8(x89122,a859,x89121),f306(f221(x89122),x89123)),x89124),x89125)) % 187.68/187.65 [8938]~P74(x89381)+E(f306(f306(f81(x89381),f306(f306(f6(a865,x89381),x89382),f277(a865,x89383,x89384))),f306(f306(f6(a865,x89381),x89382),f277(a865,f306(f306(f81(a865),x89384),f79(a865)),f306(f306(f81(a865),x89384),x89385)))),f306(f306(f6(a865,x89381),x89382),f277(a865,x89383,f306(f306(f81(a865),x89384),x89385))))+~P1(f306(f306(f220(a865),x89383),f306(f306(f81(a865),x89384),f79(a865)))) % 187.68/187.65 [8939]~P1(f306(f306(f308(x89391),x89394),x89395))+~P1(f306(f306(f220(f872(x89391,a859)),f306(f164(x89391),x89392)),x89395))+P1(f306(f306(f220(f872(x89391,a859)),f306(f164(x89391),f306(f306(f151(x89391,x89392),x89393),x89394))),x89395)) % 187.68/187.65 [9167]~P6(x91672)+~P1(f306(f63(x91671),x91675))+E(f306(f306(f66(x91671,x91672,f306(f306(f8(x91672,f872(x91672,x91672),x91671),f108(x91672)),x91673)),x91674),x91675),f306(f306(f108(x91672),x91674),f306(f306(f43(x91671,x91672),x91675),x91673))) % 187.68/187.65 [9168]~P6(x91682)+~P1(f306(f63(x91681),x91685))+E(f306(f306(f66(x91681,x91682,f306(f306(f8(x91682,f872(x91682,x91682),x91681),f109(x91682)),x91683)),x91684),x91685),f306(f306(f109(x91682),x91684),f306(f306(f44(x91681,x91682),x91685),x91683))) % 187.68/187.65 [9216]E(f306(x92161,x92162),f306(x92161,x92163))+P1(f306(f306(f221(a865),f306(x92161,x92162)),f306(x92161,x92163)))+~P1(f306(f306(f308(f871(x92164,x92164)),f306(f306(f236(x92164,x92164),x92162),x92163)),f145(x92164,f306(f306(f143(f872(x92164,a865)),x92161),x92165)))) % 187.68/187.65 [9248]~E(f306(x92484,x92482),f306(x92484,x92483))+~P1(f306(f306(f308(f871(x92481,x92481)),f306(f306(f236(x92481,x92481),x92482),x92483)),f145(x92481,x92485)))+P1(f306(f306(f308(f871(x92481,x92481)),f306(f306(f236(x92481,x92481),x92482),x92483)),f145(x92481,f306(f306(f143(f872(x92481,a865)),x92484),x92485)))) % 187.68/187.65 [9271]~P28(x92711,x92712,x92713,x92715)+P28(x92711,x92712,x92713,f306(f306(f284(x92711),x92714),x92715))+P1(f306(f306(f308(x92712),f306(x92713,x92714)),f306(f285(x92711,x92712,x92713),f306(f306(f22(f872(x92711,a859)),x92715),f306(f306(f284(x92711),x92714),f185(f872(x92711,a859))))))) % 187.68/187.65 [9275]P1(f306(x92752,x92755))+~P1(f306(f306(f308(x92751),x92755),f306(f164(x92751),x92753)))+E(f306(f306(f130(x92751),f306(f186(f866(x92751)),f168(x92751,x92752,f306(f306(f122(x92751),x92753),x92754)))),f306(f306(f122(x92751),x92753),x92754)),f306(f306(f122(x92751),f306(f306(f130(x92751),f306(f186(f866(x92751)),f168(x92751,x92752,x92753))),x92753)),x92754)) % 187.68/187.65 [9278]~P1(f306(f306(f308(f871(x92781,x92781)),f306(f306(f236(x92781,x92781),x92782),x92783)),f145(x92781,x92785)))+~P1(f306(f306(f220(a865),f306(x92784,x92782)),f306(x92784,x92783)))+P1(f306(f306(f308(f871(x92781,x92781)),f306(f306(f236(x92781,x92781),x92782),x92783)),f145(x92781,f306(f306(f143(f872(x92781,a865)),x92784),x92785)))) % 187.68/187.65 [9343]P1(f306(f306(f308(f871(x93434,x93434)),f306(f306(f236(x93434,x93434),x93432),x93433)),f145(x93434,x93435)))+P1(f306(f306(f221(a865),f306(x93431,x93432)),f306(x93431,x93433)))+~P1(f306(f306(f308(f871(x93434,x93434)),f306(f306(f236(x93434,x93434),x93432),x93433)),f145(x93434,f306(f306(f143(f872(x93434,a865)),x93431),x93435)))) % 187.68/187.65 [9487]~P1(f306(f306(f308(f871(f866(x94871),f866(x94871))),f306(f306(f236(f866(x94871),f866(x94871)),x94872),x94874)),f150(x94871,x94875)))+~P1(f306(f306(f221(a865),x94873),f306(f186(f866(x94871)),x94872)))+P1(f306(f306(f308(f871(x94871,x94871)),f306(f306(f236(x94871,x94871),f306(f306(f157(x94871),x94872),x94873)),f306(f306(f157(x94871),x94874),x94873))),x94875)) % 187.68/187.65 [9732]E(x97321,f2(a1))+~P1(f306(f50(x97323,x97321),f306(f306(f236(a1,a1),x97324),x97325)))+P1(f306(f50(f306(f306(f82(a1),x97322),x97323),x97321),f306(f306(f236(a1,a1),f306(f306(f81(a1),f306(f306(f82(a1),x97322),x97324)),f306(f306(f40(a1),f306(f306(f82(a1),x97322),x97325)),x97321))),f46(a1,f306(f306(f82(a1),x97322),x97325),x97321)))) % 187.68/187.65 [9735]~P1(f306(f306(f221(a865),f2(a865)),x97353))+~P1(f306(f49(x97352,x97353),f306(f306(f236(a865,a865),x97354),x97355)))+P1(f306(f49(f306(f306(f82(a865),x97351),x97352),x97353),f306(f306(f236(a865,a865),f306(f306(f81(a865),f306(f306(f82(a865),x97351),x97354)),f306(f306(f40(a865),f306(f306(f82(a865),x97351),x97355)),x97353))),f46(a865,f306(f306(f82(a865),x97351),x97355),x97353)))) % 187.68/187.65 [10048]~P74(x100482)+~P1(f306(f63(x100481),x100484))+E(f306(f306(f6(x100481,x100482),x100483),f306(f228(x100481),f306(f306(f18(x100481,a859,a859),f306(f306(f8(a859,f872(a859,a859),x100481),a304),f306(f306(f7(x100481,f872(x100481,a859),a859),f308(x100481)),x100484))),f306(f306(f7(x100481,f872(x100481,a859),a859),f308(x100481)),x100485)))),f306(f306(f6(x100481,x100482),f306(f306(f7(x100481,x100482,x100482),f306(f306(f18(x100481,x100482,f872(x100482,x100482)),f306(f306(f8(a859,f872(x100482,f872(x100482,x100482)),x100481),f101(x100482)),f306(f306(f7(x100481,f872(x100481,a859),a859),f308(x100481)),x100485))),x100483)),f2(x100482))),x100484)) % 187.68/187.65 [8219]~E(f306(f306(f122(x82191),x82192),x82195),f306(f306(f122(x82191),x82193),x82194))+E(f306(f306(f122(x82191),f306(f306(f130(x82191),f306(f186(f866(x82191)),x82192)),x82193)),x82194),x82195)+P1(f306(f306(f220(a865),f306(f186(f866(x82191)),x82193)),f306(f186(f866(x82191)),x82192))) % 187.68/187.65 [8419]~E(f306(f306(f122(x84192),x84193),x84191),f306(f306(f122(x84192),x84194),x84195))+E(x84191,f306(f306(f122(x84192),f306(f306(f130(x84192),f306(f186(f866(x84192)),x84193)),x84194)),x84195))+~P1(f306(f306(f220(a865),f306(f186(f866(x84192)),x84193)),f306(f186(f866(x84192)),x84194))) % 187.68/187.65 [8511]~E(f306(f306(f81(a865),f306(f306(f82(a865),x85113),x85114)),x85111),f306(f306(f81(a865),f306(f306(f82(a865),x85112),x85114)),x85115))+~P1(f306(f306(f220(a865),x85113),x85112))+E(x85111,f306(f306(f81(a865),f306(f306(f82(a865),f306(f306(f22(a865),x85112),x85113)),x85114)),x85115)) % 187.68/187.65 [8512]~E(f306(f306(f81(a865),f306(f306(f82(a865),x85121),x85123)),x85124),f306(f306(f81(a865),f306(f306(f82(a865),x85122),x85123)),x85125))+~P1(f306(f306(f220(a865),x85122),x85121))+E(f306(f306(f81(a865),f306(f306(f82(a865),f306(f306(f22(a865),x85121),x85122)),x85123)),x85124),x85125) % 187.68/187.65 [8667]E(f306(f306(f81(a865),f306(f306(f82(a865),x86671),x86672)),x86673),f306(f306(f81(a865),f306(f306(f82(a865),x86674),x86672)),x86675))+~P1(f306(f306(f220(a865),x86674),x86671))+~E(x86675,f306(f306(f81(a865),f306(f306(f82(a865),f306(f306(f22(a865),x86671),x86674)),x86672)),x86673)) % 187.68/187.65 [8668]E(f306(f306(f81(a865),f306(f306(f82(a865),x86681),x86682)),x86683),f306(f306(f81(a865),f306(f306(f82(a865),x86684),x86682)),x86685))+~P1(f306(f306(f220(a865),x86684),x86681))+~E(f306(f306(f81(a865),f306(f306(f82(a865),f306(f306(f22(a865),x86681),x86684)),x86682)),x86683),x86685) % 187.68/187.65 [9540]~P61(x95402)+~P1(f306(f63(x95401),x95405))+E(f306(f306(f9(x95401,x95402),f306(f306(f18(x95401,x95402,x95402),f306(f306(f8(x95402,f872(x95402,x95402),x95401),f264(x95402)),x95403)),x95404)),x95405),f306(f306(f264(x95402),f306(f306(f9(x95401,x95402),x95403),x95405)),f306(f306(f9(x95401,x95402),x95404),x95405))) % 187.68/187.65 [9666]~E(f605(x96665,x96664,x96663,x96662,x96661),f606(x96665,x96664,x96663,x96662,x96661))+P1(f306(f306(f308(f871(x96661,x96661)),f306(f306(f236(x96661,x96661),x96662),x96663)),f282(x96661,x96664)))+~P1(f306(f306(f308(f871(x96661,x96661)),f306(f306(f236(x96661,x96661),x96662),x96663)),f282(x96661,f306(f306(f108(f872(f871(x96661,x96661),a859)),x96664),x96665)))) % 187.68/187.65 [9667]~E(f616(x96675,x96674,x96673,x96672,x96671),f617(x96675,x96674,x96673,x96672,x96671))+P1(f306(f306(f308(f871(x96671,x96671)),f306(f306(f236(x96671,x96671),x96672),x96673)),f282(x96671,x96674)))+~P1(f306(f306(f308(f871(x96671,x96671)),f306(f306(f236(x96671,x96671),x96672),x96673)),f282(x96671,f306(f306(f108(f872(f871(x96671,x96671),a859)),x96674),x96675)))) % 187.68/187.65 [9878]P1(f306(f306(f308(f871(x98781,x98781)),f306(f306(f236(x98781,x98781),x98782),f606(x98785,x98784,x98783,x98782,x98781))),f282(x98781,x98784)))+P1(f306(f306(f308(f871(x98781,x98781)),f306(f306(f236(x98781,x98781),x98782),x98783)),f282(x98781,x98784)))+~P1(f306(f306(f308(f871(x98781,x98781)),f306(f306(f236(x98781,x98781),x98782),x98783)),f282(x98781,f306(f306(f108(f872(f871(x98781,x98781),a859)),x98784),x98785)))) % 187.68/187.65 [9959]P1(f306(f306(f308(f871(x99591,x99591)),f306(f306(f236(x99591,x99591),f617(x99595,x99594,x99593,x99592,x99591)),x99593)),f282(x99591,x99594)))+P1(f306(f306(f308(f871(x99591,x99591)),f306(f306(f236(x99591,x99591),x99592),x99593)),f282(x99591,x99594)))+~P1(f306(f306(f308(f871(x99591,x99591)),f306(f306(f236(x99591,x99591),x99592),x99593)),f282(x99591,f306(f306(f108(f872(f871(x99591,x99591),a859)),x99594),x99595)))) % 187.68/187.65 [9997]P1(f306(f306(f308(f871(x99971,x99971)),f306(f306(f236(x99971,x99971),x99972),x99973)),f282(x99971,x99974)))+P1(f306(f306(f308(f871(x99971,x99971)),f306(f306(f236(x99971,x99971),f606(x99975,x99974,x99973,x99972,x99971)),f605(x99975,x99974,x99973,x99972,x99971))),x99975))+~P1(f306(f306(f308(f871(x99971,x99971)),f306(f306(f236(x99971,x99971),x99972),x99973)),f282(x99971,f306(f306(f108(f872(f871(x99971,x99971),a859)),x99974),x99975)))) % 187.68/187.65 [9998]P1(f306(f306(f308(f871(x99981,x99981)),f306(f306(f236(x99981,x99981),x99982),x99983)),f282(x99981,x99984)))+P1(f306(f306(f308(f871(x99981,x99981)),f306(f306(f236(x99981,x99981),f616(x99985,x99984,x99983,x99982,x99981)),f617(x99985,x99984,x99983,x99982,x99981))),x99985))+~P1(f306(f306(f308(f871(x99981,x99981)),f306(f306(f236(x99981,x99981),x99982),x99983)),f282(x99981,f306(f306(f108(f872(f871(x99981,x99981),a859)),x99984),x99985)))) % 187.68/187.65 [10125]~P1(f306(f306(f308(f871(f866(x101251),f866(x101251))),f306(f306(f236(f866(x101251),f866(x101251)),x101254),x101255)),f150(x101251,x101252)))+~P1(f306(f306(f308(f871(x101251,x101251)),x101253),f306(f164(f871(x101251,x101251)),f306(f306(f173(x101251,x101251),x101254),x101255))))+P1(f306(f306(f245(x101251,x101251,a859),f306(f306(f7(x101251,f872(f871(x101251,x101251),a859),f872(x101251,a859)),f306(f306(f8(f872(x101251,f872(f872(f871(x101251,x101251),a859),a859)),f872(f872(f871(x101251,x101251),a859),f872(x101251,a859)),x101251),f7(x101251,f872(f871(x101251,x101251),a859),a859)),f306(f306(f8(f872(x101251,f871(x101251,x101251)),f872(x101251,f872(f872(f871(x101251,x101251),a859),a859)),x101251),f306(f8(f871(x101251,x101251),f872(f872(f871(x101251,x101251),a859),a859),x101251),f308(f871(x101251,x101251)))),f236(x101251,x101251)))),x101252)),x101253)) % 187.68/187.65 [9570]~P1(f306(f306(f220(a865),x95703),x95702))+~P1(f306(f306(f220(a865),f306(f306(f81(a865),f306(f306(f82(a865),x95703),x95704)),x95701)),f306(f306(f81(a865),f306(f306(f82(a865),x95702),x95704)),x95705)))+P1(f306(f306(f220(a865),x95701),f306(f306(f81(a865),f306(f306(f82(a865),f306(f306(f22(a865),x95702),x95703)),x95704)),x95705))) % 187.68/187.65 [9571]~P1(f306(f306(f220(a865),x95713),x95712))+~P1(f306(f306(f221(a865),f306(f306(f81(a865),f306(f306(f82(a865),x95713),x95714)),x95711)),f306(f306(f81(a865),f306(f306(f82(a865),x95712),x95714)),x95715)))+P1(f306(f306(f221(a865),x95711),f306(f306(f81(a865),f306(f306(f82(a865),f306(f306(f22(a865),x95712),x95713)),x95714)),x95715))) % 187.68/187.65 [9589]~P1(f306(f306(f220(a865),x95891),x95894))+P1(f306(f306(f220(a865),f306(f306(f81(a865),f306(f306(f82(a865),x95891),x95892)),x95893)),f306(f306(f81(a865),f306(f306(f82(a865),x95894),x95892)),x95895)))+~P1(f306(f306(f220(a865),x95893),f306(f306(f81(a865),f306(f306(f82(a865),f306(f306(f22(a865),x95894),x95891)),x95892)),x95895))) % 187.68/187.65 [9590]~P1(f306(f306(f220(a865),x95901),x95904))+P1(f306(f306(f221(a865),f306(f306(f81(a865),f306(f306(f82(a865),x95901),x95902)),x95903)),f306(f306(f81(a865),f306(f306(f82(a865),x95904),x95902)),x95905)))+~P1(f306(f306(f221(a865),x95903),f306(f306(f81(a865),f306(f306(f82(a865),f306(f306(f22(a865),x95904),x95901)),x95902)),x95905))) % 187.68/187.65 [9701]~P1(f306(f306(f220(a865),x97012),x97011))+~P1(f306(f306(f220(a865),f306(f306(f81(a865),f306(f306(f82(a865),x97011),x97013)),x97014)),f306(f306(f81(a865),f306(f306(f82(a865),x97012),x97013)),x97015)))+P1(f306(f306(f220(a865),f306(f306(f81(a865),f306(f306(f82(a865),f306(f306(f22(a865),x97011),x97012)),x97013)),x97014)),x97015)) % 187.68/187.65 [9702]~P1(f306(f306(f220(a865),x97022),x97021))+~P1(f306(f306(f221(a865),f306(f306(f81(a865),f306(f306(f82(a865),x97021),x97023)),x97024)),f306(f306(f81(a865),f306(f306(f82(a865),x97022),x97023)),x97025)))+P1(f306(f306(f221(a865),f306(f306(f81(a865),f306(f306(f82(a865),f306(f306(f22(a865),x97021),x97022)),x97023)),x97024)),x97025)) % 187.68/187.65 [9757]~P1(f306(f306(f220(a865),x97574),x97571))+P1(f306(f306(f220(a865),f306(f306(f81(a865),f306(f306(f82(a865),x97571),x97572)),x97573)),f306(f306(f81(a865),f306(f306(f82(a865),x97574),x97572)),x97575)))+~P1(f306(f306(f220(a865),f306(f306(f81(a865),f306(f306(f82(a865),f306(f306(f22(a865),x97571),x97574)),x97572)),x97573)),x97575)) % 187.68/187.65 [9758]~P1(f306(f306(f220(a865),x97584),x97581))+P1(f306(f306(f221(a865),f306(f306(f81(a865),f306(f306(f82(a865),x97581),x97582)),x97583)),f306(f306(f81(a865),f306(f306(f82(a865),x97584),x97582)),x97585)))+~P1(f306(f306(f221(a865),f306(f306(f81(a865),f306(f306(f82(a865),f306(f306(f22(a865),x97581),x97584)),x97582)),x97583)),x97585)) % 187.68/187.65 [9982]~P15(x99821,x99822,x99825,x99823)+~P1(f306(f306(f308(f871(x99821,x99821)),x99824),x99825))+P1(f306(f306(f245(x99821,x99821,a859),f306(f306(f7(x99821,f872(x99821,x99822),f872(x99821,a859)),f306(f306(f8(f872(x99822,a859),f872(f872(x99821,x99822),f872(x99821,a859)),x99821),f8(x99822,a859,x99821)),f306(f306(f8(x99822,f872(x99822,a859),x99821),a303),x99823))),x99823)),x99824)) % 187.68/187.65 [10006]~P109(x100061)+~P41(x100061,f872(x100062,a859),x100063)+P41(x100061,f872(x100062,a859),f306(f306(f7(x100061,f872(x100062,a859),f872(x100062,a859)),f306(f306(f8(f872(x100062,a859),f872(f872(x100062,a859),f872(x100062,a859)),x100061),f108(f872(x100062,a859))),f306(f306(f7(x100061,f872(x100062,a859),f872(x100062,a859)),f306(f306(f8(f872(x100062,a859),f872(f872(x100062,a859),f872(x100062,a859)),x100061),f108(f872(x100062,a859))),x100063)),x100064))),x100065)) % 187.68/187.65 [6763]~E(f306(x67634,x67635),f188(x67632))+E(f306(f176(x67631,x67632,x67633,x67634),x67635),f306(f214(x67632),x67636))+~E(f306(x67633,x67635),f306(f214(x67632),x67636)) % 187.68/187.65 [6861]~E(f306(x68613,x68616),f188(x68611))+E(f306(f216(f869(x68611),x68612,f188(x68611),x68613),f306(x68614,x68615)),f188(x68611))+~E(f306(x68614,x68615),f306(f214(x68612),x68616)) % 187.68/187.65 [7445]E(f306(x74451,x74452),f188(x74453))+~E(f306(f176(x74455,x74453,x74456,x74451),x74452),f306(f214(x74453),x74454))+E(f306(x74451,x74452),f306(f214(x74453),x74454)) % 187.68/187.65 [7478]~E(f306(f176(x74786,x74783,x74785,x74781),x74782),f306(f214(x74783),x74784))+E(f306(x74781,x74782),f306(f214(x74783),x74784))+E(f306(x74785,x74782),f306(f214(x74783),x74784)) % 187.68/187.65 [8378]~P22(x83786,x83781,x83782,x83784)+E(f306(f74(x83781,x83781,x83781,f306(x83782,x83783)),f306(x83784,x83785)),f306(f74(x83781,x83781,x83781,f306(x83784,x83785)),f306(x83782,x83783)))+~P1(f306(f63(x83786),x83785)) % 187.68/187.65 [8801]~P28(x88011,x88013,x88015,x88016)+~P28(x88013,x88012,x88014,f306(f285(x88011,x88013,x88015),x88016))+P28(x88011,x88012,f306(f74(x88013,x88012,x88011,x88014),x88015),x88016) % 187.68/187.65 [9376]~P1(f306(f306(x93763,x93762),x93766))+~P1(f306(f306(x93764,x93765),x93762))+P1(f306(f306(f308(x93761),x93762),f274(x93761,x93763,x93764,x93765,x93766))) % 187.68/187.65 [9377]~P1(f306(f306(x93774,x93772),x93776))+~P1(f306(f306(x93773,x93775),x93772))+P1(f306(f306(f308(x93771),x93772),f271(x93771,x93773,x93774,x93775,x93776))) % 187.68/187.65 [9488]E(x94881,x94882)+E(x94883,x94884)+~P1(f306(f306(f308(f871(f866(x94885),f866(x94885))),f306(f306(f236(f866(x94885),f866(x94885)),f306(f306(f143(x94885),x94883),x94881)),f306(f306(f143(x94885),x94884),x94882))),f149(x94885,x94886))) % 187.68/187.65 [9498]~E(x94982,x94984)+P1(f306(f306(f308(f871(f866(x94981),f866(x94981))),f306(f306(f236(f866(x94981),f866(x94981)),f306(f306(f143(x94981),x94982),x94983)),f306(f306(f143(x94981),x94984),x94985))),f137(x94981,x94986)))+~P1(f306(f306(f308(f871(f866(x94981),f866(x94981))),f306(f306(f236(f866(x94981),f866(x94981)),x94983),x94985)),f137(x94981,x94986))) % 187.68/187.65 [9499]~E(x94992,x94994)+P1(f306(f306(f308(f871(f866(x94991),f866(x94991))),f306(f306(f236(f866(x94991),f866(x94991)),f306(f306(f143(x94991),x94992),x94993)),f306(f306(f143(x94991),x94994),x94995))),f139(x94991,x94996)))+~P1(f306(f306(f308(f871(f866(x94991),f866(x94991))),f306(f306(f236(f866(x94991),f866(x94991)),x94993),x94995)),f139(x94991,x94996))) % 187.68/187.65 [9500]~E(x95002,x95004)+P1(f306(f306(f308(f871(f866(x95001),f866(x95001))),f306(f306(f236(f866(x95001),f866(x95001)),f306(f306(f143(x95001),x95002),x95003)),f306(f306(f143(x95001),x95004),x95005))),f149(x95001,x95006)))+~P1(f306(f306(f308(f871(f866(x95001),f866(x95001))),f306(f306(f236(f866(x95001),f866(x95001)),x95003),x95005)),f149(x95001,x95006))) % 187.68/187.65 [9501]~E(x95012,x95014)+P1(f306(f306(f308(f871(f866(x95011),f866(x95011))),f306(f306(f236(f866(x95011),f866(x95011)),f306(f306(f122(x95011),x95012),x95013)),f306(f306(f122(x95011),x95014),x95015))),f149(x95011,x95016)))+~P1(f306(f306(f308(f871(f866(x95011),f866(x95011))),f306(f306(f236(f866(x95011),f866(x95011)),x95013),x95015)),f149(x95011,x95016))) % 187.68/187.65 [9502]~E(x95023,x95025)+P1(f306(f306(f308(f871(f866(x95021),f866(x95021))),f306(f306(f236(f866(x95021),f866(x95021)),f306(f306(f122(x95021),x95022),x95023)),f306(f306(f122(x95021),x95024),x95025))),f149(x95021,x95026)))+~P1(f306(f306(f308(f871(f866(x95021),f866(x95021))),f306(f306(f236(f866(x95021),f866(x95021)),x95022),x95024)),f149(x95021,x95026))) % 187.68/187.65 [9558]E(x95581,x95582)+P1(f306(f306(f308(f871(f866(x95583),f866(x95583))),f306(f306(f236(f866(x95583),f866(x95583)),x95581),x95582)),f149(x95583,x95584)))+~P1(f306(f306(f308(f871(f866(x95583),f866(x95583))),f306(f306(f236(f866(x95583),f866(x95583)),f306(f306(f143(x95583),x95585),x95581)),f306(f306(f143(x95583),x95586),x95582))),f149(x95583,x95584))) % 187.68/187.65 [9705]~E(x97053,x97055)+P1(f306(f306(f308(f871(f866(x97051),f866(x97051))),f306(f306(f236(f866(x97051),f866(x97051)),f306(f306(f122(x97051),x97052),f306(f306(f143(x97051),x97053),f120(x97051)))),f306(f306(f122(x97051),x97054),f306(f306(f143(x97051),x97055),f120(x97051))))),f149(x97051,x97056)))+~P1(f306(f306(f308(f871(f866(x97051),f866(x97051))),f306(f306(f236(f866(x97051),f866(x97051)),x97052),x97054)),f149(x97051,x97056))) % 187.68/187.65 [9722]E(f306(x97221,x97222),f188(x97223))+~E(f306(f216(f869(x97226),x97223,f188(x97226),x97224),f306(x97221,x97222)),f188(x97226))+E(f306(x97224,f663(x97222,x97221,x97224,x97225,x97226,x97223)),f188(x97226)) % 187.68/187.65 [9723]E(f306(x97231,x97232),f188(x97233))+~E(f306(f216(f869(x97236),x97233,f188(x97236),x97234),f306(x97231,x97232)),f188(x97236))+E(f306(f214(x97233),f663(x97232,x97231,x97234,x97235,x97236,x97233)),f306(x97231,x97232)) % 187.68/187.65 [9761]E(x97611,x97612)+E(x97613,x97614)+~P1(f306(f306(f308(f871(f866(x97615),f866(x97615))),f306(f306(f236(f866(x97615),f866(x97615)),f306(f306(f122(x97615),x97613),f306(f306(f143(x97615),x97611),f120(x97615)))),f306(f306(f122(x97615),x97614),f306(f306(f143(x97615),x97612),f120(x97615))))),f149(x97615,x97616))) % 187.68/187.65 [9785]E(x97851,x97852)+~P1(f306(f306(f308(f871(f866(x97853),f866(x97853))),f306(f306(f236(f866(x97853),f866(x97853)),f306(f306(f122(x97853),x97851),f306(f306(f143(x97853),x97855),f120(x97853)))),f306(f306(f122(x97853),x97852),f306(f306(f143(x97853),x97856),f120(x97853))))),f149(x97853,x97854)))+P1(f306(f306(f308(f871(f866(x97853),f866(x97853))),f306(f306(f236(f866(x97853),f866(x97853)),x97851),x97852)),f149(x97853,x97854))) % 187.68/187.65 [9820]~P1(f306(f306(f308(f871(f872(x98201,a859),f872(x98201,a859))),f306(f306(f236(f872(x98201,a859),f872(x98201,a859)),x98202),x98204)),f298(x98201,x98206)))+~P1(f306(f306(f308(f871(f872(x98201,a859),f872(x98201,a859))),f306(f306(f236(f872(x98201,a859),f872(x98201,a859)),x98203),x98205)),f298(x98201,x98206)))+P1(f306(f306(f308(f871(f872(x98201,a859),f872(x98201,a859))),f306(f306(f236(f872(x98201,a859),f872(x98201,a859)),f306(f306(f108(f872(x98201,a859)),x98202),x98203)),f306(f306(f108(f872(x98201,a859)),x98204),x98205))),f298(x98201,x98206))) % 187.68/187.65 [5203]~E(f306(x52033,x52036),x52035)+~E(x52034,f306(f214(x52031),x52036))+E(f306(f306(f189(x52031,x52032),x52033),x52034),f306(f214(x52032),x52035)) % 187.68/187.65 [5617]~E(f306(f306(f122(x56171),x56176),x56173),x56175)+E(f306(f306(f122(x56171),x56172),x56173),f306(f306(f143(x56171),x56174),x56175))+~E(x56172,f306(f306(f143(x56171),x56174),x56176)) % 187.68/187.65 [5618]~E(f306(f306(f122(x56181),x56186),x56183),x56185)+E(f306(f306(f122(x56181),x56182),x56183),f306(f306(f122(x56181),x56184),x56185))+~E(x56182,f306(f306(f122(x56181),x56184),x56186)) % 187.68/187.65 [5620]E(f306(f306(f122(x56201),x56202),x56203),f306(f306(f143(x56201),x56204),x56205))+~E(f306(f306(f143(x56201),x56204),x56206),x56202)+~E(x56205,f306(f306(f122(x56201),x56206),x56203)) % 187.68/187.65 [5622]~E(f306(f306(f122(x56221),x56222),x56226),x56224)+E(f306(f306(f122(x56221),x56222),x56223),f306(f306(f122(x56221),x56224),x56225))+~E(x56223,f306(f306(f122(x56221),x56226),x56225)) % 187.68/187.65 [6757]E(f306(x67571,x67572),f306(x67573,x67572))+~E(f306(f306(f146(x67574,x67575),x67571),x67576),f306(f306(f146(x67574,x67575),x67573),x67576))+~P1(f306(f306(f308(x67574),x67572),f306(f164(x67574),x67576))) % 187.68/187.65 [7140]~P22(x71404,x71405,x71406,x71401)+E(f306(f306(x71401,x71402),x71403),f306(f306(f66(x71404,x71405,x71406),x71403),x71402))+~P1(f306(f63(x71404),x71402)) % 187.68/187.65 [7206]~E(x72062,f306(x72064,x72066))+~P1(f306(f306(f308(x72063),x72066),x72065))+P1(f306(f306(f308(x72061),x72062),f306(f285(x72063,x72061,x72064),x72065))) % 187.68/187.65 [7207]~E(f306(x72074,x72072),x72076)+~P1(f306(f306(f308(x72073),x72076),x72075))+P1(f306(f306(f308(x72071),x72072),f306(f286(x72071,x72073,x72074),x72075))) % 187.68/187.65 [7657]~P35(x76571,x76572,x76574,x76576)+P35(x76571,x76572,f306(f306(f143(x76571),x76573),x76574),f306(f306(f143(x76571),x76575),x76576))+~P1(f306(f306(x76572,x76573),x76575)) % 187.68/187.65 [8675]~P56(x86754,x86755,x86751,x86752,x86756)+E(f306(x86751,f306(x86752,x86753)),x86753)+~P1(f306(f306(f308(x86755),x86753),x86756)) % 187.68/187.65 [9490]E(x94901,x94902)+E(f306(f186(f866(x94903)),x94904),f306(f186(f866(x94903)),x94905))+~P1(f306(f306(f308(f871(f866(x94903),f866(x94903))),f306(f306(f236(f866(x94903),f866(x94903)),f306(f306(f143(x94903),x94901),x94904)),f306(f306(f143(x94903),x94902),x94905))),f137(x94903,x94906))) % 187.68/187.65 [9553]~P19(x95531,x95532,x95533)+E(f306(f306(f66(x95531,x95532,x95533),x95534),x95535),x95536)+~P1(f306(f68(x95531,x95532,x95533,x95534,x95535),x95536)) % 187.68/187.65 [9561]E(f306(f186(f866(x95611)),x95612),f306(f186(f866(x95611)),x95613))+P1(f306(f306(f308(f871(f866(x95611),f866(x95611))),f306(f306(f236(f866(x95611),f866(x95611)),x95612),x95613)),f137(x95611,x95614)))+~P1(f306(f306(f308(f871(f866(x95611),f866(x95611))),f306(f306(f236(f866(x95611),f866(x95611)),f306(f306(f143(x95611),x95615),x95612)),f306(f306(f143(x95611),x95616),x95613))),f137(x95611,x95614))) % 187.68/187.65 [9583]~P1(f306(f306(f308(f871(x95831,x95831)),f306(f306(f236(x95831,x95831),x95832),x95834)),f282(x95831,x95836)))+P1(f306(f306(f308(f871(f866(x95831),f866(x95831))),f306(f306(f236(f866(x95831),f866(x95831)),f306(f306(f143(x95831),x95832),x95833)),f306(f306(f143(x95831),x95834),x95835))),f282(f866(x95831),f149(x95831,x95836))))+~P1(f306(f306(f308(f871(f866(x95831),f866(x95831))),f306(f306(f236(f866(x95831),f866(x95831)),x95833),x95835)),f282(f866(x95831),f149(x95831,x95836)))) % 187.68/187.65 [9767]~P1(f306(x97672,x97676))+~E(f306(f128(x97671,x97672),x97673),f306(f306(f143(x97671),x97674),x97675))+~P1(f306(f306(f308(x97671),x97676),f306(f164(x97671),f781(x97675,x97674,x97673,x97672,x97671)))) % 187.68/187.65 [9768]~P1(f306(x97684,x97686))+~E(f306(f306(f143(x97681),x97682),x97683),f306(f128(x97681,x97684),x97685))+~P1(f306(f306(f308(x97681),x97686),f306(f164(x97681),f778(x97685,x97684,x97683,x97682,x97681)))) % 187.68/187.65 [10077]~P74(x100772)+E(f306(f306(f6(x100771,x100772),f306(f306(f8(f872(x100773,a859),x100772,x100771),f306(f6(x100773,x100772),x100774)),f306(f306(f8(f872(x100773,a859),f872(x100773,a859),x100771),f228(x100773)),f306(f306(f8(f872(x100773,a859),f872(x100773,a859),x100771),f306(f18(x100773,a859,a859),f306(f306(f8(a859,f872(a859,a859),x100773),a304),f306(f306(f7(x100773,f872(x100773,a859),a859),f308(x100773)),x100775)))),f306(f7(x100773,x100771,a859),f306(f306(f8(x100771,f872(x100771,a859),x100773),a303),x100776)))))),f306(f285(x100773,x100771,x100776),x100775)),f306(f306(f6(x100773,x100772),x100774),x100775))+~P1(f306(f63(x100773),x100775)) % 187.68/187.65 [6814]~P108(x68143)+P1(f306(x68142,x68145))+E(f306(f128(x68141,x68142),f306(f306(f140(x68141,x68143,x68144),x68145),x68146)),f306(f128(x68141,x68142),x68146)) % 187.68/187.65 [6816]P1(f306(x68161,x68162))+~E(f159(x68163,x68161,x68164),f306(f306(f236(f866(x68163),f866(x68163)),x68165),x68166))+~P1(f306(f306(f308(x68163),x68162),f306(f164(x68163),x68165))) % 187.68/187.65 [6858]~P1(f306(x68582,x68586))+~E(f159(x68581,x68582,x68583),f306(f306(f236(f866(x68581),f866(x68581)),x68584),x68585))+~P1(f306(f306(f308(x68581),x68586),f306(f164(x68581),x68585))) % 187.68/187.65 [7522]~P18(x75221,x75222,x75223)+~P1(f306(f63(x75221),x75226))+E(f306(f306(f66(x75221,x75222,x75223),x75224),f306(f306(f284(x75221),x75225),x75226)),f306(f306(f66(x75221,x75222,x75223),f306(f306(x75223,x75225),x75224)),x75226)) % 187.68/187.65 [7572]~P108(x75722)+~P1(f306(f306(f220(x75722),f306(x75723,x75724)),f306(x75723,x75725)))+E(f306(f306(f140(x75721,x75722,x75723),x75724),f306(f306(f143(x75721),x75725),x75726)),f306(f306(f143(x75721),x75724),f306(f306(f143(x75721),x75725),x75726))) % 187.68/187.65 [7688]E(x76881,x76882)+~E(f306(f306(f243(x76883,x76884),x76881),f306(f16(f872(x76884,a859),x76883),x76885)),f306(f306(f243(x76883,x76884),x76882),f306(f16(f872(x76884,a859),x76883),x76885)))+~P1(f306(f306(f308(x76884),x76886),x76885)) % 187.68/187.65 [7752]~P18(x77521,x77522,x77523)+~P1(f306(f63(x77521),x77526))+E(f306(f306(f66(x77521,x77522,x77523),x77524),f306(f306(f284(x77521),x77525),x77526)),f306(f306(x77523,x77525),f306(f306(f66(x77521,x77522,x77523),x77524),x77526))) % 187.68/187.65 [7869]~P19(x78691,x78692,x78693)+~P1(f306(f63(x78691),x78696))+E(f306(f306(f66(x78691,x78692,x78693),f306(f306(x78693,x78694),x78695)),x78696),f306(f306(x78693,x78694),f306(f306(f66(x78691,x78692,x78693),x78695),x78696))) % 187.68/187.65 [7938]~P23(x79382,x79385,x79386,x79381)+~P1(f306(f63(x79382),x79384))+E(f306(x79381,f306(f306(f284(x79382),x79383),x79384)),f306(f74(x79385,x79385,x79385,f306(x79381,x79384)),f306(x79386,x79383))) % 187.68/187.65 [7976]~P108(x79762)+P1(f306(f306(f220(x79762),f306(x79763,x79764)),f306(x79763,x79765)))+E(f306(f306(f140(x79761,x79762,x79763),x79764),f306(f306(f143(x79761),x79765),x79766)),f306(f306(f143(x79761),x79765),f306(f306(f140(x79761,x79762,x79763),x79764),x79766))) % 187.68/187.65 [8120]~E(f306(f186(f866(x81201)),x81205),f306(f186(f866(x81202)),x81206))+~E(f306(f186(f866(x81201)),x81203),f306(f186(f866(x81202)),x81204))+E(f306(f306(f122(f871(x81201,x81202)),f306(f306(f173(x81201,x81202),x81203),x81204)),f306(f306(f173(x81201,x81202),x81205),x81206)),f306(f306(f173(x81201,x81202),f306(f306(f122(x81201),x81203),x81205)),f306(f306(f122(x81202),x81204),x81206))) % 187.68/187.65 [8234]~E(x82342,f306(f285(x82343,x82341,x82344),x82346))+P1(f306(f306(f220(f872(x82341,a859)),x82342),f306(f285(x82343,x82341,x82344),x82345)))+~P1(f306(f306(f220(f872(x82343,a859)),x82346),x82345)) % 187.68/187.65 [8336]~P108(x83365)+E(f306(x83361,x83362),f306(x83361,x83363))+E(f306(f306(f140(x83364,x83365,x83361),x83362),f306(f306(f140(x83364,x83365,x83361),x83363),x83366)),f306(f306(f140(x83364,x83365,x83361),x83363),f306(f306(f140(x83364,x83365,x83361),x83362),x83366))) % 187.68/187.65 [8372]~P28(x83723,x83721,x83724,x83725)+P28(x83723,x83721,f306(f306(f306(f73(x83723,x83721),x83724),x83726),x83722),x83725)+P1(f306(f306(f308(x83721),x83722),f306(f285(x83723,x83721,x83724),x83725))) % 187.68/187.65 [8520]~P1(f306(f306(f308(x85202),x85204),f306(x85206,x85203)))+~P1(f306(f306(f308(x85201),x85203),x85205))+P1(f306(f306(f308(f871(x85201,x85202)),f306(f306(f236(x85201,x85202),x85203),x85204)),f306(f306(f243(x85201,x85202),x85205),x85206))) % 187.68/187.65 [8982]~P75(x89822)+~P28(x89824,x89821,x89825,x89826)+E(f306(f306(f9(x89821,x89822),x89823),f306(f285(x89824,x89821,x89825),x89826)),f306(f306(f9(x89824,x89822),f306(f74(x89821,x89822,x89824,x89823),x89825)),x89826)) % 187.68/187.65 [8983]~P74(x89832)+~P28(x89834,x89831,x89835,x89836)+E(f306(f306(f6(x89831,x89832),x89833),f306(f285(x89834,x89831,x89835),x89836)),f306(f306(f6(x89834,x89832),f306(f74(x89831,x89832,x89834,x89833),x89835)),x89836)) % 187.68/187.65 [9031]~P37(x90312,x90315,x90311,x90313,x90316)+P1(f306(f306(x90311,f306(f306(f157(x90312),x90313),x90314)),f306(f306(f157(x90315),x90316),x90314)))+~P1(f306(f306(f221(a865),x90314),f306(f186(f866(x90315)),x90316))) % 187.68/187.65 [9032]~P37(x90322,x90325,x90321,x90323,x90326)+P1(f306(f306(x90321,f306(f306(f157(x90322),x90323),x90324)),f306(f306(f157(x90325),x90326),x90324)))+~P1(f306(f306(f221(a865),x90324),f306(f186(f866(x90322)),x90323))) % 187.68/187.65 [9244]~P22(x92443,x92441,x92446,x92442)+~P1(f306(f63(x92443),x92444))+E(f306(f74(x92441,x92441,x92441,f306(x92442,f306(f306(f22(f872(x92443,a859)),x92444),f306(f306(f284(x92443),x92445),f185(f872(x92443,a859)))))),f306(x92446,x92445)),f306(x92442,f306(f306(f284(x92443),x92445),x92444))) % 187.68/187.65 [9257]~P1(f306(f306(f308(x92575),x92573),x92576))+P1(f306(f306(f308(x92571),f306(x92572,x92573)),f103(f872(x92571,a859),x92574)))+~P1(f306(f306(f220(f872(x92571,a859)),f306(f285(x92575,x92571,x92572),x92576)),f306(x92574,f306(f285(x92575,x92571,x92572),x92576)))) % 187.68/187.65 [9858]~E(f306(f285(x98582,x98584,x98586),f231(f872(x98582,a859))),f231(f872(x98584,a859)))+~E(f306(f285(x98581,x98583,x98585),f231(f872(x98581,a859))),f231(f872(x98583,a859)))+E(f306(f285(f871(x98581,x98582),f871(x98583,x98584),f246(x98581,x98583,x98582,x98584,x98585,x98586)),f231(f872(f871(x98581,x98582),a859))),f231(f872(f871(x98583,x98584),a859))) % 187.68/187.65 [9908]~P28(x99083,x99084,x99085,f306(x99086,f644(x99086,x99085,x99084,x99083,x99082,x99081)))+P28(x99083,x99084,x99085,f306(f306(f44(x99082,f872(x99083,a859)),x99081),x99086))+E(x99081,f185(f872(x99082,a859))) % 187.68/187.65 [9967]P28(x99676,x99675,x99674,f306(f306(f44(x99672,f872(x99676,a859)),x99671),x99673))+E(x99671,f185(f872(x99672,a859)))+P1(f306(f306(f308(x99672),f644(x99673,x99674,x99675,x99676,x99672,x99671)),x99671)) % 187.68/187.65 [9973]P1(f306(f306(f308(x99731),f572(x99732,x99733,x99734,x99735,x99736,x99731)),x99736))+P1(f306(f306(f220(f872(f871(x99731,x99734),a859)),f306(f306(f243(x99731,x99734),x99736),x99733)),f306(f306(f243(x99731,x99734),x99735),x99732)))+~P1(f306(f306(f220(f872(x99731,a859)),x99736),x99735)) % 187.68/187.65 [10012]P27(x100126,x100125,f306(f306(f284(f864(x100126)),f306(f306(f306(f93(x100126),x100121),x100123),x100122)),f185(f872(f864(x100126),a859))))+~P27(x100126,x100125,f306(f306(f284(f864(x100126)),f306(f306(f306(f93(x100126),x100124),x100123),x100122)),f185(f872(f864(x100126),a859))))+P1(f306(f306(x100121,f535(x100121,x100122,x100123,x100124,x100125,x100126)),f650(x100121,x100122,x100123,x100124,x100125,x100126))) % 187.68/187.65 [10013]P27(x100136,x100135,f306(f306(f284(f864(x100136)),f306(f306(f306(f93(x100136),x100134),x100133),x100132)),f185(f872(f864(x100136),a859))))+~P27(x100136,x100135,f306(f306(f284(f864(x100136)),f306(f306(f306(f93(x100136),x100134),x100133),x100131)),f185(f872(f864(x100136),a859))))+P1(f306(f306(x100131,f754(x100132,x100131,x100133,x100134,x100135,x100136)),f816(x100132,x100131,x100133,x100134,x100135,x100136))) % 187.68/187.65 [10052]~P27(x100521,x100522,f306(f306(f284(f864(x100521)),f306(f306(f306(f93(x100521),x100523),x100524),x100526)),f185(f872(f864(x100521),a859))))+P27(x100521,x100522,f306(f306(f284(f864(x100521)),f306(f306(f306(f93(x100521),x100523),x100524),x100525)),f185(f872(f864(x100521),a859))))+~P1(f306(f306(x100525,f754(x100525,x100526,x100524,x100523,x100522,x100521)),f816(x100525,x100526,x100524,x100523,x100522,x100521))) % 187.68/187.65 [10053]~P27(x100531,x100532,f306(f306(f284(f864(x100531)),f306(f306(f306(f93(x100531),x100536),x100534),x100535)),f185(f872(f864(x100531),a859))))+P27(x100531,x100532,f306(f306(f284(f864(x100531)),f306(f306(f306(f93(x100531),x100533),x100534),x100535)),f185(f872(f864(x100531),a859))))+~P1(f306(f306(x100536,f535(x100533,x100535,x100534,x100536,x100532,x100531)),f650(x100533,x100535,x100534,x100536,x100532,x100531))) % 187.68/187.65 [10089]~P1(f306(f306(f220(f872(x100892,a859)),f306(x100894,f572(x100896,x100894,x100892,x100895,x100893,x100891))),f306(x100896,f572(x100896,x100894,x100892,x100895,x100893,x100891))))+~P1(f306(f306(f220(f872(x100891,a859)),x100893),x100895))+P1(f306(f306(f220(f872(f871(x100891,x100892),a859)),f306(f306(f243(x100891,x100892),x100893),x100894)),f306(f306(f243(x100891,x100892),x100895),x100896))) % 187.68/187.65 [7707]~P1(f306(x77071,x77075))+~P1(f306(x77076,x77074))+P1(f306(x77071,f306(f244(x77072,x77073),f306(f306(f236(x77072,x77073),x77074),x77075)))) % 187.68/187.65 [7708]~P1(f306(x77081,x77084))+~P1(f306(x77086,x77085))+P1(f306(x77081,f306(f235(x77082,x77083),f306(f306(f236(x77082,x77083),x77084),x77085)))) % 187.68/187.65 [7730]~E(f306(f186(f866(x77301)),x77303),f306(f186(f866(x77304)),x77305))+~E(f306(f306(f169(x77301,x77304),f306(f306(f173(x77301,x77304),x77303),x77305)),x77302),f306(f214(x77304),x77306))+P1(f306(f306(f308(x77301),x77302),f306(f164(x77301),x77303))) % 187.68/187.65 [7757]~P1(f306(f306(x77574,x77576),x77575))+~P1(f306(f306(f308(x77571),x77576),x77573))+P1(f306(f306(f306(f43(x77571,f872(x77572,a859)),x77573),x77574),x77575)) % 187.68/187.65 [8068]~P1(f306(f306(f308(x80681),x80682),f306(x80685,x80686)))+~P1(f306(f306(f308(x80683),x80686),x80684))+P1(f306(f306(f308(x80681),x80682),f306(f306(f43(x80683,f872(x80681,a859)),x80684),x80685))) % 187.68/187.65 [8112]P1(f306(f306(x81121,x81122),x81123))+~P1(f306(f306(x81124,x81122),x81123))+~P1(f306(f306(f220(f872(x81125,f872(x81126,a859))),x81124),x81121)) % 187.68/187.65 [8258]P1(f306(f306(x82581,x82582),x82583))+~P1(f306(f306(f308(x82584),x82582),x82585))+~P1(f306(f306(f306(f44(x82584,f872(x82586,a859)),x82585),x82581),x82583)) % 187.68/187.65 [8393]P1(f306(f306(f308(x83931),x83932),f306(x83933,x83934)))+~P1(f306(f306(f308(x83935),x83934),x83936))+~P1(f306(f306(f308(x83931),x83932),f306(f306(f44(x83935,f872(x83931,a859)),x83936),x83933))) % 187.68/187.65 [8590]~P1(f306(f306(f306(f306(a195,x85901),x85903),x85904),x85906))+~P1(f306(f306(f306(f306(a195,x85902),x85906),x85904),x85905))+P1(f306(f306(f306(f306(a195,f34(x85901,x85902)),x85903),x85904),x85905)) % 187.68/187.65 [8657]~P15(x86574,x86575,x86576,x86571)+E(f306(x86571,x86572),f306(x86571,x86573))+~P1(f306(f306(f308(f871(x86574,x86574)),f306(f306(f236(x86574,x86574),x86572),x86573)),x86576)) % 187.68/187.65 [8688]P1(f306(f306(f220(f872(x86881,a859)),x86882),f306(x86883,x86884)))+~P1(f306(f306(f308(x86885),x86884),x86886))+~P1(f306(f306(f220(f872(x86881,a859)),x86882),f306(f306(f44(x86885,f872(x86881,a859)),x86886),x86883))) % 187.68/187.65 [8717]~P54(x87173,x87174,f306(f261(x87174,x87173),x87175))+E(x87171,f185(f872(x87172,a859)))+E(f306(f306(f44(x87172,f872(x87173,a859)),x87171),f306(f306(f8(f872(x87174,a859),f872(x87173,a859),x87172),f260(x87174,x87173,x87175)),x87176)),f306(f260(x87174,x87173,x87175),f306(f306(f44(x87172,f872(x87174,a859)),x87171),x87176))) % 187.68/187.65 [8792]P1(f306(f306(f308(x87921),x87922),f306(f260(x87923,x87921,x87924),x87925)))+~P1(f306(f306(f308(x87923),x87926),x87925))+~P1(f306(f306(f308(f871(x87923,x87921)),f306(f306(f236(x87923,x87921),x87926),x87922)),x87924)) % 187.68/187.65 [8911]P1(f306(x89111,x89112))+~P1(f306(f306(f306(f306(a195,x89114),x89112),x89115),x89116))+P1(f306(f306(f306(f306(a195,f31(x89111,x89113,x89114)),x89112),x89115),x89116)) % 187.68/187.65 [8929]~P1(f306(x89291,x89294))+~P1(f306(f306(f306(f306(a195,x89292),x89294),x89295),x89296))+P1(f306(f306(f306(f306(a195,f31(x89291,x89292,x89293)),x89294),x89295),x89296)) % 187.68/187.65 [9105]P1(f306(f306(f220(f872(x91051,a859)),f306(f260(x91052,x91051,x91053),x91054)),f306(f260(x91052,x91051,x91055),x91056)))+~P1(f306(f306(f220(f872(x91052,a859)),x91054),x91056))+~P1(f306(f306(f220(f872(f871(x91052,x91051),a859)),x91053),x91055)) % 187.68/187.65 [9194]P1(f306(x91941,x91942))+P1(f306(f306(f306(f306(a195,x91943),x91942),x91944),x91945))+~P1(f306(f306(f306(f306(a195,f31(x91941,x91946,x91943)),x91942),x91944),x91945)) % 187.68/187.65 [9199]~P1(f306(x91995,x91992))+P1(f306(f306(f306(f306(a195,x91991),x91992),x91993),x91994))+~P1(f306(f306(f306(f306(a195,f31(x91995,x91991,x91996)),x91992),x91993),x91994)) % 187.68/187.65 [9251]P1(f306(f306(f306(f306(a195,x92511),x92512),x92513),x92514))+P1(f306(f306(f306(f306(a195,x92515),x92512),x92513),x92514))+~P1(f306(f306(f306(f306(a195,f31(x92516,x92511,x92515)),x92512),x92513),x92514)) % 187.68/187.65 [9294]~P1(f306(f306(f308(x92942),x92946),x92944))+~P1(f306(f306(f220(f872(x92941,a859)),x92943),x92945))+P1(f306(f306(f220(f872(f871(x92941,x92942),a859)),f306(f306(f243(x92941,x92942),x92943),f306(f16(f872(x92942,a859),x92941),x92944))),f306(f306(f243(x92941,x92942),x92945),f306(f16(f872(x92942,a859),x92941),x92944)))) % 187.68/187.65 [9307]~P37(x93071,x93072,x93073,x93075,x93076)+P1(f306(f306(f245(x93071,x93072,a859),x93073),x93074))+~P1(f306(f306(f308(f871(x93071,x93072)),x93074),f306(f164(f871(x93071,x93072)),f306(f306(f173(x93071,x93072),x93075),x93076)))) % 187.68/187.65 [9443]~E(x94433,x94435)+P1(f306(f306(f308(f871(f866(x94431),f866(x94431))),f306(f306(f236(f866(x94431),f866(x94431)),f306(f306(f143(x94431),x94432),x94433)),f306(f306(f143(x94431),x94434),x94435))),f149(x94431,x94436)))+~P1(f306(f306(f308(f871(x94431,x94431)),f306(f306(f236(x94431,x94431),x94432),x94434)),x94436)) % 187.68/187.65 [9449]~E(f306(f186(f866(x94491)),x94495),f306(f186(f866(x94492)),x94496))+E(f178(x94491,x94492,f179(x94491,x94492,x94493,f306(f306(f22(f872(x94491,a859)),x94494),f306(f164(x94491),x94495))),x94495,x94496),f179(x94491,x94492,f178(x94491,x94492,x94493,x94495,x94496),x94494))+~P1(f306(f306(f220(f872(x94491,a859)),f306(f164(x94491),x94495)),x94494)) % 187.68/187.65 [9450]~E(f306(f186(f866(x94501)),x94503),f306(f186(f866(x94501)),x94505))+P1(f306(f306(f308(f871(f866(x94501),f866(x94501))),f306(f306(f236(f866(x94501),f866(x94501)),f306(f306(f143(x94501),x94502),x94503)),f306(f306(f143(x94501),x94504),x94505))),f137(x94501,x94506)))+~P1(f306(f306(f308(f871(x94501,x94501)),f306(f306(f236(x94501,x94501),x94502),x94504)),x94506)) % 187.68/187.65 [9481]P1(f306(f306(f308(f871(x94811,x94811)),f306(f306(f236(x94811,x94811),x94812),x94813)),f306(f306(f180(f871(x94811,x94811),a859),f306(a119,x94814)),x94815)))+~P1(f306(f306(f308(f871(x94811,x94811)),f306(f306(f236(x94811,x94811),x94816),x94813)),x94815))+~P1(f306(f306(f308(f871(x94811,x94811)),f306(f306(f236(x94811,x94811),x94812),x94816)),f306(f306(f180(f871(x94811,x94811),a859),x94814),x94815))) % 187.68/187.65 [9482]P1(f306(f306(f308(f871(x94821,x94821)),f306(f306(f236(x94821,x94821),x94822),x94823)),f306(f306(f180(f871(x94821,x94821),a859),f306(a119,x94824)),x94825)))+~P1(f306(f306(f308(f871(x94821,x94821)),f306(f306(f236(x94821,x94821),x94822),x94826)),x94825))+~P1(f306(f306(f308(f871(x94821,x94821)),f306(f306(f236(x94821,x94821),x94826),x94823)),f306(f306(f180(f871(x94821,x94821),a859),x94824),x94825))) % 187.68/187.65 [9486]~P1(f306(f306(f308(x94864),x94865),x94866))+P1(f306(f306(f220(f872(x94861,a859)),x94862),x94863))+~P1(f306(f306(f220(f872(f871(x94861,x94864),a859)),f306(f306(f243(x94861,x94864),x94862),f306(f16(f872(x94864,a859),x94861),x94866))),f306(f306(f243(x94861,x94864),x94863),f306(f16(f872(x94864,a859),x94861),x94866)))) % 187.68/187.65 [9531]E(x95311,x95312)+~P1(f306(f306(f308(f871(f866(x95313),f866(x95313))),f306(f306(f236(f866(x95313),f866(x95313)),f306(f306(f143(x95313),x95311),x95315)),f306(f306(f143(x95313),x95312),x95316))),f137(x95313,x95314)))+P1(f306(f306(f308(f871(x95313,x95313)),f306(f306(f236(x95313,x95313),x95311),x95312)),x95314)) % 187.68/187.65 [9532]E(x95321,x95322)+~P1(f306(f306(f308(f871(f866(x95323),f866(x95323))),f306(f306(f236(f866(x95323),f866(x95323)),f306(f306(f143(x95323),x95321),x95325)),f306(f306(f143(x95323),x95322),x95326))),f139(x95323,x95324)))+P1(f306(f306(f308(f871(x95323,x95323)),f306(f306(f236(x95323,x95323),x95321),x95322)),x95324)) % 187.68/187.65 [9533]E(x95331,x95332)+~P1(f306(f306(f308(f871(f866(x95333),f866(x95333))),f306(f306(f236(f866(x95333),f866(x95333)),f306(f306(f143(x95333),x95331),x95335)),f306(f306(f143(x95333),x95332),x95336))),f149(x95333,x95334)))+P1(f306(f306(f308(f871(x95333,x95333)),f306(f306(f236(x95333,x95333),x95331),x95332)),x95334)) % 187.68/187.65 [9569]P1(f306(f306(f308(f871(f866(x95691),f866(x95691))),f306(f306(f236(f866(x95691),f866(x95691)),f306(f306(f143(x95691),x95692),x95693)),f306(f306(f143(x95691),x95694),x95695))),f150(x95691,x95696)))+~P1(f306(f306(f308(f871(f866(x95691),f866(x95691))),f306(f306(f236(f866(x95691),f866(x95691)),x95693),x95695)),f150(x95691,x95696)))+~P1(f306(f306(f308(f871(x95691,x95691)),f306(f306(f236(x95691,x95691),x95692),x95694)),x95696)) % 187.68/187.65 [9587]P1(f306(x95871,x95872))+~P1(f306(x95871,f459(x95871,x95873,x95874,x95875,x95876)))+~P1(f306(f306(f308(x95876),x95872),f306(f306(f43(x95875,f872(x95876,a859)),x95874),x95873))) % 187.68/187.65 [9592]~P1(f306(f306(f308(f871(f866(x95921),f866(x95921))),f306(f306(f236(f866(x95921),f866(x95921)),f306(f306(f143(x95921),x95922),x95925)),f306(f306(f143(x95921),x95923),x95926))),f137(x95921,x95924)))+P1(f306(f306(f308(f871(f866(x95921),f866(x95921))),f306(f306(f236(f866(x95921),f866(x95921)),x95925),x95926)),f137(x95921,x95924)))+P1(f306(f306(f308(f871(x95921,x95921)),f306(f306(f236(x95921,x95921),x95922),x95923)),x95924)) % 187.68/187.65 [9593]~P1(f306(f306(f308(f871(f866(x95931),f866(x95931))),f306(f306(f236(f866(x95931),f866(x95931)),f306(f306(f143(x95931),x95932),x95935)),f306(f306(f143(x95931),x95933),x95936))),f139(x95931,x95934)))+P1(f306(f306(f308(f871(f866(x95931),f866(x95931))),f306(f306(f236(f866(x95931),f866(x95931)),x95935),x95936)),f139(x95931,x95934)))+P1(f306(f306(f308(f871(x95931,x95931)),f306(f306(f236(x95931,x95931),x95932),x95933)),x95934)) % 187.68/187.65 [9594]~P1(f306(f306(f308(f871(f866(x95941),f866(x95941))),f306(f306(f236(f866(x95941),f866(x95941)),f306(f306(f143(x95941),x95942),x95945)),f306(f306(f143(x95941),x95943),x95946))),f149(x95941,x95944)))+P1(f306(f306(f308(f871(f866(x95941),f866(x95941))),f306(f306(f236(f866(x95941),f866(x95941)),x95945),x95946)),f149(x95941,x95944)))+P1(f306(f306(f308(f871(x95941,x95941)),f306(f306(f236(x95941,x95941),x95942),x95943)),x95944)) % 187.68/187.65 [9676]P1(f306(x96761,x96762))+P1(f306(f306(f308(x96763),f458(x96761,x96764,x96765,x96763,x96766)),x96765))+~P1(f306(f306(f308(x96766),x96762),f306(f306(f43(x96763,f872(x96766,a859)),x96765),x96764))) % 187.68/187.65 [9687]~E(x96872,x96874)+P1(f306(f306(f308(f871(f866(x96871),f866(x96871))),f306(f306(f236(f866(x96871),f866(x96871)),f306(f306(f122(x96871),x96872),f306(f306(f143(x96871),x96873),f120(x96871)))),f306(f306(f122(x96871),x96874),f306(f306(f143(x96871),x96875),f120(x96871))))),f149(x96871,x96876)))+~P1(f306(f306(f308(f871(x96871,x96871)),f306(f306(f236(x96871,x96871),x96873),x96875)),x96876)) % 187.68/187.65 [9777]E(x97771,x97772)+~P1(f306(f306(f308(f871(f866(x97773),f866(x97773))),f306(f306(f236(f866(x97773),f866(x97773)),f306(f306(f122(x97773),x97775),f306(f306(f143(x97773),x97771),f120(x97773)))),f306(f306(f122(x97773),x97776),f306(f306(f143(x97773),x97772),f120(x97773))))),f149(x97773,x97774)))+P1(f306(f306(f308(f871(x97773,x97773)),f306(f306(f236(x97773,x97773),x97771),x97772)),x97774)) % 187.68/187.65 [9803]~P1(f306(f306(f308(f871(f866(x98031),f866(x98031))),f306(f306(f236(f866(x98031),f866(x98031)),f306(f306(f122(x98031),x98035),f306(f306(f143(x98031),x98032),f120(x98031)))),f306(f306(f122(x98031),x98036),f306(f306(f143(x98031),x98033),f120(x98031))))),f149(x98031,x98034)))+P1(f306(f306(f308(f871(f866(x98031),f866(x98031))),f306(f306(f236(f866(x98031),f866(x98031)),x98035),x98036)),f149(x98031,x98034)))+P1(f306(f306(f308(f871(x98031,x98031)),f306(f306(f236(x98031,x98031),x98032),x98033)),x98034)) % 187.68/187.65 [9821]P1(f306(x98211,x98212))+P1(f306(f306(f308(x98213),f459(x98211,x98214,x98215,x98216,x98213)),f306(x98214,f458(x98211,x98214,x98215,x98216,x98213))))+~P1(f306(f306(f308(x98213),x98212),f306(f306(f43(x98216,f872(x98213,a859)),x98215),x98214))) % 187.68/187.65 [8808]~P19(x88083,x88084,x88081)+~P1(f306(f63(x88083),x88086))+E(f306(f306(x88081,x88082),f306(f306(f66(x88083,x88084,x88081),x88085),f306(f306(f22(f872(x88083,a859)),x88086),f306(f306(f284(x88083),x88082),f185(f872(x88083,a859)))))),f306(f306(f66(x88083,x88084,x88081),x88085),f306(f306(f284(x88083),x88082),x88086))) % 187.68/187.65 [8894]~E(f306(f306(f169(x88941,x88942),x88944),x88945),f306(f214(x88942),x88946))+~P1(f306(f306(x88943,x88945),x88946))+E(f306(f306(f169(x88941,x88942),f306(f128(f871(x88941,x88942),f306(f245(x88941,x88942,a859),x88943)),x88944)),x88945),f306(f214(x88942),x88946)) % 187.68/187.65 [9112]~P1(f306(f306(f308(x91125),x91123),x91126))+P1(f306(f306(f220(f872(x91121,a859)),f306(x91122,x91123)),x91124))+~P1(f306(f306(f220(f872(x91121,a859)),f306(f306(f43(x91125,f872(x91121,a859)),x91126),x91122)),x91124)) % 187.68/187.65 [9751]~P9(x97511,x97515,x97514)+P1(f306(f306(f308(f871(x97511,x97511)),f306(f306(f236(x97511,x97511),x97512),x97513)),x97514))+~P1(f306(f306(f308(x97511),x97516),f306(f306(f109(f872(x97511,a859)),f306(f260(x97511,x97511,x97514),f306(f306(f284(x97511),x97512),f185(f872(x97511,a859))))),f306(f260(x97511,x97511,x97514),f306(f306(f284(x97511),x97513),f185(f872(x97511,a859))))))) % 187.68/187.65 [8557]~P126(x85572)+~E(f306(f306(f81(x85572),f306(f306(f82(x85572),x85574),x85575)),x85571),f306(f306(f81(x85572),f306(f306(f82(x85572),x85573),x85575)),x85576))+E(x85571,f306(f306(f81(x85572),f306(f306(f82(x85572),f306(f306(f22(x85572),x85573),x85574)),x85575)),x85576)) % 187.68/187.65 [8558]~P126(x85581)+~E(f306(f306(f81(x85581),f306(f306(f82(x85581),x85582),x85584)),x85585),f306(f306(f81(x85581),f306(f306(f82(x85581),x85583),x85584)),x85586))+E(f306(f306(f81(x85581),f306(f306(f82(x85581),f306(f306(f22(x85581),x85582),x85583)),x85584)),x85585),x85586) % 187.68/187.65 [8720]~P126(x87201)+E(f306(f306(f81(x87201),f306(f306(f82(x87201),x87202),x87203)),x87204),f306(f306(f81(x87201),f306(f306(f82(x87201),x87205),x87203)),x87206))+~E(x87206,f306(f306(f81(x87201),f306(f306(f82(x87201),f306(f306(f22(x87201),x87202),x87205)),x87203)),x87204)) % 187.68/187.65 [8721]~P126(x87211)+E(f306(f306(f81(x87211),f306(f306(f82(x87211),x87212),x87213)),x87214),f306(f306(f81(x87211),f306(f306(f82(x87211),x87215),x87213)),x87216))+~E(f306(f306(f81(x87211),f306(f306(f82(x87211),f306(f306(f22(x87211),x87212),x87215)),x87213)),x87214),x87216) % 187.68/187.65 [9051]~P1(f306(f306(x90514,x90515),x90516))+~P1(f306(f306(x90513,x90515),x90516))+P1(f306(f306(f306(f306(f109(f872(x90511,f872(x90512,a859))),x90513),x90514),x90515),x90516)) % 187.68/187.65 [9315]P1(f306(f306(x93151,x93152),x93153))+P1(f306(f306(x93154,x93152),x93153))+~P1(f306(f306(f306(f306(f108(f872(x93155,f872(x93156,a859))),x93154),x93151),x93152),x93153)) % 187.68/187.65 [9607]~P134(x96071)+~P1(f306(f306(f220(x96071),f306(f306(f81(x96071),f306(f306(f82(x96071),x96074),x96075)),x96072)),f306(f306(f81(x96071),f306(f306(f82(x96071),x96073),x96075)),x96076)))+P1(f306(f306(f220(x96071),x96072),f306(f306(f81(x96071),f306(f306(f82(x96071),f306(f306(f22(x96071),x96073),x96074)),x96075)),x96076))) % 187.68/187.65 [9608]~P134(x96081)+~P1(f306(f306(f221(x96081),f306(f306(f81(x96081),f306(f306(f82(x96081),x96084),x96085)),x96082)),f306(f306(f81(x96081),f306(f306(f82(x96081),x96083),x96085)),x96086)))+P1(f306(f306(f221(x96081),x96082),f306(f306(f81(x96081),f306(f306(f82(x96081),f306(f306(f22(x96081),x96083),x96084)),x96085)),x96086))) % 187.68/187.65 [9629]~P134(x96291)+P1(f306(f306(f220(x96291),f306(f306(f81(x96291),f306(f306(f82(x96291),x96292),x96293)),x96294)),f306(f306(f81(x96291),f306(f306(f82(x96291),x96295),x96293)),x96296)))+~P1(f306(f306(f220(x96291),x96294),f306(f306(f81(x96291),f306(f306(f82(x96291),f306(f306(f22(x96291),x96295),x96292)),x96293)),x96296))) % 187.68/187.65 [9630]~P134(x96301)+P1(f306(f306(f221(x96301),f306(f306(f81(x96301),f306(f306(f82(x96301),x96302),x96303)),x96304)),f306(f306(f81(x96301),f306(f306(f82(x96301),x96305),x96303)),x96306)))+~P1(f306(f306(f221(x96301),x96304),f306(f306(f81(x96301),f306(f306(f82(x96301),f306(f306(f22(x96301),x96305),x96302)),x96303)),x96306))) % 187.68/187.65 [9739]~P134(x97391)+~P1(f306(f306(f220(x97391),f306(f306(f81(x97391),f306(f306(f82(x97391),x97392),x97394)),x97395)),f306(f306(f81(x97391),f306(f306(f82(x97391),x97393),x97394)),x97396)))+P1(f306(f306(f220(x97391),f306(f306(f81(x97391),f306(f306(f82(x97391),f306(f306(f22(x97391),x97392),x97393)),x97394)),x97395)),x97396)) % 187.68/187.65 [9740]~P134(x97401)+~P1(f306(f306(f221(x97401),f306(f306(f81(x97401),f306(f306(f82(x97401),x97402),x97404)),x97405)),f306(f306(f81(x97401),f306(f306(f82(x97401),x97403),x97404)),x97406)))+P1(f306(f306(f221(x97401),f306(f306(f81(x97401),f306(f306(f82(x97401),f306(f306(f22(x97401),x97402),x97403)),x97404)),x97405)),x97406)) % 187.68/187.65 [9787]~P134(x97871)+P1(f306(f306(f220(x97871),f306(f306(f81(x97871),f306(f306(f82(x97871),x97872),x97873)),x97874)),f306(f306(f81(x97871),f306(f306(f82(x97871),x97875),x97873)),x97876)))+~P1(f306(f306(f220(x97871),f306(f306(f81(x97871),f306(f306(f82(x97871),f306(f306(f22(x97871),x97872),x97875)),x97873)),x97874)),x97876)) % 187.68/187.65 [9788]~P134(x97881)+P1(f306(f306(f221(x97881),f306(f306(f81(x97881),f306(f306(f82(x97881),x97882),x97883)),x97884)),f306(f306(f81(x97881),f306(f306(f82(x97881),x97885),x97883)),x97886)))+~P1(f306(f306(f221(x97881),f306(f306(f81(x97881),f306(f306(f82(x97881),f306(f306(f22(x97881),x97882),x97885)),x97883)),x97884)),x97886)) % 187.68/187.65 [9960]~P74(x99602)+~P1(f306(f63(x99601),x99606))+E(f306(f306(f6(x99601,x99602),f306(f306(f18(x99601,x99602,x99602),f306(f306(f18(x99601,x99602,f872(x99602,x99602)),f306(f306(f8(a859,f872(x99602,f872(x99602,x99602)),x99601),f101(x99602)),x99603)),x99604)),x99605)),x99606),f306(f306(f81(x99602),f306(f306(f6(x99601,x99602),x99604),f306(f306(f109(f872(x99601,a859)),x99606),f306(f228(x99601),x99603)))),f306(f306(f6(x99601,x99602),x99605),f306(f306(f109(f872(x99601,a859)),x99606),f306(f80(f872(x99601,a859)),f306(f228(x99601),x99603)))))) % 187.68/187.65 [10021]P1(f306(f306(f308(x100212),x100214),x100216))+P1(f306(f306(f308(x100212),x100215),x100216))+E(f306(f286(x100211,x100212,f306(f306(f7(x100211,x100212,x100212),f306(f306(f7(x100211,x100212,f872(x100212,x100212)),f306(f306(f8(a859,f872(x100212,f872(x100212,x100212)),x100211),f101(x100212)),f306(f306(f7(x100211,f872(x100211,a859),a859),f308(x100211)),x100213))),x100214)),x100215)),x100216),f185(f872(x100211,a859))) % 187.68/187.65 [10022]P1(f306(f306(f308(x100222),x100225),x100226))+~P1(f306(f306(f308(x100222),x100224),x100226))+E(f306(f286(x100221,x100222,f306(f306(f7(x100221,x100222,x100222),f306(f306(f7(x100221,x100222,f872(x100222,x100222)),f306(f306(f8(a859,f872(x100222,f872(x100222,x100222)),x100221),f101(x100222)),f306(f306(f7(x100221,f872(x100221,a859),a859),f308(x100221)),x100223))),x100224)),x100225)),x100226),x100223) % 187.68/187.65 [10023]P1(f306(f306(f308(x100232),x100234),x100236))+~P1(f306(f306(f308(x100232),x100235),x100236))+E(f306(f286(x100231,x100232,f306(f306(f7(x100231,x100232,x100232),f306(f306(f7(x100231,x100232,f872(x100232,x100232)),f306(f306(f8(a859,f872(x100232,f872(x100232,x100232)),x100231),f101(x100232)),f306(f306(f7(x100231,f872(x100231,a859),a859),f308(x100231)),x100233))),x100234)),x100235)),x100236),f306(f80(f872(x100231,a859)),x100233)) % 187.68/187.65 [10024]~P1(f306(f306(f308(x100242),x100244),x100246))+~P1(f306(f306(f308(x100242),x100245),x100246))+E(f306(f286(x100241,x100242,f306(f306(f7(x100241,x100242,x100242),f306(f306(f7(x100241,x100242,f872(x100242,x100242)),f306(f306(f8(a859,f872(x100242,f872(x100242,x100242)),x100241),f101(x100242)),f306(f306(f7(x100241,f872(x100241,a859),a859),f308(x100241)),x100243))),x100244)),x100245)),x100246),f231(f872(x100241,a859))) % 187.68/187.65 [10160]P27(x101601,x101602,f306(f306(f284(f864(x101601)),f306(f306(f306(f93(x101601),f306(x101603,x101604)),f306(a26,x101604)),f306(x101605,x101604))),f185(f872(f864(x101601),a859))))+~P1(f306(f306(f308(a862),x101604),x101606))+~P27(x101601,f306(f306(f108(f872(f864(x101601),a859)),x101602),f306(f285(a862,f864(x101601),f306(f306(f18(a862,f872(x101601,f872(a861,a859)),f864(x101601)),f306(f306(f18(a862,a860,f872(f872(x101601,f872(a861,a859)),f864(x101601))),f306(f306(f8(f872(x101601,f872(a861,a859)),f872(a860,f872(f872(x101601,f872(a861,a859)),f864(x101601))),a862),f93(x101601)),x101603)),a26)),x101605)),x101606)),f306(f285(a862,f864(x101601),f306(f306(f18(a862,f872(x101601,f872(a861,a859)),f864(x101601)),f306(f306(f18(a862,a860,f872(f872(x101601,f872(a861,a859)),f864(x101601))),f306(f306(f8(f872(x101601,f872(a861,a859)),f872(a860,f872(f872(x101601,f872(a861,a859)),f864(x101601))),a862),f93(x101601)),x101603)),f306(f306(f8(f869(a860),a860,a862),f218(a860)),a28))),x101605)),x101606)) % 187.68/187.65 [8587]E(x85871,x85872)+~P56(x85874,x85875,x85873,x85876,x85877)+~E(f306(x85873,x85871),f306(x85873,x85872)) % 187.68/187.65 [6966]E(f306(f216(f869(x69661),x69662,f188(x69661),x69663),f306(x69664,x69665)),f306(f214(x69661),x69666))+~E(f306(x69664,x69665),f306(f214(x69662),x69667))+~E(f306(x69663,x69667),f306(f214(x69661),x69666)) % 187.68/187.65 [8615]~P12(x86156,x86155,x86157,x86154,x86151)+E(f306(f306(x86151,x86152),x86153),x86154)+P1(f306(f63(x86155),x86153)) % 187.68/187.65 [9470]P44(x94701,x94702,x94703,x94704,x94705,f306(f306(x94703,x94706),x94707))+~E(f306(f306(x94703,x94706),x94707),x94704)+~E(x94705,f185(f872(x94701,a859))) % 187.68/187.65 [9652]~P1(f306(x96526,x96523))+~P1(f306(f306(f308(f871(x96522,x96522)),f306(f306(f236(x96522,x96522),x96524),x96525)),f306(x96527,x96523)))+P1(f306(f306(f308(f871(f871(x96521,x96522),f871(x96521,x96522))),f306(f306(f236(f871(x96521,x96522),f871(x96521,x96522)),f306(f306(f236(x96521,x96522),x96523),x96524)),f306(f306(f236(x96521,x96522),x96523),x96525))),f258(x96521,x96522,x96526,x96527))) % 187.68/187.65 [10079]~P44(x100792,x100797,x100793,x100796,x100791,f306(f306(x100793,x100795),x100794))+E(f306(f306(x100793,f676(x100794,x100795,x100791,x100796,x100793,x100797,x100792)),f688(x100794,x100795,x100791,x100796,x100793,x100797,x100792)),f306(f306(x100793,x100795),x100794))+E(x100791,f185(f872(x100792,a859))) % 187.68/187.65 [10080]~P44(x100807,x100806,x100801,x100804,x100805,f306(f306(x100801,x100802),x100803))+E(f306(f306(x100801,f676(x100803,x100802,x100805,x100804,x100801,x100806,x100807)),f688(x100803,x100802,x100805,x100804,x100801,x100806,x100807)),f306(f306(x100801,x100802),x100803))+E(f306(f306(x100801,x100802),x100803),x100804) % 187.68/187.65 [9151]~P37(x91511,x91512,x91513,x91515,x91517)+P37(x91511,x91512,x91513,f306(f306(f143(x91511),x91514),x91515),f306(f306(f143(x91512),x91516),x91517))+~P1(f306(f306(x91513,x91514),x91516)) % 187.68/187.65 [9169]P37(x91691,x91692,x91693,x91694,x91695)+~P37(x91691,x91692,x91693,f306(f306(f122(x91691),x91696),x91694),f306(f306(f122(x91692),x91697),x91695))+~E(f306(f186(f866(x91691)),x91696),f306(f186(f866(x91692)),x91697)) % 187.68/187.65 [9170]P37(x91701,x91702,x91703,x91704,x91705)+~P37(x91701,x91702,x91703,f306(f306(f122(x91701),x91704),x91706),f306(f306(f122(x91702),x91705),x91707))+~E(f306(f186(f866(x91701)),x91704),f306(f186(f866(x91702)),x91705)) % 187.68/187.65 [9379]~P37(x93791,x93792,x93793,x93795,x93797)+~P37(x93791,x93792,x93793,x93794,x93796)+P37(x93791,x93792,x93793,f306(f306(f122(x93791),x93794),x93795),f306(f306(f122(x93792),x93796),x93797)) % 187.68/187.65 [9726]~P1(f306(f68(x97261,x97264,x97265,x97266,x97263),x97267))+P1(f306(f68(x97261,x97264,x97265,x97266,f306(f306(f284(x97261),x97262),x97263)),f306(f306(x97265,x97262),x97267)))+P1(f306(f306(f308(x97261),x97262),x97263)) % 187.68/187.65 [9856]~P28(x98563,x98561,x98564,f231(f872(x98563,a859)))+E(f306(f306(f169(x98561,x98562),f306(f306(f146(f871(x98563,x98562),f871(x98561,x98562)),f306(f245(x98563,x98562,f871(x98561,x98562)),f306(f306(f8(x98561,f872(x98562,f871(x98561,x98562)),x98563),f236(x98561,x98562)),x98564))),x98565)),f306(x98564,x98566)),f306(f214(x98562),x98567))+~E(f306(f306(f169(x98563,x98562),x98565),x98566),f306(f214(x98562),x98567)) % 187.68/187.65 [10101]~P44(x101012,x101017,x101016,x101015,x101011,f306(f306(x101016,x101014),x101013))+E(x101011,f185(f872(x101012,a859)))+P1(f306(f306(f308(x101012),f676(x101013,x101014,x101011,x101015,x101016,x101017,x101012)),x101011)) % 187.68/187.65 [10102]~P44(x101025,x101027,x101021,x101024,x101026,f306(f306(x101021,x101022),x101023))+E(f306(f306(x101021,x101022),x101023),x101024)+P1(f306(f306(f308(x101025),f676(x101023,x101022,x101026,x101024,x101021,x101027,x101025)),x101026)) % 187.68/187.65 [6756]~E(x67565,x67567)+~E(x67566,x67564)+E(f306(f306(f306(f306(f73(x67561,f869(x67562)),x67563),x67564),f306(f214(x67562),x67565)),x67566),f306(f214(x67562),x67567)) % 187.68/187.65 [6882]E(x68821,x68822)+~E(f306(x68825,x68821),f306(f214(x68824),x68827))+E(f306(f306(f306(f306(f73(x68823,f869(x68824)),x68825),x68822),f306(f214(x68824),x68826)),x68821),f306(f214(x68824),x68827)) % 187.68/187.65 [7597]E(x75971,x75972)+~E(x75973,x75974)+~E(f306(f306(f306(f306(f73(x75975,f869(x75976)),x75977),x75974),f306(f214(x75976),x75971)),x75973),f306(f214(x75976),x75972)) % 187.68/187.65 [7663]E(x76631,x76632)+E(f306(x76633,x76634),f306(f214(x76635),x76631))+~E(f306(f306(f306(f306(f73(x76636,f869(x76635)),x76633),x76637),f306(f214(x76635),x76632)),x76634),f306(f214(x76635),x76631)) % 187.68/187.65 [7664]E(x76641,x76642)+E(f306(x76643,x76641),f306(f214(x76644),x76645))+~E(f306(f306(f306(f306(f73(x76646,f869(x76644)),x76643),x76642),f306(f214(x76644),x76647)),x76641),f306(f214(x76644),x76645)) % 187.68/187.65 [8833]~P24(x88334,x88335,x88336,x88337,x88331)+~P1(f306(f63(x88335),x88333))+E(f306(f306(x88331,x88332),x88333),f306(f306(f306(f67(x88334,x88335,x88336),x88332),x88337),x88333)) % 187.68/187.65 [8834]~P12(x88344,x88345,x88346,x88347,x88341)+~P1(f306(f63(x88345),x88343))+E(f306(f306(x88341,x88342),x88343),f306(f306(f306(f67(x88344,x88345,x88346),x88342),x88347),x88343)) % 187.68/187.65 [9436]~P27(x94361,x94362,f306(f306(f284(f864(x94361)),f306(f306(f306(f93(x94361),x94363),x94364),x94367)),f185(f872(f864(x94361),a859))))+P27(x94361,x94362,f306(f306(f284(f864(x94361)),f306(f306(f306(f93(x94361),x94363),f34(x94364,x94365)),x94366)),f185(f872(f864(x94361),a859))))+~P27(x94361,x94362,f306(f306(f284(f864(x94361)),f306(f306(f306(f93(x94361),x94367),x94365),x94366)),f185(f872(f864(x94361),a859)))) % 187.68/187.65 [9624]~P26(x96243,x96244,x96245,x96247,x96246,x96241)+~P1(f306(f63(x96244),x96242))+E(f306(x96241,x96242),f306(f306(f306(f67(x96243,x96244,x96245),x96246),x96247),x96242)) % 187.68/187.65 [9782]P44(x97821,x97822,x97823,x97824,x97825,f306(f306(x97823,x97826),x97827))+~P44(x97821,x97822,x97823,x97824,f306(f306(f22(f872(x97821,a859)),x97825),f306(f306(f284(x97821),x97826),f185(f872(x97821,a859)))),x97827)+~P1(f306(f306(f308(x97821),x97826),x97825)) % 187.68/187.65 [10054]~P27(x100541,x100542,f306(f306(f284(f864(x100541)),f306(f306(f306(f93(x100541),f96(x100541,x100543,x100544)),x100545),x100547)),f185(f872(f864(x100541),a859))))+P27(x100541,x100542,f306(f306(f284(f864(x100541)),f306(f306(f306(f93(x100541),x100543),f31(x100544,x100545,x100546)),x100547)),f185(f872(f864(x100541),a859))))+~P27(x100541,x100542,f306(f306(f284(f864(x100541)),f306(f306(f306(f93(x100541),f96(x100541,x100543,f306(f74(a859,a859,a861,a301),x100544))),x100546),x100547)),f185(f872(f864(x100541),a859)))) % 187.68/187.66 [10121]P27(x101217,x101216,f306(f306(f284(f864(x101217)),f306(f306(f306(f93(x101217),x101211),x101214),x101212)),f185(f872(f864(x101217),a859))))+~P27(x101217,x101216,f306(f306(f284(f864(x101217)),f306(f306(f306(f93(x101217),x101215),x101214),x101213)),f185(f872(f864(x101217),a859))))+P1(f306(f306(x101211,f826(x101212,x101211,x101213,x101214,x101215,x101216,x101217)),f843(x101212,x101211,x101213,x101214,x101215,x101216,x101217))) % 187.68/187.66 [10130]~P44(x101302,x101303,x101304,x101305,x101301,f306(f306(x101304,x101307),x101306))+P44(x101302,x101303,x101304,x101305,f306(f306(f22(f872(x101302,a859)),x101301),f306(f306(f284(x101302),f676(x101306,x101307,x101301,x101305,x101304,x101303,x101302)),f185(f872(x101302,a859)))),f688(x101306,x101307,x101301,x101305,x101304,x101303,x101302))+E(x101301,f185(f872(x101302,a859))) % 187.68/187.66 [10131]~P44(x101315,x101316,x101311,x101314,x101317,f306(f306(x101311,x101312),x101313))+P44(x101315,x101316,x101311,x101314,f306(f306(f22(f872(x101315,a859)),x101317),f306(f306(f284(x101315),f676(x101313,x101312,x101317,x101314,x101311,x101316,x101315)),f185(f872(x101315,a859)))),f688(x101313,x101312,x101317,x101314,x101311,x101316,x101315))+E(f306(f306(x101311,x101312),x101313),x101314) % 187.68/187.66 [10132]~P27(x101321,x101322,f306(f306(f284(f864(x101321)),f306(f306(f306(f93(x101321),x101327),x101324),x101326)),f185(f872(f864(x101321),a859))))+P27(x101321,x101322,f306(f306(f284(f864(x101321)),f306(f306(f306(f93(x101321),x101323),x101324),x101325)),f185(f872(f864(x101321),a859))))+~P1(f306(f306(x101325,f826(x101325,x101323,x101326,x101324,x101327,x101322,x101321)),f850(x101325,x101323,x101326,x101324,x101327,x101322,x101321))) % 187.68/187.66 [9158]E(f178(x91581,x91582,x91583,x91584,f306(f306(f151(x91582,x91585),x91586),x91587)),f178(x91581,x91582,x91583,x91584,x91585))+~P1(f306(f306(f221(a865),x91586),f306(f186(f866(x91582)),x91585)))+~P1(f306(f306(f220(a865),f306(f186(f866(x91581)),x91584)),x91586)) % 187.68/187.66 [9458]P1(f306(f306(f220(f872(f871(x94581,x94582),a859)),f306(f306(f263(x94581,x94583,x94582),x94584),x94585)),f306(f306(f263(x94581,x94583,x94582),x94586),x94587)))+~P1(f306(f306(f220(f872(f871(x94583,x94582),a859)),x94585),x94587))+~P1(f306(f306(f220(f872(f871(x94581,x94583),a859)),x94584),x94586)) % 187.68/187.66 [9793]~P1(f306(f306(f308(x97931),x97936),x97935))+P1(f306(f68(x97931,x97932,x97933,x97934,x97935),f306(f306(x97933,x97936),x97937)))+~P1(f306(f68(x97931,x97932,x97933,x97934,f306(f306(f22(f872(x97931,a859)),x97935),f306(f306(f284(x97931),x97936),f185(f872(x97931,a859))))),x97937)) % 187.68/187.66 [10190]~P142(x101901)+~P28(f871(x101902,x101903),x101901,f306(f245(x101902,x101903,x101901),f306(f306(f7(x101902,f872(x101903,x101901),f872(x101903,x101901)),f306(f306(f8(f872(x101901,x101901),f872(f872(x101903,x101901),f872(x101903,x101901)),x101902),f8(x101901,x101901,x101903)),f306(f306(f8(x101901,f872(x101901,x101901),x101902),f82(x101901)),x101904))),x101905)),f306(f306(f243(x101902,x101903),x101906),f306(f16(f872(x101903,a859),x101902),x101907)))+E(f306(f306(f6(x101901,x101901),f35(x101901)),f306(f228(x101901),f306(f306(f8(f872(x101902,a859),a859,x101901),f88(x101902)),f306(f306(f8(f872(x101902,f872(x101903,a859)),f872(x101902,a859),x101901),f306(f8(f872(x101903,a859),a859,x101902),f88(x101903))),f306(f306(f7(x101901,f872(x101902,f872(x101903,a859)),f872(x101902,f872(x101903,a859))),f306(f306(f8(f872(x101902,f872(f872(x101903,a859),f872(x101903,a859))),f872(f872(x101902,f872(x101903,a859)),f872(x101902,f872(x101903,a859))),x101901),f18(x101902,f872(x101903,a859),f872(x101903,a859))),f306(f306(f8(f872(x101902,f872(x101903,f872(a859,a859))),f872(x101902,f872(f872(x101903,a859),f872(x101903,a859))),x101901),f306(f8(f872(x101903,f872(a859,a859)),f872(f872(x101903,a859),f872(x101903,a859)),x101902),f18(x101903,a859,a859))),f306(f306(f8(f872(x101902,f872(x101903,a859)),f872(x101902,f872(x101903,f872(a859,a859))),x101901),f306(f8(f872(x101903,a859),f872(x101903,f872(a859,a859)),x101902),f306(f8(a859,f872(a859,a859),x101903),a304))),f306(f306(f7(x101901,f872(x101902,f872(x101903,x101901)),f872(x101902,f872(x101903,a859))),f306(f306(f8(f872(f872(x101903,x101901),f872(x101903,a859)),f872(f872(x101902,f872(x101903,x101901)),f872(x101902,f872(x101903,a859))),x101901),f8(f872(x101903,x101901),f872(x101903,a859),x101902)),f306(f306(f8(f872(x101901,a859),f872(f872(x101903,x101901),f872(x101903,a859)),x101901),f8(x101901,a859,x101903)),a303))),f306(f306(f7(x101902,f872(x101903,x101901),f872(x101903,x101901)),f306(f306(f8(f872(x101901,x101901),f872(f872(x101903,x101901),f872(x101903,x101901)),x101902),f8(x101901,x101901,x101903)),f306(f306(f8(x101901,f872(x101901,x101901),x101902),f82(x101901)),x101904))),x101905)))))),f306(f306(f7(x101902,f872(x101903,a859),f872(x101903,a859)),f306(f306(f8(f872(a859,a859),f872(f872(x101903,a859),f872(x101903,a859)),x101902),f8(a859,a859,x101903)),f306(f306(f8(a859,f872(a859,a859),x101902),a304),f306(f306(f7(x101902,f872(x101902,a859),a859),f308(x101902)),x101906)))),f306(f306(f7(x101903,f872(x101903,a859),a859),f308(x101903)),x101907))))))),f306(f306(f82(x101901),f306(f306(f6(x101902,x101901),x101904),x101906)),f306(f306(f6(x101903,x101901),x101905),x101907))) % 187.68/187.66 [9887]P53(x98871,x98872,x98873,x98874,x98875,x98876,x98877)+~P1(f306(f306(x98874,x98876),x98878))+~P1(f306(f306(x98875,x98878),x98877)) % 187.68/187.66 [9220]~P22(x92208,x92201,x92203,x92205)+~P1(f306(f63(x92208),x92206))+E(f306(f74(x92201,x92201,x92202,f306(x92203,x92204)),f306(f74(x92201,x92201,x92202,f306(x92205,x92206)),x92207)),f306(f74(x92201,x92201,x92202,f306(x92205,x92206)),f306(f74(x92201,x92201,x92202,f306(x92203,x92204)),x92207))) % 187.68/187.66 [9614]~P25(x96147,x96142,x96145,x96148,x96146,x96141)+~P1(f306(f63(x96142),x96144))+E(f306(x96141,f306(f306(f284(x96142),x96143),x96144)),f306(f306(x96145,f306(x96146,x96143)),f306(x96141,x96144))) % 187.68/187.66 [9736]~P28(x97362,x97364,x97366,x97368)+~P28(x97361,x97363,x97365,x97367)+P28(f871(x97361,x97362),f871(x97363,x97364),f246(x97361,x97363,x97362,x97364,x97365,x97366),f306(f306(f243(x97361,x97362),x97367),f306(f16(f872(x97362,a859),x97361),x97368))) % 187.68/187.66 [9404]P1(f306(f306(f308(f871(x94041,x94042)),f306(f306(f236(x94041,x94042),x94043),x94044)),f306(f306(f263(x94041,x94045,x94042),x94046),x94047)))+~P1(f306(f306(f308(f871(x94041,x94045)),f306(f306(f236(x94041,x94045),x94043),x94048)),x94046))+~P1(f306(f306(f308(f871(x94045,x94042)),f306(f306(f236(x94045,x94042),x94048),x94044)),x94047)) % 187.68/187.66 [9595]~P1(f306(f306(f220(f872(f871(x95953,x95952),a859)),x95955),f306(f306(f243(x95953,x95952),x95958),f306(f16(f872(x95952,a859),x95953),x95957))))+~P1(f306(f306(f220(f872(f871(x95951,x95953),a859)),x95954),f306(f306(f243(x95951,x95953),x95956),f306(f16(f872(x95953,a859),x95951),x95958))))+P1(f306(f306(f220(f872(f871(x95951,x95952),a859)),f306(f306(f263(x95951,x95953,x95952),x95954),x95955)),f306(f306(f243(x95951,x95952),x95956),f306(f16(f872(x95952,a859),x95951),x95957)))) % 187.68/187.66 [9646]~E(x96463,x96465)+P1(f306(f306(f308(f871(f871(x96461,x96462),f871(x96461,x96462))),f306(f306(f236(f871(x96461,x96462),f871(x96461,x96462)),f306(f306(f236(x96461,x96462),x96463),x96464)),f306(f306(f236(x96461,x96462),x96465),x96466))),f299(x96461,x96462,x96467,x96468)))+~P1(f306(f306(f308(f871(x96462,x96462)),f306(f306(f236(x96462,x96462),x96464),x96466)),x96468)) % 187.68/187.66 [9759]E(x97591,x97592)+~P1(f306(f306(f308(f871(f871(x97593,x97595),f871(x97593,x97595))),f306(f306(f236(f871(x97593,x97595),f871(x97593,x97595)),f306(f306(f236(x97593,x97595),x97591),x97596)),f306(f306(f236(x97593,x97595),x97592),x97597))),f299(x97593,x97595,x97594,x97598)))+P1(f306(f306(f308(f871(x97593,x97593)),f306(f306(f236(x97593,x97593),x97591),x97592)),x97594)) % 187.68/187.66 [9776]~P1(f306(f306(f308(f871(f871(x97761,x97765),f871(x97761,x97765))),f306(f306(f236(f871(x97761,x97765),f871(x97761,x97765)),f306(f306(f236(x97761,x97765),x97762),x97766)),f306(f306(f236(x97761,x97765),x97763),x97767))),f299(x97761,x97765,x97764,x97768)))+P1(f306(f306(f308(f871(x97761,x97761)),f306(f306(f236(x97761,x97761),x97762),x97763)),x97764))+P1(f306(f306(f308(f871(x97765,x97765)),f306(f306(f236(x97765,x97765),x97766),x97767)),x97768)) % 187.68/187.66 [9677]~P26(x96777,x96775,x96771,x96778,x96772,x96774)+~P1(f306(f63(x96775),x96776))+E(f306(f306(x96771,f306(x96772,x96773)),f306(x96774,f306(f306(f22(f872(x96775,a859)),x96776),f306(f306(f284(x96775),x96773),f185(f872(x96775,a859)))))),f306(x96774,f306(f306(f284(x96775),x96773),x96776))) % 187.68/187.66 [9177]~P1(f306(f306(f306(x91775,x91778),x91776),x91777))+~P1(f306(f306(f308(x91771),x91778),x91774))+P1(f306(f306(f306(f306(f43(x91771,f872(x91772,f872(x91773,a859))),x91774),x91775),x91776),x91777)) % 187.68/187.66 [9390]P1(f306(f306(f306(x93901,x93902),x93903),x93904))+~P1(f306(f306(f308(x93905),x93902),x93906))+~P1(f306(f306(f306(f306(f44(x93905,f872(x93907,f872(x93908,a859))),x93906),x93901),x93903),x93904)) % 187.68/187.66 [9588]~P24(x95883,x95882,x95884,x95888,x95881)+~P1(f306(f63(x95882),x95887))+E(f306(f306(x95881,f306(f306(f18(x95882,x95883,x95883),f306(f306(f8(x95883,f872(x95883,x95883),x95882),x95884),x95885)),x95886)),x95887),f306(f306(x95884,f306(f306(x95881,x95885),x95887)),f306(f306(x95881,x95886),x95887))) % 187.68/187.66 [9864]~E(f306(f285(x98642,x98644,x98646),x98648),x986410)+~E(f306(f285(x98641,x98643,x98645),x98647),x98649)+E(f306(f285(f871(x98641,x98642),f871(x98643,x98644),f246(x98641,x98643,x98642,x98644,x98645,x98646)),f306(f306(f243(x98641,x98642),x98647),f306(f16(f872(x98642,a859),x98641),x98648))),f306(f306(f243(x98643,x98644),x98649),f306(f16(f872(x98644,a859),x98643),x986410))) % 187.68/187.66 [4790]~P108(x47902)+~P17(x47902,x47901)+P17(x47902,f121(x47902,x47901))+E(x47901,f120(x47902)) % 187.68/187.66 [4791]~P108(x47912)+~P17(x47912,x47911)+P17(x47912,f722(x47911,x47912))+E(x47911,f120(x47912)) % 187.68/187.66 [5024]~P6(x50242)+E(f10(x50242,x50241),f42(x50242,x50241))+E(x50241,f185(f872(x50242,a859)))+~P1(f306(f63(x50242),x50241)) % 187.68/187.66 [5025]~P6(x50252)+E(f13(x50252,x50251),f41(x50252,x50251))+E(x50251,f185(f872(x50252,a859)))+~P1(f306(f63(x50252),x50251)) % 187.68/187.66 [5191]~P108(x51912)+~P17(x51912,x51911)+E(x51911,f120(x51912))+E(f306(f306(f143(x51912),f756(x51911,x51912)),f722(x51911,x51912)),x51911) % 187.68/187.66 [5991]~P98(x59912)+E(x59911,f185(f872(x59912,a859)))+P1(f306(f306(f220(x59912),f10(x59912,x59911)),f13(x59912,x59911)))+~P1(f306(f63(x59912),x59911)) % 187.68/187.66 [6003]~P42(x60032)+~P42(x60031)+E(x60031,x60032)+~E(f306(f285(a1,a865,a112),x60031),f306(f285(a1,a865,a112),x60032)) % 187.68/187.66 [9033]~P112(x90331)+~P1(f306(f306(f308(x90331),x90332),f117(x90331)))+P1(f306(f306(f221(x90331),f306(f306(f81(x90331),f306(f306(f81(x90331),f79(x90331)),x90332)),x90332)),f2(x90331)))+~P1(f306(f306(f221(x90331),x90332),f2(x90331))) % 187.68/187.66 [9277]~P112(x92771)+~P1(f306(f306(f308(x92771),x92772),f117(x92771)))+~P1(f306(f306(f221(x92771),f306(f306(f81(x92771),f306(f306(f81(x92771),f79(x92771)),x92772)),x92772)),f2(x92771)))+P1(f306(f306(f221(x92771),x92772),f2(x92771))) % 187.68/187.66 [4846]~P115(x48462)+~P142(x48462)+E(x48461,f2(a865))+E(f306(f306(f237(x48462),f2(x48462)),x48461),f2(x48462)) % 187.68/187.66 [4851]~P115(x48511)+~P142(x48511)+~E(x48512,f2(a865))+E(f306(f306(f237(x48511),f2(x48511)),x48512),f79(x48511)) % 187.68/187.66 [5011]~P140(x50112)+E(x50111,f79(x50112))+E(x50111,f306(f80(x50112),f79(x50112)))+~E(f306(f306(f82(x50112),x50111),x50111),f79(x50112)) % 187.68/187.66 [5272]~P88(x52722)+E(x52721,f2(x52722))+E(f83(x52722,x52721),f306(f80(x52722),f79(x52722)))+P1(f306(f306(f221(x52722),f2(x52722)),x52721)) % 187.68/187.66 [5508]~P88(x55082)+E(f83(x55082,x55081),f79(x55082))+E(x55081,f2(x55082))+~P1(f306(f306(f221(x55082),f2(x55082)),x55081)) % 187.68/187.66 [5517]E(x55171,x55172)+~E(f306(f111(a865),x55171),f306(f111(a865),x55172))+P1(f306(a190,f306(f111(a1),x55172)))+P1(f306(a190,f306(f111(a1),x55171))) % 187.68/187.66 [5566]~P90(x55661)+~E(x55662,f2(x55661))+E(f306(f306(f81(x55661),x55662),x55662),f2(x55661))+~P1(f306(f306(f308(x55661),x55662),f117(x55661))) % 187.68/187.66 [5605]E(x56051,f2(a1))+~E(f306(f306(f40(a1),x56052),x56051),f2(a1))+P1(f306(f306(f221(a1),x56051),x56052))+P1(f306(f306(f221(a1),x56052),x56051)) % 187.68/187.66 [5636]E(x56361,f2(a1))+~E(f306(f306(f40(a1),x56362),x56361),f2(a1))+P1(f306(f306(f220(a1),x56362),f2(a1)))+P1(f306(f306(f221(a1),x56362),x56361)) % 187.68/187.66 [5669]E(x56691,f2(a1))+~E(f306(f306(f40(a1),x56692),x56691),f2(a1))+P1(f306(f306(f220(a1),f2(a1)),x56692))+P1(f306(f306(f221(a1),x56691),x56692)) % 187.68/187.66 [5705]~P90(x57052)+E(x57051,f2(x57052))+~E(f306(f306(f81(x57052),x57051),x57051),f2(x57052))+~P1(f306(f306(f308(x57052),x57051),f117(x57052))) % 187.68/187.66 [5765]E(f306(f111(a865),x57651),f306(f111(a865),x57652))+~E(f306(f111(a1),x57652),f2(a1))+P1(f306(a190,f306(f111(a1),x57652)))+~P1(f306(a190,f306(f111(a1),x57651))) % 187.68/187.66 [5793]~E(f306(f111(a865),x57932),f306(f111(a865),x57931))+E(f306(f111(a1),x57931),f2(a1))+P1(f306(a190,f306(f111(a1),x57931)))+~P1(f306(a190,f306(f111(a1),x57932))) % 187.68/187.66 [5802]~P108(x58022)+E(x58021,f185(f872(x58022,a859)))+~P1(f306(f63(x58022),x58021))+P1(f306(f306(f308(x58022),f14(x58022,x58021)),x58021)) % 187.68/187.66 [5803]~P108(x58032)+E(x58031,f185(f872(x58032,a859)))+~P1(f306(f63(x58032),x58031))+P1(f306(f306(f308(x58032),f15(x58032,x58031)),x58031)) % 187.68/187.66 [5971]~P112(x59711)+~P91(x59711)+P1(f306(f306(f220(x59711),f2(x59711)),f306(f111(x59711),x59712)))+~P1(f306(f306(f220(a1),a84),x59712)) % 187.68/187.66 [5972]~P112(x59721)+~P91(x59721)+P1(f306(f306(f221(x59721),f2(x59721)),f306(f111(x59721),x59722)))+~P1(f306(f306(f221(a1),a84),x59722)) % 187.68/187.66 [5990]~P112(x59901)+~P91(x59901)+E(f306(f76(x59901),f306(f111(x59901),x59902)),f306(f111(x59901),x59902))+P1(f306(f306(f221(x59901),f306(f111(x59901),x59902)),f2(x59901))) % 187.68/187.66 [6030]E(x60301,x60302)+~E(f306(a112,x60301),f306(a112,x60302))+~P1(f306(f306(f220(a1),f2(a1)),x60302))+~P1(f306(f306(f220(a1),f2(a1)),x60301)) % 187.68/187.66 [6224]~P91(x62242)+~P112(x62242)+~P1(f306(f306(f220(x62242),f2(x62242)),f306(f111(x62242),x62241)))+P1(f306(f306(f220(a1),a84),x62241)) % 187.68/187.66 [6225]~P91(x62252)+~P112(x62252)+~P1(f306(f306(f221(x62252),f2(x62252)),f306(f111(x62252),x62251)))+P1(f306(f306(f221(a1),a84),x62251)) % 187.68/187.66 [6230]~P112(x62301)+~P91(x62301)+P1(f306(f306(f220(x62301),f306(f111(x62301),x62302)),f2(x62301)))+~P1(f306(f306(f220(a1),x62302),a84)) % 187.68/187.66 [6231]~P112(x62311)+~P91(x62311)+P1(f306(f306(f221(x62311),f306(f111(x62311),x62312)),f2(x62311)))+~P1(f306(f306(f221(a1),x62312),a84)) % 187.68/187.66 [6541]~P91(x65412)+~P112(x65412)+~P1(f306(f306(f220(x65412),f306(f111(x65412),x65411)),f2(x65412)))+P1(f306(f306(f220(a1),x65411),a84)) % 187.68/187.66 [6542]~P91(x65422)+~P112(x65422)+~P1(f306(f306(f221(x65422),f306(f111(x65422),x65421)),f2(x65422)))+P1(f306(f306(f221(a1),x65421),a84)) % 187.68/187.66 [6635]~P112(x66351)+~P91(x66351)+E(f306(f76(x66351),f306(f111(x66351),x66352)),f306(f80(x66351),f306(f111(x66351),x66352)))+~P1(f306(f306(f221(x66351),f306(f111(x66351),x66352)),f2(x66351))) % 187.68/187.66 [6655]E(f306(f111(a865),x66551),f306(f111(a865),x66552))+~E(f306(f111(a1),x66552),f2(a1))+~P1(f306(f306(f220(a1),f306(f111(a1),x66551)),f2(a1)))+~P1(f306(a190,f306(f111(a1),x66551))) % 187.68/187.66 [7528]~P108(x75282)+E(x75281,f185(f872(x75282,a859)))+~P1(f306(f63(x75282),x75281))+P1(f306(f306(f220(x75282),f11(x75282,f225(x75282),x75281)),f12(x75282,f219(x75282),x75281))) % 187.68/187.66 [7845]~P42(x78452)+~P7(x78451)+P1(f306(f306(f308(a1),x78451),x78452))+~P1(f306(f306(f308(a865),f306(a112,x78451)),f306(f285(a1,a865,a112),x78452))) % 187.68/187.66 [8123]~P60(x81232)+P1(f306(x81231,f188(x81232)))+~P1(f306(f59(f869(x81232)),x81231))+P1(f306(f59(x81232),f306(f306(f8(f869(x81232),a859,x81232),x81231),f214(x81232)))) % 187.68/187.66 [8595]~P60(x85951)+~P1(f306(x85952,f188(x85951)))+P1(f306(f60(f869(x85951)),x85952))+~P1(f306(f60(x85951),f306(f306(f8(f869(x85951),a859,x85951),x85952),f214(x85951)))) % 187.68/187.66 [5799]~P125(x57992)+E(x57991,f2(a1))+E(f306(f80(x57992),f306(f110(x57992),f306(f80(a1),x57991))),f306(f110(x57992),x57991))+~P1(f306(f306(f221(a1),x57991),f2(a1))) % 187.68/187.66 [5872]~P90(x58721)+~P91(x58721)+~P33(x58721,f306(f111(x58721),x58722))+P33(x58721,f306(f111(x58721),f306(f306(f81(a1),x58722),x58722))) % 187.68/187.66 [6212]~P76(x62122)+E(x62121,f185(f872(x62122,a859)))+E(f15(x62122,f306(f285(x62122,x62122,f80(x62122)),x62121)),f306(f80(x62122),f14(x62122,x62121)))+~P1(f306(f63(x62122),x62121)) % 187.68/187.66 [6213]~P76(x62132)+E(x62131,f185(f872(x62132,a859)))+E(f14(x62132,f306(f285(x62132,x62132,f80(x62132)),x62131)),f306(f80(x62132),f15(x62132,x62131)))+~P1(f306(f63(x62132),x62131)) % 187.68/187.66 [6245]~P90(x62451)+~P91(x62451)+P33(x62451,f306(f111(x62451),x62452))+~P33(x62451,f306(f111(x62451),f306(f306(f81(a1),x62452),x62452))) % 187.68/187.66 [6336]E(x63361,f2(a1))+E(f306(a52,f51(f306(f80(a1),x63361),f306(f80(a1),x63362))),f47(x63361,x63362))+P1(f306(f306(f220(a1),f2(a1)),x63362))+~P1(f306(f306(f220(a1),f2(a1)),x63361)) % 187.68/187.66 [8346]~P32(a5000)+~P1(f306(a25,x83461))+P27(a861,x83462,f306(f306(f284(f864(a861)),f306(f306(f306(f93(a861),a303),x83461),f193(x83461))),f185(f872(f864(a861),a859))))+P1(f306(f306(f308(a862),f858(x83461,x83462)),f175(a862,a860,a28))) % 187.68/187.66 [8638]~P42(x86382)+~P42(x86381)+P1(f306(f306(f221(f872(a865,a859)),f306(f285(a1,a865,a112),x86381)),f306(f285(a1,a865,a112),x86382)))+~P1(f306(f306(f221(f872(a1,a859)),x86381),x86382)) % 187.68/187.66 [8851]~E(f762(x88512,x88511),f763(x88512,x88511))+~P1(f306(f129(x88511),f764(x88512,x88511)))+~P1(f306(f129(f866(x88511)),x88512))+P1(f306(f129(x88511),f306(f134(f866(x88511),f866(x88511),f122(x88511),f120(x88511)),x88512))) % 187.68/187.66 [8950]~P42(x89502)+~P42(x89501)+~P1(f306(f306(f220(f872(a865,a859)),f306(f285(a1,a865,a112),x89501)),f306(f285(a1,a865,a112),x89502)))+P1(f306(f306(f220(f872(a1,a859)),x89501),x89502)) % 187.68/187.66 [8951]~P42(x89512)+~P42(x89511)+~P1(f306(f306(f221(f872(a865,a859)),f306(f285(a1,a865,a112),x89511)),f306(f285(a1,a865,a112),x89512)))+P1(f306(f306(f221(f872(a1,a859)),x89511),x89512)) % 187.68/187.66 [8957]~E(f762(x89572,x89571),f763(x89572,x89571))+~P1(f306(f129(f866(x89571)),x89572))+P1(f306(f129(x89571),f306(f134(f866(x89571),f866(x89571),f122(x89571),f120(x89571)),x89572)))+P1(f306(f306(f308(f866(x89571)),f764(x89572,x89571)),f306(f164(f866(x89571)),x89572))) % 187.68/187.66 [9000]~P1(f306(f129(x90001),f764(x90002,x90001)))+~P1(f306(f129(f866(x90001)),x90002))+P1(f306(f129(x90001),f306(f134(f866(x90001),f866(x90001),f122(x90001),f120(x90001)),x90002)))+P1(f306(f306(f308(f866(x90001)),f763(x90002,x90001)),f306(f164(f866(x90001)),x90002))) % 187.68/187.66 [9001]~P1(f306(f129(x90011),f764(x90012,x90011)))+~P1(f306(f129(f866(x90011)),x90012))+P1(f306(f129(x90011),f306(f134(f866(x90011),f866(x90011),f122(x90011),f120(x90011)),x90012)))+P1(f306(f306(f308(f866(x90011)),f762(x90012,x90011)),f306(f164(f866(x90011)),x90012))) % 187.68/187.66 [9075]~P1(f306(f129(f866(x90751)),x90752))+P1(f306(f129(x90751),f306(f134(f866(x90751),f866(x90751),f122(x90751),f120(x90751)),x90752)))+P1(f306(f306(f308(f866(x90751)),f763(x90752,x90751)),f306(f164(f866(x90751)),x90752)))+P1(f306(f306(f308(f866(x90751)),f764(x90752,x90751)),f306(f164(f866(x90751)),x90752))) % 187.68/187.66 [9076]~P1(f306(f129(f866(x90761)),x90762))+P1(f306(f129(x90761),f306(f134(f866(x90761),f866(x90761),f122(x90761),f120(x90761)),x90762)))+P1(f306(f306(f308(f866(x90761)),f762(x90762,x90761)),f306(f164(f866(x90761)),x90762)))+P1(f306(f306(f308(f866(x90761)),f764(x90762,x90761)),f306(f164(f866(x90761)),x90762))) % 187.68/187.66 [9089]~E(f306(f306(f109(f872(x90891,a859)),f306(f164(x90891),f763(x90892,x90891))),f306(f164(x90891),f762(x90892,x90891))),f185(f872(x90891,a859)))+~P1(f306(f129(x90891),f764(x90892,x90891)))+~P1(f306(f129(f866(x90891)),x90892))+P1(f306(f129(x90891),f306(f134(f866(x90891),f866(x90891),f122(x90891),f120(x90891)),x90892))) % 187.68/187.66 [9154]~E(f306(f306(f109(f872(x91541,a859)),f306(f164(x91541),f763(x91542,x91541))),f306(f164(x91541),f762(x91542,x91541))),f185(f872(x91541,a859)))+~P1(f306(f129(f866(x91541)),x91542))+P1(f306(f129(x91541),f306(f134(f866(x91541),f866(x91541),f122(x91541),f120(x91541)),x91542)))+P1(f306(f306(f308(f866(x91541)),f764(x91542,x91541)),f306(f164(f866(x91541)),x91542))) % 187.68/187.66 [9428]E(x94281,f2(a1))+E(x94282,f2(a1))+E(f306(f306(f87(a1,f871(a1,a1)),f306(f306(a203,x94282),x94281)),f306(f306(f18(a1,a1,f871(a1,a1)),f306(f306(f8(a1,f872(a1,f871(a1,a1)),a1),f236(a1,a1)),f306(f40(a1),x94282))),f306(f40(a1),x94281))),f201(x94282,x94281))+P1(f306(f306(f221(a1),x94281),f2(a1))) % 187.68/187.66 [9492]~P32(a5000)+~P1(f306(a25,x94922))+P27(a861,x94921,f306(f306(f284(f864(a861)),f306(f306(f306(f93(a861),a303),x94922),f193(x94922))),f185(f872(f864(a861),a859))))+~P27(a861,x94921,f306(f306(f284(f864(a861)),f306(f306(f306(f93(a861),a303),f306(a26,f858(x94922,x94921))),f193(f306(a26,f858(x94922,x94921))))),f185(f872(f864(a861),a859)))) % 187.68/187.66 [8184]~P91(x81842)+~P112(x81842)+~P1(f306(f306(f220(x81842),f306(f111(x81842),x81841)),f79(x81842)))+P1(f306(f306(f220(a1),x81841),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104))) % 187.68/187.66 [8185]~P91(x81852)+~P112(x81852)+~P1(f306(f306(f221(x81852),f306(f111(x81852),x81851)),f79(x81852)))+P1(f306(f306(f221(a1),x81851),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104))) % 187.68/187.66 [8466]~P112(x84661)+~P91(x84661)+P1(f306(f306(f220(x84661),f306(f111(x84661),x84662)),f79(x84661)))+~P1(f306(f306(f220(a1),x84662),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104))) % 187.68/187.66 [8467]~P112(x84671)+~P91(x84671)+P1(f306(f306(f221(x84671),f306(f111(x84671),x84672)),f79(x84671)))+~P1(f306(f306(f221(a1),x84672),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104))) % 187.68/187.66 [8662]~P91(x86622)+~P112(x86622)+~P1(f306(f306(f220(x86622),f79(x86622)),f306(f111(x86622),x86621)))+P1(f306(f306(f220(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),x86621)) % 187.68/187.66 [8663]~P91(x86632)+~P112(x86632)+~P1(f306(f306(f221(x86632),f79(x86632)),f306(f111(x86632),x86631)))+P1(f306(f306(f221(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),x86631)) % 187.68/187.66 [9039]~P112(x90391)+~P91(x90391)+P1(f306(f306(f220(x90391),f79(x90391)),f306(f111(x90391),x90392)))+~P1(f306(f306(f220(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),x90392)) % 187.68/187.66 [9040]~P112(x90401)+~P91(x90401)+P1(f306(f306(f221(x90401),f79(x90401)),f306(f111(x90401),x90402)))+~P1(f306(f306(f221(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),x90402)) % 187.68/187.66 [9560]~P140(x95602)+E(x95601,f79(x95602))+E(x95601,f306(f80(x95602),f79(x95602)))+~E(f306(f306(f237(x95602),x95601),f306(f111(a865),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)))),f79(x95602)) % 187.68/187.66 [9833]~P91(x98331)+~P63(x98331)+~P1(f306(f306(f221(x98331),f2(x98331)),x98332))+P1(f306(f306(f221(x98331),f2(x98331)),f306(f306(f264(x98331),x98332),f306(f111(x98331),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)))))) % 187.68/187.66 [9896]~P91(x98961)+~P63(x98961)+P1(f306(f306(f221(x98961),f2(x98961)),x98962))+~P1(f306(f306(f221(x98961),f2(x98961)),f306(f306(f264(x98961),x98962),f306(f111(x98961),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)))))) % 187.68/187.66 [10159]~P125(x101592)+E(x101591,f2(a1))+P1(f306(f306(f221(a1),x101591),f2(a1)))+E(f306(f306(f245(a1,a1,x101592),f306(f306(f7(a1,f872(a1,f872(x101592,x101592)),f872(a1,x101592)),f306(f306(f8(f872(f872(x101592,x101592),x101592),f872(f872(a1,f872(x101592,x101592)),f872(a1,x101592)),a1),f8(f872(x101592,x101592),x101592,a1)),f306(f306(f8(x101592,f872(f872(x101592,x101592),x101592),a1),f87(x101592,x101592)),f110(x101592)))),f306(f306(f7(a1,f872(x101592,x101592),f872(x101592,x101592)),f306(f306(f8(f872(x101592,f872(x101592,x101592)),f872(f872(x101592,x101592),f872(x101592,x101592)),a1),f18(x101592,x101592,x101592)),f306(f306(f7(a1,f872(x101592,x101592),f872(x101592,f872(x101592,x101592))),f306(f306(f8(f872(x101592,f872(x101592,x101592)),f872(f872(x101592,x101592),f872(x101592,f872(x101592,x101592))),a1),f8(x101592,f872(x101592,x101592),x101592)),f306(f306(f8(a859,f872(x101592,f872(x101592,x101592)),a1),f101(x101592)),f306(f306(f7(a1,a1,a859),a303),f2(a1))))),f306(f306(f18(x101592,x101592,x101592),f81(x101592)),f5(x101592))))),f306(f306(f7(x101592,x101592,x101592),f306(f306(f8(x101592,f872(x101592,x101592),x101592),f81(x101592)),f306(f306(f18(x101592,x101592,x101592),f81(x101592)),f5(x101592)))),f79(x101592))))),f47(x101591,f306(f111(a1),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104))))),f306(f110(x101592),x101591)) % 187.68/187.66 [5034]~P6(x50343)+~P41(x50343,x50343,x50341)+E(f306(x50341,x50342),x50342)+~E(x50342,f103(x50343,x50341)) % 187.68/187.66 [5035]~P6(x50353)+~P41(x50353,x50353,x50351)+E(f306(x50351,x50352),x50352)+~E(x50352,f102(x50353,x50351)) % 187.68/187.66 [5186]~P60(x51863)+~P38(x51863,x51862,f57(x51863))+E(x51861,f770(x51862,x51863))+~P1(f306(x51862,x51861)) % 187.68/187.66 [5344]~P60(x53441)+P38(x53441,x53442,f57(x53441))+~E(f771(x53442,x53441,x53443),x53443)+~P1(f306(x53442,x53443)) % 187.68/187.66 [4817]~P90(x48173)+~P91(x48173)+E(x48171,x48172)+~E(f306(f111(x48173),x48171),f306(f111(x48173),x48172)) % 187.68/187.66 [5970]~P60(x59701)+P38(x59701,x59702,f57(x59701))+~P1(f306(x59702,x59703))+P1(f306(x59702,f771(x59702,x59701,x59703))) % 187.68/187.66 [5980]~P1(f306(x59801,x59802))+~P1(f306(x59801,x59803))+~P1(f306(f306(f220(a865),x59803),f757(x59802,x59801)))+P1(f306(x59801,f2(a865))) % 187.68/187.66 [6401]P146(x64012,x64013,x64011)+E(x64011,f2(a1))+P1(f306(f306(f220(a1),f2(a1)),f798(x64011,x64013,x64012)))+P1(f306(f306(f221(a1),x64011),f2(a1))) % 187.68/187.66 [6402]P145(x64022,x64023,x64021)+E(x64021,f2(a1))+P1(f306(f306(f220(a1),f2(a1)),f807(x64021,x64023,x64022)))+P1(f306(f306(f221(a1),x64021),f2(a1))) % 187.68/187.66 [6519]P145(x65191,x65192,x65193)+~P1(f306(x65191,x65192))+P1(f306(f306(f220(a1),f2(a1)),f807(x65193,x65192,x65191)))+P1(f306(f306(f221(a1),x65193),f2(a1))) % 187.68/187.66 [6547]P146(x65471,x65472,x65473)+P1(f306(f306(f220(a1),f2(a1)),f798(x65473,x65472,x65471)))+~P1(f306(x65471,f2(a1)))+P1(f306(f306(f221(a1),x65473),f2(a1))) % 187.68/187.66 [6575]P146(x65752,x65753,x65751)+E(x65751,f2(a1))+~P1(f306(x65752,f799(x65751,x65753,x65752)))+P1(f306(f306(f221(a1),x65751),f2(a1))) % 187.68/187.66 [6576]P145(x65762,x65763,x65761)+E(x65761,f2(a1))+~P1(f306(x65762,f807(x65761,x65763,x65762)))+P1(f306(f306(f221(a1),x65761),f2(a1))) % 187.68/187.66 [6680]~P108(x66801)+~P6(x66801)+~P1(f306(f306(f221(x66801),x66802),f41(x66801,x66803)))+P1(f306(f306(f221(x66801),x66802),f610(x66803,x66802,x66801))) % 187.68/187.66 [6689]P145(x66891,x66892,x66893)+~P1(f306(x66891,x66892))+~P1(f306(x66891,f807(x66893,x66892,x66891)))+P1(f306(f306(f221(a1),x66893),f2(a1))) % 187.68/187.66 [6720]P146(x67201,x67202,x67203)+~P1(f306(x67201,f799(x67203,x67202,x67201)))+~P1(f306(x67201,f2(a1)))+P1(f306(f306(f221(a1),x67203),f2(a1))) % 187.68/187.66 [6971]P146(x69712,x69713,x69711)+E(x69711,f2(a1))+P1(f306(f306(f220(a1),f2(a1)),f798(x69711,x69713,x69712)))+P1(f306(f306(f221(a1),x69711),f797(x69711,x69713,x69712))) % 187.68/187.66 [6972]P145(x69722,x69723,x69721)+E(x69721,f2(a1))+P1(f306(f306(f220(a1),f2(a1)),f807(x69721,x69723,x69722)))+P1(f306(f306(f221(a1),x69721),f806(x69721,x69723,x69722))) % 187.68/187.66 [7089]P145(x70891,x70892,x70893)+~P1(f306(x70891,x70892))+P1(f306(f306(f220(a1),f2(a1)),f807(x70893,x70892,x70891)))+P1(f306(f306(f221(a1),x70893),f806(x70893,x70892,x70891))) % 187.68/187.66 [7108]P146(x71081,x71082,x71083)+P1(f306(f306(f220(a1),f2(a1)),f798(x71083,x71082,x71081)))+P1(f306(f306(f221(a1),x71083),f797(x71083,x71082,x71081)))+~P1(f306(x71081,f2(a1))) % 187.68/187.66 [7141]P146(x71412,x71413,x71411)+E(x71411,f2(a1))+~P1(f306(x71412,f799(x71411,x71413,x71412)))+P1(f306(f306(f221(a1),x71411),f797(x71411,x71413,x71412))) % 187.68/187.66 [7142]P145(x71422,x71423,x71421)+E(x71421,f2(a1))+~P1(f306(x71422,f807(x71421,x71423,x71422)))+P1(f306(f306(f221(a1),x71421),f806(x71421,x71423,x71422))) % 187.68/187.66 [7183]P146(x71832,x71833,x71831)+E(x71831,f2(a1))+P1(f306(f306(f220(a1),f2(a1)),f798(x71831,x71833,x71832)))+~P1(f306(x71832,f805(x71831,x71833,x71832))) % 187.68/187.66 [7184]P145(x71842,x71843,x71841)+E(x71841,f2(a1))+P1(f306(f306(f220(a1),f2(a1)),f807(x71841,x71843,x71842)))+~P1(f306(x71842,f806(x71841,x71843,x71842))) % 187.68/187.66 [7272]P145(x72721,x72722,x72723)+~P1(f306(x72721,x72722))+~P1(f306(x72721,f807(x72723,x72722,x72721)))+P1(f306(f306(f221(a1),x72723),f806(x72723,x72722,x72721))) % 187.68/187.66 [7287]P146(x72871,x72872,x72873)+~P1(f306(x72871,f799(x72873,x72872,x72871)))+P1(f306(f306(f221(a1),x72873),f797(x72873,x72872,x72871)))+~P1(f306(x72871,f2(a1))) % 187.68/187.66 [7291]P145(x72911,x72912,x72913)+~P1(f306(x72911,x72912))+P1(f306(f306(f220(a1),f2(a1)),f807(x72913,x72912,x72911)))+~P1(f306(x72911,f806(x72913,x72912,x72911))) % 187.68/187.66 [7309]P146(x73091,x73092,x73093)+P1(f306(f306(f220(a1),f2(a1)),f798(x73093,x73092,x73091)))+~P1(f306(x73091,f805(x73093,x73092,x73091)))+~P1(f306(x73091,f2(a1))) % 187.68/187.66 [7333]P146(x73332,x73333,x73331)+E(x73331,f2(a1))+~P1(f306(x73332,f799(x73331,x73333,x73332)))+~P1(f306(x73332,f805(x73331,x73333,x73332))) % 187.68/187.66 [7334]P145(x73342,x73343,x73341)+E(x73341,f2(a1))+~P1(f306(x73342,f807(x73341,x73343,x73342)))+~P1(f306(x73342,f806(x73341,x73343,x73342))) % 187.68/187.66 [7426]P145(x74261,x74262,x74263)+~P1(f306(x74261,x74262))+~P1(f306(x74261,f807(x74263,x74262,x74261)))+~P1(f306(x74261,f806(x74263,x74262,x74261))) % 187.68/187.66 [7443]P146(x74431,x74432,x74433)+~P1(f306(x74431,f799(x74433,x74432,x74431)))+~P1(f306(x74431,f805(x74433,x74432,x74431)))+~P1(f306(x74431,f2(a1))) % 187.68/187.66 [7488]P146(x74882,x74883,x74881)+E(x74881,f2(a1))+P1(f306(f306(f220(a1),f2(a1)),f798(x74881,x74883,x74882)))+P1(f306(f306(f220(a1),f797(x74881,x74883,x74882)),f2(a1))) % 187.68/187.66 [7489]P145(x74892,x74893,x74891)+E(x74891,f2(a1))+P1(f306(f306(f220(a1),f2(a1)),f807(x74891,x74893,x74892)))+P1(f306(f306(f220(a1),f806(x74891,x74893,x74892)),f2(a1))) % 187.68/187.66 [7490]~P125(x74901)+~P1(f306(f306(f308(x74901),x74903),f117(x74901)))+~P1(f306(f306(f308(x74901),x74902),f117(x74901)))+P1(f306(f306(f308(x74901),f306(f306(f22(x74901),x74902),x74903)),f117(x74901))) % 187.68/187.66 [7491]~P125(x74911)+~P1(f306(f306(f308(x74911),x74913),f117(x74911)))+~P1(f306(f306(f308(x74911),x74912),f117(x74911)))+P1(f306(f306(f308(x74911),f306(f306(f81(x74911),x74912),x74913)),f117(x74911))) % 187.68/187.66 [7492]~P141(x74921)+~P1(f306(f306(f308(x74921),x74923),f183(x74921)))+~P1(f306(f306(f308(x74921),x74922),f183(x74921)))+P1(f306(f306(f308(x74921),f306(f306(f81(x74921),x74922),x74923)),f183(x74921))) % 187.68/187.66 [7493]~P125(x74931)+~P1(f306(f306(f308(x74931),x74933),f117(x74931)))+~P1(f306(f306(f308(x74931),x74932),f117(x74931)))+P1(f306(f306(f308(x74931),f306(f306(f82(x74931),x74932),x74933)),f117(x74931))) % 187.68/187.66 [7494]~P141(x74941)+~P1(f306(f306(f308(x74941),x74943),f183(x74941)))+~P1(f306(f306(f308(x74941),x74942),f183(x74941)))+P1(f306(f306(f308(x74941),f306(f306(f82(x74941),x74942),x74943)),f183(x74941))) % 187.68/187.66 [7495]~P86(x74951)+~P1(f306(f306(f220(x74951),x74953),f2(x74951)))+~P1(f306(f306(f220(x74951),x74952),f2(x74951)))+P1(f306(f306(f220(x74951),f306(f306(f81(x74951),x74952),x74953)),f2(x74951))) % 187.68/187.66 [7496]~P86(x74961)+~P1(f306(f306(f220(x74961),x74963),f2(x74961)))+~P1(f306(f306(f221(x74961),x74962),f2(x74961)))+P1(f306(f306(f221(x74961),f306(f306(f81(x74961),x74962),x74963)),f2(x74961))) % 187.68/187.66 [7497]~P86(x74971)+~P1(f306(f306(f220(x74971),x74972),f2(x74971)))+~P1(f306(f306(f221(x74971),x74973),f2(x74971)))+P1(f306(f306(f221(x74971),f306(f306(f81(x74971),x74972),x74973)),f2(x74971))) % 187.68/187.66 [7498]~P86(x74981)+~P1(f306(f306(f221(x74981),x74983),f2(x74981)))+~P1(f306(f306(f221(x74981),x74982),f2(x74981)))+P1(f306(f306(f221(x74981),f306(f306(f81(x74981),x74982),x74983)),f2(x74981))) % 187.68/187.66 [7524]P146(x75243,x75242,x75241)+E(x75241,f2(a1))+E(f306(f306(f81(a1),f306(f306(f82(a1),x75241),f799(x75241,x75242,x75243))),f798(x75241,x75242,x75243)),x75242)+P1(f306(f306(f221(a1),x75241),f2(a1))) % 187.68/187.66 [7525]P145(x75253,x75252,x75251)+E(x75251,f2(a1))+E(f306(f306(f81(a1),f306(f306(f82(a1),x75251),f808(x75251,x75252,x75253))),f807(x75251,x75252,x75253)),x75252)+P1(f306(f306(f221(a1),x75251),f2(a1))) % 187.68/187.66 [7607]P145(x76071,x76072,x76073)+~P1(f306(x76071,x76072))+P1(f306(f306(f220(a1),f2(a1)),f807(x76073,x76072,x76071)))+P1(f306(f306(f220(a1),f806(x76073,x76072,x76071)),f2(a1))) % 187.68/187.66 [7637]P146(x76371,x76372,x76373)+P1(f306(f306(f220(a1),f2(a1)),f798(x76373,x76372,x76371)))+~P1(f306(x76371,f2(a1)))+P1(f306(f306(f220(a1),f797(x76373,x76372,x76371)),f2(a1))) % 187.68/187.66 [7646]P145(x76463,x76462,x76461)+~P1(f306(x76463,x76462))+E(f306(f306(f81(a1),f306(f306(f82(a1),x76461),f808(x76461,x76462,x76463))),f807(x76461,x76462,x76463)),x76462)+P1(f306(f306(f221(a1),x76461),f2(a1))) % 187.68/187.66 [7652]P146(x76522,x76523,x76521)+E(x76521,f2(a1))+~P1(f306(x76522,f799(x76521,x76523,x76522)))+P1(f306(f306(f220(a1),f797(x76521,x76523,x76522)),f2(a1))) % 187.68/187.66 [7653]P145(x76532,x76533,x76531)+E(x76531,f2(a1))+~P1(f306(x76532,f807(x76531,x76533,x76532)))+P1(f306(f306(f220(a1),f806(x76531,x76533,x76532)),f2(a1))) % 187.68/187.66 [7658]P146(x76583,x76582,x76581)+E(f306(f306(f81(a1),f306(f306(f82(a1),x76581),f799(x76581,x76582,x76583))),f798(x76581,x76582,x76583)),x76582)+~P1(f306(x76583,f2(a1)))+P1(f306(f306(f221(a1),x76581),f2(a1))) % 187.68/187.66 [7713]P145(x77131,x77132,x77133)+~P1(f306(x77131,x77132))+~P1(f306(x77131,f807(x77133,x77132,x77131)))+P1(f306(f306(f220(a1),f806(x77133,x77132,x77131)),f2(a1))) % 187.68/187.66 [7717]P146(x77171,x77172,x77173)+~P1(f306(x77171,f799(x77173,x77172,x77171)))+~P1(f306(x77171,f2(a1)))+P1(f306(f306(f220(a1),f797(x77173,x77172,x77171)),f2(a1))) % 187.68/187.66 [7787]~P122(x77871)+~P1(f306(f306(f220(x77871),f306(f306(f82(x77871),x77873),x77872)),f2(x77871)))+P1(f306(f306(f220(x77871),x77872),f2(x77871)))+P1(f306(f306(f220(x77871),x77873),f2(x77871))) % 187.68/187.66 [7788]~P63(x77881)+~P1(f306(f306(f220(x77881),f306(f306(f264(x77881),x77883),x77882)),f2(x77881)))+P1(f306(f306(f220(x77881),x77882),f2(x77881)))+P1(f306(f306(f220(x77881),x77883),f2(x77881))) % 187.68/187.66 [7789]~P63(x77891)+~P1(f306(f306(f221(x77891),f306(f306(f264(x77891),x77893),x77892)),f2(x77891)))+P1(f306(f306(f221(x77891),x77892),f2(x77891)))+P1(f306(f306(f221(x77891),x77893),f2(x77891))) % 187.68/187.66 [7903]P146(x79033,x79032,x79031)+E(x79031,f2(a1))+E(f306(f306(f81(a1),f306(f306(f82(a1),x79031),f799(x79031,x79032,x79033))),f798(x79031,x79032,x79033)),x79032)+P1(f306(f306(f221(a1),x79031),f797(x79031,x79032,x79033))) % 187.68/187.66 [7904]P145(x79043,x79042,x79041)+E(x79041,f2(a1))+E(f306(f306(f81(a1),f306(f306(f82(a1),x79041),f808(x79041,x79042,x79043))),f807(x79041,x79042,x79043)),x79042)+P1(f306(f306(f221(a1),x79041),f806(x79041,x79042,x79043))) % 187.68/187.66 [7916]P146(x79163,x79162,x79161)+E(x79161,f2(a1))+E(f306(f306(f81(a1),f306(f306(f82(a1),x79161),f805(x79161,x79162,x79163))),f797(x79161,x79162,x79163)),x79162)+P1(f306(f306(f220(a1),f2(a1)),f798(x79161,x79162,x79163))) % 187.68/187.66 [7917]P145(x79173,x79172,x79171)+E(x79171,f2(a1))+E(f306(f306(f81(a1),f306(f306(f82(a1),x79171),f809(x79171,x79172,x79173))),f806(x79171,x79172,x79173)),x79172)+P1(f306(f306(f220(a1),f2(a1)),f807(x79171,x79172,x79173))) % 187.68/187.66 [7961]P145(x79613,x79612,x79611)+~P1(f306(x79613,x79612))+E(f306(f306(f81(a1),f306(f306(f82(a1),x79611),f808(x79611,x79612,x79613))),f807(x79611,x79612,x79613)),x79612)+P1(f306(f306(f221(a1),x79611),f806(x79611,x79612,x79613))) % 187.68/187.66 [7973]P146(x79733,x79732,x79731)+E(f306(f306(f81(a1),f306(f306(f82(a1),x79731),f799(x79731,x79732,x79733))),f798(x79731,x79732,x79733)),x79732)+P1(f306(f306(f221(a1),x79731),f797(x79731,x79732,x79733)))+~P1(f306(x79733,f2(a1))) % 187.68/187.66 [7979]P145(x79793,x79792,x79791)+~P1(f306(x79793,x79792))+E(f306(f306(f81(a1),f306(f306(f82(a1),x79791),f809(x79791,x79792,x79793))),f806(x79791,x79792,x79793)),x79792)+P1(f306(f306(f220(a1),f2(a1)),f807(x79791,x79792,x79793))) % 187.68/187.66 [7987]P146(x79873,x79872,x79871)+E(f306(f306(f81(a1),f306(f306(f82(a1),x79871),f805(x79871,x79872,x79873))),f797(x79871,x79872,x79873)),x79872)+P1(f306(f306(f220(a1),f2(a1)),f798(x79871,x79872,x79873)))+~P1(f306(x79873,f2(a1))) % 187.68/187.66 [7998]P146(x79983,x79982,x79981)+E(x79981,f2(a1))+E(f306(f306(f81(a1),f306(f306(f82(a1),x79981),f799(x79981,x79982,x79983))),f798(x79981,x79982,x79983)),x79982)+~P1(f306(x79983,f805(x79981,x79982,x79983))) % 187.68/187.66 [7999]P145(x79993,x79992,x79991)+E(x79991,f2(a1))+E(f306(f306(f81(a1),f306(f306(f82(a1),x79991),f808(x79991,x79992,x79993))),f807(x79991,x79992,x79993)),x79992)+~P1(f306(x79993,f806(x79991,x79992,x79993))) % 187.68/187.66 [8000]P146(x80003,x80002,x80001)+E(x80001,f2(a1))+E(f306(f306(f81(a1),f306(f306(f82(a1),x80001),f805(x80001,x80002,x80003))),f797(x80001,x80002,x80003)),x80002)+~P1(f306(x80003,f799(x80001,x80002,x80003))) % 187.68/187.66 [8001]P145(x80013,x80012,x80011)+E(x80011,f2(a1))+E(f306(f306(f81(a1),f306(f306(f82(a1),x80011),f809(x80011,x80012,x80013))),f806(x80011,x80012,x80013)),x80012)+~P1(f306(x80013,f807(x80011,x80012,x80013))) % 187.68/187.66 [8060]P145(x80603,x80602,x80601)+~P1(f306(x80603,x80602))+E(f306(f306(f81(a1),f306(f306(f82(a1),x80601),f808(x80601,x80602,x80603))),f807(x80601,x80602,x80603)),x80602)+~P1(f306(x80603,f806(x80601,x80602,x80603))) % 187.68/187.66 [8061]P145(x80613,x80612,x80611)+~P1(f306(x80613,x80612))+E(f306(f306(f81(a1),f306(f306(f82(a1),x80611),f809(x80611,x80612,x80613))),f806(x80611,x80612,x80613)),x80612)+~P1(f306(x80613,f807(x80611,x80612,x80613))) % 187.68/187.66 [8071]P146(x80713,x80712,x80711)+E(f306(f306(f81(a1),f306(f306(f82(a1),x80711),f799(x80711,x80712,x80713))),f798(x80711,x80712,x80713)),x80712)+~P1(f306(x80713,f805(x80711,x80712,x80713)))+~P1(f306(x80713,f2(a1))) % 187.68/187.66 [8072]P146(x80723,x80722,x80721)+E(f306(f306(f81(a1),f306(f306(f82(a1),x80721),f805(x80721,x80722,x80723))),f797(x80721,x80722,x80723)),x80722)+~P1(f306(x80723,f799(x80721,x80722,x80723)))+~P1(f306(x80723,f2(a1))) % 187.68/187.66 [8177]P146(x81773,x81772,x81771)+E(x81771,f2(a1))+E(f306(f306(f81(a1),f306(f306(f82(a1),x81771),f799(x81771,x81772,x81773))),f798(x81771,x81772,x81773)),x81772)+P1(f306(f306(f220(a1),f797(x81771,x81772,x81773)),f2(a1))) % 187.68/187.66 [8178]P145(x81783,x81782,x81781)+E(x81781,f2(a1))+E(f306(f306(f81(a1),f306(f306(f82(a1),x81781),f808(x81781,x81782,x81783))),f807(x81781,x81782,x81783)),x81782)+P1(f306(f306(f220(a1),f806(x81781,x81782,x81783)),f2(a1))) % 187.68/187.66 [8218]P145(x82183,x82182,x82181)+~P1(f306(x82183,x82182))+E(f306(f306(f81(a1),f306(f306(f82(a1),x82181),f808(x82181,x82182,x82183))),f807(x82181,x82182,x82183)),x82182)+P1(f306(f306(f220(a1),f806(x82181,x82182,x82183)),f2(a1))) % 187.68/187.66 [8223]P146(x82233,x82232,x82231)+E(f306(f306(f81(a1),f306(f306(f82(a1),x82231),f799(x82231,x82232,x82233))),f798(x82231,x82232,x82233)),x82232)+~P1(f306(x82233,f2(a1)))+P1(f306(f306(f220(a1),f797(x82231,x82232,x82233)),f2(a1))) % 187.68/187.66 [8354]P146(x83543,x83542,x83541)+E(x83541,f2(a1))+E(f306(f306(f81(a1),f306(f306(f82(a1),x83541),f805(x83541,x83542,x83543))),f797(x83541,x83542,x83543)),x83542)+E(f306(f306(f81(a1),f306(f306(f82(a1),x83541),f799(x83541,x83542,x83543))),f798(x83541,x83542,x83543)),x83542) % 187.68/187.66 [8355]P145(x83553,x83552,x83551)+E(x83551,f2(a1))+E(f306(f306(f81(a1),f306(f306(f82(a1),x83551),f809(x83551,x83552,x83553))),f806(x83551,x83552,x83553)),x83552)+E(f306(f306(f81(a1),f306(f306(f82(a1),x83551),f808(x83551,x83552,x83553))),f807(x83551,x83552,x83553)),x83552) % 187.68/187.66 [8377]P145(x83773,x83772,x83771)+~P1(f306(x83773,x83772))+E(f306(f306(f81(a1),f306(f306(f82(a1),x83771),f809(x83771,x83772,x83773))),f806(x83771,x83772,x83773)),x83772)+E(f306(f306(f81(a1),f306(f306(f82(a1),x83771),f808(x83771,x83772,x83773))),f807(x83771,x83772,x83773)),x83772) % 187.68/187.66 [8388]P146(x83883,x83882,x83881)+E(f306(f306(f81(a1),f306(f306(f82(a1),x83881),f805(x83881,x83882,x83883))),f797(x83881,x83882,x83883)),x83882)+E(f306(f306(f81(a1),f306(f306(f82(a1),x83881),f799(x83881,x83882,x83883))),f798(x83881,x83882,x83883)),x83882)+~P1(f306(x83883,f2(a1))) % 187.68/187.66 [9044]~P122(x90441)+~E(x90443,f2(x90441))+~E(x90442,f2(x90441))+P1(f306(f306(f220(x90441),f306(f306(f81(x90441),f306(f306(f82(x90441),x90442),x90442)),f306(f306(f82(x90441),x90443),x90443))),f2(x90441))) % 187.68/187.66 [10104]~P112(x101041)+~E(x101043,f2(x101041))+~E(x101042,f2(x101041))+P1(f306(f306(f220(x101041),f306(f306(f81(x101041),f306(f306(f237(x101041),x101042),f306(f111(a865),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104))))),f306(f306(f237(x101041),x101043),f306(f111(a865),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)))))),f2(x101041))) % 187.68/187.66 [4765]~E(x47653,x47651)+~P118(x47652)+E(x47651,f2(x47652))+E(f306(f306(f264(x47652),x47653),x47651),f79(x47652)) % 187.68/187.66 [4818]~P99(x48181)+~E(x48183,f185(x48181))+~E(x48182,f185(x48181))+E(f306(f306(f108(x48181),x48182),x48183),f185(x48181)) % 187.68/187.66 [4819]~P102(x48191)+~E(x48193,f231(x48191))+~E(x48192,f231(x48191))+E(f306(f306(f109(x48191),x48192),x48193),f231(x48191)) % 187.68/187.66 [4907]~P118(x49073)+E(x49071,x49072)+E(x49072,f2(x49073))+~E(f306(f306(f264(x49073),x49071),x49072),f79(x49073)) % 187.68/187.66 [4925]~P139(x49252)+E(x49251,f2(x49252))+E(x49253,f2(x49252))+~E(f306(f306(f82(x49252),x49253),x49251),f2(x49252)) % 187.68/187.66 [4927]~P132(x49272)+E(x49271,f2(x49272))+E(x49273,f2(x49272))+~E(f306(f306(f82(x49272),x49273),x49271),f2(x49272)) % 187.68/187.66 [5311]~P117(x53113)+E(x53111,x53112)+E(x53111,f306(f80(x53113),x53112))+~E(f306(f306(f82(x53113),x53111),x53111),f306(f306(f82(x53113),x53112),x53112)) % 187.68/187.66 [5351]~P94(x53511)+E(f306(f80(x53511),x53512),x53513)+~E(f306(f306(f108(x53511),x53512),x53513),f231(x53511))+~E(f306(f306(f109(x53511),x53512),x53513),f185(x53511)) % 187.68/187.66 [5430]~P112(x54303)+E(x54301,x54302)+P1(f306(f306(f221(x54303),x54302),x54301))+P1(f306(f306(f221(x54303),x54301),x54302)) % 187.68/187.66 [5431]~P108(x54313)+E(x54311,x54312)+P1(f306(f306(f221(x54313),x54312),x54311))+P1(f306(f306(f221(x54313),x54311),x54312)) % 187.68/187.66 [5432]~E(x54322,x54323)+~P108(x54321)+P1(f306(f306(f221(x54321),x54322),x54323))+P1(f306(f306(f220(x54321),x54322),x54323)) % 187.68/187.66 [5685]~P109(x56853)+E(x56851,x56852)+~P1(f306(f306(f220(x56853),x56852),x56851))+P1(f306(f306(f221(x56853),x56852),x56851)) % 187.68/187.66 [5687]~P108(x56873)+E(x56871,x56872)+~P1(f306(f306(f220(x56873),x56871),x56872))+P1(f306(f306(f221(x56873),x56871),x56872)) % 187.68/187.66 [5693]~P109(x56933)+E(x56931,x56932)+~P1(f306(f306(f220(x56933),x56931),x56932))+P1(f306(f306(f221(x56933),x56931),x56932)) % 187.68/187.66 [5796]P145(x57961,x57962,x57963)+~P1(f306(x57961,x57962))+P1(f306(f306(f221(a1),x57963),f2(a1)))+P1(f306(f306(f221(a1),f2(a1)),x57963)) % 187.68/187.66 [5843]P146(x58431,x58432,x58433)+~P1(f306(x58431,f2(a1)))+P1(f306(f306(f221(a1),x58433),f2(a1)))+P1(f306(f306(f221(a1),f2(a1)),x58433)) % 187.68/187.66 [5847]~P98(x58471)+E(f306(f306(f108(x58471),x58472),f10(x58471,x58473)),x58472)+~P1(f306(f63(x58471),x58473))+~P1(f306(f306(f308(x58471),x58472),x58473)) % 187.68/187.66 [5848]~P98(x58481)+E(f306(f306(f109(x58481),x58482),f13(x58481,x58483)),x58482)+~P1(f306(f63(x58481),x58483))+~P1(f306(f306(f308(x58481),x58482),x58483)) % 187.68/187.66 [5884]~P108(x58841)+E(f306(f306(f225(x58841),x58842),f14(x58841,x58843)),f14(x58841,x58843))+~P1(f306(f63(x58841),x58843))+~P1(f306(f306(f308(x58841),x58842),x58843)) % 187.68/187.66 [5885]~P108(x58851)+E(f306(f306(f219(x58851),x58852),f15(x58851,x58853)),f15(x58851,x58853))+~P1(f306(f63(x58851),x58853))+~P1(f306(f306(f308(x58851),x58852),x58853)) % 187.68/187.66 [5886]~P98(x58861)+E(f306(f306(f108(x58861),x58862),f13(x58861,x58863)),f13(x58861,x58863))+~P1(f306(f63(x58861),x58863))+~P1(f306(f306(f308(x58861),x58862),x58863)) % 187.68/187.66 [5887]~P98(x58871)+E(f306(f306(f109(x58871),x58872),f10(x58871,x58873)),f10(x58871,x58873))+~P1(f306(f63(x58871),x58873))+~P1(f306(f306(f308(x58871),x58872),x58873)) % 187.68/187.66 [5932]E(x59321,x59322)+~P109(x59323)+~P1(f306(f306(f220(x59323),x59322),x59321))+~P1(f306(f306(f220(x59323),x59321),x59322)) % 187.68/187.66 [6074]~P106(x60741)+P1(f306(f306(f221(x60741),x60743),x60742))+~P1(f306(f306(f220(x60741),x60743),x60742))+P1(f306(f306(f220(x60741),x60742),x60743)) % 187.68/187.66 [6095]~P108(x60951)+~P1(f306(f63(x60951),x60953))+P1(f306(f306(f220(x60951),x60952),f15(x60951,x60953)))+~P1(f306(f306(f308(x60951),x60952),x60953)) % 187.68/187.66 [6147]~P108(x61471)+E(f306(f306(f225(x61471),x61472),f12(x61471,f219(x61471),x61473)),x61472)+~P1(f306(f63(x61471),x61473))+~P1(f306(f306(f308(x61471),x61472),x61473)) % 187.68/187.66 [6148]~P108(x61481)+E(f306(f306(f219(x61481),x61482),f11(x61481,f225(x61481),x61483)),x61482)+~P1(f306(f63(x61481),x61483))+~P1(f306(f306(f308(x61481),x61482),x61483)) % 187.68/187.66 [6286]E(x62861,x62862)+~E(f306(f306(f22(a865),x62861),x62863),f306(f306(f22(a865),x62862),x62863))+~P1(f306(f306(f220(a865),x62863),x62861))+~P1(f306(f306(f220(a865),x62863),x62862)) % 187.68/187.66 [6316]~P108(x63161)+~P1(f306(f63(x63161),x63162))+~P1(f306(f306(f308(x63161),x63163),x63162))+P1(f306(f306(f220(x63161),f14(x63161,x63162)),x63163)) % 187.68/187.66 [6380]P146(x63802,x63803,x63801)+E(x63801,f2(a1))+P1(f306(f306(f221(a1),x63801),f797(x63801,x63803,x63802)))+P1(f306(f306(f221(a1),f2(a1)),x63801)) % 187.68/187.66 [6381]P145(x63812,x63813,x63811)+E(x63811,f2(a1))+P1(f306(f306(f221(a1),x63811),f806(x63811,x63813,x63812)))+P1(f306(f306(f221(a1),f2(a1)),x63811)) % 187.68/187.66 [6382]~P108(x63821)+E(f306(f306(f225(x63821),x63822),f11(x63821,f225(x63821),x63823)),f11(x63821,f225(x63821),x63823))+~P1(f306(f63(x63821),x63823))+~P1(f306(f306(f308(x63821),x63822),x63823)) % 187.68/187.66 [6383]~P108(x63831)+E(f306(f306(f219(x63831),x63832),f12(x63831,f219(x63831),x63833)),f12(x63831,f219(x63831),x63833))+~P1(f306(f63(x63831),x63833))+~P1(f306(f306(f308(x63831),x63832),x63833)) % 187.68/187.66 [6389]~P1(f306(x63891,x63892))+P1(f306(x63891,f570(x63892,x63891,x63893)))+P1(f306(x63891,f2(a865)))+~P1(f306(f306(f221(a865),x63892),x63893)) % 187.68/187.66 [6444]~P1(f306(x64441,x64442))+~P1(f306(f63(x64443),x64442))+P1(f306(x64441,f598(x64441,x64442,x64443)))+P1(f306(x64441,f185(f872(x64443,a859)))) % 187.68/187.66 [6457]~P112(x64571)+~P91(x64571)+P1(f306(f306(f220(x64571),f306(f111(x64571),x64572)),f306(f111(x64571),x64573)))+~P1(f306(f306(f220(a1),x64572),x64573)) % 187.68/187.66 [6458]~P112(x64581)+~P91(x64581)+P1(f306(f306(f221(x64581),f306(f111(x64581),x64582)),f306(f111(x64581),x64583)))+~P1(f306(f306(f221(a1),x64582),x64583)) % 187.68/187.66 [6461]~P1(f306(x64611,x64613))+~P1(f306(f63(x64612),x64613))+P1(f306(f63(x64612),f598(x64611,x64613,x64612)))+P1(f306(x64611,f185(f872(x64612,a859)))) % 187.68/187.66 [6491]P145(x64911,x64912,x64913)+~P1(f306(x64911,x64912))+P1(f306(f306(f221(a1),x64913),f806(x64913,x64912,x64911)))+P1(f306(f306(f221(a1),f2(a1)),x64913)) % 187.68/187.66 [6526]P146(x65261,x65262,x65263)+P1(f306(f306(f221(a1),x65263),f797(x65263,x65262,x65261)))+~P1(f306(x65261,f2(a1)))+P1(f306(f306(f221(a1),f2(a1)),x65263)) % 187.68/187.66 [6558]~P107(x65581)+~P92(x65581)+E(f306(f306(f225(x65581),f306(f111(x65581),x65582)),f306(f111(x65581),x65583)),f306(f111(x65581),x65583))+P1(f306(f306(f220(x65581),f306(f111(x65581),x65582)),f306(f111(x65581),x65583))) % 187.68/187.66 [6559]~P107(x65591)+~P92(x65591)+E(f306(f306(f219(x65591),f306(f111(x65591),x65592)),f306(f111(x65591),x65593)),f306(f111(x65591),x65592))+P1(f306(f306(f220(x65591),f306(f111(x65591),x65592)),f306(f111(x65591),x65593))) % 187.68/187.66 [6618]P146(x66182,x66183,x66181)+E(x66181,f2(a1))+~P1(f306(x66182,f805(x66181,x66183,x66182)))+P1(f306(f306(f221(a1),f2(a1)),x66181)) % 187.68/187.66 [6619]P145(x66192,x66193,x66191)+E(x66191,f2(a1))+~P1(f306(x66192,f806(x66191,x66193,x66192)))+P1(f306(f306(f221(a1),f2(a1)),x66191)) % 187.68/187.66 [6623]P1(f306(x66231,x66232))+~P1(f306(f63(x66233),x66232))+P1(f306(x66231,f639(x66231,x66232,x66233)))+~P1(f306(x66231,f185(f872(x66233,a859)))) % 187.68/187.66 [6645]P1(f306(x66451,x66452))+P1(f306(f63(x66453),f639(x66451,x66452,x66453)))+~P1(f306(f63(x66453),x66452))+~P1(f306(x66451,f185(f872(x66453,a859)))) % 187.68/187.66 [6710]P145(x67101,x67102,x67103)+~P1(f306(x67101,x67102))+~P1(f306(x67101,f806(x67103,x67102,x67101)))+P1(f306(f306(f221(a1),f2(a1)),x67103)) % 187.68/187.66 [6739]P146(x67391,x67392,x67393)+~P1(f306(x67391,f805(x67393,x67392,x67391)))+~P1(f306(x67391,f2(a1)))+P1(f306(f306(f221(a1),f2(a1)),x67393)) % 187.68/187.66 [6846]~P91(x68463)+~P112(x68463)+~P1(f306(f306(f220(x68463),f306(f111(x68463),x68461)),f306(f111(x68463),x68462)))+P1(f306(f306(f220(a1),x68461),x68462)) % 187.68/187.66 [6847]~P91(x68473)+~P112(x68473)+~P1(f306(f306(f221(x68473),f306(f111(x68473),x68471)),f306(f111(x68473),x68472)))+P1(f306(f306(f221(a1),x68471),x68472)) % 187.68/187.66 [6874]~P108(x68741)+~P17(x68741,x68743)+P17(x68741,f306(f306(f143(x68741),x68742),x68743))+~P1(f306(f306(f220(x68741),x68742),f727(x68743,x68742,x68741))) % 187.68/187.66 [6875]~P108(x68751)+~P17(x68751,x68753)+P17(x68751,f306(f306(f143(x68751),x68752),x68753))+~P1(f306(f306(f220(x68751),x68752),f728(x68753,x68752,x68751))) % 187.68/187.66 [6876]~P108(x68761)+~P17(x68761,x68763)+P17(x68761,f306(f306(f143(x68761),x68762),x68763))+~P1(f306(f306(f220(x68761),x68762),f773(x68762,x68763,x68761))) % 187.68/187.66 [6960]P146(x69602,x69603,x69601)+E(x69601,f2(a1))+P1(f306(f306(f221(a1),x69601),f2(a1)))+P1(f306(f306(f221(a1),f798(x69601,x69603,x69602)),x69601)) % 187.68/187.66 [6961]P145(x69612,x69613,x69611)+E(x69611,f2(a1))+P1(f306(f306(f221(a1),x69611),f2(a1)))+P1(f306(f306(f221(a1),f807(x69611,x69613,x69612)),x69611)) % 187.68/187.66 [7002]P146(x70022,x70023,x70021)+E(x70021,f2(a1))+P1(f306(f306(f220(a1),f797(x70021,x70023,x70022)),f2(a1)))+P1(f306(f306(f221(a1),f2(a1)),x70021)) % 187.68/187.66 [7003]P145(x70032,x70033,x70031)+E(x70031,f2(a1))+P1(f306(f306(f220(a1),f806(x70031,x70033,x70032)),f2(a1)))+P1(f306(f306(f221(a1),f2(a1)),x70031)) % 187.68/187.66 [7025]~P108(x70251)+~P17(x70251,x70253)+E(f306(f306(f140(x70251,x70251,f5(x70251)),x70252),f162(x70251,x70252,x70253)),x70253)+~P1(f306(f306(f308(x70251),x70252),f306(f164(x70251),x70253))) % 187.68/187.66 [7072]P145(x70721,x70722,x70723)+~P1(f306(x70721,x70722))+P1(f306(f306(f221(a1),x70723),f2(a1)))+P1(f306(f306(f221(a1),f807(x70723,x70722,x70721)),x70723)) % 187.68/187.66 [7078]~P107(x70781)+~P92(x70781)+E(f306(f306(f225(x70781),f306(f111(x70781),x70782)),f306(f111(x70781),x70783)),f306(f111(x70781),x70782))+~P1(f306(f306(f220(x70781),f306(f111(x70781),x70782)),f306(f111(x70781),x70783))) % 187.68/187.66 [7079]~P107(x70791)+~P92(x70791)+E(f306(f306(f219(x70791),f306(f111(x70791),x70792)),f306(f111(x70791),x70793)),f306(f111(x70791),x70793))+~P1(f306(f306(f220(x70791),f306(f111(x70791),x70792)),f306(f111(x70791),x70793))) % 187.68/187.66 [7093]P146(x70931,x70932,x70933)+~P1(f306(x70931,f2(a1)))+P1(f306(f306(f221(a1),x70933),f2(a1)))+P1(f306(f306(f221(a1),f798(x70933,x70932,x70931)),x70933)) % 187.68/187.66 [7101]P145(x71011,x71012,x71013)+~P1(f306(x71011,x71012))+P1(f306(f306(f220(a1),f806(x71013,x71012,x71011)),f2(a1)))+P1(f306(f306(f221(a1),f2(a1)),x71013)) % 187.68/187.66 [7125]P146(x71251,x71252,x71253)+~P1(f306(x71251,f2(a1)))+P1(f306(f306(f220(a1),f797(x71253,x71252,x71251)),f2(a1)))+P1(f306(f306(f221(a1),f2(a1)),x71253)) % 187.68/187.66 [7153]~P1(f306(x71531,x71532))+P1(f306(x71531,f2(a865)))+~P1(f306(f306(f221(a865),x71532),x71533))+P1(f306(f306(f221(a865),f570(x71532,x71531,x71533)),x71533)) % 187.68/187.66 [7170]~P108(x71701)+~P17(x71701,x71703)+P17(x71701,f306(f306(f143(x71701),x71702),x71703))+P1(f306(f306(f308(x71701),f727(x71703,x71702,x71701)),f306(f164(x71701),x71703))) % 187.68/187.66 [7171]~P108(x71711)+~P17(x71711,x71713)+P17(x71711,f306(f306(f143(x71711),x71712),x71713))+P1(f306(f306(f308(x71711),f728(x71713,x71712,x71711)),f306(f164(x71711),x71713))) % 187.68/187.66 [7172]~P108(x71721)+~P17(x71721,x71723)+P17(x71721,f306(f306(f143(x71721),x71722),x71723))+P1(f306(f306(f308(x71721),f773(x71722,x71723,x71721)),f306(f164(x71721),x71723))) % 187.68/187.66 [7276]~P108(x72761)+~P6(x72761)+~P1(f306(f306(f221(x72761),x72763),f41(x72761,x72762)))+P1(f306(f306(f308(x72761),f610(x72762,x72763,x72761)),x72762)) % 187.68/187.66 [7441]~P108(x74411)+~P6(x74411)+~P1(f306(f306(f221(x74411),f42(x74411,x74413)),x74412))+P1(f306(f306(f308(x74411),f633(x74412,x74413,x74411)),x74413)) % 187.68/187.66 [7442]~P108(x74421)+~P6(x74421)+~P1(f306(f306(f221(x74421),f42(x74421,x74423)),x74422))+P1(f306(f306(f221(x74421),f633(x74422,x74423,x74421)),x74422)) % 187.68/187.66 [7454]P146(x74542,x74543,x74541)+E(x74541,f2(a1))+P1(f306(f306(f221(a1),x74541),f797(x74541,x74543,x74542)))+P1(f306(f306(f221(a1),f798(x74541,x74543,x74542)),x74541)) % 187.68/187.66 [7455]P145(x74552,x74553,x74551)+E(x74551,f2(a1))+P1(f306(f306(f221(a1),x74551),f806(x74551,x74553,x74552)))+P1(f306(f306(f221(a1),f807(x74551,x74553,x74552)),x74551)) % 187.68/187.66 [7545]P146(x75453,x75452,x75451)+E(x75451,f2(a1))+E(f306(f306(f81(a1),f306(f306(f82(a1),x75451),f805(x75451,x75452,x75453))),f797(x75451,x75452,x75453)),x75452)+P1(f306(f306(f221(a1),f2(a1)),x75451)) % 187.68/187.66 [7546]P145(x75463,x75462,x75461)+E(x75461,f2(a1))+E(f306(f306(f81(a1),f306(f306(f82(a1),x75461),f809(x75461,x75462,x75463))),f806(x75461,x75462,x75463)),x75462)+P1(f306(f306(f221(a1),f2(a1)),x75461)) % 187.68/187.66 [7549]~P133(x75491)+~P1(f306(f306(f220(x75491),x75493),f2(x75491)))+P1(f306(f306(f220(x75491),f306(f306(f82(x75491),x75492),x75493)),f2(x75491)))+~P1(f306(f306(f220(x75491),f2(x75491)),x75492)) % 187.68/187.66 [7551]~P133(x75511)+~P1(f306(f306(f220(x75511),x75512),f2(x75511)))+P1(f306(f306(f220(x75511),f306(f306(f82(x75511),x75512),x75513)),f2(x75511)))+~P1(f306(f306(f220(x75511),f2(x75511)),x75513)) % 187.68/187.66 [7552]~P122(x75521)+~P1(f306(f306(f220(x75521),x75523),f2(x75521)))+P1(f306(f306(f220(x75521),f306(f306(f82(x75521),x75522),x75523)),f2(x75521)))+~P1(f306(f306(f220(x75521),f2(x75521)),x75522)) % 187.68/187.66 [7553]~P122(x75531)+~P1(f306(f306(f220(x75531),x75532),f2(x75531)))+P1(f306(f306(f220(x75531),f306(f306(f82(x75531),x75532),x75533)),f2(x75531)))+~P1(f306(f306(f220(x75531),f2(x75531)),x75533)) % 187.68/187.66 [7554]~P63(x75541)+~P1(f306(f306(f220(x75541),x75543),f2(x75541)))+P1(f306(f306(f220(x75541),f306(f306(f264(x75541),x75542),x75543)),f2(x75541)))+~P1(f306(f306(f220(x75541),f2(x75541)),x75542)) % 187.68/187.66 [7555]~P63(x75551)+~P1(f306(f306(f220(x75551),x75552),f2(x75551)))+P1(f306(f306(f220(x75551),f306(f306(f264(x75551),x75552),x75553)),f2(x75551)))+~P1(f306(f306(f220(x75551),f2(x75551)),x75553)) % 187.68/187.66 [7556]~P64(x75561)+~P1(f306(f306(f220(x75561),x75562),f2(x75561)))+P1(f306(f306(f220(x75561),f306(f306(f264(x75561),x75562),x75563)),f2(x75561)))+~P1(f306(f306(f221(x75561),f2(x75561)),x75563)) % 187.68/187.66 [7557]~P64(x75571)+~P1(f306(f306(f221(x75571),x75573),f2(x75571)))+P1(f306(f306(f220(x75571),f306(f306(f264(x75571),x75572),x75573)),f2(x75571)))+~P1(f306(f306(f220(x75571),f2(x75571)),x75572)) % 187.68/187.66 [7559]~P128(x75591)+~P1(f306(f306(f221(x75591),x75593),f2(x75591)))+P1(f306(f306(f221(x75591),f306(f306(f82(x75591),x75592),x75593)),f2(x75591)))+~P1(f306(f306(f221(x75591),f2(x75591)),x75592)) % 187.68/187.66 [7560]~P128(x75601)+~P1(f306(f306(f221(x75601),x75602),f2(x75601)))+P1(f306(f306(f221(x75601),f306(f306(f82(x75601),x75602),x75603)),f2(x75601)))+~P1(f306(f306(f221(x75601),f2(x75601)),x75603)) % 187.68/187.66 [7561]~P63(x75611)+~P1(f306(f306(f221(x75611),x75613),f2(x75611)))+P1(f306(f306(f221(x75611),f306(f306(f264(x75611),x75612),x75613)),f2(x75611)))+~P1(f306(f306(f221(x75611),f2(x75611)),x75612)) % 187.68/187.66 [7562]~P63(x75621)+~P1(f306(f306(f221(x75621),x75622),f2(x75621)))+P1(f306(f306(f221(x75621),f306(f306(f264(x75621),x75622),x75623)),f2(x75621)))+~P1(f306(f306(f221(x75621),f2(x75621)),x75623)) % 187.68/187.66 [7563]~P64(x75631)+~P1(f306(f306(f221(x75631),x75633),f2(x75631)))+P1(f306(f306(f221(x75631),f306(f306(f264(x75631),x75632),x75633)),f2(x75631)))+~P1(f306(f306(f221(x75631),f2(x75631)),x75632)) % 187.68/187.66 [7564]~P64(x75641)+~P1(f306(f306(f221(x75641),x75642),f2(x75641)))+P1(f306(f306(f221(x75641),f306(f306(f264(x75641),x75642),x75643)),f2(x75641)))+~P1(f306(f306(f221(x75641),f2(x75641)),x75643)) % 187.68/187.66 [7579]P145(x75791,x75792,x75793)+~P1(f306(x75791,x75792))+P1(f306(f306(f221(a1),x75793),f806(x75793,x75792,x75791)))+P1(f306(f306(f221(a1),f807(x75793,x75792,x75791)),x75793)) % 187.68/187.66 [7592]P146(x75921,x75922,x75923)+P1(f306(f306(f221(a1),x75923),f797(x75923,x75922,x75921)))+~P1(f306(x75921,f2(a1)))+P1(f306(f306(f221(a1),f798(x75923,x75922,x75921)),x75923)) % 187.68/187.66 [7643]P146(x76432,x76433,x76431)+E(x76431,f2(a1))+~P1(f306(x76432,f805(x76431,x76433,x76432)))+P1(f306(f306(f221(a1),f798(x76431,x76433,x76432)),x76431)) % 187.68/187.66 [7644]P145(x76442,x76443,x76441)+E(x76441,f2(a1))+~P1(f306(x76442,f806(x76441,x76443,x76442)))+P1(f306(f306(f221(a1),f807(x76441,x76443,x76442)),x76441)) % 187.68/187.66 [7655]P145(x76553,x76552,x76551)+~P1(f306(x76553,x76552))+E(f306(f306(f81(a1),f306(f306(f82(a1),x76551),f809(x76551,x76552,x76553))),f806(x76551,x76552,x76553)),x76552)+P1(f306(f306(f221(a1),f2(a1)),x76551)) % 187.68/187.66 [7673]P146(x76733,x76732,x76731)+E(f306(f306(f81(a1),f306(f306(f82(a1),x76731),f805(x76731,x76732,x76733))),f797(x76731,x76732,x76733)),x76732)+~P1(f306(x76733,f2(a1)))+P1(f306(f306(f221(a1),f2(a1)),x76731)) % 187.68/187.66 [7698]~P1(f306(x76981,x76983))+~P1(f306(f63(x76982),x76983))+P1(f306(f306(f308(x76982),f586(x76981,x76983,x76982)),f598(x76981,x76983,x76982)))+P1(f306(x76981,f185(f872(x76982,a859)))) % 187.68/187.66 [7709]P145(x77091,x77092,x77093)+~P1(f306(x77091,x77092))+~P1(f306(x77091,f806(x77093,x77092,x77091)))+P1(f306(f306(f221(a1),f807(x77093,x77092,x77091)),x77093)) % 187.68/187.66 [7714]P146(x77141,x77142,x77143)+~P1(f306(x77141,f805(x77143,x77142,x77141)))+~P1(f306(x77141,f2(a1)))+P1(f306(f306(f221(a1),f798(x77143,x77142,x77141)),x77143)) % 187.68/187.66 [7818]~P122(x78181)+~P1(f306(f306(f220(x78181),f306(f306(f82(x78181),x78183),x78182)),f2(x78181)))+P1(f306(f306(f220(x78181),x78182),f2(x78181)))+P1(f306(f306(f220(x78181),f2(x78181)),x78182)) % 187.68/187.66 [7819]~P122(x78191)+~P1(f306(f306(f220(x78191),f306(f306(f82(x78191),x78192),x78193)),f2(x78191)))+P1(f306(f306(f220(x78191),x78192),f2(x78191)))+P1(f306(f306(f220(x78191),f2(x78191)),x78192)) % 187.68/187.66 [7820]~P63(x78201)+~P1(f306(f306(f220(x78201),f306(f306(f264(x78201),x78203),x78202)),f2(x78201)))+P1(f306(f306(f220(x78201),x78202),f2(x78201)))+P1(f306(f306(f220(x78201),f2(x78201)),x78202)) % 187.68/187.66 [7821]~P63(x78211)+~P1(f306(f306(f220(x78211),f306(f306(f264(x78211),x78212),x78213)),f2(x78211)))+P1(f306(f306(f220(x78211),x78212),f2(x78211)))+P1(f306(f306(f220(x78211),f2(x78211)),x78212)) % 187.68/187.66 [7822]~P63(x78221)+~P1(f306(f306(f221(x78221),f306(f306(f264(x78221),x78223),x78222)),f2(x78221)))+P1(f306(f306(f221(x78221),x78222),f2(x78221)))+P1(f306(f306(f221(x78221),f2(x78221)),x78222)) % 187.68/187.66 [7823]~P63(x78231)+~P1(f306(f306(f221(x78231),f306(f306(f264(x78231),x78232),x78233)),f2(x78231)))+P1(f306(f306(f221(x78231),x78232),f2(x78231)))+P1(f306(f306(f221(x78231),f2(x78231)),x78232)) % 187.68/187.66 [7847]~P122(x78471)+~P1(f306(f306(f220(x78471),f306(f306(f82(x78471),x78472),x78473)),f2(x78471)))+P1(f306(f306(f220(x78471),f2(x78471)),x78472))+P1(f306(f306(f220(x78471),f2(x78471)),x78473)) % 187.68/187.66 [7848]~P63(x78481)+~P1(f306(f306(f220(x78481),f306(f306(f264(x78481),x78482),x78483)),f2(x78481)))+P1(f306(f306(f220(x78481),f2(x78481)),x78482))+P1(f306(f306(f220(x78481),f2(x78481)),x78483)) % 187.68/187.66 [7849]~P63(x78491)+~P1(f306(f306(f221(x78491),f306(f306(f264(x78491),x78492),x78493)),f2(x78491)))+P1(f306(f306(f221(x78491),f2(x78491)),x78492))+P1(f306(f306(f221(x78491),f2(x78491)),x78493)) % 187.68/187.66 [7870]P146(x78702,x78703,x78701)+E(x78701,f2(a1))+P1(f306(f306(f220(a1),f797(x78701,x78703,x78702)),f2(a1)))+P1(f306(f306(f221(a1),f798(x78701,x78703,x78702)),x78701)) % 187.68/187.66 [7871]P145(x78712,x78713,x78711)+E(x78711,f2(a1))+P1(f306(f306(f220(a1),f806(x78711,x78713,x78712)),f2(a1)))+P1(f306(f306(f221(a1),f807(x78711,x78713,x78712)),x78711)) % 187.68/187.66 [7878]~P111(x78781)+~P1(f306(f306(f221(x78781),x78782),f79(x78781)))+P1(f306(f306(f221(x78781),f306(f306(f237(x78781),x78782),f306(a119,x78783))),f79(x78781)))+~P1(f306(f306(f221(x78781),f2(x78781)),x78782)) % 187.68/187.66 [7933]~P108(x79331)+~E(x79333,f120(x79331))+~P17(x79331,f306(f161(x79331),x79333))+E(f306(f134(x79331,x79331,f306(f7(x79331,x79331,x79331),f219(x79331)),x79332),f306(f161(x79331),x79333)),x79332) % 187.68/187.66 [7935]P145(x79351,x79352,x79353)+~P1(f306(x79351,x79352))+P1(f306(f306(f220(a1),f806(x79353,x79352,x79351)),f2(a1)))+P1(f306(f306(f221(a1),f807(x79353,x79352,x79351)),x79353)) % 187.68/187.66 [7945]P146(x79451,x79452,x79453)+~P1(f306(x79451,f2(a1)))+P1(f306(f306(f220(a1),f797(x79453,x79452,x79451)),f2(a1)))+P1(f306(f306(f221(a1),f798(x79453,x79452,x79451)),x79453)) % 187.68/187.66 [8172]P146(x81723,x81722,x81721)+E(x81721,f2(a1))+E(f306(f306(f81(a1),f306(f306(f82(a1),x81721),f805(x81721,x81722,x81723))),f797(x81721,x81722,x81723)),x81722)+P1(f306(f306(f221(a1),f798(x81721,x81722,x81723)),x81721)) % 187.68/187.66 [8173]P145(x81733,x81732,x81731)+E(x81731,f2(a1))+E(f306(f306(f81(a1),f306(f306(f82(a1),x81731),f809(x81731,x81732,x81733))),f806(x81731,x81732,x81733)),x81732)+P1(f306(f306(f221(a1),f807(x81731,x81732,x81733)),x81731)) % 187.68/187.66 [8209]P145(x82093,x82092,x82091)+~P1(f306(x82093,x82092))+E(f306(f306(f81(a1),f306(f306(f82(a1),x82091),f809(x82091,x82092,x82093))),f806(x82091,x82092,x82093)),x82092)+P1(f306(f306(f221(a1),f807(x82091,x82092,x82093)),x82091)) % 187.68/187.66 [8210]~P74(x82101)+~P75(x82101)+~P42(x82103)+E(f306(f306(f9(a865,x82101),f306(f306(f8(a1,x82101,a865),x82102),f107(a1))),f306(f285(a1,a865,a112),x82103)),f306(f306(f9(a1,x82101),x82102),x82103)) % 187.68/187.66 [8211]~P74(x82111)+~P75(x82111)+~P42(x82113)+E(f306(f306(f6(a865,x82111),f306(f306(f8(a1,x82111,a865),x82112),f107(a1))),f306(f285(a1,a865,a112),x82113)),f306(f306(f6(a1,x82111),x82112),x82113)) % 187.68/187.66 [8220]P146(x82203,x82202,x82201)+E(f306(f306(f81(a1),f306(f306(f82(a1),x82201),f805(x82201,x82202,x82203))),f797(x82201,x82202,x82203)),x82202)+~P1(f306(x82203,f2(a1)))+P1(f306(f306(f221(a1),f798(x82201,x82202,x82203)),x82201)) % 187.68/187.66 [8239]~E(x82392,f2(a865))+~E(f306(f235(a865,a865),x82393),f2(a865))+~E(x82391,f306(f306(f81(a865),f306(f306(f82(a865),f306(f235(a865,a865),x82393)),x82392)),f306(f244(a865,a865),x82393)))+P1(f306(f49(x82391,x82392),x82393)) % 187.68/187.66 [8294]P1(f306(x82941,x82942))+~P1(f306(f306(f308(x82943),f637(x82941,x82942,x82943)),f639(x82941,x82942,x82943)))+~P1(f306(f63(x82943),x82942))+~P1(f306(x82941,f185(f872(x82943,a859)))) % 187.68/187.66 [8913]P1(f306(x89131,x89132))+~P1(f306(f63(x89133),x89132))+~P1(f306(x89131,f306(f306(f284(x89133),f637(x89131,x89132,x89133)),f639(x89131,x89132,x89133))))+~P1(f306(x89131,f185(f872(x89133,a859)))) % 187.68/187.66 [9150]P1(f306(f306(f220(a1),x91501),f2(a1)))+~P1(f306(f306(f221(a1),f306(f306(f81(a1),f306(f306(f82(a1),x91503),x91501)),x91502)),f2(a1)))+~P1(f306(f306(f220(a1),f2(a1)),x91502))+~P1(f306(f306(f221(a1),f2(a1)),x91503)) % 187.68/187.66 [5756]~P108(x57562)+E(x57561,f185(f872(x57562,a859)))+~P1(f306(f63(x57562),x57561))+E(f14(x57562,f306(f306(f284(x57562),x57563),x57561)),f306(f306(f225(x57562),x57563),f14(x57562,x57561))) % 187.68/187.66 [5757]~P108(x57572)+E(x57571,f185(f872(x57572,a859)))+~P1(f306(f63(x57572),x57571))+E(f15(x57572,f306(f306(f284(x57572),x57573),x57571)),f306(f306(f219(x57572),x57573),f15(x57572,x57571))) % 187.68/187.66 [5758]~P98(x57582)+E(x57581,f185(f872(x57582,a859)))+~P1(f306(f63(x57582),x57581))+E(f13(x57582,f306(f306(f284(x57582),x57583),x57581)),f306(f306(f108(x57582),x57583),f13(x57582,x57581))) % 187.68/187.66 [5759]~P98(x57592)+E(x57591,f185(f872(x57592,a859)))+~P1(f306(f63(x57592),x57591))+E(f10(x57592,f306(f306(f284(x57592),x57593),x57591)),f306(f306(f109(x57592),x57593),f10(x57592,x57591))) % 187.68/187.66 [6072]~P122(x60721)+~E(x60723,f2(x60721))+~E(x60722,f2(x60721))+E(f306(f306(f81(x60721),f306(f306(f82(x60721),x60722),x60722)),f306(f306(f82(x60721),x60723),x60723)),f2(x60721)) % 187.68/187.66 [6141]~P95(x61412)+E(x61411,f185(f872(x61412,a859)))+~P1(f306(f63(x61412),x61411))+E(f306(f65(x61412,f82(x61412)),f306(f306(f284(x61412),x61413),x61411)),f306(f306(f82(x61412),x61413),f306(f65(x61412,f82(x61412)),x61411))) % 187.68/187.66 [6265]~P108(x62652)+E(x62651,f185(f872(x62652,a859)))+~P1(f306(f63(x62652),x62651))+E(f11(x62652,f225(x62652),f306(f306(f284(x62652),x62653),x62651)),f306(f306(f225(x62652),x62653),f11(x62652,f225(x62652),x62651))) % 187.68/187.66 [6266]~P108(x62662)+E(x62661,f185(f872(x62662,a859)))+~P1(f306(f63(x62662),x62661))+E(f12(x62662,f219(x62662),f306(f306(f284(x62662),x62663),x62661)),f306(f306(f219(x62662),x62663),f12(x62662,f219(x62662),x62661))) % 187.68/187.66 [6774]~P72(x67741)+~P1(f306(f63(x67741),x67743))+E(f306(f65(x67741,f82(x67741)),f306(f306(f284(x67741),x67742),x67743)),f306(f306(f66(x67741,x67741,f82(x67741)),x67742),x67743))+P1(f306(f306(f308(x67741),x67742),x67743)) % 187.68/187.66 [6851]~E(f306(f306(f81(a1),x68512),f306(f306(f82(a1),x68513),x68511)),x68513)+~P1(f306(f306(f221(a1),f2(a1)),x68513))+P1(f306(f306(f220(a1),f79(a1)),x68511))+~P1(f306(f306(f221(a1),x68512),x68513)) % 187.68/187.66 [6881]~E(f306(f306(f81(a1),x68812),f306(f306(f82(a1),x68813),x68811)),x68813)+P1(f306(f306(f220(a1),x68811),f79(a1)))+~P1(f306(f306(f220(a1),f2(a1)),x68812))+~P1(f306(f306(f221(a1),f2(a1)),x68813)) % 187.68/187.66 [6897]E(x68971,f2(a865))+~P1(f306(f49(x68973,x68971),x68972))+~P1(f306(f306(f221(a865),f2(a865)),x68971))+P1(f306(f306(f221(a865),f306(f244(a865,a865),x68972)),x68971)) % 187.68/187.66 [6927]~P137(x69271)+~P1(f306(f306(f220(x69271),x69272),f2(x69271)))+~P1(f306(f306(f220(x69271),x69273),f2(x69271)))+E(f306(f306(f82(x69271),f306(f76(x69271),x69272)),f306(f76(x69271),x69273)),f306(f76(x69271),f306(f306(f82(x69271),x69272),x69273))) % 187.68/187.66 [6979]~P137(x69791)+~P1(f306(f306(f220(x69791),x69792),f2(x69791)))+E(f306(f306(f82(x69791),f306(f76(x69791),x69792)),f306(f76(x69791),x69793)),f306(f76(x69791),f306(f306(f82(x69791),x69792),x69793)))+~P1(f306(f306(f220(x69791),f2(x69791)),x69793)) % 187.68/187.66 [6980]~P137(x69801)+~P1(f306(f306(f220(x69801),x69803),f2(x69801)))+E(f306(f306(f82(x69801),f306(f76(x69801),x69802)),f306(f76(x69801),x69803)),f306(f76(x69801),f306(f306(f82(x69801),x69802),x69803)))+~P1(f306(f306(f220(x69801),f2(x69801)),x69802)) % 187.68/187.66 [7034]~P137(x70341)+E(f306(f306(f82(x70341),f306(f76(x70341),x70342)),f306(f76(x70341),x70343)),f306(f76(x70341),f306(f306(f82(x70341),x70342),x70343)))+~P1(f306(f306(f220(x70341),f2(x70341)),x70342))+~P1(f306(f306(f220(x70341),f2(x70341)),x70343)) % 187.68/187.66 [7051]~P134(x70511)+~P1(f306(f306(f220(x70511),x70513),f2(x70511)))+~P1(f306(f306(f220(x70511),x70512),f2(x70511)))+P1(f306(f306(f220(x70511),f2(x70511)),f306(f306(f82(x70511),x70512),x70513))) % 187.68/187.66 [7052]~P122(x70521)+~P1(f306(f306(f220(x70521),x70523),f2(x70521)))+~P1(f306(f306(f220(x70521),x70522),f2(x70521)))+P1(f306(f306(f220(x70521),f2(x70521)),f306(f306(f82(x70521),x70522),x70523))) % 187.68/187.66 [7053]~P63(x70531)+~P1(f306(f306(f220(x70531),x70533),f2(x70531)))+~P1(f306(f306(f220(x70531),x70532),f2(x70531)))+P1(f306(f306(f220(x70531),f2(x70531)),f306(f306(f264(x70531),x70532),x70533))) % 187.68/187.66 [7054]~P64(x70541)+~P1(f306(f306(f221(x70541),x70543),f2(x70541)))+~P1(f306(f306(f220(x70541),x70542),f2(x70541)))+P1(f306(f306(f220(x70541),f2(x70541)),f306(f306(f264(x70541),x70542),x70543))) % 187.68/187.66 [7055]~P122(x70551)+~P1(f306(f306(f221(x70551),x70553),f2(x70551)))+~P1(f306(f306(f221(x70551),x70552),f2(x70551)))+P1(f306(f306(f221(x70551),f2(x70551)),f306(f306(f82(x70551),x70552),x70553))) % 187.68/187.66 [7056]~P63(x70561)+~P1(f306(f306(f221(x70561),x70563),f2(x70561)))+~P1(f306(f306(f221(x70561),x70562),f2(x70561)))+P1(f306(f306(f221(x70561),f2(x70561)),f306(f306(f264(x70561),x70562),x70563))) % 187.68/187.66 [7057]~P64(x70571)+~P1(f306(f306(f221(x70571),x70573),f2(x70571)))+~P1(f306(f306(f221(x70571),x70572),f2(x70571)))+P1(f306(f306(f221(x70571),f2(x70571)),f306(f306(f264(x70571),x70572),x70573))) % 187.68/187.66 [7058]~P111(x70581)+~P1(f306(f306(f221(a865),f2(a865)),x70583))+~P1(f306(f306(f221(x70581),f79(x70581)),x70582))+P1(f306(f306(f221(x70581),f79(x70581)),f306(f306(f237(x70581),x70582),x70583))) % 187.68/187.66 [7155]~P133(x71551)+~P1(f306(f306(f220(x71551),f2(x71551)),x71553))+~P1(f306(f306(f220(x71551),f2(x71551)),x71552))+P1(f306(f306(f220(x71551),f2(x71551)),f306(f306(f82(x71551),x71552),x71553))) % 187.68/187.66 [7156]~P134(x71561)+~P1(f306(f306(f220(x71561),f2(x71561)),x71563))+~P1(f306(f306(f220(x71561),f2(x71561)),x71562))+P1(f306(f306(f220(x71561),f2(x71561)),f306(f306(f82(x71561),x71562),x71563))) % 187.68/187.66 [7157]~P122(x71571)+~P1(f306(f306(f220(x71571),f2(x71571)),x71573))+~P1(f306(f306(f220(x71571),f2(x71571)),x71572))+P1(f306(f306(f220(x71571),f2(x71571)),f306(f306(f82(x71571),x71572),x71573))) % 187.68/187.66 [7158]~P63(x71581)+~P1(f306(f306(f220(x71581),f2(x71581)),x71583))+~P1(f306(f306(f220(x71581),f2(x71581)),x71582))+P1(f306(f306(f220(x71581),f2(x71581)),f306(f306(f264(x71581),x71582),x71583))) % 187.68/187.66 [7159]~P64(x71591)+~P1(f306(f306(f221(x71591),f2(x71591)),x71593))+~P1(f306(f306(f220(x71591),f2(x71591)),x71592))+P1(f306(f306(f220(x71591),f2(x71591)),f306(f306(f264(x71591),x71592),x71593))) % 187.68/187.66 [7162]~P86(x71621)+~P1(f306(f306(f221(x71621),f2(x71621)),x71623))+~P1(f306(f306(f221(x71621),f2(x71621)),x71622))+P1(f306(f306(f221(x71621),f2(x71621)),f306(f306(f81(x71621),x71622),x71623))) % 187.68/187.66 [7163]~P128(x71631)+~P1(f306(f306(f221(x71631),f2(x71631)),x71633))+~P1(f306(f306(f221(x71631),f2(x71631)),x71632))+P1(f306(f306(f221(x71631),f2(x71631)),f306(f306(f82(x71631),x71632),x71633))) % 187.68/187.66 [7164]~P63(x71641)+~P1(f306(f306(f221(x71641),f2(x71641)),x71643))+~P1(f306(f306(f221(x71641),f2(x71641)),x71642))+P1(f306(f306(f221(x71641),f2(x71641)),f306(f306(f264(x71641),x71642),x71643))) % 187.68/187.66 [7165]~P64(x71651)+~P1(f306(f306(f221(x71651),f2(x71651)),x71653))+~P1(f306(f306(f221(x71651),f2(x71651)),x71652))+P1(f306(f306(f221(x71651),f2(x71651)),f306(f306(f264(x71651),x71652),x71653))) % 187.68/187.66 [7166]~P111(x71661)+~P1(f306(f306(f221(x71661),f79(x71661)),x71663))+~P1(f306(f306(f221(x71661),f79(x71661)),x71662))+P1(f306(f306(f221(x71661),f79(x71661)),f306(f306(f82(x71661),x71662),x71663))) % 187.68/187.66 [7237]~P108(x72371)+~P1(f306(f63(x72371),x72373))+E(f14(x72371,f306(f306(f284(x72371),x72372),x72373)),x72372)+~E(f306(f306(f22(f872(x72371,a859)),x72373),f306(f306(f284(x72371),x72372),f185(f872(x72371,a859)))),f185(f872(x72371,a859))) % 187.68/187.66 [7238]~P108(x72381)+~P1(f306(f63(x72381),x72383))+E(f15(x72381,f306(f306(f284(x72381),x72382),x72383)),x72382)+~E(f306(f306(f22(f872(x72381,a859)),x72383),f306(f306(f284(x72381),x72382),f185(f872(x72381,a859)))),f185(f872(x72381,a859))) % 187.68/187.66 [7239]~P98(x72391)+~P1(f306(f63(x72391),x72393))+E(f13(x72391,f306(f306(f284(x72391),x72392),x72393)),x72392)+~E(f306(f306(f22(f872(x72391,a859)),x72393),f306(f306(f284(x72391),x72392),f185(f872(x72391,a859)))),f185(f872(x72391,a859))) % 187.68/187.66 [7240]~P98(x72401)+~P1(f306(f63(x72401),x72403))+E(f10(x72401,f306(f306(f284(x72401),x72402),x72403)),x72402)+~E(f306(f306(f22(f872(x72401,a859)),x72403),f306(f306(f284(x72401),x72402),f185(f872(x72401,a859)))),f185(f872(x72401,a859))) % 187.68/187.66 [7241]~P122(x72411)+P1(f306(f306(f220(x72411),x72412),f2(x72411)))+P1(f306(f306(f220(x72411),f2(x72411)),x72413))+~P1(f306(f306(f220(x72411),f2(x72411)),f306(f306(f82(x72411),x72413),x72412))) % 187.68/187.66 [7242]~P122(x72421)+P1(f306(f306(f220(x72421),x72422),f2(x72421)))+P1(f306(f306(f220(x72421),f2(x72421)),x72423))+~P1(f306(f306(f220(x72421),f2(x72421)),f306(f306(f82(x72421),x72422),x72423))) % 187.68/187.66 [7243]~P63(x72431)+P1(f306(f306(f220(x72431),x72432),f2(x72431)))+P1(f306(f306(f220(x72431),f2(x72431)),x72433))+~P1(f306(f306(f220(x72431),f2(x72431)),f306(f306(f264(x72431),x72433),x72432))) % 187.68/187.66 [7244]~P63(x72441)+P1(f306(f306(f220(x72441),x72442),f2(x72441)))+P1(f306(f306(f220(x72441),f2(x72441)),x72443))+~P1(f306(f306(f220(x72441),f2(x72441)),f306(f306(f264(x72441),x72442),x72443))) % 187.68/187.66 [7245]~P122(x72451)+P1(f306(f306(f220(x72451),x72452),f2(x72451)))+P1(f306(f306(f220(x72451),f2(x72451)),x72452))+~P1(f306(f306(f220(x72451),f2(x72451)),f306(f306(f82(x72451),x72453),x72452))) % 187.68/187.66 [7246]~P122(x72461)+P1(f306(f306(f220(x72461),x72462),f2(x72461)))+P1(f306(f306(f220(x72461),f2(x72461)),x72462))+~P1(f306(f306(f220(x72461),f2(x72461)),f306(f306(f82(x72461),x72462),x72463))) % 187.68/187.66 [7247]~P63(x72471)+P1(f306(f306(f220(x72471),x72472),f2(x72471)))+P1(f306(f306(f220(x72471),f2(x72471)),x72472))+~P1(f306(f306(f220(x72471),f2(x72471)),f306(f306(f264(x72471),x72473),x72472))) % 187.68/187.66 [7248]~P63(x72481)+P1(f306(f306(f220(x72481),x72482),f2(x72481)))+P1(f306(f306(f220(x72481),f2(x72481)),x72482))+~P1(f306(f306(f220(x72481),f2(x72481)),f306(f306(f264(x72481),x72482),x72483))) % 187.68/187.66 [7249]~P63(x72491)+P1(f306(f306(f221(x72491),x72492),f2(x72491)))+P1(f306(f306(f221(x72491),f2(x72491)),x72493))+~P1(f306(f306(f221(x72491),f2(x72491)),f306(f306(f264(x72491),x72493),x72492))) % 187.68/187.66 [7250]~P63(x72501)+P1(f306(f306(f221(x72501),x72502),f2(x72501)))+P1(f306(f306(f221(x72501),f2(x72501)),x72503))+~P1(f306(f306(f221(x72501),f2(x72501)),f306(f306(f264(x72501),x72502),x72503))) % 187.68/187.66 [7251]~P63(x72511)+P1(f306(f306(f221(x72511),x72512),f2(x72511)))+P1(f306(f306(f221(x72511),f2(x72511)),x72512))+~P1(f306(f306(f221(x72511),f2(x72511)),f306(f306(f264(x72511),x72513),x72512))) % 187.68/187.66 [7252]~P63(x72521)+P1(f306(f306(f221(x72521),x72522),f2(x72521)))+P1(f306(f306(f221(x72521),f2(x72521)),x72522))+~P1(f306(f306(f221(x72521),f2(x72521)),f306(f306(f264(x72521),x72522),x72523))) % 187.68/187.66 [7341]~E(f306(f306(f109(f872(x73411,a859)),f306(f164(x73411),x73412)),f306(f164(x73411),x73413)),f185(f872(x73411,a859)))+~P1(f306(f129(x73411),x73413))+~P1(f306(f129(x73411),x73412))+P1(f306(f129(x73411),f306(f306(f122(x73411),x73412),x73413))) % 187.68/187.66 [7342]~P108(x73421)+~P1(f306(f63(x73421),x73423))+E(f11(x73421,f225(x73421),f306(f306(f284(x73421),x73422),x73423)),x73422)+~E(f306(f306(f22(f872(x73421,a859)),x73423),f306(f306(f284(x73421),x73422),f185(f872(x73421,a859)))),f185(f872(x73421,a859))) % 187.68/187.66 [7343]~P108(x73431)+~P1(f306(f63(x73431),x73433))+E(f12(x73431,f219(x73431),f306(f306(f284(x73431),x73432),x73433)),x73432)+~E(f306(f306(f22(f872(x73431,a859)),x73433),f306(f306(f284(x73431),x73432),f185(f872(x73431,a859)))),f185(f872(x73431,a859))) % 187.68/187.66 [7359]~P84(x73591)+~P1(f306(f306(f220(x73591),x73592),x73593))+~P1(f306(f306(f220(x73591),f306(f80(x73591),x73592)),x73593))+P1(f306(f306(f220(x73591),f306(f76(x73591),x73592)),x73593)) % 187.68/187.66 [7360]~P112(x73601)+~P1(f306(f306(f221(x73601),x73602),x73603))+~P1(f306(f306(f221(x73601),f306(f80(x73601),x73602)),x73603))+P1(f306(f306(f221(x73601),f306(f76(x73601),x73602)),x73603)) % 187.68/187.66 [7431]~P128(x74311)+P1(f306(f306(f221(x74311),f2(x74311)),x74312))+~P1(f306(f306(f221(x74311),f2(x74311)),x74313))+~P1(f306(f306(f221(x74311),f2(x74311)),f306(f306(f82(x74311),x74313),x74312))) % 187.68/187.66 [7432]~P128(x74321)+P1(f306(f306(f221(x74321),f2(x74321)),x74322))+~P1(f306(f306(f221(x74321),f2(x74321)),x74323))+~P1(f306(f306(f221(x74321),f2(x74321)),f306(f306(f82(x74321),x74322),x74323))) % 187.68/187.66 [7732]E(x77321,x77322)+~P1(f306(f63(x77323),x77321))+~P1(f306(f306(f220(a865),f306(f39(x77323),x77321)),f306(f39(x77323),x77322)))+~P1(f306(f306(f220(f872(x77323,a859)),x77322),x77321)) % 187.68/187.66 [7874]~P1(f306(f306(f221(a1),x78741),f2(a1)))+~P1(f306(f306(f221(a1),f2(a1)),x78742))+~P1(f306(f306(f220(a1),x78742),x78743))+P1(f306(f306(f220(a1),f306(f306(f40(a1),x78741),x78742)),f306(f306(f40(a1),x78741),x78743))) % 187.68/187.66 [7887]~P1(f306(f306(f220(a1),f2(a1)),x78871))+~P1(f306(f306(f221(a1),f2(a1)),x78873))+~P1(f306(f306(f220(a1),x78873),x78872))+P1(f306(f306(f220(a1),f306(f306(f40(a1),x78871),x78872)),f306(f306(f40(a1),x78871),x78873))) % 187.68/187.66 [8027]E(f306(x80271,f495(x80272,x80271,x80273)),x80272)+~P1(f306(f306(f220(a1),x80272),f306(x80271,x80273)))+P1(f306(f306(f221(a865),f496(x80272,x80271,x80273)),x80273))+~P1(f306(f306(f220(a1),f306(x80271,f2(a865))),x80272)) % 187.68/187.66 [8028]E(f306(x80281,f508(x80282,x80281,x80283)),x80282)+~P1(f306(f306(f220(a1),x80282),f306(x80281,x80283)))+P1(f306(f306(f221(a865),f509(x80282,x80281,x80283)),x80283))+~P1(f306(f306(f220(a1),f306(x80281,f2(a865))),x80282)) % 187.68/187.66 [8132]~P1(f306(f63(x81321),x81323))+~P1(f306(f306(f221(a865),f306(f39(x81321),x81322)),f306(f39(x81321),x81323)))+~P1(f306(f306(f220(f872(x81321,a859)),x81322),x81323))+P1(f306(f306(f221(f872(x81321,a859)),x81322),x81323)) % 187.68/187.66 [8161]E(f306(f306(f81(a1),f371(x81613,x81611,x81612)),f372(x81613,x81611,x81612)),x81611)+E(f306(f306(f22(a1),x81611),x81612),x81611)+~P1(f306(f306(f221(a1),f2(a1)),x81612))+~P1(f306(f306(f308(a1),f306(f306(f22(a1),x81611),f79(a1))),x81613)) % 187.68/187.66 [8162]E(f306(f306(f22(a1),f377(x81623,x81621,x81622)),f378(x81623,x81621,x81622)),x81621)+E(f306(f306(f81(a1),x81621),x81622),x81621)+~P1(f306(f306(f221(a1),f2(a1)),x81622))+~P1(f306(f306(f308(a1),f306(f306(f81(a1),x81621),f79(a1))),x81623)) % 187.68/187.66 [8215]~P1(f306(f306(f220(a865),x82153),x82151))+P1(f306(f306(f220(a865),x82151),x82152))+~P1(f306(f306(f220(a865),x82153),x82152))+~P1(f306(f306(f220(a865),f306(f306(f22(a865),x82151),x82153)),f306(f306(f22(a865),x82152),x82153))) % 187.68/187.66 [8216]~P1(f306(f306(f220(a865),x82163),x82161))+P1(f306(f306(f221(a865),x82161),x82162))+~P1(f306(f306(f220(a865),x82163),x82162))+~P1(f306(f306(f221(a865),f306(f306(f22(a865),x82161),x82163)),f306(f306(f22(a865),x82162),x82163))) % 187.68/187.66 [8232]~P108(x82322)+E(x82321,f120(x82322))+~P17(x82322,f306(f161(x82322),x82321))+E(f306(f134(x82322,x82322,f306(f7(x82322,x82322,x82322),f219(x82322)),x82323),f306(f161(x82322),x82321)),f306(f306(f219(x82322),f306(f306(f157(x82322),x82321),f2(a865))),x82323)) % 187.68/187.66 [8278]~P6(x82781)+~P41(x82781,x82781,x82783)+P1(f306(f306(f220(x82781),x82782),f103(x82781,x82783)))+~P1(f306(f306(f220(x82781),x82782),f306(x82783,f306(f306(f108(x82781),x82782),f103(x82781,x82783))))) % 187.68/187.66 [8299]E(f306(f306(f22(a1),x82991),x82992),x82991)+~P1(f306(f306(f221(a1),f2(a1)),x82992))+P1(f306(f306(f308(a1),f371(x82993,x82991,x82992)),x82993))+~P1(f306(f306(f308(a1),f306(f306(f22(a1),x82991),f79(a1))),x82993)) % 187.68/187.66 [8300]E(f306(f306(f81(a1),x83001),x83002),x83001)+~P1(f306(f306(f221(a1),f2(a1)),x83002))+P1(f306(f306(f308(a1),f377(x83003,x83001,x83002)),x83003))+~P1(f306(f306(f308(a1),f306(f306(f81(a1),x83001),f79(a1))),x83003)) % 187.68/187.66 [8375]~P1(f306(f306(f220(a1),x83751),f306(x83752,x83753)))+P1(f306(f306(f221(a865),f496(x83751,x83752,x83753)),x83753))+P1(f306(f306(f220(a865),f495(x83751,x83752,x83753)),x83753))+~P1(f306(f306(f220(a1),f306(x83752,f2(a865))),x83751)) % 187.68/187.66 [8376]~P1(f306(f306(f220(a1),x83761),f306(x83762,x83763)))+P1(f306(f306(f221(a865),f509(x83761,x83762,x83763)),x83763))+P1(f306(f306(f220(a865),f508(x83761,x83762,x83763)),x83763))+~P1(f306(f306(f220(a1),f306(x83762,f2(a865))),x83761)) % 187.68/187.66 [8457]E(f306(f306(f22(a1),x84571),x84572),x84571)+~P1(f306(f306(f221(a1),f2(a1)),x84572))+P1(f306(f306(f308(a1),f372(x84573,x84571,x84572)),f277(a1,f79(a1),x84572)))+~P1(f306(f306(f308(a1),f306(f306(f22(a1),x84571),f79(a1))),x84573)) % 187.68/187.66 [8458]E(f306(f306(f81(a1),x84581),x84582),x84581)+~P1(f306(f306(f221(a1),f2(a1)),x84582))+P1(f306(f306(f308(a1),f378(x84583,x84581,x84582)),f277(a1,f79(a1),x84582)))+~P1(f306(f306(f308(a1),f306(f306(f81(a1),x84581),f79(a1))),x84583)) % 187.68/187.66 [8588]~P111(x85881)+~P1(f306(f306(f221(x85881),x85882),f79(x85881)))+~P1(f306(f306(f221(x85881),f2(x85881)),x85882))+P1(f306(f306(f221(x85881),f306(f306(f82(x85881),x85882),f306(f306(f237(x85881),x85882),x85883))),f306(f306(f237(x85881),x85882),x85883))) % 187.68/187.66 [8669]~P1(f306(x86691,x86692))+P1(f306(x86691,f2(a865)))+~P1(f306(f306(f221(a865),x86692),x86693))+~P1(f306(x86691,f46(a865,f306(a119,f570(x86692,x86691,x86693)),x86693))) % 187.68/187.66 [8809]E(f478(x88091,x88092,x88093),f2(a865))+P1(f306(f306(x88091,x88093),x88092))+P1(f306(f306(x88091,f478(x88091,x88092,x88093)),f46(a865,f474(x88091,x88092,x88093),f478(x88091,x88092,x88093))))+~P1(f306(f294(f871(a865,a865),a205),f306(f306(f236(a865,a865),x88093),x88092))) % 187.68/187.66 [8847]~P28(x88471,x88471,x88472,x88473)+E(f306(f285(x88471,x88471,x88472),x88473),x88473)+~P1(f306(f63(x88471),x88473))+~P1(f306(f306(f220(f872(x88471,a859)),f306(f285(x88471,x88471,x88472),x88473)),x88473)) % 187.68/187.66 [8924]~P6(x89241)+~P41(x89241,x89241,x89243)+P1(f306(f306(f220(x89241),f306(f306(f108(x89241),x89242),f103(x89241,x89243))),f306(x89243,f306(f306(f108(x89241),x89242),f103(x89241,x89243)))))+~P1(f306(f306(f220(x89241),x89242),f306(x89243,f306(f306(f108(x89241),x89242),f103(x89241,x89243))))) % 187.68/187.66 [9088]P1(f306(f306(x90881,x90882),x90883))+~P1(f306(f306(f221(a1),f333(x90881,x90883,x90882)),f2(a1)))+P1(f306(f306(x90881,f306(f80(a1),f332(x90881,x90883,x90882))),f306(f80(a1),f333(x90881,x90883,x90882))))+~P1(f306(f294(f871(a1,a1),a210),f306(f306(f236(a1,a1),x90882),x90883))) % 187.68/187.66 [9281]P1(f306(f306(x92811,x92812),x92813))+P1(f306(f306(x92811,f306(f306(f81(a1),f692(x92811,x92813,x92812)),f79(a1))),f695(x92811,x92813,x92812)))+~P1(f306(f306(f220(a1),f692(x92811,x92813,x92812)),f695(x92811,x92813,x92812)))+~P1(f306(f294(f871(a1,a1),a174),f306(f306(f236(a1,a1),x92812),x92813))) % 187.68/187.66 [9710]~P60(x97102)+~P60(x97101)+~P1(f306(f59(f871(x97101,x97102)),x97103))+P1(f306(f59(x97101),f306(f306(f8(f872(x97102,a859),a859,x97101),f59(x97102)),f306(f306(f8(f872(x97102,f871(x97101,x97102)),f872(x97102,a859),x97101),f306(f8(f871(x97101,x97102),a859,x97102),x97103)),f236(x97101,x97102))))) % 187.68/187.66 [9711]~P60(x97112)+~P60(x97111)+~P1(f306(f60(f871(x97111,x97112)),x97113))+P1(f306(f60(x97111),f306(f306(f8(f872(x97112,a859),a859,x97111),f60(x97112)),f306(f306(f8(f872(x97112,f871(x97111,x97112)),f872(x97112,a859),x97111),f306(f8(f871(x97111,x97112),a859,x97112),x97113)),f236(x97111,x97112))))) % 187.68/187.66 [9813]~P60(x98132)+~P60(x98131)+P1(f306(f59(f871(x98131,x98132)),x98133))+~P1(f306(f59(x98131),f306(f306(f8(f872(x98132,a859),a859,x98131),f59(x98132)),f306(f306(f8(f872(x98132,f871(x98131,x98132)),f872(x98132,a859),x98131),f306(f8(f871(x98131,x98132),a859,x98132),x98133)),f236(x98131,x98132))))) % 187.68/187.66 [9814]~P60(x98142)+~P60(x98141)+P1(f306(f60(f871(x98141,x98142)),x98143))+~P1(f306(f60(x98141),f306(f306(f8(f872(x98142,a859),a859,x98141),f60(x98142)),f306(f306(f8(f872(x98142,f871(x98141,x98142)),f872(x98142,a859),x98141),f306(f8(f871(x98141,x98142),a859,x98142),x98143)),f236(x98141,x98142))))) % 187.68/187.66 [9987]E(f306(x99871,f495(x99872,x99871,x99873)),x99872)+~P1(f306(f306(f220(a1),x99872),f306(x99871,x99873)))+~P1(f306(f306(f220(a1),f306(f76(a1),f306(f306(f22(a1),f306(x99871,f306(f306(f81(a865),f496(x99872,x99871,x99873)),f79(a865)))),f306(x99871,f496(x99872,x99871,x99873))))),f79(a1)))+~P1(f306(f306(f220(a1),f306(x99871,f2(a865))),x99872)) % 187.68/187.66 [9988]E(f306(x99881,f508(x99882,x99881,x99883)),x99882)+~P1(f306(f306(f220(a1),x99882),f306(x99881,x99883)))+~P1(f306(f306(f220(a1),f306(f76(a1),f306(f306(f22(a1),f306(x99881,f306(f306(f81(a865),f509(x99882,x99881,x99883)),f79(a865)))),f306(x99881,f509(x99882,x99881,x99883))))),f79(a1)))+~P1(f306(f306(f220(a1),f306(x99881,f2(a865))),x99882)) % 187.68/187.66 [9992]~P1(f306(f306(f220(a1),x99921),f306(x99922,x99923)))+~P1(f306(f306(f220(a1),f306(f76(a1),f306(f306(f22(a1),f306(x99922,f306(f306(f81(a865),f496(x99921,x99922,x99923)),f79(a865)))),f306(x99922,f496(x99921,x99922,x99923))))),f79(a1)))+P1(f306(f306(f220(a865),f495(x99921,x99922,x99923)),x99923))+~P1(f306(f306(f220(a1),f306(x99922,f2(a865))),x99921)) % 187.68/187.66 [9993]~P1(f306(f306(f220(a1),x99931),f306(x99932,x99933)))+~P1(f306(f306(f220(a1),f306(f76(a1),f306(f306(f22(a1),f306(x99932,f306(f306(f81(a865),f509(x99931,x99932,x99933)),f79(a865)))),f306(x99932,f509(x99931,x99932,x99933))))),f79(a1)))+P1(f306(f306(f220(a865),f508(x99931,x99932,x99933)),x99933))+~P1(f306(f306(f220(a1),f306(x99932,f2(a865))),x99931)) % 187.68/187.66 [10049]E(x100491,x100492)+~E(f306(f134(f866(x100493),f866(x100493),f122(x100493),f120(x100493)),x100491),f306(f134(f866(x100493),f866(x100493),f122(x100493),f120(x100493)),x100492))+~E(f306(f186(f866(f866(x100493))),x100491),f306(f186(f866(f866(x100493))),x100492))+~P1(f306(f306(f245(f866(x100493),f866(x100493),a859),f306(f306(f7(f866(x100493),f872(f866(x100493),a865),f872(f866(x100493),a859)),f306(f306(f8(f872(a865,a859),f872(f872(f866(x100493),a865),f872(f866(x100493),a859)),f866(x100493)),f8(a865,a859,f866(x100493))),f306(f306(f8(a865,f872(a865,a859),f866(x100493)),a303),f186(f866(x100493))))),f186(f866(x100493)))),f737(x100492,x100491,x100493))) % 187.68/187.66 [10050]E(x100501,x100502)+~E(f306(f134(f866(x100503),f866(x100503),f122(x100503),f120(x100503)),x100501),f306(f134(f866(x100503),f866(x100503),f122(x100503),f120(x100503)),x100502))+~E(f306(f186(f866(f866(x100503))),x100501),f306(f186(f866(f866(x100503))),x100502))+~P1(f306(f306(f245(f866(x100503),f866(x100503),a859),f306(f306(f7(f866(x100503),f872(f866(x100503),a865),f872(f866(x100503),a859)),f306(f306(f8(f872(a865,a859),f872(f872(f866(x100503),a865),f872(f866(x100503),a859)),f866(x100503)),f8(a865,a859,f866(x100503))),f306(f306(f8(a865,f872(a865,a859),f866(x100503)),a303),f186(f866(x100503))))),f186(f866(x100503)))),f738(x100501,x100502,x100503))) % 187.68/187.66 [6761]~E(f79(a865),f2(a865))+~P1(f306(f63(x67611),x67613))+~P1(f306(f63(x67611),x67612))+E(f306(f306(f81(a865),f306(f39(x67611),x67612)),f306(f39(x67611),x67613)),f306(f39(x67611),f306(f306(f108(f872(x67611,a859)),x67612),x67613))) % 187.68/187.66 [7173]~P108(x71731)+~P1(f306(f63(x71731),x71732))+~P1(f306(f306(f308(x71731),x71733),x71732))+P1(f306(f306(f220(x71731),f306(f65(x71731,f225(x71731)),x71732)),x71733)) % 187.68/187.66 [7174]~P103(x71741)+~P1(f306(f63(x71741),x71742))+~P1(f306(f306(f308(x71741),x71743),x71742))+P1(f306(f306(f220(x71741),f306(f65(x71741,f109(x71741)),x71742)),x71743)) % 187.68/187.66 [7425]~P1(f306(f63(x74251),x74253))+~P1(f306(f63(x74251),x74252))+~E(f306(f306(f109(f872(x74251,a859)),x74252),x74253),f185(f872(x74251,a859)))+E(f306(f306(f81(a865),f306(f39(x74251),x74252)),f306(f39(x74251),x74253)),f306(f39(x74251),f306(f306(f108(f872(x74251,a859)),x74252),x74253))) % 187.68/187.66 [8221]~P40(x82211,x82213)+~P40(x82211,x82212)+~E(f306(f306(f109(f872(x82211,a859)),f306(f234(x82211,x82211),x82212)),f306(f232(x82211,x82211),x82213)),f185(f872(x82211,a859)))+P40(x82211,f306(f306(f108(f872(f871(x82211,x82211),a859)),x82212),x82213)) % 187.68/187.66 [8314]E(x83141,f306(f306(f40(a865),x83142),x83143))+~P1(f306(f306(f221(a865),f2(a865)),x83143))+~P1(f306(f306(f221(a865),x83142),f306(f306(f82(a865),x83143),f306(a119,x83141))))+~P1(f306(f306(f220(a865),f306(f306(f82(a865),x83143),x83141)),x83142)) % 187.68/187.66 [8455]~P1(f306(f63(x84551),x84552))+~P1(f306(f63(x84551),x84553))+E(f306(f306(f81(a865),f306(f39(x84551),x84552)),f306(f39(x84551),x84553)),f306(f39(x84551),f306(f306(f108(f872(x84551,a859)),x84552),x84553)))+P1(f306(f306(f308(x84551),f440(x84553,x84552,x84551)),f306(f306(f109(f872(x84551,a859)),x84552),x84553))) % 187.68/187.66 [8821]~P122(x88212)+~E(x88211,f2(x88212))+~E(x88213,f2(x88212))+~P1(f306(f306(f221(x88212),f2(x88212)),f306(f306(f81(x88212),f306(f306(f82(x88212),x88213),x88213)),f306(f306(f82(x88212),x88211),x88211)))) % 187.68/187.66 [9362]~P40(x93621,x93623)+~P40(x93621,x93622)+P40(x93621,f306(f306(f108(f872(f871(x93621,x93621),a859)),x93622),x93623))+~P1(f306(f306(f220(f872(f871(x93621,x93621),a859)),f306(f306(f263(x93621,x93621,x93621),x93622),x93623)),x93622)) % 187.68/187.66 [9489]~P1(f306(x94891,x94893))+~P1(f306(f63(x94892),x94893))+P1(f306(x94891,f185(f872(x94892,a859))))+~P1(f306(x94891,f306(f306(f22(f872(x94892,a859)),f598(x94891,x94893,x94892)),f306(f306(f284(x94892),f586(x94891,x94893,x94892)),f185(f872(x94892,a859)))))) % 187.68/187.66 [9743]~P60(x97431)+~P60(x97432)+P14(x97431,f306(f306(f8(f872(x97432,x97431),a859,f866(x97431)),x97433),f306(f306(f8(f872(x97432,f869(x97431)),f872(x97432,x97431),f866(x97431)),f74(f869(x97431),x97431,x97432,f218(x97431))),f306(f306(f8(f866(f871(x97432,x97431)),f872(x97432,f869(x97431)),f866(x97431)),f169(x97432,x97431)),f306(f173(x97432,x97431),f57(x97432))))),f306(f186(f866(x97432)),f57(x97432)))+~P1(f306(f60(f872(x97432,x97431)),x97433)) % 187.68/187.66 [9744]~P60(x97441)+~P60(x97442)+P13(x97441,f306(f306(f8(f872(x97442,x97441),a859,f866(x97441)),x97443),f306(f306(f8(f872(x97442,f869(x97441)),f872(x97442,x97441),f866(x97441)),f74(f869(x97441),x97441,x97442,f218(x97441))),f306(f306(f8(f866(f871(x97442,x97441)),f872(x97442,f869(x97441)),f866(x97441)),f169(x97442,x97441)),f306(f173(x97442,x97441),f57(x97442))))),f306(f186(f866(x97442)),f57(x97442)))+~P1(f306(f59(f872(x97442,x97441)),x97443)) % 187.68/187.66 [9838]~P60(x98381)+~P60(x98382)+~P13(x98382,f306(f306(f8(f872(x98381,x98382),a859,f866(x98382)),x98383),f306(f306(f8(f872(x98381,f869(x98382)),f872(x98381,x98382),f866(x98382)),f74(f869(x98382),x98382,x98381,f218(x98382))),f306(f306(f8(f866(f871(x98381,x98382)),f872(x98381,f869(x98382)),f866(x98382)),f169(x98381,x98382)),f306(f173(x98381,x98382),f57(x98381))))),f306(f186(f866(x98381)),f57(x98381)))+P1(f306(f59(f872(x98381,x98382)),x98383)) % 187.68/187.66 [9839]~P60(x98391)+~P60(x98392)+~P14(x98392,f306(f306(f8(f872(x98391,x98392),a859,f866(x98392)),x98393),f306(f306(f8(f872(x98391,f869(x98392)),f872(x98391,x98392),f866(x98392)),f74(f869(x98392),x98392,x98391,f218(x98392))),f306(f306(f8(f866(f871(x98391,x98392)),f872(x98391,f869(x98392)),f866(x98392)),f169(x98391,x98392)),f306(f173(x98391,x98392),f57(x98391))))),f306(f186(f866(x98391)),f57(x98391)))+P1(f306(f60(f872(x98391,x98392)),x98393)) % 187.68/187.66 [8623]~P1(f306(f306(f221(a1),f2(a1)),x86233))+P1(f306(f306(f220(a1),f2(a1)),x86231))+~P1(f306(f306(f221(a1),x86232),x86233))+~P1(f306(f306(f220(a1),f2(a1)),f306(f306(f81(a1),f306(f306(f82(a1),x86233),x86231)),x86232))) % 187.68/187.66 [8643]~P108(x86431)+~P1(f306(f63(x86431),x86432))+E(f306(f306(f22(f872(x86431,a859)),x86432),f306(f306(f284(x86431),x86433),f185(f872(x86431,a859)))),f185(f872(x86431,a859)))+E(f306(f306(f225(x86431),x86433),f14(x86431,f306(f306(f22(f872(x86431,a859)),x86432),f306(f306(f284(x86431),x86433),f185(f872(x86431,a859)))))),f14(x86431,f306(f306(f284(x86431),x86433),x86432))) % 187.68/187.66 [8644]~P108(x86441)+~P1(f306(f63(x86441),x86442))+E(f306(f306(f22(f872(x86441,a859)),x86442),f306(f306(f284(x86441),x86443),f185(f872(x86441,a859)))),f185(f872(x86441,a859)))+E(f306(f306(f219(x86441),x86443),f15(x86441,f306(f306(f22(f872(x86441,a859)),x86442),f306(f306(f284(x86441),x86443),f185(f872(x86441,a859)))))),f15(x86441,f306(f306(f284(x86441),x86443),x86442))) % 187.68/187.66 [8645]~P98(x86451)+~P1(f306(f63(x86451),x86452))+E(f306(f306(f22(f872(x86451,a859)),x86452),f306(f306(f284(x86451),x86453),f185(f872(x86451,a859)))),f185(f872(x86451,a859)))+E(f306(f306(f108(x86451),x86453),f13(x86451,f306(f306(f22(f872(x86451,a859)),x86452),f306(f306(f284(x86451),x86453),f185(f872(x86451,a859)))))),f13(x86451,f306(f306(f284(x86451),x86453),x86452))) % 187.68/187.66 [8646]~P98(x86461)+~P1(f306(f63(x86461),x86462))+E(f306(f306(f22(f872(x86461,a859)),x86462),f306(f306(f284(x86461),x86463),f185(f872(x86461,a859)))),f185(f872(x86461,a859)))+E(f306(f306(f109(x86461),x86463),f10(x86461,f306(f306(f22(f872(x86461,a859)),x86462),f306(f306(f284(x86461),x86463),f185(f872(x86461,a859)))))),f10(x86461,f306(f306(f284(x86461),x86463),x86462))) % 187.68/187.66 [8711]~P108(x87111)+~P1(f306(f63(x87111),x87112))+E(f306(f306(f22(f872(x87111,a859)),x87112),f306(f306(f284(x87111),x87113),f185(f872(x87111,a859)))),f185(f872(x87111,a859)))+E(f306(f306(f225(x87111),x87113),f11(x87111,f225(x87111),f306(f306(f22(f872(x87111,a859)),x87112),f306(f306(f284(x87111),x87113),f185(f872(x87111,a859)))))),f11(x87111,f225(x87111),f306(f306(f284(x87111),x87113),x87112))) % 187.68/187.66 [8712]~P108(x87121)+~P1(f306(f63(x87121),x87122))+E(f306(f306(f22(f872(x87121,a859)),x87122),f306(f306(f284(x87121),x87123),f185(f872(x87121,a859)))),f185(f872(x87121,a859)))+E(f306(f306(f219(x87121),x87123),f12(x87121,f219(x87121),f306(f306(f22(f872(x87121,a859)),x87122),f306(f306(f284(x87121),x87123),f185(f872(x87121,a859)))))),f12(x87121,f219(x87121),f306(f306(f284(x87121),x87123),x87122))) % 187.68/187.66 [9092]~P6(x90921)+~P41(x90921,x90921,x90922)+P1(f306(f306(f220(x90921),f102(x90921,x90922)),x90923))+~P1(f306(f306(f220(x90921),f306(x90922,f306(f306(f109(x90921),f102(x90921,x90922)),x90923))),x90923)) % 187.68/187.66 [9301]E(x93011,x93012)+~E(f306(f134(f866(x93013),f866(x93013),f122(x93013),f120(x93013)),x93011),f306(f134(f866(x93013),f866(x93013),f122(x93013),f120(x93013)),x93012))+~E(f306(f186(f866(f866(x93013))),x93011),f306(f186(f866(f866(x93013))),x93012))+P1(f306(f306(f308(f871(f866(x93013),f866(x93013))),f737(x93012,x93011,x93013)),f306(f164(f871(f866(x93013),f866(x93013))),f306(f306(f173(f866(x93013),f866(x93013)),x93011),x93012)))) % 187.68/187.66 [9302]E(x93021,x93022)+~E(f306(f134(f866(x93023),f866(x93023),f122(x93023),f120(x93023)),x93021),f306(f134(f866(x93023),f866(x93023),f122(x93023),f120(x93023)),x93022))+~E(f306(f186(f866(f866(x93023))),x93021),f306(f186(f866(f866(x93023))),x93022))+P1(f306(f306(f308(f871(f866(x93023),f866(x93023))),f738(x93021,x93022,x93023)),f306(f164(f871(f866(x93023),f866(x93023))),f306(f306(f173(f866(x93023),f866(x93023)),x93022),x93021)))) % 187.68/187.66 [10141]~P77(x101412)+E(x101411,f185(f872(x101412,a859)))+~P1(f306(f63(x101412),x101411))+E(f14(x101412,f306(f228(x101412),f306(f306(f8(f872(x101412,a859),a859,x101412),f88(x101412)),f306(f306(f7(x101412,f872(x101412,a859),f872(x101412,a859)),f306(f306(f8(f872(x101412,f872(a859,a859)),f872(f872(x101412,a859),f872(x101412,a859)),x101412),f18(x101412,a859,a859)),f306(f306(f8(f872(x101412,a859),f872(x101412,f872(a859,a859)),x101412),f306(f8(a859,f872(a859,a859),x101412),a304)),f306(f306(f7(x101412,f872(x101412,x101412),f872(x101412,a859)),f306(f306(f8(f872(x101412,a859),f872(f872(x101412,x101412),f872(x101412,a859)),x101412),f8(x101412,a859,x101412)),a303)),f306(f81(x101412),x101413))))),f306(f306(f7(x101412,f872(x101412,a859),a859),f308(x101412)),x101411))))),f306(f306(f81(x101412),x101413),f14(x101412,x101411))) % 187.68/187.66 [10142]~P77(x101422)+E(x101421,f185(f872(x101422,a859)))+~P1(f306(f63(x101422),x101421))+E(f15(x101422,f306(f228(x101422),f306(f306(f8(f872(x101422,a859),a859,x101422),f88(x101422)),f306(f306(f7(x101422,f872(x101422,a859),f872(x101422,a859)),f306(f306(f8(f872(x101422,f872(a859,a859)),f872(f872(x101422,a859),f872(x101422,a859)),x101422),f18(x101422,a859,a859)),f306(f306(f8(f872(x101422,a859),f872(x101422,f872(a859,a859)),x101422),f306(f8(a859,f872(a859,a859),x101422),a304)),f306(f306(f7(x101422,f872(x101422,x101422),f872(x101422,a859)),f306(f306(f8(f872(x101422,a859),f872(f872(x101422,x101422),f872(x101422,a859)),x101422),f8(x101422,a859,x101422)),a303)),f306(f81(x101422),x101423))))),f306(f306(f7(x101422,f872(x101422,a859),a859),f308(x101422)),x101421))))),f306(f306(f81(x101422),x101423),f15(x101422,x101421))) % 187.68/187.66 [10143]~P101(x101432)+E(x101431,f185(f872(x101432,a859)))+~P1(f306(f63(x101432),x101431))+E(f10(x101432,f306(f228(x101432),f306(f306(f8(f872(x101432,a859),a859,x101432),f88(x101432)),f306(f306(f7(x101432,f872(x101432,a859),f872(x101432,a859)),f306(f306(f8(f872(x101432,f872(a859,a859)),f872(f872(x101432,a859),f872(x101432,a859)),x101432),f18(x101432,a859,a859)),f306(f306(f8(f872(x101432,a859),f872(x101432,f872(a859,a859)),x101432),f306(f8(a859,f872(a859,a859),x101432),a304)),f306(f306(f7(x101432,f872(x101432,x101432),f872(x101432,a859)),f306(f306(f8(f872(x101432,a859),f872(f872(x101432,x101432),f872(x101432,a859)),x101432),f8(x101432,a859,x101432)),a303)),f306(f108(x101432),x101433))))),f306(f306(f7(x101432,f872(x101432,a859),a859),f308(x101432)),x101431))))),f306(f306(f108(x101432),x101433),f10(x101432,x101431))) % 187.68/187.66 [10144]~P101(x101442)+E(x101441,f185(f872(x101442,a859)))+~P1(f306(f63(x101442),x101441))+E(f13(x101442,f306(f228(x101442),f306(f306(f8(f872(x101442,a859),a859,x101442),f88(x101442)),f306(f306(f7(x101442,f872(x101442,a859),f872(x101442,a859)),f306(f306(f8(f872(x101442,f872(a859,a859)),f872(f872(x101442,a859),f872(x101442,a859)),x101442),f18(x101442,a859,a859)),f306(f306(f8(f872(x101442,a859),f872(x101442,f872(a859,a859)),x101442),f306(f8(a859,f872(a859,a859),x101442),a304)),f306(f306(f7(x101442,f872(x101442,x101442),f872(x101442,a859)),f306(f306(f8(f872(x101442,a859),f872(f872(x101442,x101442),f872(x101442,a859)),x101442),f8(x101442,a859,x101442)),a303)),f306(f109(x101442),x101443))))),f306(f306(f7(x101442,f872(x101442,a859),a859),f308(x101442)),x101441))))),f306(f306(f109(x101442),x101443),f13(x101442,x101441))) % 187.68/187.66 [10145]~P108(x101452)+E(x101451,f185(f872(x101452,a859)))+~P1(f306(f63(x101452),x101451))+E(f12(x101452,f219(x101452),f306(f228(x101452),f306(f306(f8(f872(x101452,a859),a859,x101452),f88(x101452)),f306(f306(f7(x101452,f872(x101452,a859),f872(x101452,a859)),f306(f306(f8(f872(x101452,f872(a859,a859)),f872(f872(x101452,a859),f872(x101452,a859)),x101452),f18(x101452,a859,a859)),f306(f306(f8(f872(x101452,a859),f872(x101452,f872(a859,a859)),x101452),f306(f8(a859,f872(a859,a859),x101452),a304)),f306(f306(f7(x101452,f872(x101452,x101452),f872(x101452,a859)),f306(f306(f8(f872(x101452,a859),f872(f872(x101452,x101452),f872(x101452,a859)),x101452),f8(x101452,a859,x101452)),a303)),f306(f225(x101452),x101453))))),f306(f306(f7(x101452,f872(x101452,a859),a859),f308(x101452)),x101451))))),f306(f306(f225(x101452),x101453),f12(x101452,f219(x101452),x101451))) % 187.68/187.66 [10146]~P108(x101462)+E(x101461,f185(f872(x101462,a859)))+~P1(f306(f63(x101462),x101461))+E(f11(x101462,f225(x101462),f306(f228(x101462),f306(f306(f8(f872(x101462,a859),a859,x101462),f88(x101462)),f306(f306(f7(x101462,f872(x101462,a859),f872(x101462,a859)),f306(f306(f8(f872(x101462,f872(a859,a859)),f872(f872(x101462,a859),f872(x101462,a859)),x101462),f18(x101462,a859,a859)),f306(f306(f8(f872(x101462,a859),f872(x101462,f872(a859,a859)),x101462),f306(f8(a859,f872(a859,a859),x101462),a304)),f306(f306(f7(x101462,f872(x101462,x101462),f872(x101462,a859)),f306(f306(f8(f872(x101462,a859),f872(f872(x101462,x101462),f872(x101462,a859)),x101462),f8(x101462,a859,x101462)),a303)),f306(f219(x101462),x101463))))),f306(f306(f7(x101462,f872(x101462,a859),a859),f308(x101462)),x101461))))),f306(f306(f219(x101462),x101463),f11(x101462,f225(x101462),x101461))) % 187.68/187.66 [9889]~P112(x98891)+~E(x98893,f2(x98891))+~E(x98892,f2(x98891))+E(f306(f306(f81(x98891),f306(f306(f237(x98891),x98892),f306(f111(a865),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104))))),f306(f306(f237(x98891),x98893),f306(f111(a865),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104))))),f2(x98891)) % 187.68/187.66 [10033]~P111(x100331)+~P1(f306(f306(f220(x100331),f2(x100331)),x100333))+P1(f306(f306(f220(x100331),x100332),x100333))+~P1(f306(f306(f220(x100331),f306(f306(f237(x100331),x100332),f306(f111(a865),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104))))),f306(f306(f237(x100331),x100333),f306(f111(a865),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)))))) % 187.68/187.66 [10081]~P112(x100812)+~E(x100811,f2(x100812))+~E(x100813,f2(x100812))+~P1(f306(f306(f221(x100812),f2(x100812)),f306(f306(f81(x100812),f306(f306(f237(x100812),x100813),f306(f111(a865),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104))))),f306(f306(f237(x100812),x100811),f306(f111(a865),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104))))))) % 187.68/187.66 [9263]E(x92631,x92632)+~E(f714(x92631,x92632,x92634,x92633),f716(x92631,x92632,x92634,x92633))+P1(f306(f306(f308(f871(f866(x92633),f866(x92633))),f306(f306(f236(f866(x92633),f866(x92633)),x92632),x92631)),f139(x92633,x92634)))+P1(f306(f306(f308(f871(f866(x92633),f866(x92633))),f306(f306(f236(f866(x92633),f866(x92633)),x92631),x92632)),f139(x92633,x92634))) % 187.68/187.66 [4804]~P61(x48042)+~E(x48044,f2(x48042))+~E(x48041,f2(x48042))+E(x48041,f306(f306(f264(x48042),x48043),x48044)) % 187.68/187.66 [4805]~P61(x48051)+~E(x48053,f2(x48051))+~E(x48054,f2(x48051))+E(f306(f306(f264(x48051),x48052),x48053),x48054) % 187.68/187.66 [4916]~P61(x49162)+E(x49161,f2(x49162))+~E(x49163,f2(x49162))+~E(x49161,f306(f306(f264(x49162),x49164),x49163)) % 187.68/187.66 [4917]~P61(x49172)+E(x49171,f2(x49172))+~E(x49173,f2(x49172))+~E(f306(f306(f264(x49172),x49174),x49173),x49171) % 187.68/187.66 [5098]~P118(x50982)+E(x50981,f2(x50982))+~E(f306(f306(f264(x50982),x50983),x50981),x50984)+E(x50983,f306(f306(f82(x50982),x50984),x50981)) % 187.68/187.66 [5100]~P118(x51002)+E(x51001,f2(x51002))+~E(f306(f306(f82(x51002),x51003),x51001),x51004)+E(x51003,f306(f306(f264(x51002),x51004),x51001)) % 187.68/187.66 [5101]~P61(x51012)+E(x51011,f2(x51012))+~E(f306(f306(f264(x51012),x51013),x51011),x51014)+E(x51013,f306(f306(f82(x51012),x51014),x51011)) % 187.68/187.66 [5102]~P61(x51022)+E(x51021,f2(x51022))+~E(f306(f306(f82(x51022),x51023),x51021),x51024)+E(x51023,f306(f306(f264(x51022),x51024),x51021)) % 187.68/187.66 [5103]~P118(x51032)+E(x51031,f2(x51032))+~E(x51033,f306(f306(f264(x51032),x51034),x51031))+E(f306(f306(f82(x51032),x51033),x51031),x51034) % 187.68/187.66 [5105]~P118(x51052)+E(x51051,f2(x51052))+~E(x51053,f306(f306(f82(x51052),x51054),x51051))+E(f306(f306(f264(x51052),x51053),x51051),x51054) % 187.68/187.66 [5106]~P61(x51062)+E(x51061,f2(x51062))+~E(x51063,f306(f306(f264(x51062),x51064),x51061))+E(f306(f306(f82(x51062),x51063),x51061),x51064) % 187.68/187.66 [5107]~P61(x51072)+E(x51071,f2(x51072))+~E(x51073,f306(f306(f82(x51072),x51074),x51071))+E(f306(f306(f264(x51072),x51073),x51071),x51074) % 187.68/187.66 [5140]~P61(x51402)+~E(x51401,f2(x51402))+~E(f306(f306(f82(x51402),x51401),x51404),x51403)+E(x51401,f306(f306(f264(x51402),x51403),x51404)) % 187.68/187.66 [5141]~P61(x51411)+~E(x51414,f2(x51411))+~E(x51412,f306(f306(f82(x51411),x51414),x51413))+E(f306(f306(f264(x51411),x51412),x51413),x51414) % 187.68/187.66 [5214]~E(x52143,x52144)+~E(x52142,x52143)+~P109(x52141)+E(f277(x52141,x52142,x52143),f306(f306(f284(x52141),x52144),f185(f872(x52141,a859)))) % 187.68/187.66 [5420]~E(f136(x54202,x54201),x54204)+~E(f121(x54202,x54201),x54203)+E(x54201,f120(x54202))+E(f306(f306(f122(x54202),x54203),f306(f306(f143(x54202),x54204),f120(x54202))),x54201) % 187.68/187.66 [6040]~P111(x60403)+E(x60401,x60402)+~E(f306(f306(f237(x60403),x60404),x60401),f306(f306(f237(x60403),x60404),x60402))+~P1(f306(f306(f221(x60403),f79(x60403)),x60404)) % 187.68/187.66 [6041]E(x60411,x60412)+~E(f306(f306(f284(x60413),x60414),x60411),f306(f306(f284(x60413),x60414),x60412))+P1(f306(f306(f308(x60413),x60414),x60412))+P1(f306(f306(f308(x60413),x60414),x60411)) % 187.68/187.66 [6078]E(f306(x60781,x60782),f2(a865))+~E(f306(f306(f6(x60783,a865),x60781),x60784),f2(a865))+~P1(f306(f63(x60783),x60784))+~P1(f306(f306(f308(x60783),x60782),x60784)) % 187.68/187.66 [6079]E(f306(x60791,x60792),f79(a865))+~E(f306(f306(f9(x60793,a865),x60791),x60794),f79(a865))+~P1(f306(f63(x60793),x60794))+~P1(f306(f306(f308(x60793),x60792),x60794)) % 187.68/187.66 [6299]~P109(x62991)+~P1(f306(f306(f220(x62991),x62994),x62993))+P1(f306(f306(f220(x62991),x62992),x62993))+~P1(f306(f306(f220(x62991),x62992),x62994)) % 187.68/187.66 [6300]~P106(x63001)+~P1(f306(f306(f220(x63001),x63002),x63004))+P1(f306(f306(f220(x63001),x63002),x63003))+~P1(f306(f306(f220(x63001),x63004),x63003)) % 187.68/187.66 [6301]~P109(x63011)+~P1(f306(f306(f221(x63011),x63014),x63013))+P1(f306(f306(f221(x63011),x63012),x63013))+~P1(f306(f306(f220(x63011),x63012),x63014)) % 187.68/187.66 [6302]~P109(x63021)+~P1(f306(f306(f221(x63021),x63022),x63024))+P1(f306(f306(f221(x63021),x63022),x63023))+~P1(f306(f306(f220(x63021),x63024),x63023)) % 187.68/187.66 [6303]~P109(x63031)+~P1(f306(f306(f221(x63031),x63034),x63033))+P1(f306(f306(f221(x63031),x63032),x63033))+~P1(f306(f306(f221(x63031),x63032),x63034)) % 187.68/187.66 [6304]~P106(x63041)+~P1(f306(f306(f221(x63041),x63042),x63044))+P1(f306(f306(f221(x63041),x63042),x63043))+~P1(f306(f306(f220(x63041),x63044),x63043)) % 187.68/187.66 [6305]~P106(x63051)+~P1(f306(f306(f221(x63051),x63054),x63053))+P1(f306(f306(f221(x63051),x63052),x63053))+~P1(f306(f306(f220(x63051),x63052),x63054)) % 187.68/187.66 [6306]~P106(x63061)+~P1(f306(f306(f221(x63061),x63062),x63064))+P1(f306(f306(f221(x63061),x63062),x63063))+~P1(f306(f306(f221(x63061),x63064),x63063)) % 187.68/187.66 [6390]~P38(x63904,x63903,x63902)+E(x63901,f796(x63902,x63903,x63904))+~P1(f306(x63903,x63901))+~P1(f306(f306(f308(x63904),x63901),f306(f164(x63904),x63902))) % 187.68/187.66 [6533]~P6(x65331)+~P1(f306(f306(f220(x65331),x65332),f42(x65331,x65334)))+P1(f306(f306(f220(x65331),x65332),x65333))+~P1(f306(f306(f308(x65331),x65333),x65334)) % 187.68/187.66 [6683]~P108(x66831)+~P17(x66831,f306(f306(f143(x66831),x66832),x66834))+~P1(f306(f306(f308(x66831),x66833),f306(f164(x66831),x66834)))+P1(f306(f306(f220(x66831),x66832),x66833)) % 187.68/187.66 [6772]~P6(x67721)+~P1(f306(f306(f220(x67721),f41(x67721,x67724)),x67723))+P1(f306(f306(f220(x67721),x67722),x67723))+~P1(f306(f306(f308(x67721),x67722),x67724)) % 187.68/187.66 [7176]~P108(x71761)+E(f306(f306(f108(f872(x71761,a859)),f306(f276(x71761,x71762),x71763)),f306(f276(x71761,x71763),x71764)),f306(f276(x71761,x71762),x71764))+~P1(f306(f306(f220(x71761),x71763),x71764))+~P1(f306(f306(f220(x71761),x71762),x71763)) % 187.68/187.66 [7213]P38(x72131,x72132,x72133)+~E(f800(x72133,x72132,x72131,x72134),x72134)+~P1(f306(x72132,x72134))+~P1(f306(f306(f308(x72131),x72134),f306(f164(x72131),x72133))) % 187.68/187.66 [7286]~P108(x72861)+E(f306(f306(f108(f872(x72861,a859)),f306(f276(x72861,x72862),x72863)),f277(x72861,x72863,x72864)),f277(x72861,x72862,x72864))+~P1(f306(f306(f220(x72861),x72863),x72864))+~P1(f306(f306(f220(x72861),x72862),x72863)) % 187.68/187.66 [7352]~P108(x73521)+E(f306(f306(f108(f872(x73521,a859)),f280(x73521,x73522,x73523)),f306(f276(x73521,x73523),x73524)),f280(x73521,x73522,x73524))+~P1(f306(f306(f220(x73521),x73523),x73524))+~P1(f306(f306(f221(x73521),x73522),x73523)) % 187.68/187.66 [7372]~P108(x73721)+E(f306(f306(f108(f872(x73721,a859)),f277(x73721,x73722,x73723)),f280(x73721,x73723,x73724)),f306(f276(x73721,x73722),x73724))+~P1(f306(f306(f220(x73721),x73722),x73723))+~P1(f306(f306(f221(x73721),x73723),x73724)) % 187.68/187.66 [7404]~P108(x74041)+E(f306(f306(f108(f872(x74041,a859)),f280(x74041,x74042,x74043)),f277(x74041,x74043,x74044)),f279(x74041,x74042,x74044))+~P1(f306(f306(f220(x74041),x74043),x74044))+~P1(f306(f306(f221(x74041),x74042),x74043)) % 187.68/187.66 [7405]~P108(x74051)+E(f306(f306(f108(f872(x74051,a859)),f279(x74051,x74052,x74053)),f280(x74051,x74053,x74054)),f280(x74051,x74052,x74054))+~P1(f306(f306(f220(x74051),x74052),x74053))+~P1(f306(f306(f221(x74051),x74053),x74054)) % 187.68/187.66 [7406]~P108(x74061)+E(f306(f306(f108(f872(x74061,a859)),f279(x74061,x74062,x74063)),f279(x74061,x74063,x74064)),f279(x74061,x74062,x74064))+~P1(f306(f306(f220(x74061),x74063),x74064))+~P1(f306(f306(f220(x74061),x74062),x74063)) % 187.68/187.66 [7407]~P108(x74071)+E(f306(f306(f108(f872(x74071,a859)),f277(x74071,x74072,x74073)),f279(x74071,x74073,x74074)),f277(x74071,x74072,x74074))+~P1(f306(f306(f220(x74071),x74073),x74074))+~P1(f306(f306(f220(x74071),x74072),x74073)) % 187.68/187.66 [8205]P28(x82051,x82052,f455(x82053,x82052,x82054,x82051),x82054)+~P1(f306(f63(x82052),x82053))+~P1(f306(f63(x82051),x82054))+~P1(f306(f306(f220(a865),f306(f39(x82051),x82054)),f306(f39(x82052),x82053))) % 187.68/187.66 [8226]P38(x82261,x82262,x82263)+~P1(f306(x82262,x82264))+P1(f306(x82262,f800(x82263,x82262,x82261,x82264)))+~P1(f306(f306(f308(x82261),x82264),f306(f164(x82261),x82263))) % 187.68/187.66 [8277]~P75(x82771)+~E(f306(x82773,f574(x82773,x82774,x82772,x82771)),f79(x82771))+E(f306(f306(f306(f67(x82771,x82772,f82(x82771)),x82773),f79(x82771)),x82774),f79(x82771))+~P1(f306(f63(x82772),x82774)) % 187.68/187.66 [8555]~P111(x85551)+~P1(f306(f306(f220(x85551),f2(x85551)),x85553))+P1(f306(f306(f220(x85551),x85552),x85553))+~P1(f306(f306(f220(x85551),f306(f306(f237(x85551),x85552),f306(a119,x85554))),f306(f306(f237(x85551),x85553),f306(a119,x85554)))) % 187.68/187.66 [8710]~P41(f872(x87104,a859),f872(x87104,a859),x87103)+P1(f306(x87101,x87102))+~P1(f306(x87101,f579(x87101,x87103,x87102,x87104)))+~P1(f306(f306(f308(x87104),x87102),f102(f872(x87104,a859),x87103))) % 187.68/187.66 [8848]P38(x88481,x88482,x88483)+~P1(f306(x88482,x88484))+~P1(f306(f306(f308(x88481),x88484),f306(f164(x88481),x88483)))+P1(f306(f306(f308(x88481),f800(x88483,x88482,x88481,x88484)),f306(f164(x88481),x88483))) % 187.68/187.66 [8935]~P75(x89351)+E(f306(f306(f306(f67(x89351,x89352,f82(x89351)),x89353),f79(x89351)),x89354),f79(x89351))+~P1(f306(f63(x89352),x89354))+P1(f306(f306(f308(x89352),f574(x89353,x89354,x89352,x89351)),x89354)) % 187.68/187.66 [9429]~P1(f306(f306(f220(a1),x94294),f2(a1)))+P1(f306(f306(f220(a1),f306(f306(f81(a1),f306(f306(f82(a1),x94291),f46(a1,x94292,x94293))),x94294)),f2(a1)))+~P1(f306(f306(f221(a1),f2(a1)),x94293))+~P1(f306(f306(f221(a1),x94291),x94294)) % 187.68/187.66 [9880]~P1(f306(f63(x98801),x98802))+~P1(f306(f306(f308(x98801),x98804),x98802))+~P1(f306(f306(f308(x98801),x98803),x98802))+P1(f306(f306(f221(a865),f306(f39(x98801),f306(f306(f22(f872(x98801,a859)),f306(f306(f22(f872(x98801,a859)),x98802),f306(f306(f284(x98801),x98803),f185(f872(x98801,a859))))),f306(f306(f284(x98801),x98804),f185(f872(x98801,a859)))))),f306(f39(x98801),x98802))) % 187.68/187.66 [6886]~P108(x68861)+~P1(f306(f306(f220(x68861),x68862),x68864))+~P1(f306(f306(f220(x68861),x68862),x68863))+P1(f306(f306(f220(x68861),x68862),f306(f306(f225(x68861),x68863),x68864))) % 187.68/187.66 [6889]~P103(x68891)+~P1(f306(f306(f220(x68891),x68892),x68894))+~P1(f306(f306(f220(x68891),x68892),x68893))+P1(f306(f306(f220(x68891),x68892),f306(f306(f109(x68891),x68893),x68894))) % 187.68/187.66 [6890]~P108(x68901)+~P1(f306(f306(f221(x68901),x68902),x68904))+~P1(f306(f306(f221(x68901),x68902),x68903))+P1(f306(f306(f221(x68901),x68902),f306(f306(f225(x68901),x68903),x68904))) % 187.68/187.66 [6909]~P62(x69092)+E(x69091,f2(x69092))+E(f306(f306(f264(x69092),f306(f306(f237(x69092),x69091),x69093)),f306(f306(f237(x69092),x69091),x69094)),f306(f306(f237(x69092),x69091),f306(f306(f22(a865),x69093),x69094)))+~P1(f306(f306(f220(a865),x69094),x69093)) % 187.68/187.66 [6954]~P108(x69541)+~P17(x69541,f306(f306(f143(x69541),x69543),x69544))+P17(x69541,f306(f306(f143(x69541),x69542),f306(f306(f143(x69541),x69543),x69544)))+~P1(f306(f306(f220(x69541),x69542),x69543)) % 187.68/187.66 [6995]~P86(x69951)+~P1(f306(f306(f220(x69951),f2(x69951)),x69954))+~P1(f306(f306(f220(x69951),x69952),x69953))+P1(f306(f306(f220(x69951),x69952),f306(f306(f81(x69951),x69953),x69954))) % 187.68/187.66 [6996]~P86(x69961)+~P1(f306(f306(f220(x69961),f2(x69961)),x69963))+~P1(f306(f306(f220(x69961),x69962),x69964))+P1(f306(f306(f220(x69961),x69962),f306(f306(f81(x69961),x69963),x69964))) % 187.68/187.66 [6997]~P111(x69971)+~P1(f306(f306(f221(x69971),f2(x69971)),x69973))+~P1(f306(f306(f221(x69971),x69972),x69974))+P1(f306(f306(f221(x69971),x69972),f306(f306(f81(x69971),x69973),x69974))) % 187.68/187.66 [6998]~P86(x69981)+~P1(f306(f306(f220(x69981),x69982),x69984))+~P1(f306(f306(f221(x69981),f2(x69981)),x69983))+P1(f306(f306(f221(x69981),x69982),f306(f306(f81(x69981),x69983),x69984))) % 187.68/187.66 [6999]~P86(x69991)+~P1(f306(f306(f220(x69991),f2(x69991)),x69993))+~P1(f306(f306(f221(x69991),x69992),x69994))+P1(f306(f306(f221(x69991),x69992),f306(f306(f81(x69991),x69993),x69994))) % 187.68/187.66 [7038]~P108(x70381)+P1(f306(f306(f220(x70381),x70382),x70383))+P1(f306(f306(f220(x70381),x70382),x70384))+~P1(f306(f306(f220(x70381),x70382),f306(f306(f219(x70381),x70384),x70383))) % 187.68/187.66 [7039]~P108(x70391)+P1(f306(f306(f221(x70391),x70392),x70393))+P1(f306(f306(f221(x70391),x70392),x70394))+~P1(f306(f306(f221(x70391),x70392),f306(f306(f219(x70391),x70394),x70393))) % 187.68/187.66 [7325]~P109(x73252)+~P60(x73251)+~P1(f306(f306(f221(f872(x73251,x73252)),x73253),x73254))+P1(f306(f306(f220(f872(x73251,x73252)),x73253),x73254)) % 187.68/187.66 [7692]~P64(x76921)+~P1(f306(f306(f221(x76921),x76924),f2(x76921)))+~P1(f306(f306(f220(x76921),x76923),f306(f306(f264(x76921),x76922),x76924)))+P1(f306(f306(f220(x76921),x76922),f306(f306(f82(x76921),x76923),x76924))) % 187.68/187.66 [7693]~P64(x76931)+~P1(f306(f306(f221(x76931),x76934),f2(x76931)))+~P1(f306(f306(f220(x76931),x76933),f306(f306(f82(x76931),x76932),x76934)))+P1(f306(f306(f220(x76931),x76932),f306(f306(f264(x76931),x76933),x76934))) % 187.68/187.66 [7694]~P64(x76941)+~P1(f306(f306(f221(x76941),x76944),f2(x76941)))+~P1(f306(f306(f221(x76941),x76943),f306(f306(f264(x76941),x76942),x76944)))+P1(f306(f306(f221(x76941),x76942),f306(f306(f82(x76941),x76943),x76944))) % 187.68/187.66 [7695]~P64(x76951)+~P1(f306(f306(f221(x76951),x76954),f2(x76951)))+~P1(f306(f306(f221(x76951),x76953),f306(f306(f82(x76951),x76952),x76954)))+P1(f306(f306(f221(x76951),x76952),f306(f306(f264(x76951),x76953),x76954))) % 187.68/187.66 [7801]~P134(x78011)+~P1(f306(f306(f220(x78011),x78012),f2(x78011)))+~P1(f306(f306(f220(x78011),x78014),x78013))+P1(f306(f306(f220(x78011),f306(f306(f82(x78011),x78012),x78013)),f306(f306(f82(x78011),x78012),x78014))) % 187.68/187.66 [7802]~P122(x78021)+~P1(f306(f306(f221(x78021),x78022),f2(x78021)))+~P1(f306(f306(f220(x78021),x78024),x78023))+P1(f306(f306(f220(x78021),f306(f306(f82(x78021),x78022),x78023)),f306(f306(f82(x78021),x78022),x78024))) % 187.68/187.66 [7803]~P134(x78031)+~P1(f306(f306(f220(x78031),x78033),f2(x78031)))+~P1(f306(f306(f220(x78031),x78034),x78032))+P1(f306(f306(f220(x78031),f306(f306(f82(x78031),x78032),x78033)),f306(f306(f82(x78031),x78034),x78033))) % 187.68/187.66 [7804]~P63(x78041)+~P1(f306(f306(f220(x78041),x78043),f2(x78041)))+~P1(f306(f306(f220(x78041),x78044),x78042))+P1(f306(f306(f220(x78041),f306(f306(f264(x78041),x78042),x78043)),f306(f306(f264(x78041),x78044),x78043))) % 187.68/187.66 [7808]~P122(x78081)+~P1(f306(f306(f221(x78081),x78083),f2(x78081)))+~P1(f306(f306(f221(x78081),x78084),x78082))+P1(f306(f306(f221(x78081),f306(f306(f82(x78081),x78082),x78083)),f306(f306(f82(x78081),x78084),x78083))) % 187.68/187.66 [7809]~P122(x78091)+~P1(f306(f306(f221(x78091),x78092),f2(x78091)))+~P1(f306(f306(f221(x78091),x78094),x78093))+P1(f306(f306(f221(x78091),f306(f306(f82(x78091),x78092),x78093)),f306(f306(f82(x78091),x78092),x78094))) % 187.68/187.66 [7810]~P64(x78101)+~P1(f306(f306(f221(x78101),x78103),f2(x78101)))+~P1(f306(f306(f221(x78101),x78104),x78102))+P1(f306(f306(f221(x78101),f306(f306(f264(x78101),x78102),x78103)),f306(f306(f264(x78101),x78104),x78103))) % 187.68/187.66 [7811]~P111(x78111)+~P1(f306(f306(f221(x78111),f79(x78111)),x78112))+~P1(f306(f306(f220(a865),x78113),x78114))+P1(f306(f306(f220(x78111),f306(f306(f237(x78111),x78112),x78113)),f306(f306(f237(x78111),x78112),x78114))) % 187.68/187.66 [7812]~P111(x78121)+~P1(f306(f306(f220(x78121),f79(x78121)),x78122))+~P1(f306(f306(f220(a865),x78123),x78124))+P1(f306(f306(f220(x78121),f306(f306(f237(x78121),x78122),x78123)),f306(f306(f237(x78121),x78122),x78124))) % 187.68/187.66 [7814]~P111(x78141)+~P1(f306(f306(f221(x78141),f79(x78141)),x78142))+~P1(f306(f306(f221(a865),x78143),x78144))+P1(f306(f306(f221(x78141),f306(f306(f237(x78141),x78142),x78143)),f306(f306(f237(x78141),x78142),x78144))) % 187.68/187.66 [7841]P1(f306(f306(f221(a865),f2(a865)),f306(x78411,x78412)))+~P1(f306(f63(x78413),x78414))+~P1(f306(f306(f308(x78413),x78412),x78414))+~P1(f306(f306(f221(a865),f2(a865)),f306(f306(f9(x78413,a865),x78411),x78414))) % 187.68/187.66 [7850]~P136(x78501)+~P1(f306(f306(f220(x78501),x78503),x78504))+~P1(f306(f306(f220(x78501),f2(x78501)),x78502))+P1(f306(f306(f220(x78501),f306(f306(f82(x78501),x78502),x78503)),f306(f306(f82(x78501),x78502),x78504))) % 187.68/187.66 [7851]~P135(x78511)+~P1(f306(f306(f220(x78511),x78513),x78514))+~P1(f306(f306(f220(x78511),f2(x78511)),x78512))+P1(f306(f306(f220(x78511),f306(f306(f82(x78511),x78512),x78513)),f306(f306(f82(x78511),x78512),x78514))) % 187.68/187.66 [7852]~P122(x78521)+~P1(f306(f306(f221(x78521),f2(x78521)),x78522))+~P1(f306(f306(f220(x78521),x78523),x78524))+P1(f306(f306(f220(x78521),f306(f306(f82(x78521),x78522),x78523)),f306(f306(f82(x78521),x78522),x78524))) % 187.68/187.66 [7853]~P136(x78531)+~P1(f306(f306(f220(x78531),x78532),x78534))+~P1(f306(f306(f220(x78531),f2(x78531)),x78533))+P1(f306(f306(f220(x78531),f306(f306(f82(x78531),x78532),x78533)),f306(f306(f82(x78531),x78534),x78533))) % 187.68/187.66 [7854]~P111(x78541)+~P1(f306(f306(f220(x78541),x78542),x78544))+~P1(f306(f306(f220(x78541),f2(x78541)),x78542))+P1(f306(f306(f220(x78541),f306(f306(f237(x78541),x78542),x78543)),f306(f306(f237(x78541),x78544),x78543))) % 187.68/187.66 [7855]~P63(x78551)+~P1(f306(f306(f220(x78551),x78552),x78554))+~P1(f306(f306(f220(x78551),f2(x78551)),x78553))+P1(f306(f306(f220(x78551),f306(f306(f264(x78551),x78552),x78553)),f306(f306(f264(x78551),x78554),x78553))) % 187.68/187.66 [7857]~P128(x78571)+~P1(f306(f306(f221(x78571),x78573),x78574))+~P1(f306(f306(f221(x78571),f2(x78571)),x78572))+P1(f306(f306(f221(x78571),f306(f306(f82(x78571),x78572),x78573)),f306(f306(f82(x78571),x78572),x78574))) % 187.68/187.66 [7858]~P120(x78581)+~P1(f306(f306(f221(x78581),x78583),x78584))+~P1(f306(f306(f221(x78581),f2(x78581)),x78582))+P1(f306(f306(f221(x78581),f306(f306(f82(x78581),x78582),x78583)),f306(f306(f82(x78581),x78582),x78584))) % 187.68/187.66 [7859]~P122(x78591)+~P1(f306(f306(f221(x78591),x78592),x78594))+~P1(f306(f306(f221(x78591),f2(x78591)),x78593))+P1(f306(f306(f221(x78591),f306(f306(f82(x78591),x78592),x78593)),f306(f306(f82(x78591),x78594),x78593))) % 187.68/187.66 [7860]~P128(x78601)+~P1(f306(f306(f221(x78601),x78602),x78604))+~P1(f306(f306(f221(x78601),f2(x78601)),x78603))+P1(f306(f306(f221(x78601),f306(f306(f82(x78601),x78602),x78603)),f306(f306(f82(x78601),x78604),x78603))) % 187.68/187.66 [7861]~P122(x78611)+~P1(f306(f306(f221(x78611),x78613),x78614))+~P1(f306(f306(f221(x78611),f2(x78611)),x78612))+P1(f306(f306(f221(x78611),f306(f306(f82(x78611),x78612),x78613)),f306(f306(f82(x78611),x78612),x78614))) % 187.68/187.66 [7862]~P64(x78621)+~P1(f306(f306(f221(x78621),x78622),x78624))+~P1(f306(f306(f221(x78621),f2(x78621)),x78623))+P1(f306(f306(f221(x78621),f306(f306(f264(x78621),x78622),x78623)),f306(f306(f264(x78621),x78624),x78623))) % 187.68/187.66 [7905]~P107(x79052)+P1(f306(f306(f221(f872(x79051,x79052)),x79054),x79053))+~P1(f306(f306(f220(f872(x79051,x79052)),x79054),x79053))+P1(f306(f306(f220(f872(x79051,x79052)),x79053),x79054)) % 187.68/187.66 [7947]P1(f306(f306(f308(x79471),x79472),x79473))+P1(f306(f306(f308(x79471),x79472),x79474))+~P1(f306(f306(f220(f872(x79471,a859)),x79474),x79473))+P1(f306(f306(f221(f872(x79471,a859)),x79474),f306(f306(f284(x79471),x79472),x79473))) % 187.68/187.66 [8110]P1(f306(f306(f308(x81101),x81102),x81103))+P1(f306(f306(f308(x81101),x81102),x81104))+~P1(f306(f306(f221(f872(x81101,a859)),x81104),f306(f306(f284(x81101),x81102),x81103)))+P1(f306(f306(f220(f872(x81101,a859)),x81104),x81103)) % 187.68/187.66 [8119]~P60(x81191)+P13(x81191,x81192,x81193)+~P1(f306(x81192,x81194))+~P1(f306(f306(f308(f866(x81191)),x81194),f306(f164(f866(x81191)),f56(x81191,x81193,f57(x81191))))) % 187.68/187.66 [8129]~P14(x81293,x81291,x81294)+~P60(x81293)+P1(f306(x81291,x81292))+~P1(f306(f306(f308(f866(x81293)),x81292),f306(f164(f866(x81293)),f56(x81293,x81294,f57(x81293))))) % 187.68/187.66 [8182]~P122(x81821)+P1(f306(f306(f221(x81821),x81823),x81822))+P1(f306(f306(f221(x81821),x81822),x81823))+~P1(f306(f306(f221(x81821),f306(f306(f82(x81821),x81824),x81822)),f306(f306(f82(x81821),x81824),x81823))) % 187.68/187.66 [8183]~P122(x81831)+P1(f306(f306(f221(x81831),x81833),x81832))+P1(f306(f306(f221(x81831),x81832),x81833))+~P1(f306(f306(f221(x81831),f306(f306(f82(x81831),x81832),x81834)),f306(f306(f82(x81831),x81833),x81834))) % 187.68/187.66 [8194]~P122(x81941)+P1(f306(f306(f221(x81941),x81944),f2(x81941)))+P1(f306(f306(f221(x81941),x81942),x81943))+~P1(f306(f306(f221(x81941),f306(f306(f82(x81941),x81942),x81944)),f306(f306(f82(x81941),x81943),x81944))) % 187.68/187.66 [8195]~P122(x81951)+P1(f306(f306(f221(x81951),x81954),f2(x81951)))+P1(f306(f306(f221(x81951),x81952),x81953))+~P1(f306(f306(f221(x81951),f306(f306(f82(x81951),x81954),x81952)),f306(f306(f82(x81951),x81954),x81953))) % 187.68/187.66 [8199]~P122(x81991)+P1(f306(f306(f221(x81991),x81992),x81993))+P1(f306(f306(f221(x81991),f2(x81991)),x81994))+~P1(f306(f306(f221(x81991),f306(f306(f82(x81991),x81994),x81993)),f306(f306(f82(x81991),x81994),x81992))) % 187.68/187.66 [8200]~P122(x82001)+P1(f306(f306(f221(x82001),x82002),x82003))+P1(f306(f306(f221(x82001),f2(x82001)),x82004))+~P1(f306(f306(f221(x82001),f306(f306(f82(x82001),x82003),x82004)),f306(f306(f82(x82001),x82002),x82004))) % 187.68/187.66 [8213]~P122(x82131)+P1(f306(f306(f221(x82131),x82132),f2(x82131)))+P1(f306(f306(f221(x82131),f2(x82131)),x82132))+~P1(f306(f306(f221(x82131),f306(f306(f82(x82131),x82133),x82132)),f306(f306(f82(x82131),x82134),x82132))) % 187.68/187.66 [8214]~P122(x82141)+P1(f306(f306(f221(x82141),x82142),f2(x82141)))+P1(f306(f306(f221(x82141),f2(x82141)),x82142))+~P1(f306(f306(f221(x82141),f306(f306(f82(x82141),x82142),x82143)),f306(f306(f82(x82141),x82142),x82144))) % 187.68/187.66 [8240]~P122(x82401)+~P1(f306(f306(f221(x82401),x82404),f2(x82401)))+P1(f306(f306(f220(x82401),x82402),x82403))+~P1(f306(f306(f220(x82401),f306(f306(f82(x82401),x82404),x82403)),f306(f306(f82(x82401),x82404),x82402))) % 187.68/187.66 [8241]~P122(x82411)+~P1(f306(f306(f221(x82411),x82414),f2(x82411)))+P1(f306(f306(f221(x82411),x82412),x82413))+~P1(f306(f306(f221(x82411),f306(f306(f82(x82411),x82414),x82413)),f306(f306(f82(x82411),x82414),x82412))) % 187.68/187.66 [8253]~P111(x82533)+~P1(f306(f306(f221(x82533),f79(x82533)),x82534))+P1(f306(f306(f220(a865),x82531),x82532))+~P1(f306(f306(f220(x82533),f306(f306(f237(x82533),x82534),x82531)),f306(f306(f237(x82533),x82534),x82532))) % 187.68/187.66 [8255]~P111(x82553)+~P1(f306(f306(f221(x82553),f79(x82553)),x82554))+P1(f306(f306(f221(a865),x82551),x82552))+~P1(f306(f306(f221(x82553),f306(f306(f237(x82553),x82554),x82551)),f306(f306(f237(x82553),x82554),x82552))) % 187.68/187.66 [8265]~P122(x82651)+P1(f306(f306(f220(x82651),x82652),x82653))+~P1(f306(f306(f221(x82651),f2(x82651)),x82654))+~P1(f306(f306(f220(x82651),f306(f306(f82(x82651),x82654),x82652)),f306(f306(f82(x82651),x82654),x82653))) % 187.68/187.66 [8266]~P128(x82661)+P1(f306(f306(f220(x82661),x82662),x82663))+~P1(f306(f306(f221(x82661),f2(x82661)),x82664))+~P1(f306(f306(f220(x82661),f306(f306(f82(x82661),x82664),x82662)),f306(f306(f82(x82661),x82664),x82663))) % 187.68/187.66 [8267]~P128(x82671)+P1(f306(f306(f220(x82671),x82672),x82673))+~P1(f306(f306(f221(x82671),f2(x82671)),x82674))+~P1(f306(f306(f220(x82671),f306(f306(f82(x82671),x82672),x82674)),f306(f306(f82(x82671),x82673),x82674))) % 187.68/187.66 [8268]~P122(x82681)+P1(f306(f306(f221(x82681),x82682),x82683))+~P1(f306(f306(f221(x82681),f2(x82681)),x82684))+~P1(f306(f306(f221(x82681),f306(f306(f82(x82681),x82684),x82682)),f306(f306(f82(x82681),x82684),x82683))) % 187.68/187.66 [8269]~P128(x82691)+P1(f306(f306(f221(x82691),x82692),x82693))+~P1(f306(f306(f220(x82691),f2(x82691)),x82694))+~P1(f306(f306(f221(x82691),f306(f306(f82(x82691),x82694),x82692)),f306(f306(f82(x82691),x82694),x82693))) % 187.68/187.66 [8270]~P129(x82701)+P1(f306(f306(f221(x82701),x82702),x82703))+~P1(f306(f306(f220(x82701),f2(x82701)),x82704))+~P1(f306(f306(f221(x82701),f306(f306(f82(x82701),x82704),x82702)),f306(f306(f82(x82701),x82704),x82703))) % 187.68/187.66 [8271]~P111(x82711)+~P1(f306(f306(f220(x82711),f2(x82711)),x82713))+P1(f306(f306(f221(x82711),x82712),x82713))+~P1(f306(f306(f221(x82711),f306(f306(f237(x82711),x82712),x82714)),f306(f306(f237(x82711),x82713),x82714))) % 187.68/187.66 [8272]~P128(x82721)+P1(f306(f306(f221(x82721),x82722),x82723))+~P1(f306(f306(f220(x82721),f2(x82721)),x82724))+~P1(f306(f306(f221(x82721),f306(f306(f82(x82721),x82722),x82724)),f306(f306(f82(x82721),x82723),x82724))) % 187.68/187.66 [8273]~P129(x82731)+P1(f306(f306(f221(x82731),x82732),x82733))+~P1(f306(f306(f220(x82731),f2(x82731)),x82734))+~P1(f306(f306(f221(x82731),f306(f306(f82(x82731),x82732),x82734)),f306(f306(f82(x82731),x82733),x82734))) % 187.68/187.66 [8317]P1(f306(f306(f308(x83171),x83172),x83173))+~P1(f306(f306(f220(f872(x83171,a859)),x83173),x83174))+~P1(f306(f306(f221(f872(x83171,a859)),x83173),x83174))+P1(f306(f306(f221(f872(x83171,a859)),x83173),f306(f306(f284(x83171),x83172),x83174))) % 187.68/187.66 [8578]~P60(x85781)+~P93(x85782)+~E(f306(x85783,f801(x85784,x85783,x85781,x85782)),f306(x85784,f801(x85784,x85783,x85781,x85782)))+P1(f306(f306(f92(f872(x85781,x85782)),x85783),x85784)) % 187.68/187.66 [8690]E(f306(f306(f22(a1),f392(x86901,x86902,x86903,x86904)),f393(x86901,x86902,x86903,x86904)),x86904)+~P1(f306(f306(f221(a1),f2(a1)),x86903))+~P1(f306(f306(f220(a1),x86901),x86904))+P1(f306(f306(f220(a1),x86901),f306(f306(f81(a1),x86904),x86903))) % 187.68/187.66 [8691]E(f306(f306(f22(a1),f399(x86911,x86912,x86913,x86914)),f400(x86911,x86912,x86913,x86914)),x86914)+~P1(f306(f306(f221(a1),f2(a1)),x86913))+~P1(f306(f306(f221(a1),x86911),x86914))+P1(f306(f306(f221(a1),x86911),f306(f306(f81(a1),x86914),x86913))) % 187.68/187.66 [8828]~E(f306(f306(f157(x88281),x88283),f719(x88284,x88283,x88281,x88282)),f306(f306(f157(x88281),x88284),f719(x88284,x88283,x88281,x88282)))+E(f306(f306(f165(x88281),x88282),x88283),f306(f306(f165(x88281),x88282),x88284))+~P1(f306(f306(f220(a865),x88282),f306(f186(f866(x88281)),x88283)))+~P1(f306(f306(f220(a865),x88282),f306(f186(f866(x88281)),x88284))) % 187.68/187.66 [8900]~P1(f306(f306(f221(a1),f2(a1)),x89003))+~P1(f306(f306(f220(a1),x89001),x89004))+P1(f306(f306(f308(a1),f392(x89001,x89002,x89003,x89004)),x89002))+P1(f306(f306(f220(a1),x89001),f306(f306(f81(a1),x89004),x89003))) % 187.68/187.66 [8901]~P1(f306(f306(f221(a1),f2(a1)),x89013))+~P1(f306(f306(f221(a1),x89011),x89014))+P1(f306(f306(f308(a1),f399(x89011,x89012,x89013,x89014)),x89012))+P1(f306(f306(f221(a1),x89011),f306(f306(f81(a1),x89014),x89013))) % 187.68/187.66 [8944]~P108(x89441)+~P1(f306(f63(x89441),x89443))+~P1(f306(f306(f308(x89441),x89444),x89443))+P1(f306(f306(f220(x89441),f306(f306(f66(x89441,x89441,f225(x89441)),x89442),x89443)),f306(f306(f225(x89441),x89444),x89442))) % 187.68/187.66 [8945]~P103(x89451)+~P1(f306(f63(x89451),x89453))+~P1(f306(f306(f308(x89451),x89454),x89453))+P1(f306(f306(f220(x89451),f306(f306(f66(x89451,x89451,f109(x89451)),x89452),x89453)),f306(f306(f109(x89451),x89454),x89452))) % 187.68/187.66 [8992]E(f306(f306(f165(x89921),x89922),x89923),f306(f306(f165(x89921),x89922),x89924))+P1(f306(f306(f221(a865),f719(x89923,x89924,x89921,x89922)),x89922))+~P1(f306(f306(f220(a865),x89922),f306(f186(f866(x89921)),x89923)))+~P1(f306(f306(f220(a865),x89922),f306(f186(f866(x89921)),x89924))) % 187.68/187.66 [8997]~P1(f306(f306(f221(a1),f2(a1)),x89973))+~P1(f306(f306(f220(a1),x89971),x89972))+P1(f306(f306(f308(a1),f393(x89971,x89974,x89973,x89972)),f277(a1,f79(a1),x89973)))+P1(f306(f306(f220(a1),x89971),f306(f306(f81(a1),x89972),x89973))) % 187.68/187.66 [8998]~P1(f306(f306(f221(a1),f2(a1)),x89983))+~P1(f306(f306(f221(a1),x89981),x89982))+P1(f306(f306(f308(a1),f400(x89981,x89984,x89983,x89982)),f277(a1,f79(a1),x89983)))+P1(f306(f306(f221(a1),x89981),f306(f306(f81(a1),x89982),x89983))) % 187.68/187.66 [9163]~E(f306(f169(x91631,x91632),x91633),f306(f169(x91631,x91632),x91634))+E(f306(f164(f871(x91631,x91632)),x91633),f306(f164(f871(x91631,x91632)),x91634))+~P1(f306(f129(x91631),f306(f306(f146(f871(x91631,x91632),x91631),f235(x91631,x91632)),x91634)))+~P1(f306(f129(x91631),f306(f306(f146(f871(x91631,x91632),x91631),f235(x91631,x91632)),x91633))) % 187.68/187.66 [9175]E(f306(f169(x91751,x91752),x91753),f306(f169(x91751,x91752),x91754))+~E(f306(f164(f871(x91751,x91752)),x91753),f306(f164(f871(x91751,x91752)),x91754))+~P1(f306(f129(x91751),f306(f306(f146(f871(x91751,x91752),x91751),f235(x91751,x91752)),x91754)))+~P1(f306(f129(x91751),f306(f306(f146(f871(x91751,x91752),x91751),f235(x91751,x91752)),x91753))) % 187.68/187.66 [9321]~P108(x93211)+~P1(f306(f63(x93211),x93214))+P1(f306(f306(f308(x93211),f648(x93212,x93213,x93214,x93211)),x93214))+P1(f306(f306(f220(x93211),f306(f306(f66(x93211,x93211,f219(x93211)),x93212),x93214)),f306(f306(f219(x93211),x93213),x93212))) % 187.68/187.66 [9322]~P97(x93221)+~P1(f306(f63(x93221),x93224))+P1(f306(f306(f308(x93221),f652(x93222,x93223,x93224,x93221)),x93224))+P1(f306(f306(f220(x93221),f306(f306(f66(x93221,x93221,f108(x93221)),x93222),x93224)),f306(f306(f108(x93221),x93223),x93222))) % 187.68/187.66 [9447]~P108(x94471)+~P1(f306(f63(x94471),x94473))+~P1(f306(f306(f220(x94471),f648(x94472,x94474,x94473,x94471)),x94474))+P1(f306(f306(f220(x94471),f306(f306(f66(x94471,x94471,f219(x94471)),x94472),x94473)),f306(f306(f219(x94471),x94474),x94472))) % 187.68/187.66 [9448]~P97(x94481)+~P1(f306(f63(x94481),x94483))+~P1(f306(f306(f220(x94481),f652(x94482,x94484,x94483,x94481)),x94484))+P1(f306(f306(f220(x94481),f306(f306(f66(x94481,x94481,f108(x94481)),x94482),x94483)),f306(f306(f108(x94481),x94484),x94482))) % 187.68/187.66 [9451]~P1(f306(f306(f220(a1),f2(a1)),x94514))+~P1(f306(f306(f221(a1),f2(a1)),x94513))+~P1(f306(f306(f221(a1),x94514),x94511))+P1(f306(f306(f221(a1),f306(f306(f81(a1),f306(f306(f82(a1),x94511),f46(a1,x94512,x94513))),x94514)),f306(f306(f82(a1),x94511),x94513))) % 187.68/187.66 [9849]E(x98491,x98492)+P1(f306(f306(f308(f871(f866(x98493),f866(x98493))),f306(f306(f236(f866(x98493),f866(x98493)),x98492),x98491)),f139(x98493,x98494)))+P1(f306(f306(f308(f871(f866(x98493),f866(x98493))),f306(f306(f236(f866(x98493),f866(x98493)),x98491),x98492)),f139(x98493,x98494)))+~P1(f306(f306(f308(f871(x98493,x98493)),f306(f306(f236(x98493,x98493),f714(x98491,x98492,x98494,x98493)),f716(x98491,x98492,x98494,x98493))),x98494)) % 187.68/187.66 [9850]E(x98501,x98502)+P1(f306(f306(f308(f871(f866(x98503),f866(x98503))),f306(f306(f236(f866(x98503),f866(x98503)),x98502),x98501)),f139(x98503,x98504)))+P1(f306(f306(f308(f871(f866(x98503),f866(x98503))),f306(f306(f236(f866(x98503),f866(x98503)),x98501),x98502)),f139(x98503,x98504)))+~P1(f306(f306(f308(f871(x98503,x98503)),f306(f306(f236(x98503,x98503),f716(x98501,x98502,x98504,x98503)),f714(x98501,x98502,x98504,x98503))),x98504)) % 187.68/187.66 [7394]~P108(x73941)+~P1(f306(f306(f220(x73941),x73943),x73944))+~P1(f306(f306(f220(x73941),x73942),x73944))+P1(f306(f306(f220(x73941),f306(f306(f219(x73941),x73942),x73943)),x73944)) % 187.68/187.66 [7397]~P97(x73971)+~P1(f306(f306(f220(x73971),x73973),x73974))+~P1(f306(f306(f220(x73971),x73972),x73974))+P1(f306(f306(f220(x73971),f306(f306(f108(x73971),x73972),x73973)),x73974)) % 187.68/187.66 [7398]~P108(x73981)+~P1(f306(f306(f221(x73981),x73983),x73984))+~P1(f306(f306(f221(x73981),x73982),x73984))+P1(f306(f306(f221(x73981),f306(f306(f219(x73981),x73982),x73983)),x73984)) % 187.68/187.66 [7715]~E(x77151,x77153)+E(f131(a865,f306(f276(a865,x77151),x77152)),f306(f306(f143(a865),x77153),x77154))+~E(f131(a865,f306(f276(a865,f306(f306(f81(a865),x77151),f79(a865))),x77152)),x77154)+~P1(f306(f306(f221(a865),x77151),x77152)) % 187.68/187.66 [7726]~P108(x77261)+P1(f306(f306(f220(x77261),x77262),x77263))+P1(f306(f306(f220(x77261),x77264),x77263))+~P1(f306(f306(f220(x77261),f306(f306(f225(x77261),x77264),x77262)),x77263)) % 187.68/187.66 [7727]~P108(x77271)+P1(f306(f306(f221(x77271),x77272),x77273))+P1(f306(f306(f221(x77271),x77274),x77273))+~P1(f306(f306(f221(x77271),f306(f306(f225(x77271),x77274),x77272)),x77273)) % 187.68/187.66 [8009]~P63(x80091)+~P1(f306(f306(f221(x80091),f2(x80091)),x80093))+~P1(f306(f306(f220(x80091),x80092),f306(f306(f264(x80091),x80094),x80093)))+P1(f306(f306(f220(x80091),f306(f306(f82(x80091),x80092),x80093)),x80094)) % 187.68/187.66 [8010]~P64(x80101)+~P1(f306(f306(f221(x80101),f2(x80101)),x80103))+~P1(f306(f306(f220(x80101),x80102),f306(f306(f264(x80101),x80104),x80103)))+P1(f306(f306(f220(x80101),f306(f306(f82(x80101),x80102),x80103)),x80104)) % 187.68/187.66 [8011]~P63(x80111)+~P1(f306(f306(f221(x80111),f2(x80111)),x80113))+~P1(f306(f306(f220(x80111),x80112),f306(f306(f82(x80111),x80114),x80113)))+P1(f306(f306(f220(x80111),f306(f306(f264(x80111),x80112),x80113)),x80114)) % 187.68/187.66 [8013]~P64(x80131)+~P1(f306(f306(f221(x80131),f2(x80131)),x80133))+~P1(f306(f306(f220(x80131),x80132),f306(f306(f82(x80131),x80134),x80133)))+P1(f306(f306(f220(x80131),f306(f306(f264(x80131),x80132),x80133)),x80134)) % 187.68/187.66 [8014]~P63(x80141)+~P1(f306(f306(f221(x80141),f2(x80141)),x80143))+~P1(f306(f306(f221(x80141),x80142),f306(f306(f264(x80141),x80144),x80143)))+P1(f306(f306(f221(x80141),f306(f306(f82(x80141),x80142),x80143)),x80144)) % 187.68/187.66 [8015]~P64(x80151)+~P1(f306(f306(f221(x80151),f2(x80151)),x80153))+~P1(f306(f306(f221(x80151),x80152),f306(f306(f264(x80151),x80154),x80153)))+P1(f306(f306(f221(x80151),f306(f306(f82(x80151),x80152),x80153)),x80154)) % 187.68/187.66 [8016]~P63(x80161)+~P1(f306(f306(f221(x80161),f2(x80161)),x80163))+~P1(f306(f306(f221(x80161),x80162),f306(f306(f82(x80161),x80164),x80163)))+P1(f306(f306(f221(x80161),f306(f306(f264(x80161),x80162),x80163)),x80164)) % 187.68/187.66 [8018]~P64(x80181)+~P1(f306(f306(f221(x80181),f2(x80181)),x80183))+~P1(f306(f306(f221(x80181),x80182),f306(f306(f82(x80181),x80184),x80183)))+P1(f306(f306(f221(x80181),f306(f306(f264(x80181),x80182),x80183)),x80184)) % 187.68/187.66 [8151]~P63(x81511)+~P1(f306(f306(f221(x81511),f2(x81511)),x81514))+P1(f306(f306(f220(x81511),x81512),f306(f306(f82(x81511),x81513),x81514)))+~P1(f306(f306(f220(x81511),f306(f306(f264(x81511),x81512),x81514)),x81513)) % 187.68/187.66 [8152]~P63(x81521)+~P1(f306(f306(f221(x81521),f2(x81521)),x81524))+P1(f306(f306(f220(x81521),x81522),f306(f306(f264(x81521),x81523),x81524)))+~P1(f306(f306(f220(x81521),f306(f306(f82(x81521),x81522),x81524)),x81523)) % 187.68/187.66 [8154]~P64(x81541)+~P1(f306(f306(f221(x81541),f2(x81541)),x81544))+P1(f306(f306(f220(x81541),x81542),f306(f306(f82(x81541),x81543),x81544)))+~P1(f306(f306(f220(x81541),f306(f306(f264(x81541),x81542),x81544)),x81543)) % 187.68/187.66 [8155]~P64(x81551)+~P1(f306(f306(f221(x81551),f2(x81551)),x81554))+P1(f306(f306(f220(x81551),x81552),f306(f306(f264(x81551),x81553),x81554)))+~P1(f306(f306(f220(x81551),f306(f306(f82(x81551),x81552),x81554)),x81553)) % 187.68/187.66 [8156]~P63(x81561)+~P1(f306(f306(f221(x81561),f2(x81561)),x81564))+P1(f306(f306(f221(x81561),x81562),f306(f306(f82(x81561),x81563),x81564)))+~P1(f306(f306(f221(x81561),f306(f306(f264(x81561),x81562),x81564)),x81563)) % 187.68/187.66 [8157]~P63(x81571)+~P1(f306(f306(f221(x81571),f2(x81571)),x81574))+P1(f306(f306(f221(x81571),x81572),f306(f306(f264(x81571),x81573),x81574)))+~P1(f306(f306(f221(x81571),f306(f306(f82(x81571),x81572),x81574)),x81573)) % 187.68/187.66 [8159]~P64(x81591)+~P1(f306(f306(f221(x81591),f2(x81591)),x81594))+P1(f306(f306(f221(x81591),x81592),f306(f306(f82(x81591),x81593),x81594)))+~P1(f306(f306(f221(x81591),f306(f306(f264(x81591),x81592),x81594)),x81593)) % 187.68/187.66 [8160]~P64(x81601)+~P1(f306(f306(f221(x81601),f2(x81601)),x81604))+P1(f306(f306(f221(x81601),x81602),f306(f306(f264(x81601),x81603),x81604)))+~P1(f306(f306(f221(x81601),f306(f306(f82(x81601),x81602),x81604)),x81603)) % 187.68/187.66 [8321]~P64(x83211)+~P1(f306(f306(f221(x83211),x83213),f2(x83211)))+~P1(f306(f306(f220(x83211),f306(f306(f264(x83211),x83214),x83213)),x83212))+P1(f306(f306(f220(x83211),f306(f306(f82(x83211),x83212),x83213)),x83214)) % 187.68/187.66 [8322]~P64(x83221)+~P1(f306(f306(f221(x83221),x83223),f2(x83221)))+~P1(f306(f306(f220(x83221),f306(f306(f82(x83221),x83224),x83223)),x83222))+P1(f306(f306(f220(x83221),f306(f306(f264(x83221),x83222),x83223)),x83224)) % 187.68/187.66 [8323]~P64(x83231)+~P1(f306(f306(f221(x83231),x83233),f2(x83231)))+~P1(f306(f306(f221(x83231),f306(f306(f264(x83231),x83234),x83233)),x83232))+P1(f306(f306(f221(x83231),f306(f306(f82(x83231),x83232),x83233)),x83234)) % 187.68/187.66 [8324]~P64(x83241)+~P1(f306(f306(f221(x83241),x83243),f2(x83241)))+~P1(f306(f306(f221(x83241),f306(f306(f82(x83241),x83244),x83243)),x83242))+P1(f306(f306(f221(x83241),f306(f306(f264(x83241),x83242),x83243)),x83244)) % 187.68/187.66 [8334]~P1(f306(x83341,x83344))+~P1(f306(f306(f221(a865),x83342),f306(f306(f82(a865),x83343),f306(a119,x83344))))+P1(f306(x83341,f306(f306(f40(a865),x83342),x83343)))+~P1(f306(f306(f220(a865),f306(f306(f82(a865),x83343),x83344)),x83342)) % 187.68/187.66 [8552]~P108(x85521)+~P1(f306(f63(x85521),x85524))+~P1(f306(f306(f308(x85521),x85522),x85524))+P1(f306(f306(f220(x85521),f306(f306(f219(x85521),x85522),x85523)),f306(f306(f66(x85521,x85521,f219(x85521)),x85523),x85524))) % 187.68/187.66 [8553]~P97(x85531)+~P1(f306(f63(x85531),x85534))+~P1(f306(f306(f308(x85531),x85532),x85534))+P1(f306(f306(f220(x85531),f306(f306(f108(x85531),x85532),x85533)),f306(f306(f66(x85531,x85531,f108(x85531)),x85533),x85534))) % 187.68/187.66 [8692]~P1(f306(f63(x86921),x86922))+E(f306(f39(x86921),f306(f306(f22(f872(x86921,a859)),x86922),f306(f306(f284(x86921),x86923),x86924))),f306(f306(f22(a865),f306(f39(x86921),f306(f306(f22(f872(x86921,a859)),x86922),x86924))),f79(a865)))+P1(f306(f306(f308(x86921),x86923),x86924))+~P1(f306(f306(f308(x86921),x86923),x86922)) % 187.68/187.66 [8762]E(f306(f306(f81(a1),f394(x87621,x87622,x87623,x87624)),f395(x87621,x87622,x87623,x87624)),x87624)+~P1(f306(f306(f221(a1),f2(a1)),x87623))+~P1(f306(f306(f220(a1),x87624),x87621))+P1(f306(f306(f220(a1),f306(f306(f22(a1),x87624),x87623)),x87621)) % 187.68/187.66 [8763]E(f306(f306(f81(a1),f402(x87631,x87632,x87633,x87634)),f403(x87631,x87632,x87633,x87634)),x87634)+~P1(f306(f306(f221(a1),f2(a1)),x87633))+~P1(f306(f306(f221(a1),x87634),x87631))+P1(f306(f306(f221(a1),f306(f306(f22(a1),x87634),x87633)),x87631)) % 187.68/187.66 [8977]~P1(f306(f306(f221(a1),f2(a1)),x89773))+~P1(f306(f306(f220(a1),x89774),x89771))+P1(f306(f306(f308(a1),f394(x89771,x89772,x89773,x89774)),x89772))+P1(f306(f306(f220(a1),f306(f306(f22(a1),x89774),x89773)),x89771)) % 187.68/187.66 [8978]~P1(f306(f306(f221(a1),f2(a1)),x89783))+~P1(f306(f306(f221(a1),x89784),x89781))+P1(f306(f306(f308(a1),f402(x89781,x89782,x89783,x89784)),x89782))+P1(f306(f306(f221(a1),f306(f306(f22(a1),x89784),x89783)),x89781)) % 187.68/187.66 [9062]~P1(f306(f306(f221(a1),f2(a1)),x90622))+~P1(f306(f306(f220(a1),x90621),x90623))+P1(f306(f306(f308(a1),f395(x90623,x90624,x90622,x90621)),f277(a1,f79(a1),x90622)))+P1(f306(f306(f220(a1),f306(f306(f22(a1),x90621),x90622)),x90623)) % 187.68/187.66 [9063]~P1(f306(f306(f221(a1),f2(a1)),x90632))+~P1(f306(f306(f221(a1),x90631),x90633))+P1(f306(f306(f308(a1),f403(x90633,x90634,x90632,x90631)),f277(a1,f79(a1),x90632)))+P1(f306(f306(f221(a1),f306(f306(f22(a1),x90631),x90632)),x90633)) % 187.68/187.66 [9079]~P1(f306(f306(f220(a1),f2(a1)),x90794))+~P1(f306(f306(f221(a1),f2(a1)),x90793))+~P1(f306(f306(f221(a1),x90794),x90791))+P1(f306(f306(f220(a1),f2(a1)),f306(f306(f81(a1),f306(f306(f82(a1),x90791),f46(a1,x90792,x90793))),x90794))) % 187.68/187.66 [9146]~P108(x91461)+~P1(f306(f63(x91461),x91464))+~P1(f306(f306(f220(x91461),x91462),f647(x91463,x91462,x91464,x91461)))+P1(f306(f306(f220(x91461),f306(f306(f225(x91461),x91462),x91463)),f306(f306(f66(x91461,x91461,f225(x91461)),x91463),x91464))) % 187.68/187.66 [9147]~P103(x91471)+~P1(f306(f63(x91471),x91474))+~P1(f306(f306(f220(x91471),x91472),f651(x91473,x91472,x91474,x91471)))+P1(f306(f306(f220(x91471),f306(f306(f109(x91471),x91472),x91473)),f306(f306(f66(x91471,x91471,f109(x91471)),x91473),x91474))) % 187.68/187.66 [9162]~P1(f306(f306(f220(a1),x91624),f2(a1)))+~P1(f306(f306(f221(a1),f2(a1)),x91622))+~P1(f306(f306(f221(a1),x91621),x91624))+P1(f306(f306(f221(a1),f306(f306(f82(a1),x91621),x91622)),f306(f306(f81(a1),f306(f306(f82(a1),x91621),f46(a1,x91623,x91622))),x91624))) % 187.68/187.66 [9184]P1(f306(f63(x91841),x91842))+~P1(f306(f63(x91841),x91843))+~P1(f306(f306(f308(f872(x91841,a859)),x91842),f306(f306(f62(x91841),x91843),x91844)))+~P1(f306(f306(f220(f872(f871(x91841,x91841),a859)),x91844),f306(f306(f243(x91841,x91841),x91843),f306(f16(f872(x91841,a859),x91841),x91843)))) % 187.68/187.66 [9213]~P108(x92131)+~P1(f306(f63(x92131),x92134))+P1(f306(f306(f308(x92131),f647(x92132,x92133,x92134,x92131)),x92134))+P1(f306(f306(f220(x92131),f306(f306(f225(x92131),x92133),x92132)),f306(f306(f66(x92131,x92131,f225(x92131)),x92132),x92134))) % 187.68/187.66 [9214]~P103(x92141)+~P1(f306(f63(x92141),x92144))+P1(f306(f306(f308(x92141),f651(x92142,x92143,x92144,x92141)),x92144))+P1(f306(f306(f220(x92141),f306(f306(f109(x92141),x92143),x92142)),f306(f306(f66(x92141,x92141,f109(x92141)),x92142),x92144))) % 187.68/187.66 [9222]~P41(f872(x92221,a859),f872(x92221,a859),x92223)+~P1(f306(f306(f308(x92221),x92222),x92224))+P1(f306(f306(f308(x92221),x92222),f103(f872(x92221,a859),x92223)))+~P1(f306(f306(f220(f872(x92221,a859)),x92224),f306(x92223,f306(f306(f108(f872(x92221,a859)),x92224),f103(f872(x92221,a859),x92223))))) % 187.68/187.66 [9402]~P41(f872(x94023,a859),f872(x94023,a859),x94024)+P1(f306(x94021,x94022))+~P1(f306(f306(f308(x94023),x94022),f102(f872(x94023,a859),x94024)))+P1(f306(f306(f308(x94023),f579(x94021,x94024,x94022,x94023)),f306(x94024,f306(f306(f109(f872(x94023,a859)),f102(f872(x94023,a859),x94024)),f306(f228(x94023),x94021))))) % 187.68/187.66 [9616]~P1(f306(f63(x96162),x96164))+~P1(f306(f63(x96161),x96163))+~P1(f306(f306(f220(a865),f306(f39(x96162),x96164)),f306(f39(x96161),x96163)))+P1(f306(f306(f220(f872(x96161,a859)),f306(f285(x96162,x96161,f455(x96163,x96161,x96164,x96162)),x96164)),x96163)) % 187.68/187.66 [9262]~P1(f306(f306(f308(x92621),x92622),x92624))+P1(f306(f306(f308(x92621),x92622),x92623))+~P1(f306(f306(f221(f872(x92621,a859)),x92624),f306(f306(f284(x92621),x92622),x92623)))+P1(f306(f306(f221(f872(x92621,a859)),f306(f306(f22(f872(x92621,a859)),x92624),f306(f306(f284(x92621),x92622),f185(f872(x92621,a859))))),x92623)) % 187.68/187.66 [9425]~P1(f306(f306(f308(x94251),x94252),x94254))+P1(f306(f306(f308(x94251),x94252),x94253))+P1(f306(f306(f221(f872(x94251,a859)),x94254),f306(f306(f284(x94251),x94252),x94253)))+~P1(f306(f306(f221(f872(x94251,a859)),f306(f306(f22(f872(x94251,a859)),x94254),f306(f306(f284(x94251),x94252),f185(f872(x94251,a859))))),x94253)) % 187.68/187.66 [9454]P1(f306(f306(f308(x94541),x94542),x94543))+~P1(f306(f306(f220(f872(x94541,a859)),x94544),x94543))+P1(f306(f306(f221(f872(x94541,a859)),x94544),f306(f306(f284(x94541),x94542),x94543)))+~P1(f306(f306(f221(f872(x94541,a859)),f306(f306(f22(f872(x94541,a859)),x94544),f306(f306(f284(x94541),x94542),f185(f872(x94541,a859))))),x94543)) % 187.68/187.66 [9459]~P1(f306(f306(f308(x94591),x94593),x94592))+~P1(f306(f306(f221(f872(x94591,a859)),x94592),x94594))+P1(f306(f306(f221(f872(x94591,a859)),x94592),f306(f306(f284(x94591),x94593),x94594)))+~P1(f306(f306(f221(f872(x94591,a859)),f306(f306(f22(f872(x94591,a859)),x94592),f306(f306(f284(x94591),x94593),f185(f872(x94591,a859))))),x94594)) % 187.68/187.66 [9472]~P1(f306(f306(f220(f872(x94721,a859)),x94722),x94724))+~P1(f306(f306(f221(f872(x94721,a859)),x94722),x94724))+P1(f306(f306(f221(f872(x94721,a859)),x94722),f306(f306(f284(x94721),x94723),x94724)))+~P1(f306(f306(f221(f872(x94721,a859)),f306(f306(f22(f872(x94721,a859)),x94722),f306(f306(f284(x94721),x94723),f185(f872(x94721,a859))))),x94724)) % 187.68/187.66 [9518]~P109(x95182)+~P60(x95181)+~P1(f306(f306(f220(f872(x95181,x95182)),x95183),x95184))+P1(f306(f60(x95181),f306(f306(f18(x95181,x95182,a859),f306(f306(f8(x95182,f872(x95182,a859),x95181),f220(x95182)),x95183)),x95184))) % 187.68/187.66 [9662]~P109(x96622)+~P60(x96621)+P1(f306(f306(f220(f872(x96621,x96622)),x96623),x96624))+~P1(f306(f60(x96621),f306(f306(f18(x96621,x96622,a859),f306(f306(f8(x96622,f872(x96622,a859),x96621),f220(x96622)),x96623)),x96624))) % 187.68/187.66 [10153]~P41(f872(x101531,a859),f872(x101531,a859),x101533)+~P1(f306(f306(f308(x101531),x101532),x101534))+P1(f306(f306(f308(x101531),x101532),f103(f872(x101531,a859),x101533)))+~P1(f306(f306(f220(f872(x101531,a859)),x101534),f306(x101533,f102(f872(x101531,a859),f306(f306(f7(f872(x101531,a859),f872(x101531,a859),f872(x101531,a859)),f306(f306(f8(f872(x101531,a859),f872(f872(x101531,a859),f872(x101531,a859)),f872(x101531,a859)),f108(f872(x101531,a859))),f306(f306(f7(f872(x101531,a859),f872(x101531,a859),f872(x101531,a859)),f306(f306(f8(f872(x101531,a859),f872(f872(x101531,a859),f872(x101531,a859)),f872(x101531,a859)),f108(f872(x101531,a859))),x101533)),x101534))),f103(f872(x101531,a859),x101533)))))) % 187.68/187.66 [9834]E(f306(f306(f157(x98341),f306(f306(f157(f866(x98341)),f171(x98341,x98342)),x98343)),x98344),f306(f306(f157(x98341),f306(f306(f157(f866(x98341)),x98342),x98344)),x98343))+~P1(f306(f306(f221(a865),x98343),f306(f186(f866(f866(x98341))),f171(x98341,x98342))))+~P17(a865,f306(f161(a865),f306(f306(f146(f866(x98341),a865),f186(f866(x98341))),x98342)))+~P1(f306(f306(f221(a865),x98344),f306(f186(f866(f866(x98341))),f306(f128(f866(x98341),f306(f306(f8(a865,a859,f866(x98341)),f306(f221(a865),x98343)),f186(f866(x98341)))),x98342)))) % 187.68/187.66 [9862]~P1(f306(f306(f308(f871(a865,a865)),x98624),x98621))+~P1(f306(f306(f308(f871(f871(a865,a865),f871(a865,a865))),f306(f306(f236(f871(a865,a865),f871(a865,a865)),x98624),x98622)),a36))+~P1(f306(f306(f308(f871(f872(f871(a865,a865),a859),f872(f871(a865,a865),a859))),f306(f306(f236(f872(f871(a865,a865),a859),f872(f871(a865,a865),a859)),x98621),x98623)),a37))+P1(f306(f306(f308(f871(f872(f871(a865,a865),a859),f872(f871(a865,a865),a859))),f306(f306(f236(f872(f871(a865,a865),a859),f872(f871(a865,a865),a859)),x98621),f306(f306(f284(f871(a865,a865)),x98622),x98623))),a37)) % 187.68/187.66 [9863]~P1(f306(f306(f308(f871(a865,a865)),x98634),x98631))+~P1(f306(f306(f308(f871(f871(a865,a865),f871(a865,a865))),f306(f306(f236(f871(a865,a865),f871(a865,a865)),x98634),x98632)),a71))+~P1(f306(f306(f308(f871(f872(f871(a865,a865),a859),f872(f871(a865,a865),a859))),f306(f306(f236(f872(f871(a865,a865),a859),f872(f871(a865,a865),a859)),x98631),x98633)),a72))+P1(f306(f306(f308(f871(f872(f871(a865,a865),a859),f872(f871(a865,a865),a859))),f306(f306(f236(f872(f871(a865,a865),a859),f872(f871(a865,a865),a859)),x98631),f306(f306(f284(f871(a865,a865)),x98632),x98633))),a72)) % 187.68/187.66 [9750]~P109(x97502)+~P60(x97501)+~P1(f306(f306(f221(f872(x97501,x97502)),x97503),x97504))+P1(f306(f59(x97501),f306(f306(f8(a859,a859,x97501),a301),f306(f306(f18(x97501,x97502,a859),f306(f306(f8(x97502,f872(x97502,a859),x97501),a303),x97503)),x97504)))) % 187.68/187.66 [9876]~P1(f306(f306(f308(f871(a865,a865)),x98764),x98763))+~P1(f306(f306(f308(f871(f871(a865,a865),f871(a865,a865))),f306(f306(f236(f871(a865,a865),f871(a865,a865)),x98761),x98764)),a36))+~P1(f306(f306(f308(f871(f872(f871(a865,a865),a859),f872(f871(a865,a865),a859))),f306(f306(f236(f872(f871(a865,a865),a859),f872(f871(a865,a865),a859)),x98762),x98763)),a38))+P1(f306(f306(f308(f871(f872(f871(a865,a865),a859),f872(f871(a865,a865),a859))),f306(f306(f236(f872(f871(a865,a865),a859),f872(f871(a865,a865),a859)),f306(f306(f284(f871(a865,a865)),x98761),x98762)),x98763)),a38)) % 187.68/187.66 [9877]~P1(f306(f306(f308(f871(a865,a865)),x98774),x98773))+~P1(f306(f306(f308(f871(f871(a865,a865),f871(a865,a865))),f306(f306(f236(f871(a865,a865),f871(a865,a865)),x98771),x98774)),a71))+~P1(f306(f306(f308(f871(f872(f871(a865,a865),a859),f872(f871(a865,a865),a859))),f306(f306(f236(f872(f871(a865,a865),a859),f872(f871(a865,a865),a859)),x98772),x98773)),a70))+P1(f306(f306(f308(f871(f872(f871(a865,a865),a859),f872(f871(a865,a865),a859))),f306(f306(f236(f872(f871(a865,a865),a859),f872(f871(a865,a865),a859)),f306(f306(f284(f871(a865,a865)),x98771),x98772)),x98773)),a70)) % 187.68/187.66 [5989]~P8(x59894,x59891)+~P1(f306(f306(x59891,x59892),x59895))+P1(f306(f306(x59891,x59892),x59893))+~P1(f306(f306(x59891,x59895),x59893)) % 187.68/187.66 [5246]~P68(x52465)+E(x52461,x52462)+~E(x52463,x52464)+~E(f306(f306(f22(x52465),x52463),x52464),f306(f306(f22(x52465),x52461),x52462)) % 187.68/187.66 [6096]~P20(x60965,x60961,x60963)+E(f306(f306(x60961,x60962),f306(x60963,x60964)),f306(x60963,x60964))+~P1(f306(f63(x60965),x60964))+~P1(f306(f306(f308(x60965),x60962),x60964)) % 187.68/187.66 [6290]~P65(x62901)+~E(f306(f306(f22(x62901),x62904),x62905),f306(f306(f22(x62901),x62902),x62903))+~P1(f306(f306(f220(x62901),x62904),x62905))+P1(f306(f306(f220(x62901),x62902),x62903)) % 187.68/187.66 [6292]~P65(x62921)+~E(f306(f306(f22(x62921),x62924),x62925),f306(f306(f22(x62921),x62922),x62923))+~P1(f306(f306(f221(x62921),x62924),x62925))+P1(f306(f306(f221(x62921),x62922),x62923)) % 187.68/187.66 [7254]~E(x72542,f306(f306(f143(x72541),x72544),x72545))+P1(f306(f306(f308(f866(x72541)),x72542),f153(x72541,x72543)))+~P1(f306(f306(f308(f866(x72541)),x72545),f153(x72541,x72543)))+~P1(f306(f306(f308(x72541),x72544),x72543)) % 187.68/187.66 [7668]~E(f306(f186(f866(x76681)),x76683),f306(f186(f866(x76682)),x76684))+~E(f306(f306(f146(f871(x76681,x76682),x76682),f244(x76681,x76682)),x76685),x76684)+~E(f306(f306(f146(f871(x76681,x76682),x76681),f235(x76681,x76682)),x76685),x76683)+E(f306(f306(f173(x76681,x76682),x76683),x76684),x76685) % 187.68/187.66 [8005]~P109(x80051)+P1(f306(f306(f221(f872(x80051,a859)),f277(x80051,x80052,x80053)),f277(x80051,x80054,x80055)))+~P1(f306(f306(f220(x80051),x80054),x80055))+P1(f306(f306(f220(x80051),x80052),x80053)) % 187.68/187.66 [8103]~P109(x81031)+P1(f306(f306(f220(f872(x81031,a859)),f277(x81031,x81032,x81033)),f277(x81031,x81034,x81035)))+~P1(f306(f306(f220(x81031),x81033),x81035))+~P1(f306(f306(f220(x81031),x81034),x81032)) % 187.68/187.66 [8228]~P108(x82281)+P1(f306(f306(f220(x82281),x82282),x82283))+P1(f306(f306(f220(x82281),x82284),x82283))+~P1(f306(f306(f220(f872(x82281,a859)),f306(f276(x82281,x82283),x82282)),f306(f276(x82281,x82284),x82285))) % 187.68/187.66 [8229]~P108(x82291)+P1(f306(f306(f220(x82291),x82292),x82293))+P1(f306(f306(f220(x82291),x82292),x82294))+~P1(f306(f306(f220(f872(x82291,a859)),f306(f276(x82291,x82293),x82292)),f306(f276(x82291,x82295),x82294))) % 187.68/187.66 [8397]~P108(x83973)+~P103(x83971)+~P41(x83973,x83971,x83972)+P1(f306(f306(f220(x83971),f306(x83972,f306(f306(f225(x83973),x83974),x83975))),f306(f306(f109(x83971),f306(x83972,x83974)),f306(x83972,x83975)))) % 187.68/187.66 [8398]~P103(x83983)+~P103(x83981)+~P41(x83983,x83981,x83982)+P1(f306(f306(f220(x83981),f306(x83982,f306(f306(f109(x83983),x83984),x83985))),f306(f306(f109(x83981),f306(x83982,x83984)),f306(x83982,x83985)))) % 187.68/187.66 [8472]~P109(x84721)+~P1(f306(f306(f220(f872(x84721,a859)),f277(x84721,x84724,x84722)),f277(x84721,x84725,x84723)))+P1(f306(f306(f220(x84721),x84722),x84723))+~P1(f306(f306(f220(x84721),x84724),x84722)) % 187.68/187.66 [8473]~P109(x84731)+~P1(f306(f306(f221(f872(x84731,a859)),f277(x84731,x84734,x84732)),f277(x84731,x84735,x84733)))+P1(f306(f306(f220(x84731),x84732),x84733))+~P1(f306(f306(f220(x84731),x84734),x84732)) % 187.68/187.66 [8474]~P109(x84741)+~P1(f306(f306(f220(f872(x84741,a859)),f277(x84741,x84743,x84744)),f277(x84741,x84742,x84745)))+P1(f306(f306(f220(x84741),x84742),x84743))+~P1(f306(f306(f220(x84741),x84743),x84744)) % 187.68/187.66 [8475]~P109(x84751)+~P1(f306(f306(f221(f872(x84751,a859)),f277(x84751,x84753,x84754)),f277(x84751,x84752,x84755)))+P1(f306(f306(f220(x84751),x84752),x84753))+~P1(f306(f306(f220(x84751),x84753),x84754)) % 187.68/187.66 [5938]~P108(x59385)+~P108(x59381)+~P41(x59385,x59381,x59382)+E(f306(f306(f225(x59381),f306(x59382,x59383)),f306(x59382,x59384)),f306(x59382,f306(f306(f225(x59385),x59383),x59384))) % 187.68/187.66 [5939]~P108(x59395)+~P108(x59391)+~P41(x59395,x59391,x59392)+E(f306(f306(f219(x59391),f306(x59392,x59393)),f306(x59392,x59394)),f306(x59392,f306(f306(f219(x59395),x59393),x59394))) % 187.68/187.66 [5988]~P20(x59882,x59885,x59883)+E(x59881,f185(f872(x59882,a859)))+~P1(f306(f63(x59882),x59881))+E(f306(x59883,f306(f306(f284(x59882),x59884),x59881)),f306(f306(x59885,x59884),f306(x59883,x59881))) % 187.68/187.66 [6759]~E(x67591,x67592)+~E(f306(f306(f109(f872(x67593,a859)),x67594),x67595),f185(f872(x67593,a859)))+~P1(f306(f306(f308(x67593),x67592),x67595))+~P1(f306(f306(f308(x67593),x67591),x67594)) % 187.68/187.66 [6840]~P21(x68402,x68405,x68401)+~P1(f306(f63(x68402),x68404))+E(f306(x68401,f306(f306(f284(x68402),x68403),x68404)),f306(f306(f66(x68402,x68402,x68405),x68403),x68404))+P1(f306(f306(f308(x68402),x68403),x68404)) % 187.68/187.66 [6905]~P75(x69052)+~P1(f306(f63(x69051),x69055))+E(f306(f306(f9(x69051,x69052),x69053),f306(f306(f284(x69051),x69054),x69055)),f306(f306(f82(x69052),f306(x69053,x69054)),f306(f306(f9(x69051,x69052),x69053),x69055)))+P1(f306(f306(f308(x69051),x69054),x69055)) % 187.68/187.66 [6907]~P74(x69072)+~P1(f306(f63(x69071),x69075))+E(f306(f306(f6(x69071,x69072),x69073),f306(f306(f284(x69071),x69074),x69075)),f306(f306(f81(x69072),f306(x69073,x69074)),f306(f306(f6(x69071,x69072),x69073),x69075)))+P1(f306(f306(f308(x69071),x69074),x69075)) % 187.68/187.66 [7410]~P21(x74102,x74105,x74101)+~P1(f306(f63(x74102),x74104))+E(f306(x74101,f306(f306(f284(x74102),x74103),x74104)),x74103)+~E(f306(f306(f22(f872(x74102,a859)),x74104),f306(f306(f284(x74102),x74103),f185(f872(x74102,a859)))),f185(f872(x74102,a859))) % 187.68/187.66 [7719]~P1(f306(x77191,x77193))+~P1(f306(f306(f193(x77192),x77193),x77195))+~P1(f306(f306(f193(f33(x77191,x77192)),x77195),x77194))+P1(f306(f306(f193(f33(x77191,x77192)),x77193),x77194)) % 187.68/187.66 [7771]~P83(x77711)+~P1(f306(f306(f220(x77711),x77713),x77715))+~P1(f306(f306(f220(x77711),x77712),x77714))+P1(f306(f306(f220(x77711),f306(f306(f81(x77711),x77712),x77713)),f306(f306(f81(x77711),x77714),x77715))) % 187.68/187.66 [7772]~P108(x77721)+~P1(f306(f306(f220(x77721),x77723),x77725))+~P1(f306(f306(f220(x77721),x77722),x77724))+P1(f306(f306(f220(x77721),f306(f306(f225(x77721),x77722),x77723)),f306(f306(f225(x77721),x77724),x77725))) % 187.68/187.66 [7773]~P108(x77731)+~P1(f306(f306(f220(x77731),x77733),x77735))+~P1(f306(f306(f220(x77731),x77732),x77734))+P1(f306(f306(f220(x77731),f306(f306(f219(x77731),x77732),x77733)),f306(f306(f219(x77731),x77734),x77735))) % 187.68/187.66 [7774]~P97(x77741)+~P1(f306(f306(f220(x77741),x77743),x77745))+~P1(f306(f306(f220(x77741),x77742),x77744))+P1(f306(f306(f220(x77741),f306(f306(f108(x77741),x77742),x77743)),f306(f306(f108(x77741),x77744),x77745))) % 187.68/187.66 [7775]~P103(x77751)+~P1(f306(f306(f220(x77751),x77753),x77755))+~P1(f306(f306(f220(x77751),x77752),x77754))+P1(f306(f306(f220(x77751),f306(f306(f109(x77751),x77752),x77753)),f306(f306(f109(x77751),x77754),x77755))) % 187.68/187.66 [7776]~P85(x77761)+~P1(f306(f306(f220(x77761),x77763),x77765))+~P1(f306(f306(f221(x77761),x77762),x77764))+P1(f306(f306(f221(x77761),f306(f306(f81(x77761),x77762),x77763)),f306(f306(f81(x77761),x77764),x77765))) % 187.68/187.66 [7777]~P85(x77771)+~P1(f306(f306(f220(x77771),x77772),x77774))+~P1(f306(f306(f221(x77771),x77773),x77775))+P1(f306(f306(f221(x77771),f306(f306(f81(x77771),x77772),x77773)),f306(f306(f81(x77771),x77774),x77775))) % 187.68/187.66 [7778]~P85(x77781)+~P1(f306(f306(f221(x77781),x77783),x77785))+~P1(f306(f306(f221(x77781),x77782),x77784))+P1(f306(f306(f221(x77781),f306(f306(f81(x77781),x77782),x77783)),f306(f306(f81(x77781),x77784),x77785))) % 187.68/187.66 [7915]~P143(x79155)+E(x79151,x79152)+E(x79153,x79154)+~E(f306(f306(f81(x79155),f306(f306(f82(x79155),x79153),x79151)),f306(f306(f82(x79155),x79154),x79152)),f306(f306(f81(x79155),f306(f306(f82(x79155),x79153),x79152)),f306(f306(f82(x79155),x79154),x79151))) % 187.68/187.66 [8057]P30(x80571,x80572,x80573)+~P31(x80571,x80574,x80575)+~P30(x80571,x80572,f552(x80575,x80574,x80571,x80572))+~P1(f306(f306(f308(f864(x80571)),x80573),x80575)) % 187.68/187.66 [8126]~P108(x81264)+~P1(f306(f129(x81261),x81263))+P1(f306(f306(f308(x81261),x81262),f306(f164(x81261),x81263)))+P1(f306(f129(x81261),f306(f306(f140(x81261,x81264,x81265),x81262),x81263))) % 187.68/187.66 [8274]~P68(x82741)+E(f306(f306(f22(x82741),f306(f306(f6(a865,x82741),x82742),f306(f276(a865,x82743),x82744))),f306(f306(f6(a865,x82741),x82742),f306(f276(a865,x82743),x82745))),f306(f306(f6(a865,x82741),x82742),f306(f276(a865,x82745),x82744)))+~P1(f306(f306(f220(a865),x82745),x82744))+~P1(f306(f306(f220(a865),x82743),x82745)) % 187.68/187.66 [8275]~P74(x82751)+E(f306(f306(f81(x82751),f306(f306(f6(a865,x82751),x82752),f306(f276(a865,x82753),x82754))),f306(f306(f6(a865,x82751),x82752),f306(f276(a865,x82754),x82755))),f306(f306(f6(a865,x82751),x82752),f306(f276(a865,x82753),x82755)))+~P1(f306(f306(f220(a865),x82754),x82755))+~P1(f306(f306(f220(a865),x82753),x82754)) % 187.68/187.66 [8609]~P62(x86092)+E(x86091,f2(x86092))+E(x86093,f2(x86092))+E(f306(f306(f264(x86092),f306(f306(f22(x86092),f306(f306(f82(x86092),x86094),x86091)),f306(f306(f82(x86092),x86095),x86093))),f306(f306(f82(x86092),x86093),x86091)),f306(f306(f22(x86092),f306(f306(f264(x86092),x86094),x86093)),f306(f306(f264(x86092),x86095),x86091))) % 187.68/187.66 [8610]~P62(x86102)+E(x86101,f2(x86102))+E(x86103,f2(x86102))+E(f306(f306(f264(x86102),f306(f306(f81(x86102),f306(f306(f82(x86102),x86104),x86101)),f306(f306(f82(x86102),x86105),x86103))),f306(f306(f82(x86102),x86103),x86101)),f306(f306(f81(x86102),f306(f306(f264(x86102),x86104),x86103)),f306(f306(f264(x86102),x86105),x86101))) % 187.68/187.66 [8619]~E(x86192,f306(x86193,x86191))+E(x86191,f479(x86192,x86193,x86194,x86195))+~P28(x86195,x86194,x86193,f231(f872(x86195,a859)))+~P1(f306(f306(f308(x86194),x86192),f306(f285(x86195,x86194,x86193),f231(f872(x86195,a859))))) % 187.68/187.66 [8813]~P112(x88131)+~P1(f306(f306(f221(x88131),f306(f76(x88131),x88132)),x88134))+P1(f306(f306(f221(x88131),f306(f306(f82(x88131),f306(f76(x88131),x88132)),f306(f76(x88131),x88133))),f306(f306(f82(x88131),x88134),x88135)))+~P1(f306(f306(f221(x88131),f306(f76(x88131),x88133)),x88135)) % 187.68/187.66 [8830]~P31(x88301,x88305,x88304)+P30(x88301,x88302,x88303)+P1(f306(f306(f308(f864(x88301)),f552(x88304,x88305,x88301,x88302)),x88305))+~P1(f306(f306(f308(f864(x88301)),x88303),x88304)) % 187.68/187.66 [8936]~P28(x89361,x89363,x89365,x89362)+~P1(f306(f63(x89363),x89364))+P1(f306(f306(f220(a865),f306(f39(x89361),x89362)),f306(f39(x89363),x89364)))+~P1(f306(f306(f220(f872(x89363,a859)),f306(f285(x89361,x89363,x89365),x89362)),x89364)) % 187.68/187.66 [9006]~P75(x90062)+~P28(x90061,x90061,x90064,x90065)+~P1(f306(f63(x90061),x90065))+E(f306(f306(f9(x90061,x90062),f306(f74(x90061,x90062,x90061,x90063),x90064)),x90065),f306(f306(f9(x90061,x90062),x90063),f306(f285(x90061,x90061,x90064),x90065))) % 187.68/187.66 [9007]~P74(x90072)+~P28(x90071,x90071,x90074,x90075)+~P1(f306(f63(x90071),x90075))+E(f306(f306(f6(x90071,x90072),f306(f74(x90071,x90072,x90071,x90073),x90074)),x90075),f306(f306(f6(x90071,x90072),x90073),f306(f285(x90071,x90071,x90074),x90075))) % 187.68/187.66 [9122]~P40(x91221,x91222)+~P1(f306(f306(f308(x91221),x91223),x91224))+~P1(f306(f306(f308(x91221),x91225),x91224))+~P1(f306(f306(f308(f871(x91221,x91221)),f306(f306(f236(x91221,x91221),x91225),f645(x91222,x91221,x91224))),x91222)) % 187.68/187.66 [9161]~P28(x91612,x91613,x91615,x91611)+E(x91611,f185(f872(x91612,a859)))+E(f306(f285(x91613,x91612,f464(x91614,x91613,x91612,x91611)),x91614),x91611)+~P1(f306(f306(f220(f872(x91613,a859)),f306(f285(x91612,x91613,x91615),x91611)),x91614)) % 187.68/187.66 [9643]~P108(x96435)+~P6(x96435)+P1(f306(f306(f308(x96431),f460(x96432,x96433,x96431,x96434,x96435)),x96433))+~P1(f306(f306(f221(x96435),x96434),f306(f306(f43(x96431,x96435),x96433),x96432))) % 187.68/187.66 [9648]~P108(x96481)+~P6(x96481)+P1(f306(f306(f221(x96481),x96482),f306(x96483,f460(x96483,x96484,x96485,x96482,x96481))))+~P1(f306(f306(f221(x96481),x96482),f306(f306(f43(x96485,x96481),x96484),x96483))) % 187.68/187.66 [9728]~P72(x97281)+~P1(f306(f68(x97281,x97281,f82(x97281),x97282,x97283),x97285))+P1(f306(f306(f308(x97281),x97282),x97283))+P1(f306(f68(x97281,x97281,f82(x97281),x97284,f306(f306(f284(x97281),x97282),x97283)),f306(f306(f82(x97281),x97284),x97285))) % 187.68/187.66 [9946]~P75(x99462)+~P1(f306(f63(x99461),x99465))+E(f306(f306(f9(x99461,x99462),f306(f306(f7(x99461,x99462,x99462),f306(f306(f18(x99461,x99462,f872(x99462,x99462)),f306(f306(f8(a859,f872(x99462,f872(x99462,x99462)),x99461),f101(x99462)),f306(a303,x99463))),x99464)),f79(x99462))),x99465),f79(x99462))+P1(f306(f306(f308(x99461),x99463),x99465)) % 187.68/187.66 [9947]~P74(x99472)+~P1(f306(f63(x99471),x99475))+E(f306(f306(f6(x99471,x99472),f306(f306(f7(x99471,x99472,x99472),f306(f306(f18(x99471,x99472,f872(x99472,x99472)),f306(f306(f8(a859,f872(x99472,f872(x99472,x99472)),x99471),f101(x99472)),f306(a303,x99473))),x99474)),f2(x99472))),x99475),f2(x99472))+P1(f306(f306(f308(x99471),x99473),x99475)) % 187.68/187.66 [9948]~P75(x99482)+~P1(f306(f63(x99481),x99485))+E(f306(f306(f9(x99481,x99482),f306(f306(f7(x99481,x99482,x99482),f306(f306(f18(x99481,x99482,f872(x99482,x99482)),f306(f306(f8(a859,f872(x99482,f872(x99482,x99482)),x99481),f101(x99482)),f306(a303,x99483))),x99484)),f79(x99482))),x99485),f306(x99484,x99483))+~P1(f306(f306(f308(x99481),x99483),x99485)) % 187.68/187.66 [9949]~P74(x99492)+~P1(f306(f63(x99491),x99495))+E(f306(f306(f6(x99491,x99492),f306(f306(f7(x99491,x99492,x99492),f306(f306(f18(x99491,x99492,f872(x99492,x99492)),f306(f306(f8(a859,f872(x99492,f872(x99492,x99492)),x99491),f101(x99492)),f306(a303,x99493))),x99494)),f2(x99492))),x99495),f306(x99494,x99493))+~P1(f306(f306(f308(x99491),x99493),x99495)) % 187.68/187.66 [10007]~P75(x100072)+~P1(f306(f63(x100071),x100075))+E(f306(f306(f9(x100071,x100072),f306(f306(f7(x100071,x100072,x100072),f306(f306(f18(x100071,x100072,f872(x100072,x100072)),f306(f306(f8(a859,f872(x100072,f872(x100072,x100072)),x100071),f101(x100072)),f306(f306(f7(x100071,x100071,a859),a303),x100073))),x100074)),f79(x100072))),x100075),f79(x100072))+P1(f306(f306(f308(x100071),x100073),x100075)) % 187.68/187.66 [10008]~P74(x100082)+~P1(f306(f63(x100081),x100085))+E(f306(f306(f6(x100081,x100082),f306(f306(f7(x100081,x100082,x100082),f306(f306(f18(x100081,x100082,f872(x100082,x100082)),f306(f306(f8(a859,f872(x100082,f872(x100082,x100082)),x100081),f101(x100082)),f306(f306(f7(x100081,x100081,a859),a303),x100083))),x100084)),f2(x100082))),x100085),f2(x100082))+P1(f306(f306(f308(x100081),x100083),x100085)) % 187.68/187.66 [10010]~P75(x100102)+~P1(f306(f63(x100101),x100105))+E(f306(f306(f9(x100101,x100102),f306(f306(f7(x100101,x100102,x100102),f306(f306(f18(x100101,x100102,f872(x100102,x100102)),f306(f306(f8(a859,f872(x100102,f872(x100102,x100102)),x100101),f101(x100102)),f306(f306(f7(x100101,x100101,a859),a303),x100103))),x100104)),f79(x100102))),x100105),f306(x100104,x100103))+~P1(f306(f306(f308(x100101),x100103),x100105)) % 187.68/187.66 [10011]~P74(x100112)+~P1(f306(f63(x100111),x100115))+E(f306(f306(f6(x100111,x100112),f306(f306(f7(x100111,x100112,x100112),f306(f306(f18(x100111,x100112,f872(x100112,x100112)),f306(f306(f8(a859,f872(x100112,f872(x100112,x100112)),x100111),f101(x100112)),f306(f306(f7(x100111,x100111,a859),a303),x100113))),x100114)),f2(x100112))),x100115),f306(x100114,x100113))+~P1(f306(f306(f308(x100111),x100113),x100115)) % 187.68/187.66 [7770]~P68(x77702)+~P1(f306(f63(x77701),x77704))+E(f306(f306(f6(x77701,x77702),x77703),f306(f306(f22(f872(x77701,a859)),x77704),f306(f306(f284(x77701),x77705),f185(f872(x77701,a859))))),f306(f306(f6(x77701,x77702),x77703),x77704))+P1(f306(f306(f308(x77701),x77705),x77704)) % 187.68/187.66 [8281]~P126(x82812)+~P1(f306(f63(x82811),x82814))+E(f306(f306(f6(x82811,x82812),x82813),f306(f306(f22(f872(x82811,a859)),x82814),f306(f306(f284(x82811),x82815),f185(f872(x82811,a859))))),f306(f306(f22(x82812),f306(f306(f6(x82811,x82812),x82813),x82814)),f306(x82813,x82815)))+~P1(f306(f306(f308(x82811),x82815),x82814)) % 187.68/187.66 [8282]~P68(x82822)+~P1(f306(f63(x82821),x82824))+E(f306(f306(f6(x82821,x82822),x82823),f306(f306(f22(f872(x82821,a859)),x82824),f306(f306(f284(x82821),x82825),f185(f872(x82821,a859))))),f306(f306(f22(x82822),f306(f306(f6(x82821,x82822),x82823),x82824)),f306(x82823,x82825)))+~P1(f306(f306(f308(x82821),x82825),x82824)) % 187.68/187.66 [8313]~P68(x83131)+~P1(f306(f63(x83132),x83134))+E(f306(f306(f22(x83131),f306(f306(f6(x83132,x83131),x83133),x83134)),f306(f306(f6(x83132,x83131),x83133),x83135)),f306(f306(f6(x83132,x83131),x83133),f306(f306(f22(f872(x83132,a859)),x83134),x83135)))+~P1(f306(f306(f220(f872(x83132,a859)),x83135),x83134)) % 187.68/187.66 [8333]P1(f306(f63(x83331),f306(x83332,x83333)))+~P1(f306(f63(x83334),x83335))+~P1(f306(f306(f308(x83334),x83333),x83335))+~P1(f306(f63(x83331),f306(f306(f43(x83334,f872(x83331,a859)),x83335),x83332))) % 187.68/187.66 [8450]~P108(x84505)+~P97(x84501)+~P41(x84505,x84501,x84502)+P1(f306(f306(f220(x84501),f306(f306(f108(x84501),f306(x84502,x84503)),f306(x84502,x84504))),f306(x84502,f306(f306(f219(x84505),x84503),x84504)))) % 187.68/187.66 [8451]~P97(x84515)+~P97(x84511)+~P41(x84515,x84511,x84512)+P1(f306(f306(f220(x84511),f306(f306(f108(x84511),f306(x84512,x84513)),f306(x84512,x84514))),f306(x84512,f306(f306(f108(x84515),x84513),x84514)))) % 187.68/187.66 [8775]~P9(x87751,x87755,x87754)+~E(f306(f260(x87751,x87751,x87754),f306(f306(f284(x87751),x87752),f185(f872(x87751,a859)))),f306(f260(x87751,x87751,x87754),f306(f306(f284(x87751),x87753),f185(f872(x87751,a859)))))+~P1(f306(f306(f308(x87751),x87753),x87755))+P1(f306(f306(f308(f871(x87751,x87751)),f306(f306(f236(x87751,x87751),x87752),x87753)),x87754)) % 187.68/187.66 [9077]~P1(f306(x90771,x90775))+P1(f306(x90771,f335(x90771,x90772,x90773,x90774)))+P1(f306(x90771,f334(x90771,x90772,x90773,x90774)))+~P1(f306(f306(f308(x90774),x90775),f306(f306(f108(f872(x90774,a859)),x90773),x90772))) % 187.68/187.66 [9267]~P1(f306(x92671,x92675))+P1(f306(x92671,f334(x92671,x92672,x92673,x92674)))+P1(f306(f306(f308(x92674),f335(x92671,x92672,x92673,x92674)),x92672))+~P1(f306(f306(f308(x92674),x92675),f306(f306(f108(f872(x92674,a859)),x92673),x92672))) % 187.68/187.66 [9268]~P1(f306(x92681,x92685))+P1(f306(x92681,f335(x92681,x92682,x92683,x92684)))+P1(f306(f306(f308(x92684),f334(x92681,x92682,x92683,x92684)),x92683))+~P1(f306(f306(f308(x92684),x92685),f306(f306(f108(f872(x92684,a859)),x92683),x92682))) % 187.68/187.66 [9274]P1(f306(x92741,x92742))+~P1(f306(x92741,f341(x92741,x92743,x92744,x92745)))+~P1(f306(x92741,f340(x92741,x92743,x92744,x92745)))+~P1(f306(f306(f308(x92745),x92742),f306(f306(f108(f872(x92745,a859)),x92744),x92743))) % 187.68/187.66 [9316]E(x93161,x93162)+~P1(f306(f306(f308(f871(x93163,x93163)),f306(f306(f236(x93163,x93163),x93161),x93162)),f282(x93163,x93165)))+P1(f306(f306(f308(x93163),x93161),x93164))+~P1(f306(f306(f220(f872(f871(x93163,x93163),a859)),x93165),f306(f306(f243(x93163,x93163),x93164),f306(f16(f872(x93163,a859),x93163),x93164)))) % 187.68/187.66 [9335]P1(f306(x93351,x93352))+~P1(f306(x93351,f340(x93351,x93354,x93355,x93353)))+P1(f306(f306(f308(x93353),f341(x93351,x93354,x93355,x93353)),x93354))+~P1(f306(f306(f308(x93353),x93352),f306(f306(f108(f872(x93353,a859)),x93355),x93354))) % 187.68/187.66 [9336]P1(f306(x93361,x93362))+~P1(f306(x93361,f341(x93361,x93364,x93365,x93363)))+P1(f306(f306(f308(x93363),f340(x93361,x93364,x93365,x93363)),x93365))+~P1(f306(f306(f308(x93363),x93362),f306(f306(f108(f872(x93363,a859)),x93365),x93364))) % 187.68/187.66 [9398]P1(f306(x93981,x93982))+P1(f306(f306(f308(x93983),f341(x93981,x93984,x93985,x93983)),x93984))+P1(f306(f306(f308(x93983),f340(x93981,x93984,x93985,x93983)),x93985))+~P1(f306(f306(f308(x93983),x93982),f306(f306(f108(f872(x93983,a859)),x93985),x93984))) % 187.68/187.66 [9400]~P1(f306(x94002,x94005))+P1(f306(f306(f308(x94001),f335(x94002,x94003,x94004,x94001)),x94003))+P1(f306(f306(f308(x94001),f334(x94002,x94003,x94004,x94001)),x94004))+~P1(f306(f306(f308(x94001),x94005),f306(f306(f108(f872(x94001,a859)),x94004),x94003))) % 187.68/187.66 [9551]~P9(x95511,x95515,x95514)+~P1(f306(f306(f308(x95511),x95513),x95515))+P1(f306(f306(f308(f871(x95511,x95511)),f306(f306(f236(x95511,x95511),x95512),x95513)),x95514))+~P1(f306(f306(f220(f872(x95511,a859)),f306(f260(x95511,x95511,x95514),f306(f306(f284(x95511),x95513),f185(f872(x95511,a859))))),f306(f260(x95511,x95511,x95514),f306(f306(f284(x95511),x95512),f185(f872(x95511,a859)))))) % 187.68/187.66 [9674]~P108(x96745)+~P6(x96745)+P1(f306(f306(f308(x96741),f625(x96742,x96743,x96744,x96741,x96745)),x96744))+~P1(f306(f306(f221(x96745),f306(f306(f44(x96741,x96745),x96744),x96743)),x96742)) % 187.68/187.66 [9707]~P83(x97075)+~P79(x97075)+P1(f306(f306(f308(x97071),f715(x97072,x97073,x97074,x97071,x97075)),f306(f164(x97071),x97074)))+P1(f306(f306(f220(x97075),f306(f158(x97075),f306(f306(f146(x97071,x97075),x97073),x97074))),f306(f158(x97075),f306(f306(f146(x97071,x97075),x97072),x97074)))) % 187.68/187.66 [9822]~P108(x98221)+~P6(x98221)+P1(f306(f306(f221(x98221),f306(x98222,f625(x98223,x98222,x98224,x98225,x98221))),x98223))+~P1(f306(f306(f221(x98221),f306(f306(f44(x98225,x98221),x98224),x98222)),x98223)) % 187.68/187.66 [9965]~P83(x99651)+~P79(x99651)+~P1(f306(f306(f220(x99651),f306(x99653,f715(x99655,x99653,x99654,x99652,x99651))),f306(x99655,f715(x99655,x99653,x99654,x99652,x99651))))+P1(f306(f306(f220(x99651),f306(f158(x99651),f306(f306(f146(x99652,x99651),x99653),x99654))),f306(f158(x99651),f306(f306(f146(x99652,x99651),x99655),x99654)))) % 187.68/187.66 [8626]~P75(x86261)+~P1(f306(f63(x86264),x86265))+~P1(f306(f306(f308(x86264),x86263),x86265))+E(f306(f306(f82(x86261),f306(x86262,x86263)),f306(f306(f9(x86264,x86261),x86262),f306(f306(f22(f872(x86264,a859)),x86265),f306(f306(f284(x86264),x86263),f185(f872(x86264,a859)))))),f306(f306(f9(x86264,x86261),x86262),x86265)) % 187.68/187.66 [8628]~P74(x86281)+~P1(f306(f63(x86284),x86285))+~P1(f306(f306(f308(x86284),x86283),x86285))+E(f306(f306(f81(x86281),f306(x86282,x86283)),f306(f306(f6(x86284,x86281),x86282),f306(f306(f22(f872(x86284,a859)),x86285),f306(f306(f284(x86284),x86283),f185(f872(x86284,a859)))))),f306(f306(f6(x86284,x86281),x86282),x86285)) % 187.68/187.66 [8681]~P21(x86811,x86814,x86815)+~P1(f306(f63(x86811),x86812))+E(f306(f306(f22(f872(x86811,a859)),x86812),f306(f306(f284(x86811),x86813),f185(f872(x86811,a859)))),f185(f872(x86811,a859)))+E(f306(f306(x86814,x86813),f306(x86815,f306(f306(f22(f872(x86811,a859)),x86812),f306(f306(f284(x86811),x86813),f185(f872(x86811,a859)))))),f306(x86815,f306(f306(f284(x86811),x86813),x86812))) % 187.68/187.66 [9057]~P74(x90571)+~P1(f306(f63(x90572),x90575))+~P1(f306(f63(x90572),x90574))+E(f306(f306(f81(x90571),f306(f306(f6(x90572,x90571),x90573),f306(f306(f108(f872(x90572,a859)),x90574),x90575))),f306(f306(f6(x90572,x90571),x90573),f306(f306(f109(f872(x90572,a859)),x90574),x90575))),f306(f306(f81(x90571),f306(f306(f6(x90572,x90571),x90573),x90574)),f306(f306(f6(x90572,x90571),x90573),x90575))) % 187.68/187.66 [9059]~P75(x90591)+~P1(f306(f63(x90592),x90595))+~P1(f306(f63(x90592),x90594))+E(f306(f306(f82(x90591),f306(f306(f9(x90592,x90591),x90593),f306(f306(f108(f872(x90592,a859)),x90594),x90595))),f306(f306(f9(x90592,x90591),x90593),f306(f306(f109(f872(x90592,a859)),x90594),x90595))),f306(f306(f82(x90591),f306(f306(f9(x90592,x90591),x90593),x90594)),f306(f306(f9(x90592,x90591),x90593),x90595))) % 187.68/187.66 [9203]~P68(x92031)+~P1(f306(f63(x92032),x92035))+~P1(f306(f63(x92032),x92034))+E(f306(f306(f22(x92031),f306(f306(f81(x92031),f306(f306(f6(x92032,x92031),x92033),x92034)),f306(f306(f6(x92032,x92031),x92033),x92035))),f306(f306(f6(x92032,x92031),x92033),f306(f306(f109(f872(x92032,a859)),x92034),x92035))),f306(f306(f6(x92032,x92031),x92033),f306(f306(f108(f872(x92032,a859)),x92034),x92035))) % 187.68/187.66 [9410]~P28(x94101,x94102,x94103,x94105)+~P28(x94101,x94102,x94103,x94104)+P28(x94101,x94102,x94103,f306(f306(f108(f872(x94101,a859)),x94104),x94105))+~E(f306(f306(f109(f872(x94102,a859)),f306(f285(x94101,x94102,x94103),f306(f306(f22(f872(x94101,a859)),x94104),x94105))),f306(f285(x94101,x94102,x94103),f306(f306(f22(f872(x94101,a859)),x94105),x94104))),f185(f872(x94102,a859))) % 187.68/187.66 [9526]E(x95261,f2(a1))+~P1(f306(f306(f221(a1),f2(a1)),x95263))+~P1(f306(f50(x95262,x95261),f306(f306(f236(a1,a1),x95264),x95265)))+P1(f306(f50(x95262,f306(f306(f82(a1),x95261),x95263)),f306(f306(f236(a1,a1),f306(f306(f40(a1),x95264),x95263)),f306(f306(f81(a1),f306(f306(f82(a1),x95261),f46(a1,x95264,x95263))),x95265)))) % 187.68/187.66 [9534]~P1(f306(f306(f221(a865),f2(a865)),x95343))+~P1(f306(f306(f221(a865),f2(a865)),x95342))+~P1(f306(f49(x95341,x95342),f306(f306(f236(a865,a865),x95344),x95345)))+P1(f306(f49(x95341,f306(f306(f82(a865),x95342),x95343)),f306(f306(f236(a865,a865),f306(f306(f40(a865),x95344),x95343)),f306(f306(f81(a865),f306(f306(f82(a865),x95342),f46(a865,x95344,x95343))),x95345)))) % 187.68/187.66 [9584]~P75(x95841)+~P1(f306(f63(x95842),x95845))+~P1(f306(f63(x95842),x95844))+E(f306(f306(f82(x95841),f306(f306(f306(f67(x95841,x95842,f82(x95841)),x95843),f79(x95841)),f306(f306(f108(f872(x95842,a859)),x95844),x95845))),f306(f306(f306(f67(x95841,x95842,f82(x95841)),x95843),f79(x95841)),f306(f306(f109(f872(x95842,a859)),x95844),x95845))),f306(f306(f82(x95841),f306(f306(f306(f67(x95841,x95842,f82(x95841)),x95843),f79(x95841)),x95844)),f306(f306(f306(f67(x95841,x95842,f82(x95841)),x95843),f79(x95841)),x95845))) % 187.68/187.66 [9586]~E(f306(f306(f165(x95861),x95865),x95862),f306(f306(f165(x95861),x95865),x95863))+P1(f306(f306(f308(f871(f866(x95861),f866(x95861))),f306(f306(f236(f866(x95861),f866(x95861)),x95862),x95863)),f139(x95861,x95864)))+~P1(f306(f306(f221(a865),x95865),f306(f306(f225(a865),f306(f186(f866(x95861)),x95862)),f306(f186(f866(x95861)),x95863))))+~P1(f306(f306(f308(f871(x95861,x95861)),f306(f306(f236(x95861,x95861),f306(f306(f157(x95861),x95862),x95865)),f306(f306(f157(x95861),x95863),x95865))),x95864)) % 187.68/187.66 [9695]~P83(x96955)+~P141(x96955)+P1(f306(f306(f308(x96951),f418(x96952,x96953,x96954,x96951,x96955)),x96954))+P1(f306(f306(f220(x96955),f306(f306(f6(x96951,x96955),x96953),x96954)),f306(f306(f82(x96955),f306(f107(x96955),f306(f39(x96951),x96954))),x96952))) % 187.68/187.66 [9892]~P83(x98921)+~P141(x98921)+~P1(f306(f306(f220(x98921),f306(x98923,f418(x98925,x98923,x98924,x98922,x98921))),x98925))+P1(f306(f306(f220(x98921),f306(f306(f6(x98922,x98921),x98923),x98924)),f306(f306(f82(x98921),f306(f107(x98921),f306(f39(x98922),x98924))),x98925))) % 187.68/187.66 [8653]E(f306(f306(f122(x86531),x86532),x86533),f306(f306(f122(x86531),x86534),x86535))+~E(f306(f306(f165(x86531),f306(f186(f866(x86531)),x86532)),x86534),x86532)+~E(f306(f306(f122(x86531),f306(f306(f130(x86531),f306(f186(f866(x86531)),x86532)),x86534)),x86535),x86533)+P1(f306(f306(f220(a865),f306(f186(f866(x86531)),x86534)),f306(f186(f866(x86531)),x86532))) % 187.68/187.66 [8774]E(f306(f306(f122(x87741),x87742),x87743),f306(f306(f122(x87741),x87744),x87745))+~E(f306(f306(f165(x87741),f306(f186(f866(x87741)),x87742)),x87744),x87742)+~E(x87743,f306(f306(f122(x87741),f306(f306(f130(x87741),f306(f186(f866(x87741)),x87742)),x87744)),x87745))+~P1(f306(f306(f220(a865),f306(f186(f866(x87741)),x87742)),f306(f186(f866(x87741)),x87744))) % 187.68/187.66 [10029]~P1(f306(x100295,x100294))+~P1(f306(f63(x100292),f306(f228(x100292),x100295)))+P1(f306(f63(x100291),f306(f228(x100291),f306(f306(f7(x100291,x100292,a859),x100293),x100294))))+~P1(f306(f63(x100291),f306(f228(x100291),f306(f306(f8(f872(x100292,a859),a859,x100291),f88(x100292)),f306(f306(f8(f872(x100292,a859),f872(x100292,a859),x100291),f306(f18(x100292,a859,a859),f306(f306(f8(a859,f872(a859,a859),x100292),a304),x100295))),x100293))))) % 187.68/187.66 [8448]~P22(x84485,x84481,x84486,x84482)+E(f306(f74(x84481,x84481,x84481,f306(x84482,x84483)),f306(x84482,x84484)),f306(f74(x84481,x84481,x84481,f306(x84482,x84484)),f306(x84482,x84483)))+~P1(f306(f63(x84485),x84484))+~P1(f306(f63(x84485),x84483)) % 187.68/187.66 [7826]~P28(x78261,x78262,x78264,x78263)+~E(f306(x78264,x78266),x78265)+E(f306(f78(x78261,x78262,x78263,x78264),x78265),x78266)+~P1(f306(f306(f308(x78261),x78266),x78263)) % 187.68/187.66 [8026]~P23(x80266,x80261,x80264,x80262)+E(f306(f74(x80261,x80261,x80261,f306(x80262,x80263)),f306(x80264,x80265)),f306(x80262,x80263))+~P1(f306(f63(x80266),x80263))+~P1(f306(f306(f308(x80266),x80265),x80263)) % 187.68/187.66 [9252]~P22(x92523,x92521,x92526,x92522)+E(f306(f74(x92521,x92521,x92521,f306(x92522,f306(f306(f22(f872(x92523,a859)),x92524),f306(f306(f284(x92523),x92525),f185(f872(x92523,a859)))))),f306(x92526,x92525)),f306(x92522,x92524))+~P1(f306(f63(x92523),x92524))+~P1(f306(f306(f308(x92523),x92525),x92524)) % 187.68/187.66 [6910]~P5(x69101)+~E(f46(x69101,x69103,x69104),f46(x69101,x69106,x69104))+~E(f46(x69101,x69102,x69104),f46(x69101,x69105,x69104))+E(f46(x69101,f306(f306(f22(x69101),x69102),x69103),x69104),f46(x69101,f306(f306(f22(x69101),x69105),x69106),x69104)) % 187.68/187.66 [6911]~P4(x69111)+~E(f46(x69111,x69113,x69114),f46(x69111,x69116,x69114))+~E(f46(x69111,x69112,x69114),f46(x69111,x69115,x69114))+E(f46(x69111,f306(f306(f81(x69111),x69112),x69113),x69114),f46(x69111,f306(f306(f81(x69111),x69115),x69116),x69114)) % 187.68/187.66 [6912]~P4(x69121)+~E(f46(x69121,x69123,x69124),f46(x69121,x69126,x69124))+~E(f46(x69121,x69122,x69124),f46(x69121,x69125,x69124))+E(f46(x69121,f306(f306(f82(x69121),x69122),x69123),x69124),f46(x69121,f306(f306(f82(x69121),x69125),x69126),x69124)) % 187.68/187.66 [7721]~P19(x77211,x77212,x77213)+~P1(f306(f63(x77211),x77216))+E(f306(f306(f66(x77211,x77212,x77213),x77214),f306(f306(f284(x77211),x77215),x77216)),f306(f306(f66(x77211,x77212,x77213),f306(f306(x77213,x77215),x77214)),x77216))+P1(f306(f306(f308(x77211),x77215),x77216)) % 187.68/187.66 [7784]~P6(x77841)+P1(f306(f306(f220(x77841),x77842),f306(x77843,x77844)))+~P1(f306(f306(f308(x77845),x77844),x77846))+~P1(f306(f306(f220(x77841),x77842),f306(f306(f44(x77845,x77841),x77846),x77843))) % 187.68/187.66 [7944]~P19(x79441,x79442,x79443)+~P1(f306(f63(x79441),x79446))+E(f306(f306(f66(x79441,x79442,x79443),x79444),f306(f306(f284(x79441),x79445),x79446)),f306(f306(x79443,x79445),f306(f306(f66(x79441,x79442,x79443),x79444),x79446)))+P1(f306(f306(f308(x79441),x79445),x79446)) % 187.68/187.66 [8042]~P108(x80423)+~P1(f306(x80422,x80425))+~P17(x80423,f306(f306(f146(x80421,x80423),x80424),x80426))+E(f306(f128(x80421,x80422),f306(f306(f140(x80421,x80423,x80424),x80425),x80426)),f306(f306(f140(x80421,x80423,x80424),x80425),f306(f128(x80421,x80422),x80426))) % 187.68/187.66 [8065]E(x80651,x80652)+E(x80653,f2(a1))+~P1(f306(f50(x80654,x80653),f306(f306(f236(a1,a1),x80655),x80652)))+~P1(f306(f50(x80654,x80653),f306(f306(f236(a1,a1),x80656),x80651))) % 187.68/187.66 [8066]E(x80661,x80662)+E(x80663,f2(a1))+~P1(f306(f50(x80664,x80663),f306(f306(f236(a1,a1),x80662),x80665)))+~P1(f306(f50(x80664,x80663),f306(f306(f236(a1,a1),x80661),x80666))) % 187.68/187.66 [8086]~P22(x80862,x80865,x80866,x80861)+~P1(f306(f63(x80862),x80864))+E(f306(x80861,f306(f306(f284(x80862),x80863),x80864)),f306(f74(x80865,x80865,x80865,f306(x80861,x80864)),f306(x80866,x80863)))+P1(f306(f306(f308(x80862),x80863),x80864)) % 187.68/187.66 [8316]~P23(x83165,x83161,x83166,x83162)+E(f306(f74(x83161,x83161,x83161,f306(x83162,x83163)),f306(x83162,x83164)),f306(x83162,x83163))+~P1(f306(f63(x83165),x83163))+~P1(f306(f306(f220(f872(x83165,a859)),x83164),x83163)) % 187.68/187.66 [9456]~P28(x94561,x94562,x94564,x94563)+~P1(f306(f306(f308(x94562),x94565),f306(f285(x94561,x94562,x94564),x94563)))+P1(f306(f306(f308(x94561),f306(f78(x94561,x94562,x94563,x94564),x94565)),x94566))+~P1(f306(f306(f220(f872(x94561,a859)),x94563),x94566)) % 187.68/187.66 [9836]~P74(x98362)+~E(f429(x98361,x98363,x98365,x98366,x98364,x98362),f421(x98361,x98363,x98365,x98366,x98364,x98362))+~P1(f306(f63(x98364),x98366))+E(f306(f306(f6(x98361,x98362),x98363),f306(f285(x98364,x98361,x98365),x98366)),f306(f306(f6(x98364,x98362),f306(f74(x98361,x98362,x98364,x98363),x98365)),x98366)) % 187.68/187.66 [9872]~P74(x98726)+E(f306(x98721,f429(x98722,x98723,x98721,x98724,x98725,x98726)),f306(x98721,f421(x98722,x98723,x98721,x98724,x98725,x98726)))+E(f306(f306(f6(x98722,x98726),x98723),f306(f285(x98725,x98722,x98721),x98724)),f306(f306(f6(x98725,x98726),f306(f74(x98722,x98726,x98725,x98723),x98721)),x98724))+~P1(f306(f63(x98725),x98724)) % 187.68/187.66 [9914]~P74(x99142)+~E(f306(x99143,f306(x99145,f421(x99141,x99143,x99145,x99146,x99144,x99142))),f2(x99142))+~P1(f306(f63(x99144),x99146))+E(f306(f306(f6(x99141,x99142),x99143),f306(f285(x99144,x99141,x99145),x99146)),f306(f306(f6(x99144,x99142),f306(f74(x99141,x99142,x99144,x99143),x99145)),x99146)) % 187.68/187.66 [9974]~P74(x99742)+~P1(f306(f63(x99744),x99746))+E(f306(f306(f6(x99741,x99742),x99743),f306(f285(x99744,x99741,x99745),x99746)),f306(f306(f6(x99744,x99742),f306(f74(x99741,x99742,x99744,x99743),x99745)),x99746))+P1(f306(f306(f308(x99744),f421(x99741,x99743,x99745,x99746,x99744,x99742)),x99746)) % 187.68/187.66 [9975]~P74(x99752)+~P1(f306(f63(x99754),x99756))+E(f306(f306(f6(x99751,x99752),x99753),f306(f285(x99754,x99751,x99755),x99756)),f306(f306(f6(x99754,x99752),f306(f74(x99751,x99752,x99754,x99753),x99755)),x99756))+P1(f306(f306(f308(x99754),f429(x99751,x99753,x99755,x99756,x99754,x99752)),x99756)) % 187.68/187.66 [10051]~P41(f872(f871(x100514,x100515),a859),f872(f871(x100514,x100515),a859),x100516)+~P1(f306(f306(x100511,f584(x100511,x100516,x100513,x100512,x100515,x100514)),f585(x100511,x100516,x100513,x100512,x100515,x100514)))+P1(f306(f306(x100511,x100512),x100513))+~P1(f306(f306(f308(f871(x100514,x100515)),f306(f306(f236(x100514,x100515),x100512),x100513)),f102(f872(f871(x100514,x100515),a859),x100516))) % 187.68/187.66 [10090]~P75(x100901)+~P1(f306(f63(x100902),x100906))+E(f306(f306(f306(f67(x100901,x100902,f82(x100901)),f306(f306(f18(x100902,f872(x100903,a859),x100901),f306(f306(f7(x100902,x100901,f872(f872(x100903,a859),x100901)),f306(f306(f8(f872(x100903,x100901),f872(x100901,f872(f872(x100903,a859),x100901)),x100902),f67(x100901,x100903,f82(x100901))),x100904)),f79(x100901))),x100905)),f79(x100901)),x100906),f306(f306(f306(f67(x100901,f871(x100902,x100903),f82(x100901)),f306(f245(x100902,x100903,x100901),x100904)),f79(x100901)),f306(f306(f243(x100902,x100903),x100906),x100905)))+P1(f306(f306(f308(x100902),f501(x100904,x100905,x100903,x100906,x100902,x100901)),x100906)) % 187.68/187.66 [10108]~P75(x101081)+~P1(f306(f63(x101082),x101086))+E(f306(f306(f306(f67(x101081,x101082,f82(x101081)),f306(f306(f18(x101082,f872(x101083,a859),x101081),f306(f306(f7(x101082,x101081,f872(f872(x101083,a859),x101081)),f306(f306(f8(f872(x101083,x101081),f872(x101081,f872(f872(x101083,a859),x101081)),x101082),f67(x101081,x101083,f82(x101081))),x101084)),f79(x101081))),x101085)),f79(x101081)),x101086),f306(f306(f306(f67(x101081,f871(x101082,x101083),f82(x101081)),f306(f245(x101082,x101083,x101081),x101084)),f79(x101081)),f306(f306(f243(x101082,x101083),x101086),x101085)))+~P1(f306(f63(x101083),f306(x101085,f501(x101084,x101085,x101083,x101086,x101082,x101081)))) % 187.68/187.66 [8227]~P23(x82272,x82275,x82276,x82271)+~P1(f306(f63(x82272),x82274))+~P1(f306(f63(x82272),x82273))+E(f306(x82271,f306(f306(f108(f872(x82272,a859)),x82273),x82274)),f306(f74(x82275,x82275,x82275,f306(x82271,x82273)),f306(x82271,x82274))) % 187.68/187.66 [8449]~P6(x84491)+P1(f306(f306(f220(x84491),f306(x84492,x84493)),x84494))+~P1(f306(f306(f308(x84495),x84493),x84496))+~P1(f306(f306(f220(x84491),f306(f306(f43(x84495,x84491),x84496),x84492)),x84494)) % 187.68/187.66 [8854]~P28(x88542,x88541,x88543,x88546)+E(f306(f306(f22(f872(x88541,a859)),f306(f285(x88542,x88541,x88543),x88544)),f306(f285(x88542,x88541,x88543),x88545)),f306(f285(x88542,x88541,x88543),f306(f306(f22(f872(x88542,a859)),x88544),x88545)))+~P1(f306(f306(f220(f872(x88542,a859)),x88545),x88546))+~P1(f306(f306(f220(f872(x88542,a859)),x88544),x88546)) % 187.68/187.66 [8855]~P28(x88552,x88551,x88553,x88556)+E(f306(f306(f109(f872(x88551,a859)),f306(f285(x88552,x88551,x88553),x88554)),f306(f285(x88552,x88551,x88553),x88555)),f306(f285(x88552,x88551,x88553),f306(f306(f109(f872(x88552,a859)),x88554),x88555)))+~P1(f306(f306(f220(f872(x88552,a859)),x88555),x88556))+~P1(f306(f306(f220(f872(x88552,a859)),x88554),x88556)) % 187.68/187.66 [8893]~P1(f306(x88931,x88933))+~P1(f306(f306(f306(f306(a195,x88932),x88933),x88934),x88936))+~P1(f306(f306(f306(f306(a195,f33(x88931,x88932)),x88936),x88934),x88935))+P1(f306(f306(f306(f306(a195,f33(x88931,x88932)),x88933),x88934),x88935)) % 187.68/187.66 [9124]E(x91241,x91242)+~P54(x91243,x91244,x91245)+~P1(f306(f306(f308(f871(x91243,x91244)),f306(f306(f236(x91243,x91244),x91246),x91242)),x91245))+~P1(f306(f306(f308(f871(x91243,x91244)),f306(f306(f236(x91243,x91244),x91246),x91241)),x91245)) % 187.68/187.66 [9909]~P72(x99091)+~E(f306(x99093,f582(x99094,x99096,x99093,x99095,x99092,x99091)),f306(x99096,f582(x99094,x99096,x99093,x99095,x99092,x99091)))+~P1(f306(f63(x99092),x99095))+E(f306(f306(f306(f67(x99091,x99092,f82(x99091)),x99093),x99094),x99095),f306(f306(f306(f67(x99091,x99092,f82(x99091)),x99096),x99094),x99095)) % 187.68/187.66 [9972]~P72(x99721)+~P1(f306(f63(x99722),x99725))+E(f306(f306(f306(f67(x99721,x99722,f82(x99721)),x99723),x99724),x99725),f306(f306(f306(f67(x99721,x99722,f82(x99721)),x99726),x99724),x99725))+P1(f306(f306(f308(x99722),f582(x99724,x99723,x99726,x99725,x99722,x99721)),x99725)) % 187.68/187.66 [8666]~P72(x86661)+~P1(f306(f63(x86662),x86666))+P1(f306(f306(f308(x86662),x86665),x86666))+E(f306(f306(f306(f67(x86661,x86662,f82(x86661)),x86663),x86664),f306(f306(f284(x86662),x86665),x86666)),f306(f306(f82(x86661),f306(x86663,x86665)),f306(f306(f306(f67(x86661,x86662,f82(x86661)),x86663),x86664),x86666))) % 187.68/187.66 [8713]~P9(x87131,x87136,x87133)+~P15(x87131,f872(x87132,a859),x87133,x87135)+~P1(f306(f306(f308(x87131),x87134),x87136))+E(f306(f306(f43(x87131,f872(x87132,a859)),f306(f260(x87131,x87131,x87133),f306(f306(f284(x87131),x87134),f185(f872(x87131,a859))))),x87135),f306(x87135,x87134)) % 187.68/187.66 [8831]~P19(x88313,x88314,x88311)+~P1(f306(f63(x88313),x88316))+~P1(f306(f306(f308(x88313),x88312),x88316))+E(f306(f306(x88311,x88312),f306(f306(f66(x88313,x88314,x88311),x88315),f306(f306(f22(f872(x88313,a859)),x88316),f306(f306(f284(x88313),x88312),f185(f872(x88313,a859)))))),f306(f306(f66(x88313,x88314,x88311),x88315),x88316)) % 187.68/187.66 [9138]~P22(x91383,x91381,x91386,x91382)+~P1(f306(f63(x91383),x91385))+~P1(f306(f63(x91383),x91384))+E(f306(f74(x91381,x91381,x91381,f306(x91382,f306(f306(f108(f872(x91383,a859)),x91384),x91385))),f306(x91382,f306(f306(f109(f872(x91383,a859)),x91384),x91385))),f306(f74(x91381,x91381,x91381,f306(x91382,x91384)),f306(x91382,x91385))) % 187.68/187.66 [10112]~P41(f872(f871(x101124,x101125),a859),f872(f871(x101124,x101125),a859),x101126)+P1(f306(f306(x101121,x101122),x101123))+~P1(f306(f306(f308(f871(x101124,x101125)),f306(f306(f236(x101124,x101125),x101122),x101123)),f102(f872(f871(x101124,x101125),a859),x101126)))+P1(f306(f306(f308(f871(x101124,x101125)),f306(f306(f236(x101124,x101125),f584(x101121,x101126,x101123,x101122,x101125,x101124)),f585(x101121,x101126,x101123,x101122,x101125,x101124))),f306(x101126,f306(f306(f109(f872(f871(x101124,x101125),a859)),f102(f872(f871(x101124,x101125),a859),x101126)),f306(f228(f871(x101124,x101125)),f306(f245(x101124,x101125,a859),x101121)))))) % 187.68/187.66 [9476]~E(x94763,f306(f306(f151(x94761,x94762),x94765),x94766))+P1(f306(f306(f308(f871(f866(x94761),f866(x94761))),f306(f306(f236(f866(x94761),f866(x94761)),x94762),x94763)),f149(x94761,x94764)))+~P1(f306(f306(f221(a865),x94765),f306(f186(f866(x94761)),x94762)))+~P1(f306(f306(f308(f871(x94761,x94761)),f306(f306(f236(x94761,x94761),f306(f306(f157(x94761),x94762),x94765)),x94766)),x94764)) % 187.68/187.66 [9985]~P75(x99852)+~P1(f306(f63(x99851),x99856))+P1(f306(f306(f308(x99851),f499(x99854,x99855,x99853,x99856,x99851,x99852)),x99856))+E(f306(f306(f9(x99851,x99852),f306(f306(f18(x99851,f872(x99853,a859),x99852),f306(f306(f8(f872(x99853,x99852),f872(f872(x99853,a859),x99852),x99851),f9(x99853,x99852)),x99854)),x99855)),x99856),f306(f306(f9(f871(x99851,x99853),x99852),f306(f245(x99851,x99853,x99852),x99854)),f306(f306(f243(x99851,x99853),x99856),x99855))) % 187.68/187.66 [9986]~P74(x99862)+~P1(f306(f63(x99861),x99866))+P1(f306(f306(f308(x99861),f500(x99864,x99865,x99863,x99866,x99861,x99862)),x99866))+E(f306(f306(f6(x99861,x99862),f306(f306(f18(x99861,f872(x99863,a859),x99862),f306(f306(f8(f872(x99863,x99862),f872(f872(x99863,a859),x99862),x99861),f6(x99863,x99862)),x99864)),x99865)),x99866),f306(f306(f6(f871(x99861,x99863),x99862),f306(f245(x99861,x99863,x99862),x99864)),f306(f306(f243(x99861,x99863),x99866),x99865))) % 187.68/187.66 [10026]~P75(x100262)+~P1(f306(f63(x100261),x100266))+~P1(f306(f63(x100263),f306(x100265,f499(x100264,x100265,x100263,x100266,x100261,x100262))))+E(f306(f306(f9(x100261,x100262),f306(f306(f18(x100261,f872(x100263,a859),x100262),f306(f306(f8(f872(x100263,x100262),f872(f872(x100263,a859),x100262),x100261),f9(x100263,x100262)),x100264)),x100265)),x100266),f306(f306(f9(f871(x100261,x100263),x100262),f306(f245(x100261,x100263,x100262),x100264)),f306(f306(f243(x100261,x100263),x100266),x100265))) % 187.68/187.66 [10027]~P74(x100272)+~P1(f306(f63(x100271),x100276))+~P1(f306(f63(x100273),f306(x100275,f500(x100274,x100275,x100273,x100276,x100271,x100272))))+E(f306(f306(f6(x100271,x100272),f306(f306(f18(x100271,f872(x100273,a859),x100272),f306(f306(f8(f872(x100273,x100272),f872(f872(x100273,a859),x100272),x100271),f6(x100273,x100272)),x100274)),x100275)),x100276),f306(f306(f6(f871(x100271,x100273),x100272),f306(f245(x100271,x100273,x100272),x100274)),f306(f306(f243(x100271,x100273),x100276),x100275))) % 187.68/187.66 [10009]~P75(x100092)+~P1(f306(f63(x100091),x100096))+P1(f306(f306(f308(x100091),x100093),x100096))+E(f306(f306(f9(x100091,x100092),f306(f306(f7(x100091,x100092,x100092),f306(f306(f18(x100091,x100092,f872(x100092,x100092)),f306(f306(f8(a859,f872(x100092,f872(x100092,x100092)),x100091),f101(x100092)),f306(f306(f7(x100091,x100091,a859),a303),x100093))),x100094)),x100095)),x100096),f306(f306(f237(x100092),x100095),f306(f39(x100091),x100096))) % 187.68/187.66 [10014]~P75(x100142)+~P1(f306(f63(x100141),x100146))+~P1(f306(f306(f308(x100141),x100143),x100146))+E(f306(f306(f9(x100141,x100142),f306(f306(f7(x100141,x100142,x100142),f306(f306(f18(x100141,x100142,f872(x100142,x100142)),f306(f306(f8(a859,f872(x100142,f872(x100142,x100142)),x100141),f101(x100142)),f306(f306(f7(x100141,x100141,a859),a303),x100143))),x100144)),x100145)),x100146),f306(f306(f82(x100142),f306(x100144,x100143)),f306(f306(f237(x100142),x100145),f306(f306(f22(a865),f306(f39(x100141),x100146)),f79(a865))))) % 187.68/187.66 [10082]~P1(f306(f63(x100821),x100825))+~P1(f306(f63(x100822),x100823))+P1(f306(f306(f308(x100822),f521(x100826,x100824,x100823,x100822,x100825,x100821)),x100823))+E(f306(f306(f6(x100821,a865),f306(f306(f8(f872(x100822,a859),a865,x100821),f39(x100822)),f306(f306(f8(f872(x100822,a859),f872(x100822,a859),x100821),f228(x100822)),f306(f306(f8(f872(x100822,a859),f872(x100822,a859),x100821),f306(f18(x100822,a859,a859),f306(f306(f8(a859,f872(a859,a859),x100822),a304),f306(f306(f7(x100822,f872(x100822,a859),a859),f308(x100822)),x100823)))),x100824)))),x100825),f306(f306(f82(a865),x100826),f306(f39(x100822),x100823))) % 187.68/187.66 [10083]~P1(f306(f63(x100831),x100835))+~P1(f306(f63(x100832),x100833))+P1(f306(f306(f308(x100832),f522(x100836,x100834,x100833,x100832,x100835,x100831)),x100833))+E(f306(f306(f6(x100831,a865),f306(f306(f8(f872(x100832,a859),a865,x100831),f39(x100832)),f306(f306(f8(f872(x100832,a859),f872(x100832,a859),x100831),f228(x100832)),f306(f306(f8(f872(x100832,a859),f872(x100832,a859),x100831),f306(f18(x100832,a859,a859),f306(f306(f8(a859,f872(a859,a859),x100832),a304),f306(f306(f7(x100832,f872(x100832,a859),a859),f308(x100832)),x100833)))),x100834)))),x100835),f306(f306(f6(x100832,a865),x100836),x100833)) % 187.68/187.66 [10116]~P1(f306(f63(x101162),x101163))+~P1(f306(f63(x101161),x101165))+~E(f306(f39(x101161),f306(f228(x101161),f306(f306(f18(x101161,a859,a859),f306(f306(f8(a859,f872(a859,a859),x101161),a304),f306(f306(f7(x101161,f872(x101161,a859),a859),f308(x101161)),x101165))),f306(f306(f7(x101161,x101162,a859),x101164),f521(x101166,x101164,x101163,x101162,x101165,x101161))))),x101166)+E(f306(f306(f6(x101161,a865),f306(f306(f8(f872(x101162,a859),a865,x101161),f39(x101162)),f306(f306(f8(f872(x101162,a859),f872(x101162,a859),x101161),f228(x101162)),f306(f306(f8(f872(x101162,a859),f872(x101162,a859),x101161),f306(f18(x101162,a859,a859),f306(f306(f8(a859,f872(a859,a859),x101162),a304),f306(f306(f7(x101162,f872(x101162,a859),a859),f308(x101162)),x101163)))),x101164)))),x101165),f306(f306(f82(a865),x101166),f306(f39(x101162),x101163))) % 187.68/187.66 [10118]~P1(f306(f63(x101182),x101183))+~P1(f306(f63(x101181),x101185))+~E(f306(f39(x101181),f306(f228(x101181),f306(f306(f18(x101181,a859,a859),f306(f306(f8(a859,f872(a859,a859),x101181),a304),f306(f306(f7(x101181,f872(x101181,a859),a859),f308(x101181)),x101185))),f306(f306(f7(x101181,x101182,a859),x101184),f522(x101186,x101184,x101183,x101182,x101185,x101181))))),f306(x101186,f522(x101186,x101184,x101183,x101182,x101185,x101181)))+E(f306(f306(f6(x101181,a865),f306(f306(f8(f872(x101182,a859),a865,x101181),f39(x101182)),f306(f306(f8(f872(x101182,a859),f872(x101182,a859),x101181),f228(x101182)),f306(f306(f8(f872(x101182,a859),f872(x101182,a859),x101181),f306(f18(x101182,a859,a859),f306(f306(f8(a859,f872(a859,a859),x101182),a304),f306(f306(f7(x101182,f872(x101182,a859),a859),f308(x101182)),x101183)))),x101184)))),x101185),f306(f306(f6(x101182,a865),x101186),x101183)) % 187.68/187.66 [9764]E(x97641,x97642)+~P19(x97643,x97644,x97645)+~P1(f306(f68(x97643,x97644,x97645,x97646,x97647),x97642))+~P1(f306(f68(x97643,x97644,x97645,x97646,x97647),x97641)) % 187.68/187.66 [9555]P1(f306(x95551,x95552))+~P1(f306(f306(f308(x95557),x95552),f306(x95556,x95554)))+~P1(f306(x95551,f457(x95551,x95556,x95555,x95553,x95557)))+~P1(f306(f306(f308(x95553),x95554),x95555)) % 187.68/187.66 [10000]~P19(x100007,x100006,x100001)+E(f306(f306(x100001,x100002),f626(x100002,x100003,x100004,x100005,x100001,x100006,x100007)),x100003)+~P1(f306(f68(x100007,x100006,x100001,x100005,x100004),x100003))+~P1(f306(f306(f308(x100007),x100002),x100004)) % 187.68/187.66 [10067]~P19(x100671,x100672,x100673)+~P1(f306(f68(x100671,x100672,x100673,x100674,x100675),x100677))+P1(f306(f68(x100671,x100672,x100673,x100674,f306(f306(f22(f872(x100671,a859)),x100675),f306(f306(f284(x100671),x100676),f185(f872(x100671,a859))))),f626(x100676,x100677,x100675,x100674,x100673,x100672,x100671)))+~P1(f306(f306(f308(x100671),x100676),x100675)) % 187.68/187.66 [9452]~P72(x94521)+~P28(x94525,x94522,x94526,x94527)+~P1(f306(f63(x94525),x94527))+E(f306(f306(f306(f67(x94521,x94522,f82(x94521)),x94523),x94524),f306(f285(x94525,x94522,x94526),x94527)),f306(f306(f306(f67(x94521,x94525,f82(x94521)),f306(f74(x94522,x94521,x94525,x94523),x94526)),x94524),x94527)) % 187.68/187.66 [9579]~E(f306(f306(f284(x95791),x95795),x95796),f306(f306(f284(x95791),x95792),x95793))+~P1(f306(f68(x95791,x95791,x95794,x95792,x95793),x95797))+P1(f306(f306(f308(x95791),x95792),x95793))+P1(f306(f64(x95791,x95794,f306(f306(f284(x95791),x95795),x95796)),x95797)) % 187.68/187.66 [9661]P1(f306(x96611,x96612))+~P1(f306(f306(f308(x96613),x96612),f306(x96614,x96617)))+~P1(f306(f306(f308(x96616),x96617),x96615))+P1(f306(f306(f308(x96613),f457(x96611,x96614,x96615,x96616,x96613)),f306(f306(f43(x96616,f872(x96613,a859)),x96615),x96614))) % 187.68/187.66 [9675]~P28(x96752,x96751,x96755,x96754)+~P28(x96751,x96753,x96756,f306(f285(x96752,x96751,x96755),x96754))+E(f306(f306(f74(x96751,x96752,x96753,f78(x96752,x96751,x96754,x96755)),f78(x96751,x96753,f306(f285(x96752,x96751,x96755),x96754),x96756)),x96757),f306(f78(x96752,x96753,x96754,f306(f74(x96751,x96753,x96752,x96756),x96755)),x96757))+~P1(f306(f306(f308(x96753),x96757),f306(f285(x96751,x96753,x96756),f306(f285(x96752,x96751,x96755),x96754)))) % 187.68/187.66 [10001]~P19(x100017,x100016,x100011)+E(f306(f306(x100011,x100012),f649(x100013,x100014,x100012,x100015,x100011,x100016,x100017)),x100013)+P1(f306(f306(f308(x100017),x100012),x100014))+~P1(f306(f68(x100017,x100016,x100011,x100015,f306(f306(f284(x100017),x100012),x100014)),x100013)) % 187.68/187.66 [10066]~P19(x100661,x100664,x100665)+P1(f306(f68(x100661,x100664,x100665,x100666,x100663),f649(x100667,x100663,x100662,x100666,x100665,x100664,x100661)))+P1(f306(f306(f308(x100661),x100662),x100663))+~P1(f306(f68(x100661,x100664,x100665,x100666,f306(f306(f284(x100661),x100662),x100663)),x100667)) % 187.68/187.66 [9747]E(x97471,f2(a1))+~P1(f306(f50(x97473,x97471),f306(f306(f236(a1,a1),x97475),x97477)))+~P1(f306(f50(x97472,x97471),f306(f306(f236(a1,a1),x97474),x97476)))+P1(f306(f50(f306(f306(f81(a1),x97472),x97473),x97471),f306(f306(f236(a1,a1),f306(f306(f81(a1),f306(f306(f81(a1),x97474),x97475)),f306(f306(f40(a1),f306(f306(f81(a1),x97476),x97477)),x97471))),f46(a1,f306(f306(f81(a1),x97476),x97477),x97471)))) % 187.68/187.66 [9749]~P1(f306(f306(f221(a865),f2(a865)),x97493))+~P1(f306(f49(x97492,x97493),f306(f306(f236(a865,a865),x97495),x97497)))+~P1(f306(f49(x97491,x97493),f306(f306(f236(a865,a865),x97494),x97496)))+P1(f306(f49(f306(f306(f81(a865),x97491),x97492),x97493),f306(f306(f236(a865,a865),f306(f306(f81(a865),f306(f306(f81(a865),x97494),x97495)),f306(f306(f40(a865),f306(f306(f81(a865),x97496),x97497)),x97493))),f46(a865,f306(f306(f81(a865),x97496),x97497),x97493)))) % 187.68/187.66 [10115]~P74(x101152)+~P1(f306(f63(x101153),x101155))+~P1(f306(f63(x101151),x101157))+E(f306(f306(f6(x101151,x101152),f306(f306(f18(x101151,f872(x101153,a859),x101152),f306(f306(f8(f872(x101153,x101152),f872(f872(x101153,a859),x101152),x101151),f6(x101153,x101152)),x101154)),f306(f306(f8(f872(x101153,a859),f872(x101153,a859),x101151),f228(x101153)),f306(f306(f8(f872(x101153,a859),f872(x101153,a859),x101151),f306(f18(x101153,a859,a859),f306(f306(f8(a859,f872(a859,a859),x101153),a304),f306(f306(f7(x101153,f872(x101153,a859),a859),f308(x101153)),x101155)))),x101156)))),x101157),f306(f306(f6(x101153,x101152),f306(f306(f18(x101153,f872(x101151,a859),x101152),f306(f306(f8(f872(x101151,x101152),f872(f872(x101151,a859),x101152),x101153),f6(x101151,x101152)),f306(f7(x101151,x101153,x101152),x101154))),f306(f306(f8(f872(x101151,a859),f872(x101151,a859),x101153),f228(x101151)),f306(f306(f8(f872(x101151,a859),f872(x101151,a859),x101153),f306(f18(x101151,a859,a859),f306(f306(f8(a859,f872(a859,a859),x101151),a304),f306(f306(f7(x101151,f872(x101151,a859),a859),f308(x101151)),x101157)))),f306(f7(x101151,x101153,a859),x101156))))),x101155)) % 187.68/187.66 [9615]~P25(x96157,x96156,x96151,x96158,x96152,x96154)+E(f306(f306(x96151,f306(x96152,x96153)),f306(x96154,x96155)),f306(x96154,x96155))+~P1(f306(f63(x96156),x96155))+~P1(f306(f306(f308(x96156),x96153),x96155)) % 187.68/187.66 [9619]~P16(x96196,x96191,x96192,x96198,x96193,x96194)+~P9(x96196,x96197,x96198)+P15(x96191,x96192,x96193,f306(x96194,x96195))+~P1(f306(f306(f308(x96196),x96195),x96197)) % 187.68/187.66 [8043]~P30(x80438,x80437,f306(f306(f306(f93(x80438),x80434),x80436),x80431))+P1(f306(f306(x80431,x80432),x80433))+~P1(f306(f306(x80434,x80432),x80435))+~P1(f306(f306(f306(f306(a195,x80436),x80435),x80437),x80433)) % 187.68/187.66 [9234]~P22(x92347,x92341,x92348,x92343)+~P1(f306(f63(x92347),x92345))+~P1(f306(f63(x92347),x92344))+E(f306(f74(x92341,x92341,x92342,f306(x92343,x92344)),f306(f74(x92341,x92341,x92342,f306(x92343,x92345)),x92346)),f306(f74(x92341,x92341,x92342,f306(x92343,x92345)),f306(f74(x92341,x92341,x92342,f306(x92343,x92344)),x92346))) % 187.68/187.66 [9242]~P37(x92421,x92422,x92423,x92424,x92427)+P37(x92421,x92422,x92423,f306(f306(f151(x92421,x92424),x92425),x92426),f306(f306(f151(x92422,x92427),x92425),x92428))+~P1(f306(f306(x92423,x92426),x92428))+~P1(f306(f306(f221(a865),x92425),f306(f186(f866(x92421)),x92424))) % 187.68/187.66 [9243]~P37(x92431,x92432,x92433,x92434,x92437)+P37(x92431,x92432,x92433,f306(f306(f151(x92431,x92434),x92435),x92436),f306(f306(f151(x92432,x92437),x92435),x92438))+~P1(f306(f306(x92433,x92436),x92438))+~P1(f306(f306(f221(a865),x92435),f306(f186(f866(x92432)),x92437))) % 187.68/187.66 [9323]~P28(x93232,x93232,x93235,x93236)+~P24(x93233,x93232,x93237,x93238,x93231)+~P1(f306(f63(x93232),x93236))+E(f306(f306(x93231,f306(f74(x93232,x93233,x93232,x93234),x93235)),x93236),f306(f306(x93231,x93234),f306(f285(x93232,x93232,x93235),x93236))) % 187.68/187.66 [9617]~P26(x96177,x96172,x96175,x96178,x96176,x96171)+~P1(f306(f63(x96172),x96174))+E(f306(x96171,f306(f306(f284(x96172),x96173),x96174)),f306(f306(x96175,f306(x96176,x96173)),f306(x96171,x96174)))+P1(f306(f306(f308(x96172),x96173),x96174)) % 187.68/187.66 [9626]~P25(x96266,x96265,x96261,x96267,x96268,x96262)+E(f306(f306(x96261,f306(x96262,x96263)),f306(x96262,x96264)),f306(x96262,x96264))+~P1(f306(f63(x96265),x96264))+~P1(f306(f306(f220(f872(x96265,a859)),x96263),x96264)) % 187.68/187.66 [10113]P27(x101138,x101137,f306(f306(f284(f864(x101138)),f306(f306(f306(f93(x101138),x101134),x101135),x101133)),f185(f872(f864(x101138),a859))))+~P27(x101138,x101137,f306(f306(f284(f864(x101138)),f306(f306(f306(f93(x101138),x101136),x101135),x101131)),f185(f872(f864(x101138),a859))))+~P1(f306(f306(x101136,x101132),f843(x101133,x101134,x101131,x101135,x101136,x101137,x101138)))+P1(f306(f306(x101131,x101132),f850(x101133,x101134,x101131,x101135,x101136,x101137,x101138))) % 187.68/187.66 [9219]P1(f306(f306(f308(f871(f866(x92191),f866(x92191))),f306(f306(f236(f866(x92191),f866(x92191)),x92192),x92193)),f149(x92191,x92194)))+~E(x92193,f306(f306(f122(x92191),x92195),f306(f306(f143(x92191),x92196),x92197)))+~E(x92192,f306(f306(f122(x92191),x92195),f306(f306(f143(x92191),x92198),x92197)))+~P1(f306(f306(f308(f871(x92191,x92191)),f306(f306(f236(x92191,x92191),x92198),x92196)),x92194)) % 187.68/187.66 [9622]~P25(x96226,x96222,x96225,x96227,x96228,x96221)+~P1(f306(f63(x96222),x96224))+~P1(f306(f63(x96222),x96223))+E(f306(x96221,f306(f306(f108(f872(x96222,a859)),x96223),x96224)),f306(f306(x96225,f306(x96221,x96223)),f306(x96221,x96224))) % 187.68/187.66 [10157]~P28(x101574,x101572,x101575,x101578)+E(f306(f306(f44(x101571,f872(x101572,a859)),x101573),f306(f306(f8(f872(x101574,a859),f872(x101572,a859),x101571),f285(x101574,x101572,x101575)),x101576)),f306(f285(x101574,x101572,x101575),f306(f306(f44(x101571,f872(x101574,a859)),x101573),x101576)))+~P1(f306(f306(f308(x101571),x101577),x101573))+P1(f306(f306(f308(x101571),f638(x101577,x101576,x101573,x101571,x101578,x101575,x101572,x101574)),x101573)) % 187.68/187.66 [10179]~P28(x101794,x101792,x101795,x101797)+E(f306(f306(f44(x101791,f872(x101792,a859)),x101793),f306(f306(f8(f872(x101794,a859),f872(x101792,a859),x101791),f285(x101794,x101792,x101795)),x101796)),f306(f285(x101794,x101792,x101795),f306(f306(f44(x101791,f872(x101794,a859)),x101793),x101796)))+~P1(f306(f306(f308(x101791),x101798),x101793))+~P1(f306(f306(f220(f872(x101794,a859)),f306(x101796,f638(x101798,x101796,x101793,x101791,x101797,x101795,x101792,x101794))),x101797)) % 187.68/187.66 [9684]~P26(x96847,x96845,x96841,x96848,x96842,x96844)+~P1(f306(f63(x96845),x96846))+~P1(f306(f306(f308(x96845),x96843),x96846))+E(f306(f306(x96841,f306(x96842,x96843)),f306(x96844,f306(f306(f22(f872(x96845,a859)),x96846),f306(f306(f284(x96845),x96843),f185(f872(x96845,a859)))))),f306(x96844,x96846)) % 187.68/187.66 [9692]~P26(x96926,x96923,x96921,x96927,x96928,x96922)+~P1(f306(f63(x96923),x96925))+~P1(f306(f63(x96923),x96924))+E(f306(f306(x96921,f306(x96922,f306(f306(f108(f872(x96923,a859)),x96924),x96925))),f306(x96922,f306(f306(f109(f872(x96923,a859)),x96924),x96925))),f306(f306(x96921,f306(x96922,x96924)),f306(x96922,x96925))) % 187.68/187.66 [9786]P44(x97861,x97862,x97863,x97864,x97865,f306(f306(x97863,x97866),x97867))+~P44(x97861,x97862,x97863,x97864,f306(f306(f22(f872(x97861,a859)),x97865),f306(f306(f284(x97861),x97868),f185(f872(x97861,a859)))),x97869)+~E(f306(f306(x97863,x97866),x97867),f306(f306(x97863,x97868),x97869))+~P1(f306(f306(f308(x97861),x97868),x97865)) % 187.68/187.66 [10194]P27(x101941,x101942,f306(f306(f284(f864(x101941)),f306(f306(f306(f93(x101941),f306(x101943,f350(x101944,x101945,x101946,x101947,x101943,x101942,x101941,x101948,x101949))),f306(x101947,f350(x101944,x101945,x101946,x101947,x101943,x101942,x101941,x101948,x101949))),f306(x101946,f350(x101944,x101945,x101946,x101947,x101943,x101942,x101941,x101948,x101949)))),f185(f872(f864(x101941),a859))))+~P1(f306(f63(x101949),x101948))+~P27(x101941,x101942,f306(f285(x101949,f864(x101941),f306(f306(f18(x101949,f872(x101941,f872(a861,a859)),f864(x101941)),f306(f306(f18(x101949,a860,f872(f872(x101941,f872(a861,a859)),f864(x101941))),f306(f306(f8(f872(x101941,f872(a861,a859)),f872(a860,f872(f872(x101941,f872(a861,a859)),f864(x101941))),x101949),f93(x101941)),x101943)),x101947)),x101946)),x101948))+P27(x101941,x101942,f306(f285(x101949,f864(x101941),f306(f306(f18(x101949,f872(x101941,f872(a861,a859)),f864(x101941)),f306(f306(f18(x101949,a860,f872(f872(x101941,f872(a861,a859)),f864(x101941))),f306(f306(f8(f872(x101941,f872(a861,a859)),f872(a860,f872(f872(x101941,f872(a861,a859)),f864(x101941))),x101949),f93(x101941)),x101945)),x101947)),x101944)),x101948)) % 187.68/187.66 [10195]~P27(x101951,x101952,f306(f306(f284(f864(x101951)),f306(f306(f306(f93(x101951),f306(x101954,f350(x101956,x101954,x101958,x101955,x101959,x101952,x101951,x101957,x101953))),f306(x101955,f350(x101956,x101954,x101958,x101955,x101959,x101952,x101951,x101957,x101953))),f306(x101956,f350(x101956,x101954,x101958,x101955,x101959,x101952,x101951,x101957,x101953)))),f185(f872(f864(x101951),a859))))+~P1(f306(f63(x101953),x101957))+~P27(x101951,x101952,f306(f285(x101953,f864(x101951),f306(f306(f18(x101953,f872(x101951,f872(a861,a859)),f864(x101951)),f306(f306(f18(x101953,a860,f872(f872(x101951,f872(a861,a859)),f864(x101951))),f306(f306(f8(f872(x101951,f872(a861,a859)),f872(a860,f872(f872(x101951,f872(a861,a859)),f864(x101951))),x101953),f93(x101951)),x101959)),x101955)),x101958)),x101957))+P27(x101951,x101952,f306(f285(x101953,f864(x101951),f306(f306(f18(x101953,f872(x101951,f872(a861,a859)),f864(x101951)),f306(f306(f18(x101953,a860,f872(f872(x101951,f872(a861,a859)),f864(x101951))),f306(f306(f8(f872(x101951,f872(a861,a859)),f872(a860,f872(f872(x101951,f872(a861,a859)),f864(x101951))),x101953),f93(x101951)),x101954)),x101955)),x101956)),x101957)) % 187.68/187.66 [9720]~P16(x97206,x97207,x97208,x97209,x972010,x97201)+E(f306(f306(x97201,x97202),x97203),f306(f306(x97201,x97204),x97205))+~P1(f306(f306(f308(f871(x97207,x97207)),f306(f306(f236(x97207,x97207),x97203),x97205)),x972010))+~P1(f306(f306(f308(f871(x97206,x97206)),f306(f306(f236(x97206,x97206),x97202),x97204)),x97209)) % 187.68/187.66 [9327]~P98(x93272)+E(x93271,f185(f872(x93272,a859)))+~P1(f306(f63(x93272),x93271))+P1(f306(f306(f308(x93272),f13(x93272,x93271)),x93271))+~P1(f306(f306(f308(x93272),f306(f306(f108(x93272),f349(x93271,x93272)),f351(x93271,x93272))),f306(f306(f284(x93272),f349(x93271,x93272)),f306(f306(f284(x93272),f351(x93271,x93272)),f185(f872(x93272,a859)))))) % 187.68/187.66 [9328]~P98(x93282)+E(x93281,f185(f872(x93282,a859)))+~P1(f306(f63(x93282),x93281))+P1(f306(f306(f308(x93282),f10(x93282,x93281)),x93281))+~P1(f306(f306(f308(x93282),f306(f306(f109(x93282),f449(x93281,x93282)),f451(x93281,x93282))),f306(f306(f284(x93282),f449(x93281,x93282)),f306(f306(f284(x93282),f451(x93281,x93282)),f185(f872(x93282,a859)))))) % 187.68/187.66 [9359]~P72(x93592)+E(x93591,f185(f872(x93592,a859)))+~P1(f306(f63(x93592),x93591))+P1(f306(f306(f308(x93592),f306(f65(x93592,f82(x93592)),x93591)),x93591))+~P1(f306(f306(f308(x93592),f306(f306(f82(x93592),f824(x93591,x93592)),f825(x93591,x93592))),f306(f306(f284(x93592),f824(x93591,x93592)),f306(f306(f284(x93592),f825(x93591,x93592)),f185(f872(x93592,a859)))))) % 187.68/187.66 [9365]~P108(x93652)+E(x93651,f185(f872(x93652,a859)))+~P1(f306(f63(x93652),x93651))+P1(f306(f306(f308(x93652),f11(x93652,f225(x93652),x93651)),x93651))+~P1(f306(f306(f308(x93652),f306(f306(f225(x93652),f841(x93651,x93652)),f842(x93651,x93652))),f306(f306(f284(x93652),f841(x93651,x93652)),f306(f306(f284(x93652),f842(x93651,x93652)),f185(f872(x93652,a859)))))) % 187.68/187.66 [9366]~P108(x93662)+E(x93661,f185(f872(x93662,a859)))+~P1(f306(f63(x93662),x93661))+P1(f306(f306(f308(x93662),f12(x93662,f219(x93662),x93661)),x93661))+~P1(f306(f306(f308(x93662),f306(f306(f219(x93662),f846(x93661,x93662)),f847(x93661,x93662))),f306(f306(f284(x93662),f846(x93661,x93662)),f306(f306(f284(x93662),f847(x93661,x93662)),f185(f872(x93662,a859)))))) % 187.68/187.66 [6479]~P86(x64792)+E(x64791,f2(x64792))+~E(f306(f306(f81(x64792),x64793),x64791),f2(x64792))+~P1(f306(f306(f220(x64792),f2(x64792)),x64793))+~P1(f306(f306(f220(x64792),f2(x64792)),x64791)) % 187.68/187.66 [6480]~P86(x64802)+E(x64801,f2(x64802))+~E(f306(f306(f81(x64802),x64801),x64803),f2(x64802))+~P1(f306(f306(f220(x64802),f2(x64802)),x64803))+~P1(f306(f306(f220(x64802),f2(x64802)),x64801)) % 187.68/187.66 [7012]~P108(x70122)+~P17(x70122,x70121)+E(x70121,f120(x70122))+~P1(f306(f306(f308(x70122),x70123),f306(f164(x70122),f722(x70121,x70122))))+P1(f306(f306(f220(x70122),f756(x70121,x70122)),x70123)) % 187.68/187.66 [7178]~P108(x71781)+E(f14(x71781,x71782),x71783)+~P1(f306(f63(x71781),x71782))+~P1(f306(f306(f220(x71781),x71783),f577(x71783,x71782,x71781)))+~P1(f306(f306(f308(x71781),x71783),x71782)) % 187.68/187.66 [7209]~P108(x72091)+~P17(x72091,x72092)+~P17(x72091,x72093)+P17(x72091,f306(f306(f122(x72091),x72092),x72093))+P1(f306(f306(f308(x72091),f729(x72093,x72092,x72091)),f306(f164(x72091),x72092))) % 187.68/187.66 [7210]~P108(x72101)+~P17(x72101,x72102)+~P17(x72101,x72103)+P17(x72101,f306(f306(f122(x72101),x72102),x72103))+P1(f306(f306(f308(x72101),f730(x72103,x72102,x72101)),f306(f164(x72101),x72103))) % 187.68/187.66 [7266]~P108(x72661)+E(f14(x72661,x72662),x72663)+~P1(f306(f63(x72661),x72662))+P1(f306(f306(f308(x72661),f577(x72663,x72662,x72661)),x72662))+~P1(f306(f306(f308(x72661),x72663),x72662)) % 187.68/187.66 [7267]~P108(x72671)+E(f15(x72671,x72672),x72673)+~P1(f306(f63(x72671),x72672))+P1(f306(f306(f308(x72671),f578(x72673,x72672,x72671)),x72672))+~P1(f306(f306(f308(x72671),x72673),x72672)) % 187.68/187.66 [7844]~P108(x78441)+E(f15(x78441,x78442),x78443)+~P1(f306(f63(x78441),x78442))+~P1(f306(f306(f308(x78441),x78443),x78442))+~P1(f306(f306(f220(x78441),f578(x78443,x78442,x78441)),x78443)) % 187.68/187.66 [8175]~P108(x81751)+~P17(x81751,x81752)+~P17(x81751,x81753)+P17(x81751,f306(f306(f122(x81751),x81752),x81753))+~P1(f306(f306(f220(x81751),f729(x81753,x81752,x81751)),f730(x81753,x81752,x81751))) % 187.68/187.66 [8960]~P108(x89602)+E(x89601,f185(f872(x89602,a859)))+~E(f306(f306(f225(x89602),f306(x89603,f344(x89601,x89603,x89602))),f306(x89603,f356(x89601,x89603,x89602))),f306(x89603,f306(f306(f225(x89602),f344(x89601,x89603,x89602)),f356(x89601,x89603,x89602))))+E(f14(x89602,f306(f285(x89602,x89602,x89603),x89601)),f306(x89603,f14(x89602,x89601)))+~P1(f306(f63(x89602),x89601)) % 187.68/187.66 [8961]~P108(x89612)+E(x89611,f185(f872(x89612,a859)))+~E(f306(f306(f219(x89612),f306(x89613,f345(x89611,x89613,x89612))),f306(x89613,f355(x89611,x89613,x89612))),f306(x89613,f306(f306(f219(x89612),f345(x89611,x89613,x89612)),f355(x89611,x89613,x89612))))+E(f15(x89612,f306(f285(x89612,x89612,x89613),x89611)),f306(x89613,f15(x89612,x89611)))+~P1(f306(f63(x89612),x89611)) % 187.68/187.66 [8962]~P98(x89622)+E(x89621,f185(f872(x89622,a859)))+~E(f306(f306(f108(x89622),f306(x89623,f357(x89621,x89623,x89622))),f306(x89623,f358(x89621,x89623,x89622))),f306(x89623,f306(f306(f108(x89622),f357(x89621,x89623,x89622)),f358(x89621,x89623,x89622))))+E(f13(x89622,f306(f285(x89622,x89622,x89623),x89621)),f306(x89623,f13(x89622,x89621)))+~P1(f306(f63(x89622),x89621)) % 187.68/187.66 [8963]~P98(x89632)+E(x89631,f185(f872(x89632,a859)))+~E(f306(f306(f109(x89632),f306(x89633,f475(x89631,x89633,x89632))),f306(x89633,f476(x89631,x89633,x89632))),f306(x89633,f306(f306(f109(x89632),f475(x89631,x89633,x89632)),f476(x89631,x89633,x89632))))+E(f10(x89632,f306(f285(x89632,x89632,x89633),x89631)),f306(x89633,f10(x89632,x89631)))+~P1(f306(f63(x89632),x89631)) % 187.68/187.66 [9034]~P108(x90342)+E(x90341,f185(f872(x90342,a859)))+~E(f306(f306(f225(x90342),f306(x90343,f346(x90341,x90343,x90342))),f306(x90343,f354(x90341,x90343,x90342))),f306(x90343,f306(f306(f225(x90342),f346(x90341,x90343,x90342)),f354(x90341,x90343,x90342))))+E(f11(x90342,f225(x90342),f306(f285(x90342,x90342,x90343),x90341)),f306(x90343,f11(x90342,f225(x90342),x90341)))+~P1(f306(f63(x90342),x90341)) % 187.68/187.66 [9035]~P108(x90352)+E(x90351,f185(f872(x90352,a859)))+~E(f306(f306(f219(x90352),f306(x90353,f347(x90351,x90353,x90352))),f306(x90353,f353(x90351,x90353,x90352))),f306(x90353,f306(f306(f219(x90352),f347(x90351,x90353,x90352)),f353(x90351,x90353,x90352))))+E(f12(x90352,f219(x90352),f306(f285(x90352,x90352,x90353),x90351)),f306(x90353,f12(x90352,f219(x90352),x90351)))+~P1(f306(f63(x90352),x90351)) % 187.68/187.66 [6493]~P72(x64932)+E(x64931,f185(f872(x64932,a859)))+~P1(f306(f63(x64932),x64931))+E(f306(f65(x64932,f82(x64932)),f306(f306(f284(x64932),x64933),x64931)),f306(f306(f82(x64932),x64933),f306(f65(x64932,f82(x64932)),x64931)))+P1(f306(f306(f308(x64932),x64933),x64931)) % 187.68/187.66 [7018]~P108(x70182)+E(f306(f306(f225(x70182),f14(x70182,x70181)),f14(x70182,x70183)),f14(x70182,x70183))+E(x70181,f185(f872(x70182,a859)))+~P1(f306(f63(x70182),x70183))+~P1(f306(f306(f220(f872(x70182,a859)),x70181),x70183)) % 187.68/187.66 [7019]~P108(x70192)+E(f306(f306(f219(x70192),f15(x70192,x70191)),f15(x70192,x70193)),f15(x70192,x70193))+E(x70191,f185(f872(x70192,a859)))+~P1(f306(f63(x70192),x70193))+~P1(f306(f306(f220(f872(x70192,a859)),x70191),x70193)) % 187.68/187.66 [7020]~P98(x70202)+E(f306(f306(f108(x70202),f13(x70202,x70201)),f13(x70202,x70203)),f13(x70202,x70203))+E(x70201,f185(f872(x70202,a859)))+~P1(f306(f63(x70202),x70203))+~P1(f306(f306(f220(f872(x70202,a859)),x70201),x70203)) % 187.68/187.66 [7021]~P98(x70212)+E(f306(f306(f109(x70212),f10(x70212,x70211)),f10(x70212,x70213)),f10(x70212,x70213))+E(x70211,f185(f872(x70212,a859)))+~P1(f306(f63(x70212),x70213))+~P1(f306(f306(f220(f872(x70212,a859)),x70211),x70213)) % 187.68/187.66 [7317]~P108(x73172)+E(x73171,f185(f872(x73172,a859)))+~P1(f306(f63(x73172),x73173))+P1(f306(f306(f220(x73172),f14(x73172,x73173)),f14(x73172,x73171)))+~P1(f306(f306(f220(f872(x73172,a859)),x73171),x73173)) % 187.68/187.66 [7318]~P108(x73182)+E(x73181,f185(f872(x73182,a859)))+~P1(f306(f63(x73182),x73183))+P1(f306(f306(f220(x73182),f15(x73182,x73181)),f15(x73182,x73183)))+~P1(f306(f306(f220(f872(x73182,a859)),x73181),x73183)) % 187.68/187.66 [7376]~P108(x73761)+E(f14(x73761,x73762),x73763)+~P1(f306(f63(x73761),x73762))+~E(f306(f306(f22(f872(x73761,a859)),x73762),f306(f306(f284(x73761),x73763),f185(f872(x73761,a859)))),f185(f872(x73761,a859)))+~P1(f306(f306(f308(x73761),x73763),x73762)) % 187.68/187.66 [7377]~P108(x73771)+E(f15(x73771,x73772),x73773)+~P1(f306(f63(x73771),x73772))+~E(f306(f306(f22(f872(x73771,a859)),x73772),f306(f306(f284(x73771),x73773),f185(f872(x73771,a859)))),f185(f872(x73771,a859)))+~P1(f306(f306(f308(x73771),x73773),x73772)) % 187.68/187.66 [7378]~P98(x73781)+E(f13(x73781,x73782),x73783)+~P1(f306(f63(x73781),x73782))+~E(f306(f306(f22(f872(x73781,a859)),x73782),f306(f306(f284(x73781),x73783),f185(f872(x73781,a859)))),f185(f872(x73781,a859)))+~P1(f306(f306(f308(x73781),x73783),x73782)) % 187.68/187.66 [7379]~P98(x73791)+E(f10(x73791,x73792),x73793)+~P1(f306(f63(x73791),x73792))+~E(f306(f306(f22(f872(x73791,a859)),x73792),f306(f306(f284(x73791),x73793),f185(f872(x73791,a859)))),f185(f872(x73791,a859)))+~P1(f306(f306(f308(x73791),x73793),x73792)) % 187.68/187.66 [7475]~P108(x74751)+E(f11(x74751,f225(x74751),x74752),x74753)+~P1(f306(f63(x74751),x74752))+~E(f306(f306(f22(f872(x74751,a859)),x74752),f306(f306(f284(x74751),x74753),f185(f872(x74751,a859)))),f185(f872(x74751,a859)))+~P1(f306(f306(f308(x74751),x74753),x74752)) % 187.68/187.66 [7476]~P108(x74761)+E(f12(x74761,f219(x74761),x74762),x74763)+~P1(f306(f63(x74761),x74762))+~E(f306(f306(f22(f872(x74761,a859)),x74762),f306(f306(f284(x74761),x74763),f185(f872(x74761,a859)))),f185(f872(x74761,a859)))+~P1(f306(f306(f308(x74761),x74763),x74762)) % 187.68/187.66 [7512]~P108(x75122)+E(x75121,f185(f872(x75122,a859)))+~P1(f306(f63(x75122),x75121))+~P1(f306(f306(f220(x75122),x75123),f835(x75123,x75121,x75122)))+P1(f306(f306(f220(x75122),x75123),f306(f65(x75122,f225(x75122)),x75121))) % 187.68/187.66 [7513]~P103(x75132)+E(x75131,f185(f872(x75132,a859)))+~P1(f306(f63(x75132),x75131))+~P1(f306(f306(f220(x75132),x75133),f437(x75133,x75131,x75132)))+P1(f306(f306(f220(x75132),x75133),f306(f65(x75132,f109(x75132)),x75131))) % 187.68/187.66 [7514]~P108(x75142)+E(x75141,f185(f872(x75142,a859)))+~P1(f306(f63(x75142),x75141))+~P1(f306(f306(f221(x75142),x75143),f836(x75143,x75141,x75142)))+P1(f306(f306(f221(x75142),x75143),f306(f65(x75142,f225(x75142)),x75141))) % 187.68/187.66 [7599]~P108(x75992)+E(x75991,f185(f872(x75992,a859)))+~P1(f306(f63(x75992),x75991))+P1(f306(f306(f308(x75992),f836(x75993,x75991,x75992)),x75991))+P1(f306(f306(f221(x75992),x75993),f306(f65(x75992,f225(x75992)),x75991))) % 187.68/187.66 [7600]~P108(x76002)+E(x76001,f185(f872(x76002,a859)))+~P1(f306(f63(x76002),x76001))+P1(f306(f306(f308(x76002),f835(x76003,x76001,x76002)),x76001))+P1(f306(f306(f220(x76002),x76003),f306(f65(x76002,f225(x76002)),x76001))) % 187.68/187.66 [7601]~P103(x76012)+E(x76011,f185(f872(x76012,a859)))+~P1(f306(f63(x76012),x76011))+P1(f306(f306(f308(x76012),f437(x76013,x76011,x76012)),x76011))+P1(f306(f306(f220(x76012),x76013),f306(f65(x76012,f109(x76012)),x76011))) % 187.68/187.66 [7723]~P108(x77232)+E(x77231,f185(f872(x77232,a859)))+E(f306(f306(f225(x77232),f11(x77232,f225(x77232),x77231)),f11(x77232,f225(x77232),x77233)),f11(x77232,f225(x77232),x77233))+~P1(f306(f63(x77232),x77233))+~P1(f306(f306(f220(f872(x77232,a859)),x77231),x77233)) % 187.68/187.66 [7724]~P108(x77242)+E(x77241,f185(f872(x77242,a859)))+E(f306(f306(f219(x77242),f12(x77242,f219(x77242),x77241)),f12(x77242,f219(x77242),x77243)),f12(x77242,f219(x77242),x77243))+~P1(f306(f63(x77242),x77243))+~P1(f306(f306(f220(f872(x77242,a859)),x77241),x77243)) % 187.68/187.66 [7923]~E(f634(x79231,x79233,x79232),f635(x79231,x79233,x79232))+~E(f306(f39(x79232),f636(x79231,x79233,x79232)),x79231)+E(f306(f306(f82(a865),x79231),f306(f39(f872(x79232,a859)),x79233)),f306(f39(x79232),f41(f872(x79232,a859),x79233)))+~P1(f306(f63(x79232),f41(f872(x79232,a859),x79233)))+~P1(f306(f63(f872(x79232,a859)),x79233)) % 187.68/187.66 [8108]~P108(x81082)+E(x81081,f185(f872(x81082,a859)))+~P1(f306(f63(x81082),x81083))+P1(f306(f306(f220(x81082),f306(f65(x81082,f225(x81082)),x81083)),f306(f65(x81082,f225(x81082)),x81081)))+~P1(f306(f306(f220(f872(x81082,a859)),x81081),x81083)) % 187.68/187.66 [8418]~E(f634(x84181,x84183,x84182),f635(x84181,x84183,x84182))+E(f306(f306(f82(a865),x84181),f306(f39(f872(x84182,a859)),x84183)),f306(f39(x84182),f41(f872(x84182,a859),x84183)))+P1(f306(f306(f308(f872(x84182,a859)),f636(x84181,x84183,x84182)),x84183))+~P1(f306(f63(x84182),f41(f872(x84182,a859),x84183)))+~P1(f306(f63(f872(x84182,a859)),x84183)) % 187.68/187.66 [8445]~E(f306(f39(x84452),f636(x84451,x84453,x84452)),x84451)+E(f306(f306(f82(a865),x84451),f306(f39(f872(x84452,a859)),x84453)),f306(f39(x84452),f41(f872(x84452,a859),x84453)))+P1(f306(f306(f308(f872(x84452,a859)),f635(x84451,x84453,x84452)),x84453))+~P1(f306(f63(x84452),f41(f872(x84452,a859),x84453)))+~P1(f306(f63(f872(x84452,a859)),x84453)) % 187.68/187.66 [8446]~E(f306(f39(x84462),f636(x84461,x84463,x84462)),x84461)+E(f306(f306(f82(a865),x84461),f306(f39(f872(x84462,a859)),x84463)),f306(f39(x84462),f41(f872(x84462,a859),x84463)))+P1(f306(f306(f308(f872(x84462,a859)),f634(x84461,x84463,x84462)),x84463))+~P1(f306(f63(x84462),f41(f872(x84462,a859),x84463)))+~P1(f306(f63(f872(x84462,a859)),x84463)) % 187.68/187.66 [8476]~E(f306(f39(x84762),f636(x84761,x84763,x84762)),x84761)+~E(f306(f306(f109(f872(x84762,a859)),f635(x84761,x84763,x84762)),f634(x84761,x84763,x84762)),f185(f872(x84762,a859)))+E(f306(f306(f82(a865),x84761),f306(f39(f872(x84762,a859)),x84763)),f306(f39(x84762),f41(f872(x84762,a859),x84763)))+~P1(f306(f63(f872(x84762,a859)),x84763))+~P1(f306(f63(x84762),f41(f872(x84762,a859),x84763))) % 187.68/187.66 [8718]E(f306(f306(f82(a865),x87181),f306(f39(f872(x87182,a859)),x87183)),f306(f39(x87182),f41(f872(x87182,a859),x87183)))+P1(f306(f306(f308(f872(x87182,a859)),f636(x87181,x87183,x87182)),x87183))+P1(f306(f306(f308(f872(x87182,a859)),f635(x87181,x87183,x87182)),x87183))+~P1(f306(f63(f872(x87182,a859)),x87183))+~P1(f306(f63(x87182),f41(f872(x87182,a859),x87183))) % 187.68/187.66 [8719]E(f306(f306(f82(a865),x87191),f306(f39(f872(x87192,a859)),x87193)),f306(f39(x87192),f41(f872(x87192,a859),x87193)))+P1(f306(f306(f308(f872(x87192,a859)),f636(x87191,x87193,x87192)),x87193))+P1(f306(f306(f308(f872(x87192,a859)),f634(x87191,x87193,x87192)),x87193))+~P1(f306(f63(f872(x87192,a859)),x87193))+~P1(f306(f63(x87192),f41(f872(x87192,a859),x87193))) % 187.68/187.66 [8744]~E(f306(f306(f109(f872(x87442,a859)),f635(x87441,x87443,x87442)),f634(x87441,x87443,x87442)),f185(f872(x87442,a859)))+E(f306(f306(f82(a865),x87441),f306(f39(f872(x87442,a859)),x87443)),f306(f39(x87442),f41(f872(x87442,a859),x87443)))+~P1(f306(f63(f872(x87442,a859)),x87443))+P1(f306(f306(f308(f872(x87442,a859)),f636(x87441,x87443,x87442)),x87443))+~P1(f306(f63(x87442),f41(f872(x87442,a859),x87443))) % 187.68/187.66 [9008]~P95(x90082)+E(x90081,f185(f872(x90082,a859)))+~E(f306(f306(f82(x90082),f306(x90083,f359(x90081,x90083,x90082))),f306(x90083,f360(x90081,x90083,x90082))),f306(x90083,f306(f306(f82(x90082),f359(x90081,x90083,x90082)),f360(x90081,x90083,x90082))))+~P1(f306(f63(x90082),x90081))+E(f306(f65(x90082,f82(x90082)),f306(f285(x90082,x90082,x90083),x90081)),f306(x90083,f306(f65(x90082,f82(x90082)),x90081))) % 187.68/187.66 [9944]P1(f306(f306(x99441,x99442),x99443))+P1(f306(f306(f221(a1),f330(x99441,x99443,x99442)),f331(x99441,x99443,x99442)))+P1(f306(f306(f220(a1),f331(x99441,x99443,x99442)),f2(a1)))+P1(f306(f306(x99441,f330(x99441,x99443,x99442)),f306(f306(f82(a1),f306(f111(a1),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)))),f331(x99441,x99443,x99442))))+~P1(f306(f294(f871(a1,a1),a58),f306(f306(f236(a1,a1),x99442),x99443))) % 187.68/187.66 [9950]P1(f306(f306(x99501,x99502),x99503))+P1(f306(f306(f220(a1),f329(x99501,x99503,x99502)),f2(a1)))+P1(f306(f306(x99501,f328(x99501,x99503,x99502)),f306(f306(f82(a1),f306(f111(a1),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)))),f329(x99501,x99503,x99502))))+P1(f306(f306(f220(a1),f2(a1)),f306(f306(f81(a1),f328(x99501,x99503,x99502)),f329(x99501,x99503,x99502))))+~P1(f306(f294(f871(a1,a1),a53),f306(f306(f236(a1,a1),x99502),x99503))) % 187.68/187.66 [7894]~P112(x78941)+~P1(f306(f306(f220(x78941),x78942),f79(x78941)))+~P1(f306(f306(f220(x78941),f2(x78941)),x78942))+~P1(f306(f306(f220(x78941),f2(x78941)),x78943))+P1(f306(f306(f220(x78941),f306(f306(f82(x78941),x78942),x78943)),x78943)) % 187.68/187.66 [7895]~P112(x78951)+~P1(f306(f306(f220(x78951),x78953),f79(x78951)))+~P1(f306(f306(f220(x78951),f2(x78951)),x78953))+~P1(f306(f306(f220(x78951),f2(x78951)),x78952))+P1(f306(f306(f220(x78951),f306(f306(f82(x78951),x78952),x78953)),x78952)) % 187.68/187.66 [8259]~P108(x82592)+E(x82591,f185(f872(x82592,a859)))+~P1(f306(f63(x82592),x82591))+P1(f306(f306(f308(x82592),f837(x82593,x82591,x82592)),x82591))+~P1(f306(f306(f221(x82592),f306(f65(x82592,f225(x82592)),x82591)),x82593)) % 187.68/187.66 [8260]~P108(x82602)+E(x82601,f185(f872(x82602,a859)))+~P1(f306(f63(x82602),x82601))+P1(f306(f306(f308(x82602),f838(x82603,x82601,x82602)),x82601))+~P1(f306(f306(f220(x82602),f306(f65(x82602,f225(x82602)),x82601)),x82603)) % 187.68/187.66 [8261]~P108(x82612)+E(x82611,f185(f872(x82612,a859)))+~P1(f306(f63(x82612),x82611))+P1(f306(f306(f220(x82612),f838(x82613,x82611,x82612)),x82613))+~P1(f306(f306(f220(x82612),f306(f65(x82612,f225(x82612)),x82611)),x82613)) % 187.68/187.66 [8262]~P108(x82622)+E(x82621,f185(f872(x82622,a859)))+~P1(f306(f63(x82622),x82621))+P1(f306(f306(f221(x82622),f837(x82623,x82621,x82622)),x82623))+~P1(f306(f306(f221(x82622),f306(f65(x82622,f225(x82622)),x82621)),x82623)) % 187.68/187.66 [8348]~P1(f306(x83481,x83483))+P1(f306(x83481,f396(x83481,x83482)))+P1(f306(x83481,f390(x83481,x83482)))+~P1(f306(f306(f221(a1),f2(a1)),x83482))+P1(f306(x83481,f306(f306(f22(a1),f390(x83481,x83482)),f306(f306(f82(a1),f397(x83481,x83482)),x83482)))) % 187.68/187.66 [8572]~P1(f306(x85721,x85723))+P1(f306(x85721,f390(x85721,x85722)))+~P1(f306(f306(f221(a1),f2(a1)),x85722))+P1(f306(f306(f308(a1),f396(x85721,x85722)),f277(a1,f79(a1),x85722)))+P1(f306(x85721,f306(f306(f22(a1),f390(x85721,x85722)),f306(f306(f82(a1),f397(x85721,x85722)),x85722)))) % 187.68/187.66 [8765]~P1(f306(x87651,x87653))+~P1(f306(x87651,f390(x87651,x87652)))+P1(f306(x87651,f396(x87651,x87652)))+~P1(f306(f306(f221(a1),f2(a1)),x87652))+~P1(f306(x87651,f306(f306(f22(a1),f390(x87651,x87652)),f306(f306(f82(a1),f397(x87651,x87652)),x87652)))) % 187.68/187.66 [8891]~P1(f306(x88911,x88913))+~P1(f306(x88911,f390(x88911,x88912)))+~P1(f306(f306(f221(a1),f2(a1)),x88912))+P1(f306(f306(f308(a1),f396(x88911,x88912)),f277(a1,f79(a1),x88912)))+~P1(f306(x88911,f306(f306(f22(a1),f390(x88911,x88912)),f306(f306(f82(a1),f397(x88911,x88912)),x88912)))) % 187.68/187.66 [8677]~P108(x86771)+~P1(f306(f63(x86771),x86772))+E(f306(f306(f22(f872(x86771,a859)),x86772),f306(f306(f284(x86771),x86773),f185(f872(x86771,a859)))),f185(f872(x86771,a859)))+~P1(f306(f306(f308(x86771),x86773),x86772))+E(f306(f306(f225(x86771),x86773),f14(x86771,f306(f306(f22(f872(x86771,a859)),x86772),f306(f306(f284(x86771),x86773),f185(f872(x86771,a859)))))),f14(x86771,x86772)) % 187.68/187.66 [8678]~P108(x86781)+~P1(f306(f63(x86781),x86782))+E(f306(f306(f22(f872(x86781,a859)),x86782),f306(f306(f284(x86781),x86783),f185(f872(x86781,a859)))),f185(f872(x86781,a859)))+~P1(f306(f306(f308(x86781),x86783),x86782))+E(f306(f306(f219(x86781),x86783),f15(x86781,f306(f306(f22(f872(x86781,a859)),x86782),f306(f306(f284(x86781),x86783),f185(f872(x86781,a859)))))),f15(x86781,x86782)) % 187.68/187.66 [8679]~P98(x86791)+~P1(f306(f63(x86791),x86792))+E(f306(f306(f22(f872(x86791,a859)),x86792),f306(f306(f284(x86791),x86793),f185(f872(x86791,a859)))),f185(f872(x86791,a859)))+~P1(f306(f306(f308(x86791),x86793),x86792))+E(f306(f306(f108(x86791),x86793),f13(x86791,f306(f306(f22(f872(x86791,a859)),x86792),f306(f306(f284(x86791),x86793),f185(f872(x86791,a859)))))),f13(x86791,x86792)) % 187.68/187.66 [8680]~P98(x86801)+~P1(f306(f63(x86801),x86802))+E(f306(f306(f22(f872(x86801,a859)),x86802),f306(f306(f284(x86801),x86803),f185(f872(x86801,a859)))),f185(f872(x86801,a859)))+~P1(f306(f306(f308(x86801),x86803),x86802))+E(f306(f306(f109(x86801),x86803),f10(x86801,f306(f306(f22(f872(x86801,a859)),x86802),f306(f306(f284(x86801),x86803),f185(f872(x86801,a859)))))),f10(x86801,x86802)) % 187.68/187.66 [8738]~P108(x87381)+~P1(f306(f63(x87381),x87382))+E(f306(f306(f22(f872(x87381,a859)),x87382),f306(f306(f284(x87381),x87383),f185(f872(x87381,a859)))),f185(f872(x87381,a859)))+~P1(f306(f306(f308(x87381),x87383),x87382))+E(f306(f306(f225(x87381),x87383),f11(x87381,f225(x87381),f306(f306(f22(f872(x87381,a859)),x87382),f306(f306(f284(x87381),x87383),f185(f872(x87381,a859)))))),f11(x87381,f225(x87381),x87382)) % 187.68/187.66 [8739]~P108(x87391)+~P1(f306(f63(x87391),x87392))+E(f306(f306(f22(f872(x87391,a859)),x87392),f306(f306(f284(x87391),x87393),f185(f872(x87391,a859)))),f185(f872(x87391,a859)))+~P1(f306(f306(f308(x87391),x87393),x87392))+E(f306(f306(f219(x87391),x87393),f12(x87391,f219(x87391),f306(f306(f22(f872(x87391,a859)),x87392),f306(f306(f284(x87391),x87393),f185(f872(x87391,a859)))))),f12(x87391,f219(x87391),x87392)) % 187.68/187.66 [8752]~P108(x87521)+~P1(f306(f63(x87521),x87523))+~P1(f306(f63(x87521),x87522))+E(f306(f306(f109(f872(x87521,a859)),x87522),x87523),f185(f872(x87521,a859)))+E(f306(f306(f225(x87521),f14(x87521,f306(f306(f108(f872(x87521,a859)),x87522),x87523))),f14(x87521,f306(f306(f109(f872(x87521,a859)),x87522),x87523))),f306(f306(f225(x87521),f14(x87521,x87522)),f14(x87521,x87523))) % 187.68/187.66 [8753]~P108(x87531)+~P1(f306(f63(x87531),x87533))+~P1(f306(f63(x87531),x87532))+E(f306(f306(f109(f872(x87531,a859)),x87532),x87533),f185(f872(x87531,a859)))+E(f306(f306(f219(x87531),f15(x87531,f306(f306(f108(f872(x87531,a859)),x87532),x87533))),f15(x87531,f306(f306(f109(f872(x87531,a859)),x87532),x87533))),f306(f306(f219(x87531),f15(x87531,x87532)),f15(x87531,x87533))) % 187.68/187.66 [8754]~P98(x87541)+~P1(f306(f63(x87541),x87543))+~P1(f306(f63(x87541),x87542))+E(f306(f306(f109(f872(x87541,a859)),x87542),x87543),f185(f872(x87541,a859)))+E(f306(f306(f108(x87541),f13(x87541,f306(f306(f108(f872(x87541,a859)),x87542),x87543))),f13(x87541,f306(f306(f109(f872(x87541,a859)),x87542),x87543))),f306(f306(f108(x87541),f13(x87541,x87542)),f13(x87541,x87543))) % 187.68/187.66 [8755]~P98(x87551)+~P1(f306(f63(x87551),x87553))+~P1(f306(f63(x87551),x87552))+E(f306(f306(f109(f872(x87551,a859)),x87552),x87553),f185(f872(x87551,a859)))+E(f306(f306(f109(x87551),f10(x87551,f306(f306(f108(f872(x87551,a859)),x87552),x87553))),f10(x87551,f306(f306(f109(f872(x87551,a859)),x87552),x87553))),f306(f306(f109(x87551),f10(x87551,x87552)),f10(x87551,x87553))) % 187.68/187.66 [8980]~P108(x89801)+~P1(f306(f63(x89801),x89803))+~P1(f306(f63(x89801),x89802))+E(f306(f306(f109(f872(x89801,a859)),x89802),x89803),f185(f872(x89801,a859)))+E(f306(f306(f225(x89801),f11(x89801,f225(x89801),f306(f306(f108(f872(x89801,a859)),x89802),x89803))),f11(x89801,f225(x89801),f306(f306(f109(f872(x89801,a859)),x89802),x89803))),f306(f306(f225(x89801),f11(x89801,f225(x89801),x89802)),f11(x89801,f225(x89801),x89803))) % 187.68/187.66 [8981]~P108(x89811)+~P1(f306(f63(x89811),x89813))+~P1(f306(f63(x89811),x89812))+E(f306(f306(f109(f872(x89811,a859)),x89812),x89813),f185(f872(x89811,a859)))+E(f306(f306(f219(x89811),f12(x89811,f219(x89811),f306(f306(f108(f872(x89811,a859)),x89812),x89813))),f12(x89811,f219(x89811),f306(f306(f109(f872(x89811,a859)),x89812),x89813))),f306(f306(f219(x89811),f12(x89811,f219(x89811),x89812)),f12(x89811,f219(x89811),x89813))) % 187.68/187.66 [9783]~P111(x97833)+E(x97831,x97832)+~P1(f306(f306(f220(x97833),f2(x97833)),x97832))+~P1(f306(f306(f220(x97833),f2(x97833)),x97831))+~E(f306(f306(f237(x97833),x97831),f306(f111(a865),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)))),f306(f306(f237(x97833),x97832),f306(f111(a865),f306(f306(f81(a1),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104)),f306(f306(f22(a1),f306(f306(f81(a1),a84),a84)),a104))))) % 187.68/187.66 [6294]E(f410(x62941,x62942,x62943),x62944)+E(f306(x62941,x62944),f2(a865))+~E(f306(f306(f6(x62943,a865),x62941),x62942),f79(a865))+~P1(f306(f63(x62943),x62942))+~P1(f306(f306(f308(x62943),x62944),x62942)) % 187.68/187.66 [6359]E(f413(x63591,x63592,x63593),x63594)+E(f306(x63591,x63594),f2(a865))+~E(f306(f306(f6(x63593,a865),x63591),x63592),f306(a119,f2(a865)))+~P1(f306(f63(x63593),x63592))+~P1(f306(f306(f308(x63593),x63594),x63592)) % 187.68/187.66 [6465]~P108(x64651)+~P6(x64651)+P1(f306(f306(f221(x64651),x64652),f41(x64651,x64653)))+~P1(f306(f306(f221(x64651),x64652),x64654))+~P1(f306(f306(f308(x64651),x64654),x64653)) % 187.68/187.66 [6638]~P108(x66381)+~P6(x66381)+~P1(f306(f306(f221(x66381),x66384),x66383))+P1(f306(f306(f221(x66381),f42(x66381,x66382)),x66383))+~P1(f306(f306(f308(x66381),x66384),x66382)) % 187.68/187.66 [6896]~P111(x68963)+E(x68961,x68962)+~E(f306(f306(f237(x68963),x68961),f306(a119,x68964)),f306(f306(f237(x68963),x68962),f306(a119,x68964)))+~P1(f306(f306(f220(x68963),f2(x68963)),x68962))+~P1(f306(f306(f220(x68963),f2(x68963)),x68961)) % 187.68/187.66 [7107]~E(f415(x71072,x71073,x71071,x71074),x71074)+~E(f306(x71072,x71074),f79(a865))+E(f306(f306(f6(x71071,a865),x71072),x71073),f79(a865))+~P1(f306(f63(x71071),x71073))+~P1(f306(f306(f308(x71071),x71074),x71073)) % 187.68/187.66 [7114]~P113(x71144)+~P132(x71144)+E(f306(x71141,f318(x71141,x71142,x71143,x71144)),f2(x71144))+~E(f306(f306(f9(x71143,x71144),x71141),x71142),f2(x71144))+~P1(f306(f63(x71143),x71142)) % 187.68/187.66 [7200]~E(f414(x72002,x72003,x72001,x72004),x72004)+~E(f306(x72002,x72004),f306(a119,f2(a865)))+E(f306(f306(f6(x72001,a865),x72002),x72003),f306(a119,f2(a865)))+~P1(f306(f63(x72001),x72003))+~P1(f306(f306(f308(x72001),x72004),x72003)) % 187.68/187.66 [7934]~E(f306(x79342,x79344),f79(a865))+~E(f306(x79342,f415(x79342,x79343,x79341,x79344)),f2(a865))+E(f306(f306(f6(x79341,a865),x79342),x79343),f79(a865))+~P1(f306(f63(x79341),x79343))+~P1(f306(f306(f308(x79341),x79344),x79343)) % 187.68/187.66 [7978]~E(f306(x79782,x79784),f306(a119,f2(a865)))+~E(f306(x79782,f414(x79782,x79783,x79781,x79784)),f2(a865))+E(f306(f306(f6(x79781,a865),x79782),x79783),f306(a119,f2(a865)))+~P1(f306(f63(x79781),x79783))+~P1(f306(f306(f308(x79781),x79784),x79783)) % 187.68/187.66 [8542]~P108(x85421)+~P17(x85421,x85424)+P17(x85421,x85422)+~E(x85422,f306(f306(f143(x85421),x85423),x85424))+~P1(f306(f306(f220(x85421),x85423),f758(x85422,x85421,x85424,x85423))) % 187.68/187.66 [8576]E(x85761,x85762)+E(f306(f306(f22(a1),f391(x85763,x85762,x85764,x85761)),f383(x85763,x85762,x85764,x85761)),x85761)+~E(f306(f306(f81(a1),x85761),x85764),x85762)+~P1(f306(f306(f221(a1),f2(a1)),x85764))+~P1(f306(f306(f308(a1),x85762),x85763)) % 187.68/187.66 [8577]E(x85771,x85772)+E(f306(f306(f81(a1),f384(x85773,x85772,x85774,x85771)),f385(x85773,x85772,x85774,x85771)),x85771)+~E(f306(f306(f22(a1),x85771),x85774),x85772)+~P1(f306(f306(f221(a1),f2(a1)),x85774))+~P1(f306(f306(f308(a1),x85772),x85773)) % 187.68/187.66 [8750]E(f306(x87501,f590(x87502,x87501,x87503,x87504)),x87502)+P1(f306(f306(f220(a865),x87504),f591(x87502,x87501,x87503,x87504)))+~P1(f306(f306(f220(a1),x87502),f306(x87501,x87503)))+~P1(f306(f306(f221(a865),x87504),x87503))+~P1(f306(f306(f220(a1),f306(x87501,x87504)),x87502)) % 187.68/187.66 [8751]~P108(x87511)+~P17(x87511,x87513)+P17(x87511,x87512)+~E(x87512,f306(f306(f143(x87511),x87514),x87513))+P1(f306(f306(f308(x87511),f758(x87512,x87511,x87513,x87514)),f306(f164(x87511),x87513))) % 187.68/187.66 [8769]~P113(x87694)+~P132(x87694)+~E(f306(f306(f9(x87691,x87694),x87692),x87693),f2(x87694))+~P1(f306(f63(x87691),x87693))+P1(f306(f306(f308(x87691),f318(x87692,x87693,x87691,x87694)),x87693)) % 187.68/187.66 [8805]~E(f306(x88052,x88054),f79(a865))+E(f306(f306(f6(x88051,a865),x88052),x88053),f79(a865))+~P1(f306(f63(x88051),x88053))+~P1(f306(f306(f308(x88051),x88054),x88053))+P1(f306(f306(f308(x88051),f415(x88052,x88053,x88051,x88054)),x88053)) % 187.68/187.66 [8814]E(x88141,x88142)+~E(f306(f306(f22(a1),x88142),x88144),x88141)+~P1(f306(f306(f221(a1),f2(a1)),x88144))+~P1(f306(f306(f308(a1),x88141),x88143))+P1(f306(f306(f308(a1),f384(x88143,x88141,x88144,x88142)),x88143)) % 187.68/187.66 [8815]E(x88151,x88152)+~E(f306(f306(f81(a1),x88152),x88154),x88151)+~P1(f306(f306(f221(a1),f2(a1)),x88154))+~P1(f306(f306(f308(a1),x88151),x88153))+P1(f306(f306(f308(a1),f391(x88153,x88151,x88154,x88152)),x88153)) % 187.68/187.66 [8817]~E(f306(x88172,x88174),f306(a119,f2(a865)))+E(f306(f306(f6(x88171,a865),x88172),x88173),f306(a119,f2(a865)))+~P1(f306(f63(x88171),x88173))+~P1(f306(f306(f308(x88171),x88174),x88173))+P1(f306(f306(f308(x88171),f414(x88172,x88173,x88171,x88174)),x88173)) % 187.68/187.66 [8822]P58(x88222,x88223,x88224,x88221)+E(x88221,f185(f872(x88222,a859)))+~P1(f306(f63(x88222),x88224))+~P1(f306(f63(x88222),x88221))+P1(f306(f306(f308(x88222),f489(x88221,x88224,x88223,x88222)),x88224)) % 187.68/187.66 [8905]E(x89051,x89052)+~E(f306(f306(f22(a1),x89052),x89054),x89051)+~P1(f306(f306(f221(a1),f2(a1)),x89054))+~P1(f306(f306(f308(a1),x89051),x89053))+P1(f306(f306(f308(a1),f385(x89053,x89051,x89054,x89052)),f277(a1,f79(a1),x89054))) % 187.68/187.66 [8906]E(x89061,x89062)+~E(f306(f306(f81(a1),x89062),x89064),x89061)+~P1(f306(f306(f221(a1),f2(a1)),x89064))+~P1(f306(f306(f308(a1),x89061),x89063))+P1(f306(f306(f308(a1),f383(x89063,x89061,x89064,x89062)),f277(a1,f79(a1),x89064))) % 187.68/187.66 [8986]P1(f306(f306(f220(a865),x89861),f590(x89862,x89863,x89864,x89861)))+~P1(f306(f306(f220(a1),x89862),f306(x89863,x89864)))+P1(f306(f306(f220(a865),x89861),f591(x89862,x89863,x89864,x89861)))+~P1(f306(f306(f221(a865),x89861),x89864))+~P1(f306(f306(f220(a1),f306(x89863,x89861)),x89862)) % 187.68/187.66 [9097]E(f306(x90971,f590(x90972,x90971,x90973,x90974)),x90972)+~P1(f306(f306(f220(a1),x90972),f306(x90971,x90973)))+P1(f306(f306(f221(a865),f591(x90972,x90971,x90973,x90974)),x90973))+~P1(f306(f306(f221(a865),x90974),x90973))+~P1(f306(f306(f220(a1),f306(x90971,x90974)),x90972)) % 187.68/187.66 [9231]~P1(f306(f306(f220(a1),x92312),f306(x92313,x92314)))+P1(f306(f306(f220(a865),x92311),f591(x92312,x92313,x92314,x92311)))+P1(f306(f306(f220(a865),f590(x92312,x92313,x92314,x92311)),x92314))+~P1(f306(f306(f221(a865),x92311),x92314))+~P1(f306(f306(f220(a1),f306(x92313,x92311)),x92312)) % 187.68/187.66 [9232]~P1(f306(f306(f220(a1),x92322),f306(x92323,x92324)))+P1(f306(f306(f220(a865),x92321),f590(x92322,x92323,x92324,x92321)))+P1(f306(f306(f221(a865),f591(x92322,x92323,x92324,x92321)),x92324))+~P1(f306(f306(f221(a865),x92321),x92324))+~P1(f306(f306(f220(a1),f306(x92323,x92321)),x92322)) % 187.68/187.66 [9340]~P1(f306(f306(f220(a1),x93401),f306(x93402,x93403)))+P1(f306(f306(f221(a865),f591(x93401,x93402,x93403,x93404)),x93403))+~P1(f306(f306(f221(a865),x93404),x93403))+~P1(f306(f306(f220(a1),f306(x93402,x93404)),x93401))+P1(f306(f306(f220(a865),f590(x93401,x93402,x93403,x93404)),x93403)) % 187.68/187.66 [9420]E(x94201,f185(f872(x94202,a859)))+~P1(f306(f63(x94202),x94204))+~P1(f306(f63(x94202),x94201))+P1(f306(f306(f308(f871(f872(x94202,a859),f872(x94202,a859))),f306(f306(f236(f872(x94202,a859),f872(x94202,a859)),x94204),x94201)),f298(x94202,x94203)))+P1(f306(f306(f308(x94202),f490(x94203,x94201,x94204,x94202)),x94204)) % 187.68/187.66 [9421]E(x94211,f185(f872(x94212,a859)))+~P1(f306(f63(x94212),x94214))+~P1(f306(f63(x94212),x94211))+P1(f306(f306(f308(f871(f872(x94212,a859),f872(x94212,a859))),f306(f306(f236(f872(x94212,a859),f872(x94212,a859)),x94214),x94211)),f298(x94212,x94213)))+P1(f306(f306(f308(x94212),f575(x94213,x94211,x94214,x94212)),x94214)) % 187.68/187.66 [10091]E(f306(x100911,f590(x100912,x100911,x100913,x100914)),x100912)+~P1(f306(f306(f220(a1),x100912),f306(x100911,x100913)))+~P1(f306(f306(f220(a1),f306(f76(a1),f306(f306(f22(a1),f306(x100911,f306(f306(f81(a865),f591(x100912,x100911,x100913,x100914)),f79(a865)))),f306(x100911,f591(x100912,x100911,x100913,x100914))))),f79(a1)))+~P1(f306(f306(f221(a865),x100914),x100913))+~P1(f306(f306(f220(a1),f306(x100911,x100914)),x100912)) % 187.68/187.66 [10092]~P1(f306(f306(f220(a1),x100922),f306(x100923,x100924)))+P1(f306(f306(f220(a865),x100921),f590(x100922,x100923,x100924,x100921)))+~P1(f306(f306(f220(a1),f306(f76(a1),f306(f306(f22(a1),f306(x100923,f306(f306(f81(a865),f591(x100922,x100923,x100924,x100921)),f79(a865)))),f306(x100923,f591(x100922,x100923,x100924,x100921))))),f79(a1)))+~P1(f306(f306(f221(a865),x100921),x100924))+~P1(f306(f306(f220(a1),f306(x100923,x100921)),x100922)) % 187.68/187.66 [10093]~P1(f306(f306(f220(a1),x100931),f306(x100932,x100933)))+~P1(f306(f306(f220(a1),f306(f76(a1),f306(f306(f22(a1),f306(x100932,f306(f306(f81(a865),f591(x100931,x100932,x100933,x100934)),f79(a865)))),f306(x100932,f591(x100931,x100932,x100933,x100934))))),f79(a1)))+~P1(f306(f306(f221(a865),x100934),x100933))+~P1(f306(f306(f220(a1),f306(x100932,x100934)),x100931))+P1(f306(f306(f220(a865),f590(x100931,x100932,x100933,x100934)),x100933)) % 187.68/187.66 [7167]~P63(x71671)+P1(f306(f306(f221(x71671),x71672),f2(x71671)))+~P1(f306(f306(f220(x71671),x71673),f2(x71671)))+P1(f306(f306(f221(x71671),f2(x71671)),x71672))+P1(f306(f306(f220(x71671),x71673),f306(f306(f264(x71671),x71674),x71672))) % 187.68/187.66 [7168]~P63(x71681)+P1(f306(f306(f221(x71681),x71682),f2(x71681)))+~P1(f306(f306(f221(x71681),x71683),f2(x71681)))+P1(f306(f306(f221(x71681),f2(x71681)),x71682))+P1(f306(f306(f221(x71681),x71683),f306(f306(f264(x71681),x71684),x71682))) % 187.68/187.66 [7416]~P63(x74161)+P1(f306(f306(f220(x74161),x74162),f2(x74161)))+P1(f306(f306(f221(x74161),x74163),f2(x74161)))+P1(f306(f306(f221(x74161),f2(x74161)),x74163))+~P1(f306(f306(f220(x74161),x74162),f306(f306(f264(x74161),x74164),x74163))) % 187.68/187.66 [7417]~P63(x74171)+P1(f306(f306(f221(x74171),x74172),f2(x74171)))+P1(f306(f306(f221(x74171),x74173),f2(x74171)))+P1(f306(f306(f221(x74171),f2(x74171)),x74173))+~P1(f306(f306(f221(x74171),x74172),f306(f306(f264(x74171),x74174),x74173))) % 187.68/187.66 [7532]E(x75321,x75322)+~E(f306(f306(f157(x75323),x75324),x75321),f306(f306(f157(x75323),x75324),x75322))+~P1(f306(f129(x75323),x75324))+~P1(f306(f306(f221(a865),x75322),f306(f186(f866(x75323)),x75324)))+~P1(f306(f306(f221(a865),x75321),f306(f186(f866(x75323)),x75324))) % 187.68/187.66 [7896]~P63(x78961)+~P1(f306(f306(f220(x78961),x78963),f2(x78961)))+P1(f306(f306(f221(x78961),f2(x78961)),x78962))+~P1(f306(f306(f220(x78961),x78964),f306(f306(f82(x78961),x78963),x78962)))+P1(f306(f306(f220(x78961),x78963),f306(f306(f264(x78961),x78964),x78962))) % 187.68/187.66 [7897]~P63(x78971)+~P1(f306(f306(f221(x78971),x78973),f2(x78971)))+P1(f306(f306(f221(x78971),f2(x78971)),x78972))+~P1(f306(f306(f221(x78971),x78974),f306(f306(f82(x78971),x78973),x78972)))+P1(f306(f306(f221(x78971),x78973),f306(f306(f264(x78971),x78974),x78972))) % 187.68/187.66 [7898]~P63(x78981)+~P1(f306(f306(f221(x78981),x78982),f2(x78981)))+P1(f306(f306(f221(x78981),f2(x78981)),x78982))+~P1(f306(f306(f220(x78981),x78984),f306(f306(f82(x78981),x78983),x78982)))+P1(f306(f306(f220(x78981),x78983),f306(f306(f264(x78981),x78984),x78982))) % 187.68/187.66 [7899]~P63(x78991)+~P1(f306(f306(f221(x78991),x78992),f2(x78991)))+P1(f306(f306(f221(x78991),f2(x78991)),x78992))+~P1(f306(f306(f220(x78991),x78994),f306(f306(f264(x78991),x78993),x78992)))+P1(f306(f306(f220(x78991),x78993),f306(f306(f82(x78991),x78994),x78992))) % 187.68/187.66 [7900]~P63(x79001)+~P1(f306(f306(f221(x79001),x79002),f2(x79001)))+P1(f306(f306(f221(x79001),f2(x79001)),x79002))+~P1(f306(f306(f221(x79001),x79004),f306(f306(f82(x79001),x79003),x79002)))+P1(f306(f306(f221(x79001),x79003),f306(f306(f264(x79001),x79004),x79002))) % 187.68/187.66 [7901]~P63(x79011)+~P1(f306(f306(f221(x79011),x79012),f2(x79011)))+P1(f306(f306(f221(x79011),f2(x79011)),x79012))+~P1(f306(f306(f221(x79011),x79014),f306(f306(f264(x79011),x79013),x79012)))+P1(f306(f306(f221(x79011),x79013),f306(f306(f82(x79011),x79014),x79012))) % 187.68/187.66 [8047]~P108(x80471)+~P17(x80471,x80472)+~P1(f306(f306(f220(a865),x80473),x80474))+P1(f306(f306(f220(x80471),f306(f306(f157(x80471),x80472),x80473)),f306(f306(f157(x80471),x80472),x80474)))+~P1(f306(f306(f221(a865),x80474),f306(f186(f866(x80471)),x80472))) % 187.68/187.66 [8099]~P111(x80991)+~P1(f306(f306(f220(x80991),x80992),f79(x80991)))+~P1(f306(f306(f220(x80991),f2(x80991)),x80992))+~P1(f306(f306(f220(a865),x80994),x80993))+P1(f306(f306(f220(x80991),f306(f306(f237(x80991),x80992),x80993)),f306(f306(f237(x80991),x80992),x80994))) % 187.68/187.66 [8100]~P111(x81001)+~P1(f306(f306(f221(x81001),x81002),f79(x81001)))+~P1(f306(f306(f221(x81001),f2(x81001)),x81002))+~P1(f306(f306(f221(a865),x81004),x81003))+P1(f306(f306(f221(x81001),f306(f306(f237(x81001),x81002),x81003)),f306(f306(f237(x81001),x81002),x81004))) % 187.68/187.66 [8101]~P111(x81011)+~P1(f306(f306(f220(x81011),f2(x81011)),x81012))+~P1(f306(f306(f221(a865),f2(a865)),x81013))+~P1(f306(f306(f221(x81011),x81012),x81014))+P1(f306(f306(f221(x81011),f306(f306(f237(x81011),x81012),x81013)),f306(f306(f237(x81011),x81014),x81013))) % 187.68/187.66 [8121]~P108(x81211)+~P17(x81211,f306(f161(x81211),x81212))+~P1(f306(f306(f220(a865),x81214),x81213))+P1(f306(f306(f220(x81211),f306(f306(f157(x81211),x81212),x81213)),f306(f306(f157(x81211),x81212),x81214)))+~P1(f306(f306(f221(a865),x81213),f306(f186(f866(x81211)),x81212))) % 187.68/187.66 [8370]~P63(x83701)+~P1(f306(f306(f220(x83701),x83702),f2(x83701)))+~P1(f306(f306(f220(x83701),x83703),x83704))+~P1(f306(f306(f221(x83701),f2(x83701)),f306(f306(f82(x83701),x83703),x83704)))+P1(f306(f306(f220(x83701),f306(f306(f264(x83701),x83702),x83703)),f306(f306(f264(x83701),x83702),x83704))) % 187.68/187.66 [8371]~P64(x83711)+~P1(f306(f306(f221(x83711),x83712),f2(x83711)))+~P1(f306(f306(f221(x83711),x83713),x83714))+~P1(f306(f306(f221(x83711),f2(x83711)),f306(f306(f82(x83711),x83713),x83714)))+P1(f306(f306(f221(x83711),f306(f306(f264(x83711),x83712),x83713)),f306(f306(f264(x83711),x83712),x83714))) % 187.68/187.66 [8380]~P64(x83801)+~P1(f306(f306(f220(x83801),x83804),x83803))+~P1(f306(f306(f220(x83801),f2(x83801)),x83802))+~P1(f306(f306(f221(x83801),f2(x83801)),f306(f306(f82(x83801),x83803),x83804)))+P1(f306(f306(f220(x83801),f306(f306(f264(x83801),x83802),x83803)),f306(f306(f264(x83801),x83802),x83804))) % 187.68/187.66 [8381]~P64(x83811)+~P1(f306(f306(f221(x83811),x83814),x83813))+~P1(f306(f306(f221(x83811),f2(x83811)),x83812))+~P1(f306(f306(f221(x83811),f2(x83811)),f306(f306(f82(x83811),x83813),x83814)))+P1(f306(f306(f221(x83811),f306(f306(f264(x83811),x83812),x83813)),f306(f306(f264(x83811),x83812),x83814))) % 187.68/187.66 [8491]P1(f306(x84911,x84912))+~P1(f306(f63(x84914),x84912))+P1(f306(x84911,f623(x84911,x84913,x84912,x84914)))+~P1(f306(x84911,f185(f872(x84914,a859))))+~P1(f306(f306(f220(f872(x84914,a859)),x84912),x84913)) % 187.68/187.66 [8499]P1(f306(x84991,x84992))+P1(f306(f63(x84993),f623(x84991,x84994,x84992,x84993)))+~P1(f306(f63(x84993),x84992))+~P1(f306(x84991,f185(f872(x84993,a859))))+~P1(f306(f306(f220(f872(x84993,a859)),x84992),x84994)) % 187.68/187.66 [8746]E(f306(f306(f81(a1),f386(x87461,x87462,x87463,x87464)),f387(x87461,x87462,x87463,x87464)),x87464)+~P1(f306(f306(f221(a1),f2(a1)),x87463))+~P1(f306(f306(f221(a1),x87462),x87464))+~P1(f306(f306(f308(a1),x87462),x87461))+P1(f306(f306(f221(a1),x87462),f306(f306(f22(a1),x87464),x87463))) % 187.68/187.66 [8966]~P1(f306(f306(f221(a1),f2(a1)),x89663))+~P1(f306(f306(f221(a1),x89662),x89664))+~P1(f306(f306(f308(a1),x89662),x89661))+P1(f306(f306(f308(a1),f386(x89661,x89662,x89663,x89664)),x89661))+P1(f306(f306(f221(a1),x89662),f306(f306(f22(a1),x89664),x89663))) % 187.68/187.66 [8979]P1(f306(x89791,x89792))+~P1(f306(f63(x89793),x89792))+P1(f306(f306(f308(x89793),f615(x89791,x89794,x89792,x89793)),x89794))+~P1(f306(x89791,f185(f872(x89793,a859))))+~P1(f306(f306(f220(f872(x89793,a859)),x89792),x89794)) % 187.68/187.66 [8996]E(f306(f306(f81(a1),f373(x89961,x89962,x89963,x89964)),f374(x89961,x89962,x89963,x89964)),x89964)+~P1(f306(f306(f221(a1),f2(a1)),x89963))+~P1(f306(f306(f220(a1),x89962),x89964))+P1(f306(f306(f220(a1),x89962),f306(f306(f22(a1),x89964),x89963)))+~P1(f306(f306(f308(a1),f306(f306(f22(a1),x89962),f79(a1))),x89961)) % 187.68/187.66 [9048]~P1(f306(f306(f221(a1),f2(a1)),x90483))+~P1(f306(f306(f221(a1),x90481),x90482))+~P1(f306(f306(f308(a1),x90481),x90484))+P1(f306(f306(f308(a1),f387(x90484,x90481,x90483,x90482)),f277(a1,f79(a1),x90483)))+P1(f306(f306(f221(a1),x90481),f306(f306(f22(a1),x90482),x90483))) % 187.68/187.66 [9145]~P1(f306(f306(f221(a1),f2(a1)),x91453))+~P1(f306(f306(f220(a1),x91452),x91454))+P1(f306(f306(f308(a1),f373(x91451,x91452,x91453,x91454)),x91451))+P1(f306(f306(f220(a1),x91452),f306(f306(f22(a1),x91454),x91453)))+~P1(f306(f306(f308(a1),f306(f306(f22(a1),x91452),f79(a1))),x91451)) % 187.68/187.66 [9185]~P1(f306(f306(f221(a1),f2(a1)),x91853))+~P1(f306(f306(f220(a1),x91851),x91852))+P1(f306(f306(f308(a1),f374(x91854,x91851,x91853,x91852)),f277(a1,f79(a1),x91853)))+P1(f306(f306(f220(a1),x91851),f306(f306(f22(a1),x91852),x91853)))+~P1(f306(f306(f308(a1),f306(f306(f22(a1),x91851),f79(a1))),x91854)) % 187.68/187.66 [9423]P1(f306(x94231,x94232))+~P1(f306(f306(f308(x94233),f615(x94231,x94234,x94232,x94233)),f623(x94231,x94234,x94232,x94233)))+~P1(f306(f63(x94233),x94232))+~P1(f306(x94231,f185(f872(x94233,a859))))+~P1(f306(f306(f220(f872(x94233,a859)),x94232),x94234)) % 187.68/187.66 [9640]P1(f306(x96401,x96402))+~P1(f306(f63(x96403),x96402))+~P1(f306(x96401,f306(f306(f284(x96403),f615(x96401,x96404,x96402,x96403)),f623(x96401,x96404,x96402,x96403))))+~P1(f306(x96401,f185(f872(x96403,a859))))+~P1(f306(f306(f220(f872(x96403,a859)),x96402),x96404)) % 187.68/187.66 [7669]~P63(x76691)+P1(f306(f306(f221(x76691),x76692),f2(x76691)))+~P1(f306(f306(f220(x76691),f2(x76691)),x76694))+P1(f306(f306(f221(x76691),f2(x76691)),x76692))+P1(f306(f306(f220(x76691),f306(f306(f264(x76691),x76693),x76692)),x76694)) % 187.68/187.66 [7670]~P63(x76701)+P1(f306(f306(f221(x76701),x76702),f2(x76701)))+P1(f306(f306(f221(x76701),f2(x76701)),x76702))+~P1(f306(f306(f221(x76701),f2(x76701)),x76704))+P1(f306(f306(f221(x76701),f306(f306(f264(x76701),x76703),x76702)),x76704)) % 187.68/187.66 [7884]~P6(x78841)+~P41(x78841,x78841,x78844)+~E(x78843,f103(x78841,x78844))+P1(f306(f306(f220(x78841),x78842),x78843))+~P1(f306(f306(f220(x78841),x78842),f306(x78844,f306(f306(f108(x78841),x78842),x78843)))) % 187.68/187.66 [7950]~P1(f306(f306(f220(a1),x79504),f2(a1)))+~E(x79502,f306(f306(f81(a1),f306(f306(f82(a1),x79501),x79503)),x79504))+P1(f306(f306(f221(a1),f2(a1)),x79501))+~P1(f306(f306(f221(a1),x79501),x79504))+P1(f306(f50(x79502,x79501),f306(f306(f236(a1,a1),x79503),x79504))) % 187.68/187.66 [7989]~P1(f306(x79891,x79894))+P1(f306(x79891,f839(x79892,x79891,x79893)))+~P1(f306(f306(f220(a1),f2(a1)),x79892))+~P1(f306(f306(f221(a1),f2(a1)),x79893))+P1(f306(x79891,f306(f306(f22(a1),x79894),f306(f306(f82(a1),x79892),x79893)))) % 187.68/187.66 [7990]~P1(f306(x79901,x79904))+P1(f306(x79901,f849(x79902,x79901,x79903)))+~P1(f306(f306(f220(a1),f2(a1)),x79902))+~P1(f306(f306(f221(a1),f2(a1)),x79903))+P1(f306(x79901,f306(f306(f81(a1),x79904),f306(f306(f82(a1),x79902),x79903)))) % 187.68/187.66 [7991]~P63(x79911)+P1(f306(f306(f221(x79911),x79912),f2(x79911)))+P1(f306(f306(f221(x79911),f2(x79911)),x79912))+P1(f306(f306(f220(x79911),f2(x79911)),x79913))+~P1(f306(f306(f220(x79911),f306(f306(f264(x79911),x79914),x79912)),x79913)) % 187.68/187.66 [7992]~P63(x79921)+P1(f306(f306(f221(x79921),x79922),f2(x79921)))+P1(f306(f306(f221(x79921),f2(x79921)),x79922))+P1(f306(f306(f221(x79921),f2(x79921)),x79923))+~P1(f306(f306(f221(x79921),f306(f306(f264(x79921),x79924),x79922)),x79923)) % 187.68/187.66 [8041]~E(x80411,f306(f306(f81(a1),f306(f306(f82(a1),x80412),x80413)),x80414))+~P1(f306(f306(f220(a1),f2(a1)),x80414))+~P1(f306(f306(f221(a1),f2(a1)),x80412))+~P1(f306(f306(f221(a1),x80414),x80412))+P1(f306(f50(x80411,x80412),f306(f306(f236(a1,a1),x80413),x80414))) % 187.68/187.66 [8165]~P63(x81651)+P1(f306(f306(f221(x81651),x81652),f2(x81651)))+~P1(f306(f306(f220(x81651),f2(x81651)),x81654))+~P1(f306(f306(f220(x81651),x81653),f306(f306(f82(x81651),x81654),x81652)))+P1(f306(f306(f220(x81651),f306(f306(f264(x81651),x81653),x81652)),x81654)) % 187.68/187.66 [8166]~P63(x81661)+P1(f306(f306(f221(x81661),x81662),f2(x81661)))+~P1(f306(f306(f221(x81661),f2(x81661)),x81664))+~P1(f306(f306(f221(x81661),x81663),f306(f306(f82(x81661),x81664),x81662)))+P1(f306(f306(f221(x81661),f306(f306(f264(x81661),x81663),x81662)),x81664)) % 187.68/187.66 [8247]~P63(x82471)+P1(f306(f306(f221(x82471),x82472),f2(x82471)))+~P1(f306(f306(f220(x82471),x82473),f2(x82471)))+P1(f306(f306(f220(x82471),x82473),f306(f306(f264(x82471),x82474),x82472)))+~P1(f306(f306(f220(x82471),f306(f306(f82(x82471),x82473),x82472)),x82474)) % 187.68/187.66 [8248]~P63(x82481)+P1(f306(f306(f221(x82481),x82482),f2(x82481)))+~P1(f306(f306(f221(x82481),x82483),f2(x82481)))+P1(f306(f306(f221(x82481),x82483),f306(f306(f264(x82481),x82484),x82482)))+~P1(f306(f306(f221(x82481),f306(f306(f82(x82481),x82483),x82482)),x82484)) % 187.68/187.66 [8407]~P63(x84071)+~P1(f306(f306(f221(x84071),x84072),f2(x84071)))+P1(f306(f306(f221(x84071),f2(x84071)),x84072))+~P1(f306(f306(f220(x84071),f306(f306(f264(x84071),x84074),x84072)),x84073))+P1(f306(f306(f220(x84071),f306(f306(f82(x84071),x84073),x84072)),x84074)) % 187.68/187.66 [8408]~P63(x84081)+~P1(f306(f306(f221(x84081),x84082),f2(x84081)))+P1(f306(f306(f221(x84081),f2(x84081)),x84082))+~P1(f306(f306(f220(x84081),f306(f306(f82(x84081),x84084),x84082)),x84083))+P1(f306(f306(f220(x84081),f306(f306(f264(x84081),x84083),x84082)),x84084)) % 187.68/187.66 [8409]~P63(x84091)+~P1(f306(f306(f221(x84091),x84092),f2(x84091)))+P1(f306(f306(f221(x84091),f2(x84091)),x84092))+~P1(f306(f306(f221(x84091),f306(f306(f264(x84091),x84094),x84092)),x84093))+P1(f306(f306(f221(x84091),f306(f306(f82(x84091),x84093),x84092)),x84094)) % 187.68/187.66 [8410]~P63(x84101)+~P1(f306(f306(f221(x84101),x84102),f2(x84101)))+P1(f306(f306(f221(x84101),f2(x84101)),x84102))+~P1(f306(f306(f221(x84101),f306(f306(f82(x84101),x84104),x84102)),x84103))+P1(f306(f306(f221(x84101),f306(f306(f264(x84101),x84103),x84102)),x84104)) % 187.68/187.66 [8432]~P63(x84321)+~P1(f306(f306(f220(x84321),f2(x84321)),x84324))+P1(f306(f306(f221(x84321),f2(x84321)),x84322))+~P1(f306(f306(f220(x84321),f306(f306(f82(x84321),x84324),x84322)),x84323))+P1(f306(f306(f220(x84321),f306(f306(f264(x84321),x84323),x84322)),x84324)) % 187.68/187.66 [8433]~P63(x84331)+~P1(f306(f306(f221(x84331),f2(x84331)),x84334))+P1(f306(f306(f221(x84331),f2(x84331)),x84332))+~P1(f306(f306(f221(x84331),f306(f306(f82(x84331),x84334),x84332)),x84333))+P1(f306(f306(f221(x84331),f306(f306(f264(x84331),x84333),x84332)),x84334)) % 187.68/187.66 [8507]~P63(x85071)+~P1(f306(f306(f221(x85071),x85074),f2(x85071)))+~P1(f306(f306(f220(x85071),x85073),f306(f306(f82(x85071),x85072),x85074)))+P1(f306(f306(f220(x85071),x85072),f306(f306(f264(x85071),x85073),x85074)))+~P1(f306(f306(f220(x85071),f306(f306(f82(x85071),x85072),x85074)),x85073)) % 187.68/187.66 [8508]~P63(x85081)+~P1(f306(f306(f220(x85081),x85082),f2(x85081)))+~P1(f306(f306(f220(x85081),x85083),f306(f306(f82(x85081),x85082),x85084)))+P1(f306(f306(f220(x85081),x85082),f306(f306(f264(x85081),x85083),x85084)))+~P1(f306(f306(f220(x85081),f306(f306(f82(x85081),x85082),x85084)),x85083)) % 187.68/187.66 [8509]~P63(x85091)+~P1(f306(f306(f221(x85091),x85094),f2(x85091)))+~P1(f306(f306(f221(x85091),x85093),f306(f306(f82(x85091),x85092),x85094)))+P1(f306(f306(f221(x85091),x85092),f306(f306(f264(x85091),x85093),x85094)))+~P1(f306(f306(f221(x85091),f306(f306(f82(x85091),x85092),x85094)),x85093)) % 187.68/187.66 [8510]~P63(x85101)+~P1(f306(f306(f221(x85101),x85102),f2(x85101)))+~P1(f306(f306(f221(x85101),x85103),f306(f306(f82(x85101),x85102),x85104)))+P1(f306(f306(f221(x85101),x85102),f306(f306(f264(x85101),x85103),x85104)))+~P1(f306(f306(f221(x85101),f306(f306(f82(x85101),x85102),x85104)),x85103)) % 187.68/187.66 [8624]~P63(x86241)+~P1(f306(f306(f221(x86241),x86243),f2(x86241)))+~P1(f306(f306(f220(x86241),x86242),f306(f306(f82(x86241),x86244),x86243)))+~P1(f306(f306(f220(x86241),f306(f306(f82(x86241),x86244),x86243)),x86242))+P1(f306(f306(f220(x86241),f306(f306(f264(x86241),x86242),x86243)),x86244)) % 187.68/187.66 [8625]~P63(x86251)+~P1(f306(f306(f221(x86251),x86253),f2(x86251)))+~P1(f306(f306(f221(x86251),x86252),f306(f306(f82(x86251),x86254),x86253)))+~P1(f306(f306(f221(x86251),f306(f306(f82(x86251),x86254),x86253)),x86252))+P1(f306(f306(f221(x86251),f306(f306(f264(x86251),x86252),x86253)),x86254)) % 187.68/187.66 [8639]~P63(x86391)+~P1(f306(f306(f220(x86391),f2(x86391)),x86394))+~P1(f306(f306(f220(x86391),x86392),f306(f306(f82(x86391),x86394),x86393)))+~P1(f306(f306(f220(x86391),f306(f306(f82(x86391),x86394),x86393)),x86392))+P1(f306(f306(f220(x86391),f306(f306(f264(x86391),x86392),x86393)),x86394)) % 187.68/187.66 [8640]~P63(x86401)+~P1(f306(f306(f221(x86401),f2(x86401)),x86404))+~P1(f306(f306(f221(x86401),x86402),f306(f306(f82(x86401),x86404),x86403)))+~P1(f306(f306(f221(x86401),f306(f306(f82(x86401),x86404),x86403)),x86402))+P1(f306(f306(f221(x86401),f306(f306(f264(x86401),x86402),x86403)),x86404)) % 187.68/187.66 [8807]E(f306(f306(f22(a1),f388(x88071,x88072,x88073,x88074)),f389(x88071,x88072,x88073,x88074)),x88074)+~P1(f306(f306(f221(a1),f2(a1)),x88073))+~P1(f306(f306(f308(a1),x88072),x88071))+~P1(f306(f306(f221(a1),x88074),x88072))+P1(f306(f306(f221(a1),f306(f306(f81(a1),x88074),x88073)),x88072)) % 187.68/187.66 [8887]~P1(f306(x88871,x88872))+~P1(f306(f306(f220(a1),f2(a1)),x88873))+~P1(f306(f306(f221(a1),f2(a1)),x88874))+~P1(f306(x88871,f306(f306(f22(a1),f839(x88873,x88871,x88874)),x88874)))+P1(f306(x88871,f306(f306(f22(a1),x88872),f306(f306(f82(a1),x88873),x88874)))) % 187.68/187.66 [8888]~P1(f306(x88881,x88882))+~P1(f306(f306(f220(a1),f2(a1)),x88883))+~P1(f306(f306(f221(a1),f2(a1)),x88884))+~P1(f306(x88881,f306(f306(f81(a1),f849(x88883,x88881,x88884)),x88884)))+P1(f306(x88881,f306(f306(f81(a1),x88882),f306(f306(f82(a1),x88883),x88884)))) % 187.68/187.66 [9042]~P1(f306(f306(f221(a1),f2(a1)),x90423))+~P1(f306(f306(f308(a1),x90422),x90421))+~P1(f306(f306(f221(a1),x90424),x90422))+P1(f306(f306(f308(a1),f388(x90421,x90422,x90423,x90424)),x90421))+P1(f306(f306(f221(a1),f306(f306(f81(a1),x90424),x90423)),x90422)) % 187.68/187.66 [9061]E(f306(f306(f22(a1),f375(x90611,x90612,x90613,x90614)),f376(x90611,x90612,x90613,x90614)),x90614)+~P1(f306(f306(f221(a1),f2(a1)),x90613))+~P1(f306(f306(f220(a1),x90614),x90612))+~P1(f306(f306(f308(a1),f306(f306(f81(a1),x90612),f79(a1))),x90611))+P1(f306(f306(f220(a1),f306(f306(f81(a1),x90614),x90613)),x90612)) % 187.68/187.66 [9087]~P1(f306(f306(f221(a1),f2(a1)),x90872))+~P1(f306(f306(f308(a1),x90873),x90874))+~P1(f306(f306(f221(a1),x90871),x90873))+P1(f306(f306(f308(a1),f389(x90874,x90873,x90872,x90871)),f277(a1,f79(a1),x90872)))+P1(f306(f306(f221(a1),f306(f306(f81(a1),x90871),x90872)),x90873)) % 187.68/187.66 [9180]~P1(f306(f306(f221(a1),f2(a1)),x91803))+~P1(f306(f306(f220(a1),x91804),x91802))+P1(f306(f306(f308(a1),f375(x91801,x91802,x91803,x91804)),x91801))+~P1(f306(f306(f308(a1),f306(f306(f81(a1),x91802),f79(a1))),x91801))+P1(f306(f306(f220(a1),f306(f306(f81(a1),x91804),x91803)),x91802)) % 187.68/187.66 [9227]~P1(f306(f306(f221(a1),f2(a1)),x92272))+~P1(f306(f306(f220(a1),x92271),x92273))+P1(f306(f306(f308(a1),f376(x92274,x92273,x92272,x92271)),f277(a1,f79(a1),x92272)))+~P1(f306(f306(f308(a1),f306(f306(f81(a1),x92273),f79(a1))),x92274))+P1(f306(f306(f220(a1),f306(f306(f81(a1),x92271),x92272)),x92273)) % 187.68/187.66 [9517]~P40(x95171,x95173)+~P29(x95171,x95174)+P40(x95171,f306(f306(f108(f872(f871(x95171,x95171),a859)),x95172),x95173))+~P1(f306(f306(f220(f872(f871(x95171,x95171),a859)),x95172),f306(f235(f872(f871(x95171,x95171),a859),f872(f871(x95171,x95171),a859)),x95174)))+~P1(f306(f306(f220(f872(f871(x95171,x95171),a859)),x95173),f306(f244(f872(f871(x95171,x95171),a859),f872(f871(x95171,x95171),a859)),x95174))) % 187.68/187.66 [9810]~E(f306(f668(x98101,x98104,x98103,x98102),f670(x98101,x98104,x98103,x98102)),f188(f866(a302)))+P1(f306(f306(f221(a1),f669(x98101,x98104,x98103,x98102)),f670(x98101,x98104,x98103,x98102)))+P1(f306(f306(f306(x98101,x98102),x98103),x98104))+P1(f306(f306(f306(x98101,f668(x98101,x98104,x98103,x98102)),f669(x98101,x98104,x98103,x98102)),f306(f306(f81(a1),f670(x98101,x98104,x98103,x98102)),f79(a1))))+~P1(f306(f294(f871(f872(a1,f869(f866(a302))),f871(a1,a1)),a292),f306(f306(f236(f872(a1,f869(f866(a302))),f871(a1,a1)),x98102),f306(f306(f236(a1,a1),x98103),x98104)))) % 187.68/187.66 [9913]~P21(x99132,x99134,x99133)+E(x99131,f185(f872(x99132,a859)))+~P1(f306(f63(x99132),x99131))+P1(f306(f306(f308(x99132),f306(x99133,x99131)),x99131))+~P1(f306(f306(f308(x99132),f306(f306(x99134,f565(x99131,x99133,x99134,x99132)),f583(x99131,x99133,x99134,x99132))),f306(f306(f284(x99132),f565(x99131,x99133,x99134,x99132)),f306(f306(f284(x99132),f583(x99131,x99133,x99134,x99132)),f185(f872(x99132,a859)))))) % 187.68/187.66 [8534]~P6(x85341)+~P41(x85341,x85341,x85344)+~E(x85342,f102(x85341,x85344))+P1(f306(f306(f220(x85341),x85342),x85343))+~P1(f306(f306(f220(x85341),f306(x85344,f306(f306(f109(x85341),x85342),x85343))),x85343)) % 187.68/187.66 [9843]~P109(x98432)+~P60(x98431)+~P1(f306(f306(f220(f872(x98431,x98432)),x98433),x98434))+P1(f306(f306(f221(f872(x98431,x98432)),x98433),x98434))+~P1(f306(f59(x98431),f306(f306(f8(a859,a859,x98431),a301),f306(f306(f18(x98431,x98432,a859),f306(f306(f8(x98432,f872(x98432,a859),x98431),a303),x98433)),x98434)))) % 187.68/187.66 [9431]~P54(x94311,x94311,x94314)+P1(f306(f306(f308(f871(x94311,x94311)),f306(f306(f236(x94311,x94311),x94312),x94313)),f282(x94311,x94314)))+P1(f306(f306(f308(f871(x94311,x94311)),f306(f306(f236(x94311,x94311),x94313),x94312)),f282(x94311,x94314)))+~P1(f306(f306(f308(f871(x94311,x94311)),f306(f306(f236(x94311,x94311),x94315),x94312)),f282(x94311,x94314)))+~P1(f306(f306(f308(f871(x94311,x94311)),f306(f306(f236(x94311,x94311),x94315),x94313)),f282(x94311,x94314))) % 187.68/187.66 [5573]E(x55731,f2(a865))+~E(f306(f39(x55732),x55735),x55731)+E(f306(f39(x55732),x55733),f306(a119,x55731))+~E(x55733,f306(f306(f284(x55732),x55734),x55735))+P1(f306(f306(f308(x55732),x55734),x55735)) % 187.68/187.66 [5699]~P62(x56992)+E(x56991,f2(x56992))+E(x56993,f2(x56992))+~E(f306(f306(f264(x56992),x56994),x56993),f306(f306(f264(x56992),x56995),x56991))+E(f306(f306(f82(x56992),x56994),x56991),f306(f306(f82(x56992),x56995),x56993)) % 187.68/187.66 [5700]~P62(x57002)+E(x57001,f2(x57002))+E(x57003,f2(x57002))+~E(f306(f306(f82(x57002),x57004),x57003),f306(f306(f82(x57002),x57005),x57001))+E(f306(f306(f264(x57002),x57004),x57001),f306(f306(f264(x57002),x57005),x57003)) % 187.68/187.66 [5766]~E(f306(f39(x57661),x57665),x57663)+~E(x57665,f185(f872(x57661,a859)))+E(f306(f39(x57661),x57662),f306(a119,x57663))+~E(x57662,f306(f306(f284(x57661),x57664),x57665))+P1(f306(f306(f308(x57661),x57664),x57665)) % 187.68/187.66 [5998]~P113(x59982)+~E(f306(x59983,x59985),f2(x59982))+E(f306(f306(f9(x59981,x59982),x59983),x59984),f2(x59982))+~P1(f306(f63(x59981),x59984))+~P1(f306(f306(f308(x59981),x59985),x59984)) % 187.68/187.66 [6372]~P108(x63723)+E(x63721,x63722)+~E(f306(f276(x63723,x63724),x63721),f306(f276(x63723,x63725),x63722))+~P1(f306(f306(f221(x63723),x63725),x63722))+~P1(f306(f306(f221(x63723),x63724),x63721)) % 187.68/187.66 [6373]~P108(x63733)+E(x63731,x63732)+~E(f306(f276(x63733,x63731),x63734),f306(f276(x63733,x63732),x63735))+~P1(f306(f306(f221(x63733),x63732),x63735))+~P1(f306(f306(f221(x63733),x63731),x63734)) % 187.68/187.66 [6532]~P109(x65321)+~P41(x65325,x65321,x65322)+~P109(x65325)+P1(f306(f306(f220(x65321),f306(x65322,x65323)),f306(x65322,x65324)))+~P1(f306(f306(f220(x65325),x65323),x65324)) % 187.68/187.66 [7433]~P108(x74331)+~P17(x74331,f306(f306(f122(x74331),x74334),x74335))+~P1(f306(f306(f308(x74331),x74333),f306(f164(x74331),x74335)))+~P1(f306(f306(f308(x74331),x74332),f306(f164(x74331),x74334)))+P1(f306(f306(f220(x74331),x74332),x74333)) % 187.68/187.66 [8544]~P109(x85441)+~P1(f306(f306(f221(f872(x85441,a859)),f277(x85441,x85445,x85442)),f277(x85441,x85444,x85443)))+~P1(f306(f306(f220(x85441),x85445),x85442))+P1(f306(f306(f221(x85441),x85442),x85443))+P1(f306(f306(f221(x85441),x85444),x85445)) % 187.68/187.66 [9554]~P41(f872(x95544,a859),f872(x95544,a859),x95545)+P1(f306(x95541,x95542))+~E(x95543,f102(f872(x95544,a859),x95545))+~P1(f306(x95541,f580(x95541,x95542,x95545,x95544,x95543)))+~P1(f306(f306(f308(x95544),x95542),x95543)) % 187.68/187.66 [9956]~P20(x99562,x99565,x99563)+E(x99561,f185(f872(x99562,a859)))+~E(f306(f306(x99565,f306(x99564,f513(x99561,x99564,x99563,x99565,x99562))),f306(x99564,f514(x99561,x99564,x99563,x99565,x99562))),f306(x99564,f306(f306(x99565,f513(x99561,x99564,x99563,x99565,x99562)),f514(x99561,x99564,x99563,x99565,x99562))))+E(f306(x99563,f306(f285(x99562,x99562,x99564),x99561)),f306(x99564,f306(x99563,x99561)))+~P1(f306(f63(x99562),x99561)) % 187.68/187.66 [6369]~P21(x63692,x63695,x63693)+E(x63691,f185(f872(x63692,a859)))+~P1(f306(f63(x63692),x63691))+E(f306(x63693,f306(f306(f284(x63692),x63694),x63691)),f306(f306(x63695,x63694),f306(x63693,x63691)))+P1(f306(f306(f308(x63692),x63694),x63691)) % 187.68/187.66 [7191]~P20(x71912,x71913,x71914)+E(f306(f306(x71913,f306(x71914,x71911)),f306(x71914,x71915)),f306(x71914,x71915))+E(x71911,f185(f872(x71912,a859)))+~P1(f306(f63(x71912),x71915))+~P1(f306(f306(f220(f872(x71912,a859)),x71911),x71915)) % 187.68/187.66 [7409]~P60(x74094)+~P93(x74095)+E(f306(x74091,x74092),f306(x74093,x74092))+~P1(f306(f306(f308(x74094),x74092),f306(f164(x74094),f57(x74094))))+~P1(f306(f306(f92(f872(x74094,x74095)),x74091),x74093)) % 187.68/187.66 [7565]~P21(x75654,x75655,x75651)+E(f306(x75651,x75652),x75653)+~P1(f306(f63(x75654),x75652))+~E(f306(f306(f22(f872(x75654,a859)),x75652),f306(f306(f284(x75654),x75653),f185(f872(x75654,a859)))),f185(f872(x75654,a859)))+~P1(f306(f306(f308(x75654),x75653),x75652)) % 187.68/187.66 [7651]E(x76511,x76512)+~E(f306(f186(f866(x76513)),x76512),f306(f186(f866(x76514)),x76515))+~E(f306(f186(f866(x76513)),x76511),f306(f186(f866(x76514)),x76515))+~E(f306(f169(x76514,x76513),f306(f306(f173(x76514,x76513),x76515),x76511)),f306(f169(x76514,x76513),f306(f306(f173(x76514,x76513),x76515),x76512)))+~P1(f306(f129(x76514),x76515)) % 187.68/187.66 [8514]E(x85141,x85142)+~P9(x85143,x85144,x85145)+E(f306(f306(f109(f872(x85143,a859)),x85141),x85142),f185(f872(x85143,a859)))+~P1(f306(f306(f308(f872(x85143,a859)),x85142),f306(f306(f62(x85143),x85144),x85145)))+~P1(f306(f306(f308(f872(x85143,a859)),x85141),f306(f306(f62(x85143),x85144),x85145))) % 187.68/187.66 [9310]~P75(x93102)+~E(f306(x93103,f342(x93103,x93104,x93105,x93101,x93102)),f79(x93102))+E(f306(f306(f9(x93101,x93102),x93103),x93104),f306(f306(f9(x93101,x93102),x93103),x93105))+~P1(f306(f63(x93101),x93105))+~P1(f306(f306(f220(f872(x93101,a859)),x93104),x93105)) % 187.68/187.66 [9311]~P75(x93112)+~E(f306(x93113,f368(x93113,x93114,x93115,x93111,x93112)),f79(x93112))+E(f306(f306(f9(x93111,x93112),x93113),x93114),f306(f306(f9(x93111,x93112),x93113),x93115))+~P1(f306(f63(x93111),x93115))+~P1(f306(f306(f220(f872(x93111,a859)),x93114),x93115)) % 187.68/187.66 [9312]~P74(x93122)+~E(f306(x93123,f426(x93123,x93124,x93125,x93121,x93122)),f2(x93122))+E(f306(f306(f6(x93121,x93122),x93123),x93124),f306(f306(f6(x93121,x93122),x93123),x93125))+~P1(f306(f63(x93121),x93125))+~P1(f306(f306(f220(f872(x93121,a859)),x93124),x93125)) % 187.68/187.66 [9313]~P74(x93132)+~E(f306(x93133,f432(x93133,x93134,x93135,x93131,x93132)),f2(x93132))+E(f306(f306(f6(x93131,x93132),x93133),x93134),f306(f306(f6(x93131,x93132),x93133),x93135))+~P1(f306(f63(x93131),x93135))+~P1(f306(f306(f220(f872(x93131,a859)),x93134),x93135)) % 187.68/187.66 [9734]~P41(f872(x97341,a859),f872(x97341,a859),f306(f306(f8(f872(x97341,a859),f872(x97341,a859),f872(x97341,a859)),f228(x97341)),x97344))+~P1(f306(f306(x97344,f306(f306(f108(f872(x97341,a859)),x97345),x97343)),f581(x97345,x97342,x97344,x97341,x97343)))+~E(x97343,f103(f872(x97341,a859),f306(f306(f8(f872(x97341,a859),f872(x97341,a859),f872(x97341,a859)),f228(x97341)),x97344)))+P1(f306(f306(f308(x97341),x97342),x97343))+~P1(f306(f306(f308(x97341),x97342),x97345)) % 187.68/187.66 [9738]~P41(f872(x97381,a859),f872(x97381,a859),f306(f306(f8(f872(x97381,a859),f872(x97381,a859),f872(x97381,a859)),f228(x97381)),x97385))+~E(x97383,f103(f872(x97381,a859),f306(f306(f8(f872(x97381,a859),f872(x97381,a859),f872(x97381,a859)),f228(x97381)),x97385)))+~P1(f306(f306(f308(x97381),x97382),x97384))+P1(f306(f306(f308(x97381),f581(x97384,x97382,x97385,x97381,x97383)),x97384))+P1(f306(f306(f308(x97381),x97382),x97383)) % 187.68/187.66 [9791]~P86(x97911)+~P1(f306(f63(x97912),x97915))+~P1(f306(f306(f220(x97911),f2(x97911)),f306(x97913,f419(x97913,x97914,x97915,x97912,x97911))))+P1(f306(f306(f220(x97911),f306(f306(f6(x97912,x97911),x97913),x97914)),f306(f306(f6(x97912,x97911),x97913),x97915)))+~P1(f306(f306(f220(f872(x97912,a859)),x97914),x97915)) % 187.68/187.66 [7430]E(x74301,f2(a865))+P1(f306(x74302,x74303))+~E(x74304,f306(f306(f81(a865),f306(f306(f82(a865),x74301),x74303)),x74305))+~P1(f306(f306(f221(a865),x74305),x74301))+~P1(f306(x74302,f306(f306(f40(a865),x74304),x74301))) % 187.68/187.66 [7506]E(x75061,f2(a865))+P1(f306(x75062,x75063))+~P1(f306(x75062,f46(a865,x75064,x75061)))+~E(x75064,f306(f306(f81(a865),f306(f306(f82(a865),x75061),x75065)),x75063))+~P1(f306(f306(f221(a865),x75063),x75061)) % 187.68/187.66 [7797]~P62(x77973)+E(f306(x77971,x77972),f2(x77973))+~P1(f306(f63(x77974),x77975))+E(f306(f306(f9(x77974,x77973),x77971),f306(f306(f22(f872(x77974,a859)),x77975),f306(f306(f284(x77974),x77972),f185(f872(x77974,a859))))),f306(f306(f9(x77974,x77973),x77971),x77975))+P1(f306(f306(f308(x77974),x77972),x77975)) % 187.68/187.66 [8207]~P75(x82071)+~P1(f306(f63(x82072),x82075))+~P1(f306(f63(x82072),x82074))+~E(f306(f306(f109(f872(x82072,a859)),x82074),x82075),f185(f872(x82072,a859)))+E(f306(f306(f82(x82071),f306(f306(f9(x82072,x82071),x82073),x82074)),f306(f306(f9(x82072,x82071),x82073),x82075)),f306(f306(f9(x82072,x82071),x82073),f306(f306(f108(f872(x82072,a859)),x82074),x82075))) % 187.68/187.66 [8208]~P74(x82081)+~P1(f306(f63(x82082),x82085))+~P1(f306(f63(x82082),x82084))+~E(f306(f306(f109(f872(x82082,a859)),x82084),x82085),f185(f872(x82082,a859)))+E(f306(f306(f81(x82081),f306(f306(f6(x82082,x82081),x82083),x82084)),f306(f306(f6(x82082,x82081),x82083),x82085)),f306(f306(f6(x82082,x82081),x82083),f306(f306(f108(f872(x82082,a859)),x82084),x82085))) % 187.68/187.66 [8302]~P62(x83023)+E(f306(x83021,x83022),f2(x83023))+~P1(f306(f63(x83024),x83025))+E(f306(f306(f9(x83024,x83023),x83021),f306(f306(f22(f872(x83024,a859)),x83025),f306(f306(f284(x83024),x83022),f185(f872(x83024,a859))))),f306(f306(f264(x83023),f306(f306(f9(x83024,x83023),x83021),x83025)),f306(x83021,x83022)))+~P1(f306(f306(f308(x83024),x83022),x83025)) % 187.68/187.66 [9021]~P9(x90211,x90215,x90214)+~E(f306(f306(f62(x90211),f306(f306(f284(x90211),x90212),f185(f872(x90211,a859)))),x90214),f306(f306(f62(x90211),f306(f306(f284(x90211),x90213),f185(f872(x90211,a859)))),x90214))+~P1(f306(f306(f308(x90211),x90213),x90215))+~P1(f306(f306(f308(x90211),x90212),x90215))+P1(f306(f306(f308(f871(x90211,x90211)),f306(f306(f236(x90211,x90211),x90212),x90213)),x90214)) % 187.68/187.66 [9041]~P9(x90411,x90415,x90413)+E(f306(f306(f62(x90411),f306(f306(f284(x90411),x90412),f185(f872(x90411,a859)))),x90413),f306(f306(f62(x90411),f306(f306(f284(x90411),x90414),f185(f872(x90411,a859)))),x90413))+~P1(f306(f306(f308(x90411),x90414),x90415))+~P1(f306(f306(f308(x90411),x90412),x90415))+~P1(f306(f306(f308(f871(x90411,x90411)),f306(f306(f236(x90411,x90411),x90412),x90414)),x90413)) % 187.68/187.66 [9339]~P75(x93391)+~P1(f306(f63(x93392),x93395))+~P1(f306(f63(x93392),x93394))+~E(f306(f306(f109(f872(x93392,a859)),x93394),x93395),f185(f872(x93392,a859)))+E(f306(f306(f82(x93391),f306(f306(f306(f67(x93391,x93392,f82(x93391)),x93393),f79(x93391)),x93394)),f306(f306(f306(f67(x93391,x93392,f82(x93391)),x93393),f79(x93391)),x93395)),f306(f306(f306(f67(x93391,x93392,f82(x93391)),x93393),f79(x93391)),f306(f306(f108(f872(x93392,a859)),x93394),x93395))) % 187.68/187.66 [9348]~P75(x93481)+~E(f306(x93483,f446(x93483,x93485,x93484,x93482,x93481)),f79(x93481))+~P1(f306(f63(x93482),x93484))+~P1(f306(f63(x93482),x93485))+E(f306(f306(f82(x93481),f306(f306(f9(x93482,x93481),x93483),x93484)),f306(f306(f9(x93482,x93481),x93483),x93485)),f306(f306(f9(x93482,x93481),x93483),f306(f306(f108(f872(x93482,a859)),x93484),x93485))) % 187.68/187.66 [9349]~P75(x93491)+~E(f306(x93493,f447(x93493,x93495,x93494,x93492,x93491)),f79(x93491))+~P1(f306(f63(x93492),x93494))+~P1(f306(f63(x93492),x93495))+E(f306(f306(f82(x93491),f306(f306(f9(x93492,x93491),x93493),x93494)),f306(f306(f9(x93492,x93491),x93493),x93495)),f306(f306(f9(x93492,x93491),x93493),f306(f306(f108(f872(x93492,a859)),x93494),x93495))) % 187.68/187.66 [9350]~P74(x93501)+~E(f306(x93503,f448(x93503,x93505,x93504,x93502,x93501)),f2(x93501))+~P1(f306(f63(x93502),x93504))+~P1(f306(f63(x93502),x93505))+E(f306(f306(f81(x93501),f306(f306(f6(x93502,x93501),x93503),x93504)),f306(f306(f6(x93502,x93501),x93503),x93505)),f306(f306(f6(x93502,x93501),x93503),f306(f306(f108(f872(x93502,a859)),x93504),x93505))) % 187.68/187.66 [9351]~P74(x93511)+~E(f306(x93513,f450(x93513,x93515,x93514,x93512,x93511)),f2(x93511))+~P1(f306(f63(x93512),x93514))+~P1(f306(f63(x93512),x93515))+E(f306(f306(f81(x93511),f306(f306(f6(x93512,x93511),x93513),x93514)),f306(f306(f6(x93512,x93511),x93513),x93515)),f306(f306(f6(x93512,x93511),x93513),f306(f306(f108(f872(x93512,a859)),x93514),x93515))) % 187.68/187.66 [9562]~P75(x95621)+~E(f306(x95623,f443(x95623,x95625,x95624,x95622,x95621)),f79(x95621))+~P1(f306(f63(x95622),x95624))+~P1(f306(f63(x95622),x95625))+E(f306(f306(f82(x95621),f306(f306(f306(f67(x95621,x95622,f82(x95621)),x95623),f79(x95621)),x95624)),f306(f306(f306(f67(x95621,x95622,f82(x95621)),x95623),f79(x95621)),x95625)),f306(f306(f306(f67(x95621,x95622,f82(x95621)),x95623),f79(x95621)),f306(f306(f108(f872(x95622,a859)),x95624),x95625))) % 187.68/187.66 [9668]~P75(x96682)+E(f306(f306(f9(x96681,x96682),x96683),x96684),f306(f306(f9(x96681,x96682),x96683),x96685))+~P1(f306(f63(x96681),x96685))+~P1(f306(f306(f220(f872(x96681,a859)),x96684),x96685))+P1(f306(f306(f308(x96681),f342(x96683,x96684,x96685,x96681,x96682)),f306(f306(f22(f872(x96681,a859)),x96685),x96684))) % 187.68/187.66 [9669]~P75(x96692)+E(f306(f306(f9(x96691,x96692),x96693),x96694),f306(f306(f9(x96691,x96692),x96693),x96695))+~P1(f306(f63(x96691),x96695))+~P1(f306(f306(f220(f872(x96691,a859)),x96694),x96695))+P1(f306(f306(f308(x96691),f368(x96693,x96694,x96695,x96691,x96692)),f306(f306(f22(f872(x96691,a859)),x96695),x96694))) % 187.68/187.66 [9670]~P74(x96702)+E(f306(f306(f6(x96701,x96702),x96703),x96704),f306(f306(f6(x96701,x96702),x96703),x96705))+~P1(f306(f63(x96701),x96705))+~P1(f306(f306(f220(f872(x96701,a859)),x96704),x96705))+P1(f306(f306(f308(x96701),f426(x96703,x96704,x96705,x96701,x96702)),f306(f306(f22(f872(x96701,a859)),x96705),x96704))) % 187.68/187.66 [9671]~P74(x96712)+E(f306(f306(f6(x96711,x96712),x96713),x96714),f306(f306(f6(x96711,x96712),x96713),x96715))+~P1(f306(f63(x96711),x96715))+~P1(f306(f306(f220(f872(x96711,a859)),x96714),x96715))+P1(f306(f306(f308(x96711),f432(x96713,x96714,x96715,x96711,x96712)),f306(f306(f22(f872(x96711,a859)),x96715),x96714))) % 187.68/187.66 [9688]~P75(x96881)+~P1(f306(f63(x96882),x96884))+~P1(f306(f63(x96882),x96885))+E(f306(f306(f82(x96881),f306(f306(f9(x96882,x96881),x96883),x96884)),f306(f306(f9(x96882,x96881),x96883),x96885)),f306(f306(f9(x96882,x96881),x96883),f306(f306(f108(f872(x96882,a859)),x96884),x96885)))+P1(f306(f306(f308(x96882),f446(x96883,x96885,x96884,x96882,x96881)),f306(f306(f109(f872(x96882,a859)),x96884),x96885))) % 187.68/187.66 [9689]~P75(x96891)+~P1(f306(f63(x96892),x96894))+~P1(f306(f63(x96892),x96895))+E(f306(f306(f82(x96891),f306(f306(f9(x96892,x96891),x96893),x96894)),f306(f306(f9(x96892,x96891),x96893),x96895)),f306(f306(f9(x96892,x96891),x96893),f306(f306(f108(f872(x96892,a859)),x96894),x96895)))+P1(f306(f306(f308(x96892),f447(x96893,x96895,x96894,x96892,x96891)),f306(f306(f109(f872(x96892,a859)),x96894),x96895))) % 187.68/187.66 [9690]~P74(x96901)+~P1(f306(f63(x96902),x96904))+~P1(f306(f63(x96902),x96905))+E(f306(f306(f81(x96901),f306(f306(f6(x96902,x96901),x96903),x96904)),f306(f306(f6(x96902,x96901),x96903),x96905)),f306(f306(f6(x96902,x96901),x96903),f306(f306(f108(f872(x96902,a859)),x96904),x96905)))+P1(f306(f306(f308(x96902),f448(x96903,x96905,x96904,x96902,x96901)),f306(f306(f109(f872(x96902,a859)),x96904),x96905))) % 187.68/187.66 [9691]~P74(x96911)+~P1(f306(f63(x96912),x96914))+~P1(f306(f63(x96912),x96915))+E(f306(f306(f81(x96911),f306(f306(f6(x96912,x96911),x96913),x96914)),f306(f306(f6(x96912,x96911),x96913),x96915)),f306(f306(f6(x96912,x96911),x96913),f306(f306(f108(f872(x96912,a859)),x96914),x96915)))+P1(f306(f306(f308(x96912),f450(x96913,x96915,x96914,x96912,x96911)),f306(f306(f109(f872(x96912,a859)),x96914),x96915))) % 187.68/187.66 [9694]~P41(f872(x96943,a859),f872(x96943,a859),x96944)+P1(f306(x96941,x96942))+~E(x96945,f102(f872(x96943,a859),x96944))+~P1(f306(f306(f308(x96943),x96942),x96945))+P1(f306(f306(f308(x96943),f580(x96941,x96942,x96944,x96943,x96945)),f306(x96944,f306(f306(f109(f872(x96943,a859)),x96945),f306(f228(x96943),x96941))))) % 187.68/187.66 [9699]~P86(x96995)+~P1(f306(f63(x96991),x96994))+P1(f306(f306(f220(x96995),f306(f306(f6(x96991,x96995),x96992),x96993)),f306(f306(f6(x96991,x96995),x96992),x96994)))+~P1(f306(f306(f220(f872(x96991,a859)),x96993),x96994))+P1(f306(f306(f308(x96991),f419(x96992,x96993,x96994,x96991,x96995)),f306(f306(f22(f872(x96991,a859)),x96994),x96993))) % 187.68/187.66 [9755]~P75(x97551)+~P1(f306(f63(x97552),x97554))+~P1(f306(f63(x97552),x97555))+E(f306(f306(f82(x97551),f306(f306(f306(f67(x97551,x97552,f82(x97551)),x97553),f79(x97551)),x97554)),f306(f306(f306(f67(x97551,x97552,f82(x97551)),x97553),f79(x97551)),x97555)),f306(f306(f306(f67(x97551,x97552,f82(x97551)),x97553),f79(x97551)),f306(f306(f108(f872(x97552,a859)),x97554),x97555)))+P1(f306(f306(f308(x97552),f443(x97553,x97555,x97554,x97552,x97551)),f306(f306(f109(f872(x97552,a859)),x97554),x97555))) % 187.68/187.66 [8706]~P21(x87061,x87064,x87065)+~P1(f306(f63(x87061),x87062))+E(f306(f306(f22(f872(x87061,a859)),x87062),f306(f306(f284(x87061),x87063),f185(f872(x87061,a859)))),f185(f872(x87061,a859)))+~P1(f306(f306(f308(x87061),x87063),x87062))+E(f306(f306(x87064,x87063),f306(x87065,f306(f306(f22(f872(x87061,a859)),x87062),f306(f306(f284(x87061),x87063),f185(f872(x87061,a859)))))),f306(x87065,x87062)) % 187.68/187.66 [8780]~P21(x87801,x87804,x87805)+~P1(f306(f63(x87801),x87803))+~P1(f306(f63(x87801),x87802))+E(f306(f306(f109(f872(x87801,a859)),x87802),x87803),f185(f872(x87801,a859)))+E(f306(f306(x87804,f306(x87805,f306(f306(f108(f872(x87801,a859)),x87802),x87803))),f306(x87805,f306(f306(f109(f872(x87801,a859)),x87802),x87803))),f306(f306(x87804,f306(x87805,x87802)),f306(x87805,x87803))) % 187.68/187.66 [8969]~P41(f872(x89691,a859),f872(x89691,a859),x89694)+~E(x89693,f103(f872(x89691,a859),x89694))+P1(f306(f306(f308(x89691),x89692),x89693))+~P1(f306(f306(f308(x89691),x89692),x89695))+~P1(f306(f306(f220(f872(x89691,a859)),x89695),f306(x89694,f306(f306(f108(f872(x89691,a859)),x89695),x89693)))) % 187.68/187.66 [9353]~P1(f306(f306(f220(a1),x93534),f2(a1)))+~P1(f306(f306(f221(a1),x93533),x93535))+P1(f306(f306(f220(a1),x93531),x93532))+~P1(f306(f306(f221(a1),x93533),x93534))+~P1(f306(f306(f220(a1),f306(f306(f81(a1),f306(f306(f82(a1),x93533),x93532)),x93535)),f306(f306(f81(a1),f306(f306(f82(a1),x93533),x93531)),x93534))) % 187.68/187.66 [9355]~P1(f306(f306(f220(a1),f2(a1)),x93555))+P1(f306(f306(f220(a1),x93551),x93552))+~P1(f306(f306(f221(a1),x93553),x93554))+~P1(f306(f306(f221(a1),x93555),x93554))+~P1(f306(f306(f220(a1),f306(f306(f81(a1),f306(f306(f82(a1),x93554),x93551)),x93555)),f306(f306(f81(a1),f306(f306(f82(a1),x93554),x93552)),x93553))) % 187.68/187.66 [9468]~P62(x94685)+E(f306(x94681,f442(x94681,x94682,x94683,x94684,x94685)),f2(x94685))+~P1(f306(f63(x94684),x94683))+~P1(f306(f63(x94684),x94682))+E(f306(f306(f264(x94685),f306(f306(f82(x94685),f306(f306(f9(x94684,x94685),x94681),x94683)),f306(f306(f9(x94684,x94685),x94681),x94682))),f306(f306(f9(x94684,x94685),x94681),f306(f306(f109(f872(x94684,a859)),x94683),x94682))),f306(f306(f9(x94684,x94685),x94681),f306(f306(f108(f872(x94684,a859)),x94683),x94682))) % 187.68/187.66 [9748]~P62(x97481)+~P1(f306(f63(x97482),x97484))+~P1(f306(f63(x97482),x97485))+E(f306(f306(f264(x97481),f306(f306(f82(x97481),f306(f306(f9(x97482,x97481),x97483),x97484)),f306(f306(f9(x97482,x97481),x97483),x97485))),f306(f306(f9(x97482,x97481),x97483),f306(f306(f109(f872(x97482,a859)),x97484),x97485))),f306(f306(f9(x97482,x97481),x97483),f306(f306(f108(f872(x97482,a859)),x97484),x97485)))+P1(f306(f306(f308(x97482),f442(x97483,x97485,x97484,x97482,x97481)),f306(f306(f109(f872(x97482,a859)),x97484),x97485))) % 187.68/187.66 [9060]E(f306(f306(f122(x90601),x90602),x90603),f306(f306(f122(x90601),x90604),x90605))+~E(f306(f306(f165(x90601),f306(f186(f866(x90601)),x90604)),x90602),x90604)+~E(f306(f306(f165(x90601),f306(f186(f866(x90601)),x90602)),x90604),x90602)+~E(x90605,f306(f306(f122(x90601),f306(f306(f130(x90601),f306(f186(f866(x90601)),x90604)),x90602)),x90603))+~E(f306(f306(f122(x90601),f306(f306(f130(x90601),f306(f186(f866(x90601)),x90602)),x90604)),x90605),x90603) % 187.68/187.66 [9466]~P108(x94662)+E(f306(f306(f140(x94661,x94662,x94663),x94664),f162(x94661,x94664,x94665)),x94665)+~P17(x94662,f306(f306(f146(x94661,x94662),x94663),x94665))+~P1(f306(f306(f308(x94661),x94664),f306(f164(x94661),x94665)))+~E(f306(f133(x94661),f306(f128(x94661,f306(f306(f8(x94662,a859,x94661),f306(a303,f306(x94663,x94664))),x94663)),x94665)),x94664) % 187.68/187.66 [9807]~P72(x98071)+~P1(f306(f68(x98071,x98071,f82(x98071),x98072,x98073),x98075))+~P1(f306(f306(f308(x98071),x98074),x98073))+P1(f306(f306(f308(x98071),x98072),x98073))+P1(f306(f68(x98071,x98071,f82(x98071),x98074,f306(f306(f284(x98071),x98072),f306(f306(f22(f872(x98071,a859)),x98073),f306(f306(f284(x98071),x98074),f185(f872(x98071,a859)))))),x98075)) % 187.68/187.66 [10152]~P41(f872(x101521,a859),f872(x101521,a859),x101524)+~E(x101523,f103(f872(x101521,a859),x101524))+P1(f306(f306(f308(x101521),x101522),x101523))+~P1(f306(f306(f308(x101521),x101522),x101525))+~P1(f306(f306(f220(f872(x101521,a859)),x101525),f306(x101524,f102(f872(x101521,a859),f306(f306(f7(f872(x101521,a859),f872(x101521,a859),f872(x101521,a859)),f306(f306(f8(f872(x101521,a859),f872(f872(x101521,a859),f872(x101521,a859)),f872(x101521,a859)),f108(f872(x101521,a859))),f306(f306(f7(f872(x101521,a859),f872(x101521,a859),f872(x101521,a859)),f306(f306(f8(f872(x101521,a859),f872(f872(x101521,a859),f872(x101521,a859)),f872(x101521,a859)),f108(f872(x101521,a859))),x101524)),x101525))),x101523))))) % 187.68/187.66 [7199]E(x71991,x71992)+~P28(x71994,x71995,x71993,x71996)+~E(f306(x71993,x71991),f306(x71993,x71992))+~P1(f306(f306(f308(x71994),x71992),x71996))+~P1(f306(f306(f308(x71994),x71991),x71996)) % 187.68/187.66 [6460]~P143(x64604)+E(x64601,x64602)+~E(x64605,x64606)+E(x64603,f2(x64604))+~E(f306(f306(f81(x64604),x64605),f306(f306(f82(x64604),x64603),x64601)),f306(f306(f81(x64604),x64606),f306(f306(f82(x64604),x64603),x64602))) % 187.68/187.66 [7487]~P108(x74871)+~P6(x74871)+~P1(f306(f306(f221(x74871),x74872),f306(x74875,x74876)))+~P1(f306(f306(f308(x74873),x74876),x74874))+P1(f306(f306(f221(x74871),x74872),f306(f306(f43(x74873,x74871),x74874),x74875))) % 187.68/187.66 [8176]~P108(x81761)+~P6(x81761)+~P1(f306(f306(f221(x81761),f306(x81764,x81766)),x81765))+~P1(f306(f306(f308(x81762),x81766),x81763))+P1(f306(f306(f221(x81761),f306(f306(f44(x81762,x81761),x81763),x81764)),x81765)) % 187.68/187.66 [8439]~P22(x84392,x84395,x84396,x84391)+~P1(f306(f63(x84392),x84394))+~P1(f306(f63(x84392),x84393))+~E(f306(f306(f109(f872(x84392,a859)),x84393),x84394),f185(f872(x84392,a859)))+E(f306(x84391,f306(f306(f108(f872(x84392,a859)),x84393),x84394)),f306(f74(x84395,x84395,x84395,f306(x84391,x84393)),f306(x84391,x84394))) % 187.68/187.66 [8749]E(x87491,x87492)+~P56(x87494,x87495,x87496,x87493,x87497)+~E(f306(x87493,x87491),f306(x87493,x87492))+~P1(f306(f306(f308(x87495),x87492),x87497))+~P1(f306(f306(f308(x87495),x87491),x87497)) % 187.68/187.66 [10058]~P1(f306(x100582,x100584))+~E(x100585,f306(f128(x100581,x100582),x100587))+E(f306(f128(x100581,x100582),x100583),f306(f306(f143(x100581),x100584),x100585))+~E(x100583,f306(f306(f122(x100581),x100586),f306(f306(f143(x100581),x100584),x100587)))+P1(f306(x100582,f783(x100585,x100584,x100583,x100582,x100581,x100586,x100587))) % 187.68/187.66 [10059]~P1(f306(x100594,x100592))+~E(x100593,f306(f128(x100591,x100594),x100597))+E(f306(f306(f143(x100591),x100592),x100593),f306(f128(x100591,x100594),x100595))+~E(x100595,f306(f306(f122(x100591),x100596),f306(f306(f143(x100591),x100592),x100597)))+P1(f306(x100594,f782(x100595,x100594,x100593,x100592,x100591,x100596,x100597))) % 187.68/187.66 [10094]~P1(f306(x100942,x100944))+~E(x100945,f306(f128(x100941,x100942),x100947))+E(f306(f128(x100941,x100942),x100943),f306(f306(f143(x100941),x100944),x100945))+~E(x100943,f306(f306(f122(x100941),x100946),f306(f306(f143(x100941),x100944),x100947)))+P1(f306(f306(f308(x100941),f783(x100945,x100944,x100943,x100942,x100941,x100946,x100947)),f306(f164(x100941),x100946))) % 187.68/187.66 [10095]~P1(f306(x100954,x100952))+~E(x100953,f306(f128(x100951,x100954),x100957))+E(f306(f306(f143(x100951),x100952),x100953),f306(f128(x100951,x100954),x100955))+~E(x100955,f306(f306(f122(x100951),x100956),f306(f306(f143(x100951),x100952),x100957)))+P1(f306(f306(f308(x100951),f782(x100955,x100954,x100953,x100952,x100951,x100956,x100957)),f306(f164(x100951),x100956))) % 187.68/187.66 [10098]~P9(x100981,x100987,x100986)+~P15(x100981,f872(x100985,a859),x100986,x100984)+P1(f306(f306(f308(x100981),f470(x100982,x100983,x100984,x100985,x100986,x100987,x100981)),x100987))+~P1(f306(f306(f308(f872(x100981,a859)),x100983),f306(f306(f62(x100981),x100987),x100986)))+P1(f306(f306(f308(f872(x100985,a859)),f306(f306(f43(x100981,f872(x100985,a859)),x100983),x100984)),x100982)) % 187.68/187.66 [10148]~P9(x101482,x101486,x101487)+~P15(x101482,f872(x101481,a859),x101487,x101484)+~P1(f306(f306(f308(f872(x101482,a859)),x101483),f306(f306(f62(x101482),x101486),x101487)))+~P1(f306(f306(f308(f872(x101481,a859)),f306(x101484,f470(x101485,x101483,x101484,x101481,x101487,x101486,x101482))),x101485))+P1(f306(f306(f308(f872(x101481,a859)),f306(f306(f43(x101482,f872(x101481,a859)),x101483),x101484)),x101485)) % 187.68/187.66 [8347]~P75(x83472)+~P28(x83471,x83475,x83478,x83474)+~E(x83473,f306(f74(x83475,x83472,x83471,x83476),x83478))+~E(x83477,f306(f285(x83471,x83475,x83478),x83474))+E(f306(f306(f9(x83471,x83472),x83473),x83474),f306(f306(f9(x83475,x83472),x83476),x83477)) % 187.68/187.66 [10151]~P75(x101512)+~P28(x101515,x101511,x101518,x101517)+~E(f306(x101516,f477(x101513,x101516,x101514,x101517,x101518,x101511,x101515,x101512)),f306(f306(f74(x101511,x101512,x101515,x101513),x101518),f477(x101513,x101516,x101514,x101517,x101518,x101511,x101515,x101512)))+~E(x101514,f306(f285(x101515,x101511,x101518),x101517))+E(f306(f306(f9(x101511,x101512),x101513),x101514),f306(f306(f9(x101515,x101512),x101516),x101517)) % 187.68/187.66 [10155]~P75(x101552)+~P28(x101551,x101555,x101558,x101554)+~E(x101557,f306(f285(x101551,x101555,x101558),x101554))+E(f306(f306(f9(x101551,x101552),x101553),x101554),f306(f306(f9(x101555,x101552),x101556),x101557))+P1(f306(f306(f308(x101551),f477(x101556,x101553,x101557,x101554,x101558,x101555,x101551,x101552)),x101554)) % 187.68/187.66 [10156]~P74(x101562)+~P28(x101561,x101565,x101568,x101564)+~E(x101567,f306(f285(x101561,x101565,x101568),x101564))+E(f306(f306(f6(x101561,x101562),x101563),x101564),f306(f306(f6(x101565,x101562),x101566),x101567))+P1(f306(f306(f308(x101561),f589(x101566,x101563,x101567,x101564,x101568,x101565,x101561,x101562)),x101564)) % 187.68/187.66 [10161]~P74(x101612)+~P28(x101615,x101611,x101618,x101617)+~E(x101614,f306(f285(x101615,x101611,x101618),x101617))+~E(f306(x101616,f589(x101613,x101616,x101614,x101617,x101618,x101611,x101615,x101612)),f306(x101613,f306(x101618,f589(x101613,x101616,x101614,x101617,x101618,x101611,x101615,x101612))))+E(f306(f306(f6(x101611,x101612),x101613),x101614),f306(f306(f6(x101615,x101612),x101616),x101617)) % 187.68/187.66 [9523]~E(f306(f186(f866(x95232)),x95235),f306(f186(f866(x95231)),x95233))+~E(f306(f186(f866(x95232)),x95234),f306(f186(f866(x95231)),x95233))+~E(f306(f306(f306(f73(x95231,f869(x95232)),f306(f169(x95231,x95232),f306(f306(f173(x95231,x95232),x95233),x95234))),x95236),f306(f214(x95232),x95237)),f306(f306(f306(f73(x95231,f869(x95232)),f306(f169(x95231,x95232),f306(f306(f173(x95231,x95232),x95233),x95235))),x95236),f306(f214(x95232),x95238)))+E(f306(f169(x95231,x95232),f306(f306(f173(x95231,x95232),x95233),x95234)),f306(f169(x95231,x95232),f306(f306(f173(x95231,x95232),x95233),x95235)))+P1(f306(f306(f308(x95231),x95236),f306(f164(x95231),x95233))) % 187.68/187.66 [9635]~P26(x96356,x96352,x96355,x96357,x96358,x96351)+~P1(f306(f63(x96352),x96354))+~P1(f306(f63(x96352),x96353))+~E(f306(f306(f109(f872(x96352,a859)),x96353),x96354),f185(f872(x96352,a859)))+E(f306(x96351,f306(f306(f108(f872(x96352,a859)),x96353),x96354)),f306(f306(x96355,f306(x96351,x96353)),f306(x96351,x96354))) % 187.68/187.66 [10044]~P26(x100448,x100442,x100445,x100447,x100446,x100441)+~E(f306(x100446,f515(x100444,x100443,x100441,x100446,x100447,x100445,x100442)),x100447)+~P1(f306(f63(x100442),x100443))+~P1(f306(f63(x100442),x100444))+E(f306(x100441,f306(f306(f108(f872(x100442,a859)),x100443),x100444)),f306(f306(x100445,f306(x100441,x100443)),f306(x100441,x100444))) % 187.68/187.66 [10103]~P26(x101038,x101032,x101035,x101037,x101036,x101031)+~P1(f306(f63(x101032),x101033))+~P1(f306(f63(x101032),x101034))+E(f306(x101031,f306(f306(f108(f872(x101032,a859)),x101033),x101034)),f306(f306(x101035,f306(x101031,x101033)),f306(x101031,x101034)))+P1(f306(f306(f308(x101032),f515(x101034,x101033,x101031,x101036,x101037,x101035,x101032)),f306(f306(f109(f872(x101032,a859)),x101033),x101034))) % 187.68/187.66 [9796]~P9(x97964,x97968,x97965)+~P9(x97961,x97969,x97963)+~P16(x97961,x97964,f872(x97962,a859),x97963,x97965,x97967)+P15(x97961,f872(x97962,a859),x97963,f306(f306(f8(f872(x97964,f872(x97962,a859)),f872(x97962,a859),x97961),f306(f43(x97964,f872(x97962,a859)),f306(f260(x97964,x97964,x97965),f306(f306(f284(x97964),x97966),f185(f872(x97964,a859)))))),x97967))+~P1(f306(f306(f308(x97964),x97966),x97968)) % 187.68/187.66 [5380]~P108(x53803)+~P17(x53803,x53801)+E(x53801,f755(x53802,x53803))+~E(f306(f164(x53803),x53801),x53802)+~P1(f306(f63(x53803),x53802))+~P1(f306(f129(x53803),x53801)) % 187.68/187.66 [4996]~P124(x49962)+~P127(x49962)+~P132(x49962)+~P115(x49962)+E(x49961,f2(x49962))+~E(f306(f306(f237(x49962),x49961),x49963),f2(x49962)) % 187.68/187.66 [4997]~P124(x49972)+~P127(x49972)+~P132(x49972)+~P115(x49972)+~E(x49971,f2(a865))+~E(f306(f306(f237(x49972),x49973),x49971),f2(x49972)) % 187.68/187.66 [6442]~P86(x64421)+~E(x64423,f2(x64421))+~E(x64422,f2(x64421))+E(f306(f306(f81(x64421),x64422),x64423),f2(x64421))+~P1(f306(f306(f220(x64421),f2(x64421)),x64423))+~P1(f306(f306(f220(x64421),f2(x64421)),x64422)) % 187.68/187.66 [8812]~E(f306(f235(a865,a865),x88123),f2(a865))+~E(x88121,f306(f306(f81(a865),f306(f306(f82(a865),f306(f235(a865,a865),x88123)),x88122)),f306(f244(a865,a865),x88123)))+P1(f306(f49(x88121,x88122),x88123))+~P1(f306(f306(f220(a865),f306(f244(a865,a865),x88123)),f2(a865)))+P1(f306(f306(f221(a865),f2(a865)),x88122))+~P1(f306(f306(f221(a865),x88122),f306(f244(a865,a865),x88123))) % 187.68/187.66 [8820]E(x88201,f2(a865))+~E(x88202,f306(f306(f81(a865),f306(f306(f82(a865),f306(f235(a865,a865),x88203)),x88201)),f306(f244(a865,a865),x88203)))+P1(f306(f49(x88202,x88201),x88203))+~P1(f306(f306(f221(a865),f2(a865)),x88201))+~P1(f306(f306(f220(a865),f2(a865)),f306(f244(a865,a865),x88203)))+~P1(f306(f306(f221(a865),f306(f244(a865,a865),x88203)),x88201)) % 187.68/187.66 [8838]~E(f306(f235(a865,a865),x88383),f2(a865))+~E(x88381,f306(f306(f81(a865),f306(f306(f82(a865),f306(f235(a865,a865),x88383)),x88382)),f306(f244(a865,a865),x88383)))+P1(f306(f49(x88381,x88382),x88383))+~P1(f306(f306(f221(a865),f2(a865)),x88382))+~P1(f306(f306(f220(a865),f2(a865)),f306(f244(a865,a865),x88383)))+~P1(f306(f306(f221(a865),f306(f244(a865,a865),x88383)),x88382)) % 187.68/187.66 [6824]~P108(x68242)+E(x68241,f185(f872(x68242,a859)))+E(x68243,f185(f872(x68242,a859)))+~P1(f306(f63(x68242),x68241))+~P1(f306(f63(x68242),x68243))+E(f14(x68242,f306(f306(f108(f872(x68242,a859)),x68243),x68241)),f306(f306(f225(x68242),f14(x68242,x68243)),f14(x68242,x68241))) % 187.68/187.66 [6825]~P108(x68252)+E(x68251,f185(f872(x68252,a859)))+E(x68253,f185(f872(x68252,a859)))+~P1(f306(f63(x68252),x68251))+~P1(f306(f63(x68252),x68253))+E(f15(x68252,f306(f306(f108(f872(x68252,a859)),x68253),x68251)),f306(f306(f219(x68252),f15(x68252,x68253)),f15(x68252,x68251))) % 187.68/187.66 [6826]~P98(x68262)+E(x68261,f185(f872(x68262,a859)))+E(x68263,f185(f872(x68262,a859)))+~P1(f306(f63(x68262),x68261))+~P1(f306(f63(x68262),x68263))+E(f13(x68262,f306(f306(f108(f872(x68262,a859)),x68263),x68261)),f306(f306(f108(x68262),f13(x68262,x68263)),f13(x68262,x68261))) % 187.68/187.66 [6827]~P98(x68272)+E(x68271,f185(f872(x68272,a859)))+E(x68273,f185(f872(x68272,a859)))+~P1(f306(f63(x68272),x68271))+~P1(f306(f63(x68272),x68273))+E(f10(x68272,f306(f306(f108(f872(x68272,a859)),x68273),x68271)),f306(f306(f109(x68272),f10(x68272,x68273)),f10(x68272,x68271))) % 187.68/187.66 [7462]~P95(x74622)+E(x74621,f185(f872(x74622,a859)))+E(x74623,f185(f872(x74622,a859)))+~P1(f306(f63(x74622),x74621))+~P1(f306(f63(x74622),x74623))+E(f306(f306(f82(x74622),f306(f65(x74622,f82(x74622)),x74623)),f306(f65(x74622,f82(x74622)),x74621)),f306(f65(x74622,f82(x74622)),f306(f306(f108(f872(x74622,a859)),x74623),x74621))) % 187.68/187.66 [7619]~P108(x76192)+E(x76191,f185(f872(x76192,a859)))+E(x76193,f185(f872(x76192,a859)))+~P1(f306(f63(x76192),x76191))+~P1(f306(f63(x76192),x76193))+E(f306(f306(f225(x76192),f11(x76192,f225(x76192),x76193)),f11(x76192,f225(x76192),x76191)),f11(x76192,f225(x76192),f306(f306(f108(f872(x76192,a859)),x76193),x76191))) % 187.68/187.66 [7620]~P108(x76202)+E(x76201,f185(f872(x76202,a859)))+E(x76203,f185(f872(x76202,a859)))+~P1(f306(f63(x76202),x76201))+~P1(f306(f63(x76202),x76203))+E(f306(f306(f219(x76202),f12(x76202,f219(x76202),x76203)),f12(x76202,f219(x76202),x76201)),f12(x76202,f219(x76202),f306(f306(f108(f872(x76202,a859)),x76203),x76201))) % 187.68/187.66 [8659]~P1(f306(x86591,x86593))+P1(f306(x86591,f398(x86591,x86592)))+P1(f306(x86591,f390(x86591,x86592)))+~P1(f306(f306(f221(a1),f2(a1)),x86592))+~P1(f306(f306(f308(a1),x86593),f277(a1,f79(a1),x86592)))+P1(f306(x86591,f306(f306(f22(a1),f390(x86591,x86592)),f306(f306(f82(a1),f397(x86591,x86592)),x86592)))) % 187.68/187.66 [8959]~P1(f306(x89591,x89593))+~P1(f306(x89591,f390(x89591,x89592)))+P1(f306(x89591,f398(x89591,x89592)))+~P1(f306(f306(f221(a1),f2(a1)),x89592))+~P1(f306(f306(f308(a1),x89593),f277(a1,f79(a1),x89592)))+~P1(f306(x89591,f306(f306(f22(a1),f390(x89591,x89592)),f306(f306(f82(a1),f397(x89591,x89592)),x89592)))) % 187.68/187.66 [10185]~P101(x101852)+E(x101851,f185(f872(x101852,a859)))+E(x101853,f185(f872(x101852,a859)))+~P1(f306(f63(x101852),x101851))+~P1(f306(f63(x101852),x101853))+E(f10(x101852,f306(f228(x101852),f306(f306(f8(f872(x101852,a859),a859,x101852),f88(x101852)),f306(f306(f8(f872(x101852,f872(x101852,a859)),f872(x101852,a859),x101852),f306(f8(f872(x101852,a859),a859,x101852),f88(x101852))),f306(f306(f7(x101852,f872(x101852,f872(x101852,a859)),f872(x101852,f872(x101852,a859))),f306(f306(f8(f872(x101852,f872(f872(x101852,a859),f872(x101852,a859))),f872(f872(x101852,f872(x101852,a859)),f872(x101852,f872(x101852,a859))),x101852),f18(x101852,f872(x101852,a859),f872(x101852,a859))),f306(f306(f8(f872(x101852,f872(x101852,f872(a859,a859))),f872(x101852,f872(f872(x101852,a859),f872(x101852,a859))),x101852),f306(f8(f872(x101852,f872(a859,a859)),f872(f872(x101852,a859),f872(x101852,a859)),x101852),f18(x101852,a859,a859))),f306(f306(f8(f872(x101852,f872(x101852,a859)),f872(x101852,f872(x101852,f872(a859,a859))),x101852),f306(f8(f872(x101852,a859),f872(x101852,f872(a859,a859)),x101852),f306(f8(a859,f872(a859,a859),x101852),a304))),f306(f306(f7(x101852,f872(x101852,f872(x101852,x101852)),f872(x101852,f872(x101852,a859))),f306(f306(f8(f872(f872(x101852,x101852),f872(x101852,a859)),f872(f872(x101852,f872(x101852,x101852)),f872(x101852,f872(x101852,a859))),x101852),f8(f872(x101852,x101852),f872(x101852,a859),x101852)),f306(f306(f8(f872(x101852,a859),f872(f872(x101852,x101852),f872(x101852,a859)),x101852),f8(x101852,a859,x101852)),a303))),f108(x101852)))))),f306(f306(f7(x101852,f872(x101852,a859),f872(x101852,a859)),f306(f306(f8(f872(a859,a859),f872(f872(x101852,a859),f872(x101852,a859)),x101852),f8(a859,a859,x101852)),f306(f306(f8(a859,f872(a859,a859),x101852),a304),f306(f306(f7(x101852,f872(x101852,a859),a859),f308(x101852)),x101853)))),f306(f306(f7(x101852,f872(x101852,a859),a859),f308(x101852)),x101851))))))),f306(f306(f108(x101852),f10(x101852,x101853)),f10(x101852,x101851))) % 187.68/187.66 [10186]~P101(x101862)+E(x101861,f185(f872(x101862,a859)))+E(x101863,f185(f872(x101862,a859)))+~P1(f306(f63(x101862),x101861))+~P1(f306(f63(x101862),x101863))+E(f13(x101862,f306(f228(x101862),f306(f306(f8(f872(x101862,a859),a859,x101862),f88(x101862)),f306(f306(f8(f872(x101862,f872(x101862,a859)),f872(x101862,a859),x101862),f306(f8(f872(x101862,a859),a859,x101862),f88(x101862))),f306(f306(f7(x101862,f872(x101862,f872(x101862,a859)),f872(x101862,f872(x101862,a859))),f306(f306(f8(f872(x101862,f872(f872(x101862,a859),f872(x101862,a859))),f872(f872(x101862,f872(x101862,a859)),f872(x101862,f872(x101862,a859))),x101862),f18(x101862,f872(x101862,a859),f872(x101862,a859))),f306(f306(f8(f872(x101862,f872(x101862,f872(a859,a859))),f872(x101862,f872(f872(x101862,a859),f872(x101862,a859))),x101862),f306(f8(f872(x101862,f872(a859,a859)),f872(f872(x101862,a859),f872(x101862,a859)),x101862),f18(x101862,a859,a859))),f306(f306(f8(f872(x101862,f872(x101862,a859)),f872(x101862,f872(x101862,f872(a859,a859))),x101862),f306(f8(f872(x101862,a859),f872(x101862,f872(a859,a859)),x101862),f306(f8(a859,f872(a859,a859),x101862),a304))),f306(f306(f7(x101862,f872(x101862,f872(x101862,x101862)),f872(x101862,f872(x101862,a859))),f306(f306(f8(f872(f872(x101862,x101862),f872(x101862,a859)),f872(f872(x101862,f872(x101862,x101862)),f872(x101862,f872(x101862,a859))),x101862),f8(f872(x101862,x101862),f872(x101862,a859),x101862)),f306(f306(f8(f872(x101862,a859),f872(f872(x101862,x101862),f872(x101862,a859)),x101862),f8(x101862,a859,x101862)),a303))),f109(x101862)))))),f306(f306(f7(x101862,f872(x101862,a859),f872(x101862,a859)),f306(f306(f8(f872(a859,a859),f872(f872(x101862,a859),f872(x101862,a859)),x101862),f8(a859,a859,x101862)),f306(f306(f8(a859,f872(a859,a859),x101862),a304),f306(f306(f7(x101862,f872(x101862,a859),a859),f308(x101862)),x101863)))),f306(f306(f7(x101862,f872(x101862,a859),a859),f308(x101862)),x101861))))))),f306(f306(f109(x101862),f13(x101862,x101863)),f13(x101862,x101861))) % 187.68/187.66 [10187]~P108(x101872)+E(x101871,f185(f872(x101872,a859)))+E(x101873,f185(f872(x101872,a859)))+~P1(f306(f63(x101872),x101871))+~P1(f306(f63(x101872),x101873))+E(f12(x101872,f219(x101872),f306(f228(x101872),f306(f306(f8(f872(x101872,a859),a859,x101872),f88(x101872)),f306(f306(f8(f872(x101872,f872(x101872,a859)),f872(x101872,a859),x101872),f306(f8(f872(x101872,a859),a859,x101872),f88(x101872))),f306(f306(f7(x101872,f872(x101872,f872(x101872,a859)),f872(x101872,f872(x101872,a859))),f306(f306(f8(f872(x101872,f872(f872(x101872,a859),f872(x101872,a859))),f872(f872(x101872,f872(x101872,a859)),f872(x101872,f872(x101872,a859))),x101872),f18(x101872,f872(x101872,a859),f872(x101872,a859))),f306(f306(f8(f872(x101872,f872(x101872,f872(a859,a859))),f872(x101872,f872(f872(x101872,a859),f872(x101872,a859))),x101872),f306(f8(f872(x101872,f872(a859,a859)),f872(f872(x101872,a859),f872(x101872,a859)),x101872),f18(x101872,a859,a859))),f306(f306(f8(f872(x101872,f872(x101872,a859)),f872(x101872,f872(x101872,f872(a859,a859))),x101872),f306(f8(f872(x101872,a859),f872(x101872,f872(a859,a859)),x101872),f306(f8(a859,f872(a859,a859),x101872),a304))),f306(f306(f7(x101872,f872(x101872,f872(x101872,x101872)),f872(x101872,f872(x101872,a859))),f306(f306(f8(f872(f872(x101872,x101872),f872(x101872,a859)),f872(f872(x101872,f872(x101872,x101872)),f872(x101872,f872(x101872,a859))),x101872),f8(f872(x101872,x101872),f872(x101872,a859),x101872)),f306(f306(f8(f872(x101872,a859),f872(f872(x101872,x101872),f872(x101872,a859)),x101872),f8(x101872,a859,x101872)),a303))),f225(x101872)))))),f306(f306(f7(x101872,f872(x101872,a859),f872(x101872,a859)),f306(f306(f8(f872(a859,a859),f872(f872(x101872,a859),f872(x101872,a859)),x101872),f8(a859,a859,x101872)),f306(f306(f8(a859,f872(a859,a859),x101872),a304),f306(f306(f7(x101872,f872(x101872,a859),a859),f308(x101872)),x101873)))),f306(f306(f7(x101872,f872(x101872,a859),a859),f308(x101872)),x101871))))))),f306(f306(f225(x101872),f12(x101872,f219(x101872),x101873)),f12(x101872,f219(x101872),x101871))) % 187.68/187.66 [10188]~P108(x101882)+E(x101881,f185(f872(x101882,a859)))+E(x101883,f185(f872(x101882,a859)))+~P1(f306(f63(x101882),x101881))+~P1(f306(f63(x101882),x101883))+E(f11(x101882,f225(x101882),f306(f228(x101882),f306(f306(f8(f872(x101882,a859),a859,x101882),f88(x101882)),f306(f306(f8(f872(x101882,f872(x101882,a859)),f872(x101882,a859),x101882),f306(f8(f872(x101882,a859),a859,x101882),f88(x101882))),f306(f306(f7(x101882,f872(x101882,f872(x101882,a859)),f872(x101882,f872(x101882,a859))),f306(f306(f8(f872(x101882,f872(f872(x101882,a859),f872(x101882,a859))),f872(f872(x101882,f872(x101882,a859)),f872(x101882,f872(x101882,a859))),x101882),f18(x101882,f872(x101882,a859),f872(x101882,a859))),f306(f306(f8(f872(x101882,f872(x101882,f872(a859,a859))),f872(x101882,f872(f872(x101882,a859),f872(x101882,a859))),x101882),f306(f8(f872(x101882,f872(a859,a859)),f872(f872(x101882,a859),f872(x101882,a859)),x101882),f18(x101882,a859,a859))),f306(f306(f8(f872(x101882,f872(x101882,a859)),f872(x101882,f872(x101882,f872(a859,a859))),x101882),f306(f8(f872(x101882,a859),f872(x101882,f872(a859,a859)),x101882),f306(f8(a859,f872(a859,a859),x101882),a304))),f306(f306(f7(x101882,f872(x101882,f872(x101882,x101882)),f872(x101882,f872(x101882,a859))),f306(f306(f8(f872(f872(x101882,x101882),f872(x101882,a859)),f872(f872(x101882,f872(x101882,x101882)),f872(x101882,f872(x101882,a859))),x101882),f8(f872(x101882,x101882),f872(x101882,a859),x101882)),f306(f306(f8(f872(x101882,a859),f872(f872(x101882,x101882),f872(x101882,a859)),x101882),f8(x101882,a859,x101882)),a303))),f219(x101882)))))),f306(f306(f7(x101882,f872(x101882,a859),f872(x101882,a859)),f306(f306(f8(f872(a859,a859),f872(f872(x101882,a859),f872(x101882,a859)),x101882),f8(a859,a859,x101882)),f306(f306(f8(a859,f872(a859,a859),x101882),a304),f306(f306(f7(x101882,f872(x101882,a859),a859),f308(x101882)),x101883)))),f306(f306(f7(x101882,f872(x101882,a859),a859),f308(x101882)),x101881))))))),f306(f306(f219(x101882),f11(x101882,f225(x101882),x101883)),f11(x101882,f225(x101882),x101881))) % 187.68/187.66 [7150]~P111(x71503)+E(x71501,x71502)+~E(f306(f306(f237(x71503),x71501),x71504),f306(f306(f237(x71503),x71502),x71504))+~P1(f306(f306(f220(x71503),f2(x71503)),x71502))+~P1(f306(f306(f220(x71503),f2(x71503)),x71501))+~P1(f306(f306(f221(a865),f2(a865)),x71504)) % 187.68/187.66 [9095]~P1(f306(x90952,x90953))+~P1(f306(x90951,x90954))+E(f224(a865,x90951),f306(a119,f224(a865,x90952)))+P1(f306(x90952,f512(x90953,x90952,x90954,x90951)))+P1(f306(x90951,f2(a865)))+P1(f306(x90951,f306(a119,f512(x90953,x90952,x90954,x90951)))) % 187.68/187.66 [9358]~P1(f306(x93582,x93583))+~P1(f306(x93581,x93584))+E(f224(a865,x93581),f306(a119,f224(a865,x93582)))+~P1(f306(x93582,f512(x93583,x93582,x93584,x93581)))+P1(f306(x93581,f2(a865)))+~P1(f306(x93581,f306(a119,f512(x93583,x93582,x93584,x93581)))) % 187.68/187.66 [7422]~P108(x74222)+E(x74221,f185(f872(x74222,a859)))+~P1(f306(f63(x74222),x74221))+~P1(f306(f306(f308(x74222),x74224),x74221))+P1(f306(f306(f220(x74222),x74223),x74224))+~P1(f306(f306(f220(x74222),x74223),f306(f65(x74222,f225(x74222)),x74221))) % 187.68/187.66 [7423]~P103(x74232)+E(x74231,f185(f872(x74232,a859)))+~P1(f306(f63(x74232),x74231))+~P1(f306(f306(f308(x74232),x74234),x74231))+P1(f306(f306(f220(x74232),x74233),x74234))+~P1(f306(f306(f220(x74232),x74233),f306(f65(x74232,f109(x74232)),x74231))) % 187.68/187.66 [7424]~P108(x74242)+E(x74241,f185(f872(x74242,a859)))+~P1(f306(f63(x74242),x74241))+~P1(f306(f306(f308(x74242),x74244),x74241))+P1(f306(f306(f221(x74242),x74243),x74244))+~P1(f306(f306(f221(x74242),x74243),f306(f65(x74242,f225(x74242)),x74241))) % 187.68/187.66 [7323]E(x73231,f2(a1))+E(f306(f306(f40(a1),x73232),x73231),x73233)+~P1(f306(f306(f220(a1),x73234),f2(a1)))+~E(x73232,f306(f306(f81(a1),f306(f306(f82(a1),x73231),x73233)),x73234))+P1(f306(f306(f221(a1),f2(a1)),x73231))+~P1(f306(f306(f221(a1),x73231),x73234)) % 187.68/187.66 [7338]E(f46(a1,x73382,x73381),x73383)+E(x73381,f2(a1))+~P1(f306(f306(f220(a1),x73383),f2(a1)))+~E(x73382,f306(f306(f81(a1),f306(f306(f82(a1),x73381),x73384)),x73383))+P1(f306(f306(f221(a1),f2(a1)),x73381))+~P1(f306(f306(f221(a1),x73381),x73383)) % 187.68/187.66 [7461]E(x74611,f2(a1))+E(f306(f306(f40(a1),x74612),x74611),x74613)+~E(x74612,f306(f306(f81(a1),f306(f306(f82(a1),x74611),x74613)),x74614))+~P1(f306(f306(f220(a1),f2(a1)),x74614))+~P1(f306(f306(f221(a1),f2(a1)),x74611))+~P1(f306(f306(f221(a1),x74614),x74611)) % 187.68/187.66 [7483]E(f46(a1,x74832,x74831),x74833)+E(x74831,f2(a1))+~E(x74832,f306(f306(f81(a1),f306(f306(f82(a1),x74831),x74834)),x74833))+~P1(f306(f306(f220(a1),f2(a1)),x74833))+~P1(f306(f306(f221(a1),f2(a1)),x74831))+~P1(f306(f306(f221(a1),x74833),x74831)) % 187.68/187.66 [7623]~P108(x76232)+E(x76231,f185(f872(x76232,a859)))+~P1(f306(f63(x76232),x76231))+~P1(f306(f306(f220(x76232),x76234),x76233))+~P1(f306(f306(f308(x76232),x76234),x76231))+P1(f306(f306(f220(x76232),f306(f65(x76232,f225(x76232)),x76231)),x76233)) % 187.68/187.66 [7624]~P108(x76242)+E(x76241,f185(f872(x76242,a859)))+~P1(f306(f63(x76242),x76241))+~P1(f306(f306(f221(x76242),x76244),x76243))+~P1(f306(f306(f308(x76242),x76244),x76241))+P1(f306(f306(f221(x76242),f306(f65(x76242,f225(x76242)),x76241)),x76243)) % 187.68/187.66 [8201]~P1(f306(f306(f220(a1),x82014),f2(a1)))+~E(x82011,f306(f306(f81(a1),f306(f306(f82(a1),x82012),x82013)),x82014))+~P1(f306(f306(f220(a1),f2(a1)),x82014))+~P1(f306(f306(f221(a1),x82014),x82012))+~P1(f306(f306(f221(a1),x82012),x82014))+P1(f306(f50(x82011,x82012),f306(f306(f236(a1,a1),x82013),x82014))) % 187.68/187.66 [9155]~P60(x91553)+~P60(x91554)+E(x91551,x91552)+~E(f306(f186(f866(x91553)),x91552),f306(f186(f866(x91554)),f57(x91554)))+~E(f306(f186(f866(x91553)),x91551),f306(f186(f866(x91554)),f57(x91554)))+~E(f306(f74(f869(x91553),x91553,x91554,f218(x91553)),f306(f169(x91554,x91553),f306(f306(f173(x91554,x91553),f57(x91554)),x91551))),f306(f74(f869(x91553),x91553,x91554,f218(x91553)),f306(f169(x91554,x91553),f306(f306(f173(x91554,x91553),f57(x91554)),x91552)))) % 187.68/187.66 [8368]~P109(x83681)+P1(f306(f306(f221(f872(x83681,a859)),f277(x83681,x83682,x83683)),f277(x83681,x83684,x83685)))+~P1(f306(f306(f220(x83681),x83684),x83682))+~P1(f306(f306(f220(x83681),x83684),x83685))+~P1(f306(f306(f220(x83681),x83683),x83685))+~P1(f306(f306(f221(x83681),x83683),x83685)) % 187.68/187.66 [8369]~P109(x83691)+P1(f306(f306(f221(f872(x83691,a859)),f277(x83691,x83692,x83693)),f277(x83691,x83694,x83695)))+~P1(f306(f306(f220(x83691),x83693),x83695))+~P1(f306(f306(f220(x83691),x83694),x83695))+~P1(f306(f306(f220(x83691),x83694),x83692))+~P1(f306(f306(f221(x83691),x83694),x83692)) % 187.68/187.66 [9221]P58(x92212,x92213,x92214,x92211)+E(x92211,f185(f872(x92212,a859)))+~P1(f306(f63(x92212),x92214))+~P1(f306(f63(x92212),x92211))+~P1(f306(f306(x92213,f489(x92211,x92214,x92213,x92212)),x92215))+~P1(f306(f306(f308(x92212),x92215),x92211)) % 187.68/187.66 [9373]~E(x93733,x93735)+~P74(x93731)+~P75(x93731)+~P42(x93733)+E(f306(f306(f9(a1,x93731),x93732),x93733),f306(f306(f9(a1,x93731),x93734),x93735))+P1(f306(f306(f220(a1),f2(a1)),f435(x93732,x93734,x93733,x93735,x93731))) % 187.68/187.66 [9374]~E(x93743,x93745)+~P74(x93741)+~P75(x93741)+~P42(x93743)+E(f306(f306(f6(a1,x93741),x93742),x93743),f306(f306(f6(a1,x93741),x93744),x93745))+P1(f306(f306(f220(a1),f2(a1)),f480(x93742,x93744,x93743,x93745,x93741))) % 187.68/187.66 [9544]~E(x95445,x95443)+~P74(x95441)+~P75(x95441)+~P42(x95445)+~E(f306(x95442,f435(x95444,x95442,x95445,x95443,x95441)),f306(x95444,f435(x95444,x95442,x95445,x95443,x95441)))+E(f306(f306(f9(a1,x95441),x95442),x95443),f306(f306(f9(a1,x95441),x95444),x95445)) % 187.68/187.66 [9545]~E(x95455,x95453)+~P74(x95451)+~P75(x95451)+~P42(x95455)+~E(f306(x95452,f480(x95454,x95452,x95455,x95453,x95451)),f306(x95454,f480(x95454,x95452,x95455,x95453,x95451)))+E(f306(f306(f6(a1,x95451),x95452),x95453),f306(f306(f6(a1,x95451),x95454),x95455)) % 187.68/187.66 [9632]~P65(x96323)+E(f306(x96321,x96322),f2(x96323))+~E(f306(f306(f6(x96324,x96323),x96321),x96325),f2(x96323))+~P1(f306(f63(x96324),x96325))+P1(f306(f306(f308(x96324),f428(x96322,x96321,x96325,x96324,x96323)),x96325))+~P1(f306(f306(f308(x96324),x96322),x96325)) % 187.68/187.66 [9771]~P65(x97713)+E(f306(x97711,x97712),f2(x97713))+~E(f306(f306(f6(x97714,x97713),x97711),x97715),f2(x97713))+~P1(f306(f63(x97714),x97715))+~P1(f306(f306(f308(x97714),x97712),x97715))+~P1(f306(f306(f220(x97713),f2(x97713)),f306(x97711,f428(x97712,x97711,x97715,x97714,x97713)))) % 187.68/187.66 [8283]~P136(x82831)+~P1(f306(f306(f220(x82831),x82833),x82835))+~P1(f306(f306(f220(x82831),x82832),x82834))+~P1(f306(f306(f220(x82831),f2(x82831)),x82833))+~P1(f306(f306(f220(x82831),f2(x82831)),x82834))+P1(f306(f306(f220(x82831),f306(f306(f82(x82831),x82832),x82833)),f306(f306(f82(x82831),x82834),x82835))) % 187.68/187.66 [8284]~P136(x82841)+~P1(f306(f306(f220(x82841),x82843),x82845))+~P1(f306(f306(f220(x82841),x82842),x82844))+~P1(f306(f306(f220(x82841),f2(x82841)),x82843))+~P1(f306(f306(f220(x82841),f2(x82841)),x82842))+P1(f306(f306(f220(x82841),f306(f306(f82(x82841),x82842),x82843)),f306(f306(f82(x82841),x82844),x82845))) % 187.68/187.66 [8285]~P64(x82851)+~P1(f306(f306(f221(x82851),f2(x82851)),x82855))+~P1(f306(f306(f220(x82851),x82855),x82853))+~P1(f306(f306(f220(x82851),x82852),x82854))+~P1(f306(f306(f220(x82851),f2(x82851)),x82852))+P1(f306(f306(f220(x82851),f306(f306(f264(x82851),x82852),x82853)),f306(f306(f264(x82851),x82854),x82855))) % 187.68/187.66 [8286]~P128(x82861)+~P1(f306(f306(f220(x82861),x82863),x82865))+~P1(f306(f306(f220(x82861),f2(x82861)),x82862))+~P1(f306(f306(f221(x82861),x82862),x82864))+~P1(f306(f306(f221(x82861),f2(x82861)),x82863))+P1(f306(f306(f221(x82861),f306(f306(f82(x82861),x82862),x82863)),f306(f306(f82(x82861),x82864),x82865))) % 187.68/187.66 [8287]~P128(x82871)+~P1(f306(f306(f220(x82871),x82872),x82874))+~P1(f306(f306(f220(x82871),f2(x82871)),x82873))+~P1(f306(f306(f221(x82871),x82873),x82875))+~P1(f306(f306(f221(x82871),f2(x82871)),x82872))+P1(f306(f306(f221(x82871),f306(f306(f82(x82871),x82872),x82873)),f306(f306(f82(x82871),x82874),x82875))) % 187.68/187.66 [8288]~P128(x82881)+~P1(f306(f306(f220(x82881),f2(x82881)),x82883))+~P1(f306(f306(f220(x82881),f2(x82881)),x82882))+~P1(f306(f306(f221(x82881),x82883),x82885))+~P1(f306(f306(f221(x82881),x82882),x82884))+P1(f306(f306(f221(x82881),f306(f306(f82(x82881),x82882),x82883)),f306(f306(f82(x82881),x82884),x82885))) % 187.68/187.66 [8289]~P128(x82891)+~P1(f306(f306(f220(x82891),f2(x82891)),x82893))+~P1(f306(f306(f221(x82891),x82893),x82895))+~P1(f306(f306(f221(x82891),x82892),x82894))+~P1(f306(f306(f221(x82891),f2(x82891)),x82894))+P1(f306(f306(f221(x82891),f306(f306(f82(x82891),x82892),x82893)),f306(f306(f82(x82891),x82894),x82895))) % 187.68/187.66 [8290]~P64(x82901)+~P1(f306(f306(f220(x82901),x82905),x82903))+~P1(f306(f306(f220(x82901),f2(x82901)),x82902))+~P1(f306(f306(f221(x82901),x82902),x82904))+~P1(f306(f306(f221(x82901),f2(x82901)),x82905))+P1(f306(f306(f221(x82901),f306(f306(f264(x82901),x82902),x82903)),f306(f306(f264(x82901),x82904),x82905))) % 187.68/187.66 [8291]~P64(x82911)+~P1(f306(f306(f220(x82911),x82912),x82914))+~P1(f306(f306(f221(x82911),x82915),x82913))+~P1(f306(f306(f221(x82911),f2(x82911)),x82915))+~P1(f306(f306(f221(x82911),f2(x82911)),x82912))+P1(f306(f306(f221(x82911),f306(f306(f264(x82911),x82912),x82913)),f306(f306(f264(x82911),x82914),x82915))) % 187.68/187.66 [9672]~P74(x96725)+~P85(x96725)+E(x96721,f185(f872(x96722,a859)))+~P1(f306(f63(x96722),x96721))+P1(f306(f306(f308(x96722),f433(x96723,x96724,x96721,x96722,x96725)),x96721))+P1(f306(f306(f221(x96725),f306(f306(f6(x96722,x96725),x96724),x96721)),f306(f306(f6(x96722,x96725),x96723),x96721))) % 187.68/187.66 [9792]~P83(x97921)+~P74(x97921)+~P1(f306(f63(x97922),x97925))+~P1(f306(f306(f220(x97921),f2(x97921)),f306(x97923,f420(x97923,x97924,x97925,x97922,x97921))))+P1(f306(f306(f220(x97921),f306(f306(f6(x97922,x97921),x97923),x97924)),f306(f306(f6(x97922,x97921),x97923),x97925)))+~P1(f306(f306(f220(f872(x97922,a859)),x97924),x97925)) % 187.68/187.66 [9961]~P74(x99613)+~P85(x99613)+E(x99611,f185(f872(x99612,a859)))+~P1(f306(f63(x99612),x99611))+~P1(f306(f306(f221(x99613),f306(x99614,f433(x99615,x99614,x99611,x99612,x99613))),f306(x99615,f433(x99615,x99614,x99611,x99612,x99613))))+P1(f306(f306(f221(x99613),f306(f306(f6(x99612,x99613),x99614),x99611)),f306(f306(f6(x99612,x99613),x99615),x99611))) % 187.68/187.66 [7009]~P20(x70092,x70095,x70094)+E(x70091,f185(f872(x70092,a859)))+E(x70093,f185(f872(x70092,a859)))+~P1(f306(f63(x70092),x70091))+~P1(f306(f63(x70092),x70093))+E(f306(x70094,f306(f306(f108(f872(x70092,a859)),x70093),x70091)),f306(f306(x70095,f306(x70094,x70093)),f306(x70094,x70091))) % 187.68/187.66 [7589]~P146(x75891,x75893,x75894)+P1(f306(x75891,x75892))+~P1(f306(f306(f221(a1),x75894),f2(a1)))+~P1(f306(f306(f220(a1),x75895),f2(a1)))+~E(x75893,f306(f306(f81(a1),f306(f306(f82(a1),x75894),x75892)),x75895))+~P1(f306(f306(f221(a1),x75894),x75895)) % 187.68/187.66 [7590]~P145(x75901,x75903,x75904)+P1(f306(x75901,x75902))+~P1(f306(f306(f221(a1),x75904),f2(a1)))+~P1(f306(f306(f220(a1),x75902),f2(a1)))+~E(x75903,f306(f306(f81(a1),f306(f306(f82(a1),x75904),x75905)),x75902))+~P1(f306(f306(f221(a1),x75904),x75902)) % 187.68/187.66 [7633]~P146(x76331,x76333,x76334)+P1(f306(x76331,x76332))+~E(x76333,f306(f306(f81(a1),f306(f306(f82(a1),x76334),x76332)),x76335))+~P1(f306(f306(f220(a1),f2(a1)),x76335))+~P1(f306(f306(f221(a1),f2(a1)),x76334))+~P1(f306(f306(f221(a1),x76335),x76334)) % 187.68/187.66 [7634]~P145(x76341,x76343,x76344)+P1(f306(x76341,x76342))+~E(x76343,f306(f306(f81(a1),f306(f306(f82(a1),x76344),x76345)),x76342))+~P1(f306(f306(f220(a1),f2(a1)),x76342))+~P1(f306(f306(f221(a1),f2(a1)),x76344))+~P1(f306(f306(f221(a1),x76342),x76344)) % 187.68/187.66 [8583]P1(f306(f306(x85831,x85832),x85833))+~P1(f306(f306(x85831,f306(f306(f40(a1),x85834),x85835)),f46(a1,x85834,x85835)))+~P1(f306(f306(f221(a1),x85835),f2(a1)))+~P1(f306(f306(f220(a1),x85833),f2(a1)))+~E(x85834,f306(f306(f81(a1),f306(f306(f82(a1),x85835),x85832)),x85833))+~P1(f306(f306(f221(a1),x85835),x85833)) % 187.68/187.66 [8592]P1(f306(f306(x85921,x85922),x85923))+~P1(f306(f306(x85921,f306(f306(f40(a1),x85924),x85925)),f46(a1,x85924,x85925)))+~E(x85924,f306(f306(f81(a1),f306(f306(f82(a1),x85925),x85922)),x85923))+~P1(f306(f306(f220(a1),f2(a1)),x85923))+~P1(f306(f306(f221(a1),f2(a1)),x85925))+~P1(f306(f306(f221(a1),x85923),x85925)) % 187.68/187.66 [8826]E(x88261,x88262)+~P55(x88263,x88265,x88264)+~P1(f306(f306(f308(x88263),x88262),x88265))+~P1(f306(f306(f308(x88263),x88261),x88265))+P1(f306(f306(f308(f871(x88263,x88263)),f306(f306(f236(x88263,x88263),x88261),x88262)),x88264))+P1(f306(f306(f308(f871(x88263,x88263)),f306(f306(f236(x88263,x88263),x88262),x88261)),x88264)) % 187.68/187.66 [9651]~P109(x96511)+~P109(x96512)+~P41(x96512,x96511,x96513)+~P1(f306(f306(f220(x96512),x96515),f370(x96514,x96513,x96512,x96511,x96515)))+E(f224(x96511,f306(f306(f7(x96511,f872(x96511,a859),a859),f308(x96511)),f306(f285(x96512,x96511,x96513),x96514))),f306(x96513,f224(x96512,f306(f306(f7(x96512,f872(x96512,a859),a859),f308(x96512)),x96514))))+~P1(f306(f306(f308(x96512),x96515),x96514)) % 187.68/187.66 [9700]~P83(x97005)+~P74(x97005)+~P1(f306(f63(x97001),x97004))+P1(f306(f306(f220(x97005),f306(f306(f6(x97001,x97005),x97002),x97003)),f306(f306(f6(x97001,x97005),x97002),x97004)))+~P1(f306(f306(f220(f872(x97001,a859)),x97003),x97004))+P1(f306(f306(f308(x97001),f420(x97002,x97003,x97004,x97001,x97005)),f306(f306(f22(f872(x97001,a859)),x97004),x97003))) % 187.68/187.66 [9716]~P109(x97161)+~P109(x97162)+~P41(x97162,x97161,x97163)+E(f224(x97161,f306(f306(f7(x97161,f872(x97161,a859),a859),f308(x97161)),f306(f285(x97162,x97161,x97163),x97164))),f306(x97163,f224(x97162,f306(f306(f7(x97162,f872(x97162,a859),a859),f308(x97162)),x97164))))+~P1(f306(f306(f308(x97162),x97165),x97164))+P1(f306(f306(f308(x97162),f370(x97164,x97163,x97162,x97161,x97165)),x97164)) % 187.68/187.66 [9799]E(x97991,f185(f872(x97992,a859)))+~P1(f306(f63(x97992),x97993))+~P1(f306(f63(x97992),x97991))+P1(f306(f306(f308(f871(f872(x97992,a859),f872(x97992,a859))),f306(f306(f236(f872(x97992,a859),f872(x97992,a859)),x97993),x97991)),f298(x97992,x97994)))+~P1(f306(f306(f308(x97992),x97995),x97991))+~P1(f306(f306(f308(f871(x97992,x97992)),f306(f306(f236(x97992,x97992),f490(x97994,x97991,x97993,x97992)),x97995)),x97994)) % 187.68/187.66 [9800]E(x98001,f185(f872(x98002,a859)))+~P1(f306(f63(x98002),x98003))+~P1(f306(f63(x98002),x98001))+P1(f306(f306(f308(f871(f872(x98002,a859),f872(x98002,a859))),f306(f306(f236(f872(x98002,a859),f872(x98002,a859)),x98003),x98001)),f298(x98002,x98004)))+~P1(f306(f306(f308(x98002),x98005),x98001))+~P1(f306(f306(f308(f871(x98002,x98002)),f306(f306(f236(x98002,x98002),f575(x98004,x98001,x98003,x98002)),x98005)),x98004)) % 187.68/187.66 [9966]~P65(x99661)+~E(f306(f306(f6(x99665,x99661),x99662),x99666),x99664)+~P1(f306(f63(x99665),x99666))+P1(f306(f306(f308(x99665),f430(x99663,x99664,x99662,x99666,x99665,x99661)),x99666))+P1(f306(f306(f220(x99661),f306(x99662,x99663)),x99664))+~P1(f306(f306(f308(x99665),x99663),x99666)) % 187.68/187.66 [10015]~P65(x100151)+~E(f306(f306(f6(x100155,x100151),x100152),x100156),x100154)+~P1(f306(f63(x100155),x100156))+~P1(f306(f306(f308(x100155),x100153),x100156))+~P1(f306(f306(f220(x100151),f2(x100151)),f306(x100152,f430(x100153,x100154,x100152,x100156,x100155,x100151))))+P1(f306(f306(f220(x100151),f306(x100152,x100153)),x100154)) % 187.68/187.66 [10134]~E(x101345,x101348)+~E(x101344,x101347)+~P107(x101341)+~P74(x101342)+E(f306(f306(f6(x101341,x101342),x101343),f306(f276(x101341,x101344),x101345)),f306(f306(f6(x101341,x101342),x101346),f306(f276(x101341,x101347),x101348)))+P1(f306(f306(f220(x101341),x101344),f588(x101343,x101346,x101345,x101348,x101344,x101347,x101341,x101342))) % 187.68/187.66 [10150]~E(x101507,x101504)+~E(x101508,x101505)+~P107(x101501)+~P74(x101502)+~E(f306(x101503,f588(x101506,x101503,x101508,x101505,x101507,x101504,x101501,x101502)),f306(x101506,f588(x101506,x101503,x101508,x101505,x101507,x101504,x101501,x101502)))+E(f306(f306(f6(x101501,x101502),x101503),f306(f276(x101501,x101504),x101505)),f306(f306(f6(x101501,x101502),x101506),f306(f276(x101501,x101507),x101508))) % 187.68/187.66 [10154]~E(x101544,x101547)+~E(x101545,x101548)+~P107(x101541)+~P74(x101542)+E(f306(f306(f6(x101541,x101542),x101543),f306(f276(x101541,x101544),x101545)),f306(f306(f6(x101541,x101542),x101546),f306(f276(x101541,x101547),x101548)))+P1(f306(f306(f221(x101541),f588(x101543,x101546,x101545,x101548,x101544,x101547,x101541,x101542)),x101545)) % 187.68/187.66 [9805]~P9(x98055,x98059,x98056)+~P9(x98051,x980510,x98053)+~P16(x98051,x98055,f872(x98052,a859),x98053,x98056,x98058)+~P1(f306(f306(f308(x98055),x98057),x98059))+~P1(f306(f306(f308(x98051),x98054),x980510))+E(f306(f306(f43(x98051,f872(x98052,a859)),f306(f260(x98051,x98051,x98053),f306(f306(f284(x98051),x98054),f185(f872(x98051,a859))))),f306(f306(f8(f872(x98055,f872(x98052,a859)),f872(x98052,a859),x98051),f306(f43(x98055,f872(x98052,a859)),f306(f260(x98055,x98055,x98056),f306(f306(f284(x98055),x98057),f185(f872(x98055,a859)))))),x98058)),f306(f306(x98058,x98054),x98057)) % 187.68/187.66 [5546]~P108(x55463)+~P17(x55463,x55462)+~P17(x55463,x55461)+E(x55461,x55462)+~E(f306(f164(x55463),x55461),f306(f164(x55463),x55462))+~P1(f306(f129(x55463),x55462))+~P1(f306(f129(x55463),x55461)) % 187.68/187.66 [4878]~P124(x48782)+~P127(x48782)+~P132(x48782)+~P115(x48782)+~E(x48783,f2(x48782))+E(x48781,f2(a865))+E(f306(f306(f237(x48782),x48783),x48781),f2(x48782)) % 187.68/187.66 [9094]E(x90941,f2(a865))+~E(x90942,f306(f306(f81(a865),f306(f306(f82(a865),f306(f235(a865,a865),x90943)),x90941)),f306(f244(a865,a865),x90943)))+P1(f306(f49(x90942,x90941),x90943))+~P1(f306(f306(f220(a865),f306(f244(a865,a865),x90943)),f2(a865)))+~P1(f306(f306(f220(a865),f2(a865)),f306(f244(a865,a865),x90943)))+~P1(f306(f306(f221(a865),x90941),f306(f244(a865,a865),x90943)))+~P1(f306(f306(f221(a865),f306(f244(a865,a865),x90943)),x90941)) % 187.68/187.66 [9104]~E(f306(f235(a865,a865),x91043),f2(a865))+~E(x91041,f306(f306(f81(a865),f306(f306(f82(a865),f306(f235(a865,a865),x91043)),x91042)),f306(f244(a865,a865),x91043)))+P1(f306(f49(x91041,x91042),x91043))+~P1(f306(f306(f220(a865),f306(f244(a865,a865),x91043)),f2(a865)))+~P1(f306(f306(f220(a865),f2(a865)),f306(f244(a865,a865),x91043)))+~P1(f306(f306(f221(a865),x91042),f306(f244(a865,a865),x91043)))+~P1(f306(f306(f221(a865),f306(f244(a865,a865),x91043)),x91042)) % 187.68/187.66 [7946]~P72(x79462)+E(x79461,f185(f872(x79462,a859)))+E(x79463,f185(f872(x79462,a859)))+~P1(f306(f63(x79462),x79461))+~P1(f306(f63(x79462),x79463))+~E(f306(f306(f109(f872(x79462,a859)),x79463),x79461),f185(f872(x79462,a859)))+E(f306(f306(f82(x79462),f306(f65(x79462,f82(x79462)),x79463)),f306(f65(x79462,f82(x79462)),x79461)),f306(f65(x79462,f82(x79462)),f306(f306(f108(f872(x79462,a859)),x79463),x79461))) % 187.68/187.66 [7729]E(x77291,f2(a1))+E(f306(f306(f40(a1),x77292),x77291),x77293)+~P1(f306(f306(f220(a1),x77294),f2(a1)))+~E(x77292,f306(f306(f81(a1),f306(f306(f82(a1),x77291),x77293)),x77294))+~P1(f306(f306(f220(a1),f2(a1)),x77294))+~P1(f306(f306(f221(a1),x77294),x77291))+~P1(f306(f306(f221(a1),x77291),x77294)) % 187.68/187.66 [7736]E(f46(a1,x77362,x77361),x77363)+E(x77361,f2(a1))+~P1(f306(f306(f220(a1),x77363),f2(a1)))+~E(x77362,f306(f306(f81(a1),f306(f306(f82(a1),x77361),x77364)),x77363))+~P1(f306(f306(f220(a1),f2(a1)),x77363))+~P1(f306(f306(f221(a1),x77363),x77361))+~P1(f306(f306(f221(a1),x77361),x77363)) % 187.68/187.66 [7641]~P21(x76412,x76415,x76414)+E(x76411,f185(f872(x76412,a859)))+E(x76413,f185(f872(x76412,a859)))+~P1(f306(f63(x76412),x76411))+~P1(f306(f63(x76412),x76413))+~E(f306(f306(f109(f872(x76412,a859)),x76413),x76411),f185(f872(x76412,a859)))+E(f306(x76414,f306(f306(f108(f872(x76412,a859)),x76413),x76411)),f306(f306(x76415,f306(x76414,x76413)),f306(x76414,x76411))) % 187.68/187.66 [9344]~P28(x93443,x93441,x93445,x93444)+~P28(x93441,x93443,x93446,x93442)+E(f306(f39(x93441),x93442),f306(f39(x93443),x93444))+~P1(f306(f63(x93443),x93444))+~P1(f306(f63(x93441),x93442))+~P1(f306(f306(f220(f872(x93443,a859)),f306(f285(x93441,x93443,x93446),x93442)),x93444))+~P1(f306(f306(f220(f872(x93441,a859)),f306(f285(x93443,x93441,x93445),x93444)),x93442)) % 187.68/187.66 [9288]~P1(f306(f306(f221(a1),f306(f306(f81(a1),f306(f306(f82(a1),x92885),x92881)),x92886)),f2(a1)))+~E(f306(f306(f81(a1),f306(f306(f82(a1),x92883),x92882)),x92884),f306(f306(f81(a1),f306(f306(f82(a1),x92885),x92881)),x92886))+~P1(f306(f306(f220(a1),f2(a1)),x92886))+~P1(f306(f306(f221(a1),f2(a1)),x92885))+~P1(f306(f306(f220(a1),x92885),x92883))+~P1(f306(f306(f221(a1),x92884),x92883))+P1(f306(f306(f220(a1),x92881),x92882)) % 187.68/187.66 [9047]~E(f306(f306(f81(a1),f306(f306(f82(a1),x90473),x90471)),x90474),f306(f306(f81(a1),f306(f306(f82(a1),x90475),x90472)),x90476))+~P1(f306(f306(f220(a1),f2(a1)),x90474))+~P1(f306(f306(f221(a1),f2(a1)),x90475))+~P1(f306(f306(f220(a1),x90475),x90473))+~P1(f306(f306(f221(a1),x90476),x90475))+P1(f306(f306(f220(a1),x90471),x90472))+~P1(f306(f306(f220(a1),f2(a1)),f306(f306(f81(a1),f306(f306(f82(a1),x90475),x90472)),x90476))) % 187.68/187.66 [9228]~P130(x92281)+~E(f306(f306(f81(x92281),x92282),x92284),f79(x92281))+~P1(f306(f306(f220(x92281),x92285),x92286))+~P1(f306(f306(f220(x92281),x92283),x92286))+~P1(f306(f306(f220(x92281),f2(x92281)),x92284))+~P1(f306(f306(f220(x92281),f2(x92281)),x92282))+P1(f306(f306(f220(x92281),f306(f306(f81(x92281),f306(f306(f82(x92281),x92282),x92283)),f306(f306(f82(x92281),x92284),x92285))),x92286)) % 187.68/187.66 [9229]~P131(x92291)+~E(f306(f306(f81(x92291),x92292),x92294),f79(x92291))+~P1(f306(f306(f220(x92291),f2(x92291)),x92294))+~P1(f306(f306(f220(x92291),f2(x92291)),x92292))+~P1(f306(f306(f221(x92291),x92295),x92296))+~P1(f306(f306(f221(x92291),x92293),x92296))+P1(f306(f306(f221(x92291),f306(f306(f81(x92291),f306(f306(f82(x92291),x92292),x92293)),f306(f306(f82(x92291),x92294),x92295))),x92296)) % 187.68/187.66 [10061]~P9(x100617,x100616,x100615)+E(x100611,x100612)+~P15(x100617,f872(x100614,a859),x100615,x100613)+E(f306(x100613,f469(x100611,x100612,x100613,x100614,x100615,x100616,x100617)),f306(x100613,f468(x100611,x100612,x100613,x100614,x100615,x100616,x100617)))+~E(f306(f306(f43(x100617,f872(x100614,a859)),x100611),x100613),f306(f306(f43(x100617,f872(x100614,a859)),x100612),x100613))+~P1(f306(f306(f308(f872(x100617,a859)),x100612),f306(f306(f62(x100617),x100616),x100615)))+~P1(f306(f306(f308(f872(x100617,a859)),x100611),f306(f306(f62(x100617),x100616),x100615))) % 187.68/187.66 [10096]~P9(x100963,x100967,x100966)+E(x100961,x100962)+~P15(x100963,f872(x100965,a859),x100966,x100964)+~E(f306(f306(f43(x100963,f872(x100965,a859)),x100961),x100964),f306(f306(f43(x100963,f872(x100965,a859)),x100962),x100964))+P1(f306(f306(f308(x100963),f468(x100961,x100962,x100964,x100965,x100966,x100967,x100963)),x100967))+~P1(f306(f306(f308(f872(x100963,a859)),x100962),f306(f306(f62(x100963),x100967),x100966)))+~P1(f306(f306(f308(f872(x100963,a859)),x100961),f306(f306(f62(x100963),x100967),x100966))) % 187.68/187.66 [10097]~P9(x100973,x100977,x100976)+E(x100971,x100972)+~P15(x100973,f872(x100975,a859),x100976,x100974)+~E(f306(f306(f43(x100973,f872(x100975,a859)),x100971),x100974),f306(f306(f43(x100973,f872(x100975,a859)),x100972),x100974))+P1(f306(f306(f308(x100973),f469(x100971,x100972,x100974,x100975,x100976,x100977,x100973)),x100977))+~P1(f306(f306(f308(f872(x100973,a859)),x100972),f306(f306(f62(x100973),x100977),x100976)))+~P1(f306(f306(f308(f872(x100973,a859)),x100971),f306(f306(f62(x100973),x100977),x100976))) % 187.68/187.66 [10169]E(x101691,x101692)+~P9(x101693,x101696,x101697)+~P15(x101693,f872(x101694,a859),x101697,x101695)+~E(f306(f306(f43(x101693,f872(x101694,a859)),x101691),x101695),f306(f306(f43(x101693,f872(x101694,a859)),x101692),x101695))+~P1(f306(f306(f308(f871(x101693,x101693)),f306(f306(f236(x101693,x101693),f468(x101691,x101692,x101695,x101694,x101697,x101696,x101693)),f469(x101691,x101692,x101695,x101694,x101697,x101696,x101693))),x101697))+~P1(f306(f306(f308(f872(x101693,a859)),x101692),f306(f306(f62(x101693),x101696),x101697)))+~P1(f306(f306(f308(f872(x101693,a859)),x101691),f306(f306(f62(x101693),x101696),x101697))) % 187.68/187.66 [9046]~P9(x90461,x90467,x90464)+~E(x90465,x90466)+~P1(f306(f306(f308(x90461),x90463),x90466))+~P1(f306(f306(f308(x90461),x90462),x90465))+~P1(f306(f306(f308(f872(x90461,a859)),x90466),f306(f306(f62(x90461),x90467),x90464)))+~P1(f306(f306(f308(f872(x90461,a859)),x90465),f306(f306(f62(x90461),x90467),x90464)))+P1(f306(f306(f308(f871(x90461,x90461)),f306(f306(f236(x90461,x90461),x90462),x90463)),x90464)) % 187.68/187.66 [9183]E(x91831,x91832)+~P9(x91833,x91834,x91835)+~P1(f306(f306(f308(x91833),x91836),x91832))+~P1(f306(f306(f308(x91833),x91837),x91831))+~P1(f306(f306(f308(f872(x91833,a859)),x91832),f306(f306(f62(x91833),x91834),x91835)))+~P1(f306(f306(f308(f872(x91833,a859)),x91831),f306(f306(f62(x91833),x91834),x91835)))+~P1(f306(f306(f308(f871(x91833,x91833)),f306(f306(f236(x91833,x91833),x91837),x91836)),x91835)) % 187.68/187.66 [10192]~P9(x101929,x101928,x101927)+~P9(x101921,x1019211,x1019210)+~P16(x101921,x101929,f872(x101926,a859),x1019210,x101927,x101925)+P1(f306(f306(f308(x101921),f472(x101922,x101923,x101924,x101925,x101926,x101927,x101928,x101929,x1019210,x1019211,x101921)),x1019211))+~P1(f306(f306(f308(f872(x101929,a859)),x101923),f306(f306(f62(x101929),x101928),x101927)))+~P1(f306(f306(f308(f872(x101921,a859)),x101924),f306(f306(f62(x101921),x1019211),x1019210)))+P1(f306(f306(f308(f872(x101926,a859)),f306(f306(f43(x101921,f872(x101926,a859)),x101924),f306(f306(f8(f872(x101929,f872(x101926,a859)),f872(x101926,a859),x101921),f306(f43(x101929,f872(x101926,a859)),x101923)),x101925))),x101922)) % 187.68/187.66 [10193]~P9(x1019311,x1019310,x101939)+~P9(x101931,x101938,x101937)+~P16(x1019311,x101931,f872(x101936,a859),x101939,x101937,x101935)+P1(f306(f306(f308(x101931),f473(x101932,x101933,x101934,x101935,x101936,x101937,x101938,x101931,x101939,x1019310,x1019311)),x101938))+~P1(f306(f306(f308(f872(x1019311,a859)),x101934),f306(f306(f62(x1019311),x1019310),x101939)))+~P1(f306(f306(f308(f872(x101931,a859)),x101933),f306(f306(f62(x101931),x101938),x101937)))+P1(f306(f306(f308(f872(x101936,a859)),f306(f306(f43(x1019311,f872(x101936,a859)),x101934),f306(f306(f8(f872(x101931,f872(x101936,a859)),f872(x101936,a859),x1019311),f306(f43(x101931,f872(x101936,a859)),x101933)),x101935))),x101932)) % 187.68/187.66 [10196]~P9(x101962,x101968,x101969)+~P9(x101964,x1019610,x1019611)+~P16(x101962,x101964,f872(x101961,a859),x101969,x1019611,x101966)+~P1(f306(f306(f308(f872(x101962,a859)),x101963),f306(f306(f62(x101962),x101968),x101969)))+~P1(f306(f306(f308(f872(x101964,a859)),x101965),f306(f306(f62(x101964),x1019610),x1019611)))+~P1(f306(f306(f308(f872(x101961,a859)),f306(f306(x101966,f472(x101967,x101965,x101963,x101966,x101961,x1019611,x1019610,x101964,x101969,x101968,x101962)),f473(x101967,x101965,x101963,x101966,x101961,x1019611,x1019610,x101964,x101969,x101968,x101962))),x101967))+P1(f306(f306(f308(f872(x101961,a859)),f306(f306(f43(x101962,f872(x101961,a859)),x101963),f306(f306(f8(f872(x101964,f872(x101961,a859)),f872(x101961,a859),x101962),f306(f43(x101964,f872(x101961,a859)),x101965)),x101966))),x101967)) % 187.68/187.66 [9080]E(x90801,x90802)+~P108(x90804)+~P28(x90803,x90804,x90805,f306(f306(f108(f872(x90803,a859)),f306(f164(x90803),x90801)),f306(f164(x90803),x90802)))+~E(f306(f164(x90803),x90801),f306(f164(x90803),x90802))+~P17(x90804,f306(f306(f146(x90803,x90804),x90805),x90802))+~P17(x90804,f306(f306(f146(x90803,x90804),x90805),x90801))+~P1(f306(f129(x90804),f306(f306(f146(x90803,x90804),x90805),x90802)))+~P1(f306(f129(x90804),f306(f306(f146(x90803,x90804),x90805),x90801))) % 187.68/187.66 %EqnAxiom % 187.68/187.66 [1]E(x11,x11) % 187.68/187.66 [2]E(x22,x21)+~E(x21,x22) % 187.68/187.66 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 187.68/187.66 [4]~E(x41,x42)+E(f2(x41),f2(x42)) % 187.68/187.66 [5]~E(x51,x52)+E(f107(x51),f107(x52)) % 187.68/187.66 [6]~E(x61,x62)+E(f22(x61),f22(x62)) % 187.68/187.66 [7]~E(x71,x72)+E(f185(x71),f185(x72)) % 187.68/187.66 [8]~E(x81,x82)+E(f306(x81,x83),f306(x82,x83)) % 187.68/187.66 [9]~E(x91,x92)+E(f306(x93,x91),f306(x93,x92)) % 187.68/187.66 [10]~E(x101,x102)+E(f32(x101),f32(x102)) % 187.68/187.66 [11]~E(x111,x112)+E(f143(x111),f143(x112)) % 187.68/187.66 [12]~E(x121,x122)+E(f219(x121),f219(x122)) % 187.68/187.66 [13]~E(x131,x132)+E(f108(x131),f108(x132)) % 187.68/187.66 [14]~E(x141,x142)+E(f225(x141),f225(x142)) % 187.68/187.66 [15]~E(x151,x152)+E(f109(x151),f109(x152)) % 187.68/187.66 [16]~E(x161,x162)+E(f110(x161),f110(x162)) % 187.68/187.66 [17]~E(x171,x172)+E(f35(x171),f35(x172)) % 187.68/187.66 [18]~E(x181,x182)+E(f85(x181),f85(x182)) % 187.68/187.66 [19]~E(x191,x192)+E(f220(x191),f220(x192)) % 187.68/187.66 [20]~E(x201,x202)+E(f872(x201,x203),f872(x202,x203)) % 187.68/187.66 [21]~E(x211,x212)+E(f872(x213,x211),f872(x213,x212)) % 187.68/187.66 [22]~E(x221,x222)+E(f473(x221,x223,x224,x225,x226,x227,x228,x229,x2210,x2211,x2212),f473(x222,x223,x224,x225,x226,x227,x228,x229,x2210,x2211,x2212)) % 187.68/187.66 [23]~E(x231,x232)+E(f473(x233,x231,x234,x235,x236,x237,x238,x239,x2310,x2311,x2312),f473(x233,x232,x234,x235,x236,x237,x238,x239,x2310,x2311,x2312)) % 187.68/187.66 [24]~E(x241,x242)+E(f473(x243,x244,x241,x245,x246,x247,x248,x249,x2410,x2411,x2412),f473(x243,x244,x242,x245,x246,x247,x248,x249,x2410,x2411,x2412)) % 187.68/187.66 [25]~E(x251,x252)+E(f473(x253,x254,x255,x251,x256,x257,x258,x259,x2510,x2511,x2512),f473(x253,x254,x255,x252,x256,x257,x258,x259,x2510,x2511,x2512)) % 187.68/187.66 [26]~E(x261,x262)+E(f473(x263,x264,x265,x266,x261,x267,x268,x269,x2610,x2611,x2612),f473(x263,x264,x265,x266,x262,x267,x268,x269,x2610,x2611,x2612)) % 187.68/187.66 [27]~E(x271,x272)+E(f473(x273,x274,x275,x276,x277,x271,x278,x279,x2710,x2711,x2712),f473(x273,x274,x275,x276,x277,x272,x278,x279,x2710,x2711,x2712)) % 187.68/187.66 [28]~E(x281,x282)+E(f473(x283,x284,x285,x286,x287,x288,x281,x289,x2810,x2811,x2812),f473(x283,x284,x285,x286,x287,x288,x282,x289,x2810,x2811,x2812)) % 187.68/187.66 [29]~E(x291,x292)+E(f473(x293,x294,x295,x296,x297,x298,x299,x291,x2910,x2911,x2912),f473(x293,x294,x295,x296,x297,x298,x299,x292,x2910,x2911,x2912)) % 187.68/187.66 [30]~E(x301,x302)+E(f473(x303,x304,x305,x306,x307,x308,x309,x3010,x301,x3011,x3012),f473(x303,x304,x305,x306,x307,x308,x309,x3010,x302,x3011,x3012)) % 187.68/187.66 [31]~E(x311,x312)+E(f473(x313,x314,x315,x316,x317,x318,x319,x3110,x3111,x311,x3112),f473(x313,x314,x315,x316,x317,x318,x319,x3110,x3111,x312,x3112)) % 187.68/187.66 [32]~E(x321,x322)+E(f473(x323,x324,x325,x326,x327,x328,x329,x3210,x3211,x3212,x321),f473(x323,x324,x325,x326,x327,x328,x329,x3210,x3211,x3212,x322)) % 187.68/187.66 [33]~E(x331,x332)+E(f866(x331),f866(x332)) % 187.68/187.66 [34]~E(x341,x342)+E(f79(x341),f79(x342)) % 187.68/187.66 [35]~E(x351,x352)+E(f472(x351,x353,x354,x355,x356,x357,x358,x359,x3510,x3511,x3512),f472(x352,x353,x354,x355,x356,x357,x358,x359,x3510,x3511,x3512)) % 187.68/187.66 [36]~E(x361,x362)+E(f472(x363,x361,x364,x365,x366,x367,x368,x369,x3610,x3611,x3612),f472(x363,x362,x364,x365,x366,x367,x368,x369,x3610,x3611,x3612)) % 187.68/187.66 [37]~E(x371,x372)+E(f472(x373,x374,x371,x375,x376,x377,x378,x379,x3710,x3711,x3712),f472(x373,x374,x372,x375,x376,x377,x378,x379,x3710,x3711,x3712)) % 187.68/187.66 [38]~E(x381,x382)+E(f472(x383,x384,x385,x381,x386,x387,x388,x389,x3810,x3811,x3812),f472(x383,x384,x385,x382,x386,x387,x388,x389,x3810,x3811,x3812)) % 187.68/187.66 [39]~E(x391,x392)+E(f472(x393,x394,x395,x396,x391,x397,x398,x399,x3910,x3911,x3912),f472(x393,x394,x395,x396,x392,x397,x398,x399,x3910,x3911,x3912)) % 187.68/187.66 [40]~E(x401,x402)+E(f472(x403,x404,x405,x406,x407,x401,x408,x409,x4010,x4011,x4012),f472(x403,x404,x405,x406,x407,x402,x408,x409,x4010,x4011,x4012)) % 187.68/187.66 [41]~E(x411,x412)+E(f472(x413,x414,x415,x416,x417,x418,x411,x419,x4110,x4111,x4112),f472(x413,x414,x415,x416,x417,x418,x412,x419,x4110,x4111,x4112)) % 187.68/187.66 [42]~E(x421,x422)+E(f472(x423,x424,x425,x426,x427,x428,x429,x421,x4210,x4211,x4212),f472(x423,x424,x425,x426,x427,x428,x429,x422,x4210,x4211,x4212)) % 187.68/187.66 [43]~E(x431,x432)+E(f472(x433,x434,x435,x436,x437,x438,x439,x4310,x431,x4311,x4312),f472(x433,x434,x435,x436,x437,x438,x439,x4310,x432,x4311,x4312)) % 187.68/187.66 [44]~E(x441,x442)+E(f472(x443,x444,x445,x446,x447,x448,x449,x4410,x4411,x441,x4412),f472(x443,x444,x445,x446,x447,x448,x449,x4410,x4411,x442,x4412)) % 187.68/187.66 [45]~E(x451,x452)+E(f472(x453,x454,x455,x456,x457,x458,x459,x4510,x4511,x4512,x451),f472(x453,x454,x455,x456,x457,x458,x459,x4510,x4511,x4512,x452)) % 187.68/187.66 [46]~E(x461,x462)+E(f118(x461),f118(x462)) % 187.68/187.66 [47]~E(x471,x472)+E(f308(x471),f308(x472)) % 187.68/187.66 [48]~E(x481,x482)+E(f162(x481,x483,x484),f162(x482,x483,x484)) % 187.68/187.66 [49]~E(x491,x492)+E(f162(x493,x491,x494),f162(x493,x492,x494)) % 187.68/187.66 [50]~E(x501,x502)+E(f162(x503,x504,x501),f162(x503,x504,x502)) % 187.68/187.66 [51]~E(x511,x512)+E(f4(x511),f4(x512)) % 187.68/187.66 [52]~E(x521,x522)+E(f171(x521,x523),f171(x522,x523)) % 187.68/187.66 [53]~E(x531,x532)+E(f171(x533,x531),f171(x533,x532)) % 187.68/187.66 [54]~E(x541,x542)+E(f864(x541),f864(x542)) % 187.68/187.66 [55]~E(x551,x552)+E(f869(x551),f869(x552)) % 187.68/187.66 [56]~E(x561,x562)+E(f111(x561),f111(x562)) % 187.68/187.66 [57]~E(x571,x572)+E(f867(x571),f867(x572)) % 187.68/187.66 [58]~E(x581,x582)+E(f33(x581,x583),f33(x582,x583)) % 187.68/187.66 [59]~E(x591,x592)+E(f33(x593,x591),f33(x593,x592)) % 187.68/187.66 [60]~E(x601,x602)+E(f46(x601,x603,x604),f46(x602,x603,x604)) % 187.68/187.66 [61]~E(x611,x612)+E(f46(x613,x611,x614),f46(x613,x612,x614)) % 187.68/187.66 [62]~E(x621,x622)+E(f46(x623,x624,x621),f46(x623,x624,x622)) % 187.68/187.66 [63]~E(x631,x632)+E(f871(x631,x633),f871(x632,x633)) % 187.68/187.66 [64]~E(x641,x642)+E(f871(x643,x641),f871(x643,x642)) % 187.68/187.66 [65]~E(x651,x652)+E(f221(x651),f221(x652)) % 187.68/187.66 [66]~E(x661,x662)+E(f80(x661),f80(x662)) % 187.68/187.66 [67]~E(x671,x672)+E(f148(x671,x673,x674,x675),f148(x672,x673,x674,x675)) % 187.68/187.66 [68]~E(x681,x682)+E(f148(x683,x681,x684,x685),f148(x683,x682,x684,x685)) % 187.68/187.66 [69]~E(x691,x692)+E(f148(x693,x694,x691,x695),f148(x693,x694,x692,x695)) % 187.68/187.66 [70]~E(x701,x702)+E(f148(x703,x704,x705,x701),f148(x703,x704,x705,x702)) % 187.68/187.66 [71]~E(x711,x712)+E(f186(x711),f186(x712)) % 187.68/187.66 [72]~E(x721,x722)+E(f120(x721),f120(x722)) % 187.68/187.66 [73]~E(x731,x732)+E(f129(x731),f129(x732)) % 187.68/187.66 [74]~E(x741,x742)+E(f63(x741),f63(x742)) % 187.68/187.66 [75]~E(x751,x752)+E(f81(x751),f81(x752)) % 187.68/187.66 [76]~E(x761,x762)+E(f39(x761),f39(x762)) % 187.68/187.66 [77]~E(x771,x772)+E(f7(x771,x773,x774),f7(x772,x773,x774)) % 187.68/187.66 [78]~E(x781,x782)+E(f7(x783,x781,x784),f7(x783,x782,x784)) % 187.68/187.66 [79]~E(x791,x792)+E(f7(x793,x794,x791),f7(x793,x794,x792)) % 187.68/187.66 [80]~E(x801,x802)+E(f62(x801),f62(x802)) % 187.68/187.66 [81]~E(x811,x812)+E(f598(x811,x813,x814),f598(x812,x813,x814)) % 187.68/187.66 [82]~E(x821,x822)+E(f598(x823,x821,x824),f598(x823,x822,x824)) % 187.68/187.66 [83]~E(x831,x832)+E(f598(x833,x834,x831),f598(x833,x834,x832)) % 187.68/187.66 [84]~E(x841,x842)+E(f82(x841),f82(x842)) % 187.68/187.66 [85]~E(x851,x852)+E(f40(x851),f40(x852)) % 187.68/187.66 [86]~E(x861,x862)+E(f264(x861),f264(x862)) % 187.68/187.66 [87]~E(x871,x872)+E(f285(x871,x873,x874),f285(x872,x873,x874)) % 187.68/187.66 [88]~E(x881,x882)+E(f285(x883,x881,x884),f285(x883,x882,x884)) % 187.68/187.66 [89]~E(x891,x892)+E(f285(x893,x894,x891),f285(x893,x894,x892)) % 187.68/187.66 [90]~E(x901,x902)+E(f170(x901,x903),f170(x902,x903)) % 187.68/187.66 [91]~E(x911,x912)+E(f170(x913,x911),f170(x913,x912)) % 187.68/187.66 [92]~E(x921,x922)+E(f51(x921,x923),f51(x922,x923)) % 187.68/187.66 [93]~E(x931,x932)+E(f51(x933,x931),f51(x933,x932)) % 187.68/187.66 [94]~E(x941,x942)+E(f164(x941),f164(x942)) % 187.68/187.66 [95]~E(x951,x952)+E(f236(x951,x953),f236(x952,x953)) % 187.68/187.66 [96]~E(x961,x962)+E(f236(x963,x961),f236(x963,x962)) % 187.68/187.66 [97]~E(x971,x972)+E(f14(x971,x973),f14(x972,x973)) % 187.68/187.66 [98]~E(x981,x982)+E(f14(x983,x981),f14(x983,x982)) % 187.68/187.66 [99]~E(x991,x992)+E(f74(x991,x993,x994,x995),f74(x992,x993,x994,x995)) % 187.68/187.66 [100]~E(x1001,x1002)+E(f74(x1003,x1001,x1004,x1005),f74(x1003,x1002,x1004,x1005)) % 187.68/187.66 [101]~E(x1011,x1012)+E(f74(x1013,x1014,x1011,x1015),f74(x1013,x1014,x1012,x1015)) % 187.68/187.66 [102]~E(x1021,x1022)+E(f74(x1023,x1024,x1025,x1021),f74(x1023,x1024,x1025,x1022)) % 187.68/187.66 [103]~E(x1031,x1032)+E(f44(x1031,x1033),f44(x1032,x1033)) % 187.68/187.66 [104]~E(x1041,x1042)+E(f44(x1043,x1041),f44(x1043,x1042)) % 187.68/187.66 [105]~E(x1051,x1052)+E(f16(x1051,x1053),f16(x1052,x1053)) % 187.68/187.66 [106]~E(x1061,x1062)+E(f16(x1063,x1061),f16(x1063,x1062)) % 187.68/187.66 [107]~E(x1071,x1072)+E(f117(x1071),f117(x1072)) % 187.68/187.66 [108]~E(x1081,x1082)+E(f804(x1081,x1083),f804(x1082,x1083)) % 187.68/187.66 [109]~E(x1091,x1092)+E(f804(x1093,x1091),f804(x1093,x1092)) % 187.68/187.66 [110]~E(x1101,x1102)+E(f8(x1101,x1103,x1104),f8(x1102,x1103,x1104)) % 187.68/187.66 [111]~E(x1111,x1112)+E(f8(x1113,x1111,x1114),f8(x1113,x1112,x1114)) % 187.68/187.66 [112]~E(x1121,x1122)+E(f8(x1123,x1124,x1121),f8(x1123,x1124,x1122)) % 187.68/187.66 [113]~E(x1131,x1132)+E(f229(x1131),f229(x1132)) % 187.68/187.66 [114]~E(x1141,x1142)+E(f146(x1141,x1143),f146(x1142,x1143)) % 187.68/187.66 [115]~E(x1151,x1152)+E(f146(x1153,x1151),f146(x1153,x1152)) % 187.68/187.66 [116]~E(x1161,x1162)+E(f42(x1161,x1163),f42(x1162,x1163)) % 187.68/187.66 [117]~E(x1171,x1172)+E(f42(x1173,x1171),f42(x1173,x1172)) % 187.68/187.66 [118]~E(x1181,x1182)+E(f188(x1181),f188(x1182)) % 187.68/187.66 [119]~E(x1191,x1192)+E(f168(x1191,x1193,x1194),f168(x1192,x1193,x1194)) % 187.68/187.66 [120]~E(x1201,x1202)+E(f168(x1203,x1201,x1204),f168(x1203,x1202,x1204)) % 187.68/187.66 [121]~E(x1211,x1212)+E(f168(x1213,x1214,x1211),f168(x1213,x1214,x1212)) % 187.68/187.66 [122]~E(x1221,x1222)+E(f276(x1221,x1223),f276(x1222,x1223)) % 187.68/187.66 [123]~E(x1231,x1232)+E(f276(x1233,x1231),f276(x1233,x1232)) % 187.68/187.66 [124]~E(x1241,x1242)+E(f18(x1241,x1243,x1244),f18(x1242,x1243,x1244)) % 187.68/187.66 [125]~E(x1251,x1252)+E(f18(x1253,x1251,x1254),f18(x1253,x1252,x1254)) % 187.68/187.66 [126]~E(x1261,x1262)+E(f18(x1263,x1264,x1261),f18(x1263,x1264,x1262)) % 187.68/187.66 [127]~E(x1271,x1272)+E(f288(x1271,x1273,x1274),f288(x1272,x1273,x1274)) % 187.68/187.66 [128]~E(x1281,x1282)+E(f288(x1283,x1281,x1284),f288(x1283,x1282,x1284)) % 187.68/187.66 [129]~E(x1291,x1292)+E(f288(x1293,x1294,x1291),f288(x1293,x1294,x1292)) % 187.68/187.66 [130]~E(x1301,x1302)+E(f6(x1301,x1303),f6(x1302,x1303)) % 187.68/187.66 [131]~E(x1311,x1312)+E(f6(x1313,x1311),f6(x1313,x1312)) % 187.68/187.66 [132]~E(x1321,x1322)+E(f281(x1321),f281(x1322)) % 187.68/187.66 [133]~E(x1331,x1332)+E(f91(x1331,x1333),f91(x1332,x1333)) % 187.68/187.66 [134]~E(x1341,x1342)+E(f91(x1343,x1341),f91(x1343,x1342)) % 187.68/187.66 [135]~E(x1351,x1352)+E(f278(x1351),f278(x1352)) % 187.68/187.66 [136]~E(x1361,x1362)+E(f260(x1361,x1363,x1364),f260(x1362,x1363,x1364)) % 187.68/187.66 [137]~E(x1371,x1372)+E(f260(x1373,x1371,x1374),f260(x1373,x1372,x1374)) % 187.68/187.66 [138]~E(x1381,x1382)+E(f260(x1383,x1384,x1381),f260(x1383,x1384,x1382)) % 187.68/187.66 [139]~E(x1391,x1392)+E(f175(x1391,x1393,x1394),f175(x1392,x1393,x1394)) % 187.68/187.66 [140]~E(x1401,x1402)+E(f175(x1403,x1401,x1404),f175(x1403,x1402,x1404)) % 187.68/187.66 [141]~E(x1411,x1412)+E(f175(x1413,x1414,x1411),f175(x1413,x1414,x1412)) % 187.68/187.66 [142]~E(x1421,x1422)+E(f231(x1421),f231(x1422)) % 187.68/187.66 [143]~E(x1431,x1432)+E(f284(x1431),f284(x1432)) % 187.68/187.66 [144]~E(x1441,x1442)+E(f76(x1441),f76(x1442)) % 187.68/187.66 [145]~E(x1451,x1452)+E(f134(x1451,x1453,x1454,x1455),f134(x1452,x1453,x1454,x1455)) % 187.68/187.66 [146]~E(x1461,x1462)+E(f134(x1463,x1461,x1464,x1465),f134(x1463,x1462,x1464,x1465)) % 187.68/187.66 [147]~E(x1471,x1472)+E(f134(x1473,x1474,x1471,x1475),f134(x1473,x1474,x1472,x1475)) % 187.68/187.66 [148]~E(x1481,x1482)+E(f134(x1483,x1484,x1485,x1481),f134(x1483,x1484,x1485,x1482)) % 187.68/187.66 [149]~E(x1491,x1492)+E(f757(x1491,x1493),f757(x1492,x1493)) % 187.68/187.66 [150]~E(x1501,x1502)+E(f757(x1503,x1501),f757(x1503,x1502)) % 187.68/187.66 [151]~E(x1511,x1512)+E(f113(x1511),f113(x1512)) % 187.68/187.66 [152]~E(x1521,x1522)+E(f115(x1521),f115(x1522)) % 187.68/187.66 [153]~E(x1531,x1532)+E(f307(x1531),f307(x1532)) % 187.68/187.66 [154]~E(x1541,x1542)+E(f383(x1541,x1543,x1544,x1545),f383(x1542,x1543,x1544,x1545)) % 187.68/187.66 [155]~E(x1551,x1552)+E(f383(x1553,x1551,x1554,x1555),f383(x1553,x1552,x1554,x1555)) % 187.68/187.66 [156]~E(x1561,x1562)+E(f383(x1563,x1564,x1561,x1565),f383(x1563,x1564,x1562,x1565)) % 187.68/187.66 [157]~E(x1571,x1572)+E(f383(x1573,x1574,x1575,x1571),f383(x1573,x1574,x1575,x1572)) % 187.68/187.66 [158]~E(x1581,x1582)+E(f228(x1581),f228(x1582)) % 187.68/187.66 [159]~E(x1591,x1592)+E(f224(x1591,x1593),f224(x1592,x1593)) % 187.68/187.66 [160]~E(x1601,x1602)+E(f224(x1603,x1601),f224(x1603,x1602)) % 187.68/187.66 [161]~E(x1611,x1612)+E(f233(x1611,x1613),f233(x1612,x1613)) % 187.68/187.66 [162]~E(x1621,x1622)+E(f233(x1623,x1621),f233(x1623,x1622)) % 187.68/187.66 [163]~E(x1631,x1632)+E(f5(x1631),f5(x1632)) % 187.68/187.66 [164]~E(x1641,x1642)+E(f131(x1641,x1643),f131(x1642,x1643)) % 187.68/187.66 [165]~E(x1651,x1652)+E(f131(x1653,x1651),f131(x1653,x1652)) % 187.68/187.66 [166]~E(x1661,x1662)+E(f295(x1661,x1663),f295(x1662,x1663)) % 187.68/187.66 [167]~E(x1671,x1672)+E(f295(x1673,x1671),f295(x1673,x1672)) % 187.68/187.66 [168]~E(x1681,x1682)+E(f161(x1681),f161(x1682)) % 187.68/187.66 [169]~E(x1691,x1692)+E(f75(x1691,x1693),f75(x1692,x1693)) % 187.68/187.66 [170]~E(x1701,x1702)+E(f75(x1703,x1701),f75(x1703,x1702)) % 187.68/187.66 [171]~E(x1711,x1712)+E(f122(x1711),f122(x1712)) % 187.68/187.66 [172]~E(x1721,x1722)+E(f245(x1721,x1723,x1724),f245(x1722,x1723,x1724)) % 187.68/187.66 [173]~E(x1731,x1732)+E(f245(x1733,x1731,x1734),f245(x1733,x1732,x1734)) % 187.68/187.66 [174]~E(x1741,x1742)+E(f245(x1743,x1744,x1741),f245(x1743,x1744,x1742)) % 187.68/187.66 [175]~E(x1751,x1752)+E(f141(x1751,x1753,x1754,x1755,x1756),f141(x1752,x1753,x1754,x1755,x1756)) % 187.68/187.66 [176]~E(x1761,x1762)+E(f141(x1763,x1761,x1764,x1765,x1766),f141(x1763,x1762,x1764,x1765,x1766)) % 187.68/187.66 [177]~E(x1771,x1772)+E(f141(x1773,x1774,x1771,x1775,x1776),f141(x1773,x1774,x1772,x1775,x1776)) % 187.68/187.66 [178]~E(x1781,x1782)+E(f141(x1783,x1784,x1785,x1781,x1786),f141(x1783,x1784,x1785,x1782,x1786)) % 187.68/187.66 [179]~E(x1791,x1792)+E(f141(x1793,x1794,x1795,x1796,x1791),f141(x1793,x1794,x1795,x1796,x1792)) % 187.68/187.66 [180]~E(x1801,x1802)+E(f173(x1801,x1803),f173(x1802,x1803)) % 187.68/187.66 [181]~E(x1811,x1812)+E(f173(x1813,x1811),f173(x1813,x1812)) % 187.68/187.66 [182]~E(x1821,x1822)+E(f15(x1821,x1823),f15(x1822,x1823)) % 187.68/187.66 [183]~E(x1831,x1832)+E(f15(x1833,x1831),f15(x1833,x1832)) % 187.68/187.66 [184]~E(x1841,x1842)+E(f654(x1841,x1843,x1844),f654(x1842,x1843,x1844)) % 187.68/187.66 [185]~E(x1851,x1852)+E(f654(x1853,x1851,x1854),f654(x1853,x1852,x1854)) % 187.68/187.66 [186]~E(x1861,x1862)+E(f654(x1863,x1864,x1861),f654(x1863,x1864,x1862)) % 187.68/187.66 [187]~E(x1871,x1872)+E(f218(x1871),f218(x1872)) % 187.68/187.66 [188]~E(x1881,x1882)+E(f583(x1881,x1883,x1884,x1885),f583(x1882,x1883,x1884,x1885)) % 187.68/187.66 [189]~E(x1891,x1892)+E(f583(x1893,x1891,x1894,x1895),f583(x1893,x1892,x1894,x1895)) % 187.68/187.66 [190]~E(x1901,x1902)+E(f583(x1903,x1904,x1901,x1905),f583(x1903,x1904,x1902,x1905)) % 187.68/187.66 [191]~E(x1911,x1912)+E(f583(x1913,x1914,x1915,x1911),f583(x1913,x1914,x1915,x1912)) % 187.68/187.66 [192]~E(x1921,x1922)+E(f157(x1921),f157(x1922)) % 187.68/187.66 [193]~E(x1931,x1932)+E(f656(x1931,x1933),f656(x1932,x1933)) % 187.68/187.66 [194]~E(x1941,x1942)+E(f656(x1943,x1941),f656(x1943,x1942)) % 187.68/187.66 [195]~E(x1951,x1952)+E(f167(x1951,x1953,x1954),f167(x1952,x1953,x1954)) % 187.68/187.66 [196]~E(x1961,x1962)+E(f167(x1963,x1961,x1964),f167(x1963,x1962,x1964)) % 187.68/187.66 [197]~E(x1971,x1972)+E(f167(x1973,x1974,x1971),f167(x1973,x1974,x1972)) % 187.68/187.66 [198]~E(x1981,x1982)+E(f158(x1981),f158(x1982)) % 187.68/187.66 [199]~E(x1991,x1992)+E(f73(x1991,x1993),f73(x1992,x1993)) % 187.68/187.66 [200]~E(x2001,x2002)+E(f73(x2003,x2001),f73(x2003,x2002)) % 187.68/187.66 [201]~E(x2011,x2012)+E(f41(x2011,x2013),f41(x2012,x2013)) % 187.68/187.66 [202]~E(x2021,x2022)+E(f41(x2023,x2021),f41(x2023,x2022)) % 187.68/187.66 [203]~E(x2031,x2032)+E(f263(x2031,x2033,x2034),f263(x2032,x2033,x2034)) % 187.68/187.66 [204]~E(x2041,x2042)+E(f263(x2043,x2041,x2044),f263(x2043,x2042,x2044)) % 187.68/187.66 [205]~E(x2051,x2052)+E(f263(x2053,x2054,x2051),f263(x2053,x2054,x2052)) % 187.68/187.66 [206]~E(x2061,x2062)+E(f366(x2061,x2063),f366(x2062,x2063)) % 187.68/187.66 [207]~E(x2071,x2072)+E(f366(x2073,x2071),f366(x2073,x2072)) % 187.68/187.66 [208]~E(x2081,x2082)+E(f201(x2081,x2083),f201(x2082,x2083)) % 187.68/187.66 [209]~E(x2091,x2092)+E(f201(x2093,x2091),f201(x2093,x2092)) % 187.68/187.66 [210]~E(x2101,x2102)+E(f150(x2101,x2103),f150(x2102,x2103)) % 187.68/187.66 [211]~E(x2111,x2112)+E(f150(x2113,x2111),f150(x2113,x2112)) % 187.68/187.66 [212]~E(x2121,x2122)+E(f405(x2121,x2123),f405(x2122,x2123)) % 187.68/187.66 [213]~E(x2131,x2132)+E(f405(x2133,x2131),f405(x2133,x2132)) % 187.68/187.66 [214]~E(x2141,x2142)+E(f66(x2141,x2143,x2144),f66(x2142,x2143,x2144)) % 187.68/187.66 [215]~E(x2151,x2152)+E(f66(x2153,x2151,x2154),f66(x2153,x2152,x2154)) % 187.68/187.66 [216]~E(x2161,x2162)+E(f66(x2163,x2164,x2161),f66(x2163,x2164,x2162)) % 187.68/187.66 [217]~E(x2171,x2172)+E(f43(x2171,x2173),f43(x2172,x2173)) % 187.68/187.66 [218]~E(x2181,x2182)+E(f43(x2183,x2181),f43(x2183,x2182)) % 187.68/187.66 [219]~E(x2191,x2192)+E(f92(x2191),f92(x2192)) % 187.68/187.66 [220]~E(x2201,x2202)+E(f643(x2201,x2203,x2204,x2205),f643(x2202,x2203,x2204,x2205)) % 187.68/187.66 [221]~E(x2211,x2212)+E(f643(x2213,x2211,x2214,x2215),f643(x2213,x2212,x2214,x2215)) % 187.68/187.66 [222]~E(x2221,x2222)+E(f643(x2223,x2224,x2221,x2225),f643(x2223,x2224,x2222,x2225)) % 187.68/187.66 [223]~E(x2231,x2232)+E(f643(x2233,x2234,x2235,x2231),f643(x2233,x2234,x2235,x2232)) % 187.68/187.66 [224]~E(x2241,x2242)+E(f180(x2241,x2243),f180(x2242,x2243)) % 187.68/187.66 [225]~E(x2251,x2252)+E(f180(x2253,x2251),f180(x2253,x2252)) % 187.68/187.66 [226]~E(x2261,x2262)+E(f166(x2261,x2263,x2264),f166(x2262,x2263,x2264)) % 187.68/187.66 [227]~E(x2271,x2272)+E(f166(x2273,x2271,x2274),f166(x2273,x2272,x2274)) % 187.68/187.66 [228]~E(x2281,x2282)+E(f166(x2283,x2284,x2281),f166(x2283,x2284,x2282)) % 187.68/187.66 [229]~E(x2291,x2292)+E(f194(x2291,x2293),f194(x2292,x2293)) % 187.68/187.66 [230]~E(x2301,x2302)+E(f194(x2303,x2301),f194(x2303,x2302)) % 187.68/187.66 [231]~E(x2311,x2312)+E(f243(x2311,x2313),f243(x2312,x2313)) % 187.68/187.66 [232]~E(x2321,x2322)+E(f243(x2323,x2321),f243(x2323,x2322)) % 187.68/187.66 [233]~E(x2331,x2332)+E(f797(x2331,x2333,x2334),f797(x2332,x2333,x2334)) % 187.68/187.66 [234]~E(x2341,x2342)+E(f797(x2343,x2341,x2344),f797(x2343,x2342,x2344)) % 187.68/187.66 [235]~E(x2351,x2352)+E(f797(x2353,x2354,x2351),f797(x2353,x2354,x2352)) % 187.68/187.66 [236]~E(x2361,x2362)+E(f790(x2361,x2363,x2364),f790(x2362,x2363,x2364)) % 187.68/187.66 [237]~E(x2371,x2372)+E(f790(x2373,x2371,x2374),f790(x2373,x2372,x2374)) % 187.68/187.66 [238]~E(x2381,x2382)+E(f790(x2383,x2384,x2381),f790(x2383,x2384,x2382)) % 187.68/187.66 [239]~E(x2391,x2392)+E(f140(x2391,x2393,x2394),f140(x2392,x2393,x2394)) % 187.68/187.66 [240]~E(x2401,x2402)+E(f140(x2403,x2401,x2404),f140(x2403,x2402,x2404)) % 187.68/187.66 [241]~E(x2411,x2412)+E(f140(x2413,x2414,x2411),f140(x2413,x2414,x2412)) % 187.68/187.66 [242]~E(x2421,x2422)+E(f93(x2421),f93(x2422)) % 187.68/187.66 [243]~E(x2431,x2432)+E(f620(x2431,x2433,x2434,x2435,x2436),f620(x2432,x2433,x2434,x2435,x2436)) % 187.68/187.66 [244]~E(x2441,x2442)+E(f620(x2443,x2441,x2444,x2445,x2446),f620(x2443,x2442,x2444,x2445,x2446)) % 187.68/187.66 [245]~E(x2451,x2452)+E(f620(x2453,x2454,x2451,x2455,x2456),f620(x2453,x2454,x2452,x2455,x2456)) % 187.68/187.66 [246]~E(x2461,x2462)+E(f620(x2463,x2464,x2465,x2461,x2466),f620(x2463,x2464,x2465,x2462,x2466)) % 187.68/187.66 [247]~E(x2471,x2472)+E(f620(x2473,x2474,x2475,x2476,x2471),f620(x2473,x2474,x2475,x2476,x2472)) % 187.68/187.66 [248]~E(x2481,x2482)+E(f121(x2481,x2483),f121(x2482,x2483)) % 187.68/187.66 [249]~E(x2491,x2492)+E(f121(x2493,x2491),f121(x2493,x2492)) % 187.68/187.66 [250]~E(x2501,x2502)+E(f286(x2501,x2503,x2504),f286(x2502,x2503,x2504)) % 187.68/187.66 [251]~E(x2511,x2512)+E(f286(x2513,x2511,x2514),f286(x2513,x2512,x2514)) % 187.68/187.66 [252]~E(x2521,x2522)+E(f286(x2523,x2524,x2521),f286(x2523,x2524,x2522)) % 187.68/187.66 [253]~E(x2531,x2532)+E(f128(x2531,x2533),f128(x2532,x2533)) % 187.68/187.66 [254]~E(x2541,x2542)+E(f128(x2543,x2541),f128(x2543,x2542)) % 187.68/187.66 [255]~E(x2551,x2552)+E(f144(x2551,x2553),f144(x2552,x2553)) % 187.68/187.66 [256]~E(x2561,x2562)+E(f144(x2563,x2561),f144(x2563,x2562)) % 187.68/187.66 [257]~E(x2571,x2572)+E(f311(x2571),f311(x2572)) % 187.68/187.66 [258]~E(x2581,x2582)+E(f409(x2581,x2583),f409(x2582,x2583)) % 187.68/187.66 [259]~E(x2591,x2592)+E(f409(x2593,x2591),f409(x2593,x2592)) % 187.68/187.66 [260]~E(x2601,x2602)+E(f160(x2601),f160(x2602)) % 187.68/187.66 [261]~E(x2611,x2612)+E(f29(x2611,x2613,x2614),f29(x2612,x2613,x2614)) % 187.68/187.66 [262]~E(x2621,x2622)+E(f29(x2623,x2621,x2624),f29(x2623,x2622,x2624)) % 187.68/187.66 [263]~E(x2631,x2632)+E(f29(x2633,x2634,x2631),f29(x2633,x2634,x2632)) % 187.68/187.66 [264]~E(x2641,x2642)+E(f103(x2641,x2643),f103(x2642,x2643)) % 187.68/187.66 [265]~E(x2651,x2652)+E(f103(x2653,x2651),f103(x2653,x2652)) % 187.68/187.66 [266]~E(x2661,x2662)+E(f149(x2661,x2663),f149(x2662,x2663)) % 187.68/187.66 [267]~E(x2671,x2672)+E(f149(x2673,x2671),f149(x2673,x2672)) % 187.68/187.66 [268]~E(x2681,x2682)+E(f870(x2681,x2683),f870(x2682,x2683)) % 187.68/187.66 [269]~E(x2691,x2692)+E(f870(x2693,x2691),f870(x2693,x2692)) % 187.68/187.66 [270]~E(x2701,x2702)+E(f47(x2701,x2703),f47(x2702,x2703)) % 187.68/187.66 [271]~E(x2711,x2712)+E(f47(x2713,x2711),f47(x2713,x2712)) % 187.68/187.66 [272]~E(x2721,x2722)+E(f855(x2721,x2723,x2724),f855(x2722,x2723,x2724)) % 187.68/187.66 [273]~E(x2731,x2732)+E(f855(x2733,x2731,x2734),f855(x2733,x2732,x2734)) % 187.68/187.66 [274]~E(x2741,x2742)+E(f855(x2743,x2744,x2741),f855(x2743,x2744,x2742)) % 187.68/187.66 [275]~E(x2751,x2752)+E(f49(x2751,x2753),f49(x2752,x2753)) % 187.68/187.66 [276]~E(x2761,x2762)+E(f49(x2763,x2761),f49(x2763,x2762)) % 187.68/187.66 [277]~E(x2771,x2772)+E(f603(x2771,x2773,x2774,x2775,x2776),f603(x2772,x2773,x2774,x2775,x2776)) % 187.68/187.66 [278]~E(x2781,x2782)+E(f603(x2783,x2781,x2784,x2785,x2786),f603(x2783,x2782,x2784,x2785,x2786)) % 187.68/187.66 [279]~E(x2791,x2792)+E(f603(x2793,x2794,x2791,x2795,x2796),f603(x2793,x2794,x2792,x2795,x2796)) % 187.68/187.66 [280]~E(x2801,x2802)+E(f603(x2803,x2804,x2805,x2801,x2806),f603(x2803,x2804,x2805,x2802,x2806)) % 187.68/187.66 [281]~E(x2811,x2812)+E(f603(x2813,x2814,x2815,x2816,x2811),f603(x2813,x2814,x2815,x2816,x2812)) % 187.68/187.66 [282]~E(x2821,x2822)+E(f130(x2821),f130(x2822)) % 187.68/187.66 [283]~E(x2831,x2832)+E(f193(x2831),f193(x2832)) % 187.68/187.66 [284]~E(x2841,x2842)+E(f10(x2841,x2843),f10(x2842,x2843)) % 187.68/187.66 [285]~E(x2851,x2852)+E(f10(x2853,x2851),f10(x2853,x2852)) % 187.68/187.66 [286]~E(x2861,x2862)+E(f163(x2861),f163(x2862)) % 187.68/187.66 [287]~E(x2871,x2872)+E(f244(x2871,x2873),f244(x2872,x2873)) % 187.68/187.66 [288]~E(x2881,x2882)+E(f244(x2883,x2881),f244(x2883,x2882)) % 187.68/187.66 [289]~E(x2891,x2892)+E(f48(x2891,x2893),f48(x2892,x2893)) % 187.68/187.66 [290]~E(x2901,x2902)+E(f48(x2903,x2901),f48(x2903,x2902)) % 187.68/187.66 [291]~E(x2911,x2912)+E(f400(x2911,x2913,x2914,x2915),f400(x2912,x2913,x2914,x2915)) % 187.68/187.66 [292]~E(x2921,x2922)+E(f400(x2923,x2921,x2924,x2925),f400(x2923,x2922,x2924,x2925)) % 187.68/187.66 [293]~E(x2931,x2932)+E(f400(x2933,x2934,x2931,x2935),f400(x2933,x2934,x2932,x2935)) % 187.68/187.66 [294]~E(x2941,x2942)+E(f400(x2943,x2944,x2945,x2941),f400(x2943,x2944,x2945,x2942)) % 187.68/187.66 [295]~E(x2951,x2952)+E(f630(x2951,x2953,x2954,x2955,x2956),f630(x2952,x2953,x2954,x2955,x2956)) % 187.68/187.66 [296]~E(x2961,x2962)+E(f630(x2963,x2961,x2964,x2965,x2966),f630(x2963,x2962,x2964,x2965,x2966)) % 187.68/187.66 [297]~E(x2971,x2972)+E(f630(x2973,x2974,x2971,x2975,x2976),f630(x2973,x2974,x2972,x2975,x2976)) % 187.68/187.66 [298]~E(x2981,x2982)+E(f630(x2983,x2984,x2985,x2981,x2986),f630(x2983,x2984,x2985,x2982,x2986)) % 187.68/187.66 [299]~E(x2991,x2992)+E(f630(x2993,x2994,x2995,x2996,x2991),f630(x2993,x2994,x2995,x2996,x2992)) % 187.68/187.66 [300]~E(x3001,x3002)+E(f13(x3001,x3003),f13(x3002,x3003)) % 187.68/187.66 [301]~E(x3011,x3012)+E(f13(x3013,x3011),f13(x3013,x3012)) % 187.68/187.66 [302]~E(x3021,x3022)+E(f261(x3021,x3023),f261(x3022,x3023)) % 187.68/187.66 [303]~E(x3031,x3032)+E(f261(x3033,x3031),f261(x3033,x3032)) % 187.68/187.66 [304]~E(x3041,x3042)+E(f101(x3041),f101(x3042)) % 187.68/187.66 [305]~E(x3051,x3052)+E(f68(x3051,x3053,x3054,x3055,x3056),f68(x3052,x3053,x3054,x3055,x3056)) % 187.68/187.66 [306]~E(x3061,x3062)+E(f68(x3063,x3061,x3064,x3065,x3066),f68(x3063,x3062,x3064,x3065,x3066)) % 187.68/187.66 [307]~E(x3071,x3072)+E(f68(x3073,x3074,x3071,x3075,x3076),f68(x3073,x3074,x3072,x3075,x3076)) % 187.68/187.66 [308]~E(x3081,x3082)+E(f68(x3083,x3084,x3085,x3081,x3086),f68(x3083,x3084,x3085,x3082,x3086)) % 187.68/187.66 [309]~E(x3091,x3092)+E(f68(x3093,x3094,x3095,x3096,x3091),f68(x3093,x3094,x3095,x3096,x3092)) % 187.68/187.66 [310]~E(x3101,x3102)+E(f237(x3101),f237(x3102)) % 187.68/187.66 [311]~E(x3111,x3112)+E(f151(x3111,x3113),f151(x3112,x3113)) % 187.68/187.66 [312]~E(x3121,x3122)+E(f151(x3123,x3121),f151(x3123,x3122)) % 187.68/187.66 [313]~E(x3131,x3132)+E(f9(x3131,x3133),f9(x3132,x3133)) % 187.68/187.66 [314]~E(x3141,x3142)+E(f9(x3143,x3141),f9(x3143,x3142)) % 187.68/187.66 [315]~E(x3151,x3152)+E(f169(x3151,x3153),f169(x3152,x3153)) % 187.68/187.66 [316]~E(x3161,x3162)+E(f169(x3163,x3161),f169(x3163,x3162)) % 187.68/187.66 [317]~E(x3171,x3172)+E(f189(x3171,x3173),f189(x3172,x3173)) % 187.68/187.66 [318]~E(x3181,x3182)+E(f189(x3183,x3181),f189(x3183,x3182)) % 187.68/187.66 [319]~E(x3191,x3192)+E(f213(x3191,x3193),f213(x3192,x3193)) % 187.68/187.66 [320]~E(x3201,x3202)+E(f213(x3203,x3201),f213(x3203,x3202)) % 187.68/187.66 [321]~E(x3211,x3212)+E(f297(x3211,x3213),f297(x3212,x3213)) % 187.68/187.66 [322]~E(x3221,x3222)+E(f297(x3223,x3221),f297(x3223,x3222)) % 187.68/187.66 [323]~E(x3231,x3232)+E(f279(x3231,x3233,x3234),f279(x3232,x3233,x3234)) % 187.68/187.66 [324]~E(x3241,x3242)+E(f279(x3243,x3241,x3244),f279(x3243,x3242,x3244)) % 187.68/187.66 [325]~E(x3251,x3252)+E(f279(x3253,x3254,x3251),f279(x3253,x3254,x3252)) % 187.68/187.66 [326]~E(x3261,x3262)+E(f298(x3261,x3263),f298(x3262,x3263)) % 187.68/187.66 [327]~E(x3271,x3272)+E(f298(x3273,x3271),f298(x3273,x3272)) % 187.68/187.66 [328]~E(x3281,x3282)+E(f179(x3281,x3283,x3284,x3285),f179(x3282,x3283,x3284,x3285)) % 187.68/187.66 [329]~E(x3291,x3292)+E(f179(x3293,x3291,x3294,x3295),f179(x3293,x3292,x3294,x3295)) % 187.68/187.66 [330]~E(x3301,x3302)+E(f179(x3303,x3304,x3301,x3305),f179(x3303,x3304,x3302,x3305)) % 187.68/187.66 [331]~E(x3311,x3312)+E(f179(x3313,x3314,x3315,x3311),f179(x3313,x3314,x3315,x3312)) % 187.68/187.66 [332]~E(x3321,x3322)+E(f57(x3321),f57(x3322)) % 187.68/187.66 [333]~E(x3331,x3332)+E(f153(x3331,x3333),f153(x3332,x3333)) % 187.68/187.66 [334]~E(x3341,x3342)+E(f153(x3343,x3341),f153(x3343,x3342)) % 187.68/187.66 [335]~E(x3351,x3352)+E(f548(x3351,x3353),f548(x3352,x3353)) % 187.68/187.66 [336]~E(x3361,x3362)+E(f548(x3363,x3361),f548(x3363,x3362)) % 187.68/187.66 [337]~E(x3371,x3372)+E(f277(x3371,x3373,x3374),f277(x3372,x3373,x3374)) % 187.68/187.66 [338]~E(x3381,x3382)+E(f277(x3383,x3381,x3384),f277(x3383,x3382,x3384)) % 187.68/187.66 [339]~E(x3391,x3392)+E(f277(x3393,x3394,x3391),f277(x3393,x3394,x3392)) % 187.68/187.66 [340]~E(x3401,x3402)+E(f357(x3401,x3403,x3404),f357(x3402,x3403,x3404)) % 187.68/187.66 [341]~E(x3411,x3412)+E(f357(x3413,x3411,x3414),f357(x3413,x3412,x3414)) % 187.68/187.66 [342]~E(x3421,x3422)+E(f357(x3423,x3424,x3421),f357(x3423,x3424,x3422)) % 187.68/187.66 [343]~E(x3431,x3432)+E(f136(x3431,x3433),f136(x3432,x3433)) % 187.68/187.66 [344]~E(x3441,x3442)+E(f136(x3443,x3441),f136(x3443,x3442)) % 187.68/187.66 [345]~E(x3451,x3452)+E(f259(x3451),f259(x3452)) % 187.68/187.66 [346]~E(x3461,x3462)+E(f449(x3461,x3463),f449(x3462,x3463)) % 187.68/187.66 [347]~E(x3471,x3472)+E(f449(x3473,x3471),f449(x3473,x3472)) % 187.68/187.66 [348]~E(x3481,x3482)+E(f176(x3481,x3483,x3484,x3485),f176(x3482,x3483,x3484,x3485)) % 187.68/187.66 [349]~E(x3491,x3492)+E(f176(x3493,x3491,x3494,x3495),f176(x3493,x3492,x3494,x3495)) % 187.68/187.66 [350]~E(x3501,x3502)+E(f176(x3503,x3504,x3501,x3505),f176(x3503,x3504,x3502,x3505)) % 187.68/187.66 [351]~E(x3511,x3512)+E(f176(x3513,x3514,x3515,x3511),f176(x3513,x3514,x3515,x3512)) % 187.68/187.66 [352]~E(x3521,x3522)+E(f239(x3521,x3523,x3524),f239(x3522,x3523,x3524)) % 187.68/187.66 [353]~E(x3531,x3532)+E(f239(x3533,x3531,x3534),f239(x3533,x3532,x3534)) % 187.68/187.66 [354]~E(x3541,x3542)+E(f239(x3543,x3544,x3541),f239(x3543,x3544,x3542)) % 187.68/187.66 [355]~E(x3551,x3552)+E(f477(x3551,x3553,x3554,x3555,x3556,x3557,x3558,x3559),f477(x3552,x3553,x3554,x3555,x3556,x3557,x3558,x3559)) % 187.68/187.66 [356]~E(x3561,x3562)+E(f477(x3563,x3561,x3564,x3565,x3566,x3567,x3568,x3569),f477(x3563,x3562,x3564,x3565,x3566,x3567,x3568,x3569)) % 187.68/187.66 [357]~E(x3571,x3572)+E(f477(x3573,x3574,x3571,x3575,x3576,x3577,x3578,x3579),f477(x3573,x3574,x3572,x3575,x3576,x3577,x3578,x3579)) % 187.68/187.66 [358]~E(x3581,x3582)+E(f477(x3583,x3584,x3585,x3581,x3586,x3587,x3588,x3589),f477(x3583,x3584,x3585,x3582,x3586,x3587,x3588,x3589)) % 187.68/187.66 [359]~E(x3591,x3592)+E(f477(x3593,x3594,x3595,x3596,x3591,x3597,x3598,x3599),f477(x3593,x3594,x3595,x3596,x3592,x3597,x3598,x3599)) % 187.68/187.66 [360]~E(x3601,x3602)+E(f477(x3603,x3604,x3605,x3606,x3607,x3601,x3608,x3609),f477(x3603,x3604,x3605,x3606,x3607,x3602,x3608,x3609)) % 187.68/187.66 [361]~E(x3611,x3612)+E(f477(x3613,x3614,x3615,x3616,x3617,x3618,x3611,x3619),f477(x3613,x3614,x3615,x3616,x3617,x3618,x3612,x3619)) % 187.68/187.66 [362]~E(x3621,x3622)+E(f477(x3623,x3624,x3625,x3626,x3627,x3628,x3629,x3621),f477(x3623,x3624,x3625,x3626,x3627,x3628,x3629,x3622)) % 187.68/187.66 [363]~E(x3631,x3632)+E(f670(x3631,x3633,x3634,x3635),f670(x3632,x3633,x3634,x3635)) % 187.68/187.66 [364]~E(x3641,x3642)+E(f670(x3643,x3641,x3644,x3645),f670(x3643,x3642,x3644,x3645)) % 187.68/187.66 [365]~E(x3651,x3652)+E(f670(x3653,x3654,x3651,x3655),f670(x3653,x3654,x3652,x3655)) % 187.68/187.66 [366]~E(x3661,x3662)+E(f670(x3663,x3664,x3665,x3661),f670(x3663,x3664,x3665,x3662)) % 187.68/187.66 [367]~E(x3671,x3672)+E(f429(x3671,x3673,x3674,x3675,x3676,x3677),f429(x3672,x3673,x3674,x3675,x3676,x3677)) % 187.68/187.66 [368]~E(x3681,x3682)+E(f429(x3683,x3681,x3684,x3685,x3686,x3687),f429(x3683,x3682,x3684,x3685,x3686,x3687)) % 187.68/187.66 [369]~E(x3691,x3692)+E(f429(x3693,x3694,x3691,x3695,x3696,x3697),f429(x3693,x3694,x3692,x3695,x3696,x3697)) % 187.68/187.66 [370]~E(x3701,x3702)+E(f429(x3703,x3704,x3705,x3701,x3706,x3707),f429(x3703,x3704,x3705,x3702,x3706,x3707)) % 187.68/187.66 [371]~E(x3711,x3712)+E(f429(x3713,x3714,x3715,x3716,x3711,x3717),f429(x3713,x3714,x3715,x3716,x3712,x3717)) % 187.68/187.66 [372]~E(x3721,x3722)+E(f429(x3723,x3724,x3725,x3726,x3727,x3721),f429(x3723,x3724,x3725,x3726,x3727,x3722)) % 187.68/187.66 [373]~E(x3731,x3732)+E(f155(x3731,x3733,x3734,x3735),f155(x3732,x3733,x3734,x3735)) % 187.68/187.66 [374]~E(x3741,x3742)+E(f155(x3743,x3741,x3744,x3745),f155(x3743,x3742,x3744,x3745)) % 187.68/187.66 [375]~E(x3751,x3752)+E(f155(x3753,x3754,x3751,x3755),f155(x3753,x3754,x3752,x3755)) % 187.68/187.66 [376]~E(x3761,x3762)+E(f155(x3763,x3764,x3765,x3761),f155(x3763,x3764,x3765,x3762)) % 187.68/187.66 [377]~E(x3771,x3772)+E(f520(x3771,x3773,x3774,x3775),f520(x3772,x3773,x3774,x3775)) % 187.68/187.66 [378]~E(x3781,x3782)+E(f520(x3783,x3781,x3784,x3785),f520(x3783,x3782,x3784,x3785)) % 187.68/187.66 [379]~E(x3791,x3792)+E(f520(x3793,x3794,x3791,x3795),f520(x3793,x3794,x3792,x3795)) % 187.68/187.66 [380]~E(x3801,x3802)+E(f520(x3803,x3804,x3805,x3801),f520(x3803,x3804,x3805,x3802)) % 187.68/187.66 [381]~E(x3811,x3812)+E(f86(x3811,x3813),f86(x3812,x3813)) % 187.68/187.66 [382]~E(x3821,x3822)+E(f86(x3823,x3821),f86(x3823,x3822)) % 187.68/187.66 [383]~E(x3831,x3832)+E(f437(x3831,x3833,x3834),f437(x3832,x3833,x3834)) % 187.68/187.66 [384]~E(x3841,x3842)+E(f437(x3843,x3841,x3844),f437(x3843,x3842,x3844)) % 187.68/187.66 [385]~E(x3851,x3852)+E(f437(x3853,x3854,x3851),f437(x3853,x3854,x3852)) % 187.68/187.66 [386]~E(x3861,x3862)+E(f89(x3861),f89(x3862)) % 187.68/187.66 [387]~E(x3871,x3872)+E(f65(x3871,x3873),f65(x3872,x3873)) % 187.68/187.66 [388]~E(x3881,x3882)+E(f65(x3883,x3881),f65(x3883,x3882)) % 187.68/187.66 [389]~E(x3891,x3892)+E(f145(x3891,x3893),f145(x3892,x3893)) % 187.68/187.66 [390]~E(x3901,x3902)+E(f145(x3903,x3901),f145(x3903,x3902)) % 187.68/187.66 [391]~E(x3911,x3912)+E(f715(x3911,x3913,x3914,x3915,x3916),f715(x3912,x3913,x3914,x3915,x3916)) % 187.68/187.66 [392]~E(x3921,x3922)+E(f715(x3923,x3921,x3924,x3925,x3926),f715(x3923,x3922,x3924,x3925,x3926)) % 187.68/187.66 [393]~E(x3931,x3932)+E(f715(x3933,x3934,x3931,x3935,x3936),f715(x3933,x3934,x3932,x3935,x3936)) % 187.68/187.66 [394]~E(x3941,x3942)+E(f715(x3943,x3944,x3945,x3941,x3946),f715(x3943,x3944,x3945,x3942,x3946)) % 187.68/187.66 [395]~E(x3951,x3952)+E(f715(x3953,x3954,x3955,x3956,x3951),f715(x3953,x3954,x3955,x3956,x3952)) % 187.68/187.66 [396]~E(x3961,x3962)+E(f795(x3961,x3963,x3964),f795(x3962,x3963,x3964)) % 187.68/187.66 [397]~E(x3971,x3972)+E(f795(x3973,x3971,x3974),f795(x3973,x3972,x3974)) % 187.68/187.66 [398]~E(x3981,x3982)+E(f795(x3983,x3984,x3981),f795(x3983,x3984,x3982)) % 187.68/187.66 [399]~E(x3991,x3992)+E(f607(x3991,x3993),f607(x3992,x3993)) % 187.68/187.66 [400]~E(x4001,x4002)+E(f607(x4003,x4001),f607(x4003,x4002)) % 187.68/187.66 [401]~E(x4011,x4012)+E(f246(x4011,x4013,x4014,x4015,x4016,x4017),f246(x4012,x4013,x4014,x4015,x4016,x4017)) % 187.68/187.66 [402]~E(x4021,x4022)+E(f246(x4023,x4021,x4024,x4025,x4026,x4027),f246(x4023,x4022,x4024,x4025,x4026,x4027)) % 187.68/187.66 [403]~E(x4031,x4032)+E(f246(x4033,x4034,x4031,x4035,x4036,x4037),f246(x4033,x4034,x4032,x4035,x4036,x4037)) % 187.68/187.66 [404]~E(x4041,x4042)+E(f246(x4043,x4044,x4045,x4041,x4046,x4047),f246(x4043,x4044,x4045,x4042,x4046,x4047)) % 187.68/187.66 [405]~E(x4051,x4052)+E(f246(x4053,x4054,x4055,x4056,x4051,x4057),f246(x4053,x4054,x4055,x4056,x4052,x4057)) % 187.68/187.66 [406]~E(x4061,x4062)+E(f246(x4063,x4064,x4065,x4066,x4067,x4061),f246(x4063,x4064,x4065,x4066,x4067,x4062)) % 187.68/187.66 [407]~E(x4071,x4072)+E(f17(x4071,x4073,x4074,x4075),f17(x4072,x4073,x4074,x4075)) % 187.68/187.66 [408]~E(x4081,x4082)+E(f17(x4083,x4081,x4084,x4085),f17(x4083,x4082,x4084,x4085)) % 187.68/187.66 [409]~E(x4091,x4092)+E(f17(x4093,x4094,x4091,x4095),f17(x4093,x4094,x4092,x4095)) % 187.68/187.66 [410]~E(x4101,x4102)+E(f17(x4103,x4104,x4105,x4101),f17(x4103,x4104,x4105,x4102)) % 187.68/187.66 [411]~E(x4111,x4112)+E(f242(x4111,x4113,x4114),f242(x4112,x4113,x4114)) % 187.68/187.66 [412]~E(x4121,x4122)+E(f242(x4123,x4121,x4124),f242(x4123,x4122,x4124)) % 187.68/187.66 [413]~E(x4131,x4132)+E(f242(x4133,x4134,x4131),f242(x4133,x4134,x4132)) % 187.68/187.66 [414]~E(x4141,x4142)+E(f139(x4141,x4143),f139(x4142,x4143)) % 187.68/187.66 [415]~E(x4151,x4152)+E(f139(x4153,x4151),f139(x4153,x4152)) % 187.68/187.66 [416]~E(x4161,x4162)+E(f385(x4161,x4163,x4164,x4165),f385(x4162,x4163,x4164,x4165)) % 187.68/187.66 [417]~E(x4171,x4172)+E(f385(x4173,x4171,x4174,x4175),f385(x4173,x4172,x4174,x4175)) % 187.68/187.66 [418]~E(x4181,x4182)+E(f385(x4183,x4184,x4181,x4185),f385(x4183,x4184,x4182,x4185)) % 187.68/187.66 [419]~E(x4191,x4192)+E(f385(x4193,x4194,x4195,x4191),f385(x4193,x4194,x4195,x4192)) % 187.68/187.66 [420]~E(x4201,x4202)+E(f500(x4201,x4203,x4204,x4205,x4206,x4207),f500(x4202,x4203,x4204,x4205,x4206,x4207)) % 187.68/187.66 [421]~E(x4211,x4212)+E(f500(x4213,x4211,x4214,x4215,x4216,x4217),f500(x4213,x4212,x4214,x4215,x4216,x4217)) % 187.68/187.66 [422]~E(x4221,x4222)+E(f500(x4223,x4224,x4221,x4225,x4226,x4227),f500(x4223,x4224,x4222,x4225,x4226,x4227)) % 187.68/187.66 [423]~E(x4231,x4232)+E(f500(x4233,x4234,x4235,x4231,x4236,x4237),f500(x4233,x4234,x4235,x4232,x4236,x4237)) % 187.68/187.66 [424]~E(x4241,x4242)+E(f500(x4243,x4244,x4245,x4246,x4241,x4247),f500(x4243,x4244,x4245,x4246,x4242,x4247)) % 187.68/187.66 [425]~E(x4251,x4252)+E(f500(x4253,x4254,x4255,x4256,x4257,x4251),f500(x4253,x4254,x4255,x4256,x4257,x4252)) % 187.68/187.66 [426]~E(x4261,x4262)+E(f147(x4261,x4263,x4264),f147(x4262,x4263,x4264)) % 187.68/187.66 [427]~E(x4271,x4272)+E(f147(x4273,x4271,x4274),f147(x4273,x4272,x4274)) % 187.68/187.66 [428]~E(x4281,x4282)+E(f147(x4283,x4284,x4281),f147(x4283,x4284,x4282)) % 187.68/187.66 [429]~E(x4291,x4292)+E(f31(x4291,x4293,x4294),f31(x4292,x4293,x4294)) % 187.68/187.66 [430]~E(x4301,x4302)+E(f31(x4303,x4301,x4304),f31(x4303,x4302,x4304)) % 187.68/187.66 [431]~E(x4311,x4312)+E(f31(x4313,x4314,x4311),f31(x4313,x4314,x4312)) % 187.68/187.66 [432]~E(x4321,x4322)+E(f34(x4321,x4323),f34(x4322,x4323)) % 187.68/187.66 [433]~E(x4331,x4332)+E(f34(x4333,x4331),f34(x4333,x4332)) % 187.68/187.66 [434]~E(x4341,x4342)+E(f413(x4341,x4343,x4344),f413(x4342,x4343,x4344)) % 187.68/187.66 [435]~E(x4351,x4352)+E(f413(x4353,x4351,x4354),f413(x4353,x4352,x4354)) % 187.68/187.66 [436]~E(x4361,x4362)+E(f413(x4363,x4364,x4361),f413(x4363,x4364,x4362)) % 187.68/187.66 [437]~E(x4371,x4372)+E(f132(x4371,x4373,x4374),f132(x4372,x4373,x4374)) % 187.68/187.66 [438]~E(x4381,x4382)+E(f132(x4383,x4381,x4384),f132(x4383,x4382,x4384)) % 187.68/187.66 [439]~E(x4391,x4392)+E(f132(x4393,x4394,x4391),f132(x4393,x4394,x4392)) % 187.68/187.66 [440]~E(x4401,x4402)+E(f234(x4401,x4403),f234(x4402,x4403)) % 187.68/187.66 [441]~E(x4411,x4412)+E(f234(x4413,x4411),f234(x4413,x4412)) % 187.68/187.66 [442]~E(x4421,x4422)+E(f56(x4421,x4423,x4424),f56(x4422,x4423,x4424)) % 187.68/187.66 [443]~E(x4431,x4432)+E(f56(x4433,x4431,x4434),f56(x4433,x4432,x4434)) % 187.68/187.66 [444]~E(x4441,x4442)+E(f56(x4443,x4444,x4441),f56(x4443,x4444,x4442)) % 187.68/187.66 [445]~E(x4451,x4452)+E(f805(x4451,x4453,x4454),f805(x4452,x4453,x4454)) % 187.68/187.66 [446]~E(x4461,x4462)+E(f805(x4463,x4461,x4464),f805(x4463,x4462,x4464)) % 187.68/187.66 [447]~E(x4471,x4472)+E(f805(x4473,x4474,x4471),f805(x4473,x4474,x4472)) % 187.68/187.66 [448]~E(x4481,x4482)+E(f125(x4481,x4483,x4484,x4485),f125(x4482,x4483,x4484,x4485)) % 187.68/187.66 [449]~E(x4491,x4492)+E(f125(x4493,x4491,x4494,x4495),f125(x4493,x4492,x4494,x4495)) % 187.68/187.66 [450]~E(x4501,x4502)+E(f125(x4503,x4504,x4501,x4505),f125(x4503,x4504,x4502,x4505)) % 187.68/187.66 [451]~E(x4511,x4512)+E(f125(x4513,x4514,x4515,x4511),f125(x4513,x4514,x4515,x4512)) % 187.68/187.66 [452]~E(x4521,x4522)+E(f293(x4521,x4523,x4524,x4525),f293(x4522,x4523,x4524,x4525)) % 187.68/187.66 [453]~E(x4531,x4532)+E(f293(x4533,x4531,x4534,x4535),f293(x4533,x4532,x4534,x4535)) % 187.68/187.66 [454]~E(x4541,x4542)+E(f293(x4543,x4544,x4541,x4545),f293(x4543,x4544,x4542,x4545)) % 187.68/187.66 [455]~E(x4551,x4552)+E(f293(x4553,x4554,x4555,x4551),f293(x4553,x4554,x4555,x4552)) % 187.68/187.66 [456]~E(x4561,x4562)+E(f574(x4561,x4563,x4564,x4565),f574(x4562,x4563,x4564,x4565)) % 187.68/187.66 [457]~E(x4571,x4572)+E(f574(x4573,x4571,x4574,x4575),f574(x4573,x4572,x4574,x4575)) % 187.68/187.66 [458]~E(x4581,x4582)+E(f574(x4583,x4584,x4581,x4585),f574(x4583,x4584,x4582,x4585)) % 187.68/187.66 [459]~E(x4591,x4592)+E(f574(x4593,x4594,x4595,x4591),f574(x4593,x4594,x4595,x4592)) % 187.68/187.66 [460]~E(x4601,x4602)+E(f214(x4601),f214(x4602)) % 187.68/187.66 [461]~E(x4611,x4612)+E(f807(x4611,x4613,x4614),f807(x4612,x4613,x4614)) % 187.68/187.66 [462]~E(x4621,x4622)+E(f807(x4623,x4621,x4624),f807(x4623,x4622,x4624)) % 187.68/187.66 [463]~E(x4631,x4632)+E(f807(x4633,x4634,x4631),f807(x4633,x4634,x4632)) % 187.68/187.66 [464]~E(x4641,x4642)+E(f282(x4641,x4643),f282(x4642,x4643)) % 187.68/187.66 [465]~E(x4651,x4652)+E(f282(x4653,x4651),f282(x4653,x4652)) % 187.68/187.66 [466]~E(x4661,x4662)+E(f198(x4661),f198(x4662)) % 187.68/187.66 [467]~E(x4671,x4672)+E(f847(x4671,x4673),f847(x4672,x4673)) % 187.68/187.66 [468]~E(x4681,x4682)+E(f847(x4683,x4681),f847(x4683,x4682)) % 187.68/187.66 [469]~E(x4691,x4692)+E(f165(x4691),f165(x4692)) % 187.68/187.66 [470]~E(x4701,x4702)+E(f575(x4701,x4703,x4704,x4705),f575(x4702,x4703,x4704,x4705)) % 187.68/187.66 [471]~E(x4711,x4712)+E(f575(x4713,x4711,x4714,x4715),f575(x4713,x4712,x4714,x4715)) % 187.68/187.66 [472]~E(x4721,x4722)+E(f575(x4723,x4724,x4721,x4725),f575(x4723,x4724,x4722,x4725)) % 187.68/187.66 [473]~E(x4731,x4732)+E(f575(x4733,x4734,x4735,x4731),f575(x4733,x4734,x4735,x4732)) % 187.68/187.66 [474]~E(x4741,x4742)+E(f694(x4741,x4743,x4744,x4745),f694(x4742,x4743,x4744,x4745)) % 187.68/187.66 [475]~E(x4751,x4752)+E(f694(x4753,x4751,x4754,x4755),f694(x4753,x4752,x4754,x4755)) % 187.68/187.66 [476]~E(x4761,x4762)+E(f694(x4763,x4764,x4761,x4765),f694(x4763,x4764,x4762,x4765)) % 187.68/187.66 [477]~E(x4771,x4772)+E(f694(x4773,x4774,x4775,x4771),f694(x4773,x4774,x4775,x4772)) % 187.68/187.66 [478]~E(x4781,x4782)+E(f209(x4781,x4783,x4784),f209(x4782,x4783,x4784)) % 187.68/187.66 [479]~E(x4791,x4792)+E(f209(x4793,x4791,x4794),f209(x4793,x4792,x4794)) % 187.68/187.66 [480]~E(x4801,x4802)+E(f209(x4803,x4804,x4801),f209(x4803,x4804,x4802)) % 187.68/187.66 [481]~E(x4811,x4812)+E(f254(x4811,x4813),f254(x4812,x4813)) % 187.68/187.66 [482]~E(x4821,x4822)+E(f254(x4823,x4821),f254(x4823,x4822)) % 187.68/187.66 [483]~E(x4831,x4832)+E(f294(x4831,x4833),f294(x4832,x4833)) % 187.68/187.66 [484]~E(x4841,x4842)+E(f294(x4843,x4841),f294(x4843,x4842)) % 187.68/187.66 [485]~E(x4851,x4852)+E(f669(x4851,x4853,x4854,x4855),f669(x4852,x4853,x4854,x4855)) % 187.68/187.66 [486]~E(x4861,x4862)+E(f669(x4863,x4861,x4864,x4865),f669(x4863,x4862,x4864,x4865)) % 187.68/187.66 [487]~E(x4871,x4872)+E(f669(x4873,x4874,x4871,x4875),f669(x4873,x4874,x4872,x4875)) % 187.68/187.66 [488]~E(x4881,x4882)+E(f669(x4883,x4884,x4885,x4881),f669(x4883,x4884,x4885,x4882)) % 187.68/187.66 [489]~E(x4891,x4892)+E(f87(x4891,x4893),f87(x4892,x4893)) % 187.68/187.66 [490]~E(x4901,x4902)+E(f87(x4903,x4901),f87(x4903,x4902)) % 187.68/187.66 [491]~E(x4911,x4912)+E(f60(x4911),f60(x4912)) % 187.68/187.66 [492]~E(x4921,x4922)+E(f235(x4921,x4923),f235(x4922,x4923)) % 187.68/187.66 [493]~E(x4931,x4932)+E(f235(x4933,x4931),f235(x4933,x4932)) % 187.68/187.66 [494]~E(x4941,x4942)+E(f593(x4941,x4943),f593(x4942,x4943)) % 187.68/187.66 [495]~E(x4951,x4952)+E(f593(x4953,x4951),f593(x4953,x4952)) % 187.68/187.66 [496]~E(x4961,x4962)+E(f354(x4961,x4963,x4964),f354(x4962,x4963,x4964)) % 187.68/187.66 [497]~E(x4971,x4972)+E(f354(x4973,x4971,x4974),f354(x4973,x4972,x4974)) % 187.68/187.66 [498]~E(x4981,x4982)+E(f354(x4983,x4984,x4981),f354(x4983,x4984,x4982)) % 187.68/187.66 [499]~E(x4991,x4992)+E(f222(x4991,x4993),f222(x4992,x4993)) % 187.68/187.66 [500]~E(x5001,x5002)+E(f222(x5003,x5001),f222(x5003,x5002)) % 187.68/187.66 [501]~E(x5011,x5012)+E(f432(x5011,x5013,x5014,x5015,x5016),f432(x5012,x5013,x5014,x5015,x5016)) % 187.68/187.66 [502]~E(x5021,x5022)+E(f432(x5023,x5021,x5024,x5025,x5026),f432(x5023,x5022,x5024,x5025,x5026)) % 187.68/187.66 [503]~E(x5031,x5032)+E(f432(x5033,x5034,x5031,x5035,x5036),f432(x5033,x5034,x5032,x5035,x5036)) % 187.68/187.66 [504]~E(x5041,x5042)+E(f432(x5043,x5044,x5045,x5041,x5046),f432(x5043,x5044,x5045,x5042,x5046)) % 187.68/187.66 [505]~E(x5051,x5052)+E(f432(x5053,x5054,x5055,x5056,x5051),f432(x5053,x5054,x5055,x5056,x5052)) % 187.68/187.66 [506]~E(x5061,x5062)+E(f384(x5061,x5063,x5064,x5065),f384(x5062,x5063,x5064,x5065)) % 187.68/187.66 [507]~E(x5071,x5072)+E(f384(x5073,x5071,x5074,x5075),f384(x5073,x5072,x5074,x5075)) % 187.68/187.66 [508]~E(x5081,x5082)+E(f384(x5083,x5084,x5081,x5085),f384(x5083,x5084,x5082,x5085)) % 187.68/187.66 [509]~E(x5091,x5092)+E(f384(x5093,x5094,x5095,x5091),f384(x5093,x5094,x5095,x5092)) % 187.68/187.66 [510]~E(x5101,x5102)+E(f443(x5101,x5103,x5104,x5105,x5106),f443(x5102,x5103,x5104,x5105,x5106)) % 187.68/187.66 [511]~E(x5111,x5112)+E(f443(x5113,x5111,x5114,x5115,x5116),f443(x5113,x5112,x5114,x5115,x5116)) % 187.68/187.66 [512]~E(x5121,x5122)+E(f443(x5123,x5124,x5121,x5125,x5126),f443(x5123,x5124,x5122,x5125,x5126)) % 187.68/187.66 [513]~E(x5131,x5132)+E(f443(x5133,x5134,x5135,x5131,x5136),f443(x5133,x5134,x5135,x5132,x5136)) % 187.68/187.66 [514]~E(x5141,x5142)+E(f443(x5143,x5144,x5145,x5146,x5141),f443(x5143,x5144,x5145,x5146,x5142)) % 187.68/187.66 [515]~E(x5151,x5152)+E(f230(x5151),f230(x5152)) % 187.68/187.66 [516]~E(x5161,x5162)+E(f102(x5161,x5163),f102(x5162,x5163)) % 187.68/187.66 [517]~E(x5171,x5172)+E(f102(x5173,x5171),f102(x5173,x5172)) % 187.68/187.66 [518]~E(x5181,x5182)+E(f390(x5181,x5183),f390(x5182,x5183)) % 187.68/187.66 [519]~E(x5191,x5192)+E(f390(x5193,x5191),f390(x5193,x5192)) % 187.68/187.66 [520]~E(x5201,x5202)+E(f570(x5201,x5203,x5204),f570(x5202,x5203,x5204)) % 187.68/187.66 [521]~E(x5211,x5212)+E(f570(x5213,x5211,x5214),f570(x5213,x5212,x5214)) % 187.68/187.66 [522]~E(x5221,x5222)+E(f570(x5223,x5224,x5221),f570(x5223,x5224,x5222)) % 187.68/187.66 [523]~E(x5231,x5232)+E(f352(x5231,x5233,x5234,x5235,x5236),f352(x5232,x5233,x5234,x5235,x5236)) % 187.68/187.66 [524]~E(x5241,x5242)+E(f352(x5243,x5241,x5244,x5245,x5246),f352(x5243,x5242,x5244,x5245,x5246)) % 187.68/187.66 [525]~E(x5251,x5252)+E(f352(x5253,x5254,x5251,x5255,x5256),f352(x5253,x5254,x5252,x5255,x5256)) % 187.68/187.66 [526]~E(x5261,x5262)+E(f352(x5263,x5264,x5265,x5261,x5266),f352(x5263,x5264,x5265,x5262,x5266)) % 187.68/187.66 [527]~E(x5271,x5272)+E(f352(x5273,x5274,x5275,x5276,x5271),f352(x5273,x5274,x5275,x5276,x5272)) % 187.68/187.66 [528]~E(x5281,x5282)+E(f88(x5281),f88(x5282)) % 187.68/187.66 [529]~E(x5291,x5292)+E(f680(x5291,x5293,x5294,x5295,x5296),f680(x5292,x5293,x5294,x5295,x5296)) % 187.68/187.66 [530]~E(x5301,x5302)+E(f680(x5303,x5301,x5304,x5305,x5306),f680(x5303,x5302,x5304,x5305,x5306)) % 187.68/187.66 [531]~E(x5311,x5312)+E(f680(x5313,x5314,x5311,x5315,x5316),f680(x5313,x5314,x5312,x5315,x5316)) % 187.68/187.66 [532]~E(x5321,x5322)+E(f680(x5323,x5324,x5325,x5321,x5326),f680(x5323,x5324,x5325,x5322,x5326)) % 187.68/187.66 [533]~E(x5331,x5332)+E(f680(x5333,x5334,x5335,x5336,x5331),f680(x5333,x5334,x5335,x5336,x5332)) % 187.68/187.66 [534]~E(x5341,x5342)+E(f806(x5341,x5343,x5344),f806(x5342,x5343,x5344)) % 187.68/187.66 [535]~E(x5351,x5352)+E(f806(x5353,x5351,x5354),f806(x5353,x5352,x5354)) % 187.68/187.66 [536]~E(x5361,x5362)+E(f806(x5363,x5364,x5361),f806(x5363,x5364,x5362)) % 187.68/187.66 [537]~E(x5371,x5372)+E(f329(x5371,x5373,x5374),f329(x5372,x5373,x5374)) % 187.68/187.66 [538]~E(x5381,x5382)+E(f329(x5383,x5381,x5384),f329(x5383,x5382,x5384)) % 187.68/187.66 [539]~E(x5391,x5392)+E(f329(x5393,x5394,x5391),f329(x5393,x5394,x5392)) % 187.68/187.66 [540]~E(x5401,x5402)+E(f100(x5401,x5403,x5404,x5405),f100(x5402,x5403,x5404,x5405)) % 187.68/187.66 [541]~E(x5411,x5412)+E(f100(x5413,x5411,x5414,x5415),f100(x5413,x5412,x5414,x5415)) % 187.68/187.66 [542]~E(x5421,x5422)+E(f100(x5423,x5424,x5421,x5425),f100(x5423,x5424,x5422,x5425)) % 187.68/187.66 [543]~E(x5431,x5432)+E(f100(x5433,x5434,x5435,x5431),f100(x5433,x5434,x5435,x5432)) % 187.68/187.66 [544]~E(x5441,x5442)+E(f540(x5441,x5443,x5444),f540(x5442,x5443,x5444)) % 187.68/187.66 [545]~E(x5451,x5452)+E(f540(x5453,x5451,x5454),f540(x5453,x5452,x5454)) % 187.68/187.66 [546]~E(x5461,x5462)+E(f540(x5463,x5464,x5461),f540(x5463,x5464,x5462)) % 187.68/187.66 [547]~E(x5471,x5472)+E(f425(x5471,x5473,x5474),f425(x5472,x5473,x5474)) % 187.68/187.66 [548]~E(x5481,x5482)+E(f425(x5483,x5481,x5484),f425(x5483,x5482,x5484)) % 187.68/187.66 [549]~E(x5491,x5492)+E(f425(x5493,x5494,x5491),f425(x5493,x5494,x5492)) % 187.68/187.66 [550]~E(x5501,x5502)+E(f599(x5501,x5503,x5504,x5505,x5506),f599(x5502,x5503,x5504,x5505,x5506)) % 187.68/187.66 [551]~E(x5511,x5512)+E(f599(x5513,x5511,x5514,x5515,x5516),f599(x5513,x5512,x5514,x5515,x5516)) % 187.68/187.66 [552]~E(x5521,x5522)+E(f599(x5523,x5524,x5521,x5525,x5526),f599(x5523,x5524,x5522,x5525,x5526)) % 187.68/187.66 [553]~E(x5531,x5532)+E(f599(x5533,x5534,x5535,x5531,x5536),f599(x5533,x5534,x5535,x5532,x5536)) % 187.68/187.66 [554]~E(x5541,x5542)+E(f599(x5543,x5544,x5545,x5546,x5541),f599(x5543,x5544,x5545,x5546,x5542)) % 187.68/187.66 [555]~E(x5551,x5552)+E(f632(x5551,x5553,x5554),f632(x5552,x5553,x5554)) % 187.68/187.66 [556]~E(x5561,x5562)+E(f632(x5563,x5561,x5564),f632(x5563,x5562,x5564)) % 187.68/187.66 [557]~E(x5571,x5572)+E(f632(x5573,x5574,x5571),f632(x5573,x5574,x5572)) % 187.68/187.66 [558]~E(x5581,x5582)+E(f83(x5581,x5583),f83(x5582,x5583)) % 187.68/187.66 [559]~E(x5591,x5592)+E(f83(x5593,x5591),f83(x5593,x5592)) % 187.68/187.66 [560]~E(x5601,x5602)+E(f216(x5601,x5603,x5604,x5605),f216(x5602,x5603,x5604,x5605)) % 187.68/187.66 [561]~E(x5611,x5612)+E(f216(x5613,x5611,x5614,x5615),f216(x5613,x5612,x5614,x5615)) % 187.68/187.66 [562]~E(x5621,x5622)+E(f216(x5623,x5624,x5621,x5625),f216(x5623,x5624,x5622,x5625)) % 187.68/187.66 [563]~E(x5631,x5632)+E(f216(x5633,x5634,x5635,x5631),f216(x5633,x5634,x5635,x5632)) % 187.68/187.66 [564]~E(x5641,x5642)+E(f96(x5641,x5643,x5644),f96(x5642,x5643,x5644)) % 187.68/187.66 [565]~E(x5651,x5652)+E(f96(x5653,x5651,x5654),f96(x5653,x5652,x5654)) % 187.68/187.66 [566]~E(x5661,x5662)+E(f96(x5663,x5664,x5661),f96(x5663,x5664,x5662)) % 187.68/187.66 [567]~E(x5671,x5672)+E(f813(x5671),f813(x5672)) % 187.68/187.66 [568]~E(x5681,x5682)+E(f784(x5681,x5683,x5684),f784(x5682,x5683,x5684)) % 187.68/187.66 [569]~E(x5691,x5692)+E(f784(x5693,x5691,x5694),f784(x5693,x5692,x5694)) % 187.68/187.66 [570]~E(x5701,x5702)+E(f784(x5703,x5704,x5701),f784(x5703,x5704,x5702)) % 187.68/187.66 [571]~E(x5711,x5712)+E(f133(x5711),f133(x5712)) % 187.68/187.66 [572]~E(x5721,x5722)+E(f333(x5721,x5723,x5724),f333(x5722,x5723,x5724)) % 187.68/187.66 [573]~E(x5731,x5732)+E(f333(x5733,x5731,x5734),f333(x5733,x5732,x5734)) % 187.68/187.66 [574]~E(x5741,x5742)+E(f333(x5743,x5744,x5741),f333(x5743,x5744,x5742)) % 187.68/187.66 [575]~E(x5751,x5752)+E(f590(x5751,x5753,x5754,x5755),f590(x5752,x5753,x5754,x5755)) % 187.68/187.66 [576]~E(x5761,x5762)+E(f590(x5763,x5761,x5764,x5765),f590(x5763,x5762,x5764,x5765)) % 187.68/187.66 [577]~E(x5771,x5772)+E(f590(x5773,x5774,x5771,x5775),f590(x5773,x5774,x5772,x5775)) % 187.68/187.66 [578]~E(x5781,x5782)+E(f590(x5783,x5784,x5785,x5781),f590(x5783,x5784,x5785,x5782)) % 187.68/187.66 [579]~E(x5791,x5792)+E(f314(x5791),f314(x5792)) % 187.68/187.66 [580]~E(x5801,x5802)+E(f842(x5801,x5803),f842(x5802,x5803)) % 187.68/187.66 [581]~E(x5811,x5812)+E(f842(x5813,x5811),f842(x5813,x5812)) % 187.68/187.66 [582]~E(x5821,x5822)+E(f137(x5821,x5823),f137(x5822,x5823)) % 187.68/187.66 [583]~E(x5831,x5832)+E(f137(x5833,x5831),f137(x5833,x5832)) % 187.68/187.66 [584]~E(x5841,x5842)+E(f764(x5841,x5843),f764(x5842,x5843)) % 187.68/187.66 [585]~E(x5851,x5852)+E(f764(x5853,x5851),f764(x5853,x5852)) % 187.68/187.66 [586]~E(x5861,x5862)+E(f573(x5861,x5863,x5864),f573(x5862,x5863,x5864)) % 187.68/187.66 [587]~E(x5871,x5872)+E(f573(x5873,x5871,x5874),f573(x5873,x5872,x5874)) % 187.68/187.66 [588]~E(x5881,x5882)+E(f573(x5883,x5884,x5881),f573(x5883,x5884,x5882)) % 187.68/187.66 [589]~E(x5891,x5892)+E(f546(x5891),f546(x5892)) % 187.68/187.66 [590]~E(x5901,x5902)+E(f794(x5901,x5903,x5904),f794(x5902,x5903,x5904)) % 187.68/187.66 [591]~E(x5911,x5912)+E(f794(x5913,x5911,x5914),f794(x5913,x5912,x5914)) % 187.68/187.66 [592]~E(x5921,x5922)+E(f794(x5923,x5924,x5921),f794(x5923,x5924,x5922)) % 187.68/187.66 [593]~E(x5931,x5932)+E(f371(x5931,x5933,x5934),f371(x5932,x5933,x5934)) % 187.68/187.66 [594]~E(x5941,x5942)+E(f371(x5943,x5941,x5944),f371(x5943,x5942,x5944)) % 187.68/187.66 [595]~E(x5951,x5952)+E(f371(x5953,x5954,x5951),f371(x5953,x5954,x5952)) % 187.68/187.66 [596]~E(x5961,x5962)+E(f64(x5961,x5963,x5964),f64(x5962,x5963,x5964)) % 187.68/187.66 [597]~E(x5971,x5972)+E(f64(x5973,x5971,x5974),f64(x5973,x5972,x5974)) % 187.68/187.66 [598]~E(x5981,x5982)+E(f64(x5983,x5984,x5981),f64(x5983,x5984,x5982)) % 187.68/187.66 [599]~E(x5991,x5992)+E(f421(x5991,x5993,x5994,x5995,x5996,x5997),f421(x5992,x5993,x5994,x5995,x5996,x5997)) % 187.68/187.66 [600]~E(x6001,x6002)+E(f421(x6003,x6001,x6004,x6005,x6006,x6007),f421(x6003,x6002,x6004,x6005,x6006,x6007)) % 187.68/187.66 [601]~E(x6011,x6012)+E(f421(x6013,x6014,x6011,x6015,x6016,x6017),f421(x6013,x6014,x6012,x6015,x6016,x6017)) % 187.68/187.66 [602]~E(x6021,x6022)+E(f421(x6023,x6024,x6025,x6021,x6026,x6027),f421(x6023,x6024,x6025,x6022,x6026,x6027)) % 187.68/187.66 [603]~E(x6031,x6032)+E(f421(x6033,x6034,x6035,x6036,x6031,x6037),f421(x6033,x6034,x6035,x6036,x6032,x6037)) % 187.68/187.66 [604]~E(x6041,x6042)+E(f421(x6043,x6044,x6045,x6046,x6047,x6041),f421(x6043,x6044,x6045,x6046,x6047,x6042)) % 187.68/187.66 [605]~E(x6051,x6052)+E(f404(x6051,x6053),f404(x6052,x6053)) % 187.68/187.66 [606]~E(x6061,x6062)+E(f404(x6063,x6061),f404(x6063,x6062)) % 187.68/187.66 [607]~E(x6071,x6072)+E(f774(x6071,x6073,x6074,x6075),f774(x6072,x6073,x6074,x6075)) % 187.68/187.66 [608]~E(x6081,x6082)+E(f774(x6083,x6081,x6084,x6085),f774(x6083,x6082,x6084,x6085)) % 187.68/187.66 [609]~E(x6091,x6092)+E(f774(x6093,x6094,x6091,x6095),f774(x6093,x6094,x6092,x6095)) % 187.68/187.66 [610]~E(x6101,x6102)+E(f774(x6103,x6104,x6105,x6101),f774(x6103,x6104,x6105,x6102)) % 187.68/187.66 [611]~E(x6111,x6112)+E(f59(x6111),f59(x6112)) % 187.68/187.66 [612]~E(x6121,x6122)+E(f676(x6121,x6123,x6124,x6125,x6126,x6127,x6128),f676(x6122,x6123,x6124,x6125,x6126,x6127,x6128)) % 187.68/187.66 [613]~E(x6131,x6132)+E(f676(x6133,x6131,x6134,x6135,x6136,x6137,x6138),f676(x6133,x6132,x6134,x6135,x6136,x6137,x6138)) % 187.68/187.66 [614]~E(x6141,x6142)+E(f676(x6143,x6144,x6141,x6145,x6146,x6147,x6148),f676(x6143,x6144,x6142,x6145,x6146,x6147,x6148)) % 187.68/187.66 [615]~E(x6151,x6152)+E(f676(x6153,x6154,x6155,x6151,x6156,x6157,x6158),f676(x6153,x6154,x6155,x6152,x6156,x6157,x6158)) % 187.68/187.66 [616]~E(x6161,x6162)+E(f676(x6163,x6164,x6165,x6166,x6161,x6167,x6168),f676(x6163,x6164,x6165,x6166,x6162,x6167,x6168)) % 187.68/187.66 [617]~E(x6171,x6172)+E(f676(x6173,x6174,x6175,x6176,x6177,x6171,x6178),f676(x6173,x6174,x6175,x6176,x6177,x6172,x6178)) % 187.68/187.66 [618]~E(x6181,x6182)+E(f676(x6183,x6184,x6185,x6186,x6187,x6188,x6181),f676(x6183,x6184,x6185,x6186,x6187,x6188,x6182)) % 187.68/187.66 [619]~E(x6191,x6192)+E(f67(x6191,x6193,x6194),f67(x6192,x6193,x6194)) % 187.68/187.66 [620]~E(x6201,x6202)+E(f67(x6203,x6201,x6204),f67(x6203,x6202,x6204)) % 187.68/187.66 [621]~E(x6211,x6212)+E(f67(x6213,x6214,x6211),f67(x6213,x6214,x6212)) % 187.68/187.66 [622]~E(x6221,x6222)+E(f12(x6221,x6223,x6224),f12(x6222,x6223,x6224)) % 187.68/187.66 [623]~E(x6231,x6232)+E(f12(x6233,x6231,x6234),f12(x6233,x6232,x6234)) % 187.68/187.66 [624]~E(x6241,x6242)+E(f12(x6243,x6244,x6241),f12(x6243,x6244,x6242)) % 187.68/187.66 [625]~E(x6251,x6252)+E(f786(x6251,x6253,x6254),f786(x6252,x6253,x6254)) % 187.68/187.66 [626]~E(x6261,x6262)+E(f786(x6263,x6261,x6264),f786(x6263,x6262,x6264)) % 187.68/187.66 [627]~E(x6271,x6272)+E(f786(x6273,x6274,x6271),f786(x6273,x6274,x6272)) % 187.68/187.66 [628]~E(x6281,x6282)+E(f730(x6281,x6283,x6284),f730(x6282,x6283,x6284)) % 187.68/187.66 [629]~E(x6291,x6292)+E(f730(x6293,x6291,x6294),f730(x6293,x6292,x6294)) % 187.68/187.66 [630]~E(x6301,x6302)+E(f730(x6303,x6304,x6301),f730(x6303,x6304,x6302)) % 187.68/187.66 [631]~E(x6311,x6312)+E(f159(x6311,x6313,x6314),f159(x6312,x6313,x6314)) % 187.68/187.66 [632]~E(x6321,x6322)+E(f159(x6323,x6321,x6324),f159(x6323,x6322,x6324)) % 187.68/187.66 [633]~E(x6331,x6332)+E(f159(x6333,x6334,x6331),f159(x6333,x6334,x6332)) % 187.68/187.66 [634]~E(x6341,x6342)+E(f789(x6341,x6343,x6344),f789(x6342,x6343,x6344)) % 187.68/187.66 [635]~E(x6351,x6352)+E(f789(x6353,x6351,x6354),f789(x6353,x6352,x6354)) % 187.68/187.66 [636]~E(x6361,x6362)+E(f789(x6363,x6364,x6361),f789(x6363,x6364,x6362)) % 187.68/187.66 [637]~E(x6371,x6372)+E(f280(x6371,x6373,x6374),f280(x6372,x6373,x6374)) % 187.68/187.66 [638]~E(x6381,x6382)+E(f280(x6383,x6381,x6384),f280(x6383,x6382,x6384)) % 187.68/187.66 [639]~E(x6391,x6392)+E(f280(x6393,x6394,x6391),f280(x6393,x6394,x6392)) % 187.68/187.66 [640]~E(x6401,x6402)+E(f262(x6401,x6403),f262(x6402,x6403)) % 187.68/187.66 [641]~E(x6411,x6412)+E(f262(x6413,x6411),f262(x6413,x6412)) % 187.68/187.66 [642]~E(x6421,x6422)+E(f397(x6421,x6423),f397(x6422,x6423)) % 187.68/187.66 [643]~E(x6431,x6432)+E(f397(x6433,x6431),f397(x6433,x6432)) % 187.68/187.66 [644]~E(x6441,x6442)+E(f456(x6441,x6443,x6444,x6445),f456(x6442,x6443,x6444,x6445)) % 187.68/187.66 [645]~E(x6451,x6452)+E(f456(x6453,x6451,x6454,x6455),f456(x6453,x6452,x6454,x6455)) % 187.68/187.66 [646]~E(x6461,x6462)+E(f456(x6463,x6464,x6461,x6465),f456(x6463,x6464,x6462,x6465)) % 187.68/187.66 [647]~E(x6471,x6472)+E(f456(x6473,x6474,x6475,x6471),f456(x6473,x6474,x6475,x6472)) % 187.68/187.66 [648]~E(x6481,x6482)+E(f687(x6481,x6483),f687(x6482,x6483)) % 187.68/187.66 [649]~E(x6491,x6492)+E(f687(x6493,x6491),f687(x6493,x6492)) % 187.68/187.66 [650]~E(x6501,x6502)+E(f567(x6501,x6503),f567(x6502,x6503)) % 187.68/187.66 [651]~E(x6511,x6512)+E(f567(x6513,x6511),f567(x6513,x6512)) % 187.68/187.66 [652]~E(x6521,x6522)+E(f232(x6521,x6523),f232(x6522,x6523)) % 187.68/187.66 [653]~E(x6531,x6532)+E(f232(x6533,x6531),f232(x6533,x6532)) % 187.68/187.66 [654]~E(x6541,x6542)+E(f539(x6541,x6543),f539(x6542,x6543)) % 187.68/187.66 [655]~E(x6551,x6552)+E(f539(x6553,x6551),f539(x6553,x6552)) % 187.68/187.66 [656]~E(x6561,x6562)+E(f247(x6561,x6563,x6564,x6565),f247(x6562,x6563,x6564,x6565)) % 187.68/187.66 [657]~E(x6571,x6572)+E(f247(x6573,x6571,x6574,x6575),f247(x6573,x6572,x6574,x6575)) % 187.68/187.66 [658]~E(x6581,x6582)+E(f247(x6583,x6584,x6581,x6585),f247(x6583,x6584,x6582,x6585)) % 187.68/187.66 [659]~E(x6591,x6592)+E(f247(x6593,x6594,x6595,x6591),f247(x6593,x6594,x6595,x6592)) % 187.68/187.66 [660]~E(x6601,x6602)+E(f808(x6601,x6603,x6604),f808(x6602,x6603,x6604)) % 187.68/187.66 [661]~E(x6611,x6612)+E(f808(x6613,x6611,x6614),f808(x6613,x6612,x6614)) % 187.68/187.66 [662]~E(x6621,x6622)+E(f808(x6623,x6624,x6621),f808(x6623,x6624,x6622)) % 187.68/187.66 [663]~E(x6631,x6632)+E(f572(x6631,x6633,x6634,x6635,x6636,x6637),f572(x6632,x6633,x6634,x6635,x6636,x6637)) % 187.68/187.66 [664]~E(x6641,x6642)+E(f572(x6643,x6641,x6644,x6645,x6646,x6647),f572(x6643,x6642,x6644,x6645,x6646,x6647)) % 187.68/187.66 [665]~E(x6651,x6652)+E(f572(x6653,x6654,x6651,x6655,x6656,x6657),f572(x6653,x6654,x6652,x6655,x6656,x6657)) % 187.68/187.66 [666]~E(x6661,x6662)+E(f572(x6663,x6664,x6665,x6661,x6666,x6667),f572(x6663,x6664,x6665,x6662,x6666,x6667)) % 187.68/187.66 [667]~E(x6671,x6672)+E(f572(x6673,x6674,x6675,x6676,x6671,x6677),f572(x6673,x6674,x6675,x6676,x6672,x6677)) % 187.68/187.66 [668]~E(x6681,x6682)+E(f572(x6683,x6684,x6685,x6686,x6687,x6681),f572(x6683,x6684,x6685,x6686,x6687,x6682)) % 187.68/187.66 [669]~E(x6691,x6692)+E(f135(x6691,x6693),f135(x6692,x6693)) % 187.68/187.66 [670]~E(x6701,x6702)+E(f135(x6703,x6701),f135(x6703,x6702)) % 187.68/187.66 [671]~E(x6711,x6712)+E(f389(x6711,x6713,x6714,x6715),f389(x6712,x6713,x6714,x6715)) % 187.68/187.66 [672]~E(x6721,x6722)+E(f389(x6723,x6721,x6724,x6725),f389(x6723,x6722,x6724,x6725)) % 187.68/187.66 [673]~E(x6731,x6732)+E(f389(x6733,x6734,x6731,x6735),f389(x6733,x6734,x6732,x6735)) % 187.68/187.66 [674]~E(x6741,x6742)+E(f389(x6743,x6744,x6745,x6741),f389(x6743,x6744,x6745,x6742)) % 187.68/187.66 [675]~E(x6751,x6752)+E(f832(x6751,x6753),f832(x6752,x6753)) % 187.68/187.66 [676]~E(x6761,x6762)+E(f832(x6763,x6761),f832(x6763,x6762)) % 187.68/187.66 [677]~E(x6771,x6772)+E(f659(x6771,x6773,x6774,x6775),f659(x6772,x6773,x6774,x6775)) % 187.68/187.66 [678]~E(x6781,x6782)+E(f659(x6783,x6781,x6784,x6785),f659(x6783,x6782,x6784,x6785)) % 187.68/187.66 [679]~E(x6791,x6792)+E(f659(x6793,x6794,x6791,x6795),f659(x6793,x6794,x6792,x6795)) % 187.68/187.66 [680]~E(x6801,x6802)+E(f659(x6803,x6804,x6805,x6801),f659(x6803,x6804,x6805,x6802)) % 187.68/187.66 [681]~E(x6811,x6812)+E(f30(x6811,x6813,x6814),f30(x6812,x6813,x6814)) % 187.68/187.66 [682]~E(x6821,x6822)+E(f30(x6823,x6821,x6824),f30(x6823,x6822,x6824)) % 187.68/187.66 [683]~E(x6831,x6832)+E(f30(x6833,x6834,x6831),f30(x6833,x6834,x6832)) % 187.68/187.66 [684]~E(x6841,x6842)+E(f768(x6841,x6843,x6844,x6845,x6846),f768(x6842,x6843,x6844,x6845,x6846)) % 187.68/187.66 [685]~E(x6851,x6852)+E(f768(x6853,x6851,x6854,x6855,x6856),f768(x6853,x6852,x6854,x6855,x6856)) % 187.68/187.66 [686]~E(x6861,x6862)+E(f768(x6863,x6864,x6861,x6865,x6866),f768(x6863,x6864,x6862,x6865,x6866)) % 187.68/187.66 [687]~E(x6871,x6872)+E(f768(x6873,x6874,x6875,x6871,x6876),f768(x6873,x6874,x6875,x6872,x6876)) % 187.68/187.66 [688]~E(x6881,x6882)+E(f768(x6883,x6884,x6885,x6886,x6881),f768(x6883,x6884,x6885,x6886,x6882)) % 187.68/187.66 [689]~E(x6891,x6892)+E(f391(x6891,x6893,x6894,x6895),f391(x6892,x6893,x6894,x6895)) % 187.68/187.66 [690]~E(x6901,x6902)+E(f391(x6903,x6901,x6904,x6905),f391(x6903,x6902,x6904,x6905)) % 187.68/187.66 [691]~E(x6911,x6912)+E(f391(x6913,x6914,x6911,x6915),f391(x6913,x6914,x6912,x6915)) % 187.68/187.66 [692]~E(x6921,x6922)+E(f391(x6923,x6924,x6925,x6921),f391(x6923,x6924,x6925,x6922)) % 187.68/187.66 [693]~E(x6931,x6932)+E(f252(x6931,x6933),f252(x6932,x6933)) % 187.68/187.66 [694]~E(x6941,x6942)+E(f252(x6943,x6941),f252(x6943,x6942)) % 187.68/187.66 [695]~E(x6951,x6952)+E(f126(x6951,x6953,x6954,x6955),f126(x6952,x6953,x6954,x6955)) % 187.68/187.66 [696]~E(x6961,x6962)+E(f126(x6963,x6961,x6964,x6965),f126(x6963,x6962,x6964,x6965)) % 187.68/187.66 [697]~E(x6971,x6972)+E(f126(x6973,x6974,x6971,x6975),f126(x6973,x6974,x6972,x6975)) % 187.68/187.66 [698]~E(x6981,x6982)+E(f126(x6983,x6984,x6985,x6981),f126(x6983,x6984,x6985,x6982)) % 187.68/187.66 [699]~E(x6991,x6992)+E(f283(x6991),f283(x6992)) % 187.68/187.66 [700]~E(x7001,x7002)+E(f11(x7001,x7003,x7004),f11(x7002,x7003,x7004)) % 187.68/187.66 [701]~E(x7011,x7012)+E(f11(x7013,x7011,x7014),f11(x7013,x7012,x7014)) % 187.68/187.66 [702]~E(x7021,x7022)+E(f11(x7023,x7024,x7021),f11(x7023,x7024,x7022)) % 187.68/187.66 [703]~E(x7031,x7032)+E(f408(x7031),f408(x7032)) % 187.68/187.66 [704]~E(x7041,x7042)+E(f799(x7041,x7043,x7044),f799(x7042,x7043,x7044)) % 187.68/187.66 [705]~E(x7051,x7052)+E(f799(x7053,x7051,x7054),f799(x7053,x7052,x7054)) % 187.68/187.66 [706]~E(x7061,x7062)+E(f799(x7063,x7064,x7061),f799(x7063,x7064,x7062)) % 187.68/187.66 [707]~E(x7071,x7072)+E(f453(x7071,x7073,x7074,x7075),f453(x7072,x7073,x7074,x7075)) % 187.68/187.66 [708]~E(x7081,x7082)+E(f453(x7083,x7081,x7084,x7085),f453(x7083,x7082,x7084,x7085)) % 187.68/187.66 [709]~E(x7091,x7092)+E(f453(x7093,x7094,x7091,x7095),f453(x7093,x7094,x7092,x7095)) % 187.68/187.66 [710]~E(x7101,x7102)+E(f453(x7103,x7104,x7105,x7101),f453(x7103,x7104,x7105,x7102)) % 187.68/187.66 [711]~E(x7111,x7112)+E(f339(x7111,x7113,x7114,x7115,x7116),f339(x7112,x7113,x7114,x7115,x7116)) % 187.68/187.66 [712]~E(x7121,x7122)+E(f339(x7123,x7121,x7124,x7125,x7126),f339(x7123,x7122,x7124,x7125,x7126)) % 187.68/187.66 [713]~E(x7131,x7132)+E(f339(x7133,x7134,x7131,x7135,x7136),f339(x7133,x7134,x7132,x7135,x7136)) % 187.68/187.66 [714]~E(x7141,x7142)+E(f339(x7143,x7144,x7145,x7141,x7146),f339(x7143,x7144,x7145,x7142,x7146)) % 187.68/187.66 [715]~E(x7151,x7152)+E(f339(x7153,x7154,x7155,x7156,x7151),f339(x7153,x7154,x7155,x7156,x7152)) % 187.68/187.66 [716]~E(x7161,x7162)+E(f317(x7161,x7163,x7164),f317(x7162,x7163,x7164)) % 187.68/187.66 [717]~E(x7171,x7172)+E(f317(x7173,x7171,x7174),f317(x7173,x7172,x7174)) % 187.68/187.66 [718]~E(x7181,x7182)+E(f317(x7183,x7184,x7181),f317(x7183,x7184,x7182)) % 187.68/187.66 [719]~E(x7191,x7192)+E(f152(x7191,x7193),f152(x7192,x7193)) % 187.68/187.66 [720]~E(x7201,x7202)+E(f152(x7203,x7201),f152(x7203,x7202)) % 187.68/187.66 [721]~E(x7211,x7212)+E(f686(x7211,x7213,x7214),f686(x7212,x7213,x7214)) % 187.68/187.66 [722]~E(x7221,x7222)+E(f686(x7223,x7221,x7224),f686(x7223,x7222,x7224)) % 187.68/187.66 [723]~E(x7231,x7232)+E(f686(x7233,x7234,x7231),f686(x7233,x7234,x7232)) % 187.68/187.66 [724]~E(x7241,x7242)+E(f368(x7241,x7243,x7244,x7245,x7246),f368(x7242,x7243,x7244,x7245,x7246)) % 187.68/187.66 [725]~E(x7251,x7252)+E(f368(x7253,x7251,x7254,x7255,x7256),f368(x7253,x7252,x7254,x7255,x7256)) % 187.68/187.66 [726]~E(x7261,x7262)+E(f368(x7263,x7264,x7261,x7265,x7266),f368(x7263,x7264,x7262,x7265,x7266)) % 187.68/187.66 [727]~E(x7271,x7272)+E(f368(x7273,x7274,x7275,x7271,x7276),f368(x7273,x7274,x7275,x7272,x7276)) % 187.68/187.66 [728]~E(x7281,x7282)+E(f368(x7283,x7284,x7285,x7286,x7281),f368(x7283,x7284,x7285,x7286,x7282)) % 187.68/187.66 [729]~E(x7291,x7292)+E(f690(x7291,x7293),f690(x7292,x7293)) % 187.68/187.66 [730]~E(x7301,x7302)+E(f690(x7303,x7301),f690(x7303,x7302)) % 187.68/187.66 [731]~E(x7311,x7312)+E(f275(x7311),f275(x7312)) % 187.68/187.66 [732]~E(x7321,x7322)+E(f512(x7321,x7323,x7324,x7325),f512(x7322,x7323,x7324,x7325)) % 187.68/187.66 [733]~E(x7331,x7332)+E(f512(x7333,x7331,x7334,x7335),f512(x7333,x7332,x7334,x7335)) % 187.68/187.66 [734]~E(x7341,x7342)+E(f512(x7343,x7344,x7341,x7345),f512(x7343,x7344,x7342,x7345)) % 187.68/187.66 [735]~E(x7351,x7352)+E(f512(x7353,x7354,x7355,x7351),f512(x7353,x7354,x7355,x7352)) % 187.68/187.66 [736]~E(x7361,x7362)+E(f781(x7361,x7363,x7364,x7365,x7366),f781(x7362,x7363,x7364,x7365,x7366)) % 187.68/187.66 [737]~E(x7371,x7372)+E(f781(x7373,x7371,x7374,x7375,x7376),f781(x7373,x7372,x7374,x7375,x7376)) % 187.68/187.66 [738]~E(x7381,x7382)+E(f781(x7383,x7384,x7381,x7385,x7386),f781(x7383,x7384,x7382,x7385,x7386)) % 187.68/187.66 [739]~E(x7391,x7392)+E(f781(x7393,x7394,x7395,x7391,x7396),f781(x7393,x7394,x7395,x7392,x7396)) % 187.68/187.66 [740]~E(x7401,x7402)+E(f781(x7403,x7404,x7405,x7406,x7401),f781(x7403,x7404,x7405,x7406,x7402)) % 187.68/187.66 [741]~E(x7411,x7412)+E(f287(x7411,x7413),f287(x7412,x7413)) % 187.68/187.66 [742]~E(x7421,x7422)+E(f287(x7423,x7421),f287(x7423,x7422)) % 187.68/187.66 [743]~E(x7431,x7432)+E(f50(x7431,x7433),f50(x7432,x7433)) % 187.68/187.66 [744]~E(x7441,x7442)+E(f50(x7443,x7441),f50(x7443,x7442)) % 187.68/187.66 [745]~E(x7451,x7452)+E(f664(x7451,x7453,x7454,x7455,x7456,x7457,x7458),f664(x7452,x7453,x7454,x7455,x7456,x7457,x7458)) % 187.68/187.66 [746]~E(x7461,x7462)+E(f664(x7463,x7461,x7464,x7465,x7466,x7467,x7468),f664(x7463,x7462,x7464,x7465,x7466,x7467,x7468)) % 187.68/187.66 [747]~E(x7471,x7472)+E(f664(x7473,x7474,x7471,x7475,x7476,x7477,x7478),f664(x7473,x7474,x7472,x7475,x7476,x7477,x7478)) % 187.68/187.66 [748]~E(x7481,x7482)+E(f664(x7483,x7484,x7485,x7481,x7486,x7487,x7488),f664(x7483,x7484,x7485,x7482,x7486,x7487,x7488)) % 187.68/187.66 [749]~E(x7491,x7492)+E(f664(x7493,x7494,x7495,x7496,x7491,x7497,x7498),f664(x7493,x7494,x7495,x7496,x7492,x7497,x7498)) % 187.68/187.66 [750]~E(x7501,x7502)+E(f664(x7503,x7504,x7505,x7506,x7507,x7501,x7508),f664(x7503,x7504,x7505,x7506,x7507,x7502,x7508)) % 187.68/187.66 [751]~E(x7511,x7512)+E(f664(x7513,x7514,x7515,x7516,x7517,x7518,x7511),f664(x7513,x7514,x7515,x7516,x7517,x7518,x7512)) % 187.68/187.66 [752]~E(x7521,x7522)+E(f407(x7521,x7523,x7524,x7525,x7526),f407(x7522,x7523,x7524,x7525,x7526)) % 187.68/187.66 [753]~E(x7531,x7532)+E(f407(x7533,x7531,x7534,x7535,x7536),f407(x7533,x7532,x7534,x7535,x7536)) % 187.68/187.66 [754]~E(x7541,x7542)+E(f407(x7543,x7544,x7541,x7545,x7546),f407(x7543,x7544,x7542,x7545,x7546)) % 187.68/187.66 [755]~E(x7551,x7552)+E(f407(x7553,x7554,x7555,x7551,x7556),f407(x7553,x7554,x7555,x7552,x7556)) % 187.68/187.66 [756]~E(x7561,x7562)+E(f407(x7563,x7564,x7565,x7566,x7561),f407(x7563,x7564,x7565,x7566,x7562)) % 187.68/187.66 [757]~E(x7571,x7572)+E(f595(x7571,x7573,x7574),f595(x7572,x7573,x7574)) % 187.68/187.66 [758]~E(x7581,x7582)+E(f595(x7583,x7581,x7584),f595(x7583,x7582,x7584)) % 187.68/187.66 [759]~E(x7591,x7592)+E(f595(x7593,x7594,x7591),f595(x7593,x7594,x7592)) % 187.68/187.66 [760]~E(x7601,x7602)+E(f727(x7601,x7603,x7604),f727(x7602,x7603,x7604)) % 187.68/187.66 [761]~E(x7611,x7612)+E(f727(x7613,x7611,x7614),f727(x7613,x7612,x7614)) % 187.68/187.66 [762]~E(x7621,x7622)+E(f727(x7623,x7624,x7621),f727(x7623,x7624,x7622)) % 187.68/187.66 [763]~E(x7631,x7632)+E(f703(x7631,x7633,x7634,x7635,x7636),f703(x7632,x7633,x7634,x7635,x7636)) % 187.68/187.66 [764]~E(x7641,x7642)+E(f703(x7643,x7641,x7644,x7645,x7646),f703(x7643,x7642,x7644,x7645,x7646)) % 187.68/187.66 [765]~E(x7651,x7652)+E(f703(x7653,x7654,x7651,x7655,x7656),f703(x7653,x7654,x7652,x7655,x7656)) % 187.68/187.66 [766]~E(x7661,x7662)+E(f703(x7663,x7664,x7665,x7661,x7666),f703(x7663,x7664,x7665,x7662,x7666)) % 187.68/187.66 [767]~E(x7671,x7672)+E(f703(x7673,x7674,x7675,x7676,x7671),f703(x7673,x7674,x7675,x7676,x7672)) % 187.68/187.66 [768]~E(x7681,x7682)+E(f489(x7681,x7683,x7684,x7685),f489(x7682,x7683,x7684,x7685)) % 187.68/187.66 [769]~E(x7691,x7692)+E(f489(x7693,x7691,x7694,x7695),f489(x7693,x7692,x7694,x7695)) % 187.68/187.66 [770]~E(x7701,x7702)+E(f489(x7703,x7704,x7701,x7705),f489(x7703,x7704,x7702,x7705)) % 187.68/187.66 [771]~E(x7711,x7712)+E(f489(x7713,x7714,x7715,x7711),f489(x7713,x7714,x7715,x7712)) % 187.68/187.66 [772]~E(x7721,x7722)+E(f182(x7721,x7723,x7724,x7725),f182(x7722,x7723,x7724,x7725)) % 187.68/187.66 [773]~E(x7731,x7732)+E(f182(x7733,x7731,x7734,x7735),f182(x7733,x7732,x7734,x7735)) % 187.68/187.66 [774]~E(x7741,x7742)+E(f182(x7743,x7744,x7741,x7745),f182(x7743,x7744,x7742,x7745)) % 187.68/187.66 [775]~E(x7751,x7752)+E(f182(x7753,x7754,x7755,x7751),f182(x7753,x7754,x7755,x7752)) % 187.68/187.66 [776]~E(x7761,x7762)+E(f559(x7761,x7763,x7764),f559(x7762,x7763,x7764)) % 187.68/187.66 [777]~E(x7771,x7772)+E(f559(x7773,x7771,x7774),f559(x7773,x7772,x7774)) % 187.68/187.66 [778]~E(x7781,x7782)+E(f559(x7783,x7784,x7781),f559(x7783,x7784,x7782)) % 187.68/187.66 [779]~E(x7791,x7792)+E(f592(x7791,x7793,x7794),f592(x7792,x7793,x7794)) % 187.68/187.66 [780]~E(x7801,x7802)+E(f592(x7803,x7801,x7804),f592(x7803,x7802,x7804)) % 187.68/187.66 [781]~E(x7811,x7812)+E(f592(x7813,x7814,x7811),f592(x7813,x7814,x7812)) % 187.68/187.66 [782]~E(x7821,x7822)+E(f820(x7821),f820(x7822)) % 187.68/187.66 [783]~E(x7831,x7832)+E(f624(x7831,x7833,x7834,x7835,x7836),f624(x7832,x7833,x7834,x7835,x7836)) % 187.68/187.66 [784]~E(x7841,x7842)+E(f624(x7843,x7841,x7844,x7845,x7846),f624(x7843,x7842,x7844,x7845,x7846)) % 187.68/187.66 [785]~E(x7851,x7852)+E(f624(x7853,x7854,x7851,x7855,x7856),f624(x7853,x7854,x7852,x7855,x7856)) % 187.68/187.66 [786]~E(x7861,x7862)+E(f624(x7863,x7864,x7865,x7861,x7866),f624(x7863,x7864,x7865,x7862,x7866)) % 187.68/187.66 [787]~E(x7871,x7872)+E(f624(x7873,x7874,x7875,x7876,x7871),f624(x7873,x7874,x7875,x7876,x7872)) % 187.68/187.66 [788]~E(x7881,x7882)+E(f191(x7881),f191(x7882)) % 187.68/187.66 [789]~E(x7891,x7892)+E(f776(x7891,x7893,x7894,x7895,x7896),f776(x7892,x7893,x7894,x7895,x7896)) % 187.68/187.66 [790]~E(x7901,x7902)+E(f776(x7903,x7901,x7904,x7905,x7906),f776(x7903,x7902,x7904,x7905,x7906)) % 187.68/187.66 [791]~E(x7911,x7912)+E(f776(x7913,x7914,x7911,x7915,x7916),f776(x7913,x7914,x7912,x7915,x7916)) % 187.68/187.66 [792]~E(x7921,x7922)+E(f776(x7923,x7924,x7925,x7921,x7926),f776(x7923,x7924,x7925,x7922,x7926)) % 187.68/187.66 [793]~E(x7931,x7932)+E(f776(x7933,x7934,x7935,x7936,x7931),f776(x7933,x7934,x7935,x7936,x7932)) % 187.68/187.66 [794]~E(x7941,x7942)+E(f809(x7941,x7943,x7944),f809(x7942,x7943,x7944)) % 187.68/187.66 [795]~E(x7951,x7952)+E(f809(x7953,x7951,x7954),f809(x7953,x7952,x7954)) % 187.68/187.66 [796]~E(x7961,x7962)+E(f809(x7963,x7964,x7961),f809(x7963,x7964,x7962)) % 187.68/187.66 [797]~E(x7971,x7972)+E(f123(x7971,x7973),f123(x7972,x7973)) % 187.68/187.66 [798]~E(x7981,x7982)+E(f123(x7983,x7981),f123(x7983,x7982)) % 187.68/187.66 [799]~E(x7991,x7992)+E(f647(x7991,x7993,x7994,x7995),f647(x7992,x7993,x7994,x7995)) % 187.68/187.66 [800]~E(x8001,x8002)+E(f647(x8003,x8001,x8004,x8005),f647(x8003,x8002,x8004,x8005)) % 187.68/187.66 [801]~E(x8011,x8012)+E(f647(x8013,x8014,x8011,x8015),f647(x8013,x8014,x8012,x8015)) % 187.68/187.66 [802]~E(x8021,x8022)+E(f647(x8023,x8024,x8025,x8021),f647(x8023,x8024,x8025,x8022)) % 187.68/187.66 [803]~E(x8031,x8032)+E(f522(x8031,x8033,x8034,x8035,x8036,x8037),f522(x8032,x8033,x8034,x8035,x8036,x8037)) % 187.68/187.66 [804]~E(x8041,x8042)+E(f522(x8043,x8041,x8044,x8045,x8046,x8047),f522(x8043,x8042,x8044,x8045,x8046,x8047)) % 187.68/187.66 [805]~E(x8051,x8052)+E(f522(x8053,x8054,x8051,x8055,x8056,x8057),f522(x8053,x8054,x8052,x8055,x8056,x8057)) % 187.68/187.66 [806]~E(x8061,x8062)+E(f522(x8063,x8064,x8065,x8061,x8066,x8067),f522(x8063,x8064,x8065,x8062,x8066,x8067)) % 187.68/187.66 [807]~E(x8071,x8072)+E(f522(x8073,x8074,x8075,x8076,x8071,x8077),f522(x8073,x8074,x8075,x8076,x8072,x8077)) % 187.68/187.66 [808]~E(x8081,x8082)+E(f522(x8083,x8084,x8085,x8086,x8087,x8081),f522(x8083,x8084,x8085,x8086,x8087,x8082)) % 187.68/187.66 [809]~E(x8091,x8092)+E(f714(x8091,x8093,x8094,x8095),f714(x8092,x8093,x8094,x8095)) % 187.68/187.66 [810]~E(x8101,x8102)+E(f714(x8103,x8101,x8104,x8105),f714(x8103,x8102,x8104,x8105)) % 187.68/187.66 [811]~E(x8111,x8112)+E(f714(x8113,x8114,x8111,x8115),f714(x8113,x8114,x8112,x8115)) % 187.68/187.66 [812]~E(x8121,x8122)+E(f714(x8123,x8124,x8125,x8121),f714(x8123,x8124,x8125,x8122)) % 187.68/187.66 [813]~E(x8131,x8132)+E(f557(x8131,x8133,x8134),f557(x8132,x8133,x8134)) % 187.68/187.66 [814]~E(x8141,x8142)+E(f557(x8143,x8141,x8144),f557(x8143,x8142,x8144)) % 187.68/187.66 [815]~E(x8151,x8152)+E(f557(x8153,x8154,x8151),f557(x8153,x8154,x8152)) % 187.68/187.66 [816]~E(x8161,x8162)+E(f735(x8161,x8163,x8164),f735(x8162,x8163,x8164)) % 187.68/187.66 [817]~E(x8171,x8172)+E(f735(x8173,x8171,x8174),f735(x8173,x8172,x8174)) % 187.68/187.66 [818]~E(x8181,x8182)+E(f735(x8183,x8184,x8181),f735(x8183,x8184,x8182)) % 187.68/187.66 [819]~E(x8191,x8192)+E(f747(x8191,x8193,x8194),f747(x8192,x8193,x8194)) % 187.68/187.66 [820]~E(x8201,x8202)+E(f747(x8203,x8201,x8204),f747(x8203,x8202,x8204)) % 187.68/187.66 [821]~E(x8211,x8212)+E(f747(x8213,x8214,x8211),f747(x8213,x8214,x8212)) % 187.68/187.66 [822]~E(x8221,x8222)+E(f697(x8221,x8223,x8224,x8225,x8226),f697(x8222,x8223,x8224,x8225,x8226)) % 187.68/187.66 [823]~E(x8231,x8232)+E(f697(x8233,x8231,x8234,x8235,x8236),f697(x8233,x8232,x8234,x8235,x8236)) % 187.68/187.66 [824]~E(x8241,x8242)+E(f697(x8243,x8244,x8241,x8245,x8246),f697(x8243,x8244,x8242,x8245,x8246)) % 187.68/187.66 [825]~E(x8251,x8252)+E(f697(x8253,x8254,x8255,x8251,x8256),f697(x8253,x8254,x8255,x8252,x8256)) % 187.68/187.66 [826]~E(x8261,x8262)+E(f697(x8263,x8264,x8265,x8266,x8261),f697(x8263,x8264,x8265,x8266,x8262)) % 187.68/187.66 [827]~E(x8271,x8272)+E(f217(x8271,x8273,x8274,x8275,x8276),f217(x8272,x8273,x8274,x8275,x8276)) % 187.68/187.66 [828]~E(x8281,x8282)+E(f217(x8283,x8281,x8284,x8285,x8286),f217(x8283,x8282,x8284,x8285,x8286)) % 187.68/187.66 [829]~E(x8291,x8292)+E(f217(x8293,x8294,x8291,x8295,x8296),f217(x8293,x8294,x8292,x8295,x8296)) % 187.68/187.66 [830]~E(x8301,x8302)+E(f217(x8303,x8304,x8305,x8301,x8306),f217(x8303,x8304,x8305,x8302,x8306)) % 187.68/187.66 [831]~E(x8311,x8312)+E(f217(x8313,x8314,x8315,x8316,x8311),f217(x8313,x8314,x8315,x8316,x8312)) % 187.68/187.66 [832]~E(x8321,x8322)+E(f653(x8321,x8323,x8324),f653(x8322,x8323,x8324)) % 187.68/187.66 [833]~E(x8331,x8332)+E(f653(x8333,x8331,x8334),f653(x8333,x8332,x8334)) % 187.68/187.66 [834]~E(x8341,x8342)+E(f653(x8343,x8344,x8341),f653(x8343,x8344,x8342)) % 187.68/187.66 [835]~E(x8351,x8352)+E(f344(x8351,x8353,x8354),f344(x8352,x8353,x8354)) % 187.68/187.66 [836]~E(x8361,x8362)+E(f344(x8363,x8361,x8364),f344(x8363,x8362,x8364)) % 187.68/187.66 [837]~E(x8371,x8372)+E(f344(x8373,x8374,x8371),f344(x8373,x8374,x8372)) % 187.68/187.66 [838]~E(x8381,x8382)+E(f708(x8381,x8383,x8384),f708(x8382,x8383,x8384)) % 187.68/187.66 [839]~E(x8391,x8392)+E(f708(x8393,x8391,x8394),f708(x8393,x8392,x8394)) % 187.68/187.66 [840]~E(x8401,x8402)+E(f708(x8403,x8404,x8401),f708(x8403,x8404,x8402)) % 187.68/187.66 [841]~E(x8411,x8412)+E(f792(x8411,x8413,x8414,x8415,x8416),f792(x8412,x8413,x8414,x8415,x8416)) % 187.68/187.66 [842]~E(x8421,x8422)+E(f792(x8423,x8421,x8424,x8425,x8426),f792(x8423,x8422,x8424,x8425,x8426)) % 187.68/187.66 [843]~E(x8431,x8432)+E(f792(x8433,x8434,x8431,x8435,x8436),f792(x8433,x8434,x8432,x8435,x8436)) % 187.68/187.66 [844]~E(x8441,x8442)+E(f792(x8443,x8444,x8445,x8441,x8446),f792(x8443,x8444,x8445,x8442,x8446)) % 187.68/187.66 [845]~E(x8451,x8452)+E(f792(x8453,x8454,x8455,x8456,x8451),f792(x8453,x8454,x8455,x8456,x8452)) % 187.68/187.66 [846]~E(x8461,x8462)+E(f377(x8461,x8463,x8464),f377(x8462,x8463,x8464)) % 187.68/187.66 [847]~E(x8471,x8472)+E(f377(x8473,x8471,x8474),f377(x8473,x8472,x8474)) % 187.68/187.66 [848]~E(x8481,x8482)+E(f377(x8483,x8484,x8481),f377(x8483,x8484,x8482)) % 187.68/187.66 [849]~E(x8491,x8492)+E(f316(x8491,x8493,x8494),f316(x8492,x8493,x8494)) % 187.68/187.66 [850]~E(x8501,x8502)+E(f316(x8503,x8501,x8504),f316(x8503,x8502,x8504)) % 187.68/187.66 [851]~E(x8511,x8512)+E(f316(x8513,x8514,x8511),f316(x8513,x8514,x8512)) % 187.68/187.66 [852]~E(x8521,x8522)+E(f521(x8521,x8523,x8524,x8525,x8526,x8527),f521(x8522,x8523,x8524,x8525,x8526,x8527)) % 187.68/187.66 [853]~E(x8531,x8532)+E(f521(x8533,x8531,x8534,x8535,x8536,x8537),f521(x8533,x8532,x8534,x8535,x8536,x8537)) % 187.68/187.66 [854]~E(x8541,x8542)+E(f521(x8543,x8544,x8541,x8545,x8546,x8547),f521(x8543,x8544,x8542,x8545,x8546,x8547)) % 187.68/187.66 [855]~E(x8551,x8552)+E(f521(x8553,x8554,x8555,x8551,x8556,x8557),f521(x8553,x8554,x8555,x8552,x8556,x8557)) % 187.68/187.66 [856]~E(x8561,x8562)+E(f521(x8563,x8564,x8565,x8566,x8561,x8567),f521(x8563,x8564,x8565,x8566,x8562,x8567)) % 187.68/187.66 [857]~E(x8571,x8572)+E(f521(x8573,x8574,x8575,x8576,x8577,x8571),f521(x8573,x8574,x8575,x8576,x8577,x8572)) % 187.68/187.66 [858]~E(x8581,x8582)+E(f833(x8581),f833(x8582)) % 187.68/187.66 [859]~E(x8591,x8592)+E(f493(x8591),f493(x8592)) % 187.68/187.66 [860]~E(x8601,x8602)+E(f396(x8601,x8603),f396(x8602,x8603)) % 187.68/187.66 [861]~E(x8611,x8612)+E(f396(x8613,x8611),f396(x8613,x8612)) % 187.68/187.66 [862]~E(x8621,x8622)+E(f734(x8621,x8623,x8624),f734(x8622,x8623,x8624)) % 187.68/187.66 [863]~E(x8631,x8632)+E(f734(x8633,x8631,x8634),f734(x8633,x8632,x8634)) % 187.68/187.66 [864]~E(x8641,x8642)+E(f734(x8643,x8644,x8641),f734(x8643,x8644,x8642)) % 187.68/187.66 [865]~E(x8651,x8652)+E(f798(x8651,x8653,x8654),f798(x8652,x8653,x8654)) % 187.68/187.66 [866]~E(x8661,x8662)+E(f798(x8663,x8661,x8664),f798(x8663,x8662,x8664)) % 187.68/187.66 [867]~E(x8671,x8672)+E(f798(x8673,x8674,x8671),f798(x8673,x8674,x8672)) % 187.68/187.66 [868]~E(x8681,x8682)+E(f255(x8681,x8683,x8684,x8685),f255(x8682,x8683,x8684,x8685)) % 187.68/187.66 [869]~E(x8691,x8692)+E(f255(x8693,x8691,x8694,x8695),f255(x8693,x8692,x8694,x8695)) % 187.68/187.66 [870]~E(x8701,x8702)+E(f255(x8703,x8704,x8701,x8705),f255(x8703,x8704,x8702,x8705)) % 187.68/187.66 [871]~E(x8711,x8712)+E(f255(x8713,x8714,x8715,x8711),f255(x8713,x8714,x8715,x8712)) % 187.68/187.66 [872]~E(x8721,x8722)+E(f625(x8721,x8723,x8724,x8725,x8726),f625(x8722,x8723,x8724,x8725,x8726)) % 187.68/187.66 [873]~E(x8731,x8732)+E(f625(x8733,x8731,x8734,x8735,x8736),f625(x8733,x8732,x8734,x8735,x8736)) % 187.68/187.66 [874]~E(x8741,x8742)+E(f625(x8743,x8744,x8741,x8745,x8746),f625(x8743,x8744,x8742,x8745,x8746)) % 187.68/187.66 [875]~E(x8751,x8752)+E(f625(x8753,x8754,x8755,x8751,x8756),f625(x8753,x8754,x8755,x8752,x8756)) % 187.68/187.66 [876]~E(x8761,x8762)+E(f625(x8763,x8764,x8765,x8766,x8761),f625(x8763,x8764,x8765,x8766,x8762)) % 187.68/187.66 [877]~E(x8771,x8772)+E(f414(x8771,x8773,x8774,x8775),f414(x8772,x8773,x8774,x8775)) % 187.68/187.66 [878]~E(x8781,x8782)+E(f414(x8783,x8781,x8784,x8785),f414(x8783,x8782,x8784,x8785)) % 187.68/187.66 [879]~E(x8791,x8792)+E(f414(x8793,x8794,x8791,x8795),f414(x8793,x8794,x8792,x8795)) % 187.68/187.66 [880]~E(x8801,x8802)+E(f414(x8803,x8804,x8805,x8801),f414(x8803,x8804,x8805,x8802)) % 187.68/187.66 [881]~E(x8811,x8812)+E(f54(x8811,x8813),f54(x8812,x8813)) % 187.68/187.66 [882]~E(x8821,x8822)+E(f54(x8823,x8821),f54(x8823,x8822)) % 187.68/187.66 [883]~E(x8831,x8832)+E(f436(x8831,x8833,x8834),f436(x8832,x8833,x8834)) % 187.68/187.66 [884]~E(x8841,x8842)+E(f436(x8843,x8841,x8844),f436(x8843,x8842,x8844)) % 187.68/187.66 [885]~E(x8851,x8852)+E(f436(x8853,x8854,x8851),f436(x8853,x8854,x8852)) % 187.68/187.66 [886]~E(x8861,x8862)+E(f646(x8861,x8863,x8864),f646(x8862,x8863,x8864)) % 187.68/187.66 [887]~E(x8871,x8872)+E(f646(x8873,x8871,x8874),f646(x8873,x8872,x8874)) % 187.68/187.66 [888]~E(x8881,x8882)+E(f646(x8883,x8884,x8881),f646(x8883,x8884,x8882)) % 187.68/187.66 [889]~E(x8891,x8892)+E(f300(x8891,x8893,x8894),f300(x8892,x8893,x8894)) % 187.68/187.66 [890]~E(x8901,x8902)+E(f300(x8903,x8901,x8904),f300(x8903,x8902,x8904)) % 187.68/187.66 [891]~E(x8911,x8912)+E(f300(x8913,x8914,x8911),f300(x8913,x8914,x8912)) % 187.68/187.66 [892]~E(x8921,x8922)+E(f178(x8921,x8923,x8924,x8925,x8926),f178(x8922,x8923,x8924,x8925,x8926)) % 187.68/187.66 [893]~E(x8931,x8932)+E(f178(x8933,x8931,x8934,x8935,x8936),f178(x8933,x8932,x8934,x8935,x8936)) % 187.68/187.66 [894]~E(x8941,x8942)+E(f178(x8943,x8944,x8941,x8945,x8946),f178(x8943,x8944,x8942,x8945,x8946)) % 187.68/187.66 [895]~E(x8951,x8952)+E(f178(x8953,x8954,x8955,x8951,x8956),f178(x8953,x8954,x8955,x8952,x8956)) % 187.68/187.66 [896]~E(x8961,x8962)+E(f178(x8963,x8964,x8965,x8966,x8961),f178(x8963,x8964,x8965,x8966,x8962)) % 187.68/187.66 [897]~E(x8971,x8972)+E(f555(x8971,x8973,x8974),f555(x8972,x8973,x8974)) % 187.68/187.66 [898]~E(x8981,x8982)+E(f555(x8983,x8981,x8984),f555(x8983,x8982,x8984)) % 187.68/187.66 [899]~E(x8991,x8992)+E(f555(x8993,x8994,x8991),f555(x8993,x8994,x8992)) % 187.68/187.66 [900]~E(x9001,x9002)+E(f857(x9001,x9003,x9004),f857(x9002,x9003,x9004)) % 187.68/187.66 [901]~E(x9011,x9012)+E(f857(x9013,x9011,x9014),f857(x9013,x9012,x9014)) % 187.68/187.66 [902]~E(x9021,x9022)+E(f857(x9023,x9024,x9021),f857(x9023,x9024,x9022)) % 187.68/187.66 [903]~E(x9031,x9032)+E(f668(x9031,x9033,x9034,x9035),f668(x9032,x9033,x9034,x9035)) % 187.68/187.66 [904]~E(x9041,x9042)+E(f668(x9043,x9041,x9044,x9045),f668(x9043,x9042,x9044,x9045)) % 187.68/187.66 [905]~E(x9051,x9052)+E(f668(x9053,x9054,x9051,x9055),f668(x9053,x9054,x9052,x9055)) % 187.68/187.66 [906]~E(x9061,x9062)+E(f668(x9063,x9064,x9065,x9061),f668(x9063,x9064,x9065,x9062)) % 187.68/187.66 [907]~E(x9071,x9072)+E(f78(x9071,x9073,x9074,x9075),f78(x9072,x9073,x9074,x9075)) % 187.68/187.66 [908]~E(x9081,x9082)+E(f78(x9083,x9081,x9084,x9085),f78(x9083,x9082,x9084,x9085)) % 187.68/187.66 [909]~E(x9091,x9092)+E(f78(x9093,x9094,x9091,x9095),f78(x9093,x9094,x9092,x9095)) % 187.68/187.66 [910]~E(x9101,x9102)+E(f78(x9103,x9104,x9105,x9101),f78(x9103,x9104,x9105,x9102)) % 187.68/187.66 [911]~E(x9111,x9112)+E(f744(x9111,x9113,x9114),f744(x9112,x9113,x9114)) % 187.68/187.66 [912]~E(x9121,x9122)+E(f744(x9123,x9121,x9124),f744(x9123,x9122,x9124)) % 187.68/187.66 [913]~E(x9131,x9132)+E(f744(x9133,x9134,x9131),f744(x9133,x9134,x9132)) % 187.68/187.66 [914]~E(x9141,x9142)+E(f319(x9141,x9143,x9144),f319(x9142,x9143,x9144)) % 187.68/187.66 [915]~E(x9151,x9152)+E(f319(x9153,x9151,x9154),f319(x9153,x9152,x9154)) % 187.68/187.66 [916]~E(x9161,x9162)+E(f319(x9163,x9164,x9161),f319(x9163,x9164,x9162)) % 187.68/187.66 [917]~E(x9171,x9172)+E(f529(x9171,x9173,x9174,x9175),f529(x9172,x9173,x9174,x9175)) % 187.68/187.66 [918]~E(x9181,x9182)+E(f529(x9183,x9181,x9184,x9185),f529(x9183,x9182,x9184,x9185)) % 187.68/187.66 [919]~E(x9191,x9192)+E(f529(x9193,x9194,x9191,x9195),f529(x9193,x9194,x9192,x9195)) % 187.68/187.66 [920]~E(x9201,x9202)+E(f529(x9203,x9204,x9205,x9201),f529(x9203,x9204,x9205,x9202)) % 187.68/187.66 [921]~E(x9211,x9212)+E(f359(x9211,x9213,x9214),f359(x9212,x9213,x9214)) % 187.68/187.66 [922]~E(x9221,x9222)+E(f359(x9223,x9221,x9224),f359(x9223,x9222,x9224)) % 187.68/187.66 [923]~E(x9231,x9232)+E(f359(x9233,x9234,x9231),f359(x9233,x9234,x9232)) % 187.68/187.66 [924]~E(x9241,x9242)+E(f831(x9241,x9243),f831(x9242,x9243)) % 187.68/187.66 [925]~E(x9251,x9252)+E(f831(x9253,x9251),f831(x9253,x9252)) % 187.68/187.66 [926]~E(x9261,x9262)+E(f785(x9261,x9263,x9264),f785(x9262,x9263,x9264)) % 187.68/187.66 [927]~E(x9271,x9272)+E(f785(x9273,x9271,x9274),f785(x9273,x9272,x9274)) % 187.68/187.66 [928]~E(x9281,x9282)+E(f785(x9283,x9284,x9281),f785(x9283,x9284,x9282)) % 187.68/187.66 [929]~E(x9291,x9292)+E(f761(x9291,x9293,x9294,x9295,x9296),f761(x9292,x9293,x9294,x9295,x9296)) % 187.68/187.66 [930]~E(x9301,x9302)+E(f761(x9303,x9301,x9304,x9305,x9306),f761(x9303,x9302,x9304,x9305,x9306)) % 187.68/187.66 [931]~E(x9311,x9312)+E(f761(x9313,x9314,x9311,x9315,x9316),f761(x9313,x9314,x9312,x9315,x9316)) % 187.68/187.66 [932]~E(x9321,x9322)+E(f761(x9323,x9324,x9325,x9321,x9326),f761(x9323,x9324,x9325,x9322,x9326)) % 187.68/187.66 [933]~E(x9331,x9332)+E(f761(x9333,x9334,x9335,x9336,x9331),f761(x9333,x9334,x9335,x9336,x9332)) % 187.68/187.66 [934]~E(x9341,x9342)+E(f611(x9341,x9343,x9344),f611(x9342,x9343,x9344)) % 187.68/187.66 [935]~E(x9351,x9352)+E(f611(x9353,x9351,x9354),f611(x9353,x9352,x9354)) % 187.68/187.66 [936]~E(x9361,x9362)+E(f611(x9363,x9364,x9361),f611(x9363,x9364,x9362)) % 187.68/187.66 [937]~E(x9371,x9372)+E(f707(x9371,x9373,x9374,x9375),f707(x9372,x9373,x9374,x9375)) % 187.68/187.66 [938]~E(x9381,x9382)+E(f707(x9383,x9381,x9384,x9385),f707(x9383,x9382,x9384,x9385)) % 187.68/187.66 [939]~E(x9391,x9392)+E(f707(x9393,x9394,x9391,x9395),f707(x9393,x9394,x9392,x9395)) % 187.68/187.66 [940]~E(x9401,x9402)+E(f707(x9403,x9404,x9405,x9401),f707(x9403,x9404,x9405,x9402)) % 187.68/187.66 [941]~E(x9411,x9412)+E(f69(x9411,x9413,x9414),f69(x9412,x9413,x9414)) % 187.68/187.66 [942]~E(x9421,x9422)+E(f69(x9423,x9421,x9424),f69(x9423,x9422,x9424)) % 187.68/187.66 [943]~E(x9431,x9432)+E(f69(x9433,x9434,x9431),f69(x9433,x9434,x9432)) % 187.68/187.66 [944]~E(x9441,x9442)+E(f635(x9441,x9443,x9444),f635(x9442,x9443,x9444)) % 187.68/187.66 [945]~E(x9451,x9452)+E(f635(x9453,x9451,x9454),f635(x9453,x9452,x9454)) % 187.68/187.66 [946]~E(x9461,x9462)+E(f635(x9463,x9464,x9461),f635(x9463,x9464,x9462)) % 187.68/187.66 [947]~E(x9471,x9472)+E(f476(x9471,x9473,x9474),f476(x9472,x9473,x9474)) % 187.68/187.66 [948]~E(x9481,x9482)+E(f476(x9483,x9481,x9484),f476(x9483,x9482,x9484)) % 187.68/187.66 [949]~E(x9491,x9492)+E(f476(x9493,x9494,x9491),f476(x9493,x9494,x9492)) % 187.68/187.66 [950]~E(x9501,x9502)+E(f61(x9501,x9503,x9504,x9505),f61(x9502,x9503,x9504,x9505)) % 187.68/187.66 [951]~E(x9511,x9512)+E(f61(x9513,x9511,x9514,x9515),f61(x9513,x9512,x9514,x9515)) % 187.68/187.66 [952]~E(x9521,x9522)+E(f61(x9523,x9524,x9521,x9525),f61(x9523,x9524,x9522,x9525)) % 187.68/187.66 [953]~E(x9531,x9532)+E(f61(x9533,x9534,x9535,x9531),f61(x9533,x9534,x9535,x9532)) % 187.68/187.66 [954]~E(x9541,x9542)+E(f427(x9541,x9543,x9544),f427(x9542,x9543,x9544)) % 187.68/187.66 [955]~E(x9551,x9552)+E(f427(x9553,x9551,x9554),f427(x9553,x9552,x9554)) % 187.68/187.66 [956]~E(x9561,x9562)+E(f427(x9563,x9564,x9561),f427(x9563,x9564,x9562)) % 187.68/187.66 [957]~E(x9571,x9572)+E(f363(x9571,x9573),f363(x9572,x9573)) % 187.68/187.66 [958]~E(x9581,x9582)+E(f363(x9583,x9581),f363(x9583,x9582)) % 187.68/187.66 [959]~E(x9591,x9592)+E(f541(x9591,x9593,x9594),f541(x9592,x9593,x9594)) % 187.68/187.66 [960]~E(x9601,x9602)+E(f541(x9603,x9601,x9604),f541(x9603,x9602,x9604)) % 187.68/187.66 [961]~E(x9611,x9612)+E(f541(x9613,x9614,x9611),f541(x9613,x9614,x9612)) % 187.68/187.66 [962]~E(x9621,x9622)+E(f375(x9621,x9623,x9624,x9625),f375(x9622,x9623,x9624,x9625)) % 187.68/187.66 [963]~E(x9631,x9632)+E(f375(x9633,x9631,x9634,x9635),f375(x9633,x9632,x9634,x9635)) % 187.68/187.66 [964]~E(x9641,x9642)+E(f375(x9643,x9644,x9641,x9645),f375(x9643,x9644,x9642,x9645)) % 187.68/187.66 [965]~E(x9651,x9652)+E(f375(x9653,x9654,x9655,x9651),f375(x9653,x9654,x9655,x9652)) % 187.68/187.66 [966]~E(x9661,x9662)+E(f55(x9661,x9663),f55(x9662,x9663)) % 187.68/187.66 [967]~E(x9671,x9672)+E(f55(x9673,x9671),f55(x9673,x9672)) % 187.68/187.66 [968]~E(x9681,x9682)+E(f749(x9681,x9683,x9684),f749(x9682,x9683,x9684)) % 187.68/187.66 [969]~E(x9691,x9692)+E(f749(x9693,x9691,x9694),f749(x9693,x9692,x9694)) % 187.68/187.66 [970]~E(x9701,x9702)+E(f749(x9703,x9704,x9701),f749(x9703,x9704,x9702)) % 187.68/187.66 [971]~E(x9711,x9712)+E(f196(x9711),f196(x9712)) % 187.68/187.66 [972]~E(x9721,x9722)+E(f782(x9721,x9723,x9724,x9725,x9726,x9727,x9728),f782(x9722,x9723,x9724,x9725,x9726,x9727,x9728)) % 187.68/187.66 [973]~E(x9731,x9732)+E(f782(x9733,x9731,x9734,x9735,x9736,x9737,x9738),f782(x9733,x9732,x9734,x9735,x9736,x9737,x9738)) % 187.68/187.66 [974]~E(x9741,x9742)+E(f782(x9743,x9744,x9741,x9745,x9746,x9747,x9748),f782(x9743,x9744,x9742,x9745,x9746,x9747,x9748)) % 187.68/187.66 [975]~E(x9751,x9752)+E(f782(x9753,x9754,x9755,x9751,x9756,x9757,x9758),f782(x9753,x9754,x9755,x9752,x9756,x9757,x9758)) % 187.68/187.66 [976]~E(x9761,x9762)+E(f782(x9763,x9764,x9765,x9766,x9761,x9767,x9768),f782(x9763,x9764,x9765,x9766,x9762,x9767,x9768)) % 187.68/187.66 [977]~E(x9771,x9772)+E(f782(x9773,x9774,x9775,x9776,x9777,x9771,x9778),f782(x9773,x9774,x9775,x9776,x9777,x9772,x9778)) % 187.68/187.66 [978]~E(x9781,x9782)+E(f782(x9783,x9784,x9785,x9786,x9787,x9788,x9781),f782(x9783,x9784,x9785,x9786,x9787,x9788,x9782)) % 187.68/187.66 [979]~E(x9791,x9792)+E(f775(x9791,x9793,x9794,x9795),f775(x9792,x9793,x9794,x9795)) % 187.68/187.66 [980]~E(x9801,x9802)+E(f775(x9803,x9801,x9804,x9805),f775(x9803,x9802,x9804,x9805)) % 187.68/187.66 [981]~E(x9811,x9812)+E(f775(x9813,x9814,x9811,x9815),f775(x9813,x9814,x9812,x9815)) % 187.68/187.66 [982]~E(x9821,x9822)+E(f775(x9823,x9824,x9825,x9821),f775(x9823,x9824,x9825,x9822)) % 187.68/187.66 [983]~E(x9831,x9832)+E(f827(x9831),f827(x9832)) % 187.68/187.66 [984]~E(x9841,x9842)+E(f94(x9841,x9843,x9844),f94(x9842,x9843,x9844)) % 187.68/187.66 [985]~E(x9851,x9852)+E(f94(x9853,x9851,x9854),f94(x9853,x9852,x9854)) % 187.68/187.66 [986]~E(x9861,x9862)+E(f94(x9863,x9864,x9861),f94(x9863,x9864,x9862)) % 187.68/187.66 [987]~E(x9871,x9872)+E(f854(x9871,x9873,x9874),f854(x9872,x9873,x9874)) % 187.68/187.66 [988]~E(x9881,x9882)+E(f854(x9883,x9881,x9884),f854(x9883,x9882,x9884)) % 187.68/187.66 [989]~E(x9891,x9892)+E(f854(x9893,x9894,x9891),f854(x9893,x9894,x9892)) % 187.68/187.66 [990]~E(x9901,x9902)+E(f411(x9901,x9903,x9904),f411(x9902,x9903,x9904)) % 187.68/187.66 [991]~E(x9911,x9912)+E(f411(x9913,x9911,x9914),f411(x9913,x9912,x9914)) % 187.68/187.66 [992]~E(x9921,x9922)+E(f411(x9923,x9924,x9921),f411(x9923,x9924,x9922)) % 187.68/187.66 [993]~E(x9931,x9932)+E(f800(x9931,x9933,x9934,x9935),f800(x9932,x9933,x9934,x9935)) % 187.68/187.66 [994]~E(x9941,x9942)+E(f800(x9943,x9941,x9944,x9945),f800(x9943,x9942,x9944,x9945)) % 187.68/187.66 [995]~E(x9951,x9952)+E(f800(x9953,x9954,x9951,x9955),f800(x9953,x9954,x9952,x9955)) % 187.68/187.66 [996]~E(x9961,x9962)+E(f800(x9963,x9964,x9965,x9961),f800(x9963,x9964,x9965,x9962)) % 187.68/187.66 [997]~E(x9971,x9972)+E(f701(x9971,x9973,x9974,x9975),f701(x9972,x9973,x9974,x9975)) % 187.68/187.66 [998]~E(x9981,x9982)+E(f701(x9983,x9981,x9984,x9985),f701(x9983,x9982,x9984,x9985)) % 187.68/187.66 [999]~E(x9991,x9992)+E(f701(x9993,x9994,x9991,x9995),f701(x9993,x9994,x9992,x9995)) % 187.68/187.66 [1000]~E(x10001,x10002)+E(f701(x10003,x10004,x10005,x10001),f701(x10003,x10004,x10005,x10002)) % 187.68/187.66 [1001]~E(x10011,x10012)+E(f430(x10011,x10013,x10014,x10015,x10016,x10017),f430(x10012,x10013,x10014,x10015,x10016,x10017)) % 187.68/187.66 [1002]~E(x10021,x10022)+E(f430(x10023,x10021,x10024,x10025,x10026,x10027),f430(x10023,x10022,x10024,x10025,x10026,x10027)) % 187.68/187.66 [1003]~E(x10031,x10032)+E(f430(x10033,x10034,x10031,x10035,x10036,x10037),f430(x10033,x10034,x10032,x10035,x10036,x10037)) % 187.68/187.66 [1004]~E(x10041,x10042)+E(f430(x10043,x10044,x10045,x10041,x10046,x10047),f430(x10043,x10044,x10045,x10042,x10046,x10047)) % 187.68/187.66 [1005]~E(x10051,x10052)+E(f430(x10053,x10054,x10055,x10056,x10051,x10057),f430(x10053,x10054,x10055,x10056,x10052,x10057)) % 187.68/187.66 [1006]~E(x10061,x10062)+E(f430(x10063,x10064,x10065,x10066,x10067,x10061),f430(x10063,x10064,x10065,x10066,x10067,x10062)) % 187.68/187.66 [1007]~E(x10071,x10072)+E(f342(x10071,x10073,x10074,x10075,x10076),f342(x10072,x10073,x10074,x10075,x10076)) % 187.68/187.66 [1008]~E(x10081,x10082)+E(f342(x10083,x10081,x10084,x10085,x10086),f342(x10083,x10082,x10084,x10085,x10086)) % 187.68/187.66 [1009]~E(x10091,x10092)+E(f342(x10093,x10094,x10091,x10095,x10096),f342(x10093,x10094,x10092,x10095,x10096)) % 187.68/187.66 [1010]~E(x10101,x10102)+E(f342(x10103,x10104,x10105,x10101,x10106),f342(x10103,x10104,x10105,x10102,x10106)) % 187.68/187.66 [1011]~E(x10111,x10112)+E(f342(x10113,x10114,x10115,x10116,x10111),f342(x10113,x10114,x10115,x10116,x10112)) % 187.68/187.66 [1012]~E(x10121,x10122)+E(f765(x10121,x10123,x10124,x10125,x10126,x10127,x10128,x10129),f765(x10122,x10123,x10124,x10125,x10126,x10127,x10128,x10129)) % 187.68/187.66 [1013]~E(x10131,x10132)+E(f765(x10133,x10131,x10134,x10135,x10136,x10137,x10138,x10139),f765(x10133,x10132,x10134,x10135,x10136,x10137,x10138,x10139)) % 187.68/187.66 [1014]~E(x10141,x10142)+E(f765(x10143,x10144,x10141,x10145,x10146,x10147,x10148,x10149),f765(x10143,x10144,x10142,x10145,x10146,x10147,x10148,x10149)) % 187.68/187.66 [1015]~E(x10151,x10152)+E(f765(x10153,x10154,x10155,x10151,x10156,x10157,x10158,x10159),f765(x10153,x10154,x10155,x10152,x10156,x10157,x10158,x10159)) % 187.68/187.66 [1016]~E(x10161,x10162)+E(f765(x10163,x10164,x10165,x10166,x10161,x10167,x10168,x10169),f765(x10163,x10164,x10165,x10166,x10162,x10167,x10168,x10169)) % 187.68/187.66 [1017]~E(x10171,x10172)+E(f765(x10173,x10174,x10175,x10176,x10177,x10171,x10178,x10179),f765(x10173,x10174,x10175,x10176,x10177,x10172,x10178,x10179)) % 187.68/187.66 [1018]~E(x10181,x10182)+E(f765(x10183,x10184,x10185,x10186,x10187,x10188,x10181,x10189),f765(x10183,x10184,x10185,x10186,x10187,x10188,x10182,x10189)) % 187.68/187.66 [1019]~E(x10191,x10192)+E(f765(x10193,x10194,x10195,x10196,x10197,x10198,x10199,x10191),f765(x10193,x10194,x10195,x10196,x10197,x10198,x10199,x10192)) % 187.68/187.66 [1020]~E(x10201,x10202)+E(f417(x10201,x10203,x10204),f417(x10202,x10203,x10204)) % 187.68/187.66 [1021]~E(x10211,x10212)+E(f417(x10213,x10211,x10214),f417(x10213,x10212,x10214)) % 187.68/187.66 [1022]~E(x10221,x10222)+E(f417(x10223,x10224,x10221),f417(x10223,x10224,x10222)) % 187.68/187.66 [1023]~E(x10231,x10232)+E(f751(x10231,x10233,x10234,x10235),f751(x10232,x10233,x10234,x10235)) % 187.68/187.66 [1024]~E(x10241,x10242)+E(f751(x10243,x10241,x10244,x10245),f751(x10243,x10242,x10244,x10245)) % 187.68/187.66 [1025]~E(x10251,x10252)+E(f751(x10253,x10254,x10251,x10255),f751(x10253,x10254,x10252,x10255)) % 187.68/187.66 [1026]~E(x10261,x10262)+E(f751(x10263,x10264,x10265,x10261),f751(x10263,x10264,x10265,x10262)) % 187.68/187.66 [1027]~E(x10271,x10272)+E(f273(x10271,x10273,x10274,x10275),f273(x10272,x10273,x10274,x10275)) % 187.68/187.66 [1028]~E(x10281,x10282)+E(f273(x10283,x10281,x10284,x10285),f273(x10283,x10282,x10284,x10285)) % 187.68/187.66 [1029]~E(x10291,x10292)+E(f273(x10293,x10294,x10291,x10295),f273(x10293,x10294,x10292,x10295)) % 187.68/187.66 [1030]~E(x10301,x10302)+E(f273(x10303,x10304,x10305,x10301),f273(x10303,x10304,x10305,x10302)) % 187.68/187.66 [1031]~E(x10311,x10312)+E(f415(x10311,x10313,x10314,x10315),f415(x10312,x10313,x10314,x10315)) % 187.68/187.66 [1032]~E(x10321,x10322)+E(f415(x10323,x10321,x10324,x10325),f415(x10323,x10322,x10324,x10325)) % 187.68/187.66 [1033]~E(x10331,x10332)+E(f415(x10333,x10334,x10331,x10335),f415(x10333,x10334,x10332,x10335)) % 187.68/187.66 [1034]~E(x10341,x10342)+E(f415(x10343,x10344,x10345,x10341),f415(x10343,x10344,x10345,x10342)) % 187.68/187.66 [1035]~E(x10351,x10352)+E(f238(x10351,x10353,x10354),f238(x10352,x10353,x10354)) % 187.68/187.66 [1036]~E(x10361,x10362)+E(f238(x10363,x10361,x10364),f238(x10363,x10362,x10364)) % 187.68/187.66 [1037]~E(x10371,x10372)+E(f238(x10373,x10374,x10371),f238(x10373,x10374,x10372)) % 187.68/187.66 [1038]~E(x10381,x10382)+E(f738(x10381,x10383,x10384),f738(x10382,x10383,x10384)) % 187.68/187.66 [1039]~E(x10391,x10392)+E(f738(x10393,x10391,x10394),f738(x10393,x10392,x10394)) % 187.68/187.66 [1040]~E(x10401,x10402)+E(f738(x10403,x10404,x10401),f738(x10403,x10404,x10402)) % 187.68/187.66 [1041]~E(x10411,x10412)+E(f674(x10411,x10413,x10414,x10415,x10416),f674(x10412,x10413,x10414,x10415,x10416)) % 187.68/187.66 [1042]~E(x10421,x10422)+E(f674(x10423,x10421,x10424,x10425,x10426),f674(x10423,x10422,x10424,x10425,x10426)) % 187.68/187.66 [1043]~E(x10431,x10432)+E(f674(x10433,x10434,x10431,x10435,x10436),f674(x10433,x10434,x10432,x10435,x10436)) % 187.68/187.66 [1044]~E(x10441,x10442)+E(f674(x10443,x10444,x10445,x10441,x10446),f674(x10443,x10444,x10445,x10442,x10446)) % 187.68/187.66 [1045]~E(x10451,x10452)+E(f674(x10453,x10454,x10455,x10456,x10451),f674(x10453,x10454,x10455,x10456,x10452)) % 187.68/187.66 [1046]~E(x10461,x10462)+E(f495(x10461,x10463,x10464),f495(x10462,x10463,x10464)) % 187.68/187.66 [1047]~E(x10471,x10472)+E(f495(x10473,x10471,x10474),f495(x10473,x10472,x10474)) % 187.68/187.66 [1048]~E(x10481,x10482)+E(f495(x10483,x10484,x10481),f495(x10483,x10484,x10482)) % 187.68/187.66 [1049]~E(x10491,x10492)+E(f788(x10491,x10493,x10494),f788(x10492,x10493,x10494)) % 187.68/187.66 [1050]~E(x10501,x10502)+E(f788(x10503,x10501,x10504),f788(x10503,x10502,x10504)) % 187.68/187.66 [1051]~E(x10511,x10512)+E(f788(x10513,x10514,x10511),f788(x10513,x10514,x10512)) % 187.68/187.66 [1052]~E(x10521,x10522)+E(f720(x10521,x10523,x10524,x10525),f720(x10522,x10523,x10524,x10525)) % 187.68/187.66 [1053]~E(x10531,x10532)+E(f720(x10533,x10531,x10534,x10535),f720(x10533,x10532,x10534,x10535)) % 187.68/187.66 [1054]~E(x10541,x10542)+E(f720(x10543,x10544,x10541,x10545),f720(x10543,x10544,x10542,x10545)) % 187.68/187.66 [1055]~E(x10551,x10552)+E(f720(x10553,x10554,x10555,x10551),f720(x10553,x10554,x10555,x10552)) % 187.68/187.66 [1056]~E(x10561,x10562)+E(f326(x10561,x10563,x10564,x10565),f326(x10562,x10563,x10564,x10565)) % 187.68/187.66 [1057]~E(x10571,x10572)+E(f326(x10573,x10571,x10574,x10575),f326(x10573,x10572,x10574,x10575)) % 187.68/187.66 [1058]~E(x10581,x10582)+E(f326(x10583,x10584,x10581,x10585),f326(x10583,x10584,x10582,x10585)) % 187.68/187.66 [1059]~E(x10591,x10592)+E(f326(x10593,x10594,x10595,x10591),f326(x10593,x10594,x10595,x10592)) % 187.68/187.66 [1060]~E(x10601,x10602)+E(f412(x10601,x10603,x10604,x10605),f412(x10602,x10603,x10604,x10605)) % 187.68/187.66 [1061]~E(x10611,x10612)+E(f412(x10613,x10611,x10614,x10615),f412(x10613,x10612,x10614,x10615)) % 187.68/187.66 [1062]~E(x10621,x10622)+E(f412(x10623,x10624,x10621,x10625),f412(x10623,x10624,x10622,x10625)) % 187.68/187.66 [1063]~E(x10631,x10632)+E(f412(x10633,x10634,x10635,x10631),f412(x10633,x10634,x10635,x10632)) % 187.68/187.66 [1064]~E(x10641,x10642)+E(f433(x10641,x10643,x10644,x10645,x10646),f433(x10642,x10643,x10644,x10645,x10646)) % 187.68/187.66 [1065]~E(x10651,x10652)+E(f433(x10653,x10651,x10654,x10655,x10656),f433(x10653,x10652,x10654,x10655,x10656)) % 187.68/187.66 [1066]~E(x10661,x10662)+E(f433(x10663,x10664,x10661,x10665,x10666),f433(x10663,x10664,x10662,x10665,x10666)) % 187.68/187.66 [1067]~E(x10671,x10672)+E(f433(x10673,x10674,x10675,x10671,x10676),f433(x10673,x10674,x10675,x10672,x10676)) % 187.68/187.66 [1068]~E(x10681,x10682)+E(f433(x10683,x10684,x10685,x10686,x10681),f433(x10683,x10684,x10685,x10686,x10682)) % 187.68/187.66 [1069]~E(x10691,x10692)+E(f743(x10691,x10693,x10694),f743(x10692,x10693,x10694)) % 187.68/187.66 [1070]~E(x10701,x10702)+E(f743(x10703,x10701,x10704),f743(x10703,x10702,x10704)) % 187.68/187.66 [1071]~E(x10711,x10712)+E(f743(x10713,x10714,x10711),f743(x10713,x10714,x10712)) % 187.68/187.66 [1072]~E(x10721,x10722)+E(f509(x10721,x10723,x10724),f509(x10722,x10723,x10724)) % 187.68/187.66 [1073]~E(x10731,x10732)+E(f509(x10733,x10731,x10734),f509(x10733,x10732,x10734)) % 187.68/187.66 [1074]~E(x10741,x10742)+E(f509(x10743,x10744,x10741),f509(x10743,x10744,x10742)) % 187.68/187.66 [1075]~E(x10751,x10752)+E(f508(x10751,x10753,x10754),f508(x10752,x10753,x10754)) % 187.68/187.66 [1076]~E(x10761,x10762)+E(f508(x10763,x10761,x10764),f508(x10763,x10762,x10764)) % 187.68/187.66 [1077]~E(x10771,x10772)+E(f508(x10773,x10774,x10771),f508(x10773,x10774,x10772)) % 187.68/187.66 [1078]~E(x10781,x10782)+E(f142(x10781,x10783,x10784,x10785),f142(x10782,x10783,x10784,x10785)) % 187.68/187.66 [1079]~E(x10791,x10792)+E(f142(x10793,x10791,x10794,x10795),f142(x10793,x10792,x10794,x10795)) % 187.68/187.66 [1080]~E(x10801,x10802)+E(f142(x10803,x10804,x10801,x10805),f142(x10803,x10804,x10802,x10805)) % 187.68/187.66 [1081]~E(x10811,x10812)+E(f142(x10813,x10814,x10815,x10811),f142(x10813,x10814,x10815,x10812)) % 187.68/187.66 [1082]~E(x10821,x10822)+E(f844(x10821,x10823),f844(x10822,x10823)) % 187.68/187.66 [1083]~E(x10831,x10832)+E(f844(x10833,x10831),f844(x10833,x10832)) % 187.68/187.66 [1084]~E(x10841,x10842)+E(f349(x10841,x10843),f349(x10842,x10843)) % 187.68/187.66 [1085]~E(x10851,x10852)+E(f349(x10853,x10851),f349(x10853,x10852)) % 187.68/187.66 [1086]~E(x10861,x10862)+E(f45(x10861),f45(x10862)) % 187.68/187.66 [1087]~E(x10871,x10872)+E(f623(x10871,x10873,x10874,x10875),f623(x10872,x10873,x10874,x10875)) % 187.68/187.66 [1088]~E(x10881,x10882)+E(f623(x10883,x10881,x10884,x10885),f623(x10883,x10882,x10884,x10885)) % 187.68/187.66 [1089]~E(x10891,x10892)+E(f623(x10893,x10894,x10891,x10895),f623(x10893,x10894,x10892,x10895)) % 187.68/187.66 [1090]~E(x10901,x10902)+E(f623(x10903,x10904,x10905,x10901),f623(x10903,x10904,x10905,x10902)) % 187.68/187.66 [1091]~E(x10911,x10912)+E(f498(x10911,x10913,x10914,x10915),f498(x10912,x10913,x10914,x10915)) % 187.68/187.66 [1092]~E(x10921,x10922)+E(f498(x10923,x10921,x10924,x10925),f498(x10923,x10922,x10924,x10925)) % 187.68/187.66 [1093]~E(x10931,x10932)+E(f498(x10933,x10934,x10931,x10935),f498(x10933,x10934,x10932,x10935)) % 187.68/187.66 [1094]~E(x10941,x10942)+E(f498(x10943,x10944,x10945,x10941),f498(x10943,x10944,x10945,x10942)) % 187.68/187.66 [1095]~E(x10951,x10952)+E(f361(x10951,x10953),f361(x10952,x10953)) % 187.68/187.66 [1096]~E(x10961,x10962)+E(f361(x10963,x10961),f361(x10963,x10962)) % 187.68/187.66 [1097]~E(x10971,x10972)+E(f250(x10971,x10973),f250(x10972,x10973)) % 187.68/187.66 [1098]~E(x10981,x10982)+E(f250(x10983,x10981),f250(x10983,x10982)) % 187.68/187.66 [1099]~E(x10991,x10992)+E(f564(x10991,x10993,x10994,x10995,x10996,x10997),f564(x10992,x10993,x10994,x10995,x10996,x10997)) % 187.68/187.66 [1100]~E(x11001,x11002)+E(f564(x11003,x11001,x11004,x11005,x11006,x11007),f564(x11003,x11002,x11004,x11005,x11006,x11007)) % 187.68/187.66 [1101]~E(x11011,x11012)+E(f564(x11013,x11014,x11011,x11015,x11016,x11017),f564(x11013,x11014,x11012,x11015,x11016,x11017)) % 187.68/187.66 [1102]~E(x11021,x11022)+E(f564(x11023,x11024,x11025,x11021,x11026,x11027),f564(x11023,x11024,x11025,x11022,x11026,x11027)) % 187.68/187.66 [1103]~E(x11031,x11032)+E(f564(x11033,x11034,x11035,x11036,x11031,x11037),f564(x11033,x11034,x11035,x11036,x11032,x11037)) % 187.68/187.66 [1104]~E(x11041,x11042)+E(f564(x11043,x11044,x11045,x11046,x11047,x11041),f564(x11043,x11044,x11045,x11046,x11047,x11042)) % 187.68/187.66 [1105]~E(x11051,x11052)+E(f269(x11051,x11053,x11054),f269(x11052,x11053,x11054)) % 187.68/187.66 [1106]~E(x11061,x11062)+E(f269(x11063,x11061,x11064),f269(x11063,x11062,x11064)) % 187.68/187.66 [1107]~E(x11071,x11072)+E(f269(x11073,x11074,x11071),f269(x11073,x11074,x11072)) % 187.68/187.66 [1108]~E(x11081,x11082)+E(f637(x11081,x11083,x11084),f637(x11082,x11083,x11084)) % 187.68/187.66 [1109]~E(x11091,x11092)+E(f637(x11093,x11091,x11094),f637(x11093,x11092,x11094)) % 187.68/187.66 [1110]~E(x11101,x11102)+E(f637(x11103,x11104,x11101),f637(x11103,x11104,x11102)) % 187.68/187.66 [1111]~E(x11111,x11112)+E(f504(x11111,x11113,x11114,x11115,x11116),f504(x11112,x11113,x11114,x11115,x11116)) % 187.68/187.66 [1112]~E(x11121,x11122)+E(f504(x11123,x11121,x11124,x11125,x11126),f504(x11123,x11122,x11124,x11125,x11126)) % 187.68/187.66 [1113]~E(x11131,x11132)+E(f504(x11133,x11134,x11131,x11135,x11136),f504(x11133,x11134,x11132,x11135,x11136)) % 187.68/187.66 [1114]~E(x11141,x11142)+E(f504(x11143,x11144,x11145,x11141,x11146),f504(x11143,x11144,x11145,x11142,x11146)) % 187.68/187.66 [1115]~E(x11151,x11152)+E(f504(x11153,x11154,x11155,x11156,x11151),f504(x11153,x11154,x11155,x11156,x11152)) % 187.68/187.66 [1116]~E(x11161,x11162)+E(f733(x11161,x11163),f733(x11162,x11163)) % 187.68/187.66 [1117]~E(x11171,x11172)+E(f733(x11173,x11171),f733(x11173,x11172)) % 187.68/187.66 [1118]~E(x11181,x11182)+E(f348(x11181,x11183,x11184,x11185,x11186),f348(x11182,x11183,x11184,x11185,x11186)) % 187.68/187.66 [1119]~E(x11191,x11192)+E(f348(x11193,x11191,x11194,x11195,x11196),f348(x11193,x11192,x11194,x11195,x11196)) % 187.68/187.66 [1120]~E(x11201,x11202)+E(f348(x11203,x11204,x11201,x11205,x11206),f348(x11203,x11204,x11202,x11205,x11206)) % 187.68/187.66 [1121]~E(x11211,x11212)+E(f348(x11213,x11214,x11215,x11211,x11216),f348(x11213,x11214,x11215,x11212,x11216)) % 187.68/187.66 [1122]~E(x11221,x11222)+E(f348(x11223,x11224,x11225,x11226,x11221),f348(x11223,x11224,x11225,x11226,x11222)) % 187.68/187.66 [1123]~E(x11231,x11232)+E(f530(x11231,x11233),f530(x11232,x11233)) % 187.68/187.66 [1124]~E(x11241,x11242)+E(f530(x11243,x11241),f530(x11243,x11242)) % 187.68/187.66 [1125]~E(x11251,x11252)+E(f702(x11251,x11253,x11254,x11255),f702(x11252,x11253,x11254,x11255)) % 187.68/187.66 [1126]~E(x11261,x11262)+E(f702(x11263,x11261,x11264,x11265),f702(x11263,x11262,x11264,x11265)) % 187.68/187.66 [1127]~E(x11271,x11272)+E(f702(x11273,x11274,x11271,x11275),f702(x11273,x11274,x11272,x11275)) % 187.68/187.66 [1128]~E(x11281,x11282)+E(f702(x11283,x11284,x11285,x11281),f702(x11283,x11284,x11285,x11282)) % 187.68/187.66 [1129]~E(x11291,x11292)+E(f525(x11291,x11293),f525(x11292,x11293)) % 187.68/187.66 [1130]~E(x11301,x11302)+E(f525(x11303,x11301),f525(x11303,x11302)) % 187.68/187.66 [1131]~E(x11311,x11312)+E(f693(x11311,x11313,x11314,x11315),f693(x11312,x11313,x11314,x11315)) % 187.68/187.66 [1132]~E(x11321,x11322)+E(f693(x11323,x11321,x11324,x11325),f693(x11323,x11322,x11324,x11325)) % 187.68/187.66 [1133]~E(x11331,x11332)+E(f693(x11333,x11334,x11331,x11335),f693(x11333,x11334,x11332,x11335)) % 187.68/187.66 [1134]~E(x11341,x11342)+E(f693(x11343,x11344,x11345,x11341),f693(x11343,x11344,x11345,x11342)) % 187.68/187.66 [1135]~E(x11351,x11352)+E(f442(x11351,x11353,x11354,x11355,x11356),f442(x11352,x11353,x11354,x11355,x11356)) % 187.68/187.66 [1136]~E(x11361,x11362)+E(f442(x11363,x11361,x11364,x11365,x11366),f442(x11363,x11362,x11364,x11365,x11366)) % 187.68/187.66 [1137]~E(x11371,x11372)+E(f442(x11373,x11374,x11371,x11375,x11376),f442(x11373,x11374,x11372,x11375,x11376)) % 187.68/187.66 [1138]~E(x11381,x11382)+E(f442(x11383,x11384,x11385,x11381,x11386),f442(x11383,x11384,x11385,x11382,x11386)) % 187.68/187.66 [1139]~E(x11391,x11392)+E(f442(x11393,x11394,x11395,x11396,x11391),f442(x11393,x11394,x11395,x11396,x11392)) % 187.68/187.66 [1140]~E(x11401,x11402)+E(f817(x11401),f817(x11402)) % 187.68/187.66 [1141]~E(x11411,x11412)+E(f566(x11411,x11413,x11414),f566(x11412,x11413,x11414)) % 187.68/187.66 [1142]~E(x11421,x11422)+E(f566(x11423,x11421,x11424),f566(x11423,x11422,x11424)) % 187.68/187.66 [1143]~E(x11431,x11432)+E(f566(x11433,x11434,x11431),f566(x11433,x11434,x11432)) % 187.68/187.66 [1144]~E(x11441,x11442)+E(f496(x11441,x11443,x11444),f496(x11442,x11443,x11444)) % 187.68/187.66 [1145]~E(x11451,x11452)+E(f496(x11453,x11451,x11454),f496(x11453,x11452,x11454)) % 187.68/187.66 [1146]~E(x11461,x11462)+E(f496(x11463,x11464,x11461),f496(x11463,x11464,x11462)) % 187.68/187.66 [1147]~E(x11471,x11472)+E(f853(x11471,x11473,x11474),f853(x11472,x11473,x11474)) % 187.68/187.66 [1148]~E(x11481,x11482)+E(f853(x11483,x11481,x11484),f853(x11483,x11482,x11484)) % 187.68/187.66 [1149]~E(x11491,x11492)+E(f853(x11493,x11494,x11491),f853(x11493,x11494,x11492)) % 187.68/187.66 [1150]~E(x11501,x11502)+E(f367(x11501,x11503,x11504),f367(x11502,x11503,x11504)) % 187.68/187.66 [1151]~E(x11511,x11512)+E(f367(x11513,x11511,x11514),f367(x11513,x11512,x11514)) % 187.68/187.66 [1152]~E(x11521,x11522)+E(f367(x11523,x11524,x11521),f367(x11523,x11524,x11522)) % 187.68/187.66 [1153]~E(x11531,x11532)+E(f622(x11531,x11533,x11534,x11535,x11536),f622(x11532,x11533,x11534,x11535,x11536)) % 187.68/187.66 [1154]~E(x11541,x11542)+E(f622(x11543,x11541,x11544,x11545,x11546),f622(x11543,x11542,x11544,x11545,x11546)) % 187.68/187.66 [1155]~E(x11551,x11552)+E(f622(x11553,x11554,x11551,x11555,x11556),f622(x11553,x11554,x11552,x11555,x11556)) % 187.68/187.66 [1156]~E(x11561,x11562)+E(f622(x11563,x11564,x11565,x11561,x11566),f622(x11563,x11564,x11565,x11562,x11566)) % 187.68/187.66 [1157]~E(x11571,x11572)+E(f622(x11573,x11574,x11575,x11576,x11571),f622(x11573,x11574,x11575,x11576,x11572)) % 187.68/187.66 [1158]~E(x11581,x11582)+E(f507(x11581,x11583,x11584,x11585,x11586,x11587,x11588,x11589),f507(x11582,x11583,x11584,x11585,x11586,x11587,x11588,x11589)) % 187.68/187.66 [1159]~E(x11591,x11592)+E(f507(x11593,x11591,x11594,x11595,x11596,x11597,x11598,x11599),f507(x11593,x11592,x11594,x11595,x11596,x11597,x11598,x11599)) % 187.68/187.66 [1160]~E(x11601,x11602)+E(f507(x11603,x11604,x11601,x11605,x11606,x11607,x11608,x11609),f507(x11603,x11604,x11602,x11605,x11606,x11607,x11608,x11609)) % 187.68/187.66 [1161]~E(x11611,x11612)+E(f507(x11613,x11614,x11615,x11611,x11616,x11617,x11618,x11619),f507(x11613,x11614,x11615,x11612,x11616,x11617,x11618,x11619)) % 187.68/187.66 [1162]~E(x11621,x11622)+E(f507(x11623,x11624,x11625,x11626,x11621,x11627,x11628,x11629),f507(x11623,x11624,x11625,x11626,x11622,x11627,x11628,x11629)) % 187.68/187.66 [1163]~E(x11631,x11632)+E(f507(x11633,x11634,x11635,x11636,x11637,x11631,x11638,x11639),f507(x11633,x11634,x11635,x11636,x11637,x11632,x11638,x11639)) % 187.68/187.66 [1164]~E(x11641,x11642)+E(f507(x11643,x11644,x11645,x11646,x11647,x11648,x11641,x11649),f507(x11643,x11644,x11645,x11646,x11647,x11648,x11642,x11649)) % 187.68/187.66 [1165]~E(x11651,x11652)+E(f507(x11653,x11654,x11655,x11656,x11657,x11658,x11659,x11651),f507(x11653,x11654,x11655,x11656,x11657,x11658,x11659,x11652)) % 187.68/187.66 [1166]~E(x11661,x11662)+E(f846(x11661,x11663),f846(x11662,x11663)) % 187.68/187.66 [1167]~E(x11671,x11672)+E(f846(x11673,x11671),f846(x11673,x11672)) % 187.68/187.66 [1168]~E(x11681,x11682)+E(f77(x11681,x11683,x11684,x11685,x11686),f77(x11682,x11683,x11684,x11685,x11686)) % 187.68/187.66 [1169]~E(x11691,x11692)+E(f77(x11693,x11691,x11694,x11695,x11696),f77(x11693,x11692,x11694,x11695,x11696)) % 187.68/187.66 [1170]~E(x11701,x11702)+E(f77(x11703,x11704,x11701,x11705,x11706),f77(x11703,x11704,x11702,x11705,x11706)) % 187.68/187.66 [1171]~E(x11711,x11712)+E(f77(x11713,x11714,x11715,x11711,x11716),f77(x11713,x11714,x11715,x11712,x11716)) % 187.68/187.66 [1172]~E(x11721,x11722)+E(f77(x11723,x11724,x11725,x11726,x11721),f77(x11723,x11724,x11725,x11726,x11722)) % 187.68/187.66 [1173]~E(x11731,x11732)+E(f351(x11731,x11733),f351(x11732,x11733)) % 187.68/187.66 [1174]~E(x11741,x11742)+E(f351(x11743,x11741),f351(x11743,x11742)) % 187.68/187.66 [1175]~E(x11751,x11752)+E(f497(x11751,x11753,x11754,x11755),f497(x11752,x11753,x11754,x11755)) % 187.68/187.66 [1176]~E(x11761,x11762)+E(f497(x11763,x11761,x11764,x11765),f497(x11763,x11762,x11764,x11765)) % 187.68/187.66 [1177]~E(x11771,x11772)+E(f497(x11773,x11774,x11771,x11775),f497(x11773,x11774,x11772,x11775)) % 187.68/187.66 [1178]~E(x11781,x11782)+E(f497(x11783,x11784,x11785,x11781),f497(x11783,x11784,x11785,x11782)) % 187.68/187.66 [1179]~E(x11791,x11792)+E(f257(x11791,x11793),f257(x11792,x11793)) % 187.68/187.66 [1180]~E(x11801,x11802)+E(f257(x11803,x11801),f257(x11803,x11802)) % 187.68/187.66 [1181]~E(x11811,x11812)+E(f499(x11811,x11813,x11814,x11815,x11816,x11817),f499(x11812,x11813,x11814,x11815,x11816,x11817)) % 187.68/187.66 [1182]~E(x11821,x11822)+E(f499(x11823,x11821,x11824,x11825,x11826,x11827),f499(x11823,x11822,x11824,x11825,x11826,x11827)) % 187.68/187.66 [1183]~E(x11831,x11832)+E(f499(x11833,x11834,x11831,x11835,x11836,x11837),f499(x11833,x11834,x11832,x11835,x11836,x11837)) % 187.68/187.66 [1184]~E(x11841,x11842)+E(f499(x11843,x11844,x11845,x11841,x11846,x11847),f499(x11843,x11844,x11845,x11842,x11846,x11847)) % 187.68/187.66 [1185]~E(x11851,x11852)+E(f499(x11853,x11854,x11855,x11856,x11851,x11857),f499(x11853,x11854,x11855,x11856,x11852,x11857)) % 187.68/187.66 [1186]~E(x11861,x11862)+E(f499(x11863,x11864,x11865,x11866,x11867,x11861),f499(x11863,x11864,x11865,x11866,x11867,x11862)) % 187.68/187.66 [1187]~E(x11871,x11872)+E(f480(x11871,x11873,x11874,x11875,x11876),f480(x11872,x11873,x11874,x11875,x11876)) % 187.68/187.66 [1188]~E(x11881,x11882)+E(f480(x11883,x11881,x11884,x11885,x11886),f480(x11883,x11882,x11884,x11885,x11886)) % 187.68/187.66 [1189]~E(x11891,x11892)+E(f480(x11893,x11894,x11891,x11895,x11896),f480(x11893,x11894,x11892,x11895,x11896)) % 187.68/187.66 [1190]~E(x11901,x11902)+E(f480(x11903,x11904,x11905,x11901,x11906),f480(x11903,x11904,x11905,x11902,x11906)) % 187.68/187.66 [1191]~E(x11911,x11912)+E(f480(x11913,x11914,x11915,x11916,x11911),f480(x11913,x11914,x11915,x11916,x11912)) % 187.68/187.66 [1192]~E(x11921,x11922)+E(f488(x11921,x11923,x11924),f488(x11922,x11923,x11924)) % 187.68/187.66 [1193]~E(x11931,x11932)+E(f488(x11933,x11931,x11934),f488(x11933,x11932,x11934)) % 187.68/187.66 [1194]~E(x11941,x11942)+E(f488(x11943,x11944,x11941),f488(x11943,x11944,x11942)) % 187.68/187.66 [1195]~E(x11951,x11952)+E(f755(x11951,x11953),f755(x11952,x11953)) % 187.68/187.66 [1196]~E(x11961,x11962)+E(f755(x11963,x11961),f755(x11963,x11962)) % 187.68/187.66 [1197]~E(x11971,x11972)+E(f600(x11971,x11973,x11974,x11975,x11976),f600(x11972,x11973,x11974,x11975,x11976)) % 187.68/187.66 [1198]~E(x11981,x11982)+E(f600(x11983,x11981,x11984,x11985,x11986),f600(x11983,x11982,x11984,x11985,x11986)) % 187.68/187.66 [1199]~E(x11991,x11992)+E(f600(x11993,x11994,x11991,x11995,x11996),f600(x11993,x11994,x11992,x11995,x11996)) % 187.68/187.66 [1200]~E(x12001,x12002)+E(f600(x12003,x12004,x12005,x12001,x12006),f600(x12003,x12004,x12005,x12002,x12006)) % 187.68/187.66 [1201]~E(x12011,x12012)+E(f600(x12013,x12014,x12015,x12016,x12011),f600(x12013,x12014,x12015,x12016,x12012)) % 187.68/187.66 [1202]~E(x12021,x12022)+E(f181(x12021,x12023,x12024),f181(x12022,x12023,x12024)) % 187.68/187.66 [1203]~E(x12031,x12032)+E(f181(x12033,x12031,x12034),f181(x12033,x12032,x12034)) % 187.68/187.66 [1204]~E(x12041,x12042)+E(f181(x12043,x12044,x12041),f181(x12043,x12044,x12042)) % 187.68/187.66 [1205]~E(x12051,x12052)+E(f435(x12051,x12053,x12054,x12055,x12056),f435(x12052,x12053,x12054,x12055,x12056)) % 187.68/187.66 [1206]~E(x12061,x12062)+E(f435(x12063,x12061,x12064,x12065,x12066),f435(x12063,x12062,x12064,x12065,x12066)) % 187.68/187.66 [1207]~E(x12071,x12072)+E(f435(x12073,x12074,x12071,x12075,x12076),f435(x12073,x12074,x12072,x12075,x12076)) % 187.68/187.66 [1208]~E(x12081,x12082)+E(f435(x12083,x12084,x12085,x12081,x12086),f435(x12083,x12084,x12085,x12082,x12086)) % 187.68/187.66 [1209]~E(x12091,x12092)+E(f435(x12093,x12094,x12095,x12096,x12091),f435(x12093,x12094,x12095,x12096,x12092)) % 187.68/187.66 [1210]~E(x12101,x12102)+E(f251(x12101),f251(x12102)) % 187.68/187.66 [1211]~E(x12111,x12112)+E(f523(x12111,x12113),f523(x12112,x12113)) % 187.68/187.66 [1212]~E(x12121,x12122)+E(f523(x12123,x12121),f523(x12123,x12122)) % 187.68/187.66 [1213]~E(x12131,x12132)+E(f183(x12131),f183(x12132)) % 187.68/187.66 [1214]~E(x12141,x12142)+E(f202(x12141,x12143),f202(x12142,x12143)) % 187.68/187.66 [1215]~E(x12151,x12152)+E(f202(x12153,x12151),f202(x12153,x12152)) % 187.68/187.66 [1216]~E(x12161,x12162)+E(f445(x12161,x12163,x12164,x12165),f445(x12162,x12163,x12164,x12165)) % 187.68/187.66 [1217]~E(x12171,x12172)+E(f445(x12173,x12171,x12174,x12175),f445(x12173,x12172,x12174,x12175)) % 187.68/187.66 [1218]~E(x12181,x12182)+E(f445(x12183,x12184,x12181,x12185),f445(x12183,x12184,x12182,x12185)) % 187.68/187.66 [1219]~E(x12191,x12192)+E(f445(x12193,x12194,x12195,x12191),f445(x12193,x12194,x12195,x12192)) % 187.68/187.66 [1220]~E(x12201,x12202)+E(f440(x12201,x12203,x12204),f440(x12202,x12203,x12204)) % 187.68/187.66 [1221]~E(x12211,x12212)+E(f440(x12213,x12211,x12214),f440(x12213,x12212,x12214)) % 187.68/187.66 [1222]~E(x12221,x12222)+E(f440(x12223,x12224,x12221),f440(x12223,x12224,x12222)) % 187.68/187.66 [1223]~E(x12231,x12232)+E(f636(x12231,x12233,x12234),f636(x12232,x12233,x12234)) % 187.68/187.66 [1224]~E(x12241,x12242)+E(f636(x12243,x12241,x12244),f636(x12243,x12242,x12244)) % 187.68/187.66 [1225]~E(x12251,x12252)+E(f636(x12253,x12254,x12251),f636(x12253,x12254,x12252)) % 187.68/187.66 [1226]~E(x12261,x12262)+E(f330(x12261,x12263,x12264),f330(x12262,x12263,x12264)) % 187.68/187.66 [1227]~E(x12271,x12272)+E(f330(x12273,x12271,x12274),f330(x12273,x12272,x12274)) % 187.68/187.66 [1228]~E(x12281,x12282)+E(f330(x12283,x12284,x12281),f330(x12283,x12284,x12282)) % 187.68/187.66 [1229]~E(x12291,x12292)+E(f487(x12291,x12293,x12294,x12295,x12296),f487(x12292,x12293,x12294,x12295,x12296)) % 187.68/187.66 [1230]~E(x12301,x12302)+E(f487(x12303,x12301,x12304,x12305,x12306),f487(x12303,x12302,x12304,x12305,x12306)) % 187.68/187.66 [1231]~E(x12311,x12312)+E(f487(x12313,x12314,x12311,x12315,x12316),f487(x12313,x12314,x12312,x12315,x12316)) % 187.68/187.66 [1232]~E(x12321,x12322)+E(f487(x12323,x12324,x12325,x12321,x12326),f487(x12323,x12324,x12325,x12322,x12326)) % 187.68/187.66 [1233]~E(x12331,x12332)+E(f487(x12333,x12334,x12335,x12336,x12331),f487(x12333,x12334,x12335,x12336,x12332)) % 187.68/187.66 [1234]~E(x12341,x12342)+E(f770(x12341,x12343),f770(x12342,x12343)) % 187.68/187.66 [1235]~E(x12351,x12352)+E(f770(x12353,x12351),f770(x12353,x12352)) % 187.68/187.66 [1236]~E(x12361,x12362)+E(f563(x12361,x12363,x12364,x12365,x12366,x12367),f563(x12362,x12363,x12364,x12365,x12366,x12367)) % 187.68/187.66 [1237]~E(x12371,x12372)+E(f563(x12373,x12371,x12374,x12375,x12376,x12377),f563(x12373,x12372,x12374,x12375,x12376,x12377)) % 187.68/187.66 [1238]~E(x12381,x12382)+E(f563(x12383,x12384,x12381,x12385,x12386,x12387),f563(x12383,x12384,x12382,x12385,x12386,x12387)) % 187.68/187.66 [1239]~E(x12391,x12392)+E(f563(x12393,x12394,x12395,x12391,x12396,x12397),f563(x12393,x12394,x12395,x12392,x12396,x12397)) % 187.68/187.66 [1240]~E(x12401,x12402)+E(f563(x12403,x12404,x12405,x12406,x12401,x12407),f563(x12403,x12404,x12405,x12406,x12402,x12407)) % 187.68/187.66 [1241]~E(x12411,x12412)+E(f563(x12413,x12414,x12415,x12416,x12417,x12411),f563(x12413,x12414,x12415,x12416,x12417,x12412)) % 187.68/187.66 [1242]~E(x12421,x12422)+E(f177(x12421,x12423,x12424),f177(x12422,x12423,x12424)) % 187.68/187.66 [1243]~E(x12431,x12432)+E(f177(x12433,x12431,x12434),f177(x12433,x12432,x12434)) % 187.68/187.66 [1244]~E(x12441,x12442)+E(f177(x12443,x12444,x12441),f177(x12443,x12444,x12442)) % 187.68/187.66 [1245]~E(x12451,x12452)+E(f187(x12451,x12453,x12454,x12455),f187(x12452,x12453,x12454,x12455)) % 187.68/187.66 [1246]~E(x12461,x12462)+E(f187(x12463,x12461,x12464,x12465),f187(x12463,x12462,x12464,x12465)) % 187.68/187.66 [1247]~E(x12471,x12472)+E(f187(x12473,x12474,x12471,x12475),f187(x12473,x12474,x12472,x12475)) % 187.68/187.66 [1248]~E(x12481,x12482)+E(f187(x12483,x12484,x12485,x12481),f187(x12483,x12484,x12485,x12482)) % 187.68/187.66 [1249]~E(x12491,x12492)+E(f241(x12491,x12493,x12494),f241(x12492,x12493,x12494)) % 187.68/187.66 [1250]~E(x12501,x12502)+E(f241(x12503,x12501,x12504),f241(x12503,x12502,x12504)) % 187.68/187.66 [1251]~E(x12511,x12512)+E(f241(x12513,x12514,x12511),f241(x12513,x12514,x12512)) % 187.68/187.66 [1252]~E(x12521,x12522)+E(f312(x12521),f312(x12522)) % 187.68/187.66 [1253]~E(x12531,x12532)+E(f334(x12531,x12533,x12534,x12535),f334(x12532,x12533,x12534,x12535)) % 187.68/187.66 [1254]~E(x12541,x12542)+E(f334(x12543,x12541,x12544,x12545),f334(x12543,x12542,x12544,x12545)) % 187.68/187.66 [1255]~E(x12551,x12552)+E(f334(x12553,x12554,x12551,x12555),f334(x12553,x12554,x12552,x12555)) % 187.68/187.66 [1256]~E(x12561,x12562)+E(f334(x12563,x12564,x12565,x12561),f334(x12563,x12564,x12565,x12562)) % 187.68/187.66 [1257]~E(x12571,x12572)+E(f695(x12571,x12573,x12574),f695(x12572,x12573,x12574)) % 187.68/187.66 [1258]~E(x12581,x12582)+E(f695(x12583,x12581,x12584),f695(x12583,x12582,x12584)) % 187.68/187.66 [1259]~E(x12591,x12592)+E(f695(x12593,x12594,x12591),f695(x12593,x12594,x12592)) % 187.68/187.66 [1260]~E(x12601,x12602)+E(f172(x12601),f172(x12602)) % 187.68/187.66 [1261]~E(x12611,x12612)+E(f416(x12611,x12613,x12614),f416(x12612,x12613,x12614)) % 187.68/187.66 [1262]~E(x12621,x12622)+E(f416(x12623,x12621,x12624),f416(x12623,x12622,x12624)) % 187.68/187.66 [1263]~E(x12631,x12632)+E(f416(x12633,x12634,x12631),f416(x12633,x12634,x12632)) % 187.68/187.66 [1264]~E(x12641,x12642)+E(f640(x12641,x12643,x12644),f640(x12642,x12643,x12644)) % 187.86/187.66 [1265]~E(x12651,x12652)+E(f640(x12653,x12651,x12654),f640(x12653,x12652,x12654)) % 187.86/187.66 [1266]~E(x12661,x12662)+E(f640(x12663,x12664,x12661),f640(x12663,x12664,x12662)) % 187.86/187.66 [1267]~E(x12671,x12672)+E(f621(x12671,x12673,x12674,x12675,x12676),f621(x12672,x12673,x12674,x12675,x12676)) % 187.86/187.66 [1268]~E(x12681,x12682)+E(f621(x12683,x12681,x12684,x12685,x12686),f621(x12683,x12682,x12684,x12685,x12686)) % 187.86/187.66 [1269]~E(x12691,x12692)+E(f621(x12693,x12694,x12691,x12695,x12696),f621(x12693,x12694,x12692,x12695,x12696)) % 187.86/187.66 [1270]~E(x12701,x12702)+E(f621(x12703,x12704,x12705,x12701,x12706),f621(x12703,x12704,x12705,x12702,x12706)) % 187.86/187.66 [1271]~E(x12711,x12712)+E(f621(x12713,x12714,x12715,x12716,x12711),f621(x12713,x12714,x12715,x12716,x12712)) % 187.86/187.66 [1272]~E(x12721,x12722)+E(f478(x12721,x12723,x12724),f478(x12722,x12723,x12724)) % 187.86/187.66 [1273]~E(x12731,x12732)+E(f478(x12733,x12731,x12734),f478(x12733,x12732,x12734)) % 187.86/187.66 [1274]~E(x12741,x12742)+E(f478(x12743,x12744,x12741),f478(x12743,x12744,x12742)) % 187.86/187.66 [1275]~E(x12751,x12752)+E(f608(x12751,x12753),f608(x12752,x12753)) % 187.86/187.66 [1276]~E(x12761,x12762)+E(f608(x12763,x12761),f608(x12763,x12762)) % 187.86/187.66 [1277]~E(x12771,x12772)+E(f818(x12771),f818(x12772)) % 187.86/187.66 [1278]~E(x12781,x12782)+E(f688(x12781,x12783,x12784,x12785,x12786,x12787,x12788),f688(x12782,x12783,x12784,x12785,x12786,x12787,x12788)) % 187.86/187.66 [1279]~E(x12791,x12792)+E(f688(x12793,x12791,x12794,x12795,x12796,x12797,x12798),f688(x12793,x12792,x12794,x12795,x12796,x12797,x12798)) % 187.86/187.66 [1280]~E(x12801,x12802)+E(f688(x12803,x12804,x12801,x12805,x12806,x12807,x12808),f688(x12803,x12804,x12802,x12805,x12806,x12807,x12808)) % 187.86/187.66 [1281]~E(x12811,x12812)+E(f688(x12813,x12814,x12815,x12811,x12816,x12817,x12818),f688(x12813,x12814,x12815,x12812,x12816,x12817,x12818)) % 187.86/187.66 [1282]~E(x12821,x12822)+E(f688(x12823,x12824,x12825,x12826,x12821,x12827,x12828),f688(x12823,x12824,x12825,x12826,x12822,x12827,x12828)) % 187.86/187.66 [1283]~E(x12831,x12832)+E(f688(x12833,x12834,x12835,x12836,x12837,x12831,x12838),f688(x12833,x12834,x12835,x12836,x12837,x12832,x12838)) % 187.86/187.66 [1284]~E(x12841,x12842)+E(f688(x12843,x12844,x12845,x12846,x12847,x12848,x12841),f688(x12843,x12844,x12845,x12846,x12847,x12848,x12842)) % 187.86/187.66 [1285]~E(x12851,x12852)+E(f824(x12851,x12853),f824(x12852,x12853)) % 187.86/187.66 [1286]~E(x12861,x12862)+E(f824(x12863,x12861),f824(x12863,x12862)) % 187.86/187.66 [1287]~E(x12871,x12872)+E(f561(x12871,x12873,x12874,x12875,x12876,x12877),f561(x12872,x12873,x12874,x12875,x12876,x12877)) % 187.86/187.66 [1288]~E(x12881,x12882)+E(f561(x12883,x12881,x12884,x12885,x12886,x12887),f561(x12883,x12882,x12884,x12885,x12886,x12887)) % 187.86/187.66 [1289]~E(x12891,x12892)+E(f561(x12893,x12894,x12891,x12895,x12896,x12897),f561(x12893,x12894,x12892,x12895,x12896,x12897)) % 187.86/187.66 [1290]~E(x12901,x12902)+E(f561(x12903,x12904,x12905,x12901,x12906,x12907),f561(x12903,x12904,x12905,x12902,x12906,x12907)) % 187.86/187.66 [1291]~E(x12911,x12912)+E(f561(x12913,x12914,x12915,x12916,x12911,x12917),f561(x12913,x12914,x12915,x12916,x12912,x12917)) % 187.86/187.66 [1292]~E(x12921,x12922)+E(f561(x12923,x12924,x12925,x12926,x12927,x12921),f561(x12923,x12924,x12925,x12926,x12927,x12922)) % 187.86/187.66 [1293]~E(x12931,x12932)+E(f249(x12931,x12933,x12934,x12935,x12936),f249(x12932,x12933,x12934,x12935,x12936)) % 187.86/187.66 [1294]~E(x12941,x12942)+E(f249(x12943,x12941,x12944,x12945,x12946),f249(x12943,x12942,x12944,x12945,x12946)) % 187.86/187.66 [1295]~E(x12951,x12952)+E(f249(x12953,x12954,x12951,x12955,x12956),f249(x12953,x12954,x12952,x12955,x12956)) % 187.86/187.66 [1296]~E(x12961,x12962)+E(f249(x12963,x12964,x12965,x12961,x12966),f249(x12963,x12964,x12965,x12962,x12966)) % 187.86/187.66 [1297]~E(x12971,x12972)+E(f249(x12973,x12974,x12975,x12976,x12971),f249(x12973,x12974,x12975,x12976,x12972)) % 187.86/187.66 [1298]~E(x12981,x12982)+E(f345(x12981,x12983,x12984),f345(x12982,x12983,x12984)) % 187.86/187.66 [1299]~E(x12991,x12992)+E(f345(x12993,x12991,x12994),f345(x12993,x12992,x12994)) % 187.86/187.66 [1300]~E(x13001,x13002)+E(f345(x13003,x13004,x13001),f345(x13003,x13004,x13002)) % 187.86/187.66 [1301]~E(x13011,x13012)+E(f745(x13011,x13013),f745(x13012,x13013)) % 187.86/187.66 [1302]~E(x13021,x13022)+E(f745(x13023,x13021),f745(x13023,x13022)) % 187.86/187.66 [1303]~E(x13031,x13032)+E(f272(x13031,x13033,x13034),f272(x13032,x13033,x13034)) % 187.86/187.66 [1304]~E(x13041,x13042)+E(f272(x13043,x13041,x13044),f272(x13043,x13042,x13044)) % 187.86/187.66 [1305]~E(x13051,x13052)+E(f272(x13053,x13054,x13051),f272(x13053,x13054,x13052)) % 187.86/187.66 [1306]~E(x13061,x13062)+E(f481(x13061,x13063,x13064,x13065,x13066),f481(x13062,x13063,x13064,x13065,x13066)) % 187.86/187.66 [1307]~E(x13071,x13072)+E(f481(x13073,x13071,x13074,x13075,x13076),f481(x13073,x13072,x13074,x13075,x13076)) % 187.86/187.66 [1308]~E(x13081,x13082)+E(f481(x13083,x13084,x13081,x13085,x13086),f481(x13083,x13084,x13082,x13085,x13086)) % 187.86/187.66 [1309]~E(x13091,x13092)+E(f481(x13093,x13094,x13095,x13091,x13096),f481(x13093,x13094,x13095,x13092,x13096)) % 187.86/187.66 [1310]~E(x13101,x13102)+E(f481(x13103,x13104,x13105,x13106,x13101),f481(x13103,x13104,x13105,x13106,x13102)) % 187.86/187.66 [1311]~E(x13111,x13112)+E(f780(x13111,x13113,x13114,x13115,x13116),f780(x13112,x13113,x13114,x13115,x13116)) % 187.86/187.66 [1312]~E(x13121,x13122)+E(f780(x13123,x13121,x13124,x13125,x13126),f780(x13123,x13122,x13124,x13125,x13126)) % 187.86/187.66 [1313]~E(x13131,x13132)+E(f780(x13133,x13134,x13131,x13135,x13136),f780(x13133,x13134,x13132,x13135,x13136)) % 187.86/187.66 [1314]~E(x13141,x13142)+E(f780(x13143,x13144,x13145,x13141,x13146),f780(x13143,x13144,x13145,x13142,x13146)) % 187.86/187.66 [1315]~E(x13151,x13152)+E(f780(x13153,x13154,x13155,x13156,x13151),f780(x13153,x13154,x13155,x13156,x13152)) % 187.86/187.66 [1316]~E(x13161,x13162)+E(f406(x13161,x13163),f406(x13162,x13163)) % 187.86/187.66 [1317]~E(x13171,x13172)+E(f406(x13173,x13171),f406(x13173,x13172)) % 187.86/187.66 [1318]~E(x13181,x13182)+E(f156(x13181,x13183,x13184,x13185),f156(x13182,x13183,x13184,x13185)) % 187.86/187.66 [1319]~E(x13191,x13192)+E(f156(x13193,x13191,x13194,x13195),f156(x13193,x13192,x13194,x13195)) % 187.86/187.66 [1320]~E(x13201,x13202)+E(f156(x13203,x13204,x13201,x13205),f156(x13203,x13204,x13202,x13205)) % 187.86/187.66 [1321]~E(x13211,x13212)+E(f156(x13213,x13214,x13215,x13211),f156(x13213,x13214,x13215,x13212)) % 187.86/187.66 [1322]~E(x13221,x13222)+E(f739(x13221,x13223,x13224),f739(x13222,x13223,x13224)) % 187.86/187.66 [1323]~E(x13231,x13232)+E(f739(x13233,x13231,x13234),f739(x13233,x13232,x13234)) % 187.86/187.66 [1324]~E(x13241,x13242)+E(f739(x13243,x13244,x13241),f739(x13243,x13244,x13242)) % 187.86/187.66 [1325]~E(x13251,x13252)+E(f450(x13251,x13253,x13254,x13255,x13256),f450(x13252,x13253,x13254,x13255,x13256)) % 187.86/187.66 [1326]~E(x13261,x13262)+E(f450(x13263,x13261,x13264,x13265,x13266),f450(x13263,x13262,x13264,x13265,x13266)) % 187.86/187.66 [1327]~E(x13271,x13272)+E(f450(x13273,x13274,x13271,x13275,x13276),f450(x13273,x13274,x13272,x13275,x13276)) % 187.86/187.66 [1328]~E(x13281,x13282)+E(f450(x13283,x13284,x13285,x13281,x13286),f450(x13283,x13284,x13285,x13282,x13286)) % 187.86/187.66 [1329]~E(x13291,x13292)+E(f450(x13293,x13294,x13295,x13296,x13291),f450(x13293,x13294,x13295,x13296,x13292)) % 187.86/187.66 [1330]~E(x13301,x13302)+E(f762(x13301,x13303),f762(x13302,x13303)) % 187.86/187.66 [1331]~E(x13311,x13312)+E(f762(x13313,x13311),f762(x13313,x13312)) % 187.86/187.66 [1332]~E(x13321,x13322)+E(f577(x13321,x13323,x13324),f577(x13322,x13323,x13324)) % 187.86/187.66 [1333]~E(x13331,x13332)+E(f577(x13333,x13331,x13334),f577(x13333,x13332,x13334)) % 187.86/187.66 [1334]~E(x13341,x13342)+E(f577(x13343,x13344,x13341),f577(x13343,x13344,x13342)) % 187.86/187.66 [1335]~E(x13351,x13352)+E(f604(x13351,x13353,x13354),f604(x13352,x13353,x13354)) % 187.86/187.66 [1336]~E(x13361,x13362)+E(f604(x13363,x13361,x13364),f604(x13363,x13362,x13364)) % 187.86/187.66 [1337]~E(x13371,x13372)+E(f604(x13373,x13374,x13371),f604(x13373,x13374,x13372)) % 187.86/187.66 [1338]~E(x13381,x13382)+E(f215(x13381,x13383,x13384),f215(x13382,x13383,x13384)) % 187.86/187.66 [1339]~E(x13391,x13392)+E(f215(x13393,x13391,x13394),f215(x13393,x13392,x13394)) % 187.86/187.66 [1340]~E(x13401,x13402)+E(f215(x13403,x13404,x13401),f215(x13403,x13404,x13402)) % 187.86/187.66 [1341]~E(x13411,x13412)+E(f655(x13411,x13413,x13414),f655(x13412,x13413,x13414)) % 187.86/187.66 [1342]~E(x13421,x13422)+E(f655(x13423,x13421,x13424),f655(x13423,x13422,x13424)) % 187.86/187.66 [1343]~E(x13431,x13432)+E(f655(x13433,x13434,x13431),f655(x13433,x13434,x13432)) % 187.86/187.66 [1344]~E(x13441,x13442)+E(f616(x13441,x13443,x13444,x13445,x13446),f616(x13442,x13443,x13444,x13445,x13446)) % 187.86/187.66 [1345]~E(x13451,x13452)+E(f616(x13453,x13451,x13454,x13455,x13456),f616(x13453,x13452,x13454,x13455,x13456)) % 187.86/187.66 [1346]~E(x13461,x13462)+E(f616(x13463,x13464,x13461,x13465,x13466),f616(x13463,x13464,x13462,x13465,x13466)) % 187.86/187.66 [1347]~E(x13471,x13472)+E(f616(x13473,x13474,x13475,x13471,x13476),f616(x13473,x13474,x13475,x13472,x13476)) % 187.86/187.66 [1348]~E(x13481,x13482)+E(f616(x13483,x13484,x13485,x13486,x13481),f616(x13483,x13484,x13485,x13486,x13482)) % 187.86/187.66 [1349]~E(x13491,x13492)+E(f337(x13491,x13493),f337(x13492,x13493)) % 187.86/187.66 [1350]~E(x13501,x13502)+E(f337(x13503,x13501),f337(x13503,x13502)) % 187.86/187.66 [1351]~E(x13511,x13512)+E(f699(x13511,x13513,x13514,x13515,x13516),f699(x13512,x13513,x13514,x13515,x13516)) % 187.86/187.66 [1352]~E(x13521,x13522)+E(f699(x13523,x13521,x13524,x13525,x13526),f699(x13523,x13522,x13524,x13525,x13526)) % 187.86/187.66 [1353]~E(x13531,x13532)+E(f699(x13533,x13534,x13531,x13535,x13536),f699(x13533,x13534,x13532,x13535,x13536)) % 187.86/187.66 [1354]~E(x13541,x13542)+E(f699(x13543,x13544,x13545,x13541,x13546),f699(x13543,x13544,x13545,x13542,x13546)) % 187.86/187.66 [1355]~E(x13551,x13552)+E(f699(x13553,x13554,x13555,x13556,x13551),f699(x13553,x13554,x13555,x13556,x13552)) % 187.86/187.66 [1356]~E(x13561,x13562)+E(f355(x13561,x13563,x13564),f355(x13562,x13563,x13564)) % 187.86/187.66 [1357]~E(x13571,x13572)+E(f355(x13573,x13571,x13574),f355(x13573,x13572,x13574)) % 187.86/187.66 [1358]~E(x13581,x13582)+E(f355(x13583,x13584,x13581),f355(x13583,x13584,x13582)) % 187.86/187.66 [1359]~E(x13591,x13592)+E(f350(x13591,x13593,x13594,x13595,x13596,x13597,x13598,x13599,x135910),f350(x13592,x13593,x13594,x13595,x13596,x13597,x13598,x13599,x135910)) % 187.86/187.66 [1360]~E(x13601,x13602)+E(f350(x13603,x13601,x13604,x13605,x13606,x13607,x13608,x13609,x136010),f350(x13603,x13602,x13604,x13605,x13606,x13607,x13608,x13609,x136010)) % 187.86/187.66 [1361]~E(x13611,x13612)+E(f350(x13613,x13614,x13611,x13615,x13616,x13617,x13618,x13619,x136110),f350(x13613,x13614,x13612,x13615,x13616,x13617,x13618,x13619,x136110)) % 187.86/187.66 [1362]~E(x13621,x13622)+E(f350(x13623,x13624,x13625,x13621,x13626,x13627,x13628,x13629,x136210),f350(x13623,x13624,x13625,x13622,x13626,x13627,x13628,x13629,x136210)) % 187.86/187.66 [1363]~E(x13631,x13632)+E(f350(x13633,x13634,x13635,x13636,x13631,x13637,x13638,x13639,x136310),f350(x13633,x13634,x13635,x13636,x13632,x13637,x13638,x13639,x136310)) % 187.86/187.66 [1364]~E(x13641,x13642)+E(f350(x13643,x13644,x13645,x13646,x13647,x13641,x13648,x13649,x136410),f350(x13643,x13644,x13645,x13646,x13647,x13642,x13648,x13649,x136410)) % 187.86/187.66 [1365]~E(x13651,x13652)+E(f350(x13653,x13654,x13655,x13656,x13657,x13658,x13651,x13659,x136510),f350(x13653,x13654,x13655,x13656,x13657,x13658,x13652,x13659,x136510)) % 187.86/187.66 [1366]~E(x13661,x13662)+E(f350(x13663,x13664,x13665,x13666,x13667,x13668,x13669,x13661,x136610),f350(x13663,x13664,x13665,x13666,x13667,x13668,x13669,x13662,x136610)) % 187.86/187.66 [1367]~E(x13671,x13672)+E(f350(x13673,x13674,x13675,x13676,x13677,x13678,x13679,x136710,x13671),f350(x13673,x13674,x13675,x13676,x13677,x13678,x13679,x136710,x13672)) % 187.86/187.66 [1368]~E(x13681,x13682)+E(f322(x13681,x13683),f322(x13682,x13683)) % 187.86/187.66 [1369]~E(x13691,x13692)+E(f322(x13693,x13691),f322(x13693,x13692)) % 187.86/187.66 [1370]~E(x13701,x13702)+E(f347(x13701,x13703,x13704),f347(x13702,x13703,x13704)) % 187.86/187.66 [1371]~E(x13711,x13712)+E(f347(x13713,x13711,x13714),f347(x13713,x13712,x13714)) % 187.86/187.66 [1372]~E(x13721,x13722)+E(f347(x13723,x13724,x13721),f347(x13723,x13724,x13722)) % 187.86/187.66 [1373]~E(x13731,x13732)+E(f740(x13731,x13733,x13734,x13735,x13736),f740(x13732,x13733,x13734,x13735,x13736)) % 187.86/187.66 [1374]~E(x13741,x13742)+E(f740(x13743,x13741,x13744,x13745,x13746),f740(x13743,x13742,x13744,x13745,x13746)) % 187.86/187.66 [1375]~E(x13751,x13752)+E(f740(x13753,x13754,x13751,x13755,x13756),f740(x13753,x13754,x13752,x13755,x13756)) % 187.86/187.66 [1376]~E(x13761,x13762)+E(f740(x13763,x13764,x13765,x13761,x13766),f740(x13763,x13764,x13765,x13762,x13766)) % 187.86/187.66 [1377]~E(x13771,x13772)+E(f740(x13773,x13774,x13775,x13776,x13771),f740(x13773,x13774,x13775,x13776,x13772)) % 187.86/187.66 [1378]~E(x13781,x13782)+E(f299(x13781,x13783,x13784,x13785),f299(x13782,x13783,x13784,x13785)) % 187.86/187.66 [1379]~E(x13791,x13792)+E(f299(x13793,x13791,x13794,x13795),f299(x13793,x13792,x13794,x13795)) % 187.86/187.66 [1380]~E(x13801,x13802)+E(f299(x13803,x13804,x13801,x13805),f299(x13803,x13804,x13802,x13805)) % 187.86/187.66 [1381]~E(x13811,x13812)+E(f299(x13813,x13814,x13815,x13811),f299(x13813,x13814,x13815,x13812)) % 187.86/187.66 [1382]~E(x13821,x13822)+E(f422(x13821),f422(x13822)) % 187.86/187.66 [1383]~E(x13831,x13832)+E(f835(x13831,x13833,x13834),f835(x13832,x13833,x13834)) % 187.86/187.66 [1384]~E(x13841,x13842)+E(f835(x13843,x13841,x13844),f835(x13843,x13842,x13844)) % 187.86/187.66 [1385]~E(x13851,x13852)+E(f835(x13853,x13854,x13851),f835(x13853,x13854,x13852)) % 187.86/187.66 [1386]~E(x13861,x13862)+E(f360(x13861,x13863,x13864),f360(x13862,x13863,x13864)) % 187.86/187.66 [1387]~E(x13871,x13872)+E(f360(x13873,x13871,x13874),f360(x13873,x13872,x13874)) % 187.86/187.66 [1388]~E(x13881,x13882)+E(f360(x13883,x13884,x13881),f360(x13883,x13884,x13882)) % 187.86/187.66 [1389]~E(x13891,x13892)+E(f399(x13891,x13893,x13894,x13895),f399(x13892,x13893,x13894,x13895)) % 187.86/187.66 [1390]~E(x13901,x13902)+E(f399(x13903,x13901,x13904,x13905),f399(x13903,x13902,x13904,x13905)) % 187.86/187.66 [1391]~E(x13911,x13912)+E(f399(x13913,x13914,x13911,x13915),f399(x13913,x13914,x13912,x13915)) % 187.86/187.66 [1392]~E(x13921,x13922)+E(f399(x13923,x13924,x13925,x13921),f399(x13923,x13924,x13925,x13922)) % 187.86/187.66 [1393]~E(x13931,x13932)+E(f524(x13931,x13933),f524(x13932,x13933)) % 187.86/187.66 [1394]~E(x13941,x13942)+E(f524(x13943,x13941),f524(x13943,x13942)) % 187.86/187.66 [1395]~E(x13951,x13952)+E(f266(x13951,x13953),f266(x13952,x13953)) % 187.86/187.66 [1396]~E(x13961,x13962)+E(f266(x13963,x13961),f266(x13963,x13962)) % 187.86/187.66 [1397]~E(x13971,x13972)+E(f431(x13971,x13973,x13974,x13975,x13976),f431(x13972,x13973,x13974,x13975,x13976)) % 187.86/187.66 [1398]~E(x13981,x13982)+E(f431(x13983,x13981,x13984,x13985,x13986),f431(x13983,x13982,x13984,x13985,x13986)) % 187.86/187.66 [1399]~E(x13991,x13992)+E(f431(x13993,x13994,x13991,x13995,x13996),f431(x13993,x13994,x13992,x13995,x13996)) % 187.86/187.66 [1400]~E(x14001,x14002)+E(f431(x14003,x14004,x14005,x14001,x14006),f431(x14003,x14004,x14005,x14002,x14006)) % 187.86/187.66 [1401]~E(x14011,x14012)+E(f431(x14013,x14014,x14015,x14016,x14011),f431(x14013,x14014,x14015,x14016,x14012)) % 187.86/187.66 [1402]~E(x14021,x14022)+E(f372(x14021,x14023,x14024),f372(x14022,x14023,x14024)) % 187.86/187.66 [1403]~E(x14031,x14032)+E(f372(x14033,x14031,x14034),f372(x14033,x14032,x14034)) % 187.86/187.66 [1404]~E(x14041,x14042)+E(f372(x14043,x14044,x14041),f372(x14043,x14044,x14042)) % 187.86/187.66 [1405]~E(x14051,x14052)+E(f531(x14051,x14053),f531(x14052,x14053)) % 187.86/187.66 [1406]~E(x14061,x14062)+E(f531(x14063,x14061),f531(x14063,x14062)) % 187.86/187.66 [1407]~E(x14071,x14072)+E(f527(x14071,x14073,x14074,x14075),f527(x14072,x14073,x14074,x14075)) % 187.86/187.66 [1408]~E(x14081,x14082)+E(f527(x14083,x14081,x14084,x14085),f527(x14083,x14082,x14084,x14085)) % 187.86/187.66 [1409]~E(x14091,x14092)+E(f527(x14093,x14094,x14091,x14095),f527(x14093,x14094,x14092,x14095)) % 187.86/187.66 [1410]~E(x14101,x14102)+E(f527(x14103,x14104,x14105,x14101),f527(x14103,x14104,x14105,x14102)) % 187.86/187.66 [1411]~E(x14111,x14112)+E(f98(x14111,x14113,x14114),f98(x14112,x14113,x14114)) % 187.86/187.66 [1412]~E(x14121,x14122)+E(f98(x14123,x14121,x14124),f98(x14123,x14122,x14124)) % 187.86/187.66 [1413]~E(x14131,x14132)+E(f98(x14133,x14134,x14131),f98(x14133,x14134,x14132)) % 187.86/187.66 [1414]~E(x14141,x14142)+E(f444(x14141,x14143,x14144,x14145),f444(x14142,x14143,x14144,x14145)) % 187.86/187.66 [1415]~E(x14151,x14152)+E(f444(x14153,x14151,x14154,x14155),f444(x14153,x14152,x14154,x14155)) % 187.86/187.66 [1416]~E(x14161,x14162)+E(f444(x14163,x14164,x14161,x14165),f444(x14163,x14164,x14162,x14165)) % 187.86/187.66 [1417]~E(x14171,x14172)+E(f444(x14173,x14174,x14175,x14171),f444(x14173,x14174,x14175,x14172)) % 187.86/187.66 [1418]~E(x14181,x14182)+E(f467(x14181,x14183,x14184,x14185),f467(x14182,x14183,x14184,x14185)) % 187.86/187.66 [1419]~E(x14191,x14192)+E(f467(x14193,x14191,x14194,x14195),f467(x14193,x14192,x14194,x14195)) % 187.86/187.66 [1420]~E(x14201,x14202)+E(f467(x14203,x14204,x14201,x14205),f467(x14203,x14204,x14202,x14205)) % 187.86/187.66 [1421]~E(x14211,x14212)+E(f467(x14213,x14214,x14215,x14211),f467(x14213,x14214,x14215,x14212)) % 187.86/187.66 [1422]~E(x14221,x14222)+E(f544(x14221,x14223,x14224),f544(x14222,x14223,x14224)) % 187.86/187.66 [1423]~E(x14231,x14232)+E(f544(x14233,x14231,x14234),f544(x14233,x14232,x14234)) % 187.86/187.66 [1424]~E(x14241,x14242)+E(f544(x14243,x14244,x14241),f544(x14243,x14244,x14242)) % 187.86/187.66 [1425]~E(x14251,x14252)+E(f335(x14251,x14253,x14254,x14255),f335(x14252,x14253,x14254,x14255)) % 187.86/187.66 [1426]~E(x14261,x14262)+E(f335(x14263,x14261,x14264,x14265),f335(x14263,x14262,x14264,x14265)) % 187.86/187.66 [1427]~E(x14271,x14272)+E(f335(x14273,x14274,x14271,x14275),f335(x14273,x14274,x14272,x14275)) % 187.86/187.66 [1428]~E(x14281,x14282)+E(f335(x14283,x14284,x14285,x14281),f335(x14283,x14284,x14285,x14282)) % 187.86/187.66 [1429]~E(x14291,x14292)+E(f685(x14291,x14293,x14294),f685(x14292,x14293,x14294)) % 187.86/187.66 [1430]~E(x14301,x14302)+E(f685(x14303,x14301,x14304),f685(x14303,x14302,x14304)) % 187.86/187.66 [1431]~E(x14311,x14312)+E(f685(x14313,x14314,x14311),f685(x14313,x14314,x14312)) % 187.86/187.66 [1432]~E(x14321,x14322)+E(f725(x14321,x14323),f725(x14322,x14323)) % 187.86/187.66 [1433]~E(x14331,x14332)+E(f725(x14333,x14331),f725(x14333,x14332)) % 187.86/187.66 [1434]~E(x14341,x14342)+E(f395(x14341,x14343,x14344,x14345),f395(x14342,x14343,x14344,x14345)) % 187.86/187.66 [1435]~E(x14351,x14352)+E(f395(x14353,x14351,x14354,x14355),f395(x14353,x14352,x14354,x14355)) % 187.86/187.66 [1436]~E(x14361,x14362)+E(f395(x14363,x14364,x14361,x14365),f395(x14363,x14364,x14362,x14365)) % 187.86/187.66 [1437]~E(x14371,x14372)+E(f395(x14373,x14374,x14375,x14371),f395(x14373,x14374,x14375,x14372)) % 187.86/187.66 [1438]~E(x14381,x14382)+E(f652(x14381,x14383,x14384,x14385),f652(x14382,x14383,x14384,x14385)) % 187.86/187.66 [1439]~E(x14391,x14392)+E(f652(x14393,x14391,x14394,x14395),f652(x14393,x14392,x14394,x14395)) % 187.86/187.66 [1440]~E(x14401,x14402)+E(f652(x14403,x14404,x14401,x14405),f652(x14403,x14404,x14402,x14405)) % 187.86/187.66 [1441]~E(x14411,x14412)+E(f652(x14413,x14414,x14415,x14411),f652(x14413,x14414,x14415,x14412)) % 187.86/187.66 [1442]~E(x14421,x14422)+E(f618(x14421,x14423,x14424,x14425),f618(x14422,x14423,x14424,x14425)) % 187.86/187.66 [1443]~E(x14431,x14432)+E(f618(x14433,x14431,x14434,x14435),f618(x14433,x14432,x14434,x14435)) % 187.86/187.66 [1444]~E(x14441,x14442)+E(f618(x14443,x14444,x14441,x14445),f618(x14443,x14444,x14442,x14445)) % 187.86/187.66 [1445]~E(x14451,x14452)+E(f618(x14453,x14454,x14455,x14451),f618(x14453,x14454,x14455,x14452)) % 187.86/187.66 [1446]~E(x14461,x14462)+E(f469(x14461,x14463,x14464,x14465,x14466,x14467,x14468),f469(x14462,x14463,x14464,x14465,x14466,x14467,x14468)) % 187.86/187.66 [1447]~E(x14471,x14472)+E(f469(x14473,x14471,x14474,x14475,x14476,x14477,x14478),f469(x14473,x14472,x14474,x14475,x14476,x14477,x14478)) % 187.86/187.66 [1448]~E(x14481,x14482)+E(f469(x14483,x14484,x14481,x14485,x14486,x14487,x14488),f469(x14483,x14484,x14482,x14485,x14486,x14487,x14488)) % 187.86/187.66 [1449]~E(x14491,x14492)+E(f469(x14493,x14494,x14495,x14491,x14496,x14497,x14498),f469(x14493,x14494,x14495,x14492,x14496,x14497,x14498)) % 187.86/187.66 [1450]~E(x14501,x14502)+E(f469(x14503,x14504,x14505,x14506,x14501,x14507,x14508),f469(x14503,x14504,x14505,x14506,x14502,x14507,x14508)) % 187.86/187.66 [1451]~E(x14511,x14512)+E(f469(x14513,x14514,x14515,x14516,x14517,x14511,x14518),f469(x14513,x14514,x14515,x14516,x14517,x14512,x14518)) % 187.86/187.66 [1452]~E(x14521,x14522)+E(f469(x14523,x14524,x14525,x14526,x14527,x14528,x14521),f469(x14523,x14524,x14525,x14526,x14527,x14528,x14522)) % 187.86/187.66 [1453]~E(x14531,x14532)+E(f648(x14531,x14533,x14534,x14535),f648(x14532,x14533,x14534,x14535)) % 187.86/187.66 [1454]~E(x14541,x14542)+E(f648(x14543,x14541,x14544,x14545),f648(x14543,x14542,x14544,x14545)) % 187.86/187.66 [1455]~E(x14551,x14552)+E(f648(x14553,x14554,x14551,x14555),f648(x14553,x14554,x14552,x14555)) % 187.86/187.66 [1456]~E(x14561,x14562)+E(f648(x14563,x14564,x14565,x14561),f648(x14563,x14564,x14565,x14562)) % 187.86/187.66 [1457]~E(x14571,x14572)+E(f634(x14571,x14573,x14574),f634(x14572,x14573,x14574)) % 187.86/187.66 [1458]~E(x14581,x14582)+E(f634(x14583,x14581,x14584),f634(x14583,x14582,x14584)) % 187.86/187.66 [1459]~E(x14591,x14592)+E(f634(x14593,x14594,x14591),f634(x14593,x14594,x14592)) % 187.86/187.66 [1460]~E(x14601,x14602)+E(f475(x14601,x14603,x14604),f475(x14602,x14603,x14604)) % 187.86/187.66 [1461]~E(x14611,x14612)+E(f475(x14613,x14611,x14614),f475(x14613,x14612,x14614)) % 187.86/187.66 [1462]~E(x14621,x14622)+E(f475(x14623,x14624,x14621),f475(x14623,x14624,x14622)) % 187.86/187.66 [1463]~E(x14631,x14632)+E(f671(x14631,x14633,x14634,x14635,x14636),f671(x14632,x14633,x14634,x14635,x14636)) % 187.86/187.66 [1464]~E(x14641,x14642)+E(f671(x14643,x14641,x14644,x14645,x14646),f671(x14643,x14642,x14644,x14645,x14646)) % 187.86/187.66 [1465]~E(x14651,x14652)+E(f671(x14653,x14654,x14651,x14655,x14656),f671(x14653,x14654,x14652,x14655,x14656)) % 187.86/187.66 [1466]~E(x14661,x14662)+E(f671(x14663,x14664,x14665,x14661,x14666),f671(x14663,x14664,x14665,x14662,x14666)) % 187.86/187.66 [1467]~E(x14671,x14672)+E(f671(x14673,x14674,x14675,x14676,x14671),f671(x14673,x14674,x14675,x14676,x14672)) % 187.86/187.66 [1468]~E(x14681,x14682)+E(f596(x14681,x14683,x14684),f596(x14682,x14683,x14684)) % 187.86/187.66 [1469]~E(x14691,x14692)+E(f596(x14693,x14691,x14694),f596(x14693,x14692,x14694)) % 187.86/187.66 [1470]~E(x14701,x14702)+E(f596(x14703,x14704,x14701),f596(x14703,x14704,x14702)) % 187.86/187.66 [1471]~E(x14711,x14712)+E(f706(x14711,x14713,x14714,x14715),f706(x14712,x14713,x14714,x14715)) % 187.86/187.66 [1472]~E(x14721,x14722)+E(f706(x14723,x14721,x14724,x14725),f706(x14723,x14722,x14724,x14725)) % 187.86/187.66 [1473]~E(x14731,x14732)+E(f706(x14733,x14734,x14731,x14735),f706(x14733,x14734,x14732,x14735)) % 187.86/187.66 [1474]~E(x14741,x14742)+E(f706(x14743,x14744,x14745,x14741),f706(x14743,x14744,x14745,x14742)) % 187.86/187.66 [1475]~E(x14751,x14752)+E(f793(x14751,x14753,x14754),f793(x14752,x14753,x14754)) % 187.86/187.66 [1476]~E(x14761,x14762)+E(f793(x14763,x14761,x14764),f793(x14763,x14762,x14764)) % 187.86/187.66 [1477]~E(x14771,x14772)+E(f793(x14773,x14774,x14771),f793(x14773,x14774,x14772)) % 187.86/187.66 [1478]~E(x14781,x14782)+E(f447(x14781,x14783,x14784,x14785,x14786),f447(x14782,x14783,x14784,x14785,x14786)) % 187.86/187.66 [1479]~E(x14791,x14792)+E(f447(x14793,x14791,x14794,x14795,x14796),f447(x14793,x14792,x14794,x14795,x14796)) % 187.86/187.66 [1480]~E(x14801,x14802)+E(f447(x14803,x14804,x14801,x14805,x14806),f447(x14803,x14804,x14802,x14805,x14806)) % 187.86/187.66 [1481]~E(x14811,x14812)+E(f447(x14813,x14814,x14815,x14811,x14816),f447(x14813,x14814,x14815,x14812,x14816)) % 187.86/187.66 [1482]~E(x14821,x14822)+E(f447(x14823,x14824,x14825,x14826,x14821),f447(x14823,x14824,x14825,x14826,x14822)) % 187.86/187.66 [1483]~E(x14831,x14832)+E(f614(x14831,x14833),f614(x14832,x14833)) % 187.86/187.66 [1484]~E(x14841,x14842)+E(f614(x14843,x14841),f614(x14843,x14842)) % 187.86/187.66 [1485]~E(x14851,x14852)+E(f783(x14851,x14853,x14854,x14855,x14856,x14857,x14858),f783(x14852,x14853,x14854,x14855,x14856,x14857,x14858)) % 187.86/187.66 [1486]~E(x14861,x14862)+E(f783(x14863,x14861,x14864,x14865,x14866,x14867,x14868),f783(x14863,x14862,x14864,x14865,x14866,x14867,x14868)) % 187.86/187.66 [1487]~E(x14871,x14872)+E(f783(x14873,x14874,x14871,x14875,x14876,x14877,x14878),f783(x14873,x14874,x14872,x14875,x14876,x14877,x14878)) % 187.86/187.66 [1488]~E(x14881,x14882)+E(f783(x14883,x14884,x14885,x14881,x14886,x14887,x14888),f783(x14883,x14884,x14885,x14882,x14886,x14887,x14888)) % 187.86/187.66 [1489]~E(x14891,x14892)+E(f783(x14893,x14894,x14895,x14896,x14891,x14897,x14898),f783(x14893,x14894,x14895,x14896,x14892,x14897,x14898)) % 187.86/187.66 [1490]~E(x14901,x14902)+E(f783(x14903,x14904,x14905,x14906,x14907,x14901,x14908),f783(x14903,x14904,x14905,x14906,x14907,x14902,x14908)) % 187.86/187.66 [1491]~E(x14911,x14912)+E(f783(x14913,x14914,x14915,x14916,x14917,x14918,x14911),f783(x14913,x14914,x14915,x14916,x14917,x14918,x14912)) % 187.86/187.66 [1492]~E(x14921,x14922)+E(f206(x14921,x14923),f206(x14922,x14923)) % 187.86/187.66 [1493]~E(x14931,x14932)+E(f206(x14933,x14931),f206(x14933,x14932)) % 187.86/187.66 [1494]~E(x14941,x14942)+E(f700(x14941,x14943),f700(x14942,x14943)) % 187.86/187.66 [1495]~E(x14951,x14952)+E(f700(x14953,x14951),f700(x14953,x14952)) % 187.86/187.66 [1496]~E(x14961,x14962)+E(f658(x14961,x14963,x14964,x14965),f658(x14962,x14963,x14964,x14965)) % 187.86/187.66 [1497]~E(x14971,x14972)+E(f658(x14973,x14971,x14974,x14975),f658(x14973,x14972,x14974,x14975)) % 187.86/187.66 [1498]~E(x14981,x14982)+E(f658(x14983,x14984,x14981,x14985),f658(x14983,x14984,x14982,x14985)) % 187.86/187.66 [1499]~E(x14991,x14992)+E(f658(x14993,x14994,x14995,x14991),f658(x14993,x14994,x14995,x14992)) % 187.86/187.66 [1500]~E(x15001,x15002)+E(f819(x15001,x15003),f819(x15002,x15003)) % 187.86/187.66 [1501]~E(x15011,x15012)+E(f819(x15013,x15011),f819(x15013,x15012)) % 187.86/187.66 [1502]~E(x15021,x15022)+E(f763(x15021,x15023),f763(x15022,x15023)) % 187.86/187.66 [1503]~E(x15031,x15032)+E(f763(x15033,x15031),f763(x15033,x15032)) % 187.86/187.66 [1504]~E(x15041,x15042)+E(f816(x15041,x15043,x15044,x15045,x15046,x15047),f816(x15042,x15043,x15044,x15045,x15046,x15047)) % 187.86/187.66 [1505]~E(x15051,x15052)+E(f816(x15053,x15051,x15054,x15055,x15056,x15057),f816(x15053,x15052,x15054,x15055,x15056,x15057)) % 187.86/187.66 [1506]~E(x15061,x15062)+E(f816(x15063,x15064,x15061,x15065,x15066,x15067),f816(x15063,x15064,x15062,x15065,x15066,x15067)) % 187.86/187.66 [1507]~E(x15071,x15072)+E(f816(x15073,x15074,x15075,x15071,x15076,x15077),f816(x15073,x15074,x15075,x15072,x15076,x15077)) % 187.86/187.66 [1508]~E(x15081,x15082)+E(f816(x15083,x15084,x15085,x15086,x15081,x15087),f816(x15083,x15084,x15085,x15086,x15082,x15087)) % 187.86/187.66 [1509]~E(x15091,x15092)+E(f816(x15093,x15094,x15095,x15096,x15097,x15091),f816(x15093,x15094,x15095,x15096,x15097,x15092)) % 187.86/187.66 [1510]~E(x15101,x15102)+E(f331(x15101,x15103,x15104),f331(x15102,x15103,x15104)) % 187.86/187.66 [1511]~E(x15111,x15112)+E(f331(x15113,x15111,x15114),f331(x15113,x15112,x15114)) % 187.86/187.66 [1512]~E(x15121,x15122)+E(f331(x15123,x15124,x15121),f331(x15123,x15124,x15122)) % 187.86/187.66 [1513]~E(x15131,x15132)+E(f565(x15131,x15133,x15134,x15135),f565(x15132,x15133,x15134,x15135)) % 187.86/187.66 [1514]~E(x15141,x15142)+E(f565(x15143,x15141,x15144,x15145),f565(x15143,x15142,x15144,x15145)) % 187.86/187.66 [1515]~E(x15151,x15152)+E(f565(x15153,x15154,x15151,x15155),f565(x15153,x15154,x15152,x15155)) % 187.86/187.66 [1516]~E(x15161,x15162)+E(f565(x15163,x15164,x15165,x15161),f565(x15163,x15164,x15165,x15162)) % 187.86/187.66 [1517]~E(x15171,x15172)+E(f343(x15171,x15173,x15174,x15175),f343(x15172,x15173,x15174,x15175)) % 187.86/187.66 [1518]~E(x15181,x15182)+E(f343(x15183,x15181,x15184,x15185),f343(x15183,x15182,x15184,x15185)) % 187.86/187.66 [1519]~E(x15191,x15192)+E(f343(x15193,x15194,x15191,x15195),f343(x15193,x15194,x15192,x15195)) % 187.86/187.66 [1520]~E(x15201,x15202)+E(f343(x15203,x15204,x15205,x15201),f343(x15203,x15204,x15205,x15202)) % 187.86/187.66 [1521]~E(x15211,x15212)+E(f207(x15211,x15213,x15214),f207(x15212,x15213,x15214)) % 187.86/187.66 [1522]~E(x15221,x15222)+E(f207(x15223,x15221,x15224),f207(x15223,x15222,x15224)) % 187.86/187.66 [1523]~E(x15231,x15232)+E(f207(x15233,x15234,x15231),f207(x15233,x15234,x15232)) % 187.86/187.66 [1524]~E(x15241,x15242)+E(f591(x15241,x15243,x15244,x15245),f591(x15242,x15243,x15244,x15245)) % 187.86/187.66 [1525]~E(x15251,x15252)+E(f591(x15253,x15251,x15254,x15255),f591(x15253,x15252,x15254,x15255)) % 187.86/187.66 [1526]~E(x15261,x15262)+E(f591(x15263,x15264,x15261,x15265),f591(x15263,x15264,x15262,x15265)) % 187.86/187.66 [1527]~E(x15271,x15272)+E(f591(x15273,x15274,x15275,x15271),f591(x15273,x15274,x15275,x15272)) % 187.86/187.66 [1528]~E(x15281,x15282)+E(f841(x15281,x15283),f841(x15282,x15283)) % 187.86/187.66 [1529]~E(x15291,x15292)+E(f841(x15293,x15291),f841(x15293,x15292)) % 187.86/187.66 [1530]~E(x15301,x15302)+E(f97(x15301,x15303,x15304,x15305),f97(x15302,x15303,x15304,x15305)) % 187.86/187.66 [1531]~E(x15311,x15312)+E(f97(x15313,x15311,x15314,x15315),f97(x15313,x15312,x15314,x15315)) % 187.86/187.66 [1532]~E(x15321,x15322)+E(f97(x15323,x15324,x15321,x15325),f97(x15323,x15324,x15322,x15325)) % 187.86/187.66 [1533]~E(x15331,x15332)+E(f97(x15333,x15334,x15335,x15331),f97(x15333,x15334,x15335,x15332)) % 187.86/187.66 [1534]~E(x15341,x15342)+E(f584(x15341,x15343,x15344,x15345,x15346,x15347),f584(x15342,x15343,x15344,x15345,x15346,x15347)) % 187.86/187.66 [1535]~E(x15351,x15352)+E(f584(x15353,x15351,x15354,x15355,x15356,x15357),f584(x15353,x15352,x15354,x15355,x15356,x15357)) % 187.86/187.66 [1536]~E(x15361,x15362)+E(f584(x15363,x15364,x15361,x15365,x15366,x15367),f584(x15363,x15364,x15362,x15365,x15366,x15367)) % 187.86/187.66 [1537]~E(x15371,x15372)+E(f584(x15373,x15374,x15375,x15371,x15376,x15377),f584(x15373,x15374,x15375,x15372,x15376,x15377)) % 187.86/187.66 [1538]~E(x15381,x15382)+E(f584(x15383,x15384,x15385,x15386,x15381,x15387),f584(x15383,x15384,x15385,x15386,x15382,x15387)) % 187.86/187.66 [1539]~E(x15391,x15392)+E(f584(x15393,x15394,x15395,x15396,x15397,x15391),f584(x15393,x15394,x15395,x15396,x15397,x15392)) % 187.86/187.66 [1540]~E(x15401,x15402)+E(f856(x15401,x15403,x15404),f856(x15402,x15403,x15404)) % 187.86/187.66 [1541]~E(x15411,x15412)+E(f856(x15413,x15411,x15414),f856(x15413,x15412,x15414)) % 187.86/187.66 [1542]~E(x15421,x15422)+E(f856(x15423,x15424,x15421),f856(x15423,x15424,x15422)) % 187.86/187.66 [1543]~E(x15431,x15432)+E(f753(x15431,x15433,x15434,x15435,x15436),f753(x15432,x15433,x15434,x15435,x15436)) % 187.86/187.66 [1544]~E(x15441,x15442)+E(f753(x15443,x15441,x15444,x15445,x15446),f753(x15443,x15442,x15444,x15445,x15446)) % 187.86/187.66 [1545]~E(x15451,x15452)+E(f753(x15453,x15454,x15451,x15455,x15456),f753(x15453,x15454,x15452,x15455,x15456)) % 187.86/187.66 [1546]~E(x15461,x15462)+E(f753(x15463,x15464,x15465,x15461,x15466),f753(x15463,x15464,x15465,x15462,x15466)) % 187.86/187.66 [1547]~E(x15471,x15472)+E(f753(x15473,x15474,x15475,x15476,x15471),f753(x15473,x15474,x15475,x15476,x15472)) % 187.86/187.66 [1548]~E(x15481,x15482)+E(f791(x15481,x15483,x15484),f791(x15482,x15483,x15484)) % 187.86/187.66 [1549]~E(x15491,x15492)+E(f791(x15493,x15491,x15494),f791(x15493,x15492,x15494)) % 187.86/187.66 [1550]~E(x15501,x15502)+E(f791(x15503,x15504,x15501),f791(x15503,x15504,x15502)) % 187.86/187.66 [1551]~E(x15511,x15512)+E(f403(x15511,x15513,x15514,x15515),f403(x15512,x15513,x15514,x15515)) % 187.86/187.66 [1552]~E(x15521,x15522)+E(f403(x15523,x15521,x15524,x15525),f403(x15523,x15522,x15524,x15525)) % 187.86/187.66 [1553]~E(x15531,x15532)+E(f403(x15533,x15534,x15531,x15535),f403(x15533,x15534,x15532,x15535)) % 187.86/187.66 [1554]~E(x15541,x15542)+E(f403(x15543,x15544,x15545,x15541),f403(x15543,x15544,x15545,x15542)) % 187.86/187.66 [1555]~E(x15551,x15552)+E(f310(x15551,x15553,x15554,x15555),f310(x15552,x15553,x15554,x15555)) % 187.86/187.66 [1556]~E(x15561,x15562)+E(f310(x15563,x15561,x15564,x15565),f310(x15563,x15562,x15564,x15565)) % 187.86/187.66 [1557]~E(x15571,x15572)+E(f310(x15573,x15574,x15571,x15575),f310(x15573,x15574,x15572,x15575)) % 187.86/187.66 [1558]~E(x15581,x15582)+E(f310(x15583,x15584,x15585,x15581),f310(x15583,x15584,x15585,x15582)) % 187.86/187.66 [1559]~E(x15591,x15592)+E(f582(x15591,x15593,x15594,x15595,x15596,x15597),f582(x15592,x15593,x15594,x15595,x15596,x15597)) % 187.86/187.66 [1560]~E(x15601,x15602)+E(f582(x15603,x15601,x15604,x15605,x15606,x15607),f582(x15603,x15602,x15604,x15605,x15606,x15607)) % 187.86/187.66 [1561]~E(x15611,x15612)+E(f582(x15613,x15614,x15611,x15615,x15616,x15617),f582(x15613,x15614,x15612,x15615,x15616,x15617)) % 187.86/187.66 [1562]~E(x15621,x15622)+E(f582(x15623,x15624,x15625,x15621,x15626,x15627),f582(x15623,x15624,x15625,x15622,x15626,x15627)) % 187.86/187.66 [1563]~E(x15631,x15632)+E(f582(x15633,x15634,x15635,x15636,x15631,x15637),f582(x15633,x15634,x15635,x15636,x15632,x15637)) % 187.86/187.66 [1564]~E(x15641,x15642)+E(f582(x15643,x15644,x15645,x15646,x15647,x15641),f582(x15643,x15644,x15645,x15646,x15647,x15642)) % 187.86/187.66 [1565]~E(x15651,x15652)+E(f602(x15651,x15653,x15654,x15655,x15656),f602(x15652,x15653,x15654,x15655,x15656)) % 187.86/187.66 [1566]~E(x15661,x15662)+E(f602(x15663,x15661,x15664,x15665,x15666),f602(x15663,x15662,x15664,x15665,x15666)) % 187.86/187.66 [1567]~E(x15671,x15672)+E(f602(x15673,x15674,x15671,x15675,x15676),f602(x15673,x15674,x15672,x15675,x15676)) % 187.86/187.66 [1568]~E(x15681,x15682)+E(f602(x15683,x15684,x15685,x15681,x15686),f602(x15683,x15684,x15685,x15682,x15686)) % 187.86/187.66 [1569]~E(x15691,x15692)+E(f602(x15693,x15694,x15695,x15696,x15691),f602(x15693,x15694,x15695,x15696,x15692)) % 187.86/187.66 [1570]~E(x15701,x15702)+E(f617(x15701,x15703,x15704,x15705,x15706),f617(x15702,x15703,x15704,x15705,x15706)) % 187.86/187.66 [1571]~E(x15711,x15712)+E(f617(x15713,x15711,x15714,x15715,x15716),f617(x15713,x15712,x15714,x15715,x15716)) % 187.86/187.66 [1572]~E(x15721,x15722)+E(f617(x15723,x15724,x15721,x15725,x15726),f617(x15723,x15724,x15722,x15725,x15726)) % 187.86/187.66 [1573]~E(x15731,x15732)+E(f617(x15733,x15734,x15735,x15731,x15736),f617(x15733,x15734,x15735,x15732,x15736)) % 187.86/187.66 [1574]~E(x15741,x15742)+E(f617(x15743,x15744,x15745,x15746,x15741),f617(x15743,x15744,x15745,x15746,x15742)) % 187.86/187.66 [1575]~E(x15751,x15752)+E(f554(x15751,x15753),f554(x15752,x15753)) % 187.86/187.66 [1576]~E(x15761,x15762)+E(f554(x15763,x15761),f554(x15763,x15762)) % 187.86/187.66 [1577]~E(x15771,x15772)+E(f580(x15771,x15773,x15774,x15775,x15776),f580(x15772,x15773,x15774,x15775,x15776)) % 187.86/187.66 [1578]~E(x15781,x15782)+E(f580(x15783,x15781,x15784,x15785,x15786),f580(x15783,x15782,x15784,x15785,x15786)) % 187.86/187.66 [1579]~E(x15791,x15792)+E(f580(x15793,x15794,x15791,x15795,x15796),f580(x15793,x15794,x15792,x15795,x15796)) % 187.86/187.66 [1580]~E(x15801,x15802)+E(f580(x15803,x15804,x15805,x15801,x15806),f580(x15803,x15804,x15805,x15802,x15806)) % 187.86/187.66 [1581]~E(x15811,x15812)+E(f580(x15813,x15814,x15815,x15816,x15811),f580(x15813,x15814,x15815,x15816,x15812)) % 187.86/187.66 [1582]~E(x15821,x15822)+E(f605(x15821,x15823,x15824,x15825,x15826),f605(x15822,x15823,x15824,x15825,x15826)) % 187.86/187.66 [1583]~E(x15831,x15832)+E(f605(x15833,x15831,x15834,x15835,x15836),f605(x15833,x15832,x15834,x15835,x15836)) % 187.86/187.66 [1584]~E(x15841,x15842)+E(f605(x15843,x15844,x15841,x15845,x15846),f605(x15843,x15844,x15842,x15845,x15846)) % 187.86/187.66 [1585]~E(x15851,x15852)+E(f605(x15853,x15854,x15855,x15851,x15856),f605(x15853,x15854,x15855,x15852,x15856)) % 187.86/187.66 [1586]~E(x15861,x15862)+E(f605(x15863,x15864,x15865,x15866,x15861),f605(x15863,x15864,x15865,x15866,x15862)) % 187.86/187.66 [1587]~E(x15871,x15872)+E(f398(x15871,x15873),f398(x15872,x15873)) % 187.86/187.66 [1588]~E(x15881,x15882)+E(f398(x15883,x15881),f398(x15883,x15882)) % 187.86/187.66 [1589]~E(x15891,x15892)+E(f773(x15891,x15893,x15894),f773(x15892,x15893,x15894)) % 187.86/187.66 [1590]~E(x15901,x15902)+E(f773(x15903,x15901,x15904),f773(x15903,x15902,x15904)) % 187.86/187.66 [1591]~E(x15911,x15912)+E(f773(x15913,x15914,x15911),f773(x15913,x15914,x15912)) % 187.86/187.66 [1592]~E(x15921,x15922)+E(f629(x15921,x15923,x15924,x15925,x15926),f629(x15922,x15923,x15924,x15925,x15926)) % 187.86/187.66 [1593]~E(x15931,x15932)+E(f629(x15933,x15931,x15934,x15935,x15936),f629(x15933,x15932,x15934,x15935,x15936)) % 187.86/187.66 [1594]~E(x15941,x15942)+E(f629(x15943,x15944,x15941,x15945,x15946),f629(x15943,x15944,x15942,x15945,x15946)) % 187.86/187.66 [1595]~E(x15951,x15952)+E(f629(x15953,x15954,x15955,x15951,x15956),f629(x15953,x15954,x15955,x15952,x15956)) % 187.86/187.66 [1596]~E(x15961,x15962)+E(f629(x15963,x15964,x15965,x15966,x15961),f629(x15963,x15964,x15965,x15966,x15962)) % 187.86/187.66 [1597]~E(x15971,x15972)+E(f464(x15971,x15973,x15974,x15975),f464(x15972,x15973,x15974,x15975)) % 187.86/187.66 [1598]~E(x15981,x15982)+E(f464(x15983,x15981,x15984,x15985),f464(x15983,x15982,x15984,x15985)) % 187.86/187.66 [1599]~E(x15991,x15992)+E(f464(x15993,x15994,x15991,x15995),f464(x15993,x15994,x15992,x15995)) % 187.86/187.66 [1600]~E(x16001,x16002)+E(f464(x16003,x16004,x16005,x16001),f464(x16003,x16004,x16005,x16002)) % 187.86/187.66 [1601]~E(x16011,x16012)+E(f657(x16011,x16013,x16014,x16015,x16016),f657(x16012,x16013,x16014,x16015,x16016)) % 187.86/187.66 [1602]~E(x16021,x16022)+E(f657(x16023,x16021,x16024,x16025,x16026),f657(x16023,x16022,x16024,x16025,x16026)) % 187.86/187.66 [1603]~E(x16031,x16032)+E(f657(x16033,x16034,x16031,x16035,x16036),f657(x16033,x16034,x16032,x16035,x16036)) % 187.86/187.66 [1604]~E(x16041,x16042)+E(f657(x16043,x16044,x16045,x16041,x16046),f657(x16043,x16044,x16045,x16042,x16046)) % 187.86/187.66 [1605]~E(x16051,x16052)+E(f657(x16053,x16054,x16055,x16056,x16051),f657(x16053,x16054,x16055,x16056,x16052)) % 187.86/187.66 [1606]~E(x16061,x16062)+E(f382(x16061,x16063,x16064),f382(x16062,x16063,x16064)) % 187.86/187.66 [1607]~E(x16071,x16072)+E(f382(x16073,x16071,x16074),f382(x16073,x16072,x16074)) % 187.86/187.66 [1608]~E(x16081,x16082)+E(f382(x16083,x16084,x16081),f382(x16083,x16084,x16082)) % 187.86/187.66 [1609]~E(x16091,x16092)+E(f683(x16091,x16093),f683(x16092,x16093)) % 187.86/187.66 [1610]~E(x16101,x16102)+E(f683(x16103,x16101),f683(x16103,x16102)) % 187.86/187.66 [1611]~E(x16111,x16112)+E(f585(x16111,x16113,x16114,x16115,x16116,x16117),f585(x16112,x16113,x16114,x16115,x16116,x16117)) % 187.86/187.66 [1612]~E(x16121,x16122)+E(f585(x16123,x16121,x16124,x16125,x16126,x16127),f585(x16123,x16122,x16124,x16125,x16126,x16127)) % 187.86/187.66 [1613]~E(x16131,x16132)+E(f585(x16133,x16134,x16131,x16135,x16136,x16137),f585(x16133,x16134,x16132,x16135,x16136,x16137)) % 187.86/187.66 [1614]~E(x16141,x16142)+E(f585(x16143,x16144,x16145,x16141,x16146,x16147),f585(x16143,x16144,x16145,x16142,x16146,x16147)) % 187.86/187.66 [1615]~E(x16151,x16152)+E(f585(x16153,x16154,x16155,x16156,x16151,x16157),f585(x16153,x16154,x16155,x16156,x16152,x16157)) % 187.86/187.66 [1616]~E(x16161,x16162)+E(f585(x16163,x16164,x16165,x16166,x16167,x16161),f585(x16163,x16164,x16165,x16166,x16167,x16162)) % 187.86/187.66 [1617]~E(x16171,x16172)+E(f678(x16171,x16173,x16174,x16175,x16176),f678(x16172,x16173,x16174,x16175,x16176)) % 187.86/187.66 [1618]~E(x16181,x16182)+E(f678(x16183,x16181,x16184,x16185,x16186),f678(x16183,x16182,x16184,x16185,x16186)) % 187.86/187.66 [1619]~E(x16191,x16192)+E(f678(x16193,x16194,x16191,x16195,x16196),f678(x16193,x16194,x16192,x16195,x16196)) % 187.86/187.66 [1620]~E(x16201,x16202)+E(f678(x16203,x16204,x16205,x16201,x16206),f678(x16203,x16204,x16205,x16202,x16206)) % 187.86/187.66 [1621]~E(x16211,x16212)+E(f678(x16213,x16214,x16215,x16216,x16211),f678(x16213,x16214,x16215,x16216,x16212)) % 187.86/187.66 [1622]~E(x16221,x16222)+E(f550(x16221,x16223,x16224),f550(x16222,x16223,x16224)) % 187.86/187.66 [1623]~E(x16231,x16232)+E(f550(x16233,x16231,x16234),f550(x16233,x16232,x16234)) % 187.86/187.66 [1624]~E(x16241,x16242)+E(f550(x16243,x16244,x16241),f550(x16243,x16244,x16242)) % 187.86/187.66 [1625]~E(x16251,x16252)+E(f696(x16251,x16253,x16254,x16255,x16256),f696(x16252,x16253,x16254,x16255,x16256)) % 187.86/187.66 [1626]~E(x16261,x16262)+E(f696(x16263,x16261,x16264,x16265,x16266),f696(x16263,x16262,x16264,x16265,x16266)) % 187.86/187.66 [1627]~E(x16271,x16272)+E(f696(x16273,x16274,x16271,x16275,x16276),f696(x16273,x16274,x16272,x16275,x16276)) % 187.86/187.66 [1628]~E(x16281,x16282)+E(f696(x16283,x16284,x16285,x16281,x16286),f696(x16283,x16284,x16285,x16282,x16286)) % 187.86/187.66 [1629]~E(x16291,x16292)+E(f696(x16293,x16294,x16295,x16296,x16291),f696(x16293,x16294,x16295,x16296,x16292)) % 187.86/187.66 [1630]~E(x16301,x16302)+E(f240(x16301,x16303),f240(x16302,x16303)) % 187.86/187.66 [1631]~E(x16311,x16312)+E(f240(x16313,x16311),f240(x16313,x16312)) % 187.86/187.66 [1632]~E(x16321,x16322)+E(f402(x16321,x16323,x16324,x16325),f402(x16322,x16323,x16324,x16325)) % 187.86/187.66 [1633]~E(x16331,x16332)+E(f402(x16333,x16331,x16334,x16335),f402(x16333,x16332,x16334,x16335)) % 187.86/187.66 [1634]~E(x16341,x16342)+E(f402(x16343,x16344,x16341,x16345),f402(x16343,x16344,x16342,x16345)) % 187.86/187.66 [1635]~E(x16351,x16352)+E(f402(x16353,x16354,x16355,x16351),f402(x16353,x16354,x16355,x16352)) % 187.86/187.66 [1636]~E(x16361,x16362)+E(f502(x16361,x16363,x16364),f502(x16362,x16363,x16364)) % 187.86/187.66 [1637]~E(x16371,x16372)+E(f502(x16373,x16371,x16374),f502(x16373,x16372,x16374)) % 187.86/187.66 [1638]~E(x16381,x16382)+E(f502(x16383,x16384,x16381),f502(x16383,x16384,x16382)) % 187.86/187.66 [1639]~E(x16391,x16392)+E(f722(x16391,x16393),f722(x16392,x16393)) % 187.86/187.66 [1640]~E(x16401,x16402)+E(f722(x16403,x16401),f722(x16403,x16402)) % 187.86/187.66 [1641]~E(x16411,x16412)+E(f712(x16411,x16413,x16414),f712(x16412,x16413,x16414)) % 187.86/187.66 [1642]~E(x16421,x16422)+E(f712(x16423,x16421,x16424),f712(x16423,x16422,x16424)) % 187.86/187.66 [1643]~E(x16431,x16432)+E(f712(x16433,x16434,x16431),f712(x16433,x16434,x16432)) % 187.86/187.66 [1644]~E(x16441,x16442)+E(f465(x16441,x16443,x16444,x16445,x16446),f465(x16442,x16443,x16444,x16445,x16446)) % 187.86/187.66 [1645]~E(x16451,x16452)+E(f465(x16453,x16451,x16454,x16455,x16456),f465(x16453,x16452,x16454,x16455,x16456)) % 187.86/187.66 [1646]~E(x16461,x16462)+E(f465(x16463,x16464,x16461,x16465,x16466),f465(x16463,x16464,x16462,x16465,x16466)) % 187.86/187.66 [1647]~E(x16471,x16472)+E(f465(x16473,x16474,x16475,x16471,x16476),f465(x16473,x16474,x16475,x16472,x16476)) % 187.86/187.66 [1648]~E(x16481,x16482)+E(f465(x16483,x16484,x16485,x16486,x16481),f465(x16483,x16484,x16485,x16486,x16482)) % 187.86/187.66 [1649]~E(x16491,x16492)+E(f394(x16491,x16493,x16494,x16495),f394(x16492,x16493,x16494,x16495)) % 187.86/187.66 [1650]~E(x16501,x16502)+E(f394(x16503,x16501,x16504,x16505),f394(x16503,x16502,x16504,x16505)) % 187.86/187.66 [1651]~E(x16511,x16512)+E(f394(x16513,x16514,x16511,x16515),f394(x16513,x16514,x16512,x16515)) % 187.86/187.66 [1652]~E(x16521,x16522)+E(f394(x16523,x16524,x16525,x16521),f394(x16523,x16524,x16525,x16522)) % 187.86/187.66 [1653]~E(x16531,x16532)+E(f737(x16531,x16533,x16534),f737(x16532,x16533,x16534)) % 187.86/187.66 [1654]~E(x16541,x16542)+E(f737(x16543,x16541,x16544),f737(x16543,x16542,x16544)) % 187.86/187.66 [1655]~E(x16551,x16552)+E(f737(x16553,x16554,x16551),f737(x16553,x16554,x16552)) % 187.86/187.66 [1656]~E(x16561,x16562)+E(f365(x16561,x16563),f365(x16562,x16563)) % 187.86/187.66 [1657]~E(x16571,x16572)+E(f365(x16573,x16571),f365(x16573,x16572)) % 187.86/187.66 [1658]~E(x16581,x16582)+E(f197(x16581,x16583,x16584,x16585,x16586),f197(x16582,x16583,x16584,x16585,x16586)) % 187.86/187.66 [1659]~E(x16591,x16592)+E(f197(x16593,x16591,x16594,x16595,x16596),f197(x16593,x16592,x16594,x16595,x16596)) % 187.86/187.66 [1660]~E(x16601,x16602)+E(f197(x16603,x16604,x16601,x16605,x16606),f197(x16603,x16604,x16602,x16605,x16606)) % 187.86/187.66 [1661]~E(x16611,x16612)+E(f197(x16613,x16614,x16615,x16611,x16616),f197(x16613,x16614,x16615,x16612,x16616)) % 187.86/187.66 [1662]~E(x16621,x16622)+E(f197(x16623,x16624,x16625,x16626,x16621),f197(x16623,x16624,x16625,x16626,x16622)) % 187.86/187.66 [1663]~E(x16631,x16632)+E(f341(x16631,x16633,x16634,x16635),f341(x16632,x16633,x16634,x16635)) % 187.86/187.66 [1664]~E(x16641,x16642)+E(f341(x16643,x16641,x16644,x16645),f341(x16643,x16642,x16644,x16645)) % 187.86/187.66 [1665]~E(x16651,x16652)+E(f341(x16653,x16654,x16651,x16655),f341(x16653,x16654,x16652,x16655)) % 187.86/187.66 [1666]~E(x16661,x16662)+E(f341(x16663,x16664,x16665,x16661),f341(x16663,x16664,x16665,x16662)) % 187.86/187.66 [1667]~E(x16671,x16672)+E(f327(x16671,x16673,x16674,x16675),f327(x16672,x16673,x16674,x16675)) % 187.86/187.66 [1668]~E(x16681,x16682)+E(f327(x16683,x16681,x16684,x16685),f327(x16683,x16682,x16684,x16685)) % 187.86/187.66 [1669]~E(x16691,x16692)+E(f327(x16693,x16694,x16691,x16695),f327(x16693,x16694,x16692,x16695)) % 187.86/187.66 [1670]~E(x16701,x16702)+E(f327(x16703,x16704,x16705,x16701),f327(x16703,x16704,x16705,x16702)) % 187.86/187.66 [1671]~E(x16711,x16712)+E(f551(x16711,x16713,x16714,x16715),f551(x16712,x16713,x16714,x16715)) % 187.86/187.66 [1672]~E(x16721,x16722)+E(f551(x16723,x16721,x16724,x16725),f551(x16723,x16722,x16724,x16725)) % 187.86/187.66 [1673]~E(x16731,x16732)+E(f551(x16733,x16734,x16731,x16735),f551(x16733,x16734,x16732,x16735)) % 187.86/187.66 [1674]~E(x16741,x16742)+E(f551(x16743,x16744,x16745,x16741),f551(x16743,x16744,x16745,x16742)) % 187.86/187.66 [1675]~E(x16751,x16752)+E(f728(x16751,x16753,x16754),f728(x16752,x16753,x16754)) % 187.86/187.66 [1676]~E(x16761,x16762)+E(f728(x16763,x16761,x16764),f728(x16763,x16762,x16764)) % 187.86/187.66 [1677]~E(x16771,x16772)+E(f728(x16773,x16774,x16771),f728(x16773,x16774,x16772)) % 187.86/187.66 [1678]~E(x16781,x16782)+E(f721(x16781,x16783,x16784),f721(x16782,x16783,x16784)) % 187.86/187.66 [1679]~E(x16791,x16792)+E(f721(x16793,x16791,x16794),f721(x16793,x16792,x16794)) % 187.86/187.66 [1680]~E(x16801,x16802)+E(f721(x16803,x16804,x16801),f721(x16803,x16804,x16802)) % 187.86/187.66 [1681]~E(x16811,x16812)+E(f562(x16811,x16813,x16814,x16815,x16816,x16817),f562(x16812,x16813,x16814,x16815,x16816,x16817)) % 187.86/187.66 [1682]~E(x16821,x16822)+E(f562(x16823,x16821,x16824,x16825,x16826,x16827),f562(x16823,x16822,x16824,x16825,x16826,x16827)) % 187.86/187.66 [1683]~E(x16831,x16832)+E(f562(x16833,x16834,x16831,x16835,x16836,x16837),f562(x16833,x16834,x16832,x16835,x16836,x16837)) % 187.86/187.66 [1684]~E(x16841,x16842)+E(f562(x16843,x16844,x16845,x16841,x16846,x16847),f562(x16843,x16844,x16845,x16842,x16846,x16847)) % 187.86/187.66 [1685]~E(x16851,x16852)+E(f562(x16853,x16854,x16855,x16856,x16851,x16857),f562(x16853,x16854,x16855,x16856,x16852,x16857)) % 187.86/187.66 [1686]~E(x16861,x16862)+E(f562(x16863,x16864,x16865,x16866,x16867,x16861),f562(x16863,x16864,x16865,x16866,x16867,x16862)) % 187.86/187.66 [1687]~E(x16871,x16872)+E(f823(x16871,x16873),f823(x16872,x16873)) % 187.86/187.66 [1688]~E(x16881,x16882)+E(f823(x16883,x16881),f823(x16883,x16882)) % 187.86/187.66 [1689]~E(x16891,x16892)+E(f609(x16891,x16893),f609(x16892,x16893)) % 187.86/187.66 [1690]~E(x16901,x16902)+E(f609(x16903,x16901),f609(x16903,x16902)) % 187.86/187.66 [1691]~E(x16911,x16912)+E(f318(x16911,x16913,x16914,x16915),f318(x16912,x16913,x16914,x16915)) % 187.86/187.66 [1692]~E(x16921,x16922)+E(f318(x16923,x16921,x16924,x16925),f318(x16923,x16922,x16924,x16925)) % 187.86/187.66 [1693]~E(x16931,x16932)+E(f318(x16933,x16934,x16931,x16935),f318(x16933,x16934,x16932,x16935)) % 187.86/187.66 [1694]~E(x16941,x16942)+E(f318(x16943,x16944,x16945,x16941),f318(x16943,x16944,x16945,x16942)) % 187.86/187.66 [1695]~E(x16951,x16952)+E(f138(x16951,x16953),f138(x16952,x16953)) % 187.86/187.66 [1696]~E(x16961,x16962)+E(f138(x16963,x16961),f138(x16963,x16962)) % 187.86/187.66 [1697]~E(x16971,x16972)+E(f638(x16971,x16973,x16974,x16975,x16976,x16977,x16978,x16979),f638(x16972,x16973,x16974,x16975,x16976,x16977,x16978,x16979)) % 187.86/187.66 [1698]~E(x16981,x16982)+E(f638(x16983,x16981,x16984,x16985,x16986,x16987,x16988,x16989),f638(x16983,x16982,x16984,x16985,x16986,x16987,x16988,x16989)) % 187.86/187.66 [1699]~E(x16991,x16992)+E(f638(x16993,x16994,x16991,x16995,x16996,x16997,x16998,x16999),f638(x16993,x16994,x16992,x16995,x16996,x16997,x16998,x16999)) % 187.86/187.66 [1700]~E(x17001,x17002)+E(f638(x17003,x17004,x17005,x17001,x17006,x17007,x17008,x17009),f638(x17003,x17004,x17005,x17002,x17006,x17007,x17008,x17009)) % 187.86/187.66 [1701]~E(x17011,x17012)+E(f638(x17013,x17014,x17015,x17016,x17011,x17017,x17018,x17019),f638(x17013,x17014,x17015,x17016,x17012,x17017,x17018,x17019)) % 187.86/187.66 [1702]~E(x17021,x17022)+E(f638(x17023,x17024,x17025,x17026,x17027,x17021,x17028,x17029),f638(x17023,x17024,x17025,x17026,x17027,x17022,x17028,x17029)) % 187.86/187.67 [1703]~E(x17031,x17032)+E(f638(x17033,x17034,x17035,x17036,x17037,x17038,x17031,x17039),f638(x17033,x17034,x17035,x17036,x17037,x17038,x17032,x17039)) % 187.86/187.67 [1704]~E(x17041,x17042)+E(f638(x17043,x17044,x17045,x17046,x17047,x17048,x17049,x17041),f638(x17043,x17044,x17045,x17046,x17047,x17048,x17049,x17042)) % 187.86/187.67 [1705]~E(x17051,x17052)+E(f742(x17051,x17053,x17054),f742(x17052,x17053,x17054)) % 187.86/187.67 [1706]~E(x17061,x17062)+E(f742(x17063,x17061,x17064),f742(x17063,x17062,x17064)) % 187.86/187.67 [1707]~E(x17071,x17072)+E(f742(x17073,x17074,x17071),f742(x17073,x17074,x17072)) % 187.86/187.67 [1708]~E(x17081,x17082)+E(f501(x17081,x17083,x17084,x17085,x17086,x17087),f501(x17082,x17083,x17084,x17085,x17086,x17087)) % 187.86/187.67 [1709]~E(x17091,x17092)+E(f501(x17093,x17091,x17094,x17095,x17096,x17097),f501(x17093,x17092,x17094,x17095,x17096,x17097)) % 187.86/187.67 [1710]~E(x17101,x17102)+E(f501(x17103,x17104,x17101,x17105,x17106,x17107),f501(x17103,x17104,x17102,x17105,x17106,x17107)) % 187.86/187.67 [1711]~E(x17111,x17112)+E(f501(x17113,x17114,x17115,x17111,x17116,x17117),f501(x17113,x17114,x17115,x17112,x17116,x17117)) % 187.86/187.67 [1712]~E(x17121,x17122)+E(f501(x17123,x17124,x17125,x17126,x17121,x17127),f501(x17123,x17124,x17125,x17126,x17122,x17127)) % 187.86/187.67 [1713]~E(x17131,x17132)+E(f501(x17133,x17134,x17135,x17136,x17137,x17131),f501(x17133,x17134,x17135,x17136,x17137,x17132)) % 187.86/187.67 [1714]~E(x17141,x17142)+E(f446(x17141,x17143,x17144,x17145,x17146),f446(x17142,x17143,x17144,x17145,x17146)) % 187.86/187.67 [1715]~E(x17151,x17152)+E(f446(x17153,x17151,x17154,x17155,x17156),f446(x17153,x17152,x17154,x17155,x17156)) % 187.86/187.67 [1716]~E(x17161,x17162)+E(f446(x17163,x17164,x17161,x17165,x17166),f446(x17163,x17164,x17162,x17165,x17166)) % 187.86/187.67 [1717]~E(x17171,x17172)+E(f446(x17173,x17174,x17175,x17171,x17176),f446(x17173,x17174,x17175,x17172,x17176)) % 187.86/187.67 [1718]~E(x17181,x17182)+E(f446(x17183,x17184,x17185,x17186,x17181),f446(x17183,x17184,x17185,x17186,x17182)) % 187.86/187.67 [1719]~E(x17191,x17192)+E(f560(x17191,x17193,x17194,x17195),f560(x17192,x17193,x17194,x17195)) % 187.86/187.67 [1720]~E(x17201,x17202)+E(f560(x17203,x17201,x17204,x17205),f560(x17203,x17202,x17204,x17205)) % 187.86/187.67 [1721]~E(x17211,x17212)+E(f560(x17213,x17214,x17211,x17215),f560(x17213,x17214,x17212,x17215)) % 187.86/187.67 [1722]~E(x17221,x17222)+E(f560(x17223,x17224,x17225,x17221),f560(x17223,x17224,x17225,x17222)) % 187.86/187.67 [1723]~E(x17231,x17232)+E(f381(x17231,x17233),f381(x17232,x17233)) % 187.86/187.67 [1724]~E(x17241,x17242)+E(f381(x17243,x17241),f381(x17243,x17242)) % 187.86/187.67 [1725]~E(x17251,x17252)+E(f766(x17251,x17253,x17254,x17255),f766(x17252,x17253,x17254,x17255)) % 187.86/187.67 [1726]~E(x17261,x17262)+E(f766(x17263,x17261,x17264,x17265),f766(x17263,x17262,x17264,x17265)) % 187.86/187.67 [1727]~E(x17271,x17272)+E(f766(x17273,x17274,x17271,x17275),f766(x17273,x17274,x17272,x17275)) % 187.86/187.67 [1728]~E(x17281,x17282)+E(f766(x17283,x17284,x17285,x17281),f766(x17283,x17284,x17285,x17282)) % 187.86/187.67 [1729]~E(x17291,x17292)+E(f772(x17291,x17293,x17294),f772(x17292,x17293,x17294)) % 187.86/187.67 [1730]~E(x17301,x17302)+E(f772(x17303,x17301,x17304),f772(x17303,x17302,x17304)) % 187.86/187.67 [1731]~E(x17311,x17312)+E(f772(x17313,x17314,x17311),f772(x17313,x17314,x17312)) % 187.86/187.67 [1732]~E(x17321,x17322)+E(f760(x17321,x17323,x17324,x17325,x17326),f760(x17322,x17323,x17324,x17325,x17326)) % 187.86/187.67 [1733]~E(x17331,x17332)+E(f760(x17333,x17331,x17334,x17335,x17336),f760(x17333,x17332,x17334,x17335,x17336)) % 187.86/187.67 [1734]~E(x17341,x17342)+E(f760(x17343,x17344,x17341,x17345,x17346),f760(x17343,x17344,x17342,x17345,x17346)) % 187.86/187.67 [1735]~E(x17351,x17352)+E(f760(x17353,x17354,x17355,x17351,x17356),f760(x17353,x17354,x17355,x17352,x17356)) % 187.86/187.67 [1736]~E(x17361,x17362)+E(f760(x17363,x17364,x17365,x17366,x17361),f760(x17363,x17364,x17365,x17366,x17362)) % 187.86/187.67 [1737]~E(x17371,x17372)+E(f731(x17371,x17373),f731(x17372,x17373)) % 187.86/187.67 [1738]~E(x17381,x17382)+E(f731(x17383,x17381),f731(x17383,x17382)) % 187.86/187.67 [1739]~E(x17391,x17392)+E(f313(x17391,x17393),f313(x17392,x17393)) % 187.86/187.67 [1740]~E(x17401,x17402)+E(f313(x17403,x17401),f313(x17403,x17402)) % 187.86/187.67 [1741]~E(x17411,x17412)+E(f483(x17411,x17413,x17414,x17415),f483(x17412,x17413,x17414,x17415)) % 187.86/187.67 [1742]~E(x17421,x17422)+E(f483(x17423,x17421,x17424,x17425),f483(x17423,x17422,x17424,x17425)) % 187.86/187.67 [1743]~E(x17431,x17432)+E(f483(x17433,x17434,x17431,x17435),f483(x17433,x17434,x17432,x17435)) % 187.86/187.67 [1744]~E(x17441,x17442)+E(f483(x17443,x17444,x17445,x17441),f483(x17443,x17444,x17445,x17442)) % 187.86/187.67 [1745]~E(x17451,x17452)+E(f615(x17451,x17453,x17454,x17455),f615(x17452,x17453,x17454,x17455)) % 187.86/187.67 [1746]~E(x17461,x17462)+E(f615(x17463,x17461,x17464,x17465),f615(x17463,x17462,x17464,x17465)) % 187.86/187.67 [1747]~E(x17471,x17472)+E(f615(x17473,x17474,x17471,x17475),f615(x17473,x17474,x17472,x17475)) % 187.86/187.67 [1748]~E(x17481,x17482)+E(f615(x17483,x17484,x17485,x17481),f615(x17483,x17484,x17485,x17482)) % 187.86/187.67 [1749]~E(x17491,x17492)+E(f588(x17491,x17493,x17494,x17495,x17496,x17497,x17498,x17499),f588(x17492,x17493,x17494,x17495,x17496,x17497,x17498,x17499)) % 187.86/187.67 [1750]~E(x17501,x17502)+E(f588(x17503,x17501,x17504,x17505,x17506,x17507,x17508,x17509),f588(x17503,x17502,x17504,x17505,x17506,x17507,x17508,x17509)) % 187.86/187.67 [1751]~E(x17511,x17512)+E(f588(x17513,x17514,x17511,x17515,x17516,x17517,x17518,x17519),f588(x17513,x17514,x17512,x17515,x17516,x17517,x17518,x17519)) % 187.86/187.67 [1752]~E(x17521,x17522)+E(f588(x17523,x17524,x17525,x17521,x17526,x17527,x17528,x17529),f588(x17523,x17524,x17525,x17522,x17526,x17527,x17528,x17529)) % 187.86/187.67 [1753]~E(x17531,x17532)+E(f588(x17533,x17534,x17535,x17536,x17531,x17537,x17538,x17539),f588(x17533,x17534,x17535,x17536,x17532,x17537,x17538,x17539)) % 187.86/187.67 [1754]~E(x17541,x17542)+E(f588(x17543,x17544,x17545,x17546,x17547,x17541,x17548,x17549),f588(x17543,x17544,x17545,x17546,x17547,x17542,x17548,x17549)) % 187.86/187.67 [1755]~E(x17551,x17552)+E(f588(x17553,x17554,x17555,x17556,x17557,x17558,x17551,x17559),f588(x17553,x17554,x17555,x17556,x17557,x17558,x17552,x17559)) % 187.86/187.67 [1756]~E(x17561,x17562)+E(f588(x17563,x17564,x17565,x17566,x17567,x17568,x17569,x17561),f588(x17563,x17564,x17565,x17566,x17567,x17568,x17569,x17562)) % 187.86/187.67 [1757]~E(x17571,x17572)+E(f374(x17571,x17573,x17574,x17575),f374(x17572,x17573,x17574,x17575)) % 187.86/187.67 [1758]~E(x17581,x17582)+E(f374(x17583,x17581,x17584,x17585),f374(x17583,x17582,x17584,x17585)) % 187.86/187.67 [1759]~E(x17591,x17592)+E(f374(x17593,x17594,x17591,x17595),f374(x17593,x17594,x17592,x17595)) % 187.86/187.67 [1760]~E(x17601,x17602)+E(f374(x17603,x17604,x17605,x17601),f374(x17603,x17604,x17605,x17602)) % 187.86/187.67 [1761]~E(x17611,x17612)+E(f270(x17611,x17613,x17614,x17615),f270(x17612,x17613,x17614,x17615)) % 187.86/187.67 [1762]~E(x17621,x17622)+E(f270(x17623,x17621,x17624,x17625),f270(x17623,x17622,x17624,x17625)) % 187.86/187.67 [1763]~E(x17631,x17632)+E(f270(x17633,x17634,x17631,x17635),f270(x17633,x17634,x17632,x17635)) % 187.86/187.67 [1764]~E(x17641,x17642)+E(f270(x17643,x17644,x17645,x17641),f270(x17643,x17644,x17645,x17642)) % 187.86/187.67 [1765]~E(x17651,x17652)+E(f852(x17651,x17653,x17654),f852(x17652,x17653,x17654)) % 187.86/187.67 [1766]~E(x17661,x17662)+E(f852(x17663,x17661,x17664),f852(x17663,x17662,x17664)) % 187.86/187.67 [1767]~E(x17671,x17672)+E(f852(x17673,x17674,x17671),f852(x17673,x17674,x17672)) % 187.86/187.67 [1768]~E(x17681,x17682)+E(f838(x17681,x17683,x17684),f838(x17682,x17683,x17684)) % 187.86/187.67 [1769]~E(x17691,x17692)+E(f838(x17693,x17691,x17694),f838(x17693,x17692,x17694)) % 187.86/187.67 [1770]~E(x17701,x17702)+E(f838(x17703,x17704,x17701),f838(x17703,x17704,x17702)) % 187.86/187.67 [1771]~E(x17711,x17712)+E(f21(x17711,x17713),f21(x17712,x17713)) % 187.86/187.67 [1772]~E(x17721,x17722)+E(f21(x17723,x17721),f21(x17723,x17722)) % 187.86/187.67 [1773]~E(x17731,x17732)+E(f271(x17731,x17733,x17734,x17735,x17736),f271(x17732,x17733,x17734,x17735,x17736)) % 187.86/187.67 [1774]~E(x17741,x17742)+E(f271(x17743,x17741,x17744,x17745,x17746),f271(x17743,x17742,x17744,x17745,x17746)) % 187.86/187.67 [1775]~E(x17751,x17752)+E(f271(x17753,x17754,x17751,x17755,x17756),f271(x17753,x17754,x17752,x17755,x17756)) % 187.86/187.67 [1776]~E(x17761,x17762)+E(f271(x17763,x17764,x17765,x17761,x17766),f271(x17763,x17764,x17765,x17762,x17766)) % 187.86/187.67 [1777]~E(x17771,x17772)+E(f271(x17773,x17774,x17775,x17776,x17771),f271(x17773,x17774,x17775,x17776,x17772)) % 187.86/187.67 [1778]~E(x17781,x17782)+E(f552(x17781,x17783,x17784,x17785),f552(x17782,x17783,x17784,x17785)) % 187.86/187.67 [1779]~E(x17791,x17792)+E(f552(x17793,x17791,x17794,x17795),f552(x17793,x17792,x17794,x17795)) % 187.86/187.67 [1780]~E(x17801,x17802)+E(f552(x17803,x17804,x17801,x17805),f552(x17803,x17804,x17802,x17805)) % 187.86/187.67 [1781]~E(x17811,x17812)+E(f552(x17813,x17814,x17815,x17811),f552(x17813,x17814,x17815,x17812)) % 187.86/187.67 [1782]~E(x17821,x17822)+E(f466(x17821,x17823,x17824),f466(x17822,x17823,x17824)) % 187.86/187.67 [1783]~E(x17831,x17832)+E(f466(x17833,x17831,x17834),f466(x17833,x17832,x17834)) % 187.86/187.67 [1784]~E(x17841,x17842)+E(f466(x17843,x17844,x17841),f466(x17843,x17844,x17842)) % 187.86/187.67 [1785]~E(x17851,x17852)+E(f474(x17851,x17853,x17854),f474(x17852,x17853,x17854)) % 187.86/187.67 [1786]~E(x17861,x17862)+E(f474(x17863,x17861,x17864),f474(x17863,x17862,x17864)) % 187.86/187.67 [1787]~E(x17871,x17872)+E(f474(x17873,x17874,x17871),f474(x17873,x17874,x17872)) % 187.86/187.67 [1788]~E(x17881,x17882)+E(f328(x17881,x17883,x17884),f328(x17882,x17883,x17884)) % 187.86/187.67 [1789]~E(x17891,x17892)+E(f328(x17893,x17891,x17894),f328(x17893,x17892,x17894)) % 187.86/187.67 [1790]~E(x17901,x17902)+E(f328(x17903,x17904,x17901),f328(x17903,x17904,x17902)) % 187.86/187.67 [1791]~E(x17911,x17912)+E(f594(x17911,x17913,x17914,x17915,x17916),f594(x17912,x17913,x17914,x17915,x17916)) % 187.86/187.67 [1792]~E(x17921,x17922)+E(f594(x17923,x17921,x17924,x17925,x17926),f594(x17923,x17922,x17924,x17925,x17926)) % 187.86/187.67 [1793]~E(x17931,x17932)+E(f594(x17933,x17934,x17931,x17935,x17936),f594(x17933,x17934,x17932,x17935,x17936)) % 187.86/187.67 [1794]~E(x17941,x17942)+E(f594(x17943,x17944,x17945,x17941,x17946),f594(x17943,x17944,x17945,x17942,x17946)) % 187.86/187.67 [1795]~E(x17951,x17952)+E(f594(x17953,x17954,x17955,x17956,x17951),f594(x17953,x17954,x17955,x17956,x17952)) % 187.86/187.67 [1796]~E(x17961,x17962)+E(f439(x17961,x17963,x17964,x17965),f439(x17962,x17963,x17964,x17965)) % 187.86/187.67 [1797]~E(x17971,x17972)+E(f439(x17973,x17971,x17974,x17975),f439(x17973,x17972,x17974,x17975)) % 187.86/187.67 [1798]~E(x17981,x17982)+E(f439(x17983,x17984,x17981,x17985),f439(x17983,x17984,x17982,x17985)) % 187.86/187.67 [1799]~E(x17991,x17992)+E(f439(x17993,x17994,x17995,x17991),f439(x17993,x17994,x17995,x17992)) % 187.86/187.67 [1800]~E(x18001,x18002)+E(f448(x18001,x18003,x18004,x18005,x18006),f448(x18002,x18003,x18004,x18005,x18006)) % 187.86/187.67 [1801]~E(x18011,x18012)+E(f448(x18013,x18011,x18014,x18015,x18016),f448(x18013,x18012,x18014,x18015,x18016)) % 187.86/187.67 [1802]~E(x18021,x18022)+E(f448(x18023,x18024,x18021,x18025,x18026),f448(x18023,x18024,x18022,x18025,x18026)) % 187.86/187.67 [1803]~E(x18031,x18032)+E(f448(x18033,x18034,x18035,x18031,x18036),f448(x18033,x18034,x18035,x18032,x18036)) % 187.86/187.67 [1804]~E(x18041,x18042)+E(f448(x18043,x18044,x18045,x18046,x18041),f448(x18043,x18044,x18045,x18046,x18042)) % 187.86/187.67 [1805]~E(x18051,x18052)+E(f581(x18051,x18053,x18054,x18055,x18056),f581(x18052,x18053,x18054,x18055,x18056)) % 187.86/187.67 [1806]~E(x18061,x18062)+E(f581(x18063,x18061,x18064,x18065,x18066),f581(x18063,x18062,x18064,x18065,x18066)) % 187.86/187.67 [1807]~E(x18071,x18072)+E(f581(x18073,x18074,x18071,x18075,x18076),f581(x18073,x18074,x18072,x18075,x18076)) % 187.86/187.67 [1808]~E(x18081,x18082)+E(f581(x18083,x18084,x18085,x18081,x18086),f581(x18083,x18084,x18085,x18082,x18086)) % 187.86/187.67 [1809]~E(x18091,x18092)+E(f581(x18093,x18094,x18095,x18096,x18091),f581(x18093,x18094,x18095,x18096,x18092)) % 187.86/187.67 [1810]~E(x18101,x18102)+E(f451(x18101,x18103),f451(x18102,x18103)) % 187.86/187.67 [1811]~E(x18111,x18112)+E(f451(x18113,x18111),f451(x18113,x18112)) % 187.86/187.67 [1812]~E(x18121,x18122)+E(f547(x18121,x18123),f547(x18122,x18123)) % 187.86/187.67 [1813]~E(x18131,x18132)+E(f547(x18133,x18131),f547(x18133,x18132)) % 187.86/187.67 [1814]~E(x18141,x18142)+E(f713(x18141,x18143,x18144),f713(x18142,x18143,x18144)) % 187.86/187.67 [1815]~E(x18151,x18152)+E(f713(x18153,x18151,x18154),f713(x18153,x18152,x18154)) % 187.86/187.67 [1816]~E(x18161,x18162)+E(f713(x18163,x18164,x18161),f713(x18163,x18164,x18162)) % 187.86/187.67 [1817]~E(x18171,x18172)+E(f536(x18171,x18173,x18174,x18175),f536(x18172,x18173,x18174,x18175)) % 187.86/187.67 [1818]~E(x18181,x18182)+E(f536(x18183,x18181,x18184,x18185),f536(x18183,x18182,x18184,x18185)) % 187.86/187.67 [1819]~E(x18191,x18192)+E(f536(x18193,x18194,x18191,x18195),f536(x18193,x18194,x18192,x18195)) % 187.86/187.67 [1820]~E(x18201,x18202)+E(f536(x18203,x18204,x18205,x18201),f536(x18203,x18204,x18205,x18202)) % 187.86/187.67 [1821]~E(x18211,x18212)+E(f698(x18211,x18213,x18214,x18215,x18216),f698(x18212,x18213,x18214,x18215,x18216)) % 187.86/187.67 [1822]~E(x18221,x18222)+E(f698(x18223,x18221,x18224,x18225,x18226),f698(x18223,x18222,x18224,x18225,x18226)) % 187.86/187.67 [1823]~E(x18231,x18232)+E(f698(x18233,x18234,x18231,x18235,x18236),f698(x18233,x18234,x18232,x18235,x18236)) % 187.86/187.67 [1824]~E(x18241,x18242)+E(f698(x18243,x18244,x18245,x18241,x18246),f698(x18243,x18244,x18245,x18242,x18246)) % 187.86/187.67 [1825]~E(x18251,x18252)+E(f698(x18253,x18254,x18255,x18256,x18251),f698(x18253,x18254,x18255,x18256,x18252)) % 187.86/187.67 [1826]~E(x18261,x18262)+E(f434(x18261,x18263,x18264,x18265),f434(x18262,x18263,x18264,x18265)) % 187.86/187.67 [1827]~E(x18271,x18272)+E(f434(x18273,x18271,x18274,x18275),f434(x18273,x18272,x18274,x18275)) % 187.86/187.67 [1828]~E(x18281,x18282)+E(f434(x18283,x18284,x18281,x18285),f434(x18283,x18284,x18282,x18285)) % 187.86/187.67 [1829]~E(x18291,x18292)+E(f434(x18293,x18294,x18295,x18291),f434(x18293,x18294,x18295,x18292)) % 187.86/187.67 [1830]~E(x18301,x18302)+E(f723(x18301,x18303),f723(x18302,x18303)) % 187.86/187.67 [1831]~E(x18311,x18312)+E(f723(x18313,x18311),f723(x18313,x18312)) % 187.86/187.67 [1832]~E(x18321,x18322)+E(f568(x18321,x18323,x18324),f568(x18322,x18323,x18324)) % 187.86/187.67 [1833]~E(x18331,x18332)+E(f568(x18333,x18331,x18334),f568(x18333,x18332,x18334)) % 187.86/187.67 [1834]~E(x18341,x18342)+E(f568(x18343,x18344,x18341),f568(x18343,x18344,x18342)) % 187.86/187.67 [1835]~E(x18351,x18352)+E(f677(x18351,x18353,x18354,x18355,x18356),f677(x18352,x18353,x18354,x18355,x18356)) % 187.86/187.67 [1836]~E(x18361,x18362)+E(f677(x18363,x18361,x18364,x18365,x18366),f677(x18363,x18362,x18364,x18365,x18366)) % 187.86/187.67 [1837]~E(x18371,x18372)+E(f677(x18373,x18374,x18371,x18375,x18376),f677(x18373,x18374,x18372,x18375,x18376)) % 187.86/187.67 [1838]~E(x18381,x18382)+E(f677(x18383,x18384,x18385,x18381,x18386),f677(x18383,x18384,x18385,x18382,x18386)) % 187.86/187.67 [1839]~E(x18391,x18392)+E(f677(x18393,x18394,x18395,x18396,x18391),f677(x18393,x18394,x18395,x18396,x18392)) % 187.86/187.67 [1840]~E(x18401,x18402)+E(f672(x18401,x18403,x18404),f672(x18402,x18403,x18404)) % 187.86/187.67 [1841]~E(x18411,x18412)+E(f672(x18413,x18411,x18414),f672(x18413,x18412,x18414)) % 187.86/187.67 [1842]~E(x18421,x18422)+E(f672(x18423,x18424,x18421),f672(x18423,x18424,x18422)) % 187.86/187.67 [1843]~E(x18431,x18432)+E(f803(x18431,x18433,x18434,x18435,x18436),f803(x18432,x18433,x18434,x18435,x18436)) % 187.86/187.67 [1844]~E(x18441,x18442)+E(f803(x18443,x18441,x18444,x18445,x18446),f803(x18443,x18442,x18444,x18445,x18446)) % 187.86/187.67 [1845]~E(x18451,x18452)+E(f803(x18453,x18454,x18451,x18455,x18456),f803(x18453,x18454,x18452,x18455,x18456)) % 187.86/187.67 [1846]~E(x18461,x18462)+E(f803(x18463,x18464,x18465,x18461,x18466),f803(x18463,x18464,x18465,x18462,x18466)) % 187.86/187.67 [1847]~E(x18471,x18472)+E(f803(x18473,x18474,x18475,x18476,x18471),f803(x18473,x18474,x18475,x18476,x18472)) % 187.86/187.67 [1848]~E(x18481,x18482)+E(f441(x18481,x18483,x18484,x18485),f441(x18482,x18483,x18484,x18485)) % 187.86/187.67 [1849]~E(x18491,x18492)+E(f441(x18493,x18491,x18494,x18495),f441(x18493,x18492,x18494,x18495)) % 187.86/187.67 [1850]~E(x18501,x18502)+E(f441(x18503,x18504,x18501,x18505),f441(x18503,x18504,x18502,x18505)) % 187.86/187.67 [1851]~E(x18511,x18512)+E(f441(x18513,x18514,x18515,x18511),f441(x18513,x18514,x18515,x18512)) % 187.86/187.67 [1852]~E(x18521,x18522)+E(f758(x18521,x18523,x18524,x18525),f758(x18522,x18523,x18524,x18525)) % 187.86/187.67 [1853]~E(x18531,x18532)+E(f758(x18533,x18531,x18534,x18535),f758(x18533,x18532,x18534,x18535)) % 187.86/187.67 [1854]~E(x18541,x18542)+E(f758(x18543,x18544,x18541,x18545),f758(x18543,x18544,x18542,x18545)) % 187.86/187.67 [1855]~E(x18551,x18552)+E(f758(x18553,x18554,x18555,x18551),f758(x18553,x18554,x18555,x18552)) % 187.86/187.67 [1856]~E(x18561,x18562)+E(f290(x18561,x18563,x18564),f290(x18562,x18563,x18564)) % 187.86/187.67 [1857]~E(x18571,x18572)+E(f290(x18573,x18571,x18574),f290(x18573,x18572,x18574)) % 187.86/187.67 [1858]~E(x18581,x18582)+E(f290(x18583,x18584,x18581),f290(x18583,x18584,x18582)) % 187.86/187.67 [1859]~E(x18591,x18592)+E(f332(x18591,x18593,x18594),f332(x18592,x18593,x18594)) % 187.86/187.67 [1860]~E(x18601,x18602)+E(f332(x18603,x18601,x18604),f332(x18603,x18602,x18604)) % 187.86/187.67 [1861]~E(x18611,x18612)+E(f332(x18613,x18614,x18611),f332(x18613,x18614,x18612)) % 187.86/187.67 [1862]~E(x18621,x18622)+E(f642(x18621,x18623,x18624),f642(x18622,x18623,x18624)) % 187.86/187.67 [1863]~E(x18631,x18632)+E(f642(x18633,x18631,x18634),f642(x18633,x18632,x18634)) % 187.86/187.67 [1864]~E(x18641,x18642)+E(f642(x18643,x18644,x18641),f642(x18643,x18644,x18642)) % 187.86/187.67 [1865]~E(x18651,x18652)+E(f851(x18651,x18653,x18654),f851(x18652,x18653,x18654)) % 187.86/187.67 [1866]~E(x18661,x18662)+E(f851(x18663,x18661,x18664),f851(x18663,x18662,x18664)) % 187.86/187.67 [1867]~E(x18671,x18672)+E(f851(x18673,x18674,x18671),f851(x18673,x18674,x18672)) % 187.86/187.67 [1868]~E(x18681,x18682)+E(f533(x18681,x18683,x18684,x18685),f533(x18682,x18683,x18684,x18685)) % 187.86/187.67 [1869]~E(x18691,x18692)+E(f533(x18693,x18691,x18694,x18695),f533(x18693,x18692,x18694,x18695)) % 187.86/187.67 [1870]~E(x18701,x18702)+E(f533(x18703,x18704,x18701,x18705),f533(x18703,x18704,x18702,x18705)) % 187.86/187.67 [1871]~E(x18711,x18712)+E(f533(x18713,x18714,x18715,x18711),f533(x18713,x18714,x18715,x18712)) % 187.86/187.67 [1872]~E(x18721,x18722)+E(f542(x18721,x18723),f542(x18722,x18723)) % 187.86/187.67 [1873]~E(x18731,x18732)+E(f542(x18733,x18731),f542(x18733,x18732)) % 187.86/187.67 [1874]~E(x18741,x18742)+E(f211(x18741,x18743,x18744),f211(x18742,x18743,x18744)) % 187.86/187.67 [1875]~E(x18751,x18752)+E(f211(x18753,x18751,x18754),f211(x18753,x18752,x18754)) % 187.86/187.67 [1876]~E(x18761,x18762)+E(f211(x18763,x18764,x18761),f211(x18763,x18764,x18762)) % 187.86/187.67 [1877]~E(x18771,x18772)+E(f452(x18771,x18773,x18774,x18775,x18776),f452(x18772,x18773,x18774,x18775,x18776)) % 187.86/187.67 [1878]~E(x18781,x18782)+E(f452(x18783,x18781,x18784,x18785,x18786),f452(x18783,x18782,x18784,x18785,x18786)) % 187.86/187.67 [1879]~E(x18791,x18792)+E(f452(x18793,x18794,x18791,x18795,x18796),f452(x18793,x18794,x18792,x18795,x18796)) % 187.86/187.67 [1880]~E(x18801,x18802)+E(f452(x18803,x18804,x18805,x18801,x18806),f452(x18803,x18804,x18805,x18802,x18806)) % 187.86/187.67 [1881]~E(x18811,x18812)+E(f452(x18813,x18814,x18815,x18816,x18811),f452(x18813,x18814,x18815,x18816,x18812)) % 187.86/187.67 [1882]~E(x18821,x18822)+E(f268(x18821,x18823,x18824),f268(x18822,x18823,x18824)) % 187.86/187.67 [1883]~E(x18831,x18832)+E(f268(x18833,x18831,x18834),f268(x18833,x18832,x18834)) % 187.86/187.67 [1884]~E(x18841,x18842)+E(f268(x18843,x18844,x18841),f268(x18843,x18844,x18842)) % 187.86/187.67 [1885]~E(x18851,x18852)+E(f613(x18851,x18853,x18854,x18855),f613(x18852,x18853,x18854,x18855)) % 187.86/187.67 [1886]~E(x18861,x18862)+E(f613(x18863,x18861,x18864,x18865),f613(x18863,x18862,x18864,x18865)) % 187.86/187.67 [1887]~E(x18871,x18872)+E(f613(x18873,x18874,x18871,x18875),f613(x18873,x18874,x18872,x18875)) % 187.86/187.67 [1888]~E(x18881,x18882)+E(f613(x18883,x18884,x18885,x18881),f613(x18883,x18884,x18885,x18882)) % 187.86/187.67 [1889]~E(x18891,x18892)+E(f843(x18891,x18893,x18894,x18895,x18896,x18897,x18898),f843(x18892,x18893,x18894,x18895,x18896,x18897,x18898)) % 187.86/187.67 [1890]~E(x18901,x18902)+E(f843(x18903,x18901,x18904,x18905,x18906,x18907,x18908),f843(x18903,x18902,x18904,x18905,x18906,x18907,x18908)) % 187.86/187.67 [1891]~E(x18911,x18912)+E(f843(x18913,x18914,x18911,x18915,x18916,x18917,x18918),f843(x18913,x18914,x18912,x18915,x18916,x18917,x18918)) % 187.86/187.67 [1892]~E(x18921,x18922)+E(f843(x18923,x18924,x18925,x18921,x18926,x18927,x18928),f843(x18923,x18924,x18925,x18922,x18926,x18927,x18928)) % 187.86/187.67 [1893]~E(x18931,x18932)+E(f843(x18933,x18934,x18935,x18936,x18931,x18937,x18938),f843(x18933,x18934,x18935,x18936,x18932,x18937,x18938)) % 187.86/187.67 [1894]~E(x18941,x18942)+E(f843(x18943,x18944,x18945,x18946,x18947,x18941,x18948),f843(x18943,x18944,x18945,x18946,x18947,x18942,x18948)) % 187.86/187.67 [1895]~E(x18951,x18952)+E(f843(x18953,x18954,x18955,x18956,x18957,x18958,x18951),f843(x18953,x18954,x18955,x18956,x18957,x18958,x18952)) % 187.86/187.67 [1896]~E(x18961,x18962)+E(f289(x18961,x18963,x18964),f289(x18962,x18963,x18964)) % 187.86/187.67 [1897]~E(x18971,x18972)+E(f289(x18973,x18971,x18974),f289(x18973,x18972,x18974)) % 187.86/187.67 [1898]~E(x18981,x18982)+E(f289(x18983,x18984,x18981),f289(x18983,x18984,x18982)) % 187.86/187.67 [1899]~E(x18991,x18992)+E(f759(x18991,x18993,x18994,x18995),f759(x18992,x18993,x18994,x18995)) % 187.86/187.67 [1900]~E(x19001,x19002)+E(f759(x19003,x19001,x19004,x19005),f759(x19003,x19002,x19004,x19005)) % 187.86/187.67 [1901]~E(x19011,x19012)+E(f759(x19013,x19014,x19011,x19015),f759(x19013,x19014,x19012,x19015)) % 187.86/187.67 [1902]~E(x19021,x19022)+E(f759(x19023,x19024,x19025,x19021),f759(x19023,x19024,x19025,x19022)) % 187.86/187.67 [1903]~E(x19031,x19032)+E(f393(x19031,x19033,x19034,x19035),f393(x19032,x19033,x19034,x19035)) % 187.86/187.67 [1904]~E(x19041,x19042)+E(f393(x19043,x19041,x19044,x19045),f393(x19043,x19042,x19044,x19045)) % 187.86/187.67 [1905]~E(x19051,x19052)+E(f393(x19053,x19054,x19051,x19055),f393(x19053,x19054,x19052,x19055)) % 187.86/187.67 [1906]~E(x19061,x19062)+E(f393(x19063,x19064,x19065,x19061),f393(x19063,x19064,x19065,x19062)) % 187.86/187.67 [1907]~E(x19071,x19072)+E(f627(x19071,x19073,x19074,x19075,x19076),f627(x19072,x19073,x19074,x19075,x19076)) % 187.86/187.67 [1908]~E(x19081,x19082)+E(f627(x19083,x19081,x19084,x19085,x19086),f627(x19083,x19082,x19084,x19085,x19086)) % 187.86/187.67 [1909]~E(x19091,x19092)+E(f627(x19093,x19094,x19091,x19095,x19096),f627(x19093,x19094,x19092,x19095,x19096)) % 187.86/187.67 [1910]~E(x19101,x19102)+E(f627(x19103,x19104,x19105,x19101,x19106),f627(x19103,x19104,x19105,x19102,x19106)) % 187.86/187.67 [1911]~E(x19111,x19112)+E(f627(x19113,x19114,x19115,x19116,x19111),f627(x19113,x19114,x19115,x19116,x19112)) % 187.86/187.67 [1912]~E(x19121,x19122)+E(f682(x19121,x19123),f682(x19122,x19123)) % 187.86/187.67 [1913]~E(x19131,x19132)+E(f682(x19133,x19131),f682(x19133,x19132)) % 187.86/187.67 [1914]~E(x19141,x19142)+E(f392(x19141,x19143,x19144,x19145),f392(x19142,x19143,x19144,x19145)) % 187.86/187.67 [1915]~E(x19151,x19152)+E(f392(x19153,x19151,x19154,x19155),f392(x19153,x19152,x19154,x19155)) % 187.86/187.67 [1916]~E(x19161,x19162)+E(f392(x19163,x19164,x19161,x19165),f392(x19163,x19164,x19162,x19165)) % 187.86/187.67 [1917]~E(x19171,x19172)+E(f392(x19173,x19174,x19175,x19171),f392(x19173,x19174,x19175,x19172)) % 187.86/187.67 [1918]~E(x19181,x19182)+E(f746(x19181,x19183),f746(x19182,x19183)) % 187.86/187.67 [1919]~E(x19191,x19192)+E(f746(x19193,x19191),f746(x19193,x19192)) % 187.86/187.67 [1920]~E(x19201,x19202)+E(f192(x19201,x19203),f192(x19202,x19203)) % 187.86/187.67 [1921]~E(x19211,x19212)+E(f192(x19213,x19211),f192(x19213,x19212)) % 187.86/187.67 [1922]~E(x19221,x19222)+E(f716(x19221,x19223,x19224,x19225),f716(x19222,x19223,x19224,x19225)) % 187.86/187.67 [1923]~E(x19231,x19232)+E(f716(x19233,x19231,x19234,x19235),f716(x19233,x19232,x19234,x19235)) % 187.86/187.67 [1924]~E(x19241,x19242)+E(f716(x19243,x19244,x19241,x19245),f716(x19243,x19244,x19242,x19245)) % 187.86/187.67 [1925]~E(x19251,x19252)+E(f716(x19253,x19254,x19255,x19251),f716(x19253,x19254,x19255,x19252)) % 187.86/187.67 [1926]~E(x19261,x19262)+E(f849(x19261,x19263,x19264),f849(x19262,x19263,x19264)) % 187.86/187.67 [1927]~E(x19271,x19272)+E(f849(x19273,x19271,x19274),f849(x19273,x19272,x19274)) % 187.86/187.67 [1928]~E(x19281,x19282)+E(f849(x19283,x19284,x19281),f849(x19283,x19284,x19282)) % 187.86/187.67 [1929]~E(x19291,x19292)+E(f569(x19291,x19293,x19294),f569(x19292,x19293,x19294)) % 187.86/187.67 [1930]~E(x19301,x19302)+E(f569(x19303,x19301,x19304),f569(x19303,x19302,x19304)) % 187.86/187.67 [1931]~E(x19311,x19312)+E(f569(x19313,x19314,x19311),f569(x19313,x19314,x19312)) % 187.86/187.67 [1932]~E(x19321,x19322)+E(f858(x19321,x19323),f858(x19322,x19323)) % 187.86/187.67 [1933]~E(x19331,x19332)+E(f858(x19333,x19331),f858(x19333,x19332)) % 187.86/187.67 [1934]~E(x19341,x19342)+E(f850(x19341,x19343,x19344,x19345,x19346,x19347,x19348),f850(x19342,x19343,x19344,x19345,x19346,x19347,x19348)) % 187.86/187.67 [1935]~E(x19351,x19352)+E(f850(x19353,x19351,x19354,x19355,x19356,x19357,x19358),f850(x19353,x19352,x19354,x19355,x19356,x19357,x19358)) % 187.86/187.67 [1936]~E(x19361,x19362)+E(f850(x19363,x19364,x19361,x19365,x19366,x19367,x19368),f850(x19363,x19364,x19362,x19365,x19366,x19367,x19368)) % 187.86/187.67 [1937]~E(x19371,x19372)+E(f850(x19373,x19374,x19375,x19371,x19376,x19377,x19378),f850(x19373,x19374,x19375,x19372,x19376,x19377,x19378)) % 187.86/187.67 [1938]~E(x19381,x19382)+E(f850(x19383,x19384,x19385,x19386,x19381,x19387,x19388),f850(x19383,x19384,x19385,x19386,x19382,x19387,x19388)) % 187.86/187.67 [1939]~E(x19391,x19392)+E(f850(x19393,x19394,x19395,x19396,x19397,x19391,x19398),f850(x19393,x19394,x19395,x19396,x19397,x19392,x19398)) % 