%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SWW354+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 : n028.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 18:08:13 EDT 2024 % Result : Theorem 172.78s 172.47s % Output : CNFRefutation 172.88s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.06/0.12 % Problem : SWW354+1 : TPTP v8.2.0. Released v5.2.0. % 0.06/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % 0.12/0.33 % Computer : n028.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 300 % 0.12/0.33 % DateTime : Wed Jun 19 07:25:09 EDT 2024 % 0.12/0.34 % CPUTime : % 0.40/0.59 start to proof:theBenchmark % 172.18/172.30 %------------------------------------------- % 172.18/172.30 % File :CSE---1.7 % 172.18/172.30 % Problem :theBenchmark % 172.18/172.30 % Transform :cnf % 172.18/172.30 % Format :tptp:raw % 172.18/172.30 % Command :java -jar mcs_scs.jar %d %s % 172.18/172.30 % 172.18/172.30 % Result :Theorem 146.890000s % 172.18/172.30 % Output :CNFRefutation 146.890000s % 172.18/172.30 %------------------------------------------- % 172.18/172.30 %------------------------------------------------------------------------------ % 172.18/172.30 % File : SWW354+1 : TPTP v8.2.0. Released v5.2.0. % 172.18/172.30 % Domain : Software Verification % 172.18/172.30 % Problem : Hoare's Logic with Procedures 435350, 5000 axioms selected % 172.18/172.30 % Version : Especial. % 172.18/172.30 % English : % 172.18/172.30 % 172.18/172.30 % Refs : [BN10] Boehme & Nipkow (2010), Sledgehammer: Judgement Day % 172.18/172.30 % : [Bla11] Blanchette (2011), Email to Geoff Sutcliffe % 172.18/172.30 % Source : [Bla11] % 172.18/172.31 % Names : hoare_435350.5000.p [Bla11] % 172.18/172.31 % 172.18/172.31 % Status : ContradictoryAxioms % 172.18/172.31 % Rating : 0.86 v8.2.0, 0.81 v7.4.0, 0.90 v7.3.0, 0.86 v7.1.0, 0.87 v7.0.0, 0.90 v6.4.0, 0.88 v6.2.0, 0.92 v6.1.0, 0.93 v6.0.0, 0.91 v5.5.0, 0.96 v5.3.0, 1.00 v5.2.0 % 172.18/172.31 % Syntax : Number of formulae : 5245 (1740 unt; 0 def) % 172.18/172.31 % Number of atoms : 12605 (4548 equ) % 172.18/172.31 % Maximal formula atoms : 13 ( 2 avg) % 172.18/172.31 % Number of connectives : 8368 (1008 ~; 156 |; 722 &) % 172.18/172.31 % ( 893 <=>;5589 =>; 0 <=; 0 <~>) % 172.18/172.31 % Maximal formula depth : 22 ( 6 avg) % 172.18/172.31 % Maximal term depth : 19 ( 2 avg) % 172.18/172.31 % Number of predicates : 144 ( 143 usr; 1 prp; 0-6 aty) % 172.18/172.31 % Number of functors : 387 ( 387 usr; 53 con; 0-7 aty) % 172.18/172.31 % Number of variables : 16682 (16537 !; 145 ?) % 172.18/172.31 % SPC : FOF_CAX_RFO_SEQ % 172.18/172.31 % 172.18/172.31 % Comments : This file was generated by Isabelle (most likely Sledgehammer) % 172.18/172.31 % 2011-03-01 12:24:52 % 172.18/172.31 %------------------------------------------------------------------------------ % 172.18/172.31 %----Relevant facts (4987) % 172.18/172.31 fof(fact_ext,axiom, % 172.18/172.31 ! [V_g_2,V_f_2] : % 172.18/172.31 ( ! [B_x] : hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) % 172.18/172.31 => V_f_2 = V_g_2 ) ). % 172.18/172.31 % 172.18/172.31 fof(fact_empty,axiom, % 172.18/172.31 ! [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))) ). % 172.18/172.31 % 172.18/172.31 fof(fact_hoare__derivs_Oequations_I1_J,axiom, % 172.18/172.31 ! [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))) ). % 172.18/172.31 % 172.18/172.31 fof(fact_cut,axiom, % 172.18/172.31 ! [V_Ga_2,V_ts_2,V_G_H_2,T_a] : % 172.18/172.31 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_H_2,V_ts_2) % 172.18/172.31 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,V_G_H_2) % 172.18/172.31 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,V_ts_2) ) ) ). % 172.18/172.31 % 172.18/172.31 fof(fact_hoare__derivs_Oinsert,axiom, % 172.18/172.31 ! [V_ts_2,V_t_2,V_Ga_2,T_a] : % 172.18/172.31 ( 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)))) % 172.18/172.31 => ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,V_ts_2) % 172.18/172.31 => 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)) ) ) ). % 172.18/172.31 % 172.18/172.31 fof(fact_derivs__insertD,axiom, % 172.18/172.31 ! [V_ts_2,V_t_2,V_Ga_2,T_a] : % 172.18/172.31 ( 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)) % 172.18/172.31 => ( 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)))) % 172.18/172.31 & c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,V_ts_2) ) ) ). % 172.18/172.31 % 172.18/172.31 fof(fact_bot__fun__def,axiom, % 172.18/172.31 ! [V_x_2,T_b,T_a] : % 172.18/172.31 ( class_Orderings_Obot(T_a) % 172.18/172.31 => hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,T_a)),V_x_2) = c_Orderings_Obot__class_Obot(T_a) ) ). % 172.18/172.31 % 172.18/172.31 fof(fact_com_Osimps_I18_J,axiom, % 172.18/172.31 ! [V_pname_H] : c_Com_Ocom_OSKIP != hAPP(c_Com_Ocom_OBODY,V_pname_H) ). % 172.18/172.31 % 172.18/172.31 fof(fact_com_Osimps_I19_J,axiom, % 172.18/172.31 ! [V_pname_H] : hAPP(c_Com_Ocom_OBODY,V_pname_H) != c_Com_Ocom_OSKIP ). % 172.18/172.31 % 172.18/172.31 fof(fact_empty__not__insert,axiom, % 172.18/172.31 ! [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) ). % 172.18/172.31 % 172.18/172.31 fof(fact_insert__not__empty,axiom, % 172.18/172.31 ! [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)) ). % 172.18/172.31 % 172.18/172.31 fof(fact_doubleton__eq__iff,axiom, % 172.18/172.31 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 172.18/172.31 ( hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = hAPP(hAPP(c_Set_Oinsert(T_a),V_ca_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_d_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) % 172.18/172.31 <=> ( ( V_a_2 = V_ca_2 % 172.18/172.31 & V_b_2 = V_d_2 ) % 172.18/172.31 | ( V_a_2 = V_d_2 % 172.18/172.31 & V_b_2 = V_ca_2 ) ) ) ). % 172.18/172.31 % 172.18/172.31 fof(fact_singleton__inject,axiom, % 172.18/172.31 ! [V_b_2,V_a_2,T_a] : % 172.18/172.31 ( 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))) % 172.18/172.31 => V_a_2 = V_b_2 ) ). % 172.18/172.31 % 172.18/172.31 fof(fact_bot__apply,axiom, % 172.18/172.31 ! [V_x_2,T_b,T_a] : % 172.18/172.31 ( class_Orderings_Obot(T_a) % 172.18/172.31 => hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_b,T_a)),V_x_2) = c_Orderings_Obot__class_Obot(T_a) ) ). % 172.18/172.31 % 172.18/172.31 fof(fact_hoare__derivs_OSkip,axiom, % 172.18/172.31 ! [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)))) ). % 172.18/172.31 % 172.18/172.31 fof(fact_hoare__derivs_Oequations_I7_J,axiom, % 172.18/172.31 ! [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)))) ). % 172.18/172.31 % 172.18/172.31 fof(fact_MGF__complete,axiom, % 172.18/172.31 ! [V_Q_2,V_P_2,V_ca_2] : % 172.18/172.31 ( c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_OMGT(V_ca_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) % 172.18/172.31 => ( c_Hoare__Mirabelle_Ohoare__valids(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),V_P_2),V_ca_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) % 172.18/172.31 => c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),V_P_2),V_ca_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) ) ) ). % 172.18/172.31 % 172.18/172.31 fof(fact_com_Osimps_I6_J,axiom, % 172.18/172.31 ! [V_pname_H_2,V_pname_2] : % 172.18/172.31 ( hAPP(c_Com_Ocom_OBODY,V_pname_2) = hAPP(c_Com_Ocom_OBODY,V_pname_H_2) % 172.18/172.31 <=> V_pname_2 = V_pname_H_2 ) ). % 172.18/172.31 % 172.18/172.31 fof(fact_triple_Oinject,axiom, % 172.18/172.31 ! [V_fun2_H_2,V_com_H_2,V_fun1_H_2,V_fun2_2,V_com_2,V_fun1_2,T_a] : % 172.18/172.31 ( 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) % 172.18/172.31 <=> ( V_fun1_2 = V_fun1_H_2 % 172.18/172.31 & V_com_2 = V_com_H_2 % 172.18/172.31 & V_fun2_2 = V_fun2_H_2 ) ) ). % 172.18/172.31 % 172.18/172.31 fof(fact_hoare__sound,axiom, % 172.18/172.31 ! [V_ts_2,V_Ga_2,T_a] : % 172.18/172.31 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,V_ts_2) % 172.18/172.31 => c_Hoare__Mirabelle_Ohoare__valids(T_a,V_Ga_2,V_ts_2) ) ). % 172.18/172.31 % 172.18/172.31 fof(fact_insert__code,axiom, % 172.18/172.31 ! [V_x_2,V_A_2,V_y_2,T_a] : % 172.18/172.31 ( hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(T_a),V_y_2),V_A_2),V_x_2)) % 172.18/172.31 <=> ( V_y_2 = V_x_2 % 172.18/172.31 | hBOOL(hAPP(V_A_2,V_x_2)) ) ) ). % 172.18/172.31 % 172.18/172.31 fof(fact_insert__commute,axiom, % 172.18/172.31 ! [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)) ). % 172.18/172.31 % 172.18/172.31 fof(fact_insert__absorb2,axiom, % 172.18/172.31 ! [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) ). % 172.18/172.31 % 172.18/172.31 fof(fact_BodyN,axiom, % 172.18/172.31 ! [V_Ga_2,V_Q_2,V_pn_2,V_P_2,T_a] : % 172.18/172.31 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),hAPP(c_Com_Ocom_OBODY,V_pn_2)),V_Q_2)),V_Ga_2),hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn_2))),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) % 172.18/172.31 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),hAPP(c_Com_Ocom_OBODY,V_pn_2)),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) ). % 172.18/172.31 % 172.18/172.31 fof(fact_weak__Body,axiom, % 172.18/172.31 ! [V_Q_2,V_pn_2,V_P_2,V_Ga_2,T_a] : % 172.18/172.31 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn_2))),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) % 172.18/172.31 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),hAPP(c_Com_Ocom_OBODY,V_pn_2)),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) ). % 172.18/172.31 % 172.18/172.31 fof(fact_the__elem__eq,axiom, % 172.18/172.31 ! [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 ). % 172.18/172.31 % 172.18/172.31 fof(fact_triple_Orecs,axiom, % 172.18/172.31 ! [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) ). % 172.18/172.31 % 172.18/172.31 fof(fact_triple_Osimps_I2_J,axiom, % 172.18/172.31 ! [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) ). % 172.18/172.31 % 172.18/172.31 fof(fact_escape,axiom, % 172.18/172.31 ! [V_Q_2,V_ca_2,V_Ga_2,T_a,V_P_2] : % 172.18/172.31 ( ! [B_Z,B_s] : % 172.18/172.31 ( hBOOL(hAPP(hAPP(V_P_2,B_Z),B_s)) % 172.18/172.31 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),T_a),hAPP(hAPP(c_COMBC(tc_Com_Ostate,tc_Com_Ostate,tc_HOL_Obool),c_fequal),B_s))),V_ca_2),hAPP(c_COMBK(tc_fun(tc_Com_Ostate,tc_HOL_Obool),T_a),hAPP(V_Q_2,B_Z)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) % 172.18/172.31 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),V_ca_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) ). % 172.18/172.31 % 172.18/172.31 fof(fact_conseq1,axiom, % 172.18/172.31 ! [V_P_2,V_Q_2,V_ca_2,V_P_H_2,V_Ga_2,T_a] : % 172.18/172.31 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_H_2),V_ca_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) % 172.18/172.31 => ( ! [B_Z,B_s] : % 172.18/172.31 ( hBOOL(hAPP(hAPP(V_P_2,B_Z),B_s)) % 172.18/172.31 => hBOOL(hAPP(hAPP(V_P_H_2,B_Z),B_s)) ) % 172.18/172.31 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),V_ca_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) ) ). % 172.18/172.31 % 172.18/172.31 fof(fact_conseq2,axiom, % 172.18/172.31 ! [V_Q_2,V_Q_H_2,V_ca_2,V_P_2,V_Ga_2,T_a] : % 172.18/172.31 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),V_ca_2),V_Q_H_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) % 172.18/172.31 => ( ! [B_Z,B_s] : % 172.18/172.31 ( hBOOL(hAPP(hAPP(V_Q_H_2,B_Z),B_s)) % 172.18/172.31 => hBOOL(hAPP(hAPP(V_Q_2,B_Z),B_s)) ) % 172.18/172.31 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),V_ca_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) ) ). % 172.18/172.31 % 172.18/172.31 fof(fact_Comp,axiom, % 172.18/172.31 ! [V_R_2,V_d_2,V_Q_2,V_ca_2,V_P_2,V_Ga_2,T_a] : % 172.18/172.31 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),V_ca_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) % 172.18/172.31 => ( 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)))) % 172.18/172.31 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),c_Com_Ocom_OSemi(V_ca_2,V_d_2)),V_R_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) ) ). % 172.18/172.31 % 172.18/172.31 fof(fact_LoopF,axiom, % 172.18/172.31 ! [V_ca_2,V_b_2,V_P_2,V_Ga_2,T_a] : c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),T_a),c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fconj)),V_P_2))),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate),c_fNot),V_b_2))),c_Com_Ocom_OWhile(V_b_2,V_ca_2)),V_P_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ). % 172.18/172.31 % 172.18/172.31 fof(fact_MGT__alternD,axiom, % 172.18/172.31 ! [V_ca_2,V_Ga_2] : % 172.18/172.31 ( c_Hoare__Mirabelle_Ostate__not__singleton % 172.18/172.31 => ( c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_Com_Ostate),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_HOL_Obool,tc_Com_Ostate),c_HOL_OAll(tc_Com_Ostate))),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Com_Ostate),hAPP(c_COMBC(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Com_Ostate),c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Com_Ostate),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fimplies)),c_Natural_Oevalc(V_ca_2))))),c_fequal))),V_ca_2),c_fequal)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) % 172.18/172.31 => c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_OMGT(V_ca_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) ) ) ). % 172.18/172.31 % 172.18/172.31 fof(fact_finite__dom__body,axiom, % 172.18/172.31 hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Com_Opname),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody))) ). % 172.18/172.31 % 172.18/172.31 fof(fact_com_Osimps_I46_J,axiom, % 172.18/172.31 ! [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) ). % 172.18/172.31 % 172.18/172.31 fof(fact_com_Osimps_I47_J,axiom, % 172.18/172.31 ! [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) ). % 172.18/172.31 % 172.18/172.31 fof(fact_com_Osimps_I3_J,axiom, % 172.18/172.31 ! [V_com2_H_2,V_com1_H_2,V_com2_2,V_com1_2] : % 172.18/172.32 ( c_Com_Ocom_OSemi(V_com1_2,V_com2_2) = c_Com_Ocom_OSemi(V_com1_H_2,V_com2_H_2) % 172.18/172.32 <=> ( V_com1_2 = V_com1_H_2 % 172.18/172.32 & V_com2_2 = V_com2_H_2 ) ) ). % 172.18/172.32 % 172.18/172.32 fof(fact_com_Osimps_I5_J,axiom, % 172.18/172.32 ! [V_com_H_2,V_fun_H_2,V_com_2,V_fun_2] : % 172.18/172.32 ( c_Com_Ocom_OWhile(V_fun_2,V_com_2) = c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) % 172.18/172.32 <=> ( V_fun_2 = V_fun_H_2 % 172.18/172.32 & V_com_2 = V_com_H_2 ) ) ). % 172.18/172.32 % 172.18/172.32 fof(fact_com_Osimps_I59_J,axiom, % 172.18/172.32 ! [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) ). % 172.18/172.32 % 172.18/172.32 fof(fact_com_Osimps_I58_J,axiom, % 172.18/172.32 ! [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) ). % 172.18/172.32 % 172.18/172.32 fof(fact_com_Osimps_I16_J,axiom, % 172.18/172.32 ! [V_com_H_2,V_fun_H_2] : c_Com_Ocom_OSKIP != c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) ). % 172.18/172.32 % 172.18/172.32 fof(fact_com_Osimps_I17_J,axiom, % 172.18/172.32 ! [V_com_H_2,V_fun_H_2] : c_Com_Ocom_OWhile(V_fun_H_2,V_com_H_2) != c_Com_Ocom_OSKIP ). % 172.18/172.32 % 172.18/172.32 fof(fact_com_Osimps_I49_J,axiom, % 172.18/172.32 ! [V_com2,V_com1,V_pname_H] : hAPP(c_Com_Ocom_OBODY,V_pname_H) != c_Com_Ocom_OSemi(V_com1,V_com2) ). % 172.18/172.32 % 172.18/172.32 fof(fact_com_Osimps_I48_J,axiom, % 172.18/172.32 ! [V_pname_H,V_com2,V_com1] : c_Com_Ocom_OSemi(V_com1,V_com2) != hAPP(c_Com_Ocom_OBODY,V_pname_H) ). % 172.18/172.32 % 172.18/172.32 fof(fact_com_Osimps_I12_J,axiom, % 172.18/172.32 ! [V_com2_H,V_com1_H] : c_Com_Ocom_OSKIP != c_Com_Ocom_OSemi(V_com1_H,V_com2_H) ). % 172.18/172.32 % 172.18/172.32 fof(fact_com_Osimps_I13_J,axiom, % 172.18/172.32 ! [V_com2_H,V_com1_H] : c_Com_Ocom_OSemi(V_com1_H,V_com2_H) != c_Com_Ocom_OSKIP ). % 172.18/172.32 % 172.18/172.32 fof(fact_MGT__def,axiom, % 172.18/172.32 ! [V_ca_2] : c_Hoare__Mirabelle_OMGT(V_ca_2) = hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),c_fequal),V_ca_2),c_Natural_Oevalc(V_ca_2)) ). % 172.18/172.32 % 172.18/172.32 fof(fact_MGT__alternI,axiom, % 172.18/172.32 ! [V_ca_2,V_Ga_2] : % 172.18/172.32 ( c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_OMGT(V_ca_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) % 172.18/172.32 => c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(tc_Com_Ostate),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_Com_Ostate),hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_HOL_Obool,tc_Com_Ostate),c_HOL_OAll(tc_Com_Ostate))),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Com_Ostate),hAPP(c_COMBC(tc_Com_Ostate,tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_fun(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_HOL_Obool)),tc_Com_Ostate),c_COMBS(tc_Com_Ostate,tc_HOL_Obool,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(tc_Com_Ostate,tc_HOL_Obool),tc_fun(tc_Com_Ostate,tc_fun(tc_HOL_Obool,tc_HOL_Obool)),tc_Com_Ostate),hAPP(c_COMBB(tc_HOL_Obool,tc_fun(tc_HOL_Obool,tc_HOL_Obool),tc_Com_Ostate),c_fimplies)),c_Natural_Oevalc(V_ca_2))))),c_fequal))),V_ca_2),c_fequal)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) ) ). % 172.27/172.32 % 172.27/172.32 fof(fact_evalc__elim__cases_I6_J,axiom, % 172.27/172.32 ! [V_s1,V_s,V_P] : % 172.27/172.32 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,V_P)),V_s),V_s1)) % 172.27/172.32 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_P))),V_s),V_s1)) ) ). % 172.27/172.32 % 172.27/172.32 fof(fact_evalc_OBody,axiom, % 172.27/172.32 ! [V_s1,V_s0,V_pn] : % 172.27/172.32 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn))),V_s0),V_s1)) % 172.27/172.32 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,V_pn)),V_s0),V_s1)) ) ). % 172.27/172.32 % 172.27/172.32 fof(fact_evalc_OSkip,axiom, % 172.27/172.32 ! [V_s] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),V_s),V_s)) ). % 172.27/172.32 % 172.27/172.32 fof(fact_evalc__elim__cases_I1_J,axiom, % 172.27/172.32 ! [V_t,V_s] : % 172.27/172.32 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),V_s),V_t)) % 172.27/172.32 => V_t = V_s ) ). % 172.27/172.32 % 172.27/172.32 fof(fact_evalc_OSemi,axiom, % 172.27/172.32 ! [V_s2,V_c1,V_s1,V_s0,V_c0] : % 172.27/172.32 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c0),V_s0),V_s1)) % 172.27/172.32 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c1),V_s1),V_s2)) % 172.27/172.32 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(V_c0,V_c1)),V_s0),V_s2)) ) ) ). % 172.27/172.32 % 172.27/172.32 fof(fact_evalc_OWhileTrue,axiom, % 172.27/172.32 ! [V_s2_2,V_s1_2,V_ca_2,V_s0_2,V_b_2] : % 172.27/172.32 ( hBOOL(hAPP(V_b_2,V_s0_2)) % 172.27/172.32 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_ca_2),V_s0_2),V_s1_2)) % 172.27/172.32 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_b_2,V_ca_2)),V_s1_2),V_s2_2)) % 172.27/172.32 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_b_2,V_ca_2)),V_s0_2),V_s2_2)) ) ) ) ). % 172.27/172.32 % 172.27/172.32 fof(fact_evalc_OWhileFalse,axiom, % 172.27/172.32 ! [V_ca_2,V_s_2,V_b_2] : % 172.27/172.32 ( ~ hBOOL(hAPP(V_b_2,V_s_2)) % 172.27/172.32 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_b_2,V_ca_2)),V_s_2),V_s_2)) ) ). % 172.27/172.32 % 172.27/172.32 fof(fact_finite_OinsertI,axiom, % 172.27/172.32 ! [V_a_2,V_A_2,T_a] : % 172.27/172.32 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.32 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2))) ) ). % 172.27/172.32 % 172.27/172.32 fof(fact_finite_OemptyI,axiom, % 172.27/172.32 ! [T_a] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ). % 172.27/172.32 % 172.27/172.32 fof(fact_evalc_Oequations_I9_J,axiom, % 172.27/172.32 ! [V_a3_2,V_a2_2,V_a1_2] : % 172.27/172.32 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,V_a1_2)),V_a2_2),V_a3_2)) % 172.27/172.32 <=> 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)) ) ). % 172.27/172.32 % 172.27/172.32 fof(fact_evalc_Oequations_I1_J,axiom, % 172.27/172.32 ! [V_a] : hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSKIP),V_a),V_a)) ). % 172.27/172.32 % 172.27/172.32 fof(fact_evalc_Oequations_I4_J,axiom, % 172.27/172.32 ! [V_a5_2,V_a2_2,V_a4_2,V_a1_2] : % 172.27/172.32 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(V_a1_2,V_a4_2)),V_a2_2),V_a5_2)) % 172.27/172.32 <=> ? [B_s1] : % 172.27/172.32 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a1_2),V_a2_2),B_s1)) % 172.27/172.32 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a4_2),B_s1),V_a5_2)) ) ) ). % 172.27/172.32 % 172.27/172.32 fof(fact_finite,axiom, % 172.27/172.32 ! [V_A_2,T_a] : % 172.27/172.32 ( class_Finite__Set_Ofinite(T_a) % 172.27/172.32 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ). % 172.27/172.32 % 172.27/172.32 fof(fact_finite__code,axiom, % 172.27/172.32 ! [V_A_2,T_a] : % 172.27/172.32 ( class_Finite__Set_Ofinite(T_a) % 172.27/172.32 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ). % 172.27/172.32 % 172.27/172.32 fof(fact_com__det,axiom, % 172.27/172.32 ! [V_u,V_t,V_s,V_c] : % 172.27/172.32 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c),V_s),V_t)) % 172.27/172.32 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c),V_s),V_u)) % 172.27/172.32 => V_u = V_t ) ) ). % 172.27/172.32 % 172.27/172.32 fof(fact_finite_Oequations_I1_J,axiom, % 172.27/172.32 ! [T_a] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ). % 172.27/172.32 % 172.27/172.32 fof(fact_finite__insert,axiom, % 172.27/172.32 ! [V_A_2,V_a_2,T_a] : % 172.27/172.32 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2))) % 172.27/172.32 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ). % 172.27/172.32 % 172.27/172.32 fof(fact_evalc_Oequations_I7_J,axiom, % 172.27/172.32 ! [V_a2_2,V_a3_2,V_a1_2] : % 172.27/172.32 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),V_a2_2),V_a2_2)) % 172.27/172.32 <=> ( hBOOL(hAPP(V_a1_2,V_a2_2)) % 172.27/172.32 => ? [B_s1] : % 172.27/172.32 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a3_2),V_a2_2),B_s1)) % 172.27/172.32 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),B_s1),V_a2_2)) ) ) ) ). % 172.27/172.32 % 172.27/172.32 fof(fact_evalc_Oequations_I8_J,axiom, % 172.27/172.32 ! [V_a5_2,V_a2_2,V_a3_2,V_a1_2] : % 172.27/172.32 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),V_a2_2),V_a5_2)) % 172.27/172.32 <=> ( ( V_a5_2 = V_a2_2 % 172.27/172.32 & ~ hBOOL(hAPP(V_a1_2,V_a2_2)) ) % 172.27/172.32 | ( hBOOL(hAPP(V_a1_2,V_a2_2)) % 172.27/172.32 & ? [B_s1] : % 172.27/172.32 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a3_2),V_a2_2),B_s1)) % 172.27/172.32 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OWhile(V_a1_2,V_a3_2)),B_s1),V_a5_2)) ) ) ) ) ). % 172.27/172.32 % 172.27/172.32 fof(fact_folding__one__idem_Oinsert__idem,axiom, % 172.27/172.32 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_a] : % 172.27/172.32 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2) % 172.27/172.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.32 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.27/172.32 => 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)) ) ) ) ). % 172.27/172.32 % 172.27/172.32 fof(fact_the__elem__def,axiom, % 172.27/172.32 ! [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))))) ). % 172.27/172.32 % 172.27/172.32 fof(fact_folding__image__simple__idem_Oinsert__idem,axiom, % 172.27/172.32 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 172.27/172.32 ( c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 172.27/172.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 172.27/172.32 => 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)) ) ) ). % 172.27/172.32 % 172.27/172.32 fof(fact_folding__one_Osingleton,axiom, % 172.27/172.32 ! [V_x_2,V_F_2,V_f_2,T_a] : % 172.27/172.32 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2) % 172.27/172.32 => 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 ) ). % 172.27/172.32 % 172.27/172.32 fof(fact_fold1Set__sing,axiom, % 172.27/172.32 ! [V_b_2,V_a_2,V_f_2,T_a] : % 172.27/172.32 ( 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)) % 172.27/172.32 <=> V_a_2 = V_b_2 ) ). % 172.27/172.32 % 172.27/172.32 fof(fact_evalc__elim__cases_I4_J,axiom, % 172.27/172.32 ! [V_t,V_s,V_c2,V_c1] : % 172.27/172.32 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(c_Com_Ocom_OSemi(V_c1,V_c2)),V_s),V_t)) % 172.27/172.32 => ~ ! [B_s1] : % 172.27/172.32 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c1),V_s),B_s1)) % 172.27/172.32 => ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c2),B_s1),V_t)) ) ) ). % 172.27/172.32 % 172.27/172.32 fof(fact_Loop__sound__lemma,axiom, % 172.27/172.32 ! [V_ca_2,V_b_2,V_P_2,V_Ga_2,T_a] : % 172.27/172.32 ( c_Hoare__Mirabelle_Ohoare__valids(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),c_Hoare__Mirabelle_Opeek__and(T_a,V_P_2,V_b_2)),V_ca_2),V_P_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) % 172.27/172.32 => c_Hoare__Mirabelle_Ohoare__valids(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),c_Com_Ocom_OWhile(V_b_2,V_ca_2)),c_Hoare__Mirabelle_Opeek__and(T_a,V_P_2,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),V_b_2)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) ). % 172.27/172.32 % 172.27/172.32 fof(fact_finite_Osimps,axiom, % 172.27/172.32 ! [V_a_2,T_a] : % 172.27/172.32 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_a_2)) % 172.27/172.32 <=> ( V_a_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.27/172.32 | ? [B_A] : % 172.27/172.32 ( ? [B_a] : V_a_2 = hAPP(hAPP(c_Set_Oinsert(T_a),B_a),B_A) % 172.27/172.32 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),B_A)) ) ) ) ). % 172.27/172.32 % 172.27/172.32 fof(fact_Loop,axiom, % 172.27/172.32 ! [V_ca_2,V_b_2,V_P_2,V_Ga_2,T_a] : % 172.27/172.32 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),c_Hoare__Mirabelle_Opeek__and(T_a,V_P_2,V_b_2)),V_ca_2),V_P_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) % 172.27/172.32 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),c_Com_Ocom_OWhile(V_b_2,V_ca_2)),c_Hoare__Mirabelle_Opeek__and(T_a,V_P_2,hAPP(c_Fun_Ocomp(tc_HOL_Obool,tc_HOL_Obool,tc_Com_Ostate,c_fNot),V_b_2)))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) ). % 172.27/172.32 % 172.27/172.32 fof(fact_Body__sound__lemma,axiom, % 172.27/172.32 ! [V_Procs_2,V_Q_2,V_P_2,V_Ga_2,T_a] : % 172.27/172.32 ( 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)) % 172.27/172.32 => 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)) ) ). % 172.27/172.32 % 172.27/172.32 fof(fact_finite__pointwise,axiom, % 172.27/172.32 ! [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] : % 172.27/172.32 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_U_2)) % 172.27/172.32 => ( ! [B_p] : % 172.27/172.32 ( 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)))) % 172.27/172.32 => 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)))) ) % 172.27/172.32 => ( 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)) % 172.27/172.32 => 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)) ) ) ) ). % 172.27/172.32 % 172.27/172.32 fof(fact_Body__triple__valid__Suc,axiom, % 172.27/172.32 ! [V_Q_2,V_pn_2,V_P_2,V_n_2,T_a] : % 172.27/172.32 ( c_Hoare__Mirabelle_Otriple__valid(T_a,V_n_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_pn_2))),V_Q_2)) % 172.27/172.32 <=> c_Hoare__Mirabelle_Otriple__valid(T_a,hAPP(c_Nat_OSuc,V_n_2),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),hAPP(c_Com_Ocom_OBODY,V_pn_2)),V_Q_2)) ) ). % 172.27/172.32 % 172.27/172.32 fof(fact_finite__imageI,axiom, % 172.27/172.32 ! [V_h_2,T_b,V_F_2,T_a] : % 172.27/172.32 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) % 172.27/172.32 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Oimage(T_a,T_b,V_h_2),V_F_2))) ) ). % 172.27/172.32 % 172.27/172.32 fof(fact_Un__absorb,axiom, % 172.27/172.32 ! [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 ). % 172.27/172.32 % 172.27/172.32 fof(fact_Un__commute,axiom, % 172.27/172.32 ! [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) ). % 172.27/172.32 % 172.27/172.32 fof(fact_Un__left__absorb,axiom, % 172.27/172.32 ! [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) ). % 172.27/172.32 % 172.27/172.32 fof(fact_Un__left__commute,axiom, % 172.27/172.32 ! [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)) ). % 172.27/172.32 % 172.27/172.32 fof(fact_image__Un,axiom, % 172.27/172.32 ! [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)) ). % 172.27/172.32 % 172.27/172.32 fof(fact_Un__assoc,axiom, % 172.27/172.32 ! [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)) ). % 172.27/172.32 % 172.27/172.32 fof(fact_bex__Un,axiom, % 172.27/172.32 ! [V_P_2,V_B_2,V_A_2,T_a] : % 172.27/172.32 ( ? [B_x] : % 172.27/172.32 ( 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))) % 172.27/172.32 & hBOOL(hAPP(V_P_2,B_x)) ) % 172.27/172.32 <=> ( ? [B_x] : % 172.27/172.32 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 172.27/172.32 & hBOOL(hAPP(V_P_2,B_x)) ) % 172.27/172.32 | ? [B_x] : % 172.27/172.32 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_B_2)) % 172.27/172.32 & hBOOL(hAPP(V_P_2,B_x)) ) ) ) ). % 172.27/172.32 % 172.27/172.32 fof(fact_ball__Un,axiom, % 172.27/172.32 ! [V_P_2,V_B_2,V_A_2,T_a] : % 172.27/172.32 ( ! [B_x] : % 172.27/172.32 ( 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))) % 172.27/172.32 => hBOOL(hAPP(V_P_2,B_x)) ) % 172.27/172.32 <=> ( ! [B_x] : % 172.27/172.32 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 172.27/172.32 => hBOOL(hAPP(V_P_2,B_x)) ) % 172.27/172.32 & ! [B_x] : % 172.27/172.32 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_B_2)) % 172.27/172.32 => hBOOL(hAPP(V_P_2,B_x)) ) ) ) ). % 172.27/172.32 % 172.27/172.32 fof(fact_triple__valid__Suc,axiom, % 172.27/172.32 ! [V_t,V_n,T_a] : % 172.27/172.32 ( c_Hoare__Mirabelle_Otriple__valid(T_a,hAPP(c_Nat_OSuc,V_n),V_t) % 172.27/172.32 => c_Hoare__Mirabelle_Otriple__valid(T_a,V_n,V_t) ) ). % 172.27/172.32 % 172.27/172.32 fof(fact_image__image,axiom, % 172.27/172.32 ! [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) ). % 172.27/172.32 % 172.27/172.32 fof(fact_folding__one__idem_Oidem,axiom, % 172.27/172.32 ! [V_x_2,V_F_2,V_f_2,T_a] : % 172.27/172.32 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2) % 172.27/172.32 => hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2 ) ). % 172.27/172.32 % 172.27/172.32 fof(fact_folding__image__simple__idem_Oidem,axiom, % 172.27/172.32 ! [V_x_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 172.27/172.32 ( c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 172.27/172.32 => hAPP(hAPP(V_f_2,V_x_2),V_x_2) = V_x_2 ) ). % 172.27/172.32 % 172.27/172.32 fof(fact_folding__image__simple__idem_Ounion__idem,axiom, % 172.27/172.32 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 172.27/172.32 ( c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 172.27/172.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 172.27/172.32 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 172.27/172.32 => 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)) ) ) ) ). % 172.27/172.32 % 172.27/172.32 fof(fact_empty__is__image,axiom, % 172.27/172.32 ! [V_A_2,V_f_2,T_b,T_a] : % 172.27/172.32 ( 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) % 172.27/172.32 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 172.27/172.32 % 172.27/172.32 fof(fact_image__empty,axiom, % 172.27/172.32 ! [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)) ). % 172.27/172.32 % 172.27/172.32 fof(fact_image__is__empty,axiom, % 172.27/172.32 ! [V_A_2,V_f_2,T_a,T_b] : % 172.27/172.32 ( 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)) % 172.27/172.33 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ). % 172.27/172.33 % 172.27/172.33 fof(fact_image__insert,axiom, % 172.27/172.33 ! [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)) ). % 172.27/172.33 % 172.27/172.33 fof(fact_Un__empty__left,axiom, % 172.27/172.33 ! [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 ). % 172.27/172.33 % 172.27/172.33 fof(fact_Un__empty__right,axiom, % 172.27/172.33 ! [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 ). % 172.27/172.33 % 172.27/172.33 fof(fact_Un__empty,axiom, % 172.27/172.33 ! [V_B_2,V_A_2,T_a] : % 172.27/172.33 ( 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)) % 172.27/172.33 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.27/172.33 & V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 172.27/172.33 % 172.27/172.33 fof(fact_finite__UnI,axiom, % 172.27/172.33 ! [V_Ga_2,V_F_2,T_a] : % 172.27/172.33 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) % 172.27/172.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_Ga_2)) % 172.27/172.33 => 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))) ) ) ). % 172.27/172.33 % 172.27/172.33 fof(fact_finite__Un,axiom, % 172.27/172.33 ! [V_Ga_2,V_F_2,T_a] : % 172.27/172.33 ( 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))) % 172.27/172.33 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) % 172.27/172.33 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_Ga_2)) ) ) ). % 172.27/172.33 % 172.27/172.33 fof(fact_Un__insert__right,axiom, % 172.27/172.33 ! [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)) ). % 172.27/172.33 % 172.27/172.33 fof(fact_Un__insert__left,axiom, % 172.27/172.33 ! [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)) ). % 172.27/172.33 % 172.27/172.33 fof(fact_peek__and__def,axiom, % 172.27/172.33 ! [V_s_2,V_Z_2,V_p_2,V_P_2,T_a] : % 172.27/172.33 ( hBOOL(hAPP(hAPP(c_Hoare__Mirabelle_Opeek__and(T_a,V_P_2,V_p_2),V_Z_2),V_s_2)) % 172.27/172.33 <=> ( hBOOL(hAPP(hAPP(V_P_2,V_Z_2),V_s_2)) % 172.27/172.33 & hBOOL(hAPP(V_p_2,V_s_2)) ) ) ). % 172.27/172.33 % 172.27/172.33 fof(fact_folding__one__idem_Ounion__idem,axiom, % 172.27/172.33 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_a] : % 172.27/172.33 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2) % 172.27/172.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.33 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.27/172.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 172.27/172.33 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.27/172.33 => 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)) ) ) ) ) ) ). % 172.27/172.33 % 172.27/172.33 fof(fact_insert__is__Un,axiom, % 172.27/172.33 ! [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) ). % 172.27/172.33 % 172.27/172.33 fof(fact_empty__fold1SetE,axiom, % 172.27/172.33 ! [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)) ). % 172.27/172.33 % 172.27/172.33 fof(fact_fold1Set__nonempty,axiom, % 172.27/172.33 ! [V_x_2,V_A_2,V_f_2,T_a] : % 172.27/172.33 ( hBOOL(hAPP(c_Finite__Set_Ofold1Set(T_a,V_f_2,V_A_2),V_x_2)) % 172.27/172.33 => V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 172.27/172.33 % 172.27/172.33 fof(fact_image__constant__conv,axiom, % 172.27/172.33 ! [V_ca_2,T_b,T_a,V_A_2] : % 172.27/172.33 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.27/172.33 => hAPP(c_Set_Oimage(T_a,T_b,hAPP(c_COMBK(T_b,T_a),V_ca_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) % 172.27/172.33 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.27/172.33 => hAPP(c_Set_Oimage(T_a,T_b,hAPP(c_COMBK(T_b,T_a),V_ca_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_ca_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ) ) ). % 172.27/172.33 % 172.27/172.33 fof(fact_hoare__derivs_OBody,axiom, % 172.27/172.33 ! [V_Procs_2,V_Q_2,V_P_2,V_Ga_2,T_a] : % 172.27/172.33 ( 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)) % 172.27/172.33 => 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)) ) ). % 172.27/172.33 % 172.27/172.33 fof(fact_Body1,axiom, % 172.27/172.33 ! [V_pn_2,V_Procs_2,V_Q_2,V_P_2,V_Ga_2,T_a] : % 172.27/172.33 ( 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)) % 172.27/172.33 => ( hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),V_pn_2),V_Procs_2)) % 172.27/172.33 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),hAPP(V_P_2,V_pn_2)),hAPP(c_Com_Ocom_OBODY,V_pn_2)),hAPP(V_Q_2,V_pn_2))),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) ) ). % 172.27/172.33 % 172.27/172.33 fof(fact_hoare__derivs_OIf,axiom, % 172.27/172.33 ! [V_d_2,V_Q_2,V_ca_2,V_b_2,V_P_2,V_Ga_2,T_a] : % 172.27/172.33 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),c_Hoare__Mirabelle_Opeek__and(T_a,V_P_2,V_b_2)),V_ca_2),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) % 172.27/172.33 => ( 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)))) % 172.27/172.33 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(T_a)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),c_Com_Ocom_OCond(V_b_2,V_ca_2,V_d_2)),V_Q_2)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(T_a),tc_HOL_Obool)))) ) ) ). % 172.27/172.33 % 172.27/172.33 fof(fact_sup1CI,axiom, % 172.27/172.33 ! [T_a,V_A_2,V_x_2,V_B_2] : % 172.27/172.33 ( ( ~ hBOOL(hAPP(V_B_2,V_x_2)) % 172.27/172.33 => hBOOL(hAPP(V_A_2,V_x_2)) ) % 172.27/172.33 => 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)) ) ). % 172.27/172.33 % 172.27/172.33 fof(fact_sup1E,axiom, % 172.27/172.33 ! [V_x_2,V_B_2,V_A_2,T_a] : % 172.27/172.33 ( 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)) % 172.27/172.33 => ( ~ hBOOL(hAPP(V_A_2,V_x_2)) % 172.27/172.33 => hBOOL(hAPP(V_B_2,V_x_2)) ) ) ). % 172.27/172.33 % 172.27/172.33 fof(fact_sup__fun__def,axiom, % 172.27/172.33 ! [V_x_2,V_g_2,V_f_2,T_b,T_a] : % 172.27/172.33 ( class_Lattices_Olattice(T_a) % 172.27/172.33 => 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)) ) ). % 172.27/172.33 % 172.27/172.33 fof(fact_image__compose,axiom, % 172.27/172.33 ! [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)) ). % 172.27/172.33 % 172.27/172.33 fof(fact_sup__apply,axiom, % 172.27/172.33 ! [V_x_2,V_g_2,V_f_2,T_b,T_a] : % 172.27/172.33 ( class_Lattices_Olattice(T_a) % 172.27/172.33 => 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)) ) ). % 172.27/172.33 % 172.27/172.33 fof(fact_sup__bot__left,axiom, % 172.27/172.33 ! [V_x,T_a] : % 172.27/172.33 ( class_Lattices_Obounded__lattice__bot(T_a) % 172.27/172.33 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x) = V_x ) ). % 172.27/172.33 % 172.27/172.33 fof(fact_sup__bot__right,axiom, % 172.27/172.33 ! [V_x,T_a] : % 172.27/172.33 ( class_Lattices_Obounded__lattice__bot(T_a) % 172.27/172.33 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),c_Orderings_Obot__class_Obot(T_a)) = V_x ) ). % 172.27/172.33 % 172.27/172.33 fof(fact_sup__eq__bot__iff,axiom, % 172.27/172.33 ! [V_y_2,V_x_2,T_a] : % 172.27/172.33 ( class_Lattices_Obounded__lattice__bot(T_a) % 172.27/172.33 => ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x_2),V_y_2) = c_Orderings_Obot__class_Obot(T_a) % 172.27/172.33 <=> ( V_x_2 = c_Orderings_Obot__class_Obot(T_a) % 172.27/172.33 & V_y_2 = c_Orderings_Obot__class_Obot(T_a) ) ) ) ). % 172.27/172.33 % 172.27/172.33 fof(fact_folding__idem_Ounion__idem,axiom, % 172.27/172.33 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 172.27/172.33 ( c_Finite__Set_Ofolding__idem(T_a,T_b,V_f_2,V_F_2) % 172.27/172.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 172.27/172.33 => 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)) ) ) ) ). % 172.27/172.33 % 172.27/172.33 fof(fact_equalityCE,axiom, % 172.27/172.33 ! [V_ca_2,T_a,V_B_2,V_A_2] : % 172.27/172.33 ( V_A_2 = V_B_2 % 172.27/172.33 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 172.27/172.33 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) % 172.27/172.33 => ~ ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 172.27/172.33 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ) ). % 172.27/172.33 % 172.27/172.33 fof(fact_emptyE,axiom, % 172.27/172.33 ! [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)))) ). % 172.27/172.33 % 172.27/172.33 fof(fact_insertCI,axiom, % 172.27/172.33 ! [V_b_2,V_B_2,V_a_2,T_a] : % 172.27/172.33 ( ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_B_2)) % 172.27/172.33 => V_a_2 = V_b_2 ) % 172.27/172.33 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),V_B_2))) ) ). % 172.27/172.33 % 172.27/172.33 fof(fact_insertE,axiom, % 172.27/172.33 ! [V_A_2,V_b_2,V_a_2,T_a] : % 172.27/172.33 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),V_A_2))) % 172.27/172.33 => ( V_a_2 != V_b_2 % 172.27/172.33 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ). % 172.27/172.33 % 172.27/172.33 fof(fact_image__eqI,axiom, % 172.27/172.33 ! [T_a,V_A_2,T_b,V_x_2,V_f_2,V_b_2] : % 172.27/172.33 ( V_b_2 = hAPP(V_f_2,V_x_2) % 172.27/172.33 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 172.27/172.33 => hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2))) ) ) ). % 172.27/172.33 % 172.27/172.33 fof(fact_UnCI,axiom, % 172.27/172.33 ! [V_A_2,V_B_2,V_ca_2,T_a] : % 172.27/172.33 ( ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) % 172.27/172.33 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) ) % 172.27/172.33 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ). % 172.27/172.33 % 172.27/172.33 fof(fact_UnE,axiom, % 172.27/172.33 ! [V_B_2,V_A_2,V_ca_2,T_a] : % 172.27/172.33 ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 172.27/172.33 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 172.27/172.33 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ). % 172.27/172.33 % 172.27/172.33 fof(fact_evalc_OIfFalse,axiom, % 172.27/172.33 ! [V_c0_2,V_s1_2,V_c1_2,V_s_2,V_b_2] : % 172.27/172.33 ( ~ hBOOL(hAPP(V_b_2,V_s_2)) % 172.27/172.33 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c1_2),V_s_2),V_s1_2)) % 172.27/172.33 => 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)) ) ) ). % 172.27/172.33 % 172.27/172.33 fof(fact_evalc_OIfTrue,axiom, % 172.27/172.33 ! [V_c1_2,V_s1_2,V_c0_2,V_s_2,V_b_2] : % 172.27/172.33 ( hBOOL(hAPP(V_b_2,V_s_2)) % 172.27/172.33 => ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c0_2),V_s_2),V_s1_2)) % 172.27/172.33 => 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)) ) ) ). % 172.27/172.33 % 172.27/172.33 fof(fact_evalc__elim__cases_I5_J,axiom, % 172.27/172.33 ! [V_t_2,V_s_2,V_c2_2,V_c1_2,V_b_2] : % 172.27/172.33 ( 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)) % 172.27/172.33 => ( ( hBOOL(hAPP(V_b_2,V_s_2)) % 172.27/172.33 => ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c1_2),V_s_2),V_t_2)) ) % 172.27/172.33 => ~ ( ~ hBOOL(hAPP(V_b_2,V_s_2)) % 172.27/172.33 => ~ hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c2_2),V_s_2),V_t_2)) ) ) ) ). % 172.27/172.33 % 172.27/172.33 fof(fact_eq__mem,axiom, % 172.27/172.33 ! [V_y_2,V_x_2,T_a] : % 172.27/172.33 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_fequal,V_y_2))) % 172.27/172.33 <=> V_x_2 = V_y_2 ) ). % 172.27/172.33 % 172.27/172.33 fof(fact_pred__equals__eq,axiom, % 172.27/172.33 ! [V_S_2,V_R_2,T_a] : % 172.27/172.33 ( 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) % 172.27/172.33 <=> V_R_2 = V_S_2 ) ). % 172.27/172.33 % 172.27/172.33 fof(fact_eq__mem__trans,axiom, % 172.27/172.33 ! [V_A_2,T_a,V_b_2,V_a_2] : % 172.27/172.33 ( V_a_2 = V_b_2 % 172.27/172.33 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),V_A_2)) % 172.27/172.33 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ). % 172.27/172.33 % 172.27/172.33 fof(fact_eqelem__imp__iff,axiom, % 172.27/172.33 ! [V_A_2,T_a,V_y_2,V_x_2] : % 172.27/172.33 ( V_x_2 = V_y_2 % 172.27/172.33 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 172.27/172.33 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) ) ) ). % 172.27/172.33 % 172.27/172.33 fof(fact_eqset__imp__iff,axiom, % 172.27/172.33 ! [V_x_2,T_a,V_B_2,V_A_2] : % 172.27/172.33 ( V_A_2 = V_B_2 % 172.27/172.33 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 172.27/172.33 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) ) ) ). % 172.27/172.33 % 172.27/172.33 fof(fact_com_Osimps_I4_J,axiom, % 172.27/172.33 ! [V_com2_H_2,V_com1_H_2,V_fun_H_2,V_com2_2,V_com1_2,V_fun_2] : % 172.27/172.33 ( 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) % 172.27/172.33 <=> ( V_fun_2 = V_fun_H_2 % 172.27/172.33 & V_com1_2 = V_com1_H_2 % 172.27/172.33 & V_com2_2 = V_com2_H_2 ) ) ). % 172.27/172.33 % 172.27/172.33 fof(fact_mem__def,axiom, % 172.27/172.33 ! [V_A_2,V_x_2,T_a] : % 172.27/172.33 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 172.27/172.33 <=> hBOOL(hAPP(V_A_2,V_x_2)) ) ). % 172.27/172.33 % 172.27/172.33 fof(fact_bot__empty__eq,axiom, % 172.27/172.33 ! [V_x_2,T_a] : % 172.27/172.33 ( hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)),V_x_2)) % 172.27/172.33 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ) ). % 172.27/172.33 % 172.27/172.33 fof(fact_sup__Un__eq,axiom, % 172.27/172.33 ! [V_x_2,V_S_2,V_R_2,T_a] : % 172.27/172.33 ( 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)) % 172.27/172.33 <=> 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))) ) ). % 172.27/172.33 % 172.27/172.33 fof(fact_equals0D,axiom, % 172.27/172.33 ! [V_a_2,T_a,V_A_2] : % 172.27/172.33 ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.27/172.33 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ). % 172.27/172.33 % 172.27/172.33 fof(fact_empty__iff,axiom, % 172.27/172.33 ! [V_ca_2,T_a] : ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ). % 172.27/172.33 % 172.27/172.33 fof(fact_ex__in__conv,axiom, % 172.27/172.33 ! [V_A_2,T_a] : % 172.27/172.33 ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 172.27/172.33 <=> V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 172.27/172.33 % 172.27/172.33 fof(fact_all__not__in__conv,axiom, % 172.27/172.33 ! [V_A_2,T_a] : % 172.27/172.33 ( ! [B_x] : ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 172.27/172.33 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 172.27/172.33 % 172.27/172.33 fof(fact_insert__absorb,axiom, % 172.27/172.33 ! [V_A_2,V_a_2,T_a] : % 172.27/172.33 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 172.27/172.33 => hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2) = V_A_2 ) ). % 172.27/172.33 % 172.27/172.33 fof(fact_insertI2,axiom, % 172.27/172.33 ! [V_b_2,V_B_2,V_a_2,T_a] : % 172.27/172.33 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_B_2)) % 172.27/172.33 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),V_B_2))) ) ). % 172.27/172.33 % 172.27/172.33 fof(fact_insert__ident,axiom, % 172.27/172.33 ! [V_B_2,V_A_2,V_x_2,T_a] : % 172.27/172.33 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 172.27/172.33 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) % 172.27/172.33 => ( 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) % 172.27/172.33 <=> V_A_2 = V_B_2 ) ) ) ). % 172.27/172.33 % 172.27/172.33 fof(fact_insert__iff,axiom, % 172.27/172.33 ! [V_A_2,V_b_2,V_a_2,T_a] : % 172.27/172.33 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),V_A_2))) % 172.27/172.33 <=> ( V_a_2 = V_b_2 % 172.27/172.33 | hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ). % 172.27/172.33 % 172.27/172.33 fof(fact_insertI1,axiom, % 172.27/172.33 ! [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))) ). % 172.27/172.33 % 172.27/172.33 fof(fact_rev__image__eqI,axiom, % 172.27/172.33 ! [T_b,V_f_2,V_b_2,V_A_2,V_x_2,T_a] : % 172.27/172.33 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 172.27/172.33 => ( V_b_2 = hAPP(V_f_2,V_x_2) % 172.27/172.33 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2))) ) ) ). % 172.27/172.33 % 172.27/172.33 fof(fact_imageI,axiom, % 172.27/172.33 ! [V_f_2,T_b,V_A_2,V_x_2,T_a] : % 172.27/172.33 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 172.27/172.33 => 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))) ) ). % 172.27/172.33 % 172.27/172.33 fof(fact_image__iff,axiom, % 172.27/172.33 ! [V_A_2,V_f_2,T_b,V_z_2,T_a] : % 172.27/172.33 ( hBOOL(hAPP(hAPP(c_member(T_a),V_z_2),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2))) % 172.27/172.33 <=> ? [B_x] : % 172.27/172.33 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 172.27/172.33 & V_z_2 = hAPP(V_f_2,B_x) ) ) ). % 172.27/172.33 % 172.27/172.33 fof(fact_UnI2,axiom, % 172.27/172.33 ! [V_A_2,V_B_2,V_ca_2,T_a] : % 172.27/172.33 ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) % 172.27/172.33 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ). % 172.27/172.33 % 172.27/172.33 fof(fact_UnI1,axiom, % 172.27/172.33 ! [V_B_2,V_A_2,V_ca_2,T_a] : % 172.27/172.33 ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 172.27/172.33 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ). % 172.27/172.33 % 172.27/172.33 fof(fact_Un__iff,axiom, % 172.27/172.33 ! [V_B_2,V_A_2,V_ca_2,T_a] : % 172.27/172.33 ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 172.27/172.33 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 172.27/172.33 | hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ). % 172.27/172.33 % 172.27/172.33 fof(fact_folding__idem_Oin__comp__idem,axiom, % 172.27/172.33 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 172.27/172.33 ( c_Finite__Set_Ofolding__idem(T_a,T_b,V_f_2,V_F_2) % 172.27/172.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.33 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 172.27/172.33 => 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) ) ) ) ). % 172.27/172.33 % 172.27/172.33 fof(fact_evalc_Oequations_I5_J,axiom, % 172.27/172.33 ! [V_a4_2,V_a2_2,V_a5_2,V_a3_2,V_a1_2] : % 172.27/172.33 ( 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)) % 172.27/172.33 <=> ( ( hBOOL(hAPP(V_a1_2,V_a2_2)) % 172.27/172.33 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a3_2),V_a2_2),V_a4_2)) ) % 172.27/172.33 | ( ~ hBOOL(hAPP(V_a1_2,V_a2_2)) % 172.27/172.33 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a5_2),V_a2_2),V_a4_2)) ) ) ) ). % 172.27/172.33 % 172.27/172.33 fof(fact_evalc_Oequations_I6_J,axiom, % 172.27/172.33 ! [V_a4_2,V_a2_2,V_a3_2,V_a5_2,V_a1_2] : % 172.27/172.33 ( 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)) % 172.27/172.33 <=> ( ( hBOOL(hAPP(V_a1_2,V_a2_2)) % 172.27/172.33 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a5_2),V_a2_2),V_a4_2)) ) % 172.27/172.33 | ( ~ hBOOL(hAPP(V_a1_2,V_a2_2)) % 172.27/172.33 & hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_a3_2),V_a2_2),V_a4_2)) ) ) ) ). % 172.27/172.33 % 172.27/172.33 fof(fact_com_Osimps_I54_J,axiom, % 172.27/172.33 ! [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) ). % 172.27/172.33 % 172.27/172.33 fof(fact_com_Osimps_I55_J,axiom, % 172.27/172.33 ! [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) ). % 172.27/172.33 % 172.27/172.33 fof(fact_com_Osimps_I52_J,axiom, % 172.27/172.33 ! [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) ). % 172.27/172.33 % 172.27/172.33 fof(fact_com_Osimps_I53_J,axiom, % 172.27/172.33 ! [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) ). % 172.27/172.33 % 172.27/172.33 fof(fact_com_Osimps_I45_J,axiom, % 172.27/172.33 ! [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) ). % 172.27/172.33 % 172.27/172.33 fof(fact_com_Osimps_I44_J,axiom, % 172.27/172.33 ! [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) ). % 172.27/172.33 % 172.27/172.33 fof(fact_com_Osimps_I15_J,axiom, % 172.27/172.33 ! [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 ). % 172.27/172.33 % 172.27/172.33 fof(fact_com_Osimps_I14_J,axiom, % 172.27/172.33 ! [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) ). % 172.27/172.33 % 172.27/172.33 fof(fact_singletonE,axiom, % 172.27/172.33 ! [V_a_2,V_b_2,T_a] : % 172.27/172.33 ( 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))))) % 172.27/172.33 => V_b_2 = V_a_2 ) ). % 172.27/172.33 % 172.27/172.33 fof(fact_singleton__iff,axiom, % 172.27/172.33 ! [V_a_2,V_b_2,T_a] : % 172.27/172.33 ( 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))))) % 172.27/172.33 <=> V_b_2 = V_a_2 ) ). % 172.27/172.33 % 172.27/172.33 fof(fact_insert__image,axiom, % 172.27/172.33 ! [V_f_2,T_b,V_A_2,V_x_2,T_a] : % 172.27/172.33 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 172.27/172.33 => 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) ) ). % 172.27/172.33 % 172.27/172.33 fof(fact_folding__idem_Oidem__left__comp,axiom, % 172.27/172.33 ! [V_g_2,V_x_2,T_c,V_F_2,V_f_2,T_b,T_a] : % 172.27/172.33 ( c_Finite__Set_Ofolding__idem(T_a,T_b,V_f_2,V_F_2) % 172.27/172.33 => 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) ) ). % 172.27/172.33 % 172.27/172.33 fof(fact_folding__idem_Oidem__comp,axiom, % 172.27/172.33 ! [V_x_2,V_F_2,V_f_2,T_b,T_a] : % 172.27/172.33 ( c_Finite__Set_Ofolding__idem(T_a,T_b,V_f_2,V_F_2) % 172.27/172.33 => 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) ) ). % 172.27/172.33 % 172.27/172.33 fof(fact_folding__one__idem_Oin__idem,axiom, % 172.27/172.33 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_a] : % 172.27/172.33 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2) % 172.27/172.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.33 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 172.27/172.33 => hAPP(hAPP(V_f_2,V_x_2),hAPP(V_F_2,V_A_2)) = hAPP(V_F_2,V_A_2) ) ) ) ). % 172.27/172.33 % 172.27/172.33 fof(fact_folding__image__simple__idem_Oin__idem,axiom, % 172.27/172.33 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 172.27/172.33 ( c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 172.27/172.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 172.27/172.33 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 172.27/172.33 => 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) ) ) ) ). % 172.27/172.33 % 172.27/172.33 fof(fact_sup_Oidem,axiom, % 172.27/172.33 ! [V_a,T_a] : % 172.27/172.33 ( class_Lattices_Osemilattice__sup(T_a) % 172.27/172.33 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_a),V_a) = V_a ) ). % 172.27/172.33 % 172.27/172.33 fof(fact_sup__idem,axiom, % 172.27/172.33 ! [V_x,T_a] : % 172.27/172.33 ( class_Lattices_Osemilattice__sup(T_a) % 172.27/172.33 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_x) = V_x ) ). % 172.27/172.33 % 172.27/172.33 fof(fact_sup_Ocommute,axiom, % 172.27/172.33 ! [V_b,V_a,T_a] : % 172.27/172.33 ( class_Lattices_Osemilattice__sup(T_a) % 172.27/172.33 => 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) ) ). % 172.27/172.33 % 172.27/172.33 fof(fact_inf__sup__aci_I5_J,axiom, % 172.27/172.33 ! [V_y,V_x,T_a] : % 172.27/172.33 ( class_Lattices_Olattice(T_a) % 172.27/172.33 => 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) ) ). % 172.27/172.33 % 172.27/172.33 fof(fact_sup__commute,axiom, % 172.27/172.33 ! [V_y,V_x,T_a] : % 172.27/172.33 ( class_Lattices_Osemilattice__sup(T_a) % 172.27/172.33 => 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) ) ). % 172.27/172.33 % 172.27/172.33 fof(fact_sup_Oleft__idem,axiom, % 172.27/172.33 ! [V_b,V_a,T_a] : % 172.27/172.33 ( class_Lattices_Osemilattice__sup(T_a) % 172.27/172.33 => 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) ) ). % 172.27/172.33 % 172.27/172.33 fof(fact_inf__sup__aci_I8_J,axiom, % 172.27/172.33 ! [V_y,V_x,T_a] : % 172.27/172.33 ( class_Lattices_Olattice(T_a) % 172.27/172.33 => 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) ) ). % 172.27/172.33 % 172.27/172.33 fof(fact_sup__left__idem,axiom, % 172.27/172.33 ! [V_y,V_x,T_a] : % 172.27/172.33 ( class_Lattices_Osemilattice__sup(T_a) % 172.27/172.33 => 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) ) ). % 172.27/172.33 % 172.27/172.33 fof(fact_sup_Oleft__commute,axiom, % 172.27/172.33 ! [V_c,V_a,V_b,T_a] : % 172.27/172.33 ( class_Lattices_Osemilattice__sup(T_a) % 172.27/172.33 => 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)) ) ). % 172.27/172.33 % 172.27/172.33 fof(fact_inf__sup__aci_I7_J,axiom, % 172.27/172.33 ! [V_z,V_y,V_x,T_a] : % 172.27/172.33 ( class_Lattices_Olattice(T_a) % 172.27/172.33 => 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)) ) ). % 172.27/172.33 % 172.27/172.33 fof(fact_sup__left__commute,axiom, % 172.27/172.33 ! [V_z,V_y,V_x,T_a] : % 172.27/172.33 ( class_Lattices_Osemilattice__sup(T_a) % 172.27/172.33 => 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)) ) ). % 172.27/172.33 % 172.27/172.33 fof(fact_sup_Oassoc,axiom, % 172.27/172.33 ! [V_c,V_b,V_a,T_a] : % 172.27/172.33 ( class_Lattices_Osemilattice__sup(T_a) % 172.27/172.33 => 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)) ) ). % 172.27/172.33 % 172.27/172.33 fof(fact_inf__sup__aci_I6_J,axiom, % 172.27/172.33 ! [V_z,V_y,V_x,T_a] : % 172.27/172.33 ( class_Lattices_Olattice(T_a) % 172.27/172.33 => 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)) ) ). % 172.27/172.33 % 172.27/172.33 fof(fact_sup__assoc,axiom, % 172.27/172.33 ! [V_z,V_y,V_x,T_a] : % 172.27/172.33 ( class_Lattices_Osemilattice__sup(T_a) % 172.27/172.33 => 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)) ) ). % 172.27/172.33 % 172.27/172.33 fof(fact_sup1I1,axiom, % 172.27/172.33 ! [V_B_2,T_a,V_x_2,V_A_2] : % 172.27/172.33 ( hBOOL(hAPP(V_A_2,V_x_2)) % 172.27/172.33 => 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)) ) ). % 172.27/172.33 % 172.27/172.33 fof(fact_sup1I2,axiom, % 172.27/172.33 ! [V_A_2,T_a,V_x_2,V_B_2] : % 172.27/172.33 ( hBOOL(hAPP(V_B_2,V_x_2)) % 172.27/172.33 => 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)) ) ). % 172.27/172.33 % 172.27/172.33 fof(fact_o__assoc,axiom, % 172.27/172.33 ! [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) ). % 172.27/172.33 % 172.27/172.33 fof(fact_o__apply,axiom, % 172.27/172.33 ! [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)) ). % 172.27/172.33 % 172.27/172.33 fof(fact_o__eq__dest,axiom, % 172.27/172.33 ! [V_v_2,V_d_2,V_ca_2,T_d,V_b_2,V_a_2,T_a,T_b,T_c] : % 172.27/172.33 ( hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_a_2),V_b_2) = hAPP(c_Fun_Ocomp(T_d,T_b,T_a,V_ca_2),V_d_2) % 172.27/172.33 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_ca_2,hAPP(V_d_2,V_v_2)) ) ). % 172.27/172.33 % 172.27/172.33 fof(fact_o__eq__elim,axiom, % 172.27/172.33 ! [V_d_2,V_ca_2,T_d,V_b_2,V_a_2,T_a,T_b,T_c] : % 172.27/172.33 ( hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_a_2),V_b_2) = hAPP(c_Fun_Ocomp(T_d,T_b,T_a,V_ca_2),V_d_2) % 172.27/172.33 => ! [B_v] : hAPP(V_a_2,hAPP(V_b_2,B_v)) = hAPP(V_ca_2,hAPP(V_d_2,B_v)) ) ). % 172.27/172.33 % 172.27/172.33 fof(fact_image__constant,axiom, % 172.27/172.33 ! [V_ca_2,T_b,V_A_2,V_x_2,T_a] : % 172.27/172.33 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 172.27/172.33 => hAPP(c_Set_Oimage(T_a,T_b,hAPP(c_COMBK(T_b,T_a),V_ca_2)),V_A_2) = hAPP(hAPP(c_Set_Oinsert(T_b),V_ca_2),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) ) ). % 172.27/172.33 % 172.27/172.33 fof(fact_folding__one_Oinsert,axiom, % 172.27/172.33 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_a] : % 172.27/172.33 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2) % 172.27/172.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.33 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 172.27/172.33 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.27/172.33 => 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)) ) ) ) ) ). % 172.27/172.33 % 172.27/172.33 fof(fact_image__ident,axiom, % 172.27/172.33 ! [V_Y_2,T_a] : hAPP(c_Set_Oimage(T_a,T_a,c_COMBI(T_a)),V_Y_2) = V_Y_2 ). % 172.27/172.33 % 172.27/172.33 fof(fact_o__def,axiom, % 172.27/172.33 ! [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)) ). % 172.27/172.33 % 172.27/172.33 fof(fact_folding__idem_Oinsert__idem,axiom, % 172.27/172.33 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 172.27/172.33 ( c_Finite__Set_Ofolding__idem(T_a,T_b,V_f_2,V_F_2) % 172.27/172.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.33 => 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)) ) ) ). % 172.27/172.33 % 172.27/172.33 fof(fact_folding__one_Oclosed,axiom, % 172.27/172.33 ! [V_A_2,V_F_2,V_f_2,T_a] : % 172.27/172.33 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2) % 172.27/172.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.33 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.27/172.33 => ( ! [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)))))) % 172.27/172.33 => hBOOL(hAPP(hAPP(c_member(T_a),hAPP(V_F_2,V_A_2)),V_A_2)) ) ) ) ) ). % 172.27/172.33 % 172.27/172.33 fof(fact_folding_Oinsert,axiom, % 172.27/172.33 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 172.27/172.33 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 172.27/172.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.33 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 172.27/172.33 => 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)) ) ) ) ). % 172.27/172.33 % 172.27/172.33 fof(fact_evaln_OBody,axiom, % 172.27/172.33 ! [V_s1,V_n,V_s0,V_pn] : % 172.27/172.33 ( 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)) % 172.27/172.33 => 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)) ) ). % 172.27/172.33 % 172.27/172.33 fof(fact_folding__one__idem_Ohom__commute,axiom, % 172.27/172.33 ! [V_N_2,V_h_2,V_F_2,V_f_2,T_a] : % 172.27/172.33 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2) % 172.27/172.33 => ( ! [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)) % 172.27/172.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 172.27/172.33 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.27/172.33 => 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)) ) ) ) ) ). % 172.27/172.33 % 172.27/172.33 fof(fact_folding__image__simple_Oinsert,axiom, % 172.27/172.33 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 172.27/172.33 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 172.27/172.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 172.27/172.33 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 172.27/172.33 => 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)) ) ) ) ). % 172.27/172.33 % 172.27/172.33 fof(fact_the__sym__eq__trivial,axiom, % 172.27/172.33 ! [V_x_2,T_a] : c_HOL_OThe(T_a,hAPP(c_fequal,V_x_2)) = V_x_2 ). % 172.27/172.33 % 172.27/172.33 fof(fact_the__eq__trivial,axiom, % 172.27/172.33 ! [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 ). % 172.27/172.33 % 172.27/172.33 fof(fact_folding__one_Oremove,axiom, % 172.27/172.33 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_a] : % 172.27/172.33 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2) % 172.27/172.33 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.33 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 172.27/172.33 => ( ( hAPP(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)) % 172.27/172.33 => hAPP(V_F_2,V_A_2) = V_x_2 ) % 172.27/172.33 & ( hAPP(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)) % 172.27/172.33 => 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)))))) ) ) ) ) ) ). % 172.27/172.33 % 172.27/172.33 fof(fact_fold1Set_Ointros,axiom, % 172.27/172.33 ! [V_x_2,V_A_2,V_a_2,V_f_2,T_a] : % 172.27/172.33 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_a,V_f_2,V_a_2,V_A_2),V_x_2)) % 172.27/172.33 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 172.27/172.34 => 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)) ) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_finite__induct,axiom, % 172.27/172.34 ! [V_P_2,V_F_2,T_a] : % 172.27/172.34 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) % 172.27/172.34 => ( hBOOL(hAPP(V_P_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) % 172.27/172.34 => ( ! [B_x,B_F] : % 172.27/172.34 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),B_F)) % 172.27/172.34 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),B_F)) % 172.27/172.34 => ( hBOOL(hAPP(V_P_2,B_F)) % 172.27/172.34 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Set_Oinsert(T_a),B_x),B_F))) ) ) ) % 172.27/172.34 => hBOOL(hAPP(V_P_2,V_F_2)) ) ) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_K__record__comp,axiom, % 172.27/172.34 ! [V_x_2,V_f_2,V_ca_2,T_c,T_a,T_b] : hAPP(hAPP(c_Fun_Ocomp(T_b,T_a,T_c,hAPP(c_COMBK(T_a,T_b),V_ca_2)),V_f_2),V_x_2) = V_ca_2 ). % 172.27/172.34 % 172.27/172.34 fof(fact_DiffI,axiom, % 172.27/172.34 ! [V_B_2,V_A_2,V_ca_2,T_a] : % 172.27/172.34 ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 172.27/172.34 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) % 172.27/172.34 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_DiffE,axiom, % 172.27/172.34 ! [V_B_2,V_A_2,V_ca_2,T_a] : % 172.27/172.34 ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 172.27/172.34 => ~ ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 172.27/172.34 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_finite__Diff,axiom, % 172.27/172.34 ! [V_B_2,V_A_2,T_a] : % 172.27/172.34 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.34 => 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))) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_evaln_OWhileTrue,axiom, % 172.27/172.34 ! [V_s2_2,V_s1_2,V_n_2,V_ca_2,V_s0_2,V_b_2] : % 172.27/172.34 ( hBOOL(hAPP(V_b_2,V_s0_2)) % 172.27/172.34 => ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_ca_2),V_s0_2),V_n_2),V_s1_2)) % 172.27/172.34 => ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(V_b_2,V_ca_2)),V_s1_2),V_n_2),V_s2_2)) % 172.27/172.34 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(V_b_2,V_ca_2)),V_s0_2),V_n_2),V_s2_2)) ) ) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_evaln_OWhileFalse,axiom, % 172.27/172.34 ! [V_n_2,V_ca_2,V_s_2,V_b_2] : % 172.27/172.34 ( ~ hBOOL(hAPP(V_b_2,V_s_2)) % 172.27/172.34 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OWhile(V_b_2,V_ca_2)),V_s_2),V_n_2),V_s_2)) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_evaln_OIfFalse,axiom, % 172.27/172.34 ! [V_c0_2,V_s1_2,V_n_2,V_c1_2,V_s_2,V_b_2] : % 172.27/172.34 ( ~ hBOOL(hAPP(V_b_2,V_s_2)) % 172.27/172.34 => ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c1_2),V_s_2),V_n_2),V_s1_2)) % 172.27/172.34 => 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)) ) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_evaln_OIfTrue,axiom, % 172.27/172.34 ! [V_c1_2,V_s1_2,V_n_2,V_c0_2,V_s_2,V_b_2] : % 172.27/172.34 ( hBOOL(hAPP(V_b_2,V_s_2)) % 172.27/172.34 => ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c0_2),V_s_2),V_n_2),V_s1_2)) % 172.27/172.34 => 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)) ) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_evaln__elim__cases_I5_J,axiom, % 172.27/172.34 ! [V_t_2,V_n_2,V_s_2,V_c2_2,V_c1_2,V_b_2] : % 172.27/172.34 ( 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)) % 172.27/172.34 => ( ( hBOOL(hAPP(V_b_2,V_s_2)) % 172.27/172.34 => ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c1_2),V_s_2),V_n_2),V_t_2)) ) % 172.27/172.34 => ~ ( ~ hBOOL(hAPP(V_b_2,V_s_2)) % 172.27/172.34 => ~ hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c2_2),V_s_2),V_n_2),V_t_2)) ) ) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_evaln_OSemi,axiom, % 172.27/172.34 ! [V_s2,V_c1,V_s1,V_n,V_s0,V_c0] : % 172.27/172.34 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c0),V_s0),V_n),V_s1)) % 172.27/172.34 => ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c1),V_s1),V_n),V_s2)) % 172.27/172.34 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OSemi(V_c0,V_c1)),V_s0),V_n),V_s2)) ) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_evaln_OSkip,axiom, % 172.27/172.34 ! [V_n,V_s] : hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OSKIP),V_s),V_n),V_s)) ). % 172.27/172.34 % 172.27/172.34 fof(fact_evaln__elim__cases_I1_J,axiom, % 172.27/172.34 ! [V_t,V_n,V_s] : % 172.27/172.34 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OSKIP),V_s),V_n),V_t)) % 172.27/172.34 => V_t = V_s ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_fun__diff__def,axiom, % 172.27/172.34 ! [V_x_2,V_B_2,V_A_2,T_b,T_a] : % 172.27/172.34 ( class_Groups_Ominus(T_a) % 172.27/172.34 => 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)) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_minus__apply,axiom, % 172.27/172.34 ! [V_x_2,V_B_2,V_A_2,T_b,T_a] : % 172.27/172.34 ( class_Groups_Ominus(T_a) % 172.27/172.34 => 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)) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_Diff__idemp,axiom, % 172.27/172.34 ! [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) ). % 172.27/172.34 % 172.27/172.34 fof(fact_Diff__iff,axiom, % 172.27/172.34 ! [V_B_2,V_A_2,V_ca_2,T_a] : % 172.27/172.34 ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 172.27/172.34 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 172.27/172.34 & ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_DiffD1,axiom, % 172.27/172.34 ! [V_B_2,V_A_2,V_ca_2,T_a] : % 172.27/172.34 ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 172.27/172.34 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_DiffD2,axiom, % 172.27/172.34 ! [V_B_2,V_A_2,V_ca_2,T_a] : % 172.27/172.34 ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 172.27/172.34 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_empty__Diff,axiom, % 172.27/172.34 ! [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)) ). % 172.27/172.34 % 172.27/172.34 fof(fact_Diff__empty,axiom, % 172.27/172.34 ! [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 ). % 172.27/172.34 % 172.27/172.34 fof(fact_Diff__cancel,axiom, % 172.27/172.34 ! [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)) ). % 172.27/172.34 % 172.27/172.34 fof(fact_finite__Diff2,axiom, % 172.27/172.34 ! [V_A_2,V_B_2,T_a] : % 172.27/172.34 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 172.27/172.34 => ( 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))) % 172.27/172.34 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_evaln__Suc,axiom, % 172.27/172.34 ! [V_s_H,V_n,V_s,V_c] : % 172.27/172.34 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c),V_s),V_n),V_s_H)) % 172.27/172.34 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c),V_s),hAPP(c_Nat_OSuc,V_n)),V_s_H)) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_Un__Diff__cancel,axiom, % 172.27/172.34 ! [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) ). % 172.27/172.34 % 172.27/172.34 fof(fact_Un__Diff__cancel2,axiom, % 172.27/172.34 ! [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) ). % 172.27/172.34 % 172.27/172.34 fof(fact_Un__Diff,axiom, % 172.27/172.34 ! [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)) ). % 172.27/172.34 % 172.27/172.34 fof(fact_evaln__evalc,axiom, % 172.27/172.34 ! [V_t,V_n,V_s,V_c] : % 172.27/172.34 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c),V_s),V_n),V_t)) % 172.27/172.34 => hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_c),V_s),V_t)) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_eval__eq,axiom, % 172.27/172.34 ! [V_t_2,V_s_2,V_ca_2] : % 172.27/172.34 ( hBOOL(hAPP(hAPP(c_Natural_Oevalc(V_ca_2),V_s_2),V_t_2)) % 172.27/172.34 <=> ? [B_n] : hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_ca_2),V_s_2),B_n),V_t_2)) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_evaln_Oequations_I8_J,axiom, % 172.27/172.34 ! [V_a6_2,V_a4_2,V_a2_2,V_a3_2,V_a1_2] : % 172.27/172.34 ( 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)) % 172.27/172.34 <=> ( ( V_a6_2 = V_a2_2 % 172.27/172.34 & ~ hBOOL(hAPP(V_a1_2,V_a2_2)) ) % 172.27/172.34 | ( hBOOL(hAPP(V_a1_2,V_a2_2)) % 172.27/172.34 & ? [B_s1] : % 172.27/172.34 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a3_2),V_a2_2),V_a4_2),B_s1)) % 172.27/172.34 & 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)) ) ) ) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_evaln_Oequations_I7_J,axiom, % 172.27/172.34 ! [V_a4_2,V_a2_2,V_a3_2,V_a1_2] : % 172.27/172.34 ( 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)) % 172.27/172.34 <=> ( hBOOL(hAPP(V_a1_2,V_a2_2)) % 172.27/172.34 => ? [B_s1] : % 172.27/172.34 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a3_2),V_a2_2),V_a4_2),B_s1)) % 172.27/172.34 & 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)) ) ) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_evaln_Oequations_I5_J,axiom, % 172.27/172.34 ! [V_a5_2,V_a4_2,V_a2_2,V_a6_2,V_a3_2,V_a1_2] : % 172.27/172.34 ( 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)) % 172.27/172.34 <=> ( ( hBOOL(hAPP(V_a1_2,V_a2_2)) % 172.27/172.34 & hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a3_2),V_a2_2),V_a4_2),V_a5_2)) ) % 172.27/172.34 | ( ~ hBOOL(hAPP(V_a1_2,V_a2_2)) % 172.27/172.34 & hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a6_2),V_a2_2),V_a4_2),V_a5_2)) ) ) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_evaln_Oequations_I6_J,axiom, % 172.27/172.34 ! [V_a5_2,V_a4_2,V_a2_2,V_a3_2,V_a6_2,V_a1_2] : % 172.27/172.34 ( 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)) % 172.27/172.34 <=> ( ( hBOOL(hAPP(V_a1_2,V_a2_2)) % 172.27/172.34 & hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a6_2),V_a2_2),V_a4_2),V_a5_2)) ) % 172.27/172.34 | ( ~ hBOOL(hAPP(V_a1_2,V_a2_2)) % 172.27/172.34 & hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a3_2),V_a2_2),V_a4_2),V_a5_2)) ) ) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_evaln_Oequations_I4_J,axiom, % 172.27/172.34 ! [V_a6_2,V_a3_2,V_a2_2,V_a5_2,V_a1_2] : % 172.27/172.34 ( 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)) % 172.27/172.34 <=> ? [B_s1] : % 172.27/172.34 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a1_2),V_a2_2),V_a3_2),B_s1)) % 172.27/172.34 & hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_a5_2),B_s1),V_a3_2),V_a6_2)) ) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_evaln_Oequations_I1_J,axiom, % 172.27/172.34 ! [V_a2,V_a1] : hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,c_Com_Ocom_OSKIP),V_a1),V_a2),V_a1)) ). % 172.27/172.34 % 172.27/172.34 fof(fact_fold__graph_Oequations_I1_J,axiom, % 172.27/172.34 ! [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)) ). % 172.27/172.34 % 172.27/172.34 fof(fact_fold__graph_OemptyI,axiom, % 172.27/172.34 ! [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)) ). % 172.27/172.34 % 172.27/172.34 fof(fact_empty__fold__graphE,axiom, % 172.27/172.34 ! [V_x_2,V_z_2,V_f_2,T_b,T_a] : % 172.27/172.34 ( 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)) % 172.27/172.34 => V_x_2 = V_z_2 ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_fold__graph__imp__finite,axiom, % 172.27/172.34 ! [V_x_2,V_A_2,V_z_2,V_f_2,T_b,T_a] : % 172.27/172.34 ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),V_x_2)) % 172.27/172.34 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_Diff1__fold__graph,axiom, % 172.27/172.34 ! [V_y_2,V_x_2,V_A_2,V_z_2,V_f_2,T_b,T_a] : % 172.27/172.34 ( 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)) % 172.27/172.34 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 172.27/172.34 => 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))) ) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_folding_Ocommute__comps_I1_J,axiom, % 172.27/172.34 ! [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] : % 172.27/172.34 ( c_Finite__Set_Ofolding(T_a,T_b,V_fa_2,V_F_2) % 172.27/172.34 => 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) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_folding_Ocommute__comp,axiom, % 172.27/172.34 ! [V_x_2,V_y_2,V_F_2,V_f_2,T_b,T_a] : % 172.27/172.34 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 172.27/172.34 => 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)) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_folding_Ocommute__left__comp,axiom, % 172.27/172.34 ! [V_g_2,V_x_2,V_y_2,T_c,V_F_2,V_f_2,T_b,T_a] : % 172.27/172.34 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 172.27/172.34 => 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)) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_folding__image__simple_Oinsert__remove,axiom, % 172.27/172.34 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 172.27/172.34 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 172.27/172.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 172.27/172.34 => 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)))))) ) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_insert__Diff1,axiom, % 172.27/172.34 ! [V_A_2,V_B_2,V_x_2,T_a] : % 172.27/172.34 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) % 172.27/172.34 => 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) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_insert__Diff__if,axiom, % 172.27/172.34 ! [V_A_2,V_B_2,V_x_2,T_a] : % 172.27/172.34 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) % 172.27/172.34 => 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) ) % 172.27/172.34 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) % 172.27/172.34 => 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)) ) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_Diff__insert,axiom, % 172.27/172.34 ! [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)))) ). % 172.27/172.34 % 172.27/172.34 fof(fact_Diff__insert2,axiom, % 172.27/172.34 ! [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) ). % 172.27/172.34 % 172.27/172.34 fof(fact_insert__Diff__single,axiom, % 172.27/172.34 ! [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) ). % 172.27/172.34 % 172.27/172.34 fof(fact_finite__Diff__insert,axiom, % 172.27/172.34 ! [V_B_2,V_a_2,V_A_2,T_a] : % 172.27/172.34 ( 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)))) % 172.27/172.34 <=> 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))) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_folding__image__simple_Oempty,axiom, % 172.27/172.34 ! [V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 172.27/172.34 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 172.27/172.34 => hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))) = V_z_2 ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_folding_Oinsert__remove,axiom, % 172.27/172.34 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 172.27/172.34 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 172.27/172.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.34 => 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)) ) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_folding__image__simple_Oremove,axiom, % 172.27/172.34 ! [V_x_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 172.27/172.34 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 172.27/172.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 172.27/172.34 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 172.27/172.34 => 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)))))) ) ) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_fold__graph_OinsertI,axiom, % 172.27/172.34 ! [V_y_2,V_z_2,V_f_2,T_b,V_A_2,V_x_2,T_a] : % 172.27/172.34 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 172.27/172.34 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),V_y_2)) % 172.27/172.34 => 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))) ) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_triple__valid__def2,axiom, % 172.27/172.34 ! [V_Q_2,V_ca_2,V_P_2,V_n_2,T_a] : % 172.27/172.34 ( c_Hoare__Mirabelle_Otriple__valid(T_a,V_n_2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),V_ca_2),V_Q_2)) % 172.27/172.34 <=> ! [B_Z,B_s] : % 172.27/172.34 ( hBOOL(hAPP(hAPP(V_P_2,B_Z),B_s)) % 172.27/172.34 => ! [B_s_H] : % 172.27/172.34 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_ca_2),B_s),V_n_2),B_s_H)) % 172.27/172.34 => hBOOL(hAPP(hAPP(V_Q_2,B_Z),B_s_H)) ) ) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_folding_Oremove,axiom, % 172.27/172.34 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 172.27/172.34 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 172.27/172.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.34 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 172.27/172.34 => 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)) ) ) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_Diff__insert__absorb,axiom, % 172.27/172.34 ! [V_A_2,V_x_2,T_a] : % 172.27/172.34 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 172.27/172.34 => 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 ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_insert__Diff,axiom, % 172.27/172.34 ! [V_A_2,V_a_2,T_a] : % 172.27/172.34 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 172.27/172.34 => 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 ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_folding_Ocommute__comp_H,axiom, % 172.27/172.34 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 172.27/172.34 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 172.27/172.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.34 => 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)) ) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_folding_Ocommute__left__comp_H,axiom, % 172.27/172.34 ! [V_g_2,V_x_2,T_c,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 172.27/172.34 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 172.27/172.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.34 => 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)) ) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_folding_Ocommute__comp_H_H,axiom, % 172.27/172.34 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 172.27/172.34 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 172.27/172.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 172.27/172.34 => 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)) ) ) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_folding_Ocommute__left__comp_H_H,axiom, % 172.27/172.34 ! [V_g_2,T_c,V_B_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 172.27/172.34 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 172.27/172.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 172.27/172.34 => 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)) ) ) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_o__eq__dest__lhs,axiom, % 172.27/172.34 ! [V_v_2,V_ca_2,V_b_2,V_a_2,T_a,T_b,T_c] : % 172.27/172.34 ( hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_a_2),V_b_2) = V_ca_2 % 172.27/172.34 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_ca_2,V_v_2) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_folding__one_Oinsert__remove,axiom, % 172.27/172.34 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_a] : % 172.27/172.34 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2) % 172.27/172.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.34 => ( ( hAPP(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)) % 172.27/172.34 => hAPP(V_F_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = V_x_2 ) % 172.27/172.34 & ( hAPP(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)) % 172.27/172.34 => 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)))))) ) ) ) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_triple__valid__def,axiom, % 172.27/172.34 ! [V_t_2,V_n_2,T_a] : % 172.27/172.34 ( c_Hoare__Mirabelle_Otriple__valid(T_a,V_n_2,V_t_2) % 172.27/172.34 <=> 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)) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_evaln_Oequations_I9_J,axiom, % 172.27/172.34 ! [V_a4_2,V_a3_2,V_a2_2,V_a1_2] : % 172.27/172.34 ( 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)) % 172.27/172.34 <=> 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)) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_evaln__elim__cases_I6_J,axiom, % 172.27/172.34 ! [V_s1,V_n,V_s,V_P] : % 172.27/172.34 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,hAPP(c_Com_Ocom_OBODY,V_P)),V_s),V_n),V_s1)) % 172.27/172.34 => ~ ! [B_n] : % 172.27/172.34 ( V_n = hAPP(c_Nat_OSuc,B_n) % 172.27/172.34 => ~ 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)) ) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_fun__upd__image,axiom, % 172.27/172.34 ! [V_y_2,V_f_2,T_b,V_A_2,V_x_2,T_a] : % 172.27/172.34 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 172.27/172.34 => 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)))))) ) % 172.27/172.34 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 172.27/172.34 => 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) ) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_finite__empty__induct,axiom, % 172.27/172.34 ! [V_P_2,V_A_2,T_a] : % 172.27/172.34 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.34 => ( hBOOL(hAPP(V_P_2,V_A_2)) % 172.27/172.34 => ( ! [B_a,B_A] : % 172.27/172.34 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),B_A)) % 172.27/172.34 => ( hBOOL(hAPP(hAPP(c_member(T_a),B_a),B_A)) % 172.27/172.34 => ( hBOOL(hAPP(V_P_2,B_A)) % 172.27/172.34 => 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)))))) ) ) ) % 172.27/172.34 => hBOOL(hAPP(V_P_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) ) ) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_insert__fold1SetE,axiom, % 172.27/172.34 ! [V_x_2,V_X_2,V_a_2,V_f_2,T_a] : % 172.27/172.34 ( 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)) % 172.27/172.34 => ~ ! [B_a,B_A] : % 172.27/172.34 ( hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_X_2) = hAPP(hAPP(c_Set_Oinsert(T_a),B_a),B_A) % 172.27/172.34 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_a,V_f_2,B_a,B_A),V_x_2)) % 172.27/172.34 => hBOOL(hAPP(hAPP(c_member(T_a),B_a),B_A)) ) ) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_fold1Set_Oequations,axiom, % 172.27/172.34 ! [V_a3_2,V_a2_2,V_a1_2,V_f_2,T_a] : % 172.27/172.34 ( 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)) % 172.27/172.34 <=> ? [B_a,B_A] : % 172.27/172.34 ( hAPP(hAPP(c_Set_Oinsert(T_a),V_a1_2),V_a2_2) = hAPP(hAPP(c_Set_Oinsert(T_a),B_a),B_A) % 172.27/172.34 & hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_a,V_f_2,B_a,B_A),V_a3_2)) % 172.27/172.34 & ~ hBOOL(hAPP(hAPP(c_member(T_a),B_a),B_A)) ) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_card__Suc__Diff1,axiom, % 172.27/172.34 ! [V_x_2,V_A_2,T_a] : % 172.27/172.34 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.34 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 172.27/172.34 => 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) ) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_fun__left__comm__idem__remove,axiom, % 172.27/172.34 ! [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))))) ). % 172.27/172.34 % 172.27/172.34 fof(fact_folding_Ounion,axiom, % 172.27/172.34 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 172.27/172.34 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 172.27/172.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 172.27/172.34 => ( 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)) % 172.27/172.34 => 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)) ) ) ) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_fold__graph__permute__diff,axiom, % 172.27/172.34 ! [V_a_2,V_x_2,V_A_2,V_b_2,T_a] : % 172.27/172.34 ( class_Groups_Oab__semigroup__mult(T_a) % 172.27/172.34 => ( 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)) % 172.27/172.34 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 172.27/172.34 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),V_A_2)) % 172.27/172.34 => 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)) ) ) ) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_fold__graph_H_Ointros_I2_J,axiom, % 172.27/172.34 ! [V_y_2,V_z_2,V_f_2,T_b,V_A_2,V_x_2,T_a] : % 172.27/172.34 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 172.27/172.34 => ( 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) % 172.27/172.34 => 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)) ) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_Sup__fin_Oremove,axiom, % 172.27/172.34 ! [V_x_2,V_A_2,T_a] : % 172.27/172.34 ( class_Lattices_Olattice(T_a) % 172.27/172.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.34 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 172.27/172.34 => ( ( hAPP(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)) % 172.27/172.34 => c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2) = V_x_2 ) % 172.27/172.34 & ( hAPP(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)) % 172.27/172.34 => 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)))))) ) ) ) ) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_inf1E,axiom, % 172.27/172.34 ! [V_x_2,V_B_2,V_A_2,T_a] : % 172.27/172.34 ( 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)) % 172.27/172.34 => ~ ( hBOOL(hAPP(V_A_2,V_x_2)) % 172.27/172.34 => ~ hBOOL(hAPP(V_B_2,V_x_2)) ) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_inf1I,axiom, % 172.27/172.34 ! [T_a,V_B_2,V_x_2,V_A_2] : % 172.27/172.34 ( hBOOL(hAPP(V_A_2,V_x_2)) % 172.27/172.34 => ( hBOOL(hAPP(V_B_2,V_x_2)) % 172.27/172.34 => 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)) ) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_fun__upd__triv,axiom, % 172.27/172.34 ! [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 ). % 172.27/172.34 % 172.27/172.34 fof(fact_IntE,axiom, % 172.27/172.34 ! [V_B_2,V_A_2,V_ca_2,T_a] : % 172.27/172.34 ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 172.27/172.34 => ~ ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 172.27/172.34 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_IntI,axiom, % 172.27/172.34 ! [V_B_2,V_A_2,V_ca_2,T_a] : % 172.27/172.34 ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 172.27/172.34 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) % 172.27/172.34 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) ) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_finite__Int,axiom, % 172.27/172.34 ! [V_Ga_2,V_F_2,T_a] : % 172.27/172.34 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) % 172.27/172.34 | hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_Ga_2)) ) % 172.27/172.34 => 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))) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_fun__left__comm__idem_Ofun__left__idem,axiom, % 172.27/172.34 ! [V_z_2,V_x_2,V_f_2,T_b,T_a] : % 172.27/172.34 ( c_Finite__Set_Ofun__left__comm__idem(T_a,T_b,V_f_2) % 172.27/172.34 => 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) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_Inf__fin_Oidem,axiom, % 172.27/172.34 ! [V_x,T_a] : % 172.27/172.34 ( class_Lattices_Olattice(T_a) % 172.27/172.34 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_x) = V_x ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_Int__assoc,axiom, % 172.27/172.34 ! [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)) ). % 172.27/172.34 % 172.27/172.34 fof(fact_Int__left__commute,axiom, % 172.27/172.34 ! [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)) ). % 172.27/172.34 % 172.27/172.34 fof(fact_Int__left__absorb,axiom, % 172.27/172.34 ! [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) ). % 172.27/172.34 % 172.27/172.34 fof(fact_Int__commute,axiom, % 172.27/172.34 ! [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) ). % 172.27/172.34 % 172.27/172.34 fof(fact_Int__absorb,axiom, % 172.27/172.34 ! [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 ). % 172.27/172.34 % 172.27/172.34 fof(fact_fun__left__comm__idem__inf,axiom, % 172.27/172.34 ! [T_a] : % 172.27/172.34 ( class_Lattices_Osemilattice__inf(T_a) % 172.27/172.34 => c_Finite__Set_Ofun__left__comm__idem(T_a,T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a)) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_fun__left__comm__idem,axiom, % 172.27/172.34 ! [T_a] : % 172.27/172.34 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 172.27/172.34 => c_Finite__Set_Ofun__left__comm__idem(T_a,T_a,c_Groups_Otimes__class_Otimes(T_a)) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_inf1D2,axiom, % 172.27/172.34 ! [V_x_2,V_B_2,V_A_2,T_a] : % 172.27/172.34 ( 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)) % 172.27/172.34 => hBOOL(hAPP(V_B_2,V_x_2)) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_inf1D1,axiom, % 172.27/172.34 ! [V_x_2,V_B_2,V_A_2,T_a] : % 172.27/172.34 ( 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)) % 172.27/172.34 => hBOOL(hAPP(V_A_2,V_x_2)) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_fun__upd__idem,axiom, % 172.27/172.34 ! [T_a,T_b,V_y_2,V_x_2,V_f_2] : % 172.27/172.34 ( hAPP(V_f_2,V_x_2) = V_y_2 % 172.27/172.34 => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_b,T_a),V_f_2),V_x_2),V_y_2) = V_f_2 ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_fun__upd__other,axiom, % 172.27/172.34 ! [V_y_2,V_f_2,T_b,T_a,V_x_2,V_z_2] : % 172.27/172.34 ( V_z_2 != V_x_2 % 172.27/172.34 => 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) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_fun__upd__twist,axiom, % 172.27/172.34 ! [V_d_2,V_b_2,V_m_2,T_b,T_a,V_ca_2,V_a_2] : % 172.27/172.34 ( V_a_2 != V_ca_2 % 172.27/172.34 => hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_m_2),V_a_2),V_b_2)),V_ca_2),V_d_2) = hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_m_2),V_ca_2),V_d_2)),V_a_2),V_b_2) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_fun__upd__apply,axiom, % 172.27/172.34 ! [V_y_2,V_f_2,T_b,T_a,V_x_2,V_z_2] : % 172.27/172.34 ( ( V_z_2 = V_x_2 % 172.27/172.34 => 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 ) % 172.27/172.34 & ( V_z_2 != V_x_2 % 172.27/172.34 => 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) ) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_fun__upd__same,axiom, % 172.27/172.34 ! [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 ). % 172.27/172.34 % 172.27/172.34 fof(fact_fun__upd__upd,axiom, % 172.27/172.34 ! [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) ). % 172.27/172.34 % 172.27/172.34 fof(fact_inf__apply,axiom, % 172.27/172.34 ! [V_x_2,V_g_2,V_f_2,T_b,T_a] : % 172.27/172.34 ( class_Lattices_Olattice(T_a) % 172.27/172.34 => 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)) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_fun__upd__idem__iff,axiom, % 172.27/172.34 ! [V_y_2,V_x_2,V_f_2,T_b,T_a] : % 172.27/172.34 ( hAPP(hAPP(hAPP(c_Fun_Ofun__upd(T_a,T_b),V_f_2),V_x_2),V_y_2) = V_f_2 % 172.27/172.34 <=> hAPP(V_f_2,V_x_2) = V_y_2 ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_inf__assoc,axiom, % 172.27/172.34 ! [V_z,V_y,V_x,T_a] : % 172.27/172.34 ( class_Lattices_Osemilattice__inf(T_a) % 172.27/172.34 => 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)) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_inf__sup__aci_I2_J,axiom, % 172.27/172.34 ! [V_z,V_y,V_x,T_a] : % 172.27/172.34 ( class_Lattices_Olattice(T_a) % 172.27/172.34 => 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)) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_inf_Oassoc,axiom, % 172.27/172.34 ! [V_c,V_b,V_a,T_a] : % 172.27/172.34 ( class_Lattices_Osemilattice__inf(T_a) % 172.27/172.34 => 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)) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_inf__left__commute,axiom, % 172.27/172.34 ! [V_z,V_y,V_x,T_a] : % 172.27/172.34 ( class_Lattices_Osemilattice__inf(T_a) % 172.27/172.34 => 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)) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_inf__sup__aci_I3_J,axiom, % 172.27/172.34 ! [V_z,V_y,V_x,T_a] : % 172.27/172.34 ( class_Lattices_Olattice(T_a) % 172.27/172.34 => 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)) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_inf_Oleft__commute,axiom, % 172.27/172.34 ! [V_c,V_a,V_b,T_a] : % 172.27/172.34 ( class_Lattices_Osemilattice__inf(T_a) % 172.27/172.34 => 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)) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_inf__left__idem,axiom, % 172.27/172.34 ! [V_y,V_x,T_a] : % 172.27/172.34 ( class_Lattices_Osemilattice__inf(T_a) % 172.27/172.34 => 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) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_inf__sup__aci_I4_J,axiom, % 172.27/172.34 ! [V_y,V_x,T_a] : % 172.27/172.34 ( class_Lattices_Olattice(T_a) % 172.27/172.34 => 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) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_inf_Oleft__idem,axiom, % 172.27/172.34 ! [V_b,V_a,T_a] : % 172.27/172.34 ( class_Lattices_Osemilattice__inf(T_a) % 172.27/172.34 => 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) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_mult__left__idem,axiom, % 172.27/172.34 ! [V_b,V_a,T_a] : % 172.27/172.34 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 172.27/172.34 => 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) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_inf__commute,axiom, % 172.27/172.34 ! [V_y,V_x,T_a] : % 172.27/172.34 ( class_Lattices_Osemilattice__inf(T_a) % 172.27/172.34 => 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) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_inf__sup__aci_I1_J,axiom, % 172.27/172.34 ! [V_y,V_x,T_a] : % 172.27/172.34 ( class_Lattices_Olattice(T_a) % 172.27/172.34 => 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) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_inf_Ocommute,axiom, % 172.27/172.34 ! [V_b,V_a,T_a] : % 172.27/172.34 ( class_Lattices_Osemilattice__inf(T_a) % 172.27/172.34 => 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) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_inf__fun__def,axiom, % 172.27/172.34 ! [V_x_2,V_g_2,V_f_2,T_b,T_a] : % 172.27/172.34 ( class_Lattices_Olattice(T_a) % 172.27/172.34 => 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)) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_inf__idem,axiom, % 172.27/172.34 ! [V_x,T_a] : % 172.27/172.34 ( class_Lattices_Osemilattice__inf(T_a) % 172.27/172.34 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_x) = V_x ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_inf_Oidem,axiom, % 172.27/172.34 ! [V_a,T_a] : % 172.27/172.34 ( class_Lattices_Osemilattice__inf(T_a) % 172.27/172.34 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a),V_a) = V_a ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_mult__idem,axiom, % 172.27/172.34 ! [V_x,T_a] : % 172.27/172.34 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 172.27/172.34 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x),V_x) = V_x ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_times_Oidem,axiom, % 172.27/172.34 ! [V_a,T_a] : % 172.27/172.34 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 172.27/172.34 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_a) = V_a ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_card__Diff__subset__Int,axiom, % 172.27/172.34 ! [V_B_2,V_A_2,T_a] : % 172.27/172.34 ( 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))) % 172.27/172.34 => 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))) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_inf__Sup__absorb,axiom, % 172.27/172.34 ! [V_a_2,V_A_2,T_a] : % 172.27/172.34 ( class_Lattices_Olattice(T_a) % 172.27/172.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.34 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 172.27/172.34 => 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 ) ) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_fun__upd__def,axiom, % 172.27/172.34 ! [V_b_2,V_f_2,T_b,T_a,V_a_2,V_x_2] : % 172.27/172.34 ( ( V_x_2 = V_a_2 % 172.27/172.34 => 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 ) % 172.27/172.34 & ( V_x_2 != V_a_2 % 172.27/172.34 => 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) ) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_fun__left__comm__idem_Ofun__left__comm__idem__apply,axiom, % 172.27/172.34 ! [V_g_2,T_c,V_f_2,T_b,T_a] : % 172.27/172.34 ( c_Finite__Set_Ofun__left__comm__idem(T_a,T_b,V_f_2) % 172.27/172.34 => 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)) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_inf__bot__right,axiom, % 172.27/172.34 ! [V_x,T_a] : % 172.27/172.34 ( class_Lattices_Obounded__lattice__bot(T_a) % 172.27/172.34 => 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) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_inf__bot__left,axiom, % 172.27/172.34 ! [V_x,T_a] : % 172.27/172.34 ( class_Lattices_Obounded__lattice__bot(T_a) % 172.27/172.34 => 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) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_inf__sup__absorb,axiom, % 172.27/172.34 ! [V_y,V_x,T_a] : % 172.27/172.34 ( class_Lattices_Olattice(T_a) % 172.27/172.34 => 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 ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_sup__inf__absorb,axiom, % 172.27/172.34 ! [V_y,V_x,T_a] : % 172.27/172.34 ( class_Lattices_Olattice(T_a) % 172.27/172.34 => 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 ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_inf__sup__distrib1,axiom, % 172.27/172.34 ! [V_z,V_y,V_x,T_a] : % 172.27/172.34 ( class_Lattices_Odistrib__lattice(T_a) % 172.27/172.34 => 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)) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_sup__inf__distrib1,axiom, % 172.27/172.34 ! [V_z,V_y,V_x,T_a] : % 172.27/172.34 ( class_Lattices_Odistrib__lattice(T_a) % 172.27/172.34 => 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)) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_inf__sup__distrib2,axiom, % 172.27/172.34 ! [V_x,V_z,V_y,T_a] : % 172.27/172.34 ( class_Lattices_Odistrib__lattice(T_a) % 172.27/172.34 => 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)) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_sup__inf__distrib2,axiom, % 172.27/172.34 ! [V_x,V_z,V_y,T_a] : % 172.27/172.34 ( class_Lattices_Odistrib__lattice(T_a) % 172.27/172.34 => 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)) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_fold__graph_H_Ointros_I1_J,axiom, % 172.27/172.34 ! [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) ). % 172.27/172.34 % 172.27/172.34 fof(fact_fold__graph_H_Oequations_I1_J,axiom, % 172.27/172.34 ! [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) ). % 172.27/172.34 % 172.27/172.34 fof(fact_IntD2,axiom, % 172.27/172.34 ! [V_B_2,V_A_2,V_ca_2,T_a] : % 172.27/172.34 ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 172.27/172.34 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_IntD1,axiom, % 172.27/172.34 ! [V_B_2,V_A_2,V_ca_2,T_a] : % 172.27/172.34 ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 172.27/172.34 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_Int__iff,axiom, % 172.27/172.34 ! [V_B_2,V_A_2,V_ca_2,T_a] : % 172.27/172.34 ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2))) % 172.27/172.34 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 172.27/172.34 & hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_disjoint__iff__not__equal,axiom, % 172.27/172.34 ! [V_B_2,V_A_2,T_a] : % 172.27/172.34 ( 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)) % 172.27/172.34 <=> ! [B_x] : % 172.27/172.34 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 172.27/172.34 => ! [B_xa] : % 172.27/172.34 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_B_2)) % 172.27/172.34 => B_x != B_xa ) ) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_Int__empty__right,axiom, % 172.27/172.34 ! [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)) ). % 172.27/172.34 % 172.27/172.34 fof(fact_Int__empty__left,axiom, % 172.27/172.34 ! [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)) ). % 172.27/172.34 % 172.27/172.34 fof(fact_insert__inter__insert,axiom, % 172.27/172.34 ! [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)) ). % 172.27/172.34 % 172.27/172.34 fof(fact_Un__Int__crazy,axiom, % 172.27/172.34 ! [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)) ). % 172.27/172.34 % 172.27/172.34 fof(fact_Un__Int__distrib2,axiom, % 172.27/172.34 ! [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)) ). % 172.27/172.34 % 172.27/172.34 fof(fact_Int__Un__distrib2,axiom, % 172.27/172.34 ! [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)) ). % 172.27/172.34 % 172.27/172.34 fof(fact_Un__Int__distrib,axiom, % 172.27/172.34 ! [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)) ). % 172.27/172.34 % 172.27/172.34 fof(fact_Int__Un__distrib,axiom, % 172.27/172.34 ! [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)) ). % 172.27/172.34 % 172.27/172.34 fof(fact_Diff__Int2,axiom, % 172.27/172.34 ! [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) ). % 172.27/172.34 % 172.27/172.34 fof(fact_Diff__Int__distrib2,axiom, % 172.27/172.34 ! [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)) ). % 172.27/172.34 % 172.27/172.34 fof(fact_Int__Diff,axiom, % 172.27/172.34 ! [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)) ). % 172.27/172.34 % 172.27/172.34 fof(fact_Diff__Int__distrib,axiom, % 172.27/172.34 ! [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)) ). % 172.27/172.34 % 172.27/172.34 fof(fact_inf__Int__eq,axiom, % 172.27/172.34 ! [V_x_2,V_S_2,V_R_2,T_a] : % 172.27/172.34 ( 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)) % 172.27/172.34 <=> 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))) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_Sup__fin_Osingleton,axiom, % 172.27/172.34 ! [V_x_2,T_a] : % 172.27/172.34 ( class_Lattices_Olattice(T_a) % 172.27/172.34 => 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 ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_fun__upd__comp,axiom, % 172.27/172.34 ! [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)) ). % 172.27/172.34 % 172.27/172.34 fof(fact_Sup__fin_Ounion__disjoint,axiom, % 172.27/172.34 ! [V_B_2,V_A_2,T_a] : % 172.27/172.34 ( class_Lattices_Olattice(T_a) % 172.27/172.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.34 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.27/172.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 172.27/172.34 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.27/172.34 => ( 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)) % 172.27/172.34 => 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)) ) ) ) ) ) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_Sup__fin_Ounion__inter,axiom, % 172.27/172.34 ! [V_B_2,V_A_2,T_a] : % 172.27/172.34 ( class_Lattices_Olattice(T_a) % 172.27/172.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 172.27/172.34 => ( 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)) % 172.27/172.34 => 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)) ) ) ) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_fun__left__comm__idem__insert,axiom, % 172.27/172.34 ! [T_a] : c_Finite__Set_Ofun__left__comm__idem(T_a,tc_fun(T_a,tc_HOL_Obool),c_Set_Oinsert(T_a)) ). % 172.27/172.34 % 172.27/172.34 fof(fact_fun__left__comm__idem__sup,axiom, % 172.27/172.34 ! [T_a] : % 172.27/172.34 ( class_Lattices_Osemilattice__sup(T_a) % 172.27/172.34 => c_Finite__Set_Ofun__left__comm__idem(T_a,T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a)) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_fun__left__comm__idem_Ofun__comp__idem,axiom, % 172.27/172.34 ! [V_x_2,V_f_2,T_b,T_a] : % 172.27/172.34 ( c_Finite__Set_Ofun__left__comm__idem(T_a,T_b,V_f_2) % 172.27/172.34 => 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) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_Int__insert__right,axiom, % 172.27/172.34 ! [V_B_2,V_A_2,V_a_2,T_a] : % 172.27/172.34 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 172.27/172.34 => 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)) ) % 172.27/172.34 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 172.27/172.34 => 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) ) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_Int__insert__left,axiom, % 172.27/172.34 ! [V_B_2,V_C_2,V_a_2,T_a] : % 172.27/172.34 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_C_2)) % 172.27/172.34 => 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)) ) % 172.27/172.34 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_C_2)) % 172.27/172.34 => 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) ) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_Int__insert__right__if0,axiom, % 172.27/172.34 ! [V_B_2,V_A_2,V_a_2,T_a] : % 172.27/172.34 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 172.27/172.34 => 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) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_Int__insert__left__if0,axiom, % 172.27/172.34 ! [V_B_2,V_C_2,V_a_2,T_a] : % 172.27/172.34 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_C_2)) % 172.27/172.34 => 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) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_Int__insert__right__if1,axiom, % 172.27/172.34 ! [V_B_2,V_A_2,V_a_2,T_a] : % 172.27/172.34 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 172.27/172.34 => 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)) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_Int__insert__left__if1,axiom, % 172.27/172.34 ! [V_B_2,V_C_2,V_a_2,T_a] : % 172.27/172.34 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_C_2)) % 172.27/172.34 => 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)) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_Diff__disjoint,axiom, % 172.27/172.34 ! [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)) ). % 172.27/172.34 % 172.27/172.34 fof(fact_Diff__triv,axiom, % 172.27/172.34 ! [V_B_2,V_A_2,T_a] : % 172.27/172.34 ( 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)) % 172.27/172.34 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_Un__Diff__Int,axiom, % 172.27/172.34 ! [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 ). % 172.27/172.34 % 172.27/172.34 fof(fact_Diff__Un,axiom, % 172.27/172.34 ! [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)) ). % 172.27/172.34 % 172.27/172.34 fof(fact_Diff__Int,axiom, % 172.27/172.34 ! [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)) ). % 172.27/172.34 % 172.27/172.34 fof(fact_Sup__fin_Oin__idem,axiom, % 172.27/172.34 ! [V_x_2,V_A_2,T_a] : % 172.27/172.34 ( class_Lattices_Olattice(T_a) % 172.27/172.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.34 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 172.27/172.34 => 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) ) ) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_Sup__fin_Oinsert__idem,axiom, % 172.27/172.34 ! [V_x_2,V_A_2,T_a] : % 172.27/172.34 ( class_Lattices_Olattice(T_a) % 172.27/172.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.34 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.27/172.34 => 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)) ) ) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_Sup__fin_Ounion__idem,axiom, % 172.27/172.34 ! [V_B_2,V_A_2,T_a] : % 172.27/172.34 ( class_Lattices_Olattice(T_a) % 172.27/172.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.34 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.27/172.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 172.27/172.34 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.27/172.34 => 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)) ) ) ) ) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_fold__graph__insert__swap,axiom, % 172.27/172.34 ! [V_z_2,V_y_2,V_A_2,V_b_2,T_a] : % 172.27/172.34 ( class_Groups_Oab__semigroup__mult(T_a) % 172.27/172.34 => ( 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)) % 172.27/172.34 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),V_A_2)) % 172.27/172.34 => 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))) ) ) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_Sup__fin_Oidem,axiom, % 172.27/172.34 ! [V_x,T_a] : % 172.27/172.34 ( class_Lattices_Olattice(T_a) % 172.27/172.34 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_x) = V_x ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_folding__image__simple_Ounion__inter,axiom, % 172.27/172.34 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 172.27/172.34 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 172.27/172.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 172.27/172.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 172.27/172.34 => 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)) ) ) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_card__insert__disjoint,axiom, % 172.27/172.34 ! [V_x_2,V_A_2,T_a] : % 172.27/172.34 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.34 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 172.27/172.34 => 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)) ) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_card__insert__if,axiom, % 172.27/172.34 ! [V_x_2,V_A_2,T_a] : % 172.27/172.34 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.34 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 172.27/172.34 => 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) ) % 172.27/172.34 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 172.27/172.34 => 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)) ) ) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_Sup__fin_Oinsert,axiom, % 172.27/172.34 ! [V_x_2,V_A_2,T_a] : % 172.27/172.34 ( class_Lattices_Olattice(T_a) % 172.27/172.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.34 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 172.27/172.34 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.27/172.34 => 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)) ) ) ) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_Sup__fin_Oinsert__remove,axiom, % 172.27/172.34 ! [V_x_2,V_A_2,T_a] : % 172.27/172.34 ( class_Lattices_Olattice(T_a) % 172.27/172.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.34 => ( ( hAPP(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)) % 172.27/172.34 => 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 ) % 172.27/172.34 & ( hAPP(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)) % 172.27/172.34 => 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)))))) ) ) ) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_folding_Ounion__inter,axiom, % 172.27/172.34 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 172.27/172.34 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 172.27/172.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 172.27/172.34 => 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)) ) ) ) ). % 172.27/172.34 % 172.27/172.34 fof(fact_folding__one_Ounion__disjoint,axiom, % 172.27/172.34 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_a] : % 172.27/172.34 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2) % 172.27/172.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.34 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.27/172.34 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 172.27/172.34 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.27/172.35 => ( 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)) % 172.27/172.35 => 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)) ) ) ) ) ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_folding__one_Ounion__inter,axiom, % 172.27/172.35 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_a] : % 172.27/172.35 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2) % 172.27/172.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 172.27/172.35 => ( 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)) % 172.27/172.35 => 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)) ) ) ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_folding__image__simple_Ounion__disjoint,axiom, % 172.27/172.35 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 172.27/172.35 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 172.27/172.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 172.27/172.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 172.27/172.35 => ( 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)) % 172.27/172.35 => 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)) ) ) ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_card__insert,axiom, % 172.27/172.35 ! [V_x_2,V_A_2,T_a] : % 172.27/172.35 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.35 => 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)))))) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_Sup__fin_Oclosed,axiom, % 172.27/172.35 ! [V_A_2,T_a] : % 172.27/172.35 ( class_Lattices_Olattice(T_a) % 172.27/172.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.35 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.27/172.35 => ( ! [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)))))) % 172.27/172.35 => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2)),V_A_2)) ) ) ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_Inf__fin_Oremove,axiom, % 172.27/172.35 ! [V_x_2,V_A_2,T_a] : % 172.27/172.35 ( class_Lattices_Olattice(T_a) % 172.27/172.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.35 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 172.27/172.35 => ( ( hAPP(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)) % 172.27/172.35 => c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2) = V_x_2 ) % 172.27/172.35 & ( hAPP(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)) % 172.27/172.35 => 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)))))) ) ) ) ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_fold__graph_H_Oequations_I2_J,axiom, % 172.27/172.35 ! [V_a5_2,V_a1_2,V_a2_2,V_a4_2,V_a3_2,T_b,T_a] : % 172.27/172.35 ( 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)) % 172.27/172.35 <=> ( ( V_a2_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.27/172.35 & hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) = V_a4_2 ) % 172.27/172.35 | ? [B_x,B_y] : % 172.27/172.35 ( hAPP(hAPP(V_a3_2,V_a1_2),V_a5_2) = hAPP(hAPP(V_a3_2,B_x),B_y) % 172.27/172.35 & hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_a2_2)) % 172.27/172.35 & 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) ) ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_Sup__fin_Ohom__commute,axiom, % 172.27/172.35 ! [V_N_2,V_h_2,T_a] : % 172.27/172.35 ( class_Lattices_Olattice(T_a) % 172.27/172.35 => ( ! [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)) % 172.27/172.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 172.27/172.35 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.27/172.35 => 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)) ) ) ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_card__Diff__singleton__if,axiom, % 172.27/172.35 ! [V_x_2,V_A_2,T_a] : % 172.27/172.35 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.35 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 172.27/172.35 => 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)) ) % 172.27/172.35 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 172.27/172.35 => 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) ) ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_card__Diff__singleton,axiom, % 172.27/172.35 ! [V_x_2,V_A_2,T_a] : % 172.27/172.35 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.35 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 172.27/172.35 => 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)) ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_card__Diff2__less,axiom, % 172.27/172.35 ! [V_y_2,V_x_2,V_A_2,T_a] : % 172.27/172.35 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.35 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 172.27/172.35 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) % 172.27/172.35 => 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))) ) ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_card__Diff1__less,axiom, % 172.27/172.35 ! [V_x_2,V_A_2,T_a] : % 172.27/172.35 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.35 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 172.27/172.35 => 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))) ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_image__eq__fold__image,axiom, % 172.27/172.35 ! [V_f_2,T_b,V_A_2,T_a] : % 172.27/172.35 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.35 => 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) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_Inf__fin_Ounion__disjoint,axiom, % 172.27/172.35 ! [V_B_2,V_A_2,T_a] : % 172.27/172.35 ( class_Lattices_Olattice(T_a) % 172.27/172.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.35 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.27/172.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 172.27/172.35 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.27/172.35 => ( 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)) % 172.27/172.35 => 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)) ) ) ) ) ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_order__less__irrefl,axiom, % 172.27/172.35 ! [V_x,T_a] : % 172.27/172.35 ( class_Orderings_Opreorder(T_a) % 172.27/172.35 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_x)) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_linorder__neq__iff,axiom, % 172.27/172.35 ! [V_y_2,V_x_2,T_a] : % 172.27/172.35 ( class_Orderings_Olinorder(T_a) % 172.27/172.35 => ( V_x_2 != V_y_2 % 172.27/172.35 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 172.27/172.35 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_x_2)) ) ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_not__less__iff__gr__or__eq,axiom, % 172.27/172.35 ! [V_y_2,V_x_2,T_a] : % 172.27/172.35 ( class_Orderings_Olinorder(T_a) % 172.27/172.35 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 172.27/172.35 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_x_2)) % 172.27/172.35 | V_x_2 = V_y_2 ) ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_linorder__less__linear,axiom, % 172.27/172.35 ! [V_y,V_x,T_a] : % 172.27/172.35 ( class_Orderings_Olinorder(T_a) % 172.27/172.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 172.27/172.35 | V_x = V_y % 172.27/172.35 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_linorder__antisym__conv3,axiom, % 172.27/172.35 ! [V_x_2,V_y_2,T_a] : % 172.27/172.35 ( class_Orderings_Olinorder(T_a) % 172.27/172.35 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_x_2)) % 172.27/172.35 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 172.27/172.35 <=> V_x_2 = V_y_2 ) ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_linorder__neqE,axiom, % 172.27/172.35 ! [V_y,V_x,T_a] : % 172.27/172.35 ( class_Orderings_Olinorder(T_a) % 172.27/172.35 => ( V_x != V_y % 172.27/172.35 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 172.27/172.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_less__imp__neq,axiom, % 172.27/172.35 ! [V_y,V_x,T_a] : % 172.27/172.35 ( class_Orderings_Oorder(T_a) % 172.27/172.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 172.27/172.35 => V_x != V_y ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_order__less__not__sym,axiom, % 172.27/172.35 ! [V_y,V_x,T_a] : % 172.27/172.35 ( class_Orderings_Opreorder(T_a) % 172.27/172.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 172.27/172.35 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_order__less__imp__not__less,axiom, % 172.27/172.35 ! [V_y,V_x,T_a] : % 172.27/172.35 ( class_Orderings_Opreorder(T_a) % 172.27/172.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 172.27/172.35 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_order__less__imp__not__eq,axiom, % 172.27/172.35 ! [V_y,V_x,T_a] : % 172.27/172.35 ( class_Orderings_Oorder(T_a) % 172.27/172.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 172.27/172.35 => V_x != V_y ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_order__less__imp__not__eq2,axiom, % 172.27/172.35 ! [V_y,V_x,T_a] : % 172.27/172.35 ( class_Orderings_Oorder(T_a) % 172.27/172.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 172.27/172.35 => V_y != V_x ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_order__less__asym_H,axiom, % 172.27/172.35 ! [V_b,V_a,T_a] : % 172.27/172.35 ( class_Orderings_Opreorder(T_a) % 172.27/172.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 172.27/172.35 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_xt1_I9_J,axiom, % 172.27/172.35 ! [V_a,V_b,T_a] : % 172.27/172.35 ( class_Orderings_Oorder(T_a) % 172.27/172.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 172.27/172.35 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_ord__eq__less__trans,axiom, % 172.27/172.35 ! [V_c,V_b,V_a,T_a] : % 172.27/172.35 ( class_Orderings_Oord(T_a) % 172.27/172.35 => ( V_a = V_b % 172.27/172.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c)) % 172.27/172.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)) ) ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_xt1_I1_J,axiom, % 172.27/172.35 ! [V_c,V_b,V_a,T_a] : % 172.27/172.35 ( class_Orderings_Oorder(T_a) % 172.27/172.35 => ( V_a = V_b % 172.27/172.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_b)) % 172.27/172.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)) ) ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_ord__less__eq__trans,axiom, % 172.27/172.35 ! [V_c,V_b,V_a,T_a] : % 172.27/172.35 ( class_Orderings_Oord(T_a) % 172.27/172.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 172.27/172.35 => ( V_b = V_c % 172.27/172.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_c)) ) ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_xt1_I2_J,axiom, % 172.27/172.35 ! [V_c,V_a,V_b,T_a] : % 172.27/172.35 ( class_Orderings_Oorder(T_a) % 172.27/172.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 172.27/172.35 => ( V_b = V_c % 172.27/172.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_a)) ) ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_order__less__trans,axiom, % 172.27/172.35 ! [V_z,V_y,V_x,T_a] : % 172.27/172.35 ( class_Orderings_Opreorder(T_a) % 172.27/172.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 172.27/172.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z)) % 172.27/172.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_xt1_I10_J,axiom, % 172.27/172.35 ! [V_z,V_x,V_y,T_a] : % 172.27/172.35 ( class_Orderings_Oorder(T_a) % 172.27/172.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) % 172.27/172.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y)) % 172.27/172.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_order__less__asym,axiom, % 172.27/172.35 ! [V_y,V_x,T_a] : % 172.27/172.35 ( class_Orderings_Opreorder(T_a) % 172.27/172.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 172.27/172.35 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_linorder__cases,axiom, % 172.27/172.35 ! [V_y,V_x,T_a] : % 172.27/172.35 ( class_Orderings_Olinorder(T_a) % 172.27/172.35 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 172.27/172.35 => ( V_x != V_y % 172.27/172.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_less__supI2,axiom, % 172.27/172.35 ! [V_a,V_b,V_x,T_a] : % 172.27/172.35 ( class_Lattices_Osemilattice__sup(T_a) % 172.27/172.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_b)) % 172.27/172.35 => 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))) ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_less__supI1,axiom, % 172.27/172.35 ! [V_b,V_a,V_x,T_a] : % 172.27/172.35 ( class_Lattices_Osemilattice__sup(T_a) % 172.27/172.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a)) % 172.27/172.35 => 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))) ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_less__infI1,axiom, % 172.27/172.35 ! [V_b,V_x,V_a,T_a] : % 172.27/172.35 ( class_Lattices_Osemilattice__inf(T_a) % 172.27/172.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_x)) % 172.27/172.35 => 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)) ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_less__infI2,axiom, % 172.27/172.35 ! [V_a,V_x,V_b,T_a] : % 172.27/172.35 ( class_Lattices_Osemilattice__inf(T_a) % 172.27/172.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_x)) % 172.27/172.35 => 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)) ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_diff__Suc__eq__diff__pred,axiom, % 172.27/172.35 ! [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) ). % 172.27/172.35 % 172.27/172.35 fof(fact_fold__image__distrib,axiom, % 172.27/172.35 ! [V_h_2,V_g_2,V_A_2,T_a,T_b] : % 172.27/172.35 ( class_Groups_Ocomm__monoid__mult(T_b) % 172.27/172.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.35 => 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)) ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_fold__image__empty,axiom, % 172.27/172.35 ! [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 ). % 172.27/172.35 % 172.27/172.35 fof(fact_fold__image__Un__Int,axiom, % 172.27/172.35 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] : % 172.27/172.35 ( class_Groups_Ocomm__monoid__mult(T_b) % 172.27/172.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 172.27/172.35 => 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))) ) ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_Inf__fin_Osingleton,axiom, % 172.27/172.35 ! [V_x_2,T_a] : % 172.27/172.35 ( class_Lattices_Olattice(T_a) % 172.27/172.35 => 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 ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_fold__Un__disjoint,axiom, % 172.27/172.35 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] : % 172.27/172.35 ( class_Groups_Ocomm__monoid__mult(T_b) % 172.27/172.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 172.27/172.35 => ( 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)) % 172.27/172.35 => 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)) ) ) ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_folding__image__simple_Oeq__fold__g,axiom, % 172.27/172.35 ! [V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 172.27/172.35 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 172.27/172.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 172.27/172.35 => 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) ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_sup__Inf__absorb,axiom, % 172.27/172.35 ! [V_a_2,V_A_2,T_a] : % 172.27/172.35 ( class_Lattices_Olattice(T_a) % 172.27/172.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.35 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 172.27/172.35 => 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 ) ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_Inf__fin_Oin__idem,axiom, % 172.27/172.35 ! [V_x_2,V_A_2,T_a] : % 172.27/172.35 ( class_Lattices_Olattice(T_a) % 172.27/172.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.35 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 172.27/172.35 => 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) ) ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_fold__image__insert,axiom, % 172.27/172.35 ! [V_z_2,V_g_2,V_a_2,V_A_2,T_a,T_b] : % 172.27/172.35 ( class_Groups_Oab__semigroup__mult(T_b) % 172.27/172.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.35 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 172.27/172.35 => 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)) ) ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_Inf__fin_Oinsert__idem,axiom, % 172.27/172.35 ! [V_x_2,V_A_2,T_a] : % 172.27/172.35 ( class_Lattices_Olattice(T_a) % 172.27/172.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.35 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.27/172.35 => 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)) ) ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_Inf__fin_Ounion__idem,axiom, % 172.27/172.35 ! [V_B_2,V_A_2,T_a] : % 172.27/172.35 ( class_Lattices_Olattice(T_a) % 172.27/172.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.35 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.27/172.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 172.27/172.35 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.27/172.35 => 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)) ) ) ) ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_card__Diff__insert,axiom, % 172.27/172.35 ! [V_B_2,V_a_2,V_A_2,T_a] : % 172.27/172.35 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.35 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 172.27/172.35 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_B_2)) % 172.27/172.35 => 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)) ) ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_Inf__fin_Oinsert,axiom, % 172.27/172.35 ! [V_x_2,V_A_2,T_a] : % 172.27/172.35 ( class_Lattices_Olattice(T_a) % 172.27/172.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.35 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 172.27/172.35 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.27/172.35 => 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)) ) ) ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_Inf__fin_Oinsert__remove,axiom, % 172.27/172.35 ! [V_x_2,V_A_2,T_a] : % 172.27/172.35 ( class_Lattices_Olattice(T_a) % 172.27/172.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.35 => ( ( hAPP(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)) % 172.27/172.35 => 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 ) % 172.27/172.35 & ( hAPP(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)) % 172.27/172.35 => 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)))))) ) ) ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_Inf__fin_Ounion__inter,axiom, % 172.27/172.35 ! [V_B_2,V_A_2,T_a] : % 172.27/172.35 ( class_Lattices_Olattice(T_a) % 172.27/172.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 172.27/172.35 => ( 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)) % 172.27/172.35 => 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)) ) ) ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_Suc__mono,axiom, % 172.27/172.35 ! [V_n,V_m] : % 172.27/172.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 172.27/172.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n))) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_lessI,axiom, % 172.27/172.35 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_n))) ). % 172.27/172.35 % 172.27/172.35 fof(fact_diff__Suc__1,axiom, % 172.27/172.35 ! [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 ). % 172.27/172.35 % 172.27/172.35 fof(fact_diff__less__Suc,axiom, % 172.27/172.35 ! [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))) ). % 172.27/172.35 % 172.27/172.35 fof(fact_less__1__mult,axiom, % 172.27/172.35 ! [V_n,V_m,T_a] : % 172.27/172.35 ( class_Rings_Olinordered__semidom(T_a) % 172.27/172.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_m)) % 172.27/172.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_n)) % 172.27/172.35 => 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))) ) ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_comm__monoid__big_OF__eq,axiom, % 172.27/172.35 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_b,T_a] : % 172.27/172.35 ( c_Big__Operators_Ocomm__monoid__big(T_a,T_b,V_f_2,V_z_2,V_F_2) % 172.27/172.35 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 172.27/172.35 => 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) ) % 172.27/172.35 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 172.27/172.35 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = V_z_2 ) ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_fold__image__Un__one,axiom, % 172.27/172.35 ! [V_f_2,V_T_2,V_S_2,T_a,T_b] : % 172.27/172.35 ( class_Groups_Ocomm__monoid__mult(T_b) % 172.27/172.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 172.27/172.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2)) % 172.27/172.35 => ( ! [B_x] : % 172.27/172.35 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2))) % 172.27/172.35 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_b) ) % 172.27/172.35 => 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)) ) ) ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_Inf__fin_Oclosed,axiom, % 172.27/172.35 ! [V_A_2,T_a] : % 172.27/172.35 ( class_Lattices_Olattice(T_a) % 172.27/172.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.35 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.27/172.35 => ( ! [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)))))) % 172.27/172.35 => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2)),V_A_2)) ) ) ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_card_Oremove,axiom, % 172.27/172.35 ! [V_x_2,V_A_2,T_a] : % 172.27/172.35 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.35 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 172.27/172.35 => 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)))))) ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_diff__less__mono2,axiom, % 172.27/172.35 ! [V_l,V_n,V_m] : % 172.27/172.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 172.27/172.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_l)) % 172.27/172.35 => 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))) ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_nat__add__commute,axiom, % 172.27/172.35 ! [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) ). % 172.27/172.35 % 172.27/172.35 fof(fact_nat__add__left__commute,axiom, % 172.27/172.35 ! [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)) ). % 172.27/172.35 % 172.27/172.35 fof(fact_nat__add__assoc,axiom, % 172.27/172.35 ! [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)) ). % 172.27/172.35 % 172.27/172.35 fof(fact_nat__add__left__cancel,axiom, % 172.27/172.35 ! [V_n_2,V_m_2,V_k_2] : % 172.27/172.35 ( 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) % 172.27/172.35 <=> V_m_2 = V_n_2 ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_nat__add__right__cancel,axiom, % 172.27/172.35 ! [V_n_2,V_k_2,V_m_2] : % 172.27/172.35 ( 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) % 172.27/172.35 <=> V_m_2 = V_n_2 ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_add__mult__distrib,axiom, % 172.27/172.35 ! [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)) ). % 172.27/172.35 % 172.27/172.35 fof(fact_add__mult__distrib2,axiom, % 172.27/172.35 ! [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)) ). % 172.27/172.35 % 172.27/172.35 fof(fact_comm__semiring__class_Odistrib,axiom, % 172.27/172.35 ! [V_c,V_b,V_a,T_a] : % 172.27/172.35 ( class_Rings_Ocomm__semiring(T_a) % 172.27/172.35 => 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)) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_combine__common__factor,axiom, % 172.27/172.35 ! [V_c,V_b,V_e,V_a,T_a] : % 172.27/172.35 ( class_Rings_Osemiring(T_a) % 172.27/172.35 => 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) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_mult__Suc,axiom, % 172.27/172.35 ! [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)) ). % 172.27/172.35 % 172.27/172.35 fof(fact_mult__Suc__right,axiom, % 172.27/172.35 ! [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)) ). % 172.27/172.35 % 172.27/172.35 fof(fact_add__Suc__right,axiom, % 172.27/172.35 ! [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)) ). % 172.27/172.35 % 172.27/172.35 fof(fact_add__Suc,axiom, % 172.27/172.35 ! [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)) ). % 172.27/172.35 % 172.27/172.35 fof(fact_add__Suc__shift,axiom, % 172.27/172.35 ! [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)) ). % 172.27/172.35 % 172.27/172.35 fof(fact_not__add__less1,axiom, % 172.27/172.35 ! [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)) ). % 172.27/172.35 % 172.27/172.35 fof(fact_not__add__less2,axiom, % 172.27/172.35 ! [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)) ). % 172.27/172.35 % 172.27/172.35 fof(fact_nat__add__left__cancel__less,axiom, % 172.27/172.35 ! [V_n_2,V_m_2,V_k_2] : % 172.27/172.35 ( 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))) % 172.27/172.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_trans__less__add1,axiom, % 172.27/172.35 ! [V_m,V_j,V_i] : % 172.27/172.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 172.27/172.35 => 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))) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_trans__less__add2,axiom, % 172.27/172.35 ! [V_m,V_j,V_i] : % 172.27/172.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 172.27/172.35 => 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))) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_add__less__mono1,axiom, % 172.27/172.35 ! [V_k,V_j,V_i] : % 172.27/172.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 172.27/172.35 => 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))) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_add__less__mono,axiom, % 172.27/172.35 ! [V_l,V_k,V_j,V_i] : % 172.27/172.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 172.27/172.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l)) % 172.27/172.35 => 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))) ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_less__add__eq__less,axiom, % 172.27/172.35 ! [V_n,V_m,V_l,V_k] : % 172.27/172.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_k),V_l)) % 172.27/172.35 => ( 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) % 172.27/172.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_add__lessD1,axiom, % 172.27/172.35 ! [V_k,V_j,V_i] : % 172.27/172.35 ( 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)) % 172.27/172.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_k)) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_diff__add__inverse2,axiom, % 172.27/172.35 ! [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 ). % 172.27/172.35 % 172.27/172.35 fof(fact_diff__add__inverse,axiom, % 172.27/172.35 ! [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 ). % 172.27/172.35 % 172.27/172.35 fof(fact_diff__diff__left,axiom, % 172.27/172.35 ! [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)) ). % 172.27/172.35 % 172.27/172.35 fof(fact_diff__cancel,axiom, % 172.27/172.35 ! [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) ). % 172.27/172.35 % 172.27/172.35 fof(fact_diff__cancel2,axiom, % 172.27/172.35 ! [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) ). % 172.27/172.35 % 172.27/172.35 fof(fact_psubsetD,axiom, % 172.27/172.35 ! [V_ca_2,V_B_2,V_A_2,T_a] : % 172.27/172.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 172.27/172.35 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 172.27/172.35 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_not__psubset__empty,axiom, % 172.27/172.35 ! [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)))) ). % 172.27/172.35 % 172.27/172.35 fof(fact_less__add__one,axiom, % 172.27/172.35 ! [V_a,T_a] : % 172.27/172.35 ( class_Rings_Olinordered__semidom(T_a) % 172.27/172.35 => 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)))) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_eq__add__iff1,axiom, % 172.27/172.35 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_a] : % 172.27/172.35 ( class_Rings_Oring(T_a) % 172.27/172.35 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_ca_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2) % 172.27/172.35 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2)),V_e_2)),V_ca_2) = V_d_2 ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_eq__add__iff2,axiom, % 172.27/172.35 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_a] : % 172.27/172.35 ( class_Rings_Oring(T_a) % 172.27/172.35 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_ca_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2) % 172.27/172.35 <=> V_ca_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_b_2),V_a_2)),V_e_2)),V_d_2) ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_less__iff__Suc__add,axiom, % 172.27/172.35 ! [V_n_2,V_m_2] : % 172.27/172.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 172.27/172.35 <=> ? [B_k] : V_n_2 = hAPP(c_Nat_OSuc,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k)) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_less__add__Suc2,axiom, % 172.27/172.35 ! [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)))) ). % 172.27/172.35 % 172.27/172.35 fof(fact_less__add__Suc1,axiom, % 172.27/172.35 ! [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)))) ). % 172.27/172.35 % 172.27/172.35 fof(fact_less__diff__conv,axiom, % 172.27/172.35 ! [V_k_2,V_j_2,V_i_2] : % 172.27/172.35 ( 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))) % 172.27/172.35 <=> 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)) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_add__diff__inverse,axiom, % 172.27/172.35 ! [V_n,V_m] : % 172.27/172.35 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 172.27/172.35 => 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 ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_less__add__iff1,axiom, % 172.27/172.35 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_a] : % 172.27/172.35 ( class_Rings_Oordered__ring(T_a) % 172.27/172.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_ca_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2))) % 172.27/172.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2)),V_e_2)),V_ca_2)),V_d_2)) ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_less__add__iff2,axiom, % 172.27/172.35 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_a] : % 172.27/172.35 ( class_Rings_Oordered__ring(T_a) % 172.27/172.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_ca_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2))) % 172.27/172.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_b_2),V_a_2)),V_e_2)),V_d_2))) ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_Suc__eq__plus1,axiom, % 172.27/172.35 ! [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)) ). % 172.27/172.35 % 172.27/172.35 fof(fact_Suc__eq__plus1__left,axiom, % 172.27/172.35 ! [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) ). % 172.27/172.35 % 172.27/172.35 fof(fact_psubset__card__mono,axiom, % 172.27/172.35 ! [V_A_2,V_B_2,T_a] : % 172.27/172.35 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 172.27/172.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 172.27/172.35 => 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))) ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_linorder__neqE__linordered__idom,axiom, % 172.27/172.35 ! [V_y,V_x,T_a] : % 172.27/172.35 ( class_Rings_Olinordered__idom(T_a) % 172.27/172.35 => ( V_x != V_y % 172.27/172.35 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 172.27/172.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_Suc__mult__cancel1,axiom, % 172.27/172.35 ! [V_n_2,V_m_2,V_k_2] : % 172.27/172.35 ( 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) % 172.27/172.35 <=> V_m_2 = V_n_2 ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_n__not__Suc__n,axiom, % 172.27/172.35 ! [V_n] : V_n != hAPP(c_Nat_OSuc,V_n) ). % 172.27/172.35 % 172.27/172.35 fof(fact_Suc__n__not__n,axiom, % 172.27/172.35 ! [V_n] : hAPP(c_Nat_OSuc,V_n) != V_n ). % 172.27/172.35 % 172.27/172.35 fof(fact_nat_Oinject,axiom, % 172.27/172.35 ! [V_nat_H_2,V_nat_2] : % 172.27/172.35 ( hAPP(c_Nat_OSuc,V_nat_2) = hAPP(c_Nat_OSuc,V_nat_H_2) % 172.27/172.35 <=> V_nat_2 = V_nat_H_2 ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_Suc__inject,axiom, % 172.27/172.35 ! [V_y,V_x] : % 172.27/172.35 ( hAPP(c_Nat_OSuc,V_x) = hAPP(c_Nat_OSuc,V_y) % 172.27/172.35 => V_x = V_y ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_less__not__refl,axiom, % 172.27/172.35 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n)) ). % 172.27/172.35 % 172.27/172.35 fof(fact_nat__neq__iff,axiom, % 172.27/172.35 ! [V_n_2,V_m_2] : % 172.27/172.35 ( V_m_2 != V_n_2 % 172.27/172.35 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 172.27/172.35 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_linorder__neqE__nat,axiom, % 172.27/172.35 ! [V_y,V_x] : % 172.27/172.35 ( V_x != V_y % 172.27/172.35 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y)) % 172.27/172.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y),V_x)) ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_less__irrefl__nat,axiom, % 172.27/172.35 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_n)) ). % 172.27/172.35 % 172.27/172.35 fof(fact_less__not__refl2,axiom, % 172.27/172.35 ! [V_m,V_n] : % 172.27/172.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m)) % 172.27/172.35 => V_m != V_n ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_less__not__refl3,axiom, % 172.27/172.35 ! [V_t,V_s] : % 172.27/172.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_s),V_t)) % 172.27/172.35 => V_s != V_t ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_nat__less__cases,axiom, % 172.27/172.35 ! [V_P_2,V_n_2,V_m_2] : % 172.27/172.35 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 172.27/172.35 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) ) % 172.27/172.35 => ( ( V_m_2 = V_n_2 % 172.27/172.35 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) ) % 172.27/172.35 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) % 172.27/172.35 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) ) % 172.27/172.35 => hBOOL(hAPP(hAPP(V_P_2,V_n_2),V_m_2)) ) ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_diff__mult__distrib2,axiom, % 172.27/172.35 ! [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)) ). % 172.27/172.35 % 172.27/172.35 fof(fact_diff__commute,axiom, % 172.27/172.35 ! [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) ). % 172.27/172.35 % 172.27/172.35 fof(fact_diff__mult__distrib,axiom, % 172.27/172.35 ! [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)) ). % 172.27/172.35 % 172.27/172.35 fof(fact_nat__mult__eq__1__iff,axiom, % 172.27/172.35 ! [V_n_2,V_m_2] : % 172.27/172.35 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 172.27/172.35 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 172.27/172.35 & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_nat__mult__1__right,axiom, % 172.27/172.35 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_n ). % 172.27/172.35 % 172.27/172.35 fof(fact_nat__1__eq__mult__iff,axiom, % 172.27/172.35 ! [V_n_2,V_m_2] : % 172.27/172.35 ( c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) % 172.27/172.35 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 172.27/172.35 & V_n_2 = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_nat__mult__1,axiom, % 172.27/172.35 ! [V_n] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n) = V_n ). % 172.27/172.35 % 172.27/172.35 fof(fact_card__Un__Int,axiom, % 172.27/172.35 ! [V_B_2,V_A_2,T_a] : % 172.27/172.35 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 172.27/172.35 => 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))) ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_card_Ounion__inter,axiom, % 172.27/172.35 ! [V_B_2,V_A_2,T_a] : % 172.27/172.35 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 172.27/172.35 => 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)) ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_comm__monoid__big_Oinfinite,axiom, % 172.27/172.35 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_b,T_a] : % 172.27/172.35 ( c_Big__Operators_Ocomm__monoid__big(T_a,T_b,V_f_2,V_z_2,V_F_2) % 172.27/172.35 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 172.27/172.35 => hAPP(hAPP(V_F_2,V_g_2),V_A_2) = V_z_2 ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_card__Un__disjoint,axiom, % 172.27/172.35 ! [V_B_2,V_A_2,T_a] : % 172.27/172.35 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 172.27/172.35 => ( 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)) % 172.27/172.35 => 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)) ) ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_card_Oinsert,axiom, % 172.27/172.35 ! [V_x_2,V_A_2,T_a] : % 172.27/172.35 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.35 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 172.27/172.35 => 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)) ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_card_Oinsert__remove,axiom, % 172.27/172.35 ! [V_x_2,V_A_2,T_a] : % 172.27/172.35 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.35 => 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)))))) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_Suc__mult__less__cancel1,axiom, % 172.27/172.35 ! [V_n_2,V_m_2,V_k_2] : % 172.27/172.35 ( 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))) % 172.27/172.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_not__less__eq,axiom, % 172.27/172.35 ! [V_n_2,V_m_2] : % 172.27/172.35 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 172.27/172.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2))) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_less__Suc__eq,axiom, % 172.27/172.35 ! [V_n_2,V_m_2] : % 172.27/172.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) % 172.27/172.35 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 172.27/172.35 | V_m_2 = V_n_2 ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_Suc__less__eq,axiom, % 172.27/172.35 ! [V_n_2,V_m_2] : % 172.27/172.35 ( 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))) % 172.27/172.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_not__less__less__Suc__eq,axiom, % 172.27/172.35 ! [V_m_2,V_n_2] : % 172.27/172.35 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) % 172.27/172.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2))) % 172.27/172.35 <=> V_n_2 = V_m_2 ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_less__antisym,axiom, % 172.27/172.35 ! [V_m,V_n] : % 172.27/172.35 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_m)) % 172.27/172.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),hAPP(c_Nat_OSuc,V_m))) % 172.27/172.35 => V_m = V_n ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_less__SucI,axiom, % 172.27/172.35 ! [V_n,V_m] : % 172.27/172.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 172.27/172.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_Suc__lessI,axiom, % 172.27/172.35 ! [V_n,V_m] : % 172.27/172.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 172.27/172.35 => ( hAPP(c_Nat_OSuc,V_m) != V_n % 172.27/172.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_less__trans__Suc,axiom, % 172.27/172.35 ! [V_k,V_j,V_i] : % 172.27/172.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 172.27/172.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),V_k)) % 172.27/172.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_i)),V_k)) ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_less__SucE,axiom, % 172.27/172.35 ! [V_n,V_m] : % 172.27/172.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) % 172.27/172.35 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 172.27/172.35 => V_m = V_n ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_Suc__lessD,axiom, % 172.27/172.35 ! [V_n,V_m] : % 172.27/172.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) % 172.27/172.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_Suc__less__SucD,axiom, % 172.27/172.35 ! [V_n,V_m] : % 172.27/172.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),hAPP(c_Nat_OSuc,V_n))) % 172.27/172.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_diff__Suc__Suc,axiom, % 172.27/172.35 ! [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) ). % 172.27/172.35 % 172.27/172.35 fof(fact_Suc__diff__diff,axiom, % 172.27/172.35 ! [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) ). % 172.27/172.35 % 172.27/172.35 fof(fact_less__imp__diff__less,axiom, % 172.27/172.35 ! [V_n,V_k,V_j] : % 172.27/172.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_j),V_k)) % 172.27/172.35 => 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)) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J,axiom, % 172.27/172.35 ! [V_m,V_a,T_a] : % 172.27/172.35 ( class_Rings_Ocomm__semiring__1(T_a) % 172.27/172.35 => 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) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J,axiom, % 172.27/172.35 ! [V_a,V_m,T_a] : % 172.27/172.35 ( class_Rings_Ocomm__semiring__1(T_a) % 172.27/172.35 => 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) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J,axiom, % 172.27/172.35 ! [V_m,T_a] : % 172.27/172.35 ( class_Rings_Ocomm__semiring__1(T_a) % 172.27/172.35 => 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) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_termination__basic__simps_I1_J,axiom, % 172.27/172.35 ! [V_z,V_y,V_x] : % 172.27/172.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y)) % 172.27/172.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z))) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_termination__basic__simps_I2_J,axiom, % 172.27/172.35 ! [V_y,V_z,V_x] : % 172.27/172.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_z)) % 172.27/172.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_y),V_z))) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_mult__1__left,axiom, % 172.27/172.35 ! [V_a,T_a] : % 172.27/172.35 ( class_Groups_Omonoid__mult(T_a) % 172.27/172.35 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J,axiom, % 172.27/172.35 ! [V_a,T_a] : % 172.27/172.35 ( class_Rings_Ocomm__semiring__1(T_a) % 172.27/172.35 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_mult__1,axiom, % 172.27/172.35 ! [V_a,T_a] : % 172.27/172.35 ( class_Groups_Ocomm__monoid__mult(T_a) % 172.27/172.35 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),c_Groups_Oone__class_Oone(T_a)),V_a) = V_a ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_mult__1__right,axiom, % 172.27/172.35 ! [V_a,T_a] : % 172.27/172.35 ( class_Groups_Omonoid__mult(T_a) % 172.27/172.35 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J,axiom, % 172.27/172.35 ! [V_a,T_a] : % 172.27/172.35 ( class_Rings_Ocomm__semiring__1(T_a) % 172.27/172.35 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_psubset__trans,axiom, % 172.27/172.35 ! [V_C_2,V_B_2,V_A_2,T_a] : % 172.27/172.35 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 172.27/172.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) % 172.27/172.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_nat__mult__assoc,axiom, % 172.27/172.35 ! [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)) ). % 172.27/172.35 % 172.27/172.35 fof(fact_nat__mult__commute,axiom, % 172.27/172.35 ! [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) ). % 172.27/172.35 % 172.27/172.35 fof(fact_add__right__imp__eq,axiom, % 172.27/172.35 ! [V_c,V_a,V_b,T_a] : % 172.27/172.35 ( class_Groups_Ocancel__semigroup__add(T_a) % 172.27/172.35 => ( 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) % 172.27/172.35 => V_b = V_c ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_add__imp__eq,axiom, % 172.27/172.35 ! [V_c,V_b,V_a,T_a] : % 172.27/172.35 ( class_Groups_Ocancel__ab__semigroup__add(T_a) % 172.27/172.35 => ( 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) % 172.27/172.35 => V_b = V_c ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_add__left__imp__eq,axiom, % 172.27/172.35 ! [V_c,V_b,V_a,T_a] : % 172.27/172.35 ( class_Groups_Ocancel__semigroup__add(T_a) % 172.27/172.35 => ( 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) % 172.27/172.35 => V_b = V_c ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J,axiom, % 172.27/172.35 ! [V_d,V_c,V_b,V_a,T_a] : % 172.27/172.35 ( class_Rings_Ocomm__semiring__1(T_a) % 172.27/172.35 => 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)) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_add__right__cancel,axiom, % 172.27/172.35 ! [V_ca_2,V_a_2,V_b_2,T_a] : % 172.27/172.35 ( class_Groups_Ocancel__semigroup__add(T_a) % 172.27/172.35 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_a_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_ca_2),V_a_2) % 172.27/172.35 <=> V_b_2 = V_ca_2 ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_add__left__cancel,axiom, % 172.27/172.35 ! [V_ca_2,V_b_2,V_a_2,T_a] : % 172.27/172.35 ( class_Groups_Ocancel__semigroup__add(T_a) % 172.27/172.35 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_ca_2) % 172.27/172.35 <=> V_b_2 = V_ca_2 ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J,axiom, % 172.27/172.35 ! [V_c,V_b,V_a,T_a] : % 172.27/172.35 ( class_Rings_Ocomm__semiring__1(T_a) % 172.27/172.35 => 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) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_ab__semigroup__add__class_Oadd__ac_I1_J,axiom, % 172.27/172.35 ! [V_c,V_b,V_a,T_a] : % 172.27/172.35 ( class_Groups_Oab__semigroup__add(T_a) % 172.27/172.35 => 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)) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J,axiom, % 172.27/172.35 ! [V_c,V_b,V_a,T_a] : % 172.27/172.35 ( class_Rings_Ocomm__semiring__1(T_a) % 172.27/172.35 => 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)) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J,axiom, % 172.27/172.35 ! [V_d,V_c,V_a,T_a] : % 172.27/172.35 ( class_Rings_Ocomm__semiring__1(T_a) % 172.27/172.35 => 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) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J,axiom, % 172.27/172.35 ! [V_d,V_c,V_a,T_a] : % 172.27/172.35 ( class_Rings_Ocomm__semiring__1(T_a) % 172.27/172.35 => 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)) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J,axiom, % 172.27/172.35 ! [V_c,V_a,T_a] : % 172.27/172.35 ( class_Rings_Ocomm__semiring__1(T_a) % 172.27/172.35 => 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) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J,axiom, % 172.27/172.35 ! [V_ry,V_rx,V_ly,V_lx,T_a] : % 172.27/172.35 ( class_Rings_Ocomm__semiring__1(T_a) % 172.27/172.35 => 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)) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J,axiom, % 172.27/172.35 ! [V_ry,V_rx,V_ly,V_lx,T_a] : % 172.27/172.35 ( class_Rings_Ocomm__semiring__1(T_a) % 172.27/172.35 => 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)) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J,axiom, % 172.27/172.35 ! [V_ry,V_rx,V_ly,V_lx,T_a] : % 172.27/172.35 ( class_Rings_Ocomm__semiring__1(T_a) % 172.27/172.35 => 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))) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J,axiom, % 172.27/172.35 ! [V_rx,V_ly,V_lx,T_a] : % 172.27/172.35 ( class_Rings_Ocomm__semiring__1(T_a) % 172.27/172.35 => 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) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J,axiom, % 172.27/172.35 ! [V_rx,V_ly,V_lx,T_a] : % 172.27/172.35 ( class_Rings_Ocomm__semiring__1(T_a) % 172.27/172.35 => 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)) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_ab__semigroup__mult__class_Omult__ac_I1_J,axiom, % 172.27/172.35 ! [V_c,V_b,V_a,T_a] : % 172.27/172.35 ( class_Groups_Oab__semigroup__mult(T_a) % 172.27/172.35 => 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)) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J,axiom, % 172.27/172.35 ! [V_ry,V_rx,V_lx,T_a] : % 172.27/172.35 ( class_Rings_Ocomm__semiring__1(T_a) % 172.27/172.35 => 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) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J,axiom, % 172.27/172.35 ! [V_ry,V_rx,V_lx,T_a] : % 172.27/172.35 ( class_Rings_Ocomm__semiring__1(T_a) % 172.27/172.35 => 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)) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J,axiom, % 172.27/172.35 ! [V_b,V_a,T_a] : % 172.27/172.35 ( class_Rings_Ocomm__semiring__1(T_a) % 172.27/172.35 => 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) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_diff__eq__diff__eq,axiom, % 172.27/172.35 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 172.27/172.35 ( class_Groups_Oab__group__add(T_a) % 172.27/172.35 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_ca_2),V_d_2) % 172.27/172.35 => ( V_a_2 = V_b_2 % 172.27/172.35 <=> V_ca_2 = V_d_2 ) ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_one__reorient,axiom, % 172.27/172.35 ! [V_x_2,T_a] : % 172.27/172.35 ( class_Groups_Oone(T_a) % 172.27/172.35 => ( c_Groups_Oone__class_Oone(T_a) = V_x_2 % 172.27/172.35 <=> V_x_2 = c_Groups_Oone__class_Oone(T_a) ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_comp__cong,axiom, % 172.27/172.35 ! [T_e,T_d,T_c,T_a,T_b,V_x_H_2,V_g_H_2,V_f_H_2,V_x_2,V_g_2,V_f_2] : % 172.27/172.35 ( hAPP(V_f_2,hAPP(V_g_2,V_x_2)) = hAPP(V_f_H_2,hAPP(V_g_H_2,V_x_H_2)) % 172.27/172.35 => hAPP(hAPP(c_Fun_Ocomp(T_b,T_a,T_c,V_f_2),V_g_2),V_x_2) = hAPP(hAPP(c_Fun_Ocomp(T_d,T_a,T_e,V_f_H_2),V_g_H_2),V_x_H_2) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_add__less__imp__less__left,axiom, % 172.27/172.35 ! [V_b,V_a,V_c,T_a] : % 172.27/172.35 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 172.27/172.35 => ( 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))) % 172.27/172.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_add__less__imp__less__right,axiom, % 172.27/172.35 ! [V_b,V_c,V_a,T_a] : % 172.27/172.35 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 172.27/172.35 => ( 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))) % 172.27/172.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_add__strict__mono,axiom, % 172.27/172.35 ! [V_d,V_c,V_b,V_a,T_a] : % 172.27/172.35 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 172.27/172.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 172.27/172.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) % 172.27/172.35 => 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))) ) ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_add__strict__left__mono,axiom, % 172.27/172.35 ! [V_c,V_b,V_a,T_a] : % 172.27/172.35 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 172.27/172.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 172.27/172.35 => 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))) ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_add__strict__right__mono,axiom, % 172.27/172.35 ! [V_c,V_b,V_a,T_a] : % 172.27/172.35 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 172.27/172.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 172.27/172.35 => 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))) ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_add__less__cancel__left,axiom, % 172.27/172.35 ! [V_b_2,V_a_2,V_ca_2,T_a] : % 172.27/172.35 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 172.27/172.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_ca_2),V_b_2))) % 172.27/172.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_add__less__cancel__right,axiom, % 172.27/172.35 ! [V_b_2,V_ca_2,V_a_2,T_a] : % 172.27/172.35 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 172.27/172.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_ca_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_ca_2))) % 172.27/172.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_diff__eq__diff__less,axiom, % 172.27/172.35 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 172.27/172.35 ( class_Groups_Oordered__ab__group__add(T_a) % 172.27/172.35 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_ca_2),V_d_2) % 172.27/172.35 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) % 172.27/172.35 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),V_d_2)) ) ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_crossproduct__eq,axiom, % 172.27/172.35 ! [V_z_2,V_x_2,V_y_2,V_w_2,T_a] : % 172.27/172.35 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a) % 172.27/172.35 => ( 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)) % 172.27/172.35 <=> ( V_w_2 = V_x_2 % 172.27/172.35 | V_y_2 = V_z_2 ) ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J,axiom, % 172.27/172.35 ! [V_b,V_m,V_a,T_a] : % 172.27/172.35 ( class_Rings_Ocomm__semiring__1(T_a) % 172.27/172.35 => 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) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J,axiom, % 172.27/172.35 ! [V_c,V_b,V_a,T_a] : % 172.27/172.35 ( class_Rings_Ocomm__semiring__1(T_a) % 172.27/172.35 => 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)) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_crossproduct__noteq,axiom, % 172.27/172.35 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 172.27/172.35 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a) % 172.27/172.35 => ( ( V_a_2 != V_b_2 % 172.27/172.35 & V_ca_2 != V_d_2 ) % 172.27/172.35 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_d_2)) != hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_d_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_ca_2)) ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J,axiom, % 172.27/172.35 ! [V_z,V_y,V_x,T_a] : % 172.27/172.35 ( class_Rings_Ocomm__semiring__1(T_a) % 172.27/172.35 => 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)) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_add__diff__cancel,axiom, % 172.27/172.35 ! [V_b,V_a,T_a] : % 172.27/172.35 ( class_Groups_Ogroup__add(T_a) % 172.27/172.35 => 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 ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_diff__add__cancel,axiom, % 172.27/172.35 ! [V_b,V_a,T_a] : % 172.27/172.35 ( class_Groups_Ogroup__add(T_a) % 172.27/172.35 => 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 ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_mult_Ocomm__neutral,axiom, % 172.27/172.35 ! [V_a,T_a] : % 172.27/172.35 ( class_Groups_Ocomm__monoid__mult(T_a) % 172.27/172.35 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_left__add__mult__distrib,axiom, % 172.27/172.35 ! [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) ). % 172.27/172.35 % 172.27/172.35 fof(fact_Inf__fin_Ohom__commute,axiom, % 172.27/172.35 ! [V_N_2,V_h_2,T_a] : % 172.27/172.35 ( class_Lattices_Olattice(T_a) % 172.27/172.35 => ( ! [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)) % 172.27/172.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 172.27/172.35 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.27/172.35 => 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)) ) ) ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_fold1__Un,axiom, % 172.27/172.35 ! [V_B_2,V_A_2,T_a] : % 172.27/172.35 ( class_Groups_Oab__semigroup__mult(T_a) % 172.27/172.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.35 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.27/172.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 172.27/172.35 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.27/172.35 => ( 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)) % 172.27/172.35 => 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)) ) ) ) ) ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_folding__image__simple_Ounion__inter__neutral,axiom, % 172.27/172.35 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 172.27/172.35 ( c_Finite__Set_Ofolding__image__simple(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 172.27/172.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 172.27/172.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 172.27/172.35 => ( ! [B_x] : % 172.27/172.35 ( 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))) % 172.27/172.35 => hAPP(V_g_2,B_x) = V_z_2 ) % 172.27/172.35 => 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)) ) ) ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_fold1__insert,axiom, % 172.27/172.35 ! [V_x_2,V_A_2,T_a] : % 172.27/172.35 ( class_Groups_Oab__semigroup__mult(T_a) % 172.27/172.35 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.27/172.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.35 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 172.27/172.35 => 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)) ) ) ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_setsum__diff1,axiom, % 172.27/172.35 ! [V_f_2,V_a_2,V_A_2,T_a,T_b] : % 172.27/172.35 ( class_Groups_Oab__group__add(T_b) % 172.27/172.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.35 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 172.27/172.35 => 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)) ) % 172.27/172.35 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 172.27/172.35 => 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) ) ) ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_setsum__diff1__ring,axiom, % 172.27/172.35 ! [V_f_2,V_a_2,V_A_2,T_a,T_b] : % 172.27/172.35 ( class_Rings_Oring(T_b) % 172.27/172.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.35 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 172.27/172.35 => 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)) ) ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_setsum__diff1_H,axiom, % 172.27/172.35 ! [V_f_2,V_a_2,V_A_2,T_a,T_b] : % 172.27/172.35 ( class_Groups_Ocomm__monoid__add(T_b) % 172.27/172.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.35 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 172.27/172.35 => 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)))))) ) ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_setsum_Oremove,axiom, % 172.27/172.35 ! [V_g_2,V_x_2,V_A_2,T_a,T_b] : % 172.27/172.35 ( class_Groups_Ocomm__monoid__add(T_b) % 172.27/172.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.35 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 172.27/172.35 => 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)))))) ) ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_setsum__commute,axiom, % 172.27/172.35 ! [V_A_2,V_B_2,V_f_2,T_c,T_b,T_a] : % 172.27/172.35 ( class_Groups_Ocomm__monoid__add(T_a) % 172.27/172.35 => 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) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_setsum__addf,axiom, % 172.27/172.35 ! [V_A_2,V_g_2,V_f_2,T_b,T_a] : % 172.27/172.35 ( class_Groups_Ocomm__monoid__add(T_a) % 172.27/172.35 => 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)) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_setsum__right__distrib,axiom, % 172.27/172.35 ! [V_A_2,V_f_2,T_b,V_r_2,T_a] : % 172.27/172.35 ( class_Rings_Osemiring__0(T_a) % 172.27/172.35 => 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) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_setsum__left__distrib,axiom, % 172.27/172.35 ! [V_r_2,V_A_2,V_f_2,T_b,T_a] : % 172.27/172.35 ( class_Rings_Osemiring__0(T_a) % 172.27/172.35 => 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) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_setsum__product,axiom, % 172.27/172.35 ! [V_B_2,V_g_2,T_c,V_A_2,V_f_2,T_b,T_a] : % 172.27/172.35 ( class_Rings_Osemiring__0(T_a) % 172.27/172.35 => 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) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_setsum__subtractf,axiom, % 172.27/172.35 ! [V_A_2,V_g_2,V_f_2,T_b,T_a] : % 172.27/172.35 ( class_Groups_Oab__group__add(T_a) % 172.27/172.35 => 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)) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_setsum_Odistrib,axiom, % 172.27/172.35 ! [V_h_2,V_g_2,V_A_2,T_a,T_b] : % 172.27/172.35 ( class_Groups_Ocomm__monoid__add(T_b) % 172.27/172.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.35 => 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)) ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_card__eq__setsum,axiom, % 172.27/172.35 ! [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) ). % 172.27/172.35 % 172.27/172.35 fof(fact_fold1__singleton__def,axiom, % 172.27/172.35 ! [V_a_2,V_f_2,T_a,V_g_2] : % 172.27/172.35 ( V_g_2 = c_Finite__Set_Ofold1(T_a,V_f_2) % 172.27/172.35 => 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 ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_fold1__singleton,axiom, % 172.27/172.35 ! [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 ). % 172.27/172.35 % 172.27/172.35 fof(fact_folding__one_Oeq__fold,axiom, % 172.27/172.35 ! [V_A_2,V_F_2,V_f_2,T_a] : % 172.27/172.35 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2) % 172.27/172.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.35 => hAPP(V_F_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_a,V_f_2),V_A_2) ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_fold1__def,axiom, % 172.27/172.35 ! [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)) ). % 172.27/172.35 % 172.27/172.35 fof(fact_setsum_Oinsert,axiom, % 172.27/172.35 ! [V_g_2,V_x_2,V_A_2,T_a,T_b] : % 172.27/172.35 ( class_Groups_Ocomm__monoid__add(T_b) % 172.27/172.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.35 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 172.27/172.35 => 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)) ) ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_setsum__insert,axiom, % 172.27/172.35 ! [V_f_2,V_a_2,V_F_2,T_a,T_b] : % 172.27/172.35 ( class_Groups_Ocomm__monoid__add(T_b) % 172.27/172.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) % 172.27/172.35 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_F_2)) % 172.27/172.35 => 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)) ) ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_Sup__fin_OF__eq,axiom, % 172.27/172.35 ! [V_A_2,T_a] : % 172.27/172.35 ( class_Lattices_Olattice(T_a) % 172.27/172.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.35 => 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) ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_Inf__fin_OF__eq,axiom, % 172.27/172.35 ! [V_A_2,T_a] : % 172.27/172.35 ( class_Lattices_Olattice(T_a) % 172.27/172.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.35 => 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) ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_setsum__Un__Int,axiom, % 172.27/172.35 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] : % 172.27/172.35 ( class_Groups_Ocomm__monoid__add(T_b) % 172.27/172.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 172.27/172.35 => 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)) ) ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_fold1__insert__idem,axiom, % 172.27/172.35 ! [V_x_2,V_A_2,T_a] : % 172.27/172.35 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 172.27/172.35 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.27/172.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.35 => 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)) ) ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_setsum_Oinsert__remove,axiom, % 172.27/172.35 ! [V_x_2,V_g_2,V_A_2,T_a,T_b] : % 172.27/172.35 ( class_Groups_Ocomm__monoid__add(T_b) % 172.27/172.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.35 => 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)))))) ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_setsum__Un__disjoint,axiom, % 172.27/172.35 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] : % 172.27/172.35 ( class_Groups_Ocomm__monoid__add(T_b) % 172.27/172.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 172.27/172.35 => ( 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)) % 172.27/172.35 => 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)) ) ) ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_setsum__Un,axiom, % 172.27/172.35 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] : % 172.27/172.35 ( class_Groups_Oab__group__add(T_b) % 172.27/172.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 172.27/172.35 => 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))) ) ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_fold1__Un2,axiom, % 172.27/172.35 ! [V_B_2,V_A_2,T_a] : % 172.27/172.35 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 172.27/172.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.35 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.27/172.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 172.27/172.35 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.27/172.35 => 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)) ) ) ) ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_setsum__diff1__nat,axiom, % 172.27/172.35 ! [V_f_2,V_A_2,V_a_2,T_a] : % 172.27/172.35 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 172.27/172.35 => 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)) ) % 172.27/172.35 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 172.27/172.35 => 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) ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_setsum__Un__nat,axiom, % 172.27/172.35 ! [V_f_2,V_B_2,V_A_2,T_a] : % 172.27/172.35 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 172.27/172.35 => 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))) ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_semilattice__big_OF__eq,axiom, % 172.27/172.35 ! [V_A_2,V_F_2,V_f_2,T_a] : % 172.27/172.35 ( c_Big__Operators_Osemilattice__big(T_a,V_f_2,V_F_2) % 172.27/172.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.35 => hAPP(V_F_2,V_A_2) = hAPP(c_Finite__Set_Ofold1(T_a,V_f_2),V_A_2) ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_fold1__in,axiom, % 172.27/172.35 ! [V_A_2,T_a] : % 172.27/172.35 ( class_Groups_Oab__semigroup__mult(T_a) % 172.27/172.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.35 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.27/172.35 => ( ! [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)))))) % 172.27/172.35 => 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)) ) ) ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_hom__fold1__commute,axiom, % 172.27/172.35 ! [V_N_2,V_h_2,T_a] : % 172.27/172.35 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 172.27/172.35 => ( ! [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)) % 172.27/172.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 172.27/172.35 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.27/172.35 => 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)) ) ) ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_setsum__strict__mono,axiom, % 172.27/172.35 ! [V_g_2,V_f_2,V_A_2,T_a,T_b] : % 172.27/172.35 ( ( class_Groups_Ocomm__monoid__add(T_b) % 172.27/172.35 & class_Groups_Oordered__cancel__ab__semigroup__add(T_b) ) % 172.27/172.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.35 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.27/172.35 => ( ! [B_x] : % 172.27/172.35 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 172.27/172.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) ) % 172.27/172.35 => 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))) ) ) ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_psubset__insert__iff,axiom, % 172.27/172.35 ! [V_B_2,V_x_2,V_A_2,T_a] : % 172.27/172.35 ( 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))) % 172.27/172.35 <=> ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) % 172.27/172.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) % 172.27/172.35 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) % 172.27/172.35 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 172.27/172.35 => 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)) ) % 172.27/172.35 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 172.27/172.35 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_setprod_Oremove,axiom, % 172.27/172.35 ! [V_g_2,V_x_2,V_A_2,T_a,T_b] : % 172.27/172.35 ( class_Groups_Ocomm__monoid__mult(T_b) % 172.27/172.35 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.35 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 172.27/172.35 => 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)))))) ) ) ) ). % 172.27/172.35 % 172.27/172.35 fof(fact_card__Diff1__le,axiom, % 172.27/172.35 ! [V_x_2,V_A_2,T_a] : % 172.27/172.35 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.35 => 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))) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_fold__image__1,axiom, % 172.27/172.36 ! [V_f_2,V_S_2,T_a,T_b] : % 172.27/172.36 ( class_Groups_Ocomm__monoid__mult(T_b) % 172.27/172.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 172.27/172.36 => ( ! [B_x] : % 172.27/172.36 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2)) % 172.27/172.36 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_b) ) % 172.27/172.36 => 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) ) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_card__Plus,axiom, % 172.27/172.36 ! [V_B_2,T_b,V_A_2,T_a] : % 172.27/172.36 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 172.27/172.36 => 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)) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_order__refl,axiom, % 172.27/172.36 ! [V_x,T_a] : % 172.27/172.36 ( class_Orderings_Opreorder(T_a) % 172.27/172.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_x)) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_equalityI,axiom, % 172.27/172.36 ! [V_B_2,V_A_2,T_a] : % 172.27/172.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 172.27/172.36 => V_A_2 = V_B_2 ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_subsetD,axiom, % 172.27/172.36 ! [V_ca_2,V_B_2,V_A_2,T_a] : % 172.27/172.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 172.27/172.36 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_B_2)) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_empty__subsetI,axiom, % 172.27/172.36 ! [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)) ). % 172.27/172.36 % 172.27/172.36 fof(fact_le__refl,axiom, % 172.27/172.36 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_n)) ). % 172.27/172.36 % 172.27/172.36 fof(fact_nat__le__linear,axiom, % 172.27/172.36 ! [V_n,V_m] : % 172.27/172.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 172.27/172.36 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_eq__imp__le,axiom, % 172.27/172.36 ! [V_n,V_m] : % 172.27/172.36 ( V_m = V_n % 172.27/172.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_le__trans,axiom, % 172.27/172.36 ! [V_k,V_j,V_i] : % 172.27/172.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_k)) % 172.27/172.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_k)) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_le__antisym,axiom, % 172.27/172.36 ! [V_n,V_m] : % 172.27/172.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 172.27/172.36 => V_m = V_n ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_rev__predicate1D,axiom, % 172.27/172.36 ! [V_Q_2,T_a,V_x_2,V_P_2] : % 172.27/172.36 ( hBOOL(hAPP(V_P_2,V_x_2)) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_P_2),V_Q_2)) % 172.27/172.36 => hBOOL(hAPP(V_Q_2,V_x_2)) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_predicate1D,axiom, % 172.27/172.36 ! [V_x_2,V_Q_2,V_P_2,T_a] : % 172.27/172.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_P_2),V_Q_2)) % 172.27/172.36 => ( hBOOL(hAPP(V_P_2,V_x_2)) % 172.27/172.36 => hBOOL(hAPP(V_Q_2,V_x_2)) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_subset__refl,axiom, % 172.27/172.36 ! [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)) ). % 172.27/172.36 % 172.27/172.36 fof(fact_le__fun__def,axiom, % 172.27/172.36 ! [V_g_2,V_f_2,T_a,T_b] : % 172.27/172.36 ( class_Orderings_Oord(T_b) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_f_2),V_g_2)) % 172.27/172.36 <=> ! [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))) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_linorder__linear,axiom, % 172.27/172.36 ! [V_y,V_x,T_a] : % 172.27/172.36 ( class_Orderings_Olinorder(T_a) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 172.27/172.36 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_set__eq__subset,axiom, % 172.27/172.36 ! [T_a,V_B_2,V_A_2] : % 172.27/172.36 ( V_A_2 = V_B_2 % 172.27/172.36 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 172.27/172.36 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_order__eq__iff,axiom, % 172.27/172.36 ! [V_y_2,V_x_2,T_a] : % 172.27/172.36 ( class_Orderings_Oorder(T_a) % 172.27/172.36 => ( V_x_2 = V_y_2 % 172.27/172.36 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 172.27/172.36 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) ) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_equalityD1,axiom, % 172.27/172.36 ! [T_a,V_B_2,V_A_2] : % 172.27/172.36 ( V_A_2 = V_B_2 % 172.27/172.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_equalityD2,axiom, % 172.27/172.36 ! [T_a,V_B_2,V_A_2] : % 172.27/172.36 ( V_A_2 = V_B_2 % 172.27/172.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_order__eq__refl,axiom, % 172.27/172.36 ! [V_y,V_x,T_a] : % 172.27/172.36 ( class_Orderings_Opreorder(T_a) % 172.27/172.36 => ( V_x = V_y % 172.27/172.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_le__funD,axiom, % 172.27/172.36 ! [V_x_2,V_g_2,V_f_2,T_a,T_b] : % 172.27/172.36 ( class_Orderings_Oord(T_b) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_f_2),V_g_2)) % 172.27/172.36 => 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))) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_order__antisym__conv,axiom, % 172.27/172.36 ! [V_x_2,V_y_2,T_a] : % 172.27/172.36 ( class_Orderings_Oorder(T_a) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 172.27/172.36 <=> V_x_2 = V_y_2 ) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_ord__eq__le__trans,axiom, % 172.27/172.36 ! [V_c,V_b,V_a,T_a] : % 172.27/172.36 ( class_Orderings_Oord(T_a) % 172.27/172.36 => ( V_a = V_b % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c)) % 172.27/172.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) ) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_xt1_I3_J,axiom, % 172.27/172.36 ! [V_c,V_b,V_a,T_a] : % 172.27/172.36 ( class_Orderings_Oorder(T_a) % 172.27/172.36 => ( V_a = V_b % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_b)) % 172.27/172.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_a)) ) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_subset__trans,axiom, % 172.27/172.36 ! [V_C_2,V_B_2,V_A_2,T_a] : % 172.27/172.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) % 172.27/172.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_ord__le__eq__trans,axiom, % 172.27/172.36 ! [V_c,V_b,V_a,T_a] : % 172.27/172.36 ( class_Orderings_Oord(T_a) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 172.27/172.36 => ( V_b = V_c % 172.27/172.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) ) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_xt1_I4_J,axiom, % 172.27/172.36 ! [V_c,V_a,V_b,T_a] : % 172.27/172.36 ( class_Orderings_Oorder(T_a) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 172.27/172.36 => ( V_b = V_c % 172.27/172.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_a)) ) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_order__antisym,axiom, % 172.27/172.36 ! [V_y,V_x,T_a] : % 172.27/172.36 ( class_Orderings_Oorder(T_a) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 172.27/172.36 => V_x = V_y ) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_order__trans,axiom, % 172.27/172.36 ! [V_z,V_y,V_x,T_a] : % 172.27/172.36 ( class_Orderings_Opreorder(T_a) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_z)) % 172.27/172.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z)) ) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_xt1_I5_J,axiom, % 172.27/172.36 ! [V_x,V_y,T_a] : % 172.27/172.36 ( class_Orderings_Oorder(T_a) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 172.27/172.36 => V_x = V_y ) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_xt1_I6_J,axiom, % 172.27/172.36 ! [V_z,V_x,V_y,T_a] : % 172.27/172.36 ( class_Orderings_Oorder(T_a) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_y)) % 172.27/172.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x)) ) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_equalityE,axiom, % 172.27/172.36 ! [T_a,V_B_2,V_A_2] : % 172.27/172.36 ( V_A_2 = V_B_2 % 172.27/172.36 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 172.27/172.36 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_le__funE,axiom, % 172.27/172.36 ! [V_x_2,V_g_2,V_f_2,T_a,T_b] : % 172.27/172.36 ( class_Orderings_Oord(T_b) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_f_2),V_g_2)) % 172.27/172.36 => 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))) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_linorder__le__cases,axiom, % 172.27/172.36 ! [V_y,V_x,T_a] : % 172.27/172.36 ( class_Orderings_Olinorder(T_a) % 172.27/172.36 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 172.27/172.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_card__seteq,axiom, % 172.27/172.36 ! [V_A_2,V_B_2,T_a] : % 172.27/172.36 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 172.27/172.36 => ( 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))) % 172.27/172.36 => V_A_2 = V_B_2 ) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_card__mono,axiom, % 172.27/172.36 ! [V_A_2,V_B_2,T_a] : % 172.27/172.36 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 172.27/172.36 => 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))) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_linorder__not__less,axiom, % 172.27/172.36 ! [V_y_2,V_x_2,T_a] : % 172.27/172.36 ( class_Orderings_Olinorder(T_a) % 172.27/172.36 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 172.27/172.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_linorder__not__le,axiom, % 172.27/172.36 ! [V_y_2,V_x_2,T_a] : % 172.27/172.36 ( class_Orderings_Olinorder(T_a) % 172.27/172.36 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 172.27/172.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_x_2)) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_linorder__le__less__linear,axiom, % 172.27/172.36 ! [V_y,V_x,T_a] : % 172.27/172.36 ( class_Orderings_Olinorder(T_a) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 172.27/172.36 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_order__less__le,axiom, % 172.27/172.36 ! [V_y_2,V_x_2,T_a] : % 172.27/172.36 ( class_Orderings_Oorder(T_a) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 172.27/172.36 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 172.27/172.36 & V_x_2 != V_y_2 ) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_less__le__not__le,axiom, % 172.27/172.36 ! [V_y_2,V_x_2,T_a] : % 172.27/172.36 ( class_Orderings_Opreorder(T_a) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 172.27/172.36 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 172.27/172.36 & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) ) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_order__le__less,axiom, % 172.27/172.36 ! [V_y_2,V_x_2,T_a] : % 172.27/172.36 ( class_Orderings_Oorder(T_a) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 172.27/172.36 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 172.27/172.36 | V_x_2 = V_y_2 ) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_leI,axiom, % 172.27/172.36 ! [V_y,V_x,T_a] : % 172.27/172.36 ( class_Orderings_Olinorder(T_a) % 172.27/172.36 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 172.27/172.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_not__leE,axiom, % 172.27/172.36 ! [V_x,V_y,T_a] : % 172.27/172.36 ( class_Orderings_Olinorder(T_a) % 172.27/172.36 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 172.27/172.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_linorder__antisym__conv1,axiom, % 172.27/172.36 ! [V_y_2,V_x_2,T_a] : % 172.27/172.36 ( class_Orderings_Olinorder(T_a) % 172.27/172.36 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 172.27/172.36 <=> V_x_2 = V_y_2 ) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_order__neq__le__trans,axiom, % 172.27/172.36 ! [V_b,V_a,T_a] : % 172.27/172.36 ( class_Orderings_Oorder(T_a) % 172.27/172.36 => ( V_a != V_b % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 172.27/172.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_xt1_I12_J,axiom, % 172.27/172.36 ! [V_b,V_a,T_a] : % 172.27/172.36 ( class_Orderings_Oorder(T_a) % 172.27/172.36 => ( V_a != V_b % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 172.27/172.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_leD,axiom, % 172.27/172.36 ! [V_x,V_y,T_a] : % 172.27/172.36 ( class_Orderings_Olinorder(T_a) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 172.27/172.36 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_order__less__imp__le,axiom, % 172.27/172.36 ! [V_y,V_x,T_a] : % 172.27/172.36 ( class_Orderings_Opreorder(T_a) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 172.27/172.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_linorder__antisym__conv2,axiom, % 172.27/172.36 ! [V_y_2,V_x_2,T_a] : % 172.27/172.36 ( class_Orderings_Olinorder(T_a) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 172.27/172.36 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_y_2)) % 172.27/172.36 <=> V_x_2 = V_y_2 ) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_order__le__imp__less__or__eq,axiom, % 172.27/172.36 ! [V_y,V_x,T_a] : % 172.27/172.36 ( class_Orderings_Oorder(T_a) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 172.27/172.36 | V_x = V_y ) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_order__le__neq__trans,axiom, % 172.27/172.36 ! [V_b,V_a,T_a] : % 172.27/172.36 ( class_Orderings_Oorder(T_a) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 172.27/172.36 => ( V_a != V_b % 172.27/172.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_xt1_I11_J,axiom, % 172.27/172.36 ! [V_a,V_b,T_a] : % 172.27/172.36 ( class_Orderings_Oorder(T_a) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 172.27/172.36 => ( V_a != V_b % 172.27/172.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) ) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_order__less__le__trans,axiom, % 172.27/172.36 ! [V_z,V_y,V_x,T_a] : % 172.27/172.36 ( class_Orderings_Opreorder(T_a) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_z)) % 172.27/172.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_xt1_I7_J,axiom, % 172.27/172.36 ! [V_z,V_x,V_y,T_a] : % 172.27/172.36 ( class_Orderings_Oorder(T_a) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_x)) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_y)) % 172.27/172.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_order__le__less__trans,axiom, % 172.27/172.36 ! [V_z,V_y,V_x,T_a] : % 172.27/172.36 ( class_Orderings_Opreorder(T_a) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_z)) % 172.27/172.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_z)) ) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_xt1_I8_J,axiom, % 172.27/172.36 ! [V_z,V_x,V_y,T_a] : % 172.27/172.36 ( class_Orderings_Oorder(T_a) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_y)) % 172.27/172.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z),V_x)) ) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_in__mono,axiom, % 172.27/172.36 ! [V_x_2,V_B_2,V_A_2,T_a] : % 172.27/172.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 172.27/172.36 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_set__rev__mp,axiom, % 172.27/172.36 ! [V_B_2,V_A_2,V_x_2,T_a] : % 172.27/172.36 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 172.27/172.36 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_set__mp,axiom, % 172.27/172.36 ! [V_x_2,V_B_2,V_A_2,T_a] : % 172.27/172.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 172.27/172.36 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_add__le__imp__le__left,axiom, % 172.27/172.36 ! [V_b,V_a,V_c,T_a] : % 172.27/172.36 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 172.27/172.36 => ( 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))) % 172.27/172.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_add__le__imp__le__right,axiom, % 172.27/172.36 ! [V_b,V_c,V_a,T_a] : % 172.27/172.36 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 172.27/172.36 => ( 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))) % 172.27/172.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_add__mono,axiom, % 172.27/172.36 ! [V_d,V_c,V_b,V_a,T_a] : % 172.27/172.36 ( class_Groups_Oordered__ab__semigroup__add(T_a) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d)) % 172.27/172.36 => 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))) ) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_add__left__mono,axiom, % 172.27/172.36 ! [V_c,V_b,V_a,T_a] : % 172.27/172.36 ( class_Groups_Oordered__ab__semigroup__add(T_a) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 172.27/172.36 => 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))) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_add__right__mono,axiom, % 172.27/172.36 ! [V_c,V_b,V_a,T_a] : % 172.27/172.36 ( class_Groups_Oordered__ab__semigroup__add(T_a) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 172.27/172.36 => 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))) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_add__le__cancel__left,axiom, % 172.27/172.36 ! [V_b_2,V_a_2,V_ca_2,T_a] : % 172.27/172.36 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_ca_2),V_b_2))) % 172.27/172.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_add__le__cancel__right,axiom, % 172.27/172.36 ! [V_b_2,V_ca_2,V_a_2,T_a] : % 172.27/172.36 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_ca_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_ca_2))) % 172.27/172.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_bot__least,axiom, % 172.27/172.36 ! [V_x,T_a] : % 172.27/172.36 ( class_Orderings_Obot(T_a) % 172.27/172.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Orderings_Obot__class_Obot(T_a)),V_x)) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_diff__eq__diff__less__eq,axiom, % 172.27/172.36 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 172.27/172.36 ( class_Groups_Oordered__ab__group__add(T_a) % 172.27/172.36 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_ca_2),V_d_2) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) % 172.27/172.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_ca_2),V_d_2)) ) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_subset__empty,axiom, % 172.27/172.36 ! [V_A_2,T_a] : % 172.27/172.36 ( 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)))) % 172.27/172.36 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_le__supE,axiom, % 172.27/172.36 ! [V_x,V_b,V_a,T_a] : % 172.27/172.36 ( class_Lattices_Osemilattice__sup(T_a) % 172.27/172.36 => ( 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)) % 172.27/172.36 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 172.27/172.36 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) ) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_sup__mono,axiom, % 172.27/172.36 ! [V_d,V_b,V_c,V_a,T_a] : % 172.27/172.36 ( class_Lattices_Osemilattice__sup(T_a) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d)) % 172.27/172.36 => 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))) ) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_sup__least,axiom, % 172.27/172.36 ! [V_z,V_x,V_y,T_a] : % 172.27/172.36 ( class_Lattices_Osemilattice__sup(T_a) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x)) % 172.27/172.36 => 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)) ) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_le__supI,axiom, % 172.27/172.36 ! [V_b,V_x,V_a,T_a] : % 172.27/172.36 ( class_Lattices_Osemilattice__sup(T_a) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) % 172.27/172.36 => 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)) ) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_sup__absorb1,axiom, % 172.27/172.36 ! [V_x,V_y,T_a] : % 172.27/172.36 ( class_Lattices_Osemilattice__sup(T_a) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 172.27/172.36 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = V_x ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_sup__absorb2,axiom, % 172.27/172.36 ! [V_y,V_x,T_a] : % 172.27/172.36 ( class_Lattices_Osemilattice__sup(T_a) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 172.27/172.36 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = V_y ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_le__supI2,axiom, % 172.27/172.36 ! [V_a,V_b,V_x,T_a] : % 172.27/172.36 ( class_Lattices_Osemilattice__sup(T_a) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) % 172.27/172.36 => 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))) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_le__supI1,axiom, % 172.27/172.36 ! [V_b,V_a,V_x,T_a] : % 172.27/172.36 ( class_Lattices_Osemilattice__sup(T_a) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 172.27/172.36 => 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))) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_le__sup__iff,axiom, % 172.27/172.36 ! [V_z_2,V_y_2,V_x_2,T_a] : % 172.27/172.36 ( class_Lattices_Osemilattice__sup(T_a) % 172.27/172.36 => ( 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)) % 172.27/172.36 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_z_2)) % 172.27/172.36 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_z_2)) ) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_le__iff__sup,axiom, % 172.27/172.36 ! [V_y_2,V_x_2,T_a] : % 172.27/172.36 ( class_Lattices_Osemilattice__sup(T_a) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 172.27/172.36 <=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x_2),V_y_2) = V_y_2 ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_sup__ge2,axiom, % 172.27/172.36 ! [V_x,V_y,T_a] : % 172.27/172.36 ( class_Lattices_Osemilattice__sup(T_a) % 172.27/172.36 => 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))) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_inf__sup__ord_I4_J,axiom, % 172.27/172.36 ! [V_x,V_y,T_a] : % 172.27/172.36 ( class_Lattices_Olattice(T_a) % 172.27/172.36 => 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))) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_sup__ge1,axiom, % 172.27/172.36 ! [V_y,V_x,T_a] : % 172.27/172.36 ( class_Lattices_Osemilattice__sup(T_a) % 172.27/172.36 => 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))) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_inf__sup__ord_I3_J,axiom, % 172.27/172.36 ! [V_y,V_x,T_a] : % 172.27/172.36 ( class_Lattices_Olattice(T_a) % 172.27/172.36 => 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))) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_finite__subset,axiom, % 172.27/172.36 ! [V_B_2,V_A_2,T_a] : % 172.27/172.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 172.27/172.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 172.27/172.36 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_rev__finite__subset,axiom, % 172.27/172.36 ! [V_A_2,V_B_2,T_a] : % 172.27/172.36 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 172.27/172.36 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_inf__sup__ord_I1_J,axiom, % 172.27/172.36 ! [V_y,V_x,T_a] : % 172.27/172.36 ( class_Lattices_Olattice(T_a) % 172.27/172.36 => 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)) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_inf__le1,axiom, % 172.27/172.36 ! [V_y,V_x,T_a] : % 172.27/172.36 ( class_Lattices_Osemilattice__inf(T_a) % 172.27/172.36 => 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)) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_inf__sup__ord_I2_J,axiom, % 172.27/172.36 ! [V_y,V_x,T_a] : % 172.27/172.36 ( class_Lattices_Olattice(T_a) % 172.27/172.36 => 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)) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_inf__le2,axiom, % 172.27/172.36 ! [V_y,V_x,T_a] : % 172.27/172.36 ( class_Lattices_Osemilattice__inf(T_a) % 172.27/172.36 => 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)) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_le__iff__inf,axiom, % 172.27/172.36 ! [V_y_2,V_x_2,T_a] : % 172.27/172.36 ( class_Lattices_Osemilattice__inf(T_a) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 172.27/172.36 <=> hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x_2),V_y_2) = V_x_2 ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_le__inf__iff,axiom, % 172.27/172.36 ! [V_z_2,V_y_2,V_x_2,T_a] : % 172.27/172.36 ( class_Lattices_Osemilattice__inf(T_a) % 172.27/172.36 => ( 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))) % 172.27/172.36 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 172.27/172.36 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_z_2)) ) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_le__infI1,axiom, % 172.27/172.36 ! [V_b,V_x,V_a,T_a] : % 172.27/172.36 ( class_Lattices_Osemilattice__inf(T_a) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 172.27/172.36 => 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)) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_le__infI2,axiom, % 172.27/172.36 ! [V_a,V_x,V_b,T_a] : % 172.27/172.36 ( class_Lattices_Osemilattice__inf(T_a) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) % 172.27/172.36 => 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)) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_inf__absorb1,axiom, % 172.27/172.36 ! [V_y,V_x,T_a] : % 172.27/172.36 ( class_Lattices_Osemilattice__inf(T_a) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 172.27/172.36 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = V_x ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_inf__absorb2,axiom, % 172.27/172.36 ! [V_x,V_y,T_a] : % 172.27/172.36 ( class_Lattices_Osemilattice__inf(T_a) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 172.27/172.36 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = V_y ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_le__infI,axiom, % 172.27/172.36 ! [V_b,V_a,V_x,T_a] : % 172.27/172.36 ( class_Lattices_Osemilattice__inf(T_a) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) % 172.27/172.36 => 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))) ) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_inf__greatest,axiom, % 172.27/172.36 ! [V_z,V_y,V_x,T_a] : % 172.27/172.36 ( class_Lattices_Osemilattice__inf(T_a) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z)) % 172.27/172.36 => 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))) ) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_inf__mono,axiom, % 172.27/172.36 ! [V_d,V_b,V_c,V_a,T_a] : % 172.27/172.36 ( class_Lattices_Osemilattice__inf(T_a) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d)) % 172.27/172.36 => 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))) ) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_le__infE,axiom, % 172.27/172.36 ! [V_b,V_a,V_x,T_a] : % 172.27/172.36 ( class_Lattices_Osemilattice__inf(T_a) % 172.27/172.36 => ( 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))) % 172.27/172.36 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 172.27/172.36 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) ) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_subset__insertI,axiom, % 172.27/172.36 ! [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))) ). % 172.27/172.36 % 172.27/172.36 fof(fact_subset__insertI2,axiom, % 172.27/172.36 ! [V_b_2,V_B_2,V_A_2,T_a] : % 172.27/172.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 172.27/172.36 => 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))) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_insert__mono,axiom, % 172.27/172.36 ! [V_a_2,V_D_2,V_C_2,T_a] : % 172.27/172.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_D_2)) % 172.27/172.36 => 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))) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_Suc__leD,axiom, % 172.27/172.36 ! [V_n,V_m] : % 172.27/172.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) % 172.27/172.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_le__SucE,axiom, % 172.27/172.36 ! [V_n,V_m] : % 172.27/172.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) % 172.27/172.36 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 172.27/172.36 => V_m = hAPP(c_Nat_OSuc,V_n) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_le__SucI,axiom, % 172.27/172.36 ! [V_n,V_m] : % 172.27/172.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 172.27/172.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_Suc__le__mono,axiom, % 172.27/172.36 ! [V_m_2,V_n_2] : % 172.27/172.36 ( 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))) % 172.27/172.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_le__Suc__eq,axiom, % 172.27/172.36 ! [V_n_2,V_m_2] : % 172.27/172.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) % 172.27/172.36 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 172.27/172.36 | V_m_2 = hAPP(c_Nat_OSuc,V_n_2) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_not__less__eq__eq,axiom, % 172.27/172.36 ! [V_n_2,V_m_2] : % 172.27/172.36 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 172.27/172.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_Suc__n__not__le__n,axiom, % 172.27/172.36 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n)),V_n)) ). % 172.27/172.36 % 172.27/172.36 fof(fact_termination__basic__simps_I5_J,axiom, % 172.27/172.36 ! [V_y,V_x] : % 172.27/172.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x),V_y)) % 172.27/172.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_y)) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_less__or__eq__imp__le,axiom, % 172.27/172.36 ! [V_n,V_m] : % 172.27/172.36 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 172.27/172.36 | V_m = V_n ) % 172.27/172.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_le__neq__implies__less,axiom, % 172.27/172.36 ! [V_n,V_m] : % 172.27/172.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 172.27/172.36 => ( V_m != V_n % 172.27/172.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_less__imp__le__nat,axiom, % 172.27/172.36 ! [V_n,V_m] : % 172.27/172.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 172.27/172.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_le__eq__less__or__eq,axiom, % 172.27/172.36 ! [V_n_2,V_m_2] : % 172.27/172.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 172.27/172.36 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 172.27/172.36 | V_m_2 = V_n_2 ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_nat__less__le,axiom, % 172.27/172.36 ! [V_n_2,V_m_2] : % 172.27/172.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 172.27/172.36 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 172.27/172.36 & V_m_2 != V_n_2 ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_subset__image__iff,axiom, % 172.27/172.36 ! [V_A_2,V_f_2,T_b,V_B_2,T_a] : % 172.27/172.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2))) % 172.27/172.36 <=> ? [B_AA] : % 172.27/172.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),B_AA),V_A_2)) % 172.27/172.36 & V_B_2 = hAPP(c_Set_Oimage(T_b,T_a,V_f_2),B_AA) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_image__mono,axiom, % 172.27/172.36 ! [V_f_2,T_b,V_B_2,V_A_2,T_a] : % 172.27/172.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 172.27/172.36 => 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))) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_termination__basic__simps_I4_J,axiom, % 172.27/172.36 ! [V_y,V_z,V_x] : % 172.27/172.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_z)) % 172.27/172.36 => 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))) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_termination__basic__simps_I3_J,axiom, % 172.27/172.36 ! [V_z,V_y,V_x] : % 172.27/172.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x),V_y)) % 172.27/172.36 => 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))) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_add__leE,axiom, % 172.27/172.36 ! [V_n,V_k,V_m] : % 172.27/172.36 ( 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)) % 172.27/172.36 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 172.27/172.36 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_add__leD1,axiom, % 172.27/172.36 ! [V_n,V_k,V_m] : % 172.27/172.36 ( 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)) % 172.27/172.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_add__leD2,axiom, % 172.27/172.36 ! [V_n,V_k,V_m] : % 172.27/172.36 ( 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)) % 172.27/172.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_add__le__mono,axiom, % 172.27/172.36 ! [V_l,V_k,V_j,V_i] : % 172.27/172.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_l)) % 172.27/172.36 => 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))) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_add__le__mono1,axiom, % 172.27/172.36 ! [V_k,V_j,V_i] : % 172.27/172.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 172.27/172.36 => 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))) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_trans__le__add2,axiom, % 172.27/172.36 ! [V_m,V_j,V_i] : % 172.27/172.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 172.27/172.36 => 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))) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_trans__le__add1,axiom, % 172.27/172.36 ! [V_m,V_j,V_i] : % 172.27/172.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 172.27/172.36 => 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))) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_nat__add__left__cancel__le,axiom, % 172.27/172.36 ! [V_n_2,V_m_2,V_k_2] : % 172.27/172.36 ( 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))) % 172.27/172.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_le__iff__add,axiom, % 172.27/172.36 ! [V_n_2,V_m_2] : % 172.27/172.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 172.27/172.36 <=> ? [B_k] : V_n_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),B_k) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_le__add1,axiom, % 172.27/172.36 ! [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))) ). % 172.27/172.36 % 172.27/172.36 fof(fact_le__add2,axiom, % 172.27/172.36 ! [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))) ). % 172.27/172.36 % 172.27/172.36 fof(fact_Un__upper1,axiom, % 172.27/172.36 ! [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))) ). % 172.27/172.36 % 172.27/172.36 fof(fact_Un__upper2,axiom, % 172.27/172.36 ! [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))) ). % 172.27/172.36 % 172.27/172.36 fof(fact_subset__Un__eq,axiom, % 172.27/172.36 ! [V_B_2,V_A_2,T_a] : % 172.27/172.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 172.27/172.36 <=> hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_Un__absorb1,axiom, % 172.27/172.36 ! [V_B_2,V_A_2,T_a] : % 172.27/172.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 172.27/172.36 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_Un__absorb2,axiom, % 172.27/172.36 ! [V_A_2,V_B_2,T_a] : % 172.27/172.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 172.27/172.36 => hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_Un__least,axiom, % 172.27/172.36 ! [V_B_2,V_C_2,V_A_2,T_a] : % 172.27/172.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) % 172.27/172.36 => 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)) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_Un__mono,axiom, % 172.27/172.36 ! [V_D_2,V_B_2,V_C_2,V_A_2,T_a] : % 172.27/172.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_D_2)) % 172.27/172.36 => 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))) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_Int__lower1,axiom, % 172.27/172.36 ! [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)) ). % 172.27/172.36 % 172.27/172.36 fof(fact_Int__lower2,axiom, % 172.27/172.36 ! [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)) ). % 172.27/172.36 % 172.27/172.36 fof(fact_Int__absorb2,axiom, % 172.27/172.36 ! [V_B_2,V_A_2,T_a] : % 172.27/172.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 172.27/172.36 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = V_A_2 ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_Int__absorb1,axiom, % 172.27/172.36 ! [V_A_2,V_B_2,T_a] : % 172.27/172.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 172.27/172.36 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = V_B_2 ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_Int__greatest,axiom, % 172.27/172.36 ! [V_B_2,V_A_2,V_C_2,T_a] : % 172.27/172.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_B_2)) % 172.27/172.36 => 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))) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_Int__mono,axiom, % 172.27/172.36 ! [V_D_2,V_B_2,V_C_2,V_A_2,T_a] : % 172.27/172.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_D_2)) % 172.27/172.36 => 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))) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_Diff__subset,axiom, % 172.27/172.36 ! [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)) ). % 172.27/172.36 % 172.27/172.36 fof(fact_Diff__mono,axiom, % 172.27/172.36 ! [V_B_2,V_D_2,V_C_2,V_A_2,T_a] : % 172.27/172.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_D_2),V_B_2)) % 172.27/172.36 => 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))) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_double__diff,axiom, % 172.27/172.36 ! [V_C_2,V_B_2,V_A_2,T_a] : % 172.27/172.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) % 172.27/172.36 => 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 ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_le__diff__iff,axiom, % 172.27/172.36 ! [V_n_2,V_m_2,V_k_2] : % 172.27/172.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2)) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2)) % 172.27/172.36 => ( 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))) % 172.27/172.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_Nat_Odiff__diff__eq,axiom, % 172.27/172.36 ! [V_n,V_m,V_k] : % 172.27/172.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_m)) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) % 172.27/172.36 => 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) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_eq__diff__iff,axiom, % 172.27/172.36 ! [V_n_2,V_m_2,V_k_2] : % 172.27/172.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2)) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2)) % 172.27/172.36 => ( 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) % 172.27/172.36 <=> V_m_2 = V_n_2 ) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_diff__diff__cancel,axiom, % 172.27/172.36 ! [V_n,V_i] : % 172.27/172.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_n)) % 172.27/172.36 => 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 ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_diff__le__mono,axiom, % 172.27/172.36 ! [V_l,V_n,V_m] : % 172.27/172.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 172.27/172.36 => 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))) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_diff__le__mono2,axiom, % 172.27/172.36 ! [V_l,V_n,V_m] : % 172.27/172.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 172.27/172.36 => 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))) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_diff__le__self,axiom, % 172.27/172.36 ! [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)) ). % 172.27/172.36 % 172.27/172.36 fof(fact_mult__le__mono,axiom, % 172.27/172.36 ! [V_l,V_k,V_j,V_i] : % 172.27/172.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_l)) % 172.27/172.36 => 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))) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_mult__le__mono2,axiom, % 172.27/172.36 ! [V_k,V_j,V_i] : % 172.27/172.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 172.27/172.36 => 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))) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_mult__le__mono1,axiom, % 172.27/172.36 ! [V_k,V_j,V_i] : % 172.27/172.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 172.27/172.36 => 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))) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_le__cube,axiom, % 172.27/172.36 ! [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)))) ). % 172.27/172.36 % 172.27/172.36 fof(fact_le__square,axiom, % 172.27/172.36 ! [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))) ). % 172.27/172.36 % 172.27/172.36 fof(fact_less__fun__def,axiom, % 172.27/172.36 ! [V_g_2,V_f_2,T_a,T_b] : % 172.27/172.36 ( class_Orderings_Oord(T_b) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b)),V_f_2),V_g_2)) % 172.27/172.36 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_f_2),V_g_2)) % 172.27/172.36 & ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_g_2),V_f_2)) ) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_evaln__nonstrict,axiom, % 172.27/172.36 ! [V_m,V_t,V_n,V_s,V_c] : % 172.27/172.36 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c),V_s),V_n),V_t)) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 172.27/172.36 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Natural_Oevaln,V_c),V_s),V_m),V_t)) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_setprod__timesf,axiom, % 172.27/172.36 ! [V_A_2,V_g_2,V_f_2,T_b,T_a] : % 172.27/172.36 ( class_Groups_Ocomm__monoid__mult(T_a) % 172.27/172.36 => 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)) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_asm,axiom, % 172.27/172.36 ! [V_Ga_2,V_ts_2,T_a] : % 172.27/172.36 ( 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)) % 172.27/172.36 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,V_ts_2) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_weaken,axiom, % 172.27/172.36 ! [V_ts_2,V_ts_H_2,V_Ga_2,T_a] : % 172.27/172.36 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,V_ts_H_2) % 172.27/172.36 => ( 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)) % 172.27/172.36 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,V_ts_2) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_thin,axiom, % 172.27/172.36 ! [V_Ga_2,V_ts_2,V_G_H_2,T_a] : % 172.27/172.36 ( c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_G_H_2,V_ts_2) % 172.27/172.36 => ( 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)) % 172.27/172.36 => c_Hoare__Mirabelle_Ohoare__derivs(T_a,V_Ga_2,V_ts_2) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_setprod__1,axiom, % 172.27/172.36 ! [V_A_2,T_b,T_a] : % 172.27/172.36 ( class_Groups_Ocomm__monoid__mult(T_a) % 172.27/172.36 => 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) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_psubset__eq,axiom, % 172.27/172.36 ! [V_B_2,V_A_2,T_a] : % 172.27/172.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 172.27/172.36 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 172.27/172.36 & V_A_2 != V_B_2 ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_subset__iff__psubset__eq,axiom, % 172.27/172.36 ! [V_B_2,V_A_2,T_a] : % 172.27/172.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 172.27/172.36 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 172.27/172.36 | V_A_2 = V_B_2 ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_psubset__imp__subset,axiom, % 172.27/172.36 ! [V_B_2,V_A_2,T_a] : % 172.27/172.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 172.27/172.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_psubset__subset__trans,axiom, % 172.27/172.36 ! [V_C_2,V_B_2,V_A_2,T_a] : % 172.27/172.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) % 172.27/172.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_subset__psubset__trans,axiom, % 172.27/172.36 ! [V_C_2,V_B_2,V_A_2,T_a] : % 172.27/172.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) % 172.27/172.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_pred__subset__eq,axiom, % 172.27/172.36 ! [V_S_2,V_R_2,T_a] : % 172.27/172.36 ( 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))) % 172.27/172.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_R_2),V_S_2)) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_setprod_Oempty,axiom, % 172.27/172.36 ! [V_g_2,T_b,T_a] : % 172.27/172.36 ( class_Groups_Ocomm__monoid__mult(T_a) % 172.27/172.36 => 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) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_setprod__empty,axiom, % 172.27/172.36 ! [V_f_2,T_b,T_a] : % 172.27/172.36 ( class_Groups_Ocomm__monoid__mult(T_a) % 172.27/172.36 => 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) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_setprod__infinite,axiom, % 172.27/172.36 ! [V_f_2,V_A_2,T_a,T_b] : % 172.27/172.36 ( class_Groups_Ocomm__monoid__mult(T_b) % 172.27/172.36 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.36 => 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) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_setprod_Oinfinite,axiom, % 172.27/172.36 ! [V_g_2,V_A_2,T_a,T_b] : % 172.27/172.36 ( class_Groups_Ocomm__monoid__mult(T_b) % 172.27/172.36 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.36 => 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) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_setprod__eq__1__iff,axiom, % 172.27/172.36 ! [V_f_2,V_F_2,T_a] : % 172.27/172.36 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) % 172.27/172.36 => ( 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) % 172.27/172.36 <=> ! [B_x] : % 172.27/172.36 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_F_2)) % 172.27/172.36 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_finite__PlusD_I2_J,axiom, % 172.27/172.36 ! [V_B_2,V_A_2,T_b,T_a] : % 172.27/172.36 ( 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))) % 172.27/172.36 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_finite__PlusD_I1_J,axiom, % 172.27/172.36 ! [V_B_2,V_A_2,T_b,T_a] : % 172.27/172.36 ( 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))) % 172.27/172.36 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_finite__Plus,axiom, % 172.27/172.36 ! [V_B_2,T_b,V_A_2,T_a] : % 172.27/172.36 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 172.27/172.36 => 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))) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_finite__Plus__iff,axiom, % 172.27/172.36 ! [V_B_2,V_A_2,T_b,T_a] : % 172.27/172.36 ( 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))) % 172.27/172.36 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.36 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_add__less__le__mono,axiom, % 172.27/172.36 ! [V_d,V_c,V_b,V_a,T_a] : % 172.27/172.36 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d)) % 172.27/172.36 => 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))) ) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_add__le__less__mono,axiom, % 172.27/172.36 ! [V_d,V_c,V_b,V_a,T_a] : % 172.27/172.36 ( class_Groups_Oordered__cancel__ab__semigroup__add(T_a) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) % 172.27/172.36 => 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))) ) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_subset__insert,axiom, % 172.27/172.36 ! [V_B_2,V_A_2,V_x_2,T_a] : % 172.27/172.36 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 172.27/172.36 => ( 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))) % 172.27/172.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_insert__subset,axiom, % 172.27/172.36 ! [V_B_2,V_A_2,V_x_2,T_a] : % 172.27/172.36 ( 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)) % 172.27/172.36 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_B_2)) % 172.27/172.36 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_setprod_Odistrib,axiom, % 172.27/172.36 ! [V_h_2,V_g_2,V_A_2,T_a,T_b] : % 172.27/172.36 ( class_Groups_Ocomm__monoid__mult(T_b) % 172.27/172.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.36 => 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)) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_distrib__sup__le,axiom, % 172.27/172.36 ! [V_z,V_y,V_x,T_a] : % 172.27/172.36 ( class_Lattices_Olattice(T_a) % 172.27/172.36 => 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)))) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_distrib__inf__le,axiom, % 172.27/172.36 ! [V_z,V_y,V_x,T_a] : % 172.27/172.36 ( class_Lattices_Olattice(T_a) % 172.27/172.36 => 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)))) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_subset__singletonD,axiom, % 172.27/172.36 ! [V_x_2,V_A_2,T_a] : % 172.27/172.36 ( 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))))) % 172.27/172.36 => ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.27/172.36 | 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))) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_finite__surj,axiom, % 172.27/172.36 ! [V_f_2,V_B_2,T_b,V_A_2,T_a] : % 172.27/172.36 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2))) % 172.27/172.36 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_less__eq__Suc__le,axiom, % 172.27/172.36 ! [V_m_2,V_n_2] : % 172.27/172.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) % 172.27/172.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_less__Suc__eq__le,axiom, % 172.27/172.36 ! [V_n_2,V_m_2] : % 172.27/172.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) % 172.27/172.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_Suc__le__eq,axiom, % 172.27/172.36 ! [V_n_2,V_m_2] : % 172.27/172.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_n_2)) % 172.27/172.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_le__imp__less__Suc,axiom, % 172.27/172.36 ! [V_n,V_m] : % 172.27/172.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 172.27/172.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),hAPP(c_Nat_OSuc,V_n))) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_Suc__leI,axiom, % 172.27/172.36 ! [V_n,V_m] : % 172.27/172.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 172.27/172.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_le__less__Suc__eq,axiom, % 172.27/172.36 ! [V_n_2,V_m_2] : % 172.27/172.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),hAPP(c_Nat_OSuc,V_m_2))) % 172.27/172.36 <=> V_n_2 = V_m_2 ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_Suc__le__lessD,axiom, % 172.27/172.36 ! [V_n,V_m] : % 172.27/172.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m)),V_n)) % 172.27/172.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_image__Int__subset,axiom, % 172.27/172.36 ! [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)))) ). % 172.27/172.36 % 172.27/172.36 fof(fact_Un__Int__assoc__eq,axiom, % 172.27/172.36 ! [V_C_2,V_B_2,V_A_2,T_a] : % 172.27/172.36 ( 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)) % 172.27/172.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_C_2),V_A_2)) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_Suc__diff__le,axiom, % 172.27/172.36 ! [V_m,V_n] : % 172.27/172.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 172.27/172.36 => 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)) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_Suc__mult__le__cancel1,axiom, % 172.27/172.36 ! [V_n_2,V_m_2,V_k_2] : % 172.27/172.36 ( 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))) % 172.27/172.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_less__diff__iff,axiom, % 172.27/172.36 ! [V_n_2,V_m_2,V_k_2] : % 172.27/172.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_m_2)) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_n_2)) % 172.27/172.36 => ( 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))) % 172.27/172.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_diff__less__mono,axiom, % 172.27/172.36 ! [V_c,V_b,V_a] : % 172.27/172.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a),V_b)) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_c),V_a)) % 172.27/172.36 => 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))) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_image__diff__subset,axiom, % 172.27/172.36 ! [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)))) ). % 172.27/172.36 % 172.27/172.36 fof(fact_diff__diff__right,axiom, % 172.27/172.36 ! [V_i,V_j,V_k] : % 172.27/172.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 172.27/172.36 => 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) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_le__diff__conv,axiom, % 172.27/172.36 ! [V_i_2,V_k_2,V_j_2] : % 172.27/172.36 ( 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)) % 172.27/172.36 <=> 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))) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_le__add__diff,axiom, % 172.27/172.36 ! [V_m,V_n,V_k] : % 172.27/172.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_n)) % 172.27/172.36 => 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))) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_le__add__diff__inverse,axiom, % 172.27/172.36 ! [V_m,V_n] : % 172.27/172.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 172.27/172.36 => 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 ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_add__diff__assoc,axiom, % 172.27/172.36 ! [V_i,V_j,V_k] : % 172.27/172.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 172.27/172.36 => 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) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_le__diff__conv2,axiom, % 172.27/172.36 ! [V_i_2,V_j_2,V_k_2] : % 172.27/172.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),V_j_2)) % 172.27/172.36 => ( 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))) % 172.27/172.36 <=> 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)) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_le__add__diff__inverse2,axiom, % 172.27/172.36 ! [V_m,V_n] : % 172.27/172.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 172.27/172.36 => 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 ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_le__imp__diff__is__add,axiom, % 172.27/172.36 ! [V_k_2,V_j_2,V_i_2] : % 172.27/172.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) % 172.27/172.36 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_j_2),V_i_2) = V_k_2 % 172.27/172.36 <=> V_j_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_k_2),V_i_2) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_diff__add__assoc,axiom, % 172.27/172.36 ! [V_i,V_j,V_k] : % 172.27/172.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 172.27/172.36 => 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)) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_add__diff__assoc2,axiom, % 172.27/172.36 ! [V_i,V_j,V_k] : % 172.27/172.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 172.27/172.36 => 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) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_diff__add__assoc2,axiom, % 172.27/172.36 ! [V_i,V_j,V_k] : % 172.27/172.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 172.27/172.36 => 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) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_Diff__subset__conv,axiom, % 172.27/172.36 ! [V_C_2,V_B_2,V_A_2,T_a] : % 172.27/172.36 ( 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)) % 172.27/172.36 <=> 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))) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_Diff__partition,axiom, % 172.27/172.36 ! [V_B_2,V_A_2,T_a] : % 172.27/172.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 172.27/172.36 => 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 ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_less__eq__Suc__le__raw,axiom, % 172.27/172.36 ! [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)) ). % 172.27/172.36 % 172.27/172.36 fof(fact_folding__image__simple__idem_Osubset__idem,axiom, % 172.27/172.36 ! [V_B_2,V_A_2,V_F_2,V_g_2,V_z_2,V_f_2,T_b,T_a] : % 172.27/172.36 ( c_Finite__Set_Ofolding__image__simple__idem(T_a,T_b,V_f_2,V_z_2,V_g_2,V_F_2) % 172.27/172.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_B_2),V_A_2)) % 172.27/172.36 => 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) ) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_setprod__delta,axiom, % 172.27/172.36 ! [V_b_2,V_a_2,V_S_2,T_a,T_b] : % 172.27/172.36 ( class_Groups_Ocomm__monoid__mult(T_b) % 172.27/172.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 172.27/172.36 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) % 172.27/172.36 => 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) ) % 172.27/172.36 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) % 172.27/172.36 => 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) ) ) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_setprod__delta_H,axiom, % 172.27/172.36 ! [V_b_2,V_a_2,V_S_2,T_a,T_b] : % 172.27/172.36 ( class_Groups_Ocomm__monoid__mult(T_b) % 172.27/172.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 172.27/172.36 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) % 172.27/172.36 => 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) ) % 172.27/172.36 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) % 172.27/172.36 => 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) ) ) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_le__add__iff2,axiom, % 172.27/172.36 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_a] : % 172.27/172.36 ( class_Rings_Oordered__ring(T_a) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_ca_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2))) % 172.27/172.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_ca_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_b_2),V_a_2)),V_e_2)),V_d_2))) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_le__add__iff1,axiom, % 172.27/172.36 ! [V_d_2,V_b_2,V_ca_2,V_e_2,V_a_2,T_a] : % 172.27/172.36 ( class_Rings_Oordered__ring(T_a) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_e_2)),V_ca_2)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_e_2)),V_d_2))) % 172.27/172.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2)),V_e_2)),V_ca_2)),V_d_2)) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_card__insert__le,axiom, % 172.27/172.36 ! [V_x_2,V_A_2,T_a] : % 172.27/172.36 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.36 => 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)))) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_card__image__le,axiom, % 172.27/172.36 ! [V_f_2,T_b,V_A_2,T_a] : % 172.27/172.36 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.36 => 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))) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_diff__Suc__diff__eq1,axiom, % 172.27/172.36 ! [V_m,V_j,V_k] : % 172.27/172.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 172.27/172.36 => 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)) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_diff__Suc__diff__eq2,axiom, % 172.27/172.36 ! [V_m,V_j,V_k] : % 172.27/172.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k),V_j)) % 172.27/172.36 => 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)) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_setsum__diff__nat,axiom, % 172.27/172.36 ! [V_f_2,V_A_2,V_B_2,T_a] : % 172.27/172.36 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 172.27/172.36 => 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)) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_nat__eq__add__iff2,axiom, % 172.27/172.36 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] : % 172.27/172.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) % 172.27/172.36 => ( 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) % 172.27/172.36 <=> 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) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_nat__diff__add__eq2,axiom, % 172.27/172.36 ! [V_n,V_m,V_u,V_j,V_i] : % 172.27/172.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 172.27/172.36 => 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)) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_nat__le__add__iff2,axiom, % 172.27/172.36 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] : % 172.27/172.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) % 172.27/172.36 => ( 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))) % 172.27/172.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),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))) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_nat__eq__add__iff1,axiom, % 172.27/172.36 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] : % 172.27/172.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) % 172.27/172.36 => ( 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) % 172.27/172.36 <=> 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 ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_nat__diff__add__eq1,axiom, % 172.27/172.36 ! [V_n,V_m,V_u,V_i,V_j] : % 172.27/172.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_i)) % 172.27/172.36 => 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) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_nat__le__add__iff1,axiom, % 172.27/172.36 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] : % 172.27/172.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) % 172.27/172.36 => ( 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))) % 172.27/172.36 <=> 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)) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_setprod_Oinsert,axiom, % 172.27/172.36 ! [V_g_2,V_x_2,V_A_2,T_a,T_b] : % 172.27/172.36 ( class_Groups_Ocomm__monoid__mult(T_b) % 172.27/172.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.36 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 172.27/172.36 => 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)) ) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_setprod__insert,axiom, % 172.27/172.36 ! [V_f_2,V_a_2,V_A_2,T_a,T_b] : % 172.27/172.36 ( class_Groups_Ocomm__monoid__mult(T_b) % 172.27/172.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.36 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 172.27/172.36 => 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)) ) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_setprod_Ounion__inter,axiom, % 172.27/172.36 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] : % 172.27/172.36 ( class_Groups_Ocomm__monoid__mult(T_b) % 172.27/172.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 172.27/172.36 => 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)) ) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_setprod__Un__Int,axiom, % 172.27/172.36 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] : % 172.27/172.36 ( class_Groups_Ocomm__monoid__mult(T_b) % 172.27/172.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 172.27/172.36 => 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)) ) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_folding__one__idem_Osubset__idem,axiom, % 172.27/172.36 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_a] : % 172.27/172.36 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2) % 172.27/172.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.36 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 172.27/172.36 => 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) ) ) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_setprod_Oeq__fold,axiom, % 172.27/172.36 ! [V_g_2,V_A_2,T_a,T_b] : % 172.27/172.36 ( class_Groups_Ocomm__monoid__mult(T_b) % 172.27/172.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.36 => 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) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_setprod_OF__eq,axiom, % 172.27/172.36 ! [V_g_2,V_A_2,T_a,T_b] : % 172.27/172.36 ( class_Groups_Ocomm__monoid__mult(T_b) % 172.27/172.36 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.36 => 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) ) % 172.27/172.36 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.36 => 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) ) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_folding__idem_Osubset__comp__idem,axiom, % 172.27/172.36 ! [V_B_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 172.27/172.36 ( c_Finite__Set_Ofolding__idem(T_a,T_b,V_f_2,V_F_2) % 172.27/172.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 172.27/172.36 => 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) ) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_subset__insert__iff,axiom, % 172.27/172.36 ! [V_B_2,V_x_2,V_A_2,T_a] : % 172.27/172.36 ( 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))) % 172.27/172.36 <=> ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 172.27/172.36 => 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)) ) % 172.27/172.36 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 172.27/172.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_diff__single__insert,axiom, % 172.27/172.36 ! [V_B_2,V_x_2,V_A_2,T_a] : % 172.27/172.36 ( 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)) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 172.27/172.36 => 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))) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_setsum__diff,axiom, % 172.27/172.36 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] : % 172.27/172.36 ( class_Groups_Oab__group__add(T_b) % 172.27/172.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 172.27/172.36 => 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)) ) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_fold1__belowI,axiom, % 172.27/172.36 ! [V_a_2,V_A_2,T_a] : % 172.27/172.36 ( class_Lattices_Osemilattice__inf(T_a) % 172.27/172.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 172.27/172.36 => 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)) ) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_nat__less__add__iff1,axiom, % 172.27/172.36 ! [V_n_2,V_m_2,V_u_2,V_i_2,V_j_2] : % 172.27/172.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_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))) % 172.27/172.36 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),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)) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_nat__less__add__iff2,axiom, % 172.27/172.36 ! [V_n_2,V_m_2,V_u_2,V_j_2,V_i_2] : % 172.27/172.36 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_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))) % 172.27/172.36 <=> 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))) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_below__fold1__iff,axiom, % 172.27/172.36 ! [V_x_2,V_A_2,T_a] : % 172.27/172.36 ( class_Lattices_Osemilattice__inf(T_a) % 172.27/172.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.36 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.27/172.36 => ( 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))) % 172.27/172.36 <=> ! [B_x] : % 172.27/172.36 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 172.27/172.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),B_x)) ) ) ) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_card__Diff__subset,axiom, % 172.27/172.36 ! [V_A_2,V_B_2,T_a] : % 172.27/172.36 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 172.27/172.36 => 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)) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_diff__card__le__card__Diff,axiom, % 172.27/172.36 ! [V_A_2,V_B_2,T_a] : % 172.27/172.36 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 172.27/172.36 => 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)))) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_Sup__fin_Osubset__idem,axiom, % 172.27/172.36 ! [V_B_2,V_A_2,T_a] : % 172.27/172.36 ( class_Lattices_Olattice(T_a) % 172.27/172.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.36 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 172.27/172.36 => 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) ) ) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_Inf__fin_Osubset__idem,axiom, % 172.27/172.36 ! [V_B_2,V_A_2,T_a] : % 172.27/172.36 ( class_Lattices_Olattice(T_a) % 172.27/172.