187.86/187.67 [1940]~E(x19401,x19402)+E(f850(x19403,x19404,x19405,x19406,x19407,x19408,x19401),f850(x19403,x19404,x19405,x19406,x19407,x19408,x19402)) % 187.86/187.67 [1941]~E(x19411,x19412)+E(f364(x19411,x19413),f364(x19412,x19413)) % 187.86/187.67 [1942]~E(x19421,x19422)+E(f364(x19423,x19421),f364(x19423,x19422)) % 187.86/187.67 [1943]~E(x19431,x19432)+E(f719(x19431,x19433,x19434,x19435),f719(x19432,x19433,x19434,x19435)) % 187.86/187.67 [1944]~E(x19441,x19442)+E(f719(x19443,x19441,x19444,x19445),f719(x19443,x19442,x19444,x19445)) % 187.86/187.67 [1945]~E(x19451,x19452)+E(f719(x19453,x19454,x19451,x19455),f719(x19453,x19454,x19452,x19455)) % 187.86/187.67 [1946]~E(x19461,x19462)+E(f719(x19463,x19464,x19465,x19461),f719(x19463,x19464,x19465,x19462)) % 187.86/187.67 [1947]~E(x19471,x19472)+E(f373(x19471,x19473,x19474,x19475),f373(x19472,x19473,x19474,x19475)) % 187.86/187.67 [1948]~E(x19481,x19482)+E(f373(x19483,x19481,x19484,x19485),f373(x19483,x19482,x19484,x19485)) % 187.86/187.67 [1949]~E(x19491,x19492)+E(f373(x19493,x19494,x19491,x19495),f373(x19493,x19494,x19492,x19495)) % 187.86/187.67 [1950]~E(x19501,x19502)+E(f373(x19503,x19504,x19505,x19501),f373(x19503,x19504,x19505,x19502)) % 187.86/187.67 [1951]~E(x19511,x19512)+E(f589(x19511,x19513,x19514,x19515,x19516,x19517,x19518,x19519),f589(x19512,x19513,x19514,x19515,x19516,x19517,x19518,x19519)) % 187.86/187.67 [1952]~E(x19521,x19522)+E(f589(x19523,x19521,x19524,x19525,x19526,x19527,x19528,x19529),f589(x19523,x19522,x19524,x19525,x19526,x19527,x19528,x19529)) % 187.86/187.67 [1953]~E(x19531,x19532)+E(f589(x19533,x19534,x19531,x19535,x19536,x19537,x19538,x19539),f589(x19533,x19534,x19532,x19535,x19536,x19537,x19538,x19539)) % 187.86/187.67 [1954]~E(x19541,x19542)+E(f589(x19543,x19544,x19545,x19541,x19546,x19547,x19548,x19549),f589(x19543,x19544,x19545,x19542,x19546,x19547,x19548,x19549)) % 187.86/187.67 [1955]~E(x19551,x19552)+E(f589(x19553,x19554,x19555,x19556,x19551,x19557,x19558,x19559),f589(x19553,x19554,x19555,x19556,x19552,x19557,x19558,x19559)) % 187.86/187.67 [1956]~E(x19561,x19562)+E(f589(x19563,x19564,x19565,x19566,x19567,x19561,x19568,x19569),f589(x19563,x19564,x19565,x19566,x19567,x19562,x19568,x19569)) % 187.86/187.67 [1957]~E(x19571,x19572)+E(f589(x19573,x19574,x19575,x19576,x19577,x19578,x19571,x19579),f589(x19573,x19574,x19575,x19576,x19577,x19578,x19572,x19579)) % 187.86/187.67 [1958]~E(x19581,x19582)+E(f589(x19583,x19584,x19585,x19586,x19587,x19588,x19589,x19581),f589(x19583,x19584,x19585,x19586,x19587,x19588,x19589,x19582)) % 187.86/187.67 [1959]~E(x19591,x19592)+E(f369(x19591,x19593,x19594,x19595,x19596),f369(x19592,x19593,x19594,x19595,x19596)) % 187.86/187.67 [1960]~E(x19601,x19602)+E(f369(x19603,x19601,x19604,x19605,x19606),f369(x19603,x19602,x19604,x19605,x19606)) % 187.86/187.67 [1961]~E(x19611,x19612)+E(f369(x19613,x19614,x19611,x19615,x19616),f369(x19613,x19614,x19612,x19615,x19616)) % 187.86/187.67 [1962]~E(x19621,x19622)+E(f369(x19623,x19624,x19625,x19621,x19626),f369(x19623,x19624,x19625,x19622,x19626)) % 187.86/187.67 [1963]~E(x19631,x19632)+E(f369(x19633,x19634,x19635,x19636,x19631),f369(x19633,x19634,x19635,x19636,x19632)) % 187.86/187.67 [1964]~E(x19641,x19642)+E(f641(x19641,x19643,x19644),f641(x19642,x19643,x19644)) % 187.86/187.67 [1965]~E(x19651,x19652)+E(f641(x19653,x19651,x19654),f641(x19653,x19652,x19654)) % 187.86/187.67 [1966]~E(x19661,x19662)+E(f641(x19663,x19664,x19661),f641(x19663,x19664,x19662)) % 187.86/187.67 [1967]~E(x19671,x19672)+E(f767(x19671,x19673,x19674,x19675),f767(x19672,x19673,x19674,x19675)) % 187.86/187.67 [1968]~E(x19681,x19682)+E(f767(x19683,x19681,x19684,x19685),f767(x19683,x19682,x19684,x19685)) % 187.86/187.67 [1969]~E(x19691,x19692)+E(f767(x19693,x19694,x19691,x19695),f767(x19693,x19694,x19692,x19695)) % 187.86/187.67 [1970]~E(x19701,x19702)+E(f767(x19703,x19704,x19705,x19701),f767(x19703,x19704,x19705,x19702)) % 187.86/187.67 [1971]~E(x19711,x19712)+E(f667(x19711,x19713,x19714,x19715,x19716),f667(x19712,x19713,x19714,x19715,x19716)) % 187.86/187.67 [1972]~E(x19721,x19722)+E(f667(x19723,x19721,x19724,x19725,x19726),f667(x19723,x19722,x19724,x19725,x19726)) % 187.86/187.67 [1973]~E(x19731,x19732)+E(f667(x19733,x19734,x19731,x19735,x19736),f667(x19733,x19734,x19732,x19735,x19736)) % 187.86/187.67 [1974]~E(x19741,x19742)+E(f667(x19743,x19744,x19745,x19741,x19746),f667(x19743,x19744,x19745,x19742,x19746)) % 187.86/187.67 [1975]~E(x19751,x19752)+E(f667(x19753,x19754,x19755,x19756,x19751),f667(x19753,x19754,x19755,x19756,x19752)) % 187.86/187.67 [1976]~E(x19761,x19762)+E(f462(x19761,x19763,x19764,x19765,x19766),f462(x19762,x19763,x19764,x19765,x19766)) % 187.86/187.67 [1977]~E(x19771,x19772)+E(f462(x19773,x19771,x19774,x19775,x19776),f462(x19773,x19772,x19774,x19775,x19776)) % 187.86/187.67 [1978]~E(x19781,x19782)+E(f462(x19783,x19784,x19781,x19785,x19786),f462(x19783,x19784,x19782,x19785,x19786)) % 187.86/187.67 [1979]~E(x19791,x19792)+E(f462(x19793,x19794,x19795,x19791,x19796),f462(x19793,x19794,x19795,x19792,x19796)) % 187.86/187.67 [1980]~E(x19801,x19802)+E(f462(x19803,x19804,x19805,x19806,x19801),f462(x19803,x19804,x19805,x19806,x19802)) % 187.86/187.67 [1981]~E(x19811,x19812)+E(f802(x19811,x19813,x19814,x19815),f802(x19812,x19813,x19814,x19815)) % 187.86/187.67 [1982]~E(x19821,x19822)+E(f802(x19823,x19821,x19824,x19825),f802(x19823,x19822,x19824,x19825)) % 187.86/187.67 [1983]~E(x19831,x19832)+E(f802(x19833,x19834,x19831,x19835),f802(x19833,x19834,x19832,x19835)) % 187.86/187.67 [1984]~E(x19841,x19842)+E(f802(x19843,x19844,x19845,x19841),f802(x19843,x19844,x19845,x19842)) % 187.86/187.67 [1985]~E(x19851,x19852)+E(f428(x19851,x19853,x19854,x19855,x19856),f428(x19852,x19853,x19854,x19855,x19856)) % 187.86/187.67 [1986]~E(x19861,x19862)+E(f428(x19863,x19861,x19864,x19865,x19866),f428(x19863,x19862,x19864,x19865,x19866)) % 187.86/187.67 [1987]~E(x19871,x19872)+E(f428(x19873,x19874,x19871,x19875,x19876),f428(x19873,x19874,x19872,x19875,x19876)) % 187.86/187.67 [1988]~E(x19881,x19882)+E(f428(x19883,x19884,x19885,x19881,x19886),f428(x19883,x19884,x19885,x19882,x19886)) % 187.86/187.67 [1989]~E(x19891,x19892)+E(f428(x19893,x19894,x19895,x19896,x19891),f428(x19893,x19894,x19895,x19896,x19892)) % 187.86/187.67 [1990]~E(x19901,x19902)+E(f420(x19901,x19903,x19904,x19905,x19906),f420(x19902,x19903,x19904,x19905,x19906)) % 187.86/187.67 [1991]~E(x19911,x19912)+E(f420(x19913,x19911,x19914,x19915,x19916),f420(x19913,x19912,x19914,x19915,x19916)) % 187.86/187.67 [1992]~E(x19921,x19922)+E(f420(x19923,x19924,x19921,x19925,x19926),f420(x19923,x19924,x19922,x19925,x19926)) % 187.86/187.67 [1993]~E(x19931,x19932)+E(f420(x19933,x19934,x19935,x19931,x19936),f420(x19933,x19934,x19935,x19932,x19936)) % 187.86/187.67 [1994]~E(x19941,x19942)+E(f420(x19943,x19944,x19945,x19946,x19941),f420(x19943,x19944,x19945,x19946,x19942)) % 187.86/187.67 [1995]~E(x19951,x19952)+E(f840(x19951,x19953),f840(x19952,x19953)) % 187.86/187.67 [1996]~E(x19961,x19962)+E(f840(x19963,x19961),f840(x19963,x19962)) % 187.86/187.67 [1997]~E(x19971,x19972)+E(f387(x19971,x19973,x19974,x19975),f387(x19972,x19973,x19974,x19975)) % 187.86/187.67 [1998]~E(x19981,x19982)+E(f387(x19983,x19981,x19984,x19985),f387(x19983,x19982,x19984,x19985)) % 187.86/187.67 [1999]~E(x19991,x19992)+E(f387(x19993,x19994,x19991,x19995),f387(x19993,x19994,x19992,x19995)) % 187.86/187.67 [2000]~E(x20001,x20002)+E(f387(x20003,x20004,x20005,x20001),f387(x20003,x20004,x20005,x20002)) % 187.86/187.67 [2001]~E(x20011,x20012)+E(f99(x20011,x20013,x20014,x20015),f99(x20012,x20013,x20014,x20015)) % 187.86/187.67 [2002]~E(x20021,x20022)+E(f99(x20023,x20021,x20024,x20025),f99(x20023,x20022,x20024,x20025)) % 187.86/187.67 [2003]~E(x20031,x20032)+E(f99(x20033,x20034,x20031,x20035),f99(x20033,x20034,x20032,x20035)) % 187.86/187.67 [2004]~E(x20041,x20042)+E(f99(x20043,x20044,x20045,x20041),f99(x20043,x20044,x20045,x20042)) % 187.86/187.67 [2005]~E(x20051,x20052)+E(f457(x20051,x20053,x20054,x20055,x20056),f457(x20052,x20053,x20054,x20055,x20056)) % 187.86/187.67 [2006]~E(x20061,x20062)+E(f457(x20063,x20061,x20064,x20065,x20066),f457(x20063,x20062,x20064,x20065,x20066)) % 187.86/187.67 [2007]~E(x20071,x20072)+E(f457(x20073,x20074,x20071,x20075,x20076),f457(x20073,x20074,x20072,x20075,x20076)) % 187.86/187.67 [2008]~E(x20081,x20082)+E(f457(x20083,x20084,x20085,x20081,x20086),f457(x20083,x20084,x20085,x20082,x20086)) % 187.86/187.67 [2009]~E(x20091,x20092)+E(f457(x20093,x20094,x20095,x20096,x20091),f457(x20093,x20094,x20095,x20096,x20092)) % 187.86/187.67 [2010]~E(x20101,x20102)+E(f514(x20101,x20103,x20104,x20105,x20106),f514(x20102,x20103,x20104,x20105,x20106)) % 187.86/187.67 [2011]~E(x20111,x20112)+E(f514(x20113,x20111,x20114,x20115,x20116),f514(x20113,x20112,x20114,x20115,x20116)) % 187.86/187.67 [2012]~E(x20121,x20122)+E(f514(x20123,x20124,x20121,x20125,x20126),f514(x20123,x20124,x20122,x20125,x20126)) % 187.86/187.67 [2013]~E(x20131,x20132)+E(f514(x20133,x20134,x20135,x20131,x20136),f514(x20133,x20134,x20135,x20132,x20136)) % 187.86/187.67 [2014]~E(x20141,x20142)+E(f514(x20143,x20144,x20145,x20146,x20141),f514(x20143,x20144,x20145,x20146,x20142)) % 187.86/187.67 [2015]~E(x20151,x20152)+E(f705(x20151,x20153,x20154,x20155),f705(x20152,x20153,x20154,x20155)) % 187.86/187.67 [2016]~E(x20161,x20162)+E(f705(x20163,x20161,x20164,x20165),f705(x20163,x20162,x20164,x20165)) % 187.86/187.67 [2017]~E(x20171,x20172)+E(f705(x20173,x20174,x20171,x20175),f705(x20173,x20174,x20172,x20175)) % 187.86/187.67 [2018]~E(x20181,x20182)+E(f705(x20183,x20184,x20185,x20181),f705(x20183,x20184,x20185,x20182)) % 187.86/187.67 [2019]~E(x20191,x20192)+E(f845(x20191,x20193),f845(x20192,x20193)) % 187.86/187.67 [2020]~E(x20201,x20202)+E(f845(x20203,x20201),f845(x20203,x20202)) % 187.86/187.67 [2021]~E(x20211,x20212)+E(f265(x20211,x20213),f265(x20212,x20213)) % 187.86/187.67 [2022]~E(x20221,x20222)+E(f265(x20223,x20221),f265(x20223,x20222)) % 187.86/187.67 [2023]~E(x20231,x20232)+E(f717(x20231,x20233,x20234),f717(x20232,x20233,x20234)) % 187.86/187.67 [2024]~E(x20241,x20242)+E(f717(x20243,x20241,x20244),f717(x20243,x20242,x20244)) % 187.86/187.67 [2025]~E(x20251,x20252)+E(f717(x20253,x20254,x20251),f717(x20253,x20254,x20252)) % 187.86/187.67 [2026]~E(x20261,x20262)+E(f471(x20261,x20263,x20264,x20265,x20266,x20267,x20268),f471(x20262,x20263,x20264,x20265,x20266,x20267,x20268)) % 187.86/187.67 [2027]~E(x20271,x20272)+E(f471(x20273,x20271,x20274,x20275,x20276,x20277,x20278),f471(x20273,x20272,x20274,x20275,x20276,x20277,x20278)) % 187.86/187.67 [2028]~E(x20281,x20282)+E(f471(x20283,x20284,x20281,x20285,x20286,x20287,x20288),f471(x20283,x20284,x20282,x20285,x20286,x20287,x20288)) % 187.86/187.67 [2029]~E(x20291,x20292)+E(f471(x20293,x20294,x20295,x20291,x20296,x20297,x20298),f471(x20293,x20294,x20295,x20292,x20296,x20297,x20298)) % 187.86/187.67 [2030]~E(x20301,x20302)+E(f471(x20303,x20304,x20305,x20306,x20301,x20307,x20308),f471(x20303,x20304,x20305,x20306,x20302,x20307,x20308)) % 187.86/187.67 [2031]~E(x20311,x20312)+E(f471(x20313,x20314,x20315,x20316,x20317,x20311,x20318),f471(x20313,x20314,x20315,x20316,x20317,x20312,x20318)) % 187.86/187.67 [2032]~E(x20321,x20322)+E(f471(x20323,x20324,x20325,x20326,x20327,x20328,x20321),f471(x20323,x20324,x20325,x20326,x20327,x20328,x20322)) % 187.86/187.67 [2033]~E(x20331,x20332)+E(f649(x20331,x20333,x20334,x20335,x20336,x20337,x20338),f649(x20332,x20333,x20334,x20335,x20336,x20337,x20338)) % 187.86/187.67 [2034]~E(x20341,x20342)+E(f649(x20343,x20341,x20344,x20345,x20346,x20347,x20348),f649(x20343,x20342,x20344,x20345,x20346,x20347,x20348)) % 187.86/187.67 [2035]~E(x20351,x20352)+E(f649(x20353,x20354,x20351,x20355,x20356,x20357,x20358),f649(x20353,x20354,x20352,x20355,x20356,x20357,x20358)) % 187.86/187.67 [2036]~E(x20361,x20362)+E(f649(x20363,x20364,x20365,x20361,x20366,x20367,x20368),f649(x20363,x20364,x20365,x20362,x20366,x20367,x20368)) % 187.86/187.67 [2037]~E(x20371,x20372)+E(f649(x20373,x20374,x20375,x20376,x20371,x20377,x20378),f649(x20373,x20374,x20375,x20376,x20372,x20377,x20378)) % 187.86/187.67 [2038]~E(x20381,x20382)+E(f649(x20383,x20384,x20385,x20386,x20387,x20381,x20388),f649(x20383,x20384,x20385,x20386,x20387,x20382,x20388)) % 187.86/187.67 [2039]~E(x20391,x20392)+E(f649(x20393,x20394,x20395,x20396,x20397,x20398,x20391),f649(x20393,x20394,x20395,x20396,x20397,x20398,x20392)) % 187.86/187.67 [2040]~E(x20401,x20402)+E(f787(x20401,x20403,x20404),f787(x20402,x20403,x20404)) % 187.86/187.67 [2041]~E(x20411,x20412)+E(f787(x20413,x20411,x20414),f787(x20413,x20412,x20414)) % 187.86/187.67 [2042]~E(x20421,x20422)+E(f787(x20423,x20424,x20421),f787(x20423,x20424,x20422)) % 187.86/187.67 [2043]~E(x20431,x20432)+E(f258(x20431,x20433,x20434,x20435),f258(x20432,x20433,x20434,x20435)) % 187.86/187.67 [2044]~E(x20441,x20442)+E(f258(x20443,x20441,x20444,x20445),f258(x20443,x20442,x20444,x20445)) % 187.86/187.67 [2045]~E(x20451,x20452)+E(f258(x20453,x20454,x20451,x20455),f258(x20453,x20454,x20452,x20455)) % 187.86/187.67 [2046]~E(x20461,x20462)+E(f258(x20463,x20464,x20465,x20461),f258(x20463,x20464,x20465,x20462)) % 187.86/187.67 [2047]~E(x20471,x20472)+E(f380(x20471,x20473),f380(x20472,x20473)) % 187.86/187.67 [2048]~E(x20481,x20482)+E(f380(x20483,x20481),f380(x20483,x20482)) % 187.86/187.67 [2049]~E(x20491,x20492)+E(f200(x20491,x20493),f200(x20492,x20493)) % 187.86/187.67 [2050]~E(x20501,x20502)+E(f200(x20503,x20501),f200(x20503,x20502)) % 187.86/187.67 [2051]~E(x20511,x20512)+E(f423(x20511,x20513),f423(x20512,x20513)) % 187.86/187.67 [2052]~E(x20521,x20522)+E(f423(x20523,x20521),f423(x20523,x20522)) % 187.86/187.67 [2053]~E(x20531,x20532)+E(f223(x20531,x20533),f223(x20532,x20533)) % 187.86/187.67 [2054]~E(x20541,x20542)+E(f223(x20543,x20541),f223(x20543,x20542)) % 187.86/187.67 [2055]~E(x20551,x20552)+E(f692(x20551,x20553,x20554),f692(x20552,x20553,x20554)) % 187.86/187.67 [2056]~E(x20561,x20562)+E(f692(x20563,x20561,x20564),f692(x20563,x20562,x20564)) % 187.86/187.67 [2057]~E(x20571,x20572)+E(f692(x20573,x20574,x20571),f692(x20573,x20574,x20572)) % 187.86/187.67 [2058]~E(x20581,x20582)+E(f537(x20581,x20583,x20584,x20585),f537(x20582,x20583,x20584,x20585)) % 187.86/187.67 [2059]~E(x20591,x20592)+E(f537(x20593,x20591,x20594,x20595),f537(x20593,x20592,x20594,x20595)) % 187.86/187.67 [2060]~E(x20601,x20602)+E(f537(x20603,x20604,x20601,x20605),f537(x20603,x20604,x20602,x20605)) % 187.86/187.67 [2061]~E(x20611,x20612)+E(f537(x20613,x20614,x20615,x20611),f537(x20613,x20614,x20615,x20612)) % 187.86/187.67 [2062]~E(x20621,x20622)+E(f379(x20621,x20623,x20624,x20625),f379(x20622,x20623,x20624,x20625)) % 187.86/187.67 [2063]~E(x20631,x20632)+E(f379(x20633,x20631,x20634,x20635),f379(x20633,x20632,x20634,x20635)) % 187.86/187.67 [2064]~E(x20641,x20642)+E(f379(x20643,x20644,x20641,x20645),f379(x20643,x20644,x20642,x20645)) % 187.86/187.67 [2065]~E(x20651,x20652)+E(f379(x20653,x20654,x20655,x20651),f379(x20653,x20654,x20655,x20652)) % 187.86/187.67 [2066]~E(x20661,x20662)+E(f538(x20661,x20663,x20664,x20665),f538(x20662,x20663,x20664,x20665)) % 187.86/187.67 [2067]~E(x20671,x20672)+E(f538(x20673,x20671,x20674,x20675),f538(x20673,x20672,x20674,x20675)) % 187.86/187.67 [2068]~E(x20681,x20682)+E(f538(x20683,x20684,x20681,x20685),f538(x20683,x20684,x20682,x20685)) % 187.86/187.67 [2069]~E(x20691,x20692)+E(f538(x20693,x20694,x20695,x20691),f538(x20693,x20694,x20695,x20692)) % 187.86/187.67 [2070]~E(x20701,x20702)+E(f358(x20701,x20703,x20704),f358(x20702,x20703,x20704)) % 187.86/187.67 [2071]~E(x20711,x20712)+E(f358(x20713,x20711,x20714),f358(x20713,x20712,x20714)) % 187.86/187.67 [2072]~E(x20721,x20722)+E(f358(x20723,x20724,x20721),f358(x20723,x20724,x20722)) % 187.86/187.67 [2073]~E(x20731,x20732)+E(f754(x20731,x20733,x20734,x20735,x20736,x20737),f754(x20732,x20733,x20734,x20735,x20736,x20737)) % 187.86/187.67 [2074]~E(x20741,x20742)+E(f754(x20743,x20741,x20744,x20745,x20746,x20747),f754(x20743,x20742,x20744,x20745,x20746,x20747)) % 187.86/187.67 [2075]~E(x20751,x20752)+E(f754(x20753,x20754,x20751,x20755,x20756,x20757),f754(x20753,x20754,x20752,x20755,x20756,x20757)) % 187.86/187.67 [2076]~E(x20761,x20762)+E(f754(x20763,x20764,x20765,x20761,x20766,x20767),f754(x20763,x20764,x20765,x20762,x20766,x20767)) % 187.86/187.67 [2077]~E(x20771,x20772)+E(f754(x20773,x20774,x20775,x20776,x20771,x20777),f754(x20773,x20774,x20775,x20776,x20772,x20777)) % 187.86/187.67 [2078]~E(x20781,x20782)+E(f754(x20783,x20784,x20785,x20786,x20787,x20781),f754(x20783,x20784,x20785,x20786,x20787,x20782)) % 187.86/187.67 [2079]~E(x20791,x20792)+E(f484(x20791,x20793,x20794,x20795),f484(x20792,x20793,x20794,x20795)) % 187.86/187.67 [2080]~E(x20801,x20802)+E(f484(x20803,x20801,x20804,x20805),f484(x20803,x20802,x20804,x20805)) % 187.86/187.67 [2081]~E(x20811,x20812)+E(f484(x20813,x20814,x20811,x20815),f484(x20813,x20814,x20812,x20815)) % 187.86/187.67 [2082]~E(x20821,x20822)+E(f484(x20823,x20824,x20825,x20821),f484(x20823,x20824,x20825,x20822)) % 187.86/187.67 [2083]~E(x20831,x20832)+E(f479(x20831,x20833,x20834,x20835),f479(x20832,x20833,x20834,x20835)) % 187.86/187.67 [2084]~E(x20841,x20842)+E(f479(x20843,x20841,x20844,x20845),f479(x20843,x20842,x20844,x20845)) % 187.86/187.67 [2085]~E(x20851,x20852)+E(f479(x20853,x20854,x20851,x20855),f479(x20853,x20854,x20852,x20855)) % 187.86/187.67 [2086]~E(x20861,x20862)+E(f479(x20863,x20864,x20865,x20861),f479(x20863,x20864,x20865,x20862)) % 187.86/187.67 [2087]~E(x20871,x20872)+E(f418(x20871,x20873,x20874,x20875,x20876),f418(x20872,x20873,x20874,x20875,x20876)) % 187.86/187.67 [2088]~E(x20881,x20882)+E(f418(x20883,x20881,x20884,x20885,x20886),f418(x20883,x20882,x20884,x20885,x20886)) % 187.86/187.67 [2089]~E(x20891,x20892)+E(f418(x20893,x20894,x20891,x20895,x20896),f418(x20893,x20894,x20892,x20895,x20896)) % 187.86/187.67 [2090]~E(x20901,x20902)+E(f418(x20903,x20904,x20905,x20901,x20906),f418(x20903,x20904,x20905,x20902,x20906)) % 187.86/187.67 [2091]~E(x20911,x20912)+E(f418(x20913,x20914,x20915,x20916,x20911),f418(x20913,x20914,x20915,x20916,x20912)) % 187.86/187.67 [2092]~E(x20921,x20922)+E(f506(x20921,x20923,x20924,x20925,x20926,x20927,x20928,x20929),f506(x20922,x20923,x20924,x20925,x20926,x20927,x20928,x20929)) % 187.86/187.67 [2093]~E(x20931,x20932)+E(f506(x20933,x20931,x20934,x20935,x20936,x20937,x20938,x20939),f506(x20933,x20932,x20934,x20935,x20936,x20937,x20938,x20939)) % 187.86/187.67 [2094]~E(x20941,x20942)+E(f506(x20943,x20944,x20941,x20945,x20946,x20947,x20948,x20949),f506(x20943,x20944,x20942,x20945,x20946,x20947,x20948,x20949)) % 187.86/187.67 [2095]~E(x20951,x20952)+E(f506(x20953,x20954,x20955,x20951,x20956,x20957,x20958,x20959),f506(x20953,x20954,x20955,x20952,x20956,x20957,x20958,x20959)) % 187.86/187.67 [2096]~E(x20961,x20962)+E(f506(x20963,x20964,x20965,x20966,x20961,x20967,x20968,x20969),f506(x20963,x20964,x20965,x20966,x20962,x20967,x20968,x20969)) % 187.86/187.67 [2097]~E(x20971,x20972)+E(f506(x20973,x20974,x20975,x20976,x20977,x20971,x20978,x20979),f506(x20973,x20974,x20975,x20976,x20977,x20972,x20978,x20979)) % 187.86/187.67 [2098]~E(x20981,x20982)+E(f506(x20983,x20984,x20985,x20986,x20987,x20988,x20981,x20989),f506(x20983,x20984,x20985,x20986,x20987,x20988,x20982,x20989)) % 187.86/187.67 [2099]~E(x20991,x20992)+E(f506(x20993,x20994,x20995,x20996,x20997,x20998,x20999,x20991),f506(x20993,x20994,x20995,x20996,x20997,x20998,x20999,x20992)) % 187.86/187.67 [2100]~E(x21001,x21002)+E(f485(x21001),f485(x21002)) % 187.86/187.67 [2101]~E(x21011,x21012)+E(f814(x21011),f814(x21012)) % 187.86/187.67 [2102]~E(x21021,x21022)+E(f691(x21021,x21023,x21024),f691(x21022,x21023,x21024)) % 187.86/187.67 [2103]~E(x21031,x21032)+E(f691(x21033,x21031,x21034),f691(x21033,x21032,x21034)) % 187.86/187.67 [2104]~E(x21041,x21042)+E(f691(x21043,x21044,x21041),f691(x21043,x21044,x21042)) % 187.86/187.67 [2105]~E(x21051,x21052)+E(f810(x21051,x21053,x21054,x21055,x21056),f810(x21052,x21053,x21054,x21055,x21056)) % 187.86/187.67 [2106]~E(x21061,x21062)+E(f810(x21063,x21061,x21064,x21065,x21066),f810(x21063,x21062,x21064,x21065,x21066)) % 187.86/187.67 [2107]~E(x21071,x21072)+E(f810(x21073,x21074,x21071,x21075,x21076),f810(x21073,x21074,x21072,x21075,x21076)) % 187.86/187.67 [2108]~E(x21081,x21082)+E(f810(x21083,x21084,x21085,x21081,x21086),f810(x21083,x21084,x21085,x21082,x21086)) % 187.86/187.67 [2109]~E(x21091,x21092)+E(f810(x21093,x21094,x21095,x21096,x21091),f810(x21093,x21094,x21095,x21096,x21092)) % 187.86/187.67 [2110]~E(x21101,x21102)+E(f256(x21101,x21103,x21104),f256(x21102,x21103,x21104)) % 187.86/187.67 [2111]~E(x21111,x21112)+E(f256(x21113,x21111,x21114),f256(x21113,x21112,x21114)) % 187.86/187.67 [2112]~E(x21121,x21122)+E(f256(x21123,x21124,x21121),f256(x21123,x21124,x21122)) % 187.86/187.67 [2113]~E(x21131,x21132)+E(f576(x21131,x21133,x21134,x21135,x21136),f576(x21132,x21133,x21134,x21135,x21136)) % 187.86/187.67 [2114]~E(x21141,x21142)+E(f576(x21143,x21141,x21144,x21145,x21146),f576(x21143,x21142,x21144,x21145,x21146)) % 187.86/187.67 [2115]~E(x21151,x21152)+E(f576(x21153,x21154,x21151,x21155,x21156),f576(x21153,x21154,x21152,x21155,x21156)) % 187.86/187.67 [2116]~E(x21161,x21162)+E(f576(x21163,x21164,x21165,x21161,x21166),f576(x21163,x21164,x21165,x21162,x21166)) % 187.86/187.67 [2117]~E(x21171,x21172)+E(f576(x21173,x21174,x21175,x21176,x21171),f576(x21173,x21174,x21175,x21176,x21172)) % 187.86/187.67 [2118]~E(x21181,x21182)+E(f801(x21181,x21183,x21184,x21185),f801(x21182,x21183,x21184,x21185)) % 187.86/187.67 [2119]~E(x21191,x21192)+E(f801(x21193,x21191,x21194,x21195),f801(x21193,x21192,x21194,x21195)) % 187.86/187.67 [2120]~E(x21201,x21202)+E(f801(x21203,x21204,x21201,x21205),f801(x21203,x21204,x21202,x21205)) % 187.86/187.67 [2121]~E(x21211,x21212)+E(f801(x21213,x21214,x21215,x21211),f801(x21213,x21214,x21215,x21212)) % 187.86/187.67 [2122]~E(x21221,x21222)+E(f401(x21221,x21223,x21224,x21225,x21226),f401(x21222,x21223,x21224,x21225,x21226)) % 187.86/187.67 [2123]~E(x21231,x21232)+E(f401(x21233,x21231,x21234,x21235,x21236),f401(x21233,x21232,x21234,x21235,x21236)) % 187.86/187.67 [2124]~E(x21241,x21242)+E(f401(x21243,x21244,x21241,x21245,x21246),f401(x21243,x21244,x21242,x21245,x21246)) % 187.86/187.67 [2125]~E(x21251,x21252)+E(f401(x21253,x21254,x21255,x21251,x21256),f401(x21253,x21254,x21255,x21252,x21256)) % 187.86/187.67 [2126]~E(x21261,x21262)+E(f401(x21263,x21264,x21265,x21266,x21261),f401(x21263,x21264,x21265,x21266,x21262)) % 187.86/187.67 [2127]~E(x21271,x21272)+E(f510(x21271,x21273,x21274),f510(x21272,x21273,x21274)) % 187.86/187.67 [2128]~E(x21281,x21282)+E(f510(x21283,x21281,x21284),f510(x21283,x21282,x21284)) % 187.86/187.67 [2129]~E(x21291,x21292)+E(f510(x21293,x21294,x21291),f510(x21293,x21294,x21292)) % 187.86/187.67 [2130]~E(x21301,x21302)+E(f438(x21301,x21303,x21304,x21305),f438(x21302,x21303,x21304,x21305)) % 187.86/187.67 [2131]~E(x21311,x21312)+E(f438(x21313,x21311,x21314,x21315),f438(x21313,x21312,x21314,x21315)) % 187.86/187.67 [2132]~E(x21321,x21322)+E(f438(x21323,x21324,x21321,x21325),f438(x21323,x21324,x21322,x21325)) % 187.86/187.67 [2133]~E(x21331,x21332)+E(f438(x21333,x21334,x21335,x21331),f438(x21333,x21334,x21335,x21332)) % 187.86/187.67 [2134]~E(x21341,x21342)+E(f212(x21341,x21343,x21344,x21345),f212(x21342,x21343,x21344,x21345)) % 187.86/187.67 [2135]~E(x21351,x21352)+E(f212(x21353,x21351,x21354,x21355),f212(x21353,x21352,x21354,x21355)) % 187.86/187.67 [2136]~E(x21361,x21362)+E(f212(x21363,x21364,x21361,x21365),f212(x21363,x21364,x21362,x21365)) % 187.86/187.67 [2137]~E(x21371,x21372)+E(f212(x21373,x21374,x21375,x21371),f212(x21373,x21374,x21375,x21372)) % 187.86/187.67 [2138]~E(x21381,x21382)+E(f771(x21381,x21383,x21384),f771(x21382,x21383,x21384)) % 187.86/187.67 [2139]~E(x21391,x21392)+E(f771(x21393,x21391,x21394),f771(x21393,x21392,x21394)) % 187.86/187.67 [2140]~E(x21401,x21402)+E(f771(x21403,x21404,x21401),f771(x21403,x21404,x21402)) % 187.86/187.67 [2141]~E(x21411,x21412)+E(f535(x21411,x21413,x21414,x21415,x21416,x21417),f535(x21412,x21413,x21414,x21415,x21416,x21417)) % 187.86/187.67 [2142]~E(x21421,x21422)+E(f535(x21423,x21421,x21424,x21425,x21426,x21427),f535(x21423,x21422,x21424,x21425,x21426,x21427)) % 187.86/187.67 [2143]~E(x21431,x21432)+E(f535(x21433,x21434,x21431,x21435,x21436,x21437),f535(x21433,x21434,x21432,x21435,x21436,x21437)) % 187.86/187.67 [2144]~E(x21441,x21442)+E(f535(x21443,x21444,x21445,x21441,x21446,x21447),f535(x21443,x21444,x21445,x21442,x21446,x21447)) % 187.86/187.67 [2145]~E(x21451,x21452)+E(f535(x21453,x21454,x21455,x21456,x21451,x21457),f535(x21453,x21454,x21455,x21456,x21452,x21457)) % 187.86/187.67 [2146]~E(x21461,x21462)+E(f535(x21463,x21464,x21465,x21466,x21467,x21461),f535(x21463,x21464,x21465,x21466,x21467,x21462)) % 187.86/187.67 [2147]~E(x21471,x21472)+E(f631(x21471,x21473,x21474,x21475,x21476,x21477,x21478),f631(x21472,x21473,x21474,x21475,x21476,x21477,x21478)) % 187.86/187.67 [2148]~E(x21481,x21482)+E(f631(x21483,x21481,x21484,x21485,x21486,x21487,x21488),f631(x21483,x21482,x21484,x21485,x21486,x21487,x21488)) % 187.86/187.67 [2149]~E(x21491,x21492)+E(f631(x21493,x21494,x21491,x21495,x21496,x21497,x21498),f631(x21493,x21494,x21492,x21495,x21496,x21497,x21498)) % 187.86/187.67 [2150]~E(x21501,x21502)+E(f631(x21503,x21504,x21505,x21501,x21506,x21507,x21508),f631(x21503,x21504,x21505,x21502,x21506,x21507,x21508)) % 187.86/187.67 [2151]~E(x21511,x21512)+E(f631(x21513,x21514,x21515,x21516,x21511,x21517,x21518),f631(x21513,x21514,x21515,x21516,x21512,x21517,x21518)) % 187.86/187.67 [2152]~E(x21521,x21522)+E(f631(x21523,x21524,x21525,x21526,x21527,x21521,x21528),f631(x21523,x21524,x21525,x21526,x21527,x21522,x21528)) % 187.86/187.67 [2153]~E(x21531,x21532)+E(f631(x21533,x21534,x21535,x21536,x21537,x21538,x21531),f631(x21533,x21534,x21535,x21536,x21537,x21538,x21532)) % 187.86/187.67 [2154]~E(x21541,x21542)+E(f511(x21541,x21543),f511(x21542,x21543)) % 187.86/187.67 [2155]~E(x21551,x21552)+E(f511(x21553,x21551),f511(x21553,x21552)) % 187.86/187.67 [2156]~E(x21561,x21562)+E(f661(x21561,x21563,x21564,x21565,x21566,x21567),f661(x21562,x21563,x21564,x21565,x21566,x21567)) % 187.86/187.67 [2157]~E(x21571,x21572)+E(f661(x21573,x21571,x21574,x21575,x21576,x21577),f661(x21573,x21572,x21574,x21575,x21576,x21577)) % 187.86/187.67 [2158]~E(x21581,x21582)+E(f661(x21583,x21584,x21581,x21585,x21586,x21587),f661(x21583,x21584,x21582,x21585,x21586,x21587)) % 187.86/187.67 [2159]~E(x21591,x21592)+E(f661(x21593,x21594,x21595,x21591,x21596,x21597),f661(x21593,x21594,x21595,x21592,x21596,x21597)) % 187.86/187.67 [2160]~E(x21601,x21602)+E(f661(x21603,x21604,x21605,x21606,x21601,x21607),f661(x21603,x21604,x21605,x21606,x21602,x21607)) % 187.86/187.67 [2161]~E(x21611,x21612)+E(f661(x21613,x21614,x21615,x21616,x21617,x21611),f661(x21613,x21614,x21615,x21616,x21617,x21612)) % 187.86/187.67 [2162]~E(x21621,x21622)+E(f353(x21621,x21623,x21624),f353(x21622,x21623,x21624)) % 187.86/187.67 [2163]~E(x21631,x21632)+E(f353(x21633,x21631,x21634),f353(x21633,x21632,x21634)) % 187.86/187.67 [2164]~E(x21641,x21642)+E(f353(x21643,x21644,x21641),f353(x21643,x21644,x21642)) % 187.86/187.67 [2165]~E(x21651,x21652)+E(f662(x21651,x21653,x21654,x21655,x21656,x21657),f662(x21652,x21653,x21654,x21655,x21656,x21657)) % 187.86/187.67 [2166]~E(x21661,x21662)+E(f662(x21663,x21661,x21664,x21665,x21666,x21667),f662(x21663,x21662,x21664,x21665,x21666,x21667)) % 187.86/187.67 [2167]~E(x21671,x21672)+E(f662(x21673,x21674,x21671,x21675,x21676,x21677),f662(x21673,x21674,x21672,x21675,x21676,x21677)) % 187.86/187.67 [2168]~E(x21681,x21682)+E(f662(x21683,x21684,x21685,x21681,x21686,x21687),f662(x21683,x21684,x21685,x21682,x21686,x21687)) % 187.86/187.67 [2169]~E(x21691,x21692)+E(f662(x21693,x21694,x21695,x21696,x21691,x21697),f662(x21693,x21694,x21695,x21696,x21692,x21697)) % 187.86/187.67 [2170]~E(x21701,x21702)+E(f662(x21703,x21704,x21705,x21706,x21707,x21701),f662(x21703,x21704,x21705,x21706,x21707,x21702)) % 187.86/187.67 [2171]~E(x21711,x21712)+E(f340(x21711,x21713,x21714,x21715),f340(x21712,x21713,x21714,x21715)) % 187.86/187.67 [2172]~E(x21721,x21722)+E(f340(x21723,x21721,x21724,x21725),f340(x21723,x21722,x21724,x21725)) % 187.86/187.67 [2173]~E(x21731,x21732)+E(f340(x21733,x21734,x21731,x21735),f340(x21733,x21734,x21732,x21735)) % 187.86/187.67 [2174]~E(x21741,x21742)+E(f340(x21743,x21744,x21745,x21741),f340(x21743,x21744,x21745,x21742)) % 187.86/187.67 [2175]~E(x21751,x21752)+E(f458(x21751,x21753,x21754,x21755,x21756),f458(x21752,x21753,x21754,x21755,x21756)) % 187.86/187.67 [2176]~E(x21761,x21762)+E(f458(x21763,x21761,x21764,x21765,x21766),f458(x21763,x21762,x21764,x21765,x21766)) % 187.86/187.67 [2177]~E(x21771,x21772)+E(f458(x21773,x21774,x21771,x21775,x21776),f458(x21773,x21774,x21772,x21775,x21776)) % 187.86/187.67 [2178]~E(x21781,x21782)+E(f458(x21783,x21784,x21785,x21781,x21786),f458(x21783,x21784,x21785,x21782,x21786)) % 187.86/187.67 [2179]~E(x21791,x21792)+E(f458(x21793,x21794,x21795,x21796,x21791),f458(x21793,x21794,x21795,x21796,x21792)) % 187.86/187.67 [2180]~E(x21801,x21802)+E(f528(x21801,x21803,x21804,x21805),f528(x21802,x21803,x21804,x21805)) % 187.86/187.67 [2181]~E(x21811,x21812)+E(f528(x21813,x21811,x21814,x21815),f528(x21813,x21812,x21814,x21815)) % 187.86/187.67 [2182]~E(x21821,x21822)+E(f528(x21823,x21824,x21821,x21825),f528(x21823,x21824,x21822,x21825)) % 187.86/187.67 [2183]~E(x21831,x21832)+E(f528(x21833,x21834,x21835,x21831),f528(x21833,x21834,x21835,x21832)) % 187.86/187.67 [2184]~E(x21841,x21842)+E(f639(x21841,x21843,x21844),f639(x21842,x21843,x21844)) % 187.86/187.67 [2185]~E(x21851,x21852)+E(f639(x21853,x21851,x21854),f639(x21853,x21852,x21854)) % 187.86/187.67 [2186]~E(x21861,x21862)+E(f639(x21863,x21864,x21861),f639(x21863,x21864,x21862)) % 187.86/187.67 [2187]~E(x21871,x21872)+E(f663(x21871,x21873,x21874,x21875,x21876,x21877),f663(x21872,x21873,x21874,x21875,x21876,x21877)) % 187.86/187.67 [2188]~E(x21881,x21882)+E(f663(x21883,x21881,x21884,x21885,x21886,x21887),f663(x21883,x21882,x21884,x21885,x21886,x21887)) % 187.86/187.67 [2189]~E(x21891,x21892)+E(f663(x21893,x21894,x21891,x21895,x21896,x21897),f663(x21893,x21894,x21892,x21895,x21896,x21897)) % 187.86/187.67 [2190]~E(x21901,x21902)+E(f663(x21903,x21904,x21905,x21901,x21906,x21907),f663(x21903,x21904,x21905,x21902,x21906,x21907)) % 187.86/187.67 [2191]~E(x21911,x21912)+E(f663(x21913,x21914,x21915,x21916,x21911,x21917),f663(x21913,x21914,x21915,x21916,x21912,x21917)) % 187.86/187.67 [2192]~E(x21921,x21922)+E(f663(x21923,x21924,x21925,x21926,x21927,x21921),f663(x21923,x21924,x21925,x21926,x21927,x21922)) % 187.86/187.67 [2193]~E(x21931,x21932)+E(f829(x21931),f829(x21932)) % 187.86/187.67 [2194]~E(x21941,x21942)+E(f645(x21941,x21943,x21944),f645(x21942,x21943,x21944)) % 187.86/187.67 [2195]~E(x21951,x21952)+E(f645(x21953,x21951,x21954),f645(x21953,x21952,x21954)) % 187.86/187.67 [2196]~E(x21961,x21962)+E(f645(x21963,x21964,x21961),f645(x21963,x21964,x21962)) % 187.86/187.67 [2197]~E(x21971,x21972)+E(f606(x21971,x21973,x21974,x21975,x21976),f606(x21972,x21973,x21974,x21975,x21976)) % 187.86/187.67 [2198]~E(x21981,x21982)+E(f606(x21983,x21981,x21984,x21985,x21986),f606(x21983,x21982,x21984,x21985,x21986)) % 187.86/187.67 [2199]~E(x21991,x21992)+E(f606(x21993,x21994,x21991,x21995,x21996),f606(x21993,x21994,x21992,x21995,x21996)) % 187.86/187.67 [2200]~E(x22001,x22002)+E(f606(x22003,x22004,x22005,x22001,x22006),f606(x22003,x22004,x22005,x22002,x22006)) % 187.86/187.67 [2201]~E(x22011,x22012)+E(f606(x22013,x22014,x22015,x22016,x22011),f606(x22013,x22014,x22015,x22016,x22012)) % 187.86/187.67 [2202]~E(x22021,x22022)+E(f338(x22021,x22023,x22024,x22025),f338(x22022,x22023,x22024,x22025)) % 187.86/187.67 [2203]~E(x22031,x22032)+E(f338(x22033,x22031,x22034,x22035),f338(x22033,x22032,x22034,x22035)) % 187.86/187.67 [2204]~E(x22041,x22042)+E(f338(x22043,x22044,x22041,x22045),f338(x22043,x22044,x22042,x22045)) % 187.86/187.67 [2205]~E(x22051,x22052)+E(f338(x22053,x22054,x22055,x22051),f338(x22053,x22054,x22055,x22052)) % 187.86/187.67 [2206]~E(x22061,x22062)+E(f571(x22061,x22063,x22064),f571(x22062,x22063,x22064)) % 187.86/187.67 [2207]~E(x22071,x22072)+E(f571(x22073,x22071,x22074),f571(x22073,x22072,x22074)) % 187.86/187.67 [2208]~E(x22081,x22082)+E(f571(x22083,x22084,x22081),f571(x22083,x22084,x22082)) % 187.86/187.67 [2209]~E(x22091,x22092)+E(f253(x22091,x22093),f253(x22092,x22093)) % 187.86/187.67 [2210]~E(x22101,x22102)+E(f253(x22103,x22101),f253(x22103,x22102)) % 187.86/187.67 [2211]~E(x22111,x22112)+E(f455(x22111,x22113,x22114,x22115),f455(x22112,x22113,x22114,x22115)) % 187.86/187.67 [2212]~E(x22121,x22122)+E(f455(x22123,x22121,x22124,x22125),f455(x22123,x22122,x22124,x22125)) % 187.86/187.67 [2213]~E(x22131,x22132)+E(f455(x22133,x22134,x22131,x22135),f455(x22133,x22134,x22132,x22135)) % 187.86/187.67 [2214]~E(x22141,x22142)+E(f455(x22143,x22144,x22145,x22141),f455(x22143,x22144,x22145,x22142)) % 187.86/187.67 [2215]~E(x22151,x22152)+E(f597(x22151,x22153,x22154),f597(x22152,x22153,x22154)) % 187.86/187.67 [2216]~E(x22161,x22162)+E(f597(x22163,x22161,x22164),f597(x22163,x22162,x22164)) % 187.86/187.67 [2217]~E(x22171,x22172)+E(f597(x22173,x22174,x22171),f597(x22173,x22174,x22172)) % 187.86/187.67 [2218]~E(x22181,x22182)+E(f321(x22181,x22183,x22184),f321(x22182,x22183,x22184)) % 187.86/187.67 [2219]~E(x22191,x22192)+E(f321(x22193,x22191,x22194),f321(x22193,x22192,x22194)) % 187.86/187.67 [2220]~E(x22201,x22202)+E(f321(x22203,x22204,x22201),f321(x22203,x22204,x22202)) % 187.86/187.67 [2221]~E(x22211,x22212)+E(f154(x22211,x22213),f154(x22212,x22213)) % 187.86/187.67 [2222]~E(x22221,x22222)+E(f154(x22223,x22221),f154(x22223,x22222)) % 187.86/187.67 [2223]~E(x22231,x22232)+E(f660(x22231,x22233,x22234,x22235,x22236,x22237),f660(x22232,x22233,x22234,x22235,x22236,x22237)) % 187.86/187.67 [2224]~E(x22241,x22242)+E(f660(x22243,x22241,x22244,x22245,x22246,x22247),f660(x22243,x22242,x22244,x22245,x22246,x22247)) % 187.86/187.67 [2225]~E(x22251,x22252)+E(f660(x22253,x22254,x22251,x22255,x22256,x22257),f660(x22253,x22254,x22252,x22255,x22256,x22257)) % 187.86/187.67 [2226]~E(x22261,x22262)+E(f660(x22263,x22264,x22265,x22261,x22266,x22267),f660(x22263,x22264,x22265,x22262,x22266,x22267)) % 187.86/187.67 [2227]~E(x22271,x22272)+E(f660(x22273,x22274,x22275,x22276,x22271,x22277),f660(x22273,x22274,x22275,x22276,x22272,x22277)) % 187.86/187.67 [2228]~E(x22281,x22282)+E(f660(x22283,x22284,x22285,x22286,x22287,x22281),f660(x22283,x22284,x22285,x22286,x22287,x22282)) % 187.86/187.67 [2229]~E(x22291,x22292)+E(f378(x22291,x22293,x22294),f378(x22292,x22293,x22294)) % 187.86/187.67 [2230]~E(x22301,x22302)+E(f378(x22303,x22301,x22304),f378(x22303,x22302,x22304)) % 187.86/187.67 [2231]~E(x22311,x22312)+E(f378(x22313,x22314,x22311),f378(x22313,x22314,x22312)) % 187.86/187.67 [2232]~E(x22321,x22322)+E(f718(x22321,x22323,x22324),f718(x22322,x22323,x22324)) % 187.86/187.67 [2233]~E(x22331,x22332)+E(f718(x22333,x22331,x22334),f718(x22333,x22332,x22334)) % 187.86/187.67 [2234]~E(x22341,x22342)+E(f718(x22343,x22344,x22341),f718(x22343,x22344,x22342)) % 187.86/187.67 [2235]~E(x22351,x22352)+E(f834(x22351),f834(x22352)) % 187.86/187.67 [2236]~E(x22361,x22362)+E(f291(x22361),f291(x22362)) % 187.86/187.67 [2237]~E(x22371,x22372)+E(f750(x22371,x22373,x22374),f750(x22372,x22373,x22374)) % 187.86/187.67 [2238]~E(x22381,x22382)+E(f750(x22383,x22381,x22384),f750(x22383,x22382,x22384)) % 187.86/187.67 [2239]~E(x22391,x22392)+E(f750(x22393,x22394,x22391),f750(x22393,x22394,x22392)) % 187.86/187.67 [2240]~E(x22401,x22402)+E(f274(x22401,x22403,x22404,x22405,x22406),f274(x22402,x22403,x22404,x22405,x22406)) % 187.86/187.67 [2241]~E(x22411,x22412)+E(f274(x22413,x22411,x22414,x22415,x22416),f274(x22413,x22412,x22414,x22415,x22416)) % 187.86/187.67 [2242]~E(x22421,x22422)+E(f274(x22423,x22424,x22421,x22425,x22426),f274(x22423,x22424,x22422,x22425,x22426)) % 187.86/187.67 [2243]~E(x22431,x22432)+E(f274(x22433,x22434,x22435,x22431,x22436),f274(x22433,x22434,x22435,x22432,x22436)) % 187.86/187.67 [2244]~E(x22441,x22442)+E(f274(x22443,x22444,x22445,x22446,x22441),f274(x22443,x22444,x22445,x22446,x22442)) % 187.86/187.67 [2245]~E(x22451,x22452)+E(f386(x22451,x22453,x22454,x22455),f386(x22452,x22453,x22454,x22455)) % 187.86/187.67 [2246]~E(x22461,x22462)+E(f386(x22463,x22461,x22464,x22465),f386(x22463,x22462,x22464,x22465)) % 187.86/187.67 [2247]~E(x22471,x22472)+E(f386(x22473,x22474,x22471,x22475),f386(x22473,x22474,x22472,x22475)) % 187.86/187.67 [2248]~E(x22481,x22482)+E(f386(x22483,x22484,x22485,x22481),f386(x22483,x22484,x22485,x22482)) % 187.86/187.67 [2249]~E(x22491,x22492)+E(f516(x22491,x22493),f516(x22492,x22493)) % 187.86/187.67 [2250]~E(x22501,x22502)+E(f516(x22503,x22501),f516(x22503,x22502)) % 187.86/187.67 [2251]~E(x22511,x22512)+E(f127(x22511),f127(x22512)) % 187.86/187.67 [2252]~E(x22521,x22522)+E(f468(x22521,x22523,x22524,x22525,x22526,x22527,x22528),f468(x22522,x22523,x22524,x22525,x22526,x22527,x22528)) % 187.86/187.67 [2253]~E(x22531,x22532)+E(f468(x22533,x22531,x22534,x22535,x22536,x22537,x22538),f468(x22533,x22532,x22534,x22535,x22536,x22537,x22538)) % 187.86/187.67 [2254]~E(x22541,x22542)+E(f468(x22543,x22544,x22541,x22545,x22546,x22547,x22548),f468(x22543,x22544,x22542,x22545,x22546,x22547,x22548)) % 187.86/187.67 [2255]~E(x22551,x22552)+E(f468(x22553,x22554,x22555,x22551,x22556,x22557,x22558),f468(x22553,x22554,x22555,x22552,x22556,x22557,x22558)) % 187.86/187.67 [2256]~E(x22561,x22562)+E(f468(x22563,x22564,x22565,x22566,x22561,x22567,x22568),f468(x22563,x22564,x22565,x22566,x22562,x22567,x22568)) % 187.86/187.67 [2257]~E(x22571,x22572)+E(f468(x22573,x22574,x22575,x22576,x22577,x22571,x22578),f468(x22573,x22574,x22575,x22576,x22577,x22572,x22578)) % 187.86/187.67 [2258]~E(x22581,x22582)+E(f468(x22583,x22584,x22585,x22586,x22587,x22588,x22581),f468(x22583,x22584,x22585,x22586,x22587,x22588,x22582)) % 187.86/187.67 [2259]~E(x22591,x22592)+E(f724(x22591,x22593),f724(x22592,x22593)) % 187.86/187.67 [2260]~E(x22601,x22602)+E(f724(x22603,x22601),f724(x22603,x22602)) % 187.86/187.67 [2261]~E(x22611,x22612)+E(f651(x22611,x22613,x22614,x22615),f651(x22612,x22613,x22614,x22615)) % 187.86/187.67 [2262]~E(x22621,x22622)+E(f651(x22623,x22621,x22624,x22625),f651(x22623,x22622,x22624,x22625)) % 187.86/187.67 [2263]~E(x22631,x22632)+E(f651(x22633,x22634,x22631,x22635),f651(x22633,x22634,x22632,x22635)) % 187.86/187.67 [2264]~E(x22641,x22642)+E(f651(x22643,x22644,x22645,x22641),f651(x22643,x22644,x22645,x22642)) % 187.86/187.67 [2265]~E(x22651,x22652)+E(f628(x22651,x22653,x22654,x22655),f628(x22652,x22653,x22654,x22655)) % 187.86/187.67 [2266]~E(x22661,x22662)+E(f628(x22663,x22661,x22664,x22665),f628(x22663,x22662,x22664,x22665)) % 187.86/187.67 [2267]~E(x22671,x22672)+E(f628(x22673,x22674,x22671,x22675),f628(x22673,x22674,x22672,x22675)) % 187.86/187.67 [2268]~E(x22681,x22682)+E(f628(x22683,x22684,x22685,x22681),f628(x22683,x22684,x22685,x22682)) % 187.86/187.67 [2269]~E(x22691,x22692)+E(f748(x22691,x22693,x22694,x22695),f748(x22692,x22693,x22694,x22695)) % 187.86/187.67 [2270]~E(x22701,x22702)+E(f748(x22703,x22701,x22704,x22705),f748(x22703,x22702,x22704,x22705)) % 187.86/187.67 [2271]~E(x22711,x22712)+E(f748(x22713,x22714,x22711,x22715),f748(x22713,x22714,x22712,x22715)) % 187.86/187.67 [2272]~E(x22721,x22722)+E(f748(x22723,x22724,x22725,x22721),f748(x22723,x22724,x22725,x22722)) % 187.86/187.67 [2273]~E(x22731,x22732)+E(f619(x22731,x22733,x22734,x22735),f619(x22732,x22733,x22734,x22735)) % 187.86/187.67 [2274]~E(x22741,x22742)+E(f619(x22743,x22741,x22744,x22745),f619(x22743,x22742,x22744,x22745)) % 187.86/187.67 [2275]~E(x22751,x22752)+E(f619(x22753,x22754,x22751,x22755),f619(x22753,x22754,x22752,x22755)) % 187.86/187.67 [2276]~E(x22761,x22762)+E(f619(x22763,x22764,x22765,x22761),f619(x22763,x22764,x22765,x22762)) % 187.86/187.67 [2277]~E(x22771,x22772)+E(f756(x22771,x22773),f756(x22772,x22773)) % 187.86/187.67 [2278]~E(x22781,x22782)+E(f756(x22783,x22781),f756(x22783,x22782)) % 187.86/187.67 [2279]~E(x22791,x22792)+E(f519(x22791,x22793,x22794),f519(x22792,x22793,x22794)) % 187.86/187.67 [2280]~E(x22801,x22802)+E(f519(x22803,x22801,x22804),f519(x22803,x22802,x22804)) % 187.86/187.67 [2281]~E(x22811,x22812)+E(f519(x22813,x22814,x22811),f519(x22813,x22814,x22812)) % 187.86/187.67 [2282]~E(x22821,x22822)+E(f836(x22821,x22823,x22824),f836(x22822,x22823,x22824)) % 187.86/187.67 [2283]~E(x22831,x22832)+E(f836(x22833,x22831,x22834),f836(x22833,x22832,x22834)) % 187.86/187.67 [2284]~E(x22841,x22842)+E(f836(x22843,x22844,x22841),f836(x22843,x22844,x22842)) % 187.86/187.67 [2285]~E(x22851,x22852)+E(f346(x22851,x22853,x22854),f346(x22852,x22853,x22854)) % 187.86/187.67 [2286]~E(x22861,x22862)+E(f346(x22863,x22861,x22864),f346(x22863,x22862,x22864)) % 187.86/187.67 [2287]~E(x22871,x22872)+E(f346(x22873,x22874,x22871),f346(x22873,x22874,x22872)) % 187.86/187.67 [2288]~E(x22881,x22882)+E(f315(x22881,x22883,x22884),f315(x22882,x22883,x22884)) % 187.86/187.67 [2289]~E(x22891,x22892)+E(f315(x22893,x22891,x22894),f315(x22893,x22892,x22894)) % 187.86/187.67 [2290]~E(x22901,x22902)+E(f315(x22903,x22904,x22901),f315(x22903,x22904,x22902)) % 187.86/187.67 [2291]~E(x22911,x22912)+E(f811(x22911,x22913,x22914,x22915),f811(x22912,x22913,x22914,x22915)) % 187.86/187.67 [2292]~E(x22921,x22922)+E(f811(x22923,x22921,x22924,x22925),f811(x22923,x22922,x22924,x22925)) % 187.86/187.67 [2293]~E(x22931,x22932)+E(f811(x22933,x22934,x22931,x22935),f811(x22933,x22934,x22932,x22935)) % 187.86/187.67 [2294]~E(x22941,x22942)+E(f811(x22943,x22944,x22945,x22941),f811(x22943,x22944,x22945,x22942)) % 187.86/187.67 [2295]~E(x22951,x22952)+E(f505(x22951,x22953,x22954,x22955,x22956),f505(x22952,x22953,x22954,x22955,x22956)) % 187.86/187.67 [2296]~E(x22961,x22962)+E(f505(x22963,x22961,x22964,x22965,x22966),f505(x22963,x22962,x22964,x22965,x22966)) % 187.86/187.67 [2297]~E(x22971,x22972)+E(f505(x22973,x22974,x22971,x22975,x22976),f505(x22973,x22974,x22972,x22975,x22976)) % 187.86/187.67 [2298]~E(x22981,x22982)+E(f505(x22983,x22984,x22985,x22981,x22986),f505(x22983,x22984,x22985,x22982,x22986)) % 187.86/187.67 [2299]~E(x22991,x22992)+E(f505(x22993,x22994,x22995,x22996,x22991),f505(x22993,x22994,x22995,x22996,x22992)) % 187.86/187.67 [2300]~E(x23001,x23002)+E(f553(x23001,x23003,x23004),f553(x23002,x23003,x23004)) % 187.86/187.67 [2301]~E(x23011,x23012)+E(f553(x23013,x23011,x23014),f553(x23013,x23012,x23014)) % 187.86/187.67 [2302]~E(x23021,x23022)+E(f553(x23023,x23024,x23021),f553(x23023,x23024,x23022)) % 187.86/187.67 [2303]~E(x23031,x23032)+E(f778(x23031,x23033,x23034,x23035,x23036),f778(x23032,x23033,x23034,x23035,x23036)) % 187.86/187.67 [2304]~E(x23041,x23042)+E(f778(x23043,x23041,x23044,x23045,x23046),f778(x23043,x23042,x23044,x23045,x23046)) % 187.86/187.67 [2305]~E(x23051,x23052)+E(f778(x23053,x23054,x23051,x23055,x23056),f778(x23053,x23054,x23052,x23055,x23056)) % 187.86/187.67 [2306]~E(x23061,x23062)+E(f778(x23063,x23064,x23065,x23061,x23066),f778(x23063,x23064,x23065,x23062,x23066)) % 187.86/187.67 [2307]~E(x23071,x23072)+E(f778(x23073,x23074,x23075,x23076,x23071),f778(x23073,x23074,x23075,x23076,x23072)) % 187.86/187.67 [2308]~E(x23081,x23082)+E(f578(x23081,x23083,x23084),f578(x23082,x23083,x23084)) % 187.86/187.67 [2309]~E(x23091,x23092)+E(f578(x23093,x23091,x23094),f578(x23093,x23092,x23094)) % 187.86/187.67 [2310]~E(x23101,x23102)+E(f578(x23103,x23104,x23101),f578(x23103,x23104,x23102)) % 187.86/187.67 [2311]~E(x23111,x23112)+E(f513(x23111,x23113,x23114,x23115,x23116),f513(x23112,x23113,x23114,x23115,x23116)) % 187.86/187.67 [2312]~E(x23121,x23122)+E(f513(x23123,x23121,x23124,x23125,x23126),f513(x23123,x23122,x23124,x23125,x23126)) % 187.86/187.67 [2313]~E(x23131,x23132)+E(f513(x23133,x23134,x23131,x23135,x23136),f513(x23133,x23134,x23132,x23135,x23136)) % 187.86/187.67 [2314]~E(x23141,x23142)+E(f513(x23143,x23144,x23145,x23141,x23146),f513(x23143,x23144,x23145,x23142,x23146)) % 187.86/187.67 [2315]~E(x23151,x23152)+E(f513(x23153,x23154,x23155,x23156,x23151),f513(x23153,x23154,x23155,x23156,x23152)) % 187.86/187.67 [2316]~E(x23161,x23162)+E(f526(x23161,x23163,x23164,x23165),f526(x23162,x23163,x23164,x23165)) % 187.86/187.67 [2317]~E(x23171,x23172)+E(f526(x23173,x23171,x23174,x23175),f526(x23173,x23172,x23174,x23175)) % 187.86/187.67 [2318]~E(x23181,x23182)+E(f526(x23183,x23184,x23181,x23185),f526(x23183,x23184,x23182,x23185)) % 187.86/187.67 [2319]~E(x23191,x23192)+E(f526(x23193,x23194,x23195,x23191),f526(x23193,x23194,x23195,x23192)) % 187.86/187.67 [2320]~E(x23201,x23202)+E(f208(x23201,x23203,x23204,x23205),f208(x23202,x23203,x23204,x23205)) % 187.86/187.67 [2321]~E(x23211,x23212)+E(f208(x23213,x23211,x23214,x23215),f208(x23213,x23212,x23214,x23215)) % 187.86/187.67 [2322]~E(x23221,x23222)+E(f208(x23223,x23224,x23221,x23225),f208(x23223,x23224,x23222,x23225)) % 187.86/187.67 [2323]~E(x23231,x23232)+E(f208(x23233,x23234,x23235,x23231),f208(x23233,x23234,x23235,x23232)) % 187.86/187.67 [2324]~E(x23241,x23242)+E(f461(x23241,x23243,x23244,x23245,x23246),f461(x23242,x23243,x23244,x23245,x23246)) % 187.86/187.67 [2325]~E(x23251,x23252)+E(f461(x23253,x23251,x23254,x23255,x23256),f461(x23253,x23252,x23254,x23255,x23256)) % 187.86/187.67 [2326]~E(x23261,x23262)+E(f461(x23263,x23264,x23261,x23265,x23266),f461(x23263,x23264,x23262,x23265,x23266)) % 187.86/187.67 [2327]~E(x23271,x23272)+E(f461(x23273,x23274,x23275,x23271,x23276),f461(x23273,x23274,x23275,x23272,x23276)) % 187.86/187.67 [2328]~E(x23281,x23282)+E(f461(x23283,x23284,x23285,x23286,x23281),f461(x23283,x23284,x23285,x23286,x23282)) % 187.86/187.67 [2329]~E(x23291,x23292)+E(f675(x23291,x23293,x23294,x23295),f675(x23292,x23293,x23294,x23295)) % 187.86/187.67 [2330]~E(x23301,x23302)+E(f675(x23303,x23301,x23304,x23305),f675(x23303,x23302,x23304,x23305)) % 187.86/187.67 [2331]~E(x23311,x23312)+E(f675(x23313,x23314,x23311,x23315),f675(x23313,x23314,x23312,x23315)) % 187.86/187.67 [2332]~E(x23321,x23322)+E(f675(x23323,x23324,x23325,x23321),f675(x23323,x23324,x23325,x23322)) % 187.86/187.67 [2333]~E(x23331,x23332)+E(f822(x23331),f822(x23332)) % 187.86/187.67 [2334]~E(x23341,x23342)+E(f388(x23341,x23343,x23344,x23345),f388(x23342,x23343,x23344,x23345)) % 187.86/187.67 [2335]~E(x23351,x23352)+E(f388(x23353,x23351,x23354,x23355),f388(x23353,x23352,x23354,x23355)) % 187.86/187.67 [2336]~E(x23361,x23362)+E(f388(x23363,x23364,x23361,x23365),f388(x23363,x23364,x23362,x23365)) % 187.86/187.67 [2337]~E(x23371,x23372)+E(f388(x23373,x23374,x23375,x23371),f388(x23373,x23374,x23375,x23372)) % 187.86/187.67 [2338]~E(x23381,x23382)+E(f644(x23381,x23383,x23384,x23385,x23386,x23387),f644(x23382,x23383,x23384,x23385,x23386,x23387)) % 187.86/187.67 [2339]~E(x23391,x23392)+E(f644(x23393,x23391,x23394,x23395,x23396,x23397),f644(x23393,x23392,x23394,x23395,x23396,x23397)) % 187.86/187.67 [2340]~E(x23401,x23402)+E(f644(x23403,x23404,x23401,x23405,x23406,x23407),f644(x23403,x23404,x23402,x23405,x23406,x23407)) % 187.86/187.67 [2341]~E(x23411,x23412)+E(f644(x23413,x23414,x23415,x23411,x23416,x23417),f644(x23413,x23414,x23415,x23412,x23416,x23417)) % 187.86/187.67 [2342]~E(x23421,x23422)+E(f644(x23423,x23424,x23425,x23426,x23421,x23427),f644(x23423,x23424,x23425,x23426,x23422,x23427)) % 187.86/187.67 [2343]~E(x23431,x23432)+E(f644(x23433,x23434,x23435,x23436,x23437,x23431),f644(x23433,x23434,x23435,x23436,x23437,x23432)) % 187.86/187.67 [2344]~E(x23441,x23442)+E(f419(x23441,x23443,x23444,x23445,x23446),f419(x23442,x23443,x23444,x23445,x23446)) % 187.86/187.67 [2345]~E(x23451,x23452)+E(f419(x23453,x23451,x23454,x23455,x23456),f419(x23453,x23452,x23454,x23455,x23456)) % 187.86/187.67 [2346]~E(x23461,x23462)+E(f419(x23463,x23464,x23461,x23465,x23466),f419(x23463,x23464,x23462,x23465,x23466)) % 187.86/187.67 [2347]~E(x23471,x23472)+E(f419(x23473,x23474,x23475,x23471,x23476),f419(x23473,x23474,x23475,x23472,x23476)) % 187.86/187.67 [2348]~E(x23481,x23482)+E(f419(x23483,x23484,x23485,x23486,x23481),f419(x23483,x23484,x23485,x23486,x23482)) % 187.86/187.67 [2349]~E(x23491,x23492)+E(f482(x23491,x23493,x23494),f482(x23492,x23493,x23494)) % 187.86/187.67 [2350]~E(x23501,x23502)+E(f482(x23503,x23501,x23504),f482(x23503,x23502,x23504)) % 187.86/187.67 [2351]~E(x23511,x23512)+E(f482(x23513,x23514,x23511),f482(x23513,x23514,x23512)) % 187.86/187.67 [2352]~E(x23521,x23522)+E(f839(x23521,x23523,x23524),f839(x23522,x23523,x23524)) % 187.86/187.67 [2353]~E(x23531,x23532)+E(f839(x23533,x23531,x23534),f839(x23533,x23532,x23534)) % 187.86/187.67 [2354]~E(x23541,x23542)+E(f839(x23543,x23544,x23541),f839(x23543,x23544,x23542)) % 187.86/187.67 [2355]~E(x23551,x23552)+E(f549(x23551,x23553,x23554),f549(x23552,x23553,x23554)) % 187.86/187.67 [2356]~E(x23561,x23562)+E(f549(x23563,x23561,x23564),f549(x23563,x23562,x23564)) % 187.86/187.67 [2357]~E(x23571,x23572)+E(f549(x23573,x23574,x23571),f549(x23573,x23574,x23572)) % 187.86/187.67 [2358]~E(x23581,x23582)+E(f424(x23581,x23583,x23584),f424(x23582,x23583,x23584)) % 187.86/187.67 [2359]~E(x23591,x23592)+E(f424(x23593,x23591,x23594),f424(x23593,x23592,x23594)) % 187.86/187.67 [2360]~E(x23601,x23602)+E(f424(x23603,x23604,x23601),f424(x23603,x23604,x23602)) % 187.86/187.67 [2361]~E(x23611,x23612)+E(f204(x23611,x23613),f204(x23612,x23613)) % 187.86/187.67 [2362]~E(x23621,x23622)+E(f204(x23623,x23621),f204(x23623,x23622)) % 187.86/187.67 [2363]~E(x23631,x23632)+E(f729(x23631,x23633,x23634),f729(x23632,x23633,x23634)) % 187.86/187.67 [2364]~E(x23641,x23642)+E(f729(x23643,x23641,x23644),f729(x23643,x23642,x23644)) % 187.86/187.67 [2365]~E(x23651,x23652)+E(f729(x23653,x23654,x23651),f729(x23653,x23654,x23652)) % 187.86/187.67 [2366]~E(x23661,x23662)+E(f779(x23661,x23663,x23664,x23665,x23666),f779(x23662,x23663,x23664,x23665,x23666)) % 187.86/187.67 [2367]~E(x23671,x23672)+E(f779(x23673,x23671,x23674,x23675,x23676),f779(x23673,x23672,x23674,x23675,x23676)) % 187.86/187.67 [2368]~E(x23681,x23682)+E(f779(x23683,x23684,x23681,x23685,x23686),f779(x23683,x23684,x23682,x23685,x23686)) % 187.86/187.67 [2369]~E(x23691,x23692)+E(f779(x23693,x23694,x23695,x23691,x23696),f779(x23693,x23694,x23695,x23692,x23696)) % 187.86/187.67 [2370]~E(x23701,x23702)+E(f779(x23703,x23704,x23705,x23706,x23701),f779(x23703,x23704,x23705,x23706,x23702)) % 187.86/187.67 [2371]~E(x23711,x23712)+E(f486(x23711,x23713),f486(x23712,x23713)) % 187.86/187.67 [2372]~E(x23721,x23722)+E(f486(x23723,x23721),f486(x23723,x23722)) % 187.86/187.67 [2373]~E(x23731,x23732)+E(f459(x23731,x23733,x23734,x23735,x23736),f459(x23732,x23733,x23734,x23735,x23736)) % 187.86/187.67 [2374]~E(x23741,x23742)+E(f459(x23743,x23741,x23744,x23745,x23746),f459(x23743,x23742,x23744,x23745,x23746)) % 187.86/187.67 [2375]~E(x23751,x23752)+E(f459(x23753,x23754,x23751,x23755,x23756),f459(x23753,x23754,x23752,x23755,x23756)) % 187.86/187.67 [2376]~E(x23761,x23762)+E(f459(x23763,x23764,x23765,x23761,x23766),f459(x23763,x23764,x23765,x23762,x23766)) % 187.86/187.67 [2377]~E(x23771,x23772)+E(f459(x23773,x23774,x23775,x23776,x23771),f459(x23773,x23774,x23775,x23776,x23772)) % 187.86/187.67 [2378]~E(x23781,x23782)+E(f370(x23781,x23783,x23784,x23785,x23786),f370(x23782,x23783,x23784,x23785,x23786)) % 187.86/187.67 [2379]~E(x23791,x23792)+E(f370(x23793,x23791,x23794,x23795,x23796),f370(x23793,x23792,x23794,x23795,x23796)) % 187.86/187.67 [2380]~E(x23801,x23802)+E(f370(x23803,x23804,x23801,x23805,x23806),f370(x23803,x23804,x23802,x23805,x23806)) % 187.86/187.67 [2381]~E(x23811,x23812)+E(f370(x23813,x23814,x23815,x23811,x23816),f370(x23813,x23814,x23815,x23812,x23816)) % 187.86/187.67 [2382]~E(x23821,x23822)+E(f370(x23823,x23824,x23825,x23826,x23821),f370(x23823,x23824,x23825,x23826,x23822)) % 187.86/187.67 [2383]~E(x23831,x23832)+E(f796(x23831,x23833,x23834),f796(x23832,x23833,x23834)) % 187.86/187.67 [2384]~E(x23841,x23842)+E(f796(x23843,x23841,x23844),f796(x23843,x23842,x23844)) % 187.86/187.67 [2385]~E(x23851,x23852)+E(f796(x23853,x23854,x23851),f796(x23853,x23854,x23852)) % 187.86/187.67 [2386]~E(x23861,x23862)+E(f830(x23861,x23863),f830(x23862,x23863)) % 187.86/187.67 [2387]~E(x23871,x23872)+E(f830(x23873,x23871),f830(x23873,x23872)) % 187.86/187.67 [2388]~E(x23881,x23882)+E(f752(x23881,x23883,x23884,x23885),f752(x23882,x23883,x23884,x23885)) % 187.86/187.67 [2389]~E(x23891,x23892)+E(f752(x23893,x23891,x23894,x23895),f752(x23893,x23892,x23894,x23895)) % 187.86/187.67 [2390]~E(x23901,x23902)+E(f752(x23903,x23904,x23901,x23905),f752(x23903,x23904,x23902,x23905)) % 187.86/187.67 [2391]~E(x23911,x23912)+E(f752(x23913,x23914,x23915,x23911),f752(x23913,x23914,x23915,x23912)) % 187.86/187.67 [2392]~E(x23921,x23922)+E(f633(x23921,x23923,x23924),f633(x23922,x23923,x23924)) % 187.86/187.67 [2393]~E(x23931,x23932)+E(f633(x23933,x23931,x23934),f633(x23933,x23932,x23934)) % 187.86/187.67 [2394]~E(x23941,x23942)+E(f633(x23943,x23944,x23941),f633(x23943,x23944,x23942)) % 187.86/187.67 [2395]~E(x23951,x23952)+E(f454(x23951,x23953,x23954,x23955),f454(x23952,x23953,x23954,x23955)) % 187.86/187.67 [2396]~E(x23961,x23962)+E(f454(x23963,x23961,x23964,x23965),f454(x23963,x23962,x23964,x23965)) % 187.86/187.67 [2397]~E(x23971,x23972)+E(f454(x23973,x23974,x23971,x23975),f454(x23973,x23974,x23972,x23975)) % 187.86/187.67 [2398]~E(x23981,x23982)+E(f454(x23983,x23984,x23985,x23981),f454(x23983,x23984,x23985,x23982)) % 187.86/187.67 [2399]~E(x23991,x23992)+E(f704(x23991,x23993,x23994,x23995),f704(x23992,x23993,x23994,x23995)) % 187.86/187.67 [2400]~E(x24001,x24002)+E(f704(x24003,x24001,x24004,x24005),f704(x24003,x24002,x24004,x24005)) % 187.86/187.67 [2401]~E(x24011,x24012)+E(f704(x24013,x24014,x24011,x24015),f704(x24013,x24014,x24012,x24015)) % 187.86/187.67 [2402]~E(x24021,x24022)+E(f704(x24023,x24024,x24025,x24021),f704(x24023,x24024,x24025,x24022)) % 187.86/187.67 [2403]~E(x24031,x24032)+E(f336(x24031,x24033,x24034,x24035),f336(x24032,x24033,x24034,x24035)) % 187.86/187.67 [2404]~E(x24041,x24042)+E(f336(x24043,x24041,x24044,x24045),f336(x24043,x24042,x24044,x24045)) % 187.86/187.67 [2405]~E(x24051,x24052)+E(f336(x24053,x24054,x24051,x24055),f336(x24053,x24054,x24052,x24055)) % 187.86/187.67 [2406]~E(x24061,x24062)+E(f336(x24063,x24064,x24065,x24061),f336(x24063,x24064,x24065,x24062)) % 187.86/187.67 [2407]~E(x24071,x24072)+E(f689(x24071),f689(x24072)) % 187.86/187.67 [2408]~E(x24081,x24082)+E(f848(x24081,x24083),f848(x24082,x24083)) % 187.86/187.67 [2409]~E(x24091,x24092)+E(f848(x24093,x24091),f848(x24093,x24092)) % 187.86/187.67 [2410]~E(x24101,x24102)+E(f470(x24101,x24103,x24104,x24105,x24106,x24107,x24108),f470(x24102,x24103,x24104,x24105,x24106,x24107,x24108)) % 187.86/187.67 [2411]~E(x24111,x24112)+E(f470(x24113,x24111,x24114,x24115,x24116,x24117,x24118),f470(x24113,x24112,x24114,x24115,x24116,x24117,x24118)) % 187.86/187.67 [2412]~E(x24121,x24122)+E(f470(x24123,x24124,x24121,x24125,x24126,x24127,x24128),f470(x24123,x24124,x24122,x24125,x24126,x24127,x24128)) % 187.86/187.67 [2413]~E(x24131,x24132)+E(f470(x24133,x24134,x24135,x24131,x24136,x24137,x24138),f470(x24133,x24134,x24135,x24132,x24136,x24137,x24138)) % 187.86/187.67 [2414]~E(x24141,x24142)+E(f470(x24143,x24144,x24145,x24146,x24141,x24147,x24148),f470(x24143,x24144,x24145,x24146,x24142,x24147,x24148)) % 187.86/187.67 [2415]~E(x24151,x24152)+E(f470(x24153,x24154,x24155,x24156,x24157,x24151,x24158),f470(x24153,x24154,x24155,x24156,x24157,x24152,x24158)) % 187.86/187.67 [2416]~E(x24161,x24162)+E(f470(x24163,x24164,x24165,x24166,x24167,x24168,x24161),f470(x24163,x24164,x24165,x24166,x24167,x24168,x24162)) % 187.86/187.67 [2417]~E(x24171,x24172)+E(f463(x24171,x24173,x24174,x24175),f463(x24172,x24173,x24174,x24175)) % 187.86/187.67 [2418]~E(x24181,x24182)+E(f463(x24183,x24181,x24184,x24185),f463(x24183,x24182,x24184,x24185)) % 187.86/187.67 [2419]~E(x24191,x24192)+E(f463(x24193,x24194,x24191,x24195),f463(x24193,x24194,x24192,x24195)) % 187.86/187.67 [2420]~E(x24201,x24202)+E(f463(x24203,x24204,x24205,x24201),f463(x24203,x24204,x24205,x24202)) % 187.86/187.67 [2421]~E(x24211,x24212)+E(f821(x24211,x24213),f821(x24212,x24213)) % 187.86/187.67 [2422]~E(x24221,x24222)+E(f821(x24223,x24221),f821(x24223,x24222)) % 187.86/187.67 [2423]~E(x24231,x24232)+E(f515(x24231,x24233,x24234,x24235,x24236,x24237,x24238),f515(x24232,x24233,x24234,x24235,x24236,x24237,x24238)) % 187.86/187.67 [2424]~E(x24241,x24242)+E(f515(x24243,x24241,x24244,x24245,x24246,x24247,x24248),f515(x24243,x24242,x24244,x24245,x24246,x24247,x24248)) % 187.86/187.67 [2425]~E(x24251,x24252)+E(f515(x24253,x24254,x24251,x24255,x24256,x24257,x24258),f515(x24253,x24254,x24252,x24255,x24256,x24257,x24258)) % 187.86/187.67 [2426]~E(x24261,x24262)+E(f515(x24263,x24264,x24265,x24261,x24266,x24267,x24268),f515(x24263,x24264,x24265,x24262,x24266,x24267,x24268)) % 187.86/187.67 [2427]~E(x24271,x24272)+E(f515(x24273,x24274,x24275,x24276,x24271,x24277,x24278),f515(x24273,x24274,x24275,x24276,x24272,x24277,x24278)) % 187.86/187.67 [2428]~E(x24281,x24282)+E(f515(x24283,x24284,x24285,x24286,x24287,x24281,x24288),f515(x24283,x24284,x24285,x24286,x24287,x24282,x24288)) % 187.86/187.67 [2429]~E(x24291,x24292)+E(f515(x24293,x24294,x24295,x24296,x24297,x24298,x24291),f515(x24293,x24294,x24295,x24296,x24297,x24298,x24292)) % 187.86/187.67 [2430]~E(x24301,x24302)+E(f666(x24301,x24303,x24304,x24305),f666(x24302,x24303,x24304,x24305)) % 187.86/187.67 [2431]~E(x24311,x24312)+E(f666(x24313,x24311,x24314,x24315),f666(x24313,x24312,x24314,x24315)) % 187.86/187.67 [2432]~E(x24321,x24322)+E(f666(x24323,x24324,x24321,x24325),f666(x24323,x24324,x24322,x24325)) % 187.86/187.67 [2433]~E(x24331,x24332)+E(f666(x24333,x24334,x24335,x24331),f666(x24333,x24334,x24335,x24332)) % 187.86/187.67 [2434]~E(x24341,x24342)+E(f490(x24341,x24343,x24344,x24345),f490(x24342,x24343,x24344,x24345)) % 187.86/187.67 [2435]~E(x24351,x24352)+E(f490(x24353,x24351,x24354,x24355),f490(x24353,x24352,x24354,x24355)) % 187.86/187.67 [2436]~E(x24361,x24362)+E(f490(x24363,x24364,x24361,x24365),f490(x24363,x24364,x24362,x24365)) % 187.86/187.67 [2437]~E(x24371,x24372)+E(f490(x24373,x24374,x24375,x24371),f490(x24373,x24374,x24375,x24372)) % 187.86/187.67 [2438]~E(x24381,x24382)+E(f726(x24381,x24383),f726(x24382,x24383)) % 187.86/187.67 [2439]~E(x24391,x24392)+E(f726(x24393,x24391),f726(x24393,x24392)) % 187.86/187.67 [2440]~E(x24401,x24402)+E(f777(x24401,x24403,x24404,x24405,x24406),f777(x24402,x24403,x24404,x24405,x24406)) % 187.86/187.67 [2441]~E(x24411,x24412)+E(f777(x24413,x24411,x24414,x24415,x24416),f777(x24413,x24412,x24414,x24415,x24416)) % 187.86/187.67 [2442]~E(x24421,x24422)+E(f777(x24423,x24424,x24421,x24425,x24426),f777(x24423,x24424,x24422,x24425,x24426)) % 187.86/187.67 [2443]~E(x24431,x24432)+E(f777(x24433,x24434,x24435,x24431,x24436),f777(x24433,x24434,x24435,x24432,x24436)) % 187.86/187.67 [2444]~E(x24441,x24442)+E(f777(x24443,x24444,x24445,x24446,x24441),f777(x24443,x24444,x24445,x24446,x24442)) % 187.86/187.67 [2445]~E(x24451,x24452)+E(f426(x24451,x24453,x24454,x24455,x24456),f426(x24452,x24453,x24454,x24455,x24456)) % 187.86/187.67 [2446]~E(x24461,x24462)+E(f426(x24463,x24461,x24464,x24465,x24466),f426(x24463,x24462,x24464,x24465,x24466)) % 187.86/187.67 [2447]~E(x24471,x24472)+E(f426(x24473,x24474,x24471,x24475,x24476),f426(x24473,x24474,x24472,x24475,x24476)) % 187.86/187.67 [2448]~E(x24481,x24482)+E(f426(x24483,x24484,x24485,x24481,x24486),f426(x24483,x24484,x24485,x24482,x24486)) % 187.86/187.67 [2449]~E(x24491,x24492)+E(f426(x24493,x24494,x24495,x24496,x24491),f426(x24493,x24494,x24495,x24496,x24492)) % 187.86/187.67 [2450]~E(x24501,x24502)+E(f558(x24501,x24503,x24504),f558(x24502,x24503,x24504)) % 187.86/187.67 [2451]~E(x24511,x24512)+E(f558(x24513,x24511,x24514),f558(x24513,x24512,x24514)) % 187.86/187.67 [2452]~E(x24521,x24522)+E(f558(x24523,x24524,x24521),f558(x24523,x24524,x24522)) % 187.86/187.67 [2453]~E(x24531,x24532)+E(f586(x24531,x24533,x24534),f586(x24532,x24533,x24534)) % 187.86/187.67 [2454]~E(x24541,x24542)+E(f586(x24543,x24541,x24544),f586(x24543,x24542,x24544)) % 187.86/187.67 [2455]~E(x24551,x24552)+E(f586(x24553,x24554,x24551),f586(x24553,x24554,x24552)) % 187.86/187.67 [2456]~E(x24561,x24562)+E(f362(x24561),f362(x24562)) % 187.86/187.67 [2457]~E(x24571,x24572)+E(f556(x24571,x24573,x24574),f556(x24572,x24573,x24574)) % 187.86/187.67 [2458]~E(x24581,x24582)+E(f556(x24583,x24581,x24584),f556(x24583,x24582,x24584)) % 187.86/187.67 [2459]~E(x24591,x24592)+E(f556(x24593,x24594,x24591),f556(x24593,x24594,x24592)) % 187.86/187.67 [2460]~E(x24601,x24602)+E(f684(x24601,x24603,x24604),f684(x24602,x24603,x24604)) % 187.86/187.67 [2461]~E(x24611,x24612)+E(f684(x24613,x24611,x24614),f684(x24613,x24612,x24614)) % 187.86/187.67 [2462]~E(x24621,x24622)+E(f684(x24623,x24624,x24621),f684(x24623,x24624,x24622)) % 187.86/187.67 [2463]~E(x24631,x24632)+E(f681(x24631,x24633),f681(x24632,x24633)) % 187.86/187.67 [2464]~E(x24641,x24642)+E(f681(x24643,x24641),f681(x24643,x24642)) % 187.86/187.67 [2465]~E(x24651,x24652)+E(f828(x24651),f828(x24652)) % 187.86/187.67 [2466]~E(x24661,x24662)+E(f534(x24661,x24663,x24664,x24665),f534(x24662,x24663,x24664,x24665)) % 187.86/187.67 [2467]~E(x24671,x24672)+E(f534(x24673,x24671,x24674,x24675),f534(x24673,x24672,x24674,x24675)) % 187.86/187.67 [2468]~E(x24681,x24682)+E(f534(x24683,x24684,x24681,x24685),f534(x24683,x24684,x24682,x24685)) % 187.86/187.67 [2469]~E(x24691,x24692)+E(f534(x24693,x24694,x24695,x24691),f534(x24693,x24694,x24695,x24692)) % 187.86/187.67 [2470]~E(x24701,x24702)+E(f825(x24701,x24703),f825(x24702,x24703)) % 187.86/187.67 [2471]~E(x24711,x24712)+E(f825(x24713,x24711),f825(x24713,x24712)) % 187.86/187.67 [2472]~E(x24721,x24722)+E(f709(x24721,x24723,x24724),f709(x24722,x24723,x24724)) % 187.86/187.67 [2473]~E(x24731,x24732)+E(f709(x24733,x24731,x24734),f709(x24733,x24732,x24734)) % 187.86/187.67 [2474]~E(x24741,x24742)+E(f709(x24743,x24744,x24741),f709(x24743,x24744,x24742)) % 187.86/187.67 [2475]~E(x24751,x24752)+E(f587(x24751,x24753,x24754),f587(x24752,x24753,x24754)) % 187.86/187.67 [2476]~E(x24761,x24762)+E(f587(x24763,x24761,x24764),f587(x24763,x24762,x24764)) % 187.86/187.67 [2477]~E(x24771,x24772)+E(f587(x24773,x24774,x24771),f587(x24773,x24774,x24772)) % 187.86/187.67 [2478]~E(x24781,x24782)+E(f579(x24781,x24783,x24784,x24785),f579(x24782,x24783,x24784,x24785)) % 187.86/187.67 [2479]~E(x24791,x24792)+E(f579(x24793,x24791,x24794,x24795),f579(x24793,x24792,x24794,x24795)) % 187.86/187.67 [2480]~E(x24801,x24802)+E(f579(x24803,x24804,x24801,x24805),f579(x24803,x24804,x24802,x24805)) % 187.86/187.67 [2481]~E(x24811,x24812)+E(f579(x24813,x24814,x24815,x24811),f579(x24813,x24814,x24815,x24812)) % 187.86/187.67 [2482]~E(x24821,x24822)+E(f492(x24821),f492(x24822)) % 187.86/187.67 [2483]~E(x24831,x24832)+E(f124(x24831),f124(x24832)) % 187.86/187.67 [2484]~E(x24841,x24842)+E(f356(x24841,x24843,x24844),f356(x24842,x24843,x24844)) % 187.86/187.67 [2485]~E(x24851,x24852)+E(f356(x24853,x24851,x24854),f356(x24853,x24852,x24854)) % 187.86/187.67 [2486]~E(x24861,x24862)+E(f356(x24863,x24864,x24861),f356(x24863,x24864,x24862)) % 187.86/187.67 [2487]~E(x24871,x24872)+E(f673(x24871,x24873,x24874,x24875,x24876),f673(x24872,x24873,x24874,x24875,x24876)) % 187.86/187.67 [2488]~E(x24881,x24882)+E(f673(x24883,x24881,x24884,x24885,x24886),f673(x24883,x24882,x24884,x24885,x24886)) % 187.86/187.67 [2489]~E(x24891,x24892)+E(f673(x24893,x24894,x24891,x24895,x24896),f673(x24893,x24894,x24892,x24895,x24896)) % 187.86/187.67 [2490]~E(x24901,x24902)+E(f673(x24903,x24904,x24905,x24901,x24906),f673(x24903,x24904,x24905,x24902,x24906)) % 187.86/187.67 [2491]~E(x24911,x24912)+E(f673(x24913,x24914,x24915,x24916,x24911),f673(x24913,x24914,x24915,x24916,x24912)) % 187.86/187.67 [2492]~E(x24921,x24922)+E(f545(x24921,x24923,x24924,x24925),f545(x24922,x24923,x24924,x24925)) % 187.86/187.67 [2493]~E(x24931,x24932)+E(f545(x24933,x24931,x24934,x24935),f545(x24933,x24932,x24934,x24935)) % 187.86/187.67 [2494]~E(x24941,x24942)+E(f545(x24943,x24944,x24941,x24945),f545(x24943,x24944,x24942,x24945)) % 187.86/187.67 [2495]~E(x24951,x24952)+E(f545(x24953,x24954,x24955,x24951),f545(x24953,x24954,x24955,x24952)) % 187.86/187.67 [2496]~E(x24961,x24962)+E(f732(x24961,x24963),f732(x24962,x24963)) % 187.86/187.67 [2497]~E(x24971,x24972)+E(f732(x24973,x24971),f732(x24973,x24972)) % 187.86/187.67 [2498]~E(x24981,x24982)+E(f410(x24981,x24983,x24984),f410(x24982,x24983,x24984)) % 187.86/187.67 [2499]~E(x24991,x24992)+E(f410(x24993,x24991,x24994),f410(x24993,x24992,x24994)) % 187.86/187.67 [2500]~E(x25001,x25002)+E(f410(x25003,x25004,x25001),f410(x25003,x25004,x25002)) % 187.86/187.67 [2501]~E(x25011,x25012)+E(f320(x25011,x25013,x25014),f320(x25012,x25013,x25014)) % 187.86/187.67 [2502]~E(x25021,x25022)+E(f320(x25023,x25021,x25024),f320(x25023,x25022,x25024)) % 187.86/187.67 [2503]~E(x25031,x25032)+E(f320(x25033,x25034,x25031),f320(x25033,x25034,x25032)) % 187.86/187.67 [2504]~E(x25041,x25042)+E(f248(x25041,x25043,x25044,x25045,x25046),f248(x25042,x25043,x25044,x25045,x25046)) % 187.86/187.67 [2505]~E(x25051,x25052)+E(f248(x25053,x25051,x25054,x25055,x25056),f248(x25053,x25052,x25054,x25055,x25056)) % 187.86/187.67 [2506]~E(x25061,x25062)+E(f248(x25063,x25064,x25061,x25065,x25066),f248(x25063,x25064,x25062,x25065,x25066)) % 187.86/187.67 [2507]~E(x25071,x25072)+E(f248(x25073,x25074,x25075,x25071,x25076),f248(x25073,x25074,x25075,x25072,x25076)) % 187.86/187.67 [2508]~E(x25081,x25082)+E(f248(x25083,x25084,x25085,x25086,x25081),f248(x25083,x25084,x25085,x25086,x25082)) % 187.86/187.67 [2509]~E(x25091,x25092)+E(f494(x25091,x25093,x25094),f494(x25092,x25093,x25094)) % 187.86/187.67 [2510]~E(x25101,x25102)+E(f494(x25103,x25101,x25104),f494(x25103,x25102,x25104)) % 187.86/187.67 [2511]~E(x25111,x25112)+E(f494(x25113,x25114,x25111),f494(x25113,x25114,x25112)) % 187.86/187.67 [2512]~E(x25121,x25122)+E(f610(x25121,x25123,x25124),f610(x25122,x25123,x25124)) % 187.86/187.67 [2513]~E(x25131,x25132)+E(f610(x25133,x25131,x25134),f610(x25133,x25132,x25134)) % 187.86/187.67 [2514]~E(x25141,x25142)+E(f610(x25143,x25144,x25141),f610(x25143,x25144,x25142)) % 187.86/187.67 [2515]~E(x25151,x25152)+E(f532(x25151,x25153,x25154),f532(x25152,x25153,x25154)) % 187.86/187.67 [2516]~E(x25161,x25162)+E(f532(x25163,x25161,x25164),f532(x25163,x25162,x25164)) % 187.86/187.67 [2517]~E(x25171,x25172)+E(f532(x25173,x25174,x25171),f532(x25173,x25174,x25172)) % 187.86/187.67 [2518]~E(x25181,x25182)+E(f837(x25181,x25183,x25184),f837(x25182,x25183,x25184)) % 187.86/187.67 [2519]~E(x25191,x25192)+E(f837(x25193,x25191,x25194),f837(x25193,x25192,x25194)) % 187.86/187.67 [2520]~E(x25201,x25202)+E(f837(x25203,x25204,x25201),f837(x25203,x25204,x25202)) % 187.86/187.67 [2521]~E(x25211,x25212)+E(f826(x25211,x25213,x25214,x25215,x25216,x25217,x25218),f826(x25212,x25213,x25214,x25215,x25216,x25217,x25218)) % 187.86/187.67 [2522]~E(x25221,x25222)+E(f826(x25223,x25221,x25224,x25225,x25226,x25227,x25228),f826(x25223,x25222,x25224,x25225,x25226,x25227,x25228)) % 187.86/187.67 [2523]~E(x25231,x25232)+E(f826(x25233,x25234,x25231,x25235,x25236,x25237,x25238),f826(x25233,x25234,x25232,x25235,x25236,x25237,x25238)) % 187.86/187.67 [2524]~E(x25241,x25242)+E(f826(x25243,x25244,x25245,x25241,x25246,x25247,x25248),f826(x25243,x25244,x25245,x25242,x25246,x25247,x25248)) % 187.86/187.67 [2525]~E(x25251,x25252)+E(f826(x25253,x25254,x25255,x25256,x25251,x25257,x25258),f826(x25253,x25254,x25255,x25256,x25252,x25257,x25258)) % 187.86/187.67 [2526]~E(x25261,x25262)+E(f826(x25263,x25264,x25265,x25266,x25267,x25261,x25268),f826(x25263,x25264,x25265,x25266,x25267,x25262,x25268)) % 187.86/187.67 [2527]~E(x25271,x25272)+E(f826(x25273,x25274,x25275,x25276,x25277,x25278,x25271),f826(x25273,x25274,x25275,x25276,x25277,x25278,x25272)) % 187.86/187.67 [2528]~E(x25281,x25282)+E(f518(x25281,x25283),f518(x25282,x25283)) % 187.86/187.67 [2529]~E(x25291,x25292)+E(f518(x25293,x25291),f518(x25293,x25292)) % 187.86/187.67 [2530]~E(x25301,x25302)+E(f711(x25301,x25303,x25304),f711(x25302,x25303,x25304)) % 187.86/187.67 [2531]~E(x25311,x25312)+E(f711(x25313,x25311,x25314),f711(x25313,x25312,x25314)) % 187.86/187.67 [2532]~E(x25321,x25322)+E(f711(x25323,x25324,x25321),f711(x25323,x25324,x25322)) % 187.86/187.67 [2533]~E(x25331,x25332)+E(f503(x25331,x25333,x25334,x25335,x25336),f503(x25332,x25333,x25334,x25335,x25336)) % 187.86/187.67 [2534]~E(x25341,x25342)+E(f503(x25343,x25341,x25344,x25345,x25346),f503(x25343,x25342,x25344,x25345,x25346)) % 187.86/187.67 [2535]~E(x25351,x25352)+E(f503(x25353,x25354,x25351,x25355,x25356),f503(x25353,x25354,x25352,x25355,x25356)) % 187.86/187.67 [2536]~E(x25361,x25362)+E(f503(x25363,x25364,x25365,x25361,x25366),f503(x25363,x25364,x25365,x25362,x25366)) % 187.86/187.67 [2537]~E(x25371,x25372)+E(f503(x25373,x25374,x25375,x25376,x25371),f503(x25373,x25374,x25375,x25376,x25372)) % 187.86/187.67 [2538]~E(x25381,x25382)+E(f601(x25381,x25383),f601(x25382,x25383)) % 187.86/187.67 [2539]~E(x25391,x25392)+E(f601(x25393,x25391),f601(x25393,x25392)) % 187.86/187.67 [2540]~E(x25401,x25402)+E(f325(x25401,x25403,x25404),f325(x25402,x25403,x25404)) % 187.86/187.67 [2541]~E(x25411,x25412)+E(f325(x25413,x25411,x25414),f325(x25413,x25412,x25414)) % 187.86/187.67 [2542]~E(x25421,x25422)+E(f325(x25423,x25424,x25421),f325(x25423,x25424,x25422)) % 187.86/187.67 [2543]~E(x25431,x25432)+E(f710(x25431,x25433),f710(x25432,x25433)) % 187.86/187.67 [2544]~E(x25441,x25442)+E(f710(x25443,x25441),f710(x25443,x25442)) % 187.86/187.67 [2545]~E(x25451,x25452)+E(f376(x25451,x25453,x25454,x25455),f376(x25452,x25453,x25454,x25455)) % 187.86/187.67 [2546]~E(x25461,x25462)+E(f376(x25463,x25461,x25464,x25465),f376(x25463,x25462,x25464,x25465)) % 187.86/187.67 [2547]~E(x25471,x25472)+E(f376(x25473,x25474,x25471,x25475),f376(x25473,x25474,x25472,x25475)) % 187.86/187.67 [2548]~E(x25481,x25482)+E(f376(x25483,x25484,x25485,x25481),f376(x25483,x25484,x25485,x25482)) % 187.86/187.67 [2549]~E(x25491,x25492)+E(f626(x25491,x25493,x25494,x25495,x25496,x25497,x25498),f626(x25492,x25493,x25494,x25495,x25496,x25497,x25498)) % 187.86/187.67 [2550]~E(x25501,x25502)+E(f626(x25503,x25501,x25504,x25505,x25506,x25507,x25508),f626(x25503,x25502,x25504,x25505,x25506,x25507,x25508)) % 187.86/187.67 [2551]~E(x25511,x25512)+E(f626(x25513,x25514,x25511,x25515,x25516,x25517,x25518),f626(x25513,x25514,x25512,x25515,x25516,x25517,x25518)) % 187.86/187.67 [2552]~E(x25521,x25522)+E(f626(x25523,x25524,x25525,x25521,x25526,x25527,x25528),f626(x25523,x25524,x25525,x25522,x25526,x25527,x25528)) % 187.86/187.67 [2553]~E(x25531,x25532)+E(f626(x25533,x25534,x25535,x25536,x25531,x25537,x25538),f626(x25533,x25534,x25535,x25536,x25532,x25537,x25538)) % 187.86/187.67 [2554]~E(x25541,x25542)+E(f626(x25543,x25544,x25545,x25546,x25547,x25541,x25548),f626(x25543,x25544,x25545,x25546,x25547,x25542,x25548)) % 187.86/187.67 [2555]~E(x25551,x25552)+E(f626(x25553,x25554,x25555,x25556,x25557,x25558,x25551),f626(x25553,x25554,x25555,x25556,x25557,x25558,x25552)) % 187.86/187.67 [2556]~E(x25561,x25562)+E(f741(x25561,x25563),f741(x25562,x25563)) % 187.86/187.67 [2557]~E(x25571,x25572)+E(f741(x25573,x25571),f741(x25573,x25572)) % 187.86/187.67 [2558]~E(x25581,x25582)+E(f812(x25581,x25583),f812(x25582,x25583)) % 187.86/187.67 [2559]~E(x25591,x25592)+E(f812(x25593,x25591),f812(x25593,x25592)) % 187.86/187.67 [2560]~E(x25601,x25602)+E(f815(x25601,x25603,x25604,x25605,x25606),f815(x25602,x25603,x25604,x25605,x25606)) % 187.86/187.67 [2561]~E(x25611,x25612)+E(f815(x25613,x25611,x25614,x25615,x25616),f815(x25613,x25612,x25614,x25615,x25616)) % 187.86/187.67 [2562]~E(x25621,x25622)+E(f815(x25623,x25624,x25621,x25625,x25626),f815(x25623,x25624,x25622,x25625,x25626)) % 187.86/187.67 [2563]~E(x25631,x25632)+E(f815(x25633,x25634,x25635,x25631,x25636),f815(x25633,x25634,x25635,x25632,x25636)) % 187.86/187.67 [2564]~E(x25641,x25642)+E(f815(x25643,x25644,x25645,x25646,x25641),f815(x25643,x25644,x25645,x25646,x25642)) % 187.86/187.67 [2565]~E(x25651,x25652)+E(f267(x25651,x25653,x25654),f267(x25652,x25653,x25654)) % 187.86/187.67 [2566]~E(x25661,x25662)+E(f267(x25663,x25661,x25664),f267(x25663,x25662,x25664)) % 187.86/187.67 [2567]~E(x25671,x25672)+E(f267(x25673,x25674,x25671),f267(x25673,x25674,x25672)) % 187.86/187.67 [2568]~E(x25681,x25682)+E(f491(x25681),f491(x25682)) % 187.86/187.67 [2569]~E(x25691,x25692)+E(f612(x25691,x25693,x25694),f612(x25692,x25693,x25694)) % 187.86/187.67 [2570]~E(x25701,x25702)+E(f612(x25703,x25701,x25704),f612(x25703,x25702,x25704)) % 187.86/187.67 [2571]~E(x25711,x25712)+E(f612(x25713,x25714,x25711),f612(x25713,x25714,x25712)) % 187.86/187.67 [2572]~E(x25721,x25722)+E(f650(x25721,x25723,x25724,x25725,x25726,x25727),f650(x25722,x25723,x25724,x25725,x25726,x25727)) % 187.86/187.67 [2573]~E(x25731,x25732)+E(f650(x25733,x25731,x25734,x25735,x25736,x25737),f650(x25733,x25732,x25734,x25735,x25736,x25737)) % 187.86/187.67 [2574]~E(x25741,x25742)+E(f650(x25743,x25744,x25741,x25745,x25746,x25747),f650(x25743,x25744,x25742,x25745,x25746,x25747)) % 187.86/187.67 [2575]~E(x25751,x25752)+E(f650(x25753,x25754,x25755,x25751,x25756,x25757),f650(x25753,x25754,x25755,x25752,x25756,x25757)) % 187.86/187.67 [2576]~E(x25761,x25762)+E(f650(x25763,x25764,x25765,x25766,x25761,x25767),f650(x25763,x25764,x25765,x25766,x25762,x25767)) % 187.86/187.67 [2577]~E(x25771,x25772)+E(f650(x25773,x25774,x25775,x25776,x25777,x25771),f650(x25773,x25774,x25775,x25776,x25777,x25772)) % 187.86/187.67 [2578]~E(x25781,x25782)+E(f460(x25781,x25783,x25784,x25785,x25786),f460(x25782,x25783,x25784,x25785,x25786)) % 187.86/187.67 [2579]~E(x25791,x25792)+E(f460(x25793,x25791,x25794,x25795,x25796),f460(x25793,x25792,x25794,x25795,x25796)) % 187.86/187.67 [2580]~E(x25801,x25802)+E(f460(x25803,x25804,x25801,x25805,x25806),f460(x25803,x25804,x25802,x25805,x25806)) % 187.86/187.67 [2581]~E(x25811,x25812)+E(f460(x25813,x25814,x25815,x25811,x25816),f460(x25813,x25814,x25815,x25812,x25816)) % 187.86/187.67 [2582]~E(x25821,x25822)+E(f460(x25823,x25824,x25825,x25826,x25821),f460(x25823,x25824,x25825,x25826,x25822)) % 187.86/187.67 [2583]~E(x25831,x25832)+E(f95(x25831),f95(x25832)) % 187.86/187.67 [2584]~E(x25841,x25842)+E(f736(x25841,x25843),f736(x25842,x25843)) % 187.86/187.67 [2585]~E(x25851,x25852)+E(f736(x25853,x25851),f736(x25853,x25852)) % 187.86/187.67 [2586]~E(x25861,x25862)+E(f769(x25861),f769(x25862)) % 187.86/187.67 [2587]~E(x25871,x25872)+E(f679(x25871,x25873,x25874,x25875,x25876),f679(x25872,x25873,x25874,x25875,x25876)) % 187.86/187.67 [2588]~E(x25881,x25882)+E(f679(x25883,x25881,x25884,x25885,x25886),f679(x25883,x25882,x25884,x25885,x25886)) % 187.86/187.67 [2589]~E(x25891,x25892)+E(f679(x25893,x25894,x25891,x25895,x25896),f679(x25893,x25894,x25892,x25895,x25896)) % 187.86/187.67 [2590]~E(x25901,x25902)+E(f679(x25903,x25904,x25905,x25901,x25906),f679(x25903,x25904,x25905,x25902,x25906)) % 187.86/187.67 [2591]~E(x25911,x25912)+E(f679(x25913,x25914,x25915,x25916,x25911),f679(x25913,x25914,x25915,x25916,x25912)) % 187.86/187.67 [2592]~E(x25921,x25922)+E(f324(x25921,x25923,x25924),f324(x25922,x25923,x25924)) % 187.86/187.67 [2593]~E(x25931,x25932)+E(f324(x25933,x25931,x25934),f324(x25933,x25932,x25934)) % 187.86/187.67 [2594]~E(x25941,x25942)+E(f324(x25943,x25944,x25941),f324(x25943,x25944,x25942)) % 187.86/187.67 [2595]~E(x25951,x25952)+E(f517(x25951,x25953),f517(x25952,x25953)) % 187.86/187.67 [2596]~E(x25961,x25962)+E(f517(x25963,x25961),f517(x25963,x25962)) % 187.86/187.67 [2597]~E(x25971,x25972)+E(f323(x25971,x25973,x25974),f323(x25972,x25973,x25974)) % 187.86/187.67 [2598]~E(x25981,x25982)+E(f323(x25983,x25981,x25984),f323(x25983,x25982,x25984)) % 187.86/187.67 [2599]~E(x25991,x25992)+E(f323(x25993,x25994,x25991),f323(x25993,x25994,x25992)) % 187.86/187.67 [2600]~E(x26001,x26002)+E(f543(x26001),f543(x26002)) % 187.86/187.67 [2601]~P1(x26011)+P1(x26012)+~E(x26011,x26012) % 187.86/187.67 [2602]~P2(x26021)+P2(x26022)+~E(x26021,x26022) % 187.86/187.67 [2603]P146(x26032,x26033,x26034)+~E(x26031,x26032)+~P146(x26031,x26033,x26034) % 187.86/187.67 [2604]P146(x26043,x26042,x26044)+~E(x26041,x26042)+~P146(x26043,x26041,x26044) % 187.86/187.67 [2605]P146(x26053,x26054,x26052)+~E(x26051,x26052)+~P146(x26053,x26054,x26051) % 187.86/187.67 [2606]~P3(x26061)+P3(x26062)+~E(x26061,x26062) % 187.86/187.67 [2607]~P6(x26071)+P6(x26072)+~E(x26071,x26072) % 187.86/187.67 [2608]~P105(x26081)+P105(x26082)+~E(x26081,x26082) % 187.86/187.67 [2609]~P106(x26091)+P106(x26092)+~E(x26091,x26092) % 187.86/187.67 [2610]~P108(x26101)+P108(x26102)+~E(x26101,x26102) % 187.86/187.67 [2611]P41(x26112,x26113,x26114)+~E(x26111,x26112)+~P41(x26111,x26113,x26114) % 187.86/187.67 [2612]P41(x26123,x26122,x26124)+~E(x26121,x26122)+~P41(x26123,x26121,x26124) % 187.86/187.67 [2613]P41(x26133,x26134,x26132)+~E(x26131,x26132)+~P41(x26133,x26134,x26131) % 187.86/187.67 [2614]~P65(x26141)+P65(x26142)+~E(x26141,x26142) % 187.86/187.67 [2615]~P107(x26151)+P107(x26152)+~E(x26151,x26152) % 187.86/187.67 [2616]P145(x26162,x26163,x26164)+~E(x26161,x26162)+~P145(x26161,x26163,x26164) % 187.86/187.67 [2617]P145(x26173,x26172,x26174)+~E(x26171,x26172)+~P145(x26173,x26171,x26174) % 187.86/187.67 [2618]P145(x26183,x26184,x26182)+~E(x26181,x26182)+~P145(x26183,x26184,x26181) % 187.86/187.67 [2619]P38(x26192,x26193,x26194)+~E(x26191,x26192)+~P38(x26191,x26193,x26194) % 187.86/187.67 [2620]P38(x26203,x26202,x26204)+~E(x26201,x26202)+~P38(x26203,x26201,x26204) % 187.86/187.67 [2621]P38(x26213,x26214,x26212)+~E(x26211,x26212)+~P38(x26213,x26214,x26211) % 187.86/187.67 [2622]P28(x26222,x26223,x26224,x26225)+~E(x26221,x26222)+~P28(x26221,x26223,x26224,x26225) % 187.86/187.67 [2623]P28(x26233,x26232,x26234,x26235)+~E(x26231,x26232)+~P28(x26233,x26231,x26234,x26235) % 187.86/187.67 [2624]P28(x26243,x26244,x26242,x26245)+~E(x26241,x26242)+~P28(x26243,x26244,x26241,x26245) % 187.86/187.67 [2625]P28(x26253,x26254,x26255,x26252)+~E(x26251,x26252)+~P28(x26253,x26254,x26255,x26251) % 187.86/187.67 [2626]~P91(x26261)+P91(x26262)+~E(x26261,x26262) % 187.86/187.67 [2627]~P112(x26271)+P112(x26272)+~E(x26271,x26272) % 187.86/187.67 [2628]P27(x26282,x26283,x26284)+~E(x26281,x26282)+~P27(x26281,x26283,x26284) % 187.86/187.67 [2629]P27(x26293,x26292,x26294)+~E(x26291,x26292)+~P27(x26293,x26291,x26294) % 187.86/187.67 [2630]P27(x26303,x26304,x26302)+~E(x26301,x26302)+~P27(x26303,x26304,x26301) % 187.86/187.67 [2631]~P109(x26311)+P109(x26312)+~E(x26311,x26312) % 187.86/187.67 [2632]~P63(x26321)+P63(x26322)+~E(x26321,x26322) % 187.86/187.67 [2633]~P113(x26331)+P113(x26332)+~E(x26331,x26332) % 187.86/187.67 [2634]~P64(x26341)+P64(x26342)+~E(x26341,x26342) % 187.86/187.67 [2635]~P98(x26351)+P98(x26352)+~E(x26351,x26352) % 187.86/187.67 [2636]~P66(x26361)+P66(x26362)+~E(x26361,x26362) % 187.86/187.67 [2637]~P111(x26371)+P111(x26372)+~E(x26371,x26372) % 187.86/187.67 [2638]P20(x26382,x26383,x26384)+~E(x26381,x26382)+~P20(x26381,x26383,x26384) % 187.86/187.67 [2639]P20(x26393,x26392,x26394)+~E(x26391,x26392)+~P20(x26393,x26391,x26394) % 187.86/187.67 [2640]P20(x26403,x26404,x26402)+~E(x26401,x26402)+~P20(x26403,x26404,x26401) % 187.86/187.67 [2641]~P126(x26411)+P126(x26412)+~E(x26411,x26412) % 187.86/187.67 [2642]~P67(x26421)+P67(x26422)+~E(x26421,x26422) % 187.86/187.67 [2643]~P81(x26431)+P81(x26432)+~E(x26431,x26432) % 187.86/187.67 [2644]P56(x26442,x26443,x26444,x26445,x26446)+~E(x26441,x26442)+~P56(x26441,x26443,x26444,x26445,x26446) % 187.86/187.67 [2645]P56(x26453,x26452,x26454,x26455,x26456)+~E(x26451,x26452)+~P56(x26453,x26451,x26454,x26455,x26456) % 187.86/187.67 [2646]P56(x26463,x26464,x26462,x26465,x26466)+~E(x26461,x26462)+~P56(x26463,x26464,x26461,x26465,x26466) % 187.86/187.67 [2647]P56(x26473,x26474,x26475,x26472,x26476)+~E(x26471,x26472)+~P56(x26473,x26474,x26475,x26471,x26476) % 187.86/187.67 [2648]P56(x26483,x26484,x26485,x26486,x26482)+~E(x26481,x26482)+~P56(x26483,x26484,x26485,x26486,x26481) % 187.86/187.67 [2649]~P92(x26491)+P92(x26492)+~E(x26491,x26492) % 187.86/187.67 [2650]~P68(x26501)+P68(x26502)+~E(x26501,x26502) % 187.86/187.67 [2651]~P78(x26511)+P78(x26512)+~E(x26511,x26512) % 187.86/187.67 [2652]~P61(x26521)+P61(x26522)+~E(x26521,x26522) % 187.86/187.67 [2653]~P42(x26531)+P42(x26532)+~E(x26531,x26532) % 187.86/187.67 [2654]~P97(x26541)+P97(x26542)+~E(x26541,x26542) % 187.86/187.67 [2655]~P103(x26551)+P103(x26552)+~E(x26551,x26552) % 187.86/187.67 [2656]~P74(x26561)+P74(x26562)+~E(x26561,x26562) % 187.86/187.67 [2657]~P124(x26571)+P124(x26572)+~E(x26571,x26572) % 187.86/187.67 [2658]P37(x26582,x26583,x26584,x26585,x26586)+~E(x26581,x26582)+~P37(x26581,x26583,x26584,x26585,x26586) % 187.86/187.67 [2659]P37(x26593,x26592,x26594,x26595,x26596)+~E(x26591,x26592)+~P37(x26593,x26591,x26594,x26595,x26596) % 187.86/187.67 [2660]P37(x26603,x26604,x26602,x26605,x26606)+~E(x26601,x26602)+~P37(x26603,x26604,x26601,x26605,x26606) % 187.86/187.67 [2661]P37(x26613,x26614,x26615,x26612,x26616)+~E(x26611,x26612)+~P37(x26613,x26614,x26615,x26611,x26616) % 187.86/187.67 [2662]P37(x26623,x26624,x26625,x26626,x26622)+~E(x26621,x26622)+~P37(x26623,x26624,x26625,x26626,x26621) % 187.86/187.67 [2663]P30(x26632,x26633,x26634)+~E(x26631,x26632)+~P30(x26631,x26633,x26634) % 187.86/187.67 [2664]P30(x26643,x26642,x26644)+~E(x26641,x26642)+~P30(x26643,x26641,x26644) % 187.86/187.67 [2665]P30(x26653,x26654,x26652)+~E(x26651,x26652)+~P30(x26653,x26654,x26651) % 187.86/187.67 [2666]~P69(x26661)+P69(x26662)+~E(x26661,x26662) % 187.86/187.67 [2667]~P4(x26671)+P4(x26672)+~E(x26671,x26672) % 187.86/187.67 [2668]~P125(x26681)+P125(x26682)+~E(x26681,x26682) % 187.86/187.67 [2669]~P70(x26691)+P70(x26692)+~E(x26691,x26692) % 187.86/187.67 [2670]~P118(x26701)+P118(x26702)+~E(x26701,x26702) % 187.86/187.67 [2671]P40(x26712,x26713)+~E(x26711,x26712)+~P40(x26711,x26713) % 187.86/187.67 [2672]P40(x26723,x26722)+~E(x26721,x26722)+~P40(x26723,x26721) % 187.86/187.67 [2673]~P71(x26731)+P71(x26732)+~E(x26731,x26732) % 187.86/187.67 [2674]P35(x26742,x26743,x26744,x26745)+~E(x26741,x26742)+~P35(x26741,x26743,x26744,x26745) % 187.86/187.67 [2675]P35(x26753,x26752,x26754,x26755)+~E(x26751,x26752)+~P35(x26753,x26751,x26754,x26755) % 187.86/187.67 [2676]P35(x26763,x26764,x26762,x26765)+~E(x26761,x26762)+~P35(x26763,x26764,x26761,x26765) % 187.86/187.67 [2677]P35(x26773,x26774,x26775,x26772)+~E(x26771,x26772)+~P35(x26773,x26774,x26775,x26771) % 187.86/187.67 [2678]P50(x26782,x26783,x26784)+~E(x26781,x26782)+~P50(x26781,x26783,x26784) % 187.86/187.67 [2679]P50(x26793,x26792,x26794)+~E(x26791,x26792)+~P50(x26793,x26791,x26794) % 187.86/187.67 [2680]P50(x26803,x26804,x26802)+~E(x26801,x26802)+~P50(x26803,x26804,x26801) % 187.86/187.67 [2681]~P82(x26811)+P82(x26812)+~E(x26811,x26812) % 187.86/187.67 [2682]P17(x26822,x26823)+~E(x26821,x26822)+~P17(x26821,x26823) % 187.86/187.67 [2683]P17(x26833,x26832)+~E(x26831,x26832)+~P17(x26833,x26831) % 187.86/187.67 [2684]~P62(x26841)+P62(x26842)+~E(x26841,x26842) % 187.86/187.67 [2685]~P83(x26851)+P83(x26852)+~E(x26851,x26852) % 187.86/187.67 [2686]P59(x26862,x26863)+~E(x26861,x26862)+~P59(x26861,x26863) % 187.86/187.67 [2687]P59(x26873,x26872)+~E(x26871,x26872)+~P59(x26873,x26871) % 187.86/187.67 [2688]P24(x26882,x26883,x26884,x26885,x26886)+~E(x26881,x26882)+~P24(x26881,x26883,x26884,x26885,x26886) % 187.86/187.67 [2689]P24(x26893,x26892,x26894,x26895,x26896)+~E(x26891,x26892)+~P24(x26893,x26891,x26894,x26895,x26896) % 187.86/187.67 [2690]P24(x26903,x26904,x26902,x26905,x26906)+~E(x26901,x26902)+~P24(x26903,x26904,x26901,x26905,x26906) % 187.86/187.67 [2691]P24(x26913,x26914,x26915,x26912,x26916)+~E(x26911,x26912)+~P24(x26913,x26914,x26915,x26911,x26916) % 187.86/187.67 [2692]P24(x26923,x26924,x26925,x26926,x26922)+~E(x26921,x26922)+~P24(x26923,x26924,x26925,x26926,x26921) % 187.86/187.67 [2693]P55(x26932,x26933,x26934)+~E(x26931,x26932)+~P55(x26931,x26933,x26934) % 187.86/187.67 [2694]P55(x26943,x26942,x26944)+~E(x26941,x26942)+~P55(x26943,x26941,x26944) % 187.86/187.67 [2695]P55(x26953,x26954,x26952)+~E(x26951,x26952)+~P55(x26953,x26954,x26951) % 187.86/187.67 [2696]~P122(x26961)+P122(x26962)+~E(x26961,x26962) % 187.86/187.67 [2697]P21(x26972,x26973,x26974)+~E(x26971,x26972)+~P21(x26971,x26973,x26974) % 187.86/187.67 [2698]P21(x26983,x26982,x26984)+~E(x26981,x26982)+~P21(x26983,x26981,x26984) % 187.86/187.67 [2699]P21(x26993,x26994,x26992)+~E(x26991,x26992)+~P21(x26993,x26994,x26991) % 187.86/187.67 [2700]~P79(x27001)+P79(x27002)+~E(x27001,x27002) % 187.86/187.67 [2701]~P93(x27011)+P93(x27012)+~E(x27011,x27012) % 187.86/187.67 [2702]~P95(x27021)+P95(x27022)+~E(x27021,x27022) % 187.86/187.67 [2703]~P76(x27031)+P76(x27032)+~E(x27031,x27032) % 187.86/187.67 [2704]~P85(x27041)+P85(x27042)+~E(x27041,x27042) % 187.86/187.67 [2705]P18(x27052,x27053,x27054)+~E(x27051,x27052)+~P18(x27051,x27053,x27054) % 187.86/187.67 [2706]P18(x27063,x27062,x27064)+~E(x27061,x27062)+~P18(x27063,x27061,x27064) % 187.86/187.67 [2707]P18(x27073,x27074,x27072)+~E(x27071,x27072)+~P18(x27073,x27074,x27071) % 187.86/187.67 [2708]P9(x27082,x27083,x27084)+~E(x27081,x27082)+~P9(x27081,x27083,x27084) % 187.86/187.67 [2709]P9(x27093,x27092,x27094)+~E(x27091,x27092)+~P9(x27093,x27091,x27094) % 187.86/187.67 [2710]P9(x27103,x27104,x27102)+~E(x27101,x27102)+~P9(x27103,x27104,x27101) % 187.86/187.67 [2711]~P86(x27111)+P86(x27112)+~E(x27111,x27112) % 187.86/187.67 [2712]P29(x27122,x27123)+~E(x27121,x27122)+~P29(x27121,x27123) % 187.86/187.67 [2713]P29(x27133,x27132)+~E(x27131,x27132)+~P29(x27133,x27131) % 187.86/187.67 [2714]P16(x27142,x27143,x27144,x27145,x27146,x27147)+~E(x27141,x27142)+~P16(x27141,x27143,x27144,x27145,x27146,x27147) % 187.86/187.67 [2715]P16(x27153,x27152,x27154,x27155,x27156,x27157)+~E(x27151,x27152)+~P16(x27153,x27151,x27154,x27155,x27156,x27157) % 187.86/187.67 [2716]P16(x27163,x27164,x27162,x27165,x27166,x27167)+~E(x27161,x27162)+~P16(x27163,x27164,x27161,x27165,x27166,x27167) % 187.86/187.67 [2717]P16(x27173,x27174,x27175,x27172,x27176,x27177)+~E(x27171,x27172)+~P16(x27173,x27174,x27175,x27171,x27176,x27177) % 187.86/187.67 [2718]P16(x27183,x27184,x27185,x27186,x27182,x27187)+~E(x27181,x27182)+~P16(x27183,x27184,x27185,x27186,x27181,x27187) % 187.86/187.67 [2719]P16(x27193,x27194,x27195,x27196,x27197,x27192)+~E(x27191,x27192)+~P16(x27193,x27194,x27195,x27196,x27197,x27191) % 187.86/187.67 [2720]~P84(x27201)+P84(x27202)+~E(x27201,x27202) % 187.86/187.67 [2721]~P143(x27211)+P143(x27212)+~E(x27211,x27212) % 187.86/187.67 [2722]~P60(x27221)+P60(x27222)+~E(x27221,x27222) % 187.86/187.67 [2723]P23(x27232,x27233,x27234,x27235)+~E(x27231,x27232)+~P23(x27231,x27233,x27234,x27235) % 187.86/187.67 [2724]P23(x27243,x27242,x27244,x27245)+~E(x27241,x27242)+~P23(x27243,x27241,x27244,x27245) % 187.86/187.67 [2725]P23(x27253,x27254,x27252,x27255)+~E(x27251,x27252)+~P23(x27253,x27254,x27251,x27255) % 187.86/187.67 [2726]P23(x27263,x27264,x27265,x27262)+~E(x27261,x27262)+~P23(x27263,x27264,x27265,x27261) % 187.86/187.67 [2727]P33(x27272,x27273)+~E(x27271,x27272)+~P33(x27271,x27273) % 187.86/187.67 [2728]P33(x27283,x27282)+~E(x27281,x27282)+~P33(x27283,x27281) % 187.86/187.67 [2729]P26(x27292,x27293,x27294,x27295,x27296,x27297)+~E(x27291,x27292)+~P26(x27291,x27293,x27294,x27295,x27296,x27297) % 187.86/187.67 [2730]P26(x27303,x27302,x27304,x27305,x27306,x27307)+~E(x27301,x27302)+~P26(x27303,x27301,x27304,x27305,x27306,x27307) % 187.86/187.67 [2731]P26(x27313,x27314,x27312,x27315,x27316,x27317)+~E(x27311,x27312)+~P26(x27313,x27314,x27311,x27315,x27316,x27317) % 187.86/187.67 [2732]P26(x27323,x27324,x27325,x27322,x27326,x27327)+~E(x27321,x27322)+~P26(x27323,x27324,x27325,x27321,x27326,x27327) % 187.86/187.67 [2733]P26(x27333,x27334,x27335,x27336,x27332,x27337)+~E(x27331,x27332)+~P26(x27333,x27334,x27335,x27336,x27331,x27337) % 187.86/187.67 [2734]P26(x27343,x27344,x27345,x27346,x27347,x27342)+~E(x27341,x27342)+~P26(x27343,x27344,x27345,x27346,x27347,x27341) % 187.86/187.67 [2735]~P90(x27351)+P90(x27352)+~E(x27351,x27352) % 187.86/187.67 [2736]~P128(x27361)+P128(x27362)+~E(x27361,x27362) % 187.86/187.67 [2737]~P94(x27371)+P94(x27372)+~E(x27371,x27372) % 187.86/187.67 [2738]~P87(x27381)+P87(x27382)+~E(x27381,x27382) % 187.86/187.67 [2739]~P102(x27391)+P102(x27392)+~E(x27391,x27392) % 187.86/187.67 [2740]~P114(x27401)+P114(x27402)+~E(x27401,x27402) % 187.86/187.67 [2741]~P88(x27411)+P88(x27412)+~E(x27411,x27412) % 187.86/187.67 [2742]~P72(x27421)+P72(x27422)+~E(x27421,x27422) % 187.86/187.67 [2743]~P75(x27431)+P75(x27432)+~E(x27431,x27432) % 187.86/187.67 [2744]~P133(x27441)+P133(x27442)+~E(x27441,x27442) % 187.86/187.67 [2745]~P129(x27451)+P129(x27452)+~E(x27451,x27452) % 187.86/187.67 [2746]P54(x27462,x27463,x27464)+~E(x27461,x27462)+~P54(x27461,x27463,x27464) % 187.86/187.67 [2747]P54(x27473,x27472,x27474)+~E(x27471,x27472)+~P54(x27473,x27471,x27474) % 187.86/187.67 [2748]P54(x27483,x27484,x27482)+~E(x27481,x27482)+~P54(x27483,x27484,x27481) % 187.86/187.67 [2749]~P99(x27491)+P99(x27492)+~E(x27491,x27492) % 187.86/187.67 [2750]P36(x27502,x27503,x27504)+~E(x27501,x27502)+~P36(x27501,x27503,x27504) % 187.86/187.67 [2751]P36(x27513,x27512,x27514)+~E(x27511,x27512)+~P36(x27513,x27511,x27514) % 187.86/187.67 [2752]P36(x27523,x27524,x27522)+~E(x27521,x27522)+~P36(x27523,x27524,x27521) % 187.86/187.67 [2753]~P140(x27531)+P140(x27532)+~E(x27531,x27532) % 187.86/187.67 [2754]~P138(x27541)+P138(x27542)+~E(x27541,x27542) % 187.86/187.67 [2755]~P141(x27551)+P141(x27552)+~E(x27551,x27552) % 187.86/187.67 [2756]P22(x27562,x27563,x27564,x27565)+~E(x27561,x27562)+~P22(x27561,x27563,x27564,x27565) % 187.86/187.67 [2757]P22(x27573,x27572,x27574,x27575)+~E(x27571,x27572)+~P22(x27573,x27571,x27574,x27575) % 187.86/187.67 [2758]P22(x27583,x27584,x27582,x27585)+~E(x27581,x27582)+~P22(x27583,x27584,x27581,x27585) % 187.86/187.67 [2759]P22(x27593,x27594,x27595,x27592)+~E(x27591,x27592)+~P22(x27593,x27594,x27595,x27591) % 187.86/187.67 [2760]~P127(x27601)+P127(x27602)+~E(x27601,x27602) % 187.86/187.67 [2761]~P80(x27611)+P80(x27612)+~E(x27611,x27612) % 187.86/187.67 [2762]P57(x27622,x27623)+~E(x27621,x27622)+~P57(x27621,x27623) % 187.86/187.67 [2763]P57(x27633,x27632)+~E(x27631,x27632)+~P57(x27633,x27631) % 187.86/187.67 [2764]~P139(x27641)+P139(x27642)+~E(x27641,x27642) % 187.86/187.67 [2765]~P132(x27651)+P132(x27652)+~E(x27651,x27652) % 187.86/187.67 [2766]~P136(x27661)+P136(x27662)+~E(x27661,x27662) % 187.86/187.67 [2767]~P7(x27671)+P7(x27672)+~E(x27671,x27672) % 187.86/187.67 [2768]~P116(x27681)+P116(x27682)+~E(x27681,x27682) % 187.86/187.67 [2769]P58(x27692,x27693,x27694,x27695)+~E(x27691,x27692)+~P58(x27691,x27693,x27694,x27695) % 187.86/187.67 [2770]P58(x27703,x27702,x27704,x27705)+~E(x27701,x27702)+~P58(x27703,x27701,x27704,x27705) % 187.86/187.67 [2771]P58(x27713,x27714,x27712,x27715)+~E(x27711,x27712)+~P58(x27713,x27714,x27711,x27715) % 187.86/187.67 [2772]P58(x27723,x27724,x27725,x27722)+~E(x27721,x27722)+~P58(x27723,x27724,x27725,x27721) % 187.86/187.67 [2773]~P100(x27731)+P100(x27732)+~E(x27731,x27732) % 187.86/187.67 [2774]~P119(x27741)+P119(x27742)+~E(x27741,x27742) % 187.86/187.67 [2775]P34(x27752,x27753,x27754)+~E(x27751,x27752)+~P34(x27751,x27753,x27754) % 187.86/187.67 [2776]P34(x27763,x27762,x27764)+~E(x27761,x27762)+~P34(x27763,x27761,x27764) % 187.86/187.67 [2777]P34(x27773,x27774,x27772)+~E(x27771,x27772)+~P34(x27773,x27774,x27771) % 187.86/187.67 [2778]P53(x27782,x27783,x27784,x27785,x27786,x27787,x27788)+~E(x27781,x27782)+~P53(x27781,x27783,x27784,x27785,x27786,x27787,x27788) % 187.86/187.67 [2779]P53(x27793,x27792,x27794,x27795,x27796,x27797,x27798)+~E(x27791,x27792)+~P53(x27793,x27791,x27794,x27795,x27796,x27797,x27798) % 187.86/187.67 [2780]P53(x27803,x27804,x27802,x27805,x27806,x27807,x27808)+~E(x27801,x27802)+~P53(x27803,x27804,x27801,x27805,x27806,x27807,x27808) % 187.86/187.67 [2781]P53(x27813,x27814,x27815,x27812,x27816,x27817,x27818)+~E(x27811,x27812)+~P53(x27813,x27814,x27815,x27811,x27816,x27817,x27818) % 187.86/187.67 [2782]P53(x27823,x27824,x27825,x27826,x27822,x27827,x27828)+~E(x27821,x27822)+~P53(x27823,x27824,x27825,x27826,x27821,x27827,x27828) % 187.86/187.67 [2783]P53(x27833,x27834,x27835,x27836,x27837,x27832,x27838)+~E(x27831,x27832)+~P53(x27833,x27834,x27835,x27836,x27837,x27831,x27838) % 187.86/187.67 [2784]P53(x27843,x27844,x27845,x27846,x27847,x27848,x27842)+~E(x27841,x27842)+~P53(x27843,x27844,x27845,x27846,x27847,x27848,x27841) % 187.86/187.67 [2785]~P5(x27851)+P5(x27852)+~E(x27851,x27852) % 187.86/187.67 [2786]P45(x27862,x27863)+~E(x27861,x27862)+~P45(x27861,x27863) % 187.86/187.67 [2787]P45(x27873,x27872)+~E(x27871,x27872)+~P45(x27873,x27871) % 187.86/187.67 [2788]P15(x27882,x27883,x27884,x27885)+~E(x27881,x27882)+~P15(x27881,x27883,x27884,x27885) % 187.86/187.67 [2789]P15(x27893,x27892,x27894,x27895)+~E(x27891,x27892)+~P15(x27893,x27891,x27894,x27895) % 187.86/187.67 [2790]P15(x27903,x27904,x27902,x27905)+~E(x27901,x27902)+~P15(x27903,x27904,x27901,x27905) % 187.86/187.67 [2791]P15(x27913,x27914,x27915,x27912)+~E(x27911,x27912)+~P15(x27913,x27914,x27915,x27911) % 187.86/187.67 [2792]~P117(x27921)+P117(x27922)+~E(x27921,x27922) % 187.86/187.67 [2793]~P144(x27931)+P144(x27932)+~E(x27931,x27932) % 187.86/187.67 [2794]P14(x27942,x27943,x27944)+~E(x27941,x27942)+~P14(x27941,x27943,x27944) % 187.86/187.67 [2795]P14(x27953,x27952,x27954)+~E(x27951,x27952)+~P14(x27953,x27951,x27954) % 187.86/187.67 [2796]P14(x27963,x27964,x27962)+~E(x27961,x27962)+~P14(x27963,x27964,x27961) % 187.86/187.67 [2797]P44(x27972,x27973,x27974,x27975,x27976,x27977)+~E(x27971,x27972)+~P44(x27971,x27973,x27974,x27975,x27976,x27977) % 187.86/187.67 [2798]P44(x27983,x27982,x27984,x27985,x27986,x27987)+~E(x27981,x27982)+~P44(x27983,x27981,x27984,x27985,x27986,x27987) % 187.86/187.67 [2799]P44(x27993,x27994,x27992,x27995,x27996,x27997)+~E(x27991,x27992)+~P44(x27993,x27994,x27991,x27995,x27996,x27997) % 187.86/187.67 [2800]P44(x28003,x28004,x28005,x28002,x28006,x28007)+~E(x28001,x28002)+~P44(x28003,x28004,x28005,x28001,x28006,x28007) % 187.86/187.67 [2801]P44(x28013,x28014,x28015,x28016,x28012,x28017)+~E(x28011,x28012)+~P44(x28013,x28014,x28015,x28016,x28011,x28017) % 187.86/187.67 [2802]P44(x28023,x28024,x28025,x28026,x28027,x28022)+~E(x28021,x28022)+~P44(x28023,x28024,x28025,x28026,x28027,x28021) % 187.86/187.67 [2803]~P134(x28031)+P134(x28032)+~E(x28031,x28032) % 187.86/187.67 [2804]P13(x28042,x28043,x28044)+~E(x28041,x28042)+~P13(x28041,x28043,x28044) % 187.86/187.67 [2805]P13(x28053,x28052,x28054)+~E(x28051,x28052)+~P13(x28053,x28051,x28054) % 187.86/187.67 [2806]P13(x28063,x28064,x28062)+~E(x28061,x28062)+~P13(x28063,x28064,x28061) % 187.86/187.67 [2807]P19(x28072,x28073,x28074)+~E(x28071,x28072)+~P19(x28071,x28073,x28074) % 187.86/187.67 [2808]P19(x28083,x28082,x28084)+~E(x28081,x28082)+~P19(x28083,x28081,x28084) % 187.86/187.67 [2809]P19(x28093,x28094,x28092)+~E(x28091,x28092)+~P19(x28093,x28094,x28091) % 187.86/187.67 [2810]~P142(x28101)+P142(x28102)+~E(x28101,x28102) % 187.86/187.67 [2811]~P135(x28111)+P135(x28112)+~E(x28111,x28112) % 187.86/187.67 [2812]P49(x28122,x28123,x28124)+~E(x28121,x28122)+~P49(x28121,x28123,x28124) % 187.86/187.67 [2813]P49(x28133,x28132,x28134)+~E(x28131,x28132)+~P49(x28133,x28131,x28134) % 187.86/187.67 [2814]P49(x28143,x28144,x28142)+~E(x28141,x28142)+~P49(x28143,x28144,x28141) % 187.86/187.67 [2815]~P123(x28151)+P123(x28152)+~E(x28151,x28152) % 187.86/187.67 [2816]P52(x28162,x28163)+~E(x28161,x28162)+~P52(x28161,x28163) % 187.86/187.67 [2817]P52(x28173,x28172)+~E(x28171,x28172)+~P52(x28173,x28171) % 187.86/187.67 [2818]~P32(x28181)+P32(x28182)+~E(x28181,x28182) % 187.86/187.67 [2819]~P10(x28191)+P10(x28192)+~E(x28191,x28192) % 187.86/187.67 [2820]P8(x28202,x28203)+~E(x28201,x28202)+~P8(x28201,x28203) % 187.86/187.67 [2821]P8(x28213,x28212)+~E(x28211,x28212)+~P8(x28213,x28211) % 187.86/187.67 [2822]~P96(x28221)+P96(x28222)+~E(x28221,x28222) % 187.86/187.67 [2823]~P120(x28231)+P120(x28232)+~E(x28231,x28232) % 187.86/187.67 [2824]P31(x28242,x28243,x28244)+~E(x28241,x28242)+~P31(x28241,x28243,x28244) % 187.86/187.67 [2825]P31(x28253,x28252,x28254)+~E(x28251,x28252)+~P31(x28253,x28251,x28254) % 187.86/187.67 [2826]P31(x28263,x28264,x28262)+~E(x28261,x28262)+~P31(x28263,x28264,x28261) % 187.86/187.67 [2827]~P115(x28271)+P115(x28272)+~E(x28271,x28272) % 187.86/187.67 [2828]~P101(x28281)+P101(x28282)+~E(x28281,x28282) % 187.86/187.67 [2829]~P39(x28291)+P39(x28292)+~E(x28291,x28292) % 187.86/187.67 [2830]P47(x28302,x28303)+~E(x28301,x28302)+~P47(x28301,x28303) % 187.86/187.67 [2831]P47(x28313,x28312)+~E(x28311,x28312)+~P47(x28313,x28311) % 187.86/187.67 [2832]P43(x28322,x28323,x28324,x28325)+~E(x28321,x28322)+~P43(x28321,x28323,x28324,x28325) % 187.86/187.67 [2833]P43(x28333,x28332,x28334,x28335)+~E(x28331,x28332)+~P43(x28333,x28331,x28334,x28335) % 187.86/187.67 [2834]P43(x28343,x28344,x28342,x28345)+~E(x28341,x28342)+~P43(x28343,x28344,x28341,x28345) % 187.86/187.67 [2835]P43(x28353,x28354,x28355,x28352)+~E(x28351,x28352)+~P43(x28353,x28354,x28355,x28351) % 187.86/187.67 [2836]~P130(x28361)+P130(x28362)+~E(x28361,x28362) % 187.86/187.67 [2837]~P131(x28371)+P131(x28372)+~E(x28371,x28372) % 187.86/187.67 [2838]~P137(x28381)+P137(x28382)+~E(x28381,x28382) % 187.86/187.67 [2839]~P121(x28391)+P121(x28392)+~E(x28391,x28392) % 187.86/187.67 [2840]~P104(x28401)+P104(x28402)+~E(x28401,x28402) % 187.86/187.67 [2841]~P46(x28411)+P46(x28412)+~E(x28411,x28412) % 187.86/187.67 [2842]P25(x28422,x28423,x28424,x28425,x28426,x28427)+~E(x28421,x28422)+~P25(x28421,x28423,x28424,x28425,x28426,x28427) % 187.86/187.67 [2843]P25(x28433,x28432,x28434,x28435,x28436,x28437)+~E(x28431,x28432)+~P25(x28433,x28431,x28434,x28435,x28436,x28437) % 187.86/187.67 [2844]P25(x28443,x28444,x28442,x28445,x28446,x28447)+~E(x28441,x28442)+~P25(x28443,x28444,x28441,x28445,x28446,x28447) % 187.86/187.67 [2845]P25(x28453,x28454,x28455,x28452,x28456,x28457)+~E(x28451,x28452)+~P25(x28453,x28454,x28455,x28451,x28456,x28457) % 187.86/187.67 [2846]P25(x28463,x28464,x28465,x28466,x28462,x28467)+~E(x28461,x28462)+~P25(x28463,x28464,x28465,x28466,x28461,x28467) % 187.86/187.67 [2847]P25(x28473,x28474,x28475,x28476,x28477,x28472)+~E(x28471,x28472)+~P25(x28473,x28474,x28475,x28476,x28477,x28471) % 187.86/187.67 [2848]~P110(x28481)+P110(x28482)+~E(x28481,x28482) % 187.86/187.67 [2849]~P77(x28491)+P77(x28492)+~E(x28491,x28492) % 187.86/187.67 [2850]P51(x28502,x28503)+~E(x28501,x28502)+~P51(x28501,x28503) % 187.86/187.67 [2851]P51(x28513,x28512)+~E(x28511,x28512)+~P51(x28513,x28511) % 187.86/187.67 [2852]~P73(x28521)+P73(x28522)+~E(x28521,x28522) % 187.86/187.67 [2853]~P89(x28531)+P89(x28532)+~E(x28531,x28532) % 187.86/187.67 [2854]P11(x28542,x28543,x28544)+~E(x28541,x28542)+~P11(x28541,x28543,x28544) % 187.86/187.67 [2855]P11(x28553,x28552,x28554)+~E(x28551,x28552)+~P11(x28553,x28551,x28554) % 187.86/187.67 [2856]P11(x28563,x28564,x28562)+~E(x28561,x28562)+~P11(x28563,x28564,x28561) % 187.86/187.67 [2857]P48(x28572,x28573,x28574)+~E(x28571,x28572)+~P48(x28571,x28573,x28574) % 187.86/187.67 [2858]P48(x28583,x28582,x28584)+~E(x28581,x28582)+~P48(x28583,x28581,x28584) % 187.86/187.67 [2859]P48(x28593,x28594,x28592)+~E(x28591,x28592)+~P48(x28593,x28594,x28591) % 187.86/187.67 [2860]P12(x28602,x28603,x28604,x28605,x28606)+~E(x28601,x28602)+~P12(x28601,x28603,x28604,x28605,x28606) % 187.86/187.67 [2861]P12(x28613,x28612,x28614,x28615,x28616)+~E(x28611,x28612)+~P12(x28613,x28611,x28614,x28615,x28616) % 187.86/187.67 [2862]P12(x28623,x28624,x28622,x28625,x28626)+~E(x28621,x28622)+~P12(x28623,x28624,x28621,x28625,x28626) % 187.86/187.67 [2863]P12(x28633,x28634,x28635,x28632,x28636)+~E(x28631,x28632)+~P12(x28633,x28634,x28635,x28631,x28636) % 187.86/187.67 [2864]P12(x28643,x28644,x28645,x28646,x28642)+~E(x28641,x28642)+~P12(x28643,x28644,x28645,x28646,x28641) % 187.86/187.67 % 187.86/187.67 %------------------------------------------- % 187.89/187.72 cnf(10200,plain, % 187.89/187.72 (~E(f306(a119,x102001),x102001)), % 187.89/187.72 inference(rename_variables,[],[4420])). % 187.89/187.72 cnf(10203,plain, % 187.89/187.72 (E(f306(f232(x102031,x102031),f233(x102031,x102032)),x102032)), % 187.89/187.72 inference(rename_variables,[],[3227])). % 187.89/187.72 cnf(10210,plain, % 187.89/187.72 (~E(f306(a119,x102101),x102101)), % 187.89/187.72 inference(rename_variables,[],[4420])). % 187.89/187.72 cnf(10221,plain, % 187.89/187.72 (~E(f306(a119,x102211),x102211)), % 187.89/187.72 inference(rename_variables,[],[4420])). % 187.89/187.72 cnf(10226,plain, % 187.89/187.72 (~P1(f306(f64(x102261,x102262,f185(f872(x102261,a859))),x102263))), % 187.89/187.72 inference(rename_variables,[],[4516])). % 187.89/187.72 cnf(10229,plain, % 187.89/187.72 (~P1(f306(f64(x102291,x102292,f185(f872(x102291,a859))),x102293))), % 187.89/187.72 inference(rename_variables,[],[4516])). % 187.89/187.72 cnf(10232,plain, % 187.89/187.72 (~P1(f306(f306(f221(a865),x102321),f2(a865)))), % 187.89/187.72 inference(rename_variables,[],[4493])). % 187.89/187.72 cnf(10235,plain, % 187.89/187.72 (~P1(f306(f306(f221(a865),x102351),f2(a865)))), % 187.89/187.72 inference(rename_variables,[],[4493])). % 187.89/187.72 cnf(10248,plain, % 187.89/187.72 (~P1(f306(f185(f872(x102481,a859)),x102482))), % 187.89/187.72 inference(scs_inference,[],[4420,10200,10210,3064,3227,3107,3170,3115,3253,4493,10232,4490,4440,4500,3244,4480,4516,10226,4519,4538,4564,4613,4615,4645,4662,4669,4670,4709,4739,4745,4830,4856,4857,4918,4919,4941,4942,4955,4959,4981,4988])). % 187.89/187.72 cnf(10252,plain, % 187.89/187.72 (~P1(f306(f306(f220(a865),f306(a119,x102521)),x102521))), % 187.89/187.72 inference(rename_variables,[],[4502])). % 187.89/187.72 cnf(10255,plain, % 187.89/187.72 (~E(f306(f306(f143(x102551),x102552),x102553),x102553)), % 187.89/187.72 inference(rename_variables,[],[4445])). % 187.89/187.72 cnf(10261,plain, % 187.89/187.72 (~P1(f306(f306(f221(a865),x102611),f2(a865)))), % 187.89/187.72 inference(rename_variables,[],[4493])). % 187.89/187.72 cnf(10263,plain, % 187.89/187.72 (E(f46(a865,f306(f232(x102631,x102631),f233(x102631,f306(f306(f82(a865),x102632),x102633))),x102632),f2(a865))), % 187.89/187.72 inference(scs_inference,[],[4420,10200,10210,3064,3227,10203,3107,3170,3134,3115,4445,3253,4493,10232,10235,4490,4440,4502,4500,3244,4480,4516,10226,4519,4538,4564,4613,4615,4645,4662,4669,4670,4709,4739,4745,4830,4856,4857,4918,4919,4941,4942,4955,4959,4981,4988,5005,5008,5009,5010,5015])). % 187.89/187.72 cnf(10264,plain, % 187.89/187.72 (E(f306(f232(x102641,x102641),f233(x102641,x102642)),x102642)), % 187.89/187.72 inference(rename_variables,[],[3227])). % 187.89/187.72 cnf(10267,plain, % 187.89/187.72 (E(f306(f232(x102671,x102671),f233(x102671,x102672)),x102672)), % 187.89/187.72 inference(rename_variables,[],[3227])). % 187.89/187.72 cnf(10274,plain, % 187.89/187.72 (~P1(f306(f306(f221(a865),f306(f306(f81(a865),x102741),x102742)),x102742))), % 187.89/187.72 inference(rename_variables,[],[4517])). % 187.89/187.72 cnf(10277,plain, % 187.89/187.72 (~P1(f306(f306(f221(a865),f306(f306(f81(a865),x102771),x102772)),x102772))), % 187.89/187.72 inference(rename_variables,[],[4517])). % 187.89/187.72 cnf(10284,plain, % 187.89/187.72 (~E(x102841,f306(a119,x102841))), % 187.89/187.72 inference(scs_inference,[],[4420,10200,10210,3064,3227,10203,10264,3107,3170,3134,3115,4445,3340,3253,4493,10232,10235,4490,4440,4502,4081,4500,3244,4480,4516,10226,4519,4517,10274,4538,4564,4613,4615,4645,4662,4669,4670,4709,4739,4745,4830,4856,4857,4918,4919,4941,4942,4955,4959,4981,4988,5005,5008,5009,5010,5015,5016,5039,5066,5067,5077,5082,5090,5135])). % 187.89/187.72 cnf(10298,plain, % 187.89/187.72 (~P1(f306(f306(f221(a865),x102981),x102981))), % 187.89/187.72 inference(rename_variables,[],[4489])). % 187.89/187.72 cnf(10301,plain, % 187.89/187.72 (P1(f306(f306(f220(a865),f46(a865,x103011,x103012)),x103011))), % 187.89/187.72 inference(rename_variables,[],[3720])). % 187.89/187.72 cnf(10322,plain, % 187.89/187.72 (E(f306(f39(a865),f306(f229(a865),x103221)),x103221)), % 187.89/187.72 inference(rename_variables,[],[3165])). % 187.89/187.72 cnf(10330,plain, % 187.89/187.72 (~E(f306(a119,x103301),x103301)), % 187.89/187.72 inference(rename_variables,[],[4420])). % 187.89/187.72 cnf(10333,plain, % 187.89/187.72 (~E(f306(a119,x103331),x103331)), % 187.89/187.72 inference(rename_variables,[],[4420])). % 187.89/187.72 cnf(10336,plain, % 187.89/187.72 (~E(f306(a119,x103361),x103361)), % 187.89/187.72 inference(rename_variables,[],[4420])). % 187.89/187.72 cnf(10338,plain, % 187.89/187.72 (P1(f306(a190,a104))), % 187.89/187.72 inference(scs_inference,[],[4420,10200,10210,10221,10330,10333,3064,3227,10203,10264,3107,3170,3134,3115,3201,4445,3165,4524,3184,3340,3253,4493,10232,10235,3847,3273,4490,4440,4489,10298,3365,3781,3720,4502,10252,4081,4500,4479,3244,4484,4480,4516,10226,4519,4517,10274,4538,4564,4613,4615,4645,4662,4669,4670,4709,4739,4745,4830,4856,4857,4918,4919,4941,4942,4955,4959,4981,4988,5005,5008,5009,5010,5015,5016,5039,5066,5067,5077,5082,5090,5135,5136,5144,5154,5158,5160,5170,5172,5178,5182,5197,5204,5207,5208,5209,5213,5248,5261,5268,5270,5271,5275,5276,5277])). % 187.89/187.72 cnf(10341,plain, % 187.89/187.72 (P1(f306(f306(f221(a865),x103411),f306(a119,x103411)))), % 187.89/187.72 inference(rename_variables,[],[3340])). % 187.89/187.72 cnf(10350,plain, % 187.89/187.72 (P1(f306(f306(f193(a24),x103501),x103501))), % 187.89/187.72 inference(rename_variables,[],[3270])). % 187.89/187.72 cnf(10357,plain, % 187.89/187.72 (E(f306(f232(x103571,x103571),f233(x103571,x103572)),x103572)), % 187.89/187.72 inference(rename_variables,[],[3227])). % 187.89/187.72 cnf(10360,plain, % 187.89/187.72 (E(f306(f232(x103601,x103601),f233(x103601,x103602)),x103602)), % 187.89/187.72 inference(rename_variables,[],[3227])). % 187.89/187.72 cnf(10387,plain, % 187.89/187.72 (~P1(f306(f306(f221(a865),x103871),x103871))), % 187.89/187.72 inference(rename_variables,[],[4489])). % 187.89/187.72 cnf(10392,plain, % 187.89/187.72 (~E(f306(f306(f306(f73(x103921,f869(x103922)),x103923),x103924),f306(f214(x103922),x103925)),f306(f16(f869(x103922),x103921),f188(x103922)))), % 187.89/187.72 inference(rename_variables,[],[4513])). % 187.89/187.72 cnf(10396,plain, % 187.89/187.72 (E(f306(f306(f81(a865),x103961),f710(x103961,x103961)),x103961)), % 187.89/187.72 inference(scs_inference,[],[4420,10200,10210,10221,10330,10333,3064,3227,10203,10264,10267,10357,3107,3170,3134,3115,3201,4513,4445,3165,4037,4524,3184,3340,10341,3253,4493,10232,10235,3702,3847,3299,3300,3273,4490,4440,3990,3270,3271,4489,10298,3365,3781,3720,10301,4502,10252,4081,4500,4479,3244,4484,3249,4480,4516,10226,4519,3741,4517,10274,4538,4564,4613,4615,4645,4662,4669,4670,4709,4739,4745,4830,4856,4857,4918,4919,4941,4942,4955,4959,4981,4988,5005,5008,5009,5010,5015,5016,5039,5066,5067,5077,5082,5090,5135,5136,5144,5154,5158,5160,5170,5172,5178,5182,5197,5204,5207,5208,5209,5213,5248,5261,5268,5270,5271,5275,5276,5277,5285,5288,5293,5294,5295,5302,5306,5307,5308,5317,5321,5322,5323,5328,5341,5350,5362,5364,5372,5373,5377,5381,5406,5412,5422,5423])). % 187.89/187.72 cnf(10419,plain, % 187.89/187.72 (~E(f306(f306(f143(x104191),x104192),x104193),x104193)), % 187.89/187.72 inference(rename_variables,[],[4445])). % 187.89/187.72 cnf(10422,plain, % 187.89/187.72 (~E(f306(a26,x104221),f34(x104222,x104223))), % 187.89/187.72 inference(rename_variables,[],[4435])). % 187.89/187.72 cnf(10433,plain, % 187.89/187.72 (P1(f306(f306(f220(a1),x104331),x104331))), % 187.89/187.72 inference(rename_variables,[],[3272])). % 187.89/187.72 cnf(10438,plain, % 187.89/187.72 (~E(f306(a119,x104381),x104381)), % 187.89/187.72 inference(rename_variables,[],[4420])). % 187.89/187.72 cnf(10445,plain, % 187.89/187.72 (P1(f306(f306(f193(a24),x104451),x104451))), % 187.89/187.72 inference(rename_variables,[],[3270])). % 187.89/187.72 cnf(10458,plain, % 187.89/187.72 (P1(f306(f306(f221(a865),x104581),f306(a119,x104581)))), % 187.89/187.72 inference(rename_variables,[],[3340])). % 187.89/187.72 cnf(10463,plain, % 187.89/187.72 (E(f306(f306(f122(x104631),f120(x104631)),x104632),x104632)), % 187.89/187.72 inference(rename_variables,[],[3222])). % 187.89/187.72 cnf(10481,plain, % 187.89/187.72 (~P1(f306(f64(x104811,x104812,f185(f872(x104811,a859))),x104813))), % 187.89/187.72 inference(rename_variables,[],[4516])). % 187.89/187.72 cnf(10500,plain, % 187.89/187.72 (~P1(f306(f306(f221(a865),x105001),x105001))), % 187.89/187.72 inference(rename_variables,[],[4489])). % 187.89/187.72 cnf(10512,plain, % 187.89/187.72 (E(f306(f306(f237(a865),f306(f111(a865),a104)),x105121),f306(f306(f237(a865),f2(a865)),x105121))), % 187.89/187.72 inference(scs_inference,[],[4420,10200,10210,10221,10330,10333,10336,4435,3064,3227,10203,10264,10267,10357,3107,3170,3134,3115,3201,3222,10463,4513,4445,10255,3165,4037,4524,3184,3628,3340,10341,10458,3253,4493,10232,10235,10261,4509,3702,3847,3299,3300,3273,4490,4440,3990,3270,10350,3271,3272,4489,10298,10387,3365,3781,3720,10301,4502,10252,4081,4500,4479,3244,3248,4481,4484,3249,4480,4516,10226,10229,4519,3741,4517,10274,4538,4564,4613,4615,4645,4662,4669,4670,4709,4739,4745,4830,4856,4857,4918,4919,4941,4942,4955,4959,4981,4988,5005,5008,5009,5010,5015,5016,5039,5066,5067,5077,5082,5090,5135,5136,5144,5154,5158,5160,5170,5172,5178,5182,5197,5204,5207,5208,5209,5213,5248,5261,5268,5270,5271,5275,5276,5277,5285,5288,5293,5294,5295,5302,5306,5307,5308,5317,5321,5322,5323,5328,5341,5350,5362,5364,5372,5373,5377,5381,5406,5412,5422,5423,5438,5451,5473,5479,5495,5496,5499,5518,5526,5527,5532,5533,5543,5544,5556,5560,5569,5570,5572,5587,5592,5603,5604,5616,5623,5637,5641,5644,5650,5651,5652,5655,5660,5697,5698,5701,5703,5706,5707,5708,5710,5712,5714,5719,5726,5741,5755,5760,5761,5774,5775,5780,5785])). % 187.89/187.72 cnf(10515,plain, % 187.89/187.72 (~E(f306(a26,x105151),f34(x105152,x105153))), % 187.89/187.72 inference(rename_variables,[],[4435])). % 187.89/187.72 cnf(10524,plain, % 187.89/187.72 (~P1(f306(f306(f221(a865),x105241),x105241))), % 187.89/187.72 inference(rename_variables,[],[4489])). % 187.89/187.72 cnf(10529,plain, % 187.89/187.72 (P1(f306(f306(f221(a865),x105291),f306(a119,x105291)))), % 187.89/187.72 inference(rename_variables,[],[3340])). % 187.89/187.72 cnf(10532,plain, % 187.89/187.72 (~P1(f306(f64(x105321,x105322,f185(f872(x105321,a859))),x105323))), % 187.89/187.72 inference(rename_variables,[],[4516])). % 187.89/187.72 cnf(10535,plain, % 187.89/187.72 (~P1(f306(f64(x105351,x105352,f185(f872(x105351,a859))),x105353))), % 187.89/187.72 inference(rename_variables,[],[4516])). % 187.89/187.72 cnf(10540,plain, % 187.89/187.72 (~P1(f306(f64(x105401,x105402,f185(f872(x105401,a859))),x105403))), % 187.89/187.72 inference(rename_variables,[],[4516])). % 187.89/187.72 cnf(10551,plain, % 187.89/187.72 (~E(f306(a119,x105511),x105511)), % 187.89/187.72 inference(rename_variables,[],[4420])). % 187.89/187.72 cnf(10569,plain, % 187.89/187.72 (P1(f306(f306(f221(a106),f306(a3,x105691)),f306(a3,f306(a119,x105691))))), % 187.89/187.72 inference(scs_inference,[],[4420,10200,10210,10221,10330,10333,10336,10438,4435,10422,3064,3227,10203,10264,10267,10357,3107,3170,3134,3115,3201,3222,10463,4513,4445,10255,3165,4037,4524,3184,3628,3340,10341,10458,10529,3715,3253,4493,10232,10235,10261,4509,3702,3847,3299,3300,3273,4490,4440,3990,3270,10350,3271,3272,4489,10298,10387,10500,3365,3781,3720,10301,4502,10252,4081,4500,4479,3244,3248,4481,4484,3249,4480,4516,10226,10229,10481,10532,10535,4519,3741,4517,10274,4538,4564,4613,4615,4645,4662,4669,4670,4709,4739,4745,4830,4856,4857,4918,4919,4941,4942,4955,4959,4981,4988,5005,5008,5009,5010,5015,5016,5039,5066,5067,5077,5082,5090,5135,5136,5144,5154,5158,5160,5170,5172,5178,5182,5197,5204,5207,5208,5209,5213,5248,5261,5268,5270,5271,5275,5276,5277,5285,5288,5293,5294,5295,5302,5306,5307,5308,5317,5321,5322,5323,5328,5341,5350,5362,5364,5372,5373,5377,5381,5406,5412,5422,5423,5438,5451,5473,5479,5495,5496,5499,5518,5526,5527,5532,5533,5543,5544,5556,5560,5569,5570,5572,5587,5592,5603,5604,5616,5623,5637,5641,5644,5650,5651,5652,5655,5660,5697,5698,5701,5703,5706,5707,5708,5710,5712,5714,5719,5726,5741,5755,5760,5761,5774,5775,5780,5785,5787,5792,5833,5845,5854,5858,5869,5873,5874,5882,5896,5902,5920,5923,5935,5965,5979,6004,6024,6025,6028,6042,6044,6046,6048])). % 187.89/187.72 cnf(10576,plain, % 187.89/187.72 (P1(f306(f306(f193(a24),x105761),x105761))), % 187.89/187.72 inference(rename_variables,[],[3270])). % 187.89/187.72 cnf(10579,plain, % 187.89/187.72 (P1(f306(f306(f220(a865),x105791),f306(f306(f82(a865),x105791),x105791)))), % 187.89/187.72 inference(rename_variables,[],[3536])). % 187.89/187.72 cnf(10581,plain, % 187.89/187.72 (P1(f306(f306(f221(a865),x105811),f306(f306(f82(a865),f306(a119,x105811)),f306(a119,x105811))))), % 187.89/187.72 inference(scs_inference,[],[4420,10200,10210,10221,10330,10333,10336,10438,4435,10422,3064,3227,10203,10264,10267,10357,3107,3170,3134,3115,3201,3222,10463,4513,4445,10255,3165,4037,4524,3184,3628,3340,10341,10458,10529,3715,3253,4493,10232,10235,10261,4509,3702,3847,3299,3300,3273,4490,4440,3990,3270,10350,10445,3271,3272,4489,10298,10387,10500,3365,3781,3720,10301,4502,10252,4081,4500,4479,3244,3248,4481,4484,3249,4480,4516,10226,10229,10481,10532,10535,3536,10579,4519,3741,4517,10274,4538,4564,4613,4615,4645,4662,4669,4670,4709,4739,4745,4830,4856,4857,4918,4919,4941,4942,4955,4959,4981,4988,5005,5008,5009,5010,5015,5016,5039,5066,5067,5077,5082,5090,5135,5136,5144,5154,5158,5160,5170,5172,5178,5182,5197,5204,5207,5208,5209,5213,5248,5261,5268,5270,5271,5275,5276,5277,5285,5288,5293,5294,5295,5302,5306,5307,5308,5317,5321,5322,5323,5328,5341,5350,5362,5364,5372,5373,5377,5381,5406,5412,5422,5423,5438,5451,5473,5479,5495,5496,5499,5518,5526,5527,5532,5533,5543,5544,5556,5560,5569,5570,5572,5587,5592,5603,5604,5616,5623,5637,5641,5644,5650,5651,5652,5655,5660,5697,5698,5701,5703,5706,5707,5708,5710,5712,5714,5719,5726,5741,5755,5760,5761,5774,5775,5780,5785,5787,5792,5833,5845,5854,5858,5869,5873,5874,5882,5896,5902,5920,5923,5935,5965,5979,6004,6024,6025,6028,6042,6044,6046,6048,6061,6062,6065,6067,6070])). % 187.89/187.72 cnf(10582,plain, % 187.89/187.72 (P1(f306(f306(f220(a865),x105821),f306(f306(f82(a865),x105821),x105821)))), % 187.89/187.72 inference(rename_variables,[],[3536])). % 187.89/187.72 cnf(10585,plain, % 187.89/187.72 (P1(f306(f306(f221(a865),x105851),f306(a119,f306(f306(f81(a865),x105852),x105851))))), % 187.89/187.72 inference(rename_variables,[],[3713])). % 187.89/187.72 cnf(10590,plain, % 187.89/187.72 (P1(f306(f306(f221(a865),x105901),f306(a119,x105901)))), % 187.89/187.72 inference(rename_variables,[],[3340])). % 187.89/187.72 cnf(10593,plain, % 187.89/187.72 (P1(f306(f306(f221(a865),x105931),f306(a119,x105931)))), % 187.89/187.72 inference(rename_variables,[],[3340])). % 187.89/187.72 cnf(10596,plain, % 187.89/187.72 (P1(f306(f306(f308(x105961),x105962),f231(f872(x105961,a859))))), % 187.89/187.72 inference(rename_variables,[],[3428])). % 187.89/187.72 cnf(10611,plain, % 187.89/187.72 (~P1(f306(f306(f220(a865),f306(a119,x106111)),x106111))), % 187.89/187.72 inference(rename_variables,[],[4502])). % 187.89/187.72 cnf(10614,plain, % 187.89/187.72 (~P1(f306(f306(f220(a865),f306(a119,x106141)),x106141))), % 187.89/187.72 inference(rename_variables,[],[4502])). % 187.89/187.72 cnf(10617,plain, % 187.89/187.72 (~P1(f306(f306(f221(a865),f306(f306(f81(a865),x106171),x106172)),x106172))), % 187.89/187.72 inference(rename_variables,[],[4517])). % 187.89/187.72 cnf(10620,plain, % 187.89/187.72 (~P1(f306(f306(f221(a865),f306(f306(f81(a865),x106201),x106202)),x106202))), % 187.89/187.72 inference(rename_variables,[],[4517])). % 187.89/187.72 cnf(10623,plain, % 187.89/187.72 (P1(f306(f231(f872(x106231,a859)),x106232))), % 187.89/187.72 inference(rename_variables,[],[3334])). % 187.89/187.72 cnf(10626,plain, % 187.89/187.72 (E(f306(f39(a865),f306(f229(a865),x106261)),x106261)), % 187.89/187.72 inference(rename_variables,[],[3165])). % 187.89/187.72 cnf(10629,plain, % 187.89/187.72 (P1(f306(f306(f221(a865),x106291),f306(a119,x106291)))), % 187.89/187.72 inference(rename_variables,[],[3340])). % 187.89/187.72 cnf(10636,plain, % 187.89/187.72 (P1(f306(f306(f193(a24),x106361),x106361))), % 187.89/187.72 inference(rename_variables,[],[3270])). % 187.89/187.72 cnf(10641,plain, % 187.89/187.72 (P1(f306(f306(f220(a1),x106411),x106411))), % 187.89/187.72 inference(rename_variables,[],[3272])). % 187.89/187.72 cnf(10650,plain, % 187.89/187.72 (E(f306(f232(x106501,x106501),f233(x106501,x106502)),x106502)), % 187.89/187.72 inference(rename_variables,[],[3227])). % 187.89/187.72 cnf(10653,plain, % 187.89/187.72 (P1(f306(f231(f872(x106531,a859)),x106532))), % 187.89/187.72 inference(rename_variables,[],[3334])). % 187.89/187.72 cnf(10656,plain, % 187.89/187.72 (P1(f306(f306(f220(a865),f2(a865)),x106561))), % 187.89/187.72 inference(rename_variables,[],[3292])). % 187.89/187.72 cnf(10659,plain, % 187.89/187.72 (P1(f306(f306(f220(f872(x106591,a859)),f185(f872(x106591,a859))),x106592))), % 187.89/187.72 inference(rename_variables,[],[3711])). % 187.89/187.72 cnf(10662,plain, % 187.89/187.72 (P1(f306(f231(f872(x106621,a859)),x106622))), % 187.89/187.72 inference(rename_variables,[],[3334])). % 187.89/187.72 cnf(10664,plain, % 187.89/187.72 (~P1(f306(f306(f220(a865),f306(f306(f82(a865),f306(a119,x106641)),f306(a119,x106641))),x106641))), % 187.89/187.72 inference(scs_inference,[],[4420,10200,10210,10221,10330,10333,10336,10438,4435,10422,3064,3227,10203,10264,10267,10357,10360,3107,3170,3134,3115,3201,3222,10463,4513,4445,10255,3165,10322,4037,4524,3184,3628,3570,3340,10341,10458,10529,10590,10593,3715,3253,4493,10232,10235,10261,4509,3702,3480,3847,3299,3300,3273,4490,4440,3990,3270,10350,10445,10576,3271,3272,10433,4489,10298,10387,10500,3428,3334,10623,10653,3365,3781,3720,10301,4502,10252,10611,3292,4081,4500,4479,3244,3248,4481,4484,3249,4480,4516,10226,10229,10481,10532,10535,4522,3711,3536,10579,10582,4519,3741,4517,10274,10277,10617,3713,4538,4564,4613,4615,4645,4662,4669,4670,4709,4739,4745,4830,4856,4857,4918,4919,4941,4942,4955,4959,4981,4988,5005,5008,5009,5010,5015,5016,5039,5066,5067,5077,5082,5090,5135,5136,5144,5154,5158,5160,5170,5172,5178,5182,5197,5204,5207,5208,5209,5213,5248,5261,5268,5270,5271,5275,5276,5277,5285,5288,5293,5294,5295,5302,5306,5307,5308,5317,5321,5322,5323,5328,5341,5350,5362,5364,5372,5373,5377,5381,5406,5412,5422,5423,5438,5451,5473,5479,5495,5496,5499,5518,5526,5527,5532,5533,5543,5544,5556,5560,5569,5570,5572,5587,5592,5603,5604,5616,5623,5637,5641,5644,5650,5651,5652,5655,5660,5697,5698,5701,5703,5706,5707,5708,5710,5712,5714,5719,5726,5741,5755,5760,5761,5774,5775,5780,5785,5787,5792,5833,5845,5854,5858,5869,5873,5874,5882,5896,5902,5920,5923,5935,5965,5979,6004,6024,6025,6028,6042,6044,6046,6048,6061,6062,6065,6067,6070,6071,6082,6088,6089,6090,6092,6094,6136,6137,6144,6154,6190,6192,6194,6196,6205,6207,6209,6215,6217,6223,6226,6234,6241,6242,6243,6248,6270,6271,6272,6274,6280])). % 187.89/187.72 cnf(10665,plain, % 187.89/187.72 (P1(f306(f306(f220(a865),x106651),f306(f306(f82(a865),x106651),x106651)))), % 187.89/187.72 inference(rename_variables,[],[3536])). % 187.89/187.72 cnf(10669,plain, % 187.89/187.72 (E(f306(f161(x106691),f217(x106692,x106693,f306(f306(f122(x106691),f306(f161(x106691),x106694)),f306(f306(f143(x106691),x106695),f120(x106691))),x106696,f188(x106693))),f306(f306(f143(x106691),x106695),x106694))), % 187.89/187.72 inference(scs_inference,[],[4420,10200,10210,10221,10330,10333,10336,10438,4435,10422,3064,3227,10203,10264,10267,10357,10360,3107,3922,3170,3134,3115,3201,3222,10463,4513,4445,10255,3165,10322,4037,4524,3184,3628,3570,3340,10341,10458,10529,10590,10593,3715,3253,4493,10232,10235,10261,4509,3702,3480,3847,3299,3300,3273,4490,4440,3990,3270,10350,10445,10576,3271,3272,10433,4489,10298,10387,10500,3428,3334,10623,10653,3365,3781,3720,10301,4502,10252,10611,3292,4081,4500,4479,3244,3248,4481,4484,3249,4480,4516,10226,10229,10481,10532,10535,4522,3711,3536,10579,10582,4519,3741,4517,10274,10277,10617,3713,4538,4564,4613,4615,4645,4662,4669,4670,4709,4739,4745,4830,4856,4857,4918,4919,4941,4942,4955,4959,4981,4988,5005,5008,5009,5010,5015,5016,5039,5066,5067,5077,5082,5090,5135,5136,5144,5154,5158,5160,5170,5172,5178,5182,5197,5204,5207,5208,5209,5213,5248,5261,5268,5270,5271,5275,5276,5277,5285,5288,5293,5294,5295,5302,5306,5307,5308,5317,5321,5322,5323,5328,5341,5350,5362,5364,5372,5373,5377,5381,5406,5412,5422,5423,5438,5451,5473,5479,5495,5496,5499,5518,5526,5527,5532,5533,5543,5544,5556,5560,5569,5570,5572,5587,5592,5603,5604,5616,5623,5637,5641,5644,5650,5651,5652,5655,5660,5697,5698,5701,5703,5706,5707,5708,5710,5712,5714,5719,5726,5741,5755,5760,5761,5774,5775,5780,5785,5787,5792,5833,5845,5854,5858,5869,5873,5874,5882,5896,5902,5920,5923,5935,5965,5979,6004,6024,6025,6028,6042,6044,6046,6048,6061,6062,6065,6067,6070,6071,6082,6088,6089,6090,6092,6094,6136,6137,6144,6154,6190,6192,6194,6196,6205,6207,6209,6215,6217,6223,6226,6234,6241,6242,6243,6248,6270,6271,6272,6274,6280,6285,6322])). % 187.89/187.72 cnf(10674,plain, % 187.89/187.72 (~P1(f306(f306(f220(a865),f306(a119,f306(a119,f306(f306(f81(a865),x106741),x106742)))),f306(a119,x106742)))), % 187.89/187.72 inference(scs_inference,[],[4420,10200,10210,10221,10330,10333,10336,10438,4435,10422,3064,3227,10203,10264,10267,10357,10360,3107,3922,3170,3134,3115,3201,3222,10463,4513,4445,10255,3165,10322,4037,4524,3184,3628,3570,3340,10341,10458,10529,10590,10593,10629,3715,3253,4493,10232,10235,10261,4509,3702,3480,3847,3299,3300,3273,4490,4440,3990,3270,10350,10445,10576,3271,3272,10433,4489,10298,10387,10500,3428,3334,10623,10653,3365,3781,3720,10301,4502,10252,10611,3292,4081,4500,4479,3244,3248,4481,4484,3249,4480,4516,10226,10229,10481,10532,10535,4522,3711,3536,10579,10582,4519,3741,4517,10274,10277,10617,3713,4538,4564,4613,4615,4645,4662,4669,4670,4709,4739,4745,4830,4856,4857,4918,4919,4941,4942,4955,4959,4981,4988,5005,5008,5009,5010,5015,5016,5039,5066,5067,5077,5082,5090,5135,5136,5144,5154,5158,5160,5170,5172,5178,5182,5197,5204,5207,5208,5209,5213,5248,5261,5268,5270,5271,5275,5276,5277,5285,5288,5293,5294,5295,5302,5306,5307,5308,5317,5321,5322,5323,5328,5341,5350,5362,5364,5372,5373,5377,5381,5406,5412,5422,5423,5438,5451,5473,5479,5495,5496,5499,5518,5526,5527,5532,5533,5543,5544,5556,5560,5569,5570,5572,5587,5592,5603,5604,5616,5623,5637,5641,5644,5650,5651,5652,5655,5660,5697,5698,5701,5703,5706,5707,5708,5710,5712,5714,5719,5726,5741,5755,5760,5761,5774,5775,5780,5785,5787,5792,5833,5845,5854,5858,5869,5873,5874,5882,5896,5902,5920,5923,5935,5965,5979,6004,6024,6025,6028,6042,6044,6046,6048,6061,6062,6065,6067,6070,6071,6082,6088,6089,6090,6092,6094,6136,6137,6144,6154,6190,6192,6194,6196,6205,6207,6209,6215,6217,6223,6226,6234,6241,6242,6243,6248,6270,6271,6272,6274,6280,6285,6322,6323,6325])). % 187.89/187.72 cnf(10682,plain, % 187.89/187.72 (~P1(f306(f306(f221(a106),f306(a3,x106821)),f306(a3,f2(a865))))), % 187.89/187.72 inference(scs_inference,[],[4420,10200,10210,10221,10330,10333,10336,10438,4435,10422,3064,3227,10203,10264,10267,10357,10360,3107,3922,3170,3134,3115,3201,3222,10463,4513,4445,10255,3165,10322,4037,4524,3184,3628,3570,3340,10341,10458,10529,10590,10593,10629,3715,3253,4493,10232,10235,10261,4509,3702,3480,3847,3299,3300,3273,4490,4440,3990,3270,10350,10445,10576,3271,3272,10433,4489,10298,10387,10500,3428,3334,10623,10653,3365,3781,3720,10301,4502,10252,10611,10614,3292,4081,4500,4479,3244,3248,4481,4484,3249,4480,4516,10226,10229,10481,10532,10535,4522,3711,3536,10579,10582,4519,3741,4517,10274,10277,10617,3713,4538,4564,4613,4615,4645,4662,4669,4670,4709,4739,4745,4830,4856,4857,4918,4919,4941,4942,4955,4959,4981,4988,5005,5008,5009,5010,5015,5016,5039,5066,5067,5077,5082,5090,5135,5136,5144,5154,5158,5160,5170,5172,5178,5182,5197,5204,5207,5208,5209,5213,5248,5261,5268,5270,5271,5275,5276,5277,5285,5288,5293,5294,5295,5302,5306,5307,5308,5317,5321,5322,5323,5328,5341,5350,5362,5364,5372,5373,5377,5381,5406,5412,5422,5423,5438,5451,5473,5479,5495,5496,5499,5518,5526,5527,5532,5533,5543,5544,5556,5560,5569,5570,5572,5587,5592,5603,5604,5616,5623,5637,5641,5644,5650,5651,5652,5655,5660,5697,5698,5701,5703,5706,5707,5708,5710,5712,5714,5719,5726,5741,5755,5760,5761,5774,5775,5780,5785,5787,5792,5833,5845,5854,5858,5869,5873,5874,5882,5896,5902,5920,5923,5935,5965,5979,6004,6024,6025,6028,6042,6044,6046,6048,6061,6062,6065,6067,6070,6071,6082,6088,6089,6090,6092,6094,6136,6137,6144,6154,6190,6192,6194,6196,6205,6207,6209,6215,6217,6223,6226,6234,6241,6242,6243,6248,6270,6271,6272,6274,6280,6285,6322,6323,6325,6326,6327,6329,6330])). % 187.89/187.72 cnf(10705,plain, % 187.89/187.72 (P1(f306(f306(f220(a865),x107051),x107051))), % 187.89/187.72 inference(rename_variables,[],[3271])). % 187.89/187.72 cnf(10716,plain, % 187.89/187.72 (~P1(f306(f306(f185(f872(x107161,f872(x107162,a859))),x107163),x107164))), % 187.89/187.72 inference(rename_variables,[],[4520])). % 187.89/187.72 cnf(10723,plain, % 187.89/187.72 (P1(f306(f306(f221(a865),x107231),f306(a119,x107231)))), % 187.89/187.72 inference(rename_variables,[],[3340])). % 187.89/187.72 cnf(10725,plain, % 187.89/187.72 (P1(f306(f306(f221(a1),f306(f306(f22(a1),x107251),f79(a1))),x107251))), % 187.89/187.72 inference(scs_inference,[],[4420,10200,10210,10221,10330,10333,10336,10438,4435,10422,3064,3227,10203,10264,10267,10357,10360,3107,3922,3170,3134,3115,3201,3222,10463,4513,4445,10255,3165,10322,4037,3897,4524,3184,3628,3570,3340,10341,10458,10529,10590,10593,10629,3715,3253,4493,10232,10235,10261,4509,3702,3480,3847,3299,3300,3273,4490,4440,3990,3270,10350,10445,10576,3271,10705,3272,10433,10641,4489,10298,10387,10500,3428,4505,3334,10623,10653,3365,3781,3720,10301,4502,10252,10611,10614,3292,4081,4500,4479,4482,3244,3248,4481,4484,3249,4480,4516,10226,10229,10481,10532,10535,4522,3711,3536,10579,10582,4519,4520,3741,4517,10274,10277,10617,3713,4538,4564,4613,4615,4645,4662,4669,4670,4709,4739,4745,4830,4856,4857,4918,4919,4941,4942,4955,4959,4981,4988,5005,5008,5009,5010,5015,5016,5039,5066,5067,5077,5082,5090,5135,5136,5144,5154,5158,5160,5170,5172,5178,5182,5197,5204,5207,5208,5209,5213,5248,5261,5268,5270,5271,5275,5276,5277,5285,5288,5293,5294,5295,5302,5306,5307,5308,5317,5321,5322,5323,5328,5341,5350,5362,5364,5372,5373,5377,5381,5406,5412,5422,5423,5438,5451,5473,5479,5495,5496,5499,5518,5526,5527,5532,5533,5543,5544,5556,5560,5569,5570,5572,5587,5592,5603,5604,5616,5623,5637,5641,5644,5650,5651,5652,5655,5660,5697,5698,5701,5703,5706,5707,5708,5710,5712,5714,5719,5726,5741,5755,5760,5761,5774,5775,5780,5785,5787,5792,5833,5845,5854,5858,5869,5873,5874,5882,5896,5902,5920,5923,5935,5965,5979,6004,6024,6025,6028,6042,6044,6046,6048,6061,6062,6065,6067,6070,6071,6082,6088,6089,6090,6092,6094,6136,6137,6144,6154,6190,6192,6194,6196,6205,6207,6209,6215,6217,6223,6226,6234,6241,6242,6243,6248,6270,6271,6272,6274,6280,6285,6322,6323,6325,6326,6327,6329,6330,6331,6332,6341,6374,6375,6384,6405,6406,6426,6429,6440,6441,6447,6476,6478,6490,6528,6530,6531,6586])). % 187.89/187.72 cnf(10726,plain, % 187.89/187.72 (P1(f306(f306(f220(a1),x107261),x107261))), % 187.89/187.72 inference(rename_variables,[],[3272])). % 187.89/187.72 cnf(10731,plain, % 187.89/187.72 (~P1(f306(f306(f221(a865),x107311),f2(a865)))), % 187.89/187.72 inference(rename_variables,[],[4493])). % 187.89/187.72 cnf(10744,plain, % 187.89/187.72 (~P1(f306(f306(f221(a865),x107441),f2(a865)))), % 187.89/187.72 inference(rename_variables,[],[4493])). % 187.89/187.72 cnf(10747,plain, % 187.89/187.72 (~P1(f306(f306(f221(f872(x107471,a859)),x107472),f185(f872(x107471,a859))))), % 187.89/187.72 inference(rename_variables,[],[4514])). % 187.89/187.72 cnf(10750,plain, % 187.89/187.72 (P1(f306(f306(f220(a865),x107501),x107501))), % 187.89/187.72 inference(rename_variables,[],[3271])). % 187.89/187.72 cnf(10753,plain, % 187.89/187.72 (P1(f306(f306(f220(a865),x107531),x107531))), % 187.89/187.72 inference(rename_variables,[],[3271])). % 187.89/187.72 cnf(10767,plain, % 187.89/187.72 (~P1(f306(f306(f221(a865),x107671),f306(f306(f22(a865),x107671),x107672)))), % 187.89/187.72 inference(scs_inference,[],[4420,10200,10210,10221,10330,10333,10336,10438,4435,10422,3064,3227,10203,10264,10267,10357,10360,3107,3922,3170,3134,3115,3201,3222,10463,4513,4445,10255,3165,10322,4037,3897,4524,3184,3628,3570,3340,10341,10458,10529,10590,10593,10629,3715,3253,4493,10232,10235,10261,10731,4509,3702,3480,3847,3299,3300,3273,4490,4440,4001,3990,4514,3270,10350,10445,10576,3271,10705,10750,10753,3272,10433,10641,4489,10298,10387,10500,10524,3428,4505,3334,10623,10653,3365,3781,3720,10301,4502,10252,10611,10614,3292,4081,4500,4479,4482,3244,3248,4481,4484,3249,4480,4516,10226,10229,10481,10532,10535,4522,3711,3536,10579,10582,4519,4520,3741,4517,10274,10277,10617,3713,4538,4564,4613,4615,4645,4662,4669,4670,4709,4739,4745,4830,4856,4857,4918,4919,4941,4942,4955,4959,4981,4988,5005,5008,5009,5010,5015,5016,5039,5066,5067,5077,5082,5090,5135,5136,5144,5154,5158,5160,5170,5172,5178,5182,5197,5204,5207,5208,5209,5213,5248,5261,5268,5270,5271,5275,5276,5277,5285,5288,5293,5294,5295,5302,5306,5307,5308,5317,5321,5322,5323,5328,5341,5350,5362,5364,5372,5373,5377,5381,5406,5412,5422,5423,5438,5451,5473,5479,5495,5496,5499,5518,5526,5527,5532,5533,5543,5544,5556,5560,5569,5570,5572,5587,5592,5603,5604,5616,5623,5637,5641,5644,5650,5651,5652,5655,5660,5697,5698,5701,5703,5706,5707,5708,5710,5712,5714,5719,5726,5741,5755,5760,5761,5774,5775,5780,5785,5787,5792,5833,5845,5854,5858,5869,5873,5874,5882,5896,5902,5920,5923,5935,5965,5979,6004,6024,6025,6028,6042,6044,6046,6048,6061,6062,6065,6067,6070,6071,6082,6088,6089,6090,6092,6094,6136,6137,6144,6154,6190,6192,6194,6196,6205,6207,6209,6215,6217,6223,6226,6234,6241,6242,6243,6248,6270,6271,6272,6274,6280,6285,6322,6323,6325,6326,6327,6329,6330,6331,6332,6341,6374,6375,6384,6405,6406,6426,6429,6440,6441,6447,6476,6478,6490,6528,6530,6531,6586,6610,6656,6676,6685,6686,6687,6688,6707,6708,6714,6726,6729,6731,6733,6734,6735,6737,6751])). % 187.89/187.72 cnf(10768,plain, % 187.89/187.72 (~P1(f306(f306(f221(a865),x107681),x107681))), % 187.89/187.72 inference(rename_variables,[],[4489])). % 187.89/187.72 cnf(10777,plain, % 187.89/187.72 (~P1(f306(f306(f308(x107771),x107772),f185(f872(x107771,a859))))), % 187.89/187.72 inference(rename_variables,[],[4505])). % 187.89/187.72 cnf(10786,plain, % 187.89/187.72 (P1(f306(f306(f220(a865),x107861),x107861))), % 187.89/187.72 inference(rename_variables,[],[3271])). % 187.89/187.72 cnf(10789,plain, % 187.89/187.72 (~P1(f306(f306(f308(x107891),x107892),f185(f872(x107891,a859))))), % 187.89/187.72 inference(rename_variables,[],[4505])). % 187.89/187.72 cnf(10792,plain, % 187.89/187.72 (P1(f306(f306(f220(f872(x107921,a859)),f306(f285(x107922,x107921,x107923),f306(f286(x107922,x107921,x107923),x107924))),x107924))), % 187.89/187.72 inference(rename_variables,[],[4140])). % 187.89/187.72 cnf(10799,plain, % 187.89/187.72 (P1(f306(f306(f220(f872(x107991,a859)),f306(f164(x107991),f306(f128(x107991,x107992),x107993))),f306(f164(x107991),x107993)))), % 187.89/187.72 inference(rename_variables,[],[3907])). % 187.89/187.72 cnf(10802,plain, % 187.89/187.72 (E(f306(f285(x108021,x108021,f5(x108021)),x108022),x108022)), % 187.89/187.72 inference(rename_variables,[],[3330])). % 187.89/187.72 cnf(10809,plain, % 187.89/187.72 (P1(f306(f306(f220(a865),f2(a865)),x108091))), % 187.89/187.72 inference(rename_variables,[],[3292])). % 187.89/187.72 cnf(10812,plain, % 187.89/187.72 (P1(f306(f306(f220(a865),x108121),x108121))), % 187.89/187.72 inference(rename_variables,[],[3271])). % 187.89/187.72 cnf(10815,plain, % 187.89/187.72 (~P1(f306(f306(f221(a865),x108151),x108151))), % 187.89/187.72 inference(rename_variables,[],[4489])). % 187.89/187.72 cnf(10818,plain, % 187.89/187.72 (~P1(f306(f306(f185(f872(x108181,f872(x108182,a859))),x108183),x108184))), % 187.89/187.72 inference(rename_variables,[],[4520])). % 187.89/187.72 cnf(10825,plain, % 187.89/187.72 (~P1(f306(f306(f221(a865),x108251),x108251))), % 187.89/187.72 inference(rename_variables,[],[4489])). % 187.89/187.72 cnf(10836,plain, % 187.89/187.72 (P1(f306(f306(f220(a865),x108361),f306(f306(f82(a865),x108361),x108361)))), % 187.89/187.72 inference(rename_variables,[],[3536])). % 187.89/187.72 cnf(10842,plain, % 187.89/187.72 (P1(f306(f306(f221(a865),x108421),f306(a119,f306(f306(f81(a865),x108422),x108421))))), % 187.89/187.72 inference(rename_variables,[],[3713])). % 187.89/187.72 cnf(10849,plain, % 187.89/187.72 (P1(f306(f306(f220(a865),x108491),x108491))), % 187.89/187.72 inference(rename_variables,[],[3271])). % 187.89/187.72 cnf(10852,plain, % 187.89/187.72 (P1(f306(f306(f220(a1),x108521),x108521))), % 187.89/187.72 inference(rename_variables,[],[3272])). % 187.89/187.72 cnf(10855,plain, % 187.89/187.72 (~E(f306(a119,x108551),x108551)), % 187.89/187.72 inference(rename_variables,[],[4420])). % 187.89/187.72 cnf(10860,plain, % 187.89/187.72 (P1(f306(f306(f308(x108601),x108602),f231(f872(x108601,a859))))), % 187.89/187.72 inference(rename_variables,[],[3428])). % 187.89/187.72 cnf(10865,plain, % 187.89/187.72 (~P1(f306(f306(f221(a865),x108651),f2(a865)))), % 187.89/187.72 inference(rename_variables,[],[4493])). % 187.89/187.72 cnf(10867,plain, % 187.89/187.72 (P1(f306(f306(f220(f872(x108671,a859)),x108672),f41(f872(x108671,a859),f306(f283(x108671),x108672))))), % 187.89/187.72 inference(scs_inference,[],[4527,4420,10200,10210,10221,10330,10333,10336,10438,10551,4435,10422,3064,3227,10203,10264,10267,10357,10360,3107,3922,3170,3134,3115,3330,3201,3222,10463,4513,4445,10255,3165,10322,4037,3897,4524,3184,3472,3628,3570,3340,10341,10458,10529,10590,10593,10629,10723,3715,3253,4493,10232,10235,10261,10731,10744,4509,3702,3480,3847,3299,3300,3273,4490,4440,4001,3907,10799,3629,3990,4514,3270,10350,10445,10576,3271,10705,10750,10753,10786,10812,3272,10433,10641,10726,4489,10298,10387,10500,10524,10768,10815,3428,10596,4505,10777,10789,3334,10623,10653,3365,3781,3720,10301,4502,10252,10611,10614,3292,10656,4081,4500,4479,4482,3244,3248,4481,4484,3249,4480,4516,10226,10229,10481,10532,10535,4522,3711,3536,10579,10582,10665,10836,4519,4520,10716,4140,3741,4517,10274,10277,10617,3713,10585,4538,4564,4613,4615,4645,4662,4669,4670,4709,4739,4745,4830,4856,4857,4918,4919,4941,4942,4955,4959,4981,4988,5005,5008,5009,5010,5015,5016,5039,5066,5067,5077,5082,5090,5135,5136,5144,5154,5158,5160,5170,5172,5178,5182,5197,5204,5207,5208,5209,5213,5248,5261,5268,5270,5271,5275,5276,5277,5285,5288,5293,5294,5295,5302,5306,5307,5308,5317,5321,5322,5323,5328,5341,5350,5362,5364,5372,5373,5377,5381,5406,5412,5422,5423,5438,5451,5473,5479,5495,5496,5499,5518,5526,5527,5532,5533,5543,5544,5556,5560,5569,5570,5572,5587,5592,5603,5604,5616,5623,5637,5641,5644,5650,5651,5652,5655,5660,5697,5698,5701,5703,5706,5707,5708,5710,5712,5714,5719,5726,5741,5755,5760,5761,5774,5775,5780,5785,5787,5792,5833,5845,5854,5858,5869,5873,5874,5882,5896,5902,5920,5923,5935,5965,5979,6004,6024,6025,6028,6042,6044,6046,6048,6061,6062,6065,6067,6070,6071,6082,6088,6089,6090,6092,6094,6136,6137,6144,6154,6190,6192,6194,6196,6205,6207,6209,6215,6217,6223,6226,6234,6241,6242,6243,6248,6270,6271,6272,6274,6280,6285,6322,6323,6325,6326,6327,6329,6330,6331,6332,6341,6374,6375,6384,6405,6406,6426,6429,6440,6441,6447,6476,6478,6490,6528,6530,6531,6586,6610,6656,6676,6685,6686,6687,6688,6707,6708,6714,6726,6729,6731,6733,6734,6735,6737,6751,6762,6764,6765,6778,6781,6832,6843,6845,6849,6864,6865,6901,6913,6944,6963,6978,7032,7060,7115,7136,7145,7148,7203,7211,7269,7271,7285,7295,7296,7297,7316,7322,7324,7373,7383,7386,7402,7451,7453,7456])). % 187.89/187.72 cnf(10880,plain, % 187.89/187.72 (P1(f306(f306(f220(a865),f2(a865)),x108801))), % 187.89/187.72 inference(rename_variables,[],[3292])). % 187.89/187.72 cnf(10887,plain, % 187.89/187.72 (P1(f306(f306(f220(a865),x108871),x108871))), % 187.89/187.72 inference(rename_variables,[],[3271])). % 187.89/187.72 cnf(10896,plain, % 187.89/187.72 (~P1(f306(f306(f308(x108961),x108962),f185(f872(x108961,a859))))), % 187.89/187.72 inference(rename_variables,[],[4505])). % 187.89/187.72 cnf(10898,plain, % 187.89/187.72 (P1(f306(f306(f220(f872(x108981,a859)),f42(f872(x108981,a859),f306(f283(x108981),x108982))),x108982))), % 187.89/187.72 inference(scs_inference,[],[4527,4420,10200,10210,10221,10330,10333,10336,10438,10551,4435,10422,3064,3227,10203,10264,10267,10357,10360,3107,3922,3170,3134,3115,3330,3201,3222,10463,4513,4445,10255,3165,10322,4037,3897,4524,3184,3472,3628,3570,3777,3340,10341,10458,10529,10590,10593,10629,10723,3715,3253,4493,10232,10235,10261,10731,10744,4509,3702,3480,3847,3299,3300,3273,4490,4440,4001,3907,10799,3629,3990,4514,3270,10350,10445,10576,3271,10705,10750,10753,10786,10812,10849,3272,10433,10641,10726,4489,10298,10387,10500,10524,10768,10815,3428,10596,10860,4505,10777,10789,3334,10623,10653,3365,3781,3720,10301,4502,10252,10611,10614,3292,10656,10809,4081,4500,3788,4479,4482,3244,3248,4481,4484,3249,4480,4516,10226,10229,10481,10532,10535,4522,3711,3536,10579,10582,10665,10836,4519,4520,10716,4140,3741,4517,10274,10277,10617,3713,10585,4538,4564,4613,4615,4645,4662,4669,4670,4709,4739,4745,4830,4856,4857,4918,4919,4941,4942,4955,4959,4981,4988,5005,5008,5009,5010,5015,5016,5039,5066,5067,5077,5082,5090,5135,5136,5144,5154,5158,5160,5170,5172,5178,5182,5197,5204,5207,5208,5209,5213,5248,5261,5268,5270,5271,5275,5276,5277,5285,5288,5293,5294,5295,5302,5306,5307,5308,5317,5321,5322,5323,5328,5341,5350,5362,5364,5372,5373,5377,5381,5406,5412,5422,5423,5438,5451,5473,5479,5495,5496,5499,5518,5526,5527,5532,5533,5543,5544,5556,5560,5569,5570,5572,5587,5592,5603,5604,5616,5623,5637,5641,5644,5650,5651,5652,5655,5660,5697,5698,5701,5703,5706,5707,5708,5710,5712,5714,5719,5726,5741,5755,5760,5761,5774,5775,5780,5785,5787,5792,5833,5845,5854,5858,5869,5873,5874,5882,5896,5902,5920,5923,5935,5965,5979,6004,6024,6025,6028,6042,6044,6046,6048,6061,6062,6065,6067,6070,6071,6082,6088,6089,6090,6092,6094,6136,6137,6144,6154,6190,6192,6194,6196,6205,6207,6209,6215,6217,6223,6226,6234,6241,6242,6243,6248,6270,6271,6272,6274,6280,6285,6322,6323,6325,6326,6327,6329,6330,6331,6332,6341,6374,6375,6384,6405,6406,6426,6429,6440,6441,6447,6476,6478,6490,6528,6530,6531,6586,6610,6656,6676,6685,6686,6687,6688,6707,6708,6714,6726,6729,6731,6733,6734,6735,6737,6751,6762,6764,6765,6778,6781,6832,6843,6845,6849,6864,6865,6901,6913,6944,6963,6978,7032,7060,7115,7136,7145,7148,7203,7211,7269,7271,7285,7295,7296,7297,7316,7322,7324,7373,7383,7386,7402,7451,7453,7456,7499,7500,7518,7585,7604,7628,7650,7665,7680,7691,7699,7700,7728,7731])). % 187.89/187.72 cnf(10900,plain, % 187.89/187.72 (E(f306(f306(f109(f872(x109001,a859)),f306(f306(f109(f872(x109001,a859)),x109002),f306(f80(f872(x109001,a859)),x109003))),x109003),f185(f872(x109001,a859)))), % 187.89/187.72 inference(scs_inference,[],[4527,4420,10200,10210,10221,10330,10333,10336,10438,10551,4435,10422,3064,3227,10203,10264,10267,10357,10360,3107,3922,3170,3134,3115,3330,3201,3222,10463,4513,4445,10255,3165,10322,4037,3897,4524,3184,3472,3628,3570,3777,3340,10341,10458,10529,10590,10593,10629,10723,3715,3253,4493,10232,10235,10261,10731,10744,4509,3702,3480,3847,3299,3300,3273,4490,4440,4001,3907,10799,3629,3990,4514,3270,10350,10445,10576,3271,10705,10750,10753,10786,10812,10849,3272,10433,10641,10726,4489,10298,10387,10500,10524,10768,10815,3428,10596,10860,4505,10777,10789,3334,10623,10653,3365,3781,3720,10301,4502,10252,10611,10614,3292,10656,10809,4081,4500,3788,4479,4482,3244,3248,4481,4484,3249,4480,4516,10226,10229,10481,10532,10535,4522,3711,3536,10579,10582,10665,10836,4519,4520,10716,4140,3741,4517,10274,10277,10617,3713,10585,3974,4538,4564,4613,4615,4645,4662,4669,4670,4709,4739,4745,4830,4856,4857,4918,4919,4941,4942,4955,4959,4981,4988,5005,5008,5009,5010,5015,5016,5039,5066,5067,5077,5082,5090,5135,5136,5144,5154,5158,5160,5170,5172,5178,5182,5197,5204,5207,5208,5209,5213,5248,5261,5268,5270,5271,5275,5276,5277,5285,5288,5293,5294,5295,5302,5306,5307,5308,5317,5321,5322,5323,5328,5341,5350,5362,5364,5372,5373,5377,5381,5406,5412,5422,5423,5438,5451,5473,5479,5495,5496,5499,5518,5526,5527,5532,5533,5543,5544,5556,5560,5569,5570,5572,5587,5592,5603,5604,5616,5623,5637,5641,5644,5650,5651,5652,5655,5660,5697,5698,5701,5703,5706,5707,5708,5710,5712,5714,5719,5726,5741,5755,5760,5761,5774,5775,5780,5785,5787,5792,5833,5845,5854,5858,5869,5873,5874,5882,5896,5902,5920,5923,5935,5965,5979,6004,6024,6025,6028,6042,6044,6046,6048,6061,6062,6065,6067,6070,6071,6082,6088,6089,6090,6092,6094,6136,6137,6144,6154,6190,6192,6194,6196,6205,6207,6209,6215,6217,6223,6226,6234,6241,6242,6243,6248,6270,6271,6272,6274,6280,6285,6322,6323,6325,6326,6327,6329,6330,6331,6332,6341,6374,6375,6384,6405,6406,6426,6429,6440,6441,6447,6476,6478,6490,6528,6530,6531,6586,6610,6656,6676,6685,6686,6687,6688,6707,6708,6714,6726,6729,6731,6733,6734,6735,6737,6751,6762,6764,6765,6778,6781,6832,6843,6845,6849,6864,6865,6901,6913,6944,6963,6978,7032,7060,7115,7136,7145,7148,7203,7211,7269,7271,7285,7295,7296,7297,7316,7322,7324,7373,7383,7386,7402,7451,7453,7456,7499,7500,7518,7585,7604,7628,7650,7665,7680,7691,7699,7700,7728,7731,7733])). % 187.89/187.72 cnf(10903,plain, % 187.89/187.72 (P1(f306(f306(f308(f866(x109031)),x109032),f153(x109031,f231(f872(x109031,a859)))))), % 187.89/187.72 inference(scs_inference,[],[4527,4420,10200,10210,10221,10330,10333,10336,10438,10551,4435,10422,3064,3227,10203,10264,10267,10357,10360,3107,3922,3170,3134,3115,3330,3201,3222,10463,4513,4445,10255,3165,10322,4037,3897,4524,3184,3472,3628,3570,3777,3340,10341,10458,10529,10590,10593,10629,10723,3715,3253,4493,10232,10235,10261,10731,10744,4509,3702,3480,3847,3299,3300,3273,4490,4440,4001,3907,10799,3629,3990,4514,3270,10350,10445,10576,3271,10705,10750,10753,10786,10812,10849,3272,10433,10641,10726,4489,10298,10387,10500,10524,10768,10815,3428,10596,10860,4505,10777,10789,3334,10623,10653,3365,3781,3720,10301,4502,10252,10611,10614,3292,10656,10809,4081,4500,3788,4479,4482,3244,3248,4481,4484,3249,4480,4516,10226,10229,10481,10532,10535,4522,3711,3536,10579,10582,10665,10836,4519,4520,10716,4140,3741,4517,10274,10277,10617,3713,10585,3974,4538,4564,4613,4615,4645,4662,4669,4670,4709,4739,4745,4830,4856,4857,4918,4919,4941,4942,4955,4959,4981,4988,5005,5008,5009,5010,5015,5016,5039,5066,5067,5077,5082,5090,5135,5136,5144,5154,5158,5160,5170,5172,5178,5182,5197,5204,5207,5208,5209,5213,5248,5261,5268,5270,5271,5275,5276,5277,5285,5288,5293,5294,5295,5302,5306,5307,5308,5317,5321,5322,5323,5328,5341,5350,5362,5364,5372,5373,5377,5381,5406,5412,5422,5423,5438,5451,5473,5479,5495,5496,5499,5518,5526,5527,5532,5533,5543,5544,5556,5560,5569,5570,5572,5587,5592,5603,5604,5616,5623,5637,5641,5644,5650,5651,5652,5655,5660,5697,5698,5701,5703,5706,5707,5708,5710,5712,5714,5719,5726,5741,5755,5760,5761,5774,5775,5780,5785,5787,5792,5833,5845,5854,5858,5869,5873,5874,5882,5896,5902,5920,5923,5935,5965,5979,6004,6024,6025,6028,6042,6044,6046,6048,6061,6062,6065,6067,6070,6071,6082,6088,6089,6090,6092,6094,6136,6137,6144,6154,6190,6192,6194,6196,6205,6207,6209,6215,6217,6223,6226,6234,6241,6242,6243,6248,6270,6271,6272,6274,6280,6285,6322,6323,6325,6326,6327,6329,6330,6331,6332,6341,6374,6375,6384,6405,6406,6426,6429,6440,6441,6447,6476,6478,6490,6528,6530,6531,6586,6610,6656,6676,6685,6686,6687,6688,6707,6708,6714,6726,6729,6731,6733,6734,6735,6737,6751,6762,6764,6765,6778,6781,6832,6843,6845,6849,6864,6865,6901,6913,6944,6963,6978,7032,7060,7115,7136,7145,7148,7203,7211,7269,7271,7285,7295,7296,7297,7316,7322,7324,7373,7383,7386,7402,7451,7453,7456,7499,7500,7518,7585,7604,7628,7650,7665,7680,7691,7699,7700,7728,7731,7733,7741])). % 187.89/187.72 cnf(10904,plain, % 187.89/187.72 (P1(f306(f306(f308(x109041),x109042),f231(f872(x109041,a859))))), % 187.89/187.72 inference(rename_variables,[],[3428])). % 187.89/187.72 cnf(10907,plain, % 187.89/187.72 (~P1(f306(f306(f308(f871(f866(x109071),f866(x109071))),f306(f306(f236(f866(x109071),f866(x109071)),x109072),f120(x109071))),f137(x109071,x109073)))), % 187.89/187.72 inference(rename_variables,[],[4524])). % 187.89/187.72 cnf(10913,plain, % 187.89/187.72 (~P1(f306(f306(f308(f871(x109131,x109131)),x109132),f233(x109131,f185(f872(x109131,a859)))))), % 187.89/187.72 inference(scs_inference,[],[4527,4420,10200,10210,10221,10330,10333,10336,10438,10551,4435,10422,3064,3227,10203,10264,10267,10357,10360,3107,3922,3170,3134,3115,3330,3201,3222,10463,4513,4445,10255,3165,10322,4037,3897,4524,3184,3472,3628,3570,3777,3340,10341,10458,10529,10590,10593,10629,10723,3715,3253,4493,10232,10235,10261,10731,10744,4509,3702,3480,3847,3299,3300,3273,4490,4440,4001,3907,10799,3629,3990,4514,3270,10350,10445,10576,3271,10705,10750,10753,10786,10812,10849,3272,10433,10641,10726,4489,10298,10387,10500,10524,10768,10815,3428,10596,10860,4505,10777,10789,10896,3334,10623,10653,3365,3781,3720,10301,4502,10252,10611,10614,3292,10656,10809,4081,4500,3788,4479,4482,3244,3248,4481,4484,3249,4480,4516,10226,10229,10481,10532,10535,4522,3711,3536,10579,10582,10665,10836,4519,4520,10716,4140,3741,4517,10274,10277,10617,3713,10585,3974,4538,4564,4613,4615,4645,4662,4669,4670,4709,4739,4745,4830,4856,4857,4918,4919,4941,4942,4955,4959,4981,4988,5005,5008,5009,5010,5015,5016,5039,5066,5067,5077,5082,5090,5135,5136,5144,5154,5158,5160,5170,5172,5178,5182,5197,5204,5207,5208,5209,5213,5248,5261,5268,5270,5271,5275,5276,5277,5285,5288,5293,5294,5295,5302,5306,5307,5308,5317,5321,5322,5323,5328,5341,5350,5362,5364,5372,5373,5377,5381,5406,5412,5422,5423,5438,5451,5473,5479,5495,5496,5499,5518,5526,5527,5532,5533,5543,5544,5556,5560,5569,5570,5572,5587,5592,5603,5604,5616,5623,5637,5641,5644,5650,5651,5652,5655,5660,5697,5698,5701,5703,5706,5707,5708,5710,5712,5714,5719,5726,5741,5755,5760,5761,5774,5775,5780,5785,5787,5792,5833,5845,5854,5858,5869,5873,5874,5882,5896,5902,5920,5923,5935,5965,5979,6004,6024,6025,6028,6042,6044,6046,6048,6061,6062,6065,6067,6070,6071,6082,6088,6089,6090,6092,6094,6136,6137,6144,6154,6190,6192,6194,6196,6205,6207,6209,6215,6217,6223,6226,6234,6241,6242,6243,6248,6270,6271,6272,6274,6280,6285,6322,6323,6325,6326,6327,6329,6330,6331,6332,6341,6374,6375,6384,6405,6406,6426,6429,6440,6441,6447,6476,6478,6490,6528,6530,6531,6586,6610,6656,6676,6685,6686,6687,6688,6707,6708,6714,6726,6729,6731,6733,6734,6735,6737,6751,6762,6764,6765,6778,6781,6832,6843,6845,6849,6864,6865,6901,6913,6944,6963,6978,7032,7060,7115,7136,7145,7148,7203,7211,7269,7271,7285,7295,7296,7297,7316,7322,7324,7373,7383,7386,7402,7451,7453,7456,7499,7500,7518,7585,7604,7628,7650,7665,7680,7691,7699,7700,7728,7731,7733,7741,7779,7790,7815,7873])). % 187.89/187.72 cnf(10914,plain, % 187.89/187.72 (~P1(f306(f306(f308(x109141),x109142),f185(f872(x109141,a859))))), % 187.89/187.72 inference(rename_variables,[],[4505])). % 187.89/187.72 cnf(10916,plain, % 187.89/187.72 (~P1(f306(f306(f308(x109161),x109162),f306(f286(x109161,x109163,x109164),f185(f872(x109163,a859)))))), % 187.89/187.72 