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.36 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 172.27/172.36 => 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) ) ) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_card__psubset,axiom, % 172.27/172.36 ! [V_A_2,V_B_2,T_a] : % 172.27/172.36 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 172.27/172.36 => ( 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))) % 172.27/172.36 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_setprod_Oinsert__remove,axiom, % 172.27/172.36 ! [V_x_2,V_g_2,V_A_2,T_a,T_b] : % 172.27/172.36 ( class_Groups_Ocomm__monoid__mult(T_b) % 172.27/172.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.36 => 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)))))) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_setprod__Un__disjoint,axiom, % 172.27/172.36 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] : % 172.27/172.36 ( class_Groups_Ocomm__monoid__mult(T_b) % 172.27/172.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 172.27/172.36 => ( 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)) % 172.27/172.36 => 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)) ) ) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_setprod_Ounion__disjoint,axiom, % 172.27/172.36 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] : % 172.27/172.36 ( class_Groups_Ocomm__monoid__mult(T_b) % 172.27/172.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 172.27/172.36 => ( 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)) % 172.27/172.36 => 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)) ) ) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_Inf__le__Sup,axiom, % 172.27/172.36 ! [V_A_2,T_a] : % 172.27/172.36 ( class_Lattices_Olattice(T_a) % 172.27/172.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.36 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.27/172.36 => 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))) ) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_flat__lub__def,axiom, % 172.27/172.36 ! [V_b_2,V_A_2,T_a] : % 172.27/172.36 ( ( 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))))) % 172.27/172.36 => c_Partial__Function_Oflat__lub(T_a,V_b_2,V_A_2) = V_b_2 ) % 172.27/172.36 & ( ~ 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))))) % 172.27/172.36 => 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)))))) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_Plus__eq__empty__conv,axiom, % 172.27/172.36 ! [V_B_2,V_A_2,T_b,T_a] : % 172.27/172.36 ( 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)) % 172.27/172.36 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.27/172.36 & V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_setprod__Un__one,axiom, % 172.27/172.36 ! [V_f_2,V_T_2,V_S_2,T_a,T_b] : % 172.27/172.36 ( class_Groups_Ocomm__monoid__mult(T_b) % 172.27/172.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 172.27/172.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2)) % 172.27/172.36 => ( ! [B_x] : % 172.27/172.36 ( 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))) % 172.27/172.36 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_b) ) % 172.27/172.36 => 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)) ) ) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_setprod_Ounion__inter__neutral,axiom, % 172.27/172.36 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] : % 172.27/172.36 ( class_Groups_Ocomm__monoid__mult(T_b) % 172.27/172.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 172.27/172.36 => ( ! [B_x] : % 172.27/172.36 ( 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))) % 172.27/172.36 => hAPP(V_g_2,B_x) = c_Groups_Oone__class_Oone(T_b) ) % 172.27/172.36 => 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)) ) ) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_setprod__gen__delta,axiom, % 172.27/172.36 ! [V_ca_2,V_b_2,V_a_2,V_S_2,T_a,T_b] : % 172.27/172.36 ( class_Groups_Ocomm__monoid__mult(T_b) % 172.27/172.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 172.27/172.36 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) % 172.27/172.36 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),hAPP(hAPP(c_COMBC(T_a,T_b,T_b),hAPP(hAPP(c_COMBS(T_a,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_a),c_If(T_b)),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),V_ca_2)),V_S_2) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_b),hAPP(V_b_2,V_a_2)),hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_ca_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),hAPP(c_Finite__Set_Ocard(T_a),V_S_2)),c_Groups_Oone__class_Oone(tc_Nat_Onat)))) ) % 172.27/172.36 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) % 172.27/172.36 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),hAPP(hAPP(c_COMBC(T_a,T_b,T_b),hAPP(hAPP(c_COMBS(T_a,T_b,tc_fun(T_b,T_b)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_b,tc_fun(T_b,T_b)),T_a),c_If(T_b)),hAPP(hAPP(c_COMBC(T_a,T_a,tc_HOL_Obool),c_fequal),V_a_2))),V_b_2)),V_ca_2)),V_S_2) = hAPP(hAPP(c_Power_Opower__class_Opower(T_b),V_ca_2),hAPP(c_Finite__Set_Ocard(T_a),V_S_2)) ) ) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_card__Plus__conv__if,axiom, % 172.27/172.36 ! [V_B_2,T_b,V_A_2,T_a] : % 172.27/172.36 ( ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.36 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) % 172.27/172.36 => 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)) ) % 172.27/172.36 & ( ~ ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.36 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) % 172.27/172.36 => 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) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_setprod__mono__one__right,axiom, % 172.27/172.36 ! [V_f_2,V_S_2,V_T_2,T_a,T_b] : % 172.27/172.36 ( class_Groups_Ocomm__monoid__mult(T_b) % 172.27/172.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2)) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2)) % 172.27/172.36 => ( ! [B_x] : % 172.27/172.36 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_T_2),V_S_2))) % 172.27/172.36 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_b) ) % 172.27/172.36 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_T_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_S_2) ) ) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_setprod__mono__one__left,axiom, % 172.27/172.36 ! [V_f_2,V_S_2,V_T_2,T_a,T_b] : % 172.27/172.36 ( class_Groups_Ocomm__monoid__mult(T_b) % 172.27/172.36 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2)) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2)) % 172.27/172.36 => ( ! [B_x] : % 172.27/172.36 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_T_2),V_S_2))) % 172.27/172.36 => hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(T_b) ) % 172.27/172.36 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_S_2) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__mult__class_Osetprod(T_a,T_b),V_f_2),V_T_2) ) ) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_finite__subset__induct,axiom, % 172.27/172.36 ! [V_P_2,V_A_2,V_F_2,T_a] : % 172.27/172.36 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_F_2),V_A_2)) % 172.27/172.36 => ( hBOOL(hAPP(V_P_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) % 172.27/172.36 => ( ! [B_a,B_F] : % 172.27/172.36 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),B_F)) % 172.27/172.36 => ( hBOOL(hAPP(hAPP(c_member(T_a),B_a),V_A_2)) % 172.27/172.36 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),B_a),B_F)) % 172.27/172.36 => ( hBOOL(hAPP(V_P_2,B_F)) % 172.27/172.36 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Set_Oinsert(T_a),B_a),B_F))) ) ) ) ) % 172.27/172.36 => hBOOL(hAPP(V_P_2,V_F_2)) ) ) ) ) ). % 172.27/172.36 % 172.27/172.36 fof(fact_less__zeroE,axiom, % 172.27/172.36 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 172.27/172.36 % 172.27/172.36 fof(fact_le0,axiom, % 172.27/172.36 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ). % 172.27/172.36 % 172.27/172.36 fof(fact_zero__less__Suc,axiom, % 172.27/172.36 ! [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))) ). % 172.27/172.36 % 172.27/172.37 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J,axiom, % 172.27/172.37 ! [V_x,T_a] : % 172.27/172.37 ( class_Rings_Ocomm__semiring__1(T_a) % 172.27/172.37 => 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) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_zero__reorient,axiom, % 172.27/172.37 ! [V_x_2,T_a] : % 172.27/172.37 ( class_Groups_Ozero(T_a) % 172.27/172.37 => ( c_Groups_Ozero__class_Ozero(T_a) = V_x_2 % 172.27/172.37 <=> V_x_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_bot__nat__def,axiom, % 172.27/172.37 c_Orderings_Obot__class_Obot(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 172.27/172.37 % 172.27/172.37 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J,axiom, % 172.27/172.37 ! [V_q,V_y,V_x,T_a] : % 172.27/172.37 ( class_Rings_Ocomm__semiring__1(T_a) % 172.27/172.37 => 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)) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J,axiom, % 172.27/172.37 ! [V_q,V_p,V_x,T_a] : % 172.27/172.37 ( class_Rings_Ocomm__semiring__1(T_a) % 172.27/172.37 => 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)) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J,axiom, % 172.27/172.37 ! [V_x,T_a] : % 172.27/172.37 ( class_Rings_Ocomm__semiring__1(T_a) % 172.27/172.37 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_x),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_x ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_add__0__left,axiom, % 172.27/172.37 ! [V_a,T_a] : % 172.27/172.37 ( class_Groups_Omonoid__add(T_a) % 172.27/172.37 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J,axiom, % 172.27/172.37 ! [V_a,T_a] : % 172.27/172.37 ( class_Rings_Ocomm__semiring__1(T_a) % 172.27/172.37 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_add__0,axiom, % 172.27/172.37 ! [V_a,T_a] : % 172.27/172.37 ( class_Groups_Ocomm__monoid__add(T_a) % 172.27/172.37 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a) = V_a ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_double__zero__sym,axiom, % 172.27/172.37 ! [V_a_2,T_a] : % 172.27/172.37 ( class_Groups_Olinordered__ab__group__add(T_a) % 172.27/172.37 => ( c_Groups_Ozero__class_Ozero(T_a) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2) % 172.27/172.37 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_add__0__right,axiom, % 172.27/172.37 ! [V_a,T_a] : % 172.27/172.37 ( class_Groups_Omonoid__add(T_a) % 172.27/172.37 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J,axiom, % 172.27/172.37 ! [V_a,T_a] : % 172.27/172.37 ( class_Rings_Ocomm__semiring__1(T_a) % 172.27/172.37 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_add_Ocomm__neutral,axiom, % 172.27/172.37 ! [V_a,T_a] : % 172.27/172.37 ( class_Groups_Ocomm__monoid__add(T_a) % 172.27/172.37 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_add__0__iff,axiom, % 172.27/172.37 ! [V_a_2,V_b_2,T_a] : % 172.27/172.37 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a) % 172.27/172.37 => ( V_b_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_b_2),V_a_2) % 172.27/172.37 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_mult__zero__left,axiom, % 172.27/172.37 ! [V_a,T_a] : % 172.27/172.37 ( class_Rings_Omult__zero(T_a) % 172.27/172.37 => 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) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_mult__zero__right,axiom, % 172.27/172.37 ! [V_a,T_a] : % 172.27/172.37 ( class_Rings_Omult__zero(T_a) % 172.27/172.37 => 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) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_mult__eq__0__iff,axiom, % 172.27/172.37 ! [V_b_2,V_a_2,T_a] : % 172.27/172.37 ( class_Rings_Oring__no__zero__divisors(T_a) % 172.27/172.37 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a) % 172.27/172.37 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a) % 172.27/172.37 | V_b_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_no__zero__divisors,axiom, % 172.27/172.37 ! [V_b,V_a,T_a] : % 172.27/172.37 ( class_Rings_Ono__zero__divisors(T_a) % 172.27/172.37 => ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 172.27/172.37 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 172.27/172.37 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_divisors__zero,axiom, % 172.27/172.37 ! [V_b,V_a,T_a] : % 172.27/172.37 ( class_Rings_Ono__zero__divisors(T_a) % 172.27/172.37 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a) % 172.27/172.37 => ( V_a = c_Groups_Ozero__class_Ozero(T_a) % 172.27/172.37 | V_b = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J,axiom, % 172.27/172.37 ! [V_a,T_a] : % 172.27/172.37 ( class_Rings_Ocomm__semiring__1(T_a) % 172.27/172.37 => 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) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J,axiom, % 172.27/172.37 ! [V_a,T_a] : % 172.27/172.37 ( class_Rings_Ocomm__semiring__1(T_a) % 172.27/172.37 => 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) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_diff__0__right,axiom, % 172.27/172.37 ! [V_a,T_a] : % 172.27/172.37 ( class_Groups_Ogroup__add(T_a) % 172.27/172.37 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_diff__self,axiom, % 172.27/172.37 ! [V_a,T_a] : % 172.27/172.37 ( class_Groups_Ogroup__add(T_a) % 172.27/172.37 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_eq__iff__diff__eq__0,axiom, % 172.27/172.37 ! [V_b_2,V_a_2,T_a] : % 172.27/172.37 ( class_Groups_Oab__group__add(T_a) % 172.27/172.37 => ( V_a_2 = V_b_2 % 172.27/172.37 <=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_right__minus__eq,axiom, % 172.27/172.37 ! [V_b_2,V_a_2,T_a] : % 172.27/172.37 ( class_Groups_Ogroup__add(T_a) % 172.27/172.37 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(T_a),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a) % 172.27/172.37 <=> V_a_2 = V_b_2 ) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_one__neq__zero,axiom, % 172.27/172.37 ! [T_a] : % 172.27/172.37 ( class_Rings_Ozero__neq__one(T_a) % 172.27/172.37 => c_Groups_Oone__class_Oone(T_a) != c_Groups_Ozero__class_Ozero(T_a) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_zero__neq__one,axiom, % 172.27/172.37 ! [T_a] : % 172.27/172.37 ( class_Rings_Ozero__neq__one(T_a) % 172.27/172.37 => c_Groups_Ozero__class_Ozero(T_a) != c_Groups_Oone__class_Oone(T_a) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_Zero__not__Suc,axiom, % 172.27/172.37 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m) ). % 172.27/172.37 % 172.27/172.37 fof(fact_nat_Osimps_I2_J,axiom, % 172.27/172.37 ! [V_nat_H] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_nat_H) ). % 172.27/172.37 % 172.27/172.37 fof(fact_Suc__not__Zero,axiom, % 172.27/172.37 ! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 172.27/172.37 % 172.27/172.37 fof(fact_nat_Osimps_I3_J,axiom, % 172.27/172.37 ! [V_nat_H_1] : hAPP(c_Nat_OSuc,V_nat_H_1) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 172.27/172.37 % 172.27/172.37 fof(fact_Zero__neq__Suc,axiom, % 172.27/172.37 ! [V_m] : c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,V_m) ). % 172.27/172.37 % 172.27/172.37 fof(fact_Suc__neq__Zero,axiom, % 172.27/172.37 ! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 172.27/172.37 % 172.27/172.37 fof(fact_not__less0,axiom, % 172.27/172.37 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 172.27/172.37 % 172.27/172.37 fof(fact_neq0__conv,axiom, % 172.27/172.37 ! [V_n_2] : % 172.27/172.37 ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 172.27/172.37 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_less__nat__zero__code,axiom, % 172.27/172.37 ! [V_n] : ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 172.27/172.37 % 172.27/172.37 fof(fact_gr__implies__not0,axiom, % 172.27/172.37 ! [V_n,V_m] : % 172.27/172.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 172.27/172.37 => V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_gr0I,axiom, % 172.27/172.37 ! [V_n] : % 172.27/172.37 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 172.27/172.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_plus__nat_Oadd__0,axiom, % 172.27/172.37 ! [V_n] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n ). % 172.27/172.37 % 172.27/172.37 fof(fact_Nat_Oadd__0__right,axiom, % 172.27/172.37 ! [V_m] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ). % 172.27/172.37 % 172.27/172.37 fof(fact_add__is__0,axiom, % 172.27/172.37 ! [V_n_2,V_m_2] : % 172.27/172.37 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 172.27/172.37 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 172.27/172.37 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_add__eq__self__zero,axiom, % 172.27/172.37 ! [V_n,V_m] : % 172.27/172.37 ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_m % 172.27/172.37 => V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_le__0__eq,axiom, % 172.27/172.37 ! [V_n_2] : % 172.27/172.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) % 172.27/172.37 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_less__eq__nat_Osimps_I1_J,axiom, % 172.27/172.37 ! [V_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) ). % 172.27/172.37 % 172.27/172.37 fof(fact_diff__0__eq__0,axiom, % 172.27/172.37 ! [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) ). % 172.27/172.37 % 172.27/172.37 fof(fact_minus__nat_Odiff__0,axiom, % 172.27/172.37 ! [V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_m ). % 172.27/172.37 % 172.27/172.37 fof(fact_diff__self__eq__0,axiom, % 172.27/172.37 ! [V_m] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 172.27/172.37 % 172.27/172.37 fof(fact_diffs0__imp__equal,axiom, % 172.27/172.37 ! [V_n,V_m] : % 172.27/172.37 ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 172.27/172.37 => ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),V_m) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 172.27/172.37 => V_m = V_n ) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_nat__mult__eq__cancel__disj,axiom, % 172.27/172.37 ! [V_n_2,V_m_2,V_k_2] : % 172.27/172.37 ( 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) % 172.27/172.37 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 172.27/172.37 | V_m_2 = V_n_2 ) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_mult__0,axiom, % 172.27/172.37 ! [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) ). % 172.27/172.37 % 172.27/172.37 fof(fact_mult__0__right,axiom, % 172.27/172.37 ! [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) ). % 172.27/172.37 % 172.27/172.37 fof(fact_mult__is__0,axiom, % 172.27/172.37 ! [V_n_2,V_m_2] : % 172.27/172.37 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 172.27/172.37 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 172.27/172.37 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_mult__cancel1,axiom, % 172.27/172.37 ! [V_n_2,V_m_2,V_k_2] : % 172.27/172.37 ( 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) % 172.27/172.37 <=> ( V_m_2 = V_n_2 % 172.27/172.37 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_mult__cancel2,axiom, % 172.27/172.37 ! [V_n_2,V_k_2,V_m_2] : % 172.27/172.37 ( 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) % 172.27/172.37 <=> ( V_m_2 = V_n_2 % 172.27/172.37 | V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_power__eq__if,axiom, % 172.27/172.37 ! [V_p,V_m] : % 172.27/172.37 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 172.27/172.37 => hAPP(hAPP(c_Power_Opower__class_Opower(tc_Nat_Onat),V_p),V_m) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) % 172.27/172.37 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 172.27/172.37 => 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)))) ) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_setsum__0,axiom, % 172.27/172.37 ! [V_A_2,T_b,T_a] : % 172.27/172.37 ( class_Groups_Ocomm__monoid__add(T_a) % 172.27/172.37 => 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) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J,axiom, % 172.27/172.37 ! [V_q,V_x,T_a] : % 172.27/172.37 ( class_Rings_Ocomm__semiring__1(T_a) % 172.27/172.37 => 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)) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J,axiom, % 172.27/172.37 ! [V_q,V_x,T_a] : % 172.27/172.37 ( class_Rings_Ocomm__semiring__1(T_a) % 172.27/172.37 => 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)) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J,axiom, % 172.27/172.37 ! [V_q,V_x,T_a] : % 172.27/172.37 ( class_Rings_Ocomm__semiring__1(T_a) % 172.27/172.37 => 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)) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J,axiom, % 172.27/172.37 ! [V_q,V_p,V_x,T_a] : % 172.27/172.37 ( class_Rings_Ocomm__semiring__1(T_a) % 172.27/172.37 => 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)) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_zero__le__double__add__iff__zero__le__single__add,axiom, % 172.27/172.37 ! [V_a_2,T_a] : % 172.27/172.37 ( class_Groups_Olinordered__ab__group__add(T_a) % 172.27/172.37 => ( 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))) % 172.27/172.37 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_double__add__le__zero__iff__single__add__le__zero,axiom, % 172.27/172.37 ! [V_a_2,T_a] : % 172.27/172.37 ( class_Groups_Olinordered__ab__group__add(T_a) % 172.27/172.37 => ( 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))) % 172.27/172.37 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_add__nonneg__nonneg,axiom, % 172.27/172.37 ! [V_b,V_a,T_a] : % 172.27/172.37 ( class_Groups_Oordered__comm__monoid__add(T_a) % 172.27/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 172.27/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 172.27/172.37 => 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))) ) ) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_add__nonneg__eq__0__iff,axiom, % 172.27/172.37 ! [V_y_2,V_x_2,T_a] : % 172.27/172.37 ( class_Groups_Oordered__comm__monoid__add(T_a) % 172.27/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x_2)) % 172.27/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y_2)) % 172.27/172.37 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_x_2),V_y_2) = c_Groups_Ozero__class_Ozero(T_a) % 172.27/172.37 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a) % 172.27/172.37 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_add__increasing,axiom, % 172.27/172.37 ! [V_c,V_b,V_a,T_a] : % 172.27/172.37 ( class_Groups_Oordered__comm__monoid__add(T_a) % 172.27/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 172.27/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c)) % 172.27/172.37 => 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))) ) ) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_add__increasing2,axiom, % 172.27/172.37 ! [V_a,V_b,V_c,T_a] : % 172.27/172.37 ( class_Groups_Oordered__comm__monoid__add(T_a) % 172.27/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 172.27/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 172.27/172.37 => 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))) ) ) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_add__nonpos__nonpos,axiom, % 172.27/172.37 ! [V_b,V_a,T_a] : % 172.27/172.37 ( class_Groups_Oordered__comm__monoid__add(T_a) % 172.27/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 172.27/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 172.27/172.37 => 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))) ) ) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_split__mult__neg__le,axiom, % 172.27/172.37 ! [V_b,V_a,T_a] : % 172.27/172.37 ( class_Rings_Oordered__cancel__semiring(T_a) % 172.27/172.37 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 172.27/172.37 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) ) % 172.27/172.37 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 172.27/172.37 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) % 172.27/172.37 => 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))) ) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_split__mult__pos__le,axiom, % 172.27/172.37 ! [V_b,V_a,T_a] : % 172.27/172.37 ( class_Rings_Oordered__ring(T_a) % 172.27/172.37 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 172.27/172.37 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) % 172.27/172.37 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 172.27/172.37 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) ) ) % 172.27/172.37 => 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))) ) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_mult__mono,axiom, % 172.27/172.37 ! [V_d,V_c,V_b,V_a,T_a] : % 172.27/172.37 ( class_Rings_Oordered__semiring(T_a) % 172.27/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 172.27/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d)) % 172.27/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 172.27/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 172.27/172.37 => 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))) ) ) ) ) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_mult__mono_H,axiom, % 172.27/172.37 ! [V_d,V_c,V_b,V_a,T_a] : % 172.27/172.37 ( class_Rings_Oordered__semiring(T_a) % 172.27/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 172.27/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d)) % 172.27/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 172.27/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 172.27/172.37 => 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))) ) ) ) ) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_mult__left__mono__neg,axiom, % 172.27/172.37 ! [V_c,V_a,V_b,T_a] : % 172.27/172.37 ( class_Rings_Oordered__ring(T_a) % 172.27/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 172.27/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 172.27/172.37 => 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))) ) ) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_mult__right__mono__neg,axiom, % 172.27/172.37 ! [V_c,V_a,V_b,T_a] : % 172.27/172.37 ( class_Rings_Oordered__ring(T_a) % 172.27/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 172.27/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 172.27/172.37 => 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))) ) ) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_comm__mult__left__mono,axiom, % 172.27/172.37 ! [V_c,V_b,V_a,T_a] : % 172.27/172.37 ( class_Rings_Oordered__comm__semiring(T_a) % 172.27/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 172.27/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 172.27/172.37 => 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))) ) ) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_mult__left__mono,axiom, % 172.27/172.37 ! [V_c,V_b,V_a,T_a] : % 172.27/172.37 ( class_Rings_Oordered__semiring(T_a) % 172.27/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 172.27/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 172.27/172.37 => 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))) ) ) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_mult__right__mono,axiom, % 172.27/172.37 ! [V_c,V_b,V_a,T_a] : % 172.27/172.37 ( class_Rings_Oordered__semiring(T_a) % 172.27/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 172.27/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 172.27/172.37 => 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))) ) ) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_mult__nonpos__nonpos,axiom, % 172.27/172.37 ! [V_b,V_a,T_a] : % 172.27/172.37 ( class_Rings_Oordered__ring(T_a) % 172.27/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 172.27/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 172.27/172.37 => 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))) ) ) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_mult__nonpos__nonneg,axiom, % 172.27/172.37 ! [V_b,V_a,T_a] : % 172.27/172.37 ( class_Rings_Oordered__cancel__semiring(T_a) % 172.27/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 172.27/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 172.27/172.37 => 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))) ) ) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_mult__nonneg__nonpos2,axiom, % 172.27/172.37 ! [V_b,V_a,T_a] : % 172.27/172.37 ( class_Rings_Oordered__cancel__semiring(T_a) % 172.27/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 172.27/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 172.27/172.37 => 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))) ) ) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_mult__nonneg__nonpos,axiom, % 172.27/172.37 ! [V_b,V_a,T_a] : % 172.27/172.37 ( class_Rings_Oordered__cancel__semiring(T_a) % 172.27/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 172.27/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 172.27/172.37 => 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))) ) ) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_mult__nonneg__nonneg,axiom, % 172.27/172.37 ! [V_b,V_a,T_a] : % 172.27/172.37 ( class_Rings_Oordered__cancel__semiring(T_a) % 172.27/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 172.27/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 172.27/172.37 => 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))) ) ) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_mult__le__0__iff,axiom, % 172.27/172.37 ! [V_b_2,V_a_2,T_a] : % 172.27/172.37 ( class_Rings_Olinordered__ring__strict(T_a) % 172.27/172.37 => ( 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))) % 172.27/172.37 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) % 172.27/172.37 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),c_Groups_Ozero__class_Ozero(T_a))) ) % 172.27/172.37 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) % 172.27/172.37 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b_2)) ) ) ) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_zero__le__mult__iff,axiom, % 172.27/172.37 ! [V_b_2,V_a_2,T_a] : % 172.27/172.37 ( class_Rings_Olinordered__ring__strict(T_a) % 172.27/172.37 => ( 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))) % 172.27/172.37 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) % 172.27/172.37 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b_2)) ) % 172.27/172.37 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) % 172.27/172.37 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_zero__le__square,axiom, % 172.27/172.37 ! [V_a,T_a] : % 172.27/172.37 ( class_Rings_Olinordered__ring(T_a) % 172.27/172.37 => 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))) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_pos__add__strict,axiom, % 172.27/172.37 ! [V_c,V_b,V_a,T_a] : % 172.27/172.37 ( class_Rings_Olinordered__semidom(T_a) % 172.27/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 172.27/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c)) % 172.27/172.37 => 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))) ) ) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_add__neg__neg,axiom, % 172.27/172.37 ! [V_b,V_a,T_a] : % 172.27/172.37 ( class_Groups_Oordered__comm__monoid__add(T_a) % 172.27/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 172.27/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 172.27/172.37 => 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))) ) ) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_add__pos__pos,axiom, % 172.27/172.37 ! [V_b,V_a,T_a] : % 172.27/172.37 ( class_Groups_Oordered__comm__monoid__add(T_a) % 172.27/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 172.27/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 172.27/172.37 => 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))) ) ) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_double__add__less__zero__iff__single__add__less__zero,axiom, % 172.27/172.37 ! [V_a_2,T_a] : % 172.27/172.37 ( class_Groups_Olinordered__ab__group__add(T_a) % 172.27/172.37 => ( 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))) % 172.27/172.37 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_zero__less__double__add__iff__zero__less__single__add,axiom, % 172.27/172.37 ! [V_a_2,T_a] : % 172.27/172.37 ( class_Groups_Olinordered__ab__group__add(T_a) % 172.27/172.37 => ( 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))) % 172.27/172.37 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_mult__strict__left__mono__neg,axiom, % 172.27/172.37 ! [V_c,V_a,V_b,T_a] : % 172.27/172.37 ( class_Rings_Olinordered__ring__strict(T_a) % 172.27/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 172.27/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 172.27/172.37 => 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))) ) ) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_mult__strict__right__mono__neg,axiom, % 172.27/172.37 ! [V_c,V_a,V_b,T_a] : % 172.27/172.37 ( class_Rings_Olinordered__ring__strict(T_a) % 172.27/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 172.27/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 172.27/172.37 => 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))) ) ) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_comm__mult__strict__left__mono,axiom, % 172.27/172.37 ! [V_c,V_b,V_a,T_a] : % 172.27/172.37 ( class_Rings_Olinordered__comm__semiring__strict(T_a) % 172.27/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 172.27/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 172.27/172.37 => 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))) ) ) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_mult__strict__left__mono,axiom, % 172.27/172.37 ! [V_c,V_b,V_a,T_a] : % 172.27/172.37 ( class_Rings_Olinordered__semiring__strict(T_a) % 172.27/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 172.27/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 172.27/172.37 => 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))) ) ) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_mult__strict__right__mono,axiom, % 172.27/172.37 ! [V_c,V_b,V_a,T_a] : % 172.27/172.37 ( class_Rings_Olinordered__semiring__strict(T_a) % 172.27/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 172.27/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 172.27/172.37 => 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))) ) ) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_mult__neg__neg,axiom, % 172.27/172.37 ! [V_b,V_a,T_a] : % 172.27/172.37 ( class_Rings_Olinordered__ring__strict(T_a) % 172.27/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 172.27/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 172.27/172.37 => 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))) ) ) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_mult__neg__pos,axiom, % 172.27/172.37 ! [V_b,V_a,T_a] : % 172.27/172.37 ( class_Rings_Olinordered__semiring__strict(T_a) % 172.27/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 172.27/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 172.27/172.37 => 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))) ) ) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_mult__less__cancel__left__neg,axiom, % 172.27/172.37 ! [V_b_2,V_a_2,V_ca_2,T_a] : % 172.27/172.37 ( class_Rings_Olinordered__ring__strict(T_a) % 172.27/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 172.27/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2))) % 172.27/172.37 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),V_a_2)) ) ) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_zero__less__mult__pos2,axiom, % 172.27/172.37 ! [V_a,V_b,T_a] : % 172.27/172.37 ( class_Rings_Olinordered__semiring__strict(T_a) % 172.27/172.37 => ( 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))) % 172.27/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 172.27/172.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_zero__less__mult__pos,axiom, % 172.27/172.37 ! [V_b,V_a,T_a] : % 172.27/172.37 ( class_Rings_Olinordered__semiring__strict(T_a) % 172.27/172.37 => ( 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))) % 172.27/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 172.27/172.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) ) ) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_mult__pos__neg2,axiom, % 172.27/172.37 ! [V_b,V_a,T_a] : % 172.27/172.37 ( class_Rings_Olinordered__semiring__strict(T_a) % 172.27/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 172.27/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 172.27/172.37 => 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))) ) ) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_mult__pos__neg,axiom, % 172.27/172.37 ! [V_b,V_a,T_a] : % 172.27/172.37 ( class_Rings_Olinordered__semiring__strict(T_a) % 172.27/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 172.27/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 172.27/172.37 => 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))) ) ) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_mult__pos__pos,axiom, % 172.27/172.37 ! [V_b,V_a,T_a] : % 172.27/172.37 ( class_Rings_Olinordered__semiring__strict(T_a) % 172.27/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 172.27/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 172.27/172.37 => 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))) ) ) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_mult__less__cancel__left__pos,axiom, % 172.27/172.37 ! [V_b_2,V_a_2,V_ca_2,T_a] : % 172.27/172.37 ( class_Rings_Olinordered__ring__strict(T_a) % 172.27/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 172.27/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2))) % 172.27/172.37 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) ) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_mult__less__cancel__left__disj,axiom, % 172.27/172.37 ! [V_b_2,V_a_2,V_ca_2,T_a] : % 172.27/172.37 ( class_Rings_Olinordered__ring__strict(T_a) % 172.27/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2))) % 172.27/172.37 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 172.27/172.37 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) % 172.27/172.37 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 172.27/172.37 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),V_a_2)) ) ) ) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_mult__less__cancel__right__disj,axiom, % 172.27/172.37 ! [V_b_2,V_ca_2,V_a_2,T_a] : % 172.27/172.37 ( class_Rings_Olinordered__ring__strict(T_a) % 172.27/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_b_2),V_ca_2))) % 172.27/172.37 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 172.27/172.37 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) % 172.27/172.37 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 172.27/172.37 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),V_a_2)) ) ) ) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_not__square__less__zero,axiom, % 172.27/172.37 ! [V_a,T_a] : % 172.27/172.37 ( class_Rings_Olinordered__ring(T_a) % 172.27/172.37 => ~ 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))) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_le__iff__diff__le__0,axiom, % 172.27/172.37 ! [V_b_2,V_a_2,T_a] : % 172.27/172.37 ( class_Groups_Oordered__ab__group__add(T_a) % 172.27/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) % 172.27/172.37 <=> 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))) ) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_less__iff__diff__less__0,axiom, % 172.27/172.37 ! [V_b_2,V_a_2,T_a] : % 172.27/172.37 ( class_Groups_Oordered__ab__group__add(T_a) % 172.27/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) % 172.27/172.37 <=> 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))) ) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_sum__squares__eq__zero__iff,axiom, % 172.27/172.37 ! [V_y_2,V_x_2,T_a] : % 172.27/172.37 ( class_Rings_Olinordered__ring__strict(T_a) % 172.27/172.37 => ( 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) % 172.27/172.37 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a) % 172.27/172.37 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_add__scale__eq__noteq,axiom, % 172.27/172.37 ! [V_d,V_c,V_b,V_a,V_r,T_a] : % 172.27/172.37 ( class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(T_a) % 172.27/172.37 => ( V_r != c_Groups_Ozero__class_Ozero(T_a) % 172.27/172.37 => ( ( V_a = V_b % 172.27/172.37 & V_c != V_d ) % 172.27/172.37 => 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)) ) ) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_not__one__le__zero,axiom, % 172.27/172.37 ! [T_a] : % 172.27/172.37 ( class_Rings_Olinordered__semidom(T_a) % 172.27/172.37 => ~ 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))) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_zero__le__one,axiom, % 172.27/172.37 ! [T_a] : % 172.27/172.37 ( class_Rings_Olinordered__semidom(T_a) % 172.27/172.37 => 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))) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_not__one__less__zero,axiom, % 172.27/172.37 ! [T_a] : % 172.27/172.37 ( class_Rings_Olinordered__semidom(T_a) % 172.27/172.37 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),c_Groups_Ozero__class_Ozero(T_a))) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_zero__less__one,axiom, % 172.27/172.37 ! [T_a] : % 172.27/172.37 ( class_Rings_Olinordered__semidom(T_a) % 172.27/172.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Groups_Oone__class_Oone(T_a))) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_setsum__empty,axiom, % 172.27/172.37 ! [V_f_2,T_b,T_a] : % 172.27/172.37 ( class_Groups_Ocomm__monoid__add(T_a) % 172.27/172.37 => 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) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_setsum_Oempty,axiom, % 172.27/172.37 ! [V_g_2,T_b,T_a] : % 172.27/172.37 ( class_Groups_Ocomm__monoid__add(T_a) % 172.27/172.37 => 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) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_setsum_Oinfinite,axiom, % 172.27/172.37 ! [V_g_2,V_A_2,T_a,T_b] : % 172.27/172.37 ( class_Groups_Ocomm__monoid__add(T_b) % 172.27/172.37 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.37 => 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) ) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_setsum__infinite,axiom, % 172.27/172.37 ! [V_f_2,V_A_2,T_a,T_b] : % 172.27/172.37 ( class_Groups_Ocomm__monoid__add(T_b) % 172.27/172.37 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.37 => 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) ) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_setprod__pos__nat__iff,axiom, % 172.27/172.37 ! [V_f_2,V_S_2,T_a] : % 172.27/172.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 172.27/172.37 => ( 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))) % 172.27/172.37 <=> ! [B_x] : % 172.27/172.37 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2)) % 172.27/172.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),hAPP(V_f_2,B_x))) ) ) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_setprod__zero,axiom, % 172.27/172.37 ! [V_f_2,V_A_2,T_a,T_b] : % 172.27/172.37 ( class_Rings_Ocomm__semiring__1(T_b) % 172.27/172.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.37 => ( ? [B_x] : % 172.27/172.37 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 172.27/172.37 & hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) ) % 172.27/172.37 => 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) ) ) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_setprod__zero__iff,axiom, % 172.27/172.37 ! [V_f_2,V_A_2,T_a,T_b] : % 172.27/172.37 ( ( class_Rings_Ocomm__semiring__1(T_b) % 172.27/172.37 & class_Rings_Ono__zero__divisors(T_b) ) % 172.27/172.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.37 => ( 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) % 172.27/172.37 <=> ? [B_x] : % 172.27/172.37 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 172.27/172.37 & hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_less__Suc__eq__0__disj,axiom, % 172.27/172.37 ! [V_n_2,V_m_2] : % 172.27/172.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) % 172.27/172.37 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 172.27/172.37 | ? [B_j] : % 172.27/172.37 ( V_m_2 = hAPP(c_Nat_OSuc,B_j) % 172.27/172.37 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_n_2)) ) ) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_less__Suc0,axiom, % 172.27/172.37 ! [V_n_2] : % 172.27/172.37 ( 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)))) % 172.27/172.37 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_gr0__conv__Suc,axiom, % 172.27/172.37 ! [V_n_2] : % 172.27/172.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) % 172.27/172.37 <=> ? [B_m] : V_n_2 = hAPP(c_Nat_OSuc,B_m) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_add__is__1,axiom, % 172.27/172.37 ! [V_n_2,V_m_2] : % 172.27/172.37 ( 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)) % 172.27/172.37 <=> ( ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 172.27/172.37 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 172.27/172.37 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 172.27/172.37 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_one__is__add,axiom, % 172.27/172.37 ! [V_n_2,V_m_2] : % 172.27/172.37 ( 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) % 172.27/172.37 <=> ( ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 172.27/172.37 & V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 172.27/172.37 | ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 172.27/172.37 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_add__gr__0,axiom, % 172.27/172.37 ! [V_n_2,V_m_2] : % 172.27/172.37 ( 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))) % 172.27/172.37 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2)) % 172.27/172.37 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_card_Oempty,axiom, % 172.27/172.37 ! [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) ). % 172.27/172.37 % 172.27/172.37 fof(fact_card__infinite,axiom, % 172.27/172.37 ! [V_A_2,T_a] : % 172.27/172.37 ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.27/172.37 => hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_mult__eq__1__iff,axiom, % 172.27/172.37 ! [V_n_2,V_m_2] : % 172.27/172.37 ( 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)) % 172.27/172.37 <=> ( V_m_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 172.27/172.37 & V_n_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_zero__less__diff,axiom, % 172.27/172.37 ! [V_m_2,V_n_2] : % 172.27/172.37 ( 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))) % 172.27/172.37 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_diff__less,axiom, % 172.27/172.37 ! [V_m,V_n] : % 172.27/172.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 172.27/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)) % 172.27/172.37 => 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)) ) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_nat__mult__less__cancel1,axiom, % 172.27/172.37 ! [V_n_2,V_m_2,V_k_2] : % 172.27/172.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 172.27/172.37 => ( 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))) % 172.27/172.37 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_nat__mult__eq__cancel1,axiom, % 172.27/172.37 ! [V_n_2,V_m_2,V_k_2] : % 172.27/172.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 172.27/172.37 => ( 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) % 172.27/172.37 <=> V_m_2 = V_n_2 ) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_mult__less__mono2,axiom, % 172.27/172.37 ! [V_k,V_j,V_i] : % 172.27/172.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 172.27/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k)) % 172.27/172.37 => 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))) ) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_mult__less__mono1,axiom, % 172.27/172.37 ! [V_k,V_j,V_i] : % 172.27/172.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 172.27/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k)) % 172.27/172.37 => 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))) ) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_mult__less__cancel2,axiom, % 172.27/172.37 ! [V_n_2,V_k_2,V_m_2] : % 172.27/172.37 ( 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))) % 172.27/172.37 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 172.27/172.37 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_mult__less__cancel1,axiom, % 172.27/172.37 ! [V_n_2,V_m_2,V_k_2] : % 172.27/172.37 ( 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))) % 172.27/172.37 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 172.27/172.37 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_nat__0__less__mult__iff,axiom, % 172.27/172.37 ! [V_n_2,V_m_2] : % 172.27/172.37 ( 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))) % 172.27/172.37 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m_2)) % 172.27/172.37 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_diff__add__0,axiom, % 172.27/172.37 ! [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) ). % 172.27/172.37 % 172.27/172.37 fof(fact_diff__is__0__eq,axiom, % 172.27/172.37 ! [V_n_2,V_m_2] : % 172.27/172.37 ( hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m_2),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 172.27/172.37 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_diff__is__0__eq_H,axiom, % 172.27/172.37 ! [V_n,V_m] : % 172.27/172.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 172.27/172.37 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_One__nat__def,axiom, % 172.27/172.37 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ). % 172.27/172.37 % 172.27/172.37 fof(fact_mult__eq__self__implies__10,axiom, % 172.27/172.37 ! [V_n,V_m] : % 172.27/172.37 ( V_m = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) % 172.27/172.37 => ( V_n = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 172.27/172.37 | V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_setsum__eq__0__iff,axiom, % 172.27/172.37 ! [V_f_2,V_F_2,T_a] : % 172.27/172.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) % 172.27/172.37 => ( 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) % 172.27/172.37 <=> ! [B_x] : % 172.27/172.37 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_F_2)) % 172.27/172.37 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_add__nonpos__neg,axiom, % 172.27/172.37 ! [V_b,V_a,T_a] : % 172.27/172.37 ( class_Groups_Oordered__comm__monoid__add(T_a) % 172.27/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 172.27/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 172.27/172.37 => 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))) ) ) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_add__neg__nonpos,axiom, % 172.27/172.37 ! [V_b,V_a,T_a] : % 172.27/172.37 ( class_Groups_Oordered__comm__monoid__add(T_a) % 172.27/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 172.27/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) % 172.27/172.37 => 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))) ) ) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_add__strict__increasing2,axiom, % 172.27/172.37 ! [V_c,V_b,V_a,T_a] : % 172.27/172.37 ( class_Groups_Oordered__comm__monoid__add(T_a) % 172.27/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 172.27/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_c)) % 172.27/172.37 => 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))) ) ) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_add__strict__increasing,axiom, % 172.27/172.37 ! [V_c,V_b,V_a,T_a] : % 172.27/172.37 ( class_Groups_Oordered__comm__monoid__add(T_a) % 172.27/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 172.27/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_c)) % 172.27/172.37 => 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))) ) ) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_add__nonneg__pos,axiom, % 172.27/172.37 ! [V_b,V_a,T_a] : % 172.27/172.37 ( class_Groups_Oordered__comm__monoid__add(T_a) % 172.27/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 172.27/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 172.27/172.37 => 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))) ) ) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_add__pos__nonneg,axiom, % 172.27/172.37 ! [V_b,V_a,T_a] : % 172.27/172.37 ( class_Groups_Oordered__comm__monoid__add(T_a) % 172.27/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 172.27/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 172.27/172.37 => 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))) ) ) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_mult__left__le__imp__le,axiom, % 172.27/172.37 ! [V_b,V_a,V_c,T_a] : % 172.27/172.37 ( class_Rings_Olinordered__semiring__strict(T_a) % 172.27/172.37 => ( 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))) % 172.27/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 172.27/172.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_mult__right__le__imp__le,axiom, % 172.27/172.37 ! [V_b,V_c,V_a,T_a] : % 172.27/172.37 ( class_Rings_Olinordered__semiring__strict(T_a) % 172.27/172.37 => ( 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))) % 172.27/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 172.27/172.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ). % 172.27/172.37 % 172.27/172.37 fof(fact_mult__less__imp__less__left,axiom, % 172.27/172.37 ! [V_b,V_a,V_c,T_a] : % 172.27/172.37 ( class_Rings_Olinordered__semiring__strict(T_a) % 172.27/172.37 => ( 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))) % 172.48/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 172.48/172.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 172.48/172.37 % 172.48/172.37 fof(fact_mult__left__less__imp__less,axiom, % 172.48/172.37 ! [V_b,V_a,V_c,T_a] : % 172.48/172.37 ( class_Rings_Olinordered__semiring(T_a) % 172.48/172.37 => ( 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))) % 172.48/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 172.48/172.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 172.48/172.37 % 172.48/172.37 fof(fact_mult__less__imp__less__right,axiom, % 172.48/172.37 ! [V_b,V_c,V_a,T_a] : % 172.48/172.37 ( class_Rings_Olinordered__semiring__strict(T_a) % 172.48/172.37 => ( 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))) % 172.48/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 172.48/172.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 172.48/172.37 % 172.48/172.37 fof(fact_mult__right__less__imp__less,axiom, % 172.48/172.37 ! [V_b,V_c,V_a,T_a] : % 172.48/172.37 ( class_Rings_Olinordered__semiring(T_a) % 172.48/172.37 => ( 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))) % 172.48/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 172.48/172.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 172.48/172.37 % 172.48/172.37 fof(fact_mult__le__less__imp__less,axiom, % 172.48/172.37 ! [V_d,V_c,V_b,V_a,T_a] : % 172.48/172.37 ( class_Rings_Olinordered__semiring__strict(T_a) % 172.48/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 172.48/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) % 172.48/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 172.48/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 172.48/172.37 => 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))) ) ) ) ) ) ). % 172.48/172.37 % 172.48/172.37 fof(fact_mult__less__le__imp__less,axiom, % 172.48/172.37 ! [V_d,V_c,V_b,V_a,T_a] : % 172.48/172.37 ( class_Rings_Olinordered__semiring__strict(T_a) % 172.48/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 172.48/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),V_d)) % 172.48/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 172.48/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 172.48/172.37 => 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))) ) ) ) ) ) ). % 172.48/172.37 % 172.48/172.37 fof(fact_mult__strict__mono_H,axiom, % 172.48/172.37 ! [V_d,V_c,V_b,V_a,T_a] : % 172.48/172.37 ( class_Rings_Olinordered__semiring__strict(T_a) % 172.48/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 172.48/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) % 172.48/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 172.48/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 172.48/172.37 => 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))) ) ) ) ) ) ). % 172.48/172.37 % 172.48/172.37 fof(fact_mult__strict__mono,axiom, % 172.48/172.37 ! [V_d,V_c,V_b,V_a,T_a] : % 172.48/172.37 ( class_Rings_Olinordered__semiring__strict(T_a) % 172.48/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 172.48/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),V_d)) % 172.48/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 172.48/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 172.48/172.37 => 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))) ) ) ) ) ) ). % 172.48/172.37 % 172.48/172.37 fof(fact_mult__le__cancel__left__neg,axiom, % 172.48/172.37 ! [V_b_2,V_a_2,V_ca_2,T_a] : % 172.48/172.37 ( class_Rings_Olinordered__ring__strict(T_a) % 172.48/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 172.48/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2))) % 172.48/172.37 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_a_2)) ) ) ) ). % 172.48/172.37 % 172.48/172.37 fof(fact_mult__le__cancel__left__pos,axiom, % 172.48/172.37 ! [V_b_2,V_a_2,V_ca_2,T_a] : % 172.48/172.37 ( class_Rings_Olinordered__ring__strict(T_a) % 172.48/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 172.48/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_a_2)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),V_b_2))) % 172.48/172.37 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) ) ) ) ). % 172.48/172.37 % 172.48/172.37 fof(fact_sum__squares__ge__zero,axiom, % 172.48/172.37 ! [V_y,V_x,T_a] : % 172.48/172.37 ( class_Rings_Olinordered__ring(T_a) % 172.48/172.37 => 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)))) ) ). % 172.48/172.37 % 172.48/172.37 fof(fact_sum__squares__le__zero__iff,axiom, % 172.48/172.37 ! [V_y_2,V_x_2,T_a] : % 172.48/172.37 ( class_Rings_Olinordered__ring__strict(T_a) % 172.48/172.37 => ( 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))) % 172.48/172.37 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a) % 172.48/172.37 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 172.48/172.37 % 172.48/172.37 fof(fact_not__sum__squares__lt__zero,axiom, % 172.48/172.37 ! [V_y,V_x,T_a] : % 172.48/172.37 ( class_Rings_Olinordered__ring(T_a) % 172.48/172.37 => ~ 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))) ) ). % 172.48/172.37 % 172.48/172.37 fof(fact_sum__squares__gt__zero__iff,axiom, % 172.48/172.37 ! [V_y_2,V_x_2,T_a] : % 172.48/172.37 ( class_Rings_Olinordered__ring__strict(T_a) % 172.48/172.37 => ( 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)))) % 172.48/172.37 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(T_a) % 172.48/172.37 | V_y_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 172.48/172.37 % 172.48/172.37 fof(fact_mult__left__le__one__le,axiom, % 172.48/172.37 ! [V_y,V_x,T_a] : % 172.48/172.37 ( class_Rings_Olinordered__idom(T_a) % 172.48/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 172.48/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 172.48/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),c_Groups_Oone__class_Oone(T_a))) % 172.48/172.37 => 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)) ) ) ) ) ). % 172.48/172.37 % 172.48/172.37 fof(fact_mult__right__le__one__le,axiom, % 172.48/172.37 ! [V_y,V_x,T_a] : % 172.48/172.37 ( class_Rings_Olinordered__idom(T_a) % 172.48/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 172.48/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 172.48/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),c_Groups_Oone__class_Oone(T_a))) % 172.48/172.37 => 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)) ) ) ) ) ). % 172.48/172.37 % 172.48/172.37 fof(fact_zero__less__two,axiom, % 172.48/172.37 ! [T_a] : % 172.48/172.37 ( class_Rings_Olinordered__semidom(T_a) % 172.48/172.37 => 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)))) ) ). % 172.48/172.37 % 172.48/172.37 fof(fact_card__eq__0__iff,axiom, % 172.48/172.37 ! [V_A_2,T_a] : % 172.48/172.37 ( hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 172.48/172.37 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.37 | ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ) ). % 172.48/172.37 % 172.48/172.37 fof(fact_setprod__constant,axiom, % 172.48/172.37 ! [V_y_2,V_A_2,T_a,T_b] : % 172.48/172.37 ( class_Groups_Ocomm__monoid__mult(T_b) % 172.48/172.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.37 => 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)) ) ) ). % 172.48/172.37 % 172.48/172.37 fof(fact_card__ge__0__finite,axiom, % 172.48/172.37 ! [V_A_2,T_a] : % 172.48/172.37 ( 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))) % 172.48/172.37 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ). % 172.48/172.37 % 172.48/172.37 fof(fact_diff__Suc__less,axiom, % 172.48/172.37 ! [V_i,V_n] : % 172.48/172.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 172.48/172.37 => 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)) ) ). % 172.48/172.37 % 172.48/172.37 fof(fact_Suc__pred,axiom, % 172.48/172.37 ! [V_n] : % 172.48/172.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 172.48/172.37 => 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 ) ). % 172.48/172.37 % 172.48/172.37 fof(fact_n__less__m__mult__n,axiom, % 172.48/172.37 ! [V_m,V_n] : % 172.48/172.37 ( 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)) % 172.48/172.37 => ( 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)) % 172.48/172.37 => 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))) ) ) ). % 172.48/172.37 % 172.48/172.37 fof(fact_n__less__n__mult__m,axiom, % 172.48/172.37 ! [V_m,V_n] : % 172.48/172.37 ( 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)) % 172.48/172.37 => ( 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)) % 172.48/172.37 => 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))) ) ) ). % 172.48/172.37 % 172.48/172.37 fof(fact_one__less__mult,axiom, % 172.48/172.37 ! [V_m,V_n] : % 172.48/172.37 ( 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)) % 172.48/172.37 => ( 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)) % 172.48/172.37 => 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))) ) ) ). % 172.48/172.37 % 172.48/172.37 fof(fact_nat__diff__split__asm,axiom, % 172.48/172.37 ! [V_b_2,V_a_2,V_P_2] : % 172.48/172.37 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2))) % 172.48/172.37 <=> ~ ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2)) % 172.48/172.37 & ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) % 172.48/172.37 | ? [B_d] : % 172.48/172.37 ( V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d) % 172.48/172.37 & ~ hBOOL(hAPP(V_P_2,B_d)) ) ) ) ). % 172.48/172.37 % 172.48/172.37 fof(fact_nat__diff__split,axiom, % 172.48/172.37 ! [V_b_2,V_a_2,V_P_2] : % 172.48/172.37 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_a_2),V_b_2))) % 172.48/172.37 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2)) % 172.48/172.37 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) % 172.48/172.37 & ! [B_d] : % 172.48/172.37 ( V_a_2 = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_b_2),B_d) % 172.48/172.37 => hBOOL(hAPP(V_P_2,B_d)) ) ) ) ). % 172.48/172.37 % 172.48/172.37 fof(fact_one__le__mult__iff,axiom, % 172.48/172.37 ! [V_n_2,V_m_2] : % 172.48/172.37 ( 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))) % 172.48/172.37 <=> ( 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)) % 172.48/172.37 & 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)) ) ) ). % 172.48/172.37 % 172.48/172.37 fof(fact_nat__mult__le__cancel1,axiom, % 172.48/172.37 ! [V_n_2,V_m_2,V_k_2] : % 172.48/172.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 172.48/172.37 => ( 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))) % 172.48/172.37 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 172.48/172.37 % 172.48/172.37 fof(fact_mult__le__cancel2,axiom, % 172.48/172.37 ! [V_n_2,V_k_2,V_m_2] : % 172.48/172.37 ( 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))) % 172.48/172.37 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 172.48/172.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 172.48/172.37 % 172.48/172.37 fof(fact_mult__le__cancel1,axiom, % 172.48/172.37 ! [V_n_2,V_m_2,V_k_2] : % 172.48/172.37 ( 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))) % 172.48/172.37 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k_2)) % 172.48/172.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 172.48/172.37 % 172.48/172.37 fof(fact_setsum__eq__Suc0__iff,axiom, % 172.48/172.37 ! [V_f_2,V_A_2,T_a] : % 172.48/172.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.37 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,tc_Nat_Onat),V_f_2),V_A_2) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 172.48/172.37 <=> ? [B_x] : % 172.48/172.37 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 172.48/172.37 & hAPP(V_f_2,B_x) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 172.48/172.37 & ! [B_xa] : % 172.48/172.37 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_A_2)) % 172.48/172.37 => ( B_x != B_xa % 172.48/172.37 => hAPP(V_f_2,B_xa) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) ) ). % 172.48/172.37 % 172.48/172.37 fof(fact_setsum__eq__1__iff,axiom, % 172.48/172.37 ! [V_f_2,V_A_2,T_a] : % 172.48/172.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.37 => ( 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) % 172.48/172.37 <=> ? [B_x] : % 172.48/172.37 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 172.48/172.37 & hAPP(V_f_2,B_x) = c_Groups_Oone__class_Oone(tc_Nat_Onat) % 172.48/172.37 & ! [B_xa] : % 172.48/172.37 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_A_2)) % 172.48/172.37 => ( B_x != B_xa % 172.48/172.37 => hAPP(V_f_2,B_xa) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ) ) ). % 172.48/172.37 % 172.48/172.37 fof(fact_setsum__delta_H,axiom, % 172.48/172.37 ! [V_b_2,V_a_2,V_S_2,T_a,T_b] : % 172.48/172.37 ( class_Groups_Ocomm__monoid__add(T_b) % 172.48/172.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 172.48/172.37 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) % 172.48/172.37 => 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) ) % 172.48/172.37 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) % 172.48/172.37 => 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) ) ) ) ) ). % 172.48/172.37 % 172.48/172.37 fof(fact_setsum__delta,axiom, % 172.48/172.37 ! [V_b_2,V_a_2,V_S_2,T_a,T_b] : % 172.48/172.37 ( class_Groups_Ocomm__monoid__add(T_b) % 172.48/172.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 172.48/172.37 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) % 172.48/172.37 => 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) ) % 172.48/172.37 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_S_2)) % 172.48/172.37 => 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) ) ) ) ) ). % 172.48/172.37 % 172.48/172.37 fof(fact_Body__triple__valid__0,axiom, % 172.48/172.37 ! [V_Q_2,V_pn_2,V_P_2,T_a] : c_Hoare__Mirabelle_Otriple__valid(T_a,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(T_a),V_P_2),hAPP(c_Com_Ocom_OBODY,V_pn_2)),V_Q_2)) ). % 172.48/172.37 % 172.48/172.37 fof(fact_convex__bound__le,axiom, % 172.48/172.37 ! [V_v,V_u,V_y,V_a,V_x,T_a] : % 172.48/172.37 ( class_Rings_Olinordered__semiring__1(T_a) % 172.48/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 172.48/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_a)) % 172.48/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_u)) % 172.48/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_v)) % 172.48/172.37 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) = c_Groups_Oone__class_Oone(T_a) % 172.48/172.37 => 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)) ) ) ) ) ) ) ). % 172.48/172.37 % 172.48/172.37 fof(fact_card__gt__0__iff,axiom, % 172.48/172.37 ! [V_A_2,T_a] : % 172.48/172.37 ( 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))) % 172.48/172.37 <=> ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.37 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ) ). % 172.48/172.37 % 172.48/172.37 fof(fact_setsum_Oeq__fold,axiom, % 172.48/172.37 ! [V_g_2,V_A_2,T_a,T_b] : % 172.48/172.37 ( class_Groups_Ocomm__monoid__add(T_b) % 172.48/172.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.37 => 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) ) ) ). % 172.48/172.37 % 172.48/172.37 fof(fact_setsum_OF__eq,axiom, % 172.48/172.37 ! [V_g_2,V_A_2,T_a,T_b] : % 172.48/172.37 ( class_Groups_Ocomm__monoid__add(T_b) % 172.48/172.37 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.37 => 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) ) % 172.48/172.37 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.37 => 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) ) ) ) ). % 172.48/172.37 % 172.48/172.37 fof(fact_Suc__diff__1,axiom, % 172.48/172.37 ! [V_n] : % 172.48/172.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 172.48/172.37 => 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 ) ). % 172.48/172.37 % 172.48/172.37 fof(fact_Suc__pred_H,axiom, % 172.48/172.37 ! [V_n] : % 172.48/172.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 172.48/172.37 => 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))) ) ). % 172.48/172.37 % 172.48/172.37 fof(fact_add__eq__if,axiom, % 172.48/172.37 ! [V_n,V_m] : % 172.48/172.37 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 172.48/172.37 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_m),V_n) = V_n ) % 172.48/172.37 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 172.48/172.37 => 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)) ) ) ). % 172.48/172.37 % 172.48/172.37 fof(fact_mult__eq__if,axiom, % 172.48/172.37 ! [V_n,V_m] : % 172.48/172.37 ( ( V_m = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 172.48/172.37 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 172.48/172.37 & ( V_m != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 172.48/172.37 => 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)) ) ) ). % 172.48/172.37 % 172.48/172.37 fof(fact_setsum__restrict__set,axiom, % 172.48/172.37 ! [V_B_2,V_f_2,V_A_2,T_a,T_b] : % 172.48/172.37 ( class_Groups_Ocomm__monoid__add(T_b) % 172.48/172.37 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.37 => 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) ) ) ). % 172.48/172.37 % 172.48/172.37 fof(fact_card__def,axiom, % 172.48/172.37 ! [V_A_2,T_a] : % 172.48/172.37 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.37 => 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) ) % 172.48/172.37 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.37 => hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 172.48/172.37 % 172.48/172.37 fof(fact_card_Oeq__fold__g,axiom, % 172.48/172.37 ! [V_A_2,T_a] : % 172.48/172.37 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.37 => 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) ) ). % 172.48/172.37 % 172.48/172.37 fof(fact_convex__bound__lt,axiom, % 172.48/172.37 ! [V_v,V_u,V_y,V_a,V_x,T_a] : % 172.48/172.37 ( class_Rings_Olinordered__semiring__1__strict(T_a) % 172.48/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a)) % 172.48/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),V_a)) % 172.48/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_u)) % 172.48/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_v)) % 172.48/172.37 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_u),V_v) = c_Groups_Oone__class_Oone(T_a) % 172.48/172.37 => 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)) ) ) ) ) ) ) ). % 172.48/172.37 % 172.48/172.37 fof(fact_power__strict__mono,axiom, % 172.48/172.37 ! [V_n,V_b,V_a,T_a] : % 172.48/172.37 ( class_Rings_Olinordered__semidom(T_a) % 172.48/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 172.48/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 172.48/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 172.48/172.37 => 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))) ) ) ) ) ). % 172.48/172.37 % 172.48/172.37 fof(fact_one__less__power,axiom, % 172.48/172.37 ! [V_n,V_a,T_a] : % 172.48/172.37 ( class_Rings_Olinordered__semidom(T_a) % 172.48/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 172.48/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 172.48/172.37 => 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))) ) ) ) ). % 172.48/172.37 % 172.48/172.37 fof(fact_power__le__imp__le__exp,axiom, % 172.48/172.37 ! [V_n,V_m,V_a,T_a] : % 172.48/172.37 ( class_Rings_Olinordered__semidom(T_a) % 172.48/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 172.48/172.37 => ( 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))) % 172.48/172.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) ) ) ) ). % 172.48/172.37 % 172.48/172.37 fof(fact_power__increasing__iff,axiom, % 172.48/172.37 ! [V_y_2,V_x_2,V_b_2,T_a] : % 172.48/172.37 ( class_Rings_Olinordered__semidom(T_a) % 172.48/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_b_2)) % 172.48/172.37 => ( 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))) % 172.48/172.37 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x_2),V_y_2)) ) ) ) ). % 172.48/172.37 % 172.48/172.37 fof(fact_power__decreasing,axiom, % 172.48/172.37 ! [V_a,V_N,V_n,T_a] : % 172.48/172.37 ( class_Rings_Olinordered__semidom(T_a) % 172.48/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_N)) % 172.48/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 172.48/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Oone__class_Oone(T_a))) % 172.48/172.37 => 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))) ) ) ) ) ). % 172.48/172.37 % 172.48/172.37 fof(fact_power__strict__decreasing,axiom, % 172.48/172.37 ! [V_a,V_N,V_n,T_a] : % 172.48/172.37 ( class_Rings_Olinordered__semidom(T_a) % 172.48/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_N)) % 172.48/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 172.48/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a))) % 172.48/172.37 => 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))) ) ) ) ) ). % 172.48/172.37 % 172.48/172.37 fof(fact_power__Suc__less__one,axiom, % 172.48/172.37 ! [V_n,V_a,T_a] : % 172.48/172.37 ( class_Rings_Olinordered__semidom(T_a) % 172.48/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 172.48/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a))) % 172.48/172.37 => 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))) ) ) ) ). % 172.48/172.37 % 172.48/172.37 fof(fact_power__eq__imp__eq__base,axiom, % 172.48/172.37 ! [V_b,V_n,V_a,T_a] : % 172.48/172.37 ( class_Rings_Olinordered__semidom(T_a) % 172.48/172.37 => ( 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) % 172.48/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 172.48/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 172.48/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 172.48/172.37 => V_a = V_b ) ) ) ) ) ). % 172.48/172.37 % 172.48/172.37 fof(fact_field__power__not__zero,axiom, % 172.48/172.37 ! [V_n,V_a,T_a] : % 172.48/172.37 ( class_Rings_Oring__1__no__zero__divisors(T_a) % 172.48/172.37 => ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 172.48/172.37 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n) != c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 172.48/172.37 % 172.48/172.37 fof(fact_power__Suc__0,axiom, % 172.48/172.37 ! [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)) ). % 172.48/172.37 % 172.48/172.37 fof(fact_nat__power__eq__Suc__0__iff,axiom, % 172.48/172.37 ! [V_m_2,V_x_2] : % 172.48/172.37 ( 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)) % 172.48/172.37 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 172.48/172.37 | V_x_2 = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ). % 172.48/172.37 % 172.48/172.37 fof(fact_nat__zero__less__power__iff,axiom, % 172.48/172.37 ! [V_n_2,V_x_2] : % 172.48/172.37 ( 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))) % 172.48/172.37 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_x_2)) % 172.48/172.37 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 172.48/172.37 % 172.48/172.37 fof(fact_nat__power__less__imp__less,axiom, % 172.48/172.37 ! [V_n,V_m,V_i] : % 172.48/172.37 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_i)) % 172.48/172.37 => ( 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))) % 172.48/172.37 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ). % 172.48/172.37 % 172.48/172.37 fof(fact_power__commutes,axiom, % 172.48/172.37 ! [V_n,V_a,T_a] : % 172.48/172.37 ( class_Groups_Omonoid__mult(T_a) % 172.48/172.37 => 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)) ) ). % 172.48/172.37 % 172.48/172.37 fof(fact_power__mult__distrib,axiom, % 172.48/172.37 ! [V_n,V_b,V_a,T_a] : % 172.48/172.37 ( class_Groups_Ocomm__monoid__mult(T_a) % 172.48/172.37 => 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)) ) ). % 172.48/172.37 % 172.48/172.37 fof(fact_power__one,axiom, % 172.48/172.37 ! [V_n,T_a] : % 172.48/172.37 ( class_Groups_Omonoid__mult(T_a) % 172.48/172.37 => 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) ) ). % 172.48/172.37 % 172.48/172.37 fof(fact_power__mult,axiom, % 172.48/172.37 ! [V_n,V_m,V_a,T_a] : % 172.48/172.37 ( class_Groups_Omonoid__mult(T_a) % 172.48/172.37 => 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) ) ). % 172.48/172.37 % 172.48/172.37 fof(fact_power__one__right,axiom, % 172.48/172.37 ! [V_a,T_a] : % 172.48/172.37 ( class_Groups_Omonoid__mult(T_a) % 172.48/172.37 => hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = V_a ) ). % 172.48/172.37 % 172.48/172.37 fof(fact_zero__le__power,axiom, % 172.48/172.37 ! [V_n,V_a,T_a] : % 172.48/172.37 ( class_Rings_Olinordered__semidom(T_a) % 172.48/172.37 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 172.48/172.37 => 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))) ) ) ). % 172.48/172.37 % 172.48/172.37 fof(fact_power__mono,axiom, % 172.48/172.38 ! [V_n,V_b,V_a,T_a] : % 172.48/172.38 ( class_Rings_Olinordered__semidom(T_a) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 172.48/172.38 => 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))) ) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_zero__less__power,axiom, % 172.48/172.38 ! [V_n,V_a,T_a] : % 172.48/172.38 ( class_Rings_Olinordered__semidom(T_a) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 172.48/172.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a),V_n))) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_power__eq__0__iff,axiom, % 172.48/172.38 ! [V_n_2,V_a_2,T_a] : % 172.48/172.38 ( ( class_Power_Opower(T_a) % 172.48/172.38 & class_Rings_Omult__zero(T_a) % 172.48/172.38 & class_Rings_Ono__zero__divisors(T_a) % 172.48/172.38 & class_Rings_Ozero__neq__one(T_a) ) % 172.48/172.38 => ( hAPP(hAPP(c_Power_Opower__class_Opower(T_a),V_a_2),V_n_2) = c_Groups_Ozero__class_Ozero(T_a) % 172.48/172.38 <=> ( V_a_2 = c_Groups_Ozero__class_Ozero(T_a) % 172.48/172.38 & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_one__le__power,axiom, % 172.48/172.38 ! [V_n,V_a,T_a] : % 172.48/172.38 ( class_Rings_Olinordered__semidom(T_a) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 172.48/172.38 => 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))) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_power__0__Suc,axiom, % 172.48/172.38 ! [V_n,T_a] : % 172.48/172.38 ( ( class_Power_Opower(T_a) % 172.48/172.38 & class_Rings_Osemiring__0(T_a) ) % 172.48/172.38 => 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) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_power__inject__exp,axiom, % 172.48/172.38 ! [V_n_2,V_m_2,V_a_2,T_a] : % 172.48/172.38 ( class_Rings_Olinordered__semidom(T_a) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a_2)) % 172.48/172.38 => ( 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) % 172.48/172.38 <=> V_m_2 = V_n_2 ) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_power__Suc,axiom, % 172.48/172.38 ! [V_n,V_a,T_a] : % 172.48/172.38 ( class_Power_Opower(T_a) % 172.48/172.38 => 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)) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_power__Suc2,axiom, % 172.48/172.38 ! [V_n,V_a,T_a] : % 172.48/172.38 ( class_Groups_Omonoid__mult(T_a) % 172.48/172.38 => 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) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_nat__one__le__power,axiom, % 172.48/172.38 ! [V_n,V_i] : % 172.48/172.38 ( 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)) % 172.48/172.38 => 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))) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_power__0,axiom, % 172.48/172.38 ! [V_a,T_a] : % 172.48/172.38 ( class_Power_Opower(T_a) % 172.48/172.38 => 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) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_power__add,axiom, % 172.48/172.38 ! [V_n,V_m,V_a,T_a] : % 172.48/172.38 ( class_Groups_Omonoid__mult(T_a) % 172.48/172.38 => 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)) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_power__less__imp__less__base,axiom, % 172.48/172.38 ! [V_b,V_n,V_a,T_a] : % 172.48/172.38 ( class_Rings_Olinordered__semidom(T_a) % 172.48/172.38 => ( 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))) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 172.48/172.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) ) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_power__le__imp__le__base,axiom, % 172.48/172.38 ! [V_b,V_n,V_a,T_a] : % 172.48/172.38 ( class_Rings_Olinordered__semidom(T_a) % 172.48/172.38 => ( 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)))) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 172.48/172.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_power__inject__base,axiom, % 172.48/172.38 ! [V_b,V_n,V_a,T_a] : % 172.48/172.38 ( class_Rings_Olinordered__semidom(T_a) % 172.48/172.38 => ( 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)) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 172.48/172.38 => V_a = V_b ) ) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_power__gt1__lemma,axiom, % 172.48/172.38 ! [V_n,V_a,T_a] : % 172.48/172.38 ( class_Rings_Olinordered__semidom(T_a) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 172.48/172.38 => 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)))) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_power__less__power__Suc,axiom, % 172.48/172.38 ! [V_n,V_a,T_a] : % 172.48/172.38 ( class_Rings_Olinordered__semidom(T_a) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 172.48/172.38 => 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)))) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_power__0__left,axiom, % 172.48/172.38 ! [V_n,T_a] : % 172.48/172.38 ( ( class_Power_Opower(T_a) % 172.48/172.38 & class_Rings_Osemiring__0(T_a) ) % 172.48/172.38 => ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 172.48/172.38 => 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) ) % 172.48/172.38 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 172.48/172.38 => 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) ) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_power__gt1,axiom, % 172.48/172.38 ! [V_n,V_a,T_a] : % 172.48/172.38 ( class_Rings_Olinordered__semidom(T_a) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 172.48/172.38 => 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)))) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_power__strict__increasing,axiom, % 172.48/172.38 ! [V_a,V_N,V_n,T_a] : % 172.48/172.38 ( class_Rings_Olinordered__semidom(T_a) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n),V_N)) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 172.48/172.38 => 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))) ) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_power__less__imp__less__exp,axiom, % 172.48/172.38 ! [V_n,V_m,V_a,T_a] : % 172.48/172.38 ( class_Rings_Olinordered__semidom(T_a) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 172.48/172.38 => ( 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))) % 172.48/172.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_power__strict__increasing__iff,axiom, % 172.48/172.38 ! [V_y_2,V_x_2,V_b_2,T_a] : % 172.48/172.38 ( class_Rings_Olinordered__semidom(T_a) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Oone__class_Oone(T_a)),V_b_2)) % 172.48/172.38 => ( 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))) % 172.48/172.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_power__increasing,axiom, % 172.48/172.38 ! [V_a,V_N,V_n,T_a] : % 172.48/172.38 ( class_Rings_Olinordered__semidom(T_a) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_N)) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Oone__class_Oone(T_a)),V_a)) % 172.48/172.38 => 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))) ) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_power__Suc__less,axiom, % 172.48/172.38 ! [V_n,V_a,T_a] : % 172.48/172.38 ( class_Rings_Olinordered__semidom(T_a) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Oone__class_Oone(T_a))) % 172.48/172.38 => 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))) ) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_triple_Osize_I1_J,axiom, % 172.48/172.38 ! [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) ). % 172.48/172.38 % 172.48/172.38 fof(fact_even__less__0__iff,axiom, % 172.48/172.38 ! [V_a_2,T_a] : % 172.48/172.38 ( class_Rings_Olinordered__idom(T_a) % 172.48/172.38 => ( 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))) % 172.48/172.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_triple_Osize_I2_J,axiom, % 172.48/172.38 ! [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) ). % 172.48/172.38 % 172.48/172.38 fof(fact_card_Ounion__inter__neutral,axiom, % 172.48/172.38 ! [V_B_2,V_A_2,T_a] : % 172.48/172.38 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 172.48/172.38 => ( ( ? [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))) % 172.48/172.38 => c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 172.48/172.38 => 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)) ) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_setsum__mono2,axiom, % 172.48/172.38 ! [V_f_2,V_A_2,V_B_2,T_a,T_b] : % 172.48/172.38 ( class_Groups_Oordered__comm__monoid__add(T_b) % 172.48/172.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 172.48/172.38 => ( ! [B_b] : % 172.48/172.38 ( 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))) % 172.48/172.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(V_f_2,B_b))) ) % 172.48/172.38 => 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))) ) ) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_power__power__power,axiom, % 172.48/172.38 ! [T_a] : % 172.48/172.38 ( class_Power_Opower(T_a) % 172.48/172.38 => 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)) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_setsum__Un__zero,axiom, % 172.48/172.38 ! [V_f_2,V_T_2,V_S_2,T_a,T_b] : % 172.48/172.38 ( class_Groups_Ocomm__monoid__add(T_b) % 172.48/172.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 172.48/172.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2)) % 172.48/172.38 => ( ! [B_x] : % 172.48/172.38 ( 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))) % 172.48/172.38 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) ) % 172.48/172.38 => 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)) ) ) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_power_Opower_Opower__0,axiom, % 172.48/172.38 ! [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 ). % 172.48/172.38 % 172.48/172.38 fof(fact_power_Opower_Opower__Suc,axiom, % 172.48/172.38 ! [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)) ). % 172.48/172.38 % 172.48/172.38 fof(fact_zpower__zadd__distrib,axiom, % 172.48/172.38 ! [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)) ). % 172.48/172.38 % 172.48/172.38 fof(fact_zpower__zpower,axiom, % 172.48/172.38 ! [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)) ). % 172.48/172.38 % 172.48/172.38 fof(fact_double__eq__0__iff,axiom, % 172.48/172.38 ! [V_a_2,T_a] : % 172.48/172.38 ( class_Groups_Olinordered__ab__group__add(T_a) % 172.48/172.38 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_a) % 172.48/172.38 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_setsum_Ounion__inter__neutral,axiom, % 172.48/172.38 ! [V_g_2,V_B_2,V_A_2,T_a,T_b] : % 172.48/172.38 ( class_Groups_Ocomm__monoid__add(T_b) % 172.48/172.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 172.48/172.38 => ( ! [B_x] : % 172.48/172.38 ( 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))) % 172.48/172.38 => hAPP(V_g_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) ) % 172.48/172.38 => 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)) ) ) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_card__Suc__eq,axiom, % 172.48/172.38 ! [V_k_2,V_A_2,T_a] : % 172.48/172.38 ( hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = hAPP(c_Nat_OSuc,V_k_2) % 172.48/172.38 <=> ? [B_b,B_B] : % 172.48/172.38 ( V_A_2 = hAPP(hAPP(c_Set_Oinsert(T_a),B_b),B_B) % 172.48/172.38 & ~ hBOOL(hAPP(hAPP(c_member(T_a),B_b),B_B)) % 172.48/172.38 & hAPP(c_Finite__Set_Ocard(T_a),B_B) = V_k_2 % 172.48/172.38 & ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 172.48/172.38 => B_B = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_setsum__mono3,axiom, % 172.48/172.38 ! [V_f_2,V_A_2,V_B_2,T_a,T_b] : % 172.48/172.38 ( ( class_Groups_Ocomm__monoid__add(T_b) % 172.48/172.38 & class_Groups_Oordered__ab__semigroup__add(T_b) ) % 172.48/172.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 172.48/172.38 => ( ! [B_x] : % 172.48/172.38 ( 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))) % 172.48/172.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(V_f_2,B_x))) ) % 172.48/172.38 => 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))) ) ) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_setsum__reindex__nonzero,axiom, % 172.48/172.38 ! [T_b,V_h_2,V_f_2,V_S_2,T_a,T_c] : % 172.48/172.38 ( class_Groups_Ocomm__monoid__add(T_c) % 172.48/172.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 172.48/172.38 => ( ! [B_x] : % 172.48/172.38 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2)) % 172.48/172.38 => ! [B_y] : % 172.48/172.38 ( hBOOL(hAPP(hAPP(c_member(T_a),B_y),V_S_2)) % 172.48/172.38 => ( B_x != B_y % 172.48/172.38 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y) % 172.48/172.38 => hAPP(V_h_2,hAPP(V_f_2,B_x)) = c_Groups_Ozero__class_Ozero(T_c) ) ) ) ) % 172.48/172.38 => 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) ) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_Ints__odd__less__0,axiom, % 172.48/172.38 ! [V_a_2,T_a] : % 172.48/172.38 ( class_Rings_Olinordered__idom(T_a) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a))) % 172.48/172.38 => ( 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))) % 172.48/172.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_com_Osize_I4_J,axiom, % 172.48/172.38 ! [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))) ). % 172.48/172.38 % 172.48/172.38 fof(fact_com_Osize_I5_J,axiom, % 172.48/172.38 ! [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))) ). % 172.48/172.38 % 172.48/172.38 fof(fact_pos__zmult__eq__1__iff,axiom, % 172.48/172.38 ! [V_n_2,V_m_2] : % 172.48/172.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m_2)) % 172.48/172.38 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint) % 172.48/172.38 <=> ( V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) % 172.48/172.38 & V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_zmult__zless__mono2,axiom, % 172.48/172.38 ! [V_k,V_j,V_i] : % 172.48/172.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j)) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k)) % 172.48/172.38 => 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))) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_zmult__1,axiom, % 172.48/172.38 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z) = V_z ). % 172.48/172.38 % 172.48/172.38 fof(fact_zmult__1__right,axiom, % 172.48/172.38 ! [V_z] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_z),c_Groups_Oone__class_Oone(tc_Int_Oint)) = V_z ). % 172.48/172.38 % 172.48/172.38 fof(fact_zadd__zmult__distrib,axiom, % 172.48/172.38 ! [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)) ). % 172.48/172.38 % 172.48/172.38 fof(fact_zadd__zmult__distrib2,axiom, % 172.48/172.38 ! [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)) ). % 172.48/172.38 % 172.48/172.38 fof(fact_zmult__commute,axiom, % 172.48/172.38 ! [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) ). % 172.48/172.38 % 172.48/172.38 fof(fact_zmult__assoc,axiom, % 172.48/172.38 ! [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)) ). % 172.48/172.38 % 172.48/172.38 fof(fact_zdiff__zmult__distrib2,axiom, % 172.48/172.38 ! [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)) ). % 172.48/172.38 % 172.48/172.38 fof(fact_zdiff__zmult__distrib,axiom, % 172.48/172.38 ! [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)) ). % 172.48/172.38 % 172.48/172.38 fof(fact_Ints__0,axiom, % 172.48/172.38 ! [T_a] : % 172.48/172.38 ( class_Rings_Oring__1(T_a) % 172.48/172.38 => hBOOL(hAPP(hAPP(c_member(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Int_Oring__1__class_OInts(T_a))) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_Ints__add,axiom, % 172.48/172.38 ! [V_b_2,V_a_2,T_a] : % 172.48/172.38 ( class_Rings_Oring__1(T_a) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a))) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Int_Oring__1__class_OInts(T_a))) % 172.48/172.38 => 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))) ) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_Ints__mult,axiom, % 172.48/172.38 ! [V_b_2,V_a_2,T_a] : % 172.48/172.38 ( class_Rings_Oring__1(T_a) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a))) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Int_Oring__1__class_OInts(T_a))) % 172.48/172.38 => 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))) ) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_Ints__diff,axiom, % 172.48/172.38 ! [V_b_2,V_a_2,T_a] : % 172.48/172.38 ( class_Rings_Oring__1(T_a) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a))) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Int_Oring__1__class_OInts(T_a))) % 172.48/172.38 => 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))) ) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_Ints__1,axiom, % 172.48/172.38 ! [T_a] : % 172.48/172.38 ( class_Rings_Oring__1(T_a) % 172.48/172.38 => hBOOL(hAPP(hAPP(c_member(T_a),c_Groups_Oone__class_Oone(T_a)),c_Int_Oring__1__class_OInts(T_a))) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_Ints__power,axiom, % 172.48/172.38 ! [V_n_2,V_a_2,T_a] : % 172.48/172.38 ( class_Rings_Oring__1(T_a) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a))) % 172.48/172.38 => 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))) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_com_Osize_I7_J,axiom, % 172.48/172.38 ! [V_pname] : c_Com_Ocom_Ocom__size(hAPP(c_Com_Ocom_OBODY,V_pname)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 172.48/172.38 % 172.48/172.38 fof(fact_com_Osize_I1_J,axiom, % 172.48/172.38 c_Com_Ocom_Ocom__size(c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 172.48/172.38 % 172.48/172.38 fof(fact_Ints__double__eq__0__iff,axiom, % 172.48/172.38 ! [V_a_2,T_a] : % 172.48/172.38 ( class_Int_Oring__char__0(T_a) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a))) % 172.48/172.38 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_a_2) = c_Groups_Ozero__class_Ozero(T_a) % 172.48/172.38 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_Ints__odd__nonzero,axiom, % 172.48/172.38 ! [V_a_2,T_a] : % 172.48/172.38 ( class_Int_Oring__char__0(T_a) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a))) % 172.48/172.38 => 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) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_com_Osize_I6_J,axiom, % 172.48/172.38 ! [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))) ). % 172.48/172.38 % 172.48/172.38 fof(fact_com_Osize_I12_J,axiom, % 172.48/172.38 ! [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))) ). % 172.48/172.38 % 172.48/172.38 fof(fact_com_Osize_I13_J,axiom, % 172.48/172.38 ! [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))) ). % 172.48/172.38 % 172.48/172.38 fof(fact_setprod__diff1,axiom, % 172.48/172.38 ! [V_a_2,V_f_2,V_A_2,T_a,T_b] : % 172.48/172.38 ( class_Fields_Ofield(T_b) % 172.48/172.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.38 => ( hAPP(V_f_2,V_a_2) != c_Groups_Ozero__class_Ozero(T_b) % 172.48/172.38 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 172.48/172.38 => 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)) ) % 172.48/172.38 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 172.48/172.38 => 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) ) ) ) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_com_Osize_I14_J,axiom, % 172.48/172.38 ! [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))) ). % 172.48/172.38 % 172.48/172.38 fof(fact_setsum__nonneg__0,axiom, % 172.48/172.38 ! [V_i_2,V_f_2,V_s_2,T_a,T_b] : % 172.48/172.38 ( class_Groups_Oordered__ab__group__add(T_b) % 172.48/172.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_s_2)) % 172.48/172.38 => ( ! [B_i] : % 172.48/172.38 ( hBOOL(hAPP(hAPP(c_member(T_a),B_i),V_s_2)) % 172.48/172.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(V_f_2,B_i))) ) % 172.48/172.38 => ( 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) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),V_s_2)) % 172.48/172.38 => hAPP(V_f_2,V_i_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_setsum__nonneg__leq__bound,axiom, % 172.48/172.38 ! [V_i_2,V_B_2,V_f_2,V_s_2,T_a,T_b] : % 172.48/172.38 ( class_Groups_Oordered__ab__group__add(T_b) % 172.48/172.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_s_2)) % 172.48/172.38 => ( ! [B_i] : % 172.48/172.38 ( hBOOL(hAPP(hAPP(c_member(T_a),B_i),V_s_2)) % 172.48/172.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(V_f_2,B_i))) ) % 172.48/172.38 => ( hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),V_s_2) = V_B_2 % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),V_s_2)) % 172.48/172.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,V_i_2)),V_B_2)) ) ) ) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_ex__least__nat__less,axiom, % 172.48/172.38 ! [V_n_2,V_P_2] : % 172.48/172.38 ( ~ hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) % 172.48/172.38 => ( hBOOL(hAPP(V_P_2,V_n_2)) % 172.48/172.38 => ? [B_k] : % 172.48/172.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_k),V_n_2)) % 172.48/172.38 & ! [B_i] : % 172.48/172.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_k)) % 172.48/172.38 => ~ hBOOL(hAPP(V_P_2,B_i)) ) % 172.48/172.38 & 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)))) ) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_zadd__left__mono,axiom, % 172.48/172.38 ! [V_k,V_j,V_i] : % 172.48/172.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j)) % 172.48/172.38 => 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))) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_zless__le,axiom, % 172.48/172.38 ! [V_w_2,V_z_2] : % 172.48/172.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),V_w_2)) % 172.48/172.38 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_2),V_w_2)) % 172.48/172.38 & V_z_2 != V_w_2 ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_zle__add1__eq__le,axiom, % 172.48/172.38 ! [V_z_2,V_w_2] : % 172.48/172.38 ( 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)))) % 172.48/172.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_add1__zle__eq,axiom, % 172.48/172.38 ! [V_z_2,V_w_2] : % 172.48/172.38 ( 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)) % 172.48/172.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_zless__imp__add1__zle,axiom, % 172.48/172.38 ! [V_z,V_w] : % 172.48/172.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w),V_z)) % 172.48/172.38 => 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)) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_zadd__zless__mono,axiom, % 172.48/172.38 ! [V_z,V_z_H,V_w,V_w_H] : % 172.48/172.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_H),V_w)) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_H),V_z)) % 172.48/172.38 => 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))) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_zle__diff1__eq,axiom, % 172.48/172.38 ! [V_z_2,V_w_2] : % 172.48/172.38 ( 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)))) % 172.48/172.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_zadd__strict__right__mono,axiom, % 172.48/172.38 ! [V_k,V_j,V_i] : % 172.48/172.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j)) % 172.48/172.38 => 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))) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_zless__add1__eq,axiom, % 172.48/172.38 ! [V_z_2,V_w_2] : % 172.48/172.38 ( 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)))) % 172.48/172.38 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) % 172.48/172.38 | V_w_2 = V_z_2 ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_zless__linear,axiom, % 172.48/172.38 ! [V_y,V_x] : % 172.48/172.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x),V_y)) % 172.48/172.38 | V_x = V_y % 172.48/172.38 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_y),V_x)) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_zadd__assoc,axiom, % 172.48/172.38 ! [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)) ). % 172.48/172.38 % 172.48/172.38 fof(fact_zadd__left__commute,axiom, % 172.48/172.38 ! [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)) ). % 172.48/172.38 % 172.48/172.38 fof(fact_zadd__commute,axiom, % 172.48/172.38 ! [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) ). % 172.48/172.38 % 172.48/172.38 fof(fact_int__0__neq__1,axiom, % 172.48/172.38 c_Groups_Ozero__class_Ozero(tc_Int_Oint) != c_Groups_Oone__class_Oone(tc_Int_Oint) ). % 172.48/172.38 % 172.48/172.38 fof(fact_zadd__0__right,axiom, % 172.48/172.38 ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_z ). % 172.48/172.38 % 172.48/172.38 fof(fact_zadd__0,axiom, % 172.48/172.38 ! [V_z] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z) = V_z ). % 172.48/172.38 % 172.48/172.38 fof(fact_odd__nonzero,axiom, % 172.48/172.38 ! [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) ). % 172.48/172.38 % 172.48/172.38 fof(fact_int__0__less__1,axiom, % 172.48/172.38 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))) ). % 172.48/172.38 % 172.48/172.38 fof(fact_odd__less__0,axiom, % 172.48/172.38 ! [V_z_2] : % 172.48/172.38 ( 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))) % 172.48/172.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_less__bin__lemma,axiom, % 172.48/172.38 ! [V_l_2,V_k_2] : % 172.48/172.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) % 172.48/172.38 <=> 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))) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_le__imp__0__less,axiom, % 172.48/172.38 ! [V_z] : % 172.48/172.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 172.48/172.38 => 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))) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_int__one__le__iff__zero__less,axiom, % 172.48/172.38 ! [V_z_2] : % 172.48/172.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)) % 172.48/172.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_divide__zero,axiom, % 172.48/172.38 ! [V_a,T_a] : % 172.48/172.38 ( class_Rings_Odivision__ring__inverse__zero(T_a) % 172.48/172.38 => 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) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_divide__zero__left,axiom, % 172.48/172.38 ! [V_a,T_a] : % 172.48/172.38 ( class_Rings_Odivision__ring(T_a) % 172.48/172.38 => 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) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_add__divide__distrib,axiom, % 172.48/172.38 ! [V_c,V_b,V_a,T_a] : % 172.48/172.38 ( class_Rings_Odivision__ring(T_a) % 172.48/172.38 => 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)) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_times__divide__eq__right,axiom, % 172.48/172.38 ! [V_c,V_b,V_a,T_a] : % 172.48/172.38 ( class_Rings_Odivision__ring(T_a) % 172.48/172.38 => 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) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_diff__divide__distrib,axiom, % 172.48/172.38 ! [V_c,V_b,V_a,T_a] : % 172.48/172.38 ( class_Rings_Odivision__ring(T_a) % 172.48/172.38 => 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)) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_divide__1,axiom, % 172.48/172.38 ! [V_a,T_a] : % 172.48/172.38 ( class_Rings_Odivision__ring(T_a) % 172.48/172.38 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_power__divide,axiom, % 172.48/172.38 ! [V_n,V_b,V_a,T_a] : % 172.48/172.38 ( class_Fields_Ofield__inverse__zero(T_a) % 172.48/172.38 => 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)) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_setsum__divide__distrib,axiom, % 172.48/172.38 ! [V_r_2,V_A_2,V_f_2,T_b,T_a] : % 172.48/172.38 ( class_Fields_Ofield(T_a) % 172.48/172.38 => 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) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_eq__divide__imp,axiom, % 172.48/172.38 ! [V_b,V_a,V_c,T_a] : % 172.48/172.38 ( class_Rings_Odivision__ring(T_a) % 172.48/172.38 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 172.48/172.38 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c) = V_b % 172.48/172.38 => V_a = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c) ) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_divide__eq__imp,axiom, % 172.48/172.38 ! [V_a,V_b,V_c,T_a] : % 172.48/172.38 ( class_Rings_Odivision__ring(T_a) % 172.48/172.38 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 172.48/172.38 => ( V_b = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a),V_c) % 172.48/172.38 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b),V_c) = V_a ) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_nonzero__divide__eq__eq,axiom, % 172.48/172.38 ! [V_a_2,V_b_2,V_ca_2,T_a] : % 172.48/172.38 ( class_Rings_Odivision__ring(T_a) % 172.48/172.38 => ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_a) % 172.48/172.38 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2) = V_a_2 % 172.48/172.38 <=> V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2) ) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_nonzero__eq__divide__eq,axiom, % 172.48/172.38 ! [V_b_2,V_a_2,V_ca_2,T_a] : % 172.48/172.38 ( class_Rings_Odivision__ring(T_a) % 172.48/172.38 => ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_a) % 172.48/172.38 => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2) % 172.48/172.38 <=> hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2) = V_b_2 ) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_divide__self__if,axiom, % 172.48/172.38 ! [V_a,T_a] : % 172.48/172.38 ( class_Rings_Odivision__ring__inverse__zero(T_a) % 172.48/172.38 => ( ( V_a = c_Groups_Ozero__class_Ozero(T_a) % 172.48/172.38 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) % 172.48/172.38 & ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 172.48/172.38 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_divide__self,axiom, % 172.48/172.38 ! [V_a,T_a] : % 172.48/172.38 ( class_Rings_Odivision__ring(T_a) % 172.48/172.38 => ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 172.48/172.38 => hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_right__inverse__eq,axiom, % 172.48/172.38 ! [V_a_2,V_b_2,T_a] : % 172.48/172.38 ( class_Rings_Odivision__ring(T_a) % 172.48/172.38 => ( V_b_2 != c_Groups_Ozero__class_Ozero(T_a) % 172.48/172.38 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a_2),V_b_2) = c_Groups_Oone__class_Oone(T_a) % 172.48/172.38 <=> V_a_2 = V_b_2 ) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_nonzero__power__divide,axiom, % 172.48/172.38 ! [V_n,V_a,V_b,T_a] : % 172.48/172.38 ( class_Fields_Ofield(T_a) % 172.48/172.38 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 172.48/172.38 => 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)) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_power__one__over,axiom, % 172.48/172.38 ! [V_n,V_a,T_a] : % 172.48/172.38 ( class_Fields_Ofield__inverse__zero(T_a) % 172.48/172.38 => 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) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_setprod__dividef,axiom, % 172.48/172.38 ! [V_g_2,V_f_2,V_A_2,T_a,T_b] : % 172.48/172.38 ( class_Fields_Ofield__inverse__zero(T_b) % 172.48/172.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.38 => 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)) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_com_Osize_I15_J,axiom, % 172.48/172.38 ! [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) ). % 172.48/172.38 % 172.48/172.38 fof(fact_com_Osize_I9_J,axiom, % 172.48/172.38 hAPP(c_Nat_Osize__class_Osize(tc_Com_Ocom),c_Com_Ocom_OSKIP) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 172.48/172.38 % 172.48/172.38 fof(fact_power__diff,axiom, % 172.48/172.38 ! [V_m,V_n,V_a,T_a] : % 172.48/172.38 ( class_Fields_Ofield(T_a) % 172.48/172.38 => ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 172.48/172.38 => 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)) ) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_self__quotient__aux1,axiom, % 172.48/172.38 ! [V_q,V_r,V_a] : % 172.48/172.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 172.48/172.38 => ( 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)) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_a)) % 172.48/172.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_q)) ) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_self__quotient__aux2,axiom, % 172.48/172.38 ! [V_q,V_r,V_a] : % 172.48/172.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 172.48/172.38 => ( 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)) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) % 172.48/172.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_le__divide__eq,axiom, % 172.48/172.38 ! [V_ca_2,V_b_2,V_a_2,T_a] : % 172.48/172.38 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2))) % 172.48/172.38 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 172.48/172.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2)),V_b_2)) ) % 172.48/172.38 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 172.48/172.38 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 172.48/172.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2))) ) % 172.48/172.38 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 172.48/172.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_divide__le__eq,axiom, % 172.48/172.38 ! [V_a_2,V_ca_2,V_b_2,T_a] : % 172.48/172.38 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2)),V_a_2)) % 172.48/172.38 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 172.48/172.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2))) ) % 172.48/172.38 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 172.48/172.38 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 172.48/172.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2)),V_b_2)) ) % 172.48/172.38 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 172.48/172.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ) ) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_pos__le__divide__eq,axiom, % 172.48/172.38 ! [V_b_2,V_a_2,V_ca_2,T_a] : % 172.48/172.38 ( class_Fields_Olinordered__field(T_a) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2))) % 172.48/172.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2)),V_b_2)) ) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_pos__divide__le__eq,axiom, % 172.48/172.38 ! [V_a_2,V_b_2,V_ca_2,T_a] : % 172.48/172.38 ( class_Fields_Olinordered__field(T_a) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2)),V_a_2)) % 172.48/172.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2))) ) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_mult__imp__div__pos__le,axiom, % 172.48/172.38 ! [V_z,V_x,V_y,T_a] : % 172.48/172.38 ( class_Fields_Olinordered__field(T_a) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 172.48/172.38 => ( 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))) % 172.48/172.38 => 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)) ) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_zle__refl,axiom, % 172.48/172.38 ! [V_w] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_w)) ). % 172.48/172.38 % 172.48/172.38 fof(fact_zle__linear,axiom, % 172.48/172.38 ! [V_w,V_z] : % 172.48/172.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_w)) % 172.48/172.38 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_z)) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_zle__trans,axiom, % 172.48/172.38 ! [V_k,V_j,V_i] : % 172.48/172.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j)) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_j),V_k)) % 172.48/172.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_k)) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_zle__antisym,axiom, % 172.48/172.38 ! [V_w,V_z] : % 172.48/172.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),V_w)) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w),V_z)) % 172.48/172.38 => V_z = V_w ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_times__divide__times__eq,axiom, % 172.48/172.38 ! [V_w,V_z,V_y,V_x,T_a] : % 172.48/172.38 ( class_Fields_Ofield__inverse__zero(T_a) % 172.48/172.38 => 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)) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_zero__le__divide__iff,axiom, % 172.48/172.38 ! [V_b_2,V_a_2,T_a] : % 172.48/172.38 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 172.48/172.38 => ( 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))) % 172.48/172.38 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) % 172.48/172.38 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b_2)) ) % 172.48/172.38 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) % 172.48/172.38 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_divide__le__0__iff,axiom, % 172.48/172.38 ! [V_b_2,V_a_2,T_a] : % 172.48/172.38 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 172.48/172.38 => ( 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))) % 172.48/172.38 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) % 172.48/172.38 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),c_Groups_Ozero__class_Ozero(T_a))) ) % 172.48/172.38 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) % 172.48/172.38 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b_2)) ) ) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_divide__right__mono,axiom, % 172.48/172.38 ! [V_c,V_b,V_a,T_a] : % 172.48/172.38 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 172.48/172.38 => 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))) ) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_divide__right__mono__neg,axiom, % 172.48/172.38 ! [V_c,V_b,V_a,T_a] : % 172.48/172.38 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 172.48/172.38 => 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))) ) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_zero__less__divide__iff,axiom, % 172.48/172.38 ! [V_b_2,V_a_2,T_a] : % 172.48/172.38 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_a_2),V_b_2))) % 172.48/172.38 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) % 172.48/172.38 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b_2)) ) % 172.48/172.38 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) % 172.48/172.38 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_divide__less__0__iff,axiom, % 172.48/172.38 ! [V_b_2,V_a_2,T_a] : % 172.48/172.38 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 172.48/172.38 => ( 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))) % 172.48/172.38 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) % 172.48/172.38 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),c_Groups_Ozero__class_Ozero(T_a))) ) % 172.48/172.38 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) % 172.48/172.38 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b_2)) ) ) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_divide__pos__pos,axiom, % 172.48/172.38 ! [V_y,V_x,T_a] : % 172.48/172.38 ( class_Fields_Olinordered__field(T_a) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 172.48/172.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y))) ) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_divide__pos__neg,axiom, % 172.48/172.38 ! [V_y,V_x,T_a] : % 172.48/172.38 ( class_Fields_Olinordered__field(T_a) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a))) % 172.48/172.38 => 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))) ) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_divide__neg__pos,axiom, % 172.48/172.38 ! [V_y,V_x,T_a] : % 172.48/172.38 ( class_Fields_Olinordered__field(T_a) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a))) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 172.48/172.38 => 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))) ) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_divide__neg__neg,axiom, % 172.48/172.38 ! [V_y,V_x,T_a] : % 172.48/172.38 ( class_Fields_Olinordered__field(T_a) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a))) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a))) % 172.48/172.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_x),V_y))) ) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_divide__strict__right__mono,axiom, % 172.48/172.38 ! [V_c,V_b,V_a,T_a] : % 172.48/172.38 ( class_Fields_Olinordered__field(T_a) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 172.48/172.38 => 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))) ) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_divide__strict__right__mono__neg,axiom, % 172.48/172.38 ! [V_c,V_a,V_b,T_a] : % 172.48/172.38 ( class_Fields_Olinordered__field(T_a) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 172.48/172.38 => 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))) ) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_frac__eq__eq,axiom, % 172.48/172.38 ! [V_w_2,V_x_2,V_z_2,V_y_2,T_a] : % 172.48/172.38 ( class_Fields_Ofield(T_a) % 172.48/172.38 => ( V_y_2 != c_Groups_Ozero__class_Ozero(T_a) % 172.48/172.38 => ( V_z_2 != c_Groups_Ozero__class_Ozero(T_a) % 172.48/172.38 => ( 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) % 172.48/172.38 <=> 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) ) ) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_mult__divide__mult__cancel__left,axiom, % 172.48/172.38 ! [V_b,V_a,V_c,T_a] : % 172.48/172.38 ( class_Fields_Ofield__inverse__zero(T_a) % 172.48/172.38 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 172.48/172.38 => 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) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_mult__divide__mult__cancel__right,axiom, % 172.48/172.38 ! [V_b,V_a,V_c,T_a] : % 172.48/172.38 ( class_Fields_Ofield__inverse__zero(T_a) % 172.48/172.38 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 172.48/172.38 => 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) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_divide__eq__eq,axiom, % 172.48/172.38 ! [V_a_2,V_ca_2,V_b_2,T_a] : % 172.48/172.38 ( class_Fields_Ofield__inverse__zero(T_a) % 172.48/172.38 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2) = V_a_2 % 172.48/172.38 <=> ( ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_a) % 172.48/172.38 => V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2) ) % 172.48/172.38 & ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_a) % 172.48/172.38 => V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_eq__divide__eq,axiom, % 172.48/172.38 ! [V_ca_2,V_b_2,V_a_2,T_a] : % 172.48/172.38 ( class_Fields_Ofield__inverse__zero(T_a) % 172.48/172.38 => ( V_a_2 = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2) % 172.48/172.38 <=> ( ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_a) % 172.48/172.38 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2) = V_b_2 ) % 172.48/172.38 & ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_a) % 172.48/172.38 => V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_divide__nonneg__pos,axiom, % 172.48/172.38 ! [V_y,V_x,T_a] : % 172.48/172.38 ( class_Fields_Olinordered__field(T_a) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 172.48/172.38 => 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))) ) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_divide__nonneg__neg,axiom, % 172.48/172.38 ! [V_y,V_x,T_a] : % 172.48/172.38 ( class_Fields_Olinordered__field(T_a) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a))) % 172.48/172.38 => 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))) ) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_frac__less2,axiom, % 172.48/172.38 ! [V_z,V_w,V_y,V_x,T_a] : % 172.48/172.38 ( class_Fields_Olinordered__field(T_a) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w)) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_w),V_z)) % 172.48/172.38 => 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))) ) ) ) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_frac__less,axiom, % 172.48/172.38 ! [V_z,V_w,V_y,V_x,T_a] : % 172.48/172.38 ( class_Fields_Olinordered__field(T_a) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w)) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_w),V_z)) % 172.48/172.38 => 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))) ) ) ) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_frac__le,axiom, % 172.48/172.38 ! [V_z,V_w,V_y,V_x,T_a] : % 172.48/172.38 ( class_Fields_Olinordered__field(T_a) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_w)) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_w),V_z)) % 172.48/172.38 => 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))) ) ) ) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_divide__nonpos__pos,axiom, % 172.48/172.38 ! [V_y,V_x,T_a] : % 172.48/172.38 ( class_Fields_Olinordered__field(T_a) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a))) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 172.48/172.38 => 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))) ) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_divide__nonpos__neg,axiom, % 172.48/172.38 ! [V_y,V_x,T_a] : % 172.48/172.38 ( class_Fields_Olinordered__field(T_a) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Groups_Ozero__class_Ozero(T_a))) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y),c_Groups_Ozero__class_Ozero(T_a))) % 172.48/172.38 => 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))) ) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_less__divide__eq,axiom, % 172.48/172.38 ! [V_ca_2,V_b_2,V_a_2,T_a] : % 172.48/172.38 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2))) % 172.48/172.38 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 172.48/172.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2)),V_b_2)) ) % 172.48/172.38 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 172.48/172.38 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 172.48/172.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2))) ) % 172.48/172.38 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 172.48/172.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_divide__less__eq,axiom, % 172.48/172.38 ! [V_a_2,V_ca_2,V_b_2,T_a] : % 172.48/172.38 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2)),V_a_2)) % 172.48/172.38 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 172.48/172.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2))) ) % 172.48/172.38 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 172.48/172.38 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 172.48/172.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2)),V_b_2)) ) % 172.48/172.38 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 172.48/172.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ) ) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_pos__less__divide__eq,axiom, % 172.48/172.38 ! [V_b_2,V_a_2,V_ca_2,T_a] : % 172.48/172.38 ( class_Fields_Olinordered__field(T_a) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2))) % 172.48/172.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2)),V_b_2)) ) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_pos__divide__less__eq,axiom, % 172.48/172.38 ! [V_a_2,V_b_2,V_ca_2,T_a] : % 172.48/172.38 ( class_Fields_Olinordered__field(T_a) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2)),V_a_2)) % 172.48/172.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2))) ) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_mult__imp__div__pos__less,axiom, % 172.48/172.38 ! [V_z,V_x,V_y,T_a] : % 172.48/172.38 ( class_Fields_Olinordered__field(T_a) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 172.48/172.38 => ( 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))) % 172.48/172.38 => 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)) ) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_mult__imp__less__div__pos,axiom, % 172.48/172.38 ! [V_x,V_z,V_y,T_a] : % 172.48/172.38 ( class_Fields_Olinordered__field(T_a) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 172.48/172.38 => ( 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)) % 172.48/172.38 => 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))) ) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_neg__less__divide__eq,axiom, % 172.48/172.38 ! [V_b_2,V_a_2,V_ca_2,T_a] : % 172.48/172.38 ( class_Fields_Olinordered__field(T_a) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2))) % 172.48/172.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2))) ) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_neg__divide__less__eq,axiom, % 172.48/172.38 ! [V_a_2,V_b_2,V_ca_2,T_a] : % 172.48/172.38 ( class_Fields_Olinordered__field(T_a) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2)),V_a_2)) % 172.48/172.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2)),V_b_2)) ) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_divide__strict__left__mono,axiom, % 172.48/172.38 ! [V_c,V_a,V_b,T_a] : % 172.48/172.38 ( class_Fields_Olinordered__field(T_a) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_a)) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 172.48/172.38 => ( 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))) % 172.48/172.38 => 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))) ) ) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_divide__strict__left__mono__neg,axiom, % 172.48/172.38 ! [V_c,V_b,V_a,T_a] : % 172.48/172.38 ( class_Fields_Olinordered__field(T_a) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 172.48/172.38 => ( 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))) % 172.48/172.38 => 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))) ) ) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_add__num__frac,axiom, % 172.48/172.38 ! [V_x,V_z,V_y,T_a] : % 172.48/172.38 ( class_Fields_Ofield__inverse__zero(T_a) % 172.48/172.38 => ( V_y != c_Groups_Ozero__class_Ozero(T_a) % 172.48/172.38 => 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) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_add__divide__eq__iff,axiom, % 172.48/172.38 ! [V_y,V_x,V_z,T_a] : % 172.48/172.38 ( class_Fields_Ofield(T_a) % 172.48/172.38 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 172.48/172.38 => 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) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_add__frac__num,axiom, % 172.48/172.38 ! [V_z,V_x,V_y,T_a] : % 172.48/172.38 ( class_Fields_Ofield__inverse__zero(T_a) % 172.48/172.38 => ( V_y != c_Groups_Ozero__class_Ozero(T_a) % 172.48/172.38 => 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) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_divide__add__eq__iff,axiom, % 172.48/172.38 ! [V_y,V_x,V_z,T_a] : % 172.48/172.38 ( class_Fields_Ofield(T_a) % 172.48/172.38 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 172.48/172.38 => 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) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_add__frac__eq,axiom, % 172.48/172.38 ! [V_w,V_x,V_z,V_y,T_a] : % 172.48/172.38 ( class_Fields_Ofield(T_a) % 172.48/172.38 => ( V_y != c_Groups_Ozero__class_Ozero(T_a) % 172.48/172.38 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 172.48/172.38 => 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)) ) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_diff__divide__eq__iff,axiom, % 172.48/172.38 ! [V_y,V_x,V_z,T_a] : % 172.48/172.38 ( class_Fields_Ofield(T_a) % 172.48/172.38 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 172.48/172.38 => 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) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_divide__diff__eq__iff,axiom, % 172.48/172.38 ! [V_y,V_x,V_z,T_a] : % 172.48/172.38 ( class_Fields_Ofield(T_a) % 172.48/172.38 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 172.48/172.38 => 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) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_diff__frac__eq,axiom, % 172.48/172.38 ! [V_w,V_x,V_z,V_y,T_a] : % 172.48/172.38 ( class_Fields_Ofield(T_a) % 172.48/172.38 => ( V_y != c_Groups_Ozero__class_Ozero(T_a) % 172.48/172.38 => ( V_z != c_Groups_Ozero__class_Ozero(T_a) % 172.48/172.38 => 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)) ) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_gt__half__sum,axiom, % 172.48/172.38 ! [V_b,V_a,T_a] : % 172.48/172.38 ( class_Fields_Olinordered__field(T_a) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 172.48/172.38 => 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)) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_less__half__sum,axiom, % 172.48/172.38 ! [V_b,V_a,T_a] : % 172.48/172.38 ( class_Fields_Olinordered__field(T_a) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_b)) % 172.48/172.38 => 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))))) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_q__pos__lemma,axiom, % 172.48/172.38 ! [V_r_H,V_q_H,V_b_H] : % 172.48/172.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H))) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b_H)) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 172.48/172.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_q_H)) ) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_q__neg__lemma,axiom, % 172.48/172.38 ! [V_r_H,V_q_H,V_b_H] : % 172.48/172.38 ( 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))) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H)) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 172.48/172.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_unique__quotient__lemma,axiom, % 172.48/172.38 ! [V_r,V_q,V_r_H,V_q_H,V_b] : % 172.48/172.38 ( 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))) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H)) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b)) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) % 172.48/172.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),V_q)) ) ) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_zdiv__mono2__lemma,axiom, % 172.48/172.38 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] : % 172.48/172.38 ( 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) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_b_H),V_q_H)),V_r_H))) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_H),V_b_H)) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b)) % 172.48/172.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),V_q_H)) ) ) ) ) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_unique__quotient__lemma__neg,axiom, % 172.48/172.38 ! [V_r,V_q,V_r_H,V_q_H,V_b] : % 172.48/172.38 ( 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))) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r)) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r_H)) % 172.48/172.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q),V_q_H)) ) ) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_zdiv__mono2__neg__lemma,axiom, % 172.48/172.38 ! [V_r_H,V_q_H,V_b_H,V_r,V_q,V_b] : % 172.48/172.38 ( 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) % 172.48/172.38 => ( 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))) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_H)) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b)) % 172.48/172.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_q_H),V_q)) ) ) ) ) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_divide__left__mono__neg,axiom, % 172.48/172.38 ! [V_c,V_b,V_a,T_a] : % 172.48/172.38 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_c),c_Groups_Ozero__class_Ozero(T_a))) % 172.48/172.38 => ( 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))) % 172.48/172.38 => 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))) ) ) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_divide__left__mono,axiom, % 172.48/172.38 ! [V_c,V_a,V_b,T_a] : % 172.48/172.38 ( class_Fields_Olinordered__field(T_a) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_a)) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_c)) % 172.48/172.38 => ( 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))) % 172.48/172.38 => 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))) ) ) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_neg__divide__le__eq,axiom, % 172.48/172.38 ! [V_a_2,V_b_2,V_ca_2,T_a] : % 172.48/172.38 ( class_Fields_Olinordered__field(T_a) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2)),V_a_2)) % 172.48/172.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2)),V_b_2)) ) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_neg__le__divide__eq,axiom, % 172.48/172.38 ! [V_b_2,V_a_2,V_ca_2,T_a] : % 172.48/172.38 ( class_Fields_Olinordered__field(T_a) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2))) % 172.48/172.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_a_2),V_ca_2))) ) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_mult__imp__le__div__pos,axiom, % 172.48/172.38 ! [V_x,V_z,V_y,T_a] : % 172.48/172.38 ( class_Fields_Olinordered__field(T_a) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 172.48/172.38 => ( 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)) % 172.48/172.38 => 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))) ) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J,axiom, % 172.48/172.38 ! [V_n,V_x] : % 172.48/172.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 172.48/172.38 => 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))) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J,axiom, % 172.48/172.38 ! [V_y,V_x] : % 172.48/172.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 172.48/172.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y))) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I6_J,axiom, % 172.48/172.38 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))) ). % 172.48/172.38 % 172.48/172.38 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J,axiom, % 172.48/172.38 ! [V_y,V_x] : % 172.48/172.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 172.48/172.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_y))) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_setprod__Un,axiom, % 172.48/172.38 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] : % 172.48/172.38 ( class_Fields_Ofield(T_b) % 172.48/172.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 172.48/172.38 => ( ! [B_x] : % 172.48/172.38 ( 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))) % 172.48/172.38 => hAPP(V_f_2,B_x) != c_Groups_Ozero__class_Ozero(T_b) ) % 172.48/172.38 => 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))) ) ) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I5_J,axiom, % 172.48/172.38 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))) ). % 172.48/172.38 % 172.48/172.38 fof(fact_int__power__div__base,axiom, % 172.48/172.38 ! [V_k,V_m] : % 172.48/172.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k)) % 172.48/172.38 => 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)))) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_zdiv__zero,axiom, % 172.48/172.38 ! [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) ). % 172.48/172.38 % 172.48/172.38 fof(fact_div__by__0,axiom, % 172.48/172.38 ! [V_a,T_a] : % 172.48/172.38 ( class_Divides_Osemiring__div(T_a) % 172.48/172.38 => 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) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_div__0,axiom, % 172.48/172.38 ! [V_a,T_a] : % 172.48/172.38 ( class_Divides_Osemiring__div(T_a) % 172.48/172.38 => 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) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_div__by__1,axiom, % 172.48/172.38 ! [V_a,T_a] : % 172.48/172.38 ( class_Divides_Osemiring__div(T_a) % 172.48/172.38 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),c_Groups_Oone__class_Oone(T_a)) = V_a ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_Divides_Otransfer__nat__int__function__closures_I1_J,axiom, % 172.48/172.38 ! [V_y,V_x] : % 172.48/172.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 172.48/172.38 => 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))) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_div__neg__pos__less0,axiom, % 172.48/172.38 ! [V_b,V_a] : % 172.48/172.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 172.48/172.38 => 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))) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_neg__imp__zdiv__neg__iff,axiom, % 172.48/172.38 ! [V_a_2,V_b_2] : % 172.48/172.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 172.48/172.38 => ( 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))) % 172.48/172.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_pos__imp__zdiv__neg__iff,axiom, % 172.48/172.38 ! [V_a_2,V_b_2] : % 172.48/172.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2)) % 172.48/172.38 => ( 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))) % 172.48/172.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_zdiv__self,axiom, % 172.48/172.38 ! [V_a] : % 172.48/172.38 ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 172.48/172.38 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_a) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_div__mult__mult1__if,axiom, % 172.48/172.38 ! [V_b,V_a,V_c,T_a] : % 172.48/172.38 ( class_Divides_Osemiring__div(T_a) % 172.48/172.38 => ( ( V_c = c_Groups_Ozero__class_Ozero(T_a) % 172.48/172.38 => 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) ) % 172.48/172.38 & ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 172.48/172.38 => 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) ) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_div__mult__self2__is__id,axiom, % 172.48/172.38 ! [V_a,V_b,T_a] : % 172.48/172.38 ( class_Divides_Osemiring__div(T_a) % 172.48/172.38 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 172.48/172.38 => 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 ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_div__mult__self1__is__id,axiom, % 172.48/172.38 ! [V_a,V_b,T_a] : % 172.48/172.38 ( class_Divides_Osemiring__div(T_a) % 172.48/172.38 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 172.48/172.38 => 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 ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_div__mult__mult2,axiom, % 172.48/172.38 ! [V_b,V_a,V_c,T_a] : % 172.48/172.38 ( class_Divides_Osemiring__div(T_a) % 172.48/172.38 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 172.48/172.38 => 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) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_div__mult__mult1,axiom, % 172.48/172.38 ! [V_b,V_a,V_c,T_a] : % 172.48/172.38 ( class_Divides_Osemiring__div(T_a) % 172.48/172.38 => ( V_c != c_Groups_Ozero__class_Ozero(T_a) % 172.48/172.38 => 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) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_div__self,axiom, % 172.48/172.38 ! [V_a,T_a] : % 172.48/172.38 ( class_Divides_Osemiring__div(T_a) % 172.48/172.38 => ( V_a != c_Groups_Ozero__class_Ozero(T_a) % 172.48/172.38 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(T_a),V_a),V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_zdiv__eq__0__iff,axiom, % 172.48/172.38 ! [V_k_2,V_i_2] : % 172.48/172.38 ( hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_i_2),V_k_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 172.48/172.38 <=> ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 172.48/172.38 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i_2)) % 172.48/172.38 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),V_k_2)) ) % 172.48/172.38 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 172.48/172.38 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_i_2)) ) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_pos__imp__zdiv__nonneg__iff,axiom, % 172.48/172.38 ! [V_a_2,V_b_2] : % 172.48/172.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2)) % 172.48/172.38 => ( 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))) % 172.48/172.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_pos__imp__zdiv__pos__iff,axiom, % 172.48/172.38 ! [V_i_2,V_k_2] : % 172.48/172.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 172.48/172.38 => ( 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))) % 172.48/172.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_i_2)) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_nonneg1__imp__zdiv__pos__iff,axiom, % 172.48/172.38 ! [V_b_2,V_a_2] : % 172.48/172.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a_2)) % 172.48/172.38 => ( 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))) % 172.48/172.38 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),V_a_2)) % 172.48/172.38 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_2)) ) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_zdiv__mono2,axiom, % 172.48/172.38 ! [V_b,V_b_H,V_a] : % 172.48/172.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b)) % 172.48/172.38 => 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))) ) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_div__nonneg__neg__le0,axiom, % 172.48/172.38 ! [V_b,V_a] : % 172.48/172.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 172.48/172.38 => 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))) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_div__pos__pos__trivial,axiom, % 172.48/172.38 ! [V_b,V_a] : % 172.48/172.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 172.48/172.38 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_neg__imp__zdiv__nonneg__iff,axiom, % 172.48/172.38 ! [V_a_2,V_b_2] : % 172.48/172.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 172.48/172.38 => ( 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))) % 172.48/172.38 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_div__nonpos__pos__le0,axiom, % 172.48/172.38 ! [V_b,V_a] : % 172.48/172.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 172.48/172.38 => 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))) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_zdiv__mono2__neg,axiom, % 172.48/172.38 ! [V_b,V_b_H,V_a] : % 172.48/172.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_H)) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_H),V_b)) % 172.48/172.38 => 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))) ) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_div__neg__neg__trivial,axiom, % 172.48/172.38 ! [V_b,V_a] : % 172.48/172.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_a)) % 172.48/172.38 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_zdiv__mono1,axiom, % 172.48/172.38 ! [V_b,V_a_H,V_a] : % 172.48/172.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),V_a_H)) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 172.48/172.38 => 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))) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_zdiv__mono1__neg,axiom, % 172.48/172.38 ! [V_b,V_a_H,V_a] : % 172.48/172.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),V_a_H)) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 172.48/172.38 => 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))) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_int__div__less__self,axiom, % 172.48/172.38 ! [V_k,V_x] : % 172.48/172.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_k)) % 172.48/172.38 => 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)) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_zdiv__zmult2__eq,axiom, % 172.48/172.38 ! [V_b,V_a,V_c] : % 172.48/172.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 172.48/172.38 => 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) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_div__mult__self1,axiom, % 172.48/172.38 ! [V_c,V_a,V_b,T_a] : % 172.48/172.38 ( class_Divides_Osemiring__div(T_a) % 172.48/172.38 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 172.48/172.38 => 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)) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_div__mult__self2,axiom, % 172.48/172.38 ! [V_c,V_a,V_b,T_a] : % 172.48/172.38 ( class_Divides_Osemiring__div(T_a) % 172.48/172.38 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 172.48/172.38 => 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)) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_div__add__self1,axiom, % 172.48/172.38 ! [V_a,V_b,T_a] : % 172.48/172.38 ( class_Divides_Osemiring__div(T_a) % 172.48/172.38 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 172.48/172.38 => 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)) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_div__add__self2,axiom, % 172.48/172.38 ! [V_a,V_b,T_a] : % 172.48/172.38 ( class_Divides_Osemiring__div(T_a) % 172.48/172.38 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 172.48/172.38 => 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)) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_split__zdiv,axiom, % 172.48/172.38 ! [V_k_2,V_n_2,V_P_2] : % 172.48/172.38 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_n_2),V_k_2))) % 172.48/172.38 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 172.48/172.38 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 172.48/172.38 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 172.48/172.38 => ! [B_i] : % 172.48/172.38 ( ? [B_j] : % 172.48/172.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) % 172.48/172.38 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2)) % 172.48/172.38 & 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) ) % 172.48/172.38 => hBOOL(hAPP(V_P_2,B_i)) ) ) % 172.48/172.38 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 172.48/172.38 => ! [B_i] : % 172.48/172.38 ( ? [B_j] : % 172.48/172.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j)) % 172.48/172.38 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 172.48/172.38 & 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) ) % 172.48/172.38 => hBOOL(hAPP(V_P_2,B_i)) ) ) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_divmod__int__rel__div__eq,axiom, % 172.48/172.38 ! [V_r_1,V_y,V_b_1,V_a_1] : % 172.48/172.38 ( 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) % 172.48/172.38 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1)) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r_1)) % 172.48/172.38 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r_1),V_b_1)) ) ) % 172.48/172.38 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1)) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_1),V_r_1)) % 172.48/172.38 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r_1),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) % 172.48/172.38 => ( V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 172.48/172.38 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a_1),V_b_1) = V_y ) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_tsub__def,axiom, % 172.48/172.38 ! [V_x,V_y] : % 172.48/172.38 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x)) % 172.48/172.38 => c_Nat__Transfer_Otsub(V_x,V_y) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y) ) % 172.48/172.38 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x)) % 172.48/172.38 => c_Nat__Transfer_Otsub(V_x,V_y) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_setsum__mono__zero__right,axiom, % 172.48/172.38 ! [V_f_2,V_S_2,V_T_2,T_a,T_b] : % 172.48/172.38 ( class_Groups_Ocomm__monoid__add(T_b) % 172.48/172.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2)) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2)) % 172.48/172.38 => ( ! [B_x] : % 172.48/172.38 ( 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))) % 172.48/172.38 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) ) % 172.48/172.38 => 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) ) ) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_setsum__mono__zero__left,axiom, % 172.48/172.38 ! [V_f_2,V_S_2,V_T_2,T_a,T_b] : % 172.48/172.38 ( class_Groups_Ocomm__monoid__add(T_b) % 172.48/172.38 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_T_2)) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_S_2),V_T_2)) % 172.48/172.38 => ( ! [B_x] : % 172.48/172.38 ( 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))) % 172.48/172.38 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) ) % 172.48/172.38 => 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) ) ) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_card__Pow,axiom, % 172.48/172.38 ! [V_A_2,T_a] : % 172.48/172.38 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.38 => 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)) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_field__le__mult__one__interval,axiom, % 172.48/172.38 ! [V_y,V_x,T_a] : % 172.48/172.38 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 172.48/172.38 => ( ! [B_z] : % 172.48/172.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),B_z)) % 172.48/172.38 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),B_z),c_Groups_Oone__class_Oone(T_a))) % 172.48/172.38 => 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)) ) ) % 172.48/172.38 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_split__pos__lemma,axiom, % 172.48/172.38 ! [V_n_2,V_P_2,V_k_2] : % 172.48/172.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 172.48/172.38 => ( 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))) % 172.48/172.38 <=> ! [B_i,B_j] : % 172.48/172.38 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) % 172.48/172.38 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2)) % 172.48/172.38 & 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) ) % 172.48/172.38 => hBOOL(hAPP(hAPP(V_P_2,B_i),B_j)) ) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_split__neg__lemma,axiom, % 172.48/172.38 ! [V_n_2,V_P_2,V_k_2] : % 172.48/172.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 172.48/172.38 => ( 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))) % 172.48/172.38 <=> ! [B_i,B_j] : % 172.48/172.38 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j)) % 172.48/172.38 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 172.48/172.38 & 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) ) % 172.48/172.38 => hBOOL(hAPP(hAPP(V_P_2,B_i),B_j)) ) ) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_PowI,axiom, % 172.48/172.38 ! [V_B_2,V_A_2,T_a] : % 172.48/172.38 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 172.48/172.38 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_a),V_B_2))) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_Cantors__paradox,axiom, % 172.48/172.38 ! [V_A_2,T_a] : % 172.48/172.38 ~ ? [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) ). % 172.48/172.38 % 172.48/172.38 fof(fact_Pow__top,axiom, % 172.48/172.38 ! [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))) ). % 172.48/172.38 % 172.48/172.38 fof(fact_Pow__not__empty,axiom, % 172.48/172.38 ! [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)) ). % 172.48/172.38 % 172.48/172.38 fof(fact_mod__mod__trivial,axiom, % 172.48/172.38 ! [V_b,V_a,T_a] : % 172.48/172.38 ( class_Divides_Osemiring__div(T_a) % 172.48/172.38 => 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) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_mod__0,axiom, % 172.48/172.38 ! [V_a,T_a] : % 172.48/172.38 ( class_Divides_Osemiring__div(T_a) % 172.48/172.38 => c_Divides_Odiv__class_Omod(T_a,c_Groups_Ozero__class_Ozero(T_a),V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_mod__by__0,axiom, % 172.48/172.38 ! [V_a,T_a] : % 172.48/172.38 ( class_Divides_Osemiring__div(T_a) % 172.48/172.38 => c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Ozero__class_Ozero(T_a)) = V_a ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_mod__self,axiom, % 172.48/172.38 ! [V_a,T_a] : % 172.48/172.38 ( class_Divides_Osemiring__div(T_a) % 172.48/172.38 => c_Divides_Odiv__class_Omod(T_a,V_a,V_a) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_mod__add__self2,axiom, % 172.48/172.38 ! [V_b,V_a,T_a] : % 172.48/172.38 ( class_Divides_Osemiring__div(T_a) % 172.48/172.38 => 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) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_mod__add__self1,axiom, % 172.48/172.38 ! [V_a,V_b,T_a] : % 172.48/172.38 ( class_Divides_Osemiring__div(T_a) % 172.48/172.38 => 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) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_mod__add__right__eq,axiom, % 172.48/172.38 ! [V_c,V_b,V_a,T_a] : % 172.48/172.38 ( class_Divides_Osemiring__div(T_a) % 172.48/172.38 => 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) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_mod__add__left__eq,axiom, % 172.48/172.38 ! [V_c,V_b,V_a,T_a] : % 172.48/172.38 ( class_Divides_Osemiring__div(T_a) % 172.48/172.38 => 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) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_mod__add__eq,axiom, % 172.48/172.38 ! [V_c,V_b,V_a,T_a] : % 172.48/172.38 ( class_Divides_Osemiring__div(T_a) % 172.48/172.38 => 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) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_zmod__simps_I2_J,axiom, % 172.48/172.38 ! [V_c,V_b,V_a,T_a] : % 172.48/172.38 ( class_Divides_Osemiring__div(T_a) % 172.48/172.38 => 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) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_zmod__simps_I1_J,axiom, % 172.48/172.38 ! [V_b,V_c,V_a,T_a] : % 172.48/172.38 ( class_Divides_Osemiring__div(T_a) % 172.48/172.38 => 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) ) ). % 172.48/172.38 % 172.48/172.38 fof(fact_mod__add__cong,axiom, % 172.48/172.38 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] : % 172.48/172.38 ( class_Divides_Osemiring__div(T_a) % 172.48/172.39 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c) % 172.48/172.39 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c) % 172.48/172.39 => 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) ) ) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_mod__mult__right__eq,axiom, % 172.48/172.39 ! [V_c,V_b,V_a,T_a] : % 172.48/172.39 ( class_Divides_Osemiring__div(T_a) % 172.48/172.39 => 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) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_mod__mult__left__eq,axiom, % 172.48/172.39 ! [V_c,V_b,V_a,T_a] : % 172.48/172.39 ( class_Divides_Osemiring__div(T_a) % 172.48/172.39 => 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) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_mod__mult__eq,axiom, % 172.48/172.39 ! [V_c,V_b,V_a,T_a] : % 172.48/172.39 ( class_Divides_Osemiring__div(T_a) % 172.48/172.39 => 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) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_mod__mult__mult1,axiom, % 172.48/172.39 ! [V_b,V_a,V_c,T_a] : % 172.48/172.39 ( class_Divides_Osemiring__div(T_a) % 172.48/172.39 => 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)) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_mod__mult__mult2,axiom, % 172.48/172.39 ! [V_b,V_c,V_a,T_a] : % 172.48/172.39 ( class_Divides_Osemiring__div(T_a) % 172.48/172.39 => 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) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_zmod__simps_I4_J,axiom, % 172.48/172.39 ! [V_b,V_c,V_a,T_a] : % 172.48/172.39 ( class_Divides_Osemiring__div(T_a) % 172.48/172.39 => 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) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_mod__mult__cong,axiom, % 172.48/172.39 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] : % 172.48/172.39 ( class_Divides_Osemiring__div(T_a) % 172.48/172.39 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c) % 172.48/172.39 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c) % 172.48/172.39 => 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) ) ) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_mod__diff__cong,axiom, % 172.48/172.39 ! [V_b_H,V_b,V_a_H,V_c,V_a,T_a] : % 172.48/172.39 ( class_Divides_Oring__div(T_a) % 172.48/172.39 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_c) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_c) % 172.48/172.39 => ( c_Divides_Odiv__class_Omod(T_a,V_b,V_c) = c_Divides_Odiv__class_Omod(T_a,V_b_H,V_c) % 172.48/172.39 => 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) ) ) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_mod__diff__eq,axiom, % 172.48/172.39 ! [V_c,V_b,V_a,T_a] : % 172.48/172.39 ( class_Divides_Oring__div(T_a) % 172.48/172.39 => 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) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_mod__diff__left__eq,axiom, % 172.48/172.39 ! [V_c,V_b,V_a,T_a] : % 172.48/172.39 ( class_Divides_Oring__div(T_a) % 172.48/172.39 => 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) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_mod__diff__right__eq,axiom, % 172.48/172.39 ! [V_c,V_b,V_a,T_a] : % 172.48/172.39 ( class_Divides_Oring__div(T_a) % 172.48/172.39 => 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) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_div__le__mono,axiom, % 172.48/172.39 ! [V_k,V_n,V_m] : % 172.48/172.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 172.48/172.39 => 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))) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_div__le__dividend,axiom, % 172.48/172.39 ! [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)) ). % 172.48/172.39 % 172.48/172.39 fof(fact_div__mult2__eq,axiom, % 172.48/172.39 ! [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) ). % 172.48/172.39 % 172.48/172.39 fof(fact_zmod__zero,axiom, % 172.48/172.39 ! [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) ). % 172.48/172.39 % 172.48/172.39 fof(fact_zmod__self,axiom, % 172.48/172.39 ! [V_a] : c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_a) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ). % 172.48/172.39 % 172.48/172.39 fof(fact_zmod__zmult1__eq,axiom, % 172.48/172.39 ! [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) ). % 172.48/172.39 % 172.48/172.39 fof(fact_zmod__simps_I3_J,axiom, % 172.48/172.39 ! [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) ). % 172.48/172.39 % 172.48/172.39 fof(fact_zdiff__zmod__left,axiom, % 172.48/172.39 ! [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) ). % 172.48/172.39 % 172.48/172.39 fof(fact_zdiff__zmod__right,axiom, % 172.48/172.39 ! [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) ). % 172.48/172.39 % 172.48/172.39 fof(fact_zpower__zmod,axiom, % 172.48/172.39 ! [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) ). % 172.48/172.39 % 172.48/172.39 fof(fact_Pow__bottom,axiom, % 172.48/172.39 ! [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))) ). % 172.48/172.39 % 172.48/172.39 fof(fact_Pow__empty,axiom, % 172.48/172.39 ! [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))) ). % 172.48/172.39 % 172.48/172.39 fof(fact_finite__Pow__iff,axiom, % 172.48/172.39 ! [V_A_2,T_a] : % 172.48/172.39 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_Set_OPow(T_a),V_A_2))) % 172.48/172.39 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_Pow__insert,axiom, % 172.48/172.39 ! [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))) ). % 172.48/172.39 % 172.48/172.39 fof(fact_Pow__mono,axiom, % 172.48/172.39 ! [V_B_2,V_A_2,T_a] : % 172.48/172.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 172.48/172.39 => 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))) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_Pow__iff,axiom, % 172.48/172.39 ! [V_B_2,V_A_2,T_a] : % 172.48/172.39 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_a),V_B_2))) % 172.48/172.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_PowD,axiom, % 172.48/172.39 ! [V_B_2,V_A_2,T_a] : % 172.48/172.39 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(c_Set_OPow(T_a),V_B_2))) % 172.48/172.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_image__Pow__surj,axiom, % 172.48/172.39 ! [V_B_2,V_A_2,V_f_2,T_a,T_b] : % 172.48/172.39 ( hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2) = V_B_2 % 172.48/172.39 => 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) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_Un__Pow__subset,axiom, % 172.48/172.39 ! [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)))) ). % 172.48/172.39 % 172.48/172.39 fof(fact_Pow__Int__eq,axiom, % 172.48/172.39 ! [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)) ). % 172.48/172.39 % 172.48/172.39 fof(fact_mod__mult__self1__is__0,axiom, % 172.48/172.39 ! [V_a,V_b,T_a] : % 172.48/172.39 ( class_Divides_Osemiring__div(T_a) % 172.48/172.39 => 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) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_mod__mult__self2__is__0,axiom, % 172.48/172.39 ! [V_b,V_a,T_a] : % 172.48/172.39 ( class_Divides_Osemiring__div(T_a) % 172.48/172.39 => 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) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_mod__mult__self2,axiom, % 172.48/172.39 ! [V_c,V_b,V_a,T_a] : % 172.48/172.39 ( class_Divides_Osemiring__div(T_a) % 172.48/172.39 => 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) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_mod__mult__self1,axiom, % 172.48/172.39 ! [V_b,V_c,V_a,T_a] : % 172.48/172.39 ( class_Divides_Osemiring__div(T_a) % 172.48/172.39 => 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) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_mod__by__1,axiom, % 172.48/172.39 ! [V_a,T_a] : % 172.48/172.39 ( class_Divides_Osemiring__div(T_a) % 172.48/172.39 => c_Divides_Odiv__class_Omod(T_a,V_a,c_Groups_Oone__class_Oone(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_mod__div__trivial,axiom, % 172.48/172.39 ! [V_b,V_a,T_a] : % 172.48/172.39 ( class_Divides_Osemiring__div(T_a) % 172.48/172.39 => 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) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_div__1,axiom, % 172.48/172.39 ! [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 ). % 172.48/172.39 % 172.48/172.39 fof(fact_div__less,axiom, % 172.48/172.39 ! [V_n,V_m] : % 172.48/172.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 172.48/172.39 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_nat__mult__div__cancel__disj,axiom, % 172.48/172.39 ! [V_n,V_m,V_k] : % 172.48/172.39 ( ( V_k = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 172.48/172.39 => 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) ) % 172.48/172.39 & ( V_k != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 172.48/172.39 => 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) ) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_Divides_Otransfer__nat__int__function__closures_I2_J,axiom, % 172.48/172.39 ! [V_y,V_x] : % 172.48/172.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 172.48/172.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 172.48/172.39 => 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))) ) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_zmod__le__nonneg__dividend,axiom, % 172.48/172.39 ! [V_k,V_m] : % 172.48/172.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_m)) % 172.48/172.39 => 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)) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_pos__mod__bound,axiom, % 172.48/172.39 ! [V_a,V_b] : % 172.48/172.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 172.48/172.39 => 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)) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_neg__mod__bound,axiom, % 172.48/172.39 ! [V_a,V_b] : % 172.48/172.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 172.48/172.39 => 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))) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_zmod__eq__0__iff,axiom, % 172.48/172.39 ! [V_d_2,V_m_2] : % 172.48/172.39 ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 172.48/172.39 <=> ? [B_q] : V_m_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_d_2),B_q) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_zmod__zdiv__trivial,axiom, % 172.48/172.39 ! [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) ). % 172.48/172.39 % 172.48/172.39 fof(fact_DIVISION__BY__ZERO,axiom, % 172.48/172.39 ! [V_a] : % 172.48/172.39 ( 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) % 172.48/172.39 & c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = V_a ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_zdiv__zadd1__eq,axiom, % 172.48/172.39 ! [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)) ). % 172.48/172.39 % 172.48/172.39 fof(fact_image__Pow__mono,axiom, % 172.48/172.39 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 172.48/172.39 ( 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)) % 172.48/172.39 => 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))) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_div__mod__equality,axiom, % 172.48/172.39 ! [V_c,V_b,V_a,T_a] : % 172.48/172.39 ( class_Divides_Osemiring__div(T_a) % 172.48/172.39 => 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) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_div__mod__equality2,axiom, % 172.48/172.39 ! [V_c,V_a,V_b,T_a] : % 172.48/172.39 ( class_Divides_Osemiring__div(T_a) % 172.48/172.39 => 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) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_mod__div__equality,axiom, % 172.48/172.39 ! [V_b,V_a,T_a] : % 172.48/172.39 ( class_Divides_Osemiring__div(T_a) % 172.48/172.39 => 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 ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_mod__div__equality2,axiom, % 172.48/172.39 ! [V_a,V_b,T_a] : % 172.48/172.39 ( class_Divides_Osemiring__div(T_a) % 172.48/172.39 => 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 ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_semiring__div__class_Omod__div__equality_H,axiom, % 172.48/172.39 ! [V_b,V_a,T_a] : % 172.48/172.39 ( class_Divides_Osemiring__div(T_a) % 172.48/172.39 => 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 ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_div__le__mono2,axiom, % 172.48/172.39 ! [V_k,V_n,V_m] : % 172.48/172.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)) % 172.48/172.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m),V_n)) % 172.48/172.39 => 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))) ) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_div__mult__self__is__m,axiom, % 172.48/172.39 ! [V_m,V_n] : % 172.48/172.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 172.48/172.39 => 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 ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_div__mult__self1__is__m,axiom, % 172.48/172.39 ! [V_m,V_n] : % 172.48/172.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 172.48/172.39 => 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 ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_nat__mult__div__cancel1,axiom, % 172.48/172.39 ! [V_n,V_m,V_k] : % 172.48/172.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k)) % 172.48/172.39 => 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) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_div__less__dividend,axiom, % 172.48/172.39 ! [V_m,V_n] : % 172.48/172.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n)) % 172.48/172.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_m)) % 172.48/172.39 => 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)) ) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_mod__neg__neg__trivial,axiom, % 172.48/172.39 ! [V_b,V_a] : % 172.48/172.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 172.48/172.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_a)) % 172.48/172.39 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a ) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_neg__mod__conj,axiom, % 172.48/172.39 ! [V_a,V_b] : % 172.48/172.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 172.48/172.39 => ( 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))) % 172.48/172.39 & 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))) ) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_neg__mod__sign,axiom, % 172.48/172.39 ! [V_a,V_b] : % 172.48/172.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 172.48/172.39 => 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))) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_mod__pos__pos__trivial,axiom, % 172.48/172.39 ! [V_b,V_a] : % 172.48/172.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 172.48/172.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 172.48/172.39 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_a ) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_pos__mod__conj,axiom, % 172.48/172.39 ! [V_a,V_b] : % 172.48/172.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 172.48/172.39 => ( 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))) % 172.48/172.39 & 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)) ) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_pos__mod__sign,axiom, % 172.48/172.39 ! [V_a,V_b] : % 172.48/172.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 172.48/172.39 => 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))) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_zmod__zdiv__equality,axiom, % 172.48/172.39 ! [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)) ). % 172.48/172.39 % 172.48/172.39 fof(fact_zdiv__zmult1__eq,axiom, % 172.48/172.39 ! [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)) ). % 172.48/172.39 % 172.48/172.39 fof(fact_zdiv__zmod__equality,axiom, % 172.48/172.39 ! [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) ). % 172.48/172.39 % 172.48/172.39 fof(fact_zdiv__zmod__equality2,axiom, % 172.48/172.39 ! [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) ). % 172.48/172.39 % 172.48/172.39 fof(fact_zmult__div__cancel,axiom, % 172.48/172.39 ! [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)) ). % 172.48/172.39 % 172.48/172.39 fof(fact_zmod__zdiv__equality_H,axiom, % 172.48/172.39 ! [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)) ). % 172.48/172.39 % 172.48/172.39 fof(fact_div__if,axiom, % 172.48/172.39 ! [V_m,V_n] : % 172.48/172.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 172.48/172.39 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 172.48/172.39 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 172.48/172.39 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 172.48/172.39 => 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)) ) ) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_div__geq,axiom, % 172.48/172.39 ! [V_m,V_n] : % 172.48/172.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 172.48/172.39 => ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 172.48/172.39 => 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)) ) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_split__div,axiom, % 172.48/172.39 ! [V_k_2,V_n_2,V_P_2] : % 172.48/172.39 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_n_2),V_k_2))) % 172.48/172.39 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 172.48/172.39 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) % 172.48/172.39 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 172.48/172.39 => ! [B_i,B_j] : % 172.48/172.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2)) % 172.48/172.39 => ( 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) % 172.48/172.39 => hBOOL(hAPP(V_P_2,B_i)) ) ) ) ) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_mod__pos__neg__trivial,axiom, % 172.48/172.39 ! [V_b,V_a] : % 172.48/172.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 172.48/172.39 => ( 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))) % 172.48/172.39 => 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) ) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_le__div__geq,axiom, % 172.48/172.39 ! [V_m,V_n] : % 172.48/172.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 172.48/172.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 172.48/172.39 => 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)) ) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_split__div__lemma,axiom, % 172.48/172.39 ! [V_m_2,V_q_2,V_n_2] : % 172.48/172.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) % 172.48/172.39 => ( ( 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)) % 172.48/172.39 & 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)))) ) % 172.48/172.39 <=> V_q_2 = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_n_2) ) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_split__div_H,axiom, % 172.48/172.39 ! [V_n_2,V_m_2,V_P_2] : % 172.48/172.39 ( hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m_2),V_n_2))) % 172.48/172.39 <=> ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 172.48/172.39 & hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) % 172.48/172.39 | ? [B_q] : % 172.48/172.39 ( 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)) % 172.48/172.39 & 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)))) % 172.48/172.39 & hBOOL(hAPP(V_P_2,B_q)) ) ) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J,axiom, % 172.48/172.39 ! [V_y,V_x] : % 172.48/172.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 172.48/172.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 172.48/172.39 => 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))) ) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_divmod__int__rel__mod__eq,axiom, % 172.48/172.39 ! [V_y,V_q_1,V_b_1,V_a_1] : % 172.48/172.39 ( 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) % 172.48/172.39 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1)) % 172.48/172.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 172.48/172.39 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_y),V_b_1)) ) ) % 172.48/172.39 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b_1)) % 172.48/172.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_1),V_y)) % 172.48/172.39 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) % 172.48/172.39 => ( V_b_1 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 172.48/172.39 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a_1,V_b_1) = V_y ) ) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_zmult2__lemma__aux2,axiom, % 172.48/172.39 ! [V_q,V_r,V_b,V_c] : % 172.48/172.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 172.48/172.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r)) % 172.48/172.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 172.48/172.39 => 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))) ) ) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_zmult2__lemma__aux1,axiom, % 172.48/172.39 ! [V_q,V_r,V_b,V_c] : % 172.48/172.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 172.48/172.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r)) % 172.48/172.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 172.48/172.39 => 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))) ) ) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_zmult2__lemma__aux4,axiom, % 172.48/172.39 ! [V_q,V_b,V_r,V_c] : % 172.48/172.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 172.48/172.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) % 172.48/172.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) % 172.48/172.39 => 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))) ) ) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_zmult2__lemma__aux3,axiom, % 172.48/172.39 ! [V_q,V_b,V_r,V_c] : % 172.48/172.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 172.48/172.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) % 172.48/172.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) % 172.48/172.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),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))) ) ) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_split__zmod,axiom, % 172.48/172.39 ! [V_k_2,V_n_2,V_P_2] : % 172.48/172.39 ( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Int_Oint,V_n_2,V_k_2))) % 172.48/172.39 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 172.48/172.39 => hBOOL(hAPP(V_P_2,V_n_2)) ) % 172.48/172.39 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 172.48/172.39 => ! [B_i,B_j] : % 172.48/172.39 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_j)) % 172.48/172.39 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_j),V_k_2)) % 172.48/172.39 & 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) ) % 172.48/172.39 => hBOOL(hAPP(V_P_2,B_j)) ) ) % 172.48/172.39 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 172.48/172.39 => ! [B_i,B_j] : % 172.48/172.39 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),B_j)) % 172.48/172.39 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_j),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 172.48/172.39 & 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) ) % 172.48/172.39 => hBOOL(hAPP(V_P_2,B_j)) ) ) ) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_zmod__zmult2__eq,axiom, % 172.48/172.39 ! [V_b,V_a,V_c] : % 172.48/172.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 172.48/172.39 => 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)) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_tsub__eq,axiom, % 172.48/172.39 ! [V_x,V_y] : % 172.48/172.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_y),V_x)) % 172.48/172.39 => c_Nat__Transfer_Otsub(V_x,V_y) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_x),V_y) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_Powp__Pow__eq,axiom, % 172.48/172.39 ! [V_x_2,V_A_2,T_a] : % 172.48/172.39 ( 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)) % 172.48/172.39 <=> hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_x_2),hAPP(c_Set_OPow(T_a),V_A_2))) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_diff__Suc,axiom, % 172.48/172.39 ! [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)) ). % 172.48/172.39 % 172.48/172.39 fof(fact_setprod__pos__nat,axiom, % 172.48/172.39 ! [V_f_2,V_S_2,T_a] : % 172.48/172.39 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 172.48/172.39 => ( ! [B_x] : % 172.48/172.39 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2)) % 172.48/172.39 => 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))) ) % 172.48/172.39 => 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))) ) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_arith__series__nat,axiom, % 172.48/172.39 ! [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)))) ). % 172.48/172.39 % 172.48/172.39 fof(fact_less__eq__nat_Osimps_I2_J,axiom, % 172.48/172.39 ! [V_n_2,V_m_2] : % 172.48/172.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_m_2)),V_n_2)) % 172.48/172.39 <=> 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)) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_setsum__SucD,axiom, % 172.48/172.39 ! [V_n_2,V_A_2,V_f_2,T_a] : % 172.48/172.39 ( 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) % 172.48/172.39 => ? [B_x] : % 172.48/172.39 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 172.48/172.39 & 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))) ) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_finite__lessThan,axiom, % 172.48/172.39 ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OlessThan(tc_Nat_Onat),V_k_2))) ). % 172.48/172.39 % 172.48/172.39 fof(fact_card__lessThan,axiom, % 172.48/172.39 ! [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 ). % 172.48/172.39 % 172.48/172.39 fof(fact_lessThan__eq__iff,axiom, % 172.48/172.39 ! [V_y_2,V_x_2,T_a] : % 172.48/172.39 ( class_Orderings_Olinorder(T_a) % 172.48/172.39 => ( hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_x_2) = hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_y_2) % 172.48/172.39 <=> V_x_2 = V_y_2 ) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_lessThan__Suc,axiom, % 172.48/172.39 ! [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)) ). % 172.48/172.39 % 172.48/172.39 fof(fact_lessThan__0,axiom, % 172.48/172.39 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)) ). % 172.48/172.39 % 172.48/172.39 fof(fact_mod__Suc__eq__Suc__mod,axiom, % 172.48/172.39 ! [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) ). % 172.48/172.39 % 172.48/172.39 fof(fact_mod__less,axiom, % 172.48/172.39 ! [V_n,V_m] : % 172.48/172.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 172.48/172.39 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_m ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_div__add1__eq,axiom, % 172.48/172.39 ! [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)) ). % 172.48/172.39 % 172.48/172.39 fof(fact_mod__less__eq__dividend,axiom, % 172.48/172.39 ! [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)) ). % 172.48/172.39 % 172.48/172.39 fof(fact_mod__mult__distrib,axiom, % 172.48/172.39 ! [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)) ). % 172.48/172.39 % 172.48/172.39 fof(fact_mod__mult__distrib2,axiom, % 172.48/172.39 ! [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)) ). % 172.48/172.39 % 172.48/172.39 fof(fact_lessThan__Suc__eq__insert__0,axiom, % 172.48/172.39 ! [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))) ). % 172.48/172.39 % 172.48/172.39 fof(fact_lessThan__iff,axiom, % 172.48/172.39 ! [V_k_2,V_i_2,T_a] : % 172.48/172.39 ( class_Orderings_Oord(T_a) % 172.48/172.39 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),hAPP(c_SetInterval_Oord__class_OlessThan(T_a),V_k_2))) % 172.48/172.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_i_2),V_k_2)) ) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_lessThan__subset__iff,axiom, % 172.48/172.39 ! [V_y_2,V_x_2,T_a] : % 172.48/172.39 ( class_Orderings_Olinorder(T_a) % 172.48/172.39 => ( 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))) % 172.48/172.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) ) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_setsum__lessThan__Suc,axiom, % 172.48/172.39 ! [V_n_2,V_f_2,T_a] : % 172.48/172.39 ( class_Groups_Ocomm__monoid__add(T_a) % 172.48/172.39 => 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)) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_lessThan__strict__subset__iff,axiom, % 172.48/172.39 ! [V_n_2,V_m_2,T_a] : % 172.48/172.39 ( class_Orderings_Olinorder(T_a) % 172.48/172.39 => ( 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))) % 172.48/172.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_m_2),V_n_2)) ) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_mod__Suc,axiom, % 172.48/172.39 ! [V_n,V_m] : % 172.48/172.39 ( ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) = V_n % 172.48/172.39 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,V_m),V_n) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 172.48/172.39 & ( hAPP(c_Nat_OSuc,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n)) != V_n % 172.48/172.39 => 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)) ) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_mod__1,axiom, % 172.48/172.39 ! [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) ). % 172.48/172.39 % 172.48/172.39 fof(fact_mod__less__divisor,axiom, % 172.48/172.39 ! [V_m,V_n] : % 172.48/172.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 172.48/172.39 => 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)) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_mod__eq__0__iff,axiom, % 172.48/172.39 ! [V_d_2,V_m_2] : % 172.48/172.39 ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m_2,V_d_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 172.48/172.39 <=> ? [B_q] : V_m_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Nat_Onat),V_d_2),B_q) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_mod__if,axiom, % 172.48/172.39 ! [V_n,V_m] : % 172.48/172.39 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 172.48/172.39 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_m ) % 172.48/172.39 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 172.48/172.39 => 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) ) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_mod__geq,axiom, % 172.48/172.39 ! [V_n,V_m] : % 172.48/172.39 ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 172.48/172.39 => 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) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_mod__mult__self3,axiom, % 172.48/172.39 ! [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) ). % 172.48/172.39 % 172.48/172.39 fof(fact_div__mult1__eq,axiom, % 172.48/172.39 ! [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)) ). % 172.48/172.39 % 172.48/172.39 fof(fact_mod__mult2__eq,axiom, % 172.48/172.39 ! [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)) ). % 172.48/172.39 % 172.48/172.39 fof(fact_le__mod__geq,axiom, % 172.48/172.39 ! [V_m,V_n] : % 172.48/172.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 172.48/172.39 => 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) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_Divides_Omod__div__equality_H,axiom, % 172.48/172.39 ! [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)) ). % 172.48/172.39 % 172.48/172.39 fof(fact_mult__div__cancel,axiom, % 172.48/172.39 ! [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)) ). % 172.48/172.39 % 172.48/172.39 fof(fact_div__mod__equality_H,axiom, % 172.48/172.39 ! [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)) ). % 172.48/172.39 % 172.48/172.39 fof(fact_nat__case__0,axiom, % 172.48/172.39 ! [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 ). % 172.48/172.39 % 172.48/172.39 fof(fact_nat__case__Suc,axiom, % 172.48/172.39 ! [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) ). % 172.48/172.39 % 172.48/172.39 fof(fact_single__Diff__lessThan,axiom, % 172.48/172.39 ! [V_k_2,T_a] : % 172.48/172.39 ( class_Orderings_Oorder(T_a) % 172.48/172.39 => 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))) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_mod__le__divisor,axiom, % 172.48/172.39 ! [V_m,V_n] : % 172.48/172.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 172.48/172.39 => 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)) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_mod__mult__self4,axiom, % 172.48/172.39 ! [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) ). % 172.48/172.39 % 172.48/172.39 fof(fact_Powp__mono,axiom, % 172.48/172.39 ! [V_B_2,V_A_2,T_a] : % 172.48/172.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 172.48/172.39 => 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))) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_finite__nat__set__iff__bounded,axiom, % 172.48/172.39 ! [V_N_2] : % 172.48/172.39 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_N_2)) % 172.48/172.39 <=> ? [B_m] : % 172.48/172.39 ! [B_x] : % 172.48/172.39 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2)) % 172.48/172.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_x),B_m)) ) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_finite__nat__set__iff__bounded__le,axiom, % 172.48/172.39 ! [V_N_2] : % 172.48/172.39 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_N_2)) % 172.48/172.39 <=> ? [B_m] : % 172.48/172.39 ! [B_x] : % 172.48/172.39 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2)) % 172.48/172.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_x),B_m)) ) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_split__mod,axiom, % 172.48/172.39 ! [V_k_2,V_n_2,V_P_2] : % 172.48/172.39 ( hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_n_2,V_k_2))) % 172.48/172.39 <=> ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 172.48/172.39 => hBOOL(hAPP(V_P_2,V_n_2)) ) % 172.48/172.39 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 172.48/172.39 => ! [B_i,B_j] : % 172.48/172.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_j),V_k_2)) % 172.48/172.39 => ( 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) % 172.48/172.39 => hBOOL(hAPP(V_P_2,B_j)) ) ) ) ) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_mod__lemma,axiom, % 172.48/172.39 ! [V_q,V_b,V_r,V_c] : % 172.48/172.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c)) % 172.48/172.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_r),V_b)) % 172.48/172.39 => 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))) ) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_Suc__times__mod__eq,axiom, % 172.48/172.39 ! [V_m,V_k] : % 172.48/172.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_k)) % 172.48/172.39 => 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) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_arith__series__general,axiom, % 172.48/172.39 ! [V_n_2,V_d_2,V_a_2,T_a] : % 172.48/172.39 ( class_Rings_Ocomm__semiring__1(T_a) % 172.48/172.39 => 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)))) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_ord_OatMost__iff,axiom, % 172.48/172.39 ! [V_k_2,V_less__eq_2,V_i_2,T_a] : % 172.48/172.39 ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OatMost(T_a,V_less__eq_2,V_k_2))) % 172.48/172.39 <=> hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_k_2)) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_ord_OatLeast__iff,axiom, % 172.48/172.39 ! [V_k_2,V_less__eq_2,V_i_2,T_a] : % 172.48/172.39 ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OatLeast(T_a,V_less__eq_2,V_k_2))) % 172.48/172.39 <=> hBOOL(hAPP(hAPP(V_less__eq_2,V_k_2),V_i_2)) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_ord_OlessThan__iff,axiom, % 172.48/172.39 ! [V_k_2,V_less_2,V_i_2,T_a] : % 172.48/172.39 ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OlessThan(T_a,V_less_2,V_k_2))) % 172.48/172.39 <=> hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_k_2)) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_ord_OgreaterThan__iff,axiom, % 172.48/172.39 ! [V_k_2,V_less_2,V_i_2,T_a] : % 172.48/172.39 ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),c_SetInterval_Oord_OgreaterThan(T_a,V_less_2,V_k_2))) % 172.48/172.39 <=> hBOOL(hAPP(hAPP(V_less_2,V_k_2),V_i_2)) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_ord_OatLeastAtMost__iff,axiom, % 172.48/172.39 ! [V_u_2,V_l_2,V_less__eq_2,V_i_2,T_a] : % 172.48/172.39 ( 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))) % 172.48/172.39 <=> ( hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2)) % 172.48/172.39 & hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2)) ) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I1_J,axiom, % 172.48/172.39 ! [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)) ). % 172.48/172.39 % 172.48/172.39 fof(fact_transfer__nat__int__set__relations_I1_J,axiom, % 172.48/172.39 ! [V_A_2] : % 172.48/172.39 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),V_A_2)) % 172.48/172.39 <=> 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))) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I2_J,axiom, % 172.48/172.39 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))) ). % 172.48/172.39 % 172.48/172.39 fof(fact_of__nat__eq__iff,axiom, % 172.48/172.39 ! [V_n_2,V_m_2,T_a] : % 172.48/172.39 ( class_Nat_Osemiring__char__0(T_a) % 172.48/172.39 => ( 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) % 172.48/172.39 <=> V_m_2 = V_n_2 ) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_Divides_Otransfer__int__nat__functions_I2_J,axiom, % 172.48/172.39 ! [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)) ). % 172.48/172.39 % 172.48/172.39 fof(fact_zmod__int,axiom, % 172.48/172.39 ! [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)) ). % 172.48/172.39 % 172.48/172.39 fof(fact_int__setsum,axiom, % 172.48/172.39 ! [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) ). % 172.48/172.39 % 172.48/172.39 fof(fact_int__setprod,axiom, % 172.48/172.39 ! [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) ). % 172.48/172.39 % 172.48/172.39 fof(fact_int__eq__0__conv,axiom, % 172.48/172.39 ! [V_n_2] : % 172.48/172.39 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 172.48/172.39 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_int__0,axiom, % 172.48/172.39 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) ). % 172.48/172.39 % 172.48/172.39 fof(fact_transfer__int__nat__numerals_I1_J,axiom, % 172.48/172.39 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)) ). % 172.48/172.39 % 172.48/172.39 fof(fact_zero__zle__int,axiom, % 172.48/172.39 ! [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))) ). % 172.48/172.39 % 172.48/172.39 fof(fact_transfer__int__nat__quantifiers_I1_J,axiom, % 172.48/172.39 ! [V_P_2] : % 172.48/172.39 ( ! [B_x] : % 172.48/172.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 172.48/172.39 => hBOOL(hAPP(V_P_2,B_x)) ) % 172.48/172.39 <=> ! [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_transfer__int__nat__quantifiers_I2_J,axiom, % 172.48/172.39 ! [V_P_2] : % 172.48/172.39 ( ? [B_x] : % 172.48/172.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 172.48/172.39 & hBOOL(hAPP(V_P_2,B_x)) ) % 172.48/172.39 <=> ? [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_x))) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J,axiom, % 172.48/172.39 ! [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))) ). % 172.48/172.39 % 172.48/172.39 fof(fact_int__less__0__conv,axiom, % 172.48/172.39 ! [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))) ). % 172.48/172.39 % 172.48/172.39 fof(fact_zless__int,axiom, % 172.48/172.39 ! [V_n_2,V_m_2] : % 172.48/172.39 ( 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))) % 172.48/172.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_transfer__int__nat__relations_I2_J,axiom, % 172.48/172.39 ! [V_y_2,V_x_2] : % 172.48/172.39 ( 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))) % 172.48/172.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_zle__int,axiom, % 172.48/172.39 ! [V_n_2,V_m_2] : % 172.48/172.39 ( 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))) % 172.48/172.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_transfer__int__nat__relations_I3_J,axiom, % 172.48/172.39 ! [V_y_2,V_x_2] : % 172.48/172.39 ( 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))) % 172.48/172.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_x_2),V_y_2)) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_zadd__int__left,axiom, % 172.48/172.39 ! [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) ). % 172.48/172.39 % 172.48/172.39 fof(fact_zadd__int,axiom, % 172.48/172.39 ! [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)) ). % 172.48/172.39 % 172.48/172.39 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I1_J,axiom, % 172.48/172.39 ! [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)) ). % 172.48/172.39 % 172.48/172.39 fof(fact_zle__iff__zadd,axiom, % 172.48/172.39 ! [V_z_2,V_w_2] : % 172.48/172.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) % 172.48/172.39 <=> ? [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)) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_of__nat__0__le__iff,axiom, % 172.48/172.39 ! [V_n,T_a] : % 172.48/172.39 ( class_Rings_Olinordered__semidom(T_a) % 172.48/172.39 => 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))) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_zero__le__imp__of__nat,axiom, % 172.48/172.39 ! [V_m,T_a] : % 172.48/172.39 ( class_Rings_Olinordered__semidom(T_a) % 172.48/172.39 => 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))) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_of__nat__less__0__iff,axiom, % 172.48/172.39 ! [V_m,T_a] : % 172.48/172.39 ( class_Rings_Olinordered__semidom(T_a) % 172.48/172.39 => ~ 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))) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_zmult__int,axiom, % 172.48/172.39 ! [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)) ). % 172.48/172.39 % 172.48/172.39 fof(fact_int__mult,axiom, % 172.48/172.39 ! [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)) ). % 172.48/172.39 % 172.48/172.39 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I2_J,axiom, % 172.48/172.39 ! [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)) ). % 172.48/172.39 % 172.48/172.39 fof(fact_of__nat__0,axiom, % 172.48/172.39 ! [T_a] : % 172.48/172.39 ( class_Rings_Osemiring__1(T_a) % 172.48/172.39 => 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) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_of__nat__less__imp__less,axiom, % 172.48/172.39 ! [V_n,V_m,T_a] : % 172.48/172.39 ( class_Rings_Olinordered__semidom(T_a) % 172.48/172.39 => ( 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))) % 172.48/172.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) ) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_less__imp__of__nat__less,axiom, % 172.48/172.39 ! [V_n,V_m,T_a] : % 172.48/172.39 ( class_Rings_Olinordered__semidom(T_a) % 172.48/172.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 172.48/172.39 => 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))) ) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_of__nat__less__iff,axiom, % 172.48/172.39 ! [V_n_2,V_m_2,T_a] : % 172.48/172.39 ( class_Rings_Olinordered__semidom(T_a) % 172.48/172.39 => ( 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))) % 172.48/172.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_int__1,axiom, % 172.48/172.39 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) ). % 172.48/172.39 % 172.48/172.39 fof(fact_transfer__int__nat__numerals_I2_J,axiom, % 172.48/172.39 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)) ). % 172.48/172.39 % 172.48/172.39 fof(fact_of__nat__le__iff,axiom, % 172.48/172.39 ! [V_n_2,V_m_2,T_a] : % 172.48/172.39 ( class_Rings_Olinordered__semidom(T_a) % 172.48/172.39 => ( 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))) % 172.48/172.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_of__nat__add,axiom, % 172.48/172.39 ! [V_n,V_m,T_a] : % 172.48/172.39 ( class_Rings_Osemiring__1(T_a) % 172.48/172.39 => 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)) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_of__nat__mult,axiom, % 172.48/172.39 ! [V_n,V_m,T_a] : % 172.48/172.39 ( class_Rings_Osemiring__1(T_a) % 172.48/172.39 => 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)) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_Divides_Otransfer__int__nat__functions_I1_J,axiom, % 172.48/172.39 ! [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)) ). % 172.48/172.39 % 172.48/172.39 fof(fact_zdiv__int,axiom, % 172.48/172.39 ! [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)) ). % 172.48/172.39 % 172.48/172.39 fof(fact_of__nat__1,axiom, % 172.48/172.39 ! [T_a] : % 172.48/172.39 ( class_Rings_Osemiring__1(T_a) % 172.48/172.39 => 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) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_Ints__of__nat,axiom, % 172.48/172.39 ! [V_n_2,T_a] : % 172.48/172.39 ( class_Rings_Oring__1(T_a) % 172.48/172.39 => 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))) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_of__nat__power,axiom, % 172.48/172.39 ! [V_n,V_m,T_a] : % 172.48/172.39 ( class_Rings_Osemiring__1(T_a) % 172.48/172.39 => 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) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_zpower__int,axiom, % 172.48/172.39 ! [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)) ). % 172.48/172.39 % 172.48/172.39 fof(fact_int__power,axiom, % 172.48/172.39 ! [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) ). % 172.48/172.39 % 172.48/172.39 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I4_J,axiom, % 172.48/172.39 ! [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)) ). % 172.48/172.39 % 172.48/172.39 fof(fact_Nat__Transfer_Otransfer__int__nat__functions_I3_J,axiom, % 172.48/172.39 ! [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)) ). % 172.48/172.39 % 172.48/172.39 fof(fact_of__nat__setsum,axiom, % 172.48/172.39 ! [V_A_2,V_f_2,T_b,T_a] : % 172.48/172.39 ( class_Rings_Osemiring__1(T_a) % 172.48/172.39 => 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) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_int__le__0__conv,axiom, % 172.48/172.39 ! [V_n_2] : % 172.48/172.39 ( 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))) % 172.48/172.39 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_int__Suc0__eq__1,axiom, % 172.48/172.39 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) ). % 172.48/172.39 % 172.48/172.39 fof(fact_zless__iff__Suc__zadd,axiom, % 172.48/172.39 ! [V_z_2,V_w_2] : % 172.48/172.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) % 172.48/172.39 <=> ? [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))) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_int__Suc,axiom, % 172.48/172.39 ! [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)) ). % 172.48/172.39 % 172.48/172.39 fof(fact_of__nat__setprod,axiom, % 172.48/172.39 ! [V_A_2,V_f_2,T_b,T_a] : % 172.48/172.39 ( ( class_Groups_Ocomm__monoid__mult(T_a) % 172.48/172.39 & class_Rings_Osemiring__1(T_a) ) % 172.48/172.39 => 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) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_zdiff__int,axiom, % 172.48/172.39 ! [V_m,V_n] : % 172.48/172.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 172.48/172.39 => 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)) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_of__nat__Suc,axiom, % 172.48/172.39 ! [V_m,T_a] : % 172.48/172.39 ( class_Rings_Osemiring__1(T_a) % 172.48/172.39 => 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)) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_of__nat__diff,axiom, % 172.48/172.39 ! [V_m,V_n,T_a] : % 172.48/172.39 ( class_Rings_Oring__1(T_a) % 172.48/172.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 172.48/172.39 => 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)) ) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_setsum__constant,axiom, % 172.48/172.39 ! [V_A_2,V_y_2,T_b,T_a] : % 172.48/172.39 ( class_Rings_Osemiring__1(T_a) % 172.48/172.39 => 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) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_zero__less__int__conv,axiom, % 172.48/172.39 ! [V_n_2] : % 172.48/172.39 ( 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))) % 172.48/172.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_zmult__zless__mono2__lemma,axiom, % 172.48/172.39 ! [V_k,V_j,V_i] : % 172.48/172.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),V_j)) % 172.48/172.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_k)) % 172.48/172.39 => 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))) ) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_of__nat__0__less__iff,axiom, % 172.48/172.39 ! [V_n_2,T_a] : % 172.48/172.39 ( class_Rings_Olinordered__semidom(T_a) % 172.48/172.39 => ( 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))) % 172.48/172.39 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) ) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_zdiff__int__split,axiom, % 172.48/172.39 ! [V_y_2,V_x_2,V_P_2] : % 172.48/172.39 ( 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)))) % 172.48/172.39 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),V_x_2)) % 172.48/172.39 => 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)))) ) % 172.48/172.39 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) % 172.48/172.39 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_semiring__1__class_Oof__nat__code,axiom, % 172.48/172.39 ! [V_n_2,T_a] : % 172.48/172.39 ( class_Rings_Osemiring__1(T_a) % 172.48/172.39 => 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)) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_setsum__bounded,axiom, % 172.48/172.39 ! [V_K_2,V_f_2,V_A_2,T_a,T_b] : % 172.48/172.39 ( ( class_Groups_Oordered__ab__semigroup__add(T_b) % 172.48/172.39 & class_Rings_Osemiring__1(T_b) ) % 172.48/172.39 => ( ! [B_i] : % 172.48/172.39 ( hBOOL(hAPP(hAPP(c_member(T_a),B_i),V_A_2)) % 172.48/172.39 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,B_i)),V_K_2)) ) % 172.48/172.39 => 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))) ) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_ord_OgreaterThanAtMost__iff,axiom, % 172.48/172.39 ! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_a] : % 172.48/172.39 ( 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))) % 172.48/172.39 <=> ( hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2)) % 172.48/172.39 & hBOOL(hAPP(hAPP(V_less__eq_2,V_i_2),V_u_2)) ) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_ord_OatLeastLessThan__iff,axiom, % 172.48/172.39 ! [V_u_2,V_l_2,V_less_2,V_less__eq_2,V_i_2,T_a] : % 172.48/172.39 ( 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))) % 172.48/172.39 <=> ( hBOOL(hAPP(hAPP(V_less__eq_2,V_l_2),V_i_2)) % 172.48/172.39 & hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2)) ) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_ord_OgreaterThanLessThan__iff,axiom, % 172.48/172.39 ! [V_u_2,V_l_2,V_less_2,V_i_2,T_a] : % 172.48/172.39 ( 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))) % 172.48/172.39 <=> ( hBOOL(hAPP(hAPP(V_less_2,V_l_2),V_i_2)) % 172.48/172.39 & hBOOL(hAPP(hAPP(V_less_2,V_i_2),V_u_2)) ) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_transfer__nat__int__set__relations_I4_J,axiom, % 172.48/172.39 ! [V_B_2,V_A_2] : % 172.48/172.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2)) % 172.48/172.39 <=> 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))) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_transfer__nat__int__set__relations_I3_J,axiom, % 172.48/172.39 ! [V_B_2,V_A_2] : % 172.48/172.39 ( V_A_2 = V_B_2 % 172.48/172.39 <=> 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) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_transfer__nat__int__set__relations_I2_J,axiom, % 172.48/172.39 ! [V_A_2,V_x_2] : % 172.48/172.39 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_x_2),V_A_2)) % 172.48/172.39 <=> 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))) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_transfer__nat__int__set__relations_I5_J,axiom, % 172.48/172.39 ! [V_B_2,V_A_2] : % 172.48/172.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Nat_Onat,tc_HOL_Obool)),V_A_2),V_B_2)) % 172.48/172.39 <=> 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))) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_transfer__int__nat__relations_I1_J,axiom, % 172.48/172.39 ! [V_y_2,V_x_2] : % 172.48/172.39 ( 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) % 172.48/172.39 <=> V_x_2 = V_y_2 ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_int__int__eq,axiom, % 172.48/172.39 ! [V_n_2,V_m_2] : % 172.48/172.39 ( 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) % 172.48/172.39 <=> V_m_2 = V_n_2 ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_of__nat__aux_Osimps_I1_J,axiom, % 172.48/172.39 ! [V_i_2,V_inc_2,T_a] : % 172.48/172.39 ( class_Rings_Osemiring__1(T_a) % 172.48/172.39 => 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 ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_of__nat__aux_Osimps_I2_J,axiom, % 172.48/172.39 ! [V_i_2,V_n_2,V_inc_2,T_a] : % 172.48/172.39 ( class_Rings_Osemiring__1(T_a) % 172.48/172.39 => 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)) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_image__minus__const__atLeastLessThan__nat,axiom, % 172.48/172.39 ! [V_x_2,V_y_2,V_ca_2] : % 172.48/172.39 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_ca_2),V_y_2)) % 172.48/172.39 => hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_ca_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_x_2),V_y_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_x_2),V_ca_2)),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_y_2),V_ca_2)) ) % 172.48/172.39 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_ca_2),V_y_2)) % 172.48/172.39 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) % 172.48/172.39 => hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_ca_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_x_2),V_y_2)) = hAPP(hAPP(c_Set_Oinsert(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool))) ) % 172.48/172.39 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) % 172.48/172.39 => hAPP(c_Set_Oimage(tc_Nat_Onat,tc_Nat_Onat,hAPP(hAPP(c_COMBC(tc_Nat_Onat,tc_Nat_Onat,tc_Nat_Onat),c_Groups_Ominus__class_Ominus(tc_Nat_Onat)),V_ca_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(tc_Nat_Onat,V_x_2),V_y_2)) = c_Orderings_Obot__class_Obot(tc_fun(tc_Nat_Onat,tc_HOL_Obool)) ) ) ) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_sum__diff__distrib,axiom, % 172.48/172.39 ! [V_n_2,V_P_2,V_Q_2] : % 172.48/172.39 ( ! [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))) % 172.48/172.39 => 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)) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_setsum__natinterval__difff,axiom, % 172.48/172.39 ! [V_f_2,V_n_2,V_m_2,T_a] : % 172.48/172.39 ( class_Groups_Oab__group__add(T_a) % 172.48/172.39 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 172.48/172.39 => 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)))) ) % 172.48/172.39 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 172.48/172.39 => 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) ) ) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_gauss__sum,axiom, % 172.48/172.39 ! [V_n_2,T_a] : % 172.48/172.39 ( class_Rings_Ocomm__semiring__1(T_a) % 172.48/172.39 => 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))) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_decr__mult__lemma,axiom, % 172.48/172.39 ! [V_k_2,V_P_2,V_d_2] : % 172.48/172.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2)) % 172.48/172.39 => ( ! [B_x] : % 172.48/172.39 ( hBOOL(hAPP(V_P_2,B_x)) % 172.48/172.39 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_d_2))) ) % 172.48/172.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 172.48/172.39 => ! [B_x] : % 172.48/172.39 ( hBOOL(hAPP(V_P_2,B_x)) % 172.48/172.39 => 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)))) ) ) ) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_incr__mult__lemma,axiom, % 172.48/172.39 ! [V_k_2,V_P_2,V_d_2] : % 172.48/172.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2)) % 172.48/172.39 => ( ! [B_x] : % 172.48/172.39 ( hBOOL(hAPP(V_P_2,B_x)) % 172.48/172.39 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_d_2))) ) % 172.48/172.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k_2)) % 172.48/172.39 => ! [B_x] : % 172.48/172.39 ( hBOOL(hAPP(V_P_2,B_x)) % 172.48/172.39 => 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)))) ) ) ) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_finite__atLeastLessThan,axiom, % 172.48/172.39 ! [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))) ). % 172.48/172.39 % 172.48/172.39 fof(fact_finite__atLeastAtMost,axiom, % 172.48/172.39 ! [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))) ). % 172.48/172.39 % 172.48/172.39 fof(fact_atLeastLessThanSuc__atLeastAtMost,axiom, % 172.48/172.39 ! [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) ). % 172.48/172.39 % 172.48/172.39 fof(fact_ivl__disj__un_I21_J,axiom, % 172.48/172.39 ! [V_u_2,V_m_2,V_l_2,T_a] : % 172.48/172.39 ( class_Orderings_Olinorder(T_a) % 172.48/172.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_m_2)) % 172.48/172.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_m_2),V_u_2)) % 172.48/172.39 => 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) ) ) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_ivl__disj__int_I15_J,axiom, % 172.48/172.39 ! [V_u_2,V_m_2,V_l_2,T_a] : % 172.48/172.39 ( class_Orderings_Oorder(T_a) % 172.48/172.39 => 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)) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_atLeastLessThan__inj_I2_J,axiom, % 172.48/172.39 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 172.48/172.39 ( class_Orderings_Olinorder(T_a) % 172.48/172.39 => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2),V_b_2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_ca_2),V_d_2) % 172.48/172.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) % 172.48/172.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),V_d_2)) % 172.48/172.39 => V_b_2 = V_d_2 ) ) ) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_atLeastLessThan__inj_I1_J,axiom, % 172.48/172.39 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 172.48/172.39 ( class_Orderings_Olinorder(T_a) % 172.48/172.39 => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2),V_b_2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_ca_2),V_d_2) % 172.48/172.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) % 172.48/172.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),V_d_2)) % 172.48/172.39 => V_a_2 = V_ca_2 ) ) ) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_atLeastLessThan__eq__iff,axiom, % 172.48/172.39 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 172.48/172.39 ( class_Orderings_Olinorder(T_a) % 172.48/172.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) % 172.48/172.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),V_d_2)) % 172.48/172.39 => ( hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2),V_b_2) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_ca_2),V_d_2) % 172.48/172.39 <=> ( V_a_2 = V_ca_2 % 172.48/172.39 & V_b_2 = V_d_2 ) ) ) ) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_atLeastLessThan__add__Un,axiom, % 172.48/172.39 ! [V_k_2,V_j_2,V_i_2] : % 172.48/172.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i_2),V_j_2)) % 172.48/172.39 => 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))) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_atLeastLessThan0,axiom, % 172.48/172.39 ! [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)) ). % 172.48/172.39 % 172.48/172.39 fof(fact_atLeast0LessThan,axiom, % 172.48/172.39 ! [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) ). % 172.48/172.39 % 172.48/172.39 fof(fact_ivl__disj__un_I6_J,axiom, % 172.48/172.39 ! [V_u_2,V_l_2,T_a] : % 172.48/172.39 ( class_Orderings_Olinorder(T_a) % 172.48/172.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2)) % 172.48/172.39 => 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) ) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_subset__card__intvl__is__intvl,axiom, % 172.48/172.39 ! [V_k_2,V_A_2] : % 172.48/172.39 ( 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))))) % 172.48/172.39 => 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))) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_card__atLeastLessThan,axiom, % 172.48/172.39 ! [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) ). % 172.48/172.39 % 172.48/172.39 fof(fact_atLeastatMost__empty__iff2,axiom, % 172.48/172.39 ! [V_b_2,V_a_2,T_a] : % 172.48/172.39 ( class_Orderings_Oorder(T_a) % 172.48/172.39 => ( 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) % 172.48/172.39 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) ) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_atLeastatMost__empty__iff,axiom, % 172.48/172.39 ! [V_b_2,V_a_2,T_a] : % 172.48/172.39 ( class_Orderings_Oorder(T_a) % 172.48/172.39 => ( 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)) % 172.48/172.39 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) ) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_atLeastatMost__empty,axiom, % 172.48/172.39 ! [V_a_2,V_b_2,T_a] : % 172.48/172.39 ( class_Orderings_Oorder(T_a) % 172.48/172.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),V_a_2)) % 172.48/172.39 => 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)) ) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_atLeastatMost__subset__iff,axiom, % 172.48/172.39 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 172.48/172.39 ( class_Orderings_Oorder(T_a) % 172.48/172.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_ca_2,V_d_2))) % 172.48/172.39 <=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) % 172.48/172.39 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_ca_2),V_a_2)) % 172.48/172.39 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_d_2)) ) ) ) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_image__Suc__atLeastLessThan,axiom, % 172.48/172.39 ! [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)) ). % 172.48/172.39 % 172.48/172.39 fof(fact_atLeastLessThan__empty,axiom, % 172.48/172.39 ! [V_a_2,V_b_2,T_a] : % 172.48/172.39 ( class_Orderings_Oorder(T_a) % 172.48/172.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_a_2)) % 172.48/172.39 => 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)) ) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_atLeastLessThan__empty__iff2,axiom, % 172.48/172.39 ! [V_b_2,V_a_2,T_a] : % 172.48/172.39 ( class_Orderings_Oorder(T_a) % 172.48/172.39 => ( 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) % 172.48/172.39 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_atLeastLessThan__empty__iff,axiom, % 172.48/172.39 ! [V_b_2,V_a_2,T_a] : % 172.48/172.39 ( class_Orderings_Oorder(T_a) % 172.48/172.39 => ( 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)) % 172.48/172.39 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_atLeastAtMost__singleton,axiom, % 172.48/172.39 ! [V_a_2,T_a] : % 172.48/172.39 ( class_Orderings_Oorder(T_a) % 172.48/172.39 => 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))) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_atLeastAtMost__singleton__iff,axiom, % 172.48/172.39 ! [V_ca_2,V_b_2,V_a_2,T_a] : % 172.48/172.39 ( class_Orderings_Oorder(T_a) % 172.48/172.39 => ( c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2) = hAPP(hAPP(c_Set_Oinsert(T_a),V_ca_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) % 172.48/172.39 <=> ( V_a_2 = V_b_2 % 172.48/172.39 & V_b_2 = V_ca_2 ) ) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_atLeastAtMost__singleton_H,axiom, % 172.48/172.39 ! [V_b_2,V_a_2,T_a] : % 172.48/172.39 ( class_Orderings_Oorder(T_a) % 172.48/172.39 => ( V_a_2 = V_b_2 % 172.48/172.39 => 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))) ) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_atLeastLessThan__subset__iff,axiom, % 172.48/172.39 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 172.48/172.39 ( class_Orderings_Olinorder(T_a) % 172.48/172.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2),V_b_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_ca_2),V_d_2))) % 172.48/172.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_a_2)) % 172.48/172.39 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_ca_2),V_a_2)) % 172.48/172.39 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_d_2)) ) ) ) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_setsum__shift__bounds__Suc__ivl,axiom, % 172.48/172.39 ! [V_n_2,V_m_2,V_f_2,T_a] : % 172.48/172.39 ( class_Groups_Ocomm__monoid__add(T_a) % 172.48/172.39 => 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)) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_ivl__disj__un_I17_J,axiom, % 172.48/172.39 ! [V_u_2,V_m_2,V_l_2,T_a] : % 172.48/172.39 ( class_Orderings_Olinorder(T_a) % 172.48/172.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_m_2)) % 172.48/172.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_m_2),V_u_2)) % 172.48/172.39 => 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) ) ) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_setsum__shift__bounds__nat__ivl,axiom, % 172.48/172.39 ! [V_n_2,V_k_2,V_m_2,V_f_2,T_a] : % 172.48/172.39 ( class_Groups_Ocomm__monoid__add(T_a) % 172.48/172.39 => 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)) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_ivl__diff,axiom, % 172.48/172.39 ! [V_m_2,V_n_2,V_i_2,T_a] : % 172.48/172.39 ( class_Orderings_Olinorder(T_a) % 172.48/172.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_i_2),V_n_2)) % 172.48/172.39 => 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) ) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_ivl__disj__int_I11_J,axiom, % 172.48/172.39 ! [V_u_2,V_m_2,V_l_2,T_a] : % 172.48/172.39 ( class_Orderings_Oorder(T_a) % 172.48/172.39 => 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)) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_image__Suc__atLeastAtMost,axiom, % 172.48/172.39 ! [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)) ). % 172.48/172.39 % 172.48/172.39 fof(fact_setsum__shift__bounds__cl__Suc__ivl,axiom, % 172.48/172.39 ! [V_n_2,V_m_2,V_f_2,T_a] : % 172.48/172.39 ( class_Groups_Ocomm__monoid__add(T_a) % 172.48/172.39 => 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)) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_setsum__shift__bounds__cl__nat__ivl,axiom, % 172.48/172.39 ! [V_n_2,V_k_2,V_m_2,V_f_2,T_a] : % 172.48/172.39 ( class_Groups_Ocomm__monoid__add(T_a) % 172.48/172.39 => 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)) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_image__add__atLeastLessThan,axiom, % 172.48/172.39 ! [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)) ). % 172.48/172.39 % 172.48/172.39 fof(fact_image__add__atLeastAtMost,axiom, % 172.48/172.39 ! [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)) ). % 172.48/172.39 % 172.48/172.39 fof(fact_setsum__add__nat__ivl,axiom, % 172.48/172.39 ! [V_f_2,V_p_2,V_n_2,V_m_2,T_a] : % 172.48/172.39 ( class_Groups_Ocomm__monoid__add(T_a) % 172.48/172.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 172.48/172.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_p_2)) % 172.48/172.39 => 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)) ) ) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_setsum__diff__nat__ivl,axiom, % 172.48/172.39 ! [V_f_2,V_p_2,V_n_2,V_m_2,T_a] : % 172.48/172.39 ( class_Groups_Oab__group__add(T_a) % 172.48/172.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 172.48/172.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_p_2)) % 172.48/172.39 => 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)) ) ) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_card__atLeastAtMost,axiom, % 172.48/172.39 ! [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) ). % 172.48/172.39 % 172.48/172.39 fof(fact_atLeastAtMostSuc__conv,axiom, % 172.48/172.39 ! [V_n_2,V_m_2] : % 172.48/172.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),hAPP(c_Nat_OSuc,V_n_2))) % 172.48/172.39 => 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)) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_atLeastLessThan__singleton,axiom, % 172.48/172.39 ! [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))) ). % 172.48/172.39 % 172.48/172.39 fof(fact_setsum__shift__lb__Suc0__0,axiom, % 172.48/172.39 ! [V_k_2,V_f_2] : % 172.48/172.39 ( hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 172.48/172.39 => 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)) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_atLeastatMost__psubset__iff,axiom, % 172.48/172.39 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 172.48/172.39 ( class_Orderings_Oorder(T_a) % 172.48/172.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_ca_2,V_d_2))) % 172.48/172.39 <=> ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) % 172.48/172.39 | ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_ca_2),V_a_2)) % 172.48/172.39 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),V_d_2)) % 172.48/172.39 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),V_a_2)) % 172.48/172.39 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),V_d_2)) ) ) ) % 172.48/172.39 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_ca_2),V_d_2)) ) ) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_ivl__disj__int_I4_J,axiom, % 172.48/172.39 ! [V_u_2,V_l_2,T_a] : % 172.48/172.39 ( class_Orderings_Oorder(T_a) % 172.48/172.39 => 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)) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_ivl__disj__un_I8_J,axiom, % 172.48/172.39 ! [V_u_2,V_l_2,T_a] : % 172.48/172.39 ( class_Orderings_Olinorder(T_a) % 172.48/172.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2)) % 172.48/172.39 => 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) ) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_ivl__disj__int_I2_J,axiom, % 172.48/172.39 ! [V_u_2,V_l_2,T_a] : % 172.48/172.39 ( class_Orderings_Oorder(T_a) % 172.48/172.39 => 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)) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_setsum__shift__lb__Suc0__0__upt,axiom, % 172.48/172.39 ! [V_k_2,V_f_2,T_a] : % 172.48/172.39 ( class_Groups_Ocomm__monoid__add(T_a) % 172.48/172.39 => ( hAPP(V_f_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(T_a) % 172.48/172.39 => 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)) ) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_setsum__head__upt__Suc,axiom, % 172.48/172.39 ! [V_f_2,V_n_2,V_m_2,T_a] : % 172.48/172.39 ( class_Groups_Ocomm__monoid__add(T_a) % 172.48/172.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 172.48/172.39 => 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))) ) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_setsum__head__Suc,axiom, % 172.48/172.39 ! [V_f_2,V_n_2,V_m_2,T_a] : % 172.48/172.39 ( class_Groups_Ocomm__monoid__add(T_a) % 172.48/172.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 172.48/172.39 => 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))) ) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_atLeastLessThanSuc,axiom, % 172.48/172.39 ! [V_n_2,V_m_2] : % 172.48/172.39 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 172.48/172.39 => 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)) ) % 172.48/172.39 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 172.48/172.39 => 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)) ) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_setsum__op__ivl__Suc,axiom, % 172.48/172.39 ! [V_f_2,V_m_2,V_n_2,T_a] : % 172.48/172.39 ( class_Groups_Ocomm__monoid__add(T_a) % 172.48/172.39 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) % 172.48/172.39 => 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) ) % 172.48/172.39 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) % 172.48/172.39 => 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)) ) ) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_setsum__cl__ivl__Suc,axiom, % 172.48/172.39 ! [V_f_2,V_m_2,V_n_2,T_a] : % 172.48/172.39 ( class_Groups_Ocomm__monoid__add(T_a) % 172.48/172.39 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) % 172.48/172.39 => 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) ) % 172.48/172.39 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Nat_OSuc,V_n_2)),V_m_2)) % 172.48/172.39 => 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))) ) ) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_setsum__ub__add__nat,axiom, % 172.48/172.39 ! [V_p_2,V_f_2,V_n_2,V_m_2,T_a] : % 172.48/172.39 ( class_Groups_Ocomm__monoid__add(T_a) % 172.48/172.39 => ( 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)))) % 172.48/172.39 => 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)))) ) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_geometric__sum,axiom, % 172.48/172.39 ! [V_n_2,V_x_2,T_a] : % 172.48/172.39 ( class_Fields_Ofield(T_a) % 172.48/172.39 => ( V_x_2 != c_Groups_Oone__class_Oone(T_a) % 172.48/172.39 => 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))) ) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_ex__nat__less,axiom, % 172.48/172.39 ! [V_P_2,V_n_2] : % 172.48/172.39 ( ? [B_m] : % 172.48/172.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2)) % 172.48/172.39 & hBOOL(hAPP(V_P_2,B_m)) ) % 172.48/172.39 <=> ? [B_x] : % 172.48/172.39 ( 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))) % 172.48/172.39 & hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_all__nat__less,axiom, % 172.48/172.39 ! [V_P_2,V_n_2] : % 172.48/172.39 ( ! [B_m] : % 172.48/172.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_m),V_n_2)) % 172.48/172.39 => hBOOL(hAPP(V_P_2,B_m)) ) % 172.48/172.39 <=> ! [B_x] : % 172.48/172.39 ( 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))) % 172.48/172.39 => hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_ex__nat__less__eq,axiom, % 172.48/172.39 ! [V_P_2,V_n_2] : % 172.48/172.39 ( ? [B_m] : % 172.48/172.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2)) % 172.48/172.39 & hBOOL(hAPP(V_P_2,B_m)) ) % 172.48/172.39 <=> ? [B_x] : % 172.48/172.39 ( 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))) % 172.48/172.39 & hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_all__nat__less__eq,axiom, % 172.48/172.39 ! [V_P_2,V_n_2] : % 172.48/172.39 ( ! [B_m] : % 172.48/172.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_m),V_n_2)) % 172.48/172.39 => hBOOL(hAPP(V_P_2,B_m)) ) % 172.48/172.39 <=> ! [B_x] : % 172.48/172.39 ( 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))) % 172.48/172.39 => hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_ivl__disj__un_I18_J,axiom, % 172.48/172.39 ! [V_u_2,V_m_2,V_l_2,T_a] : % 172.48/172.39 ( class_Orderings_Olinorder(T_a) % 172.48/172.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_m_2)) % 172.48/172.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_m_2),V_u_2)) % 172.48/172.39 => 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) ) ) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_ivl__disj__un_I3_J,axiom, % 172.48/172.39 ! [V_u_2,V_l_2,T_a] : % 172.48/172.39 ( class_Orderings_Olinorder(T_a) % 172.48/172.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_l_2),V_u_2)) % 172.48/172.39 => 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) ) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_finite__greaterThanLessThan,axiom, % 172.48/172.39 ! [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))) ). % 172.48/172.39 % 172.48/172.39 fof(fact_finite__atLeastAtMost__int,axiom, % 172.48/172.39 ! [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))) ). % 172.48/172.39 % 172.48/172.39 fof(fact_finite__atLeastLessThan__int,axiom, % 172.48/172.39 ! [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))) ). % 172.48/172.39 % 172.48/172.39 fof(fact_finite__greaterThanLessThan__int,axiom, % 172.48/172.39 ! [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))) ). % 172.48/172.39 % 172.48/172.39 fof(fact_atLeastLessThanPlusOne__atLeastAtMost__int,axiom, % 172.48/172.39 ! [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) ). % 172.48/172.39 % 172.48/172.39 fof(fact_atLeastPlusOneLessThan__greaterThanLessThan__int,axiom, % 172.48/172.39 ! [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) ). % 172.48/172.39 % 172.48/172.39 fof(fact_finite__atLeastZeroLessThan__int,axiom, % 172.48/172.39 ! [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))) ). % 172.48/172.39 % 172.48/172.39 fof(fact_greaterThanLessThan__empty,axiom, % 172.48/172.39 ! [V_k_2,V_l_2,T_a] : % 172.48/172.39 ( class_Orderings_Oorder(T_a) % 172.48/172.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_k_2)) % 172.48/172.39 => 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)) ) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_atLeastSucLessThan__greaterThanLessThan,axiom, % 172.48/172.39 ! [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) ). % 172.48/172.39 % 172.48/172.39 fof(fact_image__add__int__atLeastLessThan,axiom, % 172.48/172.39 ! [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) ). % 172.48/172.39 % 172.48/172.39 fof(fact_ivl__disj__int_I12_J,axiom, % 172.48/172.39 ! [V_u_2,V_m_2,V_l_2,T_a] : % 172.48/172.39 ( class_Orderings_Oorder(T_a) % 172.48/172.39 => 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)) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_ivl__disj__int_I13_J,axiom, % 172.48/172.39 ! [V_u_2,V_m_2,V_l_2,T_a] : % 172.48/172.39 ( class_Orderings_Oorder(T_a) % 172.48/172.39 => 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)) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_ivl__disj__int_I9_J,axiom, % 172.48/172.39 ! [V_u_2,V_m_2,V_l_2,T_a] : % 172.48/172.39 ( class_Orderings_Oorder(T_a) % 172.48/172.39 => 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)) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_card__greaterThanLessThan,axiom, % 172.48/172.39 ! [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)) ). % 172.48/172.39 % 172.48/172.39 fof(fact_simp__from__to,axiom, % 172.48/172.39 ! [V_i_2,V_j_2] : % 172.48/172.39 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j_2),V_i_2)) % 172.48/172.39 => 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)) ) % 172.48/172.39 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j_2),V_i_2)) % 172.48/172.39 => 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)) ) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_ivl__disj__un_I15_J,axiom, % 172.48/172.39 ! [V_u_2,V_m_2,V_l_2,T_a] : % 172.48/172.39 ( class_Orderings_Olinorder(T_a) % 172.48/172.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_l_2),V_m_2)) % 172.48/172.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_m_2),V_u_2)) % 172.48/172.39 => 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) ) ) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_aset_I6_J,axiom, % 172.48/172.39 ! [V_A_2,V_t_2,V_D_2] : % 172.48/172.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 172.48/172.39 => ( 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)) % 172.48/172.39 => ! [B_x] : % 172.48/172.39 ( ! [B_xa] : % 172.48/172.39 ( 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))) % 172.48/172.39 => ! [B_xb] : % 172.48/172.39 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) % 172.48/172.39 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) ) % 172.48/172.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_x),V_t_2)) % 172.48/172.39 => 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)) ) ) ) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_bset_I8_J,axiom, % 172.48/172.39 ! [V_B_2,V_t_2,V_D_2] : % 172.48/172.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 172.48/172.39 => ( 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)) % 172.48/172.39 => ! [B_x] : % 172.48/172.39 ( ! [B_xa] : % 172.48/172.39 ( 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))) % 172.48/172.39 => ! [B_xb] : % 172.48/172.39 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) % 172.48/172.39 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) ) % 172.48/172.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),B_x)) % 172.48/172.39 => 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))) ) ) ) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_aset_I4_J,axiom, % 172.48/172.39 ! [V_A_2,V_t_2,V_D_2] : % 172.48/172.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 172.48/172.39 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_A_2)) % 172.48/172.39 => ! [B_x] : % 172.48/172.39 ( ! [B_xa] : % 172.48/172.39 ( 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))) % 172.48/172.39 => ! [B_xb] : % 172.48/172.39 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) % 172.48/172.39 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) ) % 172.48/172.39 => ( B_x != V_t_2 % 172.48/172.39 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_x),V_D_2) != V_t_2 ) ) ) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_bset_I4_J,axiom, % 172.48/172.39 ! [V_B_2,V_t_2,V_D_2] : % 172.48/172.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 172.48/172.39 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_B_2)) % 172.48/172.39 => ! [B_x] : % 172.48/172.39 ( ! [B_xa] : % 172.48/172.39 ( 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))) % 172.48/172.39 => ! [B_xb] : % 172.48/172.39 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) % 172.48/172.39 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) ) % 172.48/172.39 => ( B_x != V_t_2 % 172.48/172.39 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_x),V_D_2) != V_t_2 ) ) ) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_bset_I7_J,axiom, % 172.48/172.39 ! [V_B_2,V_t_2,V_D_2] : % 172.48/172.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 172.48/172.39 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_B_2)) % 172.48/172.39 => ! [B_x] : % 172.48/172.39 ( ! [B_xa] : % 172.48/172.39 ( 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))) % 172.48/172.39 => ! [B_xb] : % 172.48/172.39 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) % 172.48/172.39 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) ) % 172.48/172.39 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),B_x)) % 172.48/172.39 => 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))) ) ) ) ) ). % 172.48/172.39 % 172.48/172.39 fof(fact_aset_I5_J,axiom, % 172.48/172.39 ! [V_A_2,V_t_2,V_D_2] : % 172.48/172.39 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 172.48/172.39 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_t_2),V_A_2)) % 172.48/172.39 => ! [B_x] : % 172.48/172.40 ( ! [B_xa] : % 172.48/172.40 ( 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))) % 172.48/172.40 => ! [B_xb] : % 172.48/172.40 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) % 172.48/172.40 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) ) % 172.48/172.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_x),V_t_2)) % 172.48/172.40 => 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)) ) ) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_bset_I3_J,axiom, % 172.48/172.40 ! [V_B_2,V_t_2,V_D_2] : % 172.48/172.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 172.48/172.40 => ( 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)) % 172.48/172.40 => ( ! [B_x] : % 172.48/172.40 ( 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))) % 172.48/172.40 => ! [B_xa] : % 172.48/172.40 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),V_B_2)) % 172.48/172.40 => V_t_2 != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xa),B_x) ) ) % 172.48/172.40 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_t_2),V_D_2) = V_t_2 ) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_aset_I3_J,axiom, % 172.48/172.40 ! [V_A_2,V_t_2,V_D_2] : % 172.48/172.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 172.48/172.40 => ( 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)) % 172.48/172.40 => ( ! [B_x] : % 172.48/172.40 ( 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))) % 172.48/172.40 => ! [B_xa] : % 172.48/172.40 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xa),V_A_2)) % 172.48/172.40 => V_t_2 != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xa),B_x) ) ) % 172.48/172.40 => hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_t_2),V_D_2) = V_t_2 ) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_bset_I6_J,axiom, % 172.48/172.40 ! [V_t_2,V_B_2,V_D_2] : % 172.48/172.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 172.48/172.40 => ! [B_x] : % 172.48/172.40 ( ! [B_xa] : % 172.48/172.40 ( 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))) % 172.48/172.40 => ! [B_xb] : % 172.48/172.40 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) % 172.48/172.40 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) ) % 172.48/172.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_x),V_t_2)) % 172.48/172.40 => 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)) ) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_aset_I8_J,axiom, % 172.48/172.40 ! [V_t_2,V_A_2,V_D_2] : % 172.48/172.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 172.48/172.40 => ! [B_x] : % 172.48/172.40 ( ! [B_xa] : % 172.48/172.40 ( 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))) % 172.48/172.40 => ! [B_xb] : % 172.48/172.40 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) % 172.48/172.40 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) ) % 172.48/172.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_t_2),B_x)) % 172.48/172.40 => 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))) ) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_periodic__finite__ex,axiom, % 172.48/172.40 ! [V_P_2,V_d_2] : % 172.48/172.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2)) % 172.48/172.40 => ( ! [B_x,B_k] : % 172.48/172.40 ( hBOOL(hAPP(V_P_2,B_x)) % 172.48/172.40 <=> 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)))) ) % 172.48/172.40 => ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) % 172.48/172.40 <=> ? [B_x] : % 172.48/172.40 ( 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))) % 172.48/172.40 & hBOOL(hAPP(V_P_2,B_x)) ) ) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_aset_I7_J,axiom, % 172.48/172.40 ! [V_t_2,V_A_2,V_D_2] : % 172.48/172.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 172.48/172.40 => ! [B_x] : % 172.48/172.40 ( ! [B_xa] : % 172.48/172.40 ( 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))) % 172.48/172.40 => ! [B_xb] : % 172.48/172.40 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_A_2)) % 172.48/172.40 => B_x != hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),B_xb),B_xa) ) ) % 172.48/172.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_t_2),B_x)) % 172.48/172.40 => 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))) ) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_bset_I5_J,axiom, % 172.48/172.40 ! [V_t_2,V_B_2,V_D_2] : % 172.48/172.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_D_2)) % 172.48/172.40 => ! [B_x] : % 172.48/172.40 ( ! [B_xa] : % 172.48/172.40 ( 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))) % 172.48/172.40 => ! [B_xb] : % 172.48/172.40 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_xb),V_B_2)) % 172.48/172.40 => B_x != hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),B_xb),B_xa) ) ) % 172.48/172.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_x),V_t_2)) % 172.48/172.40 => 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)) ) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_ivl__disj__un_I19_J,axiom, % 172.48/172.40 ! [V_u_2,V_m_2,V_l_2,T_a] : % 172.48/172.40 ( class_Orderings_Olinorder(T_a) % 172.48/172.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_l_2),V_m_2)) % 172.48/172.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_m_2),V_u_2)) % 172.48/172.40 => 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) ) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_ivl__disj__un_I4_J,axiom, % 172.48/172.40 ! [V_u_2,V_l_2,T_a] : % 172.48/172.40 ( class_Orderings_Olinorder(T_a) % 172.48/172.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_l_2),V_u_2)) % 172.48/172.40 => 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) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_ivl__disj__un_I5_J,axiom, % 172.48/172.40 ! [V_u_2,V_l_2,T_a] : % 172.48/172.40 ( class_Orderings_Olinorder(T_a) % 172.48/172.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2)) % 172.48/172.40 => 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) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_image__atLeastZeroLessThan__int,axiom, % 172.48/172.40 ! [V_u_2] : % 172.48/172.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_u_2)) % 172.48/172.40 => 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))) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_zero__less__imp__eq__int,axiom, % 172.48/172.40 ! [V_k] : % 172.48/172.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k)) % 172.48/172.40 => ? [B_n] : % 172.48/172.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n)) % 172.48/172.40 & V_k = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_finite__greaterThanAtMost,axiom, % 172.48/172.40 ! [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))) ). % 172.48/172.40 % 172.48/172.40 fof(fact_finite__greaterThanAtMost__int,axiom, % 172.48/172.40 ! [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))) ). % 172.48/172.40 % 172.48/172.40 fof(fact_nat__int,axiom, % 172.48/172.40 ! [V_n] : hAPP(c_Int_Onat,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n)) = V_n ). % 172.48/172.40 % 172.48/172.40 fof(fact_card__greaterThanAtMost__int,axiom, % 172.48/172.40 ! [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)) ). % 172.48/172.40 % 172.48/172.40 fof(fact_nat__0,axiom, % 172.48/172.40 hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 172.48/172.40 % 172.48/172.40 fof(fact_transfer__nat__int__numerals_I1_J,axiom, % 172.48/172.40 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ). % 172.48/172.40 % 172.48/172.40 fof(fact_eq__nat__nat__iff,axiom, % 172.48/172.40 ! [V_z_H_2,V_z_2] : % 172.48/172.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) % 172.48/172.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H_2)) % 172.48/172.40 => ( hAPP(c_Int_Onat,V_z_2) = hAPP(c_Int_Onat,V_z_H_2) % 172.48/172.40 <=> V_z_2 = V_z_H_2 ) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_transfer__nat__int__relations_I1_J,axiom, % 172.48/172.40 ! [V_y_2,V_x_2] : % 172.48/172.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) % 172.48/172.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2)) % 172.48/172.40 => ( hAPP(c_Int_Onat,V_x_2) = hAPP(c_Int_Onat,V_y_2) % 172.48/172.40 <=> V_x_2 = V_y_2 ) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_all__nat,axiom, % 172.48/172.40 ! [V_P_2] : % 172.48/172.40 ( ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) % 172.48/172.40 <=> ! [B_x] : % 172.48/172.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 172.48/172.40 => hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,B_x))) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_ex__nat,axiom, % 172.48/172.40 ! [V_P_2] : % 172.48/172.40 ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) % 172.48/172.40 <=> ? [B_x] : % 172.48/172.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 172.48/172.40 & hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,B_x))) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_transfer__nat__int__numerals_I2_J,axiom, % 172.48/172.40 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)) ). % 172.48/172.40 % 172.48/172.40 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I4_J,axiom, % 172.48/172.40 ! [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))) ). % 172.48/172.40 % 172.48/172.40 fof(fact_transfer__int__nat__set__return__embed,axiom, % 172.48/172.40 ! [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 ). % 172.48/172.40 % 172.48/172.40 fof(fact_transfer__nat__int__sum__prod_I2_J,axiom, % 172.48/172.40 ! [V_A_2,V_f_2,T_a] : % 172.48/172.40 ( ( class_Groups_Ocomm__monoid__add(T_a) % 172.48/172.40 & class_Groups_Ocomm__monoid__mult(T_a) ) % 172.48/172.40 => 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)) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_greaterThanAtMost__empty,axiom, % 172.48/172.40 ! [V_k_2,V_l_2,T_a] : % 172.48/172.40 ( class_Orderings_Oorder(T_a) % 172.48/172.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_k_2)) % 172.48/172.40 => 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)) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_greaterThanAtMost__empty__iff2,axiom, % 172.48/172.40 ! [V_l_2,V_k_2,T_a] : % 172.48/172.40 ( class_Orderings_Oorder(T_a) % 172.48/172.40 => ( 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) % 172.48/172.40 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_k_2),V_l_2)) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_greaterThanAtMost__empty__iff,axiom, % 172.48/172.40 ! [V_l_2,V_k_2,T_a] : % 172.48/172.40 ( class_Orderings_Oorder(T_a) % 172.48/172.40 => ( 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)) % 172.48/172.40 <=> ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_k_2),V_l_2)) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_ivl__disj__un_I20_J,axiom, % 172.48/172.40 ! [V_u_2,V_m_2,V_l_2,T_a] : % 172.48/172.40 ( class_Orderings_Olinorder(T_a) % 172.48/172.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_m_2)) % 172.48/172.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_m_2),V_u_2)) % 172.48/172.40 => 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) ) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I2_J,axiom, % 172.48/172.40 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))) ). % 172.48/172.40 % 172.48/172.40 fof(fact_ivl__disj__int_I14_J,axiom, % 172.48/172.40 ! [V_u_2,V_m_2,V_l_2,T_a] : % 172.48/172.40 ( class_Orderings_Oorder(T_a) % 172.48/172.40 => 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)) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_atLeastSucAtMost__greaterThanAtMost,axiom, % 172.48/172.40 ! [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) ). % 172.48/172.40 % 172.48/172.40 fof(fact_nat__0__iff,axiom, % 172.48/172.40 ! [V_i_2] : % 172.48/172.40 ( hAPP(c_Int_Onat,V_i_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 172.48/172.40 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_nat__le__0,axiom, % 172.48/172.40 ! [V_z] : % 172.48/172.