inference(scs_inference,[],[4527,4420,10200,10210,10221,10330,10333,10336,10438,10551,4435,10422,3064,3227,10203,10264,10267,10357,10360,3107,3922,3170,3134,3115,3330,3201,3222,10463,4513,4445,10255,3165,10322,4037,3897,4524,3184,3472,3628,3570,3777,3340,10341,10458,10529,10590,10593,10629,10723,3715,3253,4493,10232,10235,10261,10731,10744,4509,3702,3480,3847,3299,3300,3273,4490,4440,4001,3907,10799,3629,3990,4514,3270,10350,10445,10576,3271,10705,10750,10753,10786,10812,10849,3272,10433,10641,10726,4489,10298,10387,10500,10524,10768,10815,3428,10596,10860,4505,10777,10789,10896,10914,3334,10623,10653,3365,3781,3720,10301,4502,10252,10611,10614,3292,10656,10809,4081,4500,3788,4479,4482,3244,3248,4481,4484,3249,4480,4516,10226,10229,10481,10532,10535,4522,3711,3536,10579,10582,10665,10836,4519,4520,10716,4140,3741,4517,10274,10277,10617,3713,10585,3974,4538,4564,4613,4615,4645,4662,4669,4670,4709,4739,4745,4830,4856,4857,4918,4919,4941,4942,4955,4959,4981,4988,5005,5008,5009,5010,5015,5016,5039,5066,5067,5077,5082,5090,5135,5136,5144,5154,5158,5160,5170,5172,5178,5182,5197,5204,5207,5208,5209,5213,5248,5261,5268,5270,5271,5275,5276,5277,5285,5288,5293,5294,5295,5302,5306,5307,5308,5317,5321,5322,5323,5328,5341,5350,5362,5364,5372,5373,5377,5381,5406,5412,5422,5423,5438,5451,5473,5479,5495,5496,5499,5518,5526,5527,5532,5533,5543,5544,5556,5560,5569,5570,5572,5587,5592,5603,5604,5616,5623,5637,5641,5644,5650,5651,5652,5655,5660,5697,5698,5701,5703,5706,5707,5708,5710,5712,5714,5719,5726,5741,5755,5760,5761,5774,5775,5780,5785,5787,5792,5833,5845,5854,5858,5869,5873,5874,5882,5896,5902,5920,5923,5935,5965,5979,6004,6024,6025,6028,6042,6044,6046,6048,6061,6062,6065,6067,6070,6071,6082,6088,6089,6090,6092,6094,6136,6137,6144,6154,6190,6192,6194,6196,6205,6207,6209,6215,6217,6223,6226,6234,6241,6242,6243,6248,6270,6271,6272,6274,6280,6285,6322,6323,6325,6326,6327,6329,6330,6331,6332,6341,6374,6375,6384,6405,6406,6426,6429,6440,6441,6447,6476,6478,6490,6528,6530,6531,6586,6610,6656,6676,6685,6686,6687,6688,6707,6708,6714,6726,6729,6731,6733,6734,6735,6737,6751,6762,6764,6765,6778,6781,6832,6843,6845,6849,6864,6865,6901,6913,6944,6963,6978,7032,7060,7115,7136,7145,7148,7203,7211,7269,7271,7285,7295,7296,7297,7316,7322,7324,7373,7383,7386,7402,7451,7453,7456,7499,7500,7518,7585,7604,7628,7650,7665,7680,7691,7699,7700,7728,7731,7733,7741,7779,7790,7815,7873,7907])). % 187.89/187.72 cnf(10917,plain, % 187.89/187.72 (~P1(f306(f306(f308(x109171),x109172),f185(f872(x109171,a859))))), % 187.89/187.72 inference(rename_variables,[],[4505])). % 187.89/187.72 cnf(10920,plain, % 187.89/187.72 (P1(f306(f306(f220(f872(x109201,a859)),x109202),f306(f306(f284(x109201),x109203),x109202)))), % 187.89/187.72 inference(rename_variables,[],[3709])). % 187.89/187.72 cnf(10923,plain, % 187.89/187.72 (P1(f306(f306(f220(a865),x109231),x109231))), % 187.89/187.72 inference(rename_variables,[],[3271])). % 187.89/187.72 cnf(10926,plain, % 187.89/187.72 (P1(f306(f306(f220(f872(x109261,a859)),x109262),f306(f306(f284(x109261),x109263),x109262)))), % 187.89/187.72 inference(rename_variables,[],[3709])). % 187.89/187.72 cnf(10929,plain, % 187.89/187.72 (E(f306(f232(x109291,x109291),f233(x109291,x109292)),x109292)), % 187.89/187.72 inference(rename_variables,[],[3227])). % 187.89/187.72 cnf(10931,plain, % 187.89/187.72 (P37(x109311,x109312,x109313,f121(x109311,f120(x109311)),f120(x109312))), % 187.89/187.72 inference(scs_inference,[],[4527,4420,10200,10210,10221,10330,10333,10336,10438,10551,4435,10422,3064,3117,3227,10203,10264,10267,10357,10360,10650,3107,3922,3170,3134,3115,3330,3201,3222,10463,4513,4445,10255,3165,10322,4037,3897,4524,3184,3472,3628,3570,3777,3340,10341,10458,10529,10590,10593,10629,10723,3715,3253,4493,10232,10235,10261,10731,10744,4509,3702,3480,3847,3299,3300,3273,4490,4440,4001,3907,10799,3629,3990,4514,3270,10350,10445,10576,3271,10705,10750,10753,10786,10812,10849,10887,3272,10433,10641,10726,4489,10298,10387,10500,10524,10768,10815,3428,10596,10860,4505,10777,10789,10896,10914,3334,10623,10653,3365,3781,3720,10301,4502,10252,10611,10614,3292,10656,10809,4081,4500,3788,4479,4482,3244,3248,4481,4484,3249,4480,4516,10226,10229,10481,10532,10535,4522,3709,10920,3711,3536,10579,10582,10665,10836,4519,4520,10716,4140,3741,4517,10274,10277,10617,3713,10585,3974,4538,4564,4613,4615,4645,4662,4669,4670,4709,4739,4745,4830,4856,4857,4918,4919,4941,4942,4955,4959,4981,4988,5005,5008,5009,5010,5015,5016,5039,5066,5067,5077,5082,5090,5135,5136,5144,5154,5158,5160,5170,5172,5178,5182,5197,5204,5207,5208,5209,5213,5248,5261,5268,5270,5271,5275,5276,5277,5285,5288,5293,5294,5295,5302,5306,5307,5308,5317,5321,5322,5323,5328,5341,5350,5362,5364,5372,5373,5377,5381,5406,5412,5422,5423,5438,5451,5473,5479,5495,5496,5499,5518,5526,5527,5532,5533,5543,5544,5556,5560,5569,5570,5572,5587,5592,5603,5604,5616,5623,5637,5641,5644,5650,5651,5652,5655,5660,5697,5698,5701,5703,5706,5707,5708,5710,5712,5714,5719,5726,5741,5755,5760,5761,5774,5775,5780,5785,5787,5792,5833,5845,5854,5858,5869,5873,5874,5882,5896,5902,5920,5923,5935,5965,5979,6004,6024,6025,6028,6042,6044,6046,6048,6061,6062,6065,6067,6070,6071,6082,6088,6089,6090,6092,6094,6136,6137,6144,6154,6190,6192,6194,6196,6205,6207,6209,6215,6217,6223,6226,6234,6241,6242,6243,6248,6270,6271,6272,6274,6280,6285,6322,6323,6325,6326,6327,6329,6330,6331,6332,6341,6374,6375,6384,6405,6406,6426,6429,6440,6441,6447,6476,6478,6490,6528,6530,6531,6586,6610,6656,6676,6685,6686,6687,6688,6707,6708,6714,6726,6729,6731,6733,6734,6735,6737,6751,6762,6764,6765,6778,6781,6832,6843,6845,6849,6864,6865,6901,6913,6944,6963,6978,7032,7060,7115,7136,7145,7148,7203,7211,7269,7271,7285,7295,7296,7297,7316,7322,7324,7373,7383,7386,7402,7451,7453,7456,7499,7500,7518,7585,7604,7628,7650,7665,7680,7691,7699,7700,7728,7731,7733,7741,7779,7790,7815,7873,7907,7939,7986,8002,8008,8019])). % 187.89/187.72 cnf(10944,plain, % 187.89/187.72 (P1(f306(f306(f220(f872(x109441,a859)),x109442),f306(f306(f284(x109441),x109443),x109442)))), % 187.89/187.72 inference(rename_variables,[],[3709])). % 187.89/187.72 cnf(10949,plain, % 187.89/187.72 (~P1(f306(f64(x109491,x109492,f185(f872(x109491,a859))),x109493))), % 187.89/187.72 inference(rename_variables,[],[4516])). % 187.89/187.72 cnf(10953,plain, % 187.89/187.72 (~P1(f306(f306(f308(f871(a865,a865)),f306(f306(f236(a865,a865),f306(a119,x109531)),x109531)),f282(a865,a296)))), % 187.89/187.72 inference(scs_inference,[],[4527,4420,10200,10210,10221,10330,10333,10336,10438,10551,4435,10422,3064,3117,3227,10203,10264,10267,10357,10360,10650,3107,3922,3170,3134,3115,3330,3201,3222,10463,4513,4445,10255,3165,10322,4037,3897,4524,3184,3472,3628,3570,3777,3340,10341,10458,10529,10590,10593,10629,10723,3715,3253,4493,10232,10235,10261,10731,10744,4509,3702,3480,3847,3299,3300,3273,4490,4440,4001,3907,10799,3629,3990,4514,3270,10350,10445,10576,3271,10705,10750,10753,10786,10812,10849,10887,3272,10433,10641,10726,4489,10298,10387,10500,10524,10768,10815,3428,10596,10860,10904,4505,10777,10789,10896,10914,3334,10623,10653,3365,3781,3720,10301,4502,10252,10611,10614,3292,10656,10809,4081,4500,3788,4479,4482,3244,3248,4481,4484,3249,4480,4516,10226,10229,10481,10532,10535,10540,4522,3864,3709,10920,10926,3711,3536,10579,10582,10665,10836,4519,4520,10716,4140,3741,4517,10274,10277,10617,3713,10585,3974,4538,4564,4613,4615,4645,4662,4669,4670,4709,4739,4745,4830,4856,4857,4918,4919,4941,4942,4955,4959,4981,4988,5005,5008,5009,5010,5015,5016,5039,5066,5067,5077,5082,5090,5135,5136,5144,5154,5158,5160,5170,5172,5178,5182,5197,5204,5207,5208,5209,5213,5248,5261,5268,5270,5271,5275,5276,5277,5285,5288,5293,5294,5295,5302,5306,5307,5308,5317,5321,5322,5323,5328,5341,5350,5362,5364,5372,5373,5377,5381,5406,5412,5422,5423,5438,5451,5473,5479,5495,5496,5499,5518,5526,5527,5532,5533,5543,5544,5556,5560,5569,5570,5572,5587,5592,5603,5604,5616,5623,5637,5641,5644,5650,5651,5652,5655,5660,5697,5698,5701,5703,5706,5707,5708,5710,5712,5714,5719,5726,5741,5755,5760,5761,5774,5775,5780,5785,5787,5792,5833,5845,5854,5858,5869,5873,5874,5882,5896,5902,5920,5923,5935,5965,5979,6004,6024,6025,6028,6042,6044,6046,6048,6061,6062,6065,6067,6070,6071,6082,6088,6089,6090,6092,6094,6136,6137,6144,6154,6190,6192,6194,6196,6205,6207,6209,6215,6217,6223,6226,6234,6241,6242,6243,6248,6270,6271,6272,6274,6280,6285,6322,6323,6325,6326,6327,6329,6330,6331,6332,6341,6374,6375,6384,6405,6406,6426,6429,6440,6441,6447,6476,6478,6490,6528,6530,6531,6586,6610,6656,6676,6685,6686,6687,6688,6707,6708,6714,6726,6729,6731,6733,6734,6735,6737,6751,6762,6764,6765,6778,6781,6832,6843,6845,6849,6864,6865,6901,6913,6944,6963,6978,7032,7060,7115,7136,7145,7148,7203,7211,7269,7271,7285,7295,7296,7297,7316,7322,7324,7373,7383,7386,7402,7451,7453,7456,7499,7500,7518,7585,7604,7628,7650,7665,7680,7691,7699,7700,7728,7731,7733,7741,7779,7790,7815,7873,7907,7939,7986,8002,8008,8019,8020,8095,8149,8168,8192,8212,8236,8335,8337,8343])). % 187.89/187.72 cnf(10962,plain, % 187.89/187.72 (P1(f306(f306(f221(a865),x109621),f306(a119,x109621)))), % 187.89/187.72 inference(rename_variables,[],[3340])). % 187.89/187.72 cnf(10969,plain, % 187.89/187.72 (E(f306(f74(x109691,x109692,x109691,x109693),f35(x109691)),x109693)), % 187.89/187.72 inference(rename_variables,[],[3722])). % 187.89/187.72 cnf(10972,plain, % 187.89/187.72 (~E(f306(f285(x109721,f872(x109721,a859),x109722),x109723),f306(f283(x109721),x109723))), % 187.89/187.72 inference(rename_variables,[],[4503])). % 187.89/187.72 cnf(10975,plain, % 187.89/187.72 (~P1(f306(f306(f308(x109751),x109752),f185(f872(x109751,a859))))), % 187.89/187.72 inference(rename_variables,[],[4505])). % 187.89/187.72 cnf(10978,plain, % 187.89/187.72 (P1(f306(f306(f308(f871(x109781,x109781)),f306(f306(f236(x109781,x109781),x109782),x109782)),f282(x109781,x109783)))), % 187.89/187.72 inference(rename_variables,[],[3897])). % 187.89/187.72 cnf(10981,plain, % 187.89/187.72 (P1(f306(f306(f220(f872(x109811,a859)),f306(f164(x109811),f162(x109811,x109812,x109813))),f306(f164(x109811),x109813)))), % 187.89/187.72 inference(rename_variables,[],[3956])). % 187.89/187.72 cnf(10984,plain, % 187.89/187.72 (P1(f306(f306(f220(f872(x109841,a859)),x109842),f231(f872(x109841,a859))))), % 187.89/187.72 inference(rename_variables,[],[3646])). % 187.89/187.72 cnf(11000,plain, % 187.89/187.72 (P1(f306(f306(f220(f872(x110001,a859)),f185(f872(x110001,a859))),x110002))), % 187.89/187.72 inference(rename_variables,[],[3711])). % 187.89/187.72 cnf(11004,plain, % 187.89/187.72 (~P1(f306(f63(f870(a865,x110041)),f293(a865,x110041,f231(f872(a865,a859)),x110042)))), % 187.89/187.72 inference(scs_inference,[],[4527,4420,10200,10210,10221,10330,10333,10336,10438,10551,4435,10422,3064,3117,3227,10203,10264,10267,10357,10360,10650,3722,3107,3922,3170,3134,3115,3330,3201,3222,10463,4513,3895,4445,10255,4503,3165,10322,4037,3897,10978,4524,10907,3184,3472,3628,3570,3777,3340,10341,10458,10529,10590,10593,10629,10723,3715,3253,4493,10232,10235,10261,10731,10744,10865,4509,3702,3480,3847,3299,3300,3273,4490,4440,4001,3907,10799,3956,3629,3990,3646,4514,3270,10350,10445,10576,3271,10705,10750,10753,10786,10812,10849,10887,3272,10433,10641,10726,4489,10298,10387,10500,10524,10768,10815,3428,10596,10860,10904,4505,10777,10789,10896,10914,10917,3334,10623,10653,3365,3781,3720,10301,4502,10252,10611,10614,3292,10656,10809,4081,4500,3788,4479,4482,3244,3248,4481,4484,3249,4480,4516,10226,10229,10481,10532,10535,10540,4522,3864,3709,10920,10926,3711,10659,3536,10579,10582,10665,10836,4519,4520,10716,4140,3741,4517,10274,10277,10617,3713,10585,3974,4538,4564,4613,4615,4645,4662,4669,4670,4709,4739,4745,4830,4856,4857,4918,4919,4941,4942,4955,4959,4981,4988,5005,5008,5009,5010,5015,5016,5039,5066,5067,5077,5082,5090,5135,5136,5144,5154,5158,5160,5170,5172,5178,5182,5197,5204,5207,5208,5209,5213,5248,5261,5268,5270,5271,5275,5276,5277,5285,5288,5293,5294,5295,5302,5306,5307,5308,5317,5321,5322,5323,5328,5341,5350,5362,5364,5372,5373,5377,5381,5406,5412,5422,5423,5438,5451,5473,5479,5495,5496,5499,5518,5526,5527,5532,5533,5543,5544,5556,5560,5569,5570,5572,5587,5592,5603,5604,5616,5623,5637,5641,5644,5650,5651,5652,5655,5660,5697,5698,5701,5703,5706,5707,5708,5710,5712,5714,5719,5726,5741,5755,5760,5761,5774,5775,5780,5785,5787,5792,5833,5845,5854,5858,5869,5873,5874,5882,5896,5902,5920,5923,5935,5965,5979,6004,6024,6025,6028,6042,6044,6046,6048,6061,6062,6065,6067,6070,6071,6082,6088,6089,6090,6092,6094,6136,6137,6144,6154,6190,6192,6194,6196,6205,6207,6209,6215,6217,6223,6226,6234,6241,6242,6243,6248,6270,6271,6272,6274,6280,6285,6322,6323,6325,6326,6327,6329,6330,6331,6332,6341,6374,6375,6384,6405,6406,6426,6429,6440,6441,6447,6476,6478,6490,6528,6530,6531,6586,6610,6656,6676,6685,6686,6687,6688,6707,6708,6714,6726,6729,6731,6733,6734,6735,6737,6751,6762,6764,6765,6778,6781,6832,6843,6845,6849,6864,6865,6901,6913,6944,6963,6978,7032,7060,7115,7136,7145,7148,7203,7211,7269,7271,7285,7295,7296,7297,7316,7322,7324,7373,7383,7386,7402,7451,7453,7456,7499,7500,7518,7585,7604,7628,7650,7665,7680,7691,7699,7700,7728,7731,7733,7741,7779,7790,7815,7873,7907,7939,7986,8002,8008,8019,8020,8095,8149,8168,8192,8212,8236,8335,8337,8343,8361,8365,8379,8402,8413,8415,8430,8436,8440,8465,8479,8480,8496,8497,8502,8503,8504,8505,8506,8524,8525])). % 187.89/187.72 cnf(11011,plain, % 187.89/187.72 (~P1(f306(f306(f308(f871(f866(x110111),f866(x110111))),f306(f306(f236(f866(x110111),f866(x110111)),x110112),f120(x110111))),f139(x110111,x110113)))), % 187.89/187.72 inference(rename_variables,[],[4525])). % 187.89/187.72 cnf(11022,plain, % 187.89/187.72 (~E(f306(a119,x110221),x110221)), % 187.89/187.72 inference(rename_variables,[],[4420])). % 187.89/187.72 cnf(11025,plain, % 187.89/187.72 (~E(f306(a119,x110251),x110251)), % 187.89/187.72 inference(rename_variables,[],[4420])). % 187.89/187.72 cnf(11027,plain, % 187.89/187.72 (P1(f306(f306(f308(f871(f866(x110271),f866(x110271))),f306(f306(f236(f866(x110271),f866(x110271)),f120(x110271)),f120(x110271))),f306(f306(f263(f866(x110271),f866(x110271),f866(x110271)),f150(x110271,x110272)),f282(f866(x110271),f150(x110271,x110272)))))), % 187.89/187.72 inference(scs_inference,[],[4527,4420,10200,10210,10221,10330,10333,10336,10438,10551,10855,11022,4435,10422,3064,3117,3227,10203,10264,10267,10357,10360,10650,3722,3107,3922,3170,3134,3115,3330,3201,3222,10463,4513,3895,4445,10255,4503,3165,10322,4037,3897,10978,4524,10907,4525,3184,3472,3628,3570,3777,3340,10341,10458,10529,10590,10593,10629,10723,3715,3253,4493,10232,10235,10261,10731,10744,10865,4509,3702,3480,3847,3299,3300,3273,4490,4440,4001,3907,10799,3956,3629,3990,3646,4514,3270,10350,10445,10576,3271,10705,10750,10753,10786,10812,10849,10887,3272,10433,10641,10726,4489,10298,10387,10500,10524,10768,10815,3428,10596,10860,10904,4505,10777,10789,10896,10914,10917,3334,10623,10653,3365,3781,3720,10301,4502,10252,10611,10614,3292,10656,10809,4081,4500,3788,4479,4482,3244,3248,4481,4484,3249,4480,4516,10226,10229,10481,10532,10535,10540,4522,3864,3709,10920,10926,3711,10659,3536,10579,10582,10665,10836,4519,4520,10716,4140,3741,4517,10274,10277,10617,3713,10585,3974,4538,4564,4613,4615,4645,4662,4669,4670,4709,4739,4745,4830,4856,4857,4918,4919,4941,4942,4955,4959,4981,4988,5005,5008,5009,5010,5015,5016,5039,5066,5067,5077,5082,5090,5135,5136,5144,5154,5158,5160,5170,5172,5178,5182,5197,5204,5207,5208,5209,5213,5248,5261,5268,5270,5271,5275,5276,5277,5285,5288,5293,5294,5295,5302,5306,5307,5308,5317,5321,5322,5323,5328,5341,5350,5362,5364,5372,5373,5377,5381,5406,5412,5422,5423,5438,5451,5473,5479,5495,5496,5499,5518,5526,5527,5532,5533,5543,5544,5556,5560,5569,5570,5572,5587,5592,5603,5604,5616,5623,5637,5641,5644,5650,5651,5652,5655,5660,5697,5698,5701,5703,5706,5707,5708,5710,5712,5714,5719,5726,5741,5755,5760,5761,5774,5775,5780,5785,5787,5792,5833,5845,5854,5858,5869,5873,5874,5882,5896,5902,5920,5923,5935,5965,5979,6004,6024,6025,6028,6042,6044,6046,6048,6061,6062,6065,6067,6070,6071,6082,6088,6089,6090,6092,6094,6136,6137,6144,6154,6190,6192,6194,6196,6205,6207,6209,6215,6217,6223,6226,6234,6241,6242,6243,6248,6270,6271,6272,6274,6280,6285,6322,6323,6325,6326,6327,6329,6330,6331,6332,6341,6374,6375,6384,6405,6406,6426,6429,6440,6441,6447,6476,6478,6490,6528,6530,6531,6586,6610,6656,6676,6685,6686,6687,6688,6707,6708,6714,6726,6729,6731,6733,6734,6735,6737,6751,6762,6764,6765,6778,6781,6832,6843,6845,6849,6864,6865,6901,6913,6944,6963,6978,7032,7060,7115,7136,7145,7148,7203,7211,7269,7271,7285,7295,7296,7297,7316,7322,7324,7373,7383,7386,7402,7451,7453,7456,7499,7500,7518,7585,7604,7628,7650,7665,7680,7691,7699,7700,7728,7731,7733,7741,7779,7790,7815,7873,7907,7939,7986,8002,8008,8019,8020,8095,8149,8168,8192,8212,8236,8335,8337,8343,8361,8365,8379,8402,8413,8415,8430,8436,8440,8465,8479,8480,8496,8497,8502,8503,8504,8505,8506,8524,8525,8526,8535,8549,8551,8563,8567,8569,8570,8571,8579])). % 187.89/187.72 cnf(11037,plain, % 187.89/187.72 (P28(x110371,x110371,f5(x110371),x110372)), % 187.89/187.72 inference(rename_variables,[],[3510])). % 187.89/187.72 cnf(11042,plain, % 187.89/187.72 (~E(f306(f285(x110421,f872(x110421,a859),x110422),x110423),f306(f283(x110421),x110423))), % 187.89/187.72 inference(rename_variables,[],[4503])). % 187.89/187.72 cnf(11047,plain, % 187.89/187.72 (P1(f306(f306(f220(f872(x110471,a859)),x110472),f231(f872(x110471,a859))))), % 187.89/187.72 inference(rename_variables,[],[3646])). % 187.89/187.72 cnf(11061,plain, % 187.89/187.72 (~P1(f306(f306(f308(x110611),x110612),f185(f872(x110611,a859))))), % 187.89/187.72 inference(rename_variables,[],[4505])). % 187.89/187.72 cnf(11064,plain, % 187.89/187.72 (~P1(f306(f306(f220(a865),f306(a119,x110641)),x110641))), % 187.89/187.72 inference(rename_variables,[],[4502])). % 187.89/187.72 cnf(11069,plain, % 187.89/187.72 (~P1(f306(f306(f308(x110691),x110692),f185(f872(x110691,a859))))), % 187.89/187.72 inference(rename_variables,[],[4505])). % 187.89/187.72 cnf(11081,plain, % 187.89/187.72 (~P1(f306(f306(f308(a865),f306(a119,f306(f134(a865,a865,f81(a865),f2(a865)),x110811))),f306(f164(a865),x110811)))), % 187.89/187.72 inference(scs_inference,[],[4527,3510,4420,10200,10210,10221,10330,10333,10336,10438,10551,10855,11022,4435,10422,10515,3064,3117,3227,10203,10264,10267,10357,10360,10650,3722,3107,3922,3170,3134,3115,3330,3201,3222,10463,4513,3895,4445,10255,4503,10972,3376,3165,10322,4037,3897,10978,4524,10907,4525,3184,3472,3628,3570,3777,3340,10341,10458,10529,10590,10593,10629,10723,10962,3715,3253,4493,10232,10235,10261,10731,10744,10865,4509,3702,3480,3847,3299,3300,3273,4490,4440,4001,3907,10799,3956,3629,3990,3646,10984,4514,3270,10350,10445,10576,3271,10705,10750,10753,10786,10812,10849,10887,3272,10433,10641,10726,4489,10298,10387,10500,10524,10768,10815,3428,10596,10860,10904,4505,10777,10789,10896,10914,10917,10975,11061,3334,10623,10653,3365,3781,3720,10301,4502,10252,10611,10614,11064,3292,10656,10809,4081,4500,3788,4479,4482,3244,3248,4481,4484,3249,4480,4516,10226,10229,10481,10532,10535,10540,4522,3864,3709,10920,10926,3711,10659,3536,10579,10582,10665,10836,4519,4520,10716,4140,3741,4517,10274,10277,10617,3713,10585,3974,4538,4564,4613,4615,4645,4662,4669,4670,4709,4739,4745,4830,4856,4857,4918,4919,4941,4942,4955,4959,4981,4988,5005,5008,5009,5010,5015,5016,5039,5066,5067,5077,5082,5090,5135,5136,5144,5154,5158,5160,5170,5172,5178,5182,5197,5204,5207,5208,5209,5213,5248,5261,5268,5270,5271,5275,5276,5277,5285,5288,5293,5294,5295,5302,5306,5307,5308,5317,5321,5322,5323,5328,5341,5350,5362,5364,5372,5373,5377,5381,5406,5412,5422,5423,5438,5451,5473,5479,5495,5496,5499,5518,5526,5527,5532,5533,5543,5544,5556,5560,5569,5570,5572,5587,5592,5603,5604,5616,5623,5637,5641,5644,5650,5651,5652,5655,5660,5697,5698,5701,5703,5706,5707,5708,5710,5712,5714,5719,5726,5741,5755,5760,5761,5774,5775,5780,5785,5787,5792,5833,5845,5854,5858,5869,5873,5874,5882,5896,5902,5920,5923,5935,5965,5979,6004,6024,6025,6028,6042,6044,6046,6048,6061,6062,6065,6067,6070,6071,6082,6088,6089,6090,6092,6094,6136,6137,6144,6154,6190,6192,6194,6196,6205,6207,6209,6215,6217,6223,6226,6234,6241,6242,6243,6248,6270,6271,6272,6274,6280,6285,6322,6323,6325,6326,6327,6329,6330,6331,6332,6341,6374,6375,6384,6405,6406,6426,6429,6440,6441,6447,6476,6478,6490,6528,6530,6531,6586,6610,6656,6676,6685,6686,6687,6688,6707,6708,6714,6726,6729,6731,6733,6734,6735,6737,6751,6762,6764,6765,6778,6781,6832,6843,6845,6849,6864,6865,6901,6913,6944,6963,6978,7032,7060,7115,7136,7145,7148,7203,7211,7269,7271,7285,7295,7296,7297,7316,7322,7324,7373,7383,7386,7402,7451,7453,7456,7499,7500,7518,7585,7604,7628,7650,7665,7680,7691,7699,7700,7728,7731,7733,7741,7779,7790,7815,7873,7907,7939,7986,8002,8008,8019,8020,8095,8149,8168,8192,8212,8236,8335,8337,8343,8361,8365,8379,8402,8413,8415,8430,8436,8440,8465,8479,8480,8496,8497,8502,8503,8504,8505,8506,8524,8525,8526,8535,8549,8551,8563,8567,8569,8570,8571,8579,8584,8611,8612,8641,8654,8658,8676,8698,8699,8700,8701,8714,8715,8737,8747,8756,8757,8758,8759,8761,8783,8784,8795])). % 187.89/187.72 cnf(11082,plain, % 187.89/187.72 (~P1(f306(f306(f220(a865),f306(a119,x110821)),x110821))), % 187.89/187.72 inference(rename_variables,[],[4502])). % 187.89/187.72 cnf(11085,plain, % 187.89/187.72 (~P1(f306(f306(f308(x110851),x110852),f185(f872(x110851,a859))))), % 187.89/187.72 inference(rename_variables,[],[4505])). % 187.89/187.72 cnf(11093,plain, % 187.89/187.72 (E(f306(f128(x110931,f231(f872(x110932,a859))),f776(x110933,x110934,f306(f306(f143(x110931),x110934),x110933),f231(f872(x110932,a859)),x110931)),x110933)), % 187.89/187.72 inference(scs_inference,[],[4527,3510,4420,10200,10210,10221,10330,10333,10336,10438,10551,10855,11022,4435,10422,10515,3064,3117,3227,10203,10264,10267,10357,10360,10650,3722,3107,3922,3170,3134,3115,3330,3201,3222,10463,4513,3895,4445,10255,4503,10972,3376,3165,10322,4037,3897,10978,4524,10907,4525,3184,3472,3628,3570,3777,3340,10341,10458,10529,10590,10593,10629,10723,10962,3715,3253,4493,10232,10235,10261,10731,10744,10865,4509,3702,3480,3847,3299,3300,3273,4490,4440,4001,3907,10799,3956,3629,3990,3646,10984,4514,3270,10350,10445,10576,3271,10705,10750,10753,10786,10812,10849,10887,3272,10433,10641,10726,4489,10298,10387,10500,10524,10768,10815,3428,10596,10860,10904,4505,10777,10789,10896,10914,10917,10975,11061,11069,3334,10623,10653,3365,3781,3720,10301,4502,10252,10611,10614,11064,3292,10656,10809,4081,4500,3788,4479,4482,3244,3248,4481,4484,3249,4480,4516,10226,10229,10481,10532,10535,10540,4522,3864,3709,10920,10926,3711,10659,3536,10579,10582,10665,10836,4519,4520,10716,4140,3741,4517,10274,10277,10617,3713,10585,3974,4538,4564,4613,4615,4645,4662,4669,4670,4709,4739,4745,4830,4856,4857,4918,4919,4941,4942,4955,4959,4981,4988,5005,5008,5009,5010,5015,5016,5039,5066,5067,5077,5082,5090,5135,5136,5144,5154,5158,5160,5170,5172,5178,5182,5197,5204,5207,5208,5209,5213,5248,5261,5268,5270,5271,5275,5276,5277,5285,5288,5293,5294,5295,5302,5306,5307,5308,5317,5321,5322,5323,5328,5341,5350,5362,5364,5372,5373,5377,5381,5406,5412,5422,5423,5438,5451,5473,5479,5495,5496,5499,5518,5526,5527,5532,5533,5543,5544,5556,5560,5569,5570,5572,5587,5592,5603,5604,5616,5623,5637,5641,5644,5650,5651,5652,5655,5660,5697,5698,5701,5703,5706,5707,5708,5710,5712,5714,5719,5726,5741,5755,5760,5761,5774,5775,5780,5785,5787,5792,5833,5845,5854,5858,5869,5873,5874,5882,5896,5902,5920,5923,5935,5965,5979,6004,6024,6025,6028,6042,6044,6046,6048,6061,6062,6065,6067,6070,6071,6082,6088,6089,6090,6092,6094,6136,6137,6144,6154,6190,6192,6194,6196,6205,6207,6209,6215,6217,6223,6226,6234,6241,6242,6243,6248,6270,6271,6272,6274,6280,6285,6322,6323,6325,6326,6327,6329,6330,6331,6332,6341,6374,6375,6384,6405,6406,6426,6429,6440,6441,6447,6476,6478,6490,6528,6530,6531,6586,6610,6656,6676,6685,6686,6687,6688,6707,6708,6714,6726,6729,6731,6733,6734,6735,6737,6751,6762,6764,6765,6778,6781,6832,6843,6845,6849,6864,6865,6901,6913,6944,6963,6978,7032,7060,7115,7136,7145,7148,7203,7211,7269,7271,7285,7295,7296,7297,7316,7322,7324,7373,7383,7386,7402,7451,7453,7456,7499,7500,7518,7585,7604,7628,7650,7665,7680,7691,7699,7700,7728,7731,7733,7741,7779,7790,7815,7873,7907,7939,7986,8002,8008,8019,8020,8095,8149,8168,8192,8212,8236,8335,8337,8343,8361,8365,8379,8402,8413,8415,8430,8436,8440,8465,8479,8480,8496,8497,8502,8503,8504,8505,8506,8524,8525,8526,8535,8549,8551,8563,8567,8569,8570,8571,8579,8584,8611,8612,8641,8654,8658,8676,8698,8699,8700,8701,8714,8715,8737,8747,8756,8757,8758,8759,8761,8783,8784,8795,8840,8846,8852,8865,8870])). % 187.89/187.72 cnf(11095,plain, % 187.89/187.72 (E(f306(x110951,f667(f306(x110951,x110952),f306(f214(x110953),x110952),x110951,x110954,x110953)),f306(x110951,x110952))), % 187.89/187.72 inference(scs_inference,[],[4527,3510,4420,10200,10210,10221,10330,10333,10336,10438,10551,10855,11022,4435,10422,10515,3064,3117,3227,10203,10264,10267,10357,10360,10650,3722,3107,3922,3170,3134,3115,3330,3201,3222,10463,3375,4513,3895,4445,10255,4503,10972,3376,3165,10322,4037,3897,10978,4524,10907,4525,3184,3472,3628,3570,3777,3340,10341,10458,10529,10590,10593,10629,10723,10962,3715,3253,4493,10232,10235,10261,10731,10744,10865,4509,3702,3480,3847,3299,3300,3273,4490,4440,4001,3907,10799,3956,3629,3990,3646,10984,4514,3270,10350,10445,10576,3271,10705,10750,10753,10786,10812,10849,10887,3272,10433,10641,10726,4489,10298,10387,10500,10524,10768,10815,3428,10596,10860,10904,4505,10777,10789,10896,10914,10917,10975,11061,11069,3334,10623,10653,3365,3781,3720,10301,4502,10252,10611,10614,11064,3292,10656,10809,4081,4500,3788,4479,4482,3244,3248,4481,4484,3249,4480,4516,10226,10229,10481,10532,10535,10540,4522,3864,3709,10920,10926,3711,10659,3536,10579,10582,10665,10836,4519,4520,10716,4140,3741,4517,10274,10277,10617,3713,10585,3974,4538,4564,4613,4615,4645,4662,4669,4670,4709,4739,4745,4830,4856,4857,4918,4919,4941,4942,4955,4959,4981,4988,5005,5008,5009,5010,5015,5016,5039,5066,5067,5077,5082,5090,5135,5136,5144,5154,5158,5160,5170,5172,5178,5182,5197,5204,5207,5208,5209,5213,5248,5261,5268,5270,5271,5275,5276,5277,5285,5288,5293,5294,5295,5302,5306,5307,5308,5317,5321,5322,5323,5328,5341,5350,5362,5364,5372,5373,5377,5381,5406,5412,5422,5423,5438,5451,5473,5479,5495,5496,5499,5518,5526,5527,5532,5533,5543,5544,5556,5560,5569,5570,5572,5587,5592,5603,5604,5616,5623,5637,5641,5644,5650,5651,5652,5655,5660,5697,5698,5701,5703,5706,5707,5708,5710,5712,5714,5719,5726,5741,5755,5760,5761,5774,5775,5780,5785,5787,5792,5833,5845,5854,5858,5869,5873,5874,5882,5896,5902,5920,5923,5935,5965,5979,6004,6024,6025,6028,6042,6044,6046,6048,6061,6062,6065,6067,6070,6071,6082,6088,6089,6090,6092,6094,6136,6137,6144,6154,6190,6192,6194,6196,6205,6207,6209,6215,6217,6223,6226,6234,6241,6242,6243,6248,6270,6271,6272,6274,6280,6285,6322,6323,6325,6326,6327,6329,6330,6331,6332,6341,6374,6375,6384,6405,6406,6426,6429,6440,6441,6447,6476,6478,6490,6528,6530,6531,6586,6610,6656,6676,6685,6686,6687,6688,6707,6708,6714,6726,6729,6731,6733,6734,6735,6737,6751,6762,6764,6765,6778,6781,6832,6843,6845,6849,6864,6865,6901,6913,6944,6963,6978,7032,7060,7115,7136,7145,7148,7203,7211,7269,7271,7285,7295,7296,7297,7316,7322,7324,7373,7383,7386,7402,7451,7453,7456,7499,7500,7518,7585,7604,7628,7650,7665,7680,7691,7699,7700,7728,7731,7733,7741,7779,7790,7815,7873,7907,7939,7986,8002,8008,8019,8020,8095,8149,8168,8192,8212,8236,8335,8337,8343,8361,8365,8379,8402,8413,8415,8430,8436,8440,8465,8479,8480,8496,8497,8502,8503,8504,8505,8506,8524,8525,8526,8535,8549,8551,8563,8567,8569,8570,8571,8579,8584,8611,8612,8641,8654,8658,8676,8698,8699,8700,8701,8714,8715,8737,8747,8756,8757,8758,8759,8761,8783,8784,8795,8840,8846,8852,8865,8870,8872])). % 187.89/187.72 cnf(11104,plain, % 187.89/187.72 (P1(f306(f306(f308(f871(x111041,x111041)),f306(f306(f236(x111041,x111041),x111042),x111042)),f282(x111041,x111043)))), % 187.89/187.72 inference(rename_variables,[],[3897])). % 187.89/187.72 cnf(11109,plain, % 187.89/187.72 (~P1(f306(f306(f308(f871(f866(x111091),f866(x111091))),f306(f306(f236(f866(x111091),f866(x111091)),x111092),f120(x111091))),f137(x111091,x111093)))), % 187.89/187.72 inference(rename_variables,[],[4524])). % 187.89/187.72 cnf(11112,plain, % 187.89/187.72 (~P1(f306(f306(f308(f871(f866(x111121),f866(x111121))),f306(f306(f236(f866(x111121),f866(x111121)),x111122),f120(x111121))),f139(x111121,x111123)))), % 187.89/187.72 inference(rename_variables,[],[4525])). % 187.89/187.72 cnf(11115,plain, % 187.89/187.72 (~P1(f306(f306(f308(f871(f866(x111151),f866(x111151))),f306(f306(f236(f866(x111151),f866(x111151)),x111152),f120(x111151))),f149(x111151,x111153)))), % 187.89/187.72 inference(rename_variables,[],[4526])). % 187.89/187.72 cnf(11120,plain, % 187.89/187.72 (~P1(f306(f306(f221(f872(x111201,a859)),x111202),f185(f872(x111201,a859))))), % 187.89/187.72 inference(rename_variables,[],[4514])). % 187.89/187.72 cnf(11123,plain, % 187.89/187.72 (~P1(f306(f306(f308(x111231),x111232),f185(f872(x111231,a859))))), % 187.89/187.72 inference(rename_variables,[],[4505])). % 187.89/187.72 cnf(11127,plain, % 187.89/187.72 (P1(f306(f306(f220(f872(x111271,a859)),x111272),f306(f306(f108(f872(x111271,a859)),x111273),f231(f872(x111271,a859)))))), % 187.89/187.72 inference(scs_inference,[],[4527,3510,4420,10200,10210,10221,10330,10333,10336,10438,10551,10855,11022,4435,10422,10515,3064,3117,3227,10203,10264,10267,10357,10360,10650,3722,3107,3922,3170,3134,3115,3330,3201,3222,10463,3375,4513,3895,4445,10255,4503,10972,3376,3165,10322,4037,3897,10978,4524,10907,11109,4525,11011,4526,3184,3472,3628,3570,3777,3340,10341,10458,10529,10590,10593,10629,10723,10962,3715,3253,4493,10232,10235,10261,10731,10744,10865,4509,3702,3480,3847,3299,3300,3273,4490,4440,4001,3907,10799,3956,3629,3990,3646,10984,11047,4514,10747,3270,10350,10445,10576,3271,10705,10750,10753,10786,10812,10849,10887,3272,10433,10641,10726,4489,10298,10387,10500,10524,10768,10815,3428,10596,10860,10904,4505,10777,10789,10896,10914,10917,10975,11061,11069,11085,3334,10623,10653,3365,3781,3720,10301,4502,10252,10611,10614,11064,3292,10656,10809,4081,4500,3788,4479,4482,3244,3248,4481,4484,3249,4480,4516,10226,10229,10481,10532,10535,10540,4522,3864,3709,10920,10926,3711,10659,3536,10579,10582,10665,10836,4519,4520,10716,4140,3741,4517,10274,10277,10617,3713,10585,3974,4538,4564,4613,4615,4645,4662,4669,4670,4709,4739,4745,4830,4856,4857,4918,4919,4941,4942,4955,4959,4981,4988,5005,5008,5009,5010,5015,5016,5039,5066,5067,5077,5082,5090,5135,5136,5144,5154,5158,5160,5170,5172,5178,5182,5197,5204,5207,5208,5209,5213,5248,5261,5268,5270,5271,5275,5276,5277,5285,5288,5293,5294,5295,5302,5306,5307,5308,5317,5321,5322,5323,5328,5341,5350,5362,5364,5372,5373,5377,5381,5406,5412,5422,5423,5438,5451,5473,5479,5495,5496,5499,5518,5526,5527,5532,5533,5543,5544,5556,5560,5569,5570,5572,5587,5592,5603,5604,5616,5623,5637,5641,5644,5650,5651,5652,5655,5660,5697,5698,5701,5703,5706,5707,5708,5710,5712,5714,5719,5726,5741,5755,5760,5761,5774,5775,5780,5785,5787,5792,5833,5845,5854,5858,5869,5873,5874,5882,5896,5902,5920,5923,5935,5965,5979,6004,6024,6025,6028,6042,6044,6046,6048,6061,6062,6065,6067,6070,6071,6082,6088,6089,6090,6092,6094,6136,6137,6144,6154,6190,6192,6194,6196,6205,6207,6209,6215,6217,6223,6226,6234,6241,6242,6243,6248,6270,6271,6272,6274,6280,6285,6322,6323,6325,6326,6327,6329,6330,6331,6332,6341,6374,6375,6384,6405,6406,6426,6429,6440,6441,6447,6476,6478,6490,6528,6530,6531,6586,6610,6656,6676,6685,6686,6687,6688,6707,6708,6714,6726,6729,6731,6733,6734,6735,6737,6751,6762,6764,6765,6778,6781,6832,6843,6845,6849,6864,6865,6901,6913,6944,6963,6978,7032,7060,7115,7136,7145,7148,7203,7211,7269,7271,7285,7295,7296,7297,7316,7322,7324,7373,7383,7386,7402,7451,7453,7456,7499,7500,7518,7585,7604,7628,7650,7665,7680,7691,7699,7700,7728,7731,7733,7741,7779,7790,7815,7873,7907,7939,7986,8002,8008,8019,8020,8095,8149,8168,8192,8212,8236,8335,8337,8343,8361,8365,8379,8402,8413,8415,8430,8436,8440,8465,8479,8480,8496,8497,8502,8503,8504,8505,8506,8524,8525,8526,8535,8549,8551,8563,8567,8569,8570,8571,8579,8584,8611,8612,8641,8654,8658,8676,8698,8699,8700,8701,8714,8715,8737,8747,8756,8757,8758,8759,8761,8783,8784,8795,8840,8846,8852,8865,8870,8872,8875,8876,8880,8889,8972,9003,9004,9005,9020,9038,9043,9070,9071])). % 187.89/187.72 cnf(11128,plain, % 187.89/187.72 (P1(f306(f306(f220(f872(x111281,a859)),x111282),f231(f872(x111281,a859))))), % 187.89/187.72 inference(rename_variables,[],[3646])). % 187.89/187.72 cnf(11131,plain, % 187.89/187.72 (~P1(f306(f306(f185(f872(x111311,f872(x111312,a859))),x111313),x111314))), % 187.89/187.72 inference(rename_variables,[],[4520])). % 187.89/187.72 cnf(11140,plain, % 187.89/187.72 (~P1(f306(f306(f308(x111401),x111402),f185(f872(x111401,a859))))), % 187.89/187.72 inference(rename_variables,[],[4505])). % 187.89/187.72 cnf(11143,plain, % 187.89/187.72 (~P1(f306(f306(f308(f871(x111431,x111431)),f306(f306(f236(x111431,x111431),x111432),x111433)),f145(x111431,f120(f872(x111431,a865)))))), % 187.89/187.72 inference(rename_variables,[],[4522])). % 187.89/187.72 cnf(11146,plain, % 187.89/187.72 (P1(f306(f306(f220(f872(x111461,a859)),x111462),x111462))), % 187.89/187.72 inference(rename_variables,[],[3566])). % 187.89/187.72 cnf(11149,plain, % 187.89/187.72 (~P1(f306(f306(f308(x111491),x111492),f185(f872(x111491,a859))))), % 187.89/187.72 inference(rename_variables,[],[4505])). % 187.89/187.72 cnf(11151,plain, % 187.89/187.72 (P1(f306(f306(f220(f872(x111511,a859)),f306(f260(x111512,x111511,f185(f872(f871(x111512,x111511),a859))),x111513)),x111514))), % 187.89/187.72 inference(scs_inference,[],[4527,3510,4420,10200,10210,10221,10330,10333,10336,10438,10551,10855,11022,4435,10422,10515,3064,3117,3227,10203,10264,10267,10357,10360,10650,3722,3107,3922,3170,3134,3115,3330,3201,3222,10463,3375,4513,3895,4445,10255,4503,10972,3376,3165,10322,4037,3897,10978,4524,10907,11109,4525,11011,4526,3184,3472,3628,3570,3777,3340,10341,10458,10529,10590,10593,10629,10723,10962,3715,3253,4493,10232,10235,10261,10731,10744,10865,4509,3702,3480,3847,3299,3300,3273,4490,4440,4001,3907,10799,3956,3629,3990,3646,10984,11047,4514,10747,3270,10350,10445,10576,3271,10705,10750,10753,10786,10812,10849,10887,3272,10433,10641,10726,4489,10298,10387,10500,10524,10768,10815,3428,10596,10860,10904,4505,10777,10789,10896,10914,10917,10975,11061,11069,11085,11123,11140,3334,10623,10653,3365,3781,3720,10301,4502,10252,10611,10614,11064,3292,10656,10809,4081,4500,3788,4479,4482,3244,3248,4481,4484,3249,4480,4516,10226,10229,10481,10532,10535,10540,4522,3864,3709,10920,10926,3566,3711,10659,11000,3536,10579,10582,10665,10836,4519,4520,10716,10818,4140,3741,4517,10274,10277,10617,3713,10585,3974,4538,4564,4613,4615,4645,4662,4669,4670,4709,4739,4745,4830,4856,4857,4918,4919,4941,4942,4955,4959,4981,4988,5005,5008,5009,5010,5015,5016,5039,5066,5067,5077,5082,5090,5135,5136,5144,5154,5158,5160,5170,5172,5178,5182,5197,5204,5207,5208,5209,5213,5248,5261,5268,5270,5271,5275,5276,5277,5285,5288,5293,5294,5295,5302,5306,5307,5308,5317,5321,5322,5323,5328,5341,5350,5362,5364,5372,5373,5377,5381,5406,5412,5422,5423,5438,5451,5473,5479,5495,5496,5499,5518,5526,5527,5532,5533,5543,5544,5556,5560,5569,5570,5572,5587,5592,5603,5604,5616,5623,5637,5641,5644,5650,5651,5652,5655,5660,5697,5698,5701,5703,5706,5707,5708,5710,5712,5714,5719,5726,5741,5755,5760,5761,5774,5775,5780,5785,5787,5792,5833,5845,5854,5858,5869,5873,5874,5882,5896,5902,5920,5923,5935,5965,5979,6004,6024,6025,6028,6042,6044,6046,6048,6061,6062,6065,6067,6070,6071,6082,6088,6089,6090,6092,6094,6136,6137,6144,6154,6190,6192,6194,6196,6205,6207,6209,6215,6217,6223,6226,6234,6241,6242,6243,6248,6270,6271,6272,6274,6280,6285,6322,6323,6325,6326,6327,6329,6330,6331,6332,6341,6374,6375,6384,6405,6406,6426,6429,6440,6441,6447,6476,6478,6490,6528,6530,6531,6586,6610,6656,6676,6685,6686,6687,6688,6707,6708,6714,6726,6729,6731,6733,6734,6735,6737,6751,6762,6764,6765,6778,6781,6832,6843,6845,6849,6864,6865,6901,6913,6944,6963,6978,7032,7060,7115,7136,7145,7148,7203,7211,7269,7271,7285,7295,7296,7297,7316,7322,7324,7373,7383,7386,7402,7451,7453,7456,7499,7500,7518,7585,7604,7628,7650,7665,7680,7691,7699,7700,7728,7731,7733,7741,7779,7790,7815,7873,7907,7939,7986,8002,8008,8019,8020,8095,8149,8168,8192,8212,8236,8335,8337,8343,8361,8365,8379,8402,8413,8415,8430,8436,8440,8465,8479,8480,8496,8497,8502,8503,8504,8505,8506,8524,8525,8526,8535,8549,8551,8563,8567,8569,8570,8571,8579,8584,8611,8612,8641,8654,8658,8676,8698,8699,8700,8701,8714,8715,8737,8747,8756,8757,8758,8759,8761,8783,8784,8795,8840,8846,8852,8865,8870,8872,8875,8876,8880,8889,8972,9003,9004,9005,9020,9038,9043,9070,9071,9114,9117,9144,9189,9190,9191,9207,9233,9247])). % 187.89/187.72 cnf(11152,plain, % 187.89/187.72 (P1(f306(f306(f220(f872(x111521,a859)),f185(f872(x111521,a859))),x111522))), % 187.89/187.72 inference(rename_variables,[],[3711])). % 187.89/187.72 cnf(11155,plain, % 187.89/187.72 (P1(f306(f306(f308(f871(x111551,x111551)),f306(f306(f236(x111551,x111551),x111552),x111552)),f282(x111551,x111553)))), % 187.89/187.72 inference(rename_variables,[],[3897])). % 187.89/187.72 cnf(11157,plain, % 187.89/187.72 (~P37(x111571,x111572,x111573,f306(f306(f146(x111574,x111571),x111575),f306(a119,f120(x111574))),f120(x111572))), % 187.89/187.72 inference(scs_inference,[],[4527,3510,4420,10200,10210,10221,10330,10333,10336,10438,10551,10855,11022,4435,10422,10515,3064,3117,3227,10203,10264,10267,10357,10360,10650,3722,3107,3922,3170,3134,3115,3330,3201,3222,10463,3375,4513,3895,4445,10255,4503,10972,3376,3165,10322,4037,3897,10978,11104,4524,10907,11109,4525,11011,4526,3184,3472,3628,3570,3777,3340,10341,10458,10529,10590,10593,10629,10723,10962,3715,3253,4493,10232,10235,10261,10731,10744,10865,4509,3702,3480,3847,3299,3300,3273,4490,4440,4001,3907,10799,3956,3629,3990,3646,10984,11047,4514,10747,3270,10350,10445,10576,3271,10705,10750,10753,10786,10812,10849,10887,3272,10433,10641,10726,4489,10298,10387,10500,10524,10768,10815,3428,10596,10860,10904,4505,10777,10789,10896,10914,10917,10975,11061,11069,11085,11123,11140,3334,10623,10653,3365,3781,3720,10301,4502,10252,10611,10614,11064,3292,10656,10809,4081,4500,3788,4479,4482,3244,3248,4481,4484,3249,4480,4516,10226,10229,10481,10532,10535,10540,4522,3864,3709,10920,10926,3566,3711,10659,11000,3536,10579,10582,10665,10836,4519,4520,10716,10818,4140,3741,4517,10274,10277,10617,3713,10585,3974,4538,4564,4613,4615,4645,4662,4669,4670,4709,4739,4745,4830,4856,4857,4918,4919,4941,4942,4955,4959,4981,4988,5005,5008,5009,5010,5015,5016,5039,5066,5067,5077,5082,5090,5135,5136,5144,5154,5158,5160,5170,5172,5178,5182,5197,5204,5207,5208,5209,5213,5248,5261,5268,5270,5271,5275,5276,5277,5285,5288,5293,5294,5295,5302,5306,5307,5308,5317,5321,5322,5323,5328,5341,5350,5362,5364,5372,5373,5377,5381,5406,5412,5422,5423,5438,5451,5473,5479,5495,5496,5499,5518,5526,5527,5532,5533,5543,5544,5556,5560,5569,5570,5572,5587,5592,5603,5604,5616,5623,5637,5641,5644,5650,5651,5652,5655,5660,5697,5698,5701,5703,5706,5707,5708,5710,5712,5714,5719,5726,5741,5755,5760,5761,5774,5775,5780,5785,5787,5792,5833,5845,5854,5858,5869,5873,5874,5882,5896,5902,5920,5923,5935,5965,5979,6004,6024,6025,6028,6042,6044,6046,6048,6061,6062,6065,6067,6070,6071,6082,6088,6089,6090,6092,6094,6136,6137,6144,6154,6190,6192,6194,6196,6205,6207,6209,6215,6217,6223,6226,6234,6241,6242,6243,6248,6270,6271,6272,6274,6280,6285,6322,6323,6325,6326,6327,6329,6330,6331,6332,6341,6374,6375,6384,6405,6406,6426,6429,6440,6441,6447,6476,6478,6490,6528,6530,6531,6586,6610,6656,6676,6685,6686,6687,6688,6707,6708,6714,6726,6729,6731,6733,6734,6735,6737,6751,6762,6764,6765,6778,6781,6832,6843,6845,6849,6864,6865,6901,6913,6944,6963,6978,7032,7060,7115,7136,7145,7148,7203,7211,7269,7271,7285,7295,7296,7297,7316,7322,7324,7373,7383,7386,7402,7451,7453,7456,7499,7500,7518,7585,7604,7628,7650,7665,7680,7691,7699,7700,7728,7731,7733,7741,7779,7790,7815,7873,7907,7939,7986,8002,8008,8019,8020,8095,8149,8168,8192,8212,8236,8335,8337,8343,8361,8365,8379,8402,8413,8415,8430,8436,8440,8465,8479,8480,8496,8497,8502,8503,8504,8505,8506,8524,8525,8526,8535,8549,8551,8563,8567,8569,8570,8571,8579,8584,8611,8612,8641,8654,8658,8676,8698,8699,8700,8701,8714,8715,8737,8747,8756,8757,8758,8759,8761,8783,8784,8795,8840,8846,8852,8865,8870,8872,8875,8876,8880,8889,8972,9003,9004,9005,9020,9038,9043,9070,9071,9114,9117,9144,9189,9190,9191,9207,9233,9247,9253,9256])). % 187.89/187.72 cnf(11159,plain, % 187.89/187.72 (~E(f306(f306(f109(f872(f871(f866(x111591),f866(x111591)),a859)),f306(f261(f866(x111591),f866(x111591)),f150(x111591,x111592))),f282(f866(x111591),f150(x111591,x111592))),f185(f872(f871(f866(x111591),f866(x111591)),a859)))), % 187.89/187.72 inference(scs_inference,[],[4527,3510,4420,10200,10210,10221,10330,10333,10336,10438,10551,10855,11022,4435,10422,10515,3064,3117,3227,10203,10264,10267,10357,10360,10650,3722,3107,3922,3170,3134,3115,3330,3201,3222,10463,3375,4513,3895,4445,10255,4503,10972,3376,3165,10322,4037,3897,10978,11104,4524,10907,11109,4525,11011,4526,3184,3472,3628,3570,3777,3340,10341,10458,10529,10590,10593,10629,10723,10962,3715,3253,4493,10232,10235,10261,10731,10744,10865,4509,3702,3480,3847,3299,3300,3273,4490,4440,4001,3907,10799,3956,3629,3990,3646,10984,11047,4514,10747,3270,10350,10445,10576,3271,10705,10750,10753,10786,10812,10849,10887,3272,10433,10641,10726,4489,10298,10387,10500,10524,10768,10815,3428,10596,10860,10904,4505,10777,10789,10896,10914,10917,10975,11061,11069,11085,11123,11140,3334,10623,10653,3365,3781,3720,10301,4502,10252,10611,10614,11064,3292,10656,10809,4081,4500,3788,4479,4482,3244,3248,4481,4484,3249,4480,4516,10226,10229,10481,10532,10535,10540,4522,3864,3709,10920,10926,3566,3711,10659,11000,3536,10579,10582,10665,10836,4519,4520,10716,10818,4140,3741,4517,10274,10277,10617,3713,10585,3974,4538,4564,4613,4615,4645,4662,4669,4670,4709,4739,4745,4830,4856,4857,4918,4919,4941,4942,4955,4959,4981,4988,5005,5008,5009,5010,5015,5016,5039,5066,5067,5077,5082,5090,5135,5136,5144,5154,5158,5160,5170,5172,5178,5182,5197,5204,5207,5208,5209,5213,5248,5261,5268,5270,5271,5275,5276,5277,5285,5288,5293,5294,5295,5302,5306,5307,5308,5317,5321,5322,5323,5328,5341,5350,5362,5364,5372,5373,5377,5381,5406,5412,5422,5423,5438,5451,5473,5479,5495,5496,5499,5518,5526,5527,5532,5533,5543,5544,5556,5560,5569,5570,5572,5587,5592,5603,5604,5616,5623,5637,5641,5644,5650,5651,5652,5655,5660,5697,5698,5701,5703,5706,5707,5708,5710,5712,5714,5719,5726,5741,5755,5760,5761,5774,5775,5780,5785,5787,5792,5833,5845,5854,5858,5869,5873,5874,5882,5896,5902,5920,5923,5935,5965,5979,6004,6024,6025,6028,6042,6044,6046,6048,6061,6062,6065,6067,6070,6071,6082,6088,6089,6090,6092,6094,6136,6137,6144,6154,6190,6192,6194,6196,6205,6207,6209,6215,6217,6223,6226,6234,6241,6242,6243,6248,6270,6271,6272,6274,6280,6285,6322,6323,6325,6326,6327,6329,6330,6331,6332,6341,6374,6375,6384,6405,6406,6426,6429,6440,6441,6447,6476,6478,6490,6528,6530,6531,6586,6610,6656,6676,6685,6686,6687,6688,6707,6708,6714,6726,6729,6731,6733,6734,6735,6737,6751,6762,6764,6765,6778,6781,6832,6843,6845,6849,6864,6865,6901,6913,6944,6963,6978,7032,7060,7115,7136,7145,7148,7203,7211,7269,7271,7285,7295,7296,7297,7316,7322,7324,7373,7383,7386,7402,7451,7453,7456,7499,7500,7518,7585,7604,7628,7650,7665,7680,7691,7699,7700,7728,7731,7733,7741,7779,7790,7815,7873,7907,7939,7986,8002,8008,8019,8020,8095,8149,8168,8192,8212,8236,8335,8337,8343,8361,8365,8379,8402,8413,8415,8430,8436,8440,8465,8479,8480,8496,8497,8502,8503,8504,8505,8506,8524,8525,8526,8535,8549,8551,8563,8567,8569,8570,8571,8579,8584,8611,8612,8641,8654,8658,8676,8698,8699,8700,8701,8714,8715,8737,8747,8756,8757,8758,8759,8761,8783,8784,8795,8840,8846,8852,8865,8870,8872,8875,8876,8880,8889,8972,9003,9004,9005,9020,9038,9043,9070,9071,9114,9117,9144,9189,9190,9191,9207,9233,9247,9253,9256,9279])). % 187.89/187.72 cnf(11161,plain, % 187.89/187.72 (P37(x111611,x111612,x111613,f306(f306(f146(x111614,x111611),x111615),f121(x111614,f120(x111614))),f120(x111612))), % 187.89/187.72 inference(scs_inference,[],[4527,3510,4420,10200,10210,10221,10330,10333,10336,10438,10551,10855,11022,4435,10422,10515,3064,3117,3227,10203,10264,10267,10357,10360,10650,3722,3107,3922,3170,3134,3115,3330,3201,3222,10463,3375,4513,3895,4445,10255,4503,10972,3376,3165,10322,4037,3897,10978,11104,4524,10907,11109,4525,11011,4526,3184,3472,3628,3570,3777,3340,10341,10458,10529,10590,10593,10629,10723,10962,3715,3253,4493,10232,10235,10261,10731,10744,10865,4509,3702,3480,3847,3299,3300,3273,4490,4440,4001,3907,10799,3956,3629,3990,3646,10984,11047,4514,10747,3270,10350,10445,10576,3271,10705,10750,10753,10786,10812,10849,10887,3272,10433,10641,10726,4489,10298,10387,10500,10524,10768,10815,3428,10596,10860,10904,4505,10777,10789,10896,10914,10917,10975,11061,11069,11085,11123,11140,3334,10623,10653,3365,3781,3720,10301,4502,10252,10611,10614,11064,3292,10656,10809,4081,4500,3788,4479,4482,3244,3248,4481,4484,3249,4480,4516,10226,10229,10481,10532,10535,10540,4522,3864,3709,10920,10926,3566,3711,10659,11000,3536,10579,10582,10665,10836,4519,4520,10716,10818,4140,3741,4517,10274,10277,10617,3713,10585,3974,4538,4564,4613,4615,4645,4662,4669,4670,4709,4739,4745,4830,4856,4857,4918,4919,4941,4942,4955,4959,4981,4988,5005,5008,5009,5010,5015,5016,5039,5066,5067,5077,5082,5090,5135,5136,5144,5154,5158,5160,5170,5172,5178,5182,5197,5204,5207,5208,5209,5213,5248,5261,5268,5270,5271,5275,5276,5277,5285,5288,5293,5294,5295,5302,5306,5307,5308,5317,5321,5322,5323,5328,5341,5350,5362,5364,5372,5373,5377,5381,5406,5412,5422,5423,5438,5451,5473,5479,5495,5496,5499,5518,5526,5527,5532,5533,5543,5544,5556,5560,5569,5570,5572,5587,5592,5603,5604,5616,5623,5637,5641,5644,5650,5651,5652,5655,5660,5697,5698,5701,5703,5706,5707,5708,5710,5712,5714,5719,5726,5741,5755,5760,5761,5774,5775,5780,5785,5787,5792,5833,5845,5854,5858,5869,5873,5874,5882,5896,5902,5920,5923,5935,5965,5979,6004,6024,6025,6028,6042,6044,6046,6048,6061,6062,6065,6067,6070,6071,6082,6088,6089,6090,6092,6094,6136,6137,6144,6154,6190,6192,6194,6196,6205,6207,6209,6215,6217,6223,6226,6234,6241,6242,6243,6248,6270,6271,6272,6274,6280,6285,6322,6323,6325,6326,6327,6329,6330,6331,6332,6341,6374,6375,6384,6405,6406,6426,6429,6440,6441,6447,6476,6478,6490,6528,6530,6531,6586,6610,6656,6676,6685,6686,6687,6688,6707,6708,6714,6726,6729,6731,6733,6734,6735,6737,6751,6762,6764,6765,6778,6781,6832,6843,6845,6849,6864,6865,6901,6913,6944,6963,6978,7032,7060,7115,7136,7145,7148,7203,7211,7269,7271,7285,7295,7296,7297,7316,7322,7324,7373,7383,7386,7402,7451,7453,7456,7499,7500,7518,7585,7604,7628,7650,7665,7680,7691,7699,7700,7728,7731,7733,7741,7779,7790,7815,7873,7907,7939,7986,8002,8008,8019,8020,8095,8149,8168,8192,8212,8236,8335,8337,8343,8361,8365,8379,8402,8413,8415,8430,8436,8440,8465,8479,8480,8496,8497,8502,8503,8504,8505,8506,8524,8525,8526,8535,8549,8551,8563,8567,8569,8570,8571,8579,8584,8611,8612,8641,8654,8658,8676,8698,8699,8700,8701,8714,8715,8737,8747,8756,8757,8758,8759,8761,8783,8784,8795,8840,8846,8852,8865,8870,8872,8875,8876,8880,8889,8972,9003,9004,9005,9020,9038,9043,9070,9071,9114,9117,9144,9189,9190,9191,9207,9233,9247,9253,9256,9279,9280])). % 187.89/187.72 cnf(11166,plain, % 187.89/187.72 (~P1(f306(f306(f308(f871(f866(x111661),f866(x111661))),f306(f306(f236(f866(x111661),f866(x111661)),x111662),f120(x111661))),f149(x111661,x111663)))), % 187.89/187.72 inference(rename_variables,[],[4526])). % 187.89/187.72 cnf(11169,plain, % 187.89/187.72 (~P1(f306(f306(f308(f871(f866(x111691),f866(x111691))),f306(f306(f236(f866(x111691),f866(x111691)),f120(x111691)),x111692)),f137(x111691,x111693)))), % 187.89/187.72 inference(rename_variables,[],[4528])). % 187.89/187.72 cnf(11174,plain, % 187.89/187.72 (~P1(f306(f306(f308(f871(f872(x111741,a859),f872(x111741,a859))),f306(f306(f236(f872(x111741,a859),f872(x111741,a859)),x111742),f185(f872(x111741,a859)))),f281(x111741)))), % 187.89/187.72 inference(scs_inference,[],[4527,3510,4420,10200,10210,10221,10330,10333,10336,10438,10551,10855,11022,4435,10422,10515,3064,3117,3227,10203,10264,10267,10357,10360,10650,3722,3107,3922,3170,3134,3115,3330,3201,3222,10463,3375,4513,3895,4445,10255,4503,10972,3376,3165,10322,4037,3897,10978,11104,4524,10907,11109,4525,11011,4526,11115,4528,4529,3184,3472,3628,3570,3777,3340,10341,10458,10529,10590,10593,10629,10723,10962,3715,3253,4493,10232,10235,10261,10731,10744,10865,4509,3702,3480,3847,3299,3300,3273,4490,4440,4001,3907,10799,3956,3629,3990,3646,10984,11047,4514,10747,11120,3270,10350,10445,10576,3271,10705,10750,10753,10786,10812,10849,10887,3272,10433,10641,10726,4489,10298,10387,10500,10524,10768,10815,3428,10596,10860,10904,4505,10777,10789,10896,10914,10917,10975,11061,11069,11085,11123,11140,3334,10623,10653,3365,3781,3720,10301,4502,10252,10611,10614,11064,3292,10656,10809,4081,4500,3788,4479,4482,3244,3248,4481,4484,3249,4480,4516,10226,10229,10481,10532,10535,10540,4522,3864,3709,10920,10926,3566,3711,10659,11000,3536,10579,10582,10665,10836,4519,4520,10716,10818,4140,3741,4517,10274,10277,10617,3713,10585,3974,4538,4564,4613,4615,4645,4662,4669,4670,4709,4739,4745,4830,4856,4857,4918,4919,4941,4942,4955,4959,4981,4988,5005,5008,5009,5010,5015,5016,5039,5066,5067,5077,5082,5090,5135,5136,5144,5154,5158,5160,5170,5172,5178,5182,5197,5204,5207,5208,5209,5213,5248,5261,5268,5270,5271,5275,5276,5277,5285,5288,5293,5294,5295,5302,5306,5307,5308,5317,5321,5322,5323,5328,5341,5350,5362,5364,5372,5373,5377,5381,5406,5412,5422,5423,5438,5451,5473,5479,5495,5496,5499,5518,5526,5527,5532,5533,5543,5544,5556,5560,5569,5570,5572,5587,5592,5603,5604,5616,5623,5637,5641,5644,5650,5651,5652,5655,5660,5697,5698,5701,5703,5706,5707,5708,5710,5712,5714,5719,5726,5741,5755,5760,5761,5774,5775,5780,5785,5787,5792,5833,5845,5854,5858,5869,5873,5874,5882,5896,5902,5920,5923,5935,5965,5979,6004,6024,6025,6028,6042,6044,6046,6048,6061,6062,6065,6067,6070,6071,6082,6088,6089,6090,6092,6094,6136,6137,6144,6154,6190,6192,6194,6196,6205,6207,6209,6215,6217,6223,6226,6234,6241,6242,6243,6248,6270,6271,6272,6274,6280,6285,6322,6323,6325,6326,6327,6329,6330,6331,6332,6341,6374,6375,6384,6405,6406,6426,6429,6440,6441,6447,6476,6478,6490,6528,6530,6531,6586,6610,6656,6676,6685,6686,6687,6688,6707,6708,6714,6726,6729,6731,6733,6734,6735,6737,6751,6762,6764,6765,6778,6781,6832,6843,6845,6849,6864,6865,6901,6913,6944,6963,6978,7032,7060,7115,7136,7145,7148,7203,7211,7269,7271,7285,7295,7296,7297,7316,7322,7324,7373,7383,7386,7402,7451,7453,7456,7499,7500,7518,7585,7604,7628,7650,7665,7680,7691,7699,7700,7728,7731,7733,7741,7779,7790,7815,7873,7907,7939,7986,8002,8008,8019,8020,8095,8149,8168,8192,8212,8236,8335,8337,8343,8361,8365,8379,8402,8413,8415,8430,8436,8440,8465,8479,8480,8496,8497,8502,8503,8504,8505,8506,8524,8525,8526,8535,8549,8551,8563,8567,8569,8570,8571,8579,8584,8611,8612,8641,8654,8658,8676,8698,8699,8700,8701,8714,8715,8737,8747,8756,8757,8758,8759,8761,8783,8784,8795,8840,8846,8852,8865,8870,8872,8875,8876,8880,8889,8972,9003,9004,9005,9020,9038,9043,9070,9071,9114,9117,9144,9189,9190,9191,9207,9233,9247,9253,9256,9279,9280,9308,9371,9407,9408,9409])). % 187.89/187.72 cnf(11177,plain, % 187.89/187.72 (P1(f306(f306(f308(x111771),x111772),f231(f872(x111771,a859))))), % 187.89/187.72 inference(rename_variables,[],[3428])). % 187.89/187.72 cnf(11182,plain, % 187.89/187.72 (P1(f306(f306(f220(f872(x111821,a859)),f185(f872(x111821,a859))),x111822))), % 187.89/187.72 inference(rename_variables,[],[3711])). % 187.89/187.72 cnf(11185,plain, % 187.89/187.72 (~P1(f306(f306(f308(x111851),x111852),f185(f872(x111851,a859))))), % 187.89/187.72 inference(rename_variables,[],[4505])). % 187.89/187.72 cnf(11188,plain, % 187.89/187.72 (P1(f306(f306(f220(f872(x111881,a859)),x111882),f231(f872(x111881,a859))))), % 187.89/187.72 inference(rename_variables,[],[3646])). % 187.89/187.72 cnf(11192,plain, % 187.89/187.72 (P1(f306(f306(f220(f872(x111921,a859)),f306(f260(x111922,x111921,x111923),f185(f872(x111922,a859)))),x111924))), % 187.89/187.72 inference(scs_inference,[],[4527,3510,4420,10200,10210,10221,10330,10333,10336,10438,10551,10855,11022,4435,10422,10515,3064,3117,3227,10203,10264,10267,10357,10360,10650,3722,3107,3922,3170,3134,3115,3330,3201,3222,10463,3375,4513,3895,4445,10255,4503,10972,3376,3165,10322,4037,3897,10978,11104,4524,10907,11109,4525,11011,4526,11115,4528,4529,3184,3472,3628,3570,3777,3340,10341,10458,10529,10590,10593,10629,10723,10962,3715,3253,4493,10232,10235,10261,10731,10744,10865,4509,3702,3480,3847,3299,3300,3273,4490,4440,4001,3907,10799,3956,3629,3990,3646,10984,11047,11128,4514,10747,11120,3270,10350,10445,10576,3271,10705,10750,10753,10786,10812,10849,10887,3272,10433,10641,10726,4489,10298,10387,10500,10524,10768,10815,3428,10596,10860,10904,4505,10777,10789,10896,10914,10917,10975,11061,11069,11085,11123,11140,11149,3334,10623,10653,3365,3781,3720,10301,4502,10252,10611,10614,11064,3292,10656,10809,4081,4500,3788,4479,4482,3244,3248,4481,4484,3249,4480,4516,10226,10229,10481,10532,10535,10540,4522,3864,3709,10920,10926,3566,3711,10659,11000,11152,11182,3536,10579,10582,10665,10836,4519,4520,10716,10818,4140,4042,3741,4517,10274,10277,10617,3713,10585,3974,4538,4564,4613,4615,4645,4662,4669,4670,4709,4739,4745,4830,4856,4857,4918,4919,4941,4942,4955,4959,4981,4988,5005,5008,5009,5010,5015,5016,5039,5066,5067,5077,5082,5090,5135,5136,5144,5154,5158,5160,5170,5172,5178,5182,5197,5204,5207,5208,5209,5213,5248,5261,5268,5270,5271,5275,5276,5277,5285,5288,5293,5294,5295,5302,5306,5307,5308,5317,5321,5322,5323,5328,5341,5350,5362,5364,5372,5373,5377,5381,5406,5412,5422,5423,5438,5451,5473,5479,5495,5496,5499,5518,5526,5527,5532,5533,5543,5544,5556,5560,5569,5570,5572,5587,5592,5603,5604,5616,5623,5637,5641,5644,5650,5651,5652,5655,5660,5697,5698,5701,5703,5706,5707,5708,5710,5712,5714,5719,5726,5741,5755,5760,5761,5774,5775,5780,5785,5787,5792,5833,5845,5854,5858,5869,5873,5874,5882,5896,5902,5920,5923,5935,5965,5979,6004,6024,6025,6028,6042,6044,6046,6048,6061,6062,6065,6067,6070,6071,6082,6088,6089,6090,6092,6094,6136,6137,6144,6154,6190,6192,6194,6196,6205,6207,6209,6215,6217,6223,6226,6234,6241,6242,6243,6248,6270,6271,6272,6274,6280,6285,6322,6323,6325,6326,6327,6329,6330,6331,6332,6341,6374,6375,6384,6405,6406,6426,6429,6440,6441,6447,6476,6478,6490,6528,6530,6531,6586,6610,6656,6676,6685,6686,6687,6688,6707,6708,6714,6726,6729,6731,6733,6734,6735,6737,6751,6762,6764,6765,6778,6781,6832,6843,6845,6849,6864,6865,6901,6913,6944,6963,6978,7032,7060,7115,7136,7145,7148,7203,7211,7269,7271,7285,7295,7296,7297,7316,7322,7324,7373,7383,7386,7402,7451,7453,7456,7499,7500,7518,7585,7604,7628,7650,7665,7680,7691,7699,7700,7728,7731,7733,7741,7779,7790,7815,7873,7907,7939,7986,8002,8008,8019,8020,8095,8149,8168,8192,8212,8236,8335,8337,8343,8361,8365,8379,8402,8413,8415,8430,8436,8440,8465,8479,8480,8496,8497,8502,8503,8504,8505,8506,8524,8525,8526,8535,8549,8551,8563,8567,8569,8570,8571,8579,8584,8611,8612,8641,8654,8658,8676,8698,8699,8700,8701,8714,8715,8737,8747,8756,8757,8758,8759,8761,8783,8784,8795,8840,8846,8852,8865,8870,8872,8875,8876,8880,8889,8972,9003,9004,9005,9020,9038,9043,9070,9071,9114,9117,9144,9189,9190,9191,9207,9233,9247,9253,9256,9279,9280,9308,9371,9407,9408,9409,9434,9435,9453,9471,9477,9493,9516])). % 187.89/187.72 cnf(11193,plain, % 187.89/187.72 (P1(f306(f306(f220(f872(x111931,a859)),f185(f872(x111931,a859))),x111932))), % 187.89/187.72 inference(rename_variables,[],[3711])). % 187.89/187.72 cnf(11195,plain, % 187.89/187.72 (~P1(f306(f68(a865,x111951,x111952,x111953,f231(f872(a865,a859))),x111954))), % 187.89/187.72 inference(scs_inference,[],[4527,3510,4420,10200,10210,10221,10330,10333,10336,10438,10551,10855,11022,4435,10422,10515,3064,3117,3227,10203,10264,10267,10357,10360,10650,3722,3107,3922,3170,3134,3115,3330,3201,3222,10463,3375,4513,3895,4445,10255,4503,10972,3376,3165,10322,4037,3897,10978,11104,4524,10907,11109,4525,11011,4526,11115,4528,4529,3184,3472,3628,3570,3777,3340,10341,10458,10529,10590,10593,10629,10723,10962,3715,3253,4493,10232,10235,10261,10731,10744,10865,4509,3702,3480,3847,3299,3300,3273,4490,4440,4001,3907,10799,3956,3629,3990,3646,10984,11047,11128,4514,10747,11120,3270,10350,10445,10576,3271,10705,10750,10753,10786,10812,10849,10887,3272,10433,10641,10726,4489,10298,10387,10500,10524,10768,10815,3428,10596,10860,10904,4505,10777,10789,10896,10914,10917,10975,11061,11069,11085,11123,11140,11149,3334,10623,10653,3365,3781,3720,10301,4502,10252,10611,10614,11064,3292,10656,10809,4081,4500,3788,4479,4482,3244,3248,4481,4484,3249,4480,4516,10226,10229,10481,10532,10535,10540,4522,3864,3709,10920,10926,3566,3711,10659,11000,11152,11182,3536,10579,10582,10665,10836,4519,4520,10716,10818,4140,4042,3741,4517,10274,10277,10617,3713,10585,3974,4538,4564,4613,4615,4645,4662,4669,4670,4709,4739,4745,4830,4856,4857,4918,4919,4941,4942,4955,4959,4981,4988,5005,5008,5009,5010,5015,5016,5039,5066,5067,5077,5082,5090,5135,5136,5144,5154,5158,5160,5170,5172,5178,5182,5197,5204,5207,5208,5209,5213,5248,5261,5268,5270,5271,5275,5276,5277,5285,5288,5293,5294,5295,5302,5306,5307,5308,5317,5321,5322,5323,5328,5341,5350,5362,5364,5372,5373,5377,5381,5406,5412,5422,5423,5438,5451,5473,5479,5495,5496,5499,5518,5526,5527,5532,5533,5543,5544,5556,5560,5569,5570,5572,5587,5592,5603,5604,5616,5623,5637,5641,5644,5650,5651,5652,5655,5660,5697,5698,5701,5703,5706,5707,5708,5710,5712,5714,5719,5726,5741,5755,5760,5761,5774,5775,5780,5785,5787,5792,5833,5845,5854,5858,5869,5873,5874,5882,5896,5902,5920,5923,5935,5965,5979,6004,6024,6025,6028,6042,6044,6046,6048,6061,6062,6065,6067,6070,6071,6082,6088,6089,6090,6092,6094,6136,6137,6144,6154,6190,6192,6194,6196,6205,6207,6209,6215,6217,6223,6226,6234,6241,6242,6243,6248,6270,6271,6272,6274,6280,6285,6322,6323,6325,6326,6327,6329,6330,6331,6332,6341,6374,6375,6384,6405,6406,6426,6429,6440,6441,6447,6476,6478,6490,6528,6530,6531,6586,6610,6656,6676,6685,6686,6687,6688,6707,6708,6714,6726,6729,6731,6733,6734,6735,6737,6751,6762,6764,6765,6778,6781,6832,6843,6845,6849,6864,6865,6901,6913,6944,6963,6978,7032,7060,7115,7136,7145,7148,7203,7211,7269,7271,7285,7295,7296,7297,7316,7322,7324,7373,7383,7386,7402,7451,7453,7456,7499,7500,7518,7585,7604,7628,7650,7665,7680,7691,7699,7700,7728,7731,7733,7741,7779,7790,7815,7873,7907,7939,7986,8002,8008,8019,8020,8095,8149,8168,8192,8212,8236,8335,8337,8343,8361,8365,8379,8402,8413,8415,8430,8436,8440,8465,8479,8480,8496,8497,8502,8503,8504,8505,8506,8524,8525,8526,8535,8549,8551,8563,8567,8569,8570,8571,8579,8584,8611,8612,8641,8654,8658,8676,8698,8699,8700,8701,8714,8715,8737,8747,8756,8757,8758,8759,8761,8783,8784,8795,8840,8846,8852,8865,8870,8872,8875,8876,8880,8889,8972,9003,9004,9005,9020,9038,9043,9070,9071,9114,9117,9144,9189,9190,9191,9207,9233,9247,9253,9256,9279,9280,9308,9371,9407,9408,9409,9434,9435,9453,9471,9477,9493,9516,9538])). % 187.89/187.72 cnf(11206,plain, % 187.89/187.72 (P1(f306(f231(f872(x112061,a859)),x112062))), % 187.89/187.72 inference(rename_variables,[],[3334])). % 187.89/187.72 cnf(11214,plain, % 187.89/187.72 (~P1(f306(f306(f308(f871(f866(x112141),f866(x112141))),f306(f306(f236(f866(x112141),f866(x112141)),x112142),f120(x112141))),f137(x112141,x112143)))), % 187.89/187.72 inference(rename_variables,[],[4524])). % 187.89/187.72 cnf(11217,plain, % 187.89/187.72 (~P1(f306(f306(f308(f871(f866(x112171),f866(x112171))),f306(f306(f236(f866(x112171),f866(x112171)),x112172),f120(x112171))),f139(x112171,x112173)))), % 187.89/187.72 inference(rename_variables,[],[4525])). % 187.89/187.72 cnf(11220,plain, % 187.89/187.72 (~E(f306(f306(f143(x112201),x112202),x112203),x112203)), % 187.89/187.72 inference(rename_variables,[],[4445])). % 187.89/187.72 cnf(11223,plain, % 187.89/187.72 (~E(f306(a119,x112231),x112231)), % 187.89/187.72 inference(rename_variables,[],[4420])). % 187.89/187.72 cnf(11226,plain, % 187.89/187.72 (~P1(f306(f306(f308(x112261),x112262),f185(f872(x112261,a859))))), % 187.89/187.72 inference(rename_variables,[],[4505])). % 187.89/187.72 cnf(11231,plain, % 187.89/187.72 (P1(f306(f306(f308(f871(f866(x112311),f866(x112311))),f306(f306(f236(f866(x112311),f866(x112311)),x112312),x112312)),f150(x112311,f282(x112311,x112313))))), % 187.89/187.72 inference(rename_variables,[],[4031])). % 187.89/187.72 cnf(11236,plain, % 187.89/187.72 (~P1(f306(f306(f308(f871(f866(x112361),f866(x112361))),f306(f306(f236(f866(x112361),f866(x112361)),x112362),f120(x112361))),f137(x112361,x112363)))), % 187.89/187.72 inference(rename_variables,[],[4524])). % 187.89/187.72 cnf(11240,plain, % 187.89/187.72 (E(f306(f306(f143(x112401),f678(f282(x112401,x112402),f306(f306(f143(x112401),x112403),x112404),x112404,x112403,x112401)),f679(f282(x112401,x112402),f306(f306(f143(x112401),x112403),x112404),x112404,x112403,x112401)),f306(f306(f143(x112401),x112403),x112404))), % 187.89/187.72 inference(scs_inference,[],[4527,3510,4420,10200,10210,10221,10330,10333,10336,10438,10551,10855,11022,11025,4435,10422,10515,3064,3117,3227,10203,10264,10267,10357,10360,10650,3722,3107,3922,3170,3134,3115,3330,3201,3222,10463,3375,4513,3895,4445,10255,10419,4503,10972,3376,3165,10322,4037,3897,10978,11104,4524,10907,11109,11214,4525,11011,11112,4526,11115,4528,11169,4529,3184,3472,3628,3570,3777,3340,10341,10458,10529,10590,10593,10629,10723,10962,3715,3253,4493,10232,10235,10261,10731,10744,10865,4509,3702,3480,3847,3299,3300,3273,4490,4440,4031,11231,4001,3907,10799,3956,3629,3990,3646,10984,11047,11128,4514,10747,11120,3270,10350,10445,10576,3271,10705,10750,10753,10786,10812,10849,10887,3272,10433,10641,10726,4489,10298,10387,10500,10524,10768,10815,3428,10596,10860,10904,4505,10777,10789,10896,10914,10917,10975,11061,11069,11085,11123,11140,11149,11185,3334,10623,10653,10662,3365,3781,3720,10301,4502,10252,10611,10614,11064,3292,10656,10809,4081,4500,3788,4479,4482,3244,3248,4481,4484,3249,4480,4516,10226,10229,10481,10532,10535,10540,4522,3864,3709,10920,10926,3566,3711,10659,11000,11152,11182,3536,10579,10582,10665,10836,4519,4520,10716,10818,4140,4042,3741,4517,10274,10277,10617,3713,10585,3974,4538,4564,4613,4615,4645,4662,4669,4670,4709,4739,4745,4830,4856,4857,4918,4919,4941,4942,4955,4959,4981,4988,5005,5008,5009,5010,5015,5016,5039,5066,5067,5077,5082,5090,5135,5136,5144,5154,5158,5160,5170,5172,5178,5182,5197,5204,5207,5208,5209,5213,5248,5261,5268,5270,5271,5275,5276,5277,5285,5288,5293,5294,5295,5302,5306,5307,5308,5317,5321,5322,5323,5328,5341,5350,5362,5364,5372,5373,5377,5381,5406,5412,5422,5423,5438,5451,5473,5479,5495,5496,5499,5518,5526,5527,5532,5533,5543,5544,5556,5560,5569,5570,5572,5587,5592,5603,5604,5616,5623,5637,5641,5644,5650,5651,5652,5655,5660,5697,5698,5701,5703,5706,5707,5708,5710,5712,5714,5719,5726,5741,5755,5760,5761,5774,5775,5780,5785,5787,5792,5833,5845,5854,5858,5869,5873,5874,5882,5896,5902,5920,5923,5935,5965,5979,6004,6024,6025,6028,6042,6044,6046,6048,6061,6062,6065,6067,6070,6071,6082,6088,6089,6090,6092,6094,6136,6137,6144,6154,6190,6192,6194,6196,6205,6207,6209,6215,6217,6223,6226,6234,6241,6242,6243,6248,6270,6271,6272,6274,6280,6285,6322,6323,6325,6326,6327,6329,6330,6331,6332,6341,6374,6375,6384,6405,6406,6426,6429,6440,6441,6447,6476,6478,6490,6528,6530,6531,6586,6610,6656,6676,6685,6686,6687,6688,6707,6708,6714,6726,6729,6731,6733,6734,6735,6737,6751,6762,6764,6765,6778,6781,6832,6843,6845,6849,6864,6865,6901,6913,6944,6963,6978,7032,7060,7115,7136,7145,7148,7203,7211,7269,7271,7285,7295,7296,7297,7316,7322,7324,7373,7383,7386,7402,7451,7453,7456,7499,7500,7518,7585,7604,7628,7650,7665,7680,7691,7699,7700,7728,7731,7733,7741,7779,7790,7815,7873,7907,7939,7986,8002,8008,8019,8020,8095,8149,8168,8192,8212,8236,8335,8337,8343,8361,8365,8379,8402,8413,8415,8430,8436,8440,8465,8479,8480,8496,8497,8502,8503,8504,8505,8506,8524,8525,8526,8535,8549,8551,8563,8567,8569,8570,8571,8579,8584,8611,8612,8641,8654,8658,8676,8698,8699,8700,8701,8714,8715,8737,8747,8756,8757,8758,8759,8761,8783,8784,8795,8840,8846,8852,8865,8870,8872,8875,8876,8880,8889,8972,9003,9004,9005,9020,9038,9043,9070,9071,9114,9117,9144,9189,9190,9191,9207,9233,9247,9253,9256,9279,9280,9308,9371,9407,9408,9409,9434,9435,9453,9471,9477,9493,9516,9538,9546,9547,9548,9549,9565,9567,9572,9603,9604,9610,9611,9654,9655,9686,9696,9706,9708,9709])). % 187.89/187.72 cnf(11245,plain, % 187.89/187.72 (~P1(f306(f306(f308(x112451),x112452),f177(x112453,x112451,f179(x112453,x112451,x112454,f185(f872(x112453,a859))))))), % 187.89/187.72 inference(scs_inference,[],[4527,3510,4420,10200,10210,10221,10330,10333,10336,10438,10551,10855,11022,11025,4435,10422,10515,3064,3117,3227,10203,10264,10267,10357,10360,10650,3722,3107,3922,3170,3134,3115,3330,3201,3222,10463,3375,4513,3895,4445,10255,10419,4503,10972,3376,3165,10322,4037,3897,10978,11104,4524,10907,11109,11214,4525,11011,11112,4526,11115,4528,11169,4529,3184,3472,3628,3570,3777,3340,10341,10458,10529,10590,10593,10629,10723,10962,3715,3253,4493,10232,10235,10261,10731,10744,10865,4509,3702,3480,3847,3299,3300,3273,4490,4440,4031,11231,4001,3907,10799,3956,3629,3990,3646,10984,11047,11128,4514,10747,11120,3270,10350,10445,10576,3271,10705,10750,10753,10786,10812,10849,10887,3272,10433,10641,10726,4489,10298,10387,10500,10524,10768,10815,3428,10596,10860,10904,4505,10777,10789,10896,10914,10917,10975,11061,11069,11085,11123,11140,11149,11185,11226,3334,10623,10653,10662,3365,3781,3720,10301,4502,10252,10611,10614,11064,3292,10656,10809,4081,4500,3788,4479,4482,3244,3248,4481,4484,3249,4480,4516,10226,10229,10481,10532,10535,10540,4522,3864,3709,10920,10926,3566,3711,10659,11000,11152,11182,3536,10579,10582,10665,10836,4519,4520,10716,10818,4140,4042,3741,4517,10274,10277,10617,3713,10585,3974,4538,4564,4613,4615,4645,4662,4669,4670,4709,4739,4745,4830,4856,4857,4918,4919,4941,4942,4955,4959,4981,4988,5005,5008,5009,5010,5015,5016,5039,5066,5067,5077,5082,5090,5135,5136,5144,5154,5158,5160,5170,5172,5178,5182,5197,5204,5207,5208,5209,5213,5248,5261,5268,5270,5271,5275,5276,5277,5285,5288,5293,5294,5295,5302,5306,5307,5308,5317,5321,5322,5323,5328,5341,5350,5362,5364,5372,5373,5377,5381,5406,5412,5422,5423,5438,5451,5473,5479,5495,5496,5499,5518,5526,5527,5532,5533,5543,5544,5556,5560,5569,5570,5572,5587,5592,5603,5604,5616,5623,5637,5641,5644,5650,5651,5652,5655,5660,5697,5698,5701,5703,5706,5707,5708,5710,5712,5714,5719,5726,5741,5755,5760,5761,5774,5775,5780,5785,5787,5792,5833,5845,5854,5858,5869,5873,5874,5882,5896,5902,5920,5923,5935,5965,5979,6004,6024,6025,6028,6042,6044,6046,6048,6061,6062,6065,6067,6070,6071,6082,6088,6089,6090,6092,6094,6136,6137,6144,6154,6190,6192,6194,6196,6205,6207,6209,6215,6217,6223,6226,6234,6241,6242,6243,6248,6270,6271,6272,6274,6280,6285,6322,6323,6325,6326,6327,6329,6330,6331,6332,6341,6374,6375,6384,6405,6406,6426,6429,6440,6441,6447,6476,6478,6490,6528,6530,6531,6586,6610,6656,6676,6685,6686,6687,6688,6707,6708,6714,6726,6729,6731,6733,6734,6735,6737,6751,6762,6764,6765,6778,6781,6832,6843,6845,6849,6864,6865,6901,6913,6944,6963,6978,7032,7060,7115,7136,7145,7148,7203,7211,7269,7271,7285,7295,7296,7297,7316,7322,7324,7373,7383,7386,7402,7451,7453,7456,7499,7500,7518,7585,7604,7628,7650,7665,7680,7691,7699,7700,7728,7731,7733,7741,7779,7790,7815,7873,7907,7939,7986,8002,8008,8019,8020,8095,8149,8168,8192,8212,8236,8335,8337,8343,8361,8365,8379,8402,8413,8415,8430,8436,8440,8465,8479,8480,8496,8497,8502,8503,8504,8505,8506,8524,8525,8526,8535,8549,8551,8563,8567,8569,8570,8571,8579,8584,8611,8612,8641,8654,8658,8676,8698,8699,8700,8701,8714,8715,8737,8747,8756,8757,8758,8759,8761,8783,8784,8795,8840,8846,8852,8865,8870,8872,8875,8876,8880,8889,8972,9003,9004,9005,9020,9038,9043,9070,9071,9114,9117,9144,9189,9190,9191,9207,9233,9247,9253,9256,9279,9280,9308,9371,9407,9408,9409,9434,9435,9453,9471,9477,9493,9516,9538,9546,9547,9548,9549,9565,9567,9572,9603,9604,9610,9611,9654,9655,9686,9696,9706,9708,9709,9719,9733])). % 187.89/187.72 cnf(11246,plain, % 187.89/187.72 (~P1(f306(f306(f308(x112461),x112462),f185(f872(x112461,a859))))), % 187.89/187.72 inference(rename_variables,[],[4505])). % 187.89/187.72 cnf(11249,plain, % 187.89/187.72 (~P1(f306(f306(f308(x112491),x112492),f185(f872(x112491,a859))))), % 187.89/187.72 inference(rename_variables,[],[4505])). % 187.89/187.72 cnf(11252,plain, % 187.89/187.72 (~P1(f306(f306(f308(x112521),x112522),f185(f872(x112521,a859))))), % 187.89/187.72 inference(rename_variables,[],[4505])). % 187.89/187.72 cnf(11255,plain, % 187.89/187.72 (P1(f306(f306(f308(x112551),x112552),f231(f872(x112551,a859))))), % 187.89/187.72 inference(rename_variables,[],[3428])). % 187.89/187.72 cnf(11260,plain, % 187.89/187.72 (~P1(f306(f306(f308(f871(x112601,x112601)),f306(f306(f236(x112601,x112601),x112602),x112603)),f145(x112601,f120(f872(x112601,a865)))))), % 187.89/187.72 inference(rename_variables,[],[4522])). % 187.89/187.72 cnf(11263,plain, % 187.89/187.72 (~E(f306(f285(x112631,f872(x112631,a859),x112632),x112633),f306(f283(x112631),x112633))), % 187.89/187.72 inference(rename_variables,[],[4503])). % 187.89/187.72 cnf(11266,plain, % 187.89/187.72 (~E(f306(f285(x112661,f872(x112661,a859),x112662),x112663),f306(f283(x112661),x112663))), % 187.89/187.72 inference(rename_variables,[],[4503])). % 187.89/187.72 cnf(11271,plain, % 187.89/187.72 (~P1(f306(f306(f308(f871(f866(x112711),f866(x112711))),f306(f306(f236(f866(x112711),f866(x112711)),x112712),f120(x112711))),f137(x112711,x112713)))), % 187.89/187.72 inference(rename_variables,[],[4524])). % 187.89/187.72 cnf(11277,plain, % 187.89/187.72 (~P1(f306(f306(f308(f871(f866(x112771),f866(x112771))),f306(f306(f236(f866(x112771),f866(x112771)),x112772),f120(x112771))),f137(x112771,x112773)))), % 187.89/187.72 inference(rename_variables,[],[4524])). % 187.89/187.72 cnf(11280,plain, % 187.89/187.72 (~P1(f306(f306(f308(x112801),x112802),f185(f872(x112801,a859))))), % 187.89/187.72 inference(rename_variables,[],[4505])). % 187.89/187.72 cnf(11283,plain, % 187.89/187.72 (~P1(f306(f306(f185(f872(x112831,f872(x112832,a859))),x112833),x112834))), % 187.89/187.72 inference(rename_variables,[],[4520])). % 187.89/187.72 cnf(11286,plain, % 187.89/187.72 (~P1(f306(f306(f221(a865),x112861),f2(a865)))), % 187.89/187.72 inference(rename_variables,[],[4493])). % 187.89/187.72 cnf(11290,plain, % 187.89/187.72 (P1(f306(f306(f308(f871(x112901,x112902)),f306(f306(f236(x112901,x112902),f306(x112903,x112904)),f306(x112905,x112904))),f306(f285(f871(x112906,x112906),f871(x112901,x112902),f246(x112906,x112901,x112906,x112902,x112903,x112905)),f282(x112906,x112907))))), % 187.89/187.72 inference(scs_inference,[],[4527,3510,4420,10200,10210,10221,10330,10333,10336,10438,10551,10855,11022,11025,4435,10422,10515,3064,3117,3227,10203,10264,10267,10357,10360,10650,3722,3107,3922,3170,3134,3115,3330,3201,3222,10463,3375,4513,3895,4445,10255,10419,4503,10972,11042,11263,3376,3165,10322,4037,3897,10978,11104,11155,4524,10907,11109,11214,11236,11271,4525,11011,11112,11217,4526,11115,4528,11169,4529,3184,3472,3628,3570,3777,3340,10341,10458,10529,10590,10593,10629,10723,10962,3715,3253,4493,10232,10235,10261,10731,10744,10865,4509,3702,3480,3847,3299,3300,3273,4490,4440,4031,11231,4001,3907,10799,3956,3629,3990,3646,10984,11047,11128,4514,10747,11120,3270,10350,10445,10576,3271,10705,10750,10753,10786,10812,10849,10887,3272,10433,10641,10726,4489,10298,10387,10500,10524,10768,10815,3428,10596,10860,10904,11177,4505,10777,10789,10896,10914,10917,10975,11061,11069,11085,11123,11140,11149,11185,11226,11246,11249,11252,3334,10623,10653,10662,3365,3781,3720,10301,4502,10252,10611,10614,11064,3292,10656,10809,4081,4500,3788,4479,4482,3244,3248,4481,4484,3249,4480,4516,10226,10229,10481,10532,10535,10540,4522,11143,3864,3709,10920,10926,3566,3711,10659,11000,11152,11182,3536,10579,10582,10665,10836,4519,4520,10716,10818,11131,4140,4042,3741,4517,10274,10277,10617,3713,10585,3974,4538,4564,4613,4615,4645,4662,4669,4670,4709,4739,4745,4830,4856,4857,4918,4919,4941,4942,4955,4959,4981,4988,5005,5008,5009,5010,5015,5016,5039,5066,5067,5077,5082,5090,5135,5136,5144,5154,5158,5160,5170,5172,5178,5182,5197,5204,5207,5208,5209,5213,5248,5261,5268,5270,5271,5275,5276,5277,5285,5288,5293,5294,5295,5302,5306,5307,5308,5317,5321,5322,5323,5328,5341,5350,5362,5364,5372,5373,5377,5381,5406,5412,5422,5423,5438,5451,5473,5479,5495,5496,5499,5518,5526,5527,5532,5533,5543,5544,5556,5560,5569,5570,5572,5587,5592,5603,5604,5616,5623,5637,5641,5644,5650,5651,5652,5655,5660,5697,5698,5701,5703,5706,5707,5708,5710,5712,5714,5719,5726,5741,5755,5760,5761,5774,5775,5780,5785,5787,5792,5833,5845,5854,5858,5869,5873,5874,5882,5896,5902,5920,5923,5935,5965,5979,6004,6024,6025,6028,6042,6044,6046,6048,6061,6062,6065,6067,6070,6071,6082,6088,6089,6090,6092,6094,6136,6137,6144,6154,6190,6192,6194,6196,6205,6207,6209,6215,6217,6223,6226,6234,6241,6242,6243,6248,6270,6271,6272,6274,6280,6285,6322,6323,6325,6326,6327,6329,6330,6331,6332,6341,6374,6375,6384,6405,6406,6426,6429,6440,6441,6447,6476,6478,6490,6528,6530,6531,6586,6610,6656,6676,6685,6686,6687,6688,6707,6708,6714,6726,6729,6731,6733,6734,6735,6737,6751,6762,6764,6765,6778,6781,6832,6843,6845,6849,6864,6865,6901,6913,6944,6963,6978,7032,7060,7115,7136,7145,7148,7203,7211,7269,7271,7285,7295,7296,7297,7316,7322,7324,7373,7383,7386,7402,7451,7453,7456,7499,7500,7518,7585,7604,7628,7650,7665,7680,7691,7699,7700,7728,7731,7733,7741,7779,7790,7815,7873,7907,7939,7986,8002,8008,8019,8020,8095,8149,8168,8192,8212,8236,8335,8337,8343,8361,8365,8379,8402,8413,8415,8430,8436,8440,8465,8479,8480,8496,8497,8502,8503,8504,8505,8506,8524,8525,8526,8535,8549,8551,8563,8567,8569,8570,8571,8579,8584,8611,8612,8641,8654,8658,8676,8698,8699,8700,8701,8714,8715,8737,8747,8756,8757,8758,8759,8761,8783,8784,8795,8840,8846,8852,8865,8870,8872,8875,8876,8880,8889,8972,9003,9004,9005,9020,9038,9043,9070,9071,9114,9117,9144,9189,9190,9191,9207,9233,9247,9253,9256,9279,9280,9308,9371,9407,9408,9409,9434,9435,9453,9471,9477,9493,9516,9538,9546,9547,9548,9549,9565,9567,9572,9603,9604,9610,9611,9654,9655,9686,9696,9706,9708,9709,9719,9733,9737,9765,9797,9802,9859,9902,9903,9905,9915,9916,9936,9941,9964,9969,9984,10036])). % 187.89/187.72 cnf(11293,plain, % 187.89/187.72 (~P1(f306(f306(f308(x112931),x112932),f185(f872(x112931,a859))))), % 187.89/187.72 inference(rename_variables,[],[4505])). % 187.89/187.72 cnf(11296,plain, % 187.89/187.72 (~P1(f306(f306(f308(x112961),x112962),f185(f872(x112961,a859))))), % 187.89/187.72 inference(rename_variables,[],[4505])). % 187.89/187.72 cnf(11299,plain, % 187.89/187.72 (P1(f306(f306(f308(x112991),f306(x112992,x112993)),f306(f285(x112994,x112991,x112992),f231(f872(x112994,a859)))))), % 187.89/187.72 inference(rename_variables,[],[3864])). % 187.89/187.72 cnf(11302,plain, % 187.89/187.72 (~P1(f306(f306(f308(f871(x113021,x113021)),f306(f306(f236(x113021,x113021),x113022),x113023)),f145(x113021,f120(f872(x113021,a865)))))), % 187.89/187.72 inference(rename_variables,[],[4522])). % 187.89/187.72 cnf(11310,plain, % 187.89/187.72 (E(f121(x113101,f120(x113101)),f120(x113101))), % 187.89/187.72 inference(rename_variables,[],[3117])). % 187.89/187.72 cnf(11313,plain, % 187.89/187.72 (~E(f306(a119,x113131),x113131)), % 187.89/187.72 inference(rename_variables,[],[4420])). % 187.89/187.72 cnf(11320,plain, % 187.89/187.72 (~E(f306(a119,x113201),x113201)), % 187.89/187.72 inference(rename_variables,[],[4420])). % 187.89/187.72 cnf(11325,plain, % 187.89/187.72 (E(f306(f232(x113251,x113251),f233(x113251,x113252)),x113252)), % 187.89/187.72 inference(rename_variables,[],[3227])). % 187.89/187.72 cnf(11328,plain, % 187.89/187.72 (E(f306(f232(x113281,x113281),f233(x113281,x113282)),x113282)), % 187.89/187.72 inference(rename_variables,[],[3227])). % 187.89/187.72 cnf(11334,plain, % 187.89/187.72 (~E(f306(a119,x113341),x113341)), % 187.89/187.72 inference(rename_variables,[],[4420])). % 187.89/187.72 cnf(11341,plain, % 187.89/187.72 (~E(f306(f306(f81(a1),x113411),x113411),a104)), % 187.89/187.72 inference(rename_variables,[],[4443])). % 187.89/187.72 cnf(11350,plain, % 187.89/187.72 (E(f306(f306(f22(a865),f2(a865)),x113501),f2(a865))), % 187.89/187.72 inference(rename_variables,[],[3185])). % 187.89/187.72 cnf(11353,plain, % 187.89/187.72 (~P1(f306(f306(f221(a865),x113531),f2(a865)))), % 187.89/187.72 inference(rename_variables,[],[4493])). % 187.89/187.72 cnf(11360,plain, % 187.89/187.72 (E(f306(f306(f81(a1),f306(f306(f82(a1),x113601),f306(f306(f40(a1),x113602),x113601))),f46(a1,x113602,x113601)),x113602)), % 187.89/187.72 inference(rename_variables,[],[3812])). % 187.89/187.72 cnf(11384,plain, % 187.89/187.72 (~E(f306(a119,x113841),x113841)), % 187.89/187.72 inference(rename_variables,[],[4420])). % 187.89/187.72 cnf(11387,plain, % 187.89/187.72 (~E(f306(a119,x113871),x113871)), % 187.89/187.72 inference(rename_variables,[],[4420])). % 187.89/187.72 cnf(11409,plain, % 187.89/187.72 (~E(f306(a119,x114091),x114091)), % 187.89/187.72 inference(rename_variables,[],[4420])). % 187.89/187.72 cnf(11412,plain, % 187.89/187.72 (~E(f306(f306(f143(x114121),x114122),x114123),x114123)), % 187.89/187.72 inference(rename_variables,[],[4445])). % 187.89/187.72 cnf(11419,plain, % 187.89/187.72 (~P1(f306(f64(x114191,x114192,f185(f872(x114191,a859))),x114193))), % 187.89/187.72 inference(rename_variables,[],[4516])). % 187.89/187.72 cnf(11422,plain, % 187.89/187.72 (~P1(f306(f306(f185(f872(x114221,f872(x114222,a859))),x114223),x114224))), % 187.89/187.72 inference(rename_variables,[],[4520])). % 187.89/187.72 cnf(11425,plain, % 187.89/187.72 (P1(f306(f306(f308(x114251),x114252),f231(f872(x114251,a859))))), % 187.89/187.72 inference(rename_variables,[],[3428])). % 187.89/187.72 cnf(11437,plain, % 187.89/187.72 (P1(f306(f306(f193(a24),x114371),x114371))), % 187.89/187.72 inference(rename_variables,[],[3270])). % 187.89/187.72 cnf(11444,plain, % 187.89/187.72 (P1(f306(f68(x114441,x114442,x114443,x114444,f185(f872(x114441,a859))),x114444))), % 187.89/187.72 inference(rename_variables,[],[4177])). % 187.89/187.72 cnf(11445,plain, % 187.89/187.72 (E(f306(f232(x114451,x114451),f233(x114451,x114452)),x114452)), % 187.89/187.72 inference(rename_variables,[],[3227])). % 187.89/187.72 cnf(11450,plain, % 187.89/187.72 (~P1(f306(f306(f185(f872(x114501,f872(x114502,a859))),x114503),x114504))), % 187.89/187.72 inference(rename_variables,[],[4520])). % 187.89/187.72 cnf(11461,plain, % 187.89/187.72 (~P1(f306(f306(f221(a865),f306(f306(f81(a865),x114611),x114612)),x114612))), % 187.89/187.72 inference(rename_variables,[],[4517])). % 187.89/187.72 cnf(11464,plain, % 187.89/187.72 (~P1(f306(f306(f221(a1),f306(f107(a1),x114641)),f2(a1)))), % 187.89/187.72 inference(rename_variables,[],[4509])). % 187.89/187.72 cnf(11480,plain, % 187.89/187.72 (~E(f306(f306(f225(a865),f306(a119,x114801)),x114801),f306(a119,x114801))), % 187.89/187.72 inference(scs_inference,[],[4527,3510,4420,10200,10210,10221,10330,10333,10336,10438,10551,10855,11022,11025,11223,11313,11320,11334,11384,11387,4435,10422,10515,3189,2876,2882,2886,2887,2894,2911,2923,2929,2936,2937,2938,2943,2970,3004,3005,3021,3030,3033,3044,3050,3162,3064,4416,3117,11310,3227,10203,10264,10267,10357,10360,10650,10929,11325,11328,3722,3107,3922,3812,11360,3170,3134,3115,3330,3201,3222,10463,3375,4513,3895,4445,10255,10419,11220,4503,10972,11042,11263,11266,3376,3165,10322,10626,3166,3086,3185,11350,4037,3897,10978,11104,11155,4524,10907,11109,11214,11236,11271,11277,4525,11011,11112,11217,4526,11115,4528,11169,4529,3184,3472,3628,4443,3570,3777,3340,10341,10458,10529,10590,10593,10629,10723,10962,3715,3253,4493,10232,10235,10261,10731,10744,10865,11286,11353,4509,3702,3480,3847,3299,3300,3273,4490,4440,3464,4510,4031,11231,3589,4001,3907,10799,3956,3629,3990,3646,10984,11047,11128,4514,10747,11120,3270,10350,10445,10576,10636,3271,10705,10750,10753,10786,10812,10849,10887,3272,10433,10641,10726,4489,10298,10387,10500,10524,10768,10815,3428,10596,10860,10904,11177,11255,4505,10777,10789,10896,10914,10917,10975,11061,11069,11085,11123,11140,11149,11185,11226,11246,11249,11252,11280,11293,3334,10623,10653,10662,3365,3781,3720,10301,4502,10252,10611,10614,11064,11082,3292,10656,10809,4081,4500,3788,4479,4482,3244,3248,4481,4484,3249,4480,4177,4516,10226,10229,10481,10532,10535,10540,10949,4522,11143,11260,3864,3709,10920,10926,3566,3711,10659,11000,11152,11182,3536,10579,10582,10665,10836,4519,4520,10716,10818,11131,11283,11422,4140,4042,3741,4517,10274,10277,10617,10620,3713,10585,3974,4521,4538,4564,4613,4615,4645,4662,4669,4670,4709,4739,4745,4830,4856,4857,4918,4919,4941,4942,4955,4959,4981,4988,5005,5008,5009,5010,5015,5016,5039,5066,5067,5077,5082,5090,5135,5136,5144,5154,5158,5160,5170,5172,5178,5182,5197,5204,5207,5208,5209,5213,5248,5261,5268,5270,5271,5275,5276,5277,5285,5288,5293,5294,5295,5302,5306,5307,5308,5317,5321,5322,5323,5328,5341,5350,5362,5364,5372,5373,5377,5381,5406,5412,5422,5423,5438,5451,5473,5479,5495,5496,5499,5518,5526,5527,5532,5533,5543,5544,5556,5560,5569,5570,5572,5587,5592,5603,5604,5616,5623,5637,5641,5644,5650,5651,5652,5655,5660,5697,5698,5701,5703,5706,5707,5708,5710,5712,5714,5719,5726,5741,5755,5760,5761,5774,5775,5780,5785,5787,5792,5833,5845,5854,5858,5869,5873,5874,5882,5896,5902,5920,5923,5935,5965,5979,6004,6024,6025,6028,6042,6044,6046,6048,6061,6062,6065,6067,6070,6071,6082,6088,6089,6090,6092,6094,6136,6137,6144,6154,6190,6192,6194,6196,6205,6207,6209,6215,6217,6223,6226,6234,6241,6242,6243,6248,6270,6271,6272,6274,6280,6285,6322,6323,6325,6326,6327,6329,6330,6331,6332,6341,6374,6375,6384,6405,6406,6426,6429,6440,6441,6447,6476,6478,6490,6528,6530,6531,6586,6610,6656,6676,6685,6686,6687,6688,6707,6708,6714,6726,6729,6731,6733,6734,6735,6737,6751,6762,6764,6765,6778,6781,6832,6843,6845,6849,6864,6865,6901,6913,6944,6963,6978,7032,7060,7115,7136,7145,7148,7203,7211,7269,7271,7285,7295,7296,7297,7316,7322,7324,7373,7383,7386,7402,7451,7453,7456,7499,7500,7518,7585,7604,7628,7650,7665,7680,7691,7699,7700,7728,7731,7733,7741,7779,7790,7815,7873,7907,7939,7986,8002,8008,8019,8020,8095,8149,8168,8192,8212,8236,8335,8337,8343,8361,8365,8379,8402,8413,8415,8430,8436,8440,8465,8479,8480,8496,8497,8502,8503,8504,8505,8506,8524,8525,8526,8535,8549,8551,8563,8567,8569,8570,8571,8579,8584,8611,8612,8641,8654,8658,8676,8698,8699,8700,8701,8714,8715,8737,8747,8756,8757,8758,8759,8761,8783,8784,8795,8840,8846,8852,8865,8870,8872,8875,8876,8880,8889,8972,9003,9004,9005,9020,9038,9043,9070,9071,9114,9117,9144,9189,9190,9191,9207,9233,9247,9253,9256,9279,9280,9308,9371,9407,9408,9409,9434,9435,9453,9471,9477,9493,9516,9538,9546,9547,9548,9549,9565,9567,9572,9603,9604,9610,9611,9654,9655,9686,9696,9706,9708,9709,9719,9733,9737,9765,9797,9802,9859,9902,9903,9905,9915,9916,9936,9941,9964,9969,9984,10036,10110,10111,10168,10184,2,8,9,4551,4552,4570,4601,4602,4604,4631,4637,4638,4649,4698,4700,4730,4744,4774,4871,4872,4886,4906,4962,4963,4966,4967,4969,4971,4972,4984,4985,4995,5006,5007,5013,5032,5033,5054,5059,5060,5061,5062,5065,5073,5076,5083,5084,5085,5150,5156,5157,5164,5194,5205,5211,5227,5247,5254,5255,5256,5265,5274,5281,5283,5284,5290,5298,5299,5309,5313,5314,5315,5316,5318,5319,5324])). % 187.89/187.72 cnf(11489,plain, % 187.89/187.72 (E(f306(f232(x114891,x114891),f233(x114891,x114892)),x114892)), % 187.89/187.72 inference(rename_variables,[],[3227])). % 187.89/187.72 cnf(11494,plain, % 187.89/187.72 (E(f306(f232(x114941,x114941),f233(x114941,x114942)),x114942)), % 187.89/187.72 inference(rename_variables,[],[3227])). % 187.89/187.72 cnf(11497,plain, % 187.89/187.72 (~P1(f306(f306(f221(a1),f306(f107(a1),x114971)),f2(a1)))), % 187.89/187.72 inference(rename_variables,[],[4509])). % 187.89/187.72 cnf(11502,plain, % 187.89/187.72 (~E(f306(a119,x115021),x115021)), % 187.89/187.72 inference(rename_variables,[],[4420])). % 187.89/187.72 cnf(11511,plain, % 187.89/187.72 (~P1(f306(f306(f221(a865),x115111),x115111))), % 187.89/187.72 inference(rename_variables,[],[4489])). % 187.89/187.72 cnf(11532,plain, % 187.89/187.72 (~P1(f306(f306(f221(a1),f306(f107(a1),x115321)),f2(a1)))), % 187.89/187.72 inference(rename_variables,[],[4509])). % 187.89/187.72 cnf(11547,plain, % 187.89/187.72 (~P1(f306(f306(f220(a865),f306(a119,x115471)),x115471))), % 187.89/187.72 inference(rename_variables,[],[4502])). % 187.89/187.72 cnf(11548,plain, % 187.89/187.72 (~E(f306(a119,x115481),x115481)), % 187.89/187.72 inference(rename_variables,[],[4420])). % 187.89/187.72 cnf(11558,plain, % 187.89/187.72 (~P1(f306(f306(f221(a865),f306(f306(f81(a865),x115581),x115582)),x115581))), % 187.89/187.72 inference(rename_variables,[],[4518])). % 187.89/187.72 cnf(11561,plain, % 187.89/187.72 (~P1(f306(f306(f221(a1),f306(f107(a1),x115611)),f2(a1)))), % 187.89/187.72 inference(rename_variables,[],[4509])). % 187.89/187.72 cnf(11564,plain, % 187.89/187.72 (~E(f306(a119,x115641),x115641)), % 187.89/187.72 inference(rename_variables,[],[4420])). % 187.89/187.72 cnf(11577,plain, % 187.89/187.72 (P1(f306(f306(f308(x115771),x115772),f306(f306(f284(x115771),x115772),x115773)))), % 187.89/187.72 inference(rename_variables,[],[3579])). % 187.89/187.72 cnf(11578,plain, % 187.89/187.72 (~P1(f306(f306(f220(a1),f2(a1)),f306(f80(a1),f306(f107(a1),f306(a119,x115781)))))), % 187.89/187.72 inference(rename_variables,[],[4519])). % 187.89/187.72 cnf(11581,plain, % 187.89/187.72 (P1(f306(f306(f221(a865),f306(f306(f22(a865),x115811),x115812)),f306(a119,x115811)))), % 187.89/187.72 inference(rename_variables,[],[3715])). % 187.89/187.72 cnf(11584,plain, % 187.89/187.72 (P1(f306(f306(f220(a865),f46(a865,x115841,x115842)),x115841))), % 187.89/187.72 inference(rename_variables,[],[3720])). % 187.89/187.72 cnf(11590,plain, % 187.89/187.72 (E(f306(f306(f122(x115901),x115902),f120(x115901)),x115902)), % 187.89/187.72 inference(rename_variables,[],[3202])). % 187.89/187.72 cnf(11593,plain, % 187.89/187.72 (E(f306(f232(x115931,x115931),f233(x115931,x115932)),x115932)), % 187.89/187.72 inference(rename_variables,[],[3227])). % 187.89/187.72 cnf(11596,plain, % 187.89/187.72 (E(f306(f74(x115961,x115962,x115961,x115963),f35(x115961)),x115963)), % 187.89/187.72 inference(rename_variables,[],[3722])). % 187.89/187.72 cnf(11602,plain, % 187.89/187.72 (~P1(f306(f306(f220(a865),f306(a119,x116021)),x116021))), % 187.89/187.72 inference(rename_variables,[],[4502])). % 187.89/187.72 cnf(11611,plain, % 187.89/187.72 (~P1(f306(f306(f221(a865),x116111),x116111))), % 187.89/187.72 inference(rename_variables,[],[4489])). % 187.89/187.72 cnf(11614,plain, % 187.89/187.72 (P1(f306(f306(f220(a865),f46(a865,x116141,x116142)),x116141))), % 187.89/187.72 inference(rename_variables,[],[3720])). % 187.89/187.72 cnf(11615,plain, % 187.89/187.72 (P1(f306(f306(f220(a865),f2(a865)),x116151))), % 187.89/187.72 inference(rename_variables,[],[3292])). % 187.89/187.72 cnf(11617,plain, % 187.89/187.72 (~P1(f306(f306(f220(a1),f79(a1)),f2(a1)))), % 187.89/187.72 inference(scs_inference,[],[4527,3510,4420,10200,10210,10221,10330,10333,10336,10438,10551,10855,11022,11025,11223,11313,11320,11334,11384,11387,11409,11502,11548,4435,10422,10515,3189,2875,2876,2882,2883,2886,2887,2894,2911,2923,2929,2936,2937,2938,2943,2970,3004,3005,3018,3019,3021,3028,3029,3030,3031,3033,3044,3050,3162,3064,4416,3117,11310,3313,3227,10203,10264,10267,10357,10360,10650,10929,11325,11328,11445,11489,11494,3202,11590,3722,10969,11596,3107,3922,3812,11360,3170,3134,3129,3115,3330,3201,3222,10463,3375,4513,3895,4445,10255,10419,11220,4503,10972,11042,11263,11266,3376,3165,10322,10626,3166,3433,3086,3185,11350,4037,3897,10978,11104,11155,4524,10907,11109,11214,11236,11271,11277,4525,11011,11112,11217,4526,11115,4528,11169,4529,3184,3472,3628,4316,4317,4443,3570,3777,3340,10341,10458,10529,10590,10593,10629,10723,10962,3715,3253,4493,10232,10235,10261,10731,10744,10865,11286,11353,4509,11464,11497,11532,3702,3480,3847,3299,3300,3273,4490,4440,3464,4510,4031,11231,3589,4001,3907,10799,3956,3629,3990,3646,10984,11047,11128,4514,10747,11120,3270,10350,10445,10576,10636,3271,10705,10750,10753,10786,10812,10849,10887,3272,10433,10641,10726,4489,10298,10387,10500,10524,10768,10815,10825,11511,3428,10596,10860,10904,11177,11255,4505,10777,10789,10896,10914,10917,10975,11061,11069,11085,11123,11140,11149,11185,11226,11246,11249,11252,11280,11293,3334,10623,10653,10662,3371,3365,3781,3720,10301,11584,4502,10252,10611,10614,11064,11082,11547,3292,10656,10809,10880,4081,4500,3788,4479,4482,3244,3248,4481,4484,3249,4480,3579,4177,4516,10226,10229,10481,10532,10535,10540,10949,4522,11143,11260,3864,3709,10920,10926,3566,3711,10659,11000,11152,11182,3536,10579,10582,10665,10836,4519,4520,10716,10818,11131,11283,11422,4140,4042,3741,4517,10274,10277,10617,10620,4518,3713,10585,3974,4521,4538,4564,4613,4615,4645,4662,4669,4670,4709,4739,4745,4830,4856,4857,4918,4919,4941,4942,4955,4959,4981,4988,5005,5008,5009,5010,5015,5016,5039,5066,5067,5077,5082,5090,5135,5136,5144,5154,5158,5160,5170,5172,5178,5182,5197,5204,5207,5208,5209,5213,5248,5261,5268,5270,5271,5275,5276,5277,5285,5288,5293,5294,5295,5302,5306,5307,5308,5317,5321,5322,5323,5328,5341,5350,5362,5364,5372,5373,5377,5381,5406,5412,5422,5423,5438,5451,5473,5479,5495,5496,5499,5518,5526,5527,5532,5533,5543,5544,5556,5560,5569,5570,5572,5587,5592,5603,5604,5616,5623,5637,5641,5644,5650,5651,5652,5655,5660,5697,5698,5701,5703,5706,5707,5708,5710,5712,5714,5719,5726,5741,5755,5760,5761,5774,5775,5780,5785,5787,5792,5833,5845,5854,5858,5869,5873,5874,5882,5896,5902,5920,5923,5935,5965,5979,6004,6024,6025,6028,6042,6044,6046,6048,6061,6062,6065,6067,6070,6071,6082,6088,6089,6090,6092,6094,6136,6137,6144,6154,6190,6192,6194,6196,6205,6207,6209,6215,6217,6223,6226,6234,6241,6242,6243,6248,6270,6271,6272,6274,6280,6285,6322,6323,6325,6326,6327,6329,6330,6331,6332,6341,6374,6375,6384,6405,6406,6426,6429,6440,6441,6447,6476,6478,6490,6528,6530,6531,6586,6610,6656,6676,6685,6686,6687,6688,6707,6708,6714,6726,6729,6731,6733,6734,6735,6737,6751,6762,6764,6765,6778,6781,6832,6843,6845,6849,6864,6865,6901,6913,6944,6963,6978,7032,7060,7115,7136,7145,7148,7203,7211,7269,7271,7285,7295,7296,7297,7316,7322,7324,7373,7383,7386,7402,7451,7453,7456,7499,7500,7518,7585,7604,7628,7650,7665,7680,7691,7699,7700,7728,7731,7733,7741,7779,7790,7815,7873,7907,7939,7986,8002,8008,8019,8020,8095,8149,8168,8192,8212,8236,8335,8337,8343,8361,8365,8379,8402,8413,8415,8430,8436,8440,8465,8479,8480,8496,8497,8502,8503,8504,8505,8506,8524,8525,8526,8535,8549,8551,8563,8567,8569,8570,8571,8579,8584,8611,8612,8641,8654,8658,8676,8698,8699,8700,8701,8714,8715,8737,8747,8756,8757,8758,8759,8761,8783,8784,8795,8840,8846,8852,8865,8870,8872,8875,8876,8880,8889,8972,9003,9004,9005,9020,9038,9043,9070,9071,9114,9117,9144,9189,9190,9191,9207,9233,9247,9253,9256,9279,9280,9308,9371,9407,9408,9409,9434,9435,9453,9471,9477,9493,9516,9538,9546,9547,9548,9549,9565,9567,9572,9603,9604,9610,9611,9654,9655,9686,9696,9706,9708,9709,9719,9733,9737,9765,9797,9802,9859,9902,9903,9905,9915,9916,9936,9941,9964,9969,9984,10036,10110,10111,10168,10184,2,8,9,4551,4552,4570,4601,4602,4604,4631,4637,4638,4649,4698,4700,4730,4744,4774,4871,4872,4886,4906,4962,4963,4966,4967,4969,4971,4972,4984,4985,4995,5006,5007,5013,5032,5033,5054,5059,5060,5061,5062,5065,5073,5076,5083,5084,5085,5150,5156,5157,5164,5194,5205,5211,5227,5247,5254,5255,5256,5265,5274,5281,5283,5284,5290,5298,5299,5309,5313,5314,5315,5316,5318,5319,5324,5325,5326,5327,5358,5359,5360,5368,5369,5370,5371,5414,5419,5421,5458,5460,5461,5463,5464,5466,5467,5469,5478,5483,5485,5486,5487,5488,5489,5490,5497,5507,5510,5521,5537,5538,5541,5550,5552,5553,5554,5579,5589,5606,5607,5617,5618,5620,5622,5627,5662,5666,5668,5728,5762,5763])). % 187.89/187.72 cnf(11632,plain, % 187.89/187.72 (~P1(f306(f306(f221(a865),x116321),x116321))), % 187.89/187.72 inference(rename_variables,[],[4489])). % 187.89/187.72 cnf(11635,plain, % 187.89/187.72 (~P1(f306(f306(f221(a865),x116351),x116351))), % 187.89/187.72 inference(rename_variables,[],[4489])). % 187.89/187.72 cnf(11638,plain, % 187.89/187.72 (~P1(f306(f306(f221(a865),x116381),x116381))), % 187.89/187.72 inference(rename_variables,[],[4489])). % 187.89/187.72 cnf(11641,plain, % 187.89/187.72 (P1(f306(f306(f308(x116411),f306(x116412,x116413)),f306(f285(x116414,x116411,x116412),f231(f872(x116414,a859)))))), % 187.89/187.72 inference(rename_variables,[],[3864])). % 187.89/187.72 cnf(11642,plain, % 187.89/187.72 (~P1(f306(f306(f220(a865),f306(a119,x116421)),x116421))), % 187.89/187.72 inference(rename_variables,[],[4502])). % 187.89/187.72 cnf(11645,plain, % 187.89/187.72 (P1(f306(f306(f308(x116451),f306(x116452,x116453)),f306(f285(x116454,x116451,x116452),f231(f872(x116454,a859)))))), % 187.89/187.72 inference(rename_variables,[],[3864])). % 187.89/187.72 cnf(11646,plain, % 187.89/187.72 (~P1(f306(f306(f221(a865),f306(f306(f81(a865),x116461),x116462)),x116462))), % 187.89/187.72 inference(rename_variables,[],[4517])). % 187.89/187.72 cnf(11651,plain, % 187.89/187.72 (~P1(f306(f306(f221(a865),f306(f306(f81(a865),x116511),x116512)),x116511))), % 187.89/187.72 inference(rename_variables,[],[4518])). % 187.89/187.72 cnf(11654,plain, % 187.89/187.72 (~P1(f306(f306(f221(a865),x116541),x116541))), % 187.89/187.72 inference(rename_variables,[],[4489])). % 187.89/187.72 cnf(11657,plain, % 187.89/187.72 (P1(f306(f306(f193(a24),x116571),x116571))), % 187.89/187.72 inference(rename_variables,[],[3270])). % 187.89/187.72 cnf(11663,plain, % 187.89/187.72 (~P38(x116631,x116632,f120(x116631))), % 187.89/187.72 inference(rename_variables,[],[4456])). % 187.89/187.72 cnf(11666,plain, % 187.89/187.72 (P1(f306(f306(f308(x116661),x116662),f306(f306(f284(x116661),x116662),x116663)))), % 187.89/187.72 inference(rename_variables,[],[3579])). % 187.89/187.72 cnf(11669,plain, % 187.89/187.72 (~P1(f306(f64(x116691,x116692,f185(f872(x116691,a859))),x116693))), % 187.89/187.72 inference(rename_variables,[],[4516])). % 187.89/187.72 cnf(11682,plain, % 187.89/187.72 (~P1(f306(f306(f308(x116821),x116822),f185(f872(x116821,a859))))), % 187.89/187.72 inference(rename_variables,[],[4505])). % 187.89/187.72 cnf(11685,plain, % 187.89/187.72 (E(f306(f306(f16(x116851,x116852),x116853),x116854),x116853)), % 187.89/187.72 inference(rename_variables,[],[3260])). % 187.89/187.72 cnf(11688,plain, % 187.89/187.72 (E(f306(f306(f16(x116881,x116882),x116883),x116884),x116883)), % 187.89/187.72 inference(rename_variables,[],[3260])). % 187.89/187.72 cnf(11700,plain, % 187.89/187.72 (P1(f306(f306(f221(a865),f2(a865)),f306(a119,x117001)))), % 187.89/187.72 inference(rename_variables,[],[3352])). % 187.89/187.72 cnf(11703,plain, % 187.89/187.72 (P1(f306(f306(f193(a24),x117031),x117031))), % 187.89/187.72 inference(rename_variables,[],[3270])). % 187.89/187.72 cnf(11706,plain, % 187.89/187.72 (P1(f306(f306(f308(x117061),f306(x117062,x117063)),f306(f285(x117064,x117061,x117062),f231(f872(x117064,a859)))))), % 187.89/187.72 inference(rename_variables,[],[3864])). % 187.89/187.72 cnf(11709,plain, % 187.89/187.72 (P1(f306(f63(x117091),f306(f164(x117091),x117092)))), % 187.89/187.72 inference(rename_variables,[],[3312])). % 187.89/187.72 cnf(11712,plain, % 187.89/187.72 (P1(f306(f63(x117121),f306(f164(x117121),x117122)))), % 187.89/187.72 inference(rename_variables,[],[3312])). % 187.89/187.72 cnf(11715,plain, % 187.89/187.72 (P1(f306(f306(f220(a1),f306(f80(a1),f306(f107(a1),x117151))),f306(f107(a1),x117152)))), % 187.89/187.72 inference(rename_variables,[],[3742])). % 187.89/187.72 cnf(11718,plain, % 187.89/187.72 (~P1(f306(f306(f308(x117181),x117182),f185(f872(x117181,a859))))), % 187.89/187.72 inference(rename_variables,[],[4505])). % 187.89/187.72 cnf(11732,plain, % 187.89/187.72 (~P1(f306(f306(f308(a865),f2(a865)),f306(f278(a865),x117321)))), % 187.89/187.72 inference(scs_inference,[],[4527,3510,4455,4456,4420,10200,10210,10221,10330,10333,10336,10438,10551,10855,11022,11025,11223,11313,11320,11334,11384,11387,11409,11502,11548,4435,10422,10515,3189,2875,2876,2879,2882,2883,2886,2887,2894,2911,2923,2929,2936,2937,2938,2943,2970,3004,3005,3018,3019,3021,3028,3029,3030,3031,3033,3044,3050,3162,3064,4416,3117,11310,3313,3227,10203,10264,10267,10357,10360,10650,10929,11325,11328,11445,11489,11494,3202,11590,3722,10969,11596,3107,3922,3812,11360,3170,3134,3129,3115,3330,3201,3222,10463,3375,4513,3895,4445,10255,10419,11220,3260,11685,4503,10972,11042,11263,11266,3376,3165,10322,10626,3166,3433,3086,3185,11350,4037,3897,10978,11104,11155,4524,10907,11109,11214,11236,11271,11277,4525,11011,11112,11217,4526,11115,4528,11169,4529,3184,3472,3628,4316,4317,4443,3570,3777,3340,10341,10458,10529,10590,10593,10629,10723,10962,3715,11581,3253,3352,4493,10232,10235,10261,10731,10744,10865,11286,11353,4509,11464,11497,11532,3702,3480,3847,3299,3300,3273,4490,4440,3464,4510,4031,11231,3589,3312,11709,4001,3907,10799,3956,3629,3990,3646,10984,11047,11128,4514,10747,11120,3270,10350,10445,10576,10636,11437,11657,3271,10705,10750,10753,10786,10812,10849,10887,3272,10433,10641,10726,3348,4489,10298,10387,10500,10524,10768,10815,10825,11511,11611,11632,11635,11638,3428,10596,10860,10904,11177,11255,4505,10777,10789,10896,10914,10917,10975,11061,11069,11085,11123,11140,11149,11185,11226,11246,11249,11252,11280,11293,11296,11682,3334,10623,10653,10662,3371,3365,3781,3720,10301,11584,4502,10252,10611,10614,11064,11082,11547,11602,11642,3292,10656,10809,10880,3742,4081,4500,3788,4479,4482,3244,3248,4481,4484,3249,4480,3579,11577,4177,4516,10226,10229,10481,10532,10535,10540,10949,11419,4522,11143,11260,3967,3864,11299,11641,11645,3709,10920,10926,3566,3711,10659,11000,11152,11182,3536,10579,10582,10665,10836,4519,11578,4520,10716,10818,11131,11283,11422,4140,4042,3741,3689,4517,10274,10277,10617,10620,11461,4518,11558,3713,10585,3974,4521,4538,4564,4613,4615,4645,4662,4669,4670,4709,4739,4745,4830,4856,4857,4918,4919,4941,4942,4955,4959,4981,4988,5005,5008,5009,5010,5015,5016,5039,5066,5067,5077,5082,5090,5135,5136,5144,5154,5158,5160,5170,5172,5178,5182,5197,5204,5207,5208,5209,5213,5248,5261,5268,5270,5271,5275,5276,5277,5285,5288,5293,5294,5295,5302,5306,5307,5308,5317,5321,5322,5323,5328,5341,5350,5362,5364,5372,5373,5377,5381,5406,5412,5422,5423,5438,5451,5473,5479,5495,5496,5499,5518,5526,5527,5532,5533,5543,5544,5556,5560,5569,5570,5572,5587,5592,5603,5604,5616,5623,5637,5641,5644,5650,5651,5652,5655,5660,5697,5698,5701,5703,5706,5707,5708,5710,5712,5714,5719,5726,5741,5755,5760,5761,5774,5775,5780,5785,5787,5792,5833,5845,5854,5858,5869,5873,5874,5882,5896,5902,5920,5923,5935,5965,5979,6004,6024,6025,6028,6042,6044,6046,6048,6061,6062,6065,6067,6070,6071,6082,6088,6089,6090,6092,6094,6136,6137,6144,6154,6190,6192,6194,6196,6205,6207,6209,6215,6217,6223,6226,6234,6241,6242,6243,6248,6270,6271,6272,6274,6280,6285,6322,6323,6325,6326,6327,6329,6330,6331,6332,6341,6374,6375,6384,6405,6406,6426,6429,6440,6441,6447,6476,6478,6490,6528,6530,6531,6586,6610,6656,6676,6685,6686,6687,6688,6707,6708,6714,6726,6729,6731,6733,6734,6735,6737,6751,6762,6764,6765,6778,6781,6832,6843,6845,6849,6864,6865,6901,6913,6944,6963,6978,7032,7060,7115,7136,7145,7148,7203,7211,7269,7271,7285,7295,7296,7297,7316,7322,7324,7373,7383,7386,7402,7451,7453,7456,7499,7500,7518,7585,7604,7628,7650,7665,7680,7691,7699,7700,7728,7731,7733,7741,7779,7790,7815,7873,7907,7939,7986,8002,8008,8019,8020,8095,8149,8168,8192,8212,8236,8335,8337,8343,8361,8365,8379,8402,8413,8415,8430,8436,8440,8465,8479,8480,8496,8497,8502,8503,8504,8505,8506,8524,8525,8526,8535,8549,8551,8563,8567,8569,8570,8571,8579,8584,8611,8612,8641,8654,8658,8676,8698,8699,8700,8701,8714,8715,8737,8747,8756,8757,8758,8759,8761,8783,8784,8795,8840,8846,8852,8865,8870,8872,8875,8876,8880,8889,8972,9003,9004,9005,9020,9038,9043,9070,9071,9114,9117,9144,9189,9190,9191,9207,9233,9247,9253,9256,9279,9280,9308,9371,9407,9408,9409,9434,9435,9453,9471,9477,9493,9516,9538,9546,9547,9548,9549,9565,9567,9572,9603,9604,9610,9611,9654,9655,9686,9696,9706,9708,9709,9719,9733,9737,9765,9797,9802,9859,9902,9903,9905,9915,9916,9936,9941,9964,9969,9984,10036,10110,10111,10168,10184,2,8,9,4551,4552,4570,4601,4602,4604,4631,4637,4638,4649,4698,4700,4730,4744,4774,4871,4872,4886,4906,4962,4963,4966,4967,4969,4971,4972,4984,4985,4995,5006,5007,5013,5032,5033,5054,5059,5060,5061,5062,5065,5073,5076,5083,5084,5085,5150,5156,5157,5164,5194,5205,5211,5227,5247,5254,5255,5256,5265,5274,5281,5283,5284,5290,5298,5299,5309,5313,5314,5315,5316,5318,5319,5324,5325,5326,5327,5358,5359,5360,5368,5369,5370,5371,5414,5419,5421,5458,5460,5461,5463,5464,5466,5467,5469,5478,5483,5485,5486,5487,5488,5489,5490,5497,5507,5510,5521,5537,5538,5541,5550,5552,5553,5554,5579,5589,5606,5607,5617,5618,5620,5622,5627,5662,5666,5668,5728,5762,5763,5767,5773,5776,5777,5778,5779,5786,5797,5798,5800,5801,5809,5830,5861,5877,5880,5881,5883,5892,5910,5914,5917,5918,5919,5937,5950,5951,5981,5982,5986,6006,6009,6013,6032,6037,6038,6063,6066,6073,6081,6087,6091,6098,6099,6100])). % 187.89/187.72 cnf(11734,plain, % 187.89/187.72 (~P1(f306(f306(f308(a865),x117341),f306(f229(a865),f2(a865))))), % 187.89/187.72 inference(scs_inference,[],[4527,3510,4455,4456,4420,10200,10210,10221,10330,10333,10336,10438,10551,10855,11022,11025,11223,11313,11320,11334,11384,11387,11409,11502,11548,4435,10422,10515,3189,2875,2876,2879,2882,2883,2886,2887,2894,2911,2923,2929,2936,2937,2938,2943,2970,3004,3005,3018,3019,3021,3028,3029,3030,3031,3033,3044,3050,3162,3064,4416,3117,11310,3313,3227,10203,10264,10267,10357,10360,10650,10929,11325,11328,11445,11489,11494,3202,11590,3722,10969,11596,3107,3922,3812,11360,3170,3134,3129,3115,3330,3201,3222,10463,3375,4513,3895,4445,10255,10419,11220,3260,11685,4503,10972,11042,11263,11266,3376,3165,10322,10626,3166,3433,3086,3185,11350,4037,3897,10978,11104,11155,4524,10907,11109,11214,11236,11271,11277,4525,11011,11112,11217,4526,11115,4528,11169,4529,3184,3472,3628,4316,4317,4443,3570,3777,3340,10341,10458,10529,10590,10593,10629,10723,10962,3715,11581,3253,3352,4493,10232,10235,10261,10731,10744,10865,11286,11353,4509,11464,11497,11532,3702,3480,3847,3299,3300,3273,4490,4440,3464,4510,4031,11231,3589,3312,11709,4001,3907,10799,3956,3629,3990,3646,10984,11047,11128,4514,10747,11120,3270,10350,10445,10576,10636,11437,11657,3271,10705,10750,10753,10786,10812,10849,10887,3272,10433,10641,10726,3348,4489,10298,10387,10500,10524,10768,10815,10825,11511,11611,11632,11635,11638,3428,10596,10860,10904,11177,11255,4505,10777,10789,10896,10914,10917,10975,11061,11069,11085,11123,11140,11149,11185,11226,11246,11249,11252,11280,11293,11296,11682,3334,10623,10653,10662,3371,3365,3781,3720,10301,11584,4502,10252,10611,10614,11064,11082,11547,11602,11642,3292,10656,10809,10880,3742,4081,4500,3788,4479,4482,3244,3248,4481,4484,3249,4480,3579,11577,4177,4516,10226,10229,10481,10532,10535,10540,10949,11419,4522,11143,11260,3967,3864,11299,11641,11645,3709,10920,10926,3566,3711,10659,11000,11152,11182,3536,10579,10582,10665,10836,4519,11578,4520,10716,10818,11131,11283,11422,4140,4042,3741,3689,4517,10274,10277,10617,10620,11461,4518,11558,3713,10585,3974,4521,4538,4564,4613,4615,4645,4662,4669,4670,4709,4739,4745,4830,4856,4857,4918,4919,4941,4942,4955,4959,4981,4988,5005,5008,5009,5010,5015,5016,5039,5066,5067,5077,5082,5090,5135,5136,5144,5154,5158,5160,5170,5172,5178,5182,5197,5204,5207,5208,5209,5213,5248,5261,5268,5270,5271,5275,5276,5277,5285,5288,5293,5294,5295,5302,5306,5307,5308,5317,5321,5322,5323,5328,5341,5350,5362,5364,5372,5373,5377,5381,5406,5412,5422,5423,5438,5451,5473,5479,5495,5496,5499,5518,5526,5527,5532,5533,5543,5544,5556,5560,5569,5570,5572,5587,5592,5603,5604,5616,5623,5637,5641,5644,5650,5651,5652,5655,5660,5697,5698,5701,5703,5706,5707,5708,5710,5712,5714,5719,5726,5741,5755,5760,5761,5774,5775,5780,5785,5787,5792,5833,5845,5854,5858,5869,5873,5874,5882,5896,5902,5920,5923,5935,5965,5979,6004,6024,6025,6028,6042,6044,6046,6048,6061,6062,6065,6067,6070,6071,6082,6088,6089,6090,6092,6094,6136,6137,6144,6154,6190,6192,6194,6196,6205,6207,6209,6215,6217,6223,6226,6234,6241,6242,6243,6248,6270,6271,6272,6274,6280,6285,6322,6323,6325,6326,6327,6329,6330,6331,6332,6341,6374,6375,6384,6405,6406,6426,6429,6440,6441,6447,6476,6478,6490,6528,6530,6531,6586,6610,6656,6676,6685,6686,6687,6688,6707,6708,6714,6726,6729,6731,6733,6734,6735,6737,6751,6762,6764,6765,6778,6781,6832,6843,6845,6849,6864,6865,6901,6913,6944,6963,6978,7032,7060,7115,7136,7145,7148,7203,7211,7269,7271,7285,7295,7296,7297,7316,7322,7324,7373,7383,7386,7402,7451,7453,7456,7499,7500,7518,7585,7604,7628,7650,7665,7680,7691,7699,7700,7728,7731,7733,7741,7779,7790,7815,7873,7907,7939,7986,8002,8008,8019,8020,8095,8149,8168,8192,8212,8236,8335,8337,8343,8361,8365,8379,8402,8413,8415,8430,8436,8440,8465,8479,8480,8496,8497,8502,8503,8504,8505,8506,8524,8525,8526,8535,8549,8551,8563,8567,8569,8570,8571,8579,8584,8611,8612,8641,8654,8658,8676,8698,8699,8700,8701,8714,8715,8737,8747,8756,8757,8758,8759,8761,8783,8784,8795,8840,8846,8852,8865,8870,8872,8875,8876,8880,8889,8972,9003,9004,9005,9020,9038,9043,9070,9071,9114,9117,9144,9189,9190,9191,9207,9233,9247,9253,9256,9279,9280,9308,9371,9407,9408,9409,9434,9435,9453,9471,9477,9493,9516,9538,9546,9547,9548,9549,9565,9567,9572,9603,9604,9610,9611,9654,9655,9686,9696,9706,9708,9709,9719,9733,9737,9765,9797,9802,9859,9902,9903,9905,9915,9916,9936,9941,9964,9969,9984,10036,10110,10111,10168,10184,2,8,9,4551,4552,4570,4601,4602,4604,4631,4637,4638,4649,4698,4700,4730,4744,4774,4871,4872,4886,4906,4962,4963,4966,4967,4969,4971,4972,4984,4985,4995,5006,5007,5013,5032,5033,5054,5059,5060,5061,5062,5065,5073,5076,5083,5084,5085,5150,5156,5157,5164,5194,5205,5211,5227,5247,5254,5255,5256,5265,5274,5281,5283,5284,5290,5298,5299,5309,5313,5314,5315,5316,5318,5319,5324,5325,5326,5327,5358,5359,5360,5368,5369,5370,5371,5414,5419,5421,5458,5460,5461,5463,5464,5466,5467,5469,5478,5483,5485,5486,5487,5488,5489,5490,5497,5507,5510,5521,5537,5538,5541,5550,5552,5553,5554,5579,5589,5606,5607,5617,5618,5620,5622,5627,5662,5666,5668,5728,5762,5763,5767,5773,5776,5777,5778,5779,5786,5797,5798,5800,5801,5809,5830,5861,5877,5880,5881,5883,5892,5910,5914,5917,5918,5919,5937,5950,5951,5981,5982,5986,6006,6009,6013,6032,6037,6038,6063,6066,6073,6081,6087,6091,6098,6099,6100,6101])). % 187.89/187.72 cnf(11737,plain, % 187.89/187.72 (P1(f306(f306(f193(a24),x117371),x117371))), % 187.89/187.72 inference(rename_variables,[],[3270])). % 187.89/187.72 cnf(11740,plain, % 187.89/187.72 (P1(f306(f306(f220(a1),x117401),x117401))), % 187.89/187.72 inference(rename_variables,[],[3272])). % 187.89/187.72 cnf(11749,plain, % 187.89/187.72 (P1(f306(f306(f220(a1),x117491),x117491))), % 187.89/187.72 inference(rename_variables,[],[3272])). % 187.89/187.72 cnf(11752,plain, % 187.89/187.72 (~P1(f306(f306(f221(a865),x117521),f2(a865)))), % 187.89/187.72 inference(rename_variables,[],[4493])). % 187.89/187.72 cnf(11757,plain, % 187.89/187.72 (~P1(f306(f306(f221(a865),x117571),f2(a865)))), % 187.89/187.72 inference(rename_variables,[],[4493])). % 187.89/187.72 cnf(11764,plain, % 187.89/187.72 (P1(f306(f231(f872(x117641,a859)),x117642))), % 187.89/187.72 inference(rename_variables,[],[3334])). % 187.89/187.72 cnf(11769,plain, % 187.89/187.72 (P1(f306(f306(f220(a865),f2(a865)),x117691))), % 187.89/187.72 inference(rename_variables,[],[3292])). % 187.89/187.72 cnf(11770,plain, % 187.89/187.72 (~P1(f306(f306(f220(a865),f306(a119,x117701)),x117701))), % 187.89/187.72 inference(rename_variables,[],[4502])). % 187.89/187.72 cnf(11773,plain, % 187.89/187.72 (~P1(f306(f64(x117731,x117732,f185(f872(x117731,a859))),x117733))), % 187.89/187.72 inference(rename_variables,[],[4516])). % 187.89/187.72 cnf(11792,plain, % 187.89/187.72 (P1(f306(f306(f221(a1),f306(f80(a1),f79(a1))),f2(a1)))), % 187.89/187.72 inference(scs_inference,[],[4527,3510,4455,4456,4420,10200,10210,10221,10330,10333,10336,10438,10551,10855,11022,11025,11223,11313,11320,11334,11384,11387,11409,11502,11548,4435,10422,10515,3189,2875,2876,2879,2882,2883,2886,2887,2889,2894,2902,2911,2923,2929,2936,2937,2938,2943,2952,2970,3004,3005,3018,3019,3021,3028,3029,3030,3031,3033,3044,3050,3162,3064,4416,3117,11310,3313,3227,10203,10264,10267,10357,10360,10650,10929,11325,11328,11445,11489,11494,3202,11590,3722,10969,11596,3107,3922,3812,11360,3170,3134,3129,3115,3330,3201,3222,10463,3375,4513,3895,4445,10255,10419,11220,3260,11685,4503,10972,11042,11263,11266,3376,3165,10322,10626,3166,3433,3086,3185,11350,4037,3897,10978,11104,11155,4524,10907,11109,11214,11236,11271,11277,4525,11011,11112,11217,4526,11115,4528,11169,4529,3184,3472,3628,4316,4317,4443,3570,3777,3340,10341,10458,10529,10590,10593,10629,10723,10962,3715,11581,3253,3352,4493,10232,10235,10261,10731,10744,10865,11286,11353,11752,11757,4509,11464,11497,11532,11561,3702,3480,3847,3299,3300,3273,4490,4440,3464,4510,4031,11231,3589,3312,11709,4001,3907,10799,3956,3629,3990,3646,10984,11047,11128,4514,10747,11120,3270,10350,10445,10576,10636,11437,11657,11703,3271,10705,10750,10753,10786,10812,10849,10887,3272,10433,10641,10726,10852,11740,3348,4489,10298,10387,10500,10524,10768,10815,10825,11511,11611,11632,11635,11638,3428,10596,10860,10904,11177,11255,4505,10777,10789,10896,10914,10917,10975,11061,11069,11085,11123,11140,11149,11185,11226,11246,11249,11252,11280,11293,11296,11682,3334,10623,10653,10662,11206,3371,3365,3781,3720,10301,11584,11614,4502,10252,10611,10614,11064,11082,11547,11602,11642,3292,10656,10809,10880,11615,3742,4081,4500,3788,4479,4482,3244,3248,4481,4484,3249,4480,3579,11577,4177,4516,10226,10229,10481,10532,10535,10540,10949,11419,11669,11773,4522,11143,11260,3967,3864,11299,11641,11645,3709,10920,10926,3566,3711,10659,11000,11152,11182,3536,10579,10582,10665,10836,4519,11578,4520,10716,10818,11131,11283,11422,4140,4042,3741,3689,4517,10274,10277,10617,10620,11461,4518,11558,3713,10585,3974,4521,4538,4564,4613,4615,4645,4662,4669,4670,4709,4739,4745,4830,4856,4857,4918,4919,4941,4942,4955,4959,4981,4988,5005,5008,5009,5010,5015,5016,5039,5066,5067,5077,5082,5090,5135,5136,5144,5154,5158,5160,5170,5172,5178,5182,5197,5204,5207,5208,5209,5213,5248,5261,5268,5270,5271,5275,5276,5277,5285,5288,5293,5294,5295,5302,5306,5307,5308,5317,5321,5322,5323,5328,5341,5350,5362,5364,5372,5373,5377,5381,5406,5412,5422,5423,5438,5451,5473,5479,5495,5496,5499,5518,5526,5527,5532,5533,5543,5544,5556,5560,5569,5570,5572,5587,5592,5603,5604,5616,5623,5637,5641,5644,5650,5651,5652,5655,5660,5697,5698,5701,5703,5706,5707,5708,5710,5712,5714,5719,5726,5741,5755,5760,5761,5774,5775,5780,5785,5787,5792,5833,5845,5854,5858,5869,5873,5874,5882,5896,5902,5920,5923,5935,5965,5979,6004,6024,6025,6028,6042,6044,6046,6048,6061,6062,6065,6067,6070,6071,6082,6088,6089,6090,6092,6094,6136,6137,6144,6154,6190,6192,6194,6196,6205,6207,6209,6215,6217,6223,6226,6234,6241,6242,6243,6248,6270,6271,6272,6274,6280,6285,6322,6323,6325,6326,6327,6329,6330,6331,6332,6341,6374,6375,6384,6405,6406,6426,6429,6440,6441,6447,6476,6478,6490,6528,6530,6531,6586,6610,6656,6676,6685,6686,6687,6688,6707,6708,6714,6726,6729,6731,6733,6734,6735,6737,6751,6762,6764,6765,6778,6781,6832,6843,6845,6849,6864,6865,6901,6913,6944,6963,6978,7032,7060,7115,7136,7145,7148,7203,7211,7269,7271,7285,7295,7296,7297,7316,7322,7324,7373,7383,7386,7402,7451,7453,7456,7499,7500,7518,7585,7604,7628,7650,7665,7680,7691,7699,7700,7728,7731,7733,7741,7779,7790,7815,7873,7907,7939,7986,8002,8008,8019,8020,8095,8149,8168,8192,8212,8236,8335,8337,8343,8361,8365,8379,8402,8413,8415,8430,8436,8440,8465,8479,8480,8496,8497,8502,8503,8504,8505,8506,8524,8525,8526,8535,8549,8551,8563,8567,8569,8570,8571,8579,8584,8611,8612,8641,8654,8658,8676,8698,8699,8700,8701,8714,8715,8737,8747,8756,8757,8758,8759,8761,8783,8784,8795,8840,8846,8852,8865,8870,8872,8875,8876,8880,8889,8972,9003,9004,9005,9020,9038,9043,9070,9071,9114,9117,9144,9189,9190,9191,9207,9233,9247,9253,9256,9279,9280,9308,9371,9407,9408,9409,9434,9435,9453,9471,9477,9493,9516,9538,9546,9547,9548,9549,9565,9567,9572,9603,9604,9610,9611,9654,9655,9686,9696,9706,9708,9709,9719,9733,9737,9765,9797,9802,9859,9902,9903,9905,9915,9916,9936,9941,9964,9969,9984,10036,10110,10111,10168,10184,2,8,9,4551,4552,4570,4601,4602,4604,4631,4637,4638,4649,4698,4700,4730,4744,4774,4871,4872,4886,4906,4962,4963,4966,4967,4969,4971,4972,4984,4985,4995,5006,5007,5013,5032,5033,5054,5059,5060,5061,5062,5065,5073,5076,5083,5084,5085,5150,5156,5157,5164,5194,5205,5211,5227,5247,5254,5255,5256,5265,5274,5281,5283,5284,5290,5298,5299,5309,5313,5314,5315,5316,5318,5319,5324,5325,5326,5327,5358,5359,5360,5368,5369,5370,5371,5414,5419,5421,5458,5460,5461,5463,5464,5466,5467,5469,5478,5483,5485,5486,5487,5488,5489,5490,5497,5507,5510,5521,5537,5538,5541,5550,5552,5553,5554,5579,5589,5606,5607,5617,5618,5620,5622,5627,5662,5666,5668,5728,5762,5763,5767,5773,5776,5777,5778,5779,5786,5797,5798,5800,5801,5809,5830,5861,5877,5880,5881,5883,5892,5910,5914,5917,5918,5919,5937,5950,5951,5981,5982,5986,6006,6009,6013,6032,6037,6038,6063,6066,6073,6081,6087,6091,6098,6099,6100,6101,6139,6155,6208,6244,6246,6267,6268,6273,6277,6278,6281,6288,6297,6314,6334,6335,6342,6352,6367,6387,6393,6395,6410,6411])). % 187.89/187.72 cnf(11795,plain, % 187.89/187.72 (~P1(f306(f306(f220(a865),f306(a119,x117951)),x117951))), % 187.89/187.72 inference(rename_variables,[],[4502])). % 187.89/187.72 cnf(11798,plain, % 187.89/187.72 (~P1(f306(f306(f220(a865),f306(a119,x117981)),x117981))), % 187.89/187.72 inference(rename_variables,[],[4502])). % 187.89/187.72 cnf(11801,plain, % 187.89/187.72 (~P1(f306(f306(f220(a865),f306(a119,x118011)),x118011))), % 187.89/187.72 inference(rename_variables,[],[4502])). % 187.89/187.72 cnf(11804,plain, % 187.89/187.72 (~P1(f306(f306(f220(a865),f306(a119,x118041)),x118041))), % 187.89/187.72 inference(rename_variables,[],[4502])). % 187.89/187.72 cnf(11807,plain, % 187.89/187.72 (~P1(f306(f306(f221(a865),x118071),x118071))), % 187.89/187.72 inference(rename_variables,[],[4489])). % 187.89/187.72 cnf(11810,plain, % 187.89/187.72 (~P1(f306(f306(f221(a865),x118101),x118101))), % 187.89/187.72 inference(rename_variables,[],[4489])). % 187.89/187.72 cnf(11813,plain, % 187.89/187.72 (~P1(f306(f306(f221(a865),x118131),x118131))), % 187.89/187.72 inference(rename_variables,[],[4489])). % 187.89/187.72 cnf(11816,plain, % 187.89/187.72 (~P1(f306(f306(f221(a865),x118161),x118161))), % 187.89/187.72 inference(rename_variables,[],[4489])). % 187.89/187.72 cnf(11832,plain, % 187.89/187.72 (P1(f306(f306(f193(a24),f306(f306(f22(a865),x118321),f306(a119,x118321))),f2(a865)))), % 187.89/187.72 inference(scs_inference,[],[4527,3510,4455,4456,4420,10200,10210,10221,10330,10333,10336,10438,10551,10855,11022,11025,11223,11313,11320,11334,11384,11387,11409,11502,11548,4435,10422,10515,3189,2875,2876,2879,2882,2883,2886,2887,2889,2894,2902,2911,2923,2929,2936,2937,2938,2943,2952,2970,3004,3005,3018,3019,3021,3028,3029,3030,3031,3033,3044,3050,3162,3064,4416,3117,11310,3313,3227,10203,10264,10267,10357,10360,10650,10929,11325,11328,11445,11489,11494,3202,11590,3722,10969,11596,3107,3922,3812,11360,3170,3134,3129,3115,3330,3201,3222,10463,3375,4513,3895,4445,10255,10419,11220,3260,11685,4503,10972,11042,11263,11266,3376,3165,10322,10626,3166,3433,3086,3185,11350,4037,3897,10978,11104,11155,4524,10907,11109,11214,11236,11271,11277,4525,11011,11112,11217,4526,11115,4528,11169,4529,3184,3472,3628,4316,4317,4443,3570,3777,3340,10341,10458,10529,10590,10593,10629,10723,10962,3715,11581,3253,3352,4493,10232,10235,10261,10731,10744,10865,11286,11353,11752,11757,4509,11464,11497,11532,11561,3702,3480,3847,3299,3300,3273,4490,4440,3464,4510,4031,11231,3589,3312,11709,4001,3907,10799,3956,3629,3990,3646,10984,11047,11128,4514,10747,11120,3270,10350,10445,10576,10636,11437,11657,11703,11737,3271,10705,10750,10753,10786,10812,10849,10887,3272,10433,10641,10726,10852,11740,3348,4489,10298,10387,10500,10524,10768,10815,10825,11511,11611,11632,11635,11638,11654,11807,11810,11813,3428,10596,10860,10904,11177,11255,4505,10777,10789,10896,10914,10917,10975,11061,11069,11085,11123,11140,11149,11185,11226,11246,11249,11252,11280,11293,11296,11682,3334,10623,10653,10662,11206,3371,3365,3781,3720,10301,11584,11614,4502,10252,10611,10614,11064,11082,11547,11602,11642,11770,11795,11798,11801,3292,10656,10809,10880,11615,3742,4081,4500,3788,4479,4482,3244,3248,4481,4484,3249,4480,3579,11577,4177,4516,10226,10229,10481,10532,10535,10540,10949,11419,11669,11773,4522,11143,11260,3967,3864,11299,11641,11645,3709,10920,10926,3566,3711,10659,11000,11152,11182,3536,10579,10582,10665,10836,4519,11578,4520,10716,10818,11131,11283,11422,4140,4042,3741,3689,4517,10274,10277,10617,10620,11461,4518,11558,3713,10585,3974,4521,4538,4564,4613,4615,4645,4662,4669,4670,4709,4739,4745,4830,4856,4857,4918,4919,4941,4942,4955,4959,4981,4988,5005,5008,5009,5010,5015,5016,5039,5066,5067,5077,5082,5090,5135,5136,5144,5154,5158,5160,5170,5172,5178,5182,5197,5204,5207,5208,5209,5213,5248,5261,5268,5270,5271,5275,5276,5277,5285,5288,5293,5294,5295,5302,5306,5307,5308,5317,5321,5322,5323,5328,5341,5350,5362,5364,5372,5373,5377,5381,5406,5412,5422,5423,5438,5451,5473,5479,5495,5496,5499,5518,5526,5527,5532,5533,5543,5544,5556,5560,5569,5570,5572,5587,5592,5603,5604,5616,5623,5637,5641,5644,5650,5651,5652,5655,5660,5697,5698,5701,5703,5706,5707,5708,5710,5712,5714,5719,5726,5741,5755,5760,5761,5774,5775,5780,5785,5787,5792,5833,5845,5854,5858,5869,5873,5874,5882,5896,5902,5920,5923,5935,5965,5979,6004,6024,6025,6028,6042,6044,6046,6048,6061,6062,6065,6067,6070,6071,6082,6088,6089,6090,6092,6094,6136,6137,6144,6154,6190,6192,6194,6196,6205,6207,6209,6215,6217,6223,6226,6234,6241,6242,6243,6248,6270,6271,6272,6274,6280,6285,6322,6323,6325,6326,6327,6329,6330,6331,6332,6341,6374,6375,6384,6405,6406,6426,6429,6440,6441,6447,6476,6478,6490,6528,6530,6531,6586,6610,6656,6676,6685,6686,6687,6688,6707,6708,6714,6726,6729,6731,6733,6734,6735,6737,6751,6762,6764,6765,6778,6781,6832,6843,6845,6849,6864,6865,6901,6913,6944,6963,6978,7032,7060,7115,7136,7145,7148,7203,7211,7269,7271,7285,7295,7296,7297,7316,7322,7324,7373,7383,7386,7402,7451,7453,7456,7499,7500,7518,7585,7604,7628,7650,7665,7680,7691,7699,7700,7728,7731,7733,7741,7779,7790,7815,7873,7907,7939,7986,8002,8008,8019,8020,8095,8149,8168,8192,8212,8236,8335,8337,8343,8361,8365,8379,8402,8413,8415,8430,8436,8440,8465,8479,8480,8496,8497,8502,8503,8504,8505,8506,8524,8525,8526,8535,8549,8551,8563,8567,8569,8570,8571,8579,8584,8611,8612,8641,8654,8658,8676,8698,8699,8700,8701,8714,8715,8737,8747,8756,8757,8758,8759,8761,8783,8784,8795,8840,8846,8852,8865,8870,8872,8875,8876,8880,8889,8972,9003,9004,9005,9020,9038,9043,9070,9071,9114,9117,9144,9189,9190,9191,9207,9233,9247,9253,9256,9279,9280,9308,9371,9407,9408,9409,9434,9435,9453,9471,9477,9493,9516,9538,9546,9547,9548,9549,9565,9567,9572,9603,9604,9610,9611,9654,9655,9686,9696,9706,9708,9709,9719,9733,9737,9765,9797,9802,9859,9902,9903,9905,9915,9916,9936,9941,9964,9969,9984,10036,10110,10111,10168,10184,2,8,9,4551,4552,4570,4601,4602,4604,4631,4637,4638,4649,4698,4700,4730,4744,4774,4871,4872,4886,4906,4962,4963,4966,4967,4969,4971,4972,4984,4985,4995,5006,5007,5013,5032,5033,5054,5059,5060,5061,5062,5065,5073,5076,5083,5084,5085,5150,5156,5157,5164,5194,5205,5211,5227,5247,5254,5255,5256,5265,5274,5281,5283,5284,5290,5298,5299,5309,5313,5314,5315,5316,5318,5319,5324,5325,5326,5327,5358,5359,5360,5368,5369,5370,5371,5414,5419,5421,5458,5460,5461,5463,5464,5466,5467,5469,5478,5483,5485,5486,5487,5488,5489,5490,5497,5507,5510,5521,5537,5538,5541,5550,5552,5553,5554,5579,5589,5606,5607,5617,5618,5620,5622,5627,5662,5666,5668,5728,5762,5763,5767,5773,5776,5777,5778,5779,5786,5797,5798,5800,5801,5809,5830,5861,5877,5880,5881,5883,5892,5910,5914,5917,5918,5919,5937,5950,5951,5981,5982,5986,6006,6009,6013,6032,6037,6038,6063,6066,6073,6081,6087,6091,6098,6099,6100,6101,6139,6155,6208,6244,6246,6267,6268,6273,6277,6278,6281,6288,6297,6314,6334,6335,6342,6352,6367,6387,6393,6395,6410,6411,6415,6417,6418,6419,6421,6423,6424,6425,6428,6433,6434,6436,6437,6443,6445,6486])). % 187.89/187.72 cnf(11833,plain, % 187.89/187.72 (P1(f306(f306(f193(a24),x118331),x118331))), % 187.89/187.72 inference(rename_variables,[],[3270])). % 187.89/187.72 cnf(11839,plain, % 187.89/187.72 (P1(f306(f306(f220(a1),x118391),x118391))), % 187.89/187.72 inference(rename_variables,[],[3272])). % 187.89/187.72 cnf(11850,plain, % 187.89/187.72 (P1(f306(f306(f220(a1),x118501),x118501))), % 187.89/187.72 inference(rename_variables,[],[3272])). % 187.89/187.72 cnf(11853,plain, % 187.89/187.72 (P1(f306(f306(f220(f872(f871(f866(x118531),f866(x118531)),a859)),f150(x118531,x118532)),f282(f866(x118531),f149(x118531,x118532))))), % 187.89/187.72 inference(rename_variables,[],[3961])). % 187.89/187.72 cnf(11860,plain, % 187.89/187.72 (P1(f306(f306(f221(a865),x118601),f306(a119,x118601)))), % 187.89/187.72 inference(rename_variables,[],[3340])). % 187.89/187.72 cnf(11863,plain, % 187.89/187.72 (P1(f306(f306(f308(f872(x118631,a859)),x118632),f306(f283(x118631),x118632)))), % 187.89/187.72 inference(rename_variables,[],[3629])). % 187.89/187.72 cnf(11864,plain, % 187.89/187.72 (~E(f306(a119,x118641),x118641)), % 187.89/187.72 inference(rename_variables,[],[4420])). % 187.89/187.72 cnf(11869,plain, % 187.89/187.72 (P1(f306(f306(f220(a1),x118691),x118691))), % 187.89/187.72 inference(rename_variables,[],[3272])). % 187.89/187.72 cnf(11874,plain, % 187.89/187.72 (P1(f306(f306(f220(a1),x118741),x118741))), % 187.89/187.72 inference(rename_variables,[],[3272])). % 187.89/187.72 cnf(11881,plain, % 187.89/187.72 (P1(f306(f63(a865),f279(a865,x118811,x118812)))), % 187.89/187.72 inference(rename_variables,[],[3481])). % 187.89/187.72 cnf(11888,plain, % 187.89/187.72 (P1(f306(f306(f220(f872(x118881,a859)),x118882),f306(f306(f284(x118881),x118883),x118882)))), % 187.89/187.72 inference(rename_variables,[],[3709])). % 187.89/187.72 cnf(11891,plain, % 187.89/187.72 (P1(f306(f306(f193(a24),x118911),x118911))), % 187.89/187.72 inference(rename_variables,[],[3270])). % 187.89/187.72 cnf(11892,plain, % 187.89/187.72 (~E(f306(a119,x118921),x118921)), % 187.89/187.72 inference(rename_variables,[],[4420])). % 187.89/187.72 cnf(11903,plain, % 187.89/187.72 (~P1(f306(f306(f221(a865),x119031),x119031))), % 187.89/187.72 inference(rename_variables,[],[4489])). % 187.89/187.72 cnf(11904,plain, % 187.89/187.72 (~E(f306(a119,x119041),x119041)), % 187.89/187.72 inference(rename_variables,[],[4420])). % 187.89/187.72 cnf(11907,plain, % 187.89/187.72 (P1(f306(f306(f220(a865),x119071),x119071))), % 187.89/187.72 inference(rename_variables,[],[3271])). % 187.89/187.72 cnf(11910,plain, % 187.89/187.72 (P1(f306(f306(f220(a865),x119101),x119101))), % 187.89/187.72 inference(rename_variables,[],[3271])). % 187.89/187.72 cnf(11913,plain, % 187.89/187.72 (P1(f306(f306(f220(a865),x119131),x119131))), % 187.89/187.72 inference(rename_variables,[],[3271])). % 187.89/187.72 cnf(11916,plain, % 187.89/187.72 (P1(f306(f306(f220(a865),x119161),x119161))), % 187.89/187.72 inference(rename_variables,[],[3271])). % 187.89/187.72 cnf(11918,plain, % 187.89/187.72 (P1(f306(f306(f221(a865),f306(a112,f2(a1))),f306(a119,x119181)))), % 187.89/187.72 inference(scs_inference,[],[4527,3510,4455,4456,4420,10200,10210,10221,10330,10333,10336,10438,10551,10855,11022,11025,11223,11313,11320,11334,11384,11387,11409,11502,11548,11564,11864,11892,4435,10422,10515,3479,3189,2875,2876,2879,2882,2883,2886,2887,2889,2894,2902,2911,2923,2929,2936,2937,2938,2943,2952,2970,3004,3005,3018,3019,3021,3028,3029,3030,3031,3033,3044,3050,3162,3064,4416,3117,11310,3313,3227,10203,10264,10267,10357,10360,10650,10929,11325,11328,11445,11489,11494,3202,11590,3722,10969,11596,3107,3922,3812,11360,3170,3134,3129,3115,3330,3201,3222,10463,3375,4513,3895,4445,10255,10419,11220,3260,11685,4503,10972,11042,11263,11266,3376,3165,10322,10626,3166,3433,3086,3185,11350,4037,3897,10978,11104,11155,4524,10907,11109,11214,11236,11271,11277,4525,11011,11112,11217,4526,11115,4528,11169,4529,3184,3472,3628,4316,4317,4443,3570,3777,3340,10341,10458,10529,10590,10593,10629,10723,10962,11860,3715,11581,3253,3352,4493,10232,10235,10261,10731,10744,10865,11286,11353,11752,11757,4509,11464,11497,11532,11561,3702,3480,3481,3847,3299,3300,3273,4490,4440,3464,4510,4031,11231,3589,3312,11709,4001,3961,3907,10799,3956,3629,3990,3646,10984,11047,11128,4514,10747,11120,3270,10350,10445,10576,10636,11437,11657,11703,11737,11833,3271,10705,10750,10753,10786,10812,10849,10887,10923,11907,11910,11913,3272,10433,10641,10726,10852,11740,11749,11839,11850,11869,11874,3348,4489,10298,10387,10500,10524,10768,10815,10825,11511,11611,11632,11635,11638,11654,11807,11810,11813,11816,3428,10596,10860,10904,11177,11255,4505,10777,10789,10896,10914,10917,10975,11061,11069,11085,11123,11140,11149,11185,11226,11246,11249,11252,11280,11293,11296,11682,3334,10623,10653,10662,11206,3371,3365,3781,3720,10301,11584,11614,4502,10252,10611,10614,11064,11082,11547,11602,11642,11770,11795,11798,11801,3292,10656,10809,10880,11615,3742,4081,4500,3788,4479,4482,3244,3248,4481,4484,3249,4480,3579,11577,4177,4516,10226,10229,10481,10532,10535,10540,10949,11419,11669,11773,4522,11143,11260,3967,3864,11299,11641,11645,3709,10920,10926,10944,3566,3711,10659,11000,11152,11182,3536,10579,10582,10665,10836,4519,11578,4520,10716,10818,11131,11283,11422,4140,4042,3741,3689,4517,10274,10277,10617,10620,11461,4518,11558,3713,10585,3974,4521,4538,4564,4613,4615,4645,4662,4669,4670,4709,4739,4745,4830,4856,4857,4918,4919,4941,4942,4955,4959,4981,4988,5005,5008,5009,5010,5015,5016,5039,5066,5067,5077,5082,5090,5135,5136,5144,5154,5158,5160,5170,5172,5178,5182,5197,5204,5207,5208,5209,5213,5248,5261,5268,5270,5271,5275,5276,5277,5285,5288,5293,5294,5295,5302,5306,5307,5308,5317,5321,5322,5323,5328,5341,5350,5362,5364,5372,5373,5377,5381,5406,5412,5422,5423,5438,5451,5473,5479,5495,5496,5499,5518,5526,5527,5532,5533,5543,5544,5556,5560,5569,5570,5572,5587,5592,5603,5604,5616,5623,5637,5641,5644,5650,5651,5652,5655,5660,5697,5698,5701,5703,5706,5707,5708,5710,5712,5714,5719,5726,5741,5755,5760,5761,5774,5775,5780,5785,5787,5792,5833,5845,5854,5858,5869,5873,5874,5882,5896,5902,5920,5923,5935,5965,5979,6004,6024,6025,6028,6042,6044,6046,6048,6061,6062,6065,6067,6070,6071,6082,6088,6089,6090,6092,6094,6136,6137,6144,6154,6190,6192,6194,6196,6205,6207,6209,6215,6217,6223,6226,6234,6241,6242,6243,6248,6270,6271,6272,6274,6280,6285,6322,6323,6325,6326,6327,6329,6330,6331,6332,6341,6374,6375,6384,6405,6406,6426,6429,6440,6441,6447,6476,6478,6490,6528,6530,6531,6586,6610,6656,6676,6685,6686,6687,6688,6707,6708,6714,6726,6729,6731,6733,6734,6735,6737,6751,6762,6764,6765,6778,6781,6832,6843,6845,6849,6864,6865,6901,6913,6944,6963,6978,7032,7060,7115,7136,7145,7148,7203,7211,7269,7271,7285,7295,7296,7297,7316,7322,7324,7373,7383,7386,7402,7451,7453,7456,7499,7500,7518,7585,7604,7628,7650,7665,7680,7691,7699,7700,7728,7731,7733,7741,7779,7790,7815,7873,7907,7939,7986,8002,8008,8019,8020,8095,8149,8168,8192,8212,8236,8335,8337,8343,8361,8365,8379,8402,8413,8415,8430,8436,8440,8465,8479,8480,8496,8497,8502,8503,8504,8505,8506,8524,8525,8526,8535,8549,8551,8563,8567,8569,8570,8571,8579,8584,8611,8612,8641,8654,8658,8676,8698,8699,8700,8701,8714,8715,8737,8747,8756,8757,8758,8759,8761,8783,8784,8795,8840,8846,8852,8865,8870,8872,8875,8876,8880,8889,8972,9003,9004,9005,9020,9038,9043,9070,9071,9114,9117,9144,9189,9190,9191,9207,9233,9247,9253,9256,9279,9280,9308,9371,9407,9408,9409,9434,9435,9453,9471,9477,9493,9516,9538,9546,9547,9548,9549,9565,9567,9572,9603,9604,9610,9611,9654,9655,9686,9696,9706,9708,9709,9719,9733,9737,9765,9797,9802,9859,9902,9903,9905,9915,9916,9936,9941,9964,9969,9984,10036,10110,10111,10168,10184,2,8,9,4551,4552,4570,4601,4602,4604,4631,4637,4638,4649,4698,4700,4730,4744,4774,4871,4872,4886,4906,4962,4963,4966,4967,4969,4971,4972,4984,4985,4995,5006,5007,5013,5032,5033,5054,5059,5060,5061,5062,5065,5073,5076,5083,5084,5085,5150,5156,5157,5164,5194,5205,5211,5227,5247,5254,5255,5256,5265,5274,5281,5283,5284,5290,5298,5299,5309,5313,5314,5315,5316,5318,5319,5324,5325,5326,5327,5358,5359,5360,5368,5369,5370,5371,5414,5419,5421,5458,5460,5461,5463,5464,5466,5467,5469,5478,5483,5485,5486,5487,5488,5489,5490,5497,5507,5510,5521,5537,5538,5541,5550,5552,5553,5554,5579,5589,5606,5607,5617,5618,5620,5622,5627,5662,5666,5668,5728,5762,5763,5767,5773,5776,5777,5778,5779,5786,5797,5798,5800,5801,5809,5830,5861,5877,5880,5881,5883,5892,5910,5914,5917,5918,5919,5937,5950,5951,5981,5982,5986,6006,6009,6013,6032,6037,6038,6063,6066,6073,6081,6087,6091,6098,6099,6100,6101,6139,6155,6208,6244,6246,6267,6268,6273,6277,6278,6281,6288,6297,6314,6334,6335,6342,6352,6367,6387,6393,6395,6410,6411,6415,6417,6418,6419,6421,6423,6424,6425,6428,6433,6434,6436,6437,6443,6445,6486,6489,6503,6505,6506,6507,6543,6548,6550,6555,6556,6564,6568,6581,6605,6606,6608,6609,6621,6625,6627,6647,6650,6669,6702,6703,6704,6709,6722,6741,6743,6745,6747,6752])). % 187.89/187.72 cnf(11919,plain, % 187.89/187.72 (P1(f306(f306(f220(a1),x119191),x119191))), % 187.89/187.72 inference(rename_variables,[],[3272])). % 187.89/187.72 cnf(11922,plain, % 187.89/187.72 (~P1(f306(f306(f221(a865),x119221),x119221))), % 187.89/187.72 inference(rename_variables,[],[4489])). % 187.89/187.72 cnf(11925,plain, % 187.89/187.72 (~P1(f306(f306(f221(a865),x119251),x119251))), % 187.89/187.72 inference(rename_variables,[],[4489])). % 187.89/187.72 cnf(11926,plain, % 187.89/187.72 (P1(f306(f306(f221(a865),x119261),f306(a119,x119261)))), % 187.89/187.72 inference(rename_variables,[],[3340])). % 187.89/187.72 cnf(11935,plain, % 187.89/187.72 (~P1(f306(f306(f221(a865),x119351),x119351))), % 187.89/187.72 inference(rename_variables,[],[4489])). % 187.89/187.72 cnf(11936,plain, % 187.89/187.72 (~E(f306(a119,x119361),x119361)), % 187.89/187.72 inference(rename_variables,[],[4420])). % 187.89/187.72 cnf(11939,plain, % 187.89/187.72 (P1(f306(f306(f220(a1),x119391),x119391))), % 187.89/187.72 inference(rename_variables,[],[3272])). % 187.89/187.72 cnf(11956,plain, % 187.89/187.72 (P1(f306(f306(f220(a1),x119561),x119561))), % 187.89/187.72 inference(rename_variables,[],[3272])). % 187.89/187.72 cnf(11961,plain, % 187.89/187.72 (P1(f306(f306(f220(a865),f2(a865)),x119611))), % 187.89/187.72 inference(rename_variables,[],[3292])). % 187.89/187.72 cnf(11978,plain, % 187.89/187.72 (~P1(f306(f306(f221(a865),x119781),f2(a865)))), % 187.89/187.72 inference(rename_variables,[],[4493])). % 187.89/187.72 cnf(11981,plain, % 187.89/187.72 (~P1(f306(f306(f221(a865),x119811),f2(a865)))), % 187.89/187.72 inference(rename_variables,[],[4493])). % 187.89/187.72 cnf(11984,plain, % 187.89/187.72 (~P1(f306(f306(f308(x119841),x119842),f185(f872(x119841,a859))))), % 187.89/187.72 inference(rename_variables,[],[4505])). % 187.89/187.72 cnf(11987,plain, % 187.89/187.72 (~P1(f306(f306(f308(x119871),x119872),f185(f872(x119871,a859))))), % 187.89/187.72 inference(rename_variables,[],[4505])). % 187.89/187.72 cnf(11990,plain, % 187.89/187.72 (~P1(f306(f306(f221(a865),x119901),x119901))), % 187.89/187.72 inference(rename_variables,[],[4489])). % 187.89/187.72 cnf(11992,plain, % 187.89/187.72 (~P1(f306(f306(f221(a865),x119921),f306(f306(f225(a865),x119921),x119922)))), % 187.89/187.72 inference(scs_inference,[],[4527,3510,4455,4456,4420,10200,10210,10221,10330,10333,10336,10438,10551,10855,11022,11025,11223,11313,11320,11334,11384,11387,11409,11502,11548,11564,11864,11892,11904,4435,10422,10515,3479,3189,2875,2876,2879,2882,2883,2886,2887,2889,2894,2902,2911,2923,2929,2936,2937,2938,2943,2952,2970,3004,3005,3018,3019,3021,3028,3029,3030,3031,3033,3044,3050,3162,3064,4416,3117,11310,3313,3227,10203,10264,10267,10357,10360,10650,10929,11325,11328,11445,11489,11494,3202,11590,3212,3722,10969,11596,3107,3922,3552,3812,11360,3170,3134,3129,3115,3330,3201,3222,10463,3375,4513,3895,4445,10255,10419,11220,3260,11685,4503,10972,11042,11263,11266,3376,3165,10322,10626,3166,3433,3086,3185,11350,4037,3897,10978,11104,11155,4524,10907,11109,11214,11236,11271,11277,4525,11011,11112,11217,4526,11115,4528,11169,4529,3184,3472,3628,4316,4317,4443,3570,3777,3340,10341,10458,10529,10590,10593,10629,10723,10962,11860,3715,11581,3253,3352,4493,10232,10235,10261,10731,10744,10865,11286,11353,11752,11757,11978,4509,11464,11497,11532,11561,3702,3480,3481,3847,3299,3300,3273,4490,4440,3464,4510,4031,11231,3589,3312,11709,4001,3961,3907,10799,3956,3629,3990,3646,10984,11047,11128,4514,10747,11120,3270,10350,10445,10576,10636,11437,11657,11703,11737,11833,3271,10705,10750,10753,10786,10812,10849,10887,10923,11907,11910,11913,11916,3272,10433,10641,10726,10852,11740,11749,11839,11850,11869,11874,11919,11939,3348,4489,10298,10387,10500,10524,10768,10815,10825,11511,11611,11632,11635,11638,11654,11807,11810,11813,11816,11903,11922,11925,11935,11990,3428,10596,10860,10904,11177,11255,4505,10777,10789,10896,10914,10917,10975,11061,11069,11085,11123,11140,11149,11185,11226,11246,11249,11252,11280,11293,11296,11682,11718,11984,3334,10623,10653,10662,11206,3371,3365,3781,3720,10301,11584,11614,4502,10252,10611,10614,11064,11082,11547,11602,11642,11770,11795,11798,11801,11804,3292,10656,10809,10880,11615,11769,3742,4081,4500,3753,3788,4479,4482,3244,3248,4481,4484,3249,4480,3760,3579,11577,4177,4516,10226,10229,10481,10532,10535,10540,10949,11419,11669,11773,4522,11143,11260,3967,3864,11299,11641,11645,3709,10920,10926,10944,3566,3711,10659,11000,11152,11182,3536,10579,10582,10665,10836,4519,11578,4520,10716,10818,11131,11283,11422,4140,4042,3741,3689,4517,10274,10277,10617,10620,11461,4518,11558,3713,10585,3974,4521,4538,4564,4613,4615,4645,4662,4669,4670,4709,4739,4745,4830,4856,4857,4918,4919,4941,4942,4955,4959,4981,4988,5005,5008,5009,5010,5015,5016,5039,5066,5067,5077,5082,5090,5135,5136,5144,5154,5158,5160,5170,5172,5178,5182,5197,5204,5207,5208,5209,5213,5248,5261,5268,5270,5271,5275,5276,5277,5285,5288,5293,5294,5295,5302,5306,5307,5308,5317,5321,5322,5323,5328,5341,5350,5362,5364,5372,5373,5377,5381,5406,5412,5422,5423,5438,5451,5473,5479,5495,5496,5499,5518,5526,5527,5532,5533,5543,5544,5556,5560,5569,5570,5572,5587,5592,5603,5604,5616,5623,5637,5641,5644,5650,5651,5652,5655,5660,5697,5698,5701,5703,5706,5707,5708,5710,5712,5714,5719,5726,5741,5755,5760,5761,5774,5775,5780,5785,5787,5792,5833,5845,5854,5858,5869,5873,5874,5882,5896,5902,5920,5923,5935,5965,5979,6004,6024,6025,6028,6042,6044,6046,6048,6061,6062,6065,6067,6070,6071,6082,6088,6089,6090,6092,6094,6136,6137,6144,6154,6190,6192,6194,6196,6205,6207,6209,6215,6217,6223,6226,6234,6241,6242,6243,6248,6270,6271,6272,6274,6280,6285,6322,6323,6325,6326,6327,6329,6330,6331,6332,6341,6374,6375,6384,6405,6406,6426,6429,6440,6441,6447,6476,6478,6490,6528,6530,6531,6586,6610,6656,6676,6685,6686,6687,6688,6707,6708,6714,6726,6729,6731,6733,6734,6735,6737,6751,6762,6764,6765,6778,6781,6832,6843,6845,6849,6864,6865,6901,6913,6944,6963,6978,7032,7060,7115,7136,7145,7148,7203,7211,7269,7271,7285,7295,7296,7297,7316,7322,7324,7373,7383,7386,7402,7451,7453,7456,7499,7500,7518,7585,7604,7628,7650,7665,7680,7691,7699,7700,7728,7731,7733,7741,7779,7790,7815,7873,7907,7939,7986,8002,8008,8019,8020,8095,8149,8168,8192,8212,8236,8335,8337,8343,8361,8365,8379,8402,8413,8415,8430,8436,8440,8465,8479,8480,8496,8497,8502,8503,8504,8505,8506,8524,8525,8526,8535,8549,8551,8563,8567,8569,8570,8571,8579,8584,8611,8612,8641,8654,8658,8676,8698,8699,8700,8701,8714,8715,8737,8747,8756,8757,8758,8759,8761,8783,8784,8795,8840,8846,8852,8865,8870,8872,8875,8876,8880,8889,8972,9003,9004,9005,9020,9038,9043,9070,9071,9114,9117,9144,9189,9190,9191,9207,9233,9247,9253,9256,9279,9280,9308,9371,9407,9408,9409,9434,9435,9453,9471,9477,9493,9516,9538,9546,9547,9548,9549,9565,9567,9572,9603,9604,9610,9611,9654,9655,9686,9696,9706,9708,9709,9719,9733,9737,9765,9797,9802,9859,9902,9903,9905,9915,9916,9936,9941,9964,9969,9984,10036,10110,10111,10168,10184,2,8,9,4551,4552,4570,4601,4602,4604,4631,4637,4638,4649,4698,4700,4730,4744,4774,4871,4872,4886,4906,4962,4963,4966,4967,4969,4971,4972,4984,4985,4995,5006,5007,5013,5032,5033,5054,5059,5060,5061,5062,5065,5073,5076,5083,5084,5085,5150,5156,5157,5164,5194,5205,5211,5227,5247,5254,5255,5256,5265,5274,5281,5283,5284,5290,5298,5299,5309,5313,5314,5315,5316,5318,5319,5324,5325,5326,5327,5358,5359,5360,5368,5369,5370,5371,5414,5419,5421,5458,5460,5461,5463,5464,5466,5467,5469,5478,5483,5485,5486,5487,5488,5489,5490,5497,5507,5510,5521,5537,5538,5541,5550,5552,5553,5554,5579,5589,5606,5607,5617,5618,5620,5622,5627,5662,5666,5668,5728,5762,5763,5767,5773,5776,5777,5778,5779,5786,5797,5798,5800,5801,5809,5830,5861,5877,5880,5881,5883,5892,5910,5914,5917,5918,5919,5937,5950,5951,5981,5982,5986,6006,6009,6013,6032,6037,6038,6063,6066,6073,6081,6087,6091,6098,6099,6100,6101,6139,6155,6208,6244,6246,6267,6268,6273,6277,6278,6281,6288,6297,6314,6334,6335,6342,6352,6367,6387,6393,6395,6410,6411,6415,6417,6418,6419,6421,6423,6424,6425,6428,6433,6434,6436,6437,6443,6445,6486,6489,6503,6505,6506,6507,6543,6548,6550,6555,6556,6564,6568,6581,6605,6606,6608,6609,6621,6625,6627,6647,6650,6669,6702,6703,6704,6709,6722,6741,6743,6745,6747,6752,6758,6760,6775,6782,6818,6819,6820,6834,6835,6837,6838,6855,6857,6873,6899,6921,6932,6934,6936,6938,6939,6940,6975,6976,6981,6982,6990,6992])). % 187.89/187.72 cnf(11993,plain, % 187.89/187.72 (~P1(f306(f306(f221(a865),x119931),x119931))), % 187.89/187.72 inference(rename_variables,[],[4489])). % 187.89/187.72 cnf(11996,plain, % 187.89/187.72 (~P1(f306(f306(f221(a865),x119961),x119961))), % 187.89/187.72 inference(rename_variables,[],[4489])). % 187.89/187.72 cnf(11999,plain, % 187.89/187.72 (~P1(f306(f306(f221(a865),x119991),x119991))), % 187.89/187.72 inference(rename_variables,[],[4489])). % 187.89/187.72 cnf(12002,plain, % 187.89/187.72 (P1(f306(f306(f221(a865),x120021),f306(a119,x120021)))), % 187.89/187.72 inference(rename_variables,[],[3340])). % 187.89/187.72 cnf(12009,plain, % 187.89/187.72 (P1(f306(f306(f308(f872(x120091,a859)),x120092),f306(f283(x120091),x120092)))), % 187.89/187.72 inference(rename_variables,[],[3629])). % 187.89/187.72 cnf(12013,plain, % 187.89/187.72 (~P1(f306(f306(f308(a865),f306(a119,f306(f134(a865,a865,f81(a865),f2(a865)),x120131))),f306(f164(a865),f306(f128(a865,x120132),x120131))))), % 187.89/187.72 inference(scs_inference,[],[4527,3510,4455,4456,4420,10200,10210,10221,10330,10333,10336,10438,10551,10855,11022,11025,11223,11313,11320,11334,11384,11387,11409,11502,11548,11564,11864,11892,11904,4435,10422,10515,3479,3189,2875,2876,2879,2882,2883,2886,2887,2889,2894,2902,2911,2923,2929,2936,2937,2938,2943,2952,2970,3004,3005,3018,3019,3021,3028,3029,3030,3031,3033,3044,3050,3162,3064,4416,3117,11310,3313,3227,10203,10264,10267,10357,10360,10650,10929,11325,11328,11445,11489,11494,3202,11590,3212,3722,10969,11596,3107,3922,3552,3812,11360,3170,3134,3129,3115,3330,3201,3222,10463,3375,4513,3895,4445,10255,10419,11220,3260,11685,4503,10972,11042,11263,11266,3376,3165,10322,10626,3166,3433,3086,3185,11350,4037,3897,10978,11104,11155,4524,10907,11109,11214,11236,11271,11277,4525,11011,11112,11217,4526,11115,4528,11169,4529,3184,3472,3628,4316,4317,4443,3570,3777,3340,10341,10458,10529,10590,10593,10629,10723,10962,11860,11926,3715,11581,3253,3352,4493,10232,10235,10261,10731,10744,10865,11286,11353,11752,11757,11978,4509,11464,11497,11532,11561,3702,3480,3481,3847,3299,3300,3273,4490,4440,3464,4510,4031,11231,3589,3312,11709,4001,3961,3907,10799,3956,3629,11863,3990,3646,10984,11047,11128,4514,10747,11120,3270,10350,10445,10576,10636,11437,11657,11703,11737,11833,3271,10705,10750,10753,10786,10812,10849,10887,10923,11907,11910,11913,11916,3272,10433,10641,10726,10852,11740,11749,11839,11850,11869,11874,11919,11939,3348,4489,10298,10387,10500,10524,10768,10815,10825,11511,11611,11632,11635,11638,11654,11807,11810,11813,11816,11903,11922,11925,11935,11990,11993,11996,3428,10596,10860,10904,11177,11255,4505,10777,10789,10896,10914,10917,10975,11061,11069,11085,11123,11140,11149,11185,11226,11246,11249,11252,11280,11293,11296,11682,11718,11984,3334,10623,10653,10662,11206,3371,3365,3781,3720,10301,11584,11614,4502,10252,10611,10614,11064,11082,11547,11602,11642,11770,11795,11798,11801,11804,3292,10656,10809,10880,11615,11769,3742,4081,4500,3753,3788,4479,4482,3244,3248,4481,4484,3249,4480,3760,3579,11577,4177,4516,10226,10229,10481,10532,10535,10540,10949,11419,11669,11773,4522,11143,11260,3967,3864,11299,11641,11645,3709,10920,10926,10944,3566,3711,10659,11000,11152,11182,3536,10579,10582,10665,10836,4519,11578,4520,10716,10818,11131,11283,11422,4140,4042,3741,3689,4517,10274,10277,10617,10620,11461,4518,11558,3713,10585,3974,4521,4538,4564,4613,4615,4645,4662,4669,4670,4709,4739,4745,4830,4856,4857,4918,4919,4941,4942,4955,4959,4981,4988,5005,5008,5009,5010,5015,5016,5039,5066,5067,5077,5082,5090,5135,5136,5144,5154,5158,5160,5170,5172,5178,5182,5197,5204,5207,5208,5209,5213,5248,5261,5268,5270,5271,5275,5276,5277,5285,5288,5293,5294,5295,5302,5306,5307,5308,5317,5321,5322,5323,5328,5341,5350,5362,5364,5372,5373,5377,5381,5406,5412,5422,5423,5438,5451,5473,5479,5495,5496,5499,5518,5526,5527,5532,5533,5543,5544,5556,5560,5569,5570,5572,5587,5592,5603,5604,5616,5623,5637,5641,5644,5650,5651,5652,5655,5660,5697,5698,5701,5703,5706,5707,5708,5710,5712,5714,5719,5726,5741,5755,5760,5761,5774,5775,5780,5785,5787,5792,5833,5845,5854,5858,5869,5873,5874,5882,5896,5902,5920,5923,5935,5965,5979,6004,6024,6025,6028,6042,6044,6046,6048,6061,6062,6065,6067,6070,6071,6082,6088,6089,6090,6092,6094,6136,6137,6144,6154,6190,6192,6194,6196,6205,6207,6209,6215,6217,6223,6226,6234,6241,6242,6243,6248,6270,6271,6272,6274,6280,6285,6322,6323,6325,6326,6327,6329,6330,6331,6332,6341,6374,6375,6384,6405,6406,6426,6429,6440,6441,6447,6476,6478,6490,6528,6530,6531,6586,6610,6656,6676,6685,6686,6687,6688,6707,6708,6714,6726,6729,6731,6733,6734,6735,6737,6751,6762,6764,6765,6778,6781,6832,6843,6845,6849,6864,6865,6901,6913,6944,6963,6978,7032,7060,7115,7136,7145,7148,7203,7211,7269,7271,7285,7295,7296,7297,7316,7322,7324,7373,7383,7386,7402,7451,7453,7456,7499,7500,7518,7585,7604,7628,7650,7665,7680,7691,7699,7700,7728,7731,7733,7741,7779,7790,7815,7873,7907,7939,7986,8002,8008,8019,8020,8095,8149,8168,8192,8212,8236,8335,8337,8343,8361,8365,8379,8402,8413,8415,8430,8436,8440,8465,8479,8480,8496,8497,8502,8503,8504,8505,8506,8524,8525,8526,8535,8549,8551,8563,8567,8569,8570,8571,8579,8584,8611,8612,8641,8654,8658,8676,8698,8699,8700,8701,8714,8715,8737,8747,8756,8757,8758,8759,8761,8783,8784,8795,8840,8846,8852,8865,8870,8872,8875,8876,8880,8889,8972,9003,9004,9005,9020,9038,9043,9070,9071,9114,9117,9144,9189,9190,9191,9207,9233,9247,9253,9256,9279,9280,9308,9371,9407,9408,9409,9434,9435,9453,9471,9477,9493,9516,9538,9546,9547,9548,9549,9565,9567,9572,9603,9604,9610,9611,9654,9655,9686,9696,9706,9708,9709,9719,9733,9737,9765,9797,9802,9859,9902,9903,9905,9915,9916,9936,9941,9964,9969,9984,10036,10110,10111,10168,10184,2,8,9,4551,4552,4570,4601,4602,4604,4631,4637,4638,4649,4698,4700,4730,4744,4774,4871,4872,4886,4906,4962,4963,4966,4967,4969,4971,4972,4984,4985,4995,5006,5007,5013,5032,5033,5054,5059,5060,5061,5062,5065,5073,5076,5083,5084,5085,5150,5156,5157,5164,5194,5205,5211,5227,5247,5254,5255,5256,5265,5274,5281,5283,5284,5290,5298,5299,5309,5313,5314,5315,5316,5318,5319,5324,5325,5326,5327,5358,5359,5360,5368,5369,5370,5371,5414,5419,5421,5458,5460,5461,5463,5464,5466,5467,5469,5478,5483,5485,5486,5487,5488,5489,5490,5497,5507,5510,5521,5537,5538,5541,5550,5552,5553,5554,5579,5589,5606,5607,5617,5618,5620,5622,5627,5662,5666,5668,5728,5762,5763,5767,5773,5776,5777,5778,5779,5786,5797,5798,5800,5801,5809,5830,5861,5877,5880,5881,5883,5892,5910,5914,5917,5918,5919,5937,5950,5951,5981,5982,5986,6006,6009,6013,6032,6037,6038,6063,6066,6073,6081,6087,6091,6098,6099,6100,6101,6139,6155,6208,6244,6246,6267,6268,6273,6277,6278,6281,6288,6297,6314,6334,6335,6342,6352,6367,6387,6393,6395,6410,6411,6415,6417,6418,6419,6421,6423,6424,6425,6428,6433,6434,6436,6437,6443,6445,6486,6489,6503,6505,6506,6507,6543,6548,6550,6555,6556,6564,6568,6581,6605,6606,6608,6609,6621,6625,6627,6647,6650,6669,6702,6703,6704,6709,6722,6741,6743,6745,6747,6752,6758,6760,6775,6782,6818,6819,6820,6834,6835,6837,6838,6855,6857,6873,6899,6921,6932,6934,6936,6938,6939,6940,6975,6976,6981,6982,6990,6992,6993,6994,7013,7022,7023,7035,7045,7084])). % 187.89/187.72 cnf(12014,plain, % 187.89/187.72 (P1(f306(f306(f220(f872(x120141,a859)),f306(f164(x120141),f306(f128(x120141,x120142),x120143))),f306(f164(x120141),x120143)))), % 187.89/187.72 inference(rename_variables,[],[3907])). % 187.89/187.72 cnf(12021,plain, % 187.89/187.72 (~P1(f306(f306(f308(x120211),x120212),f185(f872(x120211,a859))))), % 187.89/187.72 inference(rename_variables,[],[4505])). % 187.89/187.72 cnf(12026,plain, % 187.89/187.72 (E(f306(f186(f866(x120261)),f306(f160(x120261),x120262)),f306(f186(f866(x120261)),x120262))), % 187.89/187.72 inference(rename_variables,[],[3283])). % 187.89/187.72 cnf(12033,plain, % 187.89/187.72 (P1(f306(f306(f220(f872(x120331,a859)),x120332),f231(f872(x120331,a859))))), % 187.89/187.72 inference(rename_variables,[],[3646])). % 187.89/187.72 cnf(12034,plain, % 187.89/187.72 (~E(f306(a119,x120341),x120341)), % 187.89/187.72 inference(rename_variables,[],[4420])). % 187.89/187.72 cnf(12036,plain, % 187.89/187.72 (~P27(a861,f185(f872(f864(a861),a859)),f306(f306(f284(f864(a861)),f306(f306(f306(f93(a861),a303),f306(a26,a873)),f193(f306(a26,a873)))),f185(f872(f864(a861),a859))))), % 187.89/187.72 inference(scs_inference,[],[4527,3510,4455,4456,4420,10200,10210,10221,10330,10333,10336,10438,10551,10855,11022,11025,11223,11313,11320,11334,11384,11387,11409,11502,11548,11564,11864,11892,11904,11936,4435,10422,10515,3479,3189,2875,2876,2879,2882,2883,2886,2887,2889,2894,2902,2911,2923,2929,2936,2937,2938,2943,2952,2970,3004,3005,3018,3019,3021,3028,3029,3030,3031,3033,3044,3050,3162,3064,4416,3117,11310,3313,3227,10203,10264,10267,10357,10360,10650,10929,11325,11328,11445,11489,11494,3202,11590,3212,3722,10969,11596,3107,3922,3552,3812,11360,3170,3134,3129,3115,3283,3330,3201,3222,10463,3375,4513,3895,4445,10255,10419,11220,3260,11685,4503,10972,11042,11263,11266,3376,3165,10322,10626,3166,3433,3086,3185,11350,4037,3897,10978,11104,11155,4524,10907,11109,11214,11236,11271,11277,4525,11011,11112,11217,4526,11115,4528,11169,4529,3184,3472,3628,4316,4317,4443,3570,3777,3340,10341,10458,10529,10590,10593,10629,10723,10962,11860,11926,3715,11581,3253,3352,4493,10232,10235,10261,10731,10744,10865,11286,11353,11752,11757,11978,4509,11464,11497,11532,11561,3702,3480,3481,3847,3299,3300,3273,4490,4440,3464,4510,4031,11231,3589,3312,11709,4001,3961,3907,10799,3956,3629,11863,3990,3646,10984,11047,11128,11188,4514,10747,11120,3270,10350,10445,10576,10636,11437,11657,11703,11737,11833,3271,10705,10750,10753,10786,10812,10849,10887,10923,11907,11910,11913,11916,3272,10433,10641,10726,10852,11740,11749,11839,11850,11869,11874,11919,11939,3348,4489,10298,10387,10500,10524,10768,10815,10825,11511,11611,11632,11635,11638,11654,11807,11810,11813,11816,11903,11922,11925,11935,11990,11993,11996,3428,10596,10860,10904,11177,11255,4505,10777,10789,10896,10914,10917,10975,11061,11069,11085,11123,11140,11149,11185,11226,11246,11249,11252,11280,11293,11296,11682,11718,11984,11987,3334,10623,10653,10662,11206,3371,3365,3781,3720,10301,11584,11614,4502,10252,10611,10614,11064,11082,11547,11602,11642,11770,11795,11798,11801,11804,3292,10656,10809,10880,11615,11769,3742,4081,4500,3753,3788,4479,4482,3244,3248,4481,4484,3249,4480,3760,3579,11577,4177,4516,10226,10229,10481,10532,10535,10540,10949,11419,11669,11773,4522,11143,11260,3967,3864,11299,11641,11645,3709,10920,10926,10944,3566,3711,10659,11000,11152,11182,11193,3536,10579,10582,10665,10836,4519,11578,4520,10716,10818,11131,11283,11422,4140,4042,3741,3689,4517,10274,10277,10617,10620,11461,4518,11558,3713,10585,3974,4521,4538,4564,4613,4615,4645,4662,4669,4670,4709,4739,4745,4830,4856,4857,4918,4919,4941,4942,4955,4959,4981,4988,5005,5008,5009,5010,5015,5016,5039,5066,5067,5077,5082,5090,5135,5136,5144,5154,5158,5160,5170,5172,5178,5182,5197,5204,5207,5208,5209,5213,5248,5261,5268,5270,5271,5275,5276,5277,5285,5288,5293,5294,5295,5302,5306,5307,5308,5317,5321,5322,5323,5328,5341,5350,5362,5364,5372,5373,5377,5381,5406,5412,5422,5423,5438,5451,5473,5479,5495,5496,5499,5518,5526,5527,5532,5533,5543,5544,5556,5560,5569,5570,5572,5587,5592,5603,5604,5616,5623,5637,5641,5644,5650,5651,5652,5655,5660,5697,5698,5701,5703,5706,5707,5708,5710,5712,5714,5719,5726,5741,5755,5760,5761,5774,5775,5780,5785,5787,5792,5833,5845,5854,5858,5869,5873,5874,5882,5896,5902,5920,5923,5935,5965,5979,6004,6024,6025,6028,6042,6044,6046,6048,6061,6062,6065,6067,6070,6071,6082,6088,6089,6090,6092,6094,6136,6137,6144,6154,6190,6192,6194,6196,6205,6207,6209,6215,6217,6223,6226,6234,6241,6242,6243,6248,6270,6271,6272,6274,6280,6285,6322,6323,6325,6326,6327,6329,6330,6331,6332,6341,6374,6375,6384,6405,6406,6426,6429,6440,6441,6447,6476,6478,6490,6528,6530,6531,6586,6610,6656,6676,6685,6686,6687,6688,6707,6708,6714,6726,6729,6731,6733,6734,6735,6737,6751,6762,6764,6765,6778,6781,6832,6843,6845,6849,6864,6865,6901,6913,6944,6963,6978,7032,7060,7115,7136,7145,7148,7203,7211,7269,7271,7285,7295,7296,7297,7316,7322,7324,7373,7383,7386,7402,7451,7453,7456,7499,7500,7518,7585,7604,7628,7650,7665,7680,7691,7699,7700,7728,7731,7733,7741,7779,7790,7815,7873,7907,7939,7986,8002,8008,8019,8020,8095,8149,8168,8192,8212,8236,8335,8337,8343,8361,8365,8379,8402,8413,8415,8430,8436,8440,8465,8479,8480,8496,8497,8502,8503,8504,8505,8506,8524,8525,8526,8535,8549,8551,8563,8567,8569,8570,8571,8579,8584,8611,8612,8641,8654,8658,8676,8698,8699,8700,8701,8714,8715,8737,8747,8756,8757,8758,8759,8761,8783,8784,8795,8840,8846,8852,8865,8870,8872,8875,8876,8880,8889,8972,9003,9004,9005,9020,9038,9043,9070,9071,9114,9117,9144,9189,9190,9191,9207,9233,9247,9253,9256,9279,9280,9308,9371,9407,9408,9409,9434,9435,9453,9471,9477,9493,9516,9538,9546,9547,9548,9549,9565,9567,9572,9603,9604,9610,9611,9654,9655,9686,9696,9706,9708,9709,9719,9733,9737,9765,9797,9802,9859,9902,9903,9905,9915,9916,9936,9941,9964,9969,9984,10036,10110,10111,10168,10184,2,8,9,4551,4552,4570,4601,4602,4604,4631,4637,4638,4649,4698,4700,4730,4744,4774,4871,4872,4886,4906,4962,4963,4966,4967,4969,4971,4972,4984,4985,4995,5006,5007,5013,5032,5033,5054,5059,5060,5061,5062,5065,5073,5076,5083,5084,5085,5150,5156,5157,5164,5194,5205,5211,5227,5247,5254,5255,5256,5265,5274,5281,5283,5284,5290,5298,5299,5309,5313,5314,5315,5316,5318,5319,5324,5325,5326,5327,5358,5359,5360,5368,5369,5370,5371,5414,5419,5421,5458,5460,5461,5463,5464,5466,5467,5469,5478,5483,5485,5486,5487,5488,5489,5490,5497,5507,5510,5521,5537,5538,5541,5550,5552,5553,5554,5579,5589,5606,5607,5617,5618,5620,5622,5627,5662,5666,5668,5728,5762,5763,5767,5773,5776,5777,5778,5779,5786,5797,5798,5800,5801,5809,5830,5861,5877,5880,5881,5883,5892,5910,5914,5917,5918,5919,5937,5950,5951,5981,5982,5986,6006,6009,6013,6032,6037,6038,6063,6066,6073,6081,6087,6091,6098,6099,6100,6101,6139,6155,6208,6244,6246,6267,6268,6273,6277,6278,6281,6288,6297,6314,6334,6335,6342,6352,6367,6387,6393,6395,6410,6411,6415,6417,6418,6419,6421,6423,6424,6425,6428,6433,6434,6436,6437,6443,6445,6486,6489,6503,6505,6506,6507,6543,6548,6550,6555,6556,6564,6568,6581,6605,6606,6608,6609,6621,6625,6627,6647,6650,6669,6702,6703,6704,6709,6722,6741,6743,6745,6747,6752,6758,6760,6775,6782,6818,6819,6820,6834,6835,6837,6838,6855,6857,6873,6899,6921,6932,6934,6936,6938,6939,6940,6975,6976,6981,6982,6990,6992,6993,6994,7013,7022,7023,7035,7045,7084,7094,7098,7105,7116,7117,7122,7124,7130,7138])). % 187.89/187.72 cnf(12037,plain, % 187.89/187.72 (P1(f306(f306(f220(f872(x120371,a859)),f185(f872(x120371,a859))),x120372))), % 187.89/187.72 inference(rename_variables,[],[3711])). % 187.89/187.72 cnf(12040,plain, % 187.89/187.72 (P1(f306(f306(f220(f872(x120401,a859)),f306(f164(x120401),f306(f128(x120401,x120402),x120403))),f306(f164(x120401),x120403)))), % 187.89/187.72 inference(rename_variables,[],[3907])). % 187.89/187.72 cnf(12046,plain, % 187.89/187.72 (P1(f306(f306(f221(a865),x120461),f306(a119,x120461)))), % 187.89/187.72 inference(rename_variables,[],[3340])). % 187.89/187.72 cnf(12055,plain, % 187.89/187.72 (E(f306(f232(x120551,x120551),f233(x120551,x120552)),x120552)), % 187.89/187.72 inference(rename_variables,[],[3227])). % 187.89/187.72 cnf(12066,plain, % 187.89/187.72 (~P1(f306(f306(f220(a865),f306(a119,x120661)),x120661))), % 187.89/187.72 inference(rename_variables,[],[4502])). % 187.89/187.72 cnf(12067,plain, % 187.89/187.72 (~P1(f306(f306(f221(a865),x120671),f2(a865)))), % 187.89/187.72 inference(rename_variables,[],[4493])). % 187.89/187.72 cnf(12070,plain, % 187.89/187.72 (P1(f306(f63(x120701),f185(f872(x120701,a859))))), % 187.89/187.72 inference(rename_variables,[],[3348])). % 187.89/187.72 cnf(12071,plain, % 187.89/187.72 (~P1(f306(f306(f308(x120711),x120712),f185(f872(x120711,a859))))), % 187.89/187.72 inference(rename_variables,[],[4505])). % 187.89/187.72 cnf(12076,plain, % 187.89/187.72 (~P1(f306(f306(f221(a865),x120761),f2(a865)))), % 187.89/187.72 inference(rename_variables,[],[4493])). % 187.89/187.72 cnf(12077,plain, % 187.89/187.72 (~P1(f306(f306(f221(a865),x120771),x120771))), % 187.89/187.72 inference(rename_variables,[],[4489])). % 187.89/187.72 cnf(12082,plain, % 187.89/187.72 (P1(f306(f306(f220(f872(x120821,a859)),f306(f164(x120821),f162(x120821,x120822,x120823))),f306(f164(x120821),x120823)))), % 187.89/187.72 inference(rename_variables,[],[3956])). % 187.89/187.72 cnf(12085,plain, % 187.89/187.72 (P28(x120851,x120851,f5(x120851),x120852)), % 187.89/187.72 inference(rename_variables,[],[3510])). % 187.89/187.72 cnf(12092,plain, % 187.89/187.72 (P1(f306(f306(f308(f872(x120921,a859)),x120922),f306(f283(x120921),x120922)))), % 187.89/187.72 inference(rename_variables,[],[3629])). % 187.89/187.72 cnf(12099,plain, % 187.89/187.72 (P1(f306(f306(f193(a24),x120991),x120991))), % 187.89/187.72 inference(rename_variables,[],[3270])). % 187.89/187.72 cnf(12102,plain, % 187.89/187.72 (~P1(f306(f306(f308(x121021),x121022),f185(f872(x121021,a859))))), % 187.89/187.72 inference(rename_variables,[],[4505])). % 187.89/187.72 cnf(12105,plain, % 187.89/187.72 (P1(f306(f306(f220(f872(x121051,a859)),x121052),f306(f306(f284(x121051),x121053),x121052)))), % 187.89/187.72 inference(rename_variables,[],[3709])). % 187.89/187.72 cnf(12106,plain, % 187.89/187.72 (P1(f306(f306(f220(f872(x121061,a859)),x121062),f231(f872(x121061,a859))))), % 187.89/187.72 inference(rename_variables,[],[3646])). % 187.89/187.72 cnf(12113,plain, % 187.89/187.72 (P1(f306(f306(f220(a865),x121131),x121131))), % 187.89/187.72 inference(rename_variables,[],[3271])). % 187.89/187.72 cnf(12116,plain, % 187.89/187.72 (P1(f306(f306(f220(a865),x121161),x121161))), % 187.89/187.72 inference(rename_variables,[],[3271])). % 187.89/187.72 cnf(12119,plain, % 187.89/187.72 (P1(f306(f306(f220(a865),x121191),x121191))), % 187.89/187.72 inference(rename_variables,[],[3271])). % 187.89/187.72 cnf(12122,plain, % 187.89/187.72 (P1(f306(f306(f220(a865),x121221),x121221))), % 187.89/187.72 inference(rename_variables,[],[3271])). % 187.89/187.72 cnf(12125,plain, % 187.89/187.72 (P1(f306(f306(f221(a865),x121251),f306(a119,x121251)))), % 187.89/187.72 inference(rename_variables,[],[3340])). % 187.89/187.72 cnf(12128,plain, % 187.89/187.72 (P1(f306(f306(f221(a865),x121281),f306(a119,x121281)))), % 187.89/187.72 inference(rename_variables,[],[3340])). % 187.89/187.72 cnf(12131,plain, % 187.89/187.72 (P1(f306(f306(f220(f872(x121311,a859)),x121312),x121312))), % 187.89/187.72 inference(rename_variables,[],[3566])). % 187.89/187.72 cnf(12133,plain, % 187.89/187.72 (~P1(f306(f306(f220(a1),f306(f306(f22(a1),a84),a104)),f2(a1)))), % 187.89/187.72 inference(scs_inference,[],[4527,3510,11037,4455,4456,4420,10200,10210,10221,10330,10333,10336,10438,10551,10855,11022,11025,11223,11313,11320,11334,11384,11387,11409,11502,11548,11564,11864,11892,11904,11936,4435,10422,10515,3479,3189,2875,2876,2878,2879,2882,2883,2885,2886,2887,2889,2894,2902,2911,2923,2929,2936,2937,2938,2943,2952,2970,3004,3005,3018,3019,3021,3028,3029,3030,3031,3033,3044,3050,3162,3064,4416,3117,11310,3313,3227,10203,10264,10267,10357,10360,10650,10929,11325,11328,11445,11489,11494,11593,3202,11590,3212,3722,10969,11596,3107,3922,3552,3812,11360,3170,3134,3129,3115,3283,3330,3201,3222,10463,3375,4513,3895,4445,10255,10419,11220,3260,11685,4503,10972,11042,11263,11266,3376,3165,10322,10626,3166,3433,3086,3185,11350,4037,3897,10978,11104,11155,4524,10907,11109,11214,11236,11271,11277,4525,11011,11112,11217,4526,11115,4528,11169,4529,3184,3472,3628,4316,4317,4443,3570,3777,3458,3704,3340,10341,10458,10529,10590,10593,10629,10723,10962,11860,11926,12002,12046,12125,3715,11581,4174,3253,3352,3533,4493,10232,10235,10261,10731,10744,10865,11286,11353,11752,11757,11978,11981,12067,4509,11464,11497,11532,11561,3702,3480,3481,3847,3299,3300,3273,4490,4440,3464,4510,4031,11231,3589,3312,11709,11712,4001,3961,3907,10799,12014,3956,10981,3629,11863,12009,3990,3646,10984,11047,11128,11188,12033,4514,10747,11120,3270,10350,10445,10576,10636,11437,11657,11703,11737,11833,11891,3271,10705,10750,10753,10786,10812,10849,10887,10923,11907,11910,11913,11916,12113,12116,12119,3272,10433,10641,10726,10852,11740,11749,11839,11850,11869,11874,11919,11939,3348,12070,4489,10298,10387,10500,10524,10768,10815,10825,11511,11611,11632,11635,11638,11654,11807,11810,11813,11816,11903,11922,11925,11935,11990,11993,11996,11999,3428,10596,10860,10904,11177,11255,4505,10777,10789,10896,10914,10917,10975,11061,11069,11085,11123,11140,11149,11185,11226,11246,11249,11252,11280,11293,11296,11682,11718,11984,11987,12021,12071,3334,10623,10653,10662,11206,3371,3365,3781,3720,10301,11584,11614,4502,10252,10611,10614,11064,11082,11547,11602,11642,11770,11795,11798,11801,11804,3292,10656,10809,10880,11615,11769,3742,4081,4500,3753,3788,4479,4482,3244,3248,4481,4484,3249,4480,3760,3579,11577,4177,4516,10226,10229,10481,10532,10535,10540,10949,11419,11669,11773,4522,11143,11260,3967,3864,11299,11641,11645,3709,10920,10926,10944,11888,3566,11146,3711,10659,11000,11152,11182,11193,3536,10579,10582,10665,10836,4519,11578,4520,10716,10818,11131,11283,11422,4140,4042,3741,3689,4517,10274,10277,10617,10620,11461,4518,11558,3713,10585,3974,4521,4538,4564,4613,4615,4645,4662,4669,4670,4709,4739,4745,4830,4856,4857,4918,4919,4941,4942,4955,4959,4981,4988,5005,5008,5009,5010,5015,5016,5039,5066,5067,5077,5082,5090,5135,5136,5144,5154,5158,5160,5170,5172,5178,5182,5197,5204,5207,5208,5209,5213,5248,5261,5268,5270,5271,5275,5276,5277,5285,5288,5293,5294,5295,5302,5306,5307,5308,5317,5321,5322,5323,5328,5341,5350,5362,5364,5372,5373,5377,5381,5406,5412,5422,5423,5438,5451,5473,5479,5495,5496,5499,5518,5526,5527,5532,5533,5543,5544,5556,5560,5569,5570,5572,5587,5592,5603,5604,5616,5623,5637,5641,5644,5650,5651,5652,5655,5660,5697,5698,5701,5703,5706,5707,5708,5710,5712,5714,5719,5726,5741,5755,5760,5761,5774,5775,5780,5785,5787,5792,5833,5845,5854,5858,5869,5873,5874,5882,5896,5902,5920,5923,5935,5965,5979,6004,6024,6025,6028,6042,6044,6046,6048,6061,6062,6065,6067,6070,6071,6082,6088,6089,6090,6092,6094,6136,6137,6144,6154,6190,6192,6194,6196,6205,6207,6209,6215,6217,6223,6226,6234,6241,6242,6243,6248,6270,6271,6272,6274,6280,6285,6322,6323,6325,6326,6327,6329,6330,6331,6332,6341,6374,6375,6384,6405,6406,6426,6429,6440,6441,6447,6476,6478,6490,6528,6530,6531,6586,6610,6656,6676,6685,6686,6687,6688,6707,6708,6714,6726,6729,6731,6733,6734,6735,6737,6751,6762,6764,6765,6778,6781,6832,6843,6845,6849,6864,6865,6901,6913,6944,6963,6978,7032,7060,7115,7136,7145,7148,7203,7211,7269,7271,7285,7295,7296,7297,7316,7322,7324,7373,7383,7386,7402,7451,7453,7456,7499,7500,7518,7585,7604,7628,7650,7665,7680,7691,7699,7700,7728,7731,7733,7741,7779,7790,7815,7873,7907,7939,7986,8002,8008,8019,8020,8095,8149,8168,8192,8212,8236,8335,8337,8343,8361,8365,8379,8402,8413,8415,8430,8436,8440,8465,8479,8480,8496,8497,8502,8503,8504,8505,8506,8524,8525,8526,8535,8549,8551,8563,8567,8569,8570,8571,8579,8584,8611,8612,8641,8654,8658,8676,8698,8699,8700,8701,8714,8715,8737,8747,8756,8757,8758,8759,8761,8783,8784,8795,8840,8846,8852,8865,8870,8872,8875,8876,8880,8889,8972,9003,9004,9005,9020,9038,9043,9070,9071,9114,9117,9144,9189,9190,9191,9207,9233,9247,9253,9256,9279,9280,9308,9371,9407,9408,9409,9434,9435,9453,9471,9477,9493,9516,9538,9546,9547,9548,9549,9565,9567,9572,9603,9604,9610,9611,9654,9655,9686,9696,9706,9708,9709,9719,9733,9737,9765,9797,9802,9859,9902,9903,9905,9915,9916,9936,9941,9964,9969,9984,10036,10110,10111,10168,10184,2,8,9,4551,4552,4570,4601,4602,4604,4631,4637,4638,4649,4698,4700,4730,4744,4774,4871,4872,4886,4906,4962,4963,4966,4967,4969,4971,4972,4984,4985,4995,5006,5007,5013,5032,5033,5054,5059,5060,5061,5062,5065,5073,5076,5083,5084,5085,5150,5156,5157,5164,5194,5205,5211,5227,5247,5254,5255,5256,5265,5274,5281,5283,5284,5290,5298,5299,5309,5313,5314,5315,5316,5318,5319,5324,5325,5326,5327,5358,5359,5360,5368,5369,5370,5371,5414,5419,5421,5458,5460,5461,5463,5464,5466,5467,5469,5478,5483,5485,5486,5487,5488,5489,5490,5497,5507,5510,5521,5537,5538,5541,5550,5552,5553,5554,5579,5589,5606,5607,5617,5618,5620,5622,5627,5662,5666,5668,5728,5762,5763,5767,5773,5776,5777,5778,5779,5786,5797,5798,5800,5801,5809,5830,5861,5877,5880,5881,5883,5892,5910,5914,5917,5918,5919,5937,5950,5951,5981,5982,5986,6006,6009,6013,6032,6037,6038,6063,6066,6073,6081,6087,6091,6098,6099,6100,6101,6139,6155,6208,6244,6246,6267,6268,6273,6277,6278,6281,6288,6297,6314,6334,6335,6342,6352,6367,6387,6393,6395,6410,6411,6415,6417,6418,6419,6421,6423,6424,6425,6428,6433,6434,6436,6437,6443,6445,6486,6489,6503,6505,6506,6507,6543,6548,6550,6555,6556,6564,6568,6581,6605,6606,6608,6609,6621,6625,6627,6647,6650,6669,6702,6703,6704,6709,6722,6741,6743,6745,6747,6752,6758,6760,6775,6782,6818,6819,6820,6834,6835,6837,6838,6855,6857,6873,6899,6921,6932,6934,6936,6938,6939,6940,6975,6976,6981,6982,6990,6992,6993,6994,7013,7022,7023,7035,7045,7084,7094,7098,7105,7116,7117,7122,7124,7130,7138,7139,7152,7169,7187,7189,7206,7255,7256,7257,7259,7261,7265,7270,7292,7337,7369,7384,7389,7401,7434,7437,7460,7484,7501,7504,7505,7515,7534,7536,7538,7540,7541,7542,7567,7593])). % 187.89/187.72 cnf(12138,plain, % 187.89/187.72 (P1(f306(f306(f308(f872(x121381,a859)),x121382),f306(f283(x121381),x121382)))), % 187.89/187.72 inference(rename_variables,[],[3629])). % 187.89/187.72 cnf(12144,plain, % 187.89/187.72 (~P1(f306(f306(f221(a1),f306(f306(f81(a1),a84),a84)),f2(a1)))), % 187.89/187.72 inference(scs_inference,[],[4527,3510,11037,4455,4456,4420,10200,10210,10221,10330,10333,10336,10438,10551,10855,11022,11025,11223,11313,11320,11334,11384,11387,11409,11502,11548,11564,11864,11892,11904,11936,4435,10422,10515,3479,3189,2875,2876,2878,2879,2882,2883,2885,2886,2887,2889,2894,2902,2911,2923,2929,2936,2937,2938,2943,2952,2970,3004,3005,3018,3019,3021,3028,3029,3030,3031,3033,3044,3050,3162,3064,4416,3117,11310,3313,3227,10203,10264,10267,10357,10360,10650,10929,11325,11328,11445,11489,11494,11593,3202,11590,3212,3722,10969,11596,3107,3922,3552,3812,11360,3170,3134,3129,3115,3283,3330,3201,3222,10463,3375,4513,3895,4445,10255,10419,11220,3260,11685,4503,10972,11042,11263,11266,3376,3165,10322,10626,3166,3433,3086,3185,11350,4037,3897,10978,11104,11155,4524,10907,11109,11214,11236,11271,11277,4525,11011,11112,11217,4526,11115,4528,11169,4529,3184,3472,3628,4316,4317,4443,3570,3777,3458,3704,3340,10341,10458,10529,10590,10593,10629,10723,10962,11860,11926,12002,12046,12125,3715,11581,4174,3253,3352,3533,4493,10232,10235,10261,10731,10744,10865,11286,11353,11752,11757,11978,11981,12067,4509,11464,11497,11532,11561,3702,3480,3481,3847,3299,3300,3273,4490,4440,3464,4510,4031,11231,3589,3312,11709,11712,4001,3961,3907,10799,12014,3956,10981,3629,11863,12009,12092,3990,3646,10984,11047,11128,11188,12033,4514,10747,11120,3270,10350,10445,10576,10636,11437,11657,11703,11737,11833,11891,3271,10705,10750,10753,10786,10812,10849,10887,10923,11907,11910,11913,11916,12113,12116,12119,3272,10433,10641,10726,10852,11740,11749,11839,11850,11869,11874,11919,11939,3348,12070,4489,10298,10387,10500,10524,10768,10815,10825,11511,11611,11632,11635,11638,11654,11807,11810,11813,11816,11903,11922,11925,11935,11990,11993,11996,11999,3428,10596,10860,10904,11177,11255,4505,10777,10789,10896,10914,10917,10975,11061,11069,11085,11123,11140,11149,11185,11226,11246,11249,11252,11280,11293,11296,11682,11718,11984,11987,12021,12071,3334,10623,10653,10662,11206,3371,3365,3781,3720,10301,11584,11614,4502,10252,10611,10614,11064,11082,11547,11602,11642,11770,11795,11798,11801,11804,3292,10656,10809,10880,11615,11769,3742,4081,4500,3753,3788,4479,4482,3244,3248,4481,4484,3249,4480,3760,3579,11577,4177,4516,10226,10229,10481,10532,10535,10540,10949,11419,11669,11773,4522,11143,11260,3967,3864,11299,11641,11645,3709,10920,10926,10944,11888,3566,11146,3711,10659,11000,11152,11182,11193,3536,10579,10582,10665,10836,4519,11578,4520,10716,10818,11131,11283,11422,4140,4042,3741,3689,4517,10274,10277,10617,10620,11461,4518,11558,3713,10585,3974,4521,4538,4564,4613,4615,4645,4662,4669,4670,4709,4739,4745,4830,4856,4857,4918,4919,4941,4942,4955,4959,4981,4988,5005,5008,5009,5010,5015,5016,5039,5066,5067,5077,5082,5090,5135,5136,5144,5154,5158,5160,5170,5172,5178,5182,5197,5204,5207,5208,5209,5213,5248,5261,5268,5270,5271,5275,5276,5277,5285,5288,5293,5294,5295,5302,5306,5307,5308,5317,5321,5322,5323,5328,5341,5350,5362,5364,5372,5373,5377,5381,5406,5412,5422,5423,5438,5451,5473,5479,5495,5496,5499,5518,5526,5527,5532,5533,5543,5544,5556,5560,5569,5570,5572,5587,5592,5603,5604,5616,5623,5637,5641,5644,5650,5651,5652,5655,5660,5697,5698,5701,5703,5706,5707,5708,5710,5712,5714,5719,5726,5741,5755,5760,5761,5774,5775,5780,5785,5787,5792,5833,5845,5854,5858,5869,5873,5874,5882,5896,5902,5920,5923,5935,5965,5979,6004,6024,6025,6028,6042,6044,6046,6048,6061,6062,6065,6067,6070,6071,6082,6088,6089,6090,6092,6094,6136,6137,6144,6154,6190,6192,6194,6196,6205,6207,6209,6215,6217,6223,6226,6234,6241,6242,6243,6248,6270,6271,6272,6274,6280,6285,6322,6323,6325,6326,6327,6329,6330,6331,6332,6341,6374,6375,6384,6405,6406,6426,6429,6440,6441,6447,6476,6478,6490,6528,6530,6531,6586,6610,6656,6676,6685,6686,6687,6688,6707,6708,6714,6726,6729,6731,6733,6734,6735,6737,6751,6762,6764,6765,6778,6781,6832,6843,6845,6849,6864,6865,6901,6913,6944,6963,6978,7032,7060,7115,7136,7145,7148,7203,7211,7269,7271,7285,7295,7296,7297,7316,7322,7324,7373,7383,7386,7402,7451,7453,7456,7499,7500,7518,7585,7604,7628,7650,7665,7680,7691,7699,7700,7728,7731,7733,7741,7779,7790,7815,7873,7907,7939,7986,8002,8008,8019,8020,8095,8149,8168,8192,8212,8236,8335,8337,8343,8361,8365,8379,8402,8413,8415,8430,8436,8440,8465,8479,8480,8496,8497,8502,8503,8504,8505,8506,8524,8525,8526,8535,8549,8551,8563,8567,8569,8570,8571,8579,8584,8611,8612,8641,8654,8658,8676,8698,8699,8700,8701,8714,8715,8737,8747,8756,8757,8758,8759,8761,8783,8784,8795,8840,8846,8852,8865,8870,8872,8875,8876,8880,8889,8972,9003,9004,9005,9020,9038,9043,9070,9071,9114,9117,9144,9189,9190,9191,9207,9233,9247,9253,9256,9279,9280,9308,9371,9407,9408,9409,9434,9435,9453,9471,9477,9493,9516,9538,9546,9547,9548,9549,9565,9567,9572,9603,9604,9610,9611,9654,9655,9686,9696,9706,9708,9709,9719,9733,9737,9765,9797,9802,9859,9902,9903,9905,9915,9916,9936,9941,9964,9969,9984,10036,10110,10111,10168,10184,2,8,9,4551,4552,4570,4601,4602,4604,4631,4637,4638,4649,4698,4700,4730,4744,4774,4871,4872,4886,4906,4962,4963,4966,4967,4969,4971,4972,4984,4985,4995,5006,5007,5013,5032,5033,5054,5059,5060,5061,5062,5065,5073,5076,5083,5084,5085,5150,5156,5157,5164,5194,5205,5211,5227,5247,5254,5255,5256,5265,5274,5281,5283,5284,5290,5298,5299,5309,5313,5314,5315,5316,5318,5319,5324,5325,5326,5327,5358,5359,5360,5368,5369,5370,5371,5414,5419,5421,5458,5460,5461,5463,5464,5466,5467,5469,5478,5483,5485,5486,5487,5488,5489,5490,5497,5507,5510,5521,5537,5538,5541,5550,5552,5553,5554,5579,5589,5606,5607,5617,5618,5620,5622,5627,5662,5666,5668,5728,5762,5763,5767,5773,5776,5777,5778,5779,5786,5797,5798,5800,5801,5809,5830,5861,5877,5880,5881,5883,5892,5910,5914,5917,5918,5919,5937,5950,5951,5981,5982,5986,6006,6009,6013,6032,6037,6038,6063,6066,6073,6081,6087,6091,6098,6099,6100,6101,6139,6155,6208,6244,6246,6267,6268,6273,6277,6278,6281,6288,6297,6314,6334,6335,6342,6352,6367,6387,6393,6395,6410,6411,6415,6417,6418,6419,6421,6423,6424,6425,6428,6433,6434,6436,6437,6443,6445,6486,6489,6503,6505,6506,6507,6543,6548,6550,6555,6556,6564,6568,6581,6605,6606,6608,6609,6621,6625,6627,6647,6650,6669,6702,6703,6704,6709,6722,6741,6743,6745,6747,6752,6758,6760,6775,6782,6818,6819,6820,6834,6835,6837,6838,6855,6857,6873,6899,6921,6932,6934,6936,6938,6939,6940,6975,6976,6981,6982,6990,6992,6993,6994,7013,7022,7023,7035,7045,7084,7094,7098,7105,7116,7117,7122,7124,7130,7138,7139,7152,7169,7187,7189,7206,7255,7256,7257,7259,7261,7265,7270,7292,7337,7369,7384,7389,7401,7434,7437,7460,7484,7501,7504,7505,7515,7534,7536,7538,7540,7541,7542,7567,7593,7594,7627,7629,7630,7631])). % 187.89/187.72 cnf(12147,plain, % 187.89/187.72 (~E(f306(a119,x121471),x121471)), % 187.89/187.72 inference(rename_variables,[],[4420])). % 187.89/187.72 cnf(12148,plain, % 187.89/187.72 (E(f306(f285(x121481,x121481,f5(x121481)),x121482),x121482)), % 187.89/187.72 inference(rename_variables,[],[3330])). % 187.89/187.72 cnf(12151,plain, % 187.89/187.72 (P35(x121511,x121512,f120(x121511),f120(x121511))), % 187.89/187.72 inference(rename_variables,[],[3517])). % 187.89/187.72 cnf(12154,plain, % 187.89/187.72 (~E(f306(a119,x121541),x121541)), % 187.89/187.72 inference(rename_variables,[],[4420])). % 187.89/187.72 cnf(12157,plain, % 187.89/187.72 (P1(f306(f306(f220(f872(x121571,a859)),f306(f164(x121571),f162(x121571,x121572,x121573))),f306(f164(x121571),x121573)))), % 187.89/187.72 inference(rename_variables,[],[3956])). % 187.89/187.72 cnf(12158,plain, % 187.89/187.72 (P1(f306(f63(x121581),f306(f164(x121581),x121582)))), % 187.89/187.72 inference(rename_variables,[],[3312])). % 187.89/187.72 cnf(12169,plain, % 187.89/187.72 (~P1(f306(f306(f221(a865),x121691),x121691))), % 187.89/187.72 inference(rename_variables,[],[4489])). % 187.89/187.72 cnf(12172,plain, % 187.89/187.72 (~P1(f306(f306(f221(a865),x121721),x121721))), % 187.89/187.72 inference(rename_variables,[],[4489])). % 187.89/187.72 cnf(12177,plain, % 187.89/187.72 (E(f306(f186(f866(x121771)),f306(f160(x121771),x121772)),f306(f186(f866(x121771)),x121772))), % 187.89/187.72 inference(rename_variables,[],[3283])). % 187.89/187.72 cnf(12180,plain, % 187.89/187.72 (P1(f306(f306(f220(a865),f2(a865)),x121801))), % 187.89/187.72 inference(rename_variables,[],[3292])). % 187.89/187.72 cnf(12187,plain, % 187.89/187.72 (P17(a865,f306(f161(a865),f306(f306(f146(f866(x121871),a865),f186(f866(x121871))),f171(x121871,x121872))))), % 187.89/187.72 inference(rename_variables,[],[3822])). % 187.89/187.72 cnf(12190,plain, % 187.89/187.72 (P28(x121901,x121901,f5(x121901),x121902)), % 187.89/187.72 inference(rename_variables,[],[3510])). % 187.89/187.72 cnf(12193,plain, % 187.89/187.72 (P1(f306(f306(f308(f866(x121931)),f120(x121931)),f153(x121931,x121932)))), % 187.89/187.72 inference(rename_variables,[],[3472])). % 187.89/187.72 cnf(12196,plain, % 187.89/187.72 (~P1(f306(f306(f185(f872(x121961,f872(x121962,a859))),x121963),x121964))), % 187.89/187.72 inference(rename_variables,[],[4520])). % 187.89/187.72 cnf(12201,plain, % 187.89/187.72 (P1(f306(f306(f220(a865),x122011),x122011))), % 187.89/187.72 inference(rename_variables,[],[3271])). % 187.89/187.72 cnf(12202,plain, % 187.89/187.72 (P1(f306(f306(f220(a865),f2(a865)),x122021))), % 187.89/187.72 inference(rename_variables,[],[3292])). % 187.89/187.72 cnf(12204,plain, % 187.89/187.72 (P1(f306(f306(f220(a1),f2(a1)),f853(x122041,f185(f872(x122042,f872(x122043,a859))),f79(a1))))), % 187.89/187.72 inference(scs_inference,[],[4527,3510,11037,12085,3517,4455,4456,4438,4420,10200,10210,10221,10330,10333,10336,10438,10551,10855,11022,11025,11223,11313,11320,11334,11384,11387,11409,11502,11548,11564,11864,11892,11904,11936,12034,12147,4435,10422,10515,3479,3189,2875,2876,2878,2879,2882,2883,2885,2886,2887,2889,2894,2902,2911,2923,2929,2936,2937,2938,2943,2952,2970,3004,3005,3018,3019,3021,3028,3029,3030,3031,3033,3044,3050,3162,3064,4416,3117,11310,3313,3227,10203,10264,10267,10357,10360,10650,10929,11325,11328,11445,11489,11494,11593,3202,11590,3212,3722,10969,11596,3107,3922,3552,3812,11360,3170,3134,3129,3115,3120,3149,3283,12026,3330,10802,3201,3222,10463,3375,4513,3895,4445,10255,10419,11220,3260,11685,4503,10972,11042,11263,11266,3376,3165,10322,10626,3166,3433,3086,3185,11350,4037,3897,10978,11104,11155,4524,10907,11109,11214,11236,11271,11277,4525,11011,11112,11217,4526,11115,4528,11169,4529,3184,3472,3628,4316,4317,4443,3570,3777,3822,3458,3704,3340,10341,10458,10529,10590,10593,10629,10723,10962,11860,11926,12002,12046,12125,3715,11581,4174,3253,3352,3533,4493,10232,10235,10261,10731,10744,10865,11286,11353,11752,11757,11978,11981,12067,12076,4509,11464,11497,11532,11561,3702,3480,3481,3847,3299,3300,3273,4490,4440,3464,4510,4031,11231,3589,3312,11709,11712,4001,3961,3907,10799,12014,3956,10981,12082,3629,11863,12009,12092,12138,3990,3646,10984,11047,11128,11188,12033,4514,10747,11120,3270,10350,10445,10576,10636,11437,11657,11703,11737,11833,11891,3271,10705,10750,10753,10786,10812,10849,10887,10923,11907,11910,11913,11916,12113,12116,12119,12122,3272,10433,10641,10726,10852,11740,11749,11839,11850,11869,11874,11919,11939,3348,12070,4489,10298,10387,10500,10524,10768,10815,10825,11511,11611,11632,11635,11638,11654,11807,11810,11813,11816,11903,11922,11925,11935,11990,11993,11996,11999,12077,12169,3428,10596,10860,10904,11177,11255,11425,4505,10777,10789,10896,10914,10917,10975,11061,11069,11085,11123,11140,11149,11185,11226,11246,11249,11252,11280,11293,11296,11682,11718,11984,11987,12021,12071,3334,10623,10653,10662,11206,3371,3365,3781,3720,10301,11584,11614,4502,10252,10611,10614,11064,11082,11547,11602,11642,11770,11795,11798,11801,11804,12066,3292,10656,10809,10880,11615,11769,11961,12180,3742,4081,4500,3753,3788,4479,4482,3244,3248,4481,4484,3249,4480,3760,3579,11577,4177,4516,10226,10229,10481,10532,10535,10540,10949,11419,11669,11773,4522,11143,11260,3967,3864,11299,11641,11645,3709,10920,10926,10944,11888,3566,11146,3711,10659,11000,11152,11182,11193,3536,10579,10582,10665,10836,4519,11578,4520,10716,10818,11131,11283,11422,11450,12196,4140,4042,3741,3689,4517,10274,10277,10617,10620,11461,4518,11558,3713,10585,3974,4521,4538,4564,4613,4615,4645,4662,4669,4670,4709,4739,4745,4830,4856,4857,4918,4919,4941,4942,4955,4959,4981,4988,5005,5008,5009,5010,5015,5016,5039,5066,5067,5077,5082,5090,5135,5136,5144,5154,5158,5160,5170,5172,5178,5182,5197,5204,5207,5208,5209,5213,5248,5261,5268,5270,5271,5275,5276,5277,5285,5288,5293,5294,5295,5302,5306,5307,5308,5317,5321,5322,5323,5328,5341,5350,5362,5364,5372,5373,5377,5381,5406,5412,5422,5423,5438,5451,5473,5479,5495,5496,5499,5518,5526,5527,5532,5533,5543,5544,5556,5560,5569,5570,5572,5587,5592,5603,5604,5616,5623,5637,5641,5644,5650,5651,5652,5655,5660,5697,5698,5701,5703,5706,5707,5708,5710,5712,5714,5719,5726,5741,5755,5760,5761,5774,5775,5780,5785,5787,5792,5833,5845,5854,5858,5869,5873,5874,5882,5896,5902,5920,5923,5935,5965,5979,6004,6024,6025,6028,6042,6044,6046,6048,6061,6062,6065,6067,6070,6071,6082,6088,6089,6090,6092,6094,6136,6137,6144,6154,6190,6192,6194,6196,6205,6207,6209,6215,6217,6223,6226,6234,6241,6242,6243,6248,6270,6271,6272,6274,6280,6285,6322,6323,6325,6326,6327,6329,6330,6331,6332,6341,6374,6375,6384,6405,6406,6426,6429,6440,6441,6447,6476,6478,6490,6528,6530,6531,6586,6610,6656,6676,6685,6686,6687,6688,6707,6708,6714,6726,6729,6731,6733,6734,6735,6737,6751,6762,6764,6765,6778,6781,6832,6843,6845,6849,6864,6865,6901,6913,6944,6963,6978,7032,7060,7115,7136,7145,7148,7203,7211,7269,7271,7285,7295,7296,7297,7316,7322,7324,7373,7383,7386,7402,7451,7453,7456,7499,7500,7518,7585,7604,7628,7650,7665,7680,7691,7699,7700,7728,7731,7733,7741,7779,7790,7815,7873,7907,7939,7986,8002,8008,8019,8020,8095,8149,8168,8192,8212,8236,8335,8337,8343,8361,8365,8379,8402,8413,8415,8430,8436,8440,8465,8479,8480,8496,8497,8502,8503,8504,8505,8506,8524,8525,8526,8535,8549,8551,8563,8567,8569,8570,8571,8579,8584,8611,8612,8641,8654,8658,8676,8698,8699,8700,8701,8714,8715,8737,8747,8756,8757,8758,8759,8761,8783,8784,8795,8840,8846,8852,8865,8870,8872,8875,8876,8880,8889,8972,9003,9004,9005,9020,9038,9043,9070,9071,9114,9117,9144,9189,9190,9191,9207,9233,9247,9253,9256,9279,9280,9308,9371,9407,9408,9409,9434,9435,9453,9471,9477,9493,9516,9538,9546,9547,9548,9549,9565,9567,9572,9603,9604,9610,9611,9654,9655,9686,9696,9706,9708,9709,9719,9733,9737,9765,9797,9802,9859,9902,9903,9905,9915,9916,9936,9941,9964,9969,9984,10036,10110,10111,10168,10184,2,8,9,4551,4552,4570,4601,4602,4604,4631,4637,4638,4649,4698,4700,4730,4744,4774,4871,4872,4886,4906,4962,4963,4966,4967,4969,4971,4972,4984,4985,4995,5006,5007,5013,5032,5033,5054,5059,5060,5061,5062,5065,5073,5076,5083,5084,5085,5150,5156,5157,5164,5194,5205,5211,5227,5247,5254,5255,5256,5265,5274,5281,5283,5284,5290,5298,5299,5309,5313,5314,5315,5316,5318,5319,5324,5325,5326,5327,5358,5359,5360,5368,5369,5370,5371,5414,5419,5421,5458,5460,5461,5463,5464,5466,5467,5469,5478,5483,5485,5486,5487,5488,5489,5490,5497,5507,5510,5521,5537,5538,5541,5550,5552,5553,5554,5579,5589,5606,5607,5617,5618,5620,5622,5627,5662,5666,5668,5728,5762,5763,5767,5773,5776,5777,5778,5779,5786,5797,5798,5800,5801,5809,5830,5861,5877,5880,5881,5883,5892,5910,5914,5917,5918,5919,5937,5950,5951,5981,5982,5986,6006,6009,6013,6032,6037,6038,6063,6066,6073,6081,6087,6091,6098,6099,6100,6101,6139,6155,6208,6244,6246,6267,6268,6273,6277,6278,6281,6288,6297,6314,6334,6335,6342,6352,6367,6387,6393,6395,6410,6411,6415,6417,6418,6419,6421,6423,6424,6425,6428,6433,6434,6436,6437,6443,6445,6486,6489,6503,6505,6506,6507,6543,6548,6550,6555,6556,6564,6568,6581,6605,6606,6608,6609,6621,6625,6627,6647,6650,6669,6702,6703,6704,6709,6722,6741,6743,6745,6747,6752,6758,6760,6775,6782,6818,6819,6820,6834,6835,6837,6838,6855,6857,6873,6899,6921,6932,6934,6936,6938,6939,6940,6975,6976,6981,6982,6990,6992,6993,6994,7013,7022,7023,7035,7045,7084,7094,7098,7105,7116,7117,7122,7124,7130,7138,7139,7152,7169,7187,7189,7206,7255,7256,7257,7259,7261,7265,7270,7292,7337,7369,7384,7389,7401,7434,7437,7460,7484,7501,7504,7505,7515,7534,7536,7538,7540,7541,7542,7567,7593,7594,7627,7629,7630,7631,7636,7657,7666,7677,7682,7688,7690,7696,7707,7708,7710,7730,7734,7739,7762,7828,7829,7876,7885,7886,7909,7910])). % 187.89/187.72 cnf(12205,plain, % 187.89/187.72 (~P1(f306(f306(f185(f872(x122051,f872(x122052,a859))),x122053),x122054))), % 187.89/187.72 inference(rename_variables,[],[4520])). % 187.89/187.72 cnf(12208,plain, % 187.89/187.72 (P1(f306(f306(f220(f872(f871(f866(x122081),f866(x122081)),a859)),f150(x122081,x122082)),f282(f866(x122081),f149(x122081,x122082))))), % 187.89/187.72 inference(rename_variables,[],[3961])). % 187.89/187.72 cnf(12214,plain, % 187.89/187.72 (P1(f306(f306(f220(f872(x122141,a859)),f306(f164(x122141),f162(x122141,x122142,x122143))),f306(f164(x122141),x122143)))), % 187.89/187.72 inference(rename_variables,[],[3956])). % 187.89/187.72 cnf(12215,plain, % 187.89/187.72 (P1(f306(f306(f220(f872(x122151,a859)),f306(f164(x122151),f306(f128(x122151,x122152),x122153))),f306(f164(x122151),x122153)))), % 187.89/187.72 inference(rename_variables,[],[3907])). % 187.89/187.72 cnf(12218,plain, % 187.89/187.72 (~P1(f306(f306(f221(f872(x122181,a859)),x122182),f185(f872(x122181,a859))))), % 187.89/187.72 inference(rename_variables,[],[4514])). % 187.89/187.72 cnf(12221,plain, % 187.89/187.72 (P28(x122211,f869(x122211),f214(x122211),x122212)), % 187.89/187.72 inference(rename_variables,[],[3518])). % 187.89/187.72 cnf(12226,plain, % 187.89/187.72 (P1(f306(f306(f220(f872(x122261,a859)),f306(f285(x122262,x122261,x122263),f306(f286(x122262,x122261,x122263),x122264))),x122264))), % 187.89/187.72 inference(rename_variables,[],[4140])). % 187.89/187.72 cnf(12229,plain, % 187.89/187.72 (P1(f306(f63(f869(x122291)),f306(f285(x122292,f869(x122291),f306(f169(x122292,x122291),x122293)),f231(f872(x122292,a859)))))), % 187.89/187.72 inference(rename_variables,[],[3967])). % 187.89/187.72 cnf(12234,plain, % 187.89/187.72 (P1(f306(f306(f308(f866(x122341)),f120(x122341)),f153(x122341,x122342)))), % 187.89/187.72 inference(rename_variables,[],[3472])). % 187.89/187.72 cnf(12237,plain, % 187.89/187.72 (~P1(f306(f306(f308(f871(f866(x122371),f866(x122371))),f306(f306(f236(f866(x122371),f866(x122371)),x122372),f120(x122371))),f137(x122371,x122373)))), % 187.89/187.72 inference(rename_variables,[],[4524])). % 187.89/187.72 cnf(12240,plain, % 187.89/187.72 (~P1(f306(f306(f221(a865),x122401),f2(a865)))), % 187.89/187.72 inference(rename_variables,[],[4493])). % 187.89/187.72 cnf(12242,plain, % 187.89/187.72 (~P1(f306(f63(x122421),f231(f872(x122421,a859))))), % 187.89/187.72 inference(scs_inference,[],[4527,3510,11037,12085,3517,3518,3238,4455,4456,3143,4438,4420,10200,10210,10221,10330,10333,10336,10438,10551,10855,11022,11025,11223,11313,11320,11334,11384,11387,11409,11502,11548,11564,11864,11892,11904,11936,12034,12147,4435,10422,10515,3479,3189,2875,2876,2878,2879,2882,2883,2885,2886,2887,2889,2894,2902,2911,2917,2923,2929,2936,2937,2938,2943,2952,2970,3004,3005,3018,3019,3021,3028,3029,3030,3031,3033,3044,3050,3162,3064,4416,3117,11310,3313,3227,10203,10264,10267,10357,10360,10650,10929,11325,11328,11445,11489,11494,11593,3202,11590,3212,3722,10969,11596,3107,3922,3552,3812,11360,3170,3134,3129,3115,3120,3149,3283,12026,3330,10802,3201,3222,10463,3375,4513,3895,4445,10255,10419,11220,3260,11685,4503,10972,11042,11263,11266,3376,3165,10322,10626,3166,3433,3086,3185,11350,4037,3897,10978,11104,11155,4524,10907,11109,11214,11236,11271,11277,4525,11011,11112,11217,4526,11115,4528,11169,4529,3184,3472,12193,12234,3628,4316,4317,4443,3570,3777,3822,3458,3704,3340,10341,10458,10529,10590,10593,10629,10723,10962,11860,11926,12002,12046,12125,3715,11581,4174,3253,3352,3533,4493,10232,10235,10261,10731,10744,10865,11286,11353,11752,11757,11978,11981,12067,12076,4509,11464,11497,11532,11561,3702,3480,3481,3847,3299,3300,3273,4490,4440,3464,4510,4031,11231,3589,3312,11709,11712,4001,3961,11853,12208,3907,10799,12014,12040,3956,10981,12082,12157,3629,11863,12009,12092,12138,3990,3646,10984,11047,11128,11188,12033,4514,10747,11120,3270,10350,10445,10576,10636,11437,11657,11703,11737,11833,11891,3271,10705,10750,10753,10786,10812,10849,10887,10923,11907,11910,11913,11916,12113,12116,12119,12122,3272,10433,10641,10726,10852,11740,11749,11839,11850,11869,11874,11919,11939,3348,12070,4489,10298,10387,10500,10524,10768,10815,10825,11511,11611,11632,11635,11638,11654,11807,11810,11813,11816,11903,11922,11925,11935,11990,11993,11996,11999,12077,12169,3428,10596,10860,10904,11177,11255,11425,4505,10777,10789,10896,10914,10917,10975,11061,11069,11085,11123,11140,11149,11185,11226,11246,11249,11252,11280,11293,11296,11682,11718,11984,11987,12021,12071,3334,10623,10653,10662,11206,3371,3365,3781,3720,10301,11584,11614,4502,10252,10611,10614,11064,11082,11547,11602,11642,11770,11795,11798,11801,11804,12066,3292,10656,10809,10880,11615,11769,11961,12180,3742,4081,4500,3753,3788,4479,4482,3244,3248,4481,4484,3249,4480,3760,3579,11577,4177,4516,10226,10229,10481,10532,10535,10540,10949,11419,11669,11773,4522,11143,11260,3967,3864,11299,11641,11645,3709,10920,10926,10944,11888,3566,11146,12131,3711,10659,11000,11152,11182,11193,3536,10579,10582,10665,10836,4519,11578,4520,10716,10818,11131,11283,11422,11450,12196,4140,10792,4042,3741,3689,4517,10274,10277,10617,10620,11461,4518,11558,3713,10585,3974,4521,4538,4564,4613,4615,4645,4662,4669,4670,4709,4739,4745,4830,4856,4857,4918,4919,4941,4942,4955,4959,4981,4988,5005,5008,5009,5010,5015,5016,5039,5066,5067,5077,5082,5090,5135,5136,5144,5154,5158,5160,5170,5172,5178,5182,5197,5204,5207,5208,5209,5213,5248,5261,5268,5270,5271,5275,5276,5277,5285,5288,5293,5294,5295,5302,5306,5307,5308,5317,5321,5322,5323,5328,5341,5350,5362,5364,5372,5373,5377,5381,5406,5412,5422,5423,5438,5451,5473,5479,5495,5496,5499,5518,5526,5527,5532,5533,5543,5544,5556,5560,5569,5570,5572,5587,5592,5603,5604,5616,5623,5637,5641,5644,5650,5651,5652,5655,5660,5697,5698,5701,5703,5706,5707,5708,5710,5712,5714,5719,5726,5741,5755,5760,5761,5774,5775,5780,5785,5787,5792,5833,5845,5854,5858,5869,5873,5874,5882,5896,5902,5920,5923,5935,5965,5979,6004,6024,6025,6028,6042,6044,6046,6048,6061,6062,6065,6067,6070,6071,6082,6088,6089,6090,6092,6094,6136,6137,6144,6154,6190,6192,6194,6196,6205,6207,6209,6215,6217,6223,6226,6234,6241,6242,6243,6248,6270,6271,6272,6274,6280,6285,6322,6323,6325,6326,6327,6329,6330,6331,6332,6341,6374,6375,6384,6405,6406,6426,6429,6440,6441,6447,6476,6478,6490,6528,6530,6531,6586,6610,6656,6676,6685,6686,6687,6688,6707,6708,6714,6726,6729,6731,6733,6734,6735,6737,6751,6762,6764,6765,6778,6781,6832,6843,6845,6849,6864,6865,6901,6913,6944,6963,6978,7032,7060,7115,7136,7145,7148,7203,7211,7269,7271,7285,7295,7296,7297,7316,7322,7324,7373,7383,7386,7402,7451,7453,7456,7499,7500,7518,7585,7604,7628,7650,7665,7680,7691,7699,7700,7728,7731,7733,7741,7779,7790,7815,7873,7907,7939,7986,8002,8008,8019,8020,8095,8149,8168,8192,8212,8236,8335,8337,8343,8361,8365,8379,8402,8413,8415,8430,8436,8440,8465,8479,8480,8496,8497,8502,8503,8504,8505,8506,8524,8525,8526,8535,8549,8551,8563,8567,8569,8570,8571,8579,8584,8611,8612,8641,8654,8658,8676,8698,8699,8700,8701,8714,8715,8737,8747,8756,8757,8758,8759,8761,8783,8784,8795,8840,8846,8852,8865,8870,8872,8875,8876,8880,8889,8972,9003,9004,9005,9020,9038,9043,9070,9071,9114,9117,9144,9189,9190,9191,9207,9233,9247,9253,9256,9279,9280,9308,9371,9407,9408,9409,9434,9435,9453,9471,9477,9493,9516,9538,9546,9547,9548,9549,9565,9567,9572,9603,9604,9610,9611,9654,9655,9686,9696,9706,9708,9709,9719,9733,9737,9765,9797,9802,9859,9902,9903,9905,9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% 187.89/187.72 cnf(12243,plain, % 187.89/187.72 (P1(f306(f306(f220(f872(x122431,a859)),x122432),x122432))), % 187.89/187.72 inference(rename_variables,[],[3566])). % 187.89/187.72 cnf(12246,plain, % 187.89/187.72 (~P1(f306(f306(f308(x122461),x122462),f185(f872(x122461,a859))))), % 187.89/187.72 inference(rename_variables,[],[4505])). % 187.89/187.72 cnf(12249,plain, % 187.89/187.72 (~P1(f306(f306(f185(f872(x122491,f872(x122492,a859))),x122493),x122494))), % 187.89/187.72 inference(rename_variables,[],[4520])). % 187.89/187.72 cnf(12252,plain, % 187.89/187.72 (P1(f306(f306(f220(f872(x122521,a859)),f306(f285(x122522,x122521,x122523),f306(f286(x122522,x122521,x122523),x122524))),x122524))), % 187.89/187.72 inference(rename_variables,[],[4140])). % 187.89/187.72 cnf(12253,plain, % 187.89/187.72 (P1(f306(f306(f220(f872(x122531,a859)),x122532),x122532))), % 187.89/187.72 inference(rename_variables,[],[3566])). % 187.89/187.72 cnf(12258,plain, % 187.89/187.72 (E(f306(f232(x122581,x122581),f233(x122581,x122582)),x122582)), % 187.89/187.72 inference(rename_variables,[],[3227])). % 187.89/187.72 cnf(12261,plain, % 187.89/187.72 (P1(f306(f306(f220(f872(x122611,a859)),f306(f164(x122611),f162(x122611,x122612,x122613))),f306(f164(x122611),x122613)))), % 187.89/187.72 inference(rename_variables,[],[3956])). % 187.89/187.72 cnf(12262,plain, % 187.89/187.72 (P1(f306(f63(x122621),f306(f164(x122621),x122622)))), % 187.89/187.72 inference(rename_variables,[],[3312])). % 187.89/187.72 cnf(12265,plain, % 187.89/187.72 (P1(f306(f306(f193(a24),x122651),x122651))), % 187.89/187.72 inference(rename_variables,[],[3270])). % 187.89/187.72 cnf(12268,plain, % 187.89/187.72 (~P1(f306(f306(f221(a865),x122681),x122681))), % 187.89/187.72 inference(rename_variables,[],[4489])). % 187.89/187.72 cnf(12271,plain, % 187.89/187.72 (~P1(f306(f306(f221(a865),x122711),x122711))), % 187.89/187.72 inference(rename_variables,[],[4489])). % 187.89/187.72 cnf(12282,plain, % 187.89/187.72 (P28(x122821,x122821,f5(x122821),x122822)), % 187.89/187.72 inference(rename_variables,[],[3510])). % 187.89/187.72 cnf(12289,plain, % 187.89/187.72 (~P1(f306(f306(f308(x122891),x122892),f185(f872(x122891,a859))))), % 187.89/187.72 inference(rename_variables,[],[4505])). % 187.89/187.72 cnf(12292,plain, % 187.89/187.72 (P1(f306(f306(f308(f871(x122921,x122921)),f306(f306(f236(x122921,x122921),x122922),x122922)),f282(x122921,x122923)))), % 187.89/187.72 inference(rename_variables,[],[3897])). % 187.89/187.72 cnf(12295,plain, % 187.89/187.72 (~P1(f306(f306(f308(x122951),x122952),f185(f872(x122951,a859))))), % 187.89/187.72 inference(rename_variables,[],[4505])). % 187.89/187.72 cnf(12298,plain, % 187.89/187.72 (P1(f306(f306(f308(f871(x122981,x122981)),f306(f306(f236(x122981,x122981),x122982),x122982)),f282(x122981,x122983)))), % 187.89/187.72 inference(rename_variables,[],[3897])). % 187.89/187.72 cnf(12308,plain, % 187.89/187.72 (~E(f306(f306(f143(x123081),x123082),x123083),x123083)), % 187.89/187.72 inference(rename_variables,[],[4445])). % 187.89/187.72 cnf(12311,plain, % 187.89/187.72 (P1(f306(f306(f308(x123111),x123112),f231(f872(x123111,a859))))), % 187.89/187.72 inference(rename_variables,[],[3428])). % 187.89/187.72 cnf(12312,plain, % 187.89/187.72 (~E(f306(a119,x123121),x123121)), % 187.89/187.72 inference(rename_variables,[],[4420])). % 187.89/187.72 cnf(12315,plain, % 187.89/187.72 (P1(f306(f306(f308(f866(x123151)),f120(x123151)),f153(x123151,x123152)))), % 187.89/187.72 inference(rename_variables,[],[3472])). % 187.89/187.72 cnf(12316,plain, % 187.89/187.72 (~E(f306(f306(f143(x123161),x123162),x123163),f120(x123161))), % 187.89/187.72 inference(rename_variables,[],[4454])). % 187.89/187.72 cnf(12319,plain, % 187.89/187.72 (P1(f306(f306(f308(x123191),f306(x123192,x123193)),f306(f285(x123194,x123191,x123192),f231(f872(x123194,a859)))))), % 187.89/187.72 inference(rename_variables,[],[3864])). % 187.89/187.72 cnf(12320,plain, % 187.89/187.72 (P28(x123201,x123201,f5(x123201),x123202)), % 187.89/187.72 inference(rename_variables,[],[3510])). % 187.89/187.72 cnf(12323,plain, % 187.89/187.72 (P1(f306(f306(f220(f872(x123231,a859)),f185(f872(x123231,a859))),x123232))), % 187.89/187.72 inference(rename_variables,[],[3711])). % 187.89/187.72 cnf(12324,plain, % 187.89/187.72 (P1(f306(f306(f220(f872(x123241,a859)),x123242),x123242))), % 187.89/187.72 inference(rename_variables,[],[3566])). % 187.89/187.72 cnf(12327,plain, % 187.89/187.72 (P1(f306(f306(f308(x123271),f306(x123272,x123273)),f306(f285(x123274,x123271,x123272),f231(f872(x123274,a859)))))), % 187.89/187.72 inference(rename_variables,[],[3864])). % 187.89/187.72 cnf(12328,plain, % 187.89/187.72 (P28(x123281,x123281,f5(x123281),x123282)), % 187.89/187.72 inference(rename_variables,[],[3510])). % 187.89/187.72 cnf(12331,plain, % 187.89/187.72 (P1(f306(f306(f308(f871(f866(x123311),f866(x123311))),f306(f306(f236(f866(x123311),f866(x123311)),f120(x123311)),f120(x123311))),f150(x123311,x123312)))), % 187.89/187.72 inference(rename_variables,[],[4037])). % 187.89/187.72 cnf(12334,plain, % 187.89/187.72 (~P1(f306(f306(f221(a865),x123341),x123341))), % 187.89/187.72 inference(rename_variables,[],[4489])). % 187.89/187.72 cnf(12335,plain, % 187.89/187.72 (~P1(f306(f306(f221(a865),x123351),f2(a865)))), % 187.89/187.72 inference(rename_variables,[],[4493])). % 187.89/187.72 cnf(12341,plain, % 187.89/187.72 (E(f306(f306(f122(x123411),x123412),f120(x123411)),x123412)), % 187.89/187.72 inference(rename_variables,[],[3202])). % 187.89/187.72 cnf(12342,plain, % 187.89/187.72 (~E(f306(f306(f143(x123421),x123422),x123423),x123423)), % 187.89/187.72 inference(rename_variables,[],[4445])). % 187.89/187.72 cnf(12345,plain, % 187.89/187.72 (E(f306(f306(f122(x123451),x123452),f120(x123451)),x123452)), % 187.89/187.72 inference(rename_variables,[],[3202])). % 187.89/187.72 cnf(12346,plain, % 187.89/187.72 (~E(f306(f306(f143(x123461),x123462),x123463),x123463)), % 187.89/187.72 inference(rename_variables,[],[4445])). % 187.89/187.72 cnf(12349,plain, % 187.89/187.72 (E(f306(f306(f122(x123491),x123492),f120(x123491)),x123492)), % 187.89/187.72 inference(rename_variables,[],[3202])). % 187.89/187.72 cnf(12358,plain, % 187.89/187.72 (P1(f306(f306(f220(f872(x123581,a859)),x123582),f231(f872(x123581,a859))))), % 187.89/187.72 inference(rename_variables,[],[3646])). % 187.89/187.72 cnf(12362,plain, % 187.89/187.72 (~P1(f306(f306(f221(a865),x123621),x123621))), % 187.89/187.72 inference(rename_variables,[],[4489])). % 187.89/187.72 cnf(12363,plain, % 187.89/187.72 (~E(f306(a119,x123631),x123631)), % 187.89/187.72 inference(rename_variables,[],[4420])). % 187.89/187.72 cnf(12366,plain, % 187.89/187.72 (P1(f306(f306(f220(f872(x123661,a859)),f185(f872(x123661,a859))),x123662))), % 187.89/187.72 inference(rename_variables,[],[3711])). % 187.89/187.72 cnf(12369,plain, % 187.89/187.72 (P1(f306(f306(f220(a865),x123691),x123691))), % 187.89/187.72 inference(rename_variables,[],[3271])). % 187.89/187.72 cnf(12372,plain, % 187.89/187.72 (P1(f306(f306(f220(f872(x123721,a859)),x123722),x123722))), % 187.89/187.72 inference(rename_variables,[],[3566])). % 187.89/187.72 cnf(12377,plain, % 187.89/187.72 (P1(f306(f306(f220(f872(x123771,a859)),x123772),f306(f306(f284(x123771),x123773),x123772)))), % 187.89/187.72 inference(rename_variables,[],[3709])). % 187.89/187.72 cnf(12380,plain, % 187.89/187.72 (P1(f306(f306(f220(f872(x123801,a859)),x123802),x123802))), % 187.89/187.72 inference(rename_variables,[],[3566])). % 187.89/187.72 cnf(12381,plain, % 187.89/187.72 (~P1(f306(f306(f308(x123811),x123812),f185(f872(x123811,a859))))), % 187.89/187.72 inference(rename_variables,[],[4505])). % 187.89/187.73 cnf(12384,plain, % 187.89/187.73 (~P1(f306(f306(f308(x123841),x123842),f185(f872(x123841,a859))))), % 187.89/187.73 inference(rename_variables,[],[4505])). % 187.89/187.73 cnf(12393,plain, % 187.89/187.73 (P28(x123931,x123931,f5(x123931),x123932)), % 187.89/187.73 inference(rename_variables,[],[3510])). % 187.89/187.73 cnf(12396,plain, % 187.89/187.73 (E(f306(f186(f866(x123961)),f306(f160(x123961),x123962)),f306(f186(f866(x123961)),x123962))), % 187.89/187.73 inference(rename_variables,[],[3283])). % 187.89/187.73 cnf(12399,plain, % 187.89/187.73 (~P1(f306(f306(f221(a865),x123991),x123991))), % 187.89/187.73 inference(rename_variables,[],[4489])). % 187.89/187.73 cnf(12400,plain, % 187.89/187.73 (P1(f306(f231(f872(x124001,a859)),x124002))), % 187.89/187.73 inference(rename_variables,[],[3334])). % 187.89/187.73 cnf(12403,plain, % 187.89/187.73 (~P1(f306(f306(f308(x124031),x124032),f185(f872(x124031,a859))))), % 187.89/187.73 inference(rename_variables,[],[4505])). % 187.89/187.73 cnf(12406,plain, % 187.89/187.73 (P1(f306(f306(f220(f872(x124061,a859)),x124062),f306(f306(f284(x124061),x124063),x124062)))), % 187.89/187.73 inference(rename_variables,[],[3709])). % 187.89/187.73 cnf(12409,plain, % 187.89/187.73 (P1(f306(f306(f308(x124091),f306(x124092,x124093)),f306(f285(x124094,x124091,x124092),f231(f872(x124094,a859)))))), % 187.89/187.73 inference(rename_variables,[],[3864])). % 187.89/187.73 cnf(12410,plain, % 187.89/187.73 (P1(f306(f306(f308(f871(x124101,x124101)),f306(f306(f236(x124101,x124101),x124102),x124102)),f282(x124101,x124103)))), % 187.89/187.73 inference(rename_variables,[],[3897])). % 187.89/187.73 cnf(12413,plain, % 187.89/187.73 (P1(f306(f306(f308(f871(x124131,x124131)),f306(f306(f236(x124131,x124131),x124132),x124132)),f282(x124131,x124133)))), % 187.89/187.73 inference(rename_variables,[],[3897])). % 187.89/187.73 cnf(12416,plain, % 187.89/187.73 (P1(f306(f306(f220(a865),x124161),x124161))), % 187.89/187.73 inference(rename_variables,[],[3271])). % 187.89/187.73 cnf(12417,plain, % 187.89/187.73 (P1(f306(f231(f872(x124171,a859)),x124172))), % 187.89/187.73 inference(rename_variables,[],[3334])). % 187.89/187.73 cnf(12420,plain, % 187.89/187.73 (P1(f306(f63(x124201),f306(f164(x124201),x124202)))), % 187.89/187.73 inference(rename_variables,[],[3312])). % 187.89/187.73 cnf(12425,plain, % 187.89/187.73 (P1(f306(f306(f308(f871(f866(x124251),f866(x124251))),f306(f306(f236(f866(x124251),f866(x124251)),f120(x124251)),f120(x124251))),f306(f306(f263(f866(x124251),f866(x124251),f866(x124251)),f150(x124251,x124252)),f150(x124251,x124252))))), % 187.89/187.73 inference(scs_inference,[],[4527,3510,11037,12085,12190,12282,12320,12328,3517,3518,3238,4455,4456,3143,4438,4420,10200,10210,10221,10330,10333,10336,10438,10551,10855,11022,11025,11223,11313,11320,11334,11384,11387,11409,11502,11548,11564,11864,11892,11904,11936,12034,12147,12154,12312,4435,10422,10515,3329,3479,3189,2875,2876,2878,2879,2882,2883,2885,2886,2887,2889,2894,2902,2911,2917,2923,2929,2936,2937,2938,2943,2952,2956,2970,3004,3005,3018,3019,3021,3028,3029,3030,3031,3033,3044,3050,3162,3064,4416,3117,11310,3313,3227,10203,10264,10267,10357,10360,10650,10929,11325,11328,11445,11489,11494,11593,12055,3202,11590,12341,12345,12349,3212,3722,10969,11596,3107,3922,4432,3552,3812,11360,3170,3134,3129,3115,3120,3149,3283,12026,12177,3330,10802,12148,3200,3201,3222,10463,3375,4513,3895,4445,10255,10419,11220,11412,12308,12342,4454,12316,3260,11685,4503,10972,11042,11263,11266,3376,3165,10322,10626,3166,3433,3086,3185,11350,4037,12331,3897,10978,11104,11155,12292,12298,12410,4524,10907,11109,11214,11236,11271,11277,12237,4525,11011,11112,11217,4526,11115,4528,11169,4529,3184,3472,12193,12234,12315,3628,4316,4317,4443,11341,3570,3777,3822,3458,3704,3340,10341,10458,10529,10590,10593,10629,10723,10962,11860,11926,12002,12046,12125,12128,3715,11581,4174,3253,3352,3533,4493,10232,10235,10261,10731,10744,10865,11286,11353,11752,11757,11978,11981,12067,12076,12240,4509,11464,11497,11532,11561,3702,3480,3481,3847,3299,3300,3273,4490,4440,3655,3464,4510,4031,11231,3589,3312,11709,11712,12158,12262,4001,3961,11853,12208,3907,10799,12014,12040,3956,10981,12082,12157,12214,12261,3629,11863,12009,12092,12138,3990,3646,10984,11047,11128,11188,12033,12106,4514,10747,11120,3270,10350,10445,10576,10636,11437,11657,11703,11737,11833,11891,12099,3271,10705,10750,10753,10786,10812,10849,10887,10923,11907,11910,11913,11916,12113,12116,12119,12122,12201,12369,3272,10433,10641,10726,10852,11740,11749,11839,11850,11869,11874,11919,11939,3348,12070,4489,10298,10387,10500,10524,10768,10815,10825,11511,11611,11632,11635,11638,11654,11807,11810,11813,11816,11903,11922,11925,11935,11990,11993,11996,11999,12077,12169,12172,12268,12271,12334,12362,3428,10596,10860,10904,11177,11255,11425,4505,10777,10789,10896,10914,10917,10975,11061,11069,11085,11123,11140,11149,11185,11226,11246,11249,11252,11280,11293,11296,11682,11718,11984,11987,12021,12071,12102,12246,12289,12295,12381,12384,3334,10623,10653,10662,11206,11764,12400,3371,3365,3781,3720,10301,11584,11614,4502,10252,10611,10614,11064,11082,11547,11602,11642,11770,11795,11798,11801,11804,12066,3292,10656,10809,10880,11615,11769,11961,12180,3742,4081,4500,3753,3788,4479,4482,3244,3248,4481,4484,3249,4480,3760,3579,11577,4177,4516,10226,10229,10481,10532,10535,10540,10949,11419,11669,11773,4522,11143,11260,11302,3967,3864,11299,11641,11645,11706,12319,12327,3709,10920,10926,10944,11888,12105,12377,3566,11146,12131,12243,12253,12324,12372,3711,10659,11000,11152,11182,11193,12037,12323,3536,10579,10582,10665,10836,4519,11578,4520,10716,10818,11131,11283,11422,11450,12196,12205,4140,10792,12226,4042,3741,3689,4517,10274,10277,10617,10620,11461,4518,11558,3713,10585,3974,4521,4538,4564,4613,4615,4645,4662,4669,4670,4709,4739,4745,4830,4856,4857,4918,4919,4941,4942,4955,4959,4981,4988,5005,5008,5009,5010,5015,5016,5039,5066,5067,5077,5082,5090,5135,5136,5144,5154,5158,5160,5170,5172,5178,5182,5197,5204,5207,5208,5209,5213,5248,5261,5268,5270,5271,5275,5276,5277,5285,5288,5293,5294,5295,5302,5306,5307,5308,5317,5321,5322,5323,5328,5341,5350,5362,5364,5372,5373,5377,5381,5406,5412,5422,5423,5438,5451,5473,5479,5495,5496,5499,5518,5526,5527,5532,5533,5543,5544,5556,5560,5569,5570,5572,5587,5592,5603,5604,5616,5623,5637,5641,5644,5650,5651,5652,5655,5660,5697,5698,5701,5703,5706,5707,5708,5710,5712,5714,5719,5726,5741,5755,5760,5761,5774,5775,5780,5785,5787,5792,5833,5845,5854,5858,5869,5873,5874,5882,5896,5902,5920,5923,5935,5965,5979,6004,6024,6025,6028,6042,6044,6046,6048,6061,6062,6065,6067,6070,6071,6082,6088,6089,6090,6092,6094,6136,6137,6144,6154,6190,6192,6194,6196,6205,6207,6209,6215,6217,6223,6226,6234,6241,6242,6243,6248,6270,6271,6272,6274,6280,6285,6322,6323,6325,6326,6327,6329,6330,6331,6332,6341,6374,6375,6384,6405,6406,6426,6429,6440,6441,6447,6476,6478,6490,6528,6530,6531,6586,6610,6656,6676,6685,6686,6687,6688,6707,6708,6714,6726,6729,6731,6733,6734,6735,6737,6751,6762,6764,6765,6778,6781,6832,6843,6845,6849,6864,6865,6901,6913,6944,6963,6978,7032,7060,7115,7136,7145,7148,7203,7211,7269,7271,7285,7295,7296,7297,7316,7322,7324,7373,7383,7386,7402,7451,7453,7456,7499,7500,7518,7585,7604,7628,7650,7665,7680,7691,7699,7700,7728,7731,7733,7741,7779,7790,7815,7873,7907,7939,7986,8002,8008,8019,8020,8095,8149,8168,8192,8212,8236,8335,8337,8343,8361,8365,8379,8402,8413,8415,8430,8436,8440,8465,8479,8480,8496,8497,8502,8503,8504,8505,8506,8524,8525,8526,8535,8549,8551,8563,8567,8569,8570,8571,8579,8584,8611,8612,8641,8654,8658,8676,8698,8699,8700,8701,8714,8715,8737,8747,8756,8757,8758,8759,8761,8783,8784,8795,8840,8846,8852,8865,8870,8872,8875,8876,8880,8889,8972,9003,9004,9005,9020,9038,9043,9070,9071,9114,9117,9144,9189,9190,9191,9207,9233,9247,9253,9256,9279,9280,9308,9371,9407,9408,9409,9434,9435,9453,9471,9477,9493,9516,9538,9546,9547,9548,9549,9565,9567,9572,9603,9604,9610,9611,9654,9655,9686,9696,9706,9708,9709,9719,9733,9737,9765,9797,9802,9859,9902,9903,9905,9915,9916,9936,9941,9964,9969,9984,10036,10110,10111,10168,10184,2,8,9,4551,4552,4570,4601,4602,4604,4631,4637,4638,4649,4698,4700,4730,4744,4774,4871,4872,4886,4906,4962,4963,4966,4967,4969,4971,4972,4984,4985,4995,5006,5007,5013,5032,5033,5054,5059,5060,5061,5062,5065,5073,5076,5083,5084,5085,5150,5156,5157,5164,5194,5205,5211,5227,5247,5254,5255,5256,5265,5274,5281,5283,5284,5290,5298,5299,5309,5313,5314,5315,5316,5318,5319,5324,5325,5326,5327,5358,5359,5360,5368,5369,5370,5371,5414,5419,5421,5458,5460,5461,5463,5464,5466,5467,5469,5478,5483,5485,5486,5487,5488,5489,5490,5497,5507,5510,5521,5537,5538,5541,5550,5552,5553,5554,5579,5589,5606,5607,5617,5618,5620,5622,5627,5662,5666,5668,5728,5762,5763,5767,5773,5776,5777,5778,5779,5786,5797,5798,5800,5801,5809,5830,5861,5877,5880,5881,5883,5892,5910,5914,5917,5918,5919,5937,5950,5951,5981,5982,5986,6006,6009,6013,6032,6037,6038,6063,6066,6073,6081,6087,6091,6098,6099,6100,6101,6139,6155,6208,6244,6246,6267,6268,6273,6277,6278,6281,6288,6297,6314,6334,6335,6342,6352,6367,6387,6393,6395,6410,6411,6415,6417,6418,6419,6421,6423,6424,6425,6428,6433,6434,6436,6437,6443,6445,6486,6489,6503,6505,6506,6507,6543,6548,6550,6555,6556,6564,6568,6581,6605,6606,6608,6609,6621,6625,6627,6647,6650,6669,6702,6703,6704,6709,6722,6741,6743,6745,6747,6752,6758,6760,6775,6782,6818,6819,6820,6834,6835,6837,6838,6855,6857,6873,6899,6921,6932,6934,6936,6938,6939,6940,6975,6976,6981,6982,6990,6992,6993,6994,7013,7022,7023,7035,7045,7084,7094,7098,7105,7116,7117,7122,7124,7130,7138,7139,7152,7169,7187,7189,7206,7255,7256,7257,7259,7261,7265,7270,7292,7337,7369,7384,7389,7401,7434,7437,7460,7484,7501,7504,7505,7515,7534,7536,7538,7540,7541,7542,7567,7593,7594,7627,7629,7630,7631,7636,7657,7666,7677,7682,7688,7690,7696,7707,7708,7710,7730,7734,7739,7762,7828,7829,7876,7885,7886,7909,7910,7927,7928,7993,7994,8022,8051,8062,8064,8073,8085,8118,8124,8131,8144,8163,8169,8191,8234,8264,8276,8295,8298,8328,8352,8416,8417,8420,8422,8441,8528,8529,8530,8531,8558,8587,8615,8657,8675,8731,8776,8779,8792,8799,8837,8885,8886,8903,8904,9045,9049,9068,9078,9103,9105,9108,9112,9115,9116,9129,9130,9151,9157,9169,9218,9237,9257,9292,9293,9300,9363,9368,9404])). % 187.89/187.73 cnf(12427,plain, % 187.89/187.73 (P1(f306(f306(f308(f871(x124271,x124271)),f306(f306(f236(x124271,x124271),x124272),x124272)),f306(f306(f263(x124271,x124271,x124271),f282(x124271,x124273)),f282(x124271,f282(x124271,x124273)))))), % 187.89/187.73 inference(scs_inference,[],[4527,3510,11037,12085,12190,12282,12320,12328,3517,3518,3238,4455,4456,3143,4438,4420,10200,10210,10221,10330,10333,10336,10438,10551,10855,11022,11025,11223,11313,11320,11334,11384,11387,11409,11502,11548,11564,11864,11892,11904,11936,12034,12147,12154,12312,4435,10422,10515,3329,3479,3189,2875,2876,2878,2879,2882,2883,2885,2886,2887,2889,2894,2902,2911,2917,2923,2929,2936,2937,2938,2943,2952,2956,2970,3004,3005,3018,3019,3021,3028,3029,3030,3031,3033,3044,3050,3162,3064,4416,3117,11310,3313,3227,10203,10264,10267,10357,10360,10650,10929,11325,11328,11445,11489,11494,11593,12055,3202,11590,12341,12345,12349,3212,3722,10969,11596,3107,3922,4432,3552,3812,11360,3170,3134,3129,3115,3120,3149,3283,12026,12177,3330,10802,12148,3200,3201,3222,10463,3375,4513,3895,4445,10255,10419,11220,11412,12308,12342,4454,12316,3260,11685,4503,10972,11042,11263,11266,3376,3165,10322,10626,3166,3433,3086,3185,11350,4037,12331,3897,10978,11104,11155,12292,12298,12410,12413,4524,10907,11109,11214,11236,11271,11277,12237,4525,11011,11112,11217,4526,11115,4528,11169,4529,3184,3472,12193,12234,12315,3628,4316,4317,4443,11341,3570,3777,3822,3458,3704,3340,10341,10458,10529,10590,10593,10629,10723,10962,11860,11926,12002,12046,12125,12128,3715,11581,4174,3253,3352,3533,4493,10232,10235,10261,10731,10744,10865,11286,11353,11752,11757,11978,11981,12067,12076,12240,4509,11464,11497,11532,11561,3702,3480,3481,3847,3299,3300,3273,4490,4440,3655,3464,4510,4031,11231,3589,3312,11709,11712,12158,12262,4001,3961,11853,12208,3907,10799,12014,12040,3956,10981,12082,12157,12214,12261,3629,11863,12009,12092,12138,3990,3646,10984,11047,11128,11188,12033,12106,4514,10747,11120,3270,10350,10445,10576,10636,11437,11657,11703,11737,11833,11891,12099,3271,10705,10750,10753,10786,10812,10849,10887,10923,11907,11910,11913,11916,12113,12116,12119,12122,12201,12369,3272,10433,10641,10726,10852,11740,11749,11839,11850,11869,11874,11919,11939,3348,12070,4489,10298,10387,10500,10524,10768,10815,10825,11511,11611,11632,11635,11638,11654,11807,11810,11813,11816,11903,11922,11925,11935,11990,11993,11996,11999,12077,12169,12172,12268,12271,12334,12362,3428,10596,10860,10904,11177,11255,11425,4505,10777,10789,10896,10914,10917,10975,11061,11069,11085,11123,11140,11149,11185,11226,11246,11249,11252,11280,11293,11296,11682,11718,11984,11987,12021,12071,12102,12246,12289,12295,12381,12384,3334,10623,10653,10662,11206,11764,12400,3371,3365,3781,3720,10301,11584,11614,4502,10252,10611,10614,11064,11082,11547,11602,11642,11770,11795,11798,11801,11804,12066,3292,10656,10809,10880,11615,11769,11961,12180,3742,4081,4500,3753,3788,4479,4482,3244,3248,4481,4484,3249,4480,3760,3579,11577,4177,4516,10226,10229,10481,10532,10535,10540,10949,11419,11669,11773,4522,11143,11260,11302,3967,3864,11299,11641,11645,11706,12319,12327,3709,10920,10926,10944,11888,12105,12377,3566,11146,12131,12243,12253,12324,12372,3711,10659,11000,11152,11182,11193,12037,12323,3536,10579,10582,10665,10836,4519,11578,4520,10716,10818,11131,11283,11422,11450,12196,12205,4140,10792,12226,4042,3741,3689,4517,10274,10277,10617,10620,11461,4518,11558,3713,10585,3974,4521,4538,4564,4613,4615,4645,4662,4669,4670,4709,4739,4745,4830,4856,4857,4918,4919,4941,4942,4955,4959,4981,4988,5005,5008,5009,5010,5015,5016,5039,5066,5067,5077,5082,5090,5135,5136,5144,5154,5158,5160,5170,5172,5178,5182,5197,5204,5207,5208,5209,5213,5248,5261,5268,5270,5271,5275,5276,5277,5285,5288,5293,5294,5295,5302,5306,5307,5308,5317,5321,5322,5323,5328,5341,5350,5362,5364,5372,5373,5377,5381,5406,5412,5422,5423,5438,5451,5473,5479,5495,5496,5499,5518,5526,5527,5532,5533,5543,5544,5556,5560,5569,5570,5572,5587,5592,5603,5604,5616,5623,5637,5641,5644,5650,5651,5652,5655,5660,5697,5698,5701,5703,5706,5707,5708,5710,5712,5714,5719,5726,5741,5755,5760,5761,5774,5775,5780,5785,5787,5792,5833,5845,5854,5858,5869,5873,5874,5882,5896,5902,5920,5923,5935,5965,5979,6004,6024,6025,6028,6042,6044,6046,6048,6061,6062,6065,6067,6070,6071,6082,6088,6089,6090,6092,6094,6136,6137,6144,6154,6190,6192,6194,6196,6205,6207,6209,6215,6217,6223,6226,6234,6241,6242,6243,6248,6270,6271,6272,6274,6280,6285,6322,6323,6325,6326,6327,6329,6330,6331,6332,6341,6374,6375,6384,6405,6406,6426,6429,6440,6441,6447,6476,6478,6490,6528,6530,6531,6586,6610,6656,6676,6685,6686,6687,6688,6707,6708,6714,6726,6729,6731,6733,6734,6735,6737,6751,6762,6764,6765,6778,6781,6832,6843,6845,6849,6864,6865,6901,6913,6944,6963,6978,7032,7060,7115,7136,7145,7148,7203,7211,7269,7271,7285,7295,7296,7297,7316,7322,7324,7373,7383,7386,7402,7451,7453,7456,7499,7500,7518,7585,7604,7628,7650,7665,7680,7691,7699,7700,7728,7731,7733,7741,7779,7790,7815,7873,7907,7939,7986,8002,8008,8019,8020,8095,8149,8168,8192,8212,8236,8335,8337,8343,8361,8365,8379,8402,8413,8415,8430,8436,8440,8465,8479,8480,8496,8497,8502,8503,8504,8505,8506,8524,8525,8526,8535,8549,8551,8563,8567,8569,8570,8571,8579,8584,8611,8612,8641,8654,8658,8676,8698,8699,8700,8701,8714,8715,8737,8747,8756,8757,8758,8759,8761,8783,8784,8795,8840,8846,8852,8865,8870,8872,8875,8876,8880,8889,8972,9003,9004,9005,9020,9038,9043,9070,9071,9114,9117,9144,9189,9190,9191,9207,9233,9247,9253,9256,9279,9280,9308,9371,9407,9408,9409,9434,9435,9453,9471,9477,9493,9516,9538,9546,9547,9548,9549,9565,9567,9572,9603,9604,9610,9611,9654,9655,9686,9696,9706,9708,9709,9719,9733,9737,9765,9797,9802,9859,9902,9903,9905,9915,9916,9936,9941,9964,9969,9984,10036,10110,10111,10168,10184,2,8,9,4551,4552,4570,4601,4602,4604,4631,4637,4638,4649,4698,4700,4730,4744,4774,4871,4872,4886,4906,4962,4963,4966,4967,4969,4971,4972,4984,4985,4995,5006,5007,5013,5032,5033,5054,5059,5060,5061,5062,5065,5073,5076,5083,5084,5085,5150,5156,5157,5164,5194,5205,5211,5227,5247,5254,5255,5256,5265,5274,5281,5283,5284,5290,5298,5299,5309,5313,5314,5315,5316,5318,5319,5324,5325,5326,5327,5358,5359,5360,5368,5369,5370,5371,5414,5419,5421,5458,5460,5461,5463,5464,5466,5467,5469,5478,5483,5485,5486,5487,5488,5489,5490,5497,5507,5510,5521,5537,5538,5541,5550,5552,5553,5554,5579,5589,5606,5607,5617,5618,5620,5622,5627,5662,5666,5668,5728,5762,5763,5767,5773,5776,5777,5778,5779,5786,5797,5798,5800,5801,5809,5830,5861,5877,5880,5881,5883,5892,5910,5914,5917,5918,5919,5937,5950,5951,5981,5982,5986,6006,6009,6013,6032,6037,6038,6063,6066,6073,6081,6087,6091,6098,6099,6100,6101,6139,6155,6208,6244,6246,6267,6268,6273,6277,6278,6281,6288,6297,6314,6334,6335,6342,6352,6367,6387,6393,6395,6410,6411,6415,6417,6418,6419,6421,6423,6424,6425,6428,6433,6434,6436,6437,6443,6445,6486,6489,6503,6505,6506,6507,6543,6548,6550,6555,6556,6564,6568,6581,6605,6606,6608,6609,6621,6625,6627,6647,6650,6669,6702,6703,6704,6709,6722,6741,6743,6745,6747,6752,6758,6760,6775,6782,6818,6819,6820,6834,6835,6837,6838,6855,6857,6873,6899,6921,6932,6934,6936,6938,6939,6940,6975,6976,6981,6982,6990,6992,6993,6994,7013,7022,7023,7035,7045,7084,7094,7098,7105,7116,7117,7122,7124,7130,7138,7139,7152,7169,7187,7189,7206,7255,7256,7257,7259,7261,7265,7270,7292,7337,7369,7384,7389,7401,7434,7437,7460,7484,7501,7504,7505,7515,7534,7536,7538,7540,7541,7542,7567,7593,7594,7627,7629,7630,7631,7636,7657,7666,7677,7682,7688,7690,7696,7707,7708,7710,7730,7734,7739,7762,7828,7829,7876,7885,7886,7909,7910,7927,7928,7993,7994,8022,8051,8062,8064,8073,8085,8118,8124,8131,8144,8163,8169,8191,8234,8264,8276,8295,8298,8328,8352,8416,8417,8420,8422,8441,8528,8529,8530,8531,8558,8587,8615,8657,8675,8731,8776,8779,8792,8799,8837,8885,8886,8903,8904,9045,9049,9068,9078,9103,9105,9108,9112,9115,9116,9129,9130,9151,9157,9169,9218,9237,9257,9292,9293,9300,9363,9368,9404,9411])). % 187.89/187.73 cnf(12430,plain, % 187.89/187.73 (~P1(f306(f306(f185(f872(x124301,f872(x124302,a859))),x124303),x124304))), % 187.89/187.73 inference(rename_variables,[],[4520])). % 187.89/187.73 cnf(12433,plain, % 187.89/187.73 (P1(f306(f306(f220(f872(x124331,a859)),x124332),f231(f872(x124331,a859))))), % 187.89/187.73 inference(rename_variables,[],[3646])). % 187.89/187.73 cnf(12436,plain, % 187.89/187.73 (P1(f306(f306(f308(f871(x124361,x124361)),f306(f306(f236(x124361,x124361),x124362),x124362)),f282(x124361,x124363)))), % 187.89/187.73 inference(rename_variables,[],[3897])). % 187.89/187.73 cnf(12439,plain, % 187.89/187.73 (~P1(f306(f306(f221(a865),f306(f306(f81(a865),x124391),x124392)),x124392))), % 187.89/187.73 inference(rename_variables,[],[4517])). % 187.89/187.73 cnf(12440,plain, % 187.89/187.73 (P1(f306(f306(f221(a865),x124401),f306(a119,x124401)))), % 187.89/187.73 inference(rename_variables,[],[3340])). % 187.89/187.73 cnf(12443,plain, % 187.89/187.73 (P1(f306(f306(f220(f872(x124431,a859)),f306(f164(x124431),f306(f128(x124431,x124432),x124433))),f306(f164(x124431),x124433)))), % 187.89/187.73 inference(rename_variables,[],[3907])). % 187.89/187.73 cnf(12446,plain, % 187.89/187.73 (P1(f306(f306(f220(f872(x124461,a859)),x124462),f231(f872(x124461,a859))))), % 187.89/187.73 inference(rename_variables,[],[3646])). % 187.89/187.73 cnf(12449,plain, % 187.89/187.73 (E(f306(f232(x124491,x124491),f233(x124491,x124492)),x124492)), % 187.89/187.73 inference(rename_variables,[],[3227])). % 187.89/187.73 cnf(12456,plain, % 187.89/187.73 (P1(f306(f306(f308(f871(f871(f866(x124561),f866(x124561)),f871(f866(x124561),f866(x124561)))),f541(f282(f871(f866(x124561),f866(x124561)),x124562),f137(x124561,x124563),f871(f866(x124561),f866(x124561)))),f282(f871(f866(x124561),f866(x124561)),x124562)))), % 187.89/187.73 inference(scs_inference,[],[4527,3510,11037,12085,12190,12282,12320,12328,3517,3518,3238,4455,4456,3143,4438,4420,10200,10210,10221,10330,10333,10336,10438,10551,10855,11022,11025,11223,11313,11320,11334,11384,11387,11409,11502,11548,11564,11864,11892,11904,11936,12034,12147,12154,12312,4435,10422,10515,3329,3479,3189,2875,2876,2878,2879,2882,2883,2885,2886,2887,2889,2894,2902,2911,2917,2923,2929,2936,2937,2938,2943,2952,2956,2970,3004,3005,3018,3019,3021,3028,3029,3030,3031,3033,3044,3050,3162,3064,4416,3603,3117,11310,3313,3227,10203,10264,10267,10357,10360,10650,10929,11325,11328,11445,11489,11494,11593,12055,12258,3202,11590,12341,12345,12349,3212,3722,10969,11596,3107,3922,4432,3552,3812,11360,3170,3134,3129,3115,3120,3149,3283,12026,12177,3330,10802,12148,3200,3201,3222,10463,3375,4513,3895,4445,10255,10419,11220,11412,12308,12342,4454,12316,3260,11685,4503,10972,11042,11263,11266,3376,3165,10322,10626,3166,3433,3086,3185,11350,4037,12331,3897,10978,11104,11155,12292,12298,12410,12413,12436,4524,10907,11109,11214,11236,11271,11277,12237,4525,11011,11112,11217,4526,11115,4528,11169,4529,3184,3472,12193,12234,12315,3628,4316,4317,4443,11341,3570,3777,3822,3458,3704,3340,10341,10458,10529,10590,10593,10629,10723,10962,11860,11926,12002,12046,12125,12128,3715,11581,4174,3253,3352,3533,4493,10232,10235,10261,10731,10744,10865,11286,11353,11752,11757,11978,11981,12067,12076,12240,4509,11464,11497,11532,11561,3702,3480,3481,3847,3299,3300,3273,4490,4440,3655,4171,3464,4510,4031,11231,3589,3312,11709,11712,12158,12262,4001,3961,11853,12208,3907,10799,12014,12040,12215,3956,10981,12082,12157,12214,12261,3629,11863,12009,12092,12138,3990,3646,10984,11047,11128,11188,12033,12106,12358,12433,4514,10747,11120,3270,10350,10445,10576,10636,11437,11657,11703,11737,11833,11891,12099,3271,10705,10750,10753,10786,10812,10849,10887,10923,11907,11910,11913,11916,12113,12116,12119,12122,12201,12369,3272,10433,10641,10726,10852,11740,11749,11839,11850,11869,11874,11919,11939,3348,12070,4489,10298,10387,10500,10524,10768,10815,10825,11511,11611,11632,11635,11638,11654,11807,11810,11813,11816,11903,11922,11925,11935,11990,11993,11996,11999,12077,12169,12172,12268,12271,12334,12362,3428,10596,10860,10904,11177,11255,11425,4505,10777,10789,10896,10914,10917,10975,11061,11069,11085,11123,11140,11149,11185,11226,11246,11249,11252,11280,11293,11296,11682,11718,11984,11987,12021,12071,12102,12246,12289,12295,12381,12384,3334,10623,10653,10662,11206,11764,12400,3371,3365,3781,3720,10301,11584,11614,4502,10252,10611,10614,11064,11082,11547,11602,11642,11770,11795,11798,11801,11804,12066,3292,10656,10809,10880,11615,11769,11961,12180,3742,4081,4500,3753,3788,4479,4482,3244,3248,4481,4484,3249,4480,3760,3579,11577,4177,4516,10226,10229,10481,10532,10535,10540,10949,11419,11669,11773,4522,11143,11260,11302,3967,3864,11299,11641,11645,11706,12319,12327,3709,10920,10926,10944,11888,12105,12377,3566,11146,12131,12243,12253,12324,12372,4035,3711,10659,11000,11152,11182,11193,12037,12323,3536,10579,10582,10665,10836,4519,11578,4520,10716,10818,11131,11283,11422,11450,12196,12205,12249,4140,10792,12226,4042,3741,3689,4517,10274,10277,10617,10620,11461,11646,4518,11558,3713,10585,3974,4521,4538,4564,4613,4615,4645,4662,4669,4670,4709,4739,4745,4830,4856,4857,4918,4919,4941,4942,4955,4959,4981,4988,5005,5008,5009,5010,5015,5016,5039,5066,5067,5077,5082,5090,5135,5136,5144,5154,5158,5160,5170,5172,5178,5182,5197,5204,5207,5208,5209,5213,5248,5261,5268,5270,5271,5275,5276,5277,5285,5288,5293,5294,5295,5302,5306,5307,5308,5317,5321,5322,5323,5328,5341,5350,5362,5364,5372,5373,5377,5381,5406,5412,5422,5423,5438,5451,5473,5479,5495,5496,5499,5518,5526,5527,5532,5533,5543,5544,5556,5560,5569,5570,5572,5587,5592,5603,5604,5616,5623,5637,5641,5644,5650,5651,5652,5655,5660,5697,5698,5701,5703,5706,5707,5708,5710,5712,5714,5719,5726,5741,5755,5760,5761,5774,5775,5780,5785,5787,5792,5833,5845,5854,5858,5869,5873,5874,5882,5896,5902,5920,5923,5935,5965,5979,6004,6024,6025,6028,6042,6044,6046,6048,6061,6062,6065,6067,6070,6071,6082,6088,6089,6090,6092,6094,6136,6137,6144,6154,6190,6192,6194,6196,6205,6207,6209,6215,6217,6223,6226,6234,6241,6242,6243,6248,6270,6271,6272,6274,6280,6285,6322,6323,6325,6326,6327,6329,6330,6331,6332,6341,6374,6375,6384,6405,6406,6426,6429,6440,6441,6447,6476,6478,6490,6528,6530,6531,6586,6610,6656,6676,6685,6686,6687,6688,6707,6708,6714,6726,6729,6731,6733,6734,6735,6737,6751,6762,6764,6765,6778,6781,6832,6843,6845,6849,6864,6865,6901,6913,6944,6963,6978,7032,7060,7115,7136,7145,7148,7203,7211,7269,7271,7285,7295,7296,7297,7316,7322,7324,7373,7383,7386,7402,7451,7453,7456,7499,7500,7518,7585,7604,7628,7650,7665,7680,7691,7699,7700,7728,7731,7733,7741,7779,7790,7815,7873,7907,7939,7986,8002,8008,8019,8020,8095,8149,8168,8192,8212,8236,8335,8337,8343,8361,8365,8379,8402,8413,8415,8430,8436,8440,8465,8479,8480,8496,8497,8502,8503,8504,8505,8506,8524,8525,8526,8535,8549,8551,8563,8567,8569,8570,8571,8579,8584,8611,8612,8641,8654,8658,8676,8698,8699,8700,8701,8714,8715,8737,8747,8756,8757,8758,8759,8761,8783,8784,8795,8840,8846,8852,8865,8870,8872,8875,8876,8880,8889,8972,9003,9004,9005,9020,9038,9043,9070,9071,9114,9117,9144,9189,9190,9191,9207,9233,9247,9253,9256,9279,9280,9308,9371,9407,9408,9409,9434,9435,9453,9471,9477,9493,9516,9538,9546,9547,9548,9549,9565,9567,9572,9603,9604,9610,9611,9654,9655,9686,9696,9706,9708,9709,9719,9733,9737,9765,9797,9802,9859,9902,9903,9905,9915,9916,9936,9941,9964,9969,9984,10036,10110,10111,10168,10184,2,8,9,4551,4552,4570,4601,4602,4604,4631,4637,4638,4649,4698,4700,4730,4744,4774,4871,4872,4886,4906,4962,4963,4966,4967,4969,4971,4972,4984,4985,4995,5006,5007,5013,5032,5033,5054,5059,5060,5061,5062,5065,5073,5076,5083,5084,5085,5150,5156,5157,5164,5194,5205,5211,5227,5247,5254,5255,5256,5265,5274,5281,5283,5284,5290,5298,5299,5309,5313,5314,5315,5316,5318,5319,5324,5325,5326,5327,5358,5359,5360,5368,5369,5370,5371,5414,5419,5421,5458,5460,5461,5463,5464,5466,5467,5469,5478,5483,5485,5486,5487,5488,5489,5490,5497,5507,5510,5521,5537,5538,5541,5550,5552,5553,5554,5579,5589,5606,5607,5617,5618,5620,5622,5627,5662,5666,5668,5728,5762,5763,5767,5773,5776,5777,5778,5779,5786,5797,5798,5800,5801,5809,5830,5861,5877,5880,5881,5883,5892,5910,5914,5917,5918,5919,5937,5950,5951,5981,5982,5986,6006,6009,6013,6032,6037,6038,6063,6066,6073,6081,6087,6091,6098,6099,6100,6101,6139,6155,6208,6244,6246,6267,6268,6273,6277,6278,6281,6288,6297,6314,6334,6335,6342,6352,6367,6387,6393,6395,6410,6411,6415,6417,6418,6419,6421,6423,6424,6425,6428,6433,6434,6436,6437,6443,6445,6486,6489,6503,6505,6506,6507,6543,6548,6550,6555,6556,6564,6568,6581,6605,6606,6608,6609,6621,6625,6627,6647,6650,6669,6702,6703,6704,6709,6722,6741,6743,6745,6747,6752,6758,6760,6775,6782,6818,6819,6820,6834,6835,6837,6838,6855,6857,6873,6899,6921,6932,6934,6936,6938,6939,6940,6975,6976,6981,6982,6990,6992,6993,6994,7013,7022,7023,7035,7045,7084,7094,7098,7105,7116,7117,7122,7124,7130,7138,7139,7152,7169,7187,7189,7206,7255,7256,7257,7259,7261,7265,7270,7292,7337,7369,7384,7389,7401,7434,7437,7460,7484,7501,7504,7505,7515,7534,7536,7538,7540,7541,7542,7567,7593,7594,7627,7629,7630,7631,7636,7657,7666,7677,7682,7688,7690,7696,7707,7708,7710,7730,7734,7739,7762,7828,7829,7876,7885,7886,7909,7910,7927,7928,7993,7994,8022,8051,8062,8064,8073,8085,8118,8124,8131,8144,8163,8169,8191,8234,8264,8276,8295,8298,8328,8352,8416,8417,8420,8422,8441,8528,8529,8530,8531,8558,8587,8615,8657,8675,8731,8776,8779,8792,8799,8837,8885,8886,8903,8904,9045,9049,9068,9078,9103,9105,9108,9112,9115,9116,9129,9130,9151,9157,9169,9218,9237,9257,9292,9293,9300,9363,9368,9404,9411,9414,9417,9418,9433,9449,9458,9470,9481,9482,9485])). % 187.89/187.73 cnf(12460,plain, % 187.89/187.73 (~P1(f306(f306(f308(x124601),x124602),f185(f872(x124601,a859))))), % 187.89/187.73 inference(rename_variables,[],[4505])). % 187.89/187.73 cnf(12461,plain, % 187.89/187.73 (P1(f306(f306(f308(f871(f866(x124611),f866(x124611))),f306(f306(f236(f866(x124611),f866(x124611)),f120(x124611)),f120(x124611))),f150(x124611,x124612)))), % 187.89/187.73 inference(rename_variables,[],[4037])). % 187.89/187.73 cnf(12463,plain, % 187.89/187.73 (P1(f306(f306(f308(f871(a865,a865)),f306(f306(f236(a865,a865),f306(a119,x124631)),f306(a119,f306(a119,x124631)))),f306(f306(f263(a865,a865,a865),f282(a865,a296)),f282(a865,f282(a865,a296)))))), % 187.89/187.73 inference(scs_inference,[],[4527,3510,11037,12085,12190,12282,12320,12328,3517,3518,3238,4455,4456,3143,4438,4420,10200,10210,10221,10330,10333,10336,10438,10551,10855,11022,11025,11223,11313,11320,11334,11384,11387,11409,11502,11548,11564,11864,11892,11904,11936,12034,12147,12154,12312,4435,10422,10515,3329,3479,3189,2875,2876,2878,2879,2882,2883,2885,2886,2887,2889,2894,2902,2911,2917,2923,2929,2936,2937,2938,2943,2952,2956,2970,3004,3005,3018,3019,3021,3028,3029,3030,3031,3033,3044,3050,3162,3064,4416,3603,3117,11310,3313,3227,10203,10264,10267,10357,10360,10650,10929,11325,11328,11445,11489,11494,11593,12055,12258,3202,11590,12341,12345,12349,3212,3722,10969,11596,3107,3922,4432,3552,3812,11360,3170,3134,3129,3115,3120,3149,3283,12026,12177,3330,10802,12148,3200,3201,3222,10463,3375,4513,3895,4445,10255,10419,11220,11412,12308,12342,4454,12316,3260,11685,4503,10972,11042,11263,11266,3376,3165,10322,10626,3166,3433,3086,3185,11350,4037,12331,3897,10978,11104,11155,12292,12298,12410,12413,12436,4524,10907,11109,11214,11236,11271,11277,12237,4525,11011,11112,11217,4526,11115,4528,11169,4529,3184,3472,12193,12234,12315,3628,4316,4317,4443,11341,3570,3777,3822,3458,3704,3340,10341,10458,10529,10590,10593,10629,10723,10962,11860,11926,12002,12046,12125,12128,3715,11581,4174,3253,3352,3533,4493,10232,10235,10261,10731,10744,10865,11286,11353,11752,11757,11978,11981,12067,12076,12240,4509,11464,11497,11532,11561,3702,3480,3481,3847,3299,3300,3273,4490,4440,3655,4171,3464,4510,4031,11231,3589,3312,11709,11712,12158,12262,4001,3961,11853,12208,3907,10799,12014,12040,12215,3956,10981,12082,12157,12214,12261,3629,11863,12009,12092,12138,3990,3646,10984,11047,11128,11188,12033,12106,12358,12433,4514,10747,11120,3270,10350,10445,10576,10636,11437,11657,11703,11737,11833,11891,12099,3271,10705,10750,10753,10786,10812,10849,10887,10923,11907,11910,11913,11916,12113,12116,12119,12122,12201,12369,3272,10433,10641,10726,10852,11740,11749,11839,11850,11869,11874,11919,11939,3348,12070,4489,10298,10387,10500,10524,10768,10815,10825,11511,11611,11632,11635,11638,11654,11807,11810,11813,11816,11903,11922,11925,11935,11990,11993,11996,11999,12077,12169,12172,12268,12271,12334,12362,3428,10596,10860,10904,11177,11255,11425,4505,10777,10789,10896,10914,10917,10975,11061,11069,11085,11123,11140,11149,11185,11226,11246,11249,11252,11280,11293,11296,11682,11718,11984,11987,12021,12071,12102,12246,12289,12295,12381,12384,12403,3334,10623,10653,10662,11206,11764,12400,3371,3365,3781,3720,10301,11584,11614,4502,10252,10611,10614,11064,11082,11547,11602,11642,11770,11795,11798,11801,11804,12066,3292,10656,10809,10880,11615,11769,11961,12180,3742,4081,4500,3753,3788,4479,4482,3244,3248,4481,4484,3249,4480,3760,3579,11577,4177,4516,10226,10229,10481,10532,10535,10540,10949,11419,11669,11773,4522,11143,11260,11302,3967,3864,11299,11641,11645,11706,12319,12327,3709,10920,10926,10944,11888,12105,12377,3566,11146,12131,12243,12253,12324,12372,4035,3711,10659,11000,11152,11182,11193,12037,12323,3536,10579,10582,10665,10836,4519,11578,4520,10716,10818,11131,11283,11422,11450,12196,12205,12249,4140,10792,12226,4042,3741,3689,4517,10274,10277,10617,10620,11461,11646,4518,11558,3713,10585,3974,4521,4538,4564,4613,4615,4645,4662,4669,4670,4709,4739,4745,4830,4856,4857,4918,4919,4941,4942,4955,4959,4981,4988,5005,5008,5009,5010,5015,5016,5039,5066,5067,5077,5082,5090,5135,5136,5144,5154,5158,5160,5170,5172,5178,5182,5197,5204,5207,5208,5209,5213,5248,5261,5268,5270,5271,5275,5276,5277,5285,5288,5293,5294,5295,5302,5306,5307,5308,5317,5321,5322,5323,5328,5341,5350,5362,5364,5372,5373,5377,5381,5406,5412,5422,5423,5438,5451,5473,5479,5495,5496,5499,5518,5526,5527,5532,5533,5543,5544,5556,5560,5569,5570,5572,5587,5592,5603,5604,5616,5623,5637,5641,5644,5650,5651,5652,5655,5660,5697,5698,5701,5703,5706,5707,5708,5710,5712,5714,5719,5726,5741,5755,5760,5761,5774,5775,5780,5785,5787,5792,5833,5845,5854,5858,5869,5873,5874,5882,5896,5902,5920,5923,5935,5965,5979,6004,6024,6025,6028,6042,6044,6046,6048,6061,6062,6065,6067,6070,6071,6082,6088,6089,6090,6092,6094,6136,6137,6144,6154,6190,6192,6194,6196,6205,6207,6209,6215,6217,6223,6226,6234,6241,6242,6243,6248,6270,6271,6272,6274,6280,6285,6322,6323,6325,6326,6327,6329,6330,6331,6332,6341,6374,6375,6384,6405,6406,6426,6429,6440,6441,6447,6476,6478,6490,6528,6530,6531,6586,6610,6656,6676,6685,6686,6687,6688,6707,6708,6714,6726,6729,6731,6733,6734,6735,6737,6751,6762,6764,6765,6778,6781,6832,6843,6845,6849,6864,6865,6901,6913,6944,6963,6978,7032,7060,7115,7136,7145,7148,7203,7211,7269,7271,7285,7295,7296,7297,7316,7322,7324,7373,7383,7386,7402,7451,7453,7456,7499,7500,7518,7585,7604,7628,7650,7665,7680,7691,7699,7700,7728,7731,7733,7741,7779,7790,7815,7873,7907,7939,7986,8002,8008,8019,8020,8095,8149,8168,8192,8212,8236,8335,8337,8343,8361,8365,8379,8402,8413,8415,8430,8436,8440,8465,8479,8480,8496,8497,8502,8503,8504,8505,8506,8524,8525,8526,8535,8549,8551,8563,8567,8569,8570,8571,8579,8584,8611,8612,8641,8654,8658,8676,8698,8699,8700,8701,8714,8715,8737,8747,8756,8757,8758,8759,8761,8783,8784,8795,8840,8846,8852,8865,8870,8872,8875,8876,8880,8889,8972,9003,9004,9005,9020,9038,9043,9070,9071,9114,9117,9144,9189,9190,9191,9207,9233,9247,9253,9256,9279,9280,9308,9371,9407,9408,9409,9434,9435,9453,9471,9477,9493,9516,9538,9546,9547,9548,9549,9565,9567,9572,9603,9604,9610,9611,9654,9655,9686,9696,9706,9708,9709,9719,9733,9737,9765,9797,9802,9859,9902,9903,9905,9915,9916,9936,9941,9964,9969,9984,10036,10110,10111,10168,10184,2,8,9,4551,4552,4570,4601,4602,4604,4631,4637,4638,4649,4698,4700,4730,4744,4774,4871,4872,4886,4906,4962,4963,4966,4967,4969,4971,4972,4984,4985,4995,5006,5007,5013,5032,5033,5054,5059,5060,5061,5062,5065,5073,5076,5083,5084,5085,5150,5156,5157,5164,5194,5205,5211,5227,5247,5254,5255,5256,5265,5274,5281,5283,5284,5290,5298,5299,5309,5313,5314,5315,5316,5318,5319,5324,5325,5326,5327,5358,5359,5360,5368,5369,5370,5371,5414,5419,5421,5458,5460,5461,5463,5464,5466,5467,5469,5478,5483,5485,5486,5487,5488,5489,5490,5497,5507,5510,5521,5537,5538,5541,5550,5552,5553,5554,5579,5589,5606,5607,5617,5618,5620,5622,5627,5662,5666,5668,5728,5762,5763,5767,5773,5776,5777,5778,5779,5786,5797,5798,5800,5801,5809,5830,5861,5877,5880,5881,5883,5892,5910,5914,5917,5918,5919,5937,5950,5951,5981,5982,5986,6006,6009,6013,6032,6037,6038,6063,6066,6073,6081,6087,6091,6098,6099,6100,6101,6139,6155,6208,6244,6246,6267,6268,6273,6277,6278,6281,6288,6297,6314,6334,6335,6342,6352,6367,6387,6393,6395,6410,6411,6415,6417,6418,6419,6421,6423,6424,6425,6428,6433,6434,6436,6437,6443,6445,6486,6489,6503,6505,6506,6507,6543,6548,6550,6555,6556,6564,6568,6581,6605,6606,6608,6609,6621,6625,6627,6647,6650,6669,6702,6703,6704,6709,6722,6741,6743,6745,6747,6752,6758,6760,6775,6782,6818,6819,6820,6834,6835,6837,6838,6855,6857,6873,6899,6921,6932,6934,6936,6938,6939,6940,6975,6976,6981,6982,6990,6992,6993,6994,7013,7022,7023,7035,7045,7084,7094,7098,7105,7116,7117,7122,7124,7130,7138,7139,7152,7169,7187,7189,7206,7255,7256,7257,7259,7261,7265,7270,7292,7337,7369,7384,7389,7401,7434,7437,7460,7484,7501,7504,7505,7515,7534,7536,7538,7540,7541,7542,7567,7593,7594,7627,7629,7630,7631,7636,7657,7666,7677,7682,7688,7690,7696,7707,7708,7710,7730,7734,7739,7762,7828,7829,7876,7885,7886,7909,7910,7927,7928,7993,7994,8022,8051,8062,8064,8073,8085,8118,8124,8131,8144,8163,8169,8191,8234,8264,8276,8295,8298,8328,8352,8416,8417,8420,8422,8441,8528,8529,8530,8531,8558,8587,8615,8657,8675,8731,8776,8779,8792,8799,8837,8885,8886,8903,8904,9045,9049,9068,9078,9103,9105,9108,9112,9115,9116,9129,9130,9151,9157,9169,9218,9237,9257,9292,9293,9300,9363,9368,9404,9411,9414,9417,9418,9433,9449,9458,9470,9481,9482,9485,9487,9514])). % 187.89/187.73 cnf(12466,plain, % 187.89/187.73 (~P1(f306(f306(f308(x124661),x124662),f185(f872(x124661,a859))))), % 187.89/187.73 inference(rename_variables,[],[4505])). % 187.89/187.73 cnf(12469,plain, % 187.89/187.73 (P34(x124691,x124692,f120(x124691))), % 187.89/187.73 inference(rename_variables,[],[3206])). % 187.89/187.73 cnf(12472,plain, % 187.89/187.73 (E(f306(f186(f866(x124721)),f306(f160(x124721),x124722)),f306(f186(f866(x124721)),x124722))), % 187.89/187.73 inference(rename_variables,[],[3283])). % 187.89/187.73 cnf(12475,plain, % 187.89/187.73 (~P1(f306(f306(f308(x124751),x124752),f185(f872(x124751,a859))))), % 187.89/187.73 inference(rename_variables,[],[4505])). % 187.89/187.73 cnf(12480,plain, % 187.89/187.73 (P1(f306(f306(f193(a24),x124801),x124801))), % 187.89/187.73 inference(rename_variables,[],[3270])). % 187.89/187.73 cnf(12484,plain, % 187.89/187.73 (~P1(f306(f306(f221(a865),x124841),x124841))), % 187.89/187.73 inference(rename_variables,[],[4489])). % 187.89/187.73 cnf(12486,plain, % 187.89/187.73 (P1(f306(f306(f308(f871(f866(x124861),f866(x124861))),f306(f306(f236(f866(x124861),f866(x124861)),f306(f160(x124861),x124862)),x124862)),f150(x124861,f231(f872(f871(x124861,x124861),a859)))))), % 187.89/187.73 inference(scs_inference,[],[4527,3510,11037,12085,12190,12282,12320,12328,3517,3518,3238,3206,4455,4456,3143,4438,4420,10200,10210,10221,10330,10333,10336,10438,10551,10855,11022,11025,11223,11313,11320,11334,11384,11387,11409,11502,11548,11564,11864,11892,11904,11936,12034,12147,12154,12312,4435,10422,10515,3329,3479,3189,2875,2876,2878,2879,2882,2883,2885,2886,2887,2889,2894,2902,2911,2917,2923,2929,2936,2937,2938,2943,2952,2956,2970,3004,3005,3018,3019,3021,3028,3029,3030,3031,3033,3044,3050,3162,3064,4416,3603,3117,11310,3313,3227,10203,10264,10267,10357,10360,10650,10929,11325,11328,11445,11489,11494,11593,12055,12258,3202,11590,12341,12345,12349,3212,3722,10969,11596,3107,3922,4432,3552,3812,11360,3170,3134,3129,3115,3120,3149,3283,12026,12177,12396,12472,3330,10802,12148,3200,3201,3222,10463,3375,4513,3895,4445,10255,10419,11220,11412,12308,12342,4454,12316,3260,11685,4503,10972,11042,11263,11266,3376,3165,10322,10626,3166,3433,3086,3185,11350,4037,12331,12461,3897,10978,11104,11155,12292,12298,12410,12413,12436,4524,10907,11109,11214,11236,11271,11277,12237,4525,11011,11112,11217,4526,11115,4528,11169,4529,3184,3472,12193,12234,12315,3628,4316,4317,4443,11341,3570,3777,3822,3458,3704,3340,10341,10458,10529,10590,10593,10629,10723,10962,11860,11926,12002,12046,12125,12128,3715,11581,4174,3253,3352,3533,4493,10232,10235,10261,10731,10744,10865,11286,11353,11752,11757,11978,11981,12067,12076,12240,4509,11464,11497,11532,11561,3702,3480,3481,3847,3299,3300,3273,4490,4440,3655,4171,3464,4510,4031,11231,3589,3312,11709,11712,12158,12262,4001,3961,11853,12208,3907,10799,12014,12040,12215,3956,10981,12082,12157,12214,12261,3629,11863,12009,12092,12138,3990,3646,10984,11047,11128,11188,12033,12106,12358,12433,4514,10747,11120,3270,10350,10445,10576,10636,11437,11657,11703,11737,11833,11891,12099,12265,3271,10705,10750,10753,10786,10812,10849,10887,10923,11907,11910,11913,11916,12113,12116,12119,12122,12201,12369,3272,10433,10641,10726,10852,11740,11749,11839,11850,11869,11874,11919,11939,3348,12070,4489,10298,10387,10500,10524,10768,10815,10825,11511,11611,11632,11635,11638,11654,11807,11810,11813,11816,11903,11922,11925,11935,11990,11993,11996,11999,12077,12169,12172,12268,12271,12334,12362,12399,3428,10596,10860,10904,11177,11255,11425,12311,4505,10777,10789,10896,10914,10917,10975,11061,11069,11085,11123,11140,11149,11185,11226,11246,11249,11252,11280,11293,11296,11682,11718,11984,11987,12021,12071,12102,12246,12289,12295,12381,12384,12403,12460,12466,3334,10623,10653,10662,11206,11764,12400,3371,3365,3781,3720,10301,11584,11614,4502,10252,10611,10614,11064,11082,11547,11602,11642,11770,11795,11798,11801,11804,12066,3292,10656,10809,10880,11615,11769,11961,12180,3742,4081,4500,3753,3788,4479,4482,3244,3248,4481,4484,3249,4480,3760,3579,11577,4177,11444,4516,10226,10229,10481,10532,10535,10540,10949,11419,11669,11773,4522,11143,11260,11302,3967,3864,11299,11641,11645,11706,12319,12327,3709,10920,10926,10944,11888,12105,12377,3566,11146,12131,12243,12253,12324,12372,4035,3711,10659,11000,11152,11182,11193,12037,12323,3536,10579,10582,10665,10836,4519,11578,4520,10716,10818,11131,11283,11422,11450,12196,12205,12249,4140,10792,12226,4042,3741,3689,4517,10274,10277,10617,10620,11461,11646,4518,11558,3713,10585,3974,4521,4538,4564,4613,4615,4645,4662,4669,4670,4709,4739,4745,4830,4856,4857,4918,4919,4941,4942,4955,4959,4981,4988,5005,5008,5009,5010,5015,5016,5039,5066,5067,5077,5082,5090,5135,5136,5144,5154,5158,5160,5170,5172,5178,5182,5197,5204,5207,5208,5209,5213,5248,5261,5268,5270,5271,5275,5276,5277,5285,5288,5293,5294,5295,5302,5306,5307,5308,5317,5321,5322,5323,5328,5341,5350,5362,5364,5372,5373,5377,5381,5406,5412,5422,5423,5438,5451,5473,5479,5495,5496,5499,5518,5526,5527,5532,5533,5543,5544,5556,5560,5569,5570,5572,5587,5592,5603,5604,5616,5623,5637,5641,5644,5650,5651,5652,5655,5660,5697,5698,5701,5703,5706,5707,5708,5710,5712,5714,5719,5726,5741,5755,5760,5761,5774,5775,5780,5785,5787,5792,5833,5845,5854,5858,5869,5873,5874,5882,5896,5902,5920,5923,5935,5965,5979,6004,6024,6025,6028,6042,6044,6046,6048,6061,6062,6065,6067,6070,6071,6082,6088,6089,6090,6092,6094,6136,6137,6144,6154,6190,6192,6194,6196,6205,6207,6209,6215,6217,6223,6226,6234,6241,6242,6243,6248,6270,6271,6272,6274,6280,6285,6322,6323,6325,6326,6327,6329,6330,6331,6332,6341,6374,6375,6384,6405,6406,6426,6429,6440,6441,6447,6476,6478,6490,6528,6530,6531,6586,6610,6656,6676,6685,6686,6687,6688,6707,6708,6714,6726,6729,6731,6733,6734,6735,6737,6751,6762,6764,6765,6778,6781,6832,6843,6845,6849,6864,6865,6901,6913,6944,6963,6978,7032,7060,7115,7136,7145,7148,7203,7211,7269,7271,7285,7295,7296,7297,7316,7322,7324,7373,7383,7386,7402,7451,7453,7456,7499,7500,7518,7585,7604,7628,7650,7665,7680,7691,7699,7700,7728,7731,7733,7741,7779,7790,7815,7873,7907,7939,7986,8002,8008,8019,8020,8095,8149,8168,8192,8212,8236,8335,8337,8343,8361,8365,8379,8402,8413,8415,8430,8436,8440,8465,8479,8480,8496,8497,8502,8503,8504,8505,8506,8524,8525,8526,8535,854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% 187.89/187.73 cnf(12487,plain, % 187.89/187.73 (P1(f306(f306(f308(x124871),x124872),f231(f872(x124871,a859))))), % 187.89/187.73 inference(rename_variables,[],[3428])). % 187.89/187.73 cnf(12490,plain, % 187.89/187.73 (~P1(f306(f306(f185(f872(x124901,f872(x124902,a859))),x124903),x124904))), % 187.89/187.73 inference(rename_variables,[],[4520])). % 187.89/187.73 cnf(12493,plain, % 187.89/187.73 (P1(f306(f306(f220(f872(x124931,a859)),x124932),x124932))), % 187.89/187.73 inference(rename_variables,[],[3566])). % 187.89/187.73 cnf(12496,plain, % 187.89/187.73 (~P1(f306(f306(f308(x124961),x124962),f185(f872(x124961,a859))))), % 187.89/187.73 inference(rename_variables,[],[4505])). % 187.89/187.73 cnf(12499,plain, % 187.89/187.73 (P1(f306(f306(f220(a1),f2(a1)),f306(f306(f237(a1),f306(f76(a1),x124991)),x124992)))), % 187.89/187.73 inference(rename_variables,[],[3741])). % 187.89/187.73 cnf(12502,plain, % 187.89/187.73 (~E(f306(a119,x125021),x125021)), % 187.89/187.73 inference(rename_variables,[],[4420])). % 187.89/187.73 cnf(12504,plain, % 187.89/187.73 (E(f306(f232(x125041,x125041),f233(x125041,x125042)),x125042)), % 187.89/187.73 inference(rename_variables,[],[3227])). % 187.89/187.73 cnf(12509,plain, % 187.89/187.73 (E(f306(f232(x125091,x125091),f233(x125091,x125092)),x125092)), % 187.89/187.73 inference(rename_variables,[],[3227])). % 187.89/187.73 cnf(12511,plain, % 187.89/187.73 (E(f306(f232(x125111,x125111),f233(x125111,x125112)),x125112)), % 187.89/187.73 inference(rename_variables,[],[3227])). % 187.89/187.73 cnf(12513,plain, % 187.89/187.73 (E(f306(f232(x125131,x125131),f233(x125131,x125132)),x125132)), % 187.89/187.73 inference(rename_variables,[],[3227])). % 187.89/187.73 cnf(12522,plain, % 187.89/187.73 (P28(x125221,x125221,f5(x125221),x125222)), % 187.89/187.73 inference(rename_variables,[],[3510])). % 187.89/187.73 cnf(12524,plain, % 187.89/187.73 (P28(x125241,x125241,f5(x125241),x125242)), % 187.89/187.73 inference(rename_variables,[],[3510])). % 187.89/187.73 cnf(12530,plain, % 187.89/187.73 (E(f306(f232(x125301,x125301),f233(x125301,x125302)),x125302)), % 187.89/187.73 inference(rename_variables,[],[3227])). % 187.89/187.73 cnf(12532,plain, % 187.89/187.73 (P27(x125321,x125322,f185(f872(f864(x125321),a859)))), % 187.89/187.73 inference(rename_variables,[],[3328])). % 187.89/187.73 cnf(12538,plain, % 187.89/187.73 (E(f306(f232(x125381,x125381),f233(x125381,x125382)),x125382)), % 187.89/187.73 inference(rename_variables,[],[3227])). % 187.89/187.73 cnf(12542,plain, % 187.89/187.73 (E(f306(f232(x125421,x125421),f233(x125421,x125422)),x125422)), % 187.89/187.73 inference(rename_variables,[],[3227])). % 187.89/187.73 cnf(12544,plain, % 187.89/187.73 (E(f306(f232(x125441,x125441),f233(x125441,x125442)),x125442)), % 187.89/187.73 inference(rename_variables,[],[3227])). % 187.89/187.73 cnf(12550,plain, % 187.89/187.73 (P30(x125501,f2(a865),f306(f306(f306(f93(x125501),x125502),f306(a26,x125503)),x125504))), % 187.89/187.73 inference(rename_variables,[],[3639])). % 187.89/187.73 cnf(12556,plain, % 187.89/187.73 (P40(x125561,f145(x125561,x125562))), % 187.89/187.73 inference(rename_variables,[],[3143])). % 187.89/187.73 cnf(12560,plain, % 187.89/187.73 (P35(x125601,x125602,f120(x125601),f120(x125601))), % 187.89/187.73 inference(rename_variables,[],[3517])). % 187.89/187.73 cnf(12562,plain, % 187.89/187.73 (P35(x125621,x125622,f120(x125621),f120(x125621))), % 187.89/187.73 inference(rename_variables,[],[3517])). % 187.89/187.73 cnf(12566,plain, % 187.89/187.73 (P50(x125661,x125662,f233(x125661,x125662))), % 187.89/187.73 inference(rename_variables,[],[3237])). % 187.89/187.73 cnf(12568,plain, % 187.89/187.73 (P50(x125681,x125682,f233(x125681,x125682))), % 187.89/187.73 inference(rename_variables,[],[3237])). % 187.89/187.73 cnf(12576,plain, % 187.89/187.73 (P55(x125761,f185(f872(x125761,a859)),x125762)), % 187.89/187.73 inference(rename_variables,[],[3290])). % 187.89/187.73 cnf(12580,plain, % 187.89/187.73 (P18(x125801,f872(x125801,a859),f284(x125801))), % 187.89/187.73 inference(rename_variables,[],[3241])). % 187.89/187.73 cnf(12586,plain, % 187.89/187.73 (E(f185(f872(f871(x125861,x125861),a859)),f233(x125861,f185(f872(x125861,a859))))), % 187.89/187.73 inference(rename_variables,[],[3343])). % 187.89/187.73 cnf(12589,plain, % 187.89/187.73 (P54(x125891,x125891,f233(x125891,x125892))), % 187.89/187.73 inference(rename_variables,[],[3238])). % 187.89/187.73 cnf(12595,plain, % 187.89/187.73 (E(f306(f232(x125951,x125951),f233(x125951,x125952)),x125952)), % 187.89/187.73 inference(rename_variables,[],[3227])). % 187.89/187.73 cnf(12604,plain, % 187.89/187.73 (P44(x126041,x126042,x126043,x126044,f185(f872(x126041,a859)),x126044)), % 187.89/187.73 inference(rename_variables,[],[4201])). % 187.89/187.73 cnf(12607,plain, % 187.89/187.73 (P44(x126071,x126072,x126073,x126074,f185(f872(x126071,a859)),x126074)), % 187.89/187.73 inference(rename_variables,[],[4201])). % 187.89/187.73 cnf(12615,plain, % 187.89/187.73 (E(f306(f232(x126151,x126151),f233(x126151,x126152)),x126152)), % 187.89/187.73 inference(rename_variables,[],[3227])). % 187.89/187.73 cnf(12620,plain, % 187.89/187.73 (P1(f306(f306(f221(a865),f2(a865)),f306(a119,x126201)))), % 187.89/187.73 inference(rename_variables,[],[3352])). % 187.89/187.73 cnf(12621,plain, % 187.89/187.73 (~E(f306(a119,x126211),x126211)), % 187.89/187.73 inference(rename_variables,[],[4420])). % 187.89/187.73 cnf(12627,plain, % 187.89/187.73 (P1(f306(f306(f221(a865),x126271),f306(a119,x126271)))), % 187.89/187.73 inference(rename_variables,[],[3340])). % 187.89/187.73 cnf(12632,plain, % 187.89/187.73 (~P1(f306(f306(f221(a865),x126321),f2(a865)))), % 187.89/187.73 inference(rename_variables,[],[4493])). % 187.89/187.73 cnf(12634,plain, % 187.89/187.73 (P1(f306(f306(f220(a1),a84),f2(a1)))), % 187.89/187.73 inference(scs_inference,[],[4527,3510,11037,12085,12190,12282,12320,12328,12393,12522,3517,12151,12560,12562,3518,12221,3237,12566,12568,3238,12589,3206,12469,4455,4456,11663,4201,12604,12607,3241,12580,3085,3143,12556,4438,3568,4420,10200,10210,10221,10330,10333,10336,10438,10551,10855,11022,11025,11223,11313,11320,11334,11384,11387,11409,11502,11548,11564,11864,11892,11904,11936,12034,12147,12154,12312,12363,12502,4435,10422,10515,3329,3290,12576,3479,3189,2875,2876,2878,2879,2882,2883,2885,2886,2887,2889,2894,2898,2902,2911,2917,2923,2929,2936,2937,2938,2943,2952,2956,2970,3004,3005,3018,3019,3021,3028,3029,3030,3031,3033,3044,3050,3162,4415,3064,3142,4416,3603,3117,11310,3251,3313,3224,3227,10203,10264,10267,10357,10360,10650,10929,11325,11328,11445,11489,11494,11593,12055,12258,12449,12504,12509,12511,12513,12530,12538,12542,12544,12595,3202,11590,12341,12345,12349,3212,3722,10969,11596,3107,3922,4432,3552,3812,11360,3328,12532,3170,3134,3639,12550,3129,3928,3644,3115,3120,3149,3283,12026,12177,12396,12472,3330,10802,12148,3200,3201,3222,10463,3375,4513,10392,3895,4445,10255,10419,11220,11412,12308,12342,4454,12316,3260,11685,4503,10972,11042,11263,11266,3664,3376,3590,3343,12586,3165,10322,10626,3166,3433,3157,3086,3185,11350,4037,12331,12461,3897,10978,11104,11155,12292,12298,12410,12413,12436,4524,10907,11109,11214,11236,11271,11277,12237,4525,11011,11112,11217,4526,11115,4528,11169,4529,3184,3472,12193,12234,12315,3628,4316,4317,4443,11341,3570,3777,3822,3458,3704,3340,10341,10458,10529,10590,10593,10629,10723,10962,11860,11926,12002,12046,12125,12128,12440,3715,11581,4174,3253,3352,11700,3533,4493,10232,10235,10261,10731,10744,10865,11286,11353,11752,11757,11978,11981,12067,12076,12240,12335,4509,11464,11497,11532,11561,3702,3480,3481,3847,3299,3300,3273,4490,4440,3655,4171,3962,3464,4510,4031,11231,3589,3312,11709,11712,12158,12262,4001,3961,11853,12208,3907,10799,12014,12040,12215,3956,10981,12082,12157,12214,12261,3629,11863,12009,12092,12138,3990,3646,10984,11047,11128,11188,12033,12106,12358,12433,12446,4514,10747,11120,3270,10350,10445,10576,10636,11437,11657,11703,11737,11833,11891,12099,12265,3271,10705,10750,10753,10786,10812,10849,10887,10923,11907,11910,11913,11916,12113,12116,12119,12122,12201,12369,3272,10433,10641,10726,10852,11740,11749,11839,11850,11869,11874,11919,11939,3348,12070,4489,10298,10387,10500,10524,10768,10815,10825,11511,11611,11632,11635,11638,11654,11807,11810,11813,11816,11903,11922,11925,11935,11990,11993,11996,11999,12077,12169,12172,12268,12271,12334,12362,12399,3428,10596,10860,10904,11177,11255,11425,12311,4505,10777,10789,10896,10914,10917,10975,11061,11069,11085,11123,11140,11149,11185,11226,11246,11249,11252,11280,11293,11296,11682,11718,11984,11987,12021,12071,12102,12246,12289,12295,12381,12384,12403,12460,12466,12475,3334,10623,10653,10662,11206,11764,12400,3371,3365,3781,3720,10301,11584,11614,4502,10252,10611,10614,11064,11082,11547,11602,11642,11770,11795,11798,11801,11804,12066,3292,10656,10809,10880,11615,11769,11961,12180,3742,4081,4500,3753,3788,4479,4482,3244,3248,4481,4484,3249,4480,3760,3579,11577,4177,11444,4516,10226,10229,10481,10532,10535,10540,10949,11419,11669,11773,4522,11143,11260,11302,3967,3864,11299,11641,11645,11706,12319,12327,3709,10920,10926,10944,11888,12105,12377,3566,11146,12131,12243,12253,12324,12372,12380,4035,3711,10659,11000,11152,11182,11193,12037,12323,3536,10579,10582,10665,10836,4519,11578,4520,10716,10818,11131,11283,11422,11450,12196,12205,12249,12430,4140,10792,12226,4042,3741,3689,4517,10274,10277,10617,10620,11461,11646,4518,11558,3713,10585,3974,4521,4538,4564,4613,4615,4645,4662,4669,4670,4709,4739,4745,4830,4856,4857,4918,4919,4941,4942,4955,4959,4981,4988,5005,5008,5009,5010,5015,5016,5039,5066,5067,5077,5082,5090,5135,5136,5144,5154,5158,5160,5170,5172,5178,5182,5197,5204,5207,5208,5209,5213,5248,5261,5268,5270,5271,5275,5276,5277,5285,5288,5293,5294,5295,5302,5306,5307,5308,5317,5321,5322,5323,5328,5341,5350,5362,5364,5372,5373,5377,5381,5406,5412,5422,5423,5438,5451,5473,5479,5495,5496,5499,5518,5526,5527,5532,5533,5543,5544,5556,5560,5569,5570,5572,5587,5592,5603,5604,5616,5623,5637,5641,5644,5650,5651,5652,5655,5660,5697,5698,5701,5703,5706,5707,5708,5710,5712,5714,5719,5726,5741,5755,5760,5761,5774,5775,5780,5785,5787,5792,5833,5845,5854,5858,5869,5873,5874,5882,5896,5902,5920,5923,5935,5965,5979,6004,6024,6025,6028,6042,6044,6046,6048,6061,6062,6065,6067,6070,6071,6082,6088,6089,6090,6092,6094,6136,6137,6144,6154,6190,6192,6194,6196,6205,6207,6209,6215,6217,6223,6226,6234,6241,6242,6243,6248,6270,6271,6272,6274,6280,6285,6322,6323,6325,6326,6327,6329,6330,6331,6332,6341,6374,6375,6384,6405,6406,6426,6429,6440,6441,6447,6476,6478,6490,6528,6530,6531,6586,6610,6656,6676,6685,6686,6687,6688,6707,6708,6714,6726,6729,6731,6733,6734,6735,6737,6751,6762,6764,6765,6778,6781,6832,6843,6845,6849,6864,6865,6901,6913,6944,6963,6978,7032,7060,7115,7136,7145,7148,7203,7211,7269,7271,7285,7295,7296,7297,7316,7322,7324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% 187.89/187.73 cnf(12641,plain, % 187.89/187.73 (~P1(f306(f306(f221(a1),f306(f107(a1),x126411)),f306(f80(a1),f306(f107(a1),x126412))))), % 187.89/187.73 inference(rename_variables,[],[4515])). % 187.89/187.73 cnf(12651,plain, % 187.89/187.73 (~P1(f306(f306(f221(a865),x126511),f2(a865)))), % 187.89/187.73 inference(rename_variables,[],[4493])). % 187.89/187.73 cnf(12654,plain, % 187.89/187.73 (~P1(f306(f306(f221(a865),x126541),f2(a865)))), % 187.89/187.73 inference(rename_variables,[],[4493])). % 187.89/187.73 cnf(12657,plain, % 187.89/187.73 (P1(f306(f63(a865),f279(a865,x126571,x126572)))), % 187.89/187.73 inference(rename_variables,[],[3481])). % 187.89/187.73 cnf(12660,plain, % 187.89/187.73 (P1(f306(f63(a865),f279(a865,x126601,x126602)))), % 187.89/187.73 inference(rename_variables,[],[3481])). % 187.89/187.73 cnf(12663,plain, % 187.89/187.73 (P1(f306(f63(a865),f279(a865,x126631,x126632)))), % 187.89/187.73 inference(rename_variables,[],[3481])). % 187.89/187.73 cnf(12666,plain, % 187.89/187.73 (P1(f306(f63(a865),f279(a865,x126661,x126662)))), % 187.89/187.73 inference(rename_variables,[],[3481])). % 187.89/187.73 cnf(12673,plain, % 187.89/187.73 (P1(f306(f306(f220(a1),f306(f80(a1),f306(f107(a1),x126731))),f306(f107(a1),x126732)))), % 187.89/187.73 inference(rename_variables,[],[3742])). % 187.89/187.73 cnf(12675,plain, % 187.89/187.73 (P1(f306(f306(f220(a1),f2(a1)),f306(f111(a1),f2(a1))))), % 187.89/187.73 inference(scs_inference,[],[4527,3510,11037,12085,12190,12282,12320,12328,12393,12522,3517,12151,12560,12562,3518,12221,3237,12566,12568,3238,12589,3206,12469,4455,4456,11663,4201,12604,12607,3241,12580,3085,3143,12556,4438,3568,4420,10200,10210,10221,10330,10333,10336,10438,10551,10855,11022,11025,11223,11313,11320,11334,11384,11387,11409,11502,11548,11564,11864,11892,11904,11936,12034,12147,12154,12312,12363,12502,4435,10422,10515,3329,3290,12576,3479,3189,2875,2876,2878,2879,2882,2883,2885,2886,2887,2889,2894,2898,2902,2911,2917,2923,2929,2936,2937,2938,2943,2948,2952,2956,2970,3004,3005,3018,3019,3021,3028,3029,3030,3031,3033,3044,3050,3162,4415,3064,3142,4416,3603,3117,11310,3251,3313,3224,3227,10203,10264,10267,10357,10360,10650,10929,11325,11328,11445,11489,11494,11593,12055,12258,12449,12504,12509,12511,12513,12530,12538,12542,12544,12595,3202,11590,12341,12345,12349,3212,3722,10969,11596,3107,3922,4432,3552,3812,11360,3328,12532,3170,3134,3639,12550,3129,3928,3644,3115,3095,3120,3149,3283,12026,12177,12396,12472,3330,10802,12148,3200,3201,3222,10463,3375,4513,10392,3895,4445,10255,10419,11220,11412,12308,12342,4454,12316,3260,11685,4503,10972,11042,11263,11266,3664,3376,3590,3343,12586,3165,10322,10626,3166,3433,3157,3086,3185,11350,4037,12331,12461,3897,10978,11104,11155,12292,12298,12410,12413,12436,4524,10907,11109,11214,11236,11271,11277,12237,4525,11011,11112,11217,4526,11115,4528,11169,4529,3184,3472,12193,12234,12315,3628,4316,4317,4443,11341,3570,3777,3822,3458,3704,3340,10341,10458,10529,10590,10593,10629,10723,10962,11860,11926,12002,12046,12125,12128,12440,3715,11581,4174,3253,3352,11700,3533,4493,10232,10235,10261,10731,10744,10865,11286,11353,11752,11757,11978,11981,12067,12076,12240,12335,12632,12651,4509,11464,11497,11532,11561,3702,3480,3481,11881,12657,12660,12663,3847,3299,3300,3273,4490,4440,3655,4171,3962,3464,4510,4031,11231,3589,3312,11709,11712,12158,12262,4001,3961,11853,12208,3907,10799,12014,12040,12215,3956,10981,12082,12157,12214,12261,3629,11863,12009,12092,12138,3990,3646,10984,11047,11128,11188,12033,12106,12358,12433,12446,4514,10747,11120,3270,10350,10445,10576,10636,11437,11657,11703,11737,11833,11891,12099,12265,3271,10705,10750,10753,10786,10812,10849,10887,10923,11907,11910,11913,11916,12113,12116,12119,12122,12201,12369,3272,10433,10641,10726,10852,11740,11749,11839,11850,11869,11874,11919,11939,3348,12070,4489,10298,10387,10500,10524,10768,10815,10825,11511,11611,11632,11635,11638,11654,11807,11810,11813,11816,11903,11922,11925,11935,11990,11993,11996,11999,12077,12169,12172,12268,12271,12334,12362,12399,3428,10596,10860,10904,11177,11255,11425,12311,4505,10777,10789,10896,10914,10917,10975,11061,11069,11085,11123,11140,11149,11185,11226,11246,11249,11252,11280,11293,11296,11682,11718,11984,11987,12021,12071,12102,12246,12289,12295,12381,12384,12403,12460,12466,12475,3334,10623,10653,10662,11206,11764,12400,3371,3365,3781,3720,10301,11584,11614,4502,10252,10611,10614,11064,11082,11547,11602,11642,11770,11795,11798,11801,11804,12066,3292,10656,10809,10880,11615,11769,11961,12180,3742,11715,4081,4500,3753,3788,4479,4482,4483,3244,3248,4481,4484,3249,4480,3760,3579,11577,4177,11444,4516,10226,10229,10481,10532,10535,10540,10949,11419,11669,11773,4522,11143,11260,11302,3967,3864,11299,11641,11645,11706,12319,12327,3709,10920,10926,10944,11888,12105,12377,3566,11146,12131,12243,12253,12324,12372,12380,4035,3711,10659,11000,11152,11182,11193,12037,12323,3536,10579,10582,10665,10836,3535,4519,11578,4515,12641,4520,10716,10818,11131,11283,11422,11450,12196,12205,12249,12430,4140,10792,12226,4042,3741,3689,3690,4517,10274,10277,10617,10620,11461,11646,4518,11558,3713,10585,3974,4521,4538,4564,4613,4615,4645,4662,4669,4670,4709,4739,4745,4830,4856,4857,4918,4919,4941,4942,4955,4959,4981,4988,5005,5008,5009,5010,5015,5016,5039,5066,5067,5077,5082,5090,5135,5136,5144,5154,5158,5160,5170,5172,5178,5182,5197,5204,5207,5208,5209,5213,5248,5261,5268,5270,5271,5275,5276,5277,5285,5288,5293,5294,5295,5302,5306,5307,5308,5317,5321,5322,5323,5328,5341,5350,5362,5364,5372,5373,5377,5381,5406,5412,5422,5423,5438,5451,5473,5479,5495,5496,5499,5518,5526,5527,5532,5533,5543,5544,5556,5560,5569,5570,5572,5587,5592,5603,5604,5616,5623,5637,5641,5644,5650,5651,5652,5655,5660,5697,5698,5701,5703,5706,5707,5708,5710,5712,5714,5719,5726,5741,5755,5760,5761,5774,5775,5780,5785,5787,5792,5833,5845,5854,5858,5869,5873,5874,5882,5896,5902,5920,5923,5935,5965,5979,6004,6024,6025,6028,6042,6044,6046,6048,6061,6062,6065,6067,6070,6071,6082,6088,6089,6090,6092,6094,6136,6137,6144,6154,6190,6192,6194,6196,6205,6207,6209,6215,6217,6223,6226,6234,6241,6242,6243,6248,6270,6271,6272,6274,6280,6285,6322,6323,6325,6326,6327,6329,6330,6331,6332,6341,6374,6375,6384,6405,6406,6426,6429,6440,6441,6447,6476,6478,6490,6528,6530,6531,6586,6610,6656,6676,6685,6686,6687,6688,6707,6708,6714,6726,6729,6731,6733,6734,6735,6737,6751,6762,6764,6765,6778,6781,6832,6843,6845,6849,6864,6865,6901,6913,6944,6963,6978,7032,7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% 187.89/187.73 cnf(12678,plain, % 187.89/187.73 (~P1(f306(f306(f221(a865),x126781),f2(a865)))), % 187.89/187.73 inference(rename_variables,[],[4493])). % 187.89/187.73 cnf(12679,plain, % 187.89/187.73 (P1(f306(f306(f220(a865),x126791),x126791))), % 187.89/187.73 inference(rename_variables,[],[3271])). % 187.89/187.73 cnf(12686,plain, % 187.89/187.73 (P1(f306(f306(f221(a865),x126861),f306(a119,x126861)))), % 187.89/187.73 inference(rename_variables,[],[3340])). % 187.89/187.73 cnf(12691,plain, % 187.89/187.73 (P1(f306(f306(f308(x126911),f306(x126912,x126913)),f306(f285(x126914,x126911,x126912),f231(f872(x126914,a859)))))), % 187.89/187.73 inference(rename_variables,[],[3864])). % 187.89/187.73 cnf(12692,plain, % 187.89/187.73 (~E(f306(a119,x126921),f2(a865))), % 187.89/187.73 inference(rename_variables,[],[4430])). % 187.89/187.73 cnf(12694,plain, % 187.89/187.73 (~P1(f306(f306(f221(a1),f2(a1)),f306(f111(a1),f2(a1))))), % 187.89/187.73 inference(scs_inference,[],[4527,3510,11037,12085,12190,12282,12320,12328,12393,12522,3517,12151,12560,12562,3518,12221,3237,12566,12568,3238,12589,3206,12469,4455,4456,11663,4201,12604,12607,3241,12580,3085,3143,12556,4438,3568,4420,10200,10210,10221,10330,10333,10336,10438,10551,10855,11022,11025,11223,11313,11320,11334,11384,11387,11409,11502,11548,11564,11864,11892,11904,11936,12034,12147,12154,12312,12363,12502,4435,10422,10515,3329,3290,12576,3479,3189,4430,2875,2876,2878,2879,2882,2883,2885,2886,2887,2889,2894,2898,2902,2911,2917,2923,2929,2936,2937,2938,2943,2948,2952,2956,2970,3004,3005,3018,3019,3021,3028,3029,3030,3031,3033,3044,3050,3162,4415,3064,3142,4416,3603,3117,11310,3251,3313,3224,3227,10203,10264,10267,10357,10360,10650,10929,11325,11328,11445,11489,11494,11593,12055,12258,12449,12504,12509,12511,12513,12530,12538,12542,12544,12595,3202,11590,12341,12345,12349,3212,3722,10969,11596,3107,3922,4432,3552,3812,11360,3328,12532,3170,3134,3639,12550,3129,3928,3644,3115,3095,3120,3149,3283,12026,12177,12396,12472,3330,10802,12148,3200,3201,3222,10463,3375,4513,10392,3895,4445,10255,10419,11220,11412,12308,12342,4454,12316,3260,11685,4503,10972,11042,11263,11266,3664,3376,3590,3343,12586,3165,10322,10626,3166,3433,3157,3086,3185,11350,4037,12331,12461,3897,10978,11104,11155,12292,12298,12410,12413,12436,4524,10907,11109,11214,11236,11271,11277,12237,4525,11011,11112,11217,4526,11115,4528,11169,4529,3184,3472,12193,12234,12315,3628,4316,4317,4443,11341,3570,3606,3777,3822,3458,3704,3340,10341,10458,10529,10590,10593,10629,10723,10962,11860,11926,12002,12046,12125,12128,12440,12627,3715,11581,4174,3253,3352,11700,3533,4493,10232,10235,10261,10731,10744,10865,11286,11353,11752,11757,11978,11981,12067,12076,12240,12335,12632,12651,12654,4509,11464,11497,11532,11561,3702,3480,3481,11881,12657,12660,12663,3847,3299,3300,3273,4490,3164,4440,3655,4171,3962,3464,4510,4031,11231,3589,3312,11709,11712,12158,12262,4001,3961,11853,12208,3907,10799,12014,12040,12215,3956,10981,12082,12157,12214,12261,3629,11863,12009,12092,12138,3990,3646,10984,11047,11128,11188,12033,12106,12358,12433,12446,4514,10747,11120,3270,10350,10445,10576,10636,11437,11657,11703,11737,11833,11891,12099,12265,3271,10705,10750,10753,10786,10812,10849,10887,10923,11907,11910,11913,11916,12113,12116,12119,12122,12201,12369,12416,3272,10433,10641,10726,10852,11740,11749,11839,11850,11869,11874,11919,11939,3348,12070,4489,10298,10387,10500,10524,10768,10815,10825,11511,11611,11632,11635,11638,11654,11807,11810,11813,11816,11903,11922,11925,11935,11990,11993,11996,11999,12077,12169,12172,12268,12271,12334,12362,12399,3428,10596,10860,10904,11177,11255,11425,12311,4505,10777,10789,10896,10914,10917,10975,11061,11069,11085,11123,11140,11149,11185,11226,11246,11249,11252,11280,11293,11296,11682,11718,11984,11987,12021,12071,12102,12246,12289,12295,12381,12384,12403,12460,12466,12475,3334,10623,10653,10662,11206,11764,12400,3371,3365,3781,3720,10301,11584,11614,4502,10252,10611,10614,11064,11082,11547,11602,11642,11770,11795,11798,11801,11804,12066,3292,10656,10809,10880,11615,11769,11961,12180,3742,11715,4081,3486,4500,3753,3788,4479,4482,4483,3244,3248,4481,4484,3249,4480,3760,3579,11577,4177,11444,4516,10226,10229,10481,10532,10535,10540,10949,11419,11669,11773,4522,11143,11260,11302,3967,12229,3864,11299,11641,11645,11706,12319,12327,12409,3709,10920,10926,10944,11888,12105,12377,3566,11146,12131,12243,12253,12324,12372,12380,4035,3711,10659,11000,11152,11182,11193,12037,12323,3536,10579,10582,10665,10836,3535,4519,11578,4515,12641,4520,10716,10818,11131,11283,11422,11450,12196,12205,12249,12430,4140,10792,12226,4042,3741,3689,3690,4517,10274,10277,10617,10620,11461,11646,4518,11558,3713,10585,3974,4521,4538,4564,4613,4615,4645,4662,4669,4670,4709,4739,4745,4830,4856,4857,4918,4919,4941,4942,4955,4959,4981,4988,5005,5008,5009,5010,5015,5016,5039,5066,5067,5077,5082,5090,5135,5136,5144,5154,5158,5160,5170,5172,5178,5182,5197,5204,5207,5208,5209,5213,5248,5261,5268,5270,5271,5275,5276,5277,5285,5288,5293,5294,5295,5302,5306,5307,5308,5317,5321,5322,5323,5328,5341,5350,5362,5364,5372,5373,5377,5381,5406,5412,5422,5423,5438,5451,5473,5479,5495,5496,5499,5518,5526,5527,5532,5533,5543,5544,5556,5560,5569,5570,5572,5587,5592,5603,5604,5616,5623,5637,5641,5644,5650,5651,5652,5655,5660,5697,5698,5701,5703,5706,5707,5708,5710,5712,5714,5719,5726,5741,5755,5760,5761,5774,5775,5780,5785,5787,5792,5833,5845,5854,5858,5869,5873,5874,5882,5896,5902,5920,5923,5935,5965,5979,6004,6024,6025,6028,6042,6044,6046,6048,6061,6062,6065,6067,6070,6071,6082,6088,6089,6090,6092,6094,6136,6137,6144,6154,6190,6192,6194,6196,6205,6207,6209,6215,6217,6223,6226,6234,6241,6242,6243,6248,6270,6271,6272,6274,6280,6285,6322,6323,6325,6326,6327,6329,6330,6331,6332,6341,6374,6375,6384,6405,6406,6426,6429,6440,6441,6447,6476,6478,6490,6528,6530,6531,6586,6610,6656,6676,6685,6686,6687,6688,6707,6708,6714,6726,6729,6731,6733,6734,6735,6737,6751,6762,6764,6765,6778,6781,6832,6843,6845,6849,6864,6865,6901,6913,6944,6963,6978,7032,7060,7115,7136,7145,7148,7203,7211,7269,7271,7285,7295,7296,7297,7316,7322,7324,7373,7383,7386,7402,7451,7453,7456,7499,7500,7518,7585,7604,7628,7650,7665,7680,7691,7699,7700,7728,7731,7733,7741,7779,7790,7815,7873,7907,7939,7986,8002,8008,8019,8020,8095,8149,8168,8192,8212,8236,8335,8337,8343,8361,8365,8379,8402,8413,8415,8430,8436,8440,8465,8479,8480,8496,8497,8502,8503,8504,8505,8506,8524,8525,8526,8535,8549,8551,8563,8567,8569,8570,8571,8579,8584,8611,8612,8641,8654,8658,8676,8698,8699,8700,8701,8714,8715,8737,8747,8756,8757,8758,8759,8761,8783,8784,8795,8840,8846,8852,8865,8870,8872,8875,8876,8880,8889,8972,9003,9004,9005,9020,9038,9043,9070,9071,9114,9117,9144,9189,9190,9191,9207,9233,9247,9253,9256,9279,9280,9308,9371,9407,9408,9409,9434,9435,9453,9471,9477,9493,9516,9538,9546,9547,9548,9549,9565,9567,9572,9603,9604,9610,9611,9654,9655,9686,9696,9706,9708,9709,9719,9733,9737,9765,9797,9802,9859,9902,9903,9905,9915,9916,9936,9941,9964,9969,9984,10036,10110,10111,10168,10184,2,8,9,4551,4552,4570,4601,4602,4604,4631,4637,4638,4649,4698,4700,4730,4744,4774,4871,4872,4886,4906,4962,4963,4966,4967,4969,4971,4972,4984,4985,4995,5006,5007,5013,5032,5033,5054,5059,5060,5061,5062,5065,5073,5076,5083,5084,5085,5150,5156,5157,5164,5194,5205,5211,5227,5247,5254,5255,5256,5265,5274,5281,5283,5284,5290,5298,5299,5309,5313,5314,5315,5316,5318,5319,5324,5325,5326,5327,5358,5359,5360,5368,5369,5370,5371,5414,5419,5421,5458,5460,5461,5463,5464,5466,5467,5469,5478,5483,5485,5486,5487,5488,5489,5490,5497,5507,5510,5521,5537,5538,5541,5550,5552,5553,5554,5579,5589,5606,5607,5617,5618,5620,5622,5627,5662,5666,5668,5728,5762,5763,5767,5773,5776,5777,5778,5779,5786,5797,5798,5800,5801,5809,5830,5861,5877,5880,5881,5883,5892,5910,5914,5917,5918,5919,5937,5950,5951,5981,5982,5986,6006,6009,6013,6032,6037,6038,6063,6066,6073,6081,6087,6091,6098,6099,6100,6101,6139,6155,6208,6244,6246,6267,6268,6273,6277,6278,6281,6288,6297,6314,6334,6335,6342,6352,6367,6387,6393,6395,6410,6411,6415,6417,6418,6419,6421,6423,6424,6425,6428,6433,6434,6436,6437,6443,6445,6486,6489,6503,6505,6506,6507,6543,6548,6550,6555,6556,6564,6568,6581,6605,6606,6608,6609,6621,6625,6627,6647,6650,6669,6702,6703,6704,6709,6722,6741,6743,6745,6747,6752,6758,6760,6775,6782,6818,6819,6820,6834,6835,6837,6838,6855,6857,6873,6899,6921,6932,6934,6936,6938,6939,6940,6975,6976,6981,6982,6990,6992,6993,6994,7013,7022,7023,7035,7045,7084,7094,7098,7105,7116,7117,7122,7124,7130,7138,7139,7152,7169,7187,7189,7206,7255,7256,7257,7259,7261,7265,7270,7292,7337,7369,7384,7389,7401,7434,7437,7460,7484,7501,7504,7505,7515,7534,7536,7538,7540,7541,7542,7567,7593,7594,7627,7629,7630,7631,7636,7657,7666,7677,7682,7688,7690,7696,7707,7708,7710,7730,7734,7739,7762,7828,7829,7876,7885,7886,7909,7910,7927,7928,7993,7994,8022,8051,8062,8064,8073,8085,8118,8124,8131,8144,8163,8169,8191,8234,8264,8276,8295,8298,8328,8352,8416,8417,8420,8422,8441,8528,8529,8530,8531,8558,8587,8615,8657,8675,8731,8776,8779,8792,8799,8837,8885,8886,8903,8904,9045,9049,9068,9078,9103,9105,9108,9112,9115,9116,9129,9130,9151,9157,9169,9218,9237,9257,9292,9293,9300,9363,9368,9404,9411,9414,9417,9418,9433,9449,9458,9470,9481,9482,9485,9487,9514,9636,9681,9682,9726,9772,9887,9888,9945,10013,10089,10102,10107,3,2601,2603,2604,2605,2606,2607,2614,2616,2617,2618,2619,2620,2621,2622,2623,2624,2625,2627,2628,2629,2630,2642,2646,2647,2650,2653,2658,2659,2661,2662,2663,2664,2665,2671,2672,2674,2676,2677,2678,2679,2680,2683,2686,2693,2694,2705,2707,2708,2709,2710,2728,2746,2747,2748,2767,2775,2776,2777,2781,2788,2790,2797,2800,2801,2802,2821,2824,2830,2848,2850,2851,5186,5246,5344,5430,5431,5432,5508,5605,5636,5669,5685,5687,5693,5756,5757,5758,5759,5765,5799,5932,5971,5980,6003,6040,6074,6078,6225])). % 187.89/187.73 cnf(12697,plain, % 187.89/187.73 (P1(f306(f306(f220(a1),x126971),x126971))), % 187.89/187.73 inference(rename_variables,[],[3272])). % 187.89/187.73 cnf(12700,plain, % 187.89/187.73 (P1(f306(f63(a865),f279(a865,x127001,x127002)))), % 187.89/187.73 inference(rename_variables,[],[3481])). % 187.89/187.73 cnf(12703,plain, % 187.89/187.73 (P1(f306(f63(a865),f279(a865,x127031,x127032)))), % 187.89/187.73 inference(rename_variables,[],[3481])). % 187.89/187.73 cnf(12706,plain, % 187.89/187.73 (P1(f306(f306(f220(a865),x127061),x127061))), % 187.89/187.73 inference(rename_variables,[],[3271])). % 187.89/187.73 cnf(12707,plain, % 187.89/187.73 (~E(f306(a119,x127071),f2(a865))), % 187.89/187.73 inference(rename_variables,[],[4430])). % 187.89/187.73 cnf(12724,plain, % 187.89/187.73 (P1(f306(f306(f220(a865),f46(a865,x127241,x127242)),x127241))), % 187.89/187.73 inference(rename_variables,[],[3720])). % 187.89/187.73 cnf(12729,plain, % 187.89/187.73 (P1(f306(f306(f221(a865),x127291),f306(a119,x127291)))), % 187.89/187.73 inference(rename_variables,[],[3340])). % 187.89/187.73 cnf(12732,plain, % 187.89/187.73 (P1(f306(f306(f221(a865),x127321),f306(a119,x127321)))), % 187.89/187.73 inference(rename_variables,[],[3340])). % 187.89/187.73 cnf(12733,plain, % 187.89/187.73 (~P1(f306(f306(f221(a865),x127331),f2(a865)))), % 187.89/187.73 inference(rename_variables,[],[4493])). % 187.89/187.73 cnf(12742,plain, % 187.89/187.73 (~P1(f306(f306(f221(a1),f306(f107(a1),x127421)),f2(a1)))), % 187.89/187.73 inference(rename_variables,[],[4509])). % 187.89/187.73 cnf(12743,plain, % 187.89/187.73 (P1(f306(f231(f872(x127431,a859)),x127432))), % 187.89/187.73 inference(rename_variables,[],[3334])). % 187.89/187.73 cnf(12746,plain, % 187.89/187.73 (~P1(f306(f306(f221(a1),f306(f107(a1),x127461)),f2(a1)))), % 187.89/187.73 inference(rename_variables,[],[4509])). % 187.89/187.73 cnf(12747,plain, % 187.89/187.73 (P1(f306(f231(f872(x127471,a859)),x127472))), % 187.89/187.73 inference(rename_variables,[],[3334])). % 187.89/187.73 cnf(12750,plain, % 187.89/187.73 (P1(f306(f231(f872(x127501,a859)),x127502))), % 187.89/187.73 inference(rename_variables,[],[3334])). % 187.89/187.73 cnf(12761,plain, % 187.89/187.73 (~P1(f306(f306(f308(x127611),x127612),f185(f872(x127611,a859))))), % 187.89/187.73 inference(rename_variables,[],[4505])). % 187.89/187.73 cnf(12762,plain, % 187.89/187.73 (P1(f306(f63(x127621),f185(f872(x127621,a859))))), % 187.89/187.73 inference(rename_variables,[],[3348])). % 187.89/187.73 cnf(12771,plain, % 187.89/187.73 (P1(f306(f306(f220(a865),f2(a865)),x127711))), % 187.89/187.73 inference(rename_variables,[],[3292])). % 187.89/187.73 cnf(12774,plain, % 187.89/187.73 (P1(f306(f306(f221(a865),x127741),f306(a119,x127741)))), % 187.89/187.73 inference(rename_variables,[],[3340])). % 187.89/187.73 cnf(12775,plain, % 187.89/187.73 (~E(f306(a119,x127751),x127751)), % 187.89/187.73 inference(rename_variables,[],[4420])). % 187.89/187.73 cnf(12778,plain, % 187.89/187.73 (~P1(f306(f306(f308(x127781),x127782),f185(f872(x127781,a859))))), % 187.89/187.73 inference(rename_variables,[],[4505])). % 187.89/187.73 cnf(12781,plain, % 187.89/187.73 (~P1(f306(f306(f308(x127811),x127812),f185(f872(x127811,a859))))), % 187.89/187.73 inference(rename_variables,[],[4505])). % 187.89/187.73 cnf(12784,plain, % 187.89/187.73 (P1(f306(f306(f220(a865),x127841),x127841))), % 187.89/187.73 inference(rename_variables,[],[3271])). % 187.89/187.73 cnf(12792,plain, % 187.89/187.73 (P1(f306(f306(f221(a865),x127921),f306(a119,x127921)))), % 187.89/187.73 inference(rename_variables,[],[3340])). % 187.89/187.73 cnf(12795,plain, % 187.89/187.73 (P1(f306(f306(f220(a865),x127951),x127951))), % 187.89/187.73 inference(rename_variables,[],[3271])). % 187.89/187.73 cnf(12800,plain, % 187.89/187.73 (P1(f306(f306(f220(a865),x128001),x128001))), % 187.89/187.73 inference(rename_variables,[],[3271])). % 187.89/187.73 cnf(12803,plain, % 187.89/187.73 (P1(f306(f306(f220(a865),x128031),x128031))), % 187.89/187.73 inference(rename_variables,[],[3271])). % 187.89/187.73 cnf(12806,plain, % 187.89/187.73 (P1(f306(f306(f220(a865),x128061),x128061))), % 187.89/187.73 inference(rename_variables,[],[3271])). % 187.89/187.73 cnf(12809,plain, % 187.89/187.73 (E(f306(f306(f22(f872(x128091,a859)),f185(f872(x128091,a859))),x128092),f185(f872(x128091,a859)))), % 187.89/187.73 inference(rename_variables,[],[3538])). % 187.89/187.73 cnf(12810,plain, % 187.89/187.73 (P1(f306(f63(x128101),f185(f872(x128101,a859))))), % 187.89/187.73 inference(rename_variables,[],[3348])). % 187.89/187.73 cnf(12813,plain, % 187.89/187.73 (E(f306(f306(f22(f872(x128131,a859)),f185(f872(x128131,a859))),x128132),f185(f872(x128131,a859)))), % 187.89/187.73 inference(rename_variables,[],[3538])). % 187.89/187.73 cnf(12814,plain, % 187.89/187.73 (P1(f306(f63(x128141),f185(f872(x128141,a859))))), % 187.89/187.73 inference(rename_variables,[],[3348])). % 187.89/187.73 cnf(12817,plain, % 187.89/187.73 (E(f306(f306(f22(f872(x128171,a859)),f185(f872(x128171,a859))),x128172),f185(f872(x128171,a859)))), % 187.89/187.73 inference(rename_variables,[],[3538])). % 187.89/187.73 cnf(12818,plain, % 187.89/187.73 (P1(f306(f63(x128181),f185(f872(x128181,a859))))), % 187.89/187.73 inference(rename_variables,[],[3348])). % 187.89/187.73 cnf(12821,plain, % 187.89/187.73 (E(f306(f306(f22(f872(x128211,a859)),f185(f872(x128211,a859))),x128212),f185(f872(x128211,a859)))), % 187.89/187.73 inference(rename_variables,[],[3538])). % 187.89/187.73 cnf(12822,plain, % 187.89/187.73 (P1(f306(f63(x128221),f185(f872(x128221,a859))))), % 187.89/187.73 inference(rename_variables,[],[3348])). % 187.89/187.73 cnf(12826,plain, % 187.89/187.73 (E(f306(f232(x128261,x128261),f233(x128261,x128262)),x128262)), % 187.89/187.73 inference(rename_variables,[],[3227])). % 187.89/187.73 cnf(12831,plain, % 187.89/187.73 (E(f306(f306(f22(f872(x128311,a859)),f185(f872(x128311,a859))),x128312),f185(f872(x128311,a859)))), % 187.89/187.73 inference(rename_variables,[],[3538])). % 187.89/187.73 cnf(12832,plain, % 187.89/187.73 (P1(f306(f63(x128321),f185(f872(x128321,a859))))), % 187.89/187.73 inference(rename_variables,[],[3348])). % 187.89/187.73 cnf(12836,plain, % 187.89/187.73 (P1(f306(f63(x128361),f185(f872(x128361,a859))))), % 187.89/187.73 inference(rename_variables,[],[3348])). % 187.89/187.73 cnf(12839,plain, % 187.89/187.73 (P1(f306(f306(f220(a865),x128391),x128391))), % 187.89/187.73 inference(rename_variables,[],[3271])). % 187.89/187.73 cnf(12843,plain, % 187.89/187.73 (P1(f306(f306(f220(a1),x128431),x128431))), % 187.89/187.73 inference(rename_variables,[],[3272])). % 187.89/187.73 cnf(12850,plain, % 187.89/187.73 (P1(f306(f306(f220(a865),x128501),x128501))), % 187.89/187.73 inference(rename_variables,[],[3271])). % 187.89/187.73 cnf(12863,plain, % 187.89/187.73 (P1(f306(f306(f220(a1),x128631),x128631))), % 187.89/187.73 inference(rename_variables,[],[3272])). % 187.89/187.73 cnf(12872,plain, % 187.89/187.73 (~P1(f306(f306(f308(x128721),x128722),f185(f872(x128721,a859))))), % 187.89/187.73 inference(rename_variables,[],[4505])). % 187.89/187.73 cnf(12883,plain, % 187.89/187.73 (P1(f306(f306(f308(x128831),x128832),f231(f872(x128831,a859))))), % 187.89/187.73 inference(rename_variables,[],[3428])). % 187.89/187.73 cnf(12887,plain, % 187.89/187.73 (P1(f306(f306(f220(f872(x128871,a859)),x128872),f231(f872(x128871,a859))))), % 187.89/187.73 inference(rename_variables,[],[3646])). % 187.89/187.73 cnf(12890,plain, % 187.89/187.73 (P1(f306(f306(f220(f872(x128901,a859)),f306(f164(x128901),f306(f128(x128901,x128902),x128903))),f306(f164(x128901),x128903)))), % 187.89/187.73 inference(rename_variables,[],[3907])). % 187.89/187.73 cnf(12896,plain, % 187.89/187.73 (~P1(f306(f306(f221(a865),x128961),f2(a865)))), % 187.89/187.73 inference(rename_variables,[],[4493])). % 187.89/187.73 cnf(12897,plain, % 187.89/187.73 (P1(f306(f306(f220(a1),x128971),x128971))), % 187.89/187.73 inference(rename_variables,[],[3272])). % 187.89/187.73 cnf(12901,plain, % 187.89/187.73 (~P1(f306(f306(f221(a865),x129011),f2(a865)))), % 187.89/187.73 inference(rename_variables,[],[4493])). % 187.89/187.73 cnf(12902,plain, % 187.89/187.73 (P1(f306(f306(f220(a1),x129021),x129021))), % 187.89/187.73 inference(rename_variables,[],[3272])). % 187.89/187.73 cnf(12911,plain, % 187.89/187.73 (P1(f306(f306(f220(a865),x129111),x129111))), % 187.89/187.73 inference(rename_variables,[],[3271])). % 187.89/187.73 cnf(12918,plain, % 187.89/187.73 (E(f306(f306(f16(x129181,x129182),x129183),x129184),x129183)), % 187.89/187.73 inference(rename_variables,[],[3260])). % 187.89/187.73 cnf(12921,plain, % 187.89/187.73 (P1(f306(f306(f220(f872(x129211,a859)),f306(f164(x129211),f162(x129211,x129212,x129213))),f306(f164(x129211),x129213)))), % 187.89/187.73 inference(rename_variables,[],[3956])). % 187.89/187.73 cnf(12923,plain, % 187.89/187.73 (P1(f306(f306(f220(a865),f495(f306(x129231,f2(a865)),x129231,f2(a865))),f2(a865)))), % 187.89/187.73 inference(scs_inference,[],[4527,3510,11037,12085,12190,12282,12320,12328,12393,12522,3517,12151,12560,12562,3518,12221,3237,12566,12568,3238,12589,3206,12469,4455,4456,11663,4201,12604,12607,3241,12580,3085,3143,12556,4438,3568,4420,10200,10210,10221,10330,10333,10336,10438,10551,10855,11022,11025,11223,11313,11320,11334,11384,11387,11409,11502,11548,11564,11864,11892,11904,11936,12034,12147,12154,12312,12363,12502,12621,4435,10422,10515,3329,3290,12576,3479,3189,4430,12692,2875,2876,2878,2879,2882,2883,2885,2886,2887,2889,2894,2898,2902,2911,2917,2923,2929,2930,2933,2936,2937,2938,2943,2948,2949,2952,2953,2956,2970,2978,2987,2990,3004,3005,3018,3019,3020,3021,3028,3029,3030,3031,3032,3033,3044,3050,3162,4415,3064,3142,4416,3603,3117,11310,3251,3313,3224,3227,10203,10264,10267,10357,10360,10650,10929,11325,11328,11445,11489,11494,11593,12055,12258,12449,12504,12509,12511,12513,12530,12538,12542,12544,12595,12615,3591,3838,3202,11590,12341,12345,12349,3212,3722,10969,11596,3107,3922,4432,3552,3812,11360,3328,12532,3170,3134,3639,12550,3129,3928,3644,3115,3095,3120,3149,3283,12026,12177,12396,12472,3330,10802,12148,3200,3201,3222,10463,3375,4513,10392,3895,4445,10255,10419,11220,11412,12308,12342,4454,12316,3260,11685,11688,4503,10972,11042,11263,11266,3664,3376,3590,3343,12586,3165,10322,10626,3166,3433,3157,3086,3185,11350,4037,12331,12461,3897,10978,11104,11155,12292,12298,12410,12413,12436,4524,10907,11109,11214,11236,11271,11277,12237,4525,11011,11112,11217,4526,11115,4528,11169,4529,3184,3472,12193,12234,12315,3628,4316,4317,4443,11341,3570,3606,3777,3538,12809,12813,12817,12821,12831,3822,12187,3458,3704,3340,10341,10458,10529,10590,10593,10629,10723,10962,11860,11926,12002,12046,12125,12128,12440,12627,12686,12729,12732,12774,12792,3715,11581,4174,3253,3352,11700,3533,4493,10232,10235,10261,10731,10744,10865,11286,11353,11752,11757,11978,11981,12067,12076,12240,12335,12632,12651,12654,12678,12733,12896,12901,4509,11464,11497,11532,11561,12742,12746,3702,3480,3481,11881,12657,12660,12663,12666,12700,3847,3299,3300,3273,4490,3164,4440,3655,4171,3962,3464,4510,4031,11231,3589,3312,11709,11712,12158,12262,12420,4001,3961,11853,12208,3907,10799,12014,12040,12215,12443,3956,10981,12082,12157,12214,12261,3629,11863,12009,12092,12138,3990,3646,10984,11047,11128,11188,12033,12106,12358,12433,12446,4514,10747,11120,3270,10350,10445,10576,10636,11437,11657,11703,11737,11833,11891,12099,12265,3271,10705,10750,10753,10786,10812,10849,10887,10923,11907,11910,11913,11916,12113,12116,12119,12122,12201,12369,12416,12679,12706,12784,12795,12800,12803,12806,12839,12850,12911,3272,10433,10641,10726,10852,11740,11749,11839,11850,11869,11874,11919,11939,11956,12697,12843,12863,12897,12902,3348,12070,12762,12810,12814,12818,12822,12832,12836,4489,10298,10387,10500,10524,10768,10815,10825,11511,11611,11632,11635,11638,11654,11807,11810,11813,11816,11903,11922,11925,11935,11990,11993,11996,11999,12077,12169,12172,12268,12271,12334,12362,12399,12484,3428,10596,10860,10904,11177,11255,11425,12311,12487,4505,10777,10789,10896,10914,10917,10975,11061,11069,11085,11123,11140,11149,11185,11226,11246,11249,11252,11280,11293,11296,11682,11718,11984,11987,12021,12071,12102,12246,12289,12295,12381,12384,12403,12460,12466,12475,12496,12761,12778,12781,3334,10623,10653,10662,11206,11764,12400,12417,12743,12747,12750,3371,3365,3781,3720,10301,11584,11614,12724,4502,10252,10611,10614,11064,11082,11547,11602,11642,11770,11795,11798,11801,11804,12066,3292,10656,10809,10880,11615,11769,11961,12180,12202,3742,11715,12673,4081,3486,4500,3753,3788,4479,4482,4483,3244,3248,4481,4484,3249,4480,3760,3579,11577,4177,11444,4516,10226,10229,10481,10532,10535,10540,10949,11419,11669,11773,4522,11143,11260,11302,3967,12229,3864,11299,11641,11645,11706,12319,12327,12409,3709,10920,10926,10944,11888,12105,12377,3566,11146,12131,12243,12253,12324,12372,12380,3601,4035,3711,10659,11000,11152,11182,11193,12037,12323,3536,10579,10582,10665,10836,3535,4519,11578,4515,12641,4520,10716,10818,11131,11283,11422,11450,12196,12205,12249,12430,4140,10792,12226,4042,3741,12499,3689,3690,4517,10274,10277,10617,10620,11461,11646,12439,4518,11558,11651,3713,10585,3974,4521,4538,4564,4613,4615,4645,4662,4669,4670,4709,4739,4745,4830,4856,4857,4918,4919,4941,4942,4955,4959,4981,4988,5005,5008,5009,5010,5015,5016,5039,5066,5067,5077,5082,5090,5135,5136,5144,5154,5158,5160,5170,5172,5178,5182,5197,5204,5207,5208,5209,5213,5248,5261,5268,5270,5271,5275,5276,5277,5285,5288,5293,5294,5295,5302,5306,5307,5308,5317,5321,5322,5323,5328,5341,5350,5362,5364,5372,5373,5377,5381,5406,5412,5422,5423,5438,5451,5473,5479,5495,5496,5499,5518,5526,5527,5532,5533,5543,5544,5556,5560,5569,5570,5572,5587,5592,5603,5604,5616,5623,5637,5641,5644,5650,5651,5652,5655,5660,5697,5698,5701,5703,5706,5707,5708,5710,5712,5714,5719,5726,5741,5755,5760,5761,5774,5775,5780,5785,5787,5792,5833,5845,5854,5858,5869,5873,5874,5882,5896,5902,5920,5923,5935,5965,5979,6004,6024,6025,6028,6042,6044,6046,6048,60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% 187.89/187.73 cnf(12925,plain, % 187.89/187.73 (~P1(f306(f306(f221(a865),x129251),f2(a865)))), % 187.89/187.73 inference(rename_variables,[],[4493])). % 187.89/187.73 cnf(12926,plain, % 187.89/187.73 (P1(f306(f306(f220(a1),x129261),x129261))), % 187.89/187.73 inference(rename_variables,[],[3272])). % 187.89/187.73 cnf(12930,plain, % 187.89/187.73 (~P1(f306(f306(f221(a865),x129301),f2(a865)))), % 187.89/187.73 inference(rename_variables,[],[4493])). % 187.89/187.73 cnf(12931,plain, % 187.89/187.73 (P1(f306(f306(f220(a1),x129311),x129311))), % 187.89/187.73 inference(rename_variables,[],[3272])). % 187.89/187.73 cnf(12935,plain, % 187.89/187.73 (~P1(f306(f306(f220(f872(a865,a859)),f277(a865,f306(a119,x129351),f306(a119,x129351))),f277(a865,x129352,x129351)))), % 187.89/187.73 inference(scs_inference,[],[4527,3510,11037,12085,12190,12282,12320,12328,12393,12522,3517,12151,12560,12562,3518,12221,3237,12566,12568,3238,12589,3206,12469,4455,4456,11663,4201,12604,12607,3241,12580,3085,3143,12556,4438,3568,4420,10200,10210,10221,10330,10333,10336,10438,10551,10855,11022,11025,11223,11313,11320,11334,11384,11387,11409,11502,11548,11564,11864,11892,11904,11936,12034,12147,12154,12312,12363,12502,12621,4435,10422,10515,3329,3290,12576,3479,3189,4430,12692,2875,2876,2878,2879,2882,2883,2885,2886,2887,2889,2894,2898,2902,2911,2917,2923,2929,2930,2933,2936,2937,2938,2943,2948,2949,2952,2953,2956,2970,2978,2987,2990,3004,3005,3018,3019,3020,3021,3028,3029,3030,3031,3032,3033,3044,3050,3162,4415,3064,3142,4416,3603,3117,11310,3251,3313,3224,3227,10203,10264,10267,10357,10360,10650,10929,11325,11328,11445,11489,11494,11593,12055,12258,12449,12504,12509,12511,12513,12530,12538,12542,12544,12595,12615,3591,3838,3202,11590,12341,12345,12349,3212,3722,10969,11596,3107,3922,4432,3552,3812,11360,3328,12532,3170,3134,3639,12550,3129,3928,3644,3115,3095,3120,3149,3283,12026,12177,12396,12472,3330,10802,12148,3200,3201,3222,10463,3375,4513,10392,3895,4445,10255,10419,11220,11412,12308,12342,4454,12316,3260,11685,11688,4503,10972,11042,11263,11266,3664,3376,3590,3343,12586,3165,10322,10626,3166,3433,3157,3086,3185,11350,4037,12331,12461,3897,10978,11104,11155,12292,12298,12410,12413,12436,4524,10907,11109,11214,11236,11271,11277,12237,4525,11011,11112,11217,4526,11115,4528,11169,4529,3184,3472,12193,12234,12315,3628,4316,4317,4443,11341,3570,3606,3777,3538,12809,12813,12817,12821,12831,3822,12187,3458,3704,3340,10341,10458,10529,10590,10593,10629,10723,10962,11860,11926,12002,12046,12125,12128,12440,12627,12686,12729,12732,12774,12792,3715,11581,4174,3253,3352,11700,3533,4493,10232,10235,10261,10731,10744,10865,11286,11353,11752,11757,11978,11981,12067,12076,12240,12335,12632,12651,12654,12678,12733,12896,12901,12925,4509,11464,11497,11532,11561,12742,12746,3702,3480,3481,11881,12657,12660,12663,12666,12700,3847,3299,3300,3273,4490,3164,4440,3655,4171,3962,3464,4510,4031,11231,3589,3312,11709,11712,12158,12262,12420,4001,3961,11853,12208,3907,10799,12014,12040,12215,12443,3956,10981,12082,12157,12214,12261,3629,11863,12009,12092,12138,3990,3646,10984,11047,11128,11188,12033,12106,12358,12433,12446,4514,10747,11120,3270,10350,10445,10576,10636,11437,11657,11703,11737,11833,11891,12099,12265,3271,10705,10750,10753,10786,10812,10849,10887,10923,11907,11910,11913,11916,12113,12116,12119,12122,12201,12369,12416,12679,12706,12784,12795,12800,12803,12806,12839,12850,12911,3272,10433,10641,10726,10852,11740,11749,11839,11850,11869,11874,11919,11939,11956,12697,12843,12863,12897,12902,12926,3348,12070,12762,12810,12814,12818,12822,12832,12836,4489,10298,10387,10500,10524,10768,10815,10825,11511,11611,11632,11635,11638,11654,11807,11810,11813,11816,11903,11922,11925,11935,11990,11993,11996,11999,12077,12169,12172,12268,12271,12334,12362,12399,12484,3428,10596,10860,10904,11177,11255,11425,12311,12487,4505,10777,10789,10896,10914,10917,10975,11061,11069,11085,11123,11140,11149,11185,11226,11246,11249,11252,11280,11293,11296,11682,11718,11984,11987,12021,12071,12102,12246,12289,12295,12381,12384,12403,12460,12466,12475,12496,12761,12778,12781,3334,10623,10653,10662,11206,11764,12400,12417,12743,12747,12750,3371,3365,3781,3720,10301,11584,11614,12724,4502,10252,10611,10614,11064,11082,11547,11602,11642,11770,11795,11798,11801,11804,12066,3292,10656,10809,10880,11615,11769,11961,12180,12202,3742,11715,12673,4081,3486,4500,3753,3788,4479,4482,4483,3244,3248,4481,4484,3249,4480,3760,3579,11577,4177,11444,4516,10226,10229,10481,10532,10535,10540,10949,11419,11669,11773,4522,11143,11260,11302,3967,12229,3864,11299,11641,11645,11706,12319,12327,12409,3709,10920,10926,10944,11888,12105,12377,3566,11146,12131,12243,12253,12324,12372,12380,3601,4035,3711,10659,11000,11152,11182,11193,12037,12323,3536,10579,10582,10665,10836,3535,4519,11578,4515,12641,4520,10716,10818,11131,11283,11422,11450,12196,12205,12249,12430,4140,10792,12226,4042,3741,12499,3689,3690,4517,10274,10277,10617,10620,11461,11646,12439,4518,11558,11651,3713,10585,3974,4521,4538,4564,4613,4615,4645,4662,4669,4670,4709,4739,4745,4830,4856,4857,4918,4919,4941,4942,4955,4959,4981,4988,5005,5008,5009,5010,5015,5016,5039,5066,5067,5077,5082,5090,5135,5136,5144,5154,5158,5160,5170,5172,5178,5182,5197,5204,5207,5208,5209,5213,5248,5261,5268,5270,5271,5275,5276,5277,5285,5288,5293,5294,5295,5302,5306,5307,5308,5317,5321,5322,5323,5328,5341,5350,5362,5364,5372,5373,5377,5381,5406,5412,5422,5423,5438,5451,5473,5479,5495,5496,5499,5518,5526,5527,5532,5533,5543,5544,5556,5560,5569,5570,5572,5587,5592,5603,5604,5616,5623,5637,5641,5644,5650,5651,5652,5655,5660,5697,5698,5701,5703,5706,5707,5708,5710,5712,5714,5719,5726,5741,5755,5760,5761,5774,5775,5780,5785,5787,5792,5833,5845,5854,5858,5869,5873,5874,5882,5896,5902,5920,5923,5935,5965,5979,6004,6024,6025,6028,6042,6044,6046,6048,6061,6062,6065,6067,6070,6071,6082,6088,6089,6090,6092,6094,6136,6137,6144,6154,6190,6192,6194,6196,6205,6207,6209,6215,6217,6223,6226,6234,6241,6242,6243,6248,6270,6271,6272,6274,6280,6285,6322,6323,6325,6326,6327,6329,6330,6331,6332,6341,6374,6375,6384,6405,6406,6426,6429,6440,6441,6447,6476,6478,6490,6528,6530,6531,6586,6610,6656,6676,6685,6686,6687,6688,6707,6708,6714,6726,6729,6731,6733,6734,6735,6737,6751,6762,6764,6765,6778,6781,6832,6843,6845,6849,6864,6865,6901,6913,6944,6963,6978,7032,7060,7115,7136,7145,7148,7203,7211,7269,7271,7285,7295,7296,7297,7316,7322,7324,7373,7383,7386,7402,7451,7453,7456,7499,7500,7518,7585,7604,7628,7650,7665,7680,7691,7699,7700,7728,7731,7733,7741,7779,7790,7815,7873,7907,7939,7986,8002,8008,8019,8020,8095,8149,8168,8192,8212,8236,8335,8337,8343,8361,8365,8379,8402,8413,8415,8430,8436,8440,8465,8479,8480,8496,8497,8502,8503,8504,8505,8506,8524,8525,8526,8535,8549,8551,8563,8567,8569,8570,8571,8579,8584,8611,8612,8641,8654,8658,8676,8698,8699,8700,8701,8714,8715,8737,8747,8756,8757,8758,8759,8761,8783,8784,8795,8840,8846,8852,8865,8870,8872,8875,8876,8880,8889,8972,9003,9004,9005,9020,9038,9043,9070,9071,9114,9117,9144,9189,9190,9191,9207,9233,9247,9253,9256,9279,9280,9308,9371,9407,9408,9409,9434,9435,9453,9471,9477,9493,9516,9538,9546,9547,9548,9549,9565,9567,9572,9603,9604,9610,9611,9654,9655,9686,9696,9706,9708,9709,9719,9733,9737,9765,9797,9802,9859,9902,9903,9905,9915,9916,9936,9941,9964,9969,9984,10036,10110,10111,10168,10184,2,8,9,4551,4552,4570,4601,4602,4604,4631,4637,4638,4649,4698,4700,4730,4744,4774,4871,4872,4886,4906,4962,4963,4966,4967,4969,4971,4972,4984,4985,4995,5006,5007,5013,5032,5033,5054,5059,5060,5061,5062,5065,5073,5076,5083,5084,5085,5150,5156,5157,5164,5194,5205,5211,5227,5247,5254,5255,5256,5265,5274,5281,5283,5284,5290,5298,5299,5309,5313,5314,5315,5316,5318,5319,5324,5325,5326,5327,5358,5359,5360,5368,5369,5370,5371,5414,5419,5421,5458,5460,5461,5463,5464,5466,5467,5469,5478,5483,5485,5486,5487,5488,5489,5490,5497,5507,5510,5521,5537,5538,5541,5550,5552,5553,5554,5579,5589,5606,5607,5617,5618,5620,5622,5627,5662,5666,5668,5728,5762,5763,5767,5773,5776,5777,5778,5779,5786,5797,5798,5800,5801,5809,5830,5861,5877,5880,5881,5883,5892,5910,5914,5917,5918,5919,5937,5950,5951,5981,5982,5986,6006,6009,6013,6032,6037,6038,6063,6066,6073,6081,6087,6091,6098,6099,6100,6101,6139,6155,6208,6244,6246,6267,6268,6273,6277,6278,6281,6288,6297,6314,6334,6335,6342,6352,6367,6387,6393,6395,6410,6411,6415,6417,6418,6419,6421,6423,6424,6425,6428,6433,6434,6436,6437,6443,6445,6486,6489,6503,6505,6506,6507,6543,6548,6550,6555,6556,6564,6568,6581,6605,6606,6608,6609,6621,6625,6627,6647,6650,6669,6702,6703,6704,6709,6722,6741,6743,6745,6747,6752,6758,6760,6775,6782,6818,6819,6820,6834,6835,6837,6838,6855,6857,6873,6899,6921,6932,6934,6936,6938,6939,6940,6975,6976,6981,6982,6990,6992,6993,6994,7013,7022,7023,7035,7045,7084,7094,7098,7105,7116,7117,7122,7124,7130,7138,7139,7152,7169,7187,7189,7206,7255,7256,7257,7259,7261,7265,7270,7292,7337,7369,7384,7389,7401,7434,7437,7460,7484,7501,7504,7505,7515,7534,7536,7538,7540,7541,7542,7567,7593,7594,7627,7629,7630,7631,7636,7657,7666,7677,7682,7688,7690,7696,7707,7708,7710,7730,7734,7739,7762,7828,7829,7876,7885,7886,7909,7910,7927,7928,7993,7994,8022,8051,8062,8064,8073,8085,8118,8124,8131,8144,8163,8169,8191,8234,8264,8276,8295,8298,8328,8352,8416,8417,8420,8422,8441,8528,8529,8530,8531,8558,8587,8615,8657,8675,8731,8776,8779,8792,8799,8837,8885,8886,8903,8904,9045,9049,9068,9078,9103,9105,9108,9112,9115,9116,9129,9130,9151,9157,9169,9218,9237,9257,9292,9293,9300,9363,9368,9404,9411,9414,9417,9418,9433,9449,9458,9470,9481,9482,9485,9487,9514,9636,9681,9682,9726,9772,9887,9888,9945,10013,10089,10102,10107,3,2601,2603,2604,2605,2606,2607,2614,2616,2617,2618,2619,2620,2621,2622,2623,2624,2625,2627,2628,2629,2630,2642,2646,2647,2650,2653,2658,2659,2661,2662,2663,2664,2665,2671,2672,2674,2676,2677,2678,2679,2680,2683,2686,2693,2694,2705,2707,2708,2709,2710,2728,2746,2747,2748,2767,2775,2776,2777,2781,2788,2790,2797,2800,2801,2802,2821,2824,2830,2848,2850,2851,5186,5246,5344,5430,5431,5432,5508,5605,5636,5669,5685,5687,5693,5756,5757,5758,5759,5765,5799,5932,5971,5980,6003,6040,6074,6078,6225,6230,6265,6266,6286,6290,6292,6299,6300,6301,6302,6303,6304,6305,6306,6389,6457,6458,6542,6575,6576,6618,6619,6759,6774,6846,6847,6851,6874,6897,6905,6907,6954,6979,6980,6998,6999,7034,7078,7079,7176,7237,7238,7239,7240,7254,7286,7342,7343,7352,7359,7360,7372,7404,7405,7406,7407,7549,7551,7552,7553,7559,7560,7770,7776,7777,7787,7826,7905,7947,8005,8027,8028,8043,8103,8205,8274,8275,8277,8313,8375,8376,8449,8472])). % 187.89/187.73 cnf(12936,plain, % 187.89/187.73 (P1(f306(f306(f220(a865),x129361),x129361))), % 187.89/187.73 inference(rename_variables,[],[3271])). % 187.89/187.73 cnf(12938,plain, % 187.89/187.73 (~P1(f306(f306(f221(f872(a865,a859)),f277(a865,f306(a119,x129381),f306(a119,x129381))),f277(a865,x129382,x129381)))), % 187.89/187.73 inference(scs_inference,[],[4527,3510,11037,12085,12190,12282,12320,12328,12393,12522,3517,12151,12560,12562,3518,12221,3237,12566,12568,3238,12589,3206,12469,4455,4456,11663,4201,12604,12607,3241,12580,3085,3143,12556,4438,3568,4420,10200,10210,10221,10330,10333,10336,10438,10551,10855,11022,11025,11223,11313,11320,11334,11384,11387,11409,11502,11548,11564,11864,11892,11904,11936,12034,12147,12154,12312,12363,12502,12621,4435,10422,10515,3329,3290,12576,3479,3189,4430,12692,2875,2876,2878,2879,2882,2883,2885,2886,2887,2889,2894,2898,2902,2911,2917,2923,2929,2930,2933,2936,2937,2938,2943,2948,2949,2952,2953,2956,2970,2978,2987,2990,3004,3005,3018,3019,3020,3021,3028,3029,3030,3031,3032,3033,3044,3050,3162,4415,3064,3142,4416,3603,3117,11310,3251,3313,3224,3227,10203,10264,10267,10357,10360,10650,10929,11325,11328,11445,11489,11494,11593,12055,12258,12449,12504,12509,12511,12513,12530,12538,12542,12544,12595,12615,3591,3838,3202,11590,12341,12345,12349,3212,3722,10969,11596,3107,3922,4432,3552,3812,11360,3328,12532,3170,3134,3639,12550,3129,3928,3644,3115,3095,3120,3149,3283,12026,12177,12396,12472,3330,10802,12148,3200,3201,3222,10463,3375,4513,10392,3895,4445,10255,10419,11220,11412,12308,12342,4454,12316,3260,11685,11688,4503,10972,11042,11263,11266,3664,3376,3590,3343,12586,3165,10322,10626,3166,3433,3157,3086,3185,11350,4037,12331,12461,3897,10978,11104,11155,12292,12298,12410,12413,12436,4524,10907,11109,11214,11236,11271,11277,12237,4525,11011,11112,11217,4526,11115,4528,11169,4529,3184,3472,12193,12234,12315,3628,4316,4317,4443,11341,3570,3606,3777,3538,12809,12813,12817,12821,12831,3822,12187,3458,3704,3340,10341,10458,10529,10590,10593,10629,10723,10962,11860,11926,12002,12046,12125,12128,12440,12627,12686,12729,12732,12774,12792,3715,11581,4174,3253,3352,11700,3533,4493,10232,10235,10261,10731,10744,10865,11286,11353,11752,11757,11978,11981,12067,12076,12240,12335,12632,12651,12654,12678,12733,12896,12901,12925,4509,11464,11497,11532,11561,12742,12746,3702,3480,3481,11881,12657,12660,12663,12666,12700,3847,3299,3300,3273,4490,3164,4440,3655,4171,3962,3464,4510,4031,11231,3589,3312,11709,11712,12158,12262,12420,4001,3961,11853,12208,3907,10799,12014,12040,12215,12443,3956,10981,12082,12157,12214,12261,3629,11863,12009,12092,12138,3990,3646,10984,11047,11128,11188,12033,12106,12358,12433,12446,4514,10747,11120,3270,10350,10445,10576,10636,11437,11657,11703,11737,11833,11891,12099,12265,3271,10705,10750,10753,10786,10812,10849,10887,10923,11907,11910,11913,11916,12113,12116,12119,12122,12201,12369,12416,12679,12706,12784,12795,12800,12803,12806,12839,12850,12911,12936,3272,10433,10641,10726,10852,11740,11749,11839,11850,11869,11874,11919,11939,11956,12697,12843,12863,12897,12902,12926,3348,12070,12762,12810,12814,12818,12822,12832,12836,4489,10298,10387,10500,10524,10768,10815,10825,11511,11611,11632,11635,11638,11654,11807,11810,11813,11816,11903,11922,11925,11935,11990,11993,11996,11999,12077,12169,12172,12268,12271,12334,12362,12399,12484,3428,10596,10860,10904,11177,11255,11425,12311,12487,4505,10777,10789,10896,10914,10917,10975,11061,11069,11085,11123,11140,11149,11185,11226,11246,11249,11252,11280,11293,11296,11682,11718,11984,11987,12021,12071,12102,12246,12289,12295,12381,12384,12403,12460,12466,12475,12496,12761,12778,12781,3334,10623,10653,10662,11206,11764,12400,12417,12743,12747,12750,3371,3365,3781,3720,10301,11584,11614,12724,4502,10252,10611,10614,11064,11082,11547,11602,11642,11770,11795,11798,11801,11804,12066,3292,10656,10809,10880,11615,11769,11961,12180,12202,3742,11715,12673,4081,3486,4500,3753,3788,4479,4482,4483,3244,3248,4481,4484,3249,4480,3760,3579,11577,4177,11444,4516,10226,10229,10481,10532,10535,10540,10949,11419,11669,11773,4522,11143,11260,11302,3967,12229,3864,11299,11641,11645,11706,12319,12327,12409,3709,10920,10926,10944,11888,12105,12377,3566,11146,12131,12243,12253,12324,12372,12380,3601,4035,3711,10659,11000,11152,11182,11193,12037,12323,3536,10579,10582,10665,10836,3535,4519,11578,4515,12641,4520,10716,10818,11131,11283,11422,11450,12196,12205,12249,12430,4140,10792,12226,4042,3741,12499,3689,3690,4517,10274,10277,10617,10620,11461,11646,12439,4518,11558,11651,3713,10585,3974,4521,4538,4564,4613,4615,4645,4662,4669,4670,4709,4739,4745,4830,4856,4857,4918,4919,4941,4942,4955,4959,4981,4988,5005,5008,5009,5010,5015,5016,5039,5066,5067,5077,5082,5090,5135,5136,5144,5154,5158,5160,5170,5172,5178,5182,5197,5204,5207,5208,5209,5213,5248,5261,5268,5270,5271,5275,5276,5277,5285,5288,5293,5294,5295,5302,5306,5307,5308,5317,5321,5322,5323,5328,5341,5350,5362,5364,5372,5373,5377,5381,5406,5412,5422,5423,5438,5451,5473,5479,5495,5496,5499,5518,5526,5527,5532,5533,5543,5544,5556,5560,5569,5570,5572,5587,5592,5603,5604,5616,5623,5637,5641,5644,5650,5651,5652,5655,5660,5697,5698,5701,5703,5706,5707,5708,5710,5712,5714,5719,5726,5741,5755,5760,5761,5774,5775,5780,5785,5787,5792,5833,5845,5854,5858,5869,5873,5874,5882,5896,5902,5920,5923,5935,5965,5979,6004,6024,6025,6028,6042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% 187.89/187.73 cnf(12939,plain, % 187.89/187.73 (P1(f306(f306(f220(a865),x129391),x129391))), % 187.89/187.73 inference(rename_variables,[],[3271])). % 187.89/187.73 cnf(12942,plain, % 187.89/187.73 (~P1(f306(f306(f220(a865),f306(a119,x129421)),x129421))), % 187.89/187.73 inference(rename_variables,[],[4502])). % 187.89/187.73 cnf(12947,plain, % 187.89/187.73 (E(x129471,f479(f306(f5(x129472),f306(f5(x129472),x129471)),f5(x129472),x129472,x129472))), % 187.89/187.73 inference(scs_inference,[],[4527,3510,11037,12085,12190,12282,12320,12328,12393,12522,12524,3517,12151,12560,12562,3518,12221,3237,12566,12568,3238,12589,3206,12469,4455,4456,11663,4201,12604,12607,3241,12580,3085,3143,12556,4438,3568,4420,10200,10210,10221,10330,10333,10336,10438,10551,10855,11022,11025,11223,11313,11320,11334,11384,11387,11409,11502,11548,11564,11864,11892,11904,11936,12034,12147,12154,12312,12363,12502,12621,4435,10422,10515,3329,3290,12576,3479,3189,4430,12692,2875,2876,2878,2879,2882,2883,2885,2886,2887,2889,2894,2898,2902,2911,2917,2923,2929,2930,2933,2936,2937,2938,2943,2948,2949,2952,2953,2956,2970,2978,2987,2990,3004,3005,3018,3019,3020,3021,3028,3029,3030,3031,3032,3033,3044,3050,3162,4415,3064,3142,4416,3603,3117,11310,3251,3313,3224,3227,10203,10264,10267,10357,10360,10650,10929,11325,11328,11445,11489,11494,11593,12055,12258,12449,12504,12509,12511,12513,12530,12538,12542,12544,12595,12615,3591,3838,3202,11590,12341,12345,12349,3212,3722,10969,11596,3106,3107,3922,4432,3552,3812,11360,3328,12532,3170,3134,3639,12550,3129,3928,3644,3115,3095,3120,3149,3283,12026,12177,12396,12472,3330,10802,12148,3200,3201,3222,10463,3375,4513,10392,3895,4445,10255,10419,11220,11412,12308,12342,4454,12316,3260,11685,11688,4503,10972,11042,11263,11266,3664,3376,3590,3343,12586,3165,10322,10626,3166,3433,3157,3086,3185,11350,4037,12331,12461,3897,10978,11104,11155,12292,12298,12410,12413,12436,4524,10907,11109,11214,11236,11271,11277,12237,4525,11011,11112,11217,4526,11115,4528,11169,4529,3184,3472,12193,12234,12315,3628,4316,4317,4443,11341,3570,3606,3777,3538,12809,12813,12817,12821,12831,3822,12187,3458,3704,3340,10341,10458,10529,10590,10593,10629,10723,10962,11860,11926,12002,12046,12125,12128,12440,12627,12686,12729,12732,12774,12792,3715,11581,4174,3253,3352,11700,3533,4493,10232,10235,10261,10731,10744,10865,11286,11353,11752,11757,11978,11981,12067,12076,12240,12335,12632,12651,12654,12678,12733,12896,12901,12925,4509,11464,11497,11532,11561,12742,12746,3702,3480,3481,11881,12657,12660,12663,12666,12700,3847,3299,3300,3273,4490,3164,4440,3655,4171,3962,3464,4510,4031,11231,3589,3312,11709,11712,12158,12262,12420,4001,3961,11853,12208,3907,10799,12014,12040,12215,12443,3956,10981,12082,12157,12214,12261,3629,11863,12009,12092,12138,3990,3646,10984,11047,11128,11188,12033,12106,12358,12433,12446,4514,10747,11120,3270,10350,10445,10576,10636,11437,11657,11703,11737,11833,11891,12099,12265,3271,10705,10750,10753,10786,10812,10849,10887,10923,11907,11910,11913,11916,12113,12116,12119,12122,12201,12369,12416,12679,12706,12784,12795,12800,12803,12806,12839,12850,12911,12936,12939,3272,10433,10641,10726,10852,11740,11749,11839,11850,11869,11874,11919,11939,11956,12697,12843,12863,12897,12902,12926,3348,12070,12762,12810,12814,12818,12822,12832,12836,4489,10298,10387,10500,10524,10768,10815,10825,11511,11611,11632,11635,11638,11654,11807,11810,11813,11816,11903,11922,11925,11935,11990,11993,11996,11999,12077,12169,12172,12268,12271,12334,12362,12399,12484,3428,10596,10860,10904,11177,11255,11425,12311,12487,4505,10777,10789,10896,10914,10917,10975,11061,11069,11085,11123,11140,11149,11185,11226,11246,11249,11252,11280,11293,11296,11682,11718,11984,11987,12021,12071,12102,12246,12289,12295,12381,12384,12403,12460,12466,12475,12496,12761,12778,12781,3334,10623,10653,10662,11206,11764,12400,12417,12743,12747,12750,3371,3365,3781,3720,10301,11584,11614,12724,4502,10252,10611,10614,11064,11082,11547,11602,11642,11770,11795,11798,11801,11804,12066,12942,3292,10656,10809,10880,11615,11769,11961,12180,12202,3742,11715,12673,4081,3486,4500,3753,3788,4479,4482,4483,3244,3248,4481,4484,3249,4480,3760,3579,11577,4177,11444,4516,10226,10229,10481,10532,10535,10540,10949,11419,11669,11773,4522,11143,11260,11302,3967,12229,3864,11299,11641,11645,11706,12319,12327,12409,12691,3709,10920,10926,10944,11888,12105,12377,3566,11146,12131,12243,12253,12324,12372,12380,3601,4035,3711,10659,11000,11152,11182,11193,12037,12323,3536,10579,10582,10665,10836,3535,4519,11578,4515,12641,4520,10716,10818,11131,11283,11422,11450,12196,12205,12249,12430,4140,10792,12226,4042,3741,12499,3689,3690,4517,10274,10277,10617,10620,11461,11646,12439,4518,11558,11651,3713,10585,3974,4521,4538,4564,4613,4615,4645,4662,4669,4670,4709,4739,4745,4830,4856,4857,4918,4919,4941,4942,4955,4959,4981,4988,5005,5008,5009,5010,5015,5016,5039,5066,5067,5077,5082,5090,5135,5136,5144,5154,5158,5160,5170,5172,5178,5182,5197,5204,5207,5208,5209,5213,5248,5261,5268,5270,5271,5275,5276,5277,5285,5288,5293,5294,5295,5302,5306,5307,5308,5317,5321,5322,5323,5328,5341,5350,5362,5364,5372,5373,5377,5381,5406,5412,5422,5423,5438,5451,5473,5479,5495,5496,5499,5518,5526,5527,5532,5533,5543,5544,5556,5560,5569,5570,5572,5587,5592,5603,5604,5616,5623,5637,5641,5644,5650,5651,5652,5655,5660,5697,5698,5701,5703,5706,5707,5708,5710,5712,5714,5719,5726,5741,5755,5760,5761,5774,5775,5780,5785,5787,5792,5833,5845,5854,5858,5869,5873,5874,5882,5896,5902,5920,5923,5935,5965,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% 