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 172.48/172.40 => hAPP(c_Int_Onat,V_z) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_zless__nat__conj,axiom, % 172.48/172.40 ! [V_z_2,V_w_2] : % 172.48/172.40 ( 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))) % 172.48/172.40 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) % 172.48/172.40 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_nat__mono__iff,axiom, % 172.48/172.40 ! [V_w_2,V_z_2] : % 172.48/172.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) % 172.48/172.40 => ( 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))) % 172.48/172.40 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_transfer__nat__int__relations_I3_J,axiom, % 172.48/172.40 ! [V_y_2,V_x_2] : % 172.48/172.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) % 172.48/172.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2)) % 172.48/172.40 => ( 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))) % 172.48/172.40 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),V_y_2)) ) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_nat__1,axiom, % 172.48/172.40 hAPP(c_Int_Onat,c_Groups_Oone__class_Oone(tc_Int_Oint)) = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ). % 172.48/172.40 % 172.48/172.40 fof(fact_nat__0__le,axiom, % 172.48/172.40 ! [V_z] : % 172.48/172.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 172.48/172.40 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_int__eq__iff,axiom, % 172.48/172.40 ! [V_z_2,V_m_2] : % 172.48/172.40 ( hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) = V_z_2 % 172.48/172.40 <=> ( V_m_2 = hAPP(c_Int_Onat,V_z_2) % 172.48/172.40 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_int__nat__eq,axiom, % 172.48/172.40 ! [V_z] : % 172.48/172.40 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 172.48/172.40 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ) % 172.48/172.40 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 172.48/172.40 => 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) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_zless__nat__eq__int__zless,axiom, % 172.48/172.40 ! [V_z_2,V_m_2] : % 172.48/172.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),hAPP(c_Int_Onat,V_z_2))) % 172.48/172.40 <=> 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)) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_card__greaterThanAtMost,axiom, % 172.48/172.40 ! [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) ). % 172.48/172.40 % 172.48/172.40 fof(fact_SetInterval_Otransfer__nat__int__set__functions_I2_J,axiom, % 172.48/172.40 ! [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))) ). % 172.48/172.40 % 172.48/172.40 fof(fact_transfer__nat__int__sum__prod_I1_J,axiom, % 172.48/172.40 ! [V_A_2,V_f_2,T_a] : % 172.48/172.40 ( ( class_Groups_Ocomm__monoid__add(T_a) % 172.48/172.40 & class_Groups_Ocomm__monoid__mult(T_a) ) % 172.48/172.40 => 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)) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_card__atLeastZeroLessThan__int,axiom, % 172.48/172.40 ! [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) ). % 172.48/172.40 % 172.48/172.40 fof(fact_card__atLeastLessThan__int,axiom, % 172.48/172.40 ! [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)) ). % 172.48/172.40 % 172.48/172.40 fof(fact_zero__less__nat__eq,axiom, % 172.48/172.40 ! [V_z_2] : % 172.48/172.40 ( 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))) % 172.48/172.40 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_nat__less__eq__zless,axiom, % 172.48/172.40 ! [V_z_2,V_w_2] : % 172.48/172.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 172.48/172.40 => ( 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))) % 172.48/172.40 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_transfer__nat__int__relations_I2_J,axiom, % 172.48/172.40 ! [V_y_2,V_x_2] : % 172.48/172.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) % 172.48/172.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y_2)) % 172.48/172.40 => ( 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))) % 172.48/172.40 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2)) ) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_nat__eq__iff,axiom, % 172.48/172.40 ! [V_m_2,V_w_2] : % 172.48/172.40 ( hAPP(c_Int_Onat,V_w_2) = V_m_2 % 172.48/172.40 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 172.48/172.40 => V_w_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) ) % 172.48/172.40 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 172.48/172.40 => V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_nat__eq__iff2,axiom, % 172.48/172.40 ! [V_w_2,V_m_2] : % 172.48/172.40 ( V_m_2 = hAPP(c_Int_Onat,V_w_2) % 172.48/172.40 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 172.48/172.40 => V_w_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_m_2) ) % 172.48/172.40 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 172.48/172.40 => V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_nat__le__eq__zle,axiom, % 172.48/172.40 ! [V_z_2,V_w_2] : % 172.48/172.40 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 172.48/172.40 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) % 172.48/172.40 => ( 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))) % 172.48/172.40 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_split__nat,axiom, % 172.48/172.40 ! [V_i_2,V_P_2] : % 172.48/172.40 ( hBOOL(hAPP(V_P_2,hAPP(c_Int_Onat,V_i_2))) % 172.48/172.40 <=> ( ! [B_n] : % 172.48/172.40 ( V_i_2 = hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),B_n) % 172.48/172.40 => hBOOL(hAPP(V_P_2,B_n)) ) % 172.48/172.40 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 172.48/172.40 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_nat__add__distrib,axiom, % 172.48/172.40 ! [V_z_H,V_z] : % 172.48/172.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 172.48/172.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H)) % 172.48/172.40 => 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)) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I1_J,axiom, % 172.48/172.40 ! [V_y,V_x] : % 172.48/172.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 172.48/172.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 172.48/172.40 => 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)) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_nat__mult__distrib,axiom, % 172.48/172.40 ! [V_z_H,V_z] : % 172.48/172.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 172.48/172.40 => 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)) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I2_J,axiom, % 172.48/172.40 ! [V_y,V_x] : % 172.48/172.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 172.48/172.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 172.48/172.40 => 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)) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I3_J,axiom, % 172.48/172.40 ! [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))) ). % 172.48/172.40 % 172.48/172.40 fof(fact_nat__diff__distrib,axiom, % 172.48/172.40 ! [V_z,V_z_H] : % 172.48/172.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_H)) % 172.48/172.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_H),V_z)) % 172.48/172.40 => 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)) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_transfer__nat__int__sum__prod2_I1_J,axiom, % 172.48/172.40 ! [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)) ). % 172.48/172.40 % 172.48/172.40 fof(fact_nat__mod__distrib,axiom, % 172.48/172.40 ! [V_y,V_x] : % 172.48/172.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 172.48/172.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 172.48/172.40 => 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)) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_Divides_Otransfer__nat__int__functions_I2_J,axiom, % 172.48/172.40 ! [V_y,V_x] : % 172.48/172.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 172.48/172.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 172.48/172.40 => 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)) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_nat__div__distrib,axiom, % 172.48/172.40 ! [V_y,V_x] : % 172.48/172.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 172.48/172.40 => 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)) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_Divides_Otransfer__nat__int__functions_I1_J,axiom, % 172.48/172.40 ! [V_y,V_x] : % 172.48/172.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 172.48/172.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 172.48/172.40 => 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)) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_ivl__disj__un_I22_J,axiom, % 172.48/172.40 ! [V_u_2,V_m_2,V_l_2,T_a] : % 172.48/172.40 ( class_Orderings_Olinorder(T_a) % 172.48/172.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_m_2)) % 172.48/172.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_m_2),V_u_2)) % 172.48/172.40 => 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) ) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_atLeastPlusOneAtMost__greaterThanAtMost__int,axiom, % 172.48/172.40 ! [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) ). % 172.48/172.40 % 172.48/172.40 fof(fact_ivl__disj__int_I16_J,axiom, % 172.48/172.40 ! [V_u_2,V_m_2,V_l_2,T_a] : % 172.48/172.40 ( class_Orderings_Oorder(T_a) % 172.48/172.40 => 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)) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I4_J,axiom, % 172.48/172.40 ! [V_n,V_x] : % 172.48/172.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 172.48/172.40 => 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)) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_nat__power__eq,axiom, % 172.48/172.40 ! [V_n,V_z] : % 172.48/172.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 172.48/172.40 => 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) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_transfer__nat__int__sum__prod2_I2_J,axiom, % 172.48/172.40 ! [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)) ). % 172.48/172.40 % 172.48/172.40 fof(fact_ivl__disj__int_I10_J,axiom, % 172.48/172.40 ! [V_u_2,V_m_2,V_l_2,T_a] : % 172.48/172.40 ( class_Orderings_Oorder(T_a) % 172.48/172.40 => 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)) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_Nat__Transfer_Otransfer__nat__int__functions_I3_J,axiom, % 172.48/172.40 ! [V_y,V_x] : % 172.48/172.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 172.48/172.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_y)) % 172.48/172.40 => 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)) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_one__less__nat__eq,axiom, % 172.48/172.40 ! [V_z_2] : % 172.48/172.40 ( 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))) % 172.48/172.40 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)),V_z_2)) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_nat__less__iff,axiom, % 172.48/172.40 ! [V_m_2,V_w_2] : % 172.48/172.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_w_2)) % 172.48/172.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(c_Int_Onat,V_w_2)),V_m_2)) % 172.48/172.40 <=> 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))) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_Suc__nat__eq__nat__zadd1,axiom, % 172.48/172.40 ! [V_z] : % 172.48/172.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 172.48/172.40 => 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)) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_card__atLeastAtMost__int,axiom, % 172.48/172.40 ! [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))) ). % 172.48/172.40 % 172.48/172.40 fof(fact_ivl__disj__un_I16_J,axiom, % 172.48/172.40 ! [V_u_2,V_m_2,V_l_2,T_a] : % 172.48/172.40 ( class_Orderings_Olinorder(T_a) % 172.48/172.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_m_2)) % 172.48/172.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_m_2),V_u_2)) % 172.48/172.40 => 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) ) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_setsum__head,axiom, % 172.48/172.40 ! [V_P_2,V_n_2,V_m_2,T_a] : % 172.48/172.40 ( class_Groups_Ocomm__monoid__add(T_a) % 172.48/172.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 172.48/172.40 => 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))) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_card__greaterThanLessThan__int,axiom, % 172.48/172.40 ! [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)))) ). % 172.48/172.40 % 172.48/172.40 fof(fact_nat__aux__def,axiom, % 172.48/172.40 ! [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) ). % 172.48/172.40 % 172.48/172.40 fof(fact_transfer__morphism__nat__int,axiom, % 172.48/172.40 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))) ). % 172.48/172.40 % 172.48/172.40 fof(fact_SetInterval_Otransfer__int__nat__set__functions,axiom, % 172.48/172.40 ! [V_n_2,V_m_2] : % 172.48/172.40 ( c_Nat__Transfer_Ois__nat(V_m_2) % 172.48/172.40 => ( c_Nat__Transfer_Ois__nat(V_n_2) % 172.48/172.40 => 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))) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I3_J,axiom, % 172.48/172.40 ! [V_B_2,V_A_2] : % 172.48/172.40 ( c_Nat__Transfer_Onat__set(V_A_2) % 172.48/172.40 => ( c_Nat__Transfer_Onat__set(V_B_2) % 172.48/172.40 => 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))) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_transfer__int__nat__set__relations_I4_J,axiom, % 172.48/172.40 ! [V_B_2,V_A_2] : % 172.48/172.40 ( c_Nat__Transfer_Onat__set(V_A_2) % 172.48/172.40 => ( c_Nat__Transfer_Onat__set(V_B_2) % 172.48/172.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2)) % 172.48/172.40 <=> 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))) ) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_ivl__disj__un_I7_J,axiom, % 172.48/172.40 ! [V_u_2,V_l_2,T_a] : % 172.48/172.40 ( class_Orderings_Olinorder(T_a) % 172.48/172.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_l_2),V_u_2)) % 172.48/172.40 => 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) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_finite__atMost,axiom, % 172.48/172.40 ! [V_k_2] : hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),hAPP(c_SetInterval_Oord__class_OatMost(tc_Nat_Onat),V_k_2))) ). % 172.48/172.40 % 172.48/172.40 fof(fact_SetInterval_Otransfer__int__nat__set__function__closures,axiom, % 172.48/172.40 ! [V_y_2,V_x_2] : % 172.48/172.40 ( c_Nat__Transfer_Ois__nat(V_x_2) % 172.48/172.40 => c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_x_2,V_y_2)) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I6_J,axiom, % 172.48/172.40 ! [V_x_2,V_A_2] : % 172.48/172.40 ( c_Nat__Transfer_Onat__set(V_A_2) % 172.48/172.40 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2)) % 172.48/172.40 => c_Nat__Transfer_Ois__nat(V_x_2) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I3_J,axiom, % 172.48/172.40 ! [V_B_2,V_A_2] : % 172.48/172.40 ( c_Nat__Transfer_Onat__set(V_A_2) % 172.48/172.40 => ( c_Nat__Transfer_Onat__set(V_B_2) % 172.48/172.40 => 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)) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_atMost__eq__iff,axiom, % 172.48/172.40 ! [V_y_2,V_x_2,T_a] : % 172.48/172.40 ( class_Orderings_Olinorder(T_a) % 172.48/172.40 => ( hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_x_2) = hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_y_2) % 172.48/172.40 <=> V_x_2 = V_y_2 ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I2_J,axiom, % 172.48/172.40 ! [V_B_2,V_A_2] : % 172.48/172.40 ( c_Nat__Transfer_Onat__set(V_A_2) % 172.48/172.40 => ( c_Nat__Transfer_Onat__set(V_B_2) % 172.48/172.40 => 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)) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_transfer__int__nat__set__relations_I3_J,axiom, % 172.48/172.40 ! [V_B_2,V_A_2] : % 172.48/172.40 ( c_Nat__Transfer_Onat__set(V_A_2) % 172.48/172.40 => ( c_Nat__Transfer_Onat__set(V_B_2) % 172.48/172.40 => ( V_A_2 = V_B_2 % 172.48/172.40 <=> 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) ) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I5_J,axiom, % 172.48/172.40 c_Nat__Transfer_Ois__nat(c_Groups_Ozero__class_Ozero(tc_Int_Oint)) ). % 172.48/172.40 % 172.48/172.40 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I1_J,axiom, % 172.48/172.40 ! [V_y,V_x] : % 172.48/172.40 ( c_Nat__Transfer_Ois__nat(V_x) % 172.48/172.40 => ( c_Nat__Transfer_Ois__nat(V_y) % 172.48/172.40 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_x),V_y)) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I9_J,axiom, % 172.48/172.40 ! [V_z] : c_Nat__Transfer_Ois__nat(hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_z)) ). % 172.48/172.40 % 172.48/172.40 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I6_J,axiom, % 172.48/172.40 c_Nat__Transfer_Ois__nat(c_Groups_Oone__class_Oone(tc_Int_Oint)) ). % 172.48/172.40 % 172.48/172.40 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I2_J,axiom, % 172.48/172.40 ! [V_y,V_x] : % 172.48/172.40 ( c_Nat__Transfer_Ois__nat(V_x) % 172.48/172.40 => ( c_Nat__Transfer_Ois__nat(V_y) % 172.48/172.40 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_x),V_y)) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_Divides_Otransfer__int__nat__function__closures_I2_J,axiom, % 172.48/172.40 ! [V_y,V_x] : % 172.48/172.40 ( c_Nat__Transfer_Ois__nat(V_x) % 172.48/172.40 => ( c_Nat__Transfer_Ois__nat(V_y) % 172.48/172.40 => c_Nat__Transfer_Ois__nat(c_Divides_Odiv__class_Omod(tc_Int_Oint,V_x,V_y)) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_Divides_Otransfer__int__nat__function__closures_I1_J,axiom, % 172.48/172.40 ! [V_y,V_x] : % 172.48/172.40 ( c_Nat__Transfer_Ois__nat(V_x) % 172.48/172.40 => ( c_Nat__Transfer_Ois__nat(V_y) % 172.48/172.40 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_x),V_y)) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I4_J,axiom, % 172.48/172.40 ! [V_n,V_x] : % 172.48/172.40 ( c_Nat__Transfer_Ois__nat(V_x) % 172.48/172.40 => c_Nat__Transfer_Ois__nat(hAPP(hAPP(c_Power_Opower__class_Opower(tc_Int_Oint),V_x),V_n)) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I3_J,axiom, % 172.48/172.40 ! [V_y,V_x] : % 172.48/172.40 ( c_Nat__Transfer_Ois__nat(V_x) % 172.48/172.40 => ( c_Nat__Transfer_Ois__nat(V_y) % 172.48/172.40 => c_Nat__Transfer_Ois__nat(c_Nat__Transfer_Otsub(V_x,V_y)) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_transfer__int__nat__set__relations_I2_J,axiom, % 172.48/172.40 ! [V_A_2,V_x_2] : % 172.48/172.40 ( c_Nat__Transfer_Ois__nat(V_x_2) % 172.48/172.40 => ( c_Nat__Transfer_Onat__set(V_A_2) % 172.48/172.40 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2)) % 172.48/172.40 <=> 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))) ) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I1_J,axiom, % 172.48/172.40 c_Nat__Transfer_Onat__set(c_Orderings_Obot__class_Obot(tc_fun(tc_Int_Oint,tc_HOL_Obool))) ). % 172.48/172.40 % 172.48/172.40 fof(fact_nat__set__def,axiom, % 172.48/172.40 ! [V_S_2] : % 172.48/172.40 ( c_Nat__Transfer_Onat__set(V_S_2) % 172.48/172.40 <=> ! [B_x] : % 172.48/172.40 ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),B_x),V_S_2)) % 172.48/172.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_atLeast0AtMost,axiom, % 172.48/172.40 ! [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) ). % 172.48/172.40 % 172.48/172.40 fof(fact_is__nat__def,axiom, % 172.48/172.40 ! [V_x_2] : % 172.48/172.40 ( c_Nat__Transfer_Ois__nat(V_x_2) % 172.48/172.40 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_lessThan__Suc__atMost,axiom, % 172.48/172.40 ! [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) ). % 172.48/172.40 % 172.48/172.40 fof(fact_card__atMost,axiom, % 172.48/172.40 ! [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) ). % 172.48/172.40 % 172.48/172.40 fof(fact_atMost__Suc,axiom, % 172.48/172.40 ! [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)) ). % 172.48/172.40 % 172.48/172.40 fof(fact_atMost__iff,axiom, % 172.48/172.40 ! [V_k_2,V_i_2,T_a] : % 172.48/172.40 ( class_Orderings_Oord(T_a) % 172.48/172.40 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_k_2))) % 172.48/172.40 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_i_2),V_k_2)) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I5_J,axiom, % 172.48/172.40 ! [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)) ). % 172.48/172.40 % 172.48/172.40 fof(fact_atMost__subset__iff,axiom, % 172.48/172.40 ! [V_y_2,V_x_2,T_a] : % 172.48/172.40 ( class_Orderings_Oorder(T_a) % 172.48/172.40 => ( 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))) % 172.48/172.40 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_transfer__int__nat__sum__prod_I2_J,axiom, % 172.48/172.40 ! [V_f_2,V_A_2,T_a] : % 172.48/172.40 ( ( class_Groups_Ocomm__monoid__add(T_a) % 172.48/172.40 & class_Groups_Ocomm__monoid__mult(T_a) ) % 172.48/172.40 => ( c_Nat__Transfer_Onat__set(V_A_2) % 172.48/172.40 => 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)) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_SetInterval_Otransfer__nat__int__set__function__closures,axiom, % 172.48/172.40 ! [V_y_2,V_x_2] : % 172.48/172.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) % 172.48/172.40 => c_Nat__Transfer_Onat__set(c_SetInterval_Oord__class_OatLeastAtMost(tc_Int_Oint,V_x_2,V_y_2)) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_transfer__nat__int__set__return__embed,axiom, % 172.48/172.40 ! [V_A_2] : % 172.48/172.40 ( c_Nat__Transfer_Onat__set(V_A_2) % 172.48/172.40 => 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 ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I4_J,axiom, % 172.48/172.40 ! [V_B_2,V_A_2] : % 172.48/172.40 ( c_Nat__Transfer_Onat__set(V_A_2) % 172.48/172.40 => ( c_Nat__Transfer_Onat__set(V_B_2) % 172.48/172.40 => 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))) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_Nat__Transfer_Otransfer__nat__int__set__function__closures_I6_J,axiom, % 172.48/172.40 ! [V_x_2,V_A_2] : % 172.48/172.40 ( c_Nat__Transfer_Onat__set(V_A_2) % 172.48/172.40 => ( hBOOL(hAPP(hAPP(c_member(tc_Int_Oint),V_x_2),V_A_2)) % 172.48/172.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_setsum__atMost__Suc,axiom, % 172.48/172.40 ! [V_n_2,V_f_2,T_a] : % 172.48/172.40 ( class_Groups_Ocomm__monoid__add(T_a) % 172.48/172.40 => 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))) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_atMost__0,axiom, % 172.48/172.40 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))) ). % 172.48/172.40 % 172.48/172.40 fof(fact_transfer__int__nat__sum__prod_I1_J,axiom, % 172.48/172.40 ! [V_f_2,V_A_2,T_a] : % 172.48/172.40 ( ( class_Groups_Ocomm__monoid__add(T_a) % 172.48/172.40 & class_Groups_Ocomm__monoid__mult(T_a) ) % 172.48/172.40 => ( c_Nat__Transfer_Onat__set(V_A_2) % 172.48/172.40 => 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)) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_ivl__disj__un_I9_J,axiom, % 172.48/172.40 ! [V_u_2,V_l_2,T_a] : % 172.48/172.40 ( class_Orderings_Olinorder(T_a) % 172.48/172.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2)) % 172.48/172.40 => 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) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_ivl__disj__int_I3_J,axiom, % 172.48/172.40 ! [V_u_2,V_l_2,T_a] : % 172.48/172.40 ( class_Orderings_Oorder(T_a) % 172.48/172.40 => 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)) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_ivl__disj__int_I1_J,axiom, % 172.48/172.40 ! [V_u_2,V_l_2,T_a] : % 172.48/172.40 ( class_Orderings_Oorder(T_a) % 172.48/172.40 => 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)) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_transfer__int__nat__set__relations_I1_J,axiom, % 172.48/172.40 ! [V_A_2] : % 172.48/172.40 ( c_Nat__Transfer_Onat__set(V_A_2) % 172.48/172.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),V_A_2)) % 172.48/172.40 <=> 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))) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I1_J,axiom, % 172.48/172.40 ! [V_A_2] : % 172.48/172.40 ( c_Nat__Transfer_Onat__set(V_A_2) % 172.48/172.40 => 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)) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_SetInterval_Otransfer__nat__int__set__functions_I1_J,axiom, % 172.48/172.40 ! [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))) ). % 172.48/172.40 % 172.48/172.40 fof(fact_ivl__disj__un_I2_J,axiom, % 172.48/172.40 ! [V_u_2,T_a] : % 172.48/172.40 ( class_Orderings_Olinorder(T_a) % 172.48/172.40 => 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) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_ivl__disj__un_I10_J,axiom, % 172.48/172.40 ! [V_u_2,V_l_2,T_a] : % 172.48/172.40 ( class_Orderings_Olinorder(T_a) % 172.48/172.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2)) % 172.48/172.40 => 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) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_transfer__int__nat__set__relations_I5_J,axiom, % 172.48/172.40 ! [V_B_2,V_A_2] : % 172.48/172.40 ( c_Nat__Transfer_Onat__set(V_A_2) % 172.48/172.40 => ( c_Nat__Transfer_Onat__set(V_B_2) % 172.48/172.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(tc_Int_Oint,tc_HOL_Obool)),V_A_2),V_B_2)) % 172.48/172.40 <=> 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))) ) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_transfer__int__nat__sum__prod2_I2_J,axiom, % 172.48/172.40 ! [V_f_2,V_A_2,T_a] : % 172.48/172.40 ( ! [B_x] : % 172.48/172.40 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 172.48/172.40 => c_Nat__Transfer_Ois__nat(hAPP(V_f_2,B_x)) ) % 172.48/172.40 => 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)) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_transfer__int__nat__sum__prod2_I1_J,axiom, % 172.48/172.40 ! [V_f_2,V_A_2,T_a] : % 172.48/172.40 ( ! [B_x] : % 172.48/172.40 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 172.48/172.40 => c_Nat__Transfer_Ois__nat(hAPP(V_f_2,B_x)) ) % 172.48/172.40 => 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)) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_atMost__Int__atLeast,axiom, % 172.48/172.40 ! [V_n_2,T_a] : % 172.48/172.40 ( class_Orderings_Oorder(T_a) % 172.48/172.40 => 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))) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_transfer__nat__int__sum__prod__cong_I2_J,axiom, % 172.48/172.40 ! [V_g_2,V_f_2,V_B_2,V_A_2,T_a] : % 172.48/172.40 ( ( class_Groups_Ocomm__monoid__add(T_a) % 172.48/172.40 & class_Groups_Ocomm__monoid__mult(T_a) ) % 172.48/172.40 => ( V_A_2 = V_B_2 % 172.48/172.40 => ( c_Nat__Transfer_Onat__set(V_B_2) % 172.48/172.40 => ( ! [B_x] : % 172.48/172.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 172.48/172.40 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) % 172.48/172.40 => 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) ) ) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_incr__lemma,axiom, % 172.48/172.40 ! [V_x,V_z,V_d] : % 172.48/172.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d)) % 172.48/172.40 => 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)))) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_setsum__abs,axiom, % 172.48/172.40 ! [V_A_2,V_f_2,T_b,T_a] : % 172.48/172.40 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 172.48/172.40 => 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))) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_setsum__abs__ge__zero,axiom, % 172.48/172.40 ! [V_A_2,V_f_2,T_b,T_a] : % 172.48/172.40 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 172.48/172.40 => 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))) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_abs__one,axiom, % 172.48/172.40 ! [T_a] : % 172.48/172.40 ( class_Rings_Olinordered__idom(T_a) % 172.48/172.40 => hAPP(c_Groups_Oabs__class_Oabs(T_a),c_Groups_Oone__class_Oone(T_a)) = c_Groups_Oone__class_Oone(T_a) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_power__abs,axiom, % 172.48/172.40 ! [V_n,V_a,T_a] : % 172.48/172.40 ( class_Rings_Olinordered__idom(T_a) % 172.48/172.40 => 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) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_abs__of__nat,axiom, % 172.48/172.40 ! [V_n,T_a] : % 172.48/172.40 ( class_Rings_Olinordered__idom(T_a) % 172.48/172.40 => 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) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_abs__le__D1,axiom, % 172.48/172.40 ! [V_b,V_a,T_a] : % 172.48/172.40 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 172.48/172.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b)) % 172.48/172.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_abs__ge__self,axiom, % 172.48/172.40 ! [V_a,T_a] : % 172.48/172.40 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 172.48/172.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a))) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_abs__eq__0,axiom, % 172.48/172.40 ! [V_a_2,T_a] : % 172.48/172.40 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 172.48/172.40 => ( hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a_2) = c_Groups_Ozero__class_Ozero(T_a) % 172.48/172.40 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_abs__zero,axiom, % 172.48/172.40 ! [T_a] : % 172.48/172.40 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 172.48/172.40 => hAPP(c_Groups_Oabs__class_Oabs(T_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_atLeast__eq__iff,axiom, % 172.48/172.40 ! [V_y_2,V_x_2,T_a] : % 172.48/172.40 ( class_Orderings_Olinorder(T_a) % 172.48/172.40 => ( hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_x_2) = hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_y_2) % 172.48/172.40 <=> V_x_2 = V_y_2 ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_abs__idempotent,axiom, % 172.48/172.40 ! [V_a,T_a] : % 172.48/172.40 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 172.48/172.40 => 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) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_abs__minus__commute,axiom, % 172.48/172.40 ! [V_b,V_a,T_a] : % 172.48/172.40 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 172.48/172.40 => 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)) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_abs__mult,axiom, % 172.48/172.40 ! [V_b,V_a,T_a] : % 172.48/172.40 ( class_Rings_Olinordered__idom(T_a) % 172.48/172.40 => 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)) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_abs__mult__self,axiom, % 172.48/172.40 ! [V_a,T_a] : % 172.48/172.40 ( class_Rings_Olinordered__idom(T_a) % 172.48/172.40 => 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) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_abs__add__abs,axiom, % 172.48/172.40 ! [V_b,V_a,T_a] : % 172.48/172.40 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 172.48/172.40 => 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)) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_abs__divide,axiom, % 172.48/172.40 ! [V_b,V_a,T_a] : % 172.48/172.40 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 172.48/172.40 => 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)) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_abs__int__eq,axiom, % 172.48/172.40 ! [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) ). % 172.48/172.40 % 172.48/172.40 fof(fact_abs__setsum__abs,axiom, % 172.48/172.40 ! [V_A_2,V_f_2,T_b,T_a] : % 172.48/172.40 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 172.48/172.40 => 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) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_abs__setprod,axiom, % 172.48/172.40 ! [V_A_2,V_f_2,T_b,T_a] : % 172.48/172.40 ( class_Fields_Olinordered__field(T_a) % 172.48/172.40 => 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) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_abs__of__nonneg,axiom, % 172.48/172.40 ! [V_a,T_a] : % 172.48/172.40 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 172.48/172.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 172.48/172.40 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_abs__le__zero__iff,axiom, % 172.48/172.40 ! [V_a_2,T_a] : % 172.48/172.40 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 172.48/172.40 => ( 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))) % 172.48/172.40 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_abs__ge__zero,axiom, % 172.48/172.40 ! [V_a,T_a] : % 172.48/172.40 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 172.48/172.40 => 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))) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_abs__not__less__zero,axiom, % 172.48/172.40 ! [V_a,T_a] : % 172.48/172.40 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 172.48/172.40 => ~ 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))) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_zero__less__abs__iff,axiom, % 172.48/172.40 ! [V_a_2,T_a] : % 172.48/172.40 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 172.48/172.40 => ( 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))) % 172.48/172.40 <=> V_a_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_abs__of__pos,axiom, % 172.48/172.40 ! [V_a,T_a] : % 172.48/172.40 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 172.48/172.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 172.48/172.40 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_abs__triangle__ineq,axiom, % 172.48/172.40 ! [V_b,V_a,T_a] : % 172.48/172.40 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 172.48/172.40 => 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)))) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_abs__mult__less,axiom, % 172.48/172.40 ! [V_d,V_b,V_c,V_a,T_a] : % 172.48/172.40 ( class_Rings_Olinordered__idom(T_a) % 172.48/172.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_c)) % 172.48/172.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_b)),V_d)) % 172.48/172.40 => 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))) ) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_abs__triangle__ineq2__sym,axiom, % 172.48/172.40 ! [V_b,V_a,T_a] : % 172.48/172.40 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 172.48/172.40 => 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)))) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_abs__triangle__ineq2,axiom, % 172.48/172.40 ! [V_b,V_a,T_a] : % 172.48/172.40 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 172.48/172.40 => 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)))) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_abs__triangle__ineq3,axiom, % 172.48/172.40 ! [V_b,V_a,T_a] : % 172.48/172.40 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 172.48/172.40 => 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)))) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_nonzero__abs__divide,axiom, % 172.48/172.40 ! [V_a,V_b,T_a] : % 172.48/172.40 ( class_Fields_Olinordered__field(T_a) % 172.48/172.40 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 172.48/172.40 => 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)) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_abs__zmult__eq__1,axiom, % 172.48/172.40 ! [V_n,V_m] : % 172.48/172.40 ( 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) % 172.48/172.40 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_m) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_abs__mult__pos,axiom, % 172.48/172.40 ! [V_y,V_x,T_a] : % 172.48/172.40 ( class_Rings_Olinordered__idom(T_a) % 172.48/172.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 172.48/172.40 => 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)) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_abs__eq__mult,axiom, % 172.48/172.40 ! [V_b,V_a,T_a] : % 172.48/172.40 ( class_Rings_Oordered__ring__abs(T_a) % 172.48/172.40 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 172.48/172.40 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) ) % 172.48/172.40 & ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_b)) % 172.48/172.40 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),c_Groups_Ozero__class_Ozero(T_a))) ) ) % 172.48/172.40 => 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)) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_abs__triangle__ineq4,axiom, % 172.48/172.40 ! [V_b,V_a,T_a] : % 172.48/172.40 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 172.48/172.40 => 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)))) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_abs__diff__triangle__ineq,axiom, % 172.48/172.40 ! [V_d,V_c,V_b,V_a,T_a] : % 172.48/172.40 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 172.48/172.40 => 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))))) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_zero__le__power__abs,axiom, % 172.48/172.40 ! [V_n,V_a,T_a] : % 172.48/172.40 ( class_Rings_Olinordered__idom(T_a) % 172.48/172.40 => 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))) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_abs__div__pos,axiom, % 172.48/172.40 ! [V_x,V_y,T_a] : % 172.48/172.40 ( class_Fields_Olinordered__field__inverse__zero(T_a) % 172.48/172.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 172.48/172.40 => 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)) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_atLeast__iff,axiom, % 172.48/172.40 ! [V_k_2,V_i_2,T_a] : % 172.48/172.40 ( class_Orderings_Oord(T_a) % 172.48/172.40 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_k_2))) % 172.48/172.40 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_k_2),V_i_2)) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_zabs__less__one__iff,axiom, % 172.48/172.40 ! [V_z_2] : % 172.48/172.40 ( 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))) % 172.48/172.40 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_nat__abs__mult__distrib,axiom, % 172.48/172.40 ! [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))) ). % 172.48/172.40 % 172.48/172.40 fof(fact_atLeast__subset__iff,axiom, % 172.48/172.40 ! [V_y_2,V_x_2,T_a] : % 172.48/172.40 ( class_Orderings_Oorder(T_a) % 172.48/172.40 => ( 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))) % 172.48/172.40 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_zero__le__zpower__abs,axiom, % 172.48/172.40 ! [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))) ). % 172.48/172.40 % 172.48/172.40 fof(fact_zero__less__zpower__abs__iff,axiom, % 172.48/172.40 ! [V_n_2,V_x_2] : % 172.48/172.40 ( 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))) % 172.48/172.40 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 172.48/172.40 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_ivl__disj__un_I14_J,axiom, % 172.48/172.40 ! [V_u_2,V_l_2,T_a] : % 172.48/172.40 ( class_Orderings_Olinorder(T_a) % 172.48/172.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2)) % 172.48/172.40 => 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) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_ivl__disj__int_I8_J,axiom, % 172.48/172.40 ! [V_u_2,V_l_2,T_a] : % 172.48/172.40 ( class_Orderings_Oorder(T_a) % 172.48/172.40 => 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)) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_ivl__disj__int_I6_J,axiom, % 172.48/172.40 ! [V_u_2,V_l_2,T_a] : % 172.48/172.40 ( class_Orderings_Oorder(T_a) % 172.48/172.40 => 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)) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_atLeast__Suc,axiom, % 172.48/172.40 ! [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)))) ). % 172.48/172.40 % 172.48/172.40 fof(fact_decr__lemma,axiom, % 172.48/172.40 ! [V_z,V_x,V_d] : % 172.48/172.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d)) % 172.48/172.40 => 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)) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_ivl__disj__un_I12_J,axiom, % 172.48/172.40 ! [V_u_2,V_l_2,T_a] : % 172.48/172.40 ( class_Orderings_Olinorder(T_a) % 172.48/172.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_l_2),V_u_2)) % 172.48/172.40 => 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) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_Nitpick_Oint__lcm__def,axiom, % 172.48/172.40 ! [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)))) ). % 172.48/172.40 % 172.48/172.40 fof(fact_ivl__disj__un_I13_J,axiom, % 172.48/172.40 ! [V_u_2,V_l_2,T_a] : % 172.48/172.40 ( class_Orderings_Olinorder(T_a) % 172.48/172.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2)) % 172.48/172.40 => 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) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_ivl__disj__un_I1_J,axiom, % 172.48/172.40 ! [V_l_2,T_a] : % 172.48/172.40 ( class_Orderings_Olinorder(T_a) % 172.48/172.40 => 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) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_transfer__nat__int__sum__prod__cong_I1_J,axiom, % 172.48/172.40 ! [V_g_2,V_f_2,V_B_2,V_A_2,T_a] : % 172.48/172.40 ( ( class_Groups_Ocomm__monoid__add(T_a) % 172.48/172.40 & class_Groups_Ocomm__monoid__mult(T_a) ) % 172.48/172.40 => ( V_A_2 = V_B_2 % 172.48/172.40 => ( c_Nat__Transfer_Onat__set(V_B_2) % 172.48/172.40 => ( ! [B_x] : % 172.48/172.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 172.48/172.40 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) % 172.48/172.40 => 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) ) ) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_greaterThan__eq__iff,axiom, % 172.48/172.40 ! [V_y_2,V_x_2,T_a] : % 172.48/172.40 ( class_Orderings_Olinorder(T_a) % 172.48/172.40 => ( hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_x_2) = hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_y_2) % 172.48/172.40 <=> V_x_2 = V_y_2 ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_atLeast__Suc__greaterThan,axiom, % 172.48/172.40 ! [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) ). % 172.48/172.40 % 172.48/172.40 fof(fact_greaterThan__iff,axiom, % 172.48/172.40 ! [V_k_2,V_i_2,T_a] : % 172.48/172.40 ( class_Orderings_Oord(T_a) % 172.48/172.40 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),hAPP(c_SetInterval_Oord__class_OgreaterThan(T_a),V_k_2))) % 172.48/172.40 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_k_2),V_i_2)) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_greaterThan__subset__iff,axiom, % 172.48/172.40 ! [V_y_2,V_x_2,T_a] : % 172.48/172.40 ( class_Orderings_Olinorder(T_a) % 172.48/172.40 => ( 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))) % 172.48/172.40 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_ivl__disj__int_I7_J,axiom, % 172.48/172.40 ! [V_u_2,V_l_2,T_a] : % 172.48/172.40 ( class_Orderings_Oorder(T_a) % 172.48/172.40 => 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)) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_ivl__disj__un_I11_J,axiom, % 172.48/172.40 ! [V_u_2,V_l_2,T_a] : % 172.48/172.40 ( class_Orderings_Olinorder(T_a) % 172.48/172.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_l_2),V_u_2)) % 172.48/172.40 => 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) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_ivl__disj__int_I5_J,axiom, % 172.48/172.40 ! [V_u_2,V_l_2,T_a] : % 172.48/172.40 ( class_Orderings_Oorder(T_a) % 172.48/172.40 => 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)) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_greaterThan__Suc,axiom, % 172.48/172.40 ! [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)))) ). % 172.48/172.40 % 172.48/172.40 fof(fact_Nitpick_Onat__lcm__def,axiom, % 172.48/172.40 ! [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)) ). % 172.48/172.40 % 172.48/172.40 fof(fact_nat0__intermed__int__val,axiom, % 172.48/172.40 ! [V_k_2,V_f_2,V_n_2] : % 172.48/172.40 ( ! [B_i] : % 172.48/172.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2)) % 172.48/172.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_i),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(V_f_2,B_i)))),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) % 172.48/172.40 => ( 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)) % 172.48/172.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2))) % 172.48/172.40 => ? [B_i] : % 172.48/172.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2)) % 172.48/172.40 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_int__val__lemma,axiom, % 172.48/172.40 ! [V_k_2,V_f_2,V_n_2] : % 172.48/172.40 ( ! [B_i] : % 172.48/172.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2)) % 172.48/172.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),hAPP(V_f_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),B_i),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(V_f_2,B_i)))),c_Groups_Oone__class_Oone(tc_Int_Oint))) ) % 172.48/172.40 => ( 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)) % 172.48/172.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2))) % 172.48/172.40 => ? [B_i] : % 172.48/172.40 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2)) % 172.48/172.40 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_card__less__Suc2,axiom, % 172.48/172.40 ! [V_i_2,V_M_2] : % 172.48/172.40 ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2)) % 172.48/172.40 => 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))))) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_card__less,axiom, % 172.48/172.40 ! [V_i_2,V_M_2] : % 172.48/172.40 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2)) % 172.48/172.40 => 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) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_CollectI,axiom, % 172.48/172.40 ! [T_a,V_a_2,V_P_2] : % 172.48/172.40 ( hBOOL(hAPP(V_P_2,V_a_2)) % 172.48/172.40 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_OCollect(T_a),V_P_2))) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_finite__Collect__conjI,axiom, % 172.48/172.40 ! [V_Q_2,V_P_2,T_a] : % 172.48/172.40 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_P_2))) % 172.48/172.40 | hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_Q_2))) ) % 172.48/172.40 => 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)))) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_finite__Collect__less__nat,axiom, % 172.48/172.40 ! [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)))) ). % 172.48/172.40 % 172.48/172.40 fof(fact_finite__Collect__le__nat,axiom, % 172.48/172.40 ! [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)))) ). % 172.48/172.40 % 172.48/172.40 fof(fact_Collect__empty__eq,axiom, % 172.48/172.40 ! [V_P_2,T_a] : % 172.48/172.40 ( hAPP(c_Set_OCollect(T_a),V_P_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.40 <=> ! [B_x] : ~ hBOOL(hAPP(V_P_2,B_x)) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_empty__Collect__eq,axiom, % 172.48/172.40 ! [V_P_2,T_a] : % 172.48/172.40 ( c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = hAPP(c_Set_OCollect(T_a),V_P_2) % 172.48/172.40 <=> ! [B_x] : ~ hBOOL(hAPP(V_P_2,B_x)) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_Collect__def,axiom, % 172.48/172.40 ! [V_P_2,T_a] : hAPP(c_Set_OCollect(T_a),V_P_2) = V_P_2 ). % 172.48/172.40 % 172.48/172.40 fof(fact_Collect__mem__eq,axiom, % 172.48/172.40 ! [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 ). % 172.48/172.40 % 172.48/172.40 fof(fact_mem__Collect__eq,axiom, % 172.48/172.40 ! [V_P_2,V_a_2,T_a] : % 172.48/172.40 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_OCollect(T_a),V_P_2))) % 172.48/172.40 <=> hBOOL(hAPP(V_P_2,V_a_2)) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_CollectD,axiom, % 172.48/172.40 ! [V_P_2,V_a_2,T_a] : % 172.48/172.40 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_OCollect(T_a),V_P_2))) % 172.48/172.40 => hBOOL(hAPP(V_P_2,V_a_2)) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_CollectE,axiom, % 172.48/172.40 ! [V_P_2,V_a_2,T_a] : % 172.48/172.40 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_OCollect(T_a),V_P_2))) % 172.48/172.40 => hBOOL(hAPP(V_P_2,V_a_2)) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_empty__def,axiom, % 172.48/172.40 ! [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)) ). % 172.48/172.40 % 172.48/172.40 fof(fact_finite__Collect__disjI,axiom, % 172.48/172.40 ! [V_Q_2,V_P_2,T_a] : % 172.48/172.40 ( 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)))) % 172.48/172.40 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_P_2))) % 172.48/172.40 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_Q_2))) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_insert__Collect,axiom, % 172.48/172.40 ! [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)) ). % 172.48/172.40 % 172.48/172.40 fof(fact_Collect__disj__eq,axiom, % 172.48/172.40 ! [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)) ). % 172.48/172.40 % 172.48/172.40 fof(fact_Collect__conj__eq,axiom, % 172.48/172.40 ! [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)) ). % 172.48/172.40 % 172.48/172.40 fof(fact_insert__compr,axiom, % 172.48/172.40 ! [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))) ). % 172.48/172.40 % 172.48/172.40 fof(fact_insert__compr__raw,axiom, % 172.48/172.40 ! [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))) ). % 172.48/172.40 % 172.48/172.40 fof(fact_Un__def,axiom, % 172.48/172.40 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = hAPP(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))) ). % 172.48/172.40 % 172.48/172.40 fof(fact_Int__def,axiom, % 172.48/172.40 ! [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))) ). % 172.48/172.40 % 172.48/172.40 fof(fact_Int__Collect,axiom, % 172.48/172.40 ! [V_P_2,V_A_2,V_x_2,T_a] : % 172.48/172.40 ( 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)))) % 172.48/172.40 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 172.48/172.40 & hBOOL(hAPP(V_P_2,V_x_2)) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_singleton__conv2,axiom, % 172.48/172.40 ! [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))) ). % 172.48/172.40 % 172.48/172.40 fof(fact_singleton__conv,axiom, % 172.48/172.40 ! [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))) ). % 172.48/172.40 % 172.48/172.40 fof(fact_Collect__conv__if2,axiom, % 172.48/172.40 ! [T_a,V_a_2,V_P_2] : % 172.48/172.40 ( ( hBOOL(hAPP(V_P_2,V_a_2)) % 172.48/172.40 => 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))) ) % 172.48/172.40 & ( ~ hBOOL(hAPP(V_P_2,V_a_2)) % 172.48/172.40 => 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)) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_Collect__conv__if,axiom, % 172.48/172.40 ! [T_a,V_a_2,V_P_2] : % 172.48/172.40 ( ( hBOOL(hAPP(V_P_2,V_a_2)) % 172.48/172.40 => 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))) ) % 172.48/172.40 & ( ~ hBOOL(hAPP(V_P_2,V_a_2)) % 172.48/172.40 => 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)) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_set__diff__eq,axiom, % 172.48/172.40 ! [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)))) ). % 172.48/172.40 % 172.48/172.40 fof(fact_insert__def,axiom, % 172.48/172.40 ! [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) ). % 172.48/172.40 % 172.48/172.40 fof(fact_finite__M__bounded__by__nat,axiom, % 172.48/172.40 ! [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))))) ). % 172.48/172.40 % 172.48/172.40 fof(fact_setsum__setsum__restrict,axiom, % 172.48/172.40 ! [V_R_2,V_f_2,V_T_2,T_b,V_S_2,T_a,T_c] : % 172.48/172.40 ( class_Groups_Ocomm__monoid__add(T_c) % 172.48/172.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 172.48/172.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2)) % 172.48/172.40 => 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) ) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_if__image__distrib,axiom, % 172.48/172.40 ! [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))))) ). % 172.48/172.40 % 172.48/172.40 fof(fact_nat__seg__image__imp__finite,axiom, % 172.48/172.40 ! [V_n_2,V_f_2,T_a,V_A_2] : % 172.48/172.40 ( 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))) % 172.48/172.40 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_setsum__restrict__set_H,axiom, % 172.48/172.40 ! [V_B_2,V_f_2,V_A_2,T_a,T_b] : % 172.48/172.40 ( class_Groups_Ocomm__monoid__add(T_b) % 172.48/172.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.40 => 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) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_setsum__image__gen,axiom, % 172.48/172.40 ! [V_f_2,T_c,V_g_2,V_S_2,T_a,T_b] : % 172.48/172.40 ( class_Groups_Ocomm__monoid__add(T_b) % 172.48/172.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 172.48/172.40 => 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)) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_nat__gcd_Osimps,axiom, % 172.48/172.40 ! [V_x,V_y] : % 172.48/172.40 ( ( V_y = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 172.48/172.40 => c_Nitpick_Onat__gcd(V_x,V_y) = V_x ) % 172.48/172.40 & ( V_y != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 172.48/172.40 => 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)) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_card__less__Suc,axiom, % 172.48/172.40 ! [V_i_2,V_M_2] : % 172.48/172.40 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_M_2)) % 172.48/172.40 => 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))))) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_dom__if,axiom, % 172.48/172.40 ! [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)))) ). % 172.48/172.40 % 172.48/172.40 fof(fact_Nitpick_Oint__gcd__def,axiom, % 172.48/172.40 ! [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)))) ). % 172.48/172.40 % 172.48/172.40 fof(fact_dom__override__on,axiom, % 172.48/172.40 ! [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))))) ). % 172.48/172.40 % 172.48/172.40 fof(fact_setsum__multicount,axiom, % 172.48/172.40 ! [V_k_2,V_R_2,V_T_2,T_b,V_S_2,T_a] : % 172.48/172.40 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 172.48/172.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_T_2)) % 172.48/172.40 => ( ! [B_x] : % 172.48/172.40 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_T_2)) % 172.48/172.40 => 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 ) % 172.48/172.40 => 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)) ) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_setsum__multicount__gen,axiom, % 172.48/172.40 ! [V_k_2,V_R_2,V_t_2,T_b,V_s_2,T_a] : % 172.48/172.40 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_s_2)) % 172.48/172.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_t_2)) % 172.48/172.40 => ( ! [B_x] : % 172.48/172.40 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_t_2)) % 172.48/172.40 => 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) ) % 172.48/172.40 => 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) ) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_finite__Collect__subsets,axiom, % 172.48/172.40 ! [V_A_2,T_a] : % 172.48/172.40 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.40 => 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)))) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_Pow__def,axiom, % 172.48/172.40 ! [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)) ). % 172.48/172.40 % 172.48/172.40 fof(fact_override__on__apply__notin,axiom, % 172.48/172.40 ! [V_g_2,V_f_2,T_b,V_A_2,V_a_2,T_a] : % 172.48/172.40 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 172.48/172.40 => 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) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_override__on__apply__in,axiom, % 172.48/172.40 ! [V_g_2,V_f_2,T_b,V_A_2,V_a_2,T_a] : % 172.48/172.40 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 172.48/172.40 => 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) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_override__on__emptyset,axiom, % 172.48/172.40 ! [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 ). % 172.48/172.40 % 172.48/172.40 fof(fact_Nat__Transfer_Otransfer__int__nat__set__function__closures_I4_J,axiom, % 172.48/172.40 ! [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))) ). % 172.48/172.40 % 172.48/172.40 fof(fact_override__on__def,axiom, % 172.48/172.40 ! [V_g_2,V_f_2,T_b,V_A_2,V_a_2,T_a] : % 172.48/172.40 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 172.48/172.40 => 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) ) % 172.48/172.40 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 172.48/172.40 => 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) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_Nat__Transfer_Otransfer__int__nat__set__functions_I5_J,axiom, % 172.48/172.40 ! [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)))) ). % 172.48/172.40 % 172.48/172.40 fof(fact_Nat__Transfer_Otransfer__nat__int__set__functions_I5_J,axiom, % 172.48/172.40 ! [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)))) ). % 172.48/172.40 % 172.48/172.40 fof(fact_inf__Sup2__distrib,axiom, % 172.48/172.40 ! [V_B_2,V_A_2,T_a] : % 172.48/172.40 ( class_Lattices_Odistrib__lattice(T_a) % 172.48/172.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.40 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 172.48/172.40 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.40 => 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))))))) ) ) ) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_inf__Sup1__distrib,axiom, % 172.48/172.40 ! [V_x_2,V_A_2,T_a] : % 172.48/172.40 ( class_Lattices_Odistrib__lattice(T_a) % 172.48/172.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.40 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.40 => 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))))) ) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_sup__Inf2__distrib,axiom, % 172.48/172.40 ! [V_B_2,V_A_2,T_a] : % 172.48/172.40 ( class_Lattices_Odistrib__lattice(T_a) % 172.48/172.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.40 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 172.48/172.40 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.40 => 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))))))) ) ) ) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_sup__Inf1__distrib,axiom, % 172.48/172.40 ! [V_x_2,V_A_2,T_a] : % 172.48/172.40 ( class_Lattices_Odistrib__lattice(T_a) % 172.48/172.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.40 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.40 => 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))))) ) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_finite__conv__nat__seg__image,axiom, % 172.48/172.40 ! [V_A_2,T_a] : % 172.48/172.40 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.40 <=> ? [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))) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_finite__Collect__bounded__ex,axiom, % 172.48/172.40 ! [V_Q_2,T_b,V_P_2,T_a] : % 172.48/172.40 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_P_2))) % 172.48/172.40 => ( 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))))) % 172.48/172.40 <=> ! [B_y] : % 172.48/172.40 ( hBOOL(hAPP(V_P_2,B_y)) % 172.48/172.40 => 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)))) ) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_finite__image__set,axiom, % 172.48/172.40 ! [V_f_2,T_b,V_P_2,T_a] : % 172.48/172.40 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_P_2))) % 172.48/172.40 => 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))))) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_add__Max__commute,axiom, % 172.48/172.40 ! [V_k_2,V_N_2,T_a] : % 172.48/172.40 ( class_Groups_Olinordered__ab__semigroup__add(T_a) % 172.48/172.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 172.48/172.40 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.40 => 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))))) ) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_add__Min__commute,axiom, % 172.48/172.40 ! [V_k_2,V_N_2,T_a] : % 172.48/172.40 ( class_Groups_Olinordered__ab__semigroup__add(T_a) % 172.48/172.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 172.48/172.40 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.40 => 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))))) ) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_pigeonhole__infinite,axiom, % 172.48/172.40 ! [V_f_2,T_b,V_A_2,T_a] : % 172.48/172.40 ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2))) % 172.48/172.40 => ? [B_x] : % 172.48/172.40 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 172.48/172.40 & ~ 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)))))) ) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_UN__le__eq__Un0,axiom, % 172.48/172.40 ! [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))) ). % 172.48/172.40 % 172.48/172.40 fof(fact_greaterThan__0,axiom, % 172.48/172.40 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))) ). % 172.48/172.40 % 172.48/172.40 fof(fact_top1I,axiom, % 172.48/172.40 ! [V_x_2,T_a] : hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_x_2)) ). % 172.48/172.40 % 172.48/172.40 fof(fact_UNIV__I,axiom, % 172.48/172.40 ! [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)))) ). % 172.48/172.40 % 172.48/172.40 fof(fact_SUP1__I,axiom, % 172.48/172.40 ! [T_b,V_b_2,V_B_2,V_A_2,V_a_2,T_a] : % 172.48/172.40 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 172.48/172.40 => ( hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2)) % 172.48/172.40 => 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)) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_UN__UN__finite__eq,axiom, % 172.48/172.40 ! [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) ). % 172.48/172.40 % 172.48/172.40 fof(fact_UN__atMost__UNIV,axiom, % 172.48/172.40 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)) ). % 172.48/172.40 % 172.48/172.40 fof(fact_SUP__UN__eq,axiom, % 172.48/172.40 ! [V_x_2,V_r_2,T_b,T_a] : % 172.48/172.40 ( 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)) % 172.48/172.40 <=> 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))) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_UN__lessThan__UNIV,axiom, % 172.48/172.40 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)) ). % 172.48/172.40 % 172.48/172.40 fof(fact_Pow__UNIV,axiom, % 172.48/172.40 ! [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)) ). % 172.48/172.40 % 172.48/172.40 fof(fact_SUP1__iff,axiom, % 172.48/172.40 ! [V_b_2,V_B_2,V_A_2,T_b,T_a] : % 172.48/172.40 ( 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)) % 172.48/172.40 <=> ? [B_x] : % 172.48/172.40 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 172.48/172.40 & hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2)) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_top__apply,axiom, % 172.48/172.40 ! [V_x_2,T_b,T_a] : % 172.48/172.40 ( class_Orderings_Otop(T_a) % 172.48/172.40 => hAPP(c_Orderings_Otop__class_Otop(tc_fun(T_b,T_a)),V_x_2) = c_Orderings_Otop__class_Otop(T_a) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_UNIV__Plus__UNIV,axiom, % 172.48/172.40 ! [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)) ). % 172.48/172.40 % 172.48/172.40 fof(fact_finite__option__UNIV,axiom, % 172.48/172.40 ! [T_a] : % 172.48/172.40 ( 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)))) % 172.48/172.40 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_finite__Prod__UNIV,axiom, % 172.48/172.40 ! [T_b,T_a] : % 172.48/172.40 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) % 172.48/172.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) % 172.48/172.40 => 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)))) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_finite__UN,axiom, % 172.48/172.40 ! [V_B_2,T_b,V_A_2,T_a] : % 172.48/172.40 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.40 => ( 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))) % 172.48/172.40 <=> ! [B_x] : % 172.48/172.40 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 172.48/172.40 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_x))) ) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_UN__atLeast__UNIV,axiom, % 172.48/172.40 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)) ). % 172.48/172.40 % 172.48/172.40 fof(fact_finite__fun__UNIVD2,axiom, % 172.48/172.40 ! [T_b,T_a] : % 172.48/172.40 ( 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)))) % 172.48/172.40 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_iso__tuple__UNIV__I,axiom, % 172.48/172.40 ! [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)))) ). % 172.48/172.40 % 172.48/172.40 fof(fact_UN__o,axiom, % 172.48/172.40 ! [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) ). % 172.48/172.40 % 172.48/172.40 fof(fact_UNIV__not__empty,axiom, % 172.48/172.40 ! [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)) ). % 172.48/172.40 % 172.48/172.40 fof(fact_finite__UNIV,axiom, % 172.48/172.40 ! [T_a] : % 172.48/172.40 ( class_Finite__Set_Ofinite(T_a) % 172.48/172.40 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_subset__UNIV,axiom, % 172.48/172.40 ! [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)))) ). % 172.48/172.40 % 172.48/172.40 fof(fact_Un__UNIV__right,axiom, % 172.48/172.40 ! [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)) ). % 172.48/172.40 % 172.48/172.40 fof(fact_Un__UNIV__left,axiom, % 172.48/172.40 ! [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)) ). % 172.48/172.40 % 172.48/172.40 fof(fact_Int__UNIV__right,axiom, % 172.48/172.40 ! [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 ). % 172.48/172.40 % 172.48/172.40 fof(fact_Int__UNIV__left,axiom, % 172.48/172.40 ! [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 ). % 172.48/172.40 % 172.48/172.40 fof(fact_finite__Plus__UNIV__iff,axiom, % 172.48/172.40 ! [T_b,T_a] : % 172.48/172.40 ( 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)))) % 172.48/172.40 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) % 172.48/172.40 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)))) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_infinite__UNIV__nat,axiom, % 172.48/172.40 ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Nat_Onat),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) ). % 172.48/172.40 % 172.48/172.40 fof(fact_UNIV__def,axiom, % 172.48/172.40 ! [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)) ). % 172.48/172.40 % 172.48/172.40 fof(fact_range__composition,axiom, % 172.48/172.40 ! [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)))) ). % 172.48/172.40 % 172.48/172.40 fof(fact_top__greatest,axiom, % 172.48/172.40 ! [V_x,T_a] : % 172.48/172.40 ( class_Orderings_Otop(T_a) % 172.48/172.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),c_Orderings_Otop__class_Otop(T_a))) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_sup__top__left,axiom, % 172.48/172.40 ! [V_x,T_a] : % 172.48/172.40 ( class_Lattices_Obounded__lattice__top(T_a) % 172.48/172.40 => 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) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_sup__top__right,axiom, % 172.48/172.40 ! [V_x,T_a] : % 172.48/172.40 ( class_Lattices_Obounded__lattice__top(T_a) % 172.48/172.40 => 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) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_inf__eq__top__iff,axiom, % 172.48/172.40 ! [V_y_2,V_x_2,T_a] : % 172.48/172.40 ( class_Lattices_Obounded__lattice__top(T_a) % 172.48/172.40 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x_2),V_y_2) = c_Orderings_Otop__class_Otop(T_a) % 172.48/172.40 <=> ( V_x_2 = c_Orderings_Otop__class_Otop(T_a) % 172.48/172.40 & V_y_2 = c_Orderings_Otop__class_Otop(T_a) ) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_inf__top__right,axiom, % 172.48/172.40 ! [V_x,T_a] : % 172.48/172.40 ( class_Lattices_Obounded__lattice__top(T_a) % 172.48/172.40 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),c_Orderings_Otop__class_Otop(T_a)) = V_x ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_inf__top__left,axiom, % 172.48/172.40 ! [V_x,T_a] : % 172.48/172.40 ( class_Lattices_Obounded__lattice__top(T_a) % 172.48/172.40 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),c_Orderings_Otop__class_Otop(T_a)),V_x) = V_x ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_range__eqI,axiom, % 172.48/172.40 ! [T_b,T_a,V_x_2,V_f_2,V_b_2] : % 172.48/172.40 ( V_b_2 = hAPP(V_f_2,V_x_2) % 172.48/172.40 => 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))))) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_rangeI,axiom, % 172.48/172.40 ! [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))))) ). % 172.48/172.40 % 172.48/172.40 fof(fact_Diff__UNIV,axiom, % 172.48/172.40 ! [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)) ). % 172.48/172.40 % 172.48/172.40 fof(fact_comp__surj,axiom, % 172.48/172.40 ! [V_g_2,T_c,V_f_2,T_a,T_b] : % 172.48/172.40 ( 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)) % 172.48/172.40 => ( 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)) % 172.48/172.40 => 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)) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_card__eq__UNIV__imp__eq__UNIV,axiom, % 172.48/172.40 ! [V_A_2,T_a] : % 172.48/172.40 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) % 172.48/172.40 => ( 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))) % 172.48/172.40 => V_A_2 = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_Min_Osingleton,axiom, % 172.48/172.40 ! [V_x_2,T_a] : % 172.48/172.40 ( class_Orderings_Olinorder(T_a) % 172.48/172.40 => 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 ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_Max_Osingleton,axiom, % 172.48/172.40 ! [V_x_2,T_a] : % 172.48/172.40 ( class_Orderings_Olinorder(T_a) % 172.48/172.40 => 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 ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_finite__Collect__not,axiom, % 172.48/172.40 ! [V_P_2,T_a] : % 172.48/172.40 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_OCollect(T_a),V_P_2))) % 172.48/172.40 => ( 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)))) % 172.48/172.40 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_finite__range__imageI,axiom, % 172.48/172.40 ! [V_f_2,T_c,V_g_2,T_b,T_a] : % 172.48/172.40 ( 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))))) % 172.48/172.40 => 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))))) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_atLeast__0,axiom, % 172.48/172.40 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)) ). % 172.48/172.40 % 172.48/172.40 fof(fact_Max__ge,axiom, % 172.48/172.40 ! [V_x_2,V_A_2,T_a] : % 172.48/172.40 ( class_Orderings_Olinorder(T_a) % 172.48/172.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.40 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 172.48/172.40 => 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))) ) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_Min__le,axiom, % 172.48/172.40 ! [V_x_2,V_A_2,T_a] : % 172.48/172.40 ( class_Orderings_Olinorder(T_a) % 172.48/172.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.40 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 172.48/172.40 => 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)) ) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_Min__in,axiom, % 172.48/172.40 ! [V_A_2,T_a] : % 172.48/172.40 ( class_Orderings_Olinorder(T_a) % 172.48/172.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.40 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.40 => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2)),V_A_2)) ) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_Max__in,axiom, % 172.48/172.40 ! [V_A_2,T_a] : % 172.48/172.40 ( class_Orderings_Olinorder(T_a) % 172.48/172.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.40 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.40 => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2)),V_A_2)) ) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_UN__le__add__shift,axiom, % 172.48/172.40 ! [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) ). % 172.48/172.40 % 172.48/172.40 fof(fact_finite__UNIV__card__ge__0,axiom, % 172.48/172.40 ! [T_a] : % 172.48/172.40 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) % 172.48/172.40 => 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))))) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_Max__mono,axiom, % 172.48/172.40 ! [V_N_2,V_M_2,T_a] : % 172.48/172.40 ( class_Orderings_Olinorder(T_a) % 172.48/172.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_M_2),V_N_2)) % 172.48/172.40 => ( V_M_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 172.48/172.40 => 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))) ) ) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_Min__antimono,axiom, % 172.48/172.40 ! [V_N_2,V_M_2,T_a] : % 172.48/172.40 ( class_Orderings_Olinorder(T_a) % 172.48/172.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_M_2),V_N_2)) % 172.48/172.40 => ( V_M_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.40 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 172.48/172.40 => 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))) ) ) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_finite__fun__UNIVD1,axiom, % 172.48/172.40 ! [T_b,T_a] : % 172.48/172.40 ( 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)))) % 172.48/172.40 => ( 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)) % 172.48/172.40 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_UN__I,axiom, % 172.48/172.40 ! [V_B_2,V_b_2,T_b,V_A_2,V_a_2,T_a] : % 172.48/172.40 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 172.48/172.40 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2))) % 172.48/172.40 => 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))) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_image__eq__UN,axiom, % 172.48/172.40 ! [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)))) ). % 172.48/172.40 % 172.48/172.40 fof(fact_UN__Pow__subset,axiom, % 172.48/172.40 ! [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)))) ). % 172.48/172.40 % 172.48/172.40 fof(fact_UN__insert,axiom, % 172.48/172.40 ! [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)) ). % 172.48/172.40 % 172.48/172.40 fof(fact_card__UNIV__unit,axiom, % 172.48/172.40 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) ). % 172.48/172.40 % 172.48/172.40 fof(fact_infinite__UNIV__int,axiom, % 172.48/172.40 ~ hBOOL(hAPP(c_Finite__Set_Ofinite(tc_Int_Oint),c_Orderings_Otop__class_Otop(tc_fun(tc_Int_Oint,tc_HOL_Obool)))) ). % 172.48/172.40 % 172.48/172.40 fof(fact_ball__UN,axiom, % 172.48/172.40 ! [V_P_2,V_B_2,V_A_2,T_b,T_a] : % 172.48/172.40 ( ! [B_x] : % 172.48/172.40 ( 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))) % 172.48/172.40 => hBOOL(hAPP(V_P_2,B_x)) ) % 172.48/172.40 <=> ! [B_x] : % 172.48/172.40 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 172.48/172.40 => ! [B_xa] : % 172.48/172.40 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),hAPP(V_B_2,B_x))) % 172.48/172.40 => hBOOL(hAPP(V_P_2,B_xa)) ) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_SUP__commute,axiom, % 172.48/172.40 ! [V_f_2,V_B_2,T_c,V_A_2,T_b,T_a] : % 172.48/172.40 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 172.48/172.40 => 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))) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_UN__extend__simps_I9_J,axiom, % 172.48/172.40 ! [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) ). % 172.48/172.40 % 172.48/172.40 fof(fact_UN__simps_I9_J,axiom, % 172.48/172.40 ! [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)) ). % 172.48/172.40 % 172.48/172.40 fof(fact_UN__UN__flatten,axiom, % 172.48/172.40 ! [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)) ). % 172.48/172.40 % 172.48/172.40 fof(fact_SUP__le__iff,axiom, % 172.48/172.40 ! [V_u_2,V_M_2,V_A_2,T_b,T_a] : % 172.48/172.40 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 172.48/172.40 => ( 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)) % 172.48/172.40 <=> ! [B_x] : % 172.48/172.40 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 172.48/172.40 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(V_M_2,B_x)),V_u_2)) ) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_less__SUP__iff,axiom, % 172.48/172.40 ! [V_f_2,V_A_2,T_b,V_a_2,T_a] : % 172.48/172.40 ( ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 172.48/172.40 & class_Orderings_Olinorder(T_a) ) % 172.48/172.40 => ( 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))) % 172.48/172.40 <=> ? [B_x] : % 172.48/172.40 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 172.48/172.40 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),hAPP(V_f_2,B_x))) ) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_UN__iff,axiom, % 172.48/172.40 ! [V_B_2,V_A_2,T_b,V_b_2,T_a] : % 172.48/172.40 ( 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))) % 172.48/172.40 <=> ? [B_x] : % 172.48/172.40 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 172.48/172.40 & hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(V_B_2,B_x))) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_SUP__const,axiom, % 172.48/172.40 ! [V_M_2,T_a,V_A_2,T_b] : % 172.48/172.40 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 172.48/172.40 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.40 => 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 ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_UNION__empty__conv_I1_J,axiom, % 172.48/172.40 ! [V_B_2,V_A_2,T_b,T_a] : % 172.48/172.40 ( 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) % 172.48/172.40 <=> ! [B_x] : % 172.48/172.40 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 172.48/172.40 => hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_UN__empty2,axiom, % 172.48/172.40 ! [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)) ). % 172.48/172.40 % 172.48/172.40 fof(fact_UN__constant,axiom, % 172.48/172.40 ! [V_ca_2,T_b,T_a,V_A_2] : % 172.48/172.40 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.40 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_ca_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) % 172.48/172.40 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.40 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_ca_2)) = V_ca_2 ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_UNION__empty__conv_I2_J,axiom, % 172.48/172.40 ! [V_B_2,V_A_2,T_a,T_b] : % 172.48/172.40 ( 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)) % 172.48/172.40 <=> ! [B_x] : % 172.48/172.40 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 172.48/172.40 => hAPP(V_B_2,B_x) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_UN__subset__iff,axiom, % 172.48/172.40 ! [V_B_2,V_A_2,V_I_2,T_b,T_a] : % 172.48/172.40 ( 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)) % 172.48/172.40 <=> ! [B_x] : % 172.48/172.40 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_I_2)) % 172.48/172.40 => 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)) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_UN__extend__simps_I10_J,axiom, % 172.48/172.40 ! [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) ). % 172.48/172.40 % 172.48/172.40 fof(fact_image__UN,axiom, % 172.48/172.40 ! [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)) ). % 172.48/172.40 % 172.48/172.40 fof(fact_UN__simps_I10_J,axiom, % 172.48/172.40 ! [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)) ). % 172.48/172.40 % 172.48/172.40 fof(fact_UN__Un,axiom, % 172.48/172.40 ! [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)) ). % 172.48/172.40 % 172.48/172.40 fof(fact_UN__Un__distrib,axiom, % 172.48/172.40 ! [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)) ). % 172.48/172.40 % 172.48/172.40 fof(fact_UN__simps_I5_J,axiom, % 172.48/172.40 ! [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)) ). % 172.48/172.40 % 172.48/172.40 fof(fact_UN__simps_I4_J,axiom, % 172.48/172.40 ! [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) ). % 172.48/172.40 % 172.48/172.40 fof(fact_UN__extend__simps_I5_J,axiom, % 172.48/172.40 ! [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)) ). % 172.48/172.40 % 172.48/172.40 fof(fact_Int__UN__distrib,axiom, % 172.48/172.40 ! [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)) ). % 172.48/172.40 % 172.48/172.40 fof(fact_UN__extend__simps_I4_J,axiom, % 172.48/172.40 ! [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)) ). % 172.48/172.40 % 172.48/172.40 fof(fact_Int__UN__distrib2,axiom, % 172.48/172.40 ! [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))) ). % 172.48/172.40 % 172.48/172.40 fof(fact_SUPR__apply,axiom, % 172.48/172.40 ! [V_x_2,V_f_2,V_A_2,T_c,T_b,T_a] : % 172.48/172.40 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 172.48/172.40 => 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)) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_UN__extend__simps_I6_J,axiom, % 172.48/172.40 ! [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)) ). % 172.48/172.40 % 172.48/172.40 fof(fact_UN__simps_I6_J,axiom, % 172.48/172.40 ! [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) ). % 172.48/172.40 % 172.48/172.40 fof(fact_SUP__subset,axiom, % 172.48/172.40 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] : % 172.48/172.40 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 172.48/172.40 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 172.48/172.40 => 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))) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_le__SUPI,axiom, % 172.48/172.40 ! [V_M_2,V_A_2,V_i_2,T_a,T_b] : % 172.48/172.40 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 172.48/172.40 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),V_A_2)) % 172.48/172.40 => 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))) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_UN__insert__distrib,axiom, % 172.48/172.40 ! [V_B_2,V_a_2,T_b,V_A_2,V_u_2,T_a] : % 172.48/172.40 ( hBOOL(hAPP(hAPP(c_member(T_a),V_u_2),V_A_2)) % 172.48/172.40 => 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)) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_UN__upper,axiom, % 172.48/172.40 ! [V_B_2,T_b,V_A_2,V_a_2,T_a] : % 172.48/172.40 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 172.48/172.40 => 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))) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_UN__absorb,axiom, % 172.48/172.40 ! [V_A_2,T_b,V_I_2,V_k_2,T_a] : % 172.48/172.40 ( hBOOL(hAPP(hAPP(c_member(T_a),V_k_2),V_I_2)) % 172.48/172.40 => 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) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_UN__simps_I1_J,axiom, % 172.48/172.40 ! [V_B_2,V_a_2,T_b,T_a,V_C_2] : % 172.48/172.40 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.40 => 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)) ) % 172.48/172.40 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.40 => 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)) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_UN__singleton,axiom, % 172.48/172.40 ! [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 ). % 172.48/172.40 % 172.48/172.40 fof(fact_UN__extend__simps_I1_J,axiom, % 172.48/172.40 ! [V_B_2,V_a_2,T_b,T_a,V_C_2] : % 172.48/172.40 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.40 => 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))) ) % 172.48/172.40 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.40 => 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)) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_UN__simps_I3_J,axiom, % 172.48/172.40 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 172.48/172.40 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.40 => 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)) ) % 172.48/172.40 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.40 => 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)) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_UN__simps_I2_J,axiom, % 172.48/172.40 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 172.48/172.40 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.40 => 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)) ) % 172.48/172.40 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.40 => 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) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_UN__extend__simps_I3_J,axiom, % 172.48/172.40 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 172.48/172.40 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.40 => 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 ) % 172.48/172.40 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.40 => 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)) ) ) ). % 172.48/172.40 % 172.48/172.40 fof(fact_UN__extend__simps_I2_J,axiom, % 172.48/172.40 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 172.48/172.40 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.40 => 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 ) % 172.48/172.41 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.41 => 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)) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_UN__finite2__subset,axiom, % 172.48/172.41 ! [V_B_2,V_k_2,V_A_2,T_a] : % 172.48/172.41 ( ! [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))) % 172.48/172.41 => 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))) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_UN__finite2__eq,axiom, % 172.48/172.41 ! [V_B_2,V_k_2,V_A_2,T_a] : % 172.48/172.41 ( ! [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) % 172.48/172.41 => 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) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_UN__finite__subset,axiom, % 172.48/172.41 ! [V_C_2,V_A_2,T_a] : % 172.48/172.41 ( ! [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)) % 172.48/172.41 => 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)) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_Min_Oremove,axiom, % 172.48/172.41 ! [V_x_2,V_A_2,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.41 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 172.48/172.41 => ( ( hAPP(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)) % 172.48/172.41 => c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2) = V_x_2 ) % 172.48/172.41 & ( hAPP(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)) % 172.48/172.41 => 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)))))) ) ) ) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_Max_Oremove,axiom, % 172.48/172.41 ! [V_x_2,V_A_2,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.41 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 172.48/172.41 => ( ( hAPP(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)) % 172.48/172.41 => c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2) = V_x_2 ) % 172.48/172.41 & ( hAPP(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)) % 172.48/172.41 => 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)))))) ) ) ) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_SUP2__I,axiom, % 172.48/172.41 ! [T_c,T_b,V_ca_2,V_b_2,V_B_2,V_A_2,V_a_2,T_a] : % 172.48/172.41 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 172.48/172.41 => ( hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_ca_2)) % 172.48/172.41 => hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_ca_2)) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_min__diff,axiom, % 172.48/172.41 ! [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) ). % 172.48/172.41 % 172.48/172.41 fof(fact_sup__max,axiom, % 172.48/172.41 ! [T_a] : % 172.48/172.41 ( ( class_Lattices_Osemilattice__sup(T_a) % 172.48/172.41 & class_Orderings_Olinorder(T_a) ) % 172.48/172.41 => c_Lattices_Osemilattice__sup__class_Osup(T_a) = c_Orderings_Oord__class_Omax(T_a) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_max__0L,axiom, % 172.48/172.41 ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n) = V_n ). % 172.48/172.41 % 172.48/172.41 fof(fact_max__0R,axiom, % 172.48/172.41 ! [V_n] : hAPP(hAPP(c_Orderings_Oord__class_Omax(tc_Nat_Onat),V_n),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = V_n ). % 172.48/172.41 % 172.48/172.41 fof(fact_inf__min,axiom, % 172.48/172.41 ! [T_a] : % 172.48/172.41 ( ( class_Lattices_Osemilattice__inf(T_a) % 172.48/172.41 & class_Orderings_Olinorder(T_a) ) % 172.48/172.41 => c_Lattices_Osemilattice__inf__class_Oinf(T_a) = c_Orderings_Oord__class_Omin(T_a) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_min__0L,axiom, % 172.48/172.41 ! [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) ). % 172.48/172.41 % 172.48/172.41 fof(fact_min__0R,axiom, % 172.48/172.41 ! [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) ). % 172.48/172.41 % 172.48/172.41 fof(fact_max__Suc__Suc,axiom, % 172.48/172.41 ! [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)) ). % 172.48/172.41 % 172.48/172.41 fof(fact_min__Suc__Suc,axiom, % 172.48/172.41 ! [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)) ). % 172.48/172.41 % 172.48/172.41 fof(fact_min__max_Odistrib__sup__le,axiom, % 172.48/172.41 ! [V_z,V_y,V_x,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => 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)))) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_min__max_Odistrib__inf__le,axiom, % 172.48/172.41 ! [V_z,V_y,V_x,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => 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)))) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_min__max_Oinf__sup__distrib2,axiom, % 172.48/172.41 ! [V_x,V_z,V_y,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => 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)) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_min__max_Osup__inf__distrib2,axiom, % 172.48/172.41 ! [V_x,V_z,V_y,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => 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)) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_min__max_Oinf__assoc,axiom, % 172.48/172.41 ! [V_z,V_y,V_x,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => 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)) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_min__max_Oinf_Oassoc,axiom, % 172.48/172.41 ! [V_c,V_b,V_a,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => 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)) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_min__max_Osup__assoc,axiom, % 172.48/172.41 ! [V_z,V_y,V_x,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => 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)) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_min__max_Osup_Oassoc,axiom, % 172.48/172.41 ! [V_c,V_b,V_a,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => 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)) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_min__max_Oinf__sup__distrib1,axiom, % 172.48/172.41 ! [V_z,V_y,V_x,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => 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)) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_min__max_Osup__inf__distrib1,axiom, % 172.48/172.41 ! [V_z,V_y,V_x,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => 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)) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_min__max_Oinf__left__commute,axiom, % 172.48/172.41 ! [V_z,V_y,V_x,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => 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)) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_min__max_Oinf_Oleft__commute,axiom, % 172.48/172.41 ! [V_c,V_a,V_b,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => 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)) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_min__max_Osup__left__commute,axiom, % 172.48/172.41 ! [V_z,V_y,V_x,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => 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)) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_min__max_Osup_Oleft__commute,axiom, % 172.48/172.41 ! [V_c,V_a,V_b,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => 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)) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_min__max_Oinf__left__idem,axiom, % 172.48/172.41 ! [V_y,V_x,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => 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) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_min__max_Oinf_Oleft__idem,axiom, % 172.48/172.41 ! [V_b,V_a,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => 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) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_min__max_Osup__left__idem,axiom, % 172.48/172.41 ! [V_y,V_x,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => 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) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_min__max_Osup_Oleft__idem,axiom, % 172.48/172.41 ! [V_b,V_a,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => 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) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_min__max_Oinf__sup__absorb,axiom, % 172.48/172.41 ! [V_y,V_x,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => 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 ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_min__max_Osup__inf__absorb,axiom, % 172.48/172.41 ! [V_y,V_x,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => 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 ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_min__max_Oinf__commute,axiom, % 172.48/172.41 ! [V_y,V_x,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => 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) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_min__max_Oinf_Ocommute,axiom, % 172.48/172.41 ! [V_b,V_a,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => 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) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_min__max_Osup__commute,axiom, % 172.48/172.41 ! [V_y,V_x,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => 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) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_min__max_Osup_Ocommute,axiom, % 172.48/172.41 ! [V_b,V_a,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => 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) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_min__max_Oinf_Oidem,axiom, % 172.48/172.41 ! [V_a,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_a),V_a) = V_a ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_min__max_Osup_Oidem,axiom, % 172.48/172.41 ! [V_a,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a),V_a) = V_a ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_Min_Oidem,axiom, % 172.48/172.41 ! [V_x,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_x) = V_x ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_Max_Oidem,axiom, % 172.48/172.41 ! [V_x,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_x) = V_x ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_min__add__distrib__left,axiom, % 172.48/172.41 ! [V_z,V_y,V_x,T_a] : % 172.48/172.41 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 172.48/172.41 => 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)) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_max__add__distrib__left,axiom, % 172.48/172.41 ! [V_z,V_y,V_x,T_a] : % 172.48/172.41 ( class_Groups_Oordered__ab__semigroup__add__imp__le(T_a) % 172.48/172.41 => 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)) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_min__max_Oless__infI1,axiom, % 172.48/172.41 ! [V_b,V_x,V_a,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),V_x)) % 172.48/172.41 => 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)) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_min__max_Oless__infI2,axiom, % 172.48/172.41 ! [V_a,V_x,V_b,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b),V_x)) % 172.48/172.41 => 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)) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_min__less__iff__conj,axiom, % 172.48/172.41 ! [V_y_2,V_x_2,V_z_2,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => ( 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))) % 172.48/172.41 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z_2),V_x_2)) % 172.48/172.41 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z_2),V_y_2)) ) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_min__less__iff__disj,axiom, % 172.48/172.41 ! [V_z_2,V_y_2,V_x_2,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => ( 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)) % 172.48/172.41 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_z_2)) % 172.48/172.41 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_z_2)) ) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_min__max_Oless__supI1,axiom, % 172.48/172.41 ! [V_b,V_a,V_x,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_a)) % 172.48/172.41 => 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))) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_min__max_Oless__supI2,axiom, % 172.48/172.41 ! [V_a,V_b,V_x,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_b)) % 172.48/172.41 => 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))) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_less__max__iff__disj,axiom, % 172.48/172.41 ! [V_y_2,V_x_2,V_z_2,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => ( 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))) % 172.48/172.41 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z_2),V_x_2)) % 172.48/172.41 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_z_2),V_y_2)) ) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_max__less__iff__conj,axiom, % 172.48/172.41 ! [V_z_2,V_y_2,V_x_2,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => ( 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)) % 172.48/172.41 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),V_z_2)) % 172.48/172.41 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_y_2),V_z_2)) ) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_min__max_Oinf__le1,axiom, % 172.48/172.41 ! [V_y,V_x,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => 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)) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_min__max_Oinf__le2,axiom, % 172.48/172.41 ! [V_y,V_x,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => 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)) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_min__max_Ole__iff__inf,axiom, % 172.48/172.41 ! [V_y_2,V_x_2,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 172.48/172.41 <=> hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x_2),V_y_2) = V_x_2 ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_min__max_Ole__inf__iff,axiom, % 172.48/172.41 ! [V_z_2,V_y_2,V_x_2,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => ( 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))) % 172.48/172.41 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 172.48/172.41 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_z_2)) ) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_min__max_Ole__infI1,axiom, % 172.48/172.41 ! [V_b,V_x,V_a,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 172.48/172.41 => 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)) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_min__max_Ole__infI2,axiom, % 172.48/172.41 ! [V_a,V_x,V_b,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) % 172.48/172.41 => 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)) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_min__max_Oinf__absorb1,axiom, % 172.48/172.41 ! [V_y,V_x,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 172.48/172.41 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = V_x ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_min__max_Oinf__absorb2,axiom, % 172.48/172.41 ! [V_x,V_y,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 172.48/172.41 => hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_x),V_y) = V_y ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_min__max_Ole__infI,axiom, % 172.48/172.41 ! [V_b,V_a,V_x,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 172.48/172.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) % 172.48/172.41 => 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))) ) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_min__max_Oinf__greatest,axiom, % 172.48/172.41 ! [V_z,V_y,V_x,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 172.48/172.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_z)) % 172.48/172.41 => 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))) ) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_min__max_Oinf__mono,axiom, % 172.48/172.41 ! [V_d,V_b,V_c,V_a,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) % 172.48/172.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d)) % 172.48/172.41 => 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))) ) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_min__max_Ole__infE,axiom, % 172.48/172.41 ! [V_b,V_a,V_x,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => ( 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))) % 172.48/172.41 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 172.48/172.41 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) ) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_min__le__iff__disj,axiom, % 172.48/172.41 ! [V_z_2,V_y_2,V_x_2,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => ( 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)) % 172.48/172.41 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_z_2)) % 172.48/172.41 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_z_2)) ) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_le__maxI1,axiom, % 172.48/172.41 ! [V_y,V_x,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => 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))) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_le__maxI2,axiom, % 172.48/172.41 ! [V_x,V_y,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => 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))) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_min__max_Ole__iff__sup,axiom, % 172.48/172.41 ! [V_y_2,V_x_2,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 172.48/172.41 <=> hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x_2),V_y_2) = V_y_2 ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_min__max_Ole__sup__iff,axiom, % 172.48/172.41 ! [V_z_2,V_y_2,V_x_2,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => ( 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)) % 172.48/172.41 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_z_2)) % 172.48/172.41 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_z_2)) ) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_min__max_Ole__supI1,axiom, % 172.48/172.41 ! [V_b,V_a,V_x,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_a)) % 172.48/172.41 => 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))) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_min__max_Ole__supI2,axiom, % 172.48/172.41 ! [V_a,V_b,V_x,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_b)) % 172.48/172.41 => 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))) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_min__max_Osup__absorb2,axiom, % 172.48/172.41 ! [V_y,V_x,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 172.48/172.41 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = V_y ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_min__max_Osup__absorb1,axiom, % 172.48/172.41 ! [V_x,V_y,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 172.48/172.41 => hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_x),V_y) = V_x ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_min__max_Ole__supI,axiom, % 172.48/172.41 ! [V_b,V_x,V_a,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 172.48/172.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) % 172.48/172.41 => 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)) ) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_min__max_Osup__least,axiom, % 172.48/172.41 ! [V_z,V_x,V_y,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y),V_x)) % 172.48/172.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z),V_x)) % 172.48/172.41 => 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)) ) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_min__max_Osup__mono,axiom, % 172.48/172.41 ! [V_d,V_b,V_c,V_a,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_c)) % 172.48/172.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_d)) % 172.48/172.41 => 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))) ) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_min__max_Ole__supE,axiom, % 172.48/172.41 ! [V_x,V_b,V_a,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => ( 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)) % 172.48/172.41 => ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_x)) % 172.48/172.41 => ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b),V_x)) ) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_le__max__iff__disj,axiom, % 172.48/172.41 ! [V_y_2,V_x_2,V_z_2,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => ( 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))) % 172.48/172.41 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z_2),V_x_2)) % 172.48/172.41 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_z_2),V_y_2)) ) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_Int__greaterThanLessThan,axiom, % 172.48/172.41 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_a_2,V_b_2)),c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,V_ca_2,V_d_2)) = c_SetInterval_Oord__class_OgreaterThanLessThan(T_a,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a_2),V_ca_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b_2),V_d_2)) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_Int__atLeastLessThan,axiom, % 172.48/172.41 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2),V_b_2)),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_ca_2),V_d_2)) = hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a_2),V_ca_2)),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b_2),V_d_2)) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_Int__atLeastAtMost,axiom, % 172.48/172.41 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_ca_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a_2),V_ca_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b_2),V_d_2)) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_Int__greaterThanAtMost,axiom, % 172.48/172.41 ! [V_d_2,V_ca_2,V_b_2,V_a_2,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_a_2,V_b_2)),c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,V_ca_2,V_d_2)) = c_SetInterval_Oord__class_OgreaterThanAtMost(T_a,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a_2),V_ca_2),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b_2),V_d_2)) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_max__diff__distrib__left,axiom, % 172.48/172.41 ! [V_z,V_y,V_x,T_a] : % 172.48/172.41 ( class_Groups_Oordered__ab__group__add(T_a) % 172.48/172.41 => 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)) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_min__diff__distrib__left,axiom, % 172.48/172.41 ! [V_z,V_y,V_x,T_a] : % 172.48/172.41 ( class_Groups_Oordered__ab__group__add(T_a) % 172.48/172.41 => 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)) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_min__max_Ofun__left__comm__idem__sup,axiom, % 172.48/172.41 ! [T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => c_Finite__Set_Ofun__left__comm__idem(T_a,T_a,c_Orderings_Oord__class_Omax(T_a)) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_min__max_Ofun__left__comm__idem__inf,axiom, % 172.48/172.41 ! [T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => c_Finite__Set_Ofun__left__comm__idem(T_a,T_a,c_Orderings_Oord__class_Omin(T_a)) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_nat__minus__add__max,axiom, % 172.48/172.41 ! [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) ). % 172.48/172.41 % 172.48/172.41 fof(fact_max__Suc1,axiom, % 172.48/172.41 ! [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) ). % 172.48/172.41 % 172.48/172.41 fof(fact_max__Suc2,axiom, % 172.48/172.41 ! [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) ). % 172.48/172.41 % 172.48/172.41 fof(fact_Max_Oin__idem,axiom, % 172.48/172.41 ! [V_x_2,V_A_2,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.41 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 172.48/172.41 => 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) ) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_Min_Oin__idem,axiom, % 172.48/172.41 ! [V_x_2,V_A_2,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.41 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 172.48/172.41 => 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) ) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_Int__atLeastAtMostL1,axiom, % 172.48/172.41 ! [V_d_2,V_b_2,V_a_2,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => 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)) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_Int__atLeastAtMostR1,axiom, % 172.48/172.41 ! [V_d_2,V_ca_2,V_b_2,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatMost(T_a),V_b_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_ca_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_ca_2,hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b_2),V_d_2)) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_Int__atLeastAtMostL2,axiom, % 172.48/172.41 ! [V_ca_2,V_b_2,V_a_2,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_a_2,V_b_2)),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_ca_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a_2),V_ca_2),V_b_2) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_Int__atLeastAtMostR2,axiom, % 172.48/172.41 ! [V_d_2,V_ca_2,V_a_2,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),hAPP(c_SetInterval_Oord__class_OatLeast(T_a),V_a_2)),c_SetInterval_Oord__class_OatLeastAtMost(T_a,V_ca_2,V_d_2)) = c_SetInterval_Oord__class_OatLeastAtMost(T_a,hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_a_2),V_ca_2),V_d_2) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_Max_OF__eq,axiom, % 172.48/172.41 ! [V_A_2,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.41 => 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) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_Min_OF__eq,axiom, % 172.48/172.41 ! [V_A_2,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.41 => 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) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_min__Suc1,axiom, % 172.48/172.41 ! [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) ). % 172.48/172.41 % 172.48/172.41 fof(fact_min__Suc2,axiom, % 172.48/172.41 ! [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) ). % 172.48/172.41 % 172.48/172.41 fof(fact_min__max_Ofold1__belowI,axiom, % 172.48/172.41 ! [V_a_2,V_A_2,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.41 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 172.48/172.41 => 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)) ) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_min__max_Obelow__fold1__iff,axiom, % 172.48/172.41 ! [V_x_2,V_A_2,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.41 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.41 => ( 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))) % 172.48/172.41 <=> ! [B_x] : % 172.48/172.41 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 172.48/172.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),B_x)) ) ) ) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_fold1__below__iff,axiom, % 172.48/172.41 ! [V_x_2,V_A_2,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.41 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.41 => ( 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)) % 172.48/172.41 <=> ? [B_x] : % 172.48/172.41 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 172.48/172.41 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_x),V_x_2)) ) ) ) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_strict__below__fold1__iff,axiom, % 172.48/172.41 ! [V_x_2,V_A_2,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.41 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.41 => ( 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))) % 172.48/172.41 <=> ! [B_x] : % 172.48/172.41 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 172.48/172.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x_2),B_x)) ) ) ) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_fold1__strict__below__iff,axiom, % 172.48/172.41 ! [V_x_2,V_A_2,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.41 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.41 => ( 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)) % 172.48/172.41 <=> ? [B_x] : % 172.48/172.41 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 172.48/172.41 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),B_x),V_x_2)) ) ) ) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_Max__insert,axiom, % 172.48/172.41 ! [V_x_2,V_A_2,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.41 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.41 => 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)) ) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_Min__insert,axiom, % 172.48/172.41 ! [V_x_2,V_A_2,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.41 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.41 => 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)) ) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_Max_Osubset__idem,axiom, % 172.48/172.41 ! [V_B_2,V_A_2,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.41 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 172.48/172.41 => 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) ) ) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_Min_Osubset__idem,axiom, % 172.48/172.41 ! [V_B_2,V_A_2,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.41 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 172.48/172.41 => 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) ) ) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_Max__Un,axiom, % 172.48/172.41 ! [V_B_2,V_A_2,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.41 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 172.48/172.41 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.41 => 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)) ) ) ) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_Min__Un,axiom, % 172.48/172.41 ! [V_B_2,V_A_2,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.41 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 172.48/172.41 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.41 => 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)) ) ) ) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_Max_Oinsert,axiom, % 172.48/172.41 ! [V_x_2,V_A_2,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.41 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 172.48/172.41 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.41 => 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)) ) ) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_Min_Oinsert,axiom, % 172.48/172.41 ! [V_x_2,V_A_2,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.41 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 172.48/172.41 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.41 => 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)) ) ) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_fold1__antimono,axiom, % 172.48/172.41 ! [V_B_2,V_A_2,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 172.48/172.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 172.48/172.41 => 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))) ) ) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_Max_Oinsert__remove,axiom, % 172.48/172.41 ! [V_x_2,V_A_2,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.41 => ( ( hAPP(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)) % 172.48/172.41 => c_Big__Operators_Olinorder__class_OMax(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = V_x_2 ) % 172.48/172.41 & ( hAPP(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)) % 172.48/172.41 => 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)))))) ) ) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_Max_Ounion__disjoint,axiom, % 172.48/172.41 ! [V_B_2,V_A_2,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.41 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 172.48/172.41 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.41 => ( 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)) % 172.48/172.41 => 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)) ) ) ) ) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_Max_Ounion__inter,axiom, % 172.48/172.41 ! [V_B_2,V_A_2,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 172.48/172.41 => ( 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)) % 172.48/172.41 => 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)) ) ) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_Min_Oinsert__remove,axiom, % 172.48/172.41 ! [V_x_2,V_A_2,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.41 => ( ( hAPP(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)) % 172.48/172.41 => c_Big__Operators_Olinorder__class_OMin(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),V_A_2)) = V_x_2 ) % 172.48/172.41 & ( hAPP(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)) % 172.48/172.41 => 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)))))) ) ) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_Min_Ounion__disjoint,axiom, % 172.48/172.41 ! [V_B_2,V_A_2,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.41 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 172.48/172.41 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.41 => ( 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)) % 172.48/172.41 => 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)) ) ) ) ) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_Min_Ounion__inter,axiom, % 172.48/172.41 ! [V_B_2,V_A_2,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 172.48/172.41 => ( 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)) % 172.48/172.41 => 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)) ) ) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_dual__min,axiom, % 172.48/172.41 ! [T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => 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) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_dual__max,axiom, % 172.48/172.41 ! [T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => 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) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_max__ord__max,axiom, % 172.48/172.41 ! [T_a] : % 172.48/172.41 ( class_Orderings_Oord(T_a) % 172.48/172.41 => c_Orderings_Oord__class_Omax(T_a) = c_Orderings_Oord_Omax(T_a,c_Orderings_Oord__class_Oless__eq(T_a)) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_min__ord__min,axiom, % 172.48/172.41 ! [T_a] : % 172.48/172.41 ( class_Orderings_Oord(T_a) % 172.48/172.41 => c_Orderings_Oord__class_Omin(T_a) = c_Orderings_Oord_Omin(T_a,c_Orderings_Oord__class_Oless__eq(T_a)) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_min__max_Oinf__Sup2__distrib,axiom, % 172.48/172.41 ! [V_B_2,V_A_2,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.41 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 172.48/172.41 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.41 => 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))))))) ) ) ) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_SUP2__iff,axiom, % 172.48/172.41 ! [V_ca_2,V_b_2,V_B_2,V_A_2,T_c,T_b,T_a] : % 172.48/172.41 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_ca_2)) % 172.48/172.41 <=> ? [B_x] : % 172.48/172.41 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 172.48/172.41 & hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_ca_2)) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_sup__nat__def,axiom, % 172.48/172.41 c_Lattices_Osemilattice__sup__class_Osup(tc_Nat_Onat) = c_Orderings_Oord__class_Omax(tc_Nat_Onat) ). % 172.48/172.41 % 172.48/172.41 fof(fact_inf__nat__def,axiom, % 172.48/172.41 c_Lattices_Osemilattice__inf__class_Oinf(tc_Nat_Onat) = c_Orderings_Oord__class_Omin(tc_Nat_Onat) ). % 172.48/172.41 % 172.48/172.41 fof(fact_min__max_OSup__fin_Oin__idem,axiom, % 172.48/172.41 ! [V_x_2,V_A_2,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.41 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 172.48/172.41 => 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) ) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_min__max_OSup__fin_Osingleton,axiom, % 172.48/172.41 ! [V_x_2,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => 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 ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_min__max_OSup__fin_OF__eq,axiom, % 172.48/172.41 ! [V_A_2,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.41 => 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) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_min__max_OSup__fin_Oinsert__idem,axiom, % 172.48/172.41 ! [V_x_2,V_A_2,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.41 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.41 => 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)) ) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_min__max_OSup__fin_Osubset__idem,axiom, % 172.48/172.41 ! [V_B_2,V_A_2,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.41 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 172.48/172.41 => 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) ) ) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_min__max_Oinf__Sup__absorb,axiom, % 172.48/172.41 ! [V_a_2,V_A_2,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.41 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 172.48/172.41 => 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 ) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_min__max_OSup__fin_Ounion__idem,axiom, % 172.48/172.41 ! [V_B_2,V_A_2,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.41 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 172.48/172.41 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.41 => 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)) ) ) ) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_min__max_OSup__fin_Oinsert,axiom, % 172.48/172.41 ! [V_x_2,V_A_2,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.41 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 172.48/172.41 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.41 => 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)) ) ) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_min__max_OSup__fin_Oinsert__remove,axiom, % 172.48/172.41 ! [V_x_2,V_A_2,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.41 => ( ( hAPP(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)) % 172.48/172.41 => 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 ) % 172.48/172.41 & ( hAPP(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)) % 172.48/172.41 => 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)))))) ) ) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_min__max_OSup__fin_Ounion__inter,axiom, % 172.48/172.41 ! [V_B_2,V_A_2,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 172.48/172.41 => ( 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)) % 172.48/172.41 => 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)) ) ) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_min__max_OSup__fin_Ounion__disjoint,axiom, % 172.48/172.41 ! [V_B_2,V_A_2,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.41 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 172.48/172.41 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.41 => ( 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)) % 172.48/172.41 => 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)) ) ) ) ) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_min__max_OSup__fin_Oremove,axiom, % 172.48/172.41 ! [V_x_2,V_A_2,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.41 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 172.48/172.41 => ( ( hAPP(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)) % 172.48/172.41 => c_Big__Operators_Olattice_OSup__fin(T_a,c_Orderings_Oord__class_Omax(T_a),V_A_2) = V_x_2 ) % 172.48/172.41 & ( hAPP(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)) % 172.48/172.41 => 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)))))) ) ) ) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_min__max_Oinf__Sup1__distrib,axiom, % 172.48/172.41 ! [V_x_2,V_A_2,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.41 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.41 => 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))))) ) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_min__max_Osup__Inf1__distrib,axiom, % 172.48/172.41 ! [V_x_2,V_A_2,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.41 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.41 => 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))))) ) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_min__max_Osup__Inf2__distrib,axiom, % 172.48/172.41 ! [V_B_2,V_A_2,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.41 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 172.48/172.41 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.41 => 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))))))) ) ) ) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_min__max_OSup__fin_Oclosed,axiom, % 172.48/172.41 ! [V_A_2,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.41 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.41 => ( ! [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)))))) % 172.48/172.41 => 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)) ) ) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_Max_Oclosed,axiom, % 172.48/172.41 ! [V_A_2,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.41 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.41 => ( ! [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)))))) % 172.48/172.41 => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2)),V_A_2)) ) ) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_min__max_OInf__fin_Oin__idem,axiom, % 172.48/172.41 ! [V_x_2,V_A_2,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.41 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 172.48/172.41 => 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) ) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_min__max_OInf__fin_Osingleton,axiom, % 172.48/172.41 ! [V_x_2,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => 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 ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_min__max_OInf__fin_OF__eq,axiom, % 172.48/172.41 ! [V_A_2,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.41 => 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) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_min__max_OInf__fin_Oinsert__idem,axiom, % 172.48/172.41 ! [V_x_2,V_A_2,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.41 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.41 => 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)) ) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_min__max_OInf__fin_Osubset__idem,axiom, % 172.48/172.41 ! [V_B_2,V_A_2,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.41 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 172.48/172.41 => 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) ) ) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_min__max_Osup__Inf__absorb,axiom, % 172.48/172.41 ! [V_a_2,V_A_2,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.41 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 172.48/172.41 => 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 ) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_min__max_OInf__fin_Ounion__idem,axiom, % 172.48/172.41 ! [V_B_2,V_A_2,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.41 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 172.48/172.41 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.41 => 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)) ) ) ) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_min__max_OInf__fin_Oinsert,axiom, % 172.48/172.41 ! [V_x_2,V_A_2,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.41 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 172.48/172.41 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.41 => 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)) ) ) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_min__max_OInf__fin_Oinsert__remove,axiom, % 172.48/172.41 ! [V_x_2,V_A_2,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.41 => ( ( hAPP(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)) % 172.48/172.41 => 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 ) % 172.48/172.41 & ( hAPP(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)) % 172.48/172.41 => 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)))))) ) ) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_min__max_OInf__fin_Ounion__disjoint,axiom, % 172.48/172.41 ! [V_B_2,V_A_2,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.41 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 172.48/172.41 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.41 => ( 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)) % 172.48/172.41 => 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)) ) ) ) ) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_min__max_OInf__fin_Ounion__inter,axiom, % 172.48/172.41 ! [V_B_2,V_A_2,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) % 172.48/172.41 => ( 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)) % 172.48/172.41 => 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)) ) ) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_min__max_OInf__fin_Oremove,axiom, % 172.48/172.41 ! [V_x_2,V_A_2,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.41 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 172.48/172.41 => ( ( hAPP(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)) % 172.48/172.41 => c_Big__Operators_Olattice_OInf__fin(T_a,c_Orderings_Oord__class_Omin(T_a),V_A_2) = V_x_2 ) % 172.48/172.41 & ( hAPP(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)) % 172.48/172.41 => 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)))))) ) ) ) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_min__max_OInf__le__Sup,axiom, % 172.48/172.41 ! [V_A_2,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.41 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.41 => 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))) ) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_min__max_OInf__fin_Oclosed,axiom, % 172.48/172.41 ! [V_A_2,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.41 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.41 => ( ! [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)))))) % 172.48/172.41 => 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)) ) ) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_Min_Oclosed,axiom, % 172.48/172.41 ! [V_A_2,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.41 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.41 => ( ! [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)))))) % 172.48/172.41 => hBOOL(hAPP(hAPP(c_member(T_a),c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2)),V_A_2)) ) ) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_min__max_OSup__fin_Ohom__commute,axiom, % 172.48/172.41 ! [V_N_2,V_h_2,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => ( ! [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)) % 172.48/172.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 172.48/172.41 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.41 => 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)) ) ) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_min__max_OInf__fin_Ohom__commute,axiom, % 172.48/172.41 ! [V_N_2,V_h_2,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => ( ! [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)) % 172.48/172.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 172.48/172.41 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.41 => 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)) ) ) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_Max_Ohom__commute,axiom, % 172.48/172.41 ! [V_N_2,V_h_2,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => ( ! [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)) % 172.48/172.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 172.48/172.41 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.41 => 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)) ) ) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_Min_Ohom__commute,axiom, % 172.48/172.41 ! [V_N_2,V_h_2,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => ( ! [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)) % 172.48/172.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_N_2)) % 172.48/172.41 => ( V_N_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.41 => 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)) ) ) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_finite__UN__I,axiom, % 172.48/172.41 ! [V_B_2,T_b,V_A_2,T_a] : % 172.48/172.41 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.41 => ( ! [B_a] : % 172.48/172.41 ( hBOOL(hAPP(hAPP(c_member(T_a),B_a),V_A_2)) % 172.48/172.41 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_a))) ) % 172.48/172.41 => 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))) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_diff__nat__eq__if,axiom, % 172.48/172.41 ! [V_z_2,V_z_H_2] : % 172.48/172.41 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z_H_2)) % 172.48/172.41 => 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) ) % 172.48/172.41 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z_H_2)) % 172.48/172.41 => 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)) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_not__neg__0,axiom, % 172.48/172.41 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ). % 172.48/172.41 % 172.48/172.41 fof(fact_not__neg__int,axiom, % 172.48/172.41 ! [V_n] : ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),V_n))) ). % 172.48/172.41 % 172.48/172.41 fof(fact_not__neg__1,axiom, % 172.48/172.41 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,c_Groups_Oone__class_Oone(tc_Int_Oint))) ). % 172.48/172.41 % 172.48/172.41 fof(fact_not__neg__eq__ge__0,axiom, % 172.48/172.41 ! [V_x_2] : % 172.48/172.41 ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_x_2)) % 172.48/172.41 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x_2)) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_neg__def,axiom, % 172.48/172.41 ! [V_Z_2] : % 172.48/172.41 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_Z_2)) % 172.48/172.41 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_Z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_neg__nat,axiom, % 172.48/172.41 ! [V_z] : % 172.48/172.41 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z)) % 172.48/172.41 => hAPP(c_Int_Onat,V_z) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_not__neg__nat,axiom, % 172.48/172.41 ! [V_z] : % 172.48/172.41 ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,V_z)) % 172.48/172.41 => hAPP(c_Nat_Osemiring__1__class_Oof__nat(tc_Int_Oint),hAPP(c_Int_Onat,V_z)) = V_z ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_setsum__cases,axiom, % 172.48/172.41 ! [V_g_2,V_f_2,V_P_2,V_A_2,T_a,T_b] : % 172.48/172.41 ( class_Groups_Ocomm__monoid__add(T_b) % 172.48/172.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.41 => 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))))) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_nat__mod__eq__lemma,axiom, % 172.48/172.41 ! [V_y,V_n,V_x] : % 172.48/172.41 ( c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_x,V_n) = c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_y,V_n) % 172.48/172.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y),V_x)) % 172.48/172.41 => ? [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)) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_zdiv__zminus1__eq__if,axiom, % 172.48/172.41 ! [V_a,V_b] : % 172.48/172.41 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 172.48/172.41 => ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 172.48/172.41 => 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)) ) % 172.48/172.41 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 172.48/172.41 => 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)) ) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_zdiv__zminus2__eq__if,axiom, % 172.48/172.41 ! [V_a,V_b] : % 172.48/172.41 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 172.48/172.41 => ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 172.48/172.41 => 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)) ) % 172.48/172.41 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 172.48/172.41 => 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)) ) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_ComplI,axiom, % 172.48/172.41 ! [V_A_2,V_ca_2,T_a] : % 172.48/172.41 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 172.48/172.41 => hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2))) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_negative__zle,axiom, % 172.48/172.41 ! [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))) ). % 172.48/172.41 % 172.48/172.41 fof(fact_negative__zless,axiom, % 172.48/172.41 ! [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))) ). % 172.48/172.41 % 172.48/172.41 fof(fact_zmult__zminus,axiom, % 172.48/172.41 ! [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)) ). % 172.48/172.41 % 172.48/172.41 fof(fact_minus__divide__left,axiom, % 172.48/172.41 ! [V_b,V_a,T_a] : % 172.48/172.41 ( class_Rings_Odivision__ring(T_a) % 172.48/172.41 => 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) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_minus__divide__divide,axiom, % 172.48/172.41 ! [V_b,V_a,T_a] : % 172.48/172.41 ( class_Fields_Ofield__inverse__zero(T_a) % 172.48/172.41 => 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) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_minus__divide__right,axiom, % 172.48/172.41 ! [V_b,V_a,T_a] : % 172.48/172.41 ( class_Fields_Ofield__inverse__zero(T_a) % 172.48/172.41 => 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)) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_abs__minus__cancel,axiom, % 172.48/172.41 ! [V_a,T_a] : % 172.48/172.41 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 172.48/172.41 => 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) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_zminus__zadd__distrib,axiom, % 172.48/172.41 ! [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)) ). % 172.48/172.41 % 172.48/172.41 fof(fact_minus__diff__eq,axiom, % 172.48/172.41 ! [V_b,V_a,T_a] : % 172.48/172.41 ( class_Groups_Oab__group__add(T_a) % 172.48/172.41 => 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) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_mod__minus__cong,axiom, % 172.48/172.41 ! [V_a_H,V_b,V_a,T_a] : % 172.48/172.41 ( class_Divides_Oring__div(T_a) % 172.48/172.41 => ( c_Divides_Odiv__class_Omod(T_a,V_a,V_b) = c_Divides_Odiv__class_Omod(T_a,V_a_H,V_b) % 172.48/172.41 => 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) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_mod__minus__eq,axiom, % 172.48/172.41 ! [V_b,V_a,T_a] : % 172.48/172.41 ( class_Divides_Oring__div(T_a) % 172.48/172.41 => 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) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_Compl__anti__mono,axiom, % 172.48/172.41 ! [V_B_2,V_A_2,T_a] : % 172.48/172.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 172.48/172.41 => 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))) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_Compl__subset__Compl__iff,axiom, % 172.48/172.41 ! [V_B_2,V_A_2,T_a] : % 172.48/172.41 ( 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))) % 172.48/172.41 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_zminus__0,axiom, % 172.48/172.41 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) ). % 172.48/172.41 % 172.48/172.41 fof(fact_le__imp__neg__le,axiom, % 172.48/172.41 ! [V_b,V_a,T_a] : % 172.48/172.41 ( class_Groups_Oordered__ab__group__add(T_a) % 172.48/172.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 172.48/172.41 => 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))) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_neg__le__iff__le,axiom, % 172.48/172.41 ! [V_a_2,V_b_2,T_a] : % 172.48/172.41 ( class_Groups_Oordered__ab__group__add(T_a) % 172.48/172.41 => ( 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))) % 172.48/172.41 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_minus__le__iff,axiom, % 172.48/172.41 ! [V_b_2,V_a_2,T_a] : % 172.48/172.41 ( class_Groups_Oordered__ab__group__add(T_a) % 172.48/172.41 => ( 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)) % 172.48/172.41 <=> 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)) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_le__minus__iff,axiom, % 172.48/172.41 ! [V_b_2,V_a_2,T_a] : % 172.48/172.41 ( class_Groups_Oordered__ab__group__add(T_a) % 172.48/172.41 => ( 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))) % 172.48/172.41 <=> 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))) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_compl__mono,axiom, % 172.48/172.41 ! [V_y,V_x,T_a] : % 172.48/172.41 ( class_Lattices_Oboolean__algebra(T_a) % 172.48/172.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 172.48/172.41 => 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))) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_compl__le__compl__iff,axiom, % 172.48/172.41 ! [V_y_2,V_x_2,T_a] : % 172.48/172.41 ( class_Lattices_Oboolean__algebra(T_a) % 172.48/172.41 => ( 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))) % 172.48/172.41 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_y_2),V_x_2)) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_neg__equal__zero,axiom, % 172.48/172.41 ! [V_a_2,T_a] : % 172.48/172.41 ( class_Groups_Olinordered__ab__group__add(T_a) % 172.48/172.41 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) = V_a_2 % 172.48/172.41 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_neg__equal__0__iff__equal,axiom, % 172.48/172.41 ! [V_a_2,T_a] : % 172.48/172.41 ( class_Groups_Ogroup__add(T_a) % 172.48/172.41 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) = c_Groups_Ozero__class_Ozero(T_a) % 172.48/172.41 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_equal__neg__zero,axiom, % 172.48/172.41 ! [V_a_2,T_a] : % 172.48/172.41 ( class_Groups_Olinordered__ab__group__add(T_a) % 172.48/172.41 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) % 172.48/172.41 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_neg__0__equal__iff__equal,axiom, % 172.48/172.41 ! [V_a_2,T_a] : % 172.48/172.41 ( class_Groups_Ogroup__add(T_a) % 172.48/172.41 => ( c_Groups_Ozero__class_Ozero(T_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) % 172.48/172.41 <=> c_Groups_Ozero__class_Ozero(T_a) = V_a_2 ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_minus__zero,axiom, % 172.48/172.41 ! [T_a] : % 172.48/172.41 ( class_Groups_Ogroup__add(T_a) % 172.48/172.41 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_less__minus__iff,axiom, % 172.48/172.41 ! [V_b_2,V_a_2,T_a] : % 172.48/172.41 ( class_Groups_Oordered__ab__group__add(T_a) % 172.48/172.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2))) % 172.48/172.41 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2))) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_minus__less__iff,axiom, % 172.48/172.41 ! [V_b_2,V_a_2,T_a] : % 172.48/172.41 ( class_Groups_Oordered__ab__group__add(T_a) % 172.48/172.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),V_b_2)) % 172.48/172.41 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2)),V_a_2)) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_neg__less__iff__less,axiom, % 172.48/172.41 ! [V_a_2,V_b_2,T_a] : % 172.48/172.41 ( class_Groups_Oordered__ab__group__add(T_a) % 172.48/172.41 => ( 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))) % 172.48/172.41 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_minus__add__distrib,axiom, % 172.48/172.41 ! [V_b,V_a,T_a] : % 172.48/172.41 ( class_Groups_Oab__group__add(T_a) % 172.48/172.41 => 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)) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_minus__add,axiom, % 172.48/172.41 ! [V_b,V_a,T_a] : % 172.48/172.41 ( class_Groups_Ogroup__add(T_a) % 172.48/172.41 => 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)) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_add__minus__cancel,axiom, % 172.48/172.41 ! [V_b,V_a,T_a] : % 172.48/172.41 ( class_Groups_Ogroup__add(T_a) % 172.48/172.41 => 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 ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_minus__add__cancel,axiom, % 172.48/172.41 ! [V_b,V_a,T_a] : % 172.48/172.41 ( class_Groups_Ogroup__add(T_a) % 172.48/172.41 => 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 ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_minus__mult__right,axiom, % 172.48/172.41 ! [V_b,V_a,T_a] : % 172.48/172.41 ( class_Rings_Oring(T_a) % 172.48/172.41 => 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)) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_minus__mult__left,axiom, % 172.48/172.41 ! [V_b,V_a,T_a] : % 172.48/172.41 ( class_Rings_Oring(T_a) % 172.48/172.41 => 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) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_minus__mult__commute,axiom, % 172.48/172.41 ! [V_b,V_a,T_a] : % 172.48/172.41 ( class_Rings_Oring(T_a) % 172.48/172.41 => 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)) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_minus__mult__minus,axiom, % 172.48/172.41 ! [V_b,V_a,T_a] : % 172.48/172.41 ( class_Rings_Oring(T_a) % 172.48/172.41 => 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) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_square__eq__iff,axiom, % 172.48/172.41 ! [V_b_2,V_a_2,T_a] : % 172.48/172.41 ( class_Rings_Oidom(T_a) % 172.48/172.41 => ( 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) % 172.48/172.41 <=> ( V_a_2 = V_b_2 % 172.48/172.41 | V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2) ) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_ComplE,axiom, % 172.48/172.41 ! [V_A_2,V_ca_2,T_a] : % 172.48/172.41 ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2))) % 172.48/172.41 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_ComplD,axiom, % 172.48/172.41 ! [V_A_2,V_ca_2,T_a] : % 172.48/172.41 ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2))) % 172.48/172.41 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_Compl__iff,axiom, % 172.48/172.41 ! [V_A_2,V_ca_2,T_a] : % 172.48/172.41 ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2))) % 172.48/172.41 <=> ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_zminus__zminus,axiom, % 172.48/172.41 ! [V_z] : hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_z)) = V_z ). % 172.48/172.41 % 172.48/172.41 fof(fact_fun__Compl__def,axiom, % 172.48/172.41 ! [V_x_2,V_A_2,T_b,T_a] : % 172.48/172.41 ( class_Groups_Ouminus(T_a) % 172.48/172.41 => 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)) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_double__compl,axiom, % 172.48/172.41 ! [V_x,T_a] : % 172.48/172.41 ( class_Lattices_Oboolean__algebra(T_a) % 172.48/172.41 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x)) = V_x ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_uminus__apply,axiom, % 172.48/172.41 ! [V_x_2,V_A_2,T_b,T_a] : % 172.48/172.41 ( class_Groups_Ouminus(T_a) % 172.48/172.41 => 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)) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_compl__eq__compl__iff,axiom, % 172.48/172.41 ! [V_y_2,V_x_2,T_a] : % 172.48/172.41 ( class_Lattices_Oboolean__algebra(T_a) % 172.48/172.41 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_y_2) % 172.48/172.41 <=> V_x_2 = V_y_2 ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_double__complement,axiom, % 172.48/172.41 ! [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 ). % 172.48/172.41 % 172.48/172.41 fof(fact_Compl__eq__Compl__iff,axiom, % 172.48/172.41 ! [V_B_2,V_A_2,T_a] : % 172.48/172.41 ( 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) % 172.48/172.41 <=> V_A_2 = V_B_2 ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_minus__minus,axiom, % 172.48/172.41 ! [V_a,T_a] : % 172.48/172.41 ( class_Groups_Ogroup__add(T_a) % 172.48/172.41 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)) = V_a ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_equation__minus__iff,axiom, % 172.48/172.41 ! [V_b_2,V_a_2,T_a] : % 172.48/172.41 ( class_Groups_Ogroup__add(T_a) % 172.48/172.41 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2) % 172.48/172.41 <=> V_b_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_minus__equation__iff,axiom, % 172.48/172.41 ! [V_b_2,V_a_2,T_a] : % 172.48/172.41 ( class_Groups_Ogroup__add(T_a) % 172.48/172.41 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) = V_b_2 % 172.48/172.41 <=> hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2) = V_a_2 ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_neg__equal__iff__equal,axiom, % 172.48/172.41 ! [V_b_2,V_a_2,T_a] : % 172.48/172.41 ( class_Groups_Ogroup__add(T_a) % 172.48/172.41 => ( hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2) % 172.48/172.41 <=> V_a_2 = V_b_2 ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_zdiv__zminus__zminus,axiom, % 172.48/172.41 ! [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) ). % 172.48/172.41 % 172.48/172.41 fof(fact_zdiv__zminus2,axiom, % 172.48/172.41 ! [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) ). % 172.48/172.41 % 172.48/172.41 fof(fact_zminus__zmod,axiom, % 172.48/172.41 ! [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) ). % 172.48/172.41 % 172.48/172.41 fof(fact_zmod__zminus__zminus,axiom, % 172.48/172.41 ! [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)) ). % 172.48/172.41 % 172.48/172.41 fof(fact_zmod__zminus2,axiom, % 172.48/172.41 ! [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)) ). % 172.48/172.41 % 172.48/172.41 fof(fact_setsum__negf,axiom, % 172.48/172.41 ! [V_A_2,V_f_2,T_b,T_a] : % 172.48/172.41 ( class_Groups_Oab__group__add(T_a) % 172.48/172.41 => 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)) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_Collect__neg__eq,axiom, % 172.48/172.41 ! [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)) ). % 172.48/172.41 % 172.48/172.41 fof(fact_minus__le__self__iff,axiom, % 172.48/172.41 ! [V_a_2,T_a] : % 172.48/172.41 ( class_Groups_Olinordered__ab__group__add(T_a) % 172.48/172.41 => ( 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)) % 172.48/172.41 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_neg__le__0__iff__le,axiom, % 172.48/172.41 ! [V_a_2,T_a] : % 172.48/172.41 ( class_Groups_Oordered__ab__group__add(T_a) % 172.48/172.41 => ( 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))) % 172.48/172.41 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_le__minus__self__iff,axiom, % 172.48/172.41 ! [V_a_2,T_a] : % 172.48/172.41 ( class_Groups_Olinordered__ab__group__add(T_a) % 172.48/172.41 => ( 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))) % 172.48/172.41 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_neg__0__le__iff__le,axiom, % 172.48/172.41 ! [V_a_2,T_a] : % 172.48/172.41 ( class_Groups_Oordered__ab__group__add(T_a) % 172.48/172.41 => ( 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))) % 172.48/172.41 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_neg__0__less__iff__less,axiom, % 172.48/172.41 ! [V_a_2,T_a] : % 172.48/172.41 ( class_Groups_Oordered__ab__group__add(T_a) % 172.48/172.41 => ( 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))) % 172.48/172.41 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_less__minus__self__iff,axiom, % 172.48/172.41 ! [V_a_2,T_a] : % 172.48/172.41 ( class_Rings_Olinordered__idom(T_a) % 172.48/172.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2))) % 172.48/172.41 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_neg__less__0__iff__less,axiom, % 172.48/172.41 ! [V_a_2,T_a] : % 172.48/172.41 ( class_Groups_Oordered__ab__group__add(T_a) % 172.48/172.41 => ( 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))) % 172.48/172.41 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_neg__less__nonneg,axiom, % 172.48/172.41 ! [V_a_2,T_a] : % 172.48/172.41 ( class_Groups_Olinordered__ab__group__add(T_a) % 172.48/172.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),V_a_2)) % 172.48/172.41 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_minus__unique,axiom, % 172.48/172.41 ! [V_b,V_a,T_a] : % 172.48/172.41 ( class_Groups_Ogroup__add(T_a) % 172.48/172.41 => ( hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a),V_b) = c_Groups_Ozero__class_Ozero(T_a) % 172.48/172.41 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) = V_b ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_ab__left__minus,axiom, % 172.48/172.41 ! [V_a,T_a] : % 172.48/172.41 ( class_Groups_Oab__group__add(T_a) % 172.48/172.41 => 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) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_left__minus,axiom, % 172.48/172.41 ! [V_a,T_a] : % 172.48/172.41 ( class_Groups_Ogroup__add(T_a) % 172.48/172.41 => 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) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_eq__neg__iff__add__eq__0,axiom, % 172.48/172.41 ! [V_b_2,V_a_2,T_a] : % 172.48/172.41 ( class_Groups_Ogroup__add(T_a) % 172.48/172.41 => ( V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_b_2) % 172.48/172.41 <=> hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_a_2),V_b_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_right__minus,axiom, % 172.48/172.41 ! [V_a,T_a] : % 172.48/172.41 ( class_Groups_Ogroup__add(T_a) % 172.48/172.41 => 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) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_diff__0,axiom, % 172.48/172.41 ! [V_a,T_a] : % 172.48/172.41 ( class_Groups_Ogroup__add(T_a) % 172.48/172.41 => 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) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_diff__def,axiom, % 172.48/172.41 ! [V_b,V_a,T_a] : % 172.48/172.41 ( class_Groups_Ogroup__add(T_a) % 172.48/172.41 => 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)) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_ab__diff__minus,axiom, % 172.48/172.41 ! [V_b,V_a,T_a] : % 172.48/172.41 ( class_Groups_Oab__group__add(T_a) % 172.48/172.41 => 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)) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I2_J,axiom, % 172.48/172.41 ! [V_y,V_x,T_a] : % 172.48/172.41 ( class_Rings_Ocomm__ring__1(T_a) % 172.48/172.41 => 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)) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_diff__minus__eq__add,axiom, % 172.48/172.41 ! [V_b,V_a,T_a] : % 172.48/172.41 ( class_Groups_Ogroup__add(T_a) % 172.48/172.41 => 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) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_comm__ring__1__class_Onormalizing__ring__rules_I1_J,axiom, % 172.48/172.41 ! [V_x,T_a] : % 172.48/172.41 ( class_Rings_Ocomm__ring__1(T_a) % 172.48/172.41 => 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) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_square__eq__1__iff,axiom, % 172.48/172.41 ! [V_x_2,T_a] : % 172.48/172.41 ( class_Rings_Oring__1__no__zero__divisors(T_a) % 172.48/172.41 => ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_x_2),V_x_2) = c_Groups_Oone__class_Oone(T_a) % 172.48/172.41 <=> ( V_x_2 = c_Groups_Oone__class_Oone(T_a) % 172.48/172.41 | V_x_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_inf__compl__bot,axiom, % 172.48/172.41 ! [V_x,T_a] : % 172.48/172.41 ( class_Lattices_Oboolean__algebra(T_a) % 172.48/172.41 => 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) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_compl__inf__bot,axiom, % 172.48/172.41 ! [V_x,T_a] : % 172.48/172.41 ( class_Lattices_Oboolean__algebra(T_a) % 172.48/172.41 => 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) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_diff__eq,axiom, % 172.48/172.41 ! [V_y,V_x,T_a] : % 172.48/172.41 ( class_Lattices_Oboolean__algebra(T_a) % 172.48/172.41 => 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)) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_compl__bot__eq,axiom, % 172.48/172.41 ! [T_a] : % 172.48/172.41 ( class_Lattices_Oboolean__algebra(T_a) % 172.48/172.41 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Orderings_Obot__class_Obot(T_a)) = c_Orderings_Otop__class_Otop(T_a) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_compl__top__eq,axiom, % 172.48/172.41 ! [T_a] : % 172.48/172.41 ( class_Lattices_Oboolean__algebra(T_a) % 172.48/172.41 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Orderings_Otop__class_Otop(T_a)) = c_Orderings_Obot__class_Obot(T_a) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_compl__inf,axiom, % 172.48/172.41 ! [V_y,V_x,T_a] : % 172.48/172.41 ( class_Lattices_Oboolean__algebra(T_a) % 172.48/172.41 => 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)) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_compl__sup,axiom, % 172.48/172.41 ! [V_y,V_x,T_a] : % 172.48/172.41 ( class_Lattices_Oboolean__algebra(T_a) % 172.48/172.41 => 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)) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_sup__compl__top,axiom, % 172.48/172.41 ! [V_x,T_a] : % 172.48/172.41 ( class_Lattices_Oboolean__algebra(T_a) % 172.48/172.41 => 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) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_compl__sup__top,axiom, % 172.48/172.41 ! [V_x,T_a] : % 172.48/172.41 ( class_Lattices_Oboolean__algebra(T_a) % 172.48/172.41 => 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) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_nonzero__minus__divide__right,axiom, % 172.48/172.41 ! [V_a,V_b,T_a] : % 172.48/172.41 ( class_Rings_Odivision__ring(T_a) % 172.48/172.41 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 172.48/172.41 => 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)) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_nonzero__minus__divide__divide,axiom, % 172.48/172.41 ! [V_a,V_b,T_a] : % 172.48/172.41 ( class_Rings_Odivision__ring(T_a) % 172.48/172.41 => ( V_b != c_Groups_Ozero__class_Ozero(T_a) % 172.48/172.41 => 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) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_abs__le__D2,axiom, % 172.48/172.41 ! [V_b,V_a,T_a] : % 172.48/172.41 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 172.48/172.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b)) % 172.48/172.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b)) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_abs__leI,axiom, % 172.48/172.41 ! [V_b,V_a,T_a] : % 172.48/172.41 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 172.48/172.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),V_b)) % 172.48/172.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a)),V_b)) % 172.48/172.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a)),V_b)) ) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_abs__le__iff,axiom, % 172.48/172.41 ! [V_b_2,V_a_2,T_a] : % 172.48/172.41 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 172.48/172.41 => ( 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)) % 172.48/172.41 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),V_b_2)) % 172.48/172.41 & 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)) ) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_abs__ge__minus__self,axiom, % 172.48/172.41 ! [V_a,T_a] : % 172.48/172.41 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 172.48/172.41 => 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))) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_abs__less__iff,axiom, % 172.48/172.41 ! [V_b_2,V_a_2,T_a] : % 172.48/172.41 ( class_Rings_Olinordered__idom(T_a) % 172.48/172.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a_2)),V_b_2)) % 172.48/172.41 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),V_b_2)) % 172.48/172.41 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a_2)),V_b_2)) ) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_subset__Compl__self__eq,axiom, % 172.48/172.41 ! [V_A_2,T_a] : % 172.48/172.41 ( 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))) % 172.48/172.41 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_Compl__UNIV__eq,axiom, % 172.48/172.41 ! [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)) ). % 172.48/172.41 % 172.48/172.41 fof(fact_Compl__empty__eq,axiom, % 172.48/172.41 ! [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)) ). % 172.48/172.41 % 172.48/172.41 fof(fact_finite__compl,axiom, % 172.48/172.41 ! [V_A_2,T_a] : % 172.48/172.41 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_a,tc_HOL_Obool)),V_A_2))) % 172.48/172.41 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_Compl__disjoint2,axiom, % 172.48/172.41 ! [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)) ). % 172.48/172.41 % 172.48/172.41 fof(fact_Compl__disjoint,axiom, % 172.48/172.41 ! [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)) ). % 172.48/172.41 % 172.48/172.41 fof(fact_Compl__partition,axiom, % 172.48/172.41 ! [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)) ). % 172.48/172.41 % 172.48/172.41 fof(fact_Compl__partition2,axiom, % 172.48/172.41 ! [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)) ). % 172.48/172.41 % 172.48/172.41 fof(fact_Compl__Int,axiom, % 172.48/172.41 ! [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)) ). % 172.48/172.41 % 172.48/172.41 fof(fact_Compl__Un,axiom, % 172.48/172.41 ! [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)) ). % 172.48/172.41 % 172.48/172.41 fof(fact_minus__max__eq__min,axiom, % 172.48/172.41 ! [V_y,V_x,T_a] : % 172.48/172.41 ( class_Groups_Olinordered__ab__group__add(T_a) % 172.48/172.41 => 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)) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_minus__min__eq__max,axiom, % 172.48/172.41 ! [V_y,V_x,T_a] : % 172.48/172.41 ( class_Groups_Olinordered__ab__group__add(T_a) % 172.48/172.41 => 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)) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_image__uminus__atLeastAtMost,axiom, % 172.48/172.41 ! [V_y_2,V_x_2,T_a] : % 172.48/172.41 ( class_Groups_Oordered__ab__group__add(T_a) % 172.48/172.41 => 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)) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_Compl__eq__Diff__UNIV,axiom, % 172.48/172.41 ! [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) ). % 172.48/172.41 % 172.48/172.41 fof(fact_abs__power__minus,axiom, % 172.48/172.41 ! [V_n,V_a,T_a] : % 172.48/172.41 ( class_Rings_Olinordered__idom(T_a) % 172.48/172.41 => 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)) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_zadd__zminus__inverse2,axiom, % 172.48/172.41 ! [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) ). % 172.48/172.41 % 172.48/172.41 fof(fact_Compl__Diff__eq,axiom, % 172.48/172.41 ! [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) ). % 172.48/172.41 % 172.48/172.41 fof(fact_Diff__eq,axiom, % 172.48/172.41 ! [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)) ). % 172.48/172.41 % 172.48/172.41 fof(fact_Diff__Compl,axiom, % 172.48/172.41 ! [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) ). % 172.48/172.41 % 172.48/172.41 fof(fact_negative__eq__positive,axiom, % 172.48/172.41 ! [V_m_2,V_n_2] : % 172.48/172.41 ( 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) % 172.48/172.41 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 172.48/172.41 & V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_not__int__zless__negative,axiom, % 172.48/172.41 ! [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)))) ). % 172.48/172.41 % 172.48/172.41 fof(fact_zmod__zminus1__not__zero,axiom, % 172.48/172.41 ! [V_l,V_k] : % 172.48/172.41 ( 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) % 172.48/172.41 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_zmod__zminus2__not__zero,axiom, % 172.48/172.41 ! [V_l,V_k] : % 172.48/172.41 ( 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) % 172.48/172.41 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_diff__int__def__symmetric,axiom, % 172.48/172.41 ! [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) ). % 172.48/172.41 % 172.48/172.41 fof(fact_diff__int__def,axiom, % 172.48/172.41 ! [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)) ). % 172.48/172.41 % 172.48/172.41 fof(fact_Ints__minus,axiom, % 172.48/172.41 ! [V_a_2,T_a] : % 172.48/172.41 ( class_Rings_Oring__1(T_a) % 172.48/172.41 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Int_Oring__1__class_OInts(T_a))) % 172.48/172.41 => 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))) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_image__uminus__greaterThanLessThan,axiom, % 172.48/172.41 ! [V_y_2,V_x_2,T_a] : % 172.48/172.41 ( class_Groups_Oordered__ab__group__add(T_a) % 172.48/172.41 => 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)) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_Compl__eq,axiom, % 172.48/172.41 ! [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))) ). % 172.48/172.41 % 172.48/172.41 fof(fact_Compl__lessThan,axiom, % 172.48/172.41 ! [V_k_2,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => 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) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_Compl__atLeast,axiom, % 172.48/172.41 ! [V_k_2,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => 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) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_Collect__imp__eq,axiom, % 172.48/172.41 ! [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)) ). % 172.48/172.41 % 172.48/172.41 fof(fact_Compl__atMost,axiom, % 172.48/172.41 ! [V_k_2,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => 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) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_Compl__greaterThan,axiom, % 172.48/172.41 ! [V_k_2,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => 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) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_abs__minus__le__zero,axiom, % 172.48/172.41 ! [V_a,T_a] : % 172.48/172.41 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 172.48/172.41 => 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))) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_abs__of__nonpos,axiom, % 172.48/172.41 ! [V_a,T_a] : % 172.48/172.41 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 172.48/172.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 172.48/172.41 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_abs__if,axiom, % 172.48/172.41 ! [V_a,T_a] : % 172.48/172.41 ( class_Groups_Oabs__if(T_a) % 172.48/172.41 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 172.48/172.41 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) % 172.48/172.41 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 172.48/172.41 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = V_a ) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_abs__of__neg,axiom, % 172.48/172.41 ! [V_a,T_a] : % 172.48/172.41 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 172.48/172.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 172.48/172.41 => hAPP(c_Groups_Oabs__class_Oabs(T_a),V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_a) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_power__minus,axiom, % 172.48/172.41 ! [V_n,V_a,T_a] : % 172.48/172.41 ( class_Rings_Oring__1(T_a) % 172.48/172.41 => 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)) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_disjoint__eq__subset__Compl,axiom, % 172.48/172.41 ! [V_B_2,V_A_2,T_a] : % 172.48/172.41 ( 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)) % 172.48/172.41 <=> 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))) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_surj__Compl__image__subset,axiom, % 172.48/172.41 ! [V_A_2,V_f_2,T_a,T_b] : % 172.48/172.41 ( 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)) % 172.48/172.41 => 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)))) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_int__zle__neg,axiom, % 172.48/172.41 ! [V_m_2,V_n_2] : % 172.48/172.41 ( 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)))) % 172.48/172.41 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 172.48/172.41 & V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_negative__zle__0,axiom, % 172.48/172.41 ! [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))) ). % 172.48/172.41 % 172.48/172.41 fof(fact_nat__zminus__int,axiom, % 172.48/172.41 ! [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) ). % 172.48/172.41 % 172.48/172.41 fof(fact_zmod__zminus1__eq__if,axiom, % 172.48/172.41 ! [V_b,V_a] : % 172.48/172.41 ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 172.48/172.41 => 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) ) % 172.48/172.41 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 172.48/172.41 => 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)) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_zmod__zminus2__eq__if,axiom, % 172.48/172.41 ! [V_b,V_a] : % 172.48/172.41 ( ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 172.48/172.41 => 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) ) % 172.48/172.41 & ( c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 172.48/172.41 => 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) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_zabs__def,axiom, % 172.48/172.41 ! [V_i] : % 172.48/172.41 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 172.48/172.41 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_i) ) % 172.48/172.41 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_i),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 172.48/172.41 => hAPP(c_Groups_Oabs__class_Oabs(tc_Int_Oint),V_i) = V_i ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_image__uminus__atLeastLessThan,axiom, % 172.48/172.41 ! [V_y_2,V_x_2,T_a] : % 172.48/172.41 ( class_Groups_Oordered__ab__group__add(T_a) % 172.48/172.41 => 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)) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_image__uminus__greaterThanAtMost,axiom, % 172.48/172.41 ! [V_y_2,V_x_2,T_a] : % 172.48/172.41 ( class_Groups_Oordered__ab__group__add(T_a) % 172.48/172.41 => 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)) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_neg__zminus__int,axiom, % 172.48/172.41 ! [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))))) ). % 172.48/172.41 % 172.48/172.41 fof(fact_image__uminus__greaterThan,axiom, % 172.48/172.41 ! [V_x_2,T_a] : % 172.48/172.41 ( class_Groups_Oordered__ab__group__add(T_a) % 172.48/172.41 => 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)) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_image__uminus__lessThan,axiom, % 172.48/172.41 ! [V_x_2,T_a] : % 172.48/172.41 ( class_Groups_Oordered__ab__group__add(T_a) % 172.48/172.41 => 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)) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_image__uminus__atLeast,axiom, % 172.48/172.41 ! [V_x_2,T_a] : % 172.48/172.41 ( class_Groups_Oordered__ab__group__add(T_a) % 172.48/172.41 => 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)) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_image__uminus__atMost,axiom, % 172.48/172.41 ! [V_x_2,T_a] : % 172.48/172.41 ( class_Groups_Oordered__ab__group__add(T_a) % 172.48/172.41 => 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)) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_Pow__Compl,axiom, % 172.48/172.41 ! [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))))) ). % 172.48/172.41 % 172.48/172.41 fof(fact_compl__unique,axiom, % 172.48/172.41 ! [V_y,V_x,T_a] : % 172.48/172.41 ( class_Lattices_Oboolean__algebra(T_a) % 172.48/172.41 => ( hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_x),V_y) = c_Orderings_Obot__class_Obot(T_a) % 172.48/172.41 => ( hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_x),V_y) = c_Orderings_Otop__class_Otop(T_a) % 172.48/172.41 => hAPP(c_Groups_Ouminus__class_Ouminus(T_a),V_x) = V_y ) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_not__zle__0__negative,axiom, % 172.48/172.41 ! [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))))) ). % 172.48/172.41 % 172.48/172.41 fof(fact_negative__zless__0,axiom, % 172.48/172.41 ! [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))) ). % 172.48/172.41 % 172.48/172.41 fof(fact_nat__mult__distrib__neg,axiom, % 172.48/172.41 ! [V_z_H,V_z] : % 172.48/172.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 172.48/172.41 => 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))) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_minus__Max__eq__Min,axiom, % 172.48/172.41 ! [V_S_2,T_a] : % 172.48/172.41 ( class_Groups_Olinordered__ab__group__add(T_a) % 172.48/172.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 172.48/172.41 => ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.41 => 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)) ) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_minus__Min__eq__Max,axiom, % 172.48/172.41 ! [V_S_2,T_a] : % 172.48/172.41 ( class_Groups_Olinordered__ab__group__add(T_a) % 172.48/172.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_S_2)) % 172.48/172.41 => ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.41 => 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)) ) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_z3div__def,axiom, % 172.48/172.41 ! [V_k,V_l] : % 172.48/172.41 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 172.48/172.41 => c_SMT_Oz3div(V_k,V_l) = hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_k),V_l) ) % 172.48/172.41 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 172.48/172.41 => 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))) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_z3mod__def,axiom, % 172.48/172.41 ! [V_k,V_l] : % 172.48/172.41 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 172.48/172.41 => c_SMT_Oz3mod(V_k,V_l) = c_Divides_Odiv__class_Omod(tc_Int_Oint,V_k,V_l) ) % 172.48/172.41 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 172.48/172.41 => 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)) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_of__int__of__nat,axiom, % 172.48/172.41 ! [V_k,T_a] : % 172.48/172.41 ( class_Rings_Oring__1(T_a) % 172.48/172.41 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 172.48/172.41 => 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)))) ) % 172.48/172.41 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 172.48/172.41 => 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)) ) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_negD,axiom, % 172.48/172.41 ! [V_x] : % 172.48/172.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 172.48/172.41 => ? [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))) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_of__int__int__eq,axiom, % 172.48/172.41 ! [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) ). % 172.48/172.41 % 172.48/172.41 fof(fact_of__int__eq__iff,axiom, % 172.48/172.41 ! [V_z_2,V_w_2,T_a] : % 172.48/172.41 ( class_Int_Oring__char__0(T_a) % 172.48/172.41 => ( 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) % 172.48/172.41 <=> V_w_2 = V_z_2 ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_of__int__0,axiom, % 172.48/172.41 ! [T_a] : % 172.48/172.41 ( class_Rings_Oring__1(T_a) % 172.48/172.41 => 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) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_of__int__0__eq__iff,axiom, % 172.48/172.41 ! [V_z_2,T_a] : % 172.48/172.41 ( class_Int_Oring__char__0(T_a) % 172.48/172.41 => ( c_Groups_Ozero__class_Ozero(T_a) = hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z_2) % 172.48/172.41 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_of__int__eq__0__iff,axiom, % 172.48/172.41 ! [V_z_2,T_a] : % 172.48/172.41 ( class_Int_Oring__char__0(T_a) % 172.48/172.41 => ( hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_z_2) = c_Groups_Ozero__class_Ozero(T_a) % 172.48/172.41 <=> V_z_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_of__int__le__iff,axiom, % 172.48/172.41 ! [V_z_2,V_w_2,T_a] : % 172.48/172.41 ( class_Rings_Olinordered__idom(T_a) % 172.48/172.41 => ( 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))) % 172.48/172.41 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_of__int__less__iff,axiom, % 172.48/172.41 ! [V_z_2,V_w_2,T_a] : % 172.48/172.41 ( class_Rings_Olinordered__idom(T_a) % 172.48/172.41 => ( 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))) % 172.48/172.41 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),V_z_2)) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_of__int__add,axiom, % 172.48/172.41 ! [V_z,V_w,T_a] : % 172.48/172.41 ( class_Rings_Oring__1(T_a) % 172.48/172.41 => 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)) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_of__int__mult,axiom, % 172.48/172.41 ! [V_z,V_w,T_a] : % 172.48/172.41 ( class_Rings_Oring__1(T_a) % 172.48/172.41 => 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)) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_of__int__1,axiom, % 172.48/172.41 ! [T_a] : % 172.48/172.41 ( class_Rings_Oring__1(T_a) % 172.48/172.41 => 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) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_of__int__diff,axiom, % 172.48/172.41 ! [V_z,V_w,T_a] : % 172.48/172.41 ( class_Rings_Oring__1(T_a) % 172.48/172.41 => 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)) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_of__int__of__nat__eq,axiom, % 172.48/172.41 ! [V_n,T_a] : % 172.48/172.41 ( class_Rings_Oring__1(T_a) % 172.48/172.41 => 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) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_of__int__minus,axiom, % 172.48/172.41 ! [V_z,T_a] : % 172.48/172.41 ( class_Rings_Oring__1(T_a) % 172.48/172.41 => 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)) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_Ints__of__int,axiom, % 172.48/172.41 ! [V_z_2,T_a] : % 172.48/172.41 ( class_Rings_Oring__1(T_a) % 172.48/172.41 => 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))) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_of__int__power,axiom, % 172.48/172.41 ! [V_n,V_z,T_a] : % 172.48/172.41 ( class_Rings_Oring__1(T_a) % 172.48/172.41 => 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) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_of__int__setsum,axiom, % 172.48/172.41 ! [V_A_2,V_f_2,T_b,T_a] : % 172.48/172.41 ( class_Rings_Oring__1(T_a) % 172.48/172.41 => 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) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_of__int__setprod,axiom, % 172.48/172.41 ! [V_A_2,V_f_2,T_b,T_a] : % 172.48/172.41 ( ( class_Groups_Ocomm__monoid__mult(T_a) % 172.48/172.41 & class_Rings_Oring__1(T_a) ) % 172.48/172.41 => 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) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_of__int__le__0__iff,axiom, % 172.48/172.41 ! [V_z_2,T_a] : % 172.48/172.41 ( class_Rings_Olinordered__idom(T_a) % 172.48/172.41 => ( 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))) % 172.48/172.41 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_of__int__0__le__iff,axiom, % 172.48/172.41 ! [V_z_2,T_a] : % 172.48/172.41 ( class_Rings_Olinordered__idom(T_a) % 172.48/172.41 => ( 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))) % 172.48/172.41 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_of__int__less__0__iff,axiom, % 172.48/172.41 ! [V_z_2,T_a] : % 172.48/172.41 ( class_Rings_Olinordered__idom(T_a) % 172.48/172.41 => ( 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))) % 172.48/172.41 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_z_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_of__int__0__less__iff,axiom, % 172.48/172.41 ! [V_z_2,T_a] : % 172.48/172.41 ( class_Rings_Olinordered__idom(T_a) % 172.48/172.41 => ( 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))) % 172.48/172.41 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z_2)) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_of__nat__nat,axiom, % 172.48/172.41 ! [V_z,T_a] : % 172.48/172.41 ( class_Rings_Oring__1(T_a) % 172.48/172.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_z)) % 172.48/172.41 => 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) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_sgn__neg,axiom, % 172.48/172.41 ! [V_a,T_a] : % 172.48/172.41 ( class_Rings_Olinordered__idom(T_a) % 172.48/172.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 172.48/172.41 => c_Groups_Osgn__class_Osgn(T_a,V_a) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_sgn__1__neg,axiom, % 172.48/172.41 ! [V_a_2,T_a] : % 172.48/172.41 ( class_Rings_Olinordered__idom(T_a) % 172.48/172.41 => ( 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)) % 172.48/172.41 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_sgn__if,axiom, % 172.48/172.41 ! [V_x,T_a] : % 172.48/172.41 ( class_Groups_Osgn__if(T_a) % 172.48/172.41 => ( ( V_x = c_Groups_Ozero__class_Ozero(T_a) % 172.48/172.41 => c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Ozero__class_Ozero(T_a) ) % 172.48/172.41 & ( V_x != c_Groups_Ozero__class_Ozero(T_a) % 172.48/172.41 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 172.48/172.41 => c_Groups_Osgn__class_Osgn(T_a,V_x) = c_Groups_Oone__class_Oone(T_a) ) % 172.48/172.41 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 172.48/172.41 => c_Groups_Osgn__class_Osgn(T_a,V_x) = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_zsgn__def,axiom, % 172.48/172.41 ! [V_i] : % 172.48/172.41 ( ( V_i = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 172.48/172.41 => c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 172.48/172.41 & ( V_i != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 172.48/172.41 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i)) % 172.48/172.41 => c_Groups_Osgn__class_Osgn(tc_Int_Oint,V_i) = c_Groups_Oone__class_Oone(tc_Int_Oint) ) % 172.48/172.41 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_i)) % 172.48/172.41 => 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)) ) ) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_sgn__sgn,axiom, % 172.48/172.41 ! [V_a,T_a] : % 172.48/172.41 ( class_Rings_Olinordered__idom(T_a) % 172.48/172.41 => 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) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_sgn__0__0,axiom, % 172.48/172.41 ! [V_a_2,T_a] : % 172.48/172.41 ( class_Rings_Olinordered__idom(T_a) % 172.48/172.41 => ( c_Groups_Osgn__class_Osgn(T_a,V_a_2) = c_Groups_Ozero__class_Ozero(T_a) % 172.48/172.41 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_sgn0,axiom, % 172.48/172.41 ! [T_a] : % 172.48/172.41 ( class_Groups_Osgn__if(T_a) % 172.48/172.41 => c_Groups_Osgn__class_Osgn(T_a,c_Groups_Ozero__class_Ozero(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_sgn__times,axiom, % 172.48/172.41 ! [V_b,V_a,T_a] : % 172.48/172.41 ( class_Rings_Olinordered__idom(T_a) % 172.48/172.41 => 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)) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_sgn__greater,axiom, % 172.48/172.41 ! [V_a_2,T_a] : % 172.48/172.41 ( class_Rings_Olinordered__idom(T_a) % 172.48/172.41 => ( 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))) % 172.48/172.41 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_sgn__less,axiom, % 172.48/172.41 ! [V_a_2,T_a] : % 172.48/172.41 ( class_Rings_Olinordered__idom(T_a) % 172.48/172.41 => ( 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))) % 172.48/172.41 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_abs__sgn,axiom, % 172.48/172.41 ! [V_k,T_a] : % 172.48/172.41 ( class_Rings_Olinordered__idom(T_a) % 172.48/172.41 => 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)) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_mult__sgn__abs,axiom, % 172.48/172.41 ! [V_x,T_a] : % 172.48/172.41 ( class_Rings_Olinordered__idom(T_a) % 172.48/172.41 => 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 ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_sgn__pos,axiom, % 172.48/172.41 ! [V_a,T_a] : % 172.48/172.41 ( class_Rings_Olinordered__idom(T_a) % 172.48/172.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) % 172.48/172.41 => c_Groups_Osgn__class_Osgn(T_a,V_a) = c_Groups_Oone__class_Oone(T_a) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_sgn__1__pos,axiom, % 172.48/172.41 ! [V_a_2,T_a] : % 172.48/172.41 ( class_Rings_Olinordered__idom(T_a) % 172.48/172.41 => ( c_Groups_Osgn__class_Osgn(T_a,V_a_2) = c_Groups_Oone__class_Oone(T_a) % 172.48/172.41 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_card_Oneutral,axiom, % 172.48/172.41 ! [V_A_2,T_a] : % 172.48/172.41 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.41 => ( ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 172.48/172.41 => c_Groups_Oone__class_Oone(tc_Nat_Onat) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 172.48/172.41 => hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_mod__induct__0,axiom, % 172.48/172.41 ! [V_i_2,V_P_2,V_p_2] : % 172.48/172.41 ( ! [B_i] : % 172.48/172.41 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_p_2)) % 172.48/172.41 => ( hBOOL(hAPP(V_P_2,B_i)) % 172.48/172.41 => hBOOL(hAPP(V_P_2,c_Divides_Odiv__class_Omod(tc_Nat_Onat,hAPP(c_Nat_OSuc,B_i),V_p_2))) ) ) % 172.48/172.41 => ( hBOOL(hAPP(V_P_2,V_i_2)) % 172.48/172.41 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),V_p_2)) % 172.48/172.41 => hBOOL(hAPP(V_P_2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_fold__image__cong,axiom, % 172.48/172.41 ! [V_z_2,V_h_2,V_g_2,V_A_2,T_a,T_b] : % 172.48/172.41 ( class_Groups_Oab__semigroup__mult(T_b) % 172.48/172.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.41 => ( ! [B_x] : % 172.48/172.41 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 172.48/172.41 => hAPP(V_g_2,B_x) = hAPP(V_h_2,B_x) ) % 172.48/172.41 => 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) ) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_Max__eqI,axiom, % 172.48/172.41 ! [V_x_2,V_A_2,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.41 => ( ! [B_y] : % 172.48/172.41 ( hBOOL(hAPP(hAPP(c_member(T_a),B_y),V_A_2)) % 172.48/172.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_y),V_x_2)) ) % 172.48/172.41 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 172.48/172.41 => c_Big__Operators_Olinorder__class_OMax(T_a,V_A_2) = V_x_2 ) ) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_Min__eqI,axiom, % 172.48/172.41 ! [V_x_2,V_A_2,T_a] : % 172.48/172.41 ( class_Orderings_Olinorder(T_a) % 172.48/172.41 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.41 => ( ! [B_y] : % 172.48/172.41 ( hBOOL(hAPP(hAPP(c_member(T_a),B_y),V_A_2)) % 172.48/172.41 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),B_y)) ) % 172.48/172.41 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 172.48/172.41 => c_Big__Operators_Olinorder__class_OMin(T_a,V_A_2) = V_x_2 ) ) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_expand__Suc,axiom, % 172.48/172.41 ! [V_v] : % 172.48/172.41 ( 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))) % 172.48/172.41 => 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))) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_com_Osize_I11_J,axiom, % 172.48/172.41 ! [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))) ). % 172.48/172.41 % 172.48/172.41 fof(fact_com_Osize_I3_J,axiom, % 172.48/172.41 ! [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))) ). % 172.48/172.41 % 172.48/172.41 fof(fact_of__nat__number__of__eq,axiom, % 172.48/172.41 ! [V_v,T_a] : % 172.48/172.41 ( class_Int_Onumber__ring(T_a) % 172.48/172.41 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 172.48/172.41 => 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) ) % 172.48/172.41 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 172.48/172.41 => 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) ) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_of__nat__number__of__lemma,axiom, % 172.48/172.41 ! [V_v,T_a] : % 172.48/172.41 ( class_Int_Onumber__ring(T_a) % 172.48/172.41 => ( ( 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))) % 172.48/172.41 => 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) ) % 172.48/172.41 & ( ~ 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))) % 172.48/172.41 => 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) ) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_number__of__reorient,axiom, % 172.48/172.41 ! [V_x_2,V_w_2,T_a] : % 172.48/172.41 ( class_Int_Onumber(T_a) % 172.48/172.41 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) = V_x_2 % 172.48/172.41 <=> V_x_2 = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_eq__number__of,axiom, % 172.48/172.41 ! [V_y_2,V_x_2,T_a] : % 172.48/172.41 ( ( class_Int_Onumber__ring(T_a) % 172.48/172.41 & class_Int_Oring__char__0(T_a) ) % 172.48/172.41 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2) % 172.48/172.41 <=> V_x_2 = V_y_2 ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_com_Osimps_I2_J,axiom, % 172.48/172.41 ! [V_com_H_2,V_fun_H_2,V_loc_H_2,V_com_2,V_fun_2,V_loc_2] : % 172.48/172.41 ( 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) % 172.48/172.41 <=> ( V_loc_2 = V_loc_H_2 % 172.48/172.41 & V_fun_2 = V_fun_H_2 % 172.48/172.41 & V_com_2 = V_com_H_2 ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_number__of__eq,axiom, % 172.48/172.41 ! [V_k,T_a] : % 172.48/172.41 ( class_Int_Onumber__ring(T_a) % 172.48/172.41 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_k) = hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_k) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_of__int__number__of__eq,axiom, % 172.48/172.41 ! [V_v,T_a] : % 172.48/172.41 ( class_Int_Onumber__ring(T_a) % 172.48/172.41 => 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) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_com_Osimps_I41_J,axiom, % 172.48/172.41 ! [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) ). % 172.48/172.41 % 172.48/172.41 fof(fact_com_Osimps_I40_J,axiom, % 172.48/172.41 ! [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) ). % 172.48/172.41 % 172.48/172.41 fof(fact_com_Osimps_I39_J,axiom, % 172.48/172.41 ! [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) ). % 172.48/172.41 % 172.48/172.41 fof(fact_com_Osimps_I38_J,axiom, % 172.48/172.41 ! [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) ). % 172.48/172.41 % 172.48/172.41 fof(fact_com_Osimps_I37_J,axiom, % 172.48/172.41 ! [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) ). % 172.48/172.41 % 172.48/172.41 fof(fact_com_Osimps_I36_J,axiom, % 172.48/172.41 ! [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) ). % 172.48/172.41 % 172.48/172.41 fof(fact_com_Osimps_I35_J,axiom, % 172.48/172.41 ! [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) ). % 172.48/172.41 % 172.48/172.41 fof(fact_com_Osimps_I34_J,axiom, % 172.48/172.41 ! [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) ). % 172.48/172.41 % 172.48/172.41 fof(fact_com_Osimps_I10_J,axiom, % 172.48/172.41 ! [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) ). % 172.48/172.41 % 172.48/172.41 fof(fact_com_Osimps_I11_J,axiom, % 172.48/172.41 ! [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 ). % 172.48/172.41 % 172.48/172.41 fof(fact_le__number__of__eq__not__less,axiom, % 172.48/172.41 ! [V_w_2,V_v_2,T_a] : % 172.48/172.41 ( ( class_Int_Onumber(T_a) % 172.48/172.41 & class_Orderings_Olinorder(T_a) ) % 172.48/172.41 => ( 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))) % 172.48/172.41 <=> ~ 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))) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_right__distrib__number__of,axiom, % 172.48/172.41 ! [V_c,V_b,V_v,T_b] : % 172.48/172.41 ( ( class_Int_Onumber(T_b) % 172.48/172.41 & class_Rings_Osemiring(T_b) ) % 172.48/172.41 => 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)) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_left__distrib__number__of,axiom, % 172.48/172.41 ! [V_v,V_b,V_a,T_b] : % 172.48/172.41 ( ( class_Int_Onumber(T_b) % 172.48/172.41 & class_Rings_Osemiring(T_b) ) % 172.48/172.41 => 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))) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_right__diff__distrib__number__of,axiom, % 172.48/172.41 ! [V_c,V_b,V_v,T_b] : % 172.48/172.41 ( ( class_Int_Onumber(T_b) % 172.48/172.41 & class_Rings_Oring(T_b) ) % 172.48/172.41 => 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)) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_left__diff__distrib__number__of,axiom, % 172.48/172.41 ! [V_v,V_b,V_a,T_b] : % 172.48/172.41 ( ( class_Int_Onumber(T_b) % 172.48/172.41 & class_Rings_Oring(T_b) ) % 172.48/172.41 => 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))) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_le__number__of,axiom, % 172.48/172.41 ! [V_y_2,V_x_2,T_a] : % 172.48/172.41 ( ( class_Int_Onumber__ring(T_a) % 172.48/172.41 & class_Rings_Olinordered__idom(T_a) ) % 172.48/172.41 => ( 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))) % 172.48/172.41 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),V_y_2)) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_less__number__of,axiom, % 172.48/172.41 ! [V_y_2,V_x_2,T_a] : % 172.48/172.41 ( ( class_Int_Onumber__ring(T_a) % 172.48/172.41 & class_Rings_Olinordered__idom(T_a) ) % 172.48/172.41 => ( 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))) % 172.48/172.41 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),V_y_2)) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_min__number__of,axiom, % 172.48/172.41 ! [V_v,V_u,T_b] : % 172.48/172.41 ( ( class_Int_Onumber(T_b) % 172.48/172.41 & class_Orderings_Oord(T_b) ) % 172.48/172.41 => ( ( 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))) % 172.48/172.41 => 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) ) % 172.48/172.41 & ( ~ 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))) % 172.48/172.41 => 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) ) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_max__number__of,axiom, % 172.48/172.41 ! [V_v,V_u,T_b] : % 172.48/172.41 ( ( class_Int_Onumber(T_b) % 172.48/172.41 & class_Orderings_Oord(T_b) ) % 172.48/172.41 => ( ( 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))) % 172.48/172.41 => 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) ) % 172.48/172.41 & ( ~ 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))) % 172.48/172.41 => 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) ) ) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_number__of__add,axiom, % 172.48/172.41 ! [V_w,V_v,T_a] : % 172.48/172.41 ( class_Int_Onumber__ring(T_a) % 172.48/172.41 => 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)) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_add__number__of__eq,axiom, % 172.48/172.41 ! [V_w,V_v,T_a] : % 172.48/172.41 ( class_Int_Onumber__ring(T_a) % 172.48/172.41 => 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)) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_add__number__of__left,axiom, % 172.48/172.41 ! [V_z,V_w,V_v,T_a] : % 172.48/172.41 ( class_Int_Onumber__ring(T_a) % 172.48/172.41 => 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) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_number__of__mult,axiom, % 172.48/172.41 ! [V_w,V_v,T_a] : % 172.48/172.41 ( class_Int_Onumber__ring(T_a) % 172.48/172.41 => 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)) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_arith__simps_I32_J,axiom, % 172.48/172.41 ! [V_w,V_v,T_a] : % 172.48/172.41 ( class_Int_Onumber__ring(T_a) % 172.48/172.41 => 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)) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_mult__number__of__left,axiom, % 172.48/172.41 ! [V_z,V_w,V_v,T_a] : % 172.48/172.41 ( class_Int_Onumber__ring(T_a) % 172.48/172.41 => 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) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_number__of__diff,axiom, % 172.48/172.41 ! [V_w,V_v,T_a] : % 172.48/172.41 ( class_Int_Onumber__ring(T_a) % 172.48/172.41 => 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)) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_arith__simps_I30_J,axiom, % 172.48/172.41 ! [V_w,T_a] : % 172.48/172.41 ( class_Int_Onumber__ring(T_a) % 172.48/172.41 => 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)) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_number__of__minus,axiom, % 172.48/172.41 ! [V_w,T_a] : % 172.48/172.41 ( class_Int_Onumber__ring(T_a) % 172.48/172.41 => 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)) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_Ints__number__of,axiom, % 172.48/172.41 ! [V_w_2,T_a] : % 172.48/172.41 ( class_Int_Onumber__ring(T_a) % 172.48/172.41 => 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))) ) ). % 172.48/172.41 % 172.48/172.41 fof(fact_divide__eq__eq__number__of1,axiom, % 172.48/172.41 ! [V_a_2,V_w_2,V_b_2,T_a] : % 172.48/172.41 ( ( class_Fields_Ofield__inverse__zero(T_a) % 172.48/172.41 & class_Int_Onumber(T_a) ) % 172.48/172.41 => ( 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 % 172.48/172.41 <=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) != c_Groups_Ozero__class_Ozero(T_a) % 172.48/172.41 => 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)) ) % 172.48/172.41 & ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) = c_Groups_Ozero__class_Ozero(T_a) % 172.48/172.42 => V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_divide__eq__eq__number__of,axiom, % 172.48/172.42 ! [V_w_2,V_ca_2,V_b_2,T_a] : % 172.48/172.42 ( ( class_Fields_Ofield__inverse__zero(T_a) % 172.48/172.42 & class_Int_Onumber(T_a) ) % 172.48/172.42 => ( hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) % 172.48/172.42 <=> ( ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_a) % 172.48/172.42 => V_b_2 = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),V_ca_2) ) % 172.48/172.42 & ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_a) % 172.48/172.42 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_eq__divide__eq__number__of,axiom, % 172.48/172.42 ! [V_ca_2,V_b_2,V_w_2,T_a] : % 172.48/172.42 ( ( class_Fields_Ofield__inverse__zero(T_a) % 172.48/172.42 & class_Int_Onumber(T_a) ) % 172.48/172.42 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) = hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2) % 172.48/172.42 <=> ( ( V_ca_2 != c_Groups_Ozero__class_Ozero(T_a) % 172.48/172.42 => hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),V_ca_2) = V_b_2 ) % 172.48/172.42 & ( V_ca_2 = c_Groups_Ozero__class_Ozero(T_a) % 172.48/172.42 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_eq__divide__eq__number__of1,axiom, % 172.48/172.42 ! [V_w_2,V_b_2,V_a_2,T_a] : % 172.48/172.42 ( ( class_Fields_Ofield__inverse__zero(T_a) % 172.48/172.42 & class_Int_Onumber(T_a) ) % 172.48/172.42 => ( 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)) % 172.48/172.42 <=> ( ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) != c_Groups_Ozero__class_Ozero(T_a) % 172.48/172.42 => 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 ) % 172.48/172.42 & ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2) = c_Groups_Ozero__class_Ozero(T_a) % 172.48/172.42 => V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_add__number__of__diff1,axiom, % 172.48/172.42 ! [V_c,V_w,V_v,T_a] : % 172.48/172.42 ( class_Int_Onumber__ring(T_a) % 172.48/172.42 => 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) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_minus__number__of__mult,axiom, % 172.48/172.42 ! [V_z,V_w,T_a] : % 172.48/172.42 ( class_Int_Onumber__ring(T_a) % 172.48/172.42 => 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) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_diff__number__of__eq,axiom, % 172.48/172.42 ! [V_w,V_v,T_a] : % 172.48/172.42 ( class_Int_Onumber__ring(T_a) % 172.48/172.42 => 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))) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_divide__less__eq__number__of1,axiom, % 172.48/172.42 ! [V_a_2,V_w_2,V_b_2,T_a] : % 172.48/172.42 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 172.48/172.42 & class_Int_Onumber(T_a) ) % 172.48/172.42 => ( 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)) % 172.48/172.42 <=> ( ( 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))) % 172.48/172.42 => 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)))) ) % 172.48/172.42 & ( ~ 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))) % 172.48/172.42 => ( ( 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))) % 172.48/172.42 => 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)) ) % 172.48/172.42 & ( ~ 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))) % 172.48/172.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ) ) ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_divide__less__eq__number__of,axiom, % 172.48/172.42 ! [V_w_2,V_ca_2,V_b_2,T_a] : % 172.48/172.42 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 172.48/172.42 & class_Int_Onumber(T_a) ) % 172.48/172.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))) % 172.48/172.42 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 172.48/172.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),V_ca_2))) ) % 172.48/172.42 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 172.48/172.42 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 172.48/172.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),V_ca_2)),V_b_2)) ) % 172.48/172.42 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 172.48/172.42 => 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))) ) ) ) ) ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_less__divide__eq__number__of,axiom, % 172.48/172.42 ! [V_ca_2,V_b_2,V_w_2,T_a] : % 172.48/172.42 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 172.48/172.42 & class_Int_Onumber(T_a) ) % 172.48/172.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2))) % 172.48/172.42 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 172.48/172.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),V_ca_2)),V_b_2)) ) % 172.48/172.42 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 172.48/172.42 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 172.48/172.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),V_ca_2))) ) % 172.48/172.42 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 172.48/172.42 => 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))) ) ) ) ) ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_less__divide__eq__number__of1,axiom, % 172.48/172.42 ! [V_w_2,V_b_2,V_a_2,T_a] : % 172.48/172.42 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 172.48/172.42 & class_Int_Onumber(T_a) ) % 172.48/172.42 => ( 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)))) % 172.48/172.42 <=> ( ( 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))) % 172.48/172.42 => 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)) ) % 172.48/172.42 & ( ~ 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))) % 172.48/172.42 => ( ( 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))) % 172.48/172.42 => 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)))) ) % 172.48/172.42 & ( ~ 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))) % 172.48/172.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_abs__number__of,axiom, % 172.48/172.42 ! [V_x,T_a] : % 172.48/172.42 ( ( class_Int_Onumber__ring(T_a) % 172.48/172.42 & class_Rings_Olinordered__idom(T_a) ) % 172.48/172.42 => ( ( 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))) % 172.48/172.42 => 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)) ) % 172.48/172.42 & ( ~ 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))) % 172.48/172.42 => 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) ) ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_add__number__of__diff2,axiom, % 172.48/172.42 ! [V_w,V_c,V_v,T_a] : % 172.48/172.42 ( class_Int_Onumber__ring(T_a) % 172.48/172.42 => 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) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_divide__le__eq__number__of1,axiom, % 172.48/172.42 ! [V_a_2,V_w_2,V_b_2,T_a] : % 172.48/172.42 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 172.48/172.42 & class_Int_Onumber(T_a) ) % 172.48/172.42 => ( 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)) % 172.48/172.42 <=> ( ( 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))) % 172.48/172.42 => 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)))) ) % 172.48/172.42 & ( ~ 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))) % 172.48/172.42 => ( ( 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))) % 172.48/172.42 => 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)) ) % 172.48/172.42 & ( ~ 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))) % 172.48/172.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a_2)) ) ) ) ) ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_divide__le__eq__number__of,axiom, % 172.48/172.42 ! [V_w_2,V_ca_2,V_b_2,T_a] : % 172.48/172.42 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 172.48/172.42 & class_Int_Onumber(T_a) ) % 172.48/172.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2)),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2))) % 172.48/172.42 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 172.48/172.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),V_ca_2))) ) % 172.48/172.42 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 172.48/172.42 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 172.48/172.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),V_ca_2)),V_b_2)) ) % 172.48/172.42 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 172.48/172.42 => 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))) ) ) ) ) ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_le__divide__eq__number__of,axiom, % 172.48/172.42 ! [V_ca_2,V_b_2,V_w_2,T_a] : % 172.48/172.42 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 172.48/172.42 & class_Int_Onumber(T_a) ) % 172.48/172.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),hAPP(hAPP(c_Rings_Oinverse__class_Odivide(T_a),V_b_2),V_ca_2))) % 172.48/172.42 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 172.48/172.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),V_ca_2)),V_b_2)) ) % 172.48/172.42 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_ca_2)) % 172.48/172.42 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 172.48/172.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)),V_ca_2))) ) % 172.48/172.42 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_ca_2),c_Groups_Ozero__class_Ozero(T_a))) % 172.48/172.42 => 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))) ) ) ) ) ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_le__divide__eq__number__of1,axiom, % 172.48/172.42 ! [V_w_2,V_b_2,V_a_2,T_a] : % 172.48/172.42 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 172.48/172.42 & class_Int_Onumber(T_a) ) % 172.48/172.42 => ( 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)))) % 172.48/172.42 <=> ( ( 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))) % 172.48/172.42 => 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)) ) % 172.48/172.42 & ( ~ 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))) % 172.48/172.42 => ( ( 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))) % 172.48/172.42 => 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)))) ) % 172.48/172.42 & ( ~ 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))) % 172.48/172.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a_2),c_Groups_Ozero__class_Ozero(T_a))) ) ) ) ) ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_one__mod__nat__number__of,axiom, % 172.48/172.42 ! [V_v_H] : % 172.48/172.42 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 172.48/172.42 => 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)) ) % 172.48/172.42 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 172.48/172.42 => 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))) ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_one__div__nat__number__of,axiom, % 172.48/172.42 ! [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))) ). % 172.48/172.42 % 172.48/172.42 fof(fact_power__number__of__odd__number__of,axiom, % 172.48/172.42 ! [V_v_2,V_w_2,T_a] : % 172.48/172.42 ( class_Int_Onumber__ring(T_a) % 172.48/172.42 => ( ( 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))) % 172.48/172.42 => 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))) ) % 172.48/172.42 & ( ~ 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))) % 172.48/172.42 => 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) ) ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_power__nat__number__of,axiom, % 172.48/172.42 ! [V_n,V_v] : % 172.48/172.42 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 172.48/172.42 => 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) ) % 172.48/172.42 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 172.48/172.42 => 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)) ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_minus__numeral__code_I5_J,axiom, % 172.48/172.42 ! [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)) ). % 172.48/172.42 % 172.48/172.42 fof(fact_neg__number__of__Bit1,axiom, % 172.48/172.42 ! [V_w_2] : % 172.48/172.42 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(V_w_2)))) % 172.48/172.42 <=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_less__eq__number__of__int__code,axiom, % 172.48/172.42 ! [V_l_2,V_k_2] : % 172.48/172.42 ( 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))) % 172.48/172.42 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_less__number__of__int__code,axiom, % 172.48/172.42 ! [V_l_2,V_k_2] : % 172.48/172.42 ( 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))) % 172.48/172.42 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_number__of__is__id,axiom, % 172.48/172.42 ! [V_k] : hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_k) = V_k ). % 172.48/172.42 % 172.48/172.42 fof(fact_times__numeral__code_I5_J,axiom, % 172.48/172.42 ! [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)) ). % 172.48/172.42 % 172.48/172.42 fof(fact_plus__numeral__code_I9_J,axiom, % 172.48/172.42 ! [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)) ). % 172.48/172.42 % 172.48/172.42 fof(fact_rel__simps_I51_J,axiom, % 172.48/172.42 ! [V_l_2,V_k_2] : % 172.48/172.42 ( c_Int_OBit1(V_k_2) = c_Int_OBit1(V_l_2) % 172.48/172.42 <=> V_k_2 = V_l_2 ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_rel__simps_I17_J,axiom, % 172.48/172.42 ! [V_l_2,V_k_2] : % 172.48/172.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit1(V_l_2))) % 172.48/172.42 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_less__int__code_I16_J,axiom, % 172.48/172.42 ! [V_k2_2,V_k1_2] : % 172.48/172.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2))) % 172.48/172.42 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_rel__simps_I34_J,axiom, % 172.48/172.42 ! [V_l_2,V_k_2] : % 172.48/172.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit1(V_l_2))) % 172.48/172.42 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_less__eq__int__code_I16_J,axiom, % 172.48/172.42 ! [V_k2_2,V_k1_2] : % 172.48/172.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2))) % 172.48/172.42 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_int__number__of__def,axiom, % 172.48/172.42 ! [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) ). % 172.48/172.42 % 172.48/172.42 fof(fact_bin__less__0__simps_I4_J,axiom, % 172.48/172.42 ! [V_w_2] : % 172.48/172.42 ( 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))) % 172.48/172.42 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_Bit1__def,axiom, % 172.48/172.42 ! [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) ). % 172.48/172.42 % 172.48/172.42 fof(fact_nat__number__of__def,axiom, % 172.48/172.42 ! [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)) ). % 172.48/172.42 % 172.48/172.42 fof(fact_nat__number__of,axiom, % 172.48/172.42 ! [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) ). % 172.48/172.42 % 172.48/172.42 fof(fact_nat__number__of__Bit1,axiom, % 172.48/172.42 ! [V_w_2] : % 172.48/172.42 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) % 172.48/172.42 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(V_w_2)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 172.48/172.42 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) % 172.48/172.42 => 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)))) ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_number__of__Bit1,axiom, % 172.48/172.42 ! [V_w,T_a] : % 172.48/172.42 ( class_Int_Onumber__ring(T_a) % 172.48/172.42 => 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)) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_power__number__of__odd,axiom, % 172.48/172.42 ! [V_z_2,V_w_2,T_a] : % 172.48/172.42 ( class_Int_Onumber__ring(T_a) % 172.48/172.42 => ( ( 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))) % 172.48/172.42 => 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))) ) % 172.48/172.42 & ( ~ 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))) % 172.48/172.42 => 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) ) ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_zpower__number__of__odd,axiom, % 172.48/172.42 ! [V_z_2,V_w_2] : % 172.48/172.42 ( ( 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))) % 172.48/172.42 => 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))) ) % 172.48/172.42 & ( ~ 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))) % 172.48/172.42 => 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) ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_minus__numeral__code_I6_J,axiom, % 172.48/172.42 ! [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))) ). % 172.48/172.42 % 172.48/172.42 fof(fact_neg__imp__number__of__eq__0,axiom, % 172.48/172.42 ! [V_v] : % 172.48/172.42 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 172.48/172.42 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_int__eq__iff__number__of,axiom, % 172.48/172.42 ! [V_v_2,V_m_2] : % 172.48/172.42 ( 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) % 172.48/172.42 <=> ( V_m_2 = hAPP(c_Int_Onat,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2)) % 172.48/172.42 & 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))) ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_eq__nat__number__of,axiom, % 172.48/172.42 ! [V_v_H_2,V_v_2] : % 172.48/172.42 ( 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) % 172.48/172.42 <=> ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2))) % 172.48/172.42 => 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))) ) % 172.48/172.42 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2))) % 172.48/172.42 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2))) % 172.48/172.42 => hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 172.48/172.42 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H_2))) % 172.48/172.42 => V_v_2 = V_v_H_2 ) ) ) ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_nat__number__of__add__left,axiom, % 172.48/172.42 ! [V_k,V_v_H,V_v] : % 172.48/172.42 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 172.48/172.42 => 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) ) % 172.48/172.42 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 172.48/172.42 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 172.48/172.42 => 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) ) % 172.48/172.42 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 172.48/172.42 => 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) ) ) ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_int__nat__number__of,axiom, % 172.48/172.42 ! [V_v] : % 172.48/172.42 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 172.48/172.42 => 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) ) % 172.48/172.42 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 172.48/172.42 => 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) ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_mod__nat__number__of,axiom, % 172.48/172.42 ! [V_v_H,V_v] : % 172.48/172.42 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 172.48/172.42 => 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) ) % 172.48/172.42 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 172.48/172.42 => ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 172.48/172.42 => 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) ) % 172.48/172.42 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v_H))) % 172.48/172.42 => 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))) ) ) ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_div__nat__number__of,axiom, % 172.48/172.42 ! [V_v_H,V_v] : % 172.48/172.42 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 172.48/172.42 => 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) ) % 172.48/172.42 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 172.48/172.42 => 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))) ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_power__nat__number__of__number__of,axiom, % 172.48/172.42 ! [V_w,V_v] : % 172.48/172.42 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 172.48/172.42 => 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)) ) % 172.48/172.42 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 172.48/172.42 => 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))) ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_Suc__nat__number__of__add,axiom, % 172.48/172.42 ! [V_n,V_v] : % 172.48/172.42 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 172.48/172.42 => 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) ) % 172.48/172.42 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 172.48/172.42 => 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) ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_diff__nat__number__of,axiom, % 172.48/172.42 ! [V_v_2,V_v_H_2] : % 172.48/172.42 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H_2),c_Int_OPls)) % 172.48/172.42 => 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) ) % 172.48/172.42 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H_2),c_Int_OPls)) % 172.48/172.42 => 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)) ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_min__Suc__number__of,axiom, % 172.48/172.42 ! [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)))) ). % 172.48/172.42 % 172.48/172.42 fof(fact_min__number__of__Suc,axiom, % 172.48/172.42 ! [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)))) ). % 172.48/172.42 % 172.48/172.42 fof(fact_rel__simps_I46_J,axiom, % 172.48/172.42 ! [V_k] : c_Int_OBit1(V_k) != c_Int_OPls ). % 172.48/172.42 % 172.48/172.42 fof(fact_rel__simps_I39_J,axiom, % 172.48/172.42 ! [V_l] : c_Int_OPls != c_Int_OBit1(V_l) ). % 172.48/172.42 % 172.48/172.42 fof(fact_succ__Pls,axiom, % 172.48/172.42 c_Int_Osucc(c_Int_OPls) = c_Int_OBit1(c_Int_OPls) ). % 172.48/172.42 % 172.48/172.42 fof(fact_minus__Pls,axiom, % 172.48/172.42 hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OPls) = c_Int_OPls ). % 172.48/172.42 % 172.48/172.42 fof(fact_add__Pls__right,axiom, % 172.48/172.42 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_OPls) = V_k ). % 172.48/172.42 % 172.48/172.42 fof(fact_add__Pls,axiom, % 172.48/172.42 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OPls),V_k) = V_k ). % 172.48/172.42 % 172.48/172.42 fof(fact_mult__Pls,axiom, % 172.48/172.42 ! [V_w] : hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),c_Int_OPls),V_w) = c_Int_OPls ). % 172.48/172.42 % 172.48/172.42 fof(fact_succ__pred,axiom, % 172.48/172.42 ! [V_x] : c_Int_Osucc(c_Int_Opred(V_x)) = V_x ). % 172.48/172.42 % 172.48/172.42 fof(fact_rel__simps_I2_J,axiom, % 172.48/172.42 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ). % 172.48/172.42 % 172.48/172.42 fof(fact_rel__simps_I19_J,axiom, % 172.48/172.42 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ). % 172.48/172.42 % 172.48/172.42 fof(fact_Pls__def,axiom, % 172.48/172.42 c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ). % 172.48/172.42 % 172.48/172.42 fof(fact_diff__bin__simps_I1_J,axiom, % 172.48/172.42 ! [V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Int_OPls) = V_k ). % 172.48/172.42 % 172.48/172.42 fof(fact_semiring__norm_I112_J,axiom, % 172.48/172.42 ! [T_a] : % 172.48/172.42 ( class_Int_Onumber__ring(T_a) % 172.48/172.42 => c_Groups_Ozero__class_Ozero(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_number__of__Pls,axiom, % 172.48/172.42 ! [T_a] : % 172.48/172.42 ( class_Int_Onumber__ring(T_a) % 172.48/172.42 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_add__numeral__0,axiom, % 172.48/172.42 ! [V_a,T_a] : % 172.48/172.42 ( class_Int_Onumber__ring(T_a) % 172.48/172.42 => 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 ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_add__numeral__0__right,axiom, % 172.48/172.42 ! [V_a,T_a] : % 172.48/172.42 ( class_Int_Onumber__ring(T_a) % 172.48/172.42 => 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 ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_bin__less__0__simps_I1_J,axiom, % 172.48/172.42 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ). % 172.48/172.42 % 172.48/172.42 fof(fact_nat__number__of__Pls,axiom, % 172.48/172.42 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 172.48/172.42 % 172.48/172.42 fof(fact_semiring__norm_I113_J,axiom, % 172.48/172.42 c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OPls) ). % 172.48/172.42 % 172.48/172.42 fof(fact_zero__is__num__zero,axiom, % 172.48/172.42 c_Groups_Ozero__class_Ozero(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls) ). % 172.48/172.42 % 172.48/172.42 fof(fact_rel__simps_I22_J,axiom, % 172.48/172.42 ! [V_k_2] : % 172.48/172.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k_2))) % 172.48/172.42 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_rel__simps_I12_J,axiom, % 172.48/172.42 ! [V_k_2] : % 172.48/172.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OPls)) % 172.48/172.42 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_Suc__diff__number__of,axiom, % 172.48/172.42 ! [V_m,V_v] : % 172.48/172.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v)) % 172.48/172.42 => 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))) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_not__neg__number__of__Pls,axiom, % 172.48/172.42 ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OPls))) ). % 172.48/172.42 % 172.48/172.42 fof(fact_nat__number__of__add__1,axiom, % 172.48/172.42 ! [V_v] : % 172.48/172.42 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 172.48/172.42 => 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) ) % 172.48/172.42 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 172.48/172.42 => 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)) ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_nat__1__add__number__of,axiom, % 172.48/172.42 ! [V_v] : % 172.48/172.42 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 172.48/172.42 => 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) ) % 172.48/172.42 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 172.48/172.42 => 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)) ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_le__iff__pred__less,axiom, % 172.48/172.42 ! [V_l_2,V_k_2] : % 172.48/172.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) % 172.48/172.42 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_Opred(V_k_2)),V_l_2)) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_minus__Bit1,axiom, % 172.48/172.42 ! [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))) ). % 172.48/172.42 % 172.48/172.42 fof(fact_pred__def,axiom, % 172.48/172.42 ! [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)) ). % 172.48/172.42 % 172.48/172.42 fof(fact_nat__number__of__diff__1,axiom, % 172.48/172.42 ! [V_v] : % 172.48/172.42 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v),c_Int_OPls)) % 172.48/172.42 => 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) ) % 172.48/172.42 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v),c_Int_OPls)) % 172.48/172.42 => 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)) ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_mult__numeral__1__right,axiom, % 172.48/172.42 ! [V_a,T_a] : % 172.48/172.42 ( class_Int_Onumber__ring(T_a) % 172.48/172.42 => 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 ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_mult__numeral__1,axiom, % 172.48/172.42 ! [V_a,T_a] : % 172.48/172.42 ( class_Int_Onumber__ring(T_a) % 172.48/172.42 => 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 ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_divide__Numeral0,axiom, % 172.48/172.42 ! [V_x,T_a] : % 172.48/172.42 ( ( class_Fields_Ofield__inverse__zero(T_a) % 172.48/172.42 & class_Int_Onumber__ring(T_a) ) % 172.48/172.42 => 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) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_numeral__1__eq__1,axiom, % 172.48/172.42 ! [T_a] : % 172.48/172.42 ( class_Int_Onumber__ring(T_a) % 172.48/172.42 => hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(T_a) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_semiring__norm_I110_J,axiom, % 172.48/172.42 ! [T_a] : % 172.48/172.42 ( class_Int_Onumber__ring(T_a) % 172.48/172.42 => c_Groups_Oone__class_Oone(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls)) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_eq__0__number__of,axiom, % 172.48/172.42 ! [V_v_2] : % 172.48/172.42 ( c_Groups_Ozero__class_Ozero(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) % 172.48/172.42 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_eq__number__of__0,axiom, % 172.48/172.42 ! [V_v_2] : % 172.48/172.42 ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 172.48/172.42 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_number__of2,axiom, % 172.48/172.42 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))) ). % 172.48/172.42 % 172.48/172.42 fof(fact_rel__simps_I5_J,axiom, % 172.48/172.42 ! [V_k_2] : % 172.48/172.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k_2))) % 172.48/172.42 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_rel__simps_I29_J,axiom, % 172.48/172.42 ! [V_k_2] : % 172.48/172.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OPls)) % 172.48/172.42 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_less__nat__number__of,axiom, % 172.48/172.42 ! [V_v_H_2,V_v_2] : % 172.48/172.42 ( 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))) % 172.48/172.42 <=> ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_2),V_v_H_2)) % 172.48/172.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v_H_2)) ) % 172.48/172.42 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_2),V_v_H_2)) ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_divide__numeral__1,axiom, % 172.48/172.42 ! [V_a,T_a] : % 172.48/172.42 ( ( class_Fields_Ofield(T_a) % 172.48/172.42 & class_Int_Onumber__ring(T_a) ) % 172.48/172.42 => 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 ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_divide__Numeral1,axiom, % 172.48/172.42 ! [V_x,T_a] : % 172.48/172.42 ( ( class_Fields_Ofield(T_a) % 172.48/172.42 & class_Int_Onumber__ring(T_a) ) % 172.48/172.42 => 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 ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_le__nat__number__of,axiom, % 172.48/172.42 ! [V_v_H_2,V_v_2] : % 172.48/172.42 ( 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))) % 172.48/172.42 <=> ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),V_v_H_2)) % 172.48/172.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_v_2),c_Int_OPls)) ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_one__is__num__one,axiom, % 172.48/172.42 c_Groups_Oone__class_Oone(tc_Int_Oint) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)) ). % 172.48/172.42 % 172.48/172.42 fof(fact_Numeral1__eq1__nat,axiom, % 172.48/172.42 c_Groups_Oone__class_Oone(tc_Nat_Onat) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) ). % 172.48/172.42 % 172.48/172.42 fof(fact_nat__numeral__1__eq__1,axiom, % 172.48/172.42 hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),c_Int_OBit1(c_Int_OPls)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ). % 172.48/172.42 % 172.48/172.42 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I8_J,axiom, % 172.48/172.42 c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit1(c_Int_OBit1(c_Int_OPls)))) ). % 172.48/172.42 % 172.48/172.42 fof(fact_succ__def,axiom, % 172.48/172.42 ! [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)) ). % 172.48/172.42 % 172.48/172.42 fof(fact_le__special_I3_J,axiom, % 172.48/172.42 ! [V_x_2,T_a] : % 172.48/172.42 ( ( class_Int_Onumber__ring(T_a) % 172.48/172.42 & class_Rings_Olinordered__idom(T_a) ) % 172.48/172.42 => ( 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))) % 172.48/172.42 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OPls)) ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_le__special_I1_J,axiom, % 172.48/172.42 ! [V_y_2,T_a] : % 172.48/172.42 ( ( class_Int_Onumber__ring(T_a) % 172.48/172.42 & class_Rings_Olinordered__idom(T_a) ) % 172.48/172.42 => ( 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))) % 172.48/172.42 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_y_2)) ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_less__special_I3_J,axiom, % 172.48/172.42 ! [V_x_2,T_a] : % 172.48/172.42 ( ( class_Int_Onumber__ring(T_a) % 172.48/172.42 & class_Rings_Olinordered__idom(T_a) ) % 172.48/172.42 => ( 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))) % 172.48/172.42 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OPls)) ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_less__special_I1_J,axiom, % 172.48/172.42 ! [V_y_2,T_a] : % 172.48/172.42 ( ( class_Int_Onumber__ring(T_a) % 172.48/172.42 & class_Rings_Olinordered__idom(T_a) ) % 172.48/172.42 => ( 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))) % 172.48/172.42 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_y_2)) ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_less__0__number__of,axiom, % 172.48/172.42 ! [V_v_2] : % 172.48/172.42 ( 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))) % 172.48/172.42 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_v_2)) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_numeral__1__eq__Suc__0,axiom, % 172.48/172.42 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)) ). % 172.48/172.42 % 172.48/172.42 fof(fact_numeral__3__eq__3,axiom, % 172.48/172.42 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)))) ). % 172.48/172.42 % 172.48/172.42 fof(fact_power3__eq__cube,axiom, % 172.48/172.42 ! [V_a,T_a] : % 172.48/172.42 ( class_Groups_Omonoid__mult(T_a) % 172.48/172.42 => 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) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I8_J,axiom, % 172.48/172.42 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))))) ). % 172.48/172.42 % 172.48/172.42 fof(fact_Suc3__eq__add__3,axiom, % 172.48/172.42 ! [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) ). % 172.48/172.42 % 172.48/172.42 fof(fact_add__nat__number__of,axiom, % 172.48/172.42 ! [V_v_H,V_v] : % 172.48/172.42 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 172.48/172.42 => 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) ) % 172.48/172.42 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 172.48/172.42 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H),c_Int_OPls)) % 172.48/172.42 => 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) ) % 172.48/172.42 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v_H),c_Int_OPls)) % 172.48/172.42 => 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)) ) ) ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_transfer__int__nat__numerals_I4_J,axiom, % 172.48/172.42 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)))) ). % 172.48/172.42 % 172.48/172.42 fof(fact_transfer__nat__int__numerals_I4_J,axiom, % 172.48/172.42 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)))) ). % 172.48/172.42 % 172.48/172.42 fof(fact_number__of__succ,axiom, % 172.48/172.42 ! [V_k,T_a] : % 172.48/172.42 ( class_Int_Onumber__ring(T_a) % 172.48/172.42 => 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)) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_number__of__pred,axiom, % 172.48/172.42 ! [V_w,T_a] : % 172.48/172.42 ( class_Int_Onumber__ring(T_a) % 172.48/172.42 => 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)) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_le__special_I2_J,axiom, % 172.48/172.42 ! [V_y_2,T_a] : % 172.48/172.42 ( ( class_Int_Onumber__ring(T_a) % 172.48/172.42 & class_Rings_Olinordered__idom(T_a) ) % 172.48/172.42 => ( 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))) % 172.48/172.42 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2)) ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_le__special_I4_J,axiom, % 172.48/172.42 ! [V_x_2,T_a] : % 172.48/172.42 ( ( class_Int_Onumber__ring(T_a) % 172.48/172.42 & class_Rings_Olinordered__idom(T_a) ) % 172.48/172.42 => ( 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))) % 172.48/172.42 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls))) ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_less__special_I2_J,axiom, % 172.48/172.42 ! [V_y_2,T_a] : % 172.48/172.42 ( ( class_Int_Onumber__ring(T_a) % 172.48/172.42 & class_Rings_Olinordered__idom(T_a) ) % 172.48/172.42 => ( 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))) % 172.48/172.42 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(c_Int_OPls)),V_y_2)) ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_less__special_I4_J,axiom, % 172.48/172.42 ! [V_x_2,T_a] : % 172.48/172.42 ( ( class_Int_Onumber__ring(T_a) % 172.48/172.42 & class_Rings_Olinordered__idom(T_a) ) % 172.48/172.42 => ( 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))) % 172.48/172.42 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_x_2),c_Int_OBit1(c_Int_OPls))) ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_add__special_I2_J,axiom, % 172.48/172.42 ! [V_w,T_a] : % 172.48/172.42 ( class_Int_Onumber__ring(T_a) % 172.48/172.42 => 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)) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_add__special_I3_J,axiom, % 172.48/172.42 ! [V_v,T_a] : % 172.48/172.42 ( class_Int_Onumber__ring(T_a) % 172.48/172.42 => 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))) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_Suc__diff__eq__diff__pred,axiom, % 172.48/172.42 ! [V_m,V_n] : % 172.48/172.42 ( 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)) % 172.48/172.42 => 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)))) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_mult__nat__number__of,axiom, % 172.48/172.42 ! [V_v_H,V_v] : % 172.48/172.42 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 172.48/172.42 => 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) ) % 172.48/172.42 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 172.48/172.42 => 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)) ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_nat__number__of__mult__left,axiom, % 172.48/172.42 ! [V_k,V_v_H,V_v] : % 172.48/172.42 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 172.48/172.42 => 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) ) % 172.48/172.42 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_v),c_Int_OPls)) % 172.48/172.42 => 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) ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_neg__number__of__pred__iff__0,axiom, % 172.48/172.42 ! [V_v_2] : % 172.48/172.42 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_Opred(V_v_2)))) % 172.48/172.42 <=> hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_Suc__mod__eq__add3__mod__number__of,axiom, % 172.48/172.42 ! [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)) ). % 172.48/172.42 % 172.48/172.42 fof(fact_Suc__mod__eq__add3__mod,axiom, % 172.48/172.42 ! [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) ). % 172.48/172.42 % 172.48/172.42 fof(fact_mod__Suc__eq__mod__add3,axiom, % 172.48/172.42 ! [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)) ). % 172.48/172.42 % 172.48/172.42 fof(fact_Suc__div__eq__add3__div__number__of,axiom, % 172.48/172.42 ! [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)) ). % 172.48/172.42 % 172.48/172.42 fof(fact_Suc__div__eq__add3__div,axiom, % 172.48/172.42 ! [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) ). % 172.48/172.42 % 172.48/172.42 fof(fact_div__Suc__eq__div__add3,axiom, % 172.48/172.42 ! [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)) ). % 172.48/172.42 % 172.48/172.42 fof(fact_diff__special_I2_J,axiom, % 172.48/172.42 ! [V_v,T_a] : % 172.48/172.42 ( class_Int_Onumber__ring(T_a) % 172.48/172.42 => 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)))) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_diff__special_I1_J,axiom, % 172.48/172.42 ! [V_w,T_a] : % 172.48/172.42 ( class_Int_Onumber__ring(T_a) % 172.48/172.42 => 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))) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_Suc__eq__number__of,axiom, % 172.48/172.42 ! [V_v_2,V_n_2] : % 172.48/172.42 ( hAPP(c_Nat_OSuc,V_n_2) = hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) % 172.48/172.42 <=> 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))))) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_eq__number__of__Suc,axiom, % 172.48/172.42 ! [V_n_2,V_v_2] : % 172.48/172.42 ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v_2) = hAPP(c_Nat_OSuc,V_n_2) % 172.48/172.42 <=> 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))))) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_nat__case__number__of,axiom, % 172.48/172.42 ! [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))) ). % 172.48/172.42 % 172.48/172.42 fof(fact_less__number__of__Suc,axiom, % 172.48/172.42 ! [V_n_2,V_v_2] : % 172.48/172.42 ( 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))) % 172.48/172.42 <=> 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)))) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_less__Suc__number__of,axiom, % 172.48/172.42 ! [V_v_2,V_n_2] : % 172.48/172.42 ( 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))) % 172.48/172.42 <=> 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))))) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_le__Suc__number__of,axiom, % 172.48/172.42 ! [V_v_2,V_n_2] : % 172.48/172.42 ( 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))) % 172.48/172.42 <=> 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))))) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_le__number__of__Suc,axiom, % 172.48/172.42 ! [V_n_2,V_v_2] : % 172.48/172.42 ( 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))) % 172.48/172.42 <=> 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)))) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_Suc__nat__number__of,axiom, % 172.48/172.42 ! [V_v] : % 172.48/172.42 ( ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 172.48/172.42 => hAPP(c_Nat_OSuc,hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v)) = c_Groups_Oone__class_Oone(tc_Nat_Onat) ) % 172.48/172.42 & ( ~ hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_v))) % 172.48/172.42 => 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)) ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_max__Suc__number__of,axiom, % 172.48/172.42 ! [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)))) ). % 172.48/172.42 % 172.48/172.42 fof(fact_max__number__of__Suc,axiom, % 172.48/172.42 ! [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)))) ). % 172.48/172.42 % 172.48/172.42 fof(fact_nat__case__add__eq__if,axiom, % 172.48/172.42 ! [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)))) ). % 172.48/172.42 % 172.48/172.42 fof(fact_nat__rec__add__eq__if,axiom, % 172.48/172.42 ! [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))))) ). % 172.48/172.42 % 172.48/172.42 fof(fact_eq__special_I2_J,axiom, % 172.48/172.42 ! [V_y_2,T_a] : % 172.48/172.42 ( class_Int_Onumber__ring(T_a) % 172.48/172.42 => ( c_Groups_Oone__class_Oone(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2) % 172.48/172.42 <=> 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)))) ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_eq__special_I4_J,axiom, % 172.48/172.42 ! [V_x_2,T_a] : % 172.48/172.42 ( class_Int_Onumber__ring(T_a) % 172.48/172.42 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2) = c_Groups_Oone__class_Oone(T_a) % 172.48/172.42 <=> 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))))) ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_nat__rec__number__of,axiom, % 172.48/172.42 ! [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)))) ). % 172.48/172.42 % 172.48/172.42 fof(fact_iszero__0,axiom, % 172.48/172.42 ! [T_a] : % 172.48/172.42 ( class_Rings_Osemiring__1(T_a) % 172.48/172.42 => c_Int_Oiszero(T_a,c_Groups_Ozero__class_Ozero(T_a)) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_iszero__def,axiom, % 172.48/172.42 ! [V_z_2,T_a] : % 172.48/172.42 ( class_Rings_Osemiring__1(T_a) % 172.48/172.42 => ( c_Int_Oiszero(T_a,V_z_2) % 172.48/172.42 <=> V_z_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_not__iszero__1,axiom, % 172.48/172.42 ! [T_a] : % 172.48/172.42 ( class_Rings_Osemiring__1(T_a) % 172.48/172.42 => ~ c_Int_Oiszero(T_a,c_Groups_Oone__class_Oone(T_a)) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_nat__rec__0,axiom, % 172.48/172.42 ! [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 ). % 172.48/172.42 % 172.48/172.42 fof(fact_nat__rec__Suc,axiom, % 172.48/172.42 ! [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)) ). % 172.48/172.42 % 172.48/172.42 fof(fact_iszero__Numeral0,axiom, % 172.48/172.42 ! [T_a] : % 172.48/172.42 ( class_Int_Onumber__ring(T_a) % 172.48/172.42 => c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OPls)) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_iszero__number__of__Bit1,axiom, % 172.48/172.42 ! [V_w,T_a] : % 172.48/172.42 ( ( class_Int_Onumber__ring(T_a) % 172.48/172.42 & class_Int_Oring__char__0(T_a) ) % 172.48/172.42 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(V_w))) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_not__iszero__Numeral1,axiom, % 172.48/172.42 ! [T_a] : % 172.48/172.42 ( class_Int_Onumber__ring(T_a) % 172.48/172.42 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit1(c_Int_OPls))) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_eq__number__of__eq,axiom, % 172.48/172.42 ! [V_y_2,V_x_2,T_a] : % 172.48/172.42 ( class_Int_Onumber__ring(T_a) % 172.48/172.42 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2) % 172.48/172.42 <=> 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)))) ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_eq__special_I1_J,axiom, % 172.48/172.42 ! [V_y_2,T_a] : % 172.48/172.42 ( class_Int_Onumber__ring(T_a) % 172.48/172.42 => ( c_Groups_Ozero__class_Ozero(T_a) = hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_y_2) % 172.48/172.42 <=> 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)))) ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_eq__special_I3_J,axiom, % 172.48/172.42 ! [V_x_2,T_a] : % 172.48/172.42 ( class_Int_Onumber__ring(T_a) % 172.48/172.42 => ( hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_x_2) = c_Groups_Ozero__class_Ozero(T_a) % 172.48/172.42 <=> 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)))) ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_zmod__number__of__Bit1,axiom, % 172.48/172.42 ! [V_v,V_w] : % 172.48/172.42 ( ( 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))) % 172.48/172.42 => 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)) ) % 172.48/172.42 & ( ~ 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))) % 172.48/172.42 => 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)) ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_neg__zmod__mult__2,axiom, % 172.48/172.42 ! [V_b,V_a] : % 172.48/172.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 172.48/172.42 => 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)) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_arith__series__int,axiom, % 172.48/172.42 ! [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)))) ). % 172.48/172.42 % 172.48/172.42 fof(fact_neg__zdiv__mult__2,axiom, % 172.48/172.42 ! [V_b,V_a] : % 172.48/172.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 172.48/172.42 => 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) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_rel__simps_I50_J,axiom, % 172.48/172.42 ! [V_l,V_k] : c_Int_OBit1(V_k) != c_Int_OBit0(V_l) ). % 172.48/172.42 % 172.48/172.42 fof(fact_rel__simps_I49_J,axiom, % 172.48/172.42 ! [V_l,V_k] : c_Int_OBit0(V_k) != c_Int_OBit1(V_l) ). % 172.48/172.42 % 172.48/172.42 fof(fact_minus__Bit0,axiom, % 172.48/172.42 ! [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)) ). % 172.48/172.42 % 172.48/172.42 fof(fact_mult__Bit0,axiom, % 172.48/172.42 ! [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)) ). % 172.48/172.42 % 172.48/172.42 fof(fact_less__eq__int__code_I13_J,axiom, % 172.48/172.42 ! [V_k2_2,V_k1_2] : % 172.48/172.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2))) % 172.48/172.42 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_rel__simps_I31_J,axiom, % 172.48/172.42 ! [V_l_2,V_k_2] : % 172.48/172.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit0(V_l_2))) % 172.48/172.42 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_less__int__code_I13_J,axiom, % 172.48/172.42 ! [V_k2_2,V_k1_2] : % 172.48/172.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2))) % 172.48/172.42 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_rel__simps_I14_J,axiom, % 172.48/172.42 ! [V_l_2,V_k_2] : % 172.48/172.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit0(V_l_2))) % 172.48/172.42 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_add__Bit0__Bit0,axiom, % 172.48/172.42 ! [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)) ). % 172.48/172.42 % 172.48/172.42 fof(fact_Bit0__def,axiom, % 172.48/172.42 ! [V_k] : c_Int_OBit0(V_k) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),V_k) ). % 172.48/172.42 % 172.48/172.42 fof(fact_rel__simps_I48_J,axiom, % 172.48/172.42 ! [V_l_2,V_k_2] : % 172.48/172.42 ( c_Int_OBit0(V_k_2) = c_Int_OBit0(V_l_2) % 172.48/172.42 <=> V_k_2 = V_l_2 ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_diff__bin__simps_I7_J,axiom, % 172.48/172.42 ! [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)) ). % 172.48/172.42 % 172.48/172.42 fof(fact_rel__simps_I44_J,axiom, % 172.48/172.42 ! [V_k_2] : % 172.48/172.42 ( c_Int_OBit0(V_k_2) = c_Int_OPls % 172.48/172.42 <=> V_k_2 = c_Int_OPls ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_rel__simps_I38_J,axiom, % 172.48/172.42 ! [V_l_2] : % 172.48/172.42 ( c_Int_OPls = c_Int_OBit0(V_l_2) % 172.48/172.42 <=> c_Int_OPls = V_l_2 ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_Bit0__Pls,axiom, % 172.48/172.42 c_Int_OBit0(c_Int_OPls) = c_Int_OPls ). % 172.48/172.42 % 172.48/172.42 fof(fact_bin__less__0__simps_I3_J,axiom, % 172.48/172.42 ! [V_w_2] : % 172.48/172.42 ( 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))) % 172.48/172.42 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_w_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_rel__simps_I27_J,axiom, % 172.48/172.42 ! [V_k_2] : % 172.48/172.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OPls)) % 172.48/172.42 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_rel__simps_I21_J,axiom, % 172.48/172.42 ! [V_k_2] : % 172.48/172.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k_2))) % 172.48/172.42 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_less__eq__int__code_I14_J,axiom, % 172.48/172.42 ! [V_k2_2,V_k1_2] : % 172.48/172.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit1(V_k2_2))) % 172.48/172.42 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_rel__simps_I32_J,axiom, % 172.48/172.42 ! [V_l_2,V_k_2] : % 172.48/172.