187.89/187.73 cnf(12948,plain, % 187.89/187.73 (P1(f306(f306(f308(x129481),f306(x129482,x129483)),f306(f285(x129484,x129481,x129482),f231(f872(x129484,a859)))))), % 187.89/187.73 inference(rename_variables,[],[3864])). % 187.89/187.73 cnf(12949,plain, % 187.89/187.73 (P28(x129491,x129491,f5(x129491),x129492)), % 187.89/187.73 inference(rename_variables,[],[3510])). % 187.89/187.73 cnf(12953,plain, % 187.89/187.73 (P1(f306(f306(f308(x129531),x129532),f231(f872(x129531,a859))))), % 187.89/187.73 inference(rename_variables,[],[3428])). % 187.89/187.73 cnf(12954,plain, % 187.89/187.73 (~P1(f306(f306(f308(x129541),x129542),f185(f872(x129541,a859))))), % 187.89/187.73 inference(rename_variables,[],[4505])). % 187.89/187.73 cnf(12958,plain, % 187.89/187.73 (P1(f306(f306(f220(f872(x129581,a859)),x129582),f231(f872(x129581,a859))))), % 187.89/187.73 inference(rename_variables,[],[3646])). % 187.89/187.73 cnf(12959,plain, % 187.89/187.73 (P28(x129591,x129591,f5(x129591),x129592)), % 187.89/187.73 inference(rename_variables,[],[3510])). % 187.89/187.73 cnf(12963,plain, % 187.89/187.73 (P1(f306(f306(f220(f872(x129631,a859)),x129632),f231(f872(x129631,a859))))), % 187.89/187.73 inference(rename_variables,[],[3646])). % 187.89/187.73 cnf(12964,plain, % 187.89/187.73 (P28(x129641,x129641,f5(x129641),x129642)), % 187.89/187.73 inference(rename_variables,[],[3510])). % 187.89/187.73 cnf(12968,plain, % 187.89/187.73 (P28(x129681,x129681,f5(x129681),x129682)), % 187.89/187.73 inference(rename_variables,[],[3510])). % 187.89/187.73 cnf(12971,plain, % 187.89/187.73 (~P1(f306(f306(f221(f872(x129711,a859)),x129712),f185(f872(x129711,a859))))), % 187.89/187.73 inference(rename_variables,[],[4514])). % 187.89/187.73 cnf(12974,plain, % 187.89/187.73 (P28(x129741,x129741,f5(x129741),x129742)), % 187.89/187.73 inference(rename_variables,[],[3510])). % 187.89/187.73 cnf(12977,plain, % 187.89/187.73 (P28(x129771,x129771,f5(x129771),x129772)), % 187.89/187.73 inference(rename_variables,[],[3510])). % 187.89/187.73 cnf(12988,plain, % 187.89/187.73 (P1(f306(f306(f220(f872(x129881,a859)),f185(f872(x129881,a859))),x129882))), % 187.89/187.73 inference(rename_variables,[],[3711])). % 187.89/187.73 cnf(12992,plain, % 187.89/187.73 (E(f306(f232(x129921,x129921),f233(x129921,x129922)),x129922)), % 187.89/187.73 inference(rename_variables,[],[3227])). % 187.89/187.73 cnf(12996,plain, % 187.89/187.73 (~P1(f306(f306(f308(x129961),x129962),f185(f872(x129961,a859))))), % 187.89/187.73 inference(rename_variables,[],[4505])). % 187.89/187.73 cnf(13000,plain, % 187.89/187.73 (P1(f306(f306(f308(x130001),f306(x130002,x130003)),f306(f285(x130004,x130001,x130002),f231(f872(x130004,a859)))))), % 187.89/187.73 inference(rename_variables,[],[3864])). % 187.89/187.73 cnf(13001,plain, % 187.89/187.73 (P28(x130011,x130011,f5(x130011),x130012)), % 187.89/187.73 inference(rename_variables,[],[3510])). % 187.89/187.73 cnf(13011,plain, % 187.89/187.73 (~P1(f306(f306(f308(x130111),x130112),f185(f872(x130111,a859))))), % 187.89/187.73 inference(rename_variables,[],[4505])). % 187.89/187.73 cnf(13014,plain, % 187.89/187.73 (~P1(f306(f306(f308(x130141),x130142),f185(f872(x130141,a859))))), % 187.89/187.73 inference(rename_variables,[],[4505])). % 187.89/187.73 cnf(13022,plain, % 187.89/187.73 (E(f306(f306(f16(x130221,x130222),x130223),x130224),x130223)), % 187.89/187.73 inference(rename_variables,[],[3260])). % 187.89/187.73 cnf(13025,plain, % 187.89/187.73 (P1(f306(f306(f221(a865),x130251),f306(a119,x130251)))), % 187.89/187.73 inference(rename_variables,[],[3340])). % 187.89/187.73 cnf(13026,plain, % 187.89/187.73 (~E(f306(a119,x130261),x130261)), % 187.89/187.73 inference(rename_variables,[],[4420])). % 187.89/187.73 cnf(13029,plain, % 187.89/187.73 (P1(f306(f306(f221(a865),x130291),f306(a119,f306(f306(f81(a865),x130292),x130291))))), % 187.89/187.73 inference(rename_variables,[],[3713])). % 187.89/187.73 cnf(13030,plain, % 187.89/187.73 (P1(f306(f306(f221(a865),x130301),f306(a119,x130301)))), % 187.89/187.73 inference(rename_variables,[],[3340])). % 187.89/187.73 cnf(13032,plain, % 187.89/187.73 (~E(f306(f306(f82(a865),f306(a119,f2(a865))),f34(x130321,x130322)),f306(f306(f82(a865),f306(a119,f2(a865))),f33(x130323,x130324)))), % 187.89/187.73 inference(scs_inference,[],[4527,3510,11037,12085,12190,12282,12320,12328,12393,12522,12524,12949,12959,12964,12968,12974,12977,3517,12151,12560,12562,3518,12221,3237,12566,12568,3238,12589,3206,12469,4455,4456,11663,4201,12604,12607,3241,12580,3085,3143,12556,4438,3568,4420,10200,10210,10221,10330,10333,10336,10438,10551,10855,11022,11025,11223,11313,11320,11334,11384,11387,11409,11502,11548,11564,11864,11892,11904,11936,12034,12147,12154,12312,12363,12502,12621,12775,13026,4435,10422,10515,3329,3290,12576,3479,3189,4430,12692,2875,2876,2878,2879,2882,2883,2885,2886,2887,2889,2894,2898,2902,2911,2917,2923,2929,2930,2933,2936,2937,2938,2939,2943,2948,2949,2952,2953,2956,2970,2978,2987,2990,3004,3005,3018,3019,3020,3021,3028,3029,3030,3031,3032,3033,3044,3050,3162,4415,3064,3142,4416,3603,3117,11310,3251,3313,3224,3227,10203,10264,10267,10357,10360,10650,10929,11325,11328,11445,11489,11494,11593,12055,12258,12449,12504,12509,12511,12513,12530,12538,12542,12544,12595,12615,12826,3591,3838,3202,11590,12341,12345,12349,3212,3722,10969,11596,3106,3107,3922,4432,3552,3812,11360,3328,12532,3170,3134,3639,12550,3129,3928,3150,3644,3115,3095,3120,3149,3283,12026,12177,12396,12472,3330,10802,12148,3200,3201,3222,10463,3375,4513,10392,3895,4445,10255,10419,11220,11412,12308,12342,12346,4454,12316,3260,11685,11688,12918,4503,10972,11042,11263,11266,3664,3255,3376,3590,3343,12586,3165,10322,10626,3166,4487,3433,3157,3086,3185,11350,4037,12331,12461,3897,10978,11104,11155,12292,12298,12410,12413,12436,4524,10907,11109,11214,11236,11271,11277,12237,4525,11011,11112,11217,4526,11115,11166,4528,11169,4529,3184,3472,12193,12234,12315,3628,4316,4317,4443,11341,3570,3606,3777,3538,12809,12813,12817,12821,12831,3822,12187,3458,3704,3340,10341,10458,10529,10590,10593,10629,10723,10962,11860,11926,12002,12046,12125,12128,12440,12627,12686,12729,12732,12774,12792,13025,3715,11581,4174,3253,3352,11700,3533,4493,10232,10235,10261,10731,10744,10865,11286,11353,11752,11757,11978,11981,12067,12076,12240,12335,12632,12651,12654,12678,12733,12896,12901,12925,4509,11464,11497,11532,11561,12742,12746,3702,3480,3481,11881,12657,12660,12663,12666,12700,3847,3299,3300,3273,4490,3164,4440,3655,4171,3962,3464,4510,4031,11231,3589,3312,11709,11712,12158,12262,12420,4001,3961,11853,12208,3907,10799,12014,12040,12215,12443,3956,10981,12082,12157,12214,12261,3629,11863,12009,12092,12138,3990,3646,10984,11047,11128,11188,12033,12106,12358,12433,12446,12887,12958,12963,4514,10747,11120,12218,12971,3270,10350,10445,10576,10636,11437,11657,11703,11737,11833,11891,12099,12265,12480,3271,10705,10750,10753,10786,10812,10849,10887,10923,11907,11910,11913,11916,12113,12116,12119,12122,12201,12369,12416,12679,12706,12784,12795,12800,12803,12806,12839,12850,12911,12936,12939,3272,10433,10641,10726,10852,11740,11749,11839,11850,11869,11874,11919,11939,11956,12697,12843,12863,12897,12902,12926,3348,12070,12762,12810,12814,12818,12822,12832,12836,4489,10298,10387,10500,10524,10768,10815,10825,11511,11611,11632,11635,11638,11654,11807,11810,11813,11816,11903,11922,11925,11935,11990,11993,11996,11999,12077,12169,12172,12268,12271,12334,12362,12399,12484,3428,10596,10860,10904,11177,11255,11425,12311,12487,12883,12953,4505,10777,10789,10896,10914,10917,10975,11061,11069,11085,11123,11140,11149,11185,11226,11246,11249,11252,11280,11293,11296,11682,11718,11984,11987,12021,12071,12102,12246,12289,12295,12381,12384,12403,12460,12466,12475,12496,12761,12778,12781,12872,12954,12996,13011,3334,10623,10653,10662,11206,11764,12400,12417,12743,12747,12750,3371,3365,3781,3720,10301,11584,11614,12724,4502,10252,10611,10614,11064,11082,11547,11602,11642,11770,11795,11798,11801,11804,12066,12942,3292,10656,10809,10880,11615,11769,11961,12180,12202,3742,11715,12673,4081,3486,4500,3753,3788,4479,4482,4483,3244,3248,4481,4484,3249,4480,3760,3579,11577,11666,4177,11444,4516,10226,10229,10481,10532,10535,10540,10949,11419,11669,11773,4522,11143,11260,11302,3967,12229,3864,11299,11641,11645,11706,12319,12327,12409,12691,12948,13000,3709,10920,10926,10944,11888,12105,12377,12406,3566,11146,12131,12243,12253,12324,12372,12380,3601,4035,3711,10659,11000,11152,11182,11193,12037,12323,12366,3536,10579,10582,10665,10836,3535,4519,11578,4515,12641,4520,10716,10818,11131,11283,11422,11450,12196,12205,12249,12430,12490,4140,10792,12226,12252,4042,3741,12499,3689,3690,4517,10274,10277,10617,10620,11461,11646,12439,4518,11558,11651,3713,10585,10842,3974,4521,4538,4564,4613,4615,4645,4662,4669,4670,4709,4739,4745,4830,4856,4857,4918,4919,4941,4942,4955,4959,4981,4988,5005,5008,5009,5010,5015,5016,5039,5066,5067,5077,5082,5090,5135,5136,5144,5154,5158,5160,5170,5172,5178,5182,5197,5204,5207,5208,5209,5213,5248,5261,5268,5270,5271,5275,5276,5277,5285,5288,5293,5294,5295,5302,5306,5307,5308,5317,5321,5322,5323,5328,5341,5350,5362,5364,5372,5373,5377,5381,5406,5412,5422,5423,5438,5451,5473,5479,5495,5496,5499,5518,5526,5527,5532,5533,5543,5544,5556,5560,5569,5570,5572,5587,5592,5603,5604,5616,5623,56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9219,9262,9456,9720,9914,9972,9974,10113,5998,6372,6373,6460])). % 187.89/187.73 cnf(13039,plain, % 187.89/187.73 (P1(f306(f306(f220(a1),f2(a1)),f306(f107(a1),x130391)))), % 187.89/187.73 inference(rename_variables,[],[3371])). % 187.89/187.73 cnf(13044,plain, % 187.89/187.73 (P1(f306(f306(f220(a865),f2(a865)),x130441))), % 187.89/187.73 inference(rename_variables,[],[3292])). % 187.89/187.73 cnf(13048,plain, % 187.89/187.73 (~E(f306(a119,x130481),f2(a865))), % 187.89/187.73 inference(rename_variables,[],[4430])). % 187.89/187.73 cnf(13053,plain, % 187.89/187.73 (~P1(f306(f306(f308(x130531),x130532),f185(f872(x130531,a859))))), % 187.89/187.73 inference(rename_variables,[],[4505])). % 187.89/187.73 cnf(13056,plain, % 187.89/187.73 (P1(f306(f63(a865),f279(a865,x130561,x130562)))), % 187.89/187.73 inference(rename_variables,[],[3481])). % 187.89/187.73 cnf(13057,plain, % 187.89/187.73 (E(f306(f306(f225(a865),f306(a119,x130571)),f306(a119,x130572)),f306(a119,f306(f306(f225(a865),x130571),x130572)))), % 187.89/187.73 inference(rename_variables,[],[3444])). % 187.89/187.73 cnf(13060,plain, % 187.89/187.73 (P1(f306(f63(a865),f279(a865,x130601,x130602)))), % 187.89/187.73 inference(rename_variables,[],[3481])). % 187.89/187.73 cnf(13061,plain, % 187.89/187.73 (E(f306(f306(f219(a865),f306(a119,x130611)),f306(a119,x130612)),f306(a119,f306(f306(f219(a865),x130611),x130612)))), % 187.89/187.73 inference(rename_variables,[],[3445])). % 187.89/187.73 cnf(13064,plain, % 187.89/187.73 (P1(f306(f63(a865),f279(a865,x130641,x130642)))), % 187.89/187.73 inference(rename_variables,[],[3481])). % 187.89/187.73 cnf(13072,plain, % 187.89/187.73 (P1(f306(f306(f220(f872(x130721,a859)),f306(f164(x130721),f306(f128(x130721,x130722),x130723))),f306(f164(x130721),x130723)))), % 187.89/187.73 inference(rename_variables,[],[3907])). % 187.89/187.73 cnf(13073,plain, % 187.89/187.73 (E(f306(f306(f16(x130731,x130732),x130733),x130734),x130733)), % 187.89/187.73 inference(rename_variables,[],[3260])). % 187.89/187.73 cnf(13076,plain, % 187.89/187.73 (P1(f306(f306(f220(f872(x130761,a859)),f306(f164(x130761),f306(f306(f165(x130761),x130762),x130763))),f306(f164(x130761),x130763)))), % 187.94/187.73 inference(rename_variables,[],[3951])). % 187.94/187.73 cnf(13077,plain, % 187.94/187.73 (E(f306(f306(f16(x130771,x130772),x130773),x130774),x130773)), % 187.94/187.73 inference(rename_variables,[],[3260])). % 187.94/187.73 cnf(13081,plain, % 187.94/187.73 (E(f306(f306(f16(x130811,x130812),x130813),x130814),x130813)), % 187.94/187.73 inference(rename_variables,[],[3260])). % 187.94/187.73 cnf(13094,plain, % 187.94/187.73 (P1(f306(f306(f220(a1),f2(a1)),f306(f107(a1),x130941)))), % 187.94/187.73 inference(rename_variables,[],[3371])). % 187.94/187.73 cnf(13097,plain, % 187.94/187.73 (~P1(f306(f306(f308(x130971),x130972),f185(f872(x130971,a859))))), % 187.94/187.73 inference(rename_variables,[],[4505])). % 187.94/187.73 cnf(13100,plain, % 187.94/187.73 (~P1(f306(f306(f308(x131001),x131002),f185(f872(x131001,a859))))), % 187.94/187.73 inference(rename_variables,[],[4505])). % 187.94/187.73 cnf(13101,plain, % 187.94/187.73 (E(f306(f232(x131011,x131011),f233(x131011,x131012)),x131012)), % 187.94/187.73 inference(rename_variables,[],[3227])). % 187.94/187.73 cnf(13102,plain, % 187.94/187.73 (P28(x131021,x131021,f5(x131021),x131022)), % 187.94/187.73 inference(rename_variables,[],[3510])). % 187.94/187.73 cnf(13106,plain, % 187.94/187.73 (E(f306(f232(x131061,x131061),f233(x131061,x131062)),x131062)), % 187.94/187.73 inference(rename_variables,[],[3227])). % 187.94/187.73 cnf(13111,plain, % 187.94/187.73 (P1(f306(f306(f221(f872(a1,a859)),f277(a1,f79(a1),f2(a1))),f277(a1,f2(a1),f79(a1))))), % 187.94/187.73 inference(scs_inference,[],[4527,3510,11037,12085,12190,12282,12320,12328,12393,12522,12524,12949,12959,12964,12968,12974,12977,13001,13102,3517,12151,12560,12562,3518,12221,3237,12566,12568,3238,12589,3206,12469,4455,4456,11663,4201,12604,12607,3241,12580,3085,3143,12556,4438,3568,4420,10200,10210,10221,10330,10333,10336,10438,10551,10855,11022,11025,11223,11313,11320,11334,11384,11387,11409,11502,11548,11564,11864,11892,11904,11936,12034,12147,12154,12312,12363,12502,12621,12775,13026,4435,10422,10515,3329,3290,12576,3479,3189,4430,12692,12707,2875,2876,2878,2879,2882,2883,2885,2886,2887,2889,2894,2898,2902,2911,2917,2923,2929,2930,2933,2934,2936,2937,2938,2939,2943,2948,2949,2952,2953,2956,2964,2970,2978,2987,2990,3004,3005,3018,3019,3020,3021,3028,3029,3030,3031,3032,3033,3044,3050,3162,4415,3064,3142,4416,3603,3117,11310,3251,3313,3224,3227,10203,10264,10267,10357,10360,10650,10929,11325,11328,11445,11489,11494,11593,12055,12258,12449,12504,12509,12511,12513,12530,12538,12542,12544,12595,12615,12826,12992,13101,3591,3838,3202,11590,12341,12345,12349,3212,3722,10969,11596,3106,3107,3922,4432,3552,3812,11360,3328,12532,3170,3134,3639,12550,3129,3928,3150,3644,3115,3095,3120,3149,3283,12026,12177,12396,12472,3330,10802,12148,3200,3201,3222,10463,3375,4513,10392,3895,4445,10255,10419,11220,11412,12308,12342,12346,4454,12316,3260,11685,11688,12918,13022,13073,13077,13081,4503,10972,11042,11263,11266,3664,3255,3376,3590,3368,3343,12586,3165,10322,10626,3166,4487,3433,3157,3086,3185,11350,4037,12331,12461,3897,10978,11104,11155,12292,12298,12410,12413,12436,4524,10907,11109,11214,11236,11271,11277,12237,4525,11011,11112,11217,4526,11115,11166,4528,11169,4529,3184,3472,12193,12234,12315,3628,4316,4317,4443,11341,3570,3606,3777,3538,12809,12813,12817,12821,12831,3822,12187,3458,3704,3340,10341,10458,10529,10590,10593,10629,10723,10962,11860,11926,12002,12046,12125,12128,12440,12627,12686,12729,12732,12774,12792,13025,3715,11581,4174,3253,3352,11700,3533,4493,10232,10235,10261,10731,10744,10865,11286,11353,11752,11757,11978,11981,12067,12076,12240,12335,12632,12651,12654,12678,12733,12896,12901,12925,4509,11464,11497,11532,11561,12742,12746,3702,3480,3481,11881,12657,12660,12663,12666,12700,12703,13056,13060,13064,3847,3444,13057,3445,13061,3299,3300,3273,4490,3164,4440,3655,4171,3962,3464,4510,4031,11231,3589,3312,11709,11712,12158,12262,12420,4001,3961,11853,12208,3907,10799,12014,12040,12215,12443,12890,13072,3951,13076,3956,10981,12082,12157,12214,12261,12921,3629,11863,12009,12092,12138,3990,3646,10984,11047,11128,11188,12033,12106,12358,12433,12446,12887,12958,12963,4514,10747,11120,12218,12971,3270,10350,10445,10576,10636,11437,11657,11703,11737,11833,11891,12099,12265,12480,3271,10705,10750,10753,10786,10812,10849,10887,10923,11907,11910,11913,11916,12113,12116,12119,12122,12201,12369,12416,12679,12706,12784,12795,12800,12803,12806,12839,12850,12911,12936,12939,3272,10433,10641,10726,10852,11740,11749,11839,11850,11869,11874,11919,11939,11956,12697,12843,12863,12897,12902,12926,3348,12070,12762,12810,12814,12818,12822,12832,12836,4489,10298,10387,10500,10524,10768,10815,10825,11511,11611,11632,11635,11638,11654,11807,11810,11813,11816,11903,11922,11925,11935,11990,11993,11996,11999,12077,12169,12172,12268,12271,12334,12362,12399,12484,3428,10596,10860,10904,11177,11255,11425,12311,12487,12883,12953,4505,10777,10789,10896,10914,10917,10975,11061,11069,11085,11123,11140,11149,11185,11226,11246,11249,11252,11280,11293,11296,11682,11718,11984,11987,12021,12071,12102,12246,12289,12295,12381,12384,12403,12460,12466,12475,12496,12761,12778,12781,12872,12954,12996,13011,13014,13053,13097,13100,3334,10623,10653,10662,11206,11764,12400,12417,12743,12747,12750,3371,13039,3365,3781,3720,10301,11584,11614,12724,4502,10252,10611,10614,11064,11082,11547,11602,11642,11770,11795,11798,11801,11804,12066,12942,3292,10656,10809,10880,11615,11769,11961,12180,12202,12771,3742,11715,12673,4081,3486,4500,3753,3788,4479,4482,4483,3244,3248,4481,4484,3246,3249,4480,4254,3760,3579,11577,11666,4177,11444,4516,10226,10229,10481,10532,10535,10540,10949,11419,11669,11773,4522,11143,11260,11302,3967,12229,3864,11299,11641,11645,11706,12319,12327,12409,12691,12948,13000,3709,10920,10926,10944,11888,12105,12377,12406,3566,11146,12131,12243,12253,12324,12372,12380,12493,3601,4035,3711,10659,11000,11152,11182,11193,12037,12323,12366,12988,3536,10579,10582,10665,10836,3535,4519,11578,4515,12641,4520,10716,10818,11131,11283,11422,11450,12196,12205,12249,12430,12490,4140,10792,12226,12252,4042,3741,12499,3689,3690,4517,10274,10277,10617,10620,11461,11646,12439,4518,11558,11651,3713,10585,10842,3974,4521,4538,4564,4613,4615,4645,4662,4669,4670,4709,4739,4745,4830,4856,4857,4918,4919,4941,4942,4955,4959,4981,4988,5005,5008,5009,5010,5015,5016,5039,5066,5067,5077,5082,5090,5135,5136,5144,5154,5158,5160,5170,5172,5178,5182,5197,5204,5207,5208,5209,5213,5248,5261,5268,5270,5271,5275,5276,5277,5285,5288,5293,5294,5295,5302,5306,5307,5308,5317,5321,5322,5323,5328,5341,5350,5362,5364,5372,5373,5377,5381,5406,5412,5422,5423,5438,5451,5473,5479,5495,5496,5499,5518,5526,5527,5532,5533,5543,5544,5556,5560,5569,5570,5572,5587,5592,5603,5604,5616,5623,5637,5641,5644,5650,5651,5652,5655,5660,5697,5698,5701,5703,5706,5707,5708,5710,5712,5714,5719,5726,5741,5755,5760,5761,5774,5775,5780,5785,5787,5792,5833,5845,5854,5858,5869,5873,5874,5882,5896,5902,5920,5923,5935,5965,5979,6004,6024,6025,6028,6042,6044,6046,6048,6061,6062,6065,6067,6070,6071,6082,6088,6089,6090,6092,6094,6136,6137,6144,6154,6190,6192,6194,6196,6205,6207,6209,6215,6217,6223,6226,6234,6241,6242,6243,6248,6270,6271,6272,6274,6280,6285,6322,6323,6325,6326,6327,6329,6330,6331,6332,6341,6374,6375,6384,6405,6406,6426,6429,6440,6441,6447,6476,6478,6490,6528,6530,6531,6586,6610,6656,6676,6685,6686,6687,6688,6707,6708,6714,6726,6729,6731,6733,6734,6735,6737,6751,6762,6764,6765,6778,6781,6832,6843,6845,6849,6864,6865,6901,6913,6944,6963,6978,7032,7060,7115,7136,7145,7148,7203,7211,7269,7271,7285,7295,7296,7297,7316,7322,7324,7373,7383,7386,7402,7451,7453,7456,7499,7500,7518,7585,7604,7628,7650,7665,7680,7691,7699,7700,7728,7731,7733,7741,7779,7790,7815,7873,7907,7939,7986,8002,8008,8019,8020,8095,8149,8168,8192,8212,8236,8335,8337,8343,8361,8365,8379,8402,8413,8415,8430,8436,8440,8465,8479,8480,8496,8497,8502,8503,8504,8505,8506,8524,8525,8526,8535,8549,8551,8563,8567,8569,8570,8571,8579,8584,8611,8612,8641,8654,8658,8676,8698,8699,8700,8701,8714,8715,8737,8747,8756,8757,8758,8759,8761,8783,8784,8795,8840,8846,8852,8865,8870,8872,8875,8876,8880,8889,8972,9003,9004,9005,9020,9038,9043,9070,9071,9114,9117,9144,9189,9190,9191,9207,9233,9247,9253,9256,9279,9280,9308,9371,9407,9408,9409,9434,9435,9453,9471,9477,9493,9516,9538,9546,9547,9548,9549,9565,9567,9572,9603,9604,9610,9611,9654,9655,9686,9696,9706,9708,9709,9719,9733,9737,9765,9797,9802,9859,9902,9903,9905,9915,9916,9936,9941,9964,9969,9984,10036,10110,10111,10168,10184,2,8,9,4551,4552,4570,4601,4602,4604,4631,4637,4638,4649,4698,4700,4730,4744,4774,4871,4872,4886,4906,4962,4963,4966,4967,4969,4971,4972,4984,4985,4995,5006,5007,5013,5032,5033,5054,5059,5060,5061,5062,5065,5073,5076,5083,5084,5085,5150,5156,5157,5164,5194,5205,5211,5227,5247,5254,5255,5256,5265,5274,5281,5283,5284,5290,5298,5299,5309,5313,5314,5315,5316,5318,5319,5324,5325,5326,5327,5358,5359,5360,5368,5369,5370,5371,5414,5419,5421,5458,5460,5461,5463,5464,5466,5467,5469,5478,5483,5485,5486,5487,5488,5489,5490,5497,5507,5510,5521,5537,5538,5541,5550,5552,5553,5554,5579,5589,5606,5607,5617,5618,5620,5622,5627,5662,5666,5668,5728,5762,5763,5767,5773,5776,5777,5778,5779,5786,5797,5798,5800,5801,5809,5830,5861,5877,5880,5881,5883,5892,5910,5914,5917,5918,5919,5937,5950,5951,5981,5982,5986,6006,6009,6013,6032,6037,6038,6063,6066,6073,6081,6087,6091,6098,6099,6100,6101,6139,6155,6208,6244,6246,6267,6268,6273,6277,6278,6281,6288,6297,6314,6334,6335,6342,6352,6367,6387,6393,6395,6410,6411,6415,6417,6418,6419,6421,6423,6424,6425,6428,6433,6434,6436,6437,6443,6445,6486,6489,6503,6505,6506,6507,6543,6548,6550,6555,6556,6564,6568,6581,6605,6606,6608,6609,6621,6625,6627,6647,6650,6669,6702,6703,6704,6709,6722,6741,6743,6745,6747,6752,6758,6760,6775,6782,6818,6819,6820,6834,6835,6837,6838,6855,6857,6873,6899,6921,6932,6934,6936,6938,6939,6940,6975,6976,6981,6982,6990,6992,6993,6994,7013,7022,7023,7035,7045,7084,7094,7098,7105,7116,7117,7122,7124,7130,7138,7139,7152,7169,7187,7189,7206,7255,7256,7257,7259,7261,7265,7270,7292,7337,7369,7384,7389,7401,7434,7437,7460,7484,7501,7504,7505,7515,7534,7536,7538,7540,7541,7542,7567,7593,7594,7627,7629,7630,7631,7636,7657,7666,7677,7682,7688,7690,7696,7707,7708,7710,7730,7734,7739,7762,7828,7829,7876,7885,7886,7909,7910,7927,7928,7993,7994,8022,8051,8062,8064,8073,8085,8118,8124,8131,8144,8163,8169,8191,8234,8264,8276,8295,8298,8328,8352,8416,8417,8420,8422,8441,8528,8529,8530,8531,8558,8587,8615,8657,8675,8731,8776,8779,8792,8799,8837,8885,8886,8903,8904,9045,9049,9068,9078,9103,9105,9108,9112,9115,9116,9129,9130,9151,9157,9169,9218,9237,9257,9292,9293,9300,9363,9368,9404,9411,9414,9417,9418,9433,9449,9458,9470,9481,9482,9485,9487,9514,9636,9681,9682,9726,9772,9887,9888,9945,10013,10089,10102,10107,3,2601,2603,2604,2605,2606,2607,2614,2616,2617,2618,2619,2620,2621,2622,2623,2624,2625,2627,2628,2629,2630,2642,2646,2647,2650,2653,2658,2659,2661,2662,2663,2664,2665,2671,2672,2674,2676,2677,2678,2679,2680,2683,2686,2693,2694,2705,2707,2708,2709,2710,2728,2746,2747,2748,2767,2775,2776,2777,2781,2788,2790,2797,2800,2801,2802,2821,2824,2830,2848,2850,2851,5186,5246,5344,5430,5431,5432,5508,5605,5636,5669,5685,5687,5693,5756,5757,5758,5759,5765,5799,5932,5971,5980,6003,6040,6074,6078,6225,6230,6265,6266,6286,6290,6292,6299,6300,6301,6302,6303,6304,6305,6306,6389,6457,6458,6542,6575,6576,6618,6619,6759,6774,6846,6847,6851,6874,6897,6905,6907,6954,6979,6980,6998,6999,7034,7078,7079,7176,7237,7238,7239,7240,7254,7286,7342,7343,7352,7359,7360,7372,7404,7405,7406,7407,7549,7551,7552,7553,7559,7560,7770,7776,7777,7787,7826,7905,7947,8005,8027,8028,8043,8103,8205,8274,8275,8277,8313,8375,8376,8449,8472,8473,8474,8475,8619,8830,8854,8855,8936,8951,9006,9007,9124,9161,9184,9219,9262,9456,9720,9914,9972,9974,10113,5998,6372,6373,6460,6479,6480,6532,6896,7114,8544,8769,8960,8961,9034,9035,9310,9311,9312,9313,9517,9791,10098,10155,10156,6442,8368])). % 187.94/187.73 cnf(13113,plain, % 187.94/187.73 (P1(f306(f306(f221(f872(a1,a859)),f277(a1,f2(a1),f2(a1))),f277(a1,f306(f80(a1),f306(f107(a1),f306(a119,x131131))),f2(a1))))), % 187.94/187.73 inference(scs_inference,[],[4527,3510,11037,12085,12190,12282,12320,12328,12393,12522,12524,12949,12959,12964,12968,12974,12977,13001,13102,3517,12151,12560,12562,3518,12221,3237,12566,12568,3238,12589,3206,12469,4455,4456,11663,4201,12604,12607,3241,12580,3085,3143,12556,4438,3568,4420,10200,10210,10221,10330,10333,10336,10438,10551,10855,11022,11025,11223,11313,11320,11334,11384,11387,11409,11502,11548,11564,11864,11892,11904,11936,12034,12147,12154,12312,12363,12502,12621,12775,13026,4435,10422,10515,3329,3290,12576,3479,3189,4430,12692,12707,2875,2876,2878,2879,2882,2883,2885,2886,2887,2889,2894,2898,2902,2911,2917,2923,2929,2930,2933,2934,2936,2937,2938,2939,2943,2948,2949,2952,2953,2956,2964,2970,2978,2987,2990,3004,3005,3018,3019,3020,3021,3028,3029,3030,3031,3032,3033,3044,3050,3162,4415,3064,3142,4416,3603,3117,11310,3251,3313,3224,3227,10203,10264,10267,10357,10360,10650,10929,11325,11328,11445,11489,11494,11593,12055,12258,12449,12504,12509,12511,12513,12530,12538,12542,12544,12595,12615,12826,12992,13101,3591,3838,3202,11590,12341,12345,12349,3212,3722,10969,11596,3106,3107,3922,4432,3552,3812,11360,3328,12532,3170,3134,3639,12550,3129,3928,3150,3644,3115,3095,3120,3149,3283,12026,12177,12396,12472,3330,10802,12148,3200,3201,3222,10463,3375,4513,10392,3895,4445,10255,10419,11220,11412,12308,12342,12346,4454,12316,3260,11685,11688,12918,13022,13073,13077,13081,4503,10972,11042,11263,11266,3664,3255,3376,3590,3368,3343,12586,3165,10322,10626,3166,4487,3433,3157,3086,3185,11350,4037,12331,12461,3897,10978,11104,11155,12292,12298,12410,12413,12436,4524,10907,11109,11214,11236,11271,11277,12237,4525,11011,11112,11217,4526,11115,11166,4528,11169,4529,3184,3472,12193,12234,12315,3628,4316,4317,4443,11341,3570,3606,3777,3538,12809,12813,12817,12821,12831,3822,12187,3458,3704,3340,10341,10458,10529,10590,10593,10629,10723,10962,11860,11926,12002,12046,12125,12128,12440,12627,12686,12729,12732,12774,12792,13025,3715,11581,4174,3253,3352,11700,3533,4493,10232,10235,10261,10731,10744,10865,11286,11353,11752,11757,11978,11981,12067,12076,12240,12335,12632,12651,12654,12678,12733,12896,12901,12925,4509,11464,11497,11532,11561,12742,12746,3702,3480,3481,11881,12657,12660,12663,12666,12700,12703,13056,13060,13064,3847,3444,13057,3445,13061,3299,3300,3273,4490,3164,4440,3655,4171,3962,3464,4510,4031,11231,3589,3312,11709,11712,12158,12262,12420,4001,3961,11853,12208,3907,10799,12014,12040,12215,12443,12890,13072,3951,13076,3956,10981,12082,12157,12214,12261,12921,3629,11863,12009,12092,12138,3990,3646,10984,11047,11128,11188,12033,12106,12358,12433,12446,12887,12958,12963,4514,10747,11120,12218,12971,3270,10350,10445,10576,10636,11437,11657,11703,11737,11833,11891,12099,12265,12480,3271,10705,10750,10753,10786,10812,10849,10887,10923,11907,11910,11913,11916,12113,12116,12119,12122,12201,12369,12416,12679,12706,12784,12795,12800,12803,12806,12839,12850,12911,12936,12939,3272,10433,10641,10726,10852,11740,11749,11839,11850,11869,11874,11919,11939,11956,12697,12843,12863,12897,12902,12926,12931,3348,12070,12762,12810,12814,12818,12822,12832,12836,4489,10298,10387,10500,10524,10768,10815,10825,11511,11611,11632,11635,11638,11654,11807,11810,11813,11816,11903,11922,11925,11935,11990,11993,11996,11999,12077,12169,12172,12268,12271,12334,12362,12399,12484,3428,10596,10860,10904,11177,11255,11425,12311,12487,12883,12953,4505,10777,10789,10896,10914,10917,10975,11061,11069,11085,11123,11140,11149,11185,11226,11246,11249,11252,11280,11293,11296,11682,11718,11984,11987,12021,12071,12102,12246,12289,12295,12381,12384,12403,12460,12466,12475,12496,12761,12778,12781,12872,12954,12996,13011,13014,13053,13097,13100,3334,10623,10653,10662,11206,11764,12400,12417,12743,12747,12750,3371,13039,3365,3781,3720,10301,11584,11614,12724,4502,10252,10611,10614,11064,11082,11547,11602,11642,11770,11795,11798,11801,11804,12066,12942,3292,10656,10809,10880,11615,11769,11961,12180,12202,12771,3742,11715,12673,4081,3486,4500,3753,3788,4479,4482,4483,3244,3248,4481,4484,3246,3249,4480,4254,3760,3579,11577,11666,4177,11444,4516,10226,10229,10481,10532,10535,10540,10949,11419,11669,11773,4522,11143,11260,11302,3967,12229,3864,11299,11641,11645,11706,12319,12327,12409,12691,12948,13000,3709,10920,10926,10944,11888,12105,12377,12406,3566,11146,12131,12243,12253,12324,12372,12380,12493,3601,4035,3711,10659,11000,11152,11182,11193,12037,12323,12366,12988,3536,10579,10582,10665,10836,3535,4519,11578,4515,12641,4520,10716,10818,11131,11283,11422,11450,12196,12205,12249,12430,12490,4140,10792,12226,12252,4042,3741,12499,3689,3690,4517,10274,10277,10617,10620,11461,11646,12439,4518,11558,11651,3713,10585,10842,3974,4521,4538,4564,4613,4615,4645,4662,4669,4670,4709,4739,4745,4830,4856,4857,4918,4919,4941,4942,4955,4959,4981,4988,5005,5008,5009,5010,5015,5016,5039,5066,5067,5077,5082,5090,5135,5136,5144,5154,5158,5160,5170,5172,5178,5182,5197,5204,5207,5208,5209,5213,5248,5261,5268,5270,5271,5275,5276,5277,5285,5288,5293,5294,5295,5302,5306,5307,5308,5317,5321,5322,5323,5328,5341,5350,5362,5364,5372,5373,5377,5381,5406,5412,5422,5423,5438,5451,5473,5479,5495,5496,5499,5518,5526,5527,5532,5533,5543,5544,5556,5560,5569,5570,5572,5587,5592,5603,5604,5616,5623,5637,5641,5644,5650,5651,5652,5655,5660,5697,5698,5701,5703,5706,5707,5708,5710,5712,5714,5719,5726,5741,5755,5760,5761,5774,5775,5780,5785,5787,5792,5833,5845,5854,5858,5869,5873,5874,5882,5896,5902,5920,5923,5935,5965,5979,6004,6024,6025,6028,6042,6044,6046,6048,6061,6062,6065,6067,6070,6071,6082,6088,6089,6090,6092,6094,6136,6137,6144,6154,6190,6192,6194,6196,6205,6207,6209,6215,6217,6223,6226,6234,6241,6242,6243,6248,6270,6271,6272,6274,6280,6285,6322,6323,6325,6326,6327,6329,6330,6331,6332,6341,6374,6375,6384,6405,6406,6426,6429,6440,6441,6447,6476,6478,6490,6528,6530,6531,6586,6610,6656,6676,6685,6686,6687,6688,6707,6708,6714,6726,6729,6731,6733,6734,6735,6737,6751,6762,6764,6765,6778,6781,6832,6843,6845,6849,6864,6865,6901,6913,6944,6963,6978,7032,7060,7115,7136,7145,7148,7203,7211,7269,7271,7285,7295,7296,7297,7316,7322,7324,7373,7383,7386,7402,7451,7453,7456,7499,7500,7518,7585,7604,7628,7650,7665,7680,7691,7699,7700,7728,7731,7733,7741,7779,7790,7815,7873,7907,7939,7986,8002,8008,8019,8020,8095,8149,8168,8192,8212,8236,8335,8337,8343,8361,8365,8379,8402,8413,8415,8430,8436,8440,8465,8479,8480,8496,8497,8502,8503,8504,8505,8506,8524,8525,8526,8535,8549,8551,8563,8567,8569,8570,8571,8579,8584,8611,8612,8641,8654,8658,8676,8698,8699,8700,8701,8714,8715,8737,8747,8756,8757,8758,8759,8761,8783,8784,8795,8840,8846,8852,8865,8870,8872,8875,8876,8880,8889,8972,9003,9004,9005,9020,9038,9043,9070,9071,9114,9117,9144,9189,9190,9191,9207,9233,9247,9253,9256,9279,9280,9308,9371,9407,9408,9409,9434,9435,9453,9471,9477,9493,9516,9538,9546,9547,9548,9549,9565,9567,9572,9603,9604,9610,9611,9654,9655,9686,9696,9706,9708,9709,9719,9733,9737,9765,9797,9802,9859,9902,9903,9905,9915,9916,9936,9941,9964,9969,9984,10036,10110,10111,10168,10184,2,8,9,4551,4552,4570,4601,4602,4604,4631,4637,4638,4649,4698,4700,4730,4744,4774,4871,4872,4886,4906,4962,4963,4966,4967,4969,4971,4972,4984,4985,4995,5006,5007,5013,5032,5033,5054,5059,5060,5061,5062,5065,5073,5076,5083,5084,5085,5150,5156,5157,5164,5194,5205,5211,5227,5247,5254,5255,5256,5265,5274,5281,5283,5284,5290,5298,5299,5309,5313,5314,5315,5316,5318,5319,5324,5325,5326,5327,5358,5359,5360,5368,5369,5370,5371,5414,5419,5421,5458,5460,5461,5463,5464,5466,5467,5469,5478,5483,5485,5486,5487,5488,5489,5490,5497,5507,5510,5521,5537,5538,5541,5550,5552,5553,5554,5579,5589,5606,5607,5617,5618,5620,5622,5627,5662,5666,5668,5728,5762,5763,5767,5773,5776,5777,5778,5779,5786,5797,5798,5800,5801,5809,5830,5861,5877,5880,5881,5883,5892,5910,5914,5917,5918,5919,5937,5950,5951,5981,5982,5986,6006,6009,6013,6032,6037,6038,6063,6066,6073,6081,6087,6091,6098,6099,6100,6101,6139,6155,6208,6244,6246,6267,6268,6273,6277,6278,6281,6288,6297,6314,6334,6335,6342,6352,6367,6387,6393,6395,6410,6411,6415,6417,6418,6419,6421,6423,6424,6425,6428,6433,6434,6436,6437,6443,6445,6486,6489,6503,6505,6506,6507,6543,6548,6550,6555,6556,6564,6568,6581,6605,6606,6608,6609,6621,6625,6627,6647,6650,6669,6702,6703,6704,6709,6722,6741,6743,6745,6747,6752,6758,6760,6775,6782,6818,6819,6820,6834,6835,6837,6838,6855,6857,6873,6899,6921,6932,6934,6936,6938,6939,6940,6975,6976,6981,6982,6990,6992,6993,6994,7013,7022,7023,7035,7045,7084,7094,7098,7105,7116,7117,7122,7124,7130,7138,7139,7152,7169,7187,7189,7206,7255,7256,7257,7259,7261,7265,7270,7292,7337,7369,7384,7389,7401,7434,7437,7460,7484,7501,7504,7505,7515,7534,7536,7538,7540,7541,7542,7567,7593,7594,7627,7629,7630,7631,7636,7657,7666,7677,7682,7688,7690,7696,7707,7708,7710,7730,7734,7739,7762,7828,7829,7876,7885,7886,7909,7910,7927,7928,7993,7994,8022,8051,8062,8064,8073,8085,8118,8124,8131,8144,8163,8169,8191,8234,8264,8276,8295,8298,8328,8352,8416,8417,8420,8422,8441,8528,8529,8530,8531,8558,8587,8615,8657,8675,8731,8776,8779,8792,8799,8837,8885,8886,8903,8904,9045,9049,9068,9078,9103,9105,9108,9112,9115,9116,9129,9130,9151,9157,9169,9218,9237,9257,9292,9293,9300,9363,9368,9404,9411,9414,9417,9418,9433,9449,9458,9470,9481,9482,9485,9487,9514,9636,9681,9682,9726,9772,9887,9888,9945,10013,10089,10102,10107,3,2601,2603,2604,2605,2606,2607,2614,2616,2617,2618,2619,2620,2621,2622,2623,2624,2625,2627,2628,2629,2630,2642,2646,2647,2650,2653,2658,2659,2661,2662,2663,2664,2665,2671,2672,2674,2676,2677,2678,2679,2680,2683,2686,2693,2694,2705,2707,2708,2709,2710,2728,2746,2747,2748,2767,2775,2776,2777,2781,2788,2790,2797,2800,2801,2802,2821,2824,2830,2848,2850,2851,5186,5246,5344,5430,5431,5432,5508,5605,5636,5669,5685,5687,5693,5756,5757,5758,5759,5765,5799,5932,5971,5980,6003,6040,6074,6078,6225,6230,6265,6266,6286,6290,6292,6299,6300,6301,6302,6303,6304,6305,6306,6389,6457,6458,6542,6575,6576,6618,6619,6759,6774,6846,6847,6851,6874,6897,6905,6907,6954,6979,6980,6998,6999,7034,7078,7079,7176,7237,7238,7239,7240,7254,7286,7342,7343,7352,7359,7360,7372,7404,7405,7406,7407,7549,7551,7552,7553,7559,7560,7770,7776,7777,7787,7826,7905,7947,8005,8027,8028,8043,8103,8205,8274,8275,8277,8313,8375,8376,8449,8472,8473,8474,8475,8619,8830,8854,8855,8936,8951,9006,9007,9124,9161,9184,9219,9262,9456,9720,9914,9972,9974,10113,5998,6372,6373,6460,6479,6480,6532,6896,7114,8544,8769,8960,8961,9034,9035,9310,9311,9312,9313,9517,9791,10098,10155,10156,6442,8368,8369])). % 187.94/187.73 cnf(13120,plain, % 187.94/187.73 (P1(f306(f306(f220(a865),f2(a865)),x131201))), % 187.94/187.73 inference(rename_variables,[],[3292])). % 187.94/187.73 cnf(13121,plain, % 187.94/187.73 (P1(f306(f306(f221(a865),f2(a865)),f306(a119,x131211)))), % 187.94/187.73 inference(rename_variables,[],[3352])). % 187.94/187.73 cnf(13122,plain, % 187.94/187.73 (E(f306(f232(x131221,x131221),f233(x131221,x131222)),x131222)), % 187.94/187.73 inference(rename_variables,[],[3227])). % 187.94/187.73 cnf(13125,plain, % 187.94/187.73 (P1(f306(f49(f306(f232(x131251,x131251),f233(x131251,f306(f306(f81(a865),f306(f306(f82(a865),f306(f235(a865,a865),f306(f306(f236(a865,a865),f2(a865)),x131252))),f306(a119,f306(f306(f81(a865),x131253),f306(f244(a865,a865),f306(f306(f236(a865,a865),f2(a865)),x131252)))))),f306(f244(a865,a865),f306(f306(f236(a865,a865),f2(a865)),x131252))))),f306(a119,f306(f306(f81(a865),x131253),f306(f244(a865,a865),f306(f306(f236(a865,a865),f2(a865)),x131252))))),f306(f306(f236(a865,a865),f2(a865)),x131252)))), % 187.94/187.73 inference(scs_inference,[],[4527,3510,11037,12085,12190,12282,12320,12328,12393,12522,12524,12949,12959,12964,12968,12974,12977,13001,13102,3517,12151,12560,12562,3518,12221,3237,12566,12568,3238,12589,3206,12469,4455,4456,11663,4201,12604,12607,3241,12580,3085,3143,12556,4438,3568,4420,10200,10210,10221,10330,10333,10336,10438,10551,10855,11022,11025,11223,11313,11320,11334,11384,11387,11409,11502,11548,11564,11864,11892,11904,11936,12034,12147,12154,12312,12363,12502,12621,12775,13026,4435,10422,10515,3329,3290,12576,3479,3189,4430,12692,12707,13048,2875,2876,2878,2879,2882,2883,2885,2886,2887,2889,2894,2898,2902,2911,2917,2923,2929,2930,2933,2934,2936,2937,2938,2939,2943,2948,2949,2952,2953,2956,2964,2970,2978,2987,2990,3004,3005,3018,3019,3020,3021,3028,3029,3030,3031,3032,3033,3044,3050,3162,4415,3064,3142,4416,3603,3117,11310,3251,3313,3224,3227,10203,10264,10267,10357,10360,10650,10929,11325,11328,11445,11489,11494,11593,12055,12258,12449,12504,12509,12511,12513,12530,12538,12542,12544,12595,12615,12826,12992,13101,13106,13122,3591,3838,3202,11590,12341,12345,12349,3212,3722,10969,11596,3106,3107,3922,4432,3552,3812,11360,3328,12532,3170,3134,3639,12550,3129,3928,3150,3644,3115,3095,3120,3149,3283,12026,12177,12396,12472,3330,10802,12148,3200,3201,3222,10463,3375,4513,10392,3895,4445,10255,10419,11220,11412,12308,12342,12346,4454,12316,3260,11685,11688,12918,13022,13073,13077,13081,4503,10972,11042,11263,11266,3664,3255,3376,3590,3368,3343,12586,3165,10322,10626,3166,4487,3433,3157,3086,3185,11350,4037,12331,12461,3897,10978,11104,11155,12292,12298,12410,12413,12436,4524,10907,11109,11214,11236,11271,11277,12237,4525,11011,11112,11217,4526,11115,11166,4528,11169,4529,3184,3472,12193,12234,12315,3628,4316,4317,3455,4443,11341,3570,3606,3777,3538,12809,12813,12817,12821,12831,3822,12187,3458,3704,3340,10341,10458,10529,10590,10593,10629,10723,10962,11860,11926,12002,12046,12125,12128,12440,12627,12686,12729,12732,12774,12792,13025,13030,3715,11581,4174,3253,3352,11700,12620,13121,3533,4493,10232,10235,10261,10731,10744,10865,11286,11353,11752,11757,11978,11981,12067,12076,12240,12335,12632,12651,12654,12678,12733,12896,12901,12925,4509,11464,11497,11532,11561,12742,12746,3702,3480,3481,11881,12657,12660,12663,12666,12700,12703,13056,13060,13064,3847,3444,13057,3445,13061,3299,3300,3273,4490,3164,4440,3655,4171,3962,3464,4510,4031,11231,3589,3312,11709,11712,12158,12262,12420,4001,3961,11853,12208,3907,10799,12014,12040,12215,12443,12890,13072,3951,13076,3956,10981,12082,12157,12214,12261,12921,3629,11863,12009,12092,12138,3990,3646,10984,11047,11128,11188,12033,12106,12358,12433,12446,12887,12958,12963,4514,10747,11120,12218,12971,3270,10350,10445,10576,10636,11437,11657,11703,11737,11833,11891,12099,12265,12480,3271,10705,10750,10753,10786,10812,10849,10887,10923,11907,11910,11913,11916,12113,12116,12119,12122,12201,12369,12416,12679,12706,12784,12795,12800,12803,12806,12839,12850,12911,12936,12939,3272,10433,10641,10726,10852,11740,11749,11839,11850,11869,11874,11919,11939,11956,12697,12843,12863,12897,12902,12926,12931,3348,12070,12762,12810,12814,12818,12822,12832,12836,4489,10298,10387,10500,10524,10768,10815,10825,11511,11611,11632,11635,11638,11654,11807,11810,11813,11816,11903,11922,11925,11935,11990,11993,11996,11999,12077,12169,12172,12268,12271,12334,12362,12399,12484,3428,10596,10860,10904,11177,11255,11425,12311,12487,12883,12953,4505,10777,10789,10896,10914,10917,10975,11061,11069,11085,11123,11140,11149,11185,11226,11246,11249,11252,11280,11293,11296,11682,11718,11984,11987,12021,12071,12102,12246,12289,12295,12381,12384,12403,12460,12466,12475,12496,12761,12778,12781,12872,12954,12996,13011,13014,13053,13097,13100,3334,10623,10653,10662,11206,11764,12400,12417,12743,12747,12750,3371,13039,3365,3781,3720,10301,11584,11614,12724,4502,10252,10611,10614,11064,11082,11547,11602,11642,11770,11795,11798,11801,11804,12066,12942,3292,10656,10809,10880,11615,11769,11961,12180,12202,12771,13044,13120,3742,11715,12673,4081,3486,4500,3753,3788,4479,4482,4483,3244,3248,4481,4484,3246,3249,4480,4254,3760,3579,11577,11666,4177,11444,4516,10226,10229,10481,10532,10535,10540,10949,11419,11669,11773,4522,11143,11260,11302,3967,12229,3864,11299,11641,11645,11706,12319,12327,12409,12691,12948,13000,3709,10920,10926,10944,11888,12105,12377,12406,3566,11146,12131,12243,12253,12324,12372,12380,12493,3601,4035,3711,10659,11000,11152,11182,11193,12037,12323,12366,12988,3536,10579,10582,10665,10836,3535,4519,11578,4515,12641,4520,10716,10818,11131,11283,11422,11450,12196,12205,12249,12430,12490,4140,10792,12226,12252,4042,3741,12499,3689,3690,4517,10274,10277,10617,10620,11461,11646,12439,4518,11558,11651,3713,10585,10842,13029,3974,4521,4538,4564,4613,4615,4645,4662,4669,4670,4709,4739,4745,4830,4856,4857,4918,4919,4941,4942,4955,4959,4981,4988,5005,5008,5009,5010,5015,5016,5039,5066,5067,5077,5082,5090,5135,5136,5144,5154,5158,5160,5170,5172,5178,5182,5197,5204,5207,5208,5209,5213,5248,5261,5268,5270,5271,5275,5276,5277,5285,5288,5293,5294,5295,5302,5306,5307,5308,5317,5321,5322,5323,5328,5341,5350,5362,5364,5372,5373,5377,5381,5406,5412,5422,5423,5438,5451,5473,5479,5495,5496,5499,5518,5526,5527,5532,5533,5543,5544,5556,5560,5569,5570,5572,5587,5592,5603,5604,5616,5623,5637,5641,5644,5650,5651,5652,5655,5660,5697,5698,5701,5703,5706,5707,5708,5710,5712,5714,5719,5726,5741,5755,5760,5761,5774,5775,5780,5785,5787,5792,5833,5845,5854,5858,5869,5873,5874,5882,5896,5902,5920,5923,5935,5965,5979,6004,6024,6025,6028,6042,6044,6046,6048,6061,6062,6065,6067,6070,6071,6082,6088,6089,6090,6092,6094,6136,6137,6144,6154,6190,6192,6194,6196,6205,6207,6209,6215,6217,6223,6226,6234,6241,6242,6243,6248,6270,6271,6272,6274,6280,6285,6322,6323,6325,6326,6327,6329,6330,6331,6332,6341,6374,6375,6384,6405,6406,6426,6429,6440,6441,6447,6476,6478,6490,6528,6530,6531,6586,6610,6656,6676,6685,6686,6687,6688,6707,6708,6714,6726,6729,6731,6733,6734,6735,6737,6751,6762,6764,6765,6778,6781,6832,6843,6845,6849,6864,6865,6901,6913,6944,6963,6978,7032,7060,7115,7136,7145,7148,7203,7211,7269,7271,7285,7295,7296,7297,7316,7322,7324,7373,7383,7386,7402,7451,7453,7456,7499,7500,7518,7585,7604,7628,7650,7665,7680,7691,7699,7700,7728,7731,7733,7741,7779,7790,7815,7873,7907,7939,7986,8002,8008,8019,8020,8095,8149,8168,8192,8212,8236,8335,8337,8343,8361,8365,8379,8402,8413,8415,8430,8436,8440,8465,8479,8480,8496,8497,8502,8503,8504,8505,8506,8524,8525,8526,8535,8549,8551,8563,8567,8569,8570,8571,8579,8584,8611,8612,8641,8654,8658,8676,8698,8699,8700,8701,8714,8715,8737,8747,8756,8757,8758,8759,8761,8783,8784,8795,8840,8846,8852,8865,8870,8872,8875,8876,8880,8889,8972,9003,9004,9005,9020,9038,9043,9070,9071,9114,9117,9144,9189,9190,9191,9207,9233,9247,9253,9256,9279,9280,9308,9371,9407,9408,9409,9434,9435,9453,9471,9477,9493,9516,9538,9546,9547,9548,9549,9565,9567,9572,9603,9604,9610,9611,9654,9655,9686,9696,9706,9708,9709,9719,9733,9737,9765,9797,9802,9859,9902,9903,9905,9915,9916,9936,9941,9964,9969,9984,10036,10110,10111,10168,10184,2,8,9,4551,4552,4570,4601,4602,4604,4631,4637,4638,4649,4698,4700,4730,4744,4774,4871,4872,4886,4906,4962,4963,4966,4967,4969,4971,4972,4984,4985,4995,5006,5007,5013,5032,5033,5054,5059,5060,5061,5062,5065,5073,5076,5083,5084,5085,5150,5156,5157,5164,5194,5205,5211,5227,5247,5254,5255,5256,5265,5274,5281,5283,5284,5290,5298,5299,5309,5313,5314,5315,5316,5318,5319,5324,5325,5326,5327,5358,5359,5360,5368,5369,5370,5371,5414,5419,5421,5458,5460,5461,5463,5464,5466,5467,5469,5478,5483,5485,5486,5487,5488,5489,5490,5497,5507,5510,5521,5537,5538,5541,5550,5552,5553,5554,5579,5589,5606,5607,5617,5618,5620,5622,5627,5662,5666,5668,5728,5762,5763,5767,5773,5776,5777,5778,5779,5786,5797,5798,5800,5801,5809,5830,5861,5877,5880,5881,5883,5892,5910,5914,5917,5918,5919,5937,5950,5951,5981,5982,5986,6006,6009,6013,6032,6037,6038,6063,6066,6073,6081,6087,6091,6098,6099,6100,6101,6139,6155,6208,6244,6246,6267,6268,6273,6277,6278,6281,6288,6297,6314,6334,6335,6342,6352,6367,6387,6393,6395,6410,6411,6415,6417,6418,6419,6421,6423,6424,6425,6428,6433,6434,6436,6437,6443,6445,6486,6489,6503,6505,6506,6507,6543,6548,6550,6555,6556,6564,6568,6581,6605,6606,6608,6609,6621,6625,6627,6647,6650,6669,6702,6703,6704,6709,6722,6741,6743,6745,6747,6752,6758,6760,6775,6782,6818,6819,6820,6834,6835,6837,6838,6855,6857,6873,6899,6921,6932,6934,6936,6938,6939,6940,6975,6976,6981,6982,6990,6992,6993,6994,7013,7022,7023,7035,7045,7084,7094,7098,7105,7116,7117,7122,7124,7130,7138,7139,7152,7169,7187,7189,7206,7255,7256,7257,7259,7261,7265,7270,7292,7337,7369,7384,7389,7401,7434,7437,7460,7484,7501,7504,7505,7515,7534,7536,7538,7540,7541,7542,7567,7593,7594,7627,7629,7630,7631,7636,7657,7666,7677,7682,7688,7690,7696,7707,7708,7710,7730,7734,7739,7762,7828,7829,7876,7885,7886,7909,7910,7927,7928,7993,7994,8022,8051,8062,8064,8073,8085,8118,8124,8131,8144,8163,8169,8191,8234,8264,8276,8295,8298,8328,8352,8416,8417,8420,8422,8441,8528,8529,8530,8531,8558,8587,8615,8657,8675,8731,8776,8779,8792,8799,8837,8885,8886,8903,8904,9045,9049,9068,9078,9103,9105,9108,9112,9115,9116,9129,9130,9151,9157,9169,9218,9237,9257,9292,9293,9300,9363,9368,9404,9411,9414,9417,9418,9433,9449,9458,9470,9481,9482,9485,9487,9514,9636,9681,9682,9726,9772,9887,9888,9945,10013,10089,10102,10107,3,2601,2603,2604,2605,2606,2607,2614,2616,2617,2618,2619,2620,2621,2622,2623,2624,2625,2627,2628,2629,2630,2642,2646,2647,2650,2653,2658,2659,2661,2662,2663,2664,2665,2671,2672,2674,2676,2677,2678,2679,2680,2683,2686,2693,2694,2705,2707,2708,2709,2710,2728,2746,2747,2748,2767,2775,2776,2777,2781,2788,2790,2797,2800,2801,2802,2821,2824,2830,2848,2850,2851,5186,5246,5344,5430,5431,5432,5508,5605,5636,5669,5685,5687,5693,5756,5757,5758,5759,5765,5799,5932,5971,5980,6003,6040,6074,6078,6225,6230,6265,6266,6286,6290,6292,6299,6300,6301,6302,6303,6304,6305,6306,6389,6457,6458,6542,6575,6576,6618,6619,6759,6774,6846,6847,6851,6874,6897,6905,6907,6954,6979,6980,6998,6999,7034,7078,7079,7176,7237,7238,7239,7240,7254,7286,7342,7343,7352,7359,7360,7372,7404,7405,7406,7407,7549,7551,7552,7553,7559,7560,7770,7776,7777,7787,7826,7905,7947,8005,8027,8028,8043,8103,8205,8274,8275,8277,8313,8375,8376,8449,8472,8473,8474,8475,8619,8830,8854,8855,8936,8951,9006,9007,9124,9161,9184,9219,9262,9456,9720,9914,9972,9974,10113,5998,6372,6373,6460,6479,6480,6532,6896,7114,8544,8769,8960,8961,9034,9035,9310,9311,9312,9313,9517,9791,10098,10155,10156,6442,8368,8369,8820,8838])). % 187.94/187.73 cnf(13141,plain, % 187.94/187.73 (E(f306(f306(f81(a865),f2(a865)),f732(f306(a119,f2(a865)),f2(a865))),f2(a865))), % 187.94/187.73 inference(scs_inference,[],[4527,3510,11037,12085,12190,12282,12320,12328,12393,12522,12524,12949,12959,12964,12968,12974,12977,13001,13102,3517,12151,12560,12562,3518,12221,3237,12566,12568,3238,12589,3206,12469,4455,4456,11663,4201,12604,12607,3241,12580,3085,3143,12556,4438,3568,4420,10200,10210,10221,10330,10333,10336,10438,10551,10855,11022,11025,11223,11313,11320,11334,11384,11387,11409,11502,11548,11564,11864,11892,11904,11936,12034,12147,12154,12312,12363,12502,12621,12775,13026,4435,10422,10515,3329,3290,12576,3479,3189,4430,12692,12707,13048,2875,2876,2878,2879,2882,2883,2885,2886,2887,2889,2894,2898,2902,2911,2917,2921,2923,2924,2929,2930,2933,2934,2936,2937,2938,2939,2943,2948,2949,2952,2953,2956,2964,2970,2978,2987,2990,3004,3005,3018,3019,3020,3021,3028,3029,3030,3031,3032,3033,3044,3050,3162,4415,3064,3142,4416,3603,3117,11310,3251,3313,3224,3227,10203,10264,10267,10357,10360,10650,10929,11325,11328,11445,11489,11494,11593,12055,12258,12449,12504,12509,12511,12513,12530,12538,12542,12544,12595,12615,12826,12992,13101,13106,13122,3591,3838,3202,11590,12341,12345,12349,3212,3722,10969,11596,3106,3107,3922,4432,3552,3812,11360,3328,12532,3170,3134,3639,12550,3129,3928,3150,3644,3115,3095,3120,3149,3283,12026,12177,12396,12472,3330,10802,12148,3200,3201,3222,10463,3375,4513,10392,3895,4445,10255,10419,11220,11412,12308,12342,12346,4454,12316,3260,11685,11688,12918,13022,13073,13077,13081,4503,10972,11042,11263,11266,3664,3255,3376,3590,3368,3343,12586,3165,10322,10626,3166,4487,3433,3157,3086,3185,11350,4037,12331,12461,3897,10978,11104,11155,12292,12298,12410,12413,12436,4524,10907,11109,11214,11236,11271,11277,12237,4525,11011,11112,11217,4526,11115,11166,4528,11169,4529,3184,3472,12193,12234,12315,3628,4316,4317,3455,4443,11341,3570,3606,3777,3538,12809,12813,12817,12821,12831,3822,12187,3458,3704,3340,10341,10458,10529,10590,10593,10629,10723,10962,11860,11926,12002,12046,12125,12128,12440,12627,12686,12729,12732,12774,12792,13025,13030,3715,11581,4174,3253,3352,11700,12620,13121,3533,4493,10232,10235,10261,10731,10744,10865,11286,11353,11752,11757,11978,11981,12067,12076,12240,12335,12632,12651,12654,12678,12733,12896,12901,12925,12930,4509,11464,11497,11532,11561,12742,12746,3702,3480,3481,11881,12657,12660,12663,12666,12700,12703,13056,13060,13064,3847,3444,13057,3445,13061,3299,3300,3273,4490,3164,4440,3655,4171,3962,3464,4510,4031,11231,3589,3312,11709,11712,12158,12262,12420,4001,3961,11853,12208,3907,10799,12014,12040,12215,12443,12890,13072,3951,13076,3956,10981,12082,12157,12214,12261,12921,3957,3629,11863,12009,12092,12138,3990,3646,10984,11047,11128,11188,12033,12106,12358,12433,12446,12887,12958,12963,4514,10747,11120,12218,12971,3270,10350,10445,10576,10636,11437,11657,11703,11737,11833,11891,12099,12265,12480,3271,10705,10750,10753,10786,10812,10849,10887,10923,11907,11910,11913,11916,12113,12116,12119,12122,12201,12369,12416,12679,12706,12784,12795,12800,12803,12806,12839,12850,12911,12936,12939,3272,10433,10641,10726,10852,11740,11749,11839,11850,11869,11874,11919,11939,11956,12697,12843,12863,12897,12902,12926,12931,3348,12070,12762,12810,12814,12818,12822,12832,12836,4489,10298,10387,10500,10524,10768,10815,10825,11511,11611,11632,11635,11638,11654,11807,11810,11813,11816,11903,11922,11925,11935,11990,11993,11996,11999,12077,12169,12172,12268,12271,12334,12362,12399,12484,3428,10596,10860,10904,11177,11255,11425,12311,12487,12883,12953,4505,10777,10789,10896,10914,10917,10975,11061,11069,11085,11123,11140,11149,11185,11226,11246,11249,11252,11280,11293,11296,11682,11718,11984,11987,12021,12071,12102,12246,12289,12295,12381,12384,12403,12460,12466,12475,12496,12761,12778,12781,12872,12954,12996,13011,13014,13053,13097,13100,3334,10623,10653,10662,11206,11764,12400,12417,12743,12747,12750,3371,13039,13094,3365,3781,3720,10301,11584,11614,12724,4502,10252,10611,10614,11064,11082,11547,11602,11642,11770,11795,11798,11801,11804,12066,12942,3292,10656,10809,10880,11615,11769,11961,12180,12202,12771,13044,13120,3742,11715,12673,4081,3486,4500,3753,3788,4479,4482,4483,3244,3248,4481,4484,3246,3249,4480,4254,3760,3579,11577,11666,4177,11444,4516,10226,10229,10481,10532,10535,10540,10949,11419,11669,11773,4522,11143,11260,11302,3967,12229,3864,11299,11641,11645,11706,12319,12327,12409,12691,12948,13000,3709,10920,10926,10944,11888,12105,12377,12406,3566,11146,12131,12243,12253,12324,12372,12380,12493,3601,4035,3711,10659,11000,11152,11182,11193,12037,12323,12366,12988,3536,10579,10582,10665,10836,3535,4519,11578,4515,12641,4520,10716,10818,11131,11283,11422,11450,12196,12205,12249,12430,12490,4140,10792,12226,12252,4042,3741,12499,3689,3690,4517,10274,10277,10617,10620,11461,11646,12439,4518,11558,11651,3713,10585,10842,13029,3974,4521,4538,4564,4613,4615,4645,4662,4669,4670,4709,4739,4745,4830,4856,4857,4918,4919,4941,4942,4955,4959,4981,4988,5005,5008,5009,5010,5015,5016,5039,5066,5067,5077,5082,5090,5135,5136,5144,5154,5158,5160,5170,5172,5178,5182,5197,5204,5207,5208,5209,5213,5248,5261,5268,5270,5271,5275,5276,5277,5285,5288,5293,5294,5295,5302,5306,5307,5308,5317,5321,5322,5323,5328,5341,5350,5362,5364,5372,5373,5377,5381,5406,5412,5422,5423,5438,5451,5473,5479,5495,5496,5499,5518,5526,5527,5532,5533,5543,5544,5556,5560,5569,5570,5572,5587,5592,5603,5604,5616,5623,5637,5641,5644,5650,5651,5652,5655,5660,5697,5698,5701,5703,5706,5707,5708,5710,5712,5714,5719,5726,5741,5755,5760,5761,5774,5775,5780,5785,5787,5792,5833,5845,5854,5858,5869,5873,5874,5882,5896,5902,5920,5923,5935,5965,5979,6004,6024,6025,6028,6042,6044,6046,6048,6061,6062,6065,6067,6070,6071,6082,6088,6089,6090,6092,6094,6136,6137,6144,6154,6190,6192,6194,6196,6205,6207,6209,6215,6217,6223,6226,6234,6241,6242,6243,6248,6270,6271,6272,6274,6280,6285,6322,6323,6325,6326,6327,6329,6330,6331,6332,6341,6374,6375,6384,6405,6406,6426,6429,6440,6441,6447,6476,6478,6490,6528,6530,6531,6586,6610,6656,6676,6685,6686,6687,6688,6707,6708,6714,6726,6729,6731,6733,6734,6735,6737,6751,6762,6764,6765,6778,6781,6832,6843,6845,6849,6864,6865,6901,6913,6944,6963,6978,7032,7060,7115,7136,7145,7148,7203,7211,7269,7271,7285,7295,7296,7297,7316,7322,7324,7373,7383,7386,7402,7451,7453,7456,7499,7500,7518,7585,7604,7628,7650,7665,7680,7691,7699,7700,7728,7731,7733,7741,7779,7790,7815,7873,7907,7939,7986,8002,8008,8019,8020,8095,8149,8168,8192,8212,8236,8335,8337,8343,8361,8365,8379,8402,8413,8415,8430,8436,8440,8465,8479,8480,8496,8497,8502,8503,8504,8505,8506,8524,8525,8526,8535,8549,8551,8563,8567,8569,8570,8571,8579,8584,8611,8612,8641,8654,8658,8676,8698,8699,8700,8701,8714,8715,8737,8747,8756,8757,8758,8759,8761,8783,8784,8795,8840,8846,8852,8865,8870,8872,8875,8876,8880,8889,8972,9003,9004,9005,9020,9038,9043,9070,9071,9114,9117,9144,9189,9190,9191,9207,9233,9247,9253,9256,9279,9280,9308,9371,9407,9408,9409,9434,9435,9453,9471,9477,9493,9516,9538,9546,9547,9548,9549,9565,9567,9572,9603,9604,9610,9611,9654,9655,9686,9696,9706,9708,9709,9719,9733,9737,9765,9797,9802,9859,9902,9903,9905,9915,9916,9936,9941,9964,9969,9984,10036,10110,10111,10168,10184,2,8,9,4551,4552,4570,4601,4602,4604,4631,4637,4638,4649,4698,4700,4730,4744,4774,4871,4872,4886,4906,4962,4963,4966,4967,4969,4971,4972,4984,4985,4995,5006,5007,5013,5032,5033,5054,5059,5060,5061,5062,5065,5073,5076,5083,5084,5085,5150,5156,5157,5164,5194,5205,5211,5227,5247,5254,5255,5256,5265,5274,5281,5283,5284,5290,5298,5299,5309,5313,5314,5315,5316,5318,5319,5324,5325,5326,5327,5358,5359,5360,5368,5369,5370,5371,5414,5419,5421,5458,5460,5461,5463,5464,5466,5467,5469,5478,5483,5485,5486,5487,5488,5489,5490,5497,5507,5510,5521,5537,5538,5541,5550,5552,5553,5554,5579,5589,5606,5607,5617,5618,5620,5622,5627,5662,5666,5668,5728,5762,5763,5767,5773,5776,5777,5778,5779,5786,5797,5798,5800,5801,5809,5830,5861,5877,5880,5881,5883,5892,5910,5914,5917,5918,5919,5937,5950,5951,5981,5982,5986,6006,6009,6013,6032,6037,6038,6063,6066,6073,6081,6087,6091,6098,6099,6100,6101,6139,6155,6208,6244,6246,6267,6268,6273,6277,6278,6281,6288,6297,6314,6334,6335,6342,6352,6367,6387,6393,6395,6410,6411,6415,6417,6418,6419,6421,6423,6424,6425,6428,6433,6434,6436,6437,6443,6445,6486,6489,6503,6505,6506,6507,6543,6548,6550,6555,6556,6564,6568,6581,6605,6606,6608,6609,6621,6625,6627,6647,6650,6669,6702,6703,6704,6709,6722,6741,6743,6745,6747,6752,6758,6760,6775,6782,6818,6819,6820,6834,6835,6837,6838,6855,6857,6873,6899,6921,6932,6934,6936,6938,6939,6940,6975,6976,6981,6982,6990,6992,6993,6994,7013,7022,7023,7035,7045,7084,7094,7098,7105,7116,7117,7122,7124,7130,7138,7139,7152,7169,7187,7189,7206,7255,7256,7257,7259,7261,7265,7270,7292,7337,7369,7384,7389,7401,7434,7437,7460,7484,7501,7504,7505,7515,7534,7536,7538,7540,7541,7542,7567,7593,7594,7627,7629,7630,7631,7636,7657,7666,7677,7682,7688,7690,7696,7707,7708,7710,7730,7734,7739,7762,7828,7829,7876,7885,7886,7909,7910,7927,7928,7993,7994,8022,8051,8062,8064,8073,8085,8118,8124,8131,8144,8163,8169,8191,8234,8264,8276,8295,8298,8328,8352,8416,8417,8420,8422,8441,8528,8529,8530,8531,8558,8587,8615,8657,8675,8731,8776,8779,8792,8799,8837,8885,8886,8903,8904,9045,9049,9068,9078,9103,9105,9108,9112,9115,9116,9129,9130,9151,9157,9169,9218,9237,9257,9292,9293,9300,9363,9368,9404,9411,9414,9417,9418,9433,9449,9458,9470,9481,9482,9485,9487,9514,9636,9681,9682,9726,9772,9887,9888,9945,10013,10089,10102,10107,3,2601,2603,2604,2605,2606,2607,2614,2616,2617,2618,2619,2620,2621,2622,2623,2624,2625,2627,2628,2629,2630,2642,2646,2647,2650,2653,2658,2659,2661,2662,2663,2664,2665,2671,2672,2674,2676,2677,2678,2679,2680,2683,2686,2693,2694,2705,2707,2708,2709,2710,2728,2746,2747,2748,2767,2775,2776,2777,2781,2788,2790,2797,2800,2801,2802,2821,2824,2830,2848,2850,2851,5186,5246,5344,5430,5431,5432,5508,5605,5636,5669,5685,5687,5693,5756,5757,5758,5759,5765,5799,5932,5971,5980,6003,6040,6074,6078,6225,6230,6265,6266,6286,6290,6292,6299,6300,6301,6302,6303,6304,6305,6306,6389,6457,6458,6542,6575,6576,6618,6619,6759,6774,6846,6847,6851,6874,6897,6905,6907,6954,6979,6980,6998,6999,7034,7078,7079,7176,7237,7238,7239,7240,7254,7286,7342,7343,7352,7359,7360,7372,7404,7405,7406,7407,7549,7551,7552,7553,7559,7560,7770,7776,7777,7787,7826,7905,7947,8005,8027,8028,8043,8103,8205,8274,8275,8277,8313,8375,8376,8449,8472,8473,8474,8475,8619,8830,8854,8855,8936,8951,9006,9007,9124,9161,9184,9219,9262,9456,9720,9914,9972,9974,10113,5998,6372,6373,6460,6479,6480,6532,6896,7114,8544,8769,8960,8961,9034,9035,9310,9311,9312,9313,9517,9791,10098,10155,10156,6442,8368,8369,8820,8838,9792,10154,4605,4607])). % 187.94/187.73 cnf(13197,plain, % 187.94/187.73 (~P1(f306(f306(f221(a1),f2(a1)),f2(a1)))), % 187.94/187.73 inference(scs_inference,[],[4527,3510,11037,12085,12190,12282,12320,12328,12393,12522,12524,12949,12959,12964,12968,12974,12977,13001,13102,3517,12151,12560,12562,3518,12221,3237,12566,12568,3238,12589,3206,12469,4455,4456,11663,4201,12604,12607,3241,12580,3085,3143,12556,4438,3568,4420,10200,10210,10221,10330,10333,10336,10438,10551,10855,11022,11025,11223,11313,11320,11334,11384,11387,11409,11502,11548,11564,11864,11892,11904,11936,12034,12147,12154,12312,12363,12502,12621,12775,13026,4435,10422,10515,3329,3290,12576,3479,3189,4430,12692,12707,13048,2875,2876,2878,2879,2882,2883,2885,2886,2887,2889,2894,2898,2902,2911,2917,2921,2923,2924,2929,2930,2933,2934,2936,2937,2938,2939,2943,2948,2949,2952,2953,2956,2964,2970,2978,2987,2990,3004,3005,3018,3019,3020,3021,3028,3029,3030,3031,3032,3033,3044,3050,3162,4415,3064,3142,4416,3603,3117,11310,3251,3313,3224,3227,10203,10264,10267,10357,10360,10650,10929,11325,11328,11445,11489,11494,11593,12055,12258,12449,12504,12509,12511,12513,12530,12538,12542,12544,12595,12615,12826,12992,13101,13106,13122,3591,3838,3202,11590,12341,12345,12349,3212,3722,10969,11596,3106,3107,3922,4432,3552,3812,11360,3328,12532,3170,3134,3639,12550,3129,3928,3150,3644,3115,3095,3120,3149,3283,12026,12177,12396,12472,3330,10802,12148,3200,3201,3222,10463,3375,4513,10392,3895,4445,10255,10419,11220,11412,12308,12342,12346,4454,12316,3260,11685,11688,12918,13022,13073,13077,13081,4503,10972,11042,11263,11266,3664,3255,3376,3590,3368,3343,12586,3165,10322,10626,3166,4487,3433,3157,3086,3185,11350,4037,12331,12461,3897,10978,11104,11155,12292,12298,12410,12413,12436,4524,10907,11109,11214,11236,11271,11277,12237,4525,11011,11112,11217,4526,11115,11166,4528,11169,4529,3184,3472,12193,12234,12315,3628,4316,4317,3455,4443,11341,3570,3606,3777,3538,12809,12813,12817,12821,12831,3822,12187,3458,3704,3340,10341,10458,10529,10590,10593,10629,10723,10962,11860,11926,12002,12046,12125,12128,12440,12627,12686,12729,12732,12774,12792,13025,13030,3715,11581,4174,3253,3352,11700,12620,13121,3533,4493,10232,10235,10261,10731,10744,10865,11286,11353,11752,11757,11978,11981,12067,12076,12240,12335,12632,12651,12654,12678,12733,12896,12901,12925,12930,4509,11464,11497,11532,11561,12742,12746,3702,3480,3481,11881,12657,12660,12663,12666,12700,12703,13056,13060,13064,3847,3444,13057,3445,13061,3299,3300,3273,4490,3164,4440,3655,4171,3962,3464,4510,4031,11231,3589,3312,11709,11712,12158,12262,12420,4001,3961,11853,12208,3907,10799,12014,12040,12215,12443,12890,13072,3951,13076,3956,10981,12082,12157,12214,12261,12921,3957,3629,11863,12009,12092,12138,3990,3646,10984,11047,11128,11188,12033,12106,12358,12433,12446,12887,12958,12963,4514,10747,11120,12218,12971,3270,10350,10445,10576,10636,11437,11657,11703,11737,11833,11891,12099,12265,12480,3271,10705,10750,10753,10786,10812,10849,10887,10923,11907,11910,11913,11916,12113,12116,12119,12122,12201,12369,12416,12679,12706,12784,12795,12800,12803,12806,12839,12850,12911,12936,12939,3272,10433,10641,10726,10852,11740,11749,11839,11850,11869,11874,11919,11939,11956,12697,12843,12863,12897,12902,12926,12931,3348,12070,12762,12810,12814,12818,12822,12832,12836,4489,10298,10387,10500,10524,10768,10815,10825,11511,11611,11632,11635,11638,11654,11807,11810,11813,11816,11903,11922,11925,11935,11990,11993,11996,11999,12077,12169,12172,12268,12271,12334,12362,12399,12484,3428,10596,10860,10904,11177,11255,11425,12311,12487,12883,12953,4505,10777,10789,10896,10914,10917,10975,11061,11069,11085,11123,11140,11149,11185,11226,11246,11249,11252,11280,11293,11296,11682,11718,11984,11987,12021,12071,12102,12246,12289,12295,12381,12384,12403,12460,12466,12475,12496,12761,12778,12781,12872,12954,12996,13011,13014,13053,13097,13100,3334,10623,10653,10662,11206,11764,12400,12417,12743,12747,12750,3371,13039,13094,3365,3781,3720,10301,11584,11614,12724,4502,10252,10611,10614,11064,11082,11547,11602,11642,11770,11795,11798,11801,11804,12066,12942,3292,10656,10809,10880,11615,11769,11961,12180,12202,12771,13044,13120,3742,11715,12673,4081,3486,4500,3753,3788,4479,4482,4483,3244,3248,4481,4484,3246,3249,4480,4254,3760,3579,11577,11666,4177,11444,4516,10226,10229,10481,10532,10535,10540,10949,11419,11669,11773,4522,11143,11260,11302,3967,12229,3864,11299,11641,11645,11706,12319,12327,12409,12691,12948,13000,3709,10920,10926,10944,11888,12105,12377,12406,3566,11146,12131,12243,12253,12324,12372,12380,12493,3601,4035,3711,10659,11000,11152,11182,11193,12037,12323,12366,12988,3536,10579,10582,10665,10836,3535,4519,11578,4515,12641,4520,10716,10818,11131,11283,11422,11450,12196,12205,12249,12430,12490,4140,10792,12226,12252,4042,3741,12499,3689,3690,4517,10274,10277,10617,10620,11461,11646,12439,4518,11558,11651,3713,10585,10842,13029,3974,4521,4538,4564,4613,4615,4645,4662,4669,4670,4709,4739,4745,4830,4856,4857,4918,4919,4941,4942,4955,4959,4981,4988,5005,5008,5009,5010,5015,5016,5039,5066,5067,5077,5082,5090,5135,5136,5144,5154,5158,5160,5170,5172,5178,5182,5197,5204,5207,5208,5209,5213,5248,5261,5268,5270,5271,5275,5276,5277,5285,5288,5293,5294,5295,5302,5306,5307,5308,5317,5321,5322,5323,5328,5341,5350,5362,5364,5372,5373,5377,5381,5406,5412,5422,5423,5438,5451,5473,5479,5495,5496,5499,5518,5526,5527,5532,5533,5543,5544,5556,5560,5569,5570,5572,5587,5592,5603,5604,5616,5623,5637,5641,5644,5650,5651,5652,5655,5660,5697,5698,5701,5703,5706,5707,5708,5710,5712,5714,5719,5726,5741,5755,5760,5761,5774,5775,5780,5785,5787,5792,5833,5845,5854,5858,5869,5873,5874,5882,5896,5902,5920,5923,5935,5965,5979,6004,6024,6025,6028,6042,6044,6046,6048,6061,6062,6065,6067,6070,6071,6082,6088,6089,6090,6092,6094,6136,6137,6144,6154,6190,6192,6194,6196,6205,6207,6209,6215,6217,6223,6226,6234,6241,6242,6243,6248,6270,6271,6272,6274,6280,6285,6322,6323,6325,6326,6327,6329,6330,6331,6332,6341,6374,6375,6384,6405,6406,6426,6429,6440,6441,6447,6476,6478,6490,6528,6530,6531,6586,6610,6656,6676,6685,6686,6687,6688,6707,6708,6714,6726,6729,6731,6733,6734,6735,6737,6751,6762,6764,6765,6778,6781,6832,6843,6845,6849,6864,6865,6901,6913,6944,6963,6978,7032,7060,7115,7136,7145,7148,7203,7211,7269,7271,7285,7295,7296,7297,7316,7322,7324,7373,7383,7386,7402,7451,7453,7456,7499,7500,7518,7585,7604,7628,7650,7665,7680,7691,7699,7700,7728,7731,7733,7741,7779,7790,7815,7873,7907,7939,7986,8002,8008,8019,8020,8095,8149,8168,8192,8212,8236,8335,8337,8343,8361,8365,8379,8402,8413,8415,8430,8436,8440,8465,8479,8480,8496,8497,8502,8503,8504,8505,8506,8524,8525,8526,8535,8549,8551,8563,8567,8569,8570,8571,8579,8584,8611,8612,8641,8654,8658,8676,8698,8699,8700,8701,8714,8715,8737,8747,8756,8757,8758,8759,8761,8783,8784,8795,8840,8846,8852,8865,8870,8872,8875,8876,8880,8889,8972,9003,9004,9005,9020,9038,9043,9070,9071,9114,9117,9144,9189,9190,9191,9207,9233,9247,9253,9256,9279,9280,9308,9371,9407,9408,9409,9434,9435,9453,9471,9477,9493,9516,9538,9546,9547,9548,9549,9565,9567,9572,9603,9604,9610,9611,9654,9655,9686,9696,9706,9708,9709,9719,9733,9737,9765,9797,9802,9859,9902,9903,9905,9915,9916,9936,9941,9964,9969,9984,10036,10110,10111,10168,10184,2,8,9,4551,4552,4570,4601,4602,4604,4631,4637,4638,4649,4698,4700,4730,4744,4774,4871,4872,4886,4906,4962,4963,4966,4967,4969,4971,4972,4984,4985,4995,5006,5007,5013,5032,5033,5054,5059,5060,5061,5062,5065,5073,5076,5083,5084,5085,5150,5156,5157,5164,5194,5205,5211,5227,5247,5254,5255,5256,5265,5274,5281,5283,5284,5290,5298,5299,5309,5313,5314,5315,5316,5318,5319,5324,5325,5326,5327,5358,5359,5360,5368,5369,5370,5371,5414,5419,5421,5458,5460,5461,5463,5464,5466,5467,5469,5478,5483,5485,5486,5487,5488,5489,5490,5497,5507,5510,5521,5537,5538,5541,5550,5552,5553,5554,5579,5589,5606,5607,5617,5618,5620,5622,5627,5662,5666,5668,5728,5762,5763,5767,5773,5776,5777,5778,5779,5786,5797,5798,5800,5801,5809,5830,5861,5877,5880,5881,5883,5892,5910,5914,5917,5918,5919,5937,5950,5951,5981,5982,5986,6006,6009,6013,6032,6037,6038,6063,6066,6073,6081,6087,6091,6098,6099,6100,6101,6139,6155,6208,6244,6246,6267,6268,6273,6277,6278,6281,6288,6297,6314,6334,6335,6342,6352,6367,6387,6393,6395,6410,6411,6415,6417,6418,6419,6421,6423,6424,6425,6428,6433,6434,6436,6437,6443,6445,6486,6489,6503,6505,6506,6507,6543,6548,6550,6555,6556,6564,6568,6581,6605,6606,6608,6609,6621,6625,6627,6647,6650,6669,6702,6703,6704,6709,6722,6741,6743,6745,6747,6752,6758,6760,6775,6782,6818,6819,6820,6834,6835,6837,6838,6855,6857,6873,6899,6921,6932,6934,6936,6938,6939,6940,6975,6976,6981,6982,6990,6992,6993,6994,7013,7022,7023,7035,7045,7084,7094,7098,7105,7116,7117,7122,7124,7130,7138,7139,7152,7169,7187,7189,7206,7255,7256,7257,7259,7261,7265,7270,7292,7337,7369,7384,7389,7401,7434,7437,7460,7484,7501,7504,7505,7515,7534,7536,7538,7540,7541,7542,7567,7593,7594,7627,7629,7630,7631,7636,7657,7666,7677,7682,7688,7690,7696,7707,7708,7710,7730,7734,7739,7762,7828,7829,7876,7885,7886,7909,7910,7927,7928,7993,7994,8022,8051,8062,8064,8073,8085,8118,8124,8131,8144,8163,8169,8191,8234,8264,8276,8295,8298,8328,8352,8416,8417,8420,8422,8441,8528,8529,8530,8531,8558,8587,8615,8657,8675,8731,8776,8779,8792,8799,8837,8885,8886,8903,8904,9045,9049,9068,9078,9103,9105,9108,9112,9115,9116,9129,9130,9151,9157,9169,9218,9237,9257,9292,9293,9300,9363,9368,9404,9411,9414,9417,9418,9433,9449,9458,9470,9481,9482,9485,9487,9514,9636,9681,9682,9726,9772,9887,9888,9945,10013,10089,10102,10107,3,2601,2603,2604,2605,2606,2607,2614,2616,2617,2618,2619,2620,2621,2622,2623,2624,2625,2627,2628,2629,2630,2642,2646,2647,2650,2653,2658,2659,2661,2662,2663,2664,2665,2671,2672,2674,2676,2677,2678,2679,2680,2683,2686,2693,2694,2705,2707,2708,2709,2710,2728,2746,2747,2748,2767,2775,2776,2777,2781,2788,2790,2797,2800,2801,2802,2821,2824,2830,2848,2850,2851,5186,5246,5344,5430,5431,5432,5508,5605,5636,5669,5685,5687,5693,5756,5757,5758,5759,5765,5799,5932,5971,5980,6003,6040,6074,6078,6225,6230,6265,6266,6286,6290,6292,6299,6300,6301,6302,6303,6304,6305,6306,6389,6457,6458,6542,6575,6576,6618,6619,6759,6774,6846,6847,6851,6874,6897,6905,6907,6954,6979,6980,6998,6999,7034,7078,7079,7176,7237,7238,7239,7240,7254,7286,7342,7343,7352,7359,7360,7372,7404,7405,7406,7407,7549,7551,7552,7553,7559,7560,7770,7776,7777,7787,7826,7905,7947,8005,8027,8028,8043,8103,8205,8274,8275,8277,8313,8375,8376,8449,8472,8473,8474,8475,8619,8830,8854,8855,8936,8951,9006,9007,9124,9161,9184,9219,9262,9456,9720,9914,9972,9974,10113,5998,6372,6373,6460,6479,6480,6532,6896,7114,8544,8769,8960,8961,9034,9035,9310,9311,9312,9313,9517,9791,10098,10155,10156,6442,8368,8369,8820,8838,9792,10154,4605,4607,4608,4663,4671,4808,4822,4823,4847,4854,4855,4884,4940,5002,5063,5115,5143,5179,5181,5187,5189,5190,5216,5289,5312,5447,5513,5514,5515,5632])). % 187.94/187.73 cnf(13199,plain, % 187.94/187.73 (P1(f306(f306(f221(a1),f2(a1)),f306(f76(a1),f79(a1))))), % 187.94/187.73 inference(scs_inference,[],[4527,3510,11037,12085,12190,12282,12320,12328,12393,12522,12524,12949,12959,12964,12968,12974,12977,13001,13102,3517,12151,12560,12562,3518,12221,3237,12566,12568,3238,12589,3206,12469,4455,4456,11663,4201,12604,12607,3241,12580,3085,3143,12556,4438,3568,4420,10200,10210,10221,10330,10333,10336,10438,10551,10855,11022,11025,11223,11313,11320,11334,11384,11387,11409,11502,11548,11564,11864,11892,11904,11936,12034,12147,12154,12312,12363,12502,12621,12775,13026,4435,10422,10515,3329,3290,12576,3479,3189,4430,12692,12707,13048,2875,2876,2878,2879,2882,2883,2885,2886,2887,2889,2894,2898,2902,2911,2917,2921,2923,2924,2929,2930,2933,2934,2936,2937,2938,2939,2943,2948,2949,2952,2953,2956,2964,2970,2978,2987,2990,3004,3005,3018,3019,3020,3021,3028,3029,3030,3031,3032,3033,3044,3050,3162,4415,3064,3142,4416,3603,3117,11310,3251,3313,3224,3227,10203,10264,10267,10357,10360,10650,10929,11325,11328,11445,11489,11494,11593,12055,12258,12449,12504,12509,12511,12513,12530,12538,12542,12544,12595,12615,12826,12992,13101,13106,13122,3591,3838,3202,11590,12341,12345,12349,3212,3722,10969,11596,3106,3107,3922,4432,3552,3812,11360,3328,12532,3170,3134,3639,12550,3129,3928,3150,3644,3115,3095,3120,3149,3283,12026,12177,12396,12472,3330,10802,12148,3200,3201,3222,10463,3375,4513,10392,3895,4445,10255,10419,11220,11412,12308,12342,12346,4454,12316,3260,11685,11688,12918,13022,13073,13077,13081,4503,10972,11042,11263,11266,3664,3255,3376,3590,3368,3343,12586,3165,10322,10626,3166,4487,3433,3157,3086,3185,11350,4037,12331,12461,3897,10978,11104,11155,12292,12298,12410,12413,12436,4524,10907,11109,11214,11236,11271,11277,12237,4525,11011,11112,11217,4526,11115,11166,4528,11169,4529,3184,3472,12193,12234,12315,3628,4316,4317,3455,4443,11341,3570,3606,3777,3538,12809,12813,12817,12821,12831,3822,12187,3458,3704,3340,10341,10458,10529,10590,10593,10629,10723,10962,11860,11926,12002,12046,12125,12128,12440,12627,12686,12729,12732,12774,12792,13025,13030,3715,11581,4174,3253,3352,11700,12620,13121,3533,4493,10232,10235,10261,10731,10744,10865,11286,11353,11752,11757,11978,11981,12067,12076,12240,12335,12632,12651,12654,12678,12733,12896,12901,12925,12930,4509,11464,11497,11532,11561,12742,12746,3702,3480,3481,11881,12657,12660,12663,12666,12700,12703,13056,13060,13064,3847,3444,13057,3445,13061,3299,3300,3273,4490,3164,4440,3655,4171,3962,3464,4510,4031,11231,3589,3312,11709,11712,12158,12262,12420,4001,3961,11853,12208,3907,10799,12014,12040,12215,12443,12890,13072,3951,13076,3956,10981,12082,12157,12214,12261,12921,3957,3629,11863,12009,12092,12138,3990,3646,10984,11047,11128,11188,12033,12106,12358,12433,12446,12887,12958,12963,4514,10747,11120,12218,12971,3270,10350,10445,10576,10636,11437,11657,11703,11737,11833,11891,12099,12265,12480,3271,10705,10750,10753,10786,10812,10849,10887,10923,11907,11910,11913,11916,12113,12116,12119,12122,12201,12369,12416,12679,12706,12784,12795,12800,12803,12806,12839,12850,12911,12936,12939,3272,10433,10641,10726,10852,11740,11749,11839,11850,11869,11874,11919,11939,11956,12697,12843,12863,12897,12902,12926,12931,3348,12070,12762,12810,12814,12818,12822,12832,12836,4489,10298,10387,10500,10524,10768,10815,10825,11511,11611,11632,11635,11638,11654,11807,11810,11813,11816,11903,11922,11925,11935,11990,11993,11996,11999,12077,12169,12172,12268,12271,12334,12362,12399,12484,3428,10596,10860,10904,11177,11255,11425,12311,12487,12883,12953,4505,10777,10789,10896,10914,10917,10975,11061,11069,11085,11123,11140,11149,11185,11226,11246,11249,11252,11280,11293,11296,11682,11718,11984,11987,12021,12071,12102,12246,12289,12295,12381,12384,12403,12460,12466,12475,12496,12761,12778,12781,12872,12954,12996,13011,13014,13053,13097,13100,3334,10623,10653,10662,11206,11764,12400,12417,12743,12747,12750,3371,13039,13094,3365,3781,3720,10301,11584,11614,12724,4502,10252,10611,10614,11064,11082,11547,11602,11642,11770,11795,11798,11801,11804,12066,12942,3292,10656,10809,10880,11615,11769,11961,12180,12202,12771,13044,13120,3742,11715,12673,4081,3486,4500,3753,3788,4479,4482,4483,3244,3248,4481,4484,3246,3249,4480,4254,3760,3579,11577,11666,4177,11444,4516,10226,10229,10481,10532,10535,10540,10949,11419,11669,11773,4522,11143,11260,11302,3967,12229,3864,11299,11641,11645,11706,12319,12327,12409,12691,12948,13000,3709,10920,10926,10944,11888,12105,12377,12406,3566,11146,12131,12243,12253,12324,12372,12380,12493,3601,4035,3711,10659,11000,11152,11182,11193,12037,12323,12366,12988,3536,10579,10582,10665,10836,3535,4519,11578,4515,12641,4520,10716,10818,11131,11283,11422,11450,12196,12205,12249,12430,12490,4140,10792,12226,12252,4042,3741,12499,3689,3690,4517,10274,10277,10617,10620,11461,11646,12439,4518,11558,11651,3713,10585,10842,13029,3974,4521,4538,4564,4613,4615,4645,4662,4669,4670,4709,4739,4745,4830,4856,4857,4918,4919,4941,4942,4955,4959,4981,4988,5005,5008,5009,5010,5015,5016,5039,5066,5067,5077,5082,5090,5135,5136,5144,5154,5158,5160,5170,5172,5178,5182,5197,5204,5207,5208,5209,5213,5248,5261,5268,5270,5271,5275,5276,5277,5285,5288,5293,5294,5295,5302,5306,5307,5308,5317,5321,5322,5323,5328,5341,5350,5362,5364,5372,5373,5377,5381,5406,5412,5422,5423,5438,5451,5473,5479,5495,5496,5499,5518,5526,5527,5532,5533,5543,5544,5556,5560,5569,5570,5572,5587,5592,5603,5604,5616,5623,5637,5641,5644,5650,5651,5652,5655,5660,5697,5698,5701,5703,5706,5707,5708,5710,5712,5714,5719,5726,5741,5755,5760,5761,5774,5775,5780,5785,5787,5792,5833,5845,5854,5858,5869,5873,5874,5882,5896,5902,5920,5923,5935,5965,5979,6004,6024,6025,6028,6042,6044,6046,6048,6061,6062,6065,6067,6070,6071,6082,6088,6089,6090,6092,6094,6136,6137,6144,6154,6190,6192,6194,6196,6205,6207,6209,6215,6217,6223,6226,6234,6241,6242,6243,6248,6270,6271,6272,6274,6280,6285,6322,6323,6325,6326,6327,6329,6330,6331,6332,6341,6374,6375,6384,6405,6406,6426,6429,6440,6441,6447,6476,6478,6490,6528,6530,6531,6586,6610,6656,6676,6685,6686,6687,6688,6707,6708,6714,6726,6729,6731,6733,6734,6735,6737,6751,6762,6764,6765,6778,6781,6832,6843,6845,6849,6864,6865,6901,6913,6944,6963,6978,7032,7060,7115,7136,7145,7148,7203,7211,7269,7271,7285,7295,7296,7297,7316,7322,7324,7373,7383,7386,7402,7451,7453,7456,7499,7500,7518,7585,7604,7628,7650,7665,7680,7691,7699,7700,7728,7731,7733,7741,7779,7790,7815,7873,7907,7939,7986,8002,8008,8019,8020,8095,8149,8168,8192,8212,8236,8335,8337,8343,8361,8365,8379,8402,8413,8415,8430,8436,8440,8465,8479,8480,8496,8497,8502,8503,8504,8505,8506,8524,8525,8526,8535,8549,8551,8563,8567,8569,8570,8571,8579,8584,8611,8612,8641,8654,8658,8676,8698,8699,8700,8701,8714,8715,8737,8747,8756,8757,8758,8759,8761,8783,8784,8795,8840,8846,8852,8865,8870,8872,8875,8876,8880,8889,8972,9003,9004,9005,9020,9038,9043,9070,9071,9114,9117,9144,9189,9190,9191,9207,9233,9247,9253,9256,9279,9280,9308,9371,9407,9408,9409,9434,9435,9453,9471,9477,9493,9516,9538,9546,9547,9548,9549,9565,9567,9572,9603,9604,9610,9611,9654,9655,9686,9696,9706,9708,9709,9719,9733,9737,9765,9797,9802,9859,9902,9903,9905,9915,9916,9936,9941,9964,9969,9984,10036,10110,10111,10168,10184,2,8,9,4551,4552,4570,4601,4602,4604,4631,4637,4638,4649,4698,4700,4730,4744,4774,4871,4872,4886,4906,4962,4963,4966,4967,4969,4971,4972,4984,4985,4995,5006,5007,5013,5032,5033,5054,5059,5060,5061,5062,5065,5073,5076,5083,5084,5085,5150,5156,5157,5164,5194,5205,5211,5227,5247,5254,5255,5256,5265,5274,5281,5283,5284,5290,5298,5299,5309,5313,5314,5315,5316,5318,5319,5324,5325,5326,5327,5358,5359,5360,5368,5369,5370,5371,5414,5419,5421,5458,5460,5461,5463,5464,5466,5467,5469,5478,5483,5485,5486,5487,5488,5489,5490,5497,5507,5510,5521,5537,5538,5541,5550,5552,5553,5554,5579,5589,5606,5607,5617,5618,5620,5622,5627,5662,5666,5668,5728,5762,5763,5767,5773,5776,5777,5778,5779,5786,5797,5798,5800,5801,5809,5830,5861,5877,5880,5881,5883,5892,5910,5914,5917,5918,5919,5937,5950,5951,5981,5982,5986,6006,6009,6013,6032,6037,6038,6063,6066,6073,6081,6087,6091,6098,6099,6100,6101,6139,6155,6208,6244,6246,6267,6268,6273,6277,6278,6281,6288,6297,6314,6334,6335,6342,6352,6367,6387,6393,6395,6410,6411,6415,6417,6418,6419,6421,6423,6424,6425,6428,6433,6434,6436,6437,6443,6445,6486,6489,6503,6505,6506,6507,6543,6548,6550,6555,6556,6564,6568,6581,6605,6606,6608,6609,6621,6625,6627,6647,6650,6669,6702,6703,6704,6709,6722,6741,6743,6745,6747,6752,6758,6760,6775,6782,6818,6819,6820,6834,6835,6837,6838,6855,6857,6873,6899,6921,6932,6934,6936,6938,6939,6940,6975,6976,6981,6982,6990,6992,6993,6994,7013,7022,7023,7035,7045,7084,7094,7098,7105,7116,7117,7122,7124,7130,7138,7139,7152,7169,7187,7189,7206,7255,7256,7257,7259,7261,7265,7270,7292,7337,7369,7384,7389,7401,7434,7437,7460,7484,7501,7504,7505,7515,7534,7536,7538,7540,7541,7542,7567,7593,7594,7627,7629,7630,7631,7636,7657,7666,7677,7682,7688,7690,7696,7707,7708,7710,7730,7734,7739,7762,7828,7829,7876,7885,7886,7909,7910,7927,7928,7993,7994,8022,8051,8062,8064,8073,8085,8118,8124,8131,8144,8163,8169,8191,8234,8264,8276,8295,8298,8328,8352,8416,8417,8420,8422,8441,8528,8529,8530,8531,8558,8587,8615,8657,8675,8731,8776,8779,8792,8799,8837,8885,8886,8903,8904,9045,9049,9068,9078,9103,9105,9108,9112,9115,9116,9129,9130,9151,9157,9169,9218,9237,9257,9292,9293,9300,9363,9368,9404,9411,9414,9417,9418,9433,9449,9458,9470,9481,9482,9485,9487,9514,9636,9681,9682,9726,9772,9887,9888,9945,10013,10089,10102,10107,3,2601,2603,2604,2605,2606,2607,2614,2616,2617,2618,2619,2620,2621,2622,2623,2624,2625,2627,2628,2629,2630,2642,2646,2647,2650,2653,2658,2659,2661,2662,2663,2664,2665,2671,2672,2674,2676,2677,2678,2679,2680,2683,2686,2693,2694,2705,2707,2708,2709,2710,2728,2746,2747,2748,2767,2775,2776,2777,2781,2788,2790,2797,2800,2801,2802,2821,2824,2830,2848,2850,2851,5186,5246,5344,5430,5431,5432,5508,5605,5636,5669,5685,5687,5693,5756,5757,5758,5759,5765,5799,5932,5971,5980,6003,6040,6074,6078,6225,6230,6265,6266,6286,6290,6292,6299,6300,6301,6302,6303,6304,6305,6306,6389,6457,6458,6542,6575,6576,6618,6619,6759,6774,6846,6847,6851,6874,6897,6905,6907,6954,6979,6980,6998,6999,7034,7078,7079,7176,7237,7238,7239,7240,7254,7286,7342,7343,7352,7359,7360,7372,7404,7405,7406,7407,7549,7551,7552,7553,7559,7560,7770,7776,7777,7787,7826,7905,7947,8005,8027,8028,8043,8103,8205,8274,8275,8277,8313,8375,8376,8449,8472,8473,8474,8475,8619,8830,8854,8855,8936,8951,9006,9007,9124,9161,9184,9219,9262,9456,9720,9914,9972,9974,10113,5998,6372,6373,6460,6479,6480,6532,6896,7114,8544,8769,8960,8961,9034,9035,9310,9311,9312,9313,9517,9791,10098,10155,10156,6442,8368,8369,8820,8838,9792,10154,4605,4607,4608,4663,4671,4808,4822,4823,4847,4854,4855,4884,4940,5002,5063,5115,5143,5179,5181,5187,5189,5190,5216,5289,5312,5447,5513,5514,5515,5632,5633])). % 187.94/187.73 cnf(13217,plain, % 187.94/187.73 (~P1(f306(f306(f221(a865),f306(a119,f306(f306(f81(a865),x132171),x132172))),f306(a119,x132171)))), % 187.94/187.73 inference(scs_inference,[],[4527,3510,11037,12085,12190,12282,12320,12328,12393,12522,12524,12949,12959,12964,12968,12974,12977,13001,13102,3517,12151,12560,12562,3518,12221,3237,12566,12568,3238,12589,3206,12469,4455,4456,11663,4201,12604,12607,3241,12580,3085,3143,12556,4438,3568,4420,10200,10210,10221,10330,10333,10336,10438,10551,10855,11022,11025,11223,11313,11320,11334,11384,11387,11409,11502,11548,11564,11864,11892,11904,11936,12034,12147,12154,12312,12363,12502,12621,12775,13026,4435,10422,10515,3329,3290,12576,3479,3189,4430,12692,12707,13048,2875,2876,2878,2879,2882,2883,2885,2886,2887,2889,2894,2898,2902,2911,2917,2921,2923,2924,2929,2930,2933,2934,2936,2937,2938,2939,2943,2948,2949,2952,2953,2956,2964,2970,2978,2987,2990,3004,3005,3018,3019,3020,3021,3028,3029,3030,3031,3032,3033,3044,3050,3162,4415,3064,3142,4416,3603,3117,11310,3251,3313,3224,3227,10203,10264,10267,10357,10360,10650,10929,11325,11328,11445,11489,11494,11593,12055,12258,12449,12504,12509,12511,12513,12530,12538,12542,12544,12595,12615,12826,12992,13101,13106,13122,3591,3838,3202,11590,12341,12345,12349,3212,3722,10969,11596,3106,3107,3922,4432,3552,3812,11360,3328,12532,3170,3134,3639,12550,3129,3928,3150,3644,3115,3095,3120,3149,3283,12026,12177,12396,12472,3330,10802,12148,3200,3201,3222,10463,3375,4513,10392,3895,4445,10255,10419,11220,11412,12308,12342,12346,4454,12316,3260,11685,11688,12918,13022,13073,13077,13081,4503,10972,11042,11263,11266,3664,3255,3376,3590,3368,3343,12586,3165,10322,10626,3166,4487,3433,3157,3086,3185,11350,4037,12331,12461,3897,10978,11104,11155,12292,12298,12410,12413,12436,4524,10907,11109,11214,11236,11271,11277,12237,4525,11011,11112,11217,4526,11115,11166,4528,11169,4529,3184,3472,12193,12234,12315,3628,4316,4317,3455,4443,11341,3570,3606,3777,3538,12809,12813,12817,12821,12831,3822,12187,3458,3704,3340,10341,10458,10529,10590,10593,10629,10723,10962,11860,11926,12002,12046,12125,12128,12440,12627,12686,12729,12732,12774,12792,13025,13030,3715,11581,4174,3253,3352,11700,12620,13121,3533,4493,10232,10235,10261,10731,10744,10865,11286,11353,11752,11757,11978,11981,12067,12076,12240,12335,12632,12651,12654,12678,12733,12896,12901,12925,12930,4509,11464,11497,11532,11561,12742,12746,3702,3480,3481,11881,12657,12660,12663,12666,12700,12703,13056,13060,13064,3847,3444,13057,3445,13061,3299,3300,3273,4490,3164,4440,3655,4171,3962,3464,4510,4031,11231,3589,3312,11709,11712,12158,12262,12420,4001,3961,11853,12208,3907,10799,12014,12040,12215,12443,12890,13072,3951,13076,3956,10981,12082,12157,12214,12261,12921,3957,3629,11863,12009,12092,12138,3990,3646,10984,11047,11128,11188,12033,12106,12358,12433,12446,12887,12958,12963,4514,10747,11120,12218,12971,3270,10350,10445,10576,10636,11437,11657,11703,11737,11833,11891,12099,12265,12480,3271,10705,10750,10753,10786,10812,10849,10887,10923,11907,11910,11913,11916,12113,12116,12119,12122,12201,12369,12416,12679,12706,12784,12795,12800,12803,12806,12839,12850,12911,12936,12939,3272,10433,10641,10726,10852,11740,11749,11839,11850,11869,11874,11919,11939,11956,12697,12843,12863,12897,12902,12926,12931,3348,12070,12762,12810,12814,12818,12822,12832,12836,4489,10298,10387,10500,10524,10768,10815,10825,11511,11611,11632,11635,11638,11654,11807,11810,11813,11816,11903,11922,11925,11935,11990,11993,11996,11999,12077,12169,12172,12268,12271,12334,12362,12399,12484,3428,10596,10860,10904,11177,11255,11425,12311,12487,12883,12953,4505,10777,10789,10896,10914,10917,10975,11061,11069,11085,11123,11140,11149,11185,11226,11246,11249,11252,11280,11293,11296,11682,11718,11984,11987,12021,12071,12102,12246,12289,12295,12381,12384,12403,12460,12466,12475,12496,12761,12778,12781,12872,12954,12996,13011,13014,13053,13097,13100,3334,10623,10653,10662,11206,11764,12400,12417,12743,12747,12750,3371,13039,13094,3365,3781,3720,10301,11584,11614,12724,4502,10252,10611,10614,11064,11082,11547,11602,11642,11770,11795,11798,11801,11804,12066,12942,3292,10656,10809,10880,11615,11769,11961,12180,12202,12771,13044,13120,3742,11715,12673,4081,3486,4500,3753,3788,4479,4482,4483,3244,3248,4481,4484,3246,3249,4480,4254,3760,3579,11577,11666,4177,11444,4516,10226,10229,10481,10532,10535,10540,10949,11419,11669,11773,4522,11143,11260,11302,3967,12229,3864,11299,11641,11645,11706,12319,12327,12409,12691,12948,13000,3709,10920,10926,10944,11888,12105,12377,12406,3566,11146,12131,12243,12253,12324,12372,12380,12493,3601,4035,3711,10659,11000,11152,11182,11193,12037,12323,12366,12988,3536,10579,10582,10665,10836,3535,4519,11578,4515,12641,4520,10716,10818,11131,11283,11422,11450,12196,12205,12249,12430,12490,4140,10792,12226,12252,4042,3741,12499,3689,3690,4517,10274,10277,10617,10620,11461,11646,12439,4518,11558,11651,3713,10585,10842,13029,3974,4521,4538,4564,4613,4615,4645,4662,4669,4670,4709,4739,4745,4830,4856,4857,4918,4919,4941,4942,4955,4959,4981,4988,5005,5008,5009,5010,5015,5016,5039,5066,5067,5077,5082,5090,5135,5136,5144,5154,5158,5160,5170,5172,5178,5182,5197,5204,5207,5208,5209,5213,5248,5261,5268,5270,5271,5275,5276,5277,5285,5288,5293,5294,5295,5302,5306,5307,5308,5317,5321,5322,5323,5328,5341,5350,5362,5364,5372,5373,5377,5381,5406,5412,5422,5423,5438,5451,5473,5479,5495,5496,5499,5518,5526,5527,5532,5533,5543,5544,5556,5560,5569,5570,5572,5587,5592,5603,5604,5616,5623,5637,5641,5644,5650,5651,5652,5655,5660,5697,5698,5701,5703,5706,5707,5708,5710,5712,5714,5719,5726,5741,5755,5760,5761,5774,5775,5780,5785,5787,5792,5833,5845,5854,5858,5869,5873,5874,5882,5896,5902,5920,5923,5935,5965,5979,6004,6024,6025,6028,6042,6044,6046,6048,6061,6062,6065,6067,6070,6071,6082,6088,6089,6090,6092,6094,6136,6137,6144,6154,6190,6192,6194,6196,6205,6207,6209,6215,6217,6223,6226,6234,6241,6242,6243,6248,6270,6271,6272,6274,6280,6285,6322,6323,6325,6326,6327,6329,6330,6331,6332,6341,6374,6375,6384,6405,6406,6426,6429,6440,6441,6447,6476,6478,6490,6528,6530,6531,6586,6610,6656,6676,6685,6686,6687,6688,6707,6708,6714,6726,6729,6731,6733,6734,6735,6737,6751,6762,6764,6765,6778,6781,6832,6843,6845,6849,6864,6865,6901,6913,6944,6963,6978,7032,7060,7115,7136,7145,7148,7203,7211,7269,7271,7285,7295,7296,7297,7316,7322,7324,7373,7383,7386,7402,7451,7453,7456,7499,7500,7518,7585,7604,7628,7650,7665,7680,7691,7699,7700,7728,7731,7733,7741,7779,7790,7815,7873,7907,7939,7986,8002,8008,8019,8020,8095,8149,8168,8192,8212,8236,8335,8337,8343,8361,8365,8379,8402,8413,8415,8430,8436,8440,8465,8479,8480,8496,8497,8502,8503,8504,8505,8506,8524,8525,8526,8535,8549,8551,8563,8567,8569,8570,8571,8579,8584,8611,8612,8641,8654,8658,8676,8698,8699,8700,8701,8714,8715,8737,8747,8756,8757,8758,8759,8761,8783,8784,8795,8840,8846,8852,8865,8870,8872,8875,8876,8880,8889,8972,9003,9004,9005,9020,9038,9043,9070,9071,9114,9117,9144,9189,9190,9191,9207,9233,9247,9253,9256,9279,9280,9308,9371,9407,9408,9409,9434,9435,9453,9471,9477,9493,9516,9538,9546,9547,9548,9549,9565,9567,9572,9603,9604,9610,9611,9654,9655,9686,9696,9706,9708,9709,9719,9733,9737,9765,9797,9802,9859,9902,9903,9905,9915,9916,9936,9941,9964,9969,9984,10036,10110,10111,10168,10184,2,8,9,4551,4552,4570,4601,4602,4604,4631,4637,4638,4649,4698,4700,4730,4744,4774,4871,4872,4886,4906,4962,4963,4966,4967,4969,4971,4972,4984,4985,4995,5006,5007,5013,5032,5033,5054,5059,5060,5061,5062,5065,5073,5076,5083,5084,5085,5150,5156,5157,5164,5194,5205,5211,5227,5247,5254,5255,5256,5265,5274,5281,5283,5284,5290,5298,5299,5309,5313,5314,5315,5316,5318,5319,5324,5325,5326,5327,5358,5359,5360,5368,5369,5370,5371,5414,5419,5421,5458,5460,5461,5463,5464,5466,5467,5469,5478,5483,5485,5486,5487,5488,5489,5490,5497,5507,5510,5521,5537,5538,5541,5550,5552,5553,5554,5579,5589,5606,5607,5617,5618,5620,5622,5627,5662,5666,5668,5728,5762,5763,5767,5773,5776,5777,5778,5779,5786,5797,5798,5800,5801,5809,5830,5861,5877,5880,5881,5883,5892,5910,5914,5917,5918,5919,5937,5950,5951,5981,5982,5986,6006,6009,6013,6032,6037,6038,6063,6066,6073,6081,6087,6091,6098,6099,6100,6101,6139,6155,6208,6244,6246,6267,6268,6273,6277,6278,6281,6288,6297,6314,6334,6335,6342,6352,6367,6387,6393,6395,6410,6411,6415,6417,6418,6419,6421,6423,6424,6425,6428,6433,6434,6436,6437,6443,6445,6486,6489,6503,6505,6506,6507,6543,6548,6550,6555,6556,6564,6568,6581,6605,6606,6608,6609,6621,6625,6627,6647,6650,6669,6702,6703,6704,6709,6722,6741,6743,6745,6747,6752,6758,6760,6775,6782,6818,6819,6820,6834,6835,6837,6838,6855,6857,6873,6899,6921,6932,6934,6936,6938,6939,6940,6975,6976,6981,6982,6990,6992,6993,6994,7013,7022,7023,7035,7045,7084,7094,7098,7105,7116,7117,7122,7124,7130,7138,7139,7152,7169,7187,7189,7206,7255,7256,7257,7259,7261,7265,7270,7292,7337,7369,7384,7389,7401,7434,7437,7460,7484,7501,7504,7505,7515,7534,7536,7538,7540,7541,7542,7567,7593,7594,7627,7629,7630,7631,7636,7657,7666,7677,7682,7688,7690,7696,7707,7708,7710,7730,7734,7739,7762,7828,7829,7876,7885,7886,7909,7910,7927,7928,7993,7994,8022,8051,8062,8064,8073,8085,8118,8124,8131,8144,8163,8169,8191,8234,8264,8276,8295,8298,8328,8352,8416,8417,8420,8422,8441,8528,8529,8530,8531,8558,8587,8615,8657,8675,8731,8776,8779,8792,8799,8837,8885,8886,8903,8904,9045,9049,9068,9078,9103,9105,9108,9112,9115,9116,9129,9130,9151,9157,9169,9218,9237,9257,9292,9293,9300,9363,9368,9404,9411,9414,9417,9418,9433,9449,9458,9470,9481,9482,9485,9487,9514,9636,9681,9682,9726,9772,9887,9888,9945,10013,10089,10102,10107,3,2601,2603,2604,2605,2606,2607,2614,2616,2617,2618,2619,2620,2621,2622,2623,2624,2625,2627,2628,2629,2630,2642,2646,2647,2650,2653,2658,2659,2661,2662,2663,2664,2665,2671,2672,2674,2676,2677,2678,2679,2680,2683,2686,2693,2694,2705,2707,2708,2709,2710,2728,2746,2747,2748,2767,2775,2776,2777,2781,2788,2790,2797,2800,2801,2802,2821,2824,2830,2848,2850,2851,5186,5246,5344,5430,5431,5432,5508,5605,5636,5669,5685,5687,5693,5756,5757,5758,5759,5765,5799,5932,5971,5980,6003,6040,6074,6078,6225,6230,6265,6266,6286,6290,6292,6299,6300,6301,6302,6303,6304,6305,6306,6389,6457,6458,6542,6575,6576,6618,6619,6759,6774,6846,6847,6851,6874,6897,6905,6907,6954,6979,6980,6998,6999,7034,7078,7079,7176,7237,7238,7239,7240,7254,7286,7342,7343,7352,7359,7360,7372,7404,7405,7406,7407,7549,7551,7552,7553,7559,7560,7770,7776,7777,7787,7826,7905,7947,8005,8027,8028,8043,8103,8205,8274,8275,8277,8313,8375,8376,8449,8472,8473,8474,8475,8619,8830,8854,8855,8936,8951,9006,9007,9124,9161,9184,9219,9262,9456,9720,9914,9972,9974,10113,5998,6372,6373,6460,6479,6480,6532,6896,7114,8544,8769,8960,8961,9034,9035,9310,9311,9312,9313,9517,9791,10098,10155,10156,6442,8368,8369,8820,8838,9792,10154,4605,4607,4608,4663,4671,4808,4822,4823,4847,4854,4855,4884,4940,5002,5063,5115,5143,5179,5181,5187,5189,5190,5216,5289,5312,5447,5513,5514,5515,5632,5633,5658,5659,5663,5716,5722,5724,5733,5739,5812])). % 187.94/187.73 cnf(13223,plain, % 187.94/187.73 (~E(f306(f179(x132231,f872(x132232,a859),x132233,f185(f872(x132231,a859))),x132234),f306(f214(f872(x132232,a859)),f306(f306(f43(f46(a1,x132235,x132235),f872(x132232,a859)),x132236),a119)))), % 187.94/187.73 inference(scs_inference,[],[4527,3510,11037,12085,12190,12282,12320,12328,12393,12522,12524,12949,12959,12964,12968,12974,12977,13001,13102,3517,12151,12560,12562,3518,12221,3237,12566,12568,3238,12589,3206,12469,4455,4456,11663,4201,12604,12607,3241,12580,3085,3143,12556,4438,3568,4420,10200,10210,10221,10330,10333,10336,10438,10551,10855,11022,11025,11223,11313,11320,11334,11384,11387,11409,11502,11548,11564,11864,11892,11904,11936,12034,12147,12154,12312,12363,12502,12621,12775,13026,4435,10422,10515,3329,3290,12576,3479,3189,4430,12692,12707,13048,2875,2876,2878,2879,2882,2883,2885,2886,2887,2889,2894,2898,2902,2911,2917,2921,2923,2924,2929,2930,2933,2934,2936,2937,2938,2939,2943,2948,2949,2952,2953,2956,2964,2970,2978,2987,2990,3004,3005,3018,3019,3020,3021,3028,3029,3030,3031,3032,3033,3044,3050,3162,4415,3064,3142,4416,3603,3117,11310,3251,3313,3224,3227,10203,10264,10267,10357,10360,10650,10929,11325,11328,11445,11489,11494,11593,12055,12258,12449,12504,12509,12511,12513,12530,12538,12542,12544,12595,12615,12826,12992,13101,13106,13122,3591,3838,3202,11590,12341,12345,12349,3212,3722,10969,11596,3106,3107,3922,4432,3552,3812,11360,3328,12532,3170,3134,3639,12550,3129,3928,3150,3644,3115,3095,3120,3149,3283,12026,12177,12396,12472,3330,10802,12148,3200,3201,3222,10463,3375,4513,10392,3895,4445,10255,10419,11220,11412,12308,12342,12346,4454,12316,3260,11685,11688,12918,13022,13073,13077,13081,4503,10972,11042,11263,11266,3664,3255,3376,3590,3368,3343,12586,3165,10322,10626,3166,4487,3433,3157,3086,3185,11350,4037,12331,12461,3897,10978,11104,11155,12292,12298,12410,12413,12436,4524,10907,11109,11214,11236,11271,11277,12237,4525,11011,11112,11217,4526,11115,11166,4528,11169,4529,3184,3472,12193,12234,12315,3628,4316,4317,3455,4443,11341,3570,3606,3777,3538,12809,12813,12817,12821,12831,3822,12187,3458,3704,3340,10341,10458,10529,10590,10593,10629,10723,10962,11860,11926,12002,12046,12125,12128,12440,12627,12686,12729,12732,12774,12792,13025,13030,3715,11581,4174,3253,3352,11700,12620,13121,3533,4493,10232,10235,10261,10731,10744,10865,11286,11353,11752,11757,11978,11981,12067,12076,12240,12335,12632,12651,12654,12678,12733,12896,12901,12925,12930,4509,11464,11497,11532,11561,12742,12746,3702,3480,3481,11881,12657,12660,12663,12666,12700,12703,13056,13060,13064,3847,3444,13057,3445,13061,3299,3300,3273,4490,3164,4440,3655,4171,3962,3464,4510,4031,11231,3589,3312,11709,11712,12158,12262,12420,4001,3961,11853,12208,3907,10799,12014,12040,12215,12443,12890,13072,3951,13076,3956,10981,12082,12157,12214,12261,12921,3957,3629,11863,12009,12092,12138,3990,3646,10984,11047,11128,11188,12033,12106,12358,12433,12446,12887,12958,12963,4514,10747,11120,12218,12971,3270,10350,10445,10576,10636,11437,11657,11703,11737,11833,11891,12099,12265,12480,3271,10705,10750,10753,10786,10812,10849,10887,10923,11907,11910,11913,11916,12113,12116,12119,12122,12201,12369,12416,12679,12706,12784,12795,12800,12803,12806,12839,12850,12911,12936,12939,3272,10433,10641,10726,10852,11740,11749,11839,11850,11869,11874,11919,11939,11956,12697,12843,12863,12897,12902,12926,12931,3348,12070,12762,12810,12814,12818,12822,12832,12836,4489,10298,10387,10500,10524,10768,10815,10825,11511,11611,11632,11635,11638,11654,11807,11810,11813,11816,11903,11922,11925,11935,11990,11993,11996,11999,12077,12169,12172,12268,12271,12334,12362,12399,12484,3428,10596,10860,10904,11177,11255,11425,12311,12487,12883,12953,4505,10777,10789,10896,10914,10917,10975,11061,11069,11085,11123,11140,11149,11185,11226,11246,11249,11252,11280,11293,11296,11682,11718,11984,11987,12021,12071,12102,12246,12289,12295,12381,12384,12403,12460,12466,12475,12496,12761,12778,12781,12872,12954,12996,13011,13014,13053,13097,13100,3334,10623,10653,10662,11206,11764,12400,12417,12743,12747,12750,3371,13039,13094,3365,3781,3720,10301,11584,11614,12724,4502,10252,10611,10614,11064,11082,11547,11602,11642,11770,11795,11798,11801,11804,12066,12942,3292,10656,10809,10880,11615,11769,11961,12180,12202,12771,13044,13120,3742,11715,12673,4081,3486,4500,3753,3788,4479,4482,4483,3244,3248,4481,4484,3246,3249,4480,4254,3760,3579,11577,11666,4177,11444,4516,10226,10229,10481,10532,10535,10540,10949,11419,11669,11773,4522,11143,11260,11302,3967,12229,3864,11299,11641,11645,11706,12319,12327,12409,12691,12948,13000,3709,10920,10926,10944,11888,12105,12377,12406,3566,11146,12131,12243,12253,12324,12372,12380,12493,3601,4035,3711,10659,11000,11152,11182,11193,12037,12323,12366,12988,3536,10579,10582,10665,10836,3535,4519,11578,4515,12641,4520,10716,10818,11131,11283,11422,11450,12196,12205,12249,12430,12490,4140,10792,12226,12252,4042,3741,12499,3689,3690,4517,10274,10277,10617,10620,11461,11646,12439,4518,11558,11651,3713,10585,10842,13029,3974,4521,4538,4564,4613,4615,4645,4662,4669,4670,4709,4739,4745,4830,4856,4857,4918,4919,4941,4942,4955,4959,4981,4988,5005,5008,5009,5010,5015,5016,5039,5066,5067,5077,5082,5090,5135,5136,5144,5154,5158,5160,5170,5172,5178,5182,5197,5204,5207,5208,5209,5213,5248,5261,5268,5270,5271,5275,5276,5277,5285,5288,5293,5294,5295,5302,5306,5307,5308,5317,5321,5322,5323,5328,5341,5350,5362,5364,5372,5373,5377,5381,5406,5412,5422,5423,5438,5451,5473,5479,5495,5496,5499,5518,5526,5527,5532,5533,5543,5544,5556,5560,5569,5570,5572,5587,5592,5603,5604,5616,5623,5637,5641,5644,5650,5651,5652,5655,5660,5697,5698,5701,5703,5706,5707,5708,5710,5712,5714,5719,5726,5741,5755,5760,5761,5774,5775,5780,5785,5787,5792,5833,5845,5854,5858,5869,5873,5874,5882,5896,5902,5920,5923,5935,5965,5979,6004,6024,6025,6028,6042,6044,6046,6048,6061,6062,6065,6067,6070,6071,6082,6088,6089,6090,6092,6094,6136,6137,6144,6154,6190,6192,6194,6196,6205,6207,6209,6215,6217,6223,6226,6234,6241,6242,6243,6248,6270,6271,6272,6274,6280,6285,6322,6323,6325,6326,6327,6329,6330,6331,6332,6341,6374,6375,6384,6405,6406,6426,6429,6440,6441,6447,6476,6478,6490,6528,6530,6531,6586,6610,6656,6676,6685,6686,6687,6688,6707,6708,6714,6726,6729,6731,6733,6734,6735,6737,6751,6762,6764,6765,6778,6781,6832,6843,6845,6849,6864,6865,6901,6913,6944,6963,6978,7032,7060,7115,7136,7145,7148,7203,7211,7269,7271,7285,7295,7296,7297,7316,7322,7324,7373,7383,7386,7402,7451,7453,7456,7499,7500,7518,7585,7604,7628,7650,7665,7680,7691,7699,7700,7728,7731,7733,7741,7779,7790,7815,7873,7907,7939,7986,8002,8008,8019,8020,8095,8149,8168,8192,8212,8236,8335,8337,8343,8361,8365,8379,8402,8413,8415,8430,8436,8440,8465,8479,8480,8496,8497,8502,8503,8504,8505,8506,8524,8525,8526,8535,8549,8551,8563,8567,8569,8570,8571,8579,8584,8611,8612,8641,8654,8658,8676,8698,8699,8700,8701,8714,8715,8737,8747,8756,8757,8758,8759,8761,8783,8784,8795,8840,8846,8852,8865,8870,8872,8875,8876,8880,8889,8972,9003,9004,9005,9020,9038,9043,9070,9071,9114,9117,9144,9189,9190,9191,9207,9233,9247,9253,9256,9279,9280,9308,9371,9407,9408,9409,9434,9435,9453,9471,9477,9493,9516,9538,9546,9547,9548,9549,9565,9567,9572,9603,9604,9610,9611,9654,9655,9686,9696,9706,9708,9709,9719,9733,9737,9765,9797,9802,9859,9902,9903,9905,9915,9916,9936,9941,9964,9969,9984,10036,10110,10111,10168,10184,2,8,9,4551,4552,4570,4601,4602,4604,4631,4637,4638,4649,4698,4700,4730,4744,4774,4871,4872,4886,4906,4962,4963,4966,4967,4969,4971,4972,4984,4985,4995,5006,5007,5013,5032,5033,5054,5059,5060,5061,5062,5065,5073,5076,5083,5084,5085,5150,5156,5157,5164,5194,5205,5211,5227,5247,5254,5255,5256,5265,5274,5281,5283,5284,5290,5298,5299,5309,5313,5314,5315,5316,5318,5319,5324,5325,5326,5327,5358,5359,5360,5368,5369,5370,5371,5414,5419,5421,5458,5460,5461,5463,5464,5466,5467,5469,5478,5483,5485,5486,5487,5488,5489,5490,5497,5507,5510,5521,5537,5538,5541,5550,5552,5553,5554,5579,5589,5606,5607,5617,5618,5620,5622,5627,5662,5666,5668,5728,5762,5763,5767,5773,5776,5777,5778,5779,5786,5797,5798,5800,5801,5809,5830,5861,5877,5880,5881,5883,5892,5910,5914,5917,5918,5919,5937,5950,5951,5981,5982,5986,6006,6009,6013,6032,6037,6038,6063,6066,6073,6081,6087,6091,6098,6099,6100,6101,6139,6155,6208,6244,6246,6267,6268,6273,6277,6278,6281,6288,6297,6314,6334,6335,6342,6352,6367,6387,6393,6395,6410,6411,6415,6417,6418,6419,6421,6423,6424,6425,6428,6433,6434,6436,6437,6443,6445,6486,6489,6503,6505,6506,6507,6543,6548,6550,6555,6556,6564,6568,6581,6605,6606,6608,6609,6621,6625,6627,6647,6650,6669,6702,6703,6704,6709,6722,6741,6743,6745,6747,6752,6758,6760,6775,6782,6818,6819,6820,6834,6835,6837,6838,6855,6857,6873,6899,6921,6932,6934,6936,6938,6939,6940,6975,6976,6981,6982,6990,6992,6993,6994,7013,7022,7023,7035,7045,7084,7094,7098,7105,7116,7117,7122,7124,7130,7138,7139,7152,7169,7187,7189,7206,7255,7256,7257,7259,7261,7265,7270,7292,7337,7369,7384,7389,7401,7434,7437,7460,7484,7501,7504,7505,7515,7534,7536,7538,7540,7541,7542,7567,7593,7594,7627,7629,7630,7631,7636,7657,7666,7677,7682,7688,7690,7696,7707,7708,7710,7730,7734,7739,7762,7828,7829,7876,7885,7886,7909,7910,7927,7928,7993,7994,8022,8051,8062,8064,8073,8085,8118,8124,8131,8144,8163,8169,8191,8234,8264,8276,8295,8298,8328,8352,8416,8417,8420,8422,8441,8528,8529,8530,8531,8558,8587,8615,8657,8675,8731,8776,8779,8792,8799,8837,8885,8886,8903,8904,9045,9049,9068,9078,9103,9105,9108,9112,9115,9116,9129,9130,9151,9157,9169,9218,9237,9257,9292,9293,9300,9363,9368,9404,9411,9414,9417,9418,9433,9449,9458,9470,9481,9482,9485,9487,9514,9636,9681,9682,9726,9772,9887,9888,9945,10013,10089,10102,10107,3,2601,2603,2604,2605,2606,2607,2614,2616,2617,2618,2619,2620,2621,2622,2623,2624,2625,2627,2628,2629,2630,2642,2646,2647,2650,2653,2658,2659,2661,2662,2663,2664,2665,2671,2672,2674,2676,2677,2678,2679,2680,2683,2686,2693,2694,2705,2707,2708,2709,2710,2728,2746,2747,2748,2767,2775,2776,2777,2781,2788,2790,2797,2800,2801,2802,2821,2824,2830,2848,2850,2851,5186,5246,5344,5430,5431,5432,5508,5605,5636,5669,5685,5687,5693,5756,5757,5758,5759,5765,5799,5932,5971,5980,6003,6040,6074,6078,6225,6230,6265,6266,6286,6290,6292,6299,6300,6301,6302,6303,6304,6305,6306,6389,6457,6458,6542,6575,6576,6618,6619,6759,6774,6846,6847,6851,6874,6897,6905,6907,6954,6979,6980,6998,6999,7034,7078,7079,7176,7237,7238,7239,7240,7254,7286,7342,7343,7352,7359,7360,7372,7404,7405,7406,7407,7549,7551,7552,7553,7559,7560,7770,7776,7777,7787,7826,7905,7947,8005,8027,8028,8043,8103,8205,8274,8275,8277,8313,8375,8376,8449,8472,8473,8474,8475,8619,8830,8854,8855,8936,8951,9006,9007,9124,9161,9184,9219,9262,9456,9720,9914,9972,9974,10113,5998,6372,6373,6460,6479,6480,6532,6896,7114,8544,8769,8960,8961,9034,9035,9310,9311,9312,9313,9517,9791,10098,10155,10156,6442,8368,8369,8820,8838,9792,10154,4605,4607,4608,4663,4671,4808,4822,4823,4847,4854,4855,4884,4940,5002,5063,5115,5143,5179,5181,5187,5189,5190,5216,5289,5312,5447,5513,5514,5515,5632,5633,5658,5659,5663,5716,5722,5724,5733,5739,5812,5890,5956,6021])). % 187.94/187.73 cnf(13227,plain, % 187.94/187.73 (~P1(f306(f63(x132271),f41(f872(x132271,a859),f231(f872(f872(x132271,a859),a859)))))), % 187.94/187.73 inference(scs_inference,[],[4527,3510,11037,12085,12190,12282,12320,12328,12393,12522,12524,12949,12959,12964,12968,12974,12977,13001,13102,3517,12151,12560,12562,3518,12221,3237,12566,12568,3238,12589,3206,12469,4455,4456,11663,4201,12604,12607,3241,12580,3085,3143,12556,4438,3568,4420,10200,10210,10221,10330,10333,10336,10438,10551,10855,11022,11025,11223,11313,11320,11334,11384,11387,11409,11502,11548,11564,11864,11892,11904,11936,12034,12147,12154,12312,12363,12502,12621,12775,13026,4435,10422,10515,3329,3290,12576,3479,3189,4430,12692,12707,13048,2875,2876,2878,2879,2882,2883,2885,2886,2887,2889,2894,2898,2902,2911,2917,2921,2923,2924,2929,2930,2933,2934,2936,2937,2938,2939,2943,2948,2949,2952,2953,2956,2964,2970,2978,2987,2990,3004,3005,3018,3019,3020,3021,3028,3029,3030,3031,3032,3033,3044,3050,3162,4415,3064,3142,4416,3603,3117,11310,3251,3313,3224,3227,10203,10264,10267,10357,10360,10650,10929,11325,11328,11445,11489,11494,11593,12055,12258,12449,12504,12509,12511,12513,12530,12538,12542,12544,12595,12615,12826,12992,13101,13106,13122,3591,3838,3202,11590,12341,12345,12349,3212,3722,10969,11596,3106,3107,3922,4432,3552,3812,11360,3328,12532,3170,3134,3639,12550,3129,3928,3150,3644,3115,3095,3120,3149,3283,12026,12177,12396,12472,3330,10802,12148,3200,3201,3222,10463,3375,4513,10392,3895,4445,10255,10419,11220,11412,12308,12342,12346,4454,12316,3260,11685,11688,12918,13022,13073,13077,13081,4503,10972,11042,11263,11266,3664,3255,3376,3590,3368,3343,12586,3165,10322,10626,3166,4487,3433,3157,3086,3185,11350,4037,12331,12461,3897,10978,11104,11155,12292,12298,12410,12413,12436,4524,10907,11109,11214,11236,11271,11277,12237,4525,11011,11112,11217,4526,11115,11166,4528,11169,4529,3184,3472,12193,12234,12315,3628,4316,4317,3455,4443,11341,3570,3606,3777,3538,12809,12813,12817,12821,12831,3822,12187,3458,3704,3340,10341,10458,10529,10590,10593,10629,10723,10962,11860,11926,12002,12046,12125,12128,12440,12627,12686,12729,12732,12774,12792,13025,13030,3715,11581,4174,3253,3352,11700,12620,13121,3533,4493,10232,10235,10261,10731,10744,10865,11286,11353,11752,11757,11978,11981,12067,12076,12240,12335,12632,12651,12654,12678,12733,12896,12901,12925,12930,4509,11464,11497,11532,11561,12742,12746,3702,3480,3481,11881,12657,12660,12663,12666,12700,12703,13056,13060,13064,3847,3444,13057,3445,13061,3299,3300,3273,4490,3164,4440,3655,4171,3962,3464,4510,4031,11231,3589,3312,11709,11712,12158,12262,12420,4001,3961,11853,12208,3907,10799,12014,12040,12215,12443,12890,13072,3951,13076,3956,10981,12082,12157,12214,12261,12921,3957,3629,11863,12009,12092,12138,3990,3646,10984,11047,11128,11188,12033,12106,12358,12433,12446,12887,12958,12963,4514,10747,11120,12218,12971,3270,10350,10445,10576,10636,11437,11657,11703,11737,11833,11891,12099,12265,12480,3271,10705,10750,10753,10786,10812,10849,10887,10923,11907,11910,11913,11916,12113,12116,12119,12122,12201,12369,12416,12679,12706,12784,12795,12800,12803,12806,12839,12850,12911,12936,12939,3272,10433,10641,10726,10852,11740,11749,11839,11850,11869,11874,11919,11939,11956,12697,12843,12863,12897,12902,12926,12931,3348,12070,12762,12810,12814,12818,12822,12832,12836,4489,10298,10387,10500,10524,10768,10815,10825,11511,11611,11632,11635,11638,11654,11807,11810,11813,11816,11903,11922,11925,11935,11990,11993,11996,11999,12077,12169,12172,12268,12271,12334,12362,12399,12484,3428,10596,10860,10904,11177,11255,11425,12311,12487,12883,12953,4505,10777,10789,10896,10914,10917,10975,11061,11069,11085,11123,11140,11149,11185,11226,11246,11249,11252,11280,11293,11296,11682,11718,11984,11987,12021,12071,12102,12246,12289,12295,12381,12384,12403,12460,12466,12475,12496,12761,12778,12781,12872,12954,12996,13011,13014,13053,13097,13100,3334,10623,10653,10662,11206,11764,12400,12417,12743,12747,12750,3371,13039,13094,3365,3781,3720,10301,11584,11614,12724,4502,10252,10611,10614,11064,11082,11547,11602,11642,11770,11795,11798,11801,11804,12066,12942,3292,10656,10809,10880,11615,11769,11961,12180,12202,12771,13044,13120,3742,11715,12673,4081,3486,4500,3753,3788,4479,4482,4483,3244,3248,4481,4484,3246,3249,4480,4254,3760,3579,11577,11666,4177,11444,4516,10226,10229,10481,10532,10535,10540,10949,11419,11669,11773,4522,11143,11260,11302,3967,12229,3864,11299,11641,11645,11706,12319,12327,12409,12691,12948,13000,3709,10920,10926,10944,11888,12105,12377,12406,3566,11146,12131,12243,12253,12324,12372,12380,12493,3601,4035,3711,10659,11000,11152,11182,11193,12037,12323,12366,12988,3536,10579,10582,10665,10836,3535,4519,11578,4515,12641,4520,10716,10818,11131,11283,11422,11450,12196,12205,12249,12430,12490,4140,10792,12226,12252,4042,3741,12499,3689,3690,4517,10274,10277,10617,10620,11461,11646,12439,4518,11558,11651,3713,10585,10842,13029,3974,4521,4538,4564,4613,4615,4645,4662,4669,4670,4709,4739,4745,4830,4856,4857,4918,4919,4941,4942,4955,4959,4981,4988,5005,5008,5009,5010,5015,5016,5039,5066,5067,5077,5082,5090,5135,5136,5144,5154,5158,5160,5170,5172,5178,5182,5197,5204,5207,5208,5209,5213,5248,5261,5268,5270,5271,5275,5276,5277,5285,5288,5293,5294,5295,5302,5306,5307,5308,5317,5321,5322,5323,5328,5341,5350,5362,5364,5372,5373,5377,5381,5406,5412,5422,5423,5438,5451,5473,5479,5495,5496,5499,5518,5526,5527,5532,5533,5543,5544,5556,5560,5569,5570,5572,5587,5592,5603,5604,5616,5623,5637,5641,5644,5650,5651,5652,5655,5660,5697,5698,5701,5703,5706,5707,5708,5710,5712,5714,5719,5726,5741,5755,5760,5761,5774,5775,5780,5785,5787,5792,5833,5845,5854,5858,5869,5873,5874,5882,5896,5902,5920,5923,5935,5965,5979,6004,6024,6025,6028,6042,6044,6046,6048,6061,6062,6065,6067,6070,6071,6082,6088,6089,6090,6092,6094,6136,6137,6144,6154,6190,6192,6194,6196,6205,6207,6209,6215,6217,6223,6226,6234,6241,6242,6243,6248,6270,6271,6272,6274,6280,6285,6322,6323,6325,6326,6327,6329,6330,6331,6332,6341,6374,6375,6384,6405,6406,6426,6429,6440,6441,6447,6476,6478,6490,6528,6530,6531,6586,6610,6656,6676,6685,6686,6687,6688,6707,6708,6714,6726,6729,6731,6733,6734,6735,6737,6751,6762,6764,6765,6778,6781,6832,6843,6845,6849,6864,6865,6901,6913,6944,6963,6978,7032,7060,7115,7136,7145,7148,7203,7211,7269,7271,7285,7295,7296,7297,7316,7322,7324,7373,7383,7386,7402,7451,7453,7456,7499,7500,7518,7585,7604,7628,7650,7665,7680,7691,7699,7700,7728,7731,7733,7741,7779,7790,7815,7873,7907,7939,7986,8002,8008,8019,8020,8095,8149,8168,8192,8212,8236,8335,8337,8343,8361,8365,8379,8402,8413,8415,8430,8436,8440,8465,8479,8480,8496,8497,8502,8503,8504,8505,8506,8524,8525,8526,8535,8549,8551,8563,8567,8569,8570,8571,8579,8584,8611,8612,8641,8654,8658,8676,8698,8699,8700,8701,8714,8715,8737,8747,8756,8757,8758,8759,8761,8783,8784,8795,8840,8846,8852,8865,8870,8872,8875,8876,8880,8889,8972,9003,9004,9005,9020,9038,9043,9070,9071,9114,9117,9144,9189,9190,9191,9207,9233,9247,9253,9256,9279,9280,9308,9371,9407,9408,9409,9434,9435,9453,9471,9477,9493,9516,9538,9546,9547,9548,9549,9565,9567,9572,9603,9604,9610,9611,9654,9655,9686,9696,9706,9708,9709,9719,9733,9737,9765,9797,9802,9859,9902,9903,9905,9915,9916,9936,9941,9964,9969,9984,10036,10110,10111,10168,10184,2,8,9,4551,4552,4570,4601,4602,4604,4631,4637,4638,4649,4698,4700,4730,4744,4774,4871,4872,4886,4906,4962,4963,4966,4967,4969,4971,4972,4984,4985,4995,5006,5007,5013,5032,5033,5054,5059,5060,5061,5062,5065,5073,5076,5083,5084,5085,5150,5156,5157,5164,5194,5205,5211,5227,5247,5254,5255,5256,5265,5274,5281,5283,5284,5290,5298,5299,5309,5313,5314,5315,5316,5318,5319,5324,5325,5326,5327,5358,5359,5360,5368,5369,5370,5371,5414,5419,5421,5458,5460,5461,5463,5464,5466,5467,5469,5478,5483,5485,5486,5487,5488,5489,5490,5497,5507,5510,5521,5537,5538,5541,5550,5552,5553,5554,5579,5589,5606,5607,5617,5618,5620,5622,5627,5662,5666,5668,5728,5762,5763,5767,5773,5776,5777,5778,5779,5786,5797,5798,5800,5801,5809,5830,5861,5877,5880,5881,5883,5892,5910,5914,5917,5918,5919,5937,5950,5951,5981,5982,5986,6006,6009,6013,6032,6037,6038,6063,6066,6073,6081,6087,6091,6098,6099,6100,6101,6139,6155,6208,6244,6246,6267,6268,6273,6277,6278,6281,6288,6297,6314,6334,6335,6342,6352,6367,6387,6393,6395,6410,6411,6415,6417,6418,6419,6421,6423,6424,6425,6428,6433,6434,6436,6437,6443,6445,6486,6489,6503,6505,6506,6507,6543,6548,6550,6555,6556,6564,6568,6581,6605,6606,6608,6609,6621,6625,6627,6647,6650,6669,6702,6703,6704,6709,6722,6741,6743,6745,6747,6752,6758,6760,6775,6782,6818,6819,6820,6834,6835,6837,6838,6855,6857,6873,6899,6921,6932,6934,6936,6938,6939,6940,6975,6976,6981,6982,6990,6992,6993,6994,7013,7022,7023,7035,7045,7084,7094,7098,7105,7116,7117,7122,7124,7130,7138,7139,7152,7169,7187,7189,7206,7255,7256,7257,7259,7261,7265,7270,7292,7337,7369,7384,7389,7401,7434,7437,7460,7484,7501,7504,7505,7515,7534,7536,7538,7540,7541,7542,7567,7593,7594,7627,7629,7630,7631,7636,7657,7666,7677,7682,7688,7690,7696,7707,7708,7710,7730,7734,7739,7762,7828,7829,7876,7885,7886,7909,7910,7927,7928,7993,7994,8022,8051,8062,8064,8073,8085,8118,8124,8131,8144,8163,8169,8191,8234,8264,8276,8295,8298,8328,8352,8416,8417,8420,8422,8441,8528,8529,8530,8531,8558,8587,8615,8657,8675,8731,8776,8779,8792,8799,8837,8885,8886,8903,8904,9045,9049,9068,9078,9103,9105,9108,9112,9115,9116,9129,9130,9151,9157,9169,9218,9237,9257,9292,9293,9300,9363,9368,9404,9411,9414,9417,9418,9433,9449,9458,9470,9481,9482,9485,9487,9514,9636,9681,9682,9726,9772,9887,9888,9945,10013,10089,10102,10107,3,2601,2603,2604,2605,2606,2607,2614,2616,2617,2618,2619,2620,2621,2622,2623,2624,2625,2627,2628,2629,2630,2642,2646,2647,2650,2653,2658,2659,2661,2662,2663,2664,2665,2671,2672,2674,2676,2677,2678,2679,2680,2683,2686,2693,2694,2705,2707,2708,2709,2710,2728,2746,2747,2748,2767,2775,2776,2777,2781,2788,2790,2797,2800,2801,2802,2821,2824,2830,2848,2850,2851,5186,5246,5344,5430,5431,5432,5508,5605,5636,5669,5685,5687,5693,5756,5757,5758,5759,5765,5799,5932,5971,5980,6003,6040,6074,6078,6225,6230,6265,6266,6286,6290,6292,6299,6300,6301,6302,6303,6304,6305,6306,6389,6457,6458,6542,6575,6576,6618,6619,6759,6774,6846,6847,6851,6874,6897,6905,6907,6954,6979,6980,6998,6999,7034,7078,7079,7176,7237,7238,7239,7240,7254,7286,7342,7343,7352,7359,7360,7372,7404,7405,7406,7407,7549,7551,7552,7553,7559,7560,7770,7776,7777,7787,7826,7905,7947,8005,8027,8028,8043,8103,8205,8274,8275,8277,8313,8375,8376,8449,8472,8473,8474,8475,8619,8830,8854,8855,8936,8951,9006,9007,9124,9161,9184,9219,9262,9456,9720,9914,9972,9974,10113,5998,6372,6373,6460,6479,6480,6532,6896,7114,8544,8769,8960,8961,9034,9035,9310,9311,9312,9313,9517,9791,10098,10155,10156,6442,8368,8369,8820,8838,9792,10154,4605,4607,4608,4663,4671,4808,4822,4823,4847,4854,4855,4884,4940,5002,5063,5115,5143,5179,5181,5187,5189,5190,5216,5289,5312,5447,5513,5514,5515,5632,5633,5658,5659,5663,5716,5722,5724,5733,5739,5812,5890,5956,6021,6047,6211])). % 187.94/187.73 cnf(13241,plain, % 187.94/187.73 (~P1(f306(f306(f221(a865),f2(a865)),f185(a865)))), % 187.94/187.73 inference(scs_inference,[],[4527,3510,11037,12085,12190,12282,12320,12328,12393,12522,12524,12949,12959,12964,12968,12974,12977,13001,13102,3517,12151,12560,12562,3518,12221,3237,12566,12568,3238,12589,3206,12469,4455,4456,11663,4201,12604,12607,3241,12580,3085,3143,12556,4438,3568,4420,10200,10210,10221,10330,10333,10336,10438,10551,10855,11022,11025,11223,11313,11320,11334,11384,11387,11409,11502,11548,11564,11864,11892,11904,11936,12034,12147,12154,12312,12363,12502,12621,12775,13026,4435,10422,10515,3329,3290,12576,3479,3189,4430,12692,12707,13048,2875,2876,2878,2879,2882,2883,2885,2886,2887,2889,2894,2898,2902,2911,2917,2921,2923,2924,2929,2930,2933,2934,2936,2937,2938,2939,2943,2948,2949,2952,2953,2956,2964,2970,2978,2987,2990,3004,3005,3018,3019,3020,3021,3028,3029,3030,3031,3032,3033,3044,3050,3162,4415,3064,3142,4416,3603,3117,11310,3251,3313,3224,3227,10203,10264,10267,10357,10360,10650,10929,11325,11328,11445,11489,11494,11593,12055,12258,12449,12504,12509,12511,12513,12530,12538,12542,12544,12595,12615,12826,12992,13101,13106,13122,3591,3838,3202,11590,12341,12345,12349,3212,3722,10969,11596,3106,3107,3922,4432,3552,3812,11360,3328,12532,3170,3134,3639,12550,3129,3928,3150,3644,3115,3095,3120,3149,3283,12026,12177,12396,12472,3330,10802,12148,3200,3201,3222,10463,3375,4513,10392,3895,4445,10255,10419,11220,11412,12308,12342,12346,4454,12316,3260,11685,11688,12918,13022,13073,13077,13081,4503,10972,11042,11263,11266,3664,3255,3376,3590,3368,3343,12586,3165,10322,10626,3166,4487,3433,3157,3086,3185,11350,4037,12331,12461,3897,10978,11104,11155,12292,12298,12410,12413,12436,4524,10907,11109,11214,11236,11271,11277,12237,4525,11011,11112,11217,4526,11115,11166,4528,11169,4529,3184,3472,12193,12234,12315,3628,4316,4317,3455,4443,11341,3570,3606,3777,3538,12809,12813,12817,12821,12831,3822,12187,3458,3704,3340,10341,10458,10529,10590,10593,10629,10723,10962,11860,11926,12002,12046,12125,12128,12440,12627,12686,12729,12732,12774,12792,13025,13030,3715,11581,4174,3253,3352,11700,12620,13121,3533,4493,10232,10235,10261,10731,10744,10865,11286,11353,11752,11757,11978,11981,12067,12076,12240,12335,12632,12651,12654,12678,12733,12896,12901,12925,12930,4509,11464,11497,11532,11561,12742,12746,3702,3480,3481,11881,12657,12660,12663,12666,12700,12703,13056,13060,13064,3847,3444,13057,3445,13061,3299,3300,3273,4490,3164,4440,3655,4171,3962,3464,4510,4031,11231,3589,3312,11709,11712,12158,12262,12420,4001,3961,11853,12208,3907,10799,12014,12040,12215,12443,12890,13072,3951,13076,3956,10981,12082,12157,12214,12261,12921,3957,3629,11863,12009,12092,12138,3990,3646,10984,11047,11128,11188,12033,12106,12358,12433,12446,12887,12958,12963,4514,10747,11120,12218,12971,3270,10350,10445,10576,10636,11437,11657,11703,11737,11833,11891,12099,12265,12480,3271,10705,10750,10753,10786,10812,10849,10887,10923,11907,11910,11913,11916,12113,12116,12119,12122,12201,12369,12416,12679,12706,12784,12795,12800,12803,12806,12839,12850,12911,12936,12939,3272,10433,10641,10726,10852,11740,11749,11839,11850,11869,11874,11919,11939,11956,12697,12843,12863,12897,12902,12926,12931,3348,12070,12762,12810,12814,12818,12822,12832,12836,4489,10298,10387,10500,10524,10768,10815,10825,11511,11611,11632,11635,11638,11654,11807,11810,11813,11816,11903,11922,11925,11935,11990,11993,11996,11999,12077,12169,12172,12268,12271,12334,12362,12399,12484,3428,10596,10860,10904,11177,11255,11425,12311,12487,12883,12953,4505,10777,10789,10896,10914,10917,10975,11061,11069,11085,11123,11140,11149,11185,11226,11246,11249,11252,11280,11293,11296,11682,11718,11984,11987,12021,12071,12102,12246,12289,12295,12381,12384,12403,12460,12466,12475,12496,12761,12778,12781,12872,12954,12996,13011,13014,13053,13097,13100,3334,10623,10653,10662,11206,11764,12400,12417,12743,12747,12750,3371,13039,13094,3365,3781,3720,10301,11584,11614,12724,4502,10252,10611,10614,11064,11082,11547,11602,11642,11770,11795,11798,11801,11804,12066,12942,3292,10656,10809,10880,11615,11769,11961,12180,12202,12771,13044,13120,3742,11715,12673,4081,3486,4500,3753,3788,4479,4482,4483,3244,3248,4481,4484,3246,3249,4480,4254,3760,3579,11577,11666,4177,11444,4516,10226,10229,10481,10532,10535,10540,10949,11419,11669,11773,4522,11143,11260,11302,3967,12229,3864,11299,11641,11645,11706,12319,12327,12409,12691,12948,13000,3709,10920,10926,10944,11888,12105,12377,12406,3566,11146,12131,12243,12253,12324,12372,12380,12493,3601,4035,3711,10659,11000,11152,11182,11193,12037,12323,12366,12988,3536,10579,10582,10665,10836,3535,4519,11578,4515,12641,4520,10716,10818,11131,11283,11422,11450,12196,12205,12249,12430,12490,4140,10792,12226,12252,4042,3741,12499,3689,3690,4517,10274,10277,10617,10620,11461,11646,12439,4518,11558,11651,3713,10585,10842,13029,3974,4521,4538,4564,4613,4615,4645,4662,4669,4670,4709,4739,4745,4830,4856,4857,4918,4919,4941,4942,4955,4959,4981,4988,5005,5008,5009,5010,5015,5016,5039,5066,5067,5077,5082,5090,5135,5136,5144,5154,5158,5160,5170,5172,5178,5182,5197,5204,5207,5208,5209,5213,5248,5261,5268,5270,5271,5275,5276,5277,5285,5288,5293,5294,5295,5302,5306,5307,5308,5317,5321,5322,5323,5328,5341,5350,5362,5364,5372,5373,5377,5381,5406,5412,5422,5423,5438,5451,5473,5479,5495,5496,5499,5518,5526,5527,5532,5533,5543,5544,5556,5560,5569,5570,5572,5587,5592,5603,5604,5616,5623,5637,5641,5644,5650,5651,5652,5655,5660,5697,5698,5701,5703,5706,5707,5708,5710,5712,5714,5719,5726,5741,5755,5760,5761,5774,5775,5780,5785,5787,5792,5833,5845,5854,5858,5869,5873,5874,5882,5896,5902,5920,5923,5935,5965,5979,6004,6024,6025,6028,6042,6044,6046,6048,6061,6062,6065,6067,6070,6071,6082,6088,6089,6090,6092,6094,6136,6137,6144,6154,6190,6192,6194,6196,6205,6207,6209,6215,6217,6223,6226,6234,6241,6242,6243,6248,6270,6271,6272,6274,6280,6285,6322,6323,6325,6326,6327,6329,6330,6331,6332,6341,6374,6375,6384,6405,6406,6426,6429,6440,6441,6447,6476,6478,6490,6528,6530,6531,6586,6610,6656,6676,6685,6686,6687,6688,6707,6708,6714,6726,6729,6731,6733,6734,6735,6737,6751,6762,6764,6765,6778,6781,6832,6843,6845,6849,6864,6865,6901,6913,6944,6963,6978,7032,7060,7115,7136,7145,7148,7203,7211,7269,7271,7285,7295,7296,7297,7316,7322,7324,7373,7383,7386,7402,7451,7453,7456,7499,7500,7518,7585,7604,7628,7650,7665,7680,7691,7699,7700,7728,7731,7733,7741,7779,7790,7815,7873,7907,7939,7986,8002,8008,8019,8020,8095,8149,8168,8192,8212,8236,8335,8337,8343,8361,8365,8379,8402,8413,8415,8430,8436,8440,8465,8479,8480,8496,8497,8502,8503,8504,8505,8506,8524,8525,8526,8535,8549,8551,8563,8567,8569,8570,8571,8579,8584,8611,8612,8641,8654,8658,8676,8698,8699,8700,8701,8714,8715,8737,8747,8756,8757,8758,8759,8761,8783,8784,8795,8840,8846,8852,8865,8870,8872,8875,8876,8880,8889,8972,9003,9004,9005,9020,9038,9043,9070,9071,9114,9117,9144,9189,9190,9191,9207,9233,9247,9253,9256,9279,9280,9308,9371,9407,9408,9409,9434,9435,9453,9471,9477,9493,9516,9538,9546,9547,9548,9549,9565,9567,9572,9603,9604,9610,9611,9654,9655,9686,9696,9706,9708,9709,9719,9733,9737,9765,9797,9802,9859,9902,9903,9905,9915,9916,9936,9941,9964,9969,9984,10036,10110,10111,10168,10184,2,8,9,4551,4552,4570,4601,4602,4604,4631,4637,4638,4649,4698,4700,4730,4744,4774,4871,4872,4886,4906,4962,4963,4966,4967,4969,4971,4972,4984,4985,4995,5006,5007,5013,5032,5033,5054,5059,5060,5061,5062,5065,5073,5076,5083,5084,5085,5150,5156,5157,5164,5194,5205,5211,5227,5247,5254,5255,5256,5265,5274,5281,5283,5284,5290,5298,5299,5309,5313,5314,5315,5316,5318,5319,5324,5325,5326,5327,5358,5359,5360,5368,5369,5370,5371,5414,5419,5421,5458,5460,5461,5463,5464,5466,5467,5469,5478,5483,5485,5486,5487,5488,5489,5490,5497,5507,5510,5521,5537,5538,5541,5550,5552,5553,5554,5579,5589,5606,5607,5617,5618,5620,5622,5627,5662,5666,5668,5728,5762,5763,5767,5773,5776,5777,5778,5779,5786,5797,5798,5800,5801,5809,5830,5861,5877,5880,5881,5883,5892,5910,5914,5917,5918,5919,5937,5950,5951,5981,5982,5986,6006,6009,6013,6032,6037,6038,6063,6066,6073,6081,6087,6091,6098,6099,6100,6101,6139,6155,6208,6244,6246,6267,6268,6273,6277,6278,6281,6288,6297,6314,6334,6335,6342,6352,6367,6387,6393,6395,6410,6411,6415,6417,6418,6419,6421,6423,6424,6425,6428,6433,6434,6436,6437,6443,6445,6486,6489,6503,6505,6506,6507,6543,6548,6550,6555,6556,6564,6568,6581,6605,6606,6608,6609,6621,6625,6627,6647,6650,6669,6702,6703,6704,6709,6722,6741,6743,6745,6747,6752,6758,6760,6775,6782,6818,6819,6820,6834,6835,6837,6838,6855,6857,6873,6899,6921,6932,6934,6936,6938,6939,6940,6975,6976,6981,6982,6990,6992,6993,6994,7013,7022,7023,7035,7045,7084,7094,7098,7105,7116,7117,7122,7124,7130,7138,7139,7152,7169,7187,7189,7206,7255,7256,7257,7259,7261,7265,7270,7292,7337,7369,7384,7389,7401,7434,7437,7460,7484,7501,7504,7505,7515,7534,7536,7538,7540,7541,7542,7567,7593,7594,7627,7629,7630,7631,7636,7657,7666,7677,7682,7688,7690,7696,7707,7708,7710,7730,7734,7739,7762,7828,7829,7876,7885,7886,7909,7910,7927,7928,7993,7994,8022,8051,8062,8064,8073,8085,8118,8124,8131,8144,8163,8169,8191,8234,8264,8276,8295,8298,8328,8352,8416,8417,8420,8422,8441,8528,8529,8530,8531,8558,8587,8615,8657,8675,8731,8776,8779,8792,8799,8837,8885,8886,8903,8904,9045,9049,9068,9078,9103,9105,9108,9112,9115,9116,9129,9130,9151,9157,9169,9218,9237,9257,9292,9293,9300,9363,9368,9404,9411,9414,9417,9418,9433,9449,9458,9470,9481,9482,9485,9487,9514,9636,9681,9682,9726,9772,9887,9888,9945,10013,10089,10102,10107,3,2601,2603,2604,2605,2606,2607,2614,2616,2617,2618,2619,2620,2621,2622,2623,2624,2625,2627,2628,2629,2630,2642,2646,2647,2650,2653,2658,2659,2661,2662,2663,2664,2665,2671,2672,2674,2676,2677,2678,2679,2680,2683,2686,2693,2694,2705,2707,2708,2709,2710,2728,2746,2747,2748,2767,2775,2776,2777,2781,2788,2790,2797,2800,2801,2802,2821,2824,2830,2848,2850,2851,5186,5246,5344,5430,5431,5432,5508,5605,5636,5669,5685,5687,5693,5756,5757,5758,5759,5765,5799,5932,5971,5980,6003,6040,6074,6078,6225,6230,6265,6266,6286,6290,6292,6299,6300,6301,6302,6303,6304,6305,6306,6389,6457,6458,6542,6575,6576,6618,6619,6759,6774,6846,6847,6851,6874,6897,6905,6907,6954,6979,6980,6998,6999,7034,7078,7079,7176,7237,7238,7239,7240,7254,7286,7342,7343,7352,7359,7360,7372,7404,7405,7406,7407,7549,7551,7552,7553,7559,7560,7770,7776,7777,7787,7826,7905,7947,8005,8027,8028,8043,8103,8205,8274,8275,8277,8313,8375,8376,8449,8472,8473,8474,8475,8619,8830,8854,8855,8936,8951,9006,9007,9124,9161,9184,9219,9262,9456,9720,9914,9972,9974,10113,5998,6372,6373,6460,6479,6480,6532,6896,7114,8544,8769,8960,8961,9034,9035,9310,9311,9312,9313,9517,9791,10098,10155,10156,6442,8368,8369,8820,8838,9792,10154,4605,4607,4608,4663,4671,4808,4822,4823,4847,4854,4855,4884,4940,5002,5063,5115,5143,5179,5181,5187,5189,5190,5216,5289,5312,5447,5513,5514,5515,5632,5633,5658,5659,5663,5716,5722,5724,5733,5739,5812,5890,5956,6021,6047,6211,6333,6487,6694,6695,6844,6908,6949])). % 187.94/187.73 cnf(13380,plain, % 187.94/187.73 (P1(f306(f306(f308(x133801),f306(x133802,x133803)),f306(f285(x133804,x133801,x133802),f231(f872(x133804,a859)))))), % 187.94/187.73 inference(rename_variables,[],[3864])). % 187.94/187.73 cnf(13388,plain, % 187.94/187.73 (E(f306(x133881,f667(f306(x133881,x133882),f306(f214(x133883),x133882),x133881,x133884,x133883)),f306(x133881,x133882))), % 187.94/187.73 inference(rename_variables,[],[11095])). % 187.94/187.73 cnf(13391,plain, % 187.94/187.73 (E(f306(x133911,f667(f306(x133911,x133912),f306(f214(x133913),x133912),x133911,x133914,x133913)),f306(x133911,x133912))), % 187.94/187.73 inference(rename_variables,[],[11095])). % 187.94/187.73 cnf(13394,plain, % 187.94/187.73 (~E(f306(f306(f143(x133941),x133942),x133943),x133943)), % 187.94/187.73 inference(rename_variables,[],[4445])). % 187.94/187.73 cnf(13397,plain, % 187.94/187.73 (P1(f306(f306(f220(f872(x133971,a859)),x133972),x133972))), % 187.94/187.73 inference(rename_variables,[],[3566])). % 187.94/187.73 cnf(13408,plain, % 187.94/187.73 (~P1(f306(f306(f308(a865),x134081),f306(f229(a865),f2(a865))))), % 187.94/187.73 inference(rename_variables,[],[11734])). % 187.94/187.73 cnf(13413,plain, % 187.94/187.73 (P1(f306(f306(f221(a1),f306(f306(f22(a1),x134131),f79(a1))),x134131))), % 187.94/187.73 inference(rename_variables,[],[10725])). % 187.94/187.73 cnf(13418,plain, % 187.94/187.73 (~P1(f306(f306(f220(a865),f306(a119,x134181)),x134181))), % 187.94/187.73 inference(rename_variables,[],[4502])). % 187.94/187.73 cnf(13421,plain, % 187.94/187.73 (~P1(f306(f306(f308(f871(x134211,x134211)),x134212),f233(x134211,f185(f872(x134211,a859)))))), % 187.94/187.73 inference(rename_variables,[],[10913])). % 187.94/187.73 cnf(13428,plain, % 187.94/187.73 (~P1(f306(f306(f308(a865),x134281),f306(f229(a865),f2(a865))))), % 187.94/187.73 inference(rename_variables,[],[11734])). % 187.94/187.73 cnf(13438,plain, % 187.94/187.73 (~P1(f306(f306(f308(f871(f866(x134381),f866(x134381))),f306(f306(f236(f866(x134381),f866(x134381)),f120(x134381)),x134382)),f149(x134381,x134383)))), % 187.94/187.73 inference(rename_variables,[],[4529])). % 187.94/187.73 cnf(13446,plain, % 187.94/187.73 (~E(f306(f306(f143(x134461),x134462),x134463),x134463)), % 187.94/187.73 inference(rename_variables,[],[4445])). % 187.94/187.73 cnf(13449,plain, % 187.94/187.73 (P1(f306(f306(f220(a1),x134491),x134491))), % 187.94/187.73 inference(rename_variables,[],[3272])). % 187.94/187.73 cnf(13452,plain, % 187.94/187.73 (~P1(f306(f306(f221(a865),f306(f306(f81(a865),x134521),x134522)),x134521))), % 187.94/187.73 inference(rename_variables,[],[4518])). % 187.94/187.73 cnf(13459,plain, % 187.94/187.73 (~P1(f306(f306(f308(f871(x134591,x134591)),x134592),f233(x134591,f185(f872(x134591,a859)))))), % 187.94/187.73 inference(rename_variables,[],[10913])). % 187.94/187.73 cnf(13462,plain, % 187.94/187.73 (~P1(f306(f306(f308(a865),x134621),f306(f229(a865),f2(a865))))), % 187.94/187.73 inference(rename_variables,[],[11734])). % 187.94/187.73 cnf(13465,plain, % 187.94/187.73 (~P1(f306(f306(f308(f871(x134651,x134651)),x134652),f233(x134651,f185(f872(x134651,a859)))))), % 187.94/187.73 inference(rename_variables,[],[10913])). % 187.94/187.73 cnf(13468,plain, % 187.94/187.73 (P1(f306(f306(f220(a865),f46(a865,x134681,x134682)),x134681))), % 187.94/187.73 inference(rename_variables,[],[3720])). % 187.94/187.73 cnf(13473,plain, % 187.94/187.73 (~E(f306(f306(f143(x134731),x134732),x134733),x134733)), % 187.94/187.73 inference(rename_variables,[],[4445])). % 187.94/187.73 cnf(13478,plain, % 187.94/187.73 (E(f306(f306(f122(x134781),x134782),f120(x134781)),x134782)), % 187.94/187.73 inference(rename_variables,[],[3202])). % 187.94/187.73 cnf(13496,plain, % 187.94/187.73 (P1(f306(f306(f220(a865),f2(a865)),x134961))), % 187.94/187.73 inference(rename_variables,[],[3292])). % 187.94/187.73 cnf(13513,plain, % 187.94/187.73 (~P1(f306(f306(f308(f871(x135131,x135131)),x135132),f233(x135131,f185(f872(x135131,a859)))))), % 187.94/187.73 inference(rename_variables,[],[10913])). % 187.94/187.73 cnf(13518,plain, % 187.94/187.73 (P1(f306(f306(f220(a865),x135181),f306(f306(f81(a865),x135181),x135182)))), % 187.94/187.73 inference(rename_variables,[],[3535])). % 187.94/187.73 cnf(13521,plain, % 187.94/187.73 (P1(f306(f306(f220(f872(x135211,a859)),f306(f164(x135211),f162(x135211,x135212,x135213))),f306(f164(x135211),x135213)))), % 187.94/187.73 inference(rename_variables,[],[3956])). % 187.94/187.73 cnf(13533,plain, % 187.94/187.73 (E(f306(f306(f122(x135331),x135332),f120(x135331)),x135332)), % 187.94/187.73 inference(rename_variables,[],[3202])). % 187.94/187.73 cnf(13536,plain, % 187.94/187.73 (P1(f306(f306(f220(f872(x135361,a859)),f306(f164(x135361),f162(x135361,x135362,x135363))),f306(f164(x135361),x135363)))), % 187.94/187.73 inference(rename_variables,[],[3956])). % 187.94/187.73 cnf(13542,plain, % 187.94/187.73 (~P1(f306(f306(f308(x135421),x135422),f185(f872(x135421,a859))))), % 187.94/187.73 inference(rename_variables,[],[4505])). % 187.94/187.74 cnf(13545,plain, % 187.94/187.74 (~E(f306(f306(f225(a865),f306(a119,x135451)),x135451),f306(a119,x135451))), % 187.94/187.74 inference(rename_variables,[],[11480])). % 187.94/187.74 cnf(13550,plain, % 187.94/187.74 (~P1(f306(f306(f308(x135501),x135502),f185(f872(x135501,a859))))), % 187.94/187.74 inference(rename_variables,[],[4505])). % 187.94/187.74 cnf(13555,plain, % 187.94/187.74 (~P1(f306(f306(f308(f871(f866(x135551),f866(x135551))),f306(f306(f236(f866(x135551),f866(x135551)),x135552),f120(x135551))),f139(x135551,x135553)))), % 187.94/187.74 inference(rename_variables,[],[4525])). % 187.94/187.74 cnf(13563,plain, % 187.94/187.74 (~P1(f306(f306(f308(x135631),x135632),f185(f872(x135631,a859))))), % 187.94/187.74 inference(rename_variables,[],[4505])). % 187.94/187.74 cnf(13576,plain, % 187.94/187.74 (~P1(f306(f306(f185(f872(x135761,f872(x135762,a859))),x135763),x135764))), % 187.94/187.74 inference(rename_variables,[],[4520])). % 187.94/187.74 cnf(13581,plain, % 187.94/187.74 (~P1(f306(f306(f308(a865),x135811),f306(f229(a865),f2(a865))))), % 187.94/187.74 inference(rename_variables,[],[11734])). % 187.94/187.74 cnf(13584,plain, % 187.94/187.74 (P1(f306(f306(f220(f872(x135841,a859)),x135842),f306(f306(f108(f872(x135841,a859)),x135843),f231(f872(x135841,a859)))))), % 187.94/187.74 inference(rename_variables,[],[11127])). % 187.94/187.74 cnf(13595,plain, % 187.94/187.74 (P1(f306(f306(f220(f872(x135951,a859)),x135952),x135952))), % 187.94/187.74 inference(rename_variables,[],[3566])). % 187.94/187.74 cnf(13600,plain, % 187.94/187.74 (P1(f306(f306(f308(x136001),f306(x136002,x136003)),f306(f285(x136004,x136001,x136002),f231(f872(x136004,a859)))))), % 187.94/187.74 inference(rename_variables,[],[3864])). % 187.94/187.74 cnf(13603,plain, % 187.94/187.74 (P1(f306(f306(f220(a865),f2(a865)),x136031))), % 187.94/187.74 inference(rename_variables,[],[3292])). % 187.94/187.74 cnf(13606,plain, % 187.94/187.74 (~E(x136061,f306(a119,x136061))), % 187.94/187.74 inference(rename_variables,[],[10284])). % 187.94/187.74 cnf(13627,plain, % 187.94/187.74 (E(f306(f232(x136271,x136271),f233(x136271,x136272)),x136272)), % 187.94/187.74 inference(rename_variables,[],[3227])). % 187.94/187.74 cnf(13632,plain, % 187.94/187.74 (E(f306(f306(f122(x136321),x136322),f120(x136321)),x136322)), % 187.94/187.74 inference(rename_variables,[],[3202])). % 187.94/187.74 cnf(13635,plain, % 187.94/187.74 (~P1(f306(f306(f308(x136351),x136352),f185(f872(x136351,a859))))), % 187.94/187.74 inference(rename_variables,[],[4505])). % 187.94/187.74 cnf(13644,plain, % 187.94/187.74 (~P1(f306(f306(f220(a865),f306(f306(f82(a865),f306(a119,x136441)),f306(a119,x136441))),x136441))), % 187.94/187.74 inference(rename_variables,[],[10664])). % 187.94/187.74 cnf(13647,plain, % 187.94/187.74 (~P1(f306(f306(f220(a865),f306(f306(f82(a865),f306(a119,x136471)),f306(a119,x136471))),x136471))), % 187.94/187.74 inference(rename_variables,[],[10664])). % 187.94/187.74 cnf(13652,plain, % 187.94/187.74 (~P1(f306(f306(f221(a865),f306(f306(f81(a865),x136521),x136522)),x136521))), % 187.94/187.74 inference(rename_variables,[],[4518])). % 187.94/187.74 cnf(13659,plain, % 187.94/187.74 (~P1(f306(f306(f308(x136591),x136592),f185(f872(x136591,a859))))), % 187.94/187.74 inference(rename_variables,[],[4505])). % 187.94/187.74 cnf(13681,plain, % 187.94/187.74 (~P1(f306(f306(f221(a865),f306(f306(f81(a865),x136811),x136812)),x136811))), % 187.94/187.74 inference(rename_variables,[],[4518])). % 187.94/187.74 cnf(13684,plain, % 187.94/187.74 (~P1(f306(f306(f308(x136841),x136842),f185(f872(x136841,a859))))), % 187.94/187.74 inference(rename_variables,[],[4505])). % 187.94/187.74 cnf(13691,plain, % 187.94/187.74 (P1(f306(f306(f220(f872(x136911,a859)),f306(f164(x136911),f162(x136911,x136912,x136913))),f306(f164(x136911),x136913)))), % 187.94/187.74 inference(rename_variables,[],[3956])). % 187.94/187.74 cnf(13697,plain, % 187.94/187.74 (E(f306(x136971,f667(f306(x136971,x136972),f306(f214(x136973),x136972),x136971,x136974,x136973)),f306(x136971,x136972))), % 187.94/187.74 inference(rename_variables,[],[11095])). % 187.94/187.74 cnf(13709,plain, % 187.94/187.74 (~P1(f306(f306(f308(f871(x137091,x137091)),x137092),f233(x137091,f185(f872(x137091,a859)))))), % 187.94/187.74 inference(rename_variables,[],[10913])). % 187.94/187.74 cnf(13714,plain, % 187.94/187.74 (P1(f306(f306(f221(a1),f306(f306(f22(a1),x137141),f79(a1))),x137141))), % 187.94/187.74 inference(rename_variables,[],[10725])). % 187.94/187.74 cnf(13717,plain, % 187.94/187.74 (P1(f306(f306(f220(a865),x137171),f306(f306(f82(a865),x137171),x137171)))), % 187.94/187.74 inference(rename_variables,[],[3536])). % 187.94/187.74 cnf(13726,plain, % 187.94/187.74 (P1(f306(f306(f221(a865),x137261),f306(a119,f306(f306(f81(a865),x137262),x137261))))), % 187.94/187.74 inference(rename_variables,[],[3713])). % 187.94/187.74 cnf(13745,plain, % 187.94/187.74 (P1(f306(f306(f220(f872(x137451,a859)),f306(f164(x137451),f162(x137451,x137452,x137453))),f306(f164(x137451),x137453)))), % 187.94/187.74 inference(rename_variables,[],[3956])). % 187.94/187.74 cnf(13752,plain, % 187.94/187.74 (~P1(f306(f306(f308(a865),x137521),f306(f229(a865),f2(a865))))), % 187.94/187.74 inference(rename_variables,[],[11734])). % 187.94/187.74 cnf(13772,plain, % 187.94/187.74 (~P1(f306(f306(f308(a865),x137721),f306(f229(a865),f2(a865))))), % 187.94/187.74 inference(rename_variables,[],[11734])). % 187.94/187.74 cnf(13791,plain, % 187.94/187.74 (~P1(f306(f306(f221(a865),f306(f306(f81(a865),x137911),x137912)),x137912))), % 187.94/187.74 inference(rename_variables,[],[4517])). % 187.94/187.74 cnf(13796,plain, % 187.94/187.74 (~P1(f306(f306(f308(x137961),x137962),f185(f872(x137961,a859))))), % 187.94/187.74 inference(rename_variables,[],[4505])). % 187.94/187.74 cnf(13799,plain, % 187.94/187.74 (~P1(f306(f306(f308(x137991),x137992),f306(f286(x137991,x137993,x137994),f185(f872(x137993,a859)))))), % 187.94/187.74 inference(rename_variables,[],[10916])). % 187.94/187.74 cnf(13802,plain, % 187.94/187.74 (~E(f306(a119,x138021),f2(a865))), % 187.94/187.74 inference(rename_variables,[],[4430])). % 187.94/187.74 cnf(13805,plain, % 187.94/187.74 (~P37(x138051,x138052,x138053,f306(f306(f146(x138054,x138051),x138055),f306(a119,f120(x138054))),f120(x138052))), % 187.94/187.74 inference(rename_variables,[],[11157])). % 187.94/187.74 cnf(13808,plain, % 187.94/187.74 (~P1(f306(f306(f308(f871(x138081,x138081)),x138082),f233(x138081,f185(f872(x138081,a859)))))), % 187.94/187.74 inference(rename_variables,[],[10913])). % 187.94/187.74 cnf(13815,plain, % 187.94/187.74 (~P1(f306(f306(f308(a865),x138151),f306(f229(a865),f2(a865))))), % 187.94/187.74 inference(rename_variables,[],[11734])). % 187.94/187.74 cnf(13830,plain, % 187.94/187.74 (~P1(f306(f306(f308(f871(x138301,x138301)),x138302),f233(x138301,f185(f872(x138301,a859)))))), % 187.94/187.74 inference(rename_variables,[],[10913])). % 187.94/187.74 cnf(13833,plain, % 187.94/187.74 (~P1(f306(f306(f308(f871(x138331,x138331)),x138332),f233(x138331,f185(f872(x138331,a859)))))), % 187.94/187.74 inference(rename_variables,[],[10913])). % 187.94/187.74 cnf(13836,plain, % 187.94/187.74 (~E(f306(f306(f143(x138361),x138362),x138363),x138363)), % 187.94/187.74 inference(rename_variables,[],[4445])). % 187.94/187.74 cnf(13843,plain, % 187.94/187.74 (~E(f306(a119,x138431),f2(a865))), % 187.94/187.74 inference(rename_variables,[],[4430])). % 187.94/187.74 cnf(13854,plain, % 187.94/187.74 (~P1(f306(f306(f308(f871(x138541,x138541)),x138542),f233(x138541,f185(f872(x138541,a859)))))), % 187.94/187.74 inference(rename_variables,[],[10913])). % 187.94/187.74 cnf(13857,plain, % 187.94/187.74 (P1(f306(f306(f221(a1),f306(f306(f22(a1),x138571),f79(a1))),x138571))), % 187.94/187.74 inference(rename_variables,[],[10725])). % 187.94/187.74 cnf(13869,plain, % 187.94/187.74 (P1(f306(f306(f220(a865),x138691),f306(f306(f82(a865),x138691),x138691)))), % 187.94/187.74 inference(rename_variables,[],[3536])). % 187.94/187.74 cnf(13872,plain, % 187.94/187.74 (~P1(f306(f306(f308(a865),x138721),f306(f229(a865),f2(a865))))), % 187.94/187.74 inference(rename_variables,[],[11734])). % 187.94/187.74 cnf(13875,plain, % 187.94/187.74 (~P1(f306(f306(f220(a865),f306(a119,x138751)),x138751))), % 187.94/187.74 inference(rename_variables,[],[4502])). % 187.94/187.74 cnf(13878,plain, % 187.94/187.74 (~P1(f306(f306(f185(f872(x138781,f872(x138782,a859))),x138783),x138784))), % 187.94/187.74 inference(rename_variables,[],[4520])). % 187.94/187.74 cnf(13893,plain, % 187.94/187.74 (P1(f306(f306(f220(a865),x138931),f306(f306(f82(a865),x138931),x138931)))), % 187.94/187.74 inference(rename_variables,[],[3536])). % 187.94/187.74 cnf(13903,plain, % 187.94/187.74 (P1(f306(f306(f220(a865),f2(a865)),x139031))), % 187.94/187.74 inference(rename_variables,[],[3292])). % 187.94/187.74 cnf(13906,plain, % 187.94/187.74 (~P1(f306(f306(f308(f871(x139061,x139061)),x139062),f233(x139061,f185(f872(x139061,a859)))))), % 187.94/187.74 inference(rename_variables,[],[10913])). % 187.94/187.74 cnf(13909,plain, % 187.94/187.74 (P1(f306(f306(f221(a1),f306(f306(f22(a1),x139091),f79(a1))),x139091))), % 187.94/187.74 inference(rename_variables,[],[10725])). % 187.94/187.74 cnf(13921,plain, % 187.94/187.74 (~P1(f306(f306(f308(f871(f866(x139211),f866(x139211))),f306(f306(f236(f866(x139211),f866(x139211)),x139212),f120(x139211))),f149(x139211,x139213)))), % 187.94/187.74 inference(rename_variables,[],[4526])). % 187.94/187.74 cnf(13924,plain, % 187.94/187.74 (~E(f306(f306(f143(x139241),x139242),x139243),x139243)), % 187.94/187.74 inference(rename_variables,[],[4445])). % 187.94/187.74 cnf(13927,plain, % 187.94/187.74 (~E(f306(f306(f143(x139271),x139272),x139273),x139273)), % 187.94/187.74 inference(rename_variables,[],[4445])). % 187.94/187.74 cnf(13936,plain, % 187.94/187.74 (~P1(f306(f306(f308(x139361),x139362),f185(f872(x139361,a859))))), % 187.94/187.74 inference(rename_variables,[],[4505])). % 187.94/187.74 cnf(13941,plain, % 187.94/187.74 (E(f306(f232(x139411,x139411),f233(x139411,x139412)),x139412)), % 187.94/187.74 inference(rename_variables,[],[3227])). % 187.94/187.74 cnf(13944,plain, % 187.94/187.74 (~E(f306(f306(f143(x139441),x139442),x139443),x139443)), % 187.94/187.74 inference(rename_variables,[],[4445])). % 187.94/187.74 cnf(13947,plain, % 187.94/187.74 (P1(f306(f306(f220(f872(x139471,a859)),f306(f164(x139471),f162(x139471,x139472,x139473))),f306(f164(x139471),x139473)))), % 187.94/187.74 inference(rename_variables,[],[3956])). % 187.94/187.74 cnf(13957,plain, % 187.94/187.74 (P1(f306(f306(f308(x139571),f306(x139572,x139573)),f306(f285(x139574,x139571,x139572),f231(f872(x139574,a859)))))), % 187.94/187.74 inference(rename_variables,[],[3864])). % 187.94/187.74 cnf(13964,plain, % 187.94/187.74 (P1(f306(f306(f220(f872(x139641,a859)),f306(f164(x139641),f162(x139641,x139642,x139643))),f306(f164(x139641),x139643)))), % 187.94/187.74 inference(rename_variables,[],[3956])). % 187.94/187.74 cnf(13969,plain, % 187.94/187.74 (P1(f306(f306(f220(a865),x139691),x139691))), % 187.94/187.74 inference(rename_variables,[],[3271])). % 187.94/187.74 cnf(13978,plain, % 187.94/187.74 (~E(f306(f306(f225(a865),f306(a119,x139781)),x139781),f306(a119,x139781))), % 187.94/187.74 inference(rename_variables,[],[11480])). % 187.94/187.74 cnf(13993,plain, % 187.94/187.74 (P1(f306(f306(f220(f872(x139931,a859)),f306(f164(x139931),f162(x139931,x139932,x139933))),f306(f164(x139931),x139933)))), % 187.94/187.74 inference(rename_variables,[],[3956])). % 187.94/187.74 cnf(14012,plain, % 187.94/187.74 (~P1(f306(f306(f308(a865),x140121),f306(f229(a865),f2(a865))))), % 187.94/187.74 inference(rename_variables,[],[11734])). % 187.94/187.74 cnf(14023,plain, % 187.94/187.74 (~P1(f306(f306(f308(f871(f866(x140231),f866(x140231))),f306(f306(f236(f866(x140231),f866(x140231)),x140232),f120(x140231))),f137(x140231,x140233)))), % 187.94/187.74 inference(rename_variables,[],[4524])). % 187.94/187.74 cnf(14026,plain, % 187.94/187.74 (~P1(f306(f306(f308(x140261),x140262),f185(f872(x140261,a859))))), % 187.94/187.74 inference(rename_variables,[],[4505])). % 187.94/187.74 cnf(14042,plain, % 187.94/187.74 (P1(f306(f306(f220(f872(x140421,a859)),x140422),x140422))), % 187.94/187.74 inference(rename_variables,[],[3566])). % 187.94/187.74 cnf(14048,plain, % 187.94/187.74 (P1(f306(f306(f220(a865),x140481),f306(f306(f81(a865),x140481),x140482)))), % 187.94/187.74 inference(rename_variables,[],[3535])). % 187.94/187.74 cnf(14054,plain, % 187.94/187.74 (P1(f306(f306(f220(a865),x140541),x140541))), % 187.94/187.74 inference(rename_variables,[],[3271])). % 187.94/187.74 cnf(14066,plain, % 187.94/187.74 (~P1(f306(f306(f185(f872(x140661,f872(x140662,a859))),x140663),x140664))), % 187.94/187.74 inference(rename_variables,[],[4520])). % 187.94/187.74 cnf(14079,plain, % 187.94/187.74 (P1(f306(f306(f221(a1),f306(f306(f22(a1),x140791),f79(a1))),x140791))), % 187.94/187.74 inference(rename_variables,[],[10725])). % 187.94/187.74 cnf(14094,plain, % 187.94/187.74 (E(f306(f306(f122(x140941),x140942),f120(x140941)),x140942)), % 187.94/187.74 inference(rename_variables,[],[3202])). % 187.94/187.74 cnf(14107,plain, % 187.94/187.74 (E(f306(f306(f122(x141071),x141072),f120(x141071)),x141072)), % 187.94/187.74 inference(rename_variables,[],[3202])). % 187.94/187.74 cnf(14112,plain, % 187.94/187.74 (~P1(f306(f306(f308(x141121),x141122),f306(f286(x141121,x141123,x141124),f185(f872(x141123,a859)))))), % 187.94/187.74 inference(rename_variables,[],[10916])). % 187.94/187.74 cnf(14133,plain, % 187.94/187.74 (P1(f306(f306(f308(x141331),f306(x141332,x141333)),f306(f285(x141334,x141331,x141332),f231(f872(x141334,a859)))))), % 187.94/187.74 inference(rename_variables,[],[3864])). % 187.94/187.74 cnf(14145,plain, % 187.94/187.74 (~E(f306(f306(f143(x141451),x141452),x141453),x141453)), % 187.94/187.74 inference(rename_variables,[],[4445])). % 187.94/187.74 cnf(14148,plain, % 187.94/187.74 (P1(f306(f306(f308(x141481),f306(x141482,x141483)),f306(f285(x141484,x141481,x141482),f231(f872(x141484,a859)))))), % 187.94/187.74 inference(rename_variables,[],[3864])). % 187.94/187.74 cnf(14151,plain, % 187.94/187.74 (~P1(f306(f306(f308(f871(x141511,x141511)),x141512),f233(x141511,f185(f872(x141511,a859)))))), % 187.94/187.74 inference(rename_variables,[],[10913])). % 187.94/187.74 cnf(14167,plain, % 187.94/187.74 (P1(f306(f306(f220(a865),x141671),x141671))), % 187.94/187.74 inference(rename_variables,[],[3271])). % 187.94/187.74 cnf(14196,plain, % 187.94/187.74 (E(f306(f232(x141961,x141961),f233(x141961,x141962)),x141962)), % 187.94/187.74 inference(rename_variables,[],[3227])). % 187.94/187.74 cnf(14213,plain, % 187.94/187.74 (P1(f306(f306(f220(f872(x142131,a859)),x142132),x142132))), % 187.94/187.74 inference(rename_variables,[],[3566])). % 187.94/187.74 cnf(14216,plain, % 187.94/187.74 (~P1(f306(f306(f185(f872(x142161,f872(x142162,a859))),x142163),x142164))), % 187.94/187.74 inference(rename_variables,[],[4520])). % 187.94/187.74 cnf(14219,plain, % 187.94/187.74 (P37(x142191,x142192,x142193,f306(f306(f146(x142194,x142191),x142195),f121(x142194,f120(x142194))),f120(x142192))), % 187.94/187.74 inference(rename_variables,[],[11161])). % 187.94/187.74 cnf(14234,plain, % 187.94/187.74 (P1(f306(f306(f308(f871(x142341,x142341)),f306(f306(f236(x142341,x142341),x142342),x142342)),f282(x142341,x142343)))), % 187.94/187.74 inference(rename_variables,[],[3897])). % 187.94/187.74 cnf(14297,plain, % 187.94/187.74 (P1(f306(f306(f220(a865),x142971),f306(f306(f81(a865),x142971),x142972)))), % 187.94/187.74 inference(rename_variables,[],[3535])). % 187.94/187.74 cnf(14303,plain, % 187.94/187.74 (P1(f306(f306(f221(a865),x143031),f306(a119,f306(f306(f81(a865),x143032),x143031))))), % 187.94/187.74 inference(rename_variables,[],[3713])). % 187.94/187.74 cnf(14341,plain, % 187.94/187.74 (P1(f306(f306(f220(f872(x143411,a859)),f306(f164(x143411),f162(x143411,x143412,x143413))),f306(f164(x143411),x143413)))), % 187.94/187.74 inference(rename_variables,[],[3956])). % 187.94/187.74 cnf(14372,plain, % 187.94/187.74 ($false), % 187.94/187.74 inference(scs_inference,[],[3299,3702,3300,4001,3847,4037,3064,4519,3271,13969,14054,14167,3248,4509,4490,3897,14234,3348,4524,14023,4481,3365,3715,4505,13542,13550,13563,13635,13659,13684,13796,13936,14026,3956,13521,13536,13691,13745,13947,13964,13993,14341,3864,13380,13600,13957,14133,14148,3741,3375,4435,4430,13802,13843,4513,4445,13394,13446,13473,13836,13924,13927,13944,14145,4443,3253,3352,4031,3907,3272,13449,3720,13468,3292,13496,13603,13903,3246,3579,3709,3566,13397,13595,14042,14213,3711,3536,13717,13869,13893,3535,13518,14048,14297,4140,3713,13726,14303,3227,13627,13941,14196,3202,13478,13533,13632,14094,14107,3628,4525,13555,4526,13921,4529,13438,4489,4502,13418,13875,4515,4520,13576,13878,14066,14216,4517,13791,4518,13452,13652,13681,4521,3479,11480,13545,13978,10284,13606,13032,11159,13223,10338,11918,12634,11792,11832,12923,12425,11290,13199,13111,12204,10581,12675,13113,10569,3250,11027,12427,12456,12463,10903,13125,11127,13584,10867,10725,13413,13714,13857,13909,14079,4260,3631,12486,10898,11192,11151,11095,13388,13391,13697,13141,10263,12947,10900,10396,11240,10669,10512,3211,11093,11174,10953,12935,12938,13217,10674,13197,13241,11617,12144,12133,12242,10248,12694,11732,11734,13408,13428,13462,13581,13752,13772,13815,13872,14012,10682,11081,10913,13421,13459,13465,13513,13709,13808,13830,13833,13854,13906,14151,10916,13799,14112,11195,10664,13644,13647,10767,11992,11004,12013,11245,13227,12036,11157,13805,10931,11161,14219,2871,3331,3813,9,8,5377,7456,6751,8502,4605,4608,5965,9516,6137,6331,9572,8504,9733,5526,5708,5651,5381,8840,5066,5556,6694,5010,6211,8413,9371,5739,6441,5572,5560,5067,5277,6144,8440,9655,9471,6440,6735,5271,9308,5016,5312,9117,5293,9802,6843,8880,9546,6274,5544,5499,6908,8465,9233,8612,5515,5372,6280,8551,5873,5658,6061,7920,8008,8611,9207,6656,9903,8524,9916,5197,9706,6737,7383,4918,5920,6686,5423,6242,6329,8335,9696,6778,8002,5935,7650,8875,5761,7939,5780,8415,9565,4663,5144,5341,6426,9905,6004,6089,6272,2,8714,4538,5306,5308,8676,5321,6688,9038,6192,8747,5663,6194,6021,8715,9604,7815,5002,6207,6374,6844,9547,5248,7451,8479,5077,9005,5323,5979,8337,5616,8430,4709,6217,6487,8698,9765,4941,5775,7986,4822,7604,8503,8402,6136,8361,8505,9020,6094,9686,5641,8379,6333,5362,7873,8654,5115,6530,9144,5182,8658,4981,8526,8759,5406,5869,9477,7136,5322,5833,6375,7115,7386,9407,6849,8584,9719,9737,8567,5719,8737,9279,5845,5604,5261,5364,5496,8757,10110,4564,6042,5513,5533,6901,7518,7665,8865,9654,6384,5190,4884,4613,5270,6845,8777,5755,4857,5714,5373,5136,5204,5644,7585,6714,7741,4942,5760,6205,9189,5570,5697,6944,9037,7918,9915,4745,5276,5882,7790,8236,7779,8365,8019,5275,8783,8889,6323,6685,7402,5716,6241,6913,5288,5603,8700,8852,7413,9902,5289,6196,5637,6764,8003,8480,6478,5514,6610,6963,8756,6046,7907,8758,5285,5422,6832,9434,9941,6708,5712,4615,5923,9435,5698,6729,9247,9611,6067,5170,6065,6447,9548,9969,4830,4856,5479,6687,4808,4919,5741,5774,6978,5208,4669,5569,9409,5216,5307,6226,7285,7324,9538,5451,6248,7271,7728,8192,8506,10168,8095,8168,9984,5701,6088,9253,7921,9797,5009,5543,8571,8579,10184,4670,5160,6864,7269,8497,5659,6223,5008,5473,5726,6044,7120,7500,5268,7731,6234,8212,6731,8020,8761,9603,7733,5710,5172,6781,9453,5874,8563,6092,8496,7060,8149,6325,8569,4662,6476,6865,7699,6733,5295,5956,6062,6326,6406,5652,6330,8972,9190,5213,8525,8795,9493,10036,6285,5302,10111,9567,6028,6090,6047,7295,9004,6209,6327,9280,8641,5706,6429,8436,9043,9070,5015,5181,5787,6048,7145,7700,8784,5812,5495,7322,4847,7296,9708,5143,5135,6025,8870,5703,6405,6071,4645]), % 187.94/187.74 ['proof']). % 187.94/187.74 % SZS output end Proof % 187.94/187.74 % Total time :172.460000s %------------------------------------------------------------------------------