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit1(V_l_2))) % 172.48/172.42 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_rel__simps_I4_J,axiom, % 172.48/172.42 ! [V_k_2] : % 172.48/172.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k_2))) % 172.48/172.42 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),V_k_2)) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_rel__simps_I10_J,axiom, % 172.48/172.42 ! [V_k_2] : % 172.48/172.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OPls)) % 172.48/172.42 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OPls)) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_rel__simps_I16_J,axiom, % 172.48/172.42 ! [V_l_2,V_k_2] : % 172.48/172.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit0(V_l_2))) % 172.48/172.42 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_less__int__code_I15_J,axiom, % 172.48/172.42 ! [V_k2_2,V_k1_2] : % 172.48/172.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit0(V_k2_2))) % 172.48/172.42 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_add__Bit1__Bit0,axiom, % 172.48/172.42 ! [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)) ). % 172.48/172.42 % 172.48/172.42 fof(fact_add__Bit0__Bit1,axiom, % 172.48/172.42 ! [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)) ). % 172.48/172.42 % 172.48/172.42 fof(fact_diff__bin__simps_I3_J,axiom, % 172.48/172.42 ! [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)) ). % 172.48/172.42 % 172.48/172.42 fof(fact_diff__bin__simps_I10_J,axiom, % 172.48/172.42 ! [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)) ). % 172.48/172.42 % 172.48/172.42 fof(fact_diff__bin__simps_I9_J,axiom, % 172.48/172.42 ! [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)) ). % 172.48/172.42 % 172.48/172.42 fof(fact_zdiv__number__of__Bit0,axiom, % 172.48/172.42 ! [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)) ). % 172.48/172.42 % 172.48/172.42 fof(fact_neg__number__of__Bit0,axiom, % 172.48/172.42 ! [V_w_2] : % 172.48/172.42 ( hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(V_w_2)))) % 172.48/172.42 <=> hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),V_w_2))) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_pred__Bit0,axiom, % 172.48/172.42 ! [V_k] : c_Int_Opred(c_Int_OBit0(V_k)) = c_Int_OBit1(c_Int_Opred(V_k)) ). % 172.48/172.42 % 172.48/172.42 fof(fact_pred__Bit1,axiom, % 172.48/172.42 ! [V_k] : c_Int_Opred(c_Int_OBit1(V_k)) = c_Int_OBit0(V_k) ). % 172.48/172.42 % 172.48/172.42 fof(fact_iszero__number__of__Bit0,axiom, % 172.48/172.42 ! [V_w_2,T_a] : % 172.48/172.42 ( ( class_Int_Onumber__ring(T_a) % 172.48/172.42 & class_Int_Oring__char__0(T_a) ) % 172.48/172.42 => ( c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OBit0(V_w_2))) % 172.48/172.42 <=> c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),V_w_2)) ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_succ__Bit1,axiom, % 172.48/172.42 ! [V_k] : c_Int_Osucc(c_Int_OBit1(V_k)) = c_Int_OBit0(c_Int_Osucc(V_k)) ). % 172.48/172.42 % 172.48/172.42 fof(fact_succ__Bit0,axiom, % 172.48/172.42 ! [V_k] : c_Int_Osucc(c_Int_OBit0(V_k)) = c_Int_OBit1(V_k) ). % 172.48/172.42 % 172.48/172.42 fof(fact_nat__number__of__Bit0,axiom, % 172.48/172.42 ! [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))) ). % 172.48/172.42 % 172.48/172.42 fof(fact_number__of__Bit0,axiom, % 172.48/172.42 ! [V_w,T_a] : % 172.48/172.42 ( class_Int_Onumber__ring(T_a) % 172.48/172.42 => 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)) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_rel__simps_I15_J,axiom, % 172.48/172.42 ! [V_l_2,V_k_2] : % 172.48/172.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OBit1(V_l_2))) % 172.48/172.42 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_less__int__code_I14_J,axiom, % 172.48/172.42 ! [V_k2_2,V_k1_2] : % 172.48/172.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit1(V_k2_2))) % 172.48/172.42 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_rel__simps_I33_J,axiom, % 172.48/172.42 ! [V_l_2,V_k_2] : % 172.48/172.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OBit0(V_l_2))) % 172.48/172.42 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_less__eq__int__code_I15_J,axiom, % 172.48/172.42 ! [V_k2_2,V_k1_2] : % 172.48/172.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit0(V_k2_2))) % 172.48/172.42 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_card__UNIV__bool,axiom, % 172.48/172.42 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))) ). % 172.48/172.42 % 172.48/172.42 fof(fact_mult__Bit1,axiom, % 172.48/172.42 ! [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) ). % 172.48/172.42 % 172.48/172.42 fof(fact_diff__bin__simps_I8_J,axiom, % 172.48/172.42 ! [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)) ). % 172.48/172.42 % 172.48/172.42 fof(fact_add__Bit1__Bit1,axiom, % 172.48/172.42 ! [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))) ). % 172.48/172.42 % 172.48/172.42 fof(fact_power__number__of__even,axiom, % 172.48/172.42 ! [V_w_2,V_z_2,T_a] : % 172.48/172.42 ( class_Int_Onumber__ring(T_a) % 172.48/172.42 => 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))) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_zpower__number__of__even,axiom, % 172.48/172.42 ! [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))) ). % 172.48/172.42 % 172.48/172.42 fof(fact_double__number__of__Bit0,axiom, % 172.48/172.42 ! [V_w,T_a] : % 172.48/172.42 ( class_Int_Onumber__ring(T_a) % 172.48/172.42 => 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)) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_number__of1,axiom, % 172.48/172.42 ! [V_n] : % 172.48/172.42 ( 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))) % 172.48/172.42 => ( 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)))) % 172.48/172.42 & 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)))) ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_Nat__Transfer_Otransfer__int__nat__function__closures_I7_J,axiom, % 172.48/172.42 c_Nat__Transfer_Ois__nat(hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OBit0(c_Int_OBit1(c_Int_OPls)))) ). % 172.48/172.42 % 172.48/172.42 fof(fact_power__number__of__even__number__of,axiom, % 172.48/172.42 ! [V_w_2,V_v_2,T_a] : % 172.48/172.42 ( class_Int_Onumber__ring(T_a) % 172.48/172.42 => 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))) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_mult__2__right,axiom, % 172.48/172.42 ! [V_z,T_a] : % 172.48/172.42 ( class_Int_Onumber__ring(T_a) % 172.48/172.42 => 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) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_mult__2,axiom, % 172.48/172.42 ! [V_z,T_a] : % 172.48/172.42 ( class_Int_Onumber__ring(T_a) % 172.48/172.42 => 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) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_one__add__one__is__two,axiom, % 172.48/172.42 ! [T_a] : % 172.48/172.42 ( class_Int_Onumber__ring(T_a) % 172.48/172.42 => 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))) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_zero__eq__power2,axiom, % 172.48/172.42 ! [V_a_2,T_a] : % 172.48/172.42 ( class_Rings_Oring__1__no__zero__divisors(T_a) % 172.48/172.42 => ( 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) % 172.48/172.42 <=> V_a_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_zero__power2,axiom, % 172.48/172.42 ! [T_a] : % 172.48/172.42 ( class_Rings_Osemiring__1(T_a) % 172.48/172.42 => 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) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_numeral__2__eq__2,axiom, % 172.48/172.42 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))) ). % 172.48/172.42 % 172.48/172.42 fof(fact_semiring__norm_I115_J,axiom, % 172.48/172.42 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))) ). % 172.48/172.42 % 172.48/172.42 fof(fact_power2__eq__square,axiom, % 172.48/172.42 ! [V_a,T_a] : % 172.48/172.42 ( class_Groups_Omonoid__mult(T_a) % 172.48/172.42 => 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) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J,axiom, % 172.48/172.42 ! [V_x,T_a] : % 172.48/172.42 ( class_Rings_Ocomm__semiring__1(T_a) % 172.48/172.42 => 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)))) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_Nat__Transfer_Otransfer__nat__int__function__closures_I7_J,axiom, % 172.48/172.42 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))))) ). % 172.48/172.42 % 172.48/172.42 fof(fact_add__2__eq__Suc,axiom, % 172.48/172.42 ! [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)) ). % 172.48/172.42 % 172.48/172.42 fof(fact_add__2__eq__Suc_H,axiom, % 172.48/172.42 ! [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)) ). % 172.48/172.42 % 172.48/172.42 fof(fact_one__power2,axiom, % 172.48/172.42 ! [T_a] : % 172.48/172.42 ( class_Rings_Osemiring__1(T_a) % 172.48/172.42 => 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) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_power2__minus,axiom, % 172.48/172.42 ! [V_a,T_a] : % 172.48/172.42 ( class_Rings_Oring__1(T_a) % 172.48/172.42 => 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)))) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_nat__mult__2__right,axiom, % 172.48/172.42 ! [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) ). % 172.48/172.42 % 172.48/172.42 fof(fact_nat__mult__2,axiom, % 172.48/172.42 ! [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) ). % 172.48/172.42 % 172.48/172.42 fof(fact_power__even__eq,axiom, % 172.48/172.42 ! [V_n,V_a,T_a] : % 172.48/172.42 ( class_Groups_Omonoid__mult(T_a) % 172.48/172.42 => 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)))) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_transfer__int__nat__numerals_I3_J,axiom, % 172.48/172.42 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)))) ). % 172.48/172.42 % 172.48/172.42 fof(fact_transfer__nat__int__numerals_I3_J,axiom, % 172.48/172.42 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)))) ). % 172.48/172.42 % 172.48/172.42 fof(fact_abs__power2,axiom, % 172.48/172.42 ! [V_a,T_a] : % 172.48/172.42 ( class_Rings_Olinordered__idom(T_a) % 172.48/172.42 => 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)))) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_power2__abs,axiom, % 172.48/172.42 ! [V_a,T_a] : % 172.48/172.42 ( class_Rings_Olinordered__idom(T_a) % 172.48/172.42 => 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)))) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_nat__1__add__1,axiom, % 172.48/172.42 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))) ). % 172.48/172.42 % 172.48/172.42 fof(fact_mod2__Suc__Suc,axiom, % 172.48/172.42 ! [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)))) ). % 172.48/172.42 % 172.48/172.42 fof(fact_div2__Suc__Suc,axiom, % 172.48/172.42 ! [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))))) ). % 172.48/172.42 % 172.48/172.42 fof(fact_zmod__number__of__Bit0,axiom, % 172.48/172.42 ! [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))) ). % 172.48/172.42 % 172.48/172.42 fof(fact_add__self__div__2,axiom, % 172.48/172.42 ! [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 ). % 172.48/172.42 % 172.48/172.42 fof(fact_half__gt__zero__iff,axiom, % 172.48/172.42 ! [V_r_2,T_a] : % 172.48/172.42 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 172.48/172.42 & class_Int_Onumber__ring(T_a) ) % 172.48/172.42 => ( 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)))))) % 172.48/172.42 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_r_2)) ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_half__gt__zero,axiom, % 172.48/172.42 ! [V_r,T_a] : % 172.48/172.42 ( ( class_Fields_Olinordered__field__inverse__zero(T_a) % 172.48/172.42 & class_Int_Onumber__ring(T_a) ) % 172.48/172.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_r)) % 172.48/172.42 => 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)))))) ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_power2__eq__imp__eq,axiom, % 172.48/172.42 ! [V_y,V_x,T_a] : % 172.48/172.42 ( class_Rings_Olinordered__semidom(T_a) % 172.48/172.42 => ( 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)))) % 172.48/172.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_x)) % 172.48/172.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 172.48/172.42 => V_x = V_y ) ) ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_power2__le__imp__le,axiom, % 172.48/172.42 ! [V_y,V_x,T_a] : % 172.48/172.42 ( class_Rings_Olinordered__semidom(T_a) % 172.48/172.42 => ( 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)))))) % 172.48/172.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 172.48/172.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_zero__le__power2,axiom, % 172.48/172.42 ! [V_a,T_a] : % 172.48/172.42 ( class_Rings_Olinordered__idom(T_a) % 172.48/172.42 => 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)))))) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_zero__less__power2,axiom, % 172.48/172.42 ! [V_a_2,T_a] : % 172.48/172.42 ( class_Rings_Olinordered__idom(T_a) % 172.48/172.42 => ( 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)))))) % 172.48/172.42 <=> V_a_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_power2__less__0,axiom, % 172.48/172.42 ! [V_a,T_a] : % 172.48/172.42 ( class_Rings_Olinordered__idom(T_a) % 172.48/172.42 => ~ 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))) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_sum__power2__eq__zero__iff,axiom, % 172.48/172.42 ! [V_y_2,V_x_2,T_a] : % 172.48/172.42 ( class_Rings_Olinordered__idom(T_a) % 172.48/172.42 => ( 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) % 172.48/172.42 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a) % 172.48/172.42 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_power2__eq__square__number__of,axiom, % 172.48/172.42 ! [V_w,T_b] : % 172.48/172.42 ( ( class_Groups_Omonoid__mult(T_b) % 172.48/172.42 & class_Int_Onumber(T_b) ) % 172.48/172.42 => 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)) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_less__2__cases,axiom, % 172.48/172.42 ! [V_n] : % 172.48/172.42 ( 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))))) % 172.48/172.42 => ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 172.48/172.42 | V_n = hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_nat__2,axiom, % 172.48/172.42 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))) ). % 172.48/172.42 % 172.48/172.42 fof(fact_power2__eq__1__iff,axiom, % 172.48/172.42 ! [V_a_2,T_a] : % 172.48/172.42 ( class_Rings_Oring__1__no__zero__divisors(T_a) % 172.48/172.42 => ( 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) % 172.48/172.42 <=> ( V_a_2 = c_Groups_Oone__class_Oone(T_a) % 172.48/172.42 | V_a_2 = hAPP(c_Groups_Ouminus__class_Ouminus(T_a),c_Groups_Oone__class_Oone(T_a)) ) ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J,axiom, % 172.48/172.42 ! [V_n,V_x,T_a] : % 172.48/172.42 ( class_Rings_Ocomm__semiring__1(T_a) % 172.48/172.42 => 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)) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_power__minus__even,axiom, % 172.48/172.42 ! [V_n,V_a,T_a] : % 172.48/172.42 ( class_Rings_Oring__1(T_a) % 172.48/172.42 => 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)) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_power2__less__imp__less,axiom, % 172.48/172.42 ! [V_y,V_x,T_a] : % 172.48/172.42 ( class_Rings_Olinordered__semidom(T_a) % 172.48/172.42 => ( 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)))))) % 172.48/172.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_y)) % 172.48/172.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_x),V_y)) ) ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_sum__power2__ge__zero,axiom, % 172.48/172.42 ! [V_y,V_x,T_a] : % 172.48/172.42 ( class_Rings_Olinordered__idom(T_a) % 172.48/172.42 => 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))))))) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_sum__power2__le__zero__iff,axiom, % 172.48/172.42 ! [V_y_2,V_x_2,T_a] : % 172.48/172.42 ( class_Rings_Olinordered__idom(T_a) % 172.48/172.42 => ( 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))) % 172.48/172.42 <=> ( V_x_2 = c_Groups_Ozero__class_Ozero(T_a) % 172.48/172.42 & V_y_2 = c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_sum__power2__gt__zero__iff,axiom, % 172.48/172.42 ! [V_y_2,V_x_2,T_a] : % 172.48/172.42 ( class_Rings_Olinordered__idom(T_a) % 172.48/172.42 => ( 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))))))) % 172.48/172.42 <=> ( V_x_2 != c_Groups_Ozero__class_Ozero(T_a) % 172.48/172.42 | V_y_2 != c_Groups_Ozero__class_Ozero(T_a) ) ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_not__sum__power2__lt__zero,axiom, % 172.48/172.42 ! [V_y,V_x,T_a] : % 172.48/172.42 ( class_Rings_Olinordered__idom(T_a) % 172.48/172.42 => ~ 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))) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_power2__sum,axiom, % 172.48/172.42 ! [V_y,V_x,T_a] : % 172.48/172.42 ( class_Int_Onumber__ring(T_a) % 172.48/172.42 => 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)) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_zero__le__even__power_H,axiom, % 172.48/172.42 ! [V_n,V_a,T_a] : % 172.48/172.42 ( class_Rings_Olinordered__idom(T_a) % 172.48/172.42 => 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)))) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_comm__semiring__1__class_Onormalizing__semiring__rules_I37_J,axiom, % 172.48/172.42 ! [V_n,V_x,T_a] : % 172.48/172.42 ( class_Rings_Ocomm__semiring__1(T_a) % 172.48/172.42 => 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))) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_power__odd__eq,axiom, % 172.48/172.42 ! [V_n,V_a,T_a] : % 172.48/172.42 ( class_Groups_Omonoid__mult(T_a) % 172.48/172.42 => 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))))) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_power__minus1__even,axiom, % 172.48/172.42 ! [V_n,T_a] : % 172.48/172.42 ( class_Rings_Oring__1(T_a) % 172.48/172.42 => 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) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_zdiv__number__of__Bit1,axiom, % 172.48/172.42 ! [V_v,V_w] : % 172.48/172.42 ( ( 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))) % 172.48/172.42 => 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)) ) % 172.48/172.42 & ( ~ 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))) % 172.48/172.42 => 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)) ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_mod2__gr__0,axiom, % 172.48/172.42 ! [V_m_2] : % 172.48/172.42 ( 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)))))) % 172.48/172.42 <=> 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) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_div__2__gt__zero,axiom, % 172.48/172.42 ! [V_n] : % 172.48/172.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n)) % 172.48/172.42 => 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)))))) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_power2__diff,axiom, % 172.48/172.42 ! [V_y,V_x,T_a] : % 172.48/172.42 ( class_Int_Onumber__ring(T_a) % 172.48/172.42 => 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)) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_odd__0__le__power__imp__0__le,axiom, % 172.48/172.42 ! [V_n,V_a,T_a] : % 172.48/172.42 ( class_Rings_Olinordered__idom(T_a) % 172.48/172.42 => ( 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))))) % 172.48/172.42 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),c_Groups_Ozero__class_Ozero(T_a)),V_a)) ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_odd__power__less__zero,axiom, % 172.48/172.42 ! [V_n,V_a,T_a] : % 172.48/172.42 ( class_Rings_Olinordered__idom(T_a) % 172.48/172.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a),c_Groups_Ozero__class_Ozero(T_a))) % 172.48/172.42 => 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))) ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_power__minus1__odd,axiom, % 172.48/172.42 ! [V_n,T_a] : % 172.48/172.42 ( class_Rings_Oring__1(T_a) % 172.48/172.42 => 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)) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_Suc__n__div__2__gt__zero,axiom, % 172.48/172.42 ! [V_n] : % 172.48/172.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 172.48/172.42 => 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)))))) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_of__nat__double,axiom, % 172.48/172.42 ! [V_x,T_a] : % 172.48/172.42 ( class_Rings_Osemiring__1(T_a) % 172.48/172.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_x)) % 172.48/172.42 => 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))) ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_pos__zmod__mult__2,axiom, % 172.48/172.42 ! [V_b,V_a] : % 172.48/172.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 172.48/172.42 => 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))) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_pos__zdiv__mult__2,axiom, % 172.48/172.42 ! [V_b,V_a] : % 172.48/172.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 172.48/172.42 => 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) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_int__of__code,axiom, % 172.48/172.42 ! [V_k] : % 172.48/172.42 ( ( V_k = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 172.48/172.42 => hAPP(c_Code__Numeral_Oint__of,V_k) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 172.48/172.42 & ( V_k != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 172.48/172.42 => ( ( 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) % 172.48/172.42 => 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)))))) ) % 172.48/172.42 & ( 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) % 172.48/172.42 => 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)) ) ) ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_of__int__num,axiom, % 172.48/172.42 ! [V_k_2,T_a] : % 172.48/172.42 ( class_Rings_Oring__1(T_a) % 172.48/172.42 => ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 172.48/172.42 => hAPP(c_Int_Oring__1__class_Oof__int(T_a),V_k_2) = c_Groups_Ozero__class_Ozero(T_a) ) % 172.48/172.42 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 172.48/172.42 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 172.48/172.42 => 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))) ) % 172.48/172.42 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 172.48/172.42 => 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))))) ) ) ) ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_power__m1__odd,axiom, % 172.48/172.42 ! [V_n,T_a] : % 172.48/172.42 ( class_Int_Onumber__ring(T_a) % 172.48/172.42 => 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) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_power__m1__even,axiom, % 172.48/172.42 ! [V_n,T_a] : % 172.48/172.42 ( class_Int_Onumber__ring(T_a) % 172.48/172.42 => 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) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_rel__simps_I42_J,axiom, % 172.48/172.42 ! [V_l] : c_Int_OMin != c_Int_OBit0(V_l) ). % 172.48/172.42 % 172.48/172.42 fof(fact_rel__simps_I45_J,axiom, % 172.48/172.42 ! [V_k] : c_Int_OBit0(V_k) != c_Int_OMin ). % 172.48/172.42 % 172.48/172.42 fof(fact_rel__simps_I40_J,axiom, % 172.48/172.42 c_Int_OMin != c_Int_OPls ). % 172.48/172.42 % 172.48/172.42 fof(fact_rel__simps_I37_J,axiom, % 172.48/172.42 c_Int_OPls != c_Int_OMin ). % 172.48/172.42 % 172.48/172.42 fof(fact_rel__simps_I24_J,axiom, % 172.48/172.42 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OMin)) ). % 172.48/172.42 % 172.48/172.42 fof(fact_rel__simps_I7_J,axiom, % 172.48/172.42 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OMin)) ). % 172.48/172.42 % 172.48/172.42 fof(fact_code__numeral__zero__minus__one,axiom, % 172.48/172.42 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) ). % 172.48/172.42 % 172.48/172.42 fof(fact_Bit1__Min,axiom, % 172.48/172.42 c_Int_OBit1(c_Int_OMin) = c_Int_OMin ). % 172.48/172.42 % 172.48/172.42 fof(fact_rel__simps_I43_J,axiom, % 172.48/172.42 ! [V_l_2] : % 172.48/172.42 ( c_Int_OMin = c_Int_OBit1(V_l_2) % 172.48/172.42 <=> c_Int_OMin = V_l_2 ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_rel__simps_I47_J,axiom, % 172.48/172.42 ! [V_k_2] : % 172.48/172.42 ( c_Int_OBit1(V_k_2) = c_Int_OMin % 172.48/172.42 <=> V_k_2 = c_Int_OMin ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_bin__less__0__simps_I2_J,axiom, % 172.48/172.42 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ). % 172.48/172.42 % 172.48/172.42 fof(fact_rel__simps_I23_J,axiom, % 172.48/172.42 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ). % 172.48/172.42 % 172.48/172.42 fof(fact_rel__simps_I20_J,axiom, % 172.48/172.42 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ). % 172.48/172.42 % 172.48/172.42 fof(fact_rel__simps_I26_J,axiom, % 172.48/172.42 ! [V_k_2] : % 172.48/172.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k_2))) % 172.48/172.42 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_rel__simps_I30_J,axiom, % 172.48/172.42 ! [V_k_2] : % 172.48/172.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OMin)) % 172.48/172.42 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_rel__simps_I3_J,axiom, % 172.48/172.42 ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ). % 172.48/172.42 % 172.48/172.42 fof(fact_rel__simps_I6_J,axiom, % 172.48/172.42 hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ). % 172.48/172.42 % 172.48/172.42 fof(fact_rel__simps_I13_J,axiom, % 172.48/172.42 ! [V_k_2] : % 172.48/172.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit1(V_k_2)),c_Int_OMin)) % 172.48/172.42 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_rel__simps_I9_J,axiom, % 172.48/172.42 ! [V_k_2] : % 172.48/172.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k_2))) % 172.48/172.42 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_rel__simps_I28_J,axiom, % 172.48/172.42 ! [V_k_2] : % 172.48/172.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OMin)) % 172.48/172.42 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_rel__simps_I8_J,axiom, % 172.48/172.42 ! [V_k_2] : % 172.48/172.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k_2))) % 172.48/172.42 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_eq__number__of__Pls__Min,axiom, % 172.48/172.42 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) ). % 172.48/172.42 % 172.48/172.42 fof(fact_Int_OMin__def,axiom, % 172.48/172.42 c_Int_OMin = hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)) ). % 172.48/172.42 % 172.48/172.42 fof(fact_mult__Min,axiom, % 172.48/172.42 ! [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) ). % 172.48/172.42 % 172.48/172.42 fof(fact_neg__number__of__Min,axiom, % 172.48/172.42 hBOOL(hAPP(c_Nat__Numeral_Oneg,hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin))) ). % 172.48/172.42 % 172.48/172.42 fof(fact_pred__Pls,axiom, % 172.48/172.42 c_Int_Opred(c_Int_OPls) = c_Int_OMin ). % 172.48/172.42 % 172.48/172.42 fof(fact_add__Min,axiom, % 172.48/172.42 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),c_Int_OMin),V_k) = c_Int_Opred(V_k) ). % 172.48/172.42 % 172.48/172.42 fof(fact_add__Min__right,axiom, % 172.48/172.42 ! [V_k] : hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_k),c_Int_OMin) = c_Int_Opred(V_k) ). % 172.48/172.42 % 172.48/172.42 fof(fact_pred__Min,axiom, % 172.48/172.42 c_Int_Opred(c_Int_OMin) = c_Int_OBit0(c_Int_OMin) ). % 172.48/172.42 % 172.48/172.42 fof(fact_nonzero__number__of__Min,axiom, % 172.48/172.42 ! [T_a] : % 172.48/172.42 ( class_Int_Onumber__ring(T_a) % 172.48/172.42 => ~ c_Int_Oiszero(T_a,hAPP(c_Int_Onumber__class_Onumber__of(T_a),c_Int_OMin)) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_succ__Min,axiom, % 172.48/172.42 c_Int_Osucc(c_Int_OMin) = c_Int_OPls ). % 172.48/172.42 % 172.48/172.42 fof(fact_diff__bin__simps_I2_J,axiom, % 172.48/172.42 ! [V_k] : hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k),c_Int_OMin) = c_Int_Osucc(V_k) ). % 172.48/172.42 % 172.48/172.42 fof(fact_mult__minus1__right,axiom, % 172.48/172.42 ! [V_z,T_a] : % 172.48/172.42 ( class_Int_Onumber__ring(T_a) % 172.48/172.42 => 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) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_mult__minus1,axiom, % 172.48/172.42 ! [V_z,T_a] : % 172.48/172.42 ( class_Int_Onumber__ring(T_a) % 172.48/172.42 => 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) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_arith__simps_I31_J,axiom, % 172.48/172.42 ! [T_a] : % 172.48/172.42 ( class_Int_Onumber__ring(T_a) % 172.48/172.42 => 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) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_number__of__Min,axiom, % 172.48/172.42 ! [T_a] : % 172.48/172.42 ( class_Int_Onumber__ring(T_a) % 172.48/172.42 => 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)) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_abs__minus__one,axiom, % 172.48/172.42 ! [T_a] : % 172.48/172.42 ( ( class_Int_Onumber__ring(T_a) % 172.48/172.42 & class_Rings_Olinordered__idom(T_a) ) % 172.48/172.42 => 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) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_divide__minus1,axiom, % 172.48/172.42 ! [V_x,T_a] : % 172.48/172.42 ( ( class_Fields_Ofield__inverse__zero(T_a) % 172.48/172.42 & class_Int_Onumber__ring(T_a) ) % 172.48/172.42 => 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) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_rel__simps_I11_J,axiom, % 172.48/172.42 ! [V_k_2] : % 172.48/172.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OBit0(V_k_2)),c_Int_OMin)) % 172.48/172.42 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),c_Int_OMin)) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_rel__simps_I25_J,axiom, % 172.48/172.42 ! [V_k_2] : % 172.48/172.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k_2))) % 172.48/172.42 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Int_OMin),V_k_2)) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_zmod__minus1__right,axiom, % 172.48/172.42 ! [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) ). % 172.48/172.42 % 172.48/172.42 fof(fact_diff__bin__simps_I4_J,axiom, % 172.48/172.42 ! [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)) ). % 172.48/172.42 % 172.48/172.42 fof(fact_minus__Min,axiom, % 172.48/172.42 hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),c_Int_OMin) = c_Int_OBit1(c_Int_OPls) ). % 172.48/172.42 % 172.48/172.42 fof(fact_zmult__eq__1__iff,axiom, % 172.48/172.42 ! [V_n_2,V_m_2] : % 172.48/172.42 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m_2),V_n_2) = c_Groups_Oone__class_Oone(tc_Int_Oint) % 172.48/172.42 <=> ( ( V_m_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) % 172.48/172.42 & V_n_2 = c_Groups_Oone__class_Oone(tc_Int_Oint) ) % 172.48/172.42 | ( V_m_2 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) % 172.48/172.42 & V_n_2 = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_pos__zmult__eq__1__iff__lemma,axiom, % 172.48/172.42 ! [V_n,V_m] : % 172.48/172.42 ( hAPP(hAPP(c_Groups_Otimes__class_Otimes(tc_Int_Oint),V_m),V_n) = c_Groups_Oone__class_Oone(tc_Int_Oint) % 172.48/172.42 => ( V_m = c_Groups_Oone__class_Oone(tc_Int_Oint) % 172.48/172.42 | V_m = hAPP(c_Int_Onumber__class_Onumber__of(tc_Int_Oint),c_Int_OMin) ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_diff__bin__simps_I6_J,axiom, % 172.48/172.42 ! [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)) ). % 172.48/172.42 % 172.48/172.42 fof(fact_diff__bin__simps_I5_J,axiom, % 172.48/172.42 ! [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)) ). % 172.48/172.42 % 172.48/172.42 fof(fact_of__int__m1,axiom, % 172.48/172.42 ! [T_a] : % 172.48/172.42 ( class_Int_Onumber__ring(T_a) % 172.48/172.42 => 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) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_zdiv__minus1__right,axiom, % 172.48/172.42 ! [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) ). % 172.48/172.42 % 172.48/172.42 fof(fact_zero__code__numeral__code,axiom, % 172.48/172.42 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) ). % 172.48/172.42 % 172.48/172.42 fof(fact_minus1__divide,axiom, % 172.48/172.42 ! [V_x,T_a] : % 172.48/172.42 ( ( class_Fields_Ofield__inverse__zero(T_a) % 172.48/172.42 & class_Int_Onumber__ring(T_a) ) % 172.48/172.42 => 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)) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_abs__power__minus__one,axiom, % 172.48/172.42 ! [V_n,T_a] : % 172.48/172.42 ( ( class_Int_Onumber__ring(T_a) % 172.48/172.42 & class_Rings_Olinordered__idom(T_a) ) % 172.48/172.42 => 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) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_div__eq__minus1,axiom, % 172.48/172.42 ! [V_b] : % 172.48/172.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 172.48/172.42 => 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) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_div__pos__neg__trivial,axiom, % 172.48/172.42 ! [V_b,V_a] : % 172.48/172.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 172.48/172.42 => ( 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))) % 172.48/172.42 => 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) ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_zmod__minus1,axiom, % 172.48/172.42 ! [V_b] : % 172.48/172.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 172.48/172.42 => 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)) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_one__code__numeral__code,axiom, % 172.48/172.42 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)) ). % 172.48/172.42 % 172.48/172.42 fof(fact_Nitpick_OFrac__def,axiom, % 172.48/172.42 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)))) ). % 172.48/172.42 % 172.48/172.42 fof(fact_int__ge__less__than2__def,axiom, % 172.48/172.42 ! [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)))) ). % 172.48/172.42 % 172.48/172.42 fof(fact_int__ge__less__than__def,axiom, % 172.48/172.42 ! [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)))) ). % 172.48/172.42 % 172.48/172.42 fof(fact_code__numeral_Osize_I1_J,axiom, % 172.48/172.42 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) ). % 172.48/172.42 % 172.48/172.42 fof(fact_Nitpick_Oprod__def,axiom, % 172.48/172.42 ! [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)))) ). % 172.48/172.42 % 172.48/172.42 fof(fact_nat__of__aux__code,axiom, % 172.48/172.42 ! [V_n,V_i] : % 172.48/172.42 ( ( V_i = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 172.48/172.42 => c_Code__Numeral_Onat__of__aux(V_i,V_n) = V_n ) % 172.48/172.42 & ( V_i != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 172.48/172.42 => 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)) ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_divmod__int__rel__def,axiom, % 172.48/172.42 ! [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))))))) ). % 172.48/172.42 % 172.48/172.42 fof(fact_divmod__int__correct,axiom, % 172.48/172.42 ! [V_a,V_b] : % 172.48/172.42 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 172.48/172.42 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_Odivmod__int(V_a,V_b))) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_code__numeral_Osize_I2_J,axiom, % 172.48/172.42 ! [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))) ). % 172.48/172.42 % 172.48/172.42 fof(fact_zmult2__lemma,axiom, % 172.48/172.42 ! [V_c,V_r,V_q,V_b,V_a] : % 172.48/172.42 ( 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))) % 172.48/172.42 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 172.48/172.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_c)) % 172.48/172.42 => 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)))) ) ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_Nats__number__of,axiom, % 172.48/172.42 ! [V_w_2,T_a] : % 172.48/172.42 ( class_Int_Onumber__ring(T_a) % 172.48/172.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Int_OPls),V_w_2)) % 172.48/172.42 => 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))) ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_code__numeral_Oinject,axiom, % 172.48/172.42 ! [V_code__numeral_H_2,V_code__numeral_2] : % 172.48/172.42 ( c_Code__Numeral_OSuc__code__numeral(V_code__numeral_2) = c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H_2) % 172.48/172.42 <=> V_code__numeral_2 = V_code__numeral_H_2 ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_sup__Un__eq2,axiom, % 172.48/172.42 ! [V_y_2,V_x_2,V_S_2,V_R_2,T_b,T_a] : % 172.48/172.42 ( 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)) % 172.48/172.42 <=> 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))) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_inf__Int__eq2,axiom, % 172.48/172.42 ! [V_y_2,V_x_2,V_S_2,V_R_2,T_b,T_a] : % 172.48/172.42 ( 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)) % 172.48/172.42 <=> 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))) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_pred__equals__eq2,axiom, % 172.48/172.42 ! [V_S_2,V_R_2,T_b,T_a] : % 172.48/172.42 ( 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) % 172.48/172.42 <=> V_R_2 = V_S_2 ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_pred__subset__eq2,axiom, % 172.48/172.42 ! [V_S_2,V_R_2,T_b,T_a] : % 172.48/172.42 ( 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))) % 172.48/172.42 <=> 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)) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_bot__empty__eq2,axiom, % 172.48/172.42 ! [V_y_2,V_x_2,T_b,T_a] : % 172.48/172.42 ( 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)) % 172.48/172.42 <=> 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)))) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_code__numeral_Osimps_I2_J,axiom, % 172.48/172.42 ! [V_code__numeral_H] : c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) != c_Code__Numeral_OSuc__code__numeral(V_code__numeral_H) ). % 172.48/172.42 % 172.48/172.42 fof(fact_code__numeral_Osimps_I3_J,axiom, % 172.48/172.42 ! [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) ). % 172.48/172.42 % 172.48/172.42 fof(fact_divmod__int__rel__0,axiom, % 172.48/172.42 ! [V_b] : % 172.48/172.42 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 172.48/172.42 => 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)))) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_self__remainder,axiom, % 172.48/172.42 ! [V_r,V_q,V_a] : % 172.48/172.42 ( 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))) % 172.48/172.42 => ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 172.48/172.42 => V_r = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_unique__quotient,axiom, % 172.48/172.42 ! [V_r_H,V_q_H,V_r,V_q,V_b,V_a] : % 172.48/172.42 ( 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))) % 172.48/172.42 => ( 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))) % 172.48/172.42 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 172.48/172.42 => V_q = V_q_H ) ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_unique__remainder,axiom, % 172.48/172.42 ! [V_r_H,V_q_H,V_r,V_q,V_b,V_a] : % 172.48/172.42 ( 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))) % 172.48/172.42 => ( 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))) % 172.48/172.42 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 172.48/172.42 => V_r = V_r_H ) ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_SUP__UN__eq2,axiom, % 172.48/172.42 ! [V_y_2,V_x_2,V_r_2,T_c,T_b,T_a] : % 172.48/172.42 ( 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)) % 172.48/172.42 <=> 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))) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_self__quotient,axiom, % 172.48/172.42 ! [V_r,V_q,V_a] : % 172.48/172.42 ( 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))) % 172.48/172.42 => ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 172.48/172.42 => V_q = c_Groups_Oone__class_Oone(tc_Int_Oint) ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_divmod__int__rel__mod,axiom, % 172.48/172.42 ! [V_r,V_q,V_b,V_a] : % 172.48/172.42 ( 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))) % 172.48/172.42 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 172.48/172.42 => c_Divides_Odiv__class_Omod(tc_Int_Oint,V_a,V_b) = V_r ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_divmod__int__rel__div,axiom, % 172.48/172.42 ! [V_r,V_q,V_b,V_a] : % 172.48/172.42 ( 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))) % 172.48/172.42 => ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 172.48/172.42 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Int_Oint),V_a),V_b) = V_q ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_Nats__0,axiom, % 172.48/172.42 ! [T_a] : % 172.48/172.42 ( class_Rings_Osemiring__1(T_a) % 172.48/172.42 => hBOOL(hAPP(hAPP(c_member(T_a),c_Groups_Ozero__class_Ozero(T_a)),c_Nat_Osemiring__1__class_ONats(T_a))) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_divmod__int__mod__div,axiom, % 172.48/172.42 ! [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)) ). % 172.48/172.42 % 172.48/172.42 fof(fact_Nats__add,axiom, % 172.48/172.42 ! [V_b_2,V_a_2,T_a] : % 172.48/172.42 ( class_Rings_Osemiring__1(T_a) % 172.48/172.42 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Nat_Osemiring__1__class_ONats(T_a))) % 172.48/172.42 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Nat_Osemiring__1__class_ONats(T_a))) % 172.48/172.42 => 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))) ) ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_Nats__mult,axiom, % 172.48/172.42 ! [V_b_2,V_a_2,T_a] : % 172.48/172.42 ( class_Rings_Osemiring__1(T_a) % 172.48/172.42 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Nat_Osemiring__1__class_ONats(T_a))) % 172.48/172.42 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Nat_Osemiring__1__class_ONats(T_a))) % 172.48/172.42 => 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))) ) ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_Nats__1,axiom, % 172.48/172.42 ! [T_a] : % 172.48/172.42 ( class_Rings_Osemiring__1(T_a) % 172.48/172.42 => hBOOL(hAPP(hAPP(c_member(T_a),c_Groups_Oone__class_Oone(T_a)),c_Nat_Osemiring__1__class_ONats(T_a))) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_of__nat__in__Nats,axiom, % 172.48/172.42 ! [V_n_2,T_a] : % 172.48/172.42 ( class_Rings_Osemiring__1(T_a) % 172.48/172.42 => 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))) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_Suc__code__numeral__minus__one,axiom, % 172.48/172.42 ! [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 ). % 172.48/172.42 % 172.48/172.42 fof(fact_divmod__int__rel__div__mod,axiom, % 172.48/172.42 ! [V_a,V_b] : % 172.48/172.42 ( V_b != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 172.48/172.42 => 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)))) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_zadd1__lemma,axiom, % 172.48/172.42 ! [V_br,V_bq,V_b,V_ar,V_aq,V_c,V_a] : % 172.48/172.42 ( 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))) % 172.48/172.42 => ( 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))) % 172.48/172.42 => ( V_c != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 172.48/172.42 => 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)))) ) ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_zminus1__lemma,axiom, % 172.48/172.42 ! [V_r_2,V_q_2,V_b_2,V_a_2] : % 172.48/172.42 ( 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))) % 172.48/172.42 => 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))))) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_divmod__int__relI,axiom, % 172.48/172.42 ! [V_r,V_q,V_b,V_a] : % 172.48/172.42 ( 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) % 172.48/172.42 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 172.48/172.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_r)) % 172.48/172.42 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_r),V_b)) ) ) % 172.48/172.42 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 172.48/172.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),V_r)) % 172.48/172.42 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_r),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) ) ) % 172.48/172.42 => 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))) ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_zmult1__lemma,axiom, % 172.48/172.42 ! [V_a,V_r,V_q,V_c,V_b] : % 172.48/172.42 ( 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))) % 172.48/172.42 => ( V_c != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 172.48/172.42 => 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)))) ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_pair__imageI,axiom, % 172.48/172.42 ! [V_f_2,T_c,V_A_2,V_b_2,V_a_2,T_b,T_a] : % 172.48/172.42 ( 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)) % 172.48/172.42 => 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))) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_norm__frac_Osimps,axiom, % 172.48/172.42 ! [V_a_2,V_b_2] : % 172.48/172.42 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 172.48/172.42 => 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)) ) % 172.48/172.42 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 172.48/172.42 => ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 172.48/172.42 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 172.48/172.42 => 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)) ) % 172.48/172.42 & ( ~ ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 172.48/172.42 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 172.48/172.42 => 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))) ) ) ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_adjust__eq,axiom, % 172.48/172.42 ! [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))) ). % 172.48/172.42 % 172.48/172.42 fof(fact_sup2E,axiom, % 172.48/172.42 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_b,T_a] : % 172.48/172.42 ( 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)) % 172.48/172.42 => ( ~ hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) % 172.48/172.42 => hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_sup2CI,axiom, % 172.48/172.42 ! [T_b,T_a,V_A_2,V_y_2,V_x_2,V_B_2] : % 172.48/172.42 ( ( ~ hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) % 172.48/172.42 => hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) ) % 172.48/172.42 => 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)) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_inf2I,axiom, % 172.48/172.42 ! [T_b,T_a,V_B_2,V_y_2,V_x_2,V_A_2] : % 172.48/172.42 ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) % 172.48/172.42 => ( hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) % 172.48/172.42 => 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)) ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_inf2E,axiom, % 172.48/172.42 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_b,T_a] : % 172.48/172.42 ( 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)) % 172.48/172.42 => ~ ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) % 172.48/172.42 => ~ hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_mem__splitI,axiom, % 172.48/172.42 ! [T_c,T_b,V_b_2,V_a_2,V_ca_2,V_z_2,T_a] : % 172.48/172.42 ( hBOOL(hAPP(hAPP(c_member(T_a),V_z_2),hAPP(hAPP(V_ca_2,V_a_2),V_b_2))) % 172.48/172.42 => hBOOL(hAPP(hAPP(c_member(T_a),V_z_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_fun(T_a,tc_HOL_Obool)),V_ca_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)))) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_prod__caseI,axiom, % 172.48/172.42 ! [T_b,T_a,V_b_2,V_a_2,V_f1_2] : % 172.48/172.42 ( hBOOL(hAPP(hAPP(V_f1_2,V_a_2),V_b_2)) % 172.48/172.42 => 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))) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_splitI,axiom, % 172.48/172.42 ! [T_b,T_a,V_b_2,V_a_2,V_f_2] : % 172.48/172.42 ( hBOOL(hAPP(hAPP(V_f_2,V_a_2),V_b_2)) % 172.48/172.42 => 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))) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_bot2E,axiom, % 172.48/172.42 ! [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)) ). % 172.48/172.42 % 172.48/172.42 fof(fact_splitD_H,axiom, % 172.48/172.42 ! [V_ca_2,V_b_2,V_a_2,V_R_2,T_c,T_b,T_a] : % 172.48/172.42 ( hBOOL(hAPP(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_fun(T_c,tc_HOL_Obool)),V_R_2),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_a_2),V_b_2)),V_ca_2)) % 172.48/172.42 => hBOOL(hAPP(hAPP(hAPP(V_R_2,V_a_2),V_b_2),V_ca_2)) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_less__by__empty,axiom, % 172.48/172.42 ! [V_B_2,T_a,V_A_2] : % 172.48/172.42 ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool)) % 172.48/172.42 => 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)) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_predicate2D,axiom, % 172.48/172.42 ! [V_y_2,V_x_2,V_Q_2,V_P_2,T_b,T_a] : % 172.48/172.42 ( 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)) % 172.48/172.42 => ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2)) % 172.48/172.42 => hBOOL(hAPP(hAPP(V_Q_2,V_x_2),V_y_2)) ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_rev__predicate2D,axiom, % 172.48/172.42 ! [V_Q_2,T_b,T_a,V_y_2,V_x_2,V_P_2] : % 172.48/172.42 ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2)) % 172.48/172.42 => ( 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)) % 172.48/172.42 => hBOOL(hAPP(hAPP(V_Q_2,V_x_2),V_y_2)) ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_inf2D1,axiom, % 172.48/172.42 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_b,T_a] : % 172.48/172.42 ( 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)) % 172.48/172.42 => hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_inf2D2,axiom, % 172.48/172.42 ! [V_y_2,V_x_2,V_B_2,V_A_2,T_b,T_a] : % 172.48/172.42 ( 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)) % 172.48/172.42 => hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_sup2I1,axiom, % 172.48/172.42 ! [V_B_2,T_b,T_a,V_y_2,V_x_2,V_A_2] : % 172.48/172.42 ( hBOOL(hAPP(hAPP(V_A_2,V_x_2),V_y_2)) % 172.48/172.42 => 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)) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_sup2I2,axiom, % 172.48/172.42 ! [V_A_2,T_b,T_a,V_y_2,V_x_2,V_B_2] : % 172.48/172.42 ( hBOOL(hAPP(hAPP(V_B_2,V_x_2),V_y_2)) % 172.48/172.42 => 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)) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_split__paired__All,axiom, % 172.48/172.42 ! [T_b,T_a,V_P_2] : % 172.48/172.42 ( ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) % 172.48/172.42 <=> ! [B_a,B_b] : hBOOL(hAPP(V_P_2,hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_a),B_b))) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_Pair__eq,axiom, % 172.48/172.42 ! [V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_b,T_a] : % 172.48/172.42 ( 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) % 172.48/172.42 <=> ( V_a_2 = V_a_H_2 % 172.48/172.42 & V_b_2 = V_b_H_2 ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_Pair__inject,axiom, % 172.48/172.42 ! [V_b_H,V_a_H,V_b,V_a,T_b,T_a] : % 172.48/172.42 ( 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) % 172.48/172.42 => ~ ( V_a = V_a_H % 172.48/172.42 => V_b != V_b_H ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_split__weak__cong,axiom, % 172.48/172.42 ! [V_ca_2,T_c,T_b,T_a,V_q_2,V_p_2] : % 172.48/172.42 ( V_p_2 = V_q_2 % 172.48/172.42 => hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,T_c),V_ca_2),V_p_2) = hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,T_c),V_ca_2),V_q_2) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_split__twice,axiom, % 172.48/172.42 ! [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) ). % 172.48/172.42 % 172.48/172.42 fof(fact_prod_Osimps_I2_J,axiom, % 172.48/172.42 ! [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) ). % 172.48/172.42 % 172.48/172.42 fof(fact_split__conv,axiom, % 172.48/172.42 ! [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) ). % 172.48/172.42 % 172.48/172.42 fof(fact_splitD,axiom, % 172.48/172.42 ! [V_b_2,V_a_2,V_f_2,T_b,T_a] : % 172.48/172.42 ( 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))) % 172.48/172.42 => hBOOL(hAPP(hAPP(V_f_2,V_a_2),V_b_2)) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_split__eta,axiom, % 172.48/172.42 ! [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 ). % 172.48/172.42 % 172.48/172.42 fof(fact_The__split__eq,axiom, % 172.48/172.42 ! [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) ). % 172.48/172.42 % 172.48/172.42 fof(fact_split__paired__The,axiom, % 172.48/172.42 ! [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)))) ). % 172.48/172.42 % 172.48/172.42 fof(fact_adjust__def,axiom, % 172.48/172.42 ! [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))))))) ). % 172.48/172.42 % 172.48/172.42 fof(fact_in__rel__def,axiom, % 172.48/172.42 ! [V_y_2,V_x_2,V_R_2,T_b,T_a] : % 172.48/172.42 ( hBOOL(hAPP(hAPP(c_FunDef_Oin__rel(T_a,T_b,V_R_2),V_x_2),V_y_2)) % 172.48/172.42 <=> 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)) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_div__mod__code__numeral__def,axiom, % 172.48/172.42 ! [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)) ). % 172.48/172.42 % 172.48/172.42 fof(fact_negDivAlg__eqn__1__number__of,axiom, % 172.48/172.42 ! [V_w] : % 172.48/172.42 ( 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))) % 172.48/172.42 => ( ( 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)))) % 172.48/172.42 => 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))) ) % 172.48/172.42 & ( ~ 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)))) % 172.48/172.42 => 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)))) ) ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_negDivAlg__correct,axiom, % 172.48/172.42 ! [V_b,V_a] : % 172.48/172.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 172.48/172.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 172.48/172.42 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_OnegDivAlg(V_a,V_b))) ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_negDivAlg__div__mod,axiom, % 172.48/172.42 ! [V_l,V_k] : % 172.48/172.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_k),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 172.48/172.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 172.48/172.42 => 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)) ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_negDivAlg__minus1,axiom, % 172.48/172.42 ! [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))) ). % 172.48/172.42 % 172.48/172.42 fof(fact_negDivAlg_Osimps,axiom, % 172.48/172.42 ! [V_b,V_a] : % 172.48/172.42 ( ( ( 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))) % 172.48/172.42 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 172.48/172.42 => 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)) ) % 172.48/172.42 & ( ~ ( 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))) % 172.48/172.42 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 172.48/172.42 => 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))) ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_negDivAlg__eqn__number__of,axiom, % 172.48/172.42 ! [V_w,V_v] : % 172.48/172.42 ( 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))) % 172.48/172.42 => ( ( 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)))) % 172.48/172.42 => 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))) ) % 172.48/172.42 & ( ~ 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)))) % 172.48/172.42 => 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)))) ) ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_negDivAlg__eqn,axiom, % 172.48/172.42 ! [V_a,V_b] : % 172.48/172.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 172.48/172.42 => ( ( 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))) % 172.48/172.42 => 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)) ) % 172.48/172.42 & ( ~ 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))) % 172.48/172.42 => 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))) ) ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_Nitpick_Orefl_H__def,axiom, % 172.48/172.42 ! [V_r_2,T_a] : % 172.48/172.42 ( c_Nitpick_Orefl_H(T_a,V_r_2) % 172.48/172.42 <=> ! [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)) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_posDivAlg__eqn__1__number__of,axiom, % 172.48/172.42 ! [V_w] : % 172.48/172.42 ( 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))) % 172.48/172.42 => ( ( 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))) % 172.48/172.42 => 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)) ) % 172.48/172.42 & ( ~ 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))) % 172.48/172.42 => 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)))) ) ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_posDivAlg_Osimps,axiom, % 172.48/172.42 ! [V_b,V_a] : % 172.48/172.42 ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 172.48/172.42 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 172.48/172.42 => 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) ) % 172.48/172.42 & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 172.48/172.42 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 172.48/172.42 => 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))) ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_posDivAlg__0,axiom, % 172.48/172.42 ! [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)) ). % 172.48/172.42 % 172.48/172.42 fof(fact_posDivAlg__correct,axiom, % 172.48/172.42 ! [V_b,V_a] : % 172.48/172.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 172.48/172.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 172.48/172.42 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),c_Divides_OposDivAlg(V_a,V_b))) ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_posDivAlg__div__mod,axiom, % 172.48/172.42 ! [V_l,V_k] : % 172.48/172.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_k)) % 172.48/172.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_l)) % 172.48/172.42 => 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)) ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_posDivAlg__eqn,axiom, % 172.48/172.42 ! [V_a,V_b] : % 172.48/172.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 172.48/172.42 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 172.48/172.42 => 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) ) % 172.48/172.42 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),V_b)) % 172.48/172.42 => 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))) ) ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_posDivAlg__eqn__number__of,axiom, % 172.48/172.42 ! [V_w,V_v] : % 172.48/172.42 ( 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))) % 172.48/172.42 => ( ( 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))) % 172.48/172.42 => 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)) ) % 172.48/172.42 & ( ~ 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))) % 172.48/172.42 => 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)))) ) ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_divmod__int__def,axiom, % 172.48/172.42 ! [V_b,V_a] : % 172.48/172.42 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 172.48/172.42 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 172.48/172.42 => c_Divides_Odivmod__int(V_a,V_b) = c_Divides_OposDivAlg(V_a,V_b) ) % 172.48/172.42 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 172.48/172.42 => ( ( V_a = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 172.48/172.42 => 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)) ) % 172.48/172.42 & ( V_a != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 172.48/172.42 => 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))) ) ) ) ) ) % 172.48/172.42 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 172.48/172.42 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 172.48/172.42 => c_Divides_Odivmod__int(V_a,V_b) = c_Divides_OnegDivAlg(V_a,V_b) ) % 172.48/172.42 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 172.48/172.42 => 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))) ) ) ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_divmod__nat__step,axiom, % 172.48/172.42 ! [V_m,V_n] : % 172.48/172.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n)) % 172.48/172.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n),V_m)) % 172.48/172.42 => 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)) ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_divmod__int__pdivmod,axiom, % 172.48/172.42 ! [V_l_2,V_k_2] : % 172.48/172.42 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 172.48/172.42 => 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)) ) % 172.48/172.42 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 172.48/172.42 => ( ( V_l_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 172.48/172.42 => 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) ) % 172.48/172.42 & ( V_l_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 172.48/172.42 => 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)))) ) ) ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_negateSnd__def,axiom, % 172.48/172.42 c_Divides_OnegateSnd = c_Product__Type_Oapsnd(tc_Int_Oint,tc_Int_Oint,tc_Int_Oint,c_Groups_Ouminus__class_Ouminus(tc_Int_Oint)) ). % 172.48/172.42 % 172.48/172.42 fof(fact_apsnd__conv,axiom, % 172.48/172.42 ! [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)) ). % 172.48/172.42 % 172.48/172.42 fof(fact_apsnd__compose,axiom, % 172.48/172.42 ! [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) ). % 172.48/172.42 % 172.48/172.42 fof(fact_divmod__nat__zero,axiom, % 172.48/172.42 ! [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) ). % 172.48/172.42 % 172.48/172.42 fof(fact_divmod__nat__base,axiom, % 172.48/172.42 ! [V_n,V_m] : % 172.48/172.42 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m),V_n)) % 172.48/172.42 => 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) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_negateSnd__eq,axiom, % 172.48/172.42 ! [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)) ). % 172.48/172.42 % 172.48/172.42 fof(fact_divmod__nat__div__mod,axiom, % 172.48/172.42 ! [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)) ). % 172.48/172.42 % 172.48/172.42 fof(fact_divmod__int__rel__neg,axiom, % 172.48/172.42 ! [V_qr,V_b,V_a] : % 172.48/172.42 ( 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)) % 172.48/172.42 => hBOOL(hAPP(c_Divides_Odivmod__int__rel(V_a,V_b),hAPP(c_Divides_OnegateSnd,V_qr))) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_divmod__nat__if,axiom, % 172.48/172.42 ! [V_m_2,V_n_2] : % 172.48/172.42 ( ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 172.48/172.42 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) % 172.48/172.42 => 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) ) % 172.48/172.42 & ( ~ ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 172.48/172.42 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) % 172.48/172.42 => 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)) ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_pdivmod__def,axiom, % 172.48/172.42 ! [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))) ). % 172.48/172.42 % 172.48/172.42 fof(fact_pdivmod__posDivAlg,axiom, % 172.48/172.42 ! [V_k,V_l] : % 172.48/172.42 ( ( V_l = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 172.48/172.42 => 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)) ) % 172.48/172.42 & ( V_l != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 172.48/172.42 => 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)) ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_divmod__int__code,axiom, % 172.48/172.42 ! [V_l_2,V_k_2] : % 172.48/172.42 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 172.48/172.42 => 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)) ) % 172.48/172.42 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 172.48/172.42 => ( ( V_l_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 172.48/172.42 => 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) ) % 172.48/172.42 & ( V_l_2 != c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 172.48/172.42 => 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)))) ) ) ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_code__numeral_Osize_I4_J,axiom, % 172.48/172.42 ! [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))) ). % 172.48/172.42 % 172.48/172.42 fof(fact_divmod__nat__rel__mult1__eq,axiom, % 172.48/172.42 ! [V_a,V_r,V_q,V_c,V_b] : % 172.48/172.42 ( 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))) % 172.48/172.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c)) % 172.48/172.42 => 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)))) ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_divmod__nat__rel__mult2__eq,axiom, % 172.48/172.42 ! [V_c,V_r,V_q,V_b,V_a] : % 172.48/172.42 ( 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))) % 172.48/172.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_b)) % 172.48/172.42 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c)) % 172.48/172.42 => 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)))) ) ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_divmod__nat__rel__unique,axiom, % 172.48/172.42 ! [V_qr_H,V_qr,V_n,V_m] : % 172.48/172.42 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr)) % 172.48/172.42 => ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr_H)) % 172.48/172.42 => V_qr = V_qr_H ) ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_divmod__nat__eq,axiom, % 172.48/172.42 ! [V_qr,V_n,V_m] : % 172.48/172.42 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),V_qr)) % 172.48/172.42 => c_Divides_Odivmod__nat(V_m,V_n) = V_qr ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_divmod__nat__rel__divmod__nat,axiom, % 172.48/172.42 ! [V_n,V_m] : hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m,V_n),c_Divides_Odivmod__nat(V_m,V_n))) ). % 172.48/172.42 % 172.48/172.42 fof(fact_divmod__nat__def,axiom, % 172.48/172.42 ! [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)) ). % 172.48/172.42 % 172.48/172.42 fof(fact_mod__eq,axiom, % 172.48/172.42 ! [V_r,V_q,V_n,V_m] : % 172.48/172.42 ( 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))) % 172.48/172.42 => c_Divides_Odiv__class_Omod(tc_Nat_Onat,V_m,V_n) = V_r ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_div__eq,axiom, % 172.48/172.42 ! [V_r,V_q,V_n,V_m] : % 172.48/172.42 ( 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))) % 172.48/172.42 => hAPP(hAPP(c_Divides_Odiv__class_Odiv(tc_Nat_Onat),V_m),V_n) = V_q ) ). % 172.48/172.42 % 172.48/172.42 fof(fact_divmod__nat__rel,axiom, % 172.48/172.42 ! [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)))) ). % 172.48/172.42 % 172.48/172.42 fof(fact_code__numeral_Osize_I3_J,axiom, % 172.48/172.42 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) ). % 172.48/172.42 % 172.48/172.42 fof(fact_divmod__nat__rel__add1__eq,axiom, % 172.48/172.42 ! [V_br,V_bq,V_b,V_ar,V_aq,V_c,V_a] : % 172.48/172.42 ( 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))) % 172.48/172.43 => ( 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))) % 172.48/172.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_c)) % 172.48/172.43 => 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)))) ) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_negDivAlg_Opsimps,axiom, % 172.48/172.43 ! [V_b_2,V_a_2] : % 172.48/172.43 ( 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))) % 172.48/172.43 => ( ( ( 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))) % 172.48/172.43 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 172.48/172.43 => 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)) ) % 172.48/172.43 & ( ~ ( 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))) % 172.48/172.43 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 172.48/172.43 => 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))) ) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_posDivAlg_Opsimps,axiom, % 172.48/172.43 ! [V_b_2,V_a_2] : % 172.48/172.43 ( 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))) % 172.48/172.43 => ( ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),V_b_2)) % 172.48/172.43 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 172.48/172.43 => 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) ) % 172.48/172.43 & ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a_2),V_b_2)) % 172.48/172.43 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 172.48/172.43 => 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))) ) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_mod__pos__neg__1__number__of,axiom, % 172.48/172.43 ! [V_w] : % 172.48/172.43 ( 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))) % 172.48/172.43 => 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))))) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_snd__apsnd,axiom, % 172.48/172.43 ! [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)) ). % 172.48/172.43 % 172.48/172.43 fof(fact_apsnd__eq__conv,axiom, % 172.48/172.43 ! [V_g_2,V_x_2,V_f_2,T_a,T_b,T_c] : % 172.48/172.43 ( 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) % 172.48/172.43 <=> 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)) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_snd__eqD,axiom, % 172.48/172.43 ! [V_a,V_y,V_x,T_a,T_b] : % 172.48/172.43 ( 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 % 172.48/172.43 => V_y = V_a ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_snd__conv,axiom, % 172.48/172.43 ! [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 ). % 172.48/172.43 % 172.48/172.43 fof(fact_snd__def,axiom, % 172.48/172.43 ! [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) ). % 172.48/172.43 % 172.48/172.43 fof(fact_mod__int__def,axiom, % 172.48/172.43 ! [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)) ). % 172.48/172.43 % 172.48/172.43 fof(fact_mod__neg__pos,axiom, % 172.48/172.43 ! [V_b,V_a] : % 172.48/172.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 172.48/172.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 172.48/172.43 => 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)) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_mod__pos__pos,axiom, % 172.48/172.43 ! [V_b,V_a] : % 172.48/172.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 172.48/172.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 172.48/172.43 => 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)) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_mod__pos__pos__1__number__of,axiom, % 172.48/172.43 ! [V_w] : % 172.48/172.43 ( 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))) % 172.48/172.43 => 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))) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_mod__pos__neg,axiom, % 172.48/172.43 ! [V_b,V_a] : % 172.48/172.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 172.48/172.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 172.48/172.43 => 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)))) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_mod__neg__neg,axiom, % 172.48/172.43 ! [V_b,V_a] : % 172.48/172.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 172.48/172.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 172.48/172.43 => 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)))) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_norm__frac_Opsimps,axiom, % 172.48/172.43 ! [V_b_2,V_a_2] : % 172.48/172.43 ( 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))) % 172.48/172.43 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 172.48/172.43 => 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)) ) % 172.48/172.43 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b_2),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 172.48/172.43 => ( ( ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 172.48/172.43 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 172.48/172.43 => 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)) ) % 172.48/172.43 & ( ~ ( V_a_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) % 172.48/172.43 | V_b_2 = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) % 172.48/172.43 => 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))) ) ) ) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_negDivAlg_Opinduct,axiom, % 172.48/172.43 ! [V_P_2,V_a1_2,V_a0_2] : % 172.48/172.43 ( 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))) % 172.48/172.43 => ( ! [B_a,B_b] : % 172.48/172.43 ( 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))) % 172.48/172.43 => ( ( ~ ( 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))) % 172.48/172.43 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 172.48/172.43 => 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))) ) % 172.48/172.43 => hBOOL(hAPP(hAPP(V_P_2,B_a),B_b)) ) ) % 172.48/172.43 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_posDivAlg_Opinduct,axiom, % 172.48/172.43 ! [V_P_2,V_a1_2,V_a0_2] : % 172.48/172.43 ( 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))) % 172.48/172.43 => ( ! [B_a,B_b] : % 172.48/172.43 ( 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))) % 172.48/172.43 => ( ( ~ ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_a),B_b)) % 172.48/172.43 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) ) % 172.48/172.43 => 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))) ) % 172.48/172.43 => hBOOL(hAPP(hAPP(V_P_2,B_a),B_b)) ) ) % 172.48/172.43 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_mod__nat__def,axiom, % 172.48/172.43 ! [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)) ). % 172.48/172.43 % 172.48/172.43 fof(fact_accp__subset,axiom, % 172.48/172.43 ! [V_R2_2,V_R1_2,T_a] : % 172.48/172.43 ( 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)) % 172.48/172.43 => 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))) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_norm__frac_Opinduct,axiom, % 172.48/172.43 ! [V_P_2,V_a1_2,V_a0_2] : % 172.48/172.43 ( 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))) % 172.48/172.43 => ( ! [B_a,B_b] : % 172.48/172.43 ( 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))) % 172.48/172.43 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 172.48/172.43 => 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))) ) % 172.48/172.43 => hBOOL(hAPP(hAPP(V_P_2,B_a),B_b)) ) ) % 172.48/172.43 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_div__pos__neg__1__number__of,axiom, % 172.48/172.43 ! [V_w] : % 172.48/172.43 ( 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))) % 172.48/172.43 => 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))))) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_Pair__fst__snd__eq,axiom, % 172.48/172.43 ! [T_b,T_a,V_t_2,V_s_2] : % 172.48/172.43 ( V_s_2 = V_t_2 % 172.48/172.43 <=> ( hAPP(c_Product__Type_Ofst(T_a,T_b),V_s_2) = hAPP(c_Product__Type_Ofst(T_a,T_b),V_t_2) % 172.48/172.43 & hAPP(c_Product__Type_Osnd(T_a,T_b),V_s_2) = hAPP(c_Product__Type_Osnd(T_a,T_b),V_t_2) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_prod__eqI,axiom, % 172.48/172.43 ! [V_q,V_p,T_b,T_a] : % 172.48/172.43 ( hAPP(c_Product__Type_Ofst(T_a,T_b),V_p) = hAPP(c_Product__Type_Ofst(T_a,T_b),V_q) % 172.48/172.43 => ( hAPP(c_Product__Type_Osnd(T_a,T_b),V_p) = hAPP(c_Product__Type_Osnd(T_a,T_b),V_q) % 172.48/172.43 => V_p = V_q ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_fst__apsnd,axiom, % 172.48/172.43 ! [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) ). % 172.48/172.43 % 172.48/172.43 fof(fact_fst__def,axiom, % 172.48/172.43 ! [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) ). % 172.48/172.43 % 172.48/172.43 fof(fact_fst__eqD,axiom, % 172.48/172.43 ! [V_a,V_y,V_x,T_b,T_a] : % 172.48/172.43 ( 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 % 172.48/172.43 => V_x = V_a ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_fst__conv,axiom, % 172.48/172.43 ! [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 ). % 172.48/172.43 % 172.48/172.43 fof(fact_pair__collapse,axiom, % 172.48/172.43 ! [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 ). % 172.48/172.43 % 172.48/172.43 fof(fact_surjective__pairing,axiom, % 172.48/172.43 ! [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)) ). % 172.48/172.43 % 172.48/172.43 fof(fact_prod__case__beta,axiom, % 172.48/172.43 ! [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)) ). % 172.48/172.43 % 172.48/172.43 fof(fact_div__int__def,axiom, % 172.48/172.43 ! [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)) ). % 172.48/172.43 % 172.48/172.43 fof(fact_split__comp__eq,axiom, % 172.48/172.43 ! [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)) ). % 172.48/172.43 % 172.48/172.43 fof(fact_split__beta,axiom, % 172.48/172.43 ! [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)) ). % 172.48/172.43 % 172.48/172.43 fof(fact_split__def,axiom, % 172.48/172.43 ! [V_p_2,V_ca_2,T_a,T_c,T_b] : hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,T_a),V_ca_2),V_p_2) = hAPP(hAPP(V_ca_2,hAPP(c_Product__Type_Ofst(T_b,T_c),V_p_2)),hAPP(c_Product__Type_Osnd(T_b,T_c),V_p_2)) ). % 172.48/172.43 % 172.48/172.43 fof(fact_split__comp,axiom, % 172.48/172.43 ! [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)) ). % 172.48/172.43 % 172.48/172.43 fof(fact_accp__downward,axiom, % 172.48/172.43 ! [V_a_2,V_b_2,V_r_2,T_a] : % 172.48/172.43 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_b_2)) % 172.48/172.43 => ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2)) % 172.48/172.43 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_a_2)) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_accp_Oequations,axiom, % 172.48/172.43 ! [V_a_2,V_r_2,T_a] : % 172.48/172.43 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_a_2)) % 172.48/172.43 <=> ! [B_x] : % 172.48/172.43 ( hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2)) % 172.48/172.43 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),B_x)) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_accp_Osimps,axiom, % 172.48/172.43 ! [V_a_2,V_r_2,T_a] : % 172.48/172.43 ( hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_a_2)) % 172.48/172.43 <=> ! [B_x] : % 172.48/172.43 ( hBOOL(hAPP(hAPP(V_r_2,B_x),V_a_2)) % 172.48/172.43 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),B_x)) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_The__split,axiom, % 172.48/172.43 ! [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))) ). % 172.48/172.43 % 172.48/172.43 fof(fact_div__neg__pos,axiom, % 172.48/172.43 ! [V_b,V_a] : % 172.48/172.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 172.48/172.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 172.48/172.43 => 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)) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_div__pos__pos,axiom, % 172.48/172.43 ! [V_b,V_a] : % 172.48/172.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 172.48/172.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_b)) % 172.48/172.43 => 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)) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_div__pos__pos__1__number__of,axiom, % 172.48/172.43 ! [V_w] : % 172.48/172.43 ( 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))) % 172.48/172.43 => 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))) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_div__pos__neg,axiom, % 172.48/172.43 ! [V_b,V_a] : % 172.48/172.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_a)) % 172.48/172.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 172.48/172.43 => 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)))) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_div__neg__neg,axiom, % 172.48/172.43 ! [V_b,V_a] : % 172.48/172.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_a),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 172.48/172.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_b),c_Groups_Ozero__class_Ozero(tc_Int_Oint))) % 172.48/172.43 => 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)))) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_prod__size__simp,axiom, % 172.48/172.43 ! [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))) ). % 172.48/172.43 % 172.48/172.43 fof(fact_nat__gcd_Opsimps,axiom, % 172.48/172.43 ! [V_y_2,V_x_2] : % 172.48/172.43 ( 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))) % 172.48/172.43 => ( ( V_y_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 172.48/172.43 => c_Nitpick_Onat__gcd(V_x_2,V_y_2) = V_x_2 ) % 172.48/172.43 & ( V_y_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 172.48/172.43 => 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)) ) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_exI__realizer,axiom, % 172.48/172.43 ! [T_a,T_b,V_x_2,V_y_2,V_P_2] : % 172.48/172.43 ( hBOOL(hAPP(hAPP(V_P_2,V_y_2),V_x_2)) % 172.48/172.43 => 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)))) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_div__nat__def,axiom, % 172.48/172.43 ! [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)) ). % 172.48/172.43 % 172.48/172.43 fof(fact_divmod__nat__rel__def,axiom, % 172.48/172.43 ! [V_qr_2,V_n_2,V_m_2] : % 172.48/172.43 ( hBOOL(hAPP(c_Divides_Odivmod__nat__rel(V_m_2,V_n_2),V_qr_2)) % 172.48/172.43 <=> ( 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)) % 172.48/172.43 & ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 172.48/172.43 => hAPP(c_Product__Type_Ofst(tc_Nat_Onat,tc_Nat_Onat),V_qr_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 172.48/172.43 & ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 172.48/172.43 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) % 172.48/172.43 => ( 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))) % 172.48/172.43 & 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)) ) ) % 172.48/172.43 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_n_2)) % 172.48/172.43 => ( 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))) % 172.48/172.43 & 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))) ) ) ) ) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_conjI__realizer,axiom, % 172.48/172.43 ! [T_b,T_a,V_q_2,V_Q_2,V_p_2,V_P_2] : % 172.48/172.43 ( hBOOL(hAPP(V_P_2,V_p_2)) % 172.48/172.43 => ( hBOOL(hAPP(V_Q_2,V_q_2)) % 172.48/172.43 => ( 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)))) % 172.48/172.43 & 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)))) ) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_nat_Osize_I2_J,axiom, % 172.48/172.43 ! [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))) ). % 172.48/172.43 % 172.48/172.43 fof(fact_in__measure,axiom, % 172.48/172.43 ! [V_f_2,V_y_2,V_x_2,T_a] : % 172.48/172.43 ( 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))) % 172.48/172.43 <=> 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))) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_nat__def,axiom, % 172.48/172.43 ! [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)))))) ). % 172.48/172.43 % 172.48/172.43 fof(fact_Rep__Integ__inject,axiom, % 172.48/172.43 ! [V_y_2,V_x_2] : % 172.48/172.43 ( hAPP(c_Int_ORep__Integ,V_x_2) = hAPP(c_Int_ORep__Integ,V_y_2) % 172.48/172.43 <=> V_x_2 = V_y_2 ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_nat_Osize_I1_J,axiom, % 172.48/172.43 c_Nat_Onat_Onat__size(c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 172.48/172.43 % 172.48/172.43 fof(fact_nat__gcd_Opinduct,axiom, % 172.48/172.43 ! [V_P_2,V_a1_2,V_a0_2] : % 172.48/172.43 ( 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))) % 172.48/172.43 => ( ! [B_x,B_y] : % 172.48/172.43 ( 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))) % 172.48/172.43 => ( ( B_y != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 172.48/172.43 => hBOOL(hAPP(hAPP(V_P_2,B_y),c_Divides_Odiv__class_Omod(tc_Nat_Onat,B_x,B_y))) ) % 172.48/172.43 => hBOOL(hAPP(hAPP(V_P_2,B_x),B_y)) ) ) % 172.48/172.43 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_mlex__leq,axiom, % 172.48/172.43 ! [V_R_2,T_a,V_y_2,V_x_2,V_f_2] : % 172.48/172.43 ( 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))) % 172.48/172.43 => ( 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)) % 172.48/172.43 => 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))) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_mlex__less,axiom, % 172.48/172.43 ! [V_R_2,T_a,V_y_2,V_x_2,V_f_2] : % 172.48/172.43 ( 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))) % 172.48/172.43 => 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))) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_finite__psubset__def,axiom, % 172.48/172.43 ! [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)))) ). % 172.48/172.43 % 172.48/172.43 fof(fact_nat_Osize_I4_J,axiom, % 172.48/172.43 ! [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))) ). % 172.48/172.43 % 172.48/172.43 fof(fact_prod_Orecs,axiom, % 172.48/172.43 ! [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) ). % 172.48/172.43 % 172.48/172.43 fof(fact_nat__size,axiom, % 172.48/172.43 ! [V_n] : hAPP(c_Nat_Osize__class_Osize(tc_Nat_Onat),V_n) = V_n ). % 172.48/172.43 % 172.48/172.43 fof(fact_nat_Osize_I3_J,axiom, % 172.48/172.43 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) ). % 172.48/172.43 % 172.48/172.43 fof(fact_in__finite__psubset,axiom, % 172.48/172.43 ! [V_B_2,V_A_2,T_a] : % 172.48/172.43 ( 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))) % 172.48/172.43 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 172.48/172.43 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_B_2)) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_in__lex__prod,axiom, % 172.48/172.43 ! [V_s_2,V_r_2,V_b_H_2,V_a_H_2,V_b_2,V_a_2,T_b,T_a] : % 172.48/172.43 ( 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))) % 172.48/172.43 <=> ( 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)) % 172.48/172.43 | ( V_a_2 = V_a_H_2 % 172.48/172.43 & 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)) ) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_apfst__apsnd,axiom, % 172.48/172.43 ! [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))) ). % 172.48/172.43 % 172.48/172.43 fof(fact_apsnd__apfst,axiom, % 172.48/172.43 ! [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))) ). % 172.48/172.43 % 172.48/172.43 fof(fact_apfst__conv,axiom, % 172.48/172.43 ! [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) ). % 172.48/172.43 % 172.48/172.43 fof(fact_apfst__compose,axiom, % 172.48/172.43 ! [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) ). % 172.48/172.43 % 172.48/172.43 fof(fact_apfst__eq__conv,axiom, % 172.48/172.43 ! [V_g_2,V_x_2,V_f_2,T_b,T_a,T_c] : % 172.48/172.43 ( 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) % 172.48/172.43 <=> 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)) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_fst__apfst,axiom, % 172.48/172.43 ! [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)) ). % 172.48/172.43 % 172.48/172.43 fof(fact_snd__apfst,axiom, % 172.48/172.43 ! [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) ). % 172.48/172.43 % 172.48/172.43 fof(fact_apsnd__apfst__commute,axiom, % 172.48/172.43 ! [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)) ). % 172.48/172.43 % 172.48/172.43 fof(fact_same__fstI,axiom, % 172.48/172.43 ! [T_a,V_R_2,V_y_2,V_y_H_2,T_b,V_x_2,V_P_2] : % 172.48/172.43 ( hBOOL(hAPP(V_P_2,V_x_2)) % 172.48/172.43 => ( 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))) % 172.48/172.43 => 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))) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_pair__lessI2,axiom, % 172.48/172.43 ! [V_t_2,V_s_2,V_b_2,V_a_2] : % 172.48/172.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_a_2),V_b_2)) % 172.48/172.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_s_2),V_t_2)) % 172.48/172.43 => 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)) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_max__ext__additive,axiom, % 172.48/172.43 ! [V_D_2,V_C_2,V_R_2,V_B_2,V_A_2,T_a] : % 172.48/172.43 ( 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))) % 172.48/172.43 => ( 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))) % 172.48/172.43 => 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))) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_pair__lessI1,axiom, % 172.48/172.43 ! [V_t_2,V_s_2,V_b_2,V_a_2] : % 172.48/172.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2)) % 172.48/172.43 => 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)) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_max__extp__max__ext__eq,axiom, % 172.48/172.43 ! [V_xa_2,V_x_2,V_R_2,T_a] : % 172.48/172.43 ( 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) % 172.48/172.43 <=> 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))) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_pair__leqI2,axiom, % 172.48/172.43 ! [V_t_2,V_s_2,V_b_2,V_a_2] : % 172.48/172.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_a_2),V_b_2)) % 172.48/172.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_s_2),V_t_2)) % 172.48/172.43 => 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)) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_smin__insertI,axiom, % 172.48/172.43 ! [V_YS_2,V_y_2,V_XS_2,V_x_2] : % 172.48/172.43 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2)) % 172.48/172.43 => ( 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)) % 172.48/172.43 => ( 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)) % 172.48/172.43 => 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)) ) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_smin__emptyI,axiom, % 172.48/172.43 ! [V_X_2] : % 172.48/172.43 ( V_X_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)) % 172.48/172.43 => 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)) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_pair__leqI1,axiom, % 172.48/172.43 ! [V_t_2,V_s_2,V_b_2,V_a_2] : % 172.48/172.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_a_2),V_b_2)) % 172.48/172.43 => 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)) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_wmax__insertI,axiom, % 172.48/172.43 ! [V_XS_2,V_x_2,V_YS_2,V_y_2] : % 172.48/172.43 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_YS_2)) % 172.48/172.43 => ( 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)) % 172.48/172.43 => ( 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)) % 172.48/172.43 => 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)) ) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_wmin__insertI,axiom, % 172.48/172.43 ! [V_YS_2,V_y_2,V_XS_2,V_x_2] : % 172.48/172.43 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_x_2),V_XS_2)) % 172.48/172.43 => ( 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)) % 172.48/172.43 => ( 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)) % 172.48/172.43 => 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)) ) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_smax__insertI,axiom, % 172.48/172.43 ! [V_X_2,V_x_2,V_Y_2,V_y_2] : % 172.48/172.43 ( hBOOL(hAPP(hAPP(c_member(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_y_2),V_Y_2)) % 172.48/172.43 => ( 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)) % 172.48/172.43 => ( 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)) % 172.48/172.43 => 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)) ) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_max__strict__def,axiom, % 172.48/172.43 c_FunDef_Omax__strict = c_Wellfounded_Omax__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ). % 172.48/172.43 % 172.48/172.43 fof(fact_wmin__emptyI,axiom, % 172.48/172.43 ! [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)) ). % 172.48/172.43 % 172.48/172.43 fof(fact_wmax__emptyI,axiom, % 172.48/172.43 ! [V_X_2] : % 172.48/172.43 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_X_2)) % 172.48/172.43 => 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)) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_smax__emptyI,axiom, % 172.48/172.43 ! [V_Y_2] : % 172.48/172.43 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(tc_Nat_Onat,tc_Nat_Onat)),V_Y_2)) % 172.48/172.43 => ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)) % 172.48/172.43 => 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)) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_max__weak__def,axiom, % 172.48/172.43 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)))) ). % 172.48/172.43 % 172.48/172.43 fof(fact_min__weak__def,axiom, % 172.48/172.43 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)))) ). % 172.48/172.43 % 172.48/172.43 fof(fact_max__rpair__set,axiom, % 172.48/172.43 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)) ). % 172.48/172.43 % 172.48/172.43 fof(fact_min__rpair__set,axiom, % 172.48/172.43 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)) ). % 172.48/172.43 % 172.48/172.43 fof(fact_min__strict__def,axiom, % 172.48/172.43 c_FunDef_Omin__strict = c_Wellfounded_Omin__ext(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ). % 172.48/172.43 % 172.48/172.43 fof(fact_less__than__iff,axiom, % 172.48/172.43 ! [V_y_2,V_x_2] : % 172.48/172.43 ( 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)) % 172.48/172.43 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_x_2),V_y_2)) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_intrel__iff,axiom, % 172.48/172.43 ! [V_v_2,V_u_2,V_y_2,V_x_2] : % 172.48/172.43 ( 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)) % 172.48/172.43 <=> 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) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_rp__inv__image__rp,axiom, % 172.48/172.43 ! [V_f_2,T_b,V_P_2,T_a] : % 172.48/172.43 ( c_FunDef_Oreduction__pair(T_a,V_P_2) % 172.48/172.43 => c_FunDef_Oreduction__pair(T_b,hAPP(hAPP(c_FunDef_Orp__inv__image(T_a,T_b),V_P_2),V_f_2)) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_pair__less__def,axiom, % 172.48/172.43 c_FunDef_Opair__less = c_Wellfounded_Olex__prod(tc_Nat_Onat,tc_Nat_Onat,c_Wellfounded_Oless__than,c_Wellfounded_Oless__than) ). % 172.48/172.43 % 172.48/172.43 fof(fact_mlex__prod__def,axiom, % 172.48/172.43 ! [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))) ). % 172.48/172.43 % 172.48/172.43 fof(fact_rp__inv__image__def,axiom, % 172.48/172.43 ! [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))) ). % 172.48/172.43 % 172.48/172.43 fof(fact_equiv__intrel__iff,axiom, % 172.48/172.43 ! [V_y_2,V_x_2] : % 172.48/172.43 ( 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)))) % 172.48/172.43 <=> 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)) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_measure__def,axiom, % 172.48/172.43 ! [T_a] : c_Wellfounded_Omeasure(T_a) = hAPP(c_Relation_Oinv__image(tc_Nat_Onat,T_a),c_Wellfounded_Oless__than) ). % 172.48/172.43 % 172.48/172.43 fof(fact_Image__singleton,axiom, % 172.48/172.43 ! [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)) ). % 172.48/172.43 % 172.48/172.43 fof(fact_Image__singleton__iff,axiom, % 172.48/172.43 ! [V_a_2,V_r_2,T_b,V_b_2,T_a] : % 172.48/172.43 ( 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)))))) % 172.48/172.43 <=> 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)) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_inv__image__def,axiom, % 172.48/172.43 ! [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))) ). % 172.48/172.43 % 172.48/172.43 fof(fact_Image__empty,axiom, % 172.48/172.43 ! [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)) ). % 172.48/172.43 % 172.48/172.43 fof(fact_Image__Un,axiom, % 172.48/172.43 ! [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)) ). % 172.48/172.43 % 172.48/172.43 fof(fact_Image__UN,axiom, % 172.48/172.43 ! [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)) ). % 172.48/172.43 % 172.48/172.43 fof(fact_Image__Int__subset,axiom, % 172.48/172.43 ! [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)))) ). % 172.48/172.43 % 172.48/172.43 fof(fact_Image__mono,axiom, % 172.48/172.43 ! [V_A_2,V_A_H_2,V_r_2,V_r_H_2,T_b,T_a] : % 172.48/172.43 ( 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)) % 172.48/172.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_H_2),V_A_2)) % 172.48/172.43 => 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))) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_Un__Image,axiom, % 172.48/172.43 ! [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)) ). % 172.48/172.43 % 172.48/172.43 fof(fact_in__inv__image,axiom, % 172.48/172.43 ! [V_f_2,V_r_2,T_b,V_y_2,V_x_2,T_a] : % 172.48/172.43 ( 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))) % 172.48/172.43 <=> 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)) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_Image__iff,axiom, % 172.48/172.43 ! [V_A_2,V_r_2,T_b,V_b_2,T_a] : % 172.48/172.43 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(c_Relation_OImage(T_b,T_a,V_r_2),V_A_2))) % 172.48/172.43 <=> ? [B_x] : % 172.48/172.43 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 172.48/172.43 & 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)) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_rev__ImageI,axiom, % 172.48/172.43 ! [V_r_2,V_b_2,T_b,V_A_2,V_a_2,T_a] : % 172.48/172.43 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 172.48/172.43 => ( 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)) % 172.48/172.43 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_OImage(T_a,T_b,V_r_2),V_A_2))) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_Image__eq__UN,axiom, % 172.48/172.43 ! [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))))) ). % 172.48/172.43 % 172.48/172.43 fof(fact_of__int,axiom, % 172.48/172.43 ! [V_j_2,V_i_2,T_a] : % 172.48/172.43 ( class_Rings_Oring__1(T_a) % 172.48/172.43 => 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)) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_One__int__def,axiom, % 172.48/172.43 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))))) ). % 172.48/172.43 % 172.48/172.43 fof(fact_mult,axiom, % 172.48/172.43 ! [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))))) ). % 172.48/172.43 % 172.48/172.43 fof(fact_Rep__Integ__inverse,axiom, % 172.48/172.43 ! [V_x_2] : hAPP(c_Int_OAbs__Integ,hAPP(c_Int_ORep__Integ,V_x_2)) = V_x_2 ). % 172.48/172.43 % 172.48/172.43 fof(fact_minus,axiom, % 172.48/172.43 ! [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))))) ). % 172.48/172.43 % 172.48/172.43 fof(fact_Zero__int__def,axiom, % 172.48/172.43 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))))) ). % 172.48/172.43 % 172.48/172.43 fof(fact_int__def,axiom, % 172.48/172.43 ! [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))))) ). % 172.48/172.43 % 172.48/172.43 fof(fact_add,axiom, % 172.48/172.43 ! [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))))) ). % 172.48/172.43 % 172.48/172.43 fof(fact_nat,axiom, % 172.48/172.43 ! [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) ). % 172.48/172.43 % 172.48/172.43 fof(fact_minus__int__def,axiom, % 172.48/172.43 ! [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))))))) ). % 172.48/172.43 % 172.48/172.43 fof(fact_less,axiom, % 172.48/172.43 ! [V_v_2,V_u_2,V_y_2,V_x_2] : % 172.48/172.43 ( 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))))))) % 172.48/172.43 <=> 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))) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_le,axiom, % 172.48/172.43 ! [V_v_2,V_u_2,V_y_2,V_x_2] : % 172.48/172.43 ( 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))))))) % 172.48/172.43 <=> 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))) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_irrefl__def,axiom, % 172.48/172.43 ! [V_r_2,T_a] : % 172.48/172.43 ( c_Relation_Oirrefl(T_a,V_r_2) % 172.48/172.43 <=> ! [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)) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_eq__Abs__Integ,axiom, % 172.48/172.43 ! [V_z_2] : % 172.48/172.43 ~ ! [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))))) ). % 172.48/172.43 % 172.48/172.43 fof(fact_Field__insert,axiom, % 172.48/172.43 ! [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)) ). % 172.48/172.43 % 172.48/172.43 fof(fact_Field__empty,axiom, % 172.48/172.43 ! [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)) ). % 172.48/172.43 % 172.48/172.43 fof(fact_mono__Field,axiom, % 172.48/172.43 ! [V_s_2,V_r_2,T_a] : % 172.48/172.43 ( 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)) % 172.48/172.43 => 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))) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_Field__Un,axiom, % 172.48/172.43 ! [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)) ). % 172.48/172.43 % 172.48/172.43 fof(fact_finite__Field,axiom, % 172.48/172.43 ! [V_r_2,T_a] : % 172.48/172.43 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2)) % 172.48/172.43 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Relation_OField(T_a),V_r_2))) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_Id__on__def,axiom, % 172.48/172.43 ! [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)))) ). % 172.48/172.43 % 172.48/172.43 fof(fact_quotient__def,axiom, % 172.48/172.43 ! [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)))) ). % 172.48/172.43 % 172.48/172.43 fof(fact_ImageE,axiom, % 172.48/172.43 ! [V_A_2,V_r_2,T_b,V_b_2,T_a] : % 172.48/172.43 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(c_Relation_OImage(T_b,T_a,V_r_2),V_A_2))) % 172.48/172.43 => ~ ! [B_x] : % 172.48/172.43 ( 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)) % 172.48/172.43 => ~ hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_quotient__empty,axiom, % 172.48/172.43 ! [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)) ). % 172.48/172.43 % 172.48/172.43 fof(fact_quotient__is__empty2,axiom, % 172.48/172.43 ! [V_r_2,V_A_2,T_a] : % 172.48/172.43 ( 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) % 172.48/172.43 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_quotient__is__empty,axiom, % 172.48/172.43 ! [V_r_2,V_A_2,T_a] : % 172.48/172.43 ( 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)) % 172.48/172.43 <=> V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_Id__on__def_H,axiom, % 172.48/172.43 ! [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)) ). % 172.48/172.43 % 172.48/172.43 fof(fact_Id__on__empty,axiom, % 172.48/172.43 ! [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)) ). % 172.48/172.43 % 172.48/172.43 fof(fact_Image__Id__on,axiom, % 172.48/172.43 ! [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) ). % 172.48/172.43 % 172.48/172.43 fof(fact_quotientI,axiom, % 172.48/172.43 ! [V_r_2,V_A_2,V_x_2,T_a] : % 172.48/172.43 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 172.48/172.43 => 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))) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_Id__on__eqI,axiom, % 172.48/172.43 ! [V_A_2,T_a,V_b_2,V_a_2] : % 172.48/172.43 ( V_a_2 = V_b_2 % 172.48/172.43 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 172.48/172.43 => 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))) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_Id__on__iff,axiom, % 172.48/172.43 ! [V_A_2,V_y_2,V_x_2,T_a] : % 172.48/172.43 ( 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))) % 172.48/172.43 <=> ( V_x_2 = V_y_2 % 172.48/172.43 & hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_singleton__quotient,axiom, % 172.48/172.43 ! [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))) ). % 172.48/172.43 % 172.48/172.43 fof(fact_equiv__class__nondisjoint,axiom, % 172.48/172.43 ! [V_b_2,V_a_2,V_x_2,V_r_2,V_A_2,T_a] : % 172.48/172.43 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 172.48/172.43 => ( 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))))))) % 172.48/172.43 => 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)) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_subset__equiv__class,axiom, % 172.48/172.43 ! [V_a_2,V_b_2,V_r_2,V_A_2,T_a] : % 172.48/172.43 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 172.48/172.43 => ( 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)))))) % 172.48/172.43 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),V_A_2)) % 172.48/172.43 => 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)) ) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_quotientE,axiom, % 172.48/172.43 ! [V_r_2,V_A_2,V_X_2,T_a] : % 172.48/172.43 ( 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))) % 172.48/172.43 => ~ ! [B_x] : % 172.48/172.43 ( 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)))) % 172.48/172.43 => ~ hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_equiv__intrel,axiom, % 172.48/172.43 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) ). % 172.48/172.43 % 172.48/172.43 fof(fact_equiv__class__self,axiom, % 172.48/172.43 ! [V_a_2,V_r_2,V_A_2,T_a] : % 172.48/172.43 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 172.48/172.43 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 172.48/172.43 => 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)))))) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_quotient__disj,axiom, % 172.48/172.43 ! [V_Y_2,V_X_2,V_r_2,V_A_2,T_a] : % 172.48/172.43 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 172.48/172.43 => ( 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))) % 172.48/172.43 => ( 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))) % 172.48/172.43 => ( V_X_2 = V_Y_2 % 172.48/172.43 | 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)) ) ) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_equiv__class__eq,axiom, % 172.48/172.43 ! [V_b_2,V_a_2,V_r_2,V_A_2,T_a] : % 172.48/172.43 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 172.48/172.43 => ( 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)) % 172.48/172.43 => 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)))) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_quotient__eq__iff,axiom, % 172.48/172.43 ! [V_y_2,V_x_2,V_Y_2,V_X_2,V_r_2,V_A_2,T_a] : % 172.48/172.43 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 172.48/172.43 => ( 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))) % 172.48/172.43 => ( 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))) % 172.48/172.43 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_X_2)) % 172.48/172.43 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_Y_2)) % 172.48/172.43 => ( V_X_2 = V_Y_2 % 172.48/172.43 <=> 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)) ) ) ) ) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_quotient__eqI,axiom, % 172.48/172.43 ! [V_y_2,V_x_2,V_Y_2,V_X_2,V_r_2,V_A_2,T_a] : % 172.48/172.43 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 172.48/172.43 => ( 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))) % 172.48/172.43 => ( 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))) % 172.48/172.43 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_X_2)) % 172.48/172.43 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_Y_2)) % 172.48/172.43 => ( 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)) % 172.48/172.43 => V_X_2 = V_Y_2 ) ) ) ) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_eq__equiv__class,axiom, % 172.48/172.43 ! [V_A_2,V_b_2,V_a_2,V_r_2,T_a] : % 172.48/172.43 ( 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)))) % 172.48/172.43 => ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 172.48/172.43 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),V_A_2)) % 172.48/172.43 => 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)) ) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_eq__equiv__class__iff,axiom, % 172.48/172.43 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_a] : % 172.48/172.43 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 172.48/172.43 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 172.48/172.43 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) % 172.48/172.43 => ( 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)))) % 172.48/172.43 <=> 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)) ) ) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_equiv__class__eq__iff,axiom, % 172.48/172.43 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_a] : % 172.48/172.43 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 172.48/172.43 => ( 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)) % 172.48/172.43 <=> ( 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)))) % 172.48/172.43 & hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 172.48/172.43 & hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) ) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_equiv__class__subset,axiom, % 172.48/172.43 ! [V_b_2,V_a_2,V_r_2,V_A_2,T_a] : % 172.48/172.43 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 172.48/172.43 => ( 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)) % 172.48/172.43 => 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)))))) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_eq__equiv__class__iff2,axiom, % 172.48/172.43 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_a] : % 172.48/172.43 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 172.48/172.43 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 172.48/172.43 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) % 172.48/172.43 => ( 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) % 172.48/172.43 <=> 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)) ) ) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_UN__equiv__class2,axiom, % 172.48/172.43 ! [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] : % 172.48/172.43 ( c_Equiv__Relations_Oequiv(T_a,V_A1_2,V_r1_2) % 172.48/172.43 => ( c_Equiv__Relations_Oequiv(T_b,V_A2_2,V_r2_2) % 172.48/172.43 => ( c_Equiv__Relations_Ocongruent2(T_a,T_b,tc_fun(T_c,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2) % 172.48/172.43 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a1_2),V_A1_2)) % 172.48/172.43 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a2_2),V_A2_2)) % 172.48/172.43 => 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) ) ) ) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_UN__equiv__class,axiom, % 172.48/172.43 ! [V_a_2,V_f_2,T_b,V_r_2,V_A_2,T_a] : % 172.48/172.43 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 172.48/172.43 => ( c_Equiv__Relations_Ocongruent(T_a,tc_fun(T_b,tc_HOL_Obool),V_r_2,V_f_2) % 172.48/172.43 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 172.48/172.43 => 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) ) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_equivp__equiv,axiom, % 172.48/172.43 ! [V_A_2,T_a] : % 172.48/172.43 ( c_Equiv__Relations_Oequiv(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_A_2) % 172.48/172.43 <=> 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)) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_equivp__transp,axiom, % 172.48/172.43 ! [V_z_2,V_y_2,V_x_2,V_R_2,T_a] : % 172.48/172.43 ( c_Equiv__Relations_Oequivp(T_a,V_R_2) % 172.48/172.43 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2)) % 172.48/172.43 => ( hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_z_2)) % 172.48/172.43 => hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_z_2)) ) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_equivp__symp,axiom, % 172.48/172.43 ! [V_y_2,V_x_2,V_R_2,T_a] : % 172.48/172.43 ( c_Equiv__Relations_Oequivp(T_a,V_R_2) % 172.48/172.43 => ( hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_y_2)) % 172.48/172.43 => hBOOL(hAPP(hAPP(V_R_2,V_y_2),V_x_2)) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_equivp__reflp,axiom, % 172.48/172.43 ! [V_x_2,V_R_2,T_a] : % 172.48/172.43 ( c_Equiv__Relations_Oequivp(T_a,V_R_2) % 172.48/172.43 => hBOOL(hAPP(hAPP(V_R_2,V_x_2),V_x_2)) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_equivp__def,axiom, % 172.48/172.43 ! [V_R_2,T_a] : % 172.48/172.43 ( c_Equiv__Relations_Oequivp(T_a,V_R_2) % 172.48/172.43 <=> ! [B_x,B_y] : % 172.48/172.43 ( hBOOL(hAPP(hAPP(V_R_2,B_x),B_y)) % 172.48/172.43 <=> hAPP(V_R_2,B_x) = hAPP(V_R_2,B_y) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_identity__equivp,axiom, % 172.48/172.43 ! [T_a] : c_Equiv__Relations_Oequivp(T_a,c_fequal) ). % 172.48/172.43 % 172.48/172.43 fof(fact_congruent2__implies__congruent,axiom, % 172.48/172.43 ! [V_a_2,V_f_2,V_r2_2,T_c,T_b,V_r1_2,V_A_2,T_a] : % 172.48/172.43 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r1_2) % 172.48/172.43 => ( c_Equiv__Relations_Ocongruent2(T_a,T_b,T_c,V_r1_2,V_r2_2,V_f_2) % 172.48/172.43 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 172.48/172.43 => c_Equiv__Relations_Ocongruent(T_b,T_c,V_r2_2,hAPP(V_f_2,V_a_2)) ) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_congruent2D,axiom, % 172.48/172.43 ! [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] : % 172.48/172.43 ( c_Equiv__Relations_Ocongruent2(T_a,T_b,T_c,V_r1_2,V_r2_2,V_f_2) % 172.48/172.43 => ( 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)) % 172.48/172.43 => ( 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)) % 172.48/172.43 => hAPP(hAPP(V_f_2,V_y1_2),V_y2_2) = hAPP(hAPP(V_f_2,V_z1_2),V_z2_2) ) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_congruentD,axiom, % 172.48/172.43 ! [V_z_2,V_y_2,V_f_2,V_r_2,T_b,T_a] : % 172.48/172.43 ( c_Equiv__Relations_Ocongruent(T_a,T_b,V_r_2,V_f_2) % 172.48/172.43 => ( 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)) % 172.48/172.43 => hAPP(V_f_2,V_y_2) = hAPP(V_f_2,V_z_2) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_congruent2__implies__congruent__UN,axiom, % 172.48/172.43 ! [V_a_2,V_f_2,T_c,V_r2_2,V_A2_2,T_b,V_r1_2,V_A1_2,T_a] : % 172.48/172.43 ( c_Equiv__Relations_Oequiv(T_a,V_A1_2,V_r1_2) % 172.48/172.43 => ( c_Equiv__Relations_Oequiv(T_b,V_A2_2,V_r2_2) % 172.48/172.43 => ( c_Equiv__Relations_Ocongruent2(T_a,T_b,tc_fun(T_c,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2) % 172.48/172.43 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A2_2)) % 172.48/172.43 => 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)) ) ) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_UN__equiv__class__inject,axiom, % 172.48/172.43 ! [V_Y_2,V_X_2,V_f_2,T_b,V_r_2,V_A_2,T_a] : % 172.48/172.43 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 172.48/172.43 => ( c_Equiv__Relations_Ocongruent(T_a,tc_fun(T_b,tc_HOL_Obool),V_r_2,V_f_2) % 172.48/172.43 => ( 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) % 172.48/172.43 => ( 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))) % 172.48/172.43 => ( 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))) % 172.48/172.43 => ( ! [B_x] : % 172.48/172.43 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 172.48/172.43 => ! [B_y] : % 172.48/172.43 ( hBOOL(hAPP(hAPP(c_member(T_a),B_y),V_A_2)) % 172.48/172.43 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_y) % 172.48/172.43 => 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)) ) ) ) % 172.48/172.43 => V_X_2 = V_Y_2 ) ) ) ) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_UN__equiv__class__type2,axiom, % 172.48/172.43 ! [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] : % 172.48/172.43 ( c_Equiv__Relations_Oequiv(T_a,V_A1_2,V_r1_2) % 172.48/172.43 => ( c_Equiv__Relations_Oequiv(T_b,V_A2_2,V_r2_2) % 172.48/172.43 => ( c_Equiv__Relations_Ocongruent2(T_a,T_b,tc_fun(T_c,tc_HOL_Obool),V_r1_2,V_r2_2,V_f_2) % 172.48/172.43 => ( 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))) % 172.48/172.43 => ( 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))) % 172.48/172.43 => ( ! [B_x1] : % 172.48/172.43 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x1),V_A1_2)) % 172.48/172.43 => ! [B_x2] : % 172.48/172.43 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x2),V_A2_2)) % 172.48/172.43 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(V_f_2,B_x1),B_x2)),V_B_2)) ) ) % 172.48/172.43 => 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)) ) ) ) ) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_UN__equiv__class__type,axiom, % 172.48/172.43 ! [V_B_2,V_X_2,V_f_2,T_b,V_r_2,V_A_2,T_a] : % 172.48/172.43 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 172.48/172.43 => ( c_Equiv__Relations_Ocongruent(T_a,tc_fun(T_b,tc_HOL_Obool),V_r_2,V_f_2) % 172.48/172.43 => ( 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))) % 172.48/172.43 => ( ! [B_x] : % 172.48/172.43 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 172.48/172.43 => hBOOL(hAPP(hAPP(c_member(tc_fun(T_b,tc_HOL_Obool)),hAPP(V_f_2,B_x)),V_B_2)) ) % 172.48/172.43 => 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)) ) ) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_Integ__def,axiom, % 172.48/172.43 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) ). % 172.48/172.43 % 172.48/172.43 fof(fact_Id__onE,axiom, % 172.48/172.43 ! [V_A_2,V_ca_2,T_a] : % 172.48/172.43 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_ca_2),c_Relation_OId__on(T_a,V_A_2))) % 172.48/172.43 => ~ ! [B_x] : % 172.48/172.43 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 172.48/172.43 => V_ca_2 != hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_card__quotient__disjoint,axiom, % 172.48/172.43 ! [V_r_2,V_A_2,T_a] : % 172.48/172.43 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.43 => ( 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) % 172.48/172.43 => 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) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_inj__on__empty,axiom, % 172.48/172.43 ! [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))) ). % 172.48/172.43 % 172.48/172.43 fof(fact_inj__uminus,axiom, % 172.48/172.43 ! [V_A_2,T_a] : % 172.48/172.43 ( class_Groups_Oordered__ab__group__add(T_a) % 172.48/172.43 => c_Fun_Oinj__on(T_a,T_a,c_Groups_Ouminus__class_Ouminus(T_a),V_A_2) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_inj__on__diff,axiom, % 172.48/172.43 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 172.48/172.43 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 172.48/172.43 => 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)) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_inj__on__id2,axiom, % 172.48/172.43 ! [V_A_2,T_a] : c_Fun_Oinj__on(T_a,T_a,c_COMBI(T_a),V_A_2) ). % 172.48/172.43 % 172.48/172.43 fof(fact_inj__on__def,axiom, % 172.48/172.43 ! [V_A_2,V_f_2,T_b,T_a] : % 172.48/172.43 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 172.48/172.43 <=> ! [B_x] : % 172.48/172.43 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 172.48/172.43 => ! [B_xa] : % 172.48/172.43 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_A_2)) % 172.48/172.43 => ( hAPP(V_f_2,B_x) = hAPP(V_f_2,B_xa) % 172.48/172.43 => B_x = B_xa ) ) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_inj__on__Int,axiom, % 172.48/172.43 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 172.48/172.43 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 172.48/172.43 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2) % 172.48/172.43 => 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)) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_subset__inj__on,axiom, % 172.48/172.43 ! [V_A_2,V_B_2,V_f_2,T_b,T_a] : % 172.48/172.43 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2) % 172.48/172.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 172.48/172.43 => c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_inj__on__imageI2,axiom, % 172.48/172.43 ! [V_A_2,V_f_2,V_f_H_2,T_c,T_b,T_a] : % 172.48/172.43 ( 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) % 172.48/172.43 => c_Fun_Oinj__on(T_a,T_c,V_f_2,V_A_2) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_inj__on__contraD,axiom, % 172.48/172.43 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_b,T_a] : % 172.48/172.43 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 172.48/172.43 => ( V_x_2 != V_y_2 % 172.48/172.43 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 172.48/172.43 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) % 172.48/172.43 => hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2) ) ) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_inj__on__iff,axiom, % 172.48/172.43 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_b,T_a] : % 172.48/172.43 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 172.48/172.43 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 172.48/172.43 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) % 172.48/172.43 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) % 172.48/172.43 <=> V_x_2 = V_y_2 ) ) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_inj__onD,axiom, % 172.48/172.43 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_b,T_a] : % 172.48/172.43 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 172.48/172.43 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) % 172.48/172.43 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 172.48/172.43 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) % 172.48/172.43 => V_x_2 = V_y_2 ) ) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_inj__fun,axiom, % 172.48/172.43 ! [T_c,V_f_2,T_b,T_a] : % 172.48/172.43 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 172.48/172.43 => 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))) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_inj__eq,axiom, % 172.48/172.43 ! [V_y_2,V_x_2,V_f_2,T_b,T_a] : % 172.48/172.43 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 172.48/172.43 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) % 172.48/172.43 <=> V_x_2 = V_y_2 ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_injD,axiom, % 172.48/172.43 ! [V_y_2,V_x_2,V_f_2,T_b,T_a] : % 172.48/172.43 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 172.48/172.43 => ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) % 172.48/172.43 => V_x_2 = V_y_2 ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_finite__imageD,axiom, % 172.48/172.43 ! [V_A_2,V_f_2,T_b,T_a] : % 172.48/172.43 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2))) % 172.48/172.43 => ( c_Fun_Oinj__on(T_b,T_a,V_f_2,V_A_2) % 172.48/172.43 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_inj__image__eq__iff,axiom, % 172.48/172.43 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 172.48/172.43 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 172.48/172.43 => ( 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) % 172.48/172.43 <=> V_A_2 = V_B_2 ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_inj__on__Un__image__eq__iff,axiom, % 172.48/172.43 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 172.48/172.43 ( 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)) % 172.48/172.43 => ( 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) % 172.48/172.43 <=> V_A_2 = V_B_2 ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_inj__comp,axiom, % 172.48/172.43 ! [V_g_2,T_c,V_f_2,T_b,T_a] : % 172.48/172.43 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 172.48/172.43 => ( c_Fun_Oinj__on(T_c,T_a,V_g_2,c_Orderings_Otop__class_Otop(tc_fun(T_c,tc_HOL_Obool))) % 172.48/172.43 => 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))) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_comp__inj__on__iff,axiom, % 172.48/172.43 ! [V_f_H_2,T_c,V_A_2,V_f_2,T_b,T_a] : % 172.48/172.43 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 172.48/172.43 => ( 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)) % 172.48/172.43 <=> 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) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_comp__inj__on,axiom, % 172.48/172.43 ! [V_g_2,T_c,V_A_2,V_f_2,T_b,T_a] : % 172.48/172.43 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 172.48/172.43 => ( 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)) % 172.48/172.43 => 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) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_inj__on__imageI,axiom, % 172.48/172.43 ! [V_A_2,V_f_2,V_g_2,T_c,T_b,T_a] : % 172.48/172.43 ( 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) % 172.48/172.43 => 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)) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_card__image,axiom, % 172.48/172.43 ! [V_A_2,V_f_2,T_b,T_a] : % 172.48/172.43 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 172.48/172.43 => 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) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_inj__on__strict__subset,axiom, % 172.48/172.43 ! [V_A_2,V_B_2,V_f_2,T_b,T_a] : % 172.48/172.43 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2) % 172.48/172.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 172.48/172.43 => 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))) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_range__ex1__eq,axiom, % 172.48/172.43 ! [V_b_2,V_f_2,T_b,T_a] : % 172.48/172.43 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 172.48/172.43 => ( 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))))) % 172.48/172.43 <=> ? [B_x] : % 172.48/172.43 ( V_b_2 = hAPP(V_f_2,B_x) % 172.48/172.43 & ! [B_y] : % 172.48/172.43 ( V_b_2 = hAPP(V_f_2,B_y) % 172.48/172.43 => B_y = B_x ) ) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_inj__image__mem__iff,axiom, % 172.48/172.43 ! [V_A_2,V_a_2,V_f_2,T_b,T_a] : % 172.48/172.43 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 172.48/172.43 => ( 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))) % 172.48/172.43 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_inj__on__iff__surj,axiom, % 172.48/172.43 ! [V_A_H_2,T_b,T_a,V_A_2] : % 172.48/172.43 ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.43 => ( ? [B_f] : % 172.48/172.43 ( c_Fun_Oinj__on(T_a,T_b,B_f,V_A_2) % 172.48/172.43 & 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)) ) % 172.48/172.43 <=> ? [B_g] : hAPP(c_Set_Oimage(T_b,T_a,B_g),V_A_H_2) = V_A_2 ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_finite__surj__inj,axiom, % 172.48/172.43 ! [V_f_2,V_A_2,T_a] : % 172.48/172.43 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.43 => ( 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))) % 172.48/172.43 => c_Fun_Oinj__on(T_a,T_a,V_f_2,V_A_2) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_endo__inj__surj,axiom, % 172.48/172.43 ! [V_f_2,V_A_2,T_a] : % 172.48/172.43 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.43 => ( 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)) % 172.48/172.43 => ( c_Fun_Oinj__on(T_a,T_a,V_f_2,V_A_2) % 172.48/172.43 => hAPP(c_Set_Oimage(T_a,T_a,V_f_2),V_A_2) = V_A_2 ) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_finite__UNIV__inj__surj,axiom, % 172.48/172.43 ! [V_f_2,T_a] : % 172.48/172.43 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) % 172.48/172.43 => ( c_Fun_Oinj__on(T_a,T_a,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 172.48/172.43 => 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)) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_finite__UNIV__surj__inj,axiom, % 172.48/172.43 ! [V_f_2,T_a] : % 172.48/172.43 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) % 172.48/172.43 => ( 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)) % 172.48/172.43 => c_Fun_Oinj__on(T_a,T_a,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_inj__image__subset__iff,axiom, % 172.48/172.43 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 172.48/172.43 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 172.48/172.43 => ( 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))) % 172.48/172.43 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_inj__on__image__Int,axiom, % 172.48/172.43 ! [V_B_2,V_A_2,V_C_2,V_f_2,T_b,T_a] : % 172.48/172.43 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_C_2) % 172.48/172.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) % 172.48/172.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) % 172.48/172.43 => 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)) ) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_image__Int,axiom, % 172.48/172.43 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 172.48/172.43 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 172.48/172.43 => 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)) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_inj__on__iff__eq__card,axiom, % 172.48/172.43 ! [V_f_2,T_b,V_A_2,T_a] : % 172.48/172.43 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.43 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 172.48/172.43 <=> 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) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_eq__card__imp__inj__on,axiom, % 172.48/172.43 ! [V_f_2,T_b,V_A_2,T_a] : % 172.48/172.43 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.43 => ( 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) % 172.48/172.43 => c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_inj__on__image__set__diff,axiom, % 172.48/172.43 ! [V_B_2,V_A_2,V_C_2,V_f_2,T_b,T_a] : % 172.48/172.43 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_C_2) % 172.48/172.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) % 172.48/172.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_C_2)) % 172.48/172.43 => 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)) ) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_image__set__diff,axiom, % 172.48/172.43 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 172.48/172.43 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 172.48/172.43 => 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)) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_setsum__reindex,axiom, % 172.48/172.43 ! [V_h_2,V_B_2,V_f_2,T_b,T_a,T_c] : % 172.48/172.43 ( class_Groups_Ocomm__monoid__add(T_c) % 172.48/172.43 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2) % 172.48/172.43 => 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) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_pigeonhole,axiom, % 172.48/172.43 ! [V_A_2,V_f_2,T_b,T_a] : % 172.48/172.43 ( 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))) % 172.48/172.43 => ~ c_Fun_Oinj__on(T_b,T_a,V_f_2,V_A_2) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_inj__on__fun__updI,axiom, % 172.48/172.43 ! [V_x_2,V_y_2,V_A_2,V_f_2,T_b,T_a] : % 172.48/172.43 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 172.48/172.43 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2))) % 172.48/172.43 => 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) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_setprod__reindex,axiom, % 172.48/172.43 ! [V_h_2,V_B_2,V_f_2,T_b,T_a,T_c] : % 172.48/172.43 ( class_Groups_Ocomm__monoid__mult(T_c) % 172.48/172.43 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2) % 172.48/172.43 => 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) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_setprod__reindex__cong,axiom, % 172.48/172.43 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_b,T_a,T_c] : % 172.48/172.43 ( class_Groups_Ocomm__monoid__mult(T_c) % 172.48/172.43 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 172.48/172.43 => ( V_B_2 = hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2) % 172.48/172.43 => ( V_g_2 = hAPP(c_Fun_Ocomp(T_b,T_c,T_a,V_h_2),V_f_2) % 172.48/172.43 => 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) ) ) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_inj__singleton,axiom, % 172.48/172.43 ! [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))) ). % 172.48/172.43 % 172.48/172.43 fof(fact_Rep__Integ,axiom, % 172.48/172.43 ! [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)) ). % 172.48/172.43 % 172.48/172.43 fof(fact_setsum_Oreindex,axiom, % 172.48/172.43 ! [V_g_2,V_h_2,V_A_2,T_a,T_b] : % 172.48/172.43 ( class_Groups_Ocomm__monoid__add(T_b) % 172.48/172.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.43 => ( c_Fun_Oinj__on(T_a,T_a,V_h_2,V_A_2) % 172.48/172.43 => 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) ) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_card__bij__eq,axiom, % 172.48/172.43 ! [V_g_2,V_B_2,V_A_2,V_f_2,T_b,T_a] : % 172.48/172.43 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 172.48/172.43 => ( 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)) % 172.48/172.43 => ( c_Fun_Oinj__on(T_b,T_a,V_g_2,V_B_2) % 172.48/172.43 => ( 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)) % 172.48/172.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 172.48/172.43 => hAPP(c_Finite__Set_Ocard(T_a),V_A_2) = hAPP(c_Finite__Set_Ocard(T_b),V_B_2) ) ) ) ) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_setprod_Oreindex,axiom, % 172.48/172.43 ! [V_g_2,V_h_2,V_A_2,T_a,T_b] : % 172.48/172.43 ( class_Groups_Ocomm__monoid__mult(T_b) % 172.48/172.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.43 => ( c_Fun_Oinj__on(T_a,T_a,V_h_2,V_A_2) % 172.48/172.43 => 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) ) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_inj__image__Compl__subset,axiom, % 172.48/172.43 ! [V_A_2,V_f_2,T_b,T_a] : % 172.48/172.43 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 172.48/172.43 => 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)))) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_inj__on__insert,axiom, % 172.48/172.43 ! [V_A_2,V_a_2,V_f_2,T_b,T_a] : % 172.48/172.43 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) % 172.48/172.43 <=> ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 172.48/172.43 & ~ 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))))))) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_inj__on__Un,axiom, % 172.48/172.43 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 172.48/172.43 ( 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)) % 172.48/172.43 <=> ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 172.48/172.43 & c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2) % 172.48/172.43 & 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)) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_inj__on__iff__card__le,axiom, % 172.48/172.43 ! [V_B_2,T_b,V_A_2,T_a] : % 172.48/172.43 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 172.48/172.43 => ( ? [B_f] : % 172.48/172.43 ( c_Fun_Oinj__on(T_a,T_b,B_f,V_A_2) % 172.48/172.43 & 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)) ) % 172.48/172.43 <=> 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))) ) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_card__inj__on__le,axiom, % 172.48/172.43 ! [V_B_2,V_A_2,V_f_2,T_b,T_a] : % 172.48/172.43 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 172.48/172.43 => ( 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)) % 172.48/172.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 172.48/172.43 => 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))) ) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_fold__image__reindex,axiom, % 172.48/172.43 ! [V_z_2,V_g_2,V_h_2,T_b,V_A_2,T_a,T_c] : % 172.48/172.43 ( class_Groups_Oab__semigroup__mult(T_c) % 172.48/172.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.43 => ( c_Fun_Oinj__on(T_a,T_b,V_h_2,V_A_2) % 172.48/172.43 => 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) ) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_quotient__diff1,axiom, % 172.48/172.43 ! [V_a_2,V_A_2,V_r_2,T_a] : % 172.48/172.43 ( 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) % 172.48/172.43 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 172.48/172.43 => 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)) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_folding__image_Oreindex,axiom, % 172.48/172.43 ! [V_g_2,V_h_2,V_A_2,V_F_2,V_z_2,V_f_2,T_b,T_a] : % 172.48/172.43 ( c_Finite__Set_Ofolding__image(T_a,T_b,V_f_2,V_z_2,V_F_2) % 172.48/172.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 172.48/172.43 => ( c_Fun_Oinj__on(T_b,T_b,V_h_2,V_A_2) % 172.48/172.43 => 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) ) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_type__definition__Integ,axiom, % 172.48/172.43 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) ). % 172.48/172.43 % 172.48/172.43 fof(fact_the__inv__into__comp,axiom, % 172.48/172.43 ! [V_x_2,V_A_2,V_g_2,T_c,V_f_2,T_b,T_a] : % 172.48/172.43 ( 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)) % 172.48/172.43 => ( c_Fun_Oinj__on(T_c,T_a,V_g_2,V_A_2) % 172.48/172.43 => ( 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)))) % 172.48/172.43 => 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) ) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_inj__Suc,axiom, % 172.48/172.43 ! [V_N_2] : c_Fun_Oinj__on(tc_Nat_Onat,tc_Nat_Onat,c_Nat_OSuc,V_N_2) ). % 172.48/172.43 % 172.48/172.43 fof(fact_inj__on__add__nat,axiom, % 172.48/172.43 ! [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) ). % 172.48/172.43 % 172.48/172.43 fof(fact_inj__of__nat,axiom, % 172.48/172.43 ! [T_a] : % 172.48/172.43 ( class_Nat_Osemiring__char__0(T_a) % 172.48/172.43 => 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))) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_inj__int,axiom, % 172.48/172.43 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))) ). % 172.48/172.43 % 172.48/172.43 fof(fact_swap__inj__on,axiom, % 172.48/172.43 ! [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) ). % 172.48/172.43 % 172.48/172.43 fof(fact_folding__image_Odistrib,axiom, % 172.48/172.43 ! [V_h_2,V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_b,T_a] : % 172.48/172.43 ( c_Finite__Set_Ofolding__image(T_a,T_b,V_f_2,V_z_2,V_F_2) % 172.48/172.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 172.48/172.43 => 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)) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_the__inv__into__f__f,axiom, % 172.48/172.43 ! [V_x_2,V_A_2,V_f_2,T_b,T_a] : % 172.48/172.43 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 172.48/172.43 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 172.48/172.43 => 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 ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_the__inv__into__f__eq,axiom, % 172.48/172.43 ! [V_y_2,V_x_2,V_A_2,V_f_2,T_b,T_a] : % 172.48/172.43 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 172.48/172.43 => ( hAPP(V_f_2,V_x_2) = V_y_2 % 172.48/172.43 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 172.48/172.43 => hAPP(c_Fun_Othe__inv__into(T_a,T_b,V_A_2,V_f_2),V_y_2) = V_x_2 ) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_the__inv__f__f,axiom, % 172.48/172.43 ! [V_x_2,V_f_2,T_b,T_a] : % 172.48/172.43 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 172.48/172.43 => 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 ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_inj__on__the__inv__into,axiom, % 172.48/172.43 ! [V_A_2,V_f_2,T_b,T_a] : % 172.48/172.43 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 172.48/172.43 => 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)) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_the__inv__into__onto,axiom, % 172.48/172.43 ! [V_A_2,V_f_2,T_b,T_a] : % 172.48/172.43 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 172.48/172.43 => 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 ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_inj__graph,axiom, % 172.48/172.43 ! [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))) ). % 172.48/172.43 % 172.48/172.43 fof(fact_the__inv__into__def,axiom, % 172.48/172.43 ! [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))) ). % 172.48/172.43 % 172.48/172.43 fof(fact_folding__image_Oeq__fold,axiom, % 172.48/172.43 ! [V_g_2,V_A_2,V_F_2,V_z_2,V_f_2,T_b,T_a] : % 172.48/172.43 ( c_Finite__Set_Ofolding__image(T_a,T_b,V_f_2,V_z_2,V_F_2) % 172.48/172.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_A_2)) % 172.48/172.43 => 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) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_f__the__inv__into__f,axiom, % 172.48/172.43 ! [V_y_2,V_A_2,V_f_2,T_b,T_a] : % 172.48/172.43 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 172.48/172.43 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2))) % 172.48/172.43 => 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 ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_the__inv__into__into,axiom, % 172.48/172.43 ! [V_B_2,V_x_2,V_A_2,V_f_2,T_b,T_a] : % 172.48/172.43 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 172.48/172.43 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2))) % 172.48/172.43 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 172.48/172.43 => 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)) ) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_type__definition_OAbs__image,axiom, % 172.48/172.43 ! [V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] : % 172.48/172.43 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2) % 172.48/172.43 => 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)) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_type__definition_ORep__range,axiom, % 172.48/172.43 ! [V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] : % 172.48/172.43 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2) % 172.48/172.43 => 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 ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_type__definition_ORep,axiom, % 172.48/172.43 ! [V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] : % 172.48/172.43 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2) % 172.48/172.43 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_Rep_2,V_x_2)),V_A_2)) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_type__definition_ORep__inverse,axiom, % 172.48/172.43 ! [V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] : % 172.48/172.43 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2) % 172.48/172.43 => hAPP(V_Abs_2,hAPP(V_Rep_2,V_x_2)) = V_x_2 ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_type__definition_ORep__inject,axiom, % 172.48/172.43 ! [V_y_2,V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] : % 172.48/172.43 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2) % 172.48/172.43 => ( hAPP(V_Rep_2,V_x_2) = hAPP(V_Rep_2,V_y_2) % 172.48/172.43 <=> V_x_2 = V_y_2 ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_type__definition_OAbs__inject,axiom, % 172.48/172.43 ! [V_y_2,V_x_2,V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] : % 172.48/172.43 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2) % 172.48/172.43 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),V_A_2)) % 172.48/172.43 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) % 172.48/172.43 => ( hAPP(V_Abs_2,V_x_2) = hAPP(V_Abs_2,V_y_2) % 172.48/172.43 <=> V_x_2 = V_y_2 ) ) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_type__definition_OAbs__inverse,axiom, % 172.48/172.43 ! [V_y_2,V_A_2,V_Abs_2,V_Rep_2,T_b,T_a] : % 172.48/172.43 ( c_Typedef_Otype__definition(T_a,T_b,V_Rep_2,V_Abs_2,V_A_2) % 172.48/172.43 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),V_A_2)) % 172.48/172.43 => hAPP(V_Rep_2,hAPP(V_Abs_2,V_y_2)) = V_y_2 ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_inj__vimage__singleton,axiom, % 172.48/172.43 ! [V_a_2,V_f_2,T_b,T_a] : % 172.48/172.43 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 172.48/172.43 => 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))))) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_strong__setprod__reindex__cong,axiom, % 172.48/172.43 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_b,T_a,T_c] : % 172.48/172.43 ( class_Groups_Ocomm__monoid__mult(T_c) % 172.48/172.43 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 172.48/172.43 => ( V_B_2 = hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2) % 172.48/172.43 => ( ! [B_x] : % 172.48/172.43 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 172.48/172.43 => 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) ) % 172.48/172.43 => 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) ) ) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_code__numeral_Osimps_I5_J,axiom, % 172.48/172.43 ! [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) ). % 172.48/172.43 % 172.48/172.43 fof(fact_vimageI,axiom, % 172.48/172.43 ! [T_b,V_B_2,T_a,V_b_2,V_a_2,V_f_2] : % 172.48/172.43 ( hAPP(V_f_2,V_a_2) = V_b_2 % 172.48/172.43 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),V_B_2)) % 172.48/172.43 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_a,V_f_2),V_B_2))) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_vimage__UNIV,axiom, % 172.48/172.43 ! [V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ). % 172.48/172.43 % 172.48/172.43 fof(fact_vimage__empty,axiom, % 172.48/172.43 ! [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)) ). % 172.48/172.43 % 172.48/172.43 fof(fact_vimage__Un,axiom, % 172.48/172.43 ! [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)) ). % 172.48/172.43 % 172.48/172.43 fof(fact_vimage__compose,axiom, % 172.48/172.43 ! [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)) ). % 172.48/172.43 % 172.48/172.43 fof(fact_vimage__mono,axiom, % 172.48/172.43 ! [V_f_2,T_b,V_B_2,V_A_2,T_a] : % 172.48/172.43 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 172.48/172.43 => 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))) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_vimage__Int,axiom, % 172.48/172.43 ! [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)) ). % 172.48/172.43 % 172.48/172.43 fof(fact_vimage__Compl,axiom, % 172.48/172.43 ! [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)) ). % 172.48/172.43 % 172.48/172.43 fof(fact_vimage__code,axiom, % 172.48/172.43 ! [V_x_2,V_A_2,V_f_2,T_b,T_a] : % 172.48/172.43 ( hBOOL(hAPP(hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_A_2),V_x_2)) % 172.48/172.43 <=> hBOOL(hAPP(V_A_2,hAPP(V_f_2,V_x_2))) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_vimage__ident,axiom, % 172.48/172.43 ! [V_Y_2,T_a] : hAPP(c_Set_Ovimage(T_a,T_a,c_COMBI(T_a)),V_Y_2) = V_Y_2 ). % 172.48/172.43 % 172.48/172.43 fof(fact_vimage__Collect__eq,axiom, % 172.48/172.43 ! [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)) ). % 172.48/172.43 % 172.48/172.43 fof(fact_vimage__UN,axiom, % 172.48/172.43 ! [V_B_2,V_A_2,T_c,V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_c,tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_c),c_Set_Ovimage(T_a,T_b,V_f_2)),V_B_2)) ). % 172.48/172.43 % 172.48/172.43 fof(fact_vimage__Diff,axiom, % 172.48/172.43 ! [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)) ). % 172.48/172.43 % 172.48/172.43 fof(fact_vimage__eq,axiom, % 172.48/172.43 ! [V_B_2,V_f_2,T_b,V_a_2,T_a] : % 172.48/172.43 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_B_2))) % 172.48/172.43 <=> hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_a_2)),V_B_2)) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_vimageD,axiom, % 172.48/172.43 ! [V_A_2,V_f_2,T_b,V_a_2,T_a] : % 172.48/172.43 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_A_2))) % 172.48/172.43 => hBOOL(hAPP(hAPP(c_member(T_b),hAPP(V_f_2,V_a_2)),V_A_2)) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_vimageI2,axiom, % 172.48/172.43 ! [T_b,V_A_2,V_a_2,V_f_2,T_a] : % 172.48/172.43 ( hBOOL(hAPP(hAPP(c_member(T_a),hAPP(V_f_2,V_a_2)),V_A_2)) % 172.48/172.43 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),hAPP(c_Set_Ovimage(T_b,T_a,V_f_2),V_A_2))) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_image__vimage__subset,axiom, % 172.48/172.43 ! [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)) ). % 172.48/172.43 % 172.48/172.43 fof(fact_surj__image__vimage__eq,axiom, % 172.48/172.43 ! [V_A_2,V_f_2,T_a,T_b] : % 172.48/172.43 ( hAPP(c_Set_Oimage(T_b,T_a,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.43 => hAPP(c_Set_Oimage(T_b,T_a,V_f_2),hAPP(c_Set_Ovimage(T_b,T_a,V_f_2),V_A_2)) = V_A_2 ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_vimage__def,axiom, % 172.48/172.43 ! [V_B_2,V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_B_2) = hAPP(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)) ). % 172.48/172.43 % 172.48/172.43 fof(fact_vimage__singleton__eq,axiom, % 172.48/172.43 ! [V_b_2,V_f_2,T_b,V_a_2,T_a] : % 172.48/172.43 ( 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)))))) % 172.48/172.43 <=> hAPP(V_f_2,V_a_2) = V_b_2 ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_vimage__insert,axiom, % 172.48/172.43 ! [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)) ). % 172.48/172.43 % 172.48/172.43 fof(fact_finite__vimageD,axiom, % 172.48/172.43 ! [V_F_2,V_h_2,T_b,T_a] : % 172.48/172.43 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Set_Ovimage(T_a,T_b,V_h_2),V_F_2))) % 172.48/172.43 => ( 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)) % 172.48/172.43 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_F_2)) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_vimage__subsetD,axiom, % 172.48/172.43 ! [V_A_2,V_B_2,V_f_2,T_a,T_b] : % 172.48/172.43 ( hAPP(c_Set_Oimage(T_b,T_a,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.43 => ( 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)) % 172.48/172.43 => 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))) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_image__vimage__eq,axiom, % 172.48/172.43 ! [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)))) ). % 172.48/172.43 % 172.48/172.43 fof(fact_finite__vimageI,axiom, % 172.48/172.43 ! [V_h_2,T_b,V_F_2,T_a] : % 172.48/172.43 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_F_2)) % 172.48/172.43 => ( c_Fun_Oinj__on(T_b,T_a,V_h_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 172.48/172.43 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Set_Ovimage(T_b,T_a,V_h_2),V_F_2))) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_inj__vimage__image__eq,axiom, % 172.48/172.43 ! [V_A_2,V_f_2,T_b,T_a] : % 172.48/172.43 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 172.48/172.43 => 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 ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_vimage__const,axiom, % 172.48/172.43 ! [T_b,V_A_2,V_ca_2,T_a] : % 172.48/172.43 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 172.48/172.43 => hAPP(c_Set_Ovimage(T_b,T_a,hAPP(c_COMBK(T_a,T_b),V_ca_2)),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) % 172.48/172.43 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 172.48/172.43 => hAPP(c_Set_Ovimage(T_b,T_a,hAPP(c_COMBK(T_a,T_b),V_ca_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_vimage__eq__UN,axiom, % 172.48/172.43 ! [V_B_2,V_f_2,T_b,T_a] : hAPP(c_Set_Ovimage(T_a,T_b,V_f_2),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_b,tc_fun(T_a,tc_HOL_Obool)),V_B_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_b),c_Set_Ovimage(T_a,T_b,V_f_2)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),c_Set_Oinsert(T_b)),c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool))))) ). % 172.48/172.43 % 172.48/172.43 fof(fact_vimage__subsetI,axiom, % 172.48/172.43 ! [V_A_2,V_B_2,V_f_2,T_b,T_a] : % 172.48/172.43 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 172.48/172.43 => ( 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))) % 172.48/172.43 => 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)) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_vimage__if,axiom, % 172.48/172.43 ! [V_B_2,T_b,V_d_2,V_A_2,V_ca_2,T_a] : % 172.48/172.43 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 172.48/172.43 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_d_2),V_A_2)) % 172.48/172.43 => hAPP(c_Set_Ovimage(T_b,T_a,hAPP(hAPP(c_COMBC(T_b,T_a,T_a),hAPP(hAPP(c_COMBC(T_b,T_a,tc_fun(T_a,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_a,tc_fun(T_a,T_a)),T_b),c_If(T_a)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))),V_ca_2)),V_d_2)),V_A_2) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) % 172.48/172.43 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_d_2),V_A_2)) % 172.48/172.43 => hAPP(c_Set_Ovimage(T_b,T_a,hAPP(hAPP(c_COMBC(T_b,T_a,T_a),hAPP(hAPP(c_COMBC(T_b,T_a,tc_fun(T_a,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_a,tc_fun(T_a,T_a)),T_b),c_If(T_a)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))),V_ca_2)),V_d_2)),V_A_2) = V_B_2 ) ) ) % 172.48/172.43 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_ca_2),V_A_2)) % 172.48/172.43 => ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_d_2),V_A_2)) % 172.48/172.43 => hAPP(c_Set_Ovimage(T_b,T_a,hAPP(hAPP(c_COMBC(T_b,T_a,T_a),hAPP(hAPP(c_COMBC(T_b,T_a,tc_fun(T_a,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_a,tc_fun(T_a,T_a)),T_b),c_If(T_a)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))),V_ca_2)),V_d_2)),V_A_2) = hAPP(c_Groups_Ouminus__class_Ouminus(tc_fun(T_b,tc_HOL_Obool)),V_B_2) ) % 172.48/172.43 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_d_2),V_A_2)) % 172.48/172.43 => hAPP(c_Set_Ovimage(T_b,T_a,hAPP(hAPP(c_COMBC(T_b,T_a,T_a),hAPP(hAPP(c_COMBC(T_b,T_a,tc_fun(T_a,T_a)),hAPP(hAPP(c_COMBB(tc_HOL_Obool,tc_fun(T_a,tc_fun(T_a,T_a)),T_b),c_If(T_a)),hAPP(hAPP(c_COMBC(T_b,tc_fun(T_b,tc_HOL_Obool),tc_HOL_Obool),c_member(T_b)),V_B_2))),V_ca_2)),V_d_2)),V_A_2) = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_code__numeral_Osimps_I4_J,axiom, % 172.48/172.43 ! [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 ). % 172.48/172.43 % 172.48/172.43 fof(fact_accp__acc__eq,axiom, % 172.48/172.43 ! [V_x_2,V_r_2,T_a] : % 172.48/172.43 ( 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)) % 172.48/172.43 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Wellfounded_Oacc(T_a,V_r_2))) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_rel__comp__def,axiom, % 172.48/172.43 ! [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))))) ). % 172.48/172.43 % 172.48/172.43 fof(fact_max__extp_Oequations,axiom, % 172.48/172.43 ! [V_a2_2,V_a1_2,V_R_2,T_a] : % 172.48/172.43 ( c_Wellfounded_Omax__extp(T_a,V_R_2,V_a1_2,V_a2_2) % 172.48/172.43 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_a1_2)) % 172.48/172.43 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_a2_2)) % 172.48/172.43 & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.43 & ! [B_x] : % 172.48/172.43 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_a1_2)) % 172.48/172.43 => ? [B_xa] : % 172.48/172.43 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_a2_2)) % 172.48/172.43 & hBOOL(hAPP(hAPP(V_R_2,B_x),B_xa)) ) ) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_rel__compI,axiom, % 172.48/172.43 ! [V_s_2,V_ca_2,T_c,V_r_2,V_b_2,V_a_2,T_b,T_a] : % 172.48/172.43 ( 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)) % 172.48/172.43 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_b_2),V_ca_2)),V_s_2)) % 172.48/172.43 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_c)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_c),V_a_2),V_ca_2)),hAPP(hAPP(c_Relation_Orel__comp(T_a,T_b,T_c),V_r_2),V_s_2))) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_rel__comp__UNION__distrib2,axiom, % 172.48/172.43 ! [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)) ). % 172.48/172.43 % 172.48/172.43 fof(fact_rel__comp__UNION__distrib,axiom, % 172.48/172.43 ! [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)) ). % 172.48/172.43 % 172.48/172.43 fof(fact_rel__comp__empty1,axiom, % 172.48/172.43 ! [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)) ). % 172.48/172.43 % 172.48/172.43 fof(fact_rel__comp__empty2,axiom, % 172.48/172.43 ! [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)) ). % 172.48/172.43 % 172.48/172.43 fof(fact_rel__comp__distrib2,axiom, % 172.48/172.43 ! [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)) ). % 172.48/172.43 % 172.48/172.43 fof(fact_rel__comp__distrib,axiom, % 172.48/172.43 ! [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)) ). % 172.48/172.43 % 172.48/172.43 fof(fact_rel__comp__mono,axiom, % 172.48/172.43 ! [V_s_2,V_s_H_2,T_c,V_r_2,V_r_H_2,T_b,T_a] : % 172.48/172.43 ( 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)) % 172.48/172.43 => ( 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)) % 172.48/172.43 => 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))) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_O__assoc,axiom, % 172.48/172.43 ! [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)) ). % 172.48/172.43 % 172.48/172.43 fof(fact_union__comp__emptyR,axiom, % 172.48/172.43 ! [V_C_2,V_B_2,V_A_2,T_a] : % 172.48/172.43 ( 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)) % 172.48/172.43 => ( 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)) % 172.48/172.43 => 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)) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_union__comp__emptyL,axiom, % 172.48/172.43 ! [V_B_2,V_C_2,V_A_2,T_a] : % 172.48/172.43 ( 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)) % 172.48/172.43 => ( 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)) % 172.48/172.43 => 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)) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_acc__subset,axiom, % 172.48/172.43 ! [V_R2_2,V_R1_2,T_a] : % 172.48/172.43 ( 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)) % 172.48/172.43 => 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))) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_acc__downward,axiom, % 172.48/172.43 ! [V_a_2,V_r_2,V_b_2,T_a] : % 172.48/172.43 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Wellfounded_Oacc(T_a,V_r_2))) % 172.48/172.43 => ( 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)) % 172.48/172.43 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Wellfounded_Oacc(T_a,V_r_2))) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_acc_Osimps,axiom, % 172.48/172.43 ! [V_r_2,V_a_2,T_a] : % 172.48/172.43 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Wellfounded_Oacc(T_a,V_r_2))) % 172.48/172.43 <=> ! [B_x] : % 172.48/172.43 ( 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)) % 172.48/172.43 => hBOOL(hAPP(hAPP(c_member(T_a),B_x),c_Wellfounded_Oacc(T_a,V_r_2))) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_max__ext__compat,axiom, % 172.48/172.43 ! [V_S_2,V_R_2,T_a] : % 172.48/172.43 ( 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)) % 172.48/172.43 => 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))) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_min__ext__compat,axiom, % 172.48/172.43 ! [V_S_2,V_R_2,T_a] : % 172.48/172.43 ( 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)) % 172.48/172.43 => 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))) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_pred__comp__rel__comp__eq,axiom, % 172.48/172.43 ! [V_y_2,V_x_2,V_s_2,V_r_2,T_c,T_b,T_a] : % 172.48/172.43 ( hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(T_a,T_b,T_c,hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_r_2),hAPP(hAPP(c_COMBC(T_b,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_fun(T_c,tc_HOL_Obool)),T_b),c_COMBC(T_c,tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_c,tc_prod(T_b,T_c)),tc_fun(T_c,tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool)),T_b),hAPP(c_COMBB(tc_prod(T_b,T_c),tc_fun(tc_fun(tc_prod(T_b,T_c),tc_HOL_Obool),tc_HOL_Obool),T_c),c_member(tc_prod(T_b,T_c)))),c_Product__Type_OPair(T_b,T_c)))),V_s_2)),V_x_2),V_y_2)) % 172.48/172.43 <=> 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))) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_reduction__pairI,axiom, % 172.48/172.43 ! [V_S_2,V_R_2,T_a] : % 172.48/172.43 ( c_Wellfounded_Owf(T_a,V_R_2) % 172.48/172.43 => ( 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)) % 172.48/172.43 => 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)) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_max__ext_Ointros,axiom, % 172.48/172.43 ! [V_R_2,V_Y_2,V_X_2,T_a] : % 172.48/172.43 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_X_2)) % 172.48/172.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_Y_2)) % 172.48/172.43 => ( V_Y_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.43 => ( ! [B_x] : % 172.48/172.43 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_X_2)) % 172.48/172.43 => ? [B_xa] : % 172.48/172.43 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_Y_2)) % 172.48/172.43 & 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)) ) ) % 172.48/172.43 => 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))) ) ) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_wf__less__than,axiom, % 172.48/172.43 c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Oless__than) ). % 172.48/172.43 % 172.48/172.43 fof(fact_pred__comp_Ointros,axiom, % 172.48/172.43 ! [T_c,T_b,T_a,V_ca_2,V_s_2,V_b_2,V_a_2,V_r_2] : % 172.48/172.43 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2)) % 172.48/172.43 => ( hBOOL(hAPP(hAPP(V_s_2,V_b_2),V_ca_2)) % 172.48/172.43 => hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(T_a,T_b,T_c,V_r_2,V_s_2),V_a_2),V_ca_2)) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_wf__empty,axiom, % 172.48/172.43 ! [T_a] : c_Wellfounded_Owf(T_a,c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_a),tc_HOL_Obool))) ). % 172.48/172.43 % 172.48/172.43 fof(fact_wf__inv__image,axiom, % 172.48/172.43 ! [V_f_2,T_b,V_r_2,T_a] : % 172.48/172.43 ( c_Wellfounded_Owf(T_a,V_r_2) % 172.48/172.43 => c_Wellfounded_Owf(T_b,hAPP(hAPP(c_Relation_Oinv__image(T_a,T_b),V_r_2),V_f_2)) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_wf__lex__prod,axiom, % 172.48/172.43 ! [V_rb_2,T_b,V_ra_2,T_a] : % 172.48/172.43 ( c_Wellfounded_Owf(T_a,V_ra_2) % 172.48/172.43 => ( c_Wellfounded_Owf(T_b,V_rb_2) % 172.48/172.43 => c_Wellfounded_Owf(tc_prod(T_a,T_b),c_Wellfounded_Olex__prod(T_a,T_b,V_ra_2,V_rb_2)) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_wf__measure,axiom, % 172.48/172.43 ! [V_f_2,T_a] : c_Wellfounded_Owf(T_a,hAPP(c_Wellfounded_Omeasure(T_a),V_f_2)) ). % 172.48/172.43 % 172.48/172.43 fof(fact_wf__comp__self,axiom, % 172.48/172.43 ! [V_R_2,T_a] : % 172.48/172.43 ( c_Wellfounded_Owf(T_a,V_R_2) % 172.48/172.43 <=> c_Wellfounded_Owf(T_a,hAPP(hAPP(c_Relation_Orel__comp(T_a,T_a,T_a),V_R_2),V_R_2)) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_max__ext__wf,axiom, % 172.48/172.43 ! [V_r_2,T_a] : % 172.48/172.43 ( c_Wellfounded_Owf(T_a,V_r_2) % 172.48/172.43 => c_Wellfounded_Owf(tc_fun(T_a,tc_HOL_Obool),c_Wellfounded_Omax__ext(T_a,V_r_2)) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_min__ext__wf,axiom, % 172.48/172.43 ! [V_r_2,T_a] : % 172.48/172.43 ( c_Wellfounded_Owf(T_a,V_r_2) % 172.48/172.43 => c_Wellfounded_Owf(tc_fun(T_a,tc_HOL_Obool),c_Wellfounded_Omin__ext(T_a,V_r_2)) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_wf__mlex,axiom, % 172.48/172.43 ! [V_f_2,V_R_2,T_a] : % 172.48/172.43 ( c_Wellfounded_Owf(T_a,V_R_2) % 172.48/172.43 => c_Wellfounded_Owf(T_a,c_Wellfounded_Omlex__prod(T_a,V_f_2,V_R_2)) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_pred__comp_Oequations,axiom, % 172.48/172.43 ! [V_a3_2,V_a1_2,V_s_2,V_r_2,T_c,T_b,T_a] : % 172.48/172.43 ( hBOOL(hAPP(hAPP(c_Predicate_Opred__comp(T_a,T_b,T_c,V_r_2,V_s_2),V_a1_2),V_a3_2)) % 172.48/172.43 <=> ? [B_b] : % 172.48/172.43 ( hBOOL(hAPP(hAPP(V_r_2,V_a1_2),B_b)) % 172.48/172.43 & hBOOL(hAPP(hAPP(V_s_2,B_b),V_a3_2)) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_wf__Int1,axiom, % 172.48/172.43 ! [V_r_H_2,V_r_2,T_a] : % 172.48/172.43 ( c_Wellfounded_Owf(T_a,V_r_2) % 172.48/172.43 => 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)) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_wf__Int2,axiom, % 172.48/172.43 ! [V_r_H_2,V_r_2,T_a] : % 172.48/172.43 ( c_Wellfounded_Owf(T_a,V_r_2) % 172.48/172.43 => 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)) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_wf__subset,axiom, % 172.48/172.43 ! [V_p_2,V_r_2,T_a] : % 172.48/172.43 ( c_Wellfounded_Owf(T_a,V_r_2) % 172.48/172.43 => ( 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)) % 172.48/172.43 => c_Wellfounded_Owf(T_a,V_p_2) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_wf__finite__psubset,axiom, % 172.48/172.43 ! [T_a] : c_Wellfounded_Owf(tc_fun(T_a,tc_HOL_Obool),c_Wellfounded_Ofinite__psubset(T_a)) ). % 172.48/172.43 % 172.48/172.43 fof(fact_wf__pair__less,axiom, % 172.48/172.43 c_Wellfounded_Owf(tc_prod(tc_Nat_Onat,tc_Nat_Onat),c_FunDef_Opair__less) ). % 172.48/172.43 % 172.48/172.43 fof(fact_wf__less,axiom, % 172.48/172.43 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)))) ). % 172.48/172.43 % 172.48/172.43 fof(fact_wf__irrefl,axiom, % 172.48/172.43 ! [V_a_2,V_r_2,T_a] : % 172.48/172.43 ( c_Wellfounded_Owf(T_a,V_r_2) % 172.48/172.43 => ~ 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)) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_wf__asym,axiom, % 172.48/172.43 ! [V_x_2,V_a_2,V_r_2,T_a] : % 172.48/172.43 ( c_Wellfounded_Owf(T_a,V_r_2) % 172.48/172.43 => ( 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)) % 172.48/172.43 => ~ 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)) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_wf__not__sym,axiom, % 172.48/172.43 ! [V_x_2,V_a_2,V_r_2,T_a] : % 172.48/172.43 ( c_Wellfounded_Owf(T_a,V_r_2) % 172.48/172.43 => ( 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)) % 172.48/172.43 => ~ 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)) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_wf__not__refl,axiom, % 172.48/172.43 ! [V_a_2,V_r_2,T_a] : % 172.48/172.43 ( c_Wellfounded_Owf(T_a,V_r_2) % 172.48/172.43 => ~ 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)) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_wf__int__ge__less__than,axiom, % 172.48/172.43 ! [V_d_2] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than(V_d_2)) ). % 172.48/172.43 % 172.48/172.43 fof(fact_wf__int__ge__less__than2,axiom, % 172.48/172.43 ! [V_d_2] : c_Wellfounded_Owf(tc_Int_Oint,c_Int_Oint__ge__less__than2(V_d_2)) ). % 172.48/172.43 % 172.48/172.43 fof(fact_acc__wfD,axiom, % 172.48/172.43 ! [V_x_2,V_r_2,T_a] : % 172.48/172.43 ( c_Wellfounded_Owf(T_a,V_r_2) % 172.48/172.43 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Wellfounded_Oacc(T_a,V_r_2))) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_wf__acc__iff,axiom, % 172.48/172.43 ! [V_r_2,T_a] : % 172.48/172.43 ( c_Wellfounded_Owf(T_a,V_r_2) % 172.48/172.43 <=> ! [B_x] : hBOOL(hAPP(hAPP(c_member(T_a),B_x),c_Wellfounded_Oacc(T_a,V_r_2))) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_wf__no__loop,axiom, % 172.48/172.43 ! [V_R_2,T_a] : % 172.48/172.43 ( 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)) % 172.48/172.43 => c_Wellfounded_Owf(T_a,V_R_2) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_wf__union__merge,axiom, % 172.48/172.43 ! [V_S_2,V_R_2,T_a] : % 172.48/172.43 ( 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)) % 172.48/172.43 <=> 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)) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_wf__iff__no__infinite__down__chain,axiom, % 172.48/172.43 ! [V_r_2,T_a] : % 172.48/172.43 ( c_Wellfounded_Owf(T_a,V_r_2) % 172.48/172.43 <=> ~ ? [B_f] : % 172.48/172.43 ! [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)) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_wfE__pf,axiom, % 172.48/172.43 ! [V_A_2,V_R_2,T_a] : % 172.48/172.43 ( c_Wellfounded_Owf(T_a,V_R_2) % 172.48/172.43 => ( 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))) % 172.48/172.43 => V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_wf__union__compatible,axiom, % 172.48/172.43 ! [V_S_2,V_R_2,T_a] : % 172.48/172.43 ( c_Wellfounded_Owf(T_a,V_R_2) % 172.48/172.43 => ( c_Wellfounded_Owf(T_a,V_S_2) % 172.48/172.43 => ( 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)) % 172.48/172.43 => 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)) ) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_wf,axiom, % 172.48/172.43 ! [T_a] : % 172.48/172.43 ( class_Orderings_Owellorder(T_a) % 172.48/172.43 => 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)))) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_reduction__pair__def,axiom, % 172.48/172.43 ! [V_P_2,T_a] : % 172.48/172.43 ( c_FunDef_Oreduction__pair(T_a,V_P_2) % 172.48/172.43 <=> ( 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)) % 172.48/172.43 & 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))) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_reduction__pair__lemma,axiom, % 172.48/172.43 ! [V_S_2,V_R_2,V_P_2,T_a] : % 172.48/172.43 ( c_FunDef_Oreduction__pair(T_a,V_P_2) % 172.48/172.43 => ( 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))) % 172.48/172.43 => ( 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))) % 172.48/172.43 => ( c_Wellfounded_Owf(T_a,V_S_2) % 172.48/172.43 => 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)) ) ) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_wf__lenlex,axiom, % 172.48/172.43 ! [V_r_2,T_a] : % 172.48/172.43 ( c_Wellfounded_Owf(T_a,V_r_2) % 172.48/172.43 => c_Wellfounded_Owf(tc_List_Olist(T_a),c_List_Olenlex(T_a,V_r_2)) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_wf__if__measure,axiom, % 172.48/172.43 ! [T_a,V_g_2,V_f_2,V_P_2] : % 172.48/172.43 ( ! [B_x] : % 172.48/172.43 ( hBOOL(hAPP(V_P_2,B_x)) % 172.48/172.43 => 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))) ) % 172.48/172.43 => 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))))) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_Nitpick_Ozero__frac__def,axiom, % 172.48/172.43 ! [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))) ). % 172.48/172.43 % 172.48/172.43 fof(fact_Nitpick_Oone__frac__def,axiom, % 172.48/172.43 ! [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))) ). % 172.48/172.43 % 172.48/172.43 fof(fact_Nitpick_Onumber__of__frac__def,axiom, % 172.48/172.43 ! [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))) ). % 172.48/172.43 % 172.48/172.43 fof(fact_pred__nat__def,axiom, % 172.48/172.43 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))) ). % 172.48/172.43 % 172.48/172.43 fof(fact_wf__pred__nat,axiom, % 172.48/172.43 c_Wellfounded_Owf(tc_Nat_Onat,c_Wellfounded_Opred__nat) ). % 172.48/172.43 % 172.48/172.43 fof(fact_Nitpick_Ofrac__def,axiom, % 172.48/172.43 ! [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)) ). % 172.48/172.43 % 172.48/172.43 fof(fact_wf__lex,axiom, % 172.48/172.43 ! [V_r_2,T_a] : % 172.48/172.43 ( c_Wellfounded_Owf(T_a,V_r_2) % 172.48/172.43 => c_Wellfounded_Owf(tc_List_Olist(T_a),c_List_Olex(T_a,V_r_2)) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_wf__lexn,axiom, % 172.48/172.43 ! [V_n_2,V_r_2,T_a] : % 172.48/172.43 ( c_Wellfounded_Owf(T_a,V_r_2) % 172.48/172.43 => c_Wellfounded_Owf(tc_List_Olist(T_a),hAPP(c_List_Olexn(T_a,V_r_2),V_n_2)) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_lex__def,axiom, % 172.48/172.43 ! [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)) ). % 172.48/172.43 % 172.48/172.43 fof(fact_lexn_Osimps_I1_J,axiom, % 172.48/172.43 ! [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)) ). % 172.48/172.43 % 172.48/172.43 fof(fact_wf__same__fst,axiom, % 172.48/172.43 ! [T_a,V_R_2,T_b,V_P_2] : % 172.48/172.43 ( ! [B_x] : % 172.48/172.43 ( hBOOL(hAPP(V_P_2,B_x)) % 172.48/172.43 => c_Wellfounded_Owf(T_b,hAPP(V_R_2,B_x)) ) % 172.48/172.43 => c_Wellfounded_Owf(tc_prod(T_a,T_b),c_Recdef_Osame__fst(T_a,T_b,V_P_2,V_R_2)) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_Range__Collect__split,axiom, % 172.48/172.43 ! [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))) ). % 172.48/172.43 % 172.48/172.43 fof(fact_image__split__eq__Sigma,axiom, % 172.48/172.43 ! [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))) ). % 172.48/172.43 % 172.48/172.43 fof(fact_SigmaI,axiom, % 172.48/172.43 ! [V_B_2,V_b_2,T_b,V_A_2,V_a_2,T_a] : % 172.48/172.43 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 172.48/172.43 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2))) % 172.48/172.43 => 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))) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_RangeI,axiom, % 172.48/172.43 ! [V_r_2,V_b_2,V_a_2,T_b,T_a] : % 172.48/172.43 ( 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)) % 172.48/172.43 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(c_Relation_ORange(T_a,T_b),V_r_2))) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_Range__Id__on,axiom, % 172.48/172.43 ! [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 ). % 172.48/172.43 % 172.48/172.43 fof(fact_Sigma__Diff__distrib1,axiom, % 172.48/172.43 ! [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)) ). % 172.48/172.43 % 172.48/172.43 fof(fact_Times__Diff__distrib1,axiom, % 172.48/172.43 ! [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))) ). % 172.48/172.43 % 172.48/172.43 fof(fact_Sigma__Diff__distrib2,axiom, % 172.48/172.43 ! [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)) ). % 172.48/172.43 % 172.48/172.43 fof(fact_Times__eq__cancel2,axiom, % 172.48/172.43 ! [V_B_2,V_A_2,T_b,V_C_2,V_x_2,T_a] : % 172.48/172.43 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_C_2)) % 172.48/172.43 => ( 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)) % 172.48/172.43 <=> V_A_2 = V_B_2 ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_Sigma__empty1,axiom, % 172.48/172.43 ! [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)) ). % 172.48/172.43 % 172.48/172.43 fof(fact_card__cartesian__product,axiom, % 172.48/172.43 ! [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)) ). % 172.48/172.43 % 172.48/172.43 fof(fact_setsum__cartesian__product,axiom, % 172.48/172.43 ! [V_A_2,V_B_2,V_f_2,T_c,T_b,T_a] : % 172.48/172.43 ( class_Groups_Ocomm__monoid__add(T_a) % 172.48/172.43 => 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))) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_Sigma__empty2,axiom, % 172.48/172.43 ! [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)) ). % 172.48/172.43 % 172.48/172.43 fof(fact_Times__empty,axiom, % 172.48/172.43 ! [V_B_2,V_A_2,T_b,T_a] : % 172.48/172.43 ( 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)) % 172.48/172.43 <=> ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.43 | V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_Compl__Times__UNIV2,axiom, % 172.48/172.43 ! [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)))) ). % 172.48/172.43 % 172.48/172.43 fof(fact_Compl__Times__UNIV1,axiom, % 172.48/172.43 ! [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))) ). % 172.48/172.43 % 172.48/172.43 fof(fact_setprod__cartesian__product,axiom, % 172.48/172.43 ! [V_A_2,V_B_2,V_f_2,T_c,T_b,T_a] : % 172.48/172.43 ( class_Groups_Ocomm__monoid__mult(T_a) % 172.48/172.43 => 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))) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_Sigma__Un__distrib2,axiom, % 172.48/172.43 ! [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)) ). % 172.48/172.43 % 172.48/172.43 fof(fact_Times__Un__distrib1,axiom, % 172.48/172.43 ! [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))) ). % 172.48/172.43 % 172.48/172.43 fof(fact_Sigma__Un__distrib1,axiom, % 172.48/172.43 ! [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)) ). % 172.48/172.43 % 172.48/172.43 fof(fact_rel__comp__subset__Sigma,axiom, % 172.48/172.43 ! [V_C_2,V_s_2,T_c,V_B_2,V_A_2,V_r_2,T_b,T_a] : % 172.48/172.43 ( 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)))) % 172.48/172.43 => ( 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)))) % 172.48/172.43 => 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)))) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_swap__product,axiom, % 172.48/172.43 ! [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)) ). % 172.48/172.43 % 172.48/172.43 fof(fact_finite__cartesian__product,axiom, % 172.48/172.43 ! [V_B_2,T_b,V_A_2,T_a] : % 172.48/172.43 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) % 172.48/172.43 => 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)))) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_equiv__type,axiom, % 172.48/172.43 ! [V_r_2,V_A_2,T_a] : % 172.48/172.43 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 172.48/172.43 => 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)))) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_Sigma__Int__distrib1,axiom, % 172.48/172.43 ! [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)) ). % 172.48/172.43 % 172.48/172.43 fof(fact_Times__Int__distrib1,axiom, % 172.48/172.43 ! [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))) ). % 172.48/172.43 % 172.48/172.43 fof(fact_Sigma__Int__distrib2,axiom, % 172.48/172.43 ! [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)) ). % 172.48/172.43 % 172.48/172.43 fof(fact_Id__on__subset__Times,axiom, % 172.48/172.43 ! [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)))) ). % 172.48/172.43 % 172.48/172.43 fof(fact_Range__Diff__subset,axiom, % 172.48/172.43 ! [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)))) ). % 172.48/172.43 % 172.48/172.43 fof(fact_UNIV__Times__UNIV,axiom, % 172.48/172.43 ! [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)) ). % 172.48/172.43 % 172.48/172.43 fof(fact_mem__Sigma__iff,axiom, % 172.48/172.43 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_b,T_a] : % 172.48/172.43 ( 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))) % 172.48/172.43 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 172.48/172.43 & hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_SigmaD1,axiom, % 172.48/172.43 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_b,T_a] : % 172.48/172.43 ( 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))) % 172.48/172.43 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_SigmaD2,axiom, % 172.48/172.43 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_b,T_a] : % 172.48/172.43 ( 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))) % 172.48/172.43 => hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2))) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_SigmaE2,axiom, % 172.48/172.43 ! [V_B_2,V_A_2,V_b_2,V_a_2,T_b,T_a] : % 172.48/172.43 ( 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))) % 172.48/172.43 => ~ ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 172.48/172.43 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_Range__empty,axiom, % 172.48/172.43 ! [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)) ). % 172.48/172.43 % 172.48/172.43 fof(fact_Range__empty__iff,axiom, % 172.48/172.43 ! [V_r_2,T_a,T_b] : % 172.48/172.43 ( hAPP(c_Relation_ORange(T_b,T_a),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.43 <=> V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_b,T_a),tc_HOL_Obool)) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_Range__Un__eq,axiom, % 172.48/172.43 ! [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)) ). % 172.48/172.43 % 172.48/172.43 fof(fact_finite__Range,axiom, % 172.48/172.43 ! [V_r_2,T_b,T_a] : % 172.48/172.43 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_b)),V_r_2)) % 172.48/172.43 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(c_Relation_ORange(T_a,T_b),V_r_2))) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_snd__eq__Range,axiom, % 172.48/172.43 ! [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) ). % 172.48/172.43 % 172.48/172.43 fof(fact_card__cartesian__product__singleton,axiom, % 172.48/172.43 ! [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) ). % 172.48/172.43 % 172.48/172.43 fof(fact_Times__subset__cancel2,axiom, % 172.48/172.43 ! [V_B_2,V_A_2,T_b,V_C_2,V_x_2,T_a] : % 172.48/172.43 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_C_2)) % 172.48/172.43 => ( 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)))) % 172.48/172.43 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_b,tc_HOL_Obool)),V_A_2),V_B_2)) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_Image__subset,axiom, % 172.48/172.43 ! [V_C_2,V_B_2,V_A_2,V_r_2,T_b,T_a] : % 172.48/172.43 ( 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)))) % 172.48/172.43 => 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)) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_finite__cartesian__productD2,axiom, % 172.48/172.43 ! [V_B_2,V_A_2,T_b,T_a] : % 172.48/172.43 ( 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)))) % 172.48/172.43 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.43 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),V_B_2)) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_finite__cartesian__productD1,axiom, % 172.48/172.43 ! [V_B_2,V_A_2,T_b,T_a] : % 172.48/172.43 ( 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)))) % 172.48/172.43 => ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_b,tc_HOL_Obool)) % 172.48/172.43 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_Collect__split,axiom, % 172.48/172.43 ! [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))) ). % 172.48/172.43 % 172.48/172.43 fof(fact_SetCompr__Sigma__eq,axiom, % 172.48/172.43 ! [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)) ). % 172.48/172.43 % 172.48/172.43 fof(fact_fst__image__times,axiom, % 172.48/172.43 ! [V_A_2,T_b,T_a,V_B_2] : % 172.48/172.43 ( ( V_B_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.43 => 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)) ) % 172.48/172.43 & ( V_B_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.43 => 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 ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_snd__image__times,axiom, % 172.48/172.43 ! [V_B_2,T_b,T_a,V_A_2] : % 172.48/172.43 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.43 => 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)) ) % 172.48/172.43 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.43 => 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 ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_Range__iff,axiom, % 172.48/172.43 ! [V_r_2,T_b,V_a_2,T_a] : % 172.48/172.43 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Relation_ORange(T_b,T_a),V_r_2))) % 172.48/172.43 <=> ? [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)) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_Range__insert,axiom, % 172.48/172.43 ! [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)) ). % 172.48/172.43 % 172.48/172.43 fof(fact_Range__Int__subset,axiom, % 172.48/172.43 ! [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)))) ). % 172.48/172.43 % 172.48/172.43 fof(fact_insert__times__insert,axiom, % 172.48/172.43 ! [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)))) ). % 172.48/172.43 % 172.48/172.43 fof(fact_finite__equiv__class,axiom, % 172.48/172.43 ! [V_X_2,V_r_2,V_A_2,T_a] : % 172.48/172.43 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.43 => ( 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)))) % 172.48/172.43 => ( 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))) % 172.48/172.43 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_X_2)) ) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_vimage__Times,axiom, % 172.48/172.43 ! [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)) ). % 172.48/172.43 % 172.48/172.43 fof(fact_UN__Times__distrib,axiom, % 172.48/172.43 ! [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))) ). % 172.48/172.43 % 172.48/172.43 fof(fact_Sigma__def,axiom, % 172.48/172.43 ! [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))))) ). % 172.48/172.43 % 172.48/172.43 fof(fact_finite__quotient,axiom, % 172.48/172.43 ! [V_r_2,V_A_2,T_a] : % 172.48/172.43 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.43 => ( 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)))) % 172.48/172.43 => 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))) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_setsum__mult__setsum__if__inj,axiom, % 172.48/172.43 ! [V_B_2,V_A_2,V_g_2,V_f_2,T_b,T_a,T_c] : % 172.48/172.43 ( class_Rings_Osemiring__0(T_c) % 172.48/172.43 => ( 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))) % 172.48/172.43 => 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))))))) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_RangeP__Range__eq,axiom, % 172.48/172.43 ! [V_x_2,V_r_2,T_b,T_a] : % 172.48/172.43 ( 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)) % 172.48/172.43 <=> hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_Relation_ORange(T_a,T_b),V_r_2))) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_Ex__inj__on__UNION__Sigma,axiom, % 172.48/172.43 ! [V_A_2,V_I_2,T_b,T_a] : % 172.48/172.43 ? [B_f] : % 172.48/172.43 ( 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)) % 172.48/172.43 & 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))) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_RangeP_Ointros,axiom, % 172.48/172.43 ! [T_b,T_a,V_b_2,V_a_2,V_r_2] : % 172.48/172.43 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2)) % 172.48/172.43 => hBOOL(hAPP(c_Predicate_ORangeP(T_a,T_b,V_r_2),V_b_2)) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_image__id,axiom, % 172.48/172.43 ! [V_Y_2,T_a] : hAPP(c_Set_Oimage(T_a,T_a,c_Fun_Oid(T_a)),V_Y_2) = V_Y_2 ). % 172.48/172.43 % 172.48/172.43 fof(fact_vimage__id,axiom, % 172.48/172.43 ! [V_A_2,T_a] : hAPP(c_Set_Ovimage(T_a,T_a,c_Fun_Oid(T_a)),V_A_2) = V_A_2 ). % 172.48/172.43 % 172.48/172.43 fof(fact_id__apply,axiom, % 172.48/172.43 ! [V_x,T_a] : hAPP(c_Fun_Oid(T_a),V_x) = V_x ). % 172.48/172.43 % 172.48/172.43 fof(fact_RangeP_Oequations,axiom, % 172.48/172.43 ! [V_a2_2,V_r_2,T_b,T_a] : % 172.48/172.43 ( hBOOL(hAPP(c_Predicate_ORangeP(T_a,T_b,V_r_2),V_a2_2)) % 172.48/172.43 <=> ? [B_a] : hBOOL(hAPP(hAPP(V_r_2,B_a),V_a2_2)) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_id__def,axiom, % 172.48/172.43 ! [V_x_1,T_a] : hAPP(c_Fun_Oid(T_a),V_x_1) = V_x_1 ). % 172.48/172.43 % 172.48/172.43 fof(fact_apsnd__id,axiom, % 172.48/172.43 ! [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)) ). % 172.48/172.43 % 172.48/172.43 fof(fact_id__o,axiom, % 172.48/172.43 ! [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 ). % 172.48/172.43 % 172.48/172.43 fof(fact_o__id,axiom, % 172.48/172.43 ! [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 ). % 172.48/172.43 % 172.48/172.43 fof(fact_o__eq__id__dest,axiom, % 172.48/172.43 ! [V_v_2,V_ca_2,V_b_2,V_a_2,T_a,T_b,T_c] : % 172.48/172.43 ( hAPP(c_Fun_Ocomp(T_c,T_b,T_a,V_a_2),V_b_2) = hAPP(c_Fun_Ocomp(T_b,T_b,T_a,c_Fun_Oid(T_b)),V_ca_2) % 172.48/172.43 => hAPP(V_a_2,hAPP(V_b_2,V_v_2)) = hAPP(V_ca_2,V_v_2) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_apfst__id,axiom, % 172.48/172.43 ! [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)) ). % 172.48/172.43 % 172.48/172.43 fof(fact_inj__on__id,axiom, % 172.48/172.43 ! [V_A_2,T_a] : c_Fun_Oinj__on(T_a,T_a,c_Fun_Oid(T_a),V_A_2) ). % 172.48/172.43 % 172.48/172.43 fof(fact_of__int__eq__id,axiom, % 172.48/172.43 c_Int_Oring__1__class_Oof__int(tc_Int_Oint) = c_Fun_Oid(tc_Int_Oint) ). % 172.48/172.43 % 172.48/172.43 fof(fact_surj__id,axiom, % 172.48/172.43 ! [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)) ). % 172.48/172.43 % 172.48/172.43 fof(fact_folding_Oempty,axiom, % 172.48/172.43 ! [V_F_2,V_f_2,T_b,T_a] : % 172.48/172.43 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 172.48/172.43 => hAPP(V_F_2,c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) = c_Fun_Oid(T_b) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_split__Pair,axiom, % 172.48/172.43 ! [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)) ). % 172.48/172.43 % 172.48/172.43 fof(fact_setsum__reindex__id,axiom, % 172.48/172.43 ! [V_B_2,V_f_2,T_a,T_b] : % 172.48/172.43 ( class_Groups_Ocomm__monoid__add(T_b) % 172.48/172.43 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2) % 172.48/172.43 => 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)) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_setprod__reindex__id,axiom, % 172.48/172.43 ! [V_B_2,V_f_2,T_a,T_b] : % 172.48/172.43 ( class_Groups_Ocomm__monoid__mult(T_b) % 172.48/172.43 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_B_2) % 172.48/172.43 => 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)) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_setprod__Sigma,axiom, % 172.48/172.43 ! [V_f_2,V_B_2,T_b,V_A_2,T_a,T_c] : % 172.48/172.43 ( class_Groups_Ocomm__monoid__mult(T_c) % 172.48/172.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.43 => ( ! [B_x] : % 172.48/172.43 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 172.48/172.43 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_x))) ) % 172.48/172.43 => 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)) ) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_setsum__Sigma,axiom, % 172.48/172.43 ! [V_f_2,V_B_2,T_b,V_A_2,T_a,T_c] : % 172.48/172.43 ( class_Groups_Ocomm__monoid__add(T_c) % 172.48/172.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.43 => ( ! [B_x] : % 172.48/172.43 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 172.48/172.43 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_x))) ) % 172.48/172.43 => 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)) ) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_fold__image__Sigma,axiom, % 172.48/172.43 ! [V_g_2,V_B_2,T_b,V_A_2,T_a,T_c] : % 172.48/172.43 ( class_Groups_Ocomm__monoid__mult(T_c) % 172.48/172.43 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.43 => ( ! [B_x] : % 172.48/172.43 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 172.48/172.43 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_x))) ) % 172.48/172.43 => 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)) ) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_card__SigmaI,axiom, % 172.48/172.43 ! [V_B_2,T_b,V_A_2,T_a] : % 172.48/172.43 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.43 => ( ! [B_x] : % 172.48/172.43 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 172.48/172.43 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_x))) ) % 172.48/172.43 => 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) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_finite__SigmaI,axiom, % 172.48/172.43 ! [V_B_2,T_b,V_A_2,T_a] : % 172.48/172.43 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.43 => ( ! [B_a] : % 172.48/172.43 ( hBOOL(hAPP(hAPP(c_member(T_a),B_a),V_A_2)) % 172.48/172.43 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_B_2,B_a))) ) % 172.48/172.43 => 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))) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_RangeE,axiom, % 172.48/172.43 ! [V_r_2,T_b,V_b_2,T_a] : % 172.48/172.43 ( hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(c_Relation_ORange(T_b,T_a),V_r_2))) % 172.48/172.43 => ~ ! [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)) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_SigmaE,axiom, % 172.48/172.43 ! [V_B_2,V_A_2,V_ca_2,T_b,T_a] : % 172.48/172.43 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),V_ca_2),hAPP(hAPP(c_Product__Type_OSigma(T_a,T_b),V_A_2),V_B_2))) % 172.48/172.43 => ~ ! [B_x] : % 172.48/172.43 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 172.48/172.43 => ! [B_y] : % 172.48/172.43 ( hBOOL(hAPP(hAPP(c_member(T_b),B_y),hAPP(V_B_2,B_x))) % 172.48/172.43 => V_ca_2 != hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_x),B_y) ) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_wf__Un,axiom, % 172.48/172.43 ! [V_s_2,V_r_2,T_a] : % 172.48/172.43 ( c_Wellfounded_Owf(T_a,V_r_2) % 172.48/172.43 => ( c_Wellfounded_Owf(T_a,V_s_2) % 172.48/172.43 => ( 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)) % 172.48/172.43 => 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)) ) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_map__pair__surj,axiom, % 172.48/172.43 ! [V_g_2,T_c,T_d,V_f_2,T_a,T_b] : % 172.48/172.43 ( hAPP(c_Set_Oimage(T_b,T_a,V_f_2),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.43 => ( 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)) % 172.48/172.43 => 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)) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_DomainI,axiom, % 172.48/172.43 ! [V_r_2,V_b_2,V_a_2,T_b,T_a] : % 172.48/172.43 ( 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)) % 172.48/172.43 => hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Relation_ODomain(T_a,T_b),V_r_2))) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_map__pair__imageI,axiom, % 172.48/172.43 ! [V_g_2,V_f_2,T_d,T_c,V_R_2,V_b_2,V_a_2,T_b,T_a] : % 172.48/172.43 ( 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)) % 172.48/172.43 => 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))) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_map__pair_Ocomp,axiom, % 172.48/172.43 ! [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)) ). % 172.48/172.43 % 172.48/172.43 fof(fact_map__pair__compose,axiom, % 172.48/172.43 ! [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)) ). % 172.48/172.43 % 172.48/172.43 fof(fact_map__pair_Ocompositionality,axiom, % 172.48/172.43 ! [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) ). % 172.48/172.43 % 172.48/172.43 fof(fact_snd__comp__map__pair,axiom, % 172.48/172.43 ! [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)) ). % 172.48/172.43 % 172.48/172.43 fof(fact_fst__comp__map__pair,axiom, % 172.48/172.43 ! [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)) ). % 172.48/172.43 % 172.48/172.43 fof(fact_fst__map__pair,axiom, % 172.48/172.43 ! [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)) ). % 172.48/172.43 % 172.48/172.43 fof(fact_snd__prod__fun,axiom, % 172.48/172.43 ! [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)) ). % 172.48/172.43 % 172.48/172.43 fof(fact_Domain__Id__on,axiom, % 172.48/172.43 ! [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 ). % 172.48/172.43 % 172.48/172.43 fof(fact_map__pair__simp,axiom, % 172.48/172.43 ! [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)) ). % 172.48/172.43 % 172.48/172.43 fof(fact_map__pair__ident,axiom, % 172.48/172.43 ! [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 ). % 172.48/172.43 % 172.48/172.43 fof(fact_map__pair_Oidentity,axiom, % 172.48/172.43 ! [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)) ). % 172.48/172.43 % 172.48/172.43 fof(fact_Domain__empty,axiom, % 172.48/172.43 ! [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)) ). % 172.48/172.43 % 172.48/172.43 fof(fact_Domain__empty__iff,axiom, % 172.48/172.43 ! [V_r_2,T_b,T_a] : % 172.48/172.43 ( hAPP(c_Relation_ODomain(T_a,T_b),V_r_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.43 <=> V_r_2 = c_Orderings_Obot__class_Obot(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool)) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_Domain__mono,axiom, % 172.48/172.43 ! [V_s_2,V_r_2,T_b,T_a] : % 172.48/172.43 ( 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)) % 172.48/172.43 => 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))) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_Domain__Un__eq,axiom, % 172.48/172.43 ! [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)) ). % 172.48/172.43 % 172.48/172.43 fof(fact_finite__Domain,axiom, % 172.48/172.43 ! [V_r_2,T_b,T_a] : % 172.48/172.43 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_b)),V_r_2)) % 172.48/172.43 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_Relation_ODomain(T_a,T_b),V_r_2))) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_fst__eq__Domain,axiom, % 172.48/172.43 ! [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) ). % 172.48/172.43 % 172.48/172.43 fof(fact_apfst__def,axiom, % 172.48/172.43 ! [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)) ). % 172.48/172.43 % 172.48/172.43 fof(fact_apsnd__def,axiom, % 172.48/172.43 ! [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) ). % 172.48/172.43 % 172.48/172.43 fof(fact_map__pair_Oid,axiom, % 172.48/172.43 ! [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)) ). % 172.48/172.43 % 172.48/172.43 fof(fact_map__pair__def,axiom, % 172.48/172.43 ! [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)) ). % 172.48/172.43 % 172.48/172.43 fof(fact_Domain__iff,axiom, % 172.48/172.43 ! [V_r_2,T_b,V_a_2,T_a] : % 172.48/172.43 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Relation_ODomain(T_a,T_b),V_r_2))) % 172.48/172.43 <=> ? [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)) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_Domain__insert,axiom, % 172.48/172.43 ! [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)) ). % 172.48/172.43 % 172.48/172.43 fof(fact_Domain__Int__subset,axiom, % 172.48/172.43 ! [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)))) ). % 172.48/172.43 % 172.48/172.43 fof(fact_Domain__Diff__subset,axiom, % 172.48/172.43 ! [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)))) ). % 172.48/172.43 % 172.48/172.43 fof(fact_Field__def,axiom, % 172.48/172.43 ! [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)) ). % 172.48/172.43 % 172.48/172.43 fof(fact_map__pair__surj__on,axiom, % 172.48/172.43 ! [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] : % 172.48/172.43 ( hAPP(c_Set_Oimage(T_b,T_a,V_f_2),V_A_2) = V_A_H_2 % 172.48/172.43 => ( hAPP(c_Set_Oimage(T_d,T_c,V_g_2),V_B_2) = V_B_H_2 % 172.48/172.43 => 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)) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_Domain__Collect__split,axiom, % 172.48/172.43 ! [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)) ). % 172.48/172.43 % 172.48/172.43 fof(fact_wf__map__pair__image,axiom, % 172.48/172.43 ! [V_f_2,T_b,V_r_2,T_a] : % 172.48/172.43 ( c_Wellfounded_Owf(T_a,V_r_2) % 172.48/172.43 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 172.48/172.43 => 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)) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_map__pair__inj__on,axiom, % 172.48/172.43 ! [V_B_2,V_g_2,T_d,T_c,V_A_2,V_f_2,T_b,T_a] : % 172.48/172.43 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 172.48/172.43 => ( c_Fun_Oinj__on(T_c,T_d,V_g_2,V_B_2) % 172.48/172.43 => 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))) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_DomainP__Domain__eq,axiom, % 172.48/172.43 ! [V_x_2,V_r_2,T_b,T_a] : % 172.48/172.43 ( 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)) % 172.48/172.43 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_Relation_ODomain(T_a,T_b),V_r_2))) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_prod__fun__imageE,axiom, % 172.48/172.43 ! [V_R_2,V_g_2,V_f_2,T_d,T_c,V_ca_2,T_b,T_a] : % 172.48/172.43 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_b)),V_ca_2),hAPP(c_Set_Oimage(tc_prod(T_c,T_d),tc_prod(T_a,T_b),c_Product__Type_Omap__pair(T_c,T_a,T_d,T_b,V_f_2,V_g_2)),V_R_2))) % 172.48/172.43 => ~ ! [B_x,B_y] : % 172.48/172.43 ( V_ca_2 = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_y)) % 172.48/172.43 => ~ 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)) ) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_DomainE,axiom, % 172.48/172.43 ! [V_r_2,T_b,V_a_2,T_a] : % 172.48/172.43 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_Relation_ODomain(T_a,T_b),V_r_2))) % 172.48/172.43 => ~ ! [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)) ) ). % 172.48/172.43 % 172.48/172.43 fof(fact_DomainP_Ointros,axiom, % 172.48/172.43 ! [T_b,T_a,V_b_2,V_a_2,V_r_2] : % 172.48/172.43 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2)) % 172.48/172.43 => hBOOL(hAPP(c_Predicate_ODomainP(T_a,T_b,V_r_2),V_a_2)) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_DomainP_Oequations,axiom, % 172.48/172.44 ! [V_a1_2,V_r_2,T_b,T_a] : % 172.48/172.44 ( hBOOL(hAPP(c_Predicate_ODomainP(T_a,T_b,V_r_2),V_a1_2)) % 172.48/172.44 <=> ? [B_x1] : hBOOL(hAPP(hAPP(V_r_2,V_a1_2),B_x1)) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_refl__on__def,axiom, % 172.48/172.44 ! [V_r_2,V_A_2,T_a] : % 172.48/172.44 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2) % 172.48/172.44 <=> ( 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)))) % 172.48/172.44 & ! [B_x] : % 172.48/172.44 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 172.48/172.44 => 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)) ) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_wfP__def,axiom, % 172.48/172.44 ! [V_r_2,T_a] : % 172.48/172.44 ( c_Wellfounded_OwfP(T_a,V_r_2) % 172.48/172.44 <=> 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))) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_Rep__Integ__induct,axiom, % 172.48/172.44 ! [V_P_2,V_y_2] : % 172.48/172.44 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_y_2),c_Int_OInteg)) % 172.48/172.44 => ( ! [B_x] : hBOOL(hAPP(V_P_2,hAPP(c_Int_ORep__Integ,B_x))) % 172.48/172.44 => hBOOL(hAPP(V_P_2,V_y_2)) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_wfP__empty,axiom, % 172.48/172.44 ! [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))) ). % 172.48/172.44 % 172.48/172.44 fof(fact_refl__on__Id__on,axiom, % 172.48/172.44 ! [V_A_2,T_a] : c_Relation_Orefl__on(T_a,V_A_2,c_Relation_OId__on(T_a,V_A_2)) ). % 172.48/172.44 % 172.48/172.44 fof(fact_accp__wfPD,axiom, % 172.48/172.44 ! [V_x_2,V_r_2,T_a] : % 172.48/172.44 ( c_Wellfounded_OwfP(T_a,V_r_2) % 172.48/172.44 => hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),V_x_2)) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_wfP__accp__iff,axiom, % 172.48/172.44 ! [V_r_2,T_a] : % 172.48/172.44 ( c_Wellfounded_OwfP(T_a,V_r_2) % 172.48/172.44 <=> ! [B_x1] : hBOOL(hAPP(c_Wellfounded_Oaccp(T_a,V_r_2),B_x1)) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_wfP__subset,axiom, % 172.48/172.44 ! [V_p_2,V_r_2,T_a] : % 172.48/172.44 ( c_Wellfounded_OwfP(T_a,V_r_2) % 172.48/172.44 => ( 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)) % 172.48/172.44 => c_Wellfounded_OwfP(T_a,V_p_2) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_refl__on__empty,axiom, % 172.48/172.44 ! [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))) ). % 172.48/172.44 % 172.48/172.44 fof(fact_refl__on__Un,axiom, % 172.48/172.44 ! [V_s_2,V_B_2,V_r_2,V_A_2,T_a] : % 172.48/172.44 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2) % 172.48/172.44 => ( c_Relation_Orefl__on(T_a,V_B_2,V_s_2) % 172.48/172.44 => 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)) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_refl__on__Int,axiom, % 172.48/172.44 ! [V_s_2,V_B_2,V_r_2,V_A_2,T_a] : % 172.48/172.44 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2) % 172.48/172.44 => ( c_Relation_Orefl__on(T_a,V_B_2,V_s_2) % 172.48/172.44 => 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)) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_refl__onD,axiom, % 172.48/172.44 ! [V_a_2,V_r_2,V_A_2,T_a] : % 172.48/172.44 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2) % 172.48/172.44 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 172.48/172.44 => 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)) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_refl__onD1,axiom, % 172.48/172.44 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_a] : % 172.48/172.44 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2) % 172.48/172.44 => ( 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)) % 172.48/172.44 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_refl__onD2,axiom, % 172.48/172.44 ! [V_y_2,V_x_2,V_r_2,V_A_2,T_a] : % 172.48/172.44 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2) % 172.48/172.44 => ( 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)) % 172.48/172.44 => hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),V_A_2)) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_wf__in__rel,axiom, % 172.48/172.44 ! [V_R_2,T_a] : % 172.48/172.44 ( c_Wellfounded_Owf(T_a,V_R_2) % 172.48/172.44 => c_Wellfounded_OwfP(T_a,c_FunDef_Oin__rel(T_a,T_a,V_R_2)) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_wfP__wf__eq,axiom, % 172.48/172.44 ! [V_r_2,T_a] : % 172.48/172.44 ( 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)) % 172.48/172.44 <=> c_Wellfounded_Owf(T_a,V_r_2) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_reflp__def,axiom, % 172.48/172.44 ! [V_r_2,T_a] : % 172.48/172.44 ( c_Predicate_Oreflp(T_a,V_r_2) % 172.48/172.44 <=> 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))) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_refl__onI,axiom, % 172.48/172.44 ! [V_A_2,V_r_2,T_a] : % 172.48/172.44 ( 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)))) % 172.48/172.44 => ( ! [B_x] : % 172.48/172.44 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 172.48/172.44 => 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)) ) % 172.48/172.44 => c_Relation_Orefl__on(T_a,V_A_2,V_r_2) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_wfP__acyclicP,axiom, % 172.48/172.44 ! [V_r_2,T_a] : % 172.48/172.44 ( c_Wellfounded_OwfP(T_a,V_r_2) % 172.48/172.44 => 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))) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_reflpE,axiom, % 172.48/172.44 ! [V_x_2,V_r_2,T_a] : % 172.48/172.44 ( c_Predicate_Oreflp(T_a,V_r_2) % 172.48/172.44 => hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_x_2)) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_wf__acyclic,axiom, % 172.48/172.44 ! [V_r_2,T_a] : % 172.48/172.44 ( c_Wellfounded_Owf(T_a,V_r_2) % 172.48/172.44 => c_Wellfounded_Oacyclic(T_a,V_r_2) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_acyclic__subset,axiom, % 172.48/172.44 ! [V_r_2,V_s_2,T_a] : % 172.48/172.44 ( c_Wellfounded_Oacyclic(T_a,V_s_2) % 172.48/172.44 => ( 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)) % 172.48/172.44 => c_Wellfounded_Oacyclic(T_a,V_r_2) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_finite__acyclic__wf,axiom, % 172.48/172.44 ! [V_r_2,T_a] : % 172.48/172.44 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2)) % 172.48/172.44 => ( c_Wellfounded_Oacyclic(T_a,V_r_2) % 172.48/172.44 => c_Wellfounded_Owf(T_a,V_r_2) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_wf__iff__acyclic__if__finite,axiom, % 172.48/172.44 ! [V_r_2,T_a] : % 172.48/172.44 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2)) % 172.48/172.44 => ( c_Wellfounded_Owf(T_a,V_r_2) % 172.48/172.44 <=> c_Wellfounded_Oacyclic(T_a,V_r_2) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_Nitpick_Owf_H__def,axiom, % 172.48/172.44 ! [V_r_2,T_a] : % 172.48/172.44 ( c_Nitpick_Owf_H(T_a,V_r_2) % 172.48/172.44 <=> ( c_Wellfounded_Oacyclic(T_a,V_r_2) % 172.48/172.44 & ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2)) % 172.48/172.44 | c_Nitpick_Ounknown(tc_HOL_Obool) ) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_Rep__Integ__cases,axiom, % 172.48/172.44 ! [V_y_2] : % 172.48/172.44 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),V_y_2),c_Int_OInteg)) % 172.48/172.44 => ~ ! [B_x] : V_y_2 != hAPP(c_Int_ORep__Integ,B_x) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_refl__on__def_H,axiom, % 172.48/172.44 ! [V_r_2,V_A_2,T_a] : % 172.48/172.44 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2) % 172.48/172.44 <=> ( ! [B_x] : % 172.48/172.44 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),B_x),V_r_2)) % 172.48/172.44 => 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)) ) % 172.48/172.44 & ! [B_x] : % 172.48/172.44 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 172.48/172.44 => 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)) ) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_Powp__def,axiom, % 172.48/172.44 ! [V_B_2,V_A_2,T_a] : % 172.48/172.44 ( hBOOL(hAPP(c_Predicate_OPowp(T_a,V_A_2),V_B_2)) % 172.48/172.44 <=> ! [B_x] : % 172.48/172.44 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_B_2)) % 172.48/172.44 => hBOOL(hAPP(V_A_2,B_x)) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_ball__UNIV,axiom, % 172.48/172.44 ! [V_P_2,T_a] : % 172.48/172.44 ( ! [B_x] : % 172.48/172.44 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) % 172.48/172.44 => hBOOL(hAPP(V_P_2,B_x)) ) % 172.48/172.44 <=> ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_ball__empty,axiom, % 172.48/172.44 ! [V_P_2,T_a,B_x] : % 172.48/172.44 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) % 172.48/172.44 => hBOOL(hAPP(V_P_2,B_x)) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_congruent__def,axiom, % 172.48/172.44 ! [V_f_2,V_r_2,T_b,T_a] : % 172.48/172.44 ( c_Equiv__Relations_Ocongruent(T_a,T_b,V_r_2,V_f_2) % 172.48/172.44 <=> ! [B_x] : % 172.48/172.44 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),B_x),V_r_2)) % 172.48/172.44 => 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)) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_Abs__Integ__induct,axiom, % 172.48/172.44 ! [V_x_2,V_P_2] : % 172.48/172.44 ( ! [B_y] : % 172.48/172.44 ( hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),B_y),c_Int_OInteg)) % 172.48/172.44 => hBOOL(hAPP(V_P_2,hAPP(c_Int_OAbs__Integ,B_y))) ) % 172.48/172.44 => hBOOL(hAPP(V_P_2,V_x_2)) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_Abs__Integ__cases,axiom, % 172.48/172.44 ! [V_x_2] : % 172.48/172.44 ~ ! [B_y] : % 172.48/172.44 ( V_x_2 = hAPP(c_Int_OAbs__Integ,B_y) % 172.48/172.44 => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(tc_prod(tc_Nat_Onat,tc_Nat_Onat),tc_HOL_Obool)),B_y),c_Int_OInteg)) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_inj__on__diff__nat,axiom, % 172.48/172.44 ! [V_k_2,V_N_2] : % 172.48/172.44 ( ! [B_x] : % 172.48/172.44 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),V_N_2)) % 172.48/172.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_k_2),B_x)) ) % 172.48/172.44 => 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) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_triples__valid__Suc,axiom, % 172.48/172.44 ! [V_n_2,V_ts_2,T_a] : % 172.48/172.44 ( ! [B_x] : % 172.48/172.44 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_a)),B_x),V_ts_2)) % 172.48/172.44 => c_Hoare__Mirabelle_Otriple__valid(T_a,hAPP(c_Nat_OSuc,V_n_2),B_x) ) % 172.48/172.44 => ! [B_x] : % 172.48/172.44 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_a)),B_x),V_ts_2)) % 172.48/172.44 => c_Hoare__Mirabelle_Otriple__valid(T_a,V_n_2,B_x) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_hoare__valids__def,axiom, % 172.48/172.44 ! [V_ts_2,V_Ga_2,T_a] : % 172.48/172.44 ( c_Hoare__Mirabelle_Ohoare__valids(T_a,V_Ga_2,V_ts_2) % 172.48/172.44 <=> ! [B_n] : % 172.48/172.44 ( ! [B_x] : % 172.48/172.44 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_a)),B_x),V_Ga_2)) % 172.48/172.44 => c_Hoare__Mirabelle_Otriple__valid(T_a,B_n,B_x) ) % 172.48/172.44 => ! [B_x] : % 172.48/172.44 ( hBOOL(hAPP(hAPP(c_member(tc_Hoare__Mirabelle_Otriple(T_a)),B_x),V_ts_2)) % 172.48/172.44 => c_Hoare__Mirabelle_Otriple__valid(T_a,B_n,B_x) ) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_wfP__SUP,axiom, % 172.48/172.44 ! [T_a,V_r_2,T_b] : % 172.48/172.44 ( ! [B_i] : c_Wellfounded_OwfP(T_b,hAPP(V_r_2,B_i)) % 172.48/172.44 => ( ! [B_i,B_j] : % 172.48/172.44 ( hAPP(V_r_2,B_i) != hAPP(V_r_2,B_j) % 172.48/172.44 => 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)) ) % 172.48/172.44 => 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)) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_mem__splitI2,axiom, % 172.48/172.44 ! [V_ca_2,V_z_2,T_c,T_b,T_a,V_p_2] : % 172.48/172.44 ( ! [B_a,B_b] : % 172.48/172.44 ( V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_a),B_b) % 172.48/172.44 => hBOOL(hAPP(hAPP(c_member(T_c),V_z_2),hAPP(hAPP(V_ca_2,B_a),B_b))) ) % 172.48/172.44 => hBOOL(hAPP(hAPP(c_member(T_c),V_z_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_fun(T_c,tc_HOL_Obool)),V_ca_2),V_p_2))) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_mem__splitE,axiom, % 172.48/172.44 ! [V_p_2,V_ca_2,T_c,T_b,V_z_2,T_a] : % 172.48/172.44 ( hBOOL(hAPP(hAPP(c_member(T_a),V_z_2),hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_b,T_c,tc_fun(T_a,tc_HOL_Obool)),V_ca_2),V_p_2))) % 172.48/172.44 => ~ ! [B_x,B_y] : % 172.48/172.44 ( V_p_2 = hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),B_x),B_y) % 172.48/172.44 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_z_2),hAPP(hAPP(V_ca_2,B_x),B_y))) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_Eps__split,axiom, % 172.48/172.44 ! [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))) ). % 172.48/172.44 % 172.48/172.44 fof(fact_wfI__pf,axiom, % 172.48/172.44 ! [V_R_2,T_a] : % 172.48/172.44 ( ! [B_A] : % 172.48/172.44 ( 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))) % 172.48/172.44 => B_A = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) % 172.48/172.44 => c_Wellfounded_Owf(T_a,V_R_2) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_Sigma__mono,axiom, % 172.48/172.44 ! [V_D_2,V_B_2,T_b,V_C_2,V_A_2,T_a] : % 172.48/172.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_C_2)) % 172.48/172.44 => ( ! [B_x] : % 172.48/172.44 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 172.48/172.44 => 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))) ) % 172.48/172.44 => 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))) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_some__sym__eq__trivial,axiom, % 172.48/172.44 ! [V_x_2,T_a] : c_Hilbert__Choice_OEps(T_a,hAPP(c_fequal,V_x_2)) = V_x_2 ). % 172.48/172.44 % 172.48/172.44 fof(fact_some__eq__trivial,axiom, % 172.48/172.44 ! [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 ). % 172.48/172.44 % 172.48/172.44 fof(fact_some__eq__ex,axiom, % 172.48/172.44 ! [T_a,V_P_2] : % 172.48/172.44 ( hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_a,V_P_2))) % 172.48/172.44 <=> ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_someI__ex,axiom, % 172.48/172.44 ! [T_a,V_P_2] : % 172.48/172.44 ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) % 172.48/172.44 => hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_a,V_P_2))) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_someI,axiom, % 172.48/172.44 ! [T_a,V_x_2,V_P_2] : % 172.48/172.44 ( hBOOL(hAPP(V_P_2,V_x_2)) % 172.48/172.44 => hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OEps(T_a,V_P_2))) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_tfl__some,axiom, % 172.48/172.44 ! [T_a,B_P] : % 172.48/172.44 ( ? [B_x] : hBOOL(hAPP(B_P,B_x)) % 172.48/172.44 => hBOOL(hAPP(B_P,c_Hilbert__Choice_OEps(T_a,B_P))) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_exE__some,axiom, % 172.48/172.44 ! [T_a,V_ca_2,V_P_2] : % 172.48/172.44 ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) % 172.48/172.44 => ( V_ca_2 = c_Hilbert__Choice_OEps(T_a,V_P_2) % 172.48/172.44 => hBOOL(hAPP(V_P_2,V_ca_2)) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_Eps__split__eq,axiom, % 172.48/172.44 ! [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) ). % 172.48/172.44 % 172.48/172.44 fof(fact_split__paired__Eps,axiom, % 172.48/172.44 ! [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)))) ). % 172.48/172.44 % 172.48/172.44 fof(fact_LeastM__def,axiom, % 172.48/172.44 ! [V_P_2,V_m_2,T_a,T_b] : % 172.48/172.44 ( class_Orderings_Oord(T_b) % 172.48/172.44 => 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))))) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_GreatestM__def,axiom, % 172.48/172.44 ! [V_P_2,V_m_2,T_a,T_b] : % 172.48/172.44 ( class_Orderings_Oord(T_b) % 172.48/172.44 => 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))))) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_acc_OaccI,axiom, % 172.48/172.44 ! [V_r_2,V_x_2,T_a] : % 172.48/172.44 ( ! [B_y] : % 172.48/172.44 ( 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)) % 172.48/172.44 => hBOOL(hAPP(hAPP(c_member(T_a),B_y),c_Wellfounded_Oacc(T_a,V_r_2))) ) % 172.48/172.44 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Wellfounded_Oacc(T_a,V_r_2))) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_LeastM__nat__lemma,axiom, % 172.48/172.44 ! [V_m_2,T_a,V_k_2,V_P_2] : % 172.48/172.44 ( hBOOL(hAPP(V_P_2,V_k_2)) % 172.48/172.44 => ( hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OLeastM(T_a,tc_Nat_Onat,V_m_2,V_P_2))) % 172.48/172.44 & ! [B_y] : % 172.48/172.44 ( hBOOL(hAPP(V_P_2,B_y)) % 172.48/172.44 => 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))) ) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_LeastM__nat__le,axiom, % 172.48/172.44 ! [T_a,V_m_2,V_x_2,V_P_2] : % 172.48/172.44 ( hBOOL(hAPP(V_P_2,V_x_2)) % 172.48/172.44 => 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))) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_Greatest__def,axiom, % 172.48/172.44 ! [T_a] : % 172.48/172.44 ( class_Orderings_Oord(T_a) % 172.48/172.44 => c_Hilbert__Choice_OGreatest(T_a) = c_Hilbert__Choice_OGreatestM(T_a,T_a,c_COMBI(T_a)) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_not__acc__down,axiom, % 172.48/172.44 ! [V_R_2,V_x_2,T_a] : % 172.48/172.44 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Wellfounded_Oacc(T_a,V_R_2))) % 172.48/172.44 => ~ ! [B_z] : % 172.48/172.44 ( 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)) % 172.48/172.44 => hBOOL(hAPP(hAPP(c_member(T_a),B_z),c_Wellfounded_Oacc(T_a,V_R_2))) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_max__ext_Osimps,axiom, % 172.48/172.44 ! [V_R_2,V_a2_2,V_a1_2,T_a] : % 172.48/172.44 ( 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))) % 172.48/172.44 <=> ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_a1_2)) % 172.48/172.44 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_a2_2)) % 172.48/172.44 & V_a2_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.44 & ! [B_x] : % 172.48/172.44 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_a1_2)) % 172.48/172.44 => ? [B_xa] : % 172.48/172.44 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_a2_2)) % 172.48/172.44 & 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)) ) ) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_LeastM__natI,axiom, % 172.48/172.44 ! [V_m_2,T_a,V_k_2,V_P_2] : % 172.48/172.44 ( hBOOL(hAPP(V_P_2,V_k_2)) % 172.48/172.44 => hBOOL(hAPP(V_P_2,c_Hilbert__Choice_OLeastM(T_a,tc_Nat_Onat,V_m_2,V_P_2))) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_wf__no__infinite__down__chainE,axiom, % 172.48/172.44 ! [V_f_2,V_r_2,T_a] : % 172.48/172.44 ( c_Wellfounded_Owf(T_a,V_r_2) % 172.48/172.44 => ~ ! [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)) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_setsum__reindex__cong,axiom, % 172.48/172.44 ! [V_h_2,V_g_2,V_B_2,V_A_2,V_f_2,T_b,T_a,T_c] : % 172.48/172.44 ( class_Groups_Ocomm__monoid__add(T_c) % 172.48/172.44 => ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_A_2) % 172.48/172.44 => ( V_B_2 = hAPP(c_Set_Oimage(T_a,T_b,V_f_2),V_A_2) % 172.48/172.44 => ( ! [B_a] : % 172.48/172.44 ( hBOOL(hAPP(hAPP(c_member(T_a),B_a),V_A_2)) % 172.48/172.44 => hAPP(V_g_2,B_a) = hAPP(V_h_2,hAPP(V_f_2,B_a)) ) % 172.48/172.44 => 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) ) ) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_scomp__unfold,axiom, % 172.48/172.44 ! [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))) ). % 172.48/172.44 % 172.48/172.44 fof(fact_scomp__apply,axiom, % 172.48/172.44 ! [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)) ). % 172.48/172.44 % 172.48/172.44 fof(fact_scomp__Pair,axiom, % 172.48/172.44 ! [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 ). % 172.48/172.44 % 172.48/172.44 fof(fact_scomp__scomp,axiom, % 172.48/172.44 ! [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)) ). % 172.48/172.44 % 172.48/172.44 fof(fact_Pair__scomp,axiom, % 172.48/172.44 ! [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) ). % 172.48/172.44 % 172.48/172.44 fof(fact_scomp__def,axiom, % 172.48/172.44 ! [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)) ). % 172.48/172.44 % 172.48/172.44 fof(fact_iterate_Osimps,axiom, % 172.48/172.44 ! [V_x_2,V_f_2,T_a,T_b,V_k_2] : % 172.48/172.44 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 172.48/172.44 => 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) ) % 172.48/172.44 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 172.48/172.44 => 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)) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_setsum__ivl__cong,axiom, % 172.48/172.44 ! [V_g_2,V_f_2,V_d_2,V_b_2,V_ca_2,V_a_2,T_a,T_b] : % 172.48/172.44 ( ( class_Groups_Ocomm__monoid__add(T_b) % 172.48/172.44 & class_Orderings_Oord(T_a) ) % 172.48/172.44 => ( V_a_2 = V_ca_2 % 172.48/172.44 => ( V_b_2 = V_d_2 % 172.48/172.44 => ( ! [B_x] : % 172.48/172.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_ca_2),B_x)) % 172.48/172.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),B_x),V_d_2)) % 172.48/172.44 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) ) % 172.48/172.44 => hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_f_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_a_2),V_b_2)) = hAPP(hAPP(c_Big__Operators_Ocomm__monoid__add__class_Osetsum(T_a,T_b),V_g_2),hAPP(c_SetInterval_Oord__class_OatLeastLessThan(T_a,V_ca_2),V_d_2)) ) ) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_less__eq,axiom, % 172.48/172.44 ! [V_n_2,V_m_2] : % 172.48/172.44 ( 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))) % 172.48/172.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_wf__trancl,axiom, % 172.48/172.44 ! [V_r_2,T_a] : % 172.48/172.44 ( c_Wellfounded_Owf(T_a,V_r_2) % 172.48/172.44 => c_Wellfounded_Owf(T_a,c_Transitive__Closure_Otrancl(T_a,V_r_2)) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_less__than__def,axiom, % 172.48/172.44 c_Wellfounded_Oless__than = c_Transitive__Closure_Otrancl(tc_Nat_Onat,c_Wellfounded_Opred__nat) ). % 172.48/172.44 % 172.48/172.44 fof(fact_acyclic__def,axiom, % 172.48/172.44 ! [V_r_2,T_a] : % 172.48/172.44 ( c_Wellfounded_Oacyclic(T_a,V_r_2) % 172.48/172.44 <=> ! [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))) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_trancl_Or__into__trancl,axiom, % 172.48/172.44 ! [V_r_2,V_b_2,V_a_2,T_a] : % 172.48/172.44 ( 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)) % 172.48/172.44 => 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))) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_trancl__subset__Field2,axiom, % 172.48/172.44 ! [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))))) ). % 172.48/172.44 % 172.48/172.44 fof(fact_trancl__Int__subset,axiom, % 172.48/172.44 ! [V_s_2,V_r_2,T_a] : % 172.48/172.44 ( 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)) % 172.48/172.44 => ( 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)) % 172.48/172.44 => 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)) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_r__into__trancl_H,axiom, % 172.48/172.44 ! [V_r_2,V_p_2,T_a] : % 172.48/172.44 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),V_r_2)) % 172.48/172.44 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_trancl__empty,axiom, % 172.48/172.44 ! [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)) ). % 172.48/172.44 % 172.48/172.44 fof(fact_trancl__domain,axiom, % 172.48/172.44 ! [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) ). % 172.48/172.44 % 172.48/172.44 fof(fact_trancl__range,axiom, % 172.48/172.44 ! [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) ). % 172.48/172.44 % 172.48/172.44 fof(fact_finite__trancl,axiom, % 172.48/172.44 ! [V_r_2,T_a] : % 172.48/172.44 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) % 172.48/172.44 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2)) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_trancl__trans,axiom, % 172.48/172.44 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_a] : % 172.48/172.44 ( 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))) % 172.48/172.44 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_b_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) % 172.48/172.44 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_Transitive__Closure_Otrancl__into__trancl,axiom, % 172.48/172.44 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_a] : % 172.48/172.44 ( 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))) % 172.48/172.44 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_b_2),V_ca_2)),V_r_2)) % 172.48/172.44 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_trancl__into__trancl2,axiom, % 172.48/172.44 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_a] : % 172.48/172.44 ( 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)) % 172.48/172.44 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_b_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) % 172.48/172.44 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_r__r__into__trancl,axiom, % 172.48/172.44 ! [V_ca_2,V_R_2,V_b_2,V_a_2,T_a] : % 172.48/172.44 ( 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)) % 172.48/172.44 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_b_2),V_ca_2)),V_R_2)) % 172.48/172.44 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_a,V_R_2))) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_trancl__mono,axiom, % 172.48/172.44 ! [V_s_2,V_r_2,V_p_2,T_a] : % 172.48/172.44 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Otrancl(T_a,V_r_2))) % 172.48/172.44 => ( 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)) % 172.48/172.44 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Otrancl(T_a,V_s_2))) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_trancl__unfold,axiom, % 172.48/172.44 ! [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)) ). % 172.48/172.44 % 172.48/172.44 fof(fact_trancl__subset__Sigma,axiom, % 172.48/172.44 ! [V_A_2,V_r_2,T_a] : % 172.48/172.44 ( 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)))) % 172.48/172.44 => 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)))) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_log_Osimps,axiom, % 172.48/172.44 ! [V_i,V_b] : % 172.48/172.44 ( ( ( 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))) % 172.48/172.44 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),V_b)) ) % 172.48/172.44 => c_Random_Olog(V_b,V_i) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) ) % 172.48/172.44 & ( ~ ( 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))) % 172.48/172.44 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_i),V_b)) ) % 172.48/172.44 => 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))) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_minus__shift__def,axiom, % 172.48/172.44 ! [V_r,V_l,V_k] : % 172.48/172.44 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l)) % 172.48/172.44 => 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) ) % 172.48/172.44 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_k),V_l)) % 172.48/172.44 => 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) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_inc__shift__def,axiom, % 172.48/172.44 ! [V_k,V_v] : % 172.48/172.44 ( ( V_v = V_k % 172.48/172.44 => c_Random_Oinc__shift(V_v,V_k) = c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) ) % 172.48/172.44 & ( V_v != V_k % 172.48/172.44 => 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)) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_range,axiom, % 172.48/172.44 ! [V_s,V_k] : % 172.48/172.44 ( 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)) % 172.48/172.44 => 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)) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_trancl__insert,axiom, % 172.48/172.44 ! [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)))))) ). % 172.48/172.44 % 172.48/172.44 fof(fact_reflcl__set__eq,axiom, % 172.48/172.44 ! [V_y_2,V_x_2,V_r_2,T_a] : % 172.48/172.44 ( 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)) % 172.48/172.44 <=> 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)))) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_r__into__rtrancl,axiom, % 172.48/172.44 ! [V_r_2,V_p_2,T_a] : % 172.48/172.44 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),V_r_2)) % 172.48/172.44 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_rtrancl_Ortrancl__refl,axiom, % 172.48/172.44 ! [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))) ). % 172.48/172.44 % 172.48/172.44 fof(fact_IdI,axiom, % 172.48/172.44 ! [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))) ). % 172.48/172.44 % 172.48/172.44 fof(fact_trancl__into__rtrancl,axiom, % 172.48/172.44 ! [V_r_2,V_b_2,V_a_2,T_a] : % 172.48/172.44 ( 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))) % 172.48/172.44 => 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))) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_Image__closed__trancl,axiom, % 172.48/172.44 ! [V_X_2,V_r_2,T_a] : % 172.48/172.44 ( 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)) % 172.48/172.44 => hAPP(c_Relation_OImage(T_a,T_a,c_Transitive__Closure_Ortrancl(T_a,V_r_2)),V_X_2) = V_X_2 ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_rtrancl__mono,axiom, % 172.48/172.44 ! [V_s_2,V_r_2,T_a] : % 172.48/172.44 ( 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)) % 172.48/172.44 => 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))) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_rtrancl__subset,axiom, % 172.48/172.44 ! [V_S_2,V_R_2,T_a] : % 172.48/172.44 ( 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)) % 172.48/172.44 => ( 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))) % 172.48/172.44 => c_Transitive__Closure_Ortrancl(T_a,V_S_2) = c_Transitive__Closure_Ortrancl(T_a,V_R_2) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_rtrancl__subset__rtrancl,axiom, % 172.48/172.44 ! [V_s_2,V_r_2,T_a] : % 172.48/172.44 ( 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))) % 172.48/172.44 => 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))) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_rtrancl__Int__subset,axiom, % 172.48/172.44 ! [V_r_2,V_s_2,T_a] : % 172.48/172.44 ( 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)) % 172.48/172.44 => ( 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)) % 172.48/172.44 => 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)) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_Image__Id,axiom, % 172.48/172.44 ! [V_A_2,T_a] : hAPP(c_Relation_OImage(T_a,T_a,c_Relation_OId(T_a)),V_A_2) = V_A_2 ). % 172.48/172.44 % 172.48/172.44 fof(fact_Id__O__R,axiom, % 172.48/172.44 ! [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 ). % 172.48/172.44 % 172.48/172.44 fof(fact_R__O__Id,axiom, % 172.48/172.44 ! [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 ). % 172.48/172.44 % 172.48/172.44 fof(fact_refl__rtrancl,axiom, % 172.48/172.44 ! [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)) ). % 172.48/172.44 % 172.48/172.44 fof(fact_Domain__rtrancl,axiom, % 172.48/172.44 ! [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)) ). % 172.48/172.44 % 172.48/172.44 fof(fact_Range__rtrancl,axiom, % 172.48/172.44 ! [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)) ). % 172.48/172.44 % 172.48/172.44 fof(fact_rtrancl__empty,axiom, % 172.48/172.44 ! [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) ). % 172.48/172.44 % 172.48/172.44 fof(fact_r__comp__rtrancl__eq,axiom, % 172.48/172.44 ! [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) ). % 172.48/172.44 % 172.48/172.44 fof(fact_rtrancl__idemp__self__comp,axiom, % 172.48/172.44 ! [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) ). % 172.48/172.44 % 172.48/172.44 fof(fact_rtrancl__unfold,axiom, % 172.48/172.44 ! [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)) ). % 172.48/172.44 % 172.48/172.44 fof(fact_rtrancl__reflcl__absorb,axiom, % 172.48/172.44 ! [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) ). % 172.48/172.44 % 172.48/172.44 fof(fact_rtrancl__Un__rtrancl,axiom, % 172.48/172.44 ! [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)) ). % 172.48/172.44 % 172.48/172.44 fof(fact_rtrancl__reflcl,axiom, % 172.48/172.44 ! [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) ). % 172.48/172.44 % 172.48/172.44 fof(fact_in__rtrancl__UnI,axiom, % 172.48/172.44 ! [V_S_2,V_R_2,V_x_2,T_a] : % 172.48/172.44 ( ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_x_2),c_Transitive__Closure_Ortrancl(T_a,V_R_2))) % 172.48/172.44 | hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_x_2),c_Transitive__Closure_Ortrancl(T_a,V_S_2))) ) % 172.48/172.44 => 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)))) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_converse__rtrancl__into__rtrancl,axiom, % 172.48/172.44 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_a] : % 172.48/172.44 ( 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)) % 172.48/172.44 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_b_2),V_ca_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) % 172.48/172.44 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_ca_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_rtrancl_Ortrancl__into__rtrancl,axiom, % 172.48/172.44 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_a] : % 172.48/172.44 ( 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))) % 172.48/172.44 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_b_2),V_ca_2)),V_r_2)) % 172.48/172.44 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_ca_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_rtrancl__trans,axiom, % 172.48/172.44 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_a] : % 172.48/172.44 ( 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))) % 172.48/172.44 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_b_2),V_ca_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) % 172.48/172.44 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_ca_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_rtrancl__idemp,axiom, % 172.48/172.44 ! [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) ). % 172.48/172.44 % 172.48/172.44 fof(fact_rtrancl__r__diff__Id,axiom, % 172.48/172.44 ! [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) ). % 172.48/172.44 % 172.48/172.44 fof(fact_trancl__rtrancl__absorb,axiom, % 172.48/172.44 ! [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) ). % 172.48/172.44 % 172.48/172.44 fof(fact_rtrancl__trancl__absorb,axiom, % 172.48/172.44 ! [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) ). % 172.48/172.44 % 172.48/172.44 fof(fact_trancl__reflcl,axiom, % 172.48/172.44 ! [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) ). % 172.48/172.44 % 172.48/172.44 fof(fact_reflcl__trancl,axiom, % 172.48/172.44 ! [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) ). % 172.48/172.44 % 172.48/172.44 fof(fact_trancl__unfold__right,axiom, % 172.48/172.44 ! [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) ). % 172.48/172.44 % 172.48/172.44 fof(fact_trancl__unfold__left,axiom, % 172.48/172.44 ! [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)) ). % 172.48/172.44 % 172.48/172.44 fof(fact_rtrancl__Un__subset,axiom, % 172.48/172.44 ! [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)))) ). % 172.48/172.44 % 172.48/172.44 fof(fact_pair__in__Id__conv,axiom, % 172.48/172.44 ! [V_b_2,V_a_2,T_a] : % 172.48/172.44 ( 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))) % 172.48/172.44 <=> V_a_2 = V_b_2 ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_rtrancl__eq__or__trancl,axiom, % 172.48/172.44 ! [V_R_2,V_y_2,V_x_2,T_a] : % 172.48/172.44 ( 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))) % 172.48/172.44 <=> ( V_x_2 = V_y_2 % 172.48/172.44 | ( V_x_2 != V_y_2 % 172.48/172.44 & 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))) ) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_rtrancl__into__trancl2,axiom, % 172.48/172.44 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_a] : % 172.48/172.44 ( 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)) % 172.48/172.44 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_b_2),V_ca_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) % 172.48/172.44 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_rtranclD,axiom, % 172.48/172.44 ! [V_R_2,V_b_2,V_a_2,T_a] : % 172.48/172.44 ( 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))) % 172.48/172.44 => ( V_a_2 = V_b_2 % 172.48/172.44 | ( V_a_2 != V_b_2 % 172.48/172.44 & 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))) ) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_rtrancl__into__trancl1,axiom, % 172.48/172.44 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_a] : % 172.48/172.44 ( 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))) % 172.48/172.44 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_b_2),V_ca_2)),V_r_2)) % 172.48/172.44 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_trancl__rtrancl__trancl,axiom, % 172.48/172.44 ! [V_ca_2,V_r_2,V_b_2,V_a_2,T_a] : % 172.48/172.44 ( 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))) % 172.48/172.44 => ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_b_2),V_ca_2)),c_Transitive__Closure_Ortrancl(T_a,V_r_2))) % 172.48/172.44 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),V_a_2),V_ca_2)),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_rtrancl__trancl__trancl,axiom, % 172.48/172.44 ! [V_z_2,V_r_2,V_y_2,V_x_2,T_a] : % 172.48/172.44 ( 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))) % 172.48/172.44 => ( 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))) % 172.48/172.44 => 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))) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_Domain__Id,axiom, % 172.48/172.44 ! [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)) ). % 172.48/172.44 % 172.48/172.44 fof(fact_Range__Id,axiom, % 172.48/172.44 ! [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)) ). % 172.48/172.44 % 172.48/172.44 fof(fact_refl__Id,axiom, % 172.48/172.44 ! [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)) ). % 172.48/172.44 % 172.48/172.44 fof(fact_pair__leq__def,axiom, % 172.48/172.44 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))) ). % 172.48/172.44 % 172.48/172.44 fof(fact_Not__Domain__rtrancl,axiom, % 172.48/172.44 ! [V_y_2,V_R_2,V_x_2,T_a] : % 172.48/172.44 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_Relation_ODomain(T_a,T_a),V_R_2))) % 172.48/172.44 => ( 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))) % 172.48/172.44 <=> V_x_2 = V_y_2 ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_acc__downwards,axiom, % 172.48/172.44 ! [V_b_2,V_r_2,V_a_2,T_a] : % 172.48/172.44 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Wellfounded_Oacc(T_a,V_r_2))) % 172.48/172.44 => ( 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))) % 172.48/172.44 => hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Wellfounded_Oacc(T_a,V_r_2))) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_acc__downwards__aux,axiom, % 172.48/172.44 ! [V_r_2,V_a_2,V_b_2,T_a] : % 172.48/172.44 ( 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))) % 172.48/172.44 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Wellfounded_Oacc(T_a,V_r_2))) % 172.48/172.44 => hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Wellfounded_Oacc(T_a,V_r_2))) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_wf__insert,axiom, % 172.48/172.44 ! [V_r_2,V_x_2,V_y_2,T_a] : % 172.48/172.44 ( 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)) % 172.48/172.44 <=> ( c_Wellfounded_Owf(T_a,V_r_2) % 172.48/172.44 & ~ 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))) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_acyclic__insert,axiom, % 172.48/172.44 ! [V_r_2,V_x_2,V_y_2,T_a] : % 172.48/172.44 ( 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)) % 172.48/172.44 <=> ( c_Wellfounded_Oacyclic(T_a,V_r_2) % 172.48/172.44 & ~ 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))) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_refl__reflcl,axiom, % 172.48/172.44 ! [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))) ). % 172.48/172.44 % 172.48/172.44 fof(fact_Id__def,axiom, % 172.48/172.44 ! [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))))) ). % 172.48/172.44 % 172.48/172.44 fof(fact_irrefl__diff__Id,axiom, % 172.48/172.44 ! [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))) ). % 172.48/172.44 % 172.48/172.44 fof(fact_pred__nat__trancl__eq__le,axiom, % 172.48/172.44 ! [V_n_2,V_m_2] : % 172.48/172.44 ( 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))) % 172.48/172.44 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_trancl__subset__Sigma__aux,axiom, % 172.48/172.44 ! [V_A_2,V_r_2,V_b_2,V_a_2,T_a] : % 172.48/172.44 ( 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))) % 172.48/172.44 => ( 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)))) % 172.48/172.44 => ( V_a_2 = V_b_2 % 172.48/172.44 | hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_irrefl__tranclI,axiom, % 172.48/172.44 ! [V_x_2,V_r_2,T_a] : % 172.48/172.44 ( 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)) % 172.48/172.44 => ~ 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))) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_sequence__trans,axiom, % 172.48/172.44 ! [V_k_2,V_i_2,V_r_2,V_f_2,T_a] : % 172.48/172.44 ( ! [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))) % 172.48/172.44 => 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))) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_total__on__diff__Id,axiom, % 172.48/172.44 ! [V_r_2,V_A_2,T_a] : % 172.48/172.44 ( 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))) % 172.48/172.44 <=> c_Relation_Ototal__on(T_a,V_A_2,V_r_2) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_converse__Id,axiom, % 172.48/172.44 ! [T_a] : hAPP(c_Relation_Oconverse(T_a,T_a),c_Relation_OId(T_a)) = c_Relation_OId(T_a) ). % 172.48/172.44 % 172.48/172.44 fof(fact_rtrancl__converse,axiom, % 172.48/172.44 ! [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)) ). % 172.48/172.44 % 172.48/172.44 fof(fact_trancl__converse,axiom, % 172.48/172.44 ! [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)) ). % 172.48/172.44 % 172.48/172.44 fof(fact_refl__on__converse,axiom, % 172.48/172.44 ! [V_r_2,V_A_2,T_a] : % 172.48/172.44 ( c_Relation_Orefl__on(T_a,V_A_2,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)) % 172.48/172.44 <=> c_Relation_Orefl__on(T_a,V_A_2,V_r_2) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_converse__rel__comp,axiom, % 172.48/172.44 ! [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)) ). % 172.48/172.44 % 172.48/172.44 fof(fact_converse__Un,axiom, % 172.48/172.44 ! [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)) ). % 172.48/172.44 % 172.48/172.44 fof(fact_Field__converse,axiom, % 172.48/172.44 ! [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) ). % 172.48/172.44 % 172.48/172.44 fof(fact_converse__inv__image,axiom, % 172.48/172.44 ! [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) ). % 172.48/172.44 % 172.48/172.44 fof(fact_finite__converse,axiom, % 172.48/172.44 ! [V_r_2,T_b,T_a] : % 172.48/172.44 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_b)),hAPP(c_Relation_Oconverse(T_b,T_a),V_r_2))) % 172.48/172.44 <=> hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_b,T_a)),V_r_2)) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_converse__Int,axiom, % 172.48/172.44 ! [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)) ). % 172.48/172.44 % 172.48/172.44 fof(fact_total__on__converse,axiom, % 172.48/172.44 ! [V_r_2,V_A_2,T_a] : % 172.48/172.44 ( c_Relation_Ototal__on(T_a,V_A_2,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)) % 172.48/172.44 <=> c_Relation_Ototal__on(T_a,V_A_2,V_r_2) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_converse__converse,axiom, % 172.48/172.44 ! [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 ). % 172.48/172.44 % 172.48/172.44 fof(fact_converse__Id__on,axiom, % 172.48/172.44 ! [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) ). % 172.48/172.44 % 172.48/172.44 fof(fact_converse__UNION,axiom, % 172.48/172.44 ! [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)) ). % 172.48/172.44 % 172.48/172.44 fof(fact_acyclic__converse,axiom, % 172.48/172.44 ! [V_r_2,T_a] : % 172.48/172.44 ( c_Wellfounded_Oacyclic(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)) % 172.48/172.44 <=> c_Wellfounded_Oacyclic(T_a,V_r_2) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_converse__iff,axiom, % 172.48/172.44 ! [V_r_2,V_b_2,V_a_2,T_b,T_a] : % 172.48/172.44 ( 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))) % 172.48/172.44 <=> 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)) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_converseI,axiom, % 172.48/172.44 ! [V_r_2,V_b_2,V_a_2,T_b,T_a] : % 172.48/172.44 ( 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)) % 172.48/172.44 => 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))) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_converseD,axiom, % 172.48/172.44 ! [V_r_2,V_b_2,V_a_2,T_b,T_a] : % 172.48/172.44 ( 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))) % 172.48/172.44 => 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)) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_wf__converse__trancl,axiom, % 172.48/172.44 ! [V_r_2,T_a] : % 172.48/172.44 ( c_Wellfounded_Owf(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)) % 172.48/172.44 => c_Wellfounded_Owf(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),c_Transitive__Closure_Otrancl(T_a,V_r_2))) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_equiv__comp__eq,axiom, % 172.48/172.44 ! [V_r_2,V_A_2,T_a] : % 172.48/172.44 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 172.48/172.44 => 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 ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_Range__converse,axiom, % 172.48/172.44 ! [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) ). % 172.48/172.44 % 172.48/172.44 fof(fact_Domain__converse,axiom, % 172.48/172.44 ! [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) ). % 172.48/172.44 % 172.48/172.44 fof(fact_Range__def,axiom, % 172.48/172.44 ! [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)) ). % 172.48/172.44 % 172.48/172.44 fof(fact_total__on__empty,axiom, % 172.48/172.44 ! [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) ). % 172.48/172.44 % 172.48/172.44 fof(fact_rtrancl__converseD,axiom, % 172.48/172.44 ! [V_r_2,V_y_2,V_x_2,T_a] : % 172.48/172.44 ( 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)))) % 172.48/172.44 => 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))) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_rtrancl__converseI,axiom, % 172.48/172.44 ! [V_r_2,V_x_2,V_y_2,T_a] : % 172.48/172.44 ( 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))) % 172.48/172.44 => 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)))) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_trancl__converseI,axiom, % 172.48/172.44 ! [V_r_2,V_y_2,V_x_2,T_a] : % 172.48/172.44 ( 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)))) % 172.48/172.44 => 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)))) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_trancl__converseD,axiom, % 172.48/172.44 ! [V_r_2,V_y_2,V_x_2,T_a] : % 172.48/172.44 ( 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)))) % 172.48/172.44 => 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)))) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_Image__subset__eq,axiom, % 172.48/172.44 ! [V_B_2,V_A_2,V_r_2,T_b,T_a] : % 172.48/172.44 ( 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)) % 172.48/172.44 <=> 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))))) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_refl__on__comp__subset,axiom, % 172.48/172.44 ! [V_r_2,V_A_2,T_a] : % 172.48/172.44 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2) % 172.48/172.44 => 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))) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_comp__equivI,axiom, % 172.48/172.44 ! [V_A_2,V_r_2,T_a] : % 172.48/172.44 ( 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 % 172.48/172.44 => ( hAPP(c_Relation_ODomain(T_a,T_a),V_r_2) = V_A_2 % 172.48/172.44 => c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_finite__acyclic__wf__converse,axiom, % 172.48/172.44 ! [V_r_2,T_a] : % 172.48/172.44 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_prod(T_a,T_a)),V_r_2)) % 172.48/172.44 => ( c_Wellfounded_Oacyclic(T_a,V_r_2) % 172.48/172.44 => c_Wellfounded_Owf(T_a,hAPP(c_Relation_Oconverse(T_a,T_a),V_r_2)) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_total__on__def,axiom, % 172.48/172.44 ! [V_r_2,V_A_2,T_a] : % 172.48/172.44 ( c_Relation_Ototal__on(T_a,V_A_2,V_r_2) % 172.48/172.44 <=> ! [B_x] : % 172.48/172.44 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 172.48/172.44 => ! [B_xa] : % 172.48/172.44 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),V_A_2)) % 172.48/172.44 => ( B_x != B_xa % 172.48/172.44 => ( 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)) % 172.48/172.44 | 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)) ) ) ) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_converse__def,axiom, % 172.48/172.44 ! [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))) ). % 172.48/172.44 % 172.48/172.44 fof(fact_rtrancl__imp__UN__rel__pow,axiom, % 172.48/172.44 ! [V_R_2,V_p_2,T_a] : % 172.48/172.44 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Ortrancl(T_a,V_R_2))) % 172.48/172.44 => 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)))) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_acyclicI,axiom, % 172.48/172.44 ! [V_r_2,T_a] : % 172.48/172.44 ( ! [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))) % 172.48/172.44 => c_Wellfounded_Oacyclic(T_a,V_r_2) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_Image__Int__eq,axiom, % 172.48/172.44 ! [V_B_2,V_A_2,V_R_2,T_b,T_a] : % 172.48/172.44 ( c_Relation_Osingle__valued(T_a,T_b,hAPP(c_Relation_Oconverse(T_b,T_a),V_R_2)) % 172.48/172.44 => 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)) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_single__valued__subset,axiom, % 172.48/172.44 ! [V_s_2,V_r_2,T_b,T_a] : % 172.48/172.44 ( 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)) % 172.48/172.44 => ( c_Relation_Osingle__valued(T_a,T_b,V_s_2) % 172.48/172.44 => c_Relation_Osingle__valued(T_a,T_b,V_r_2) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_comp__funpow,axiom, % 172.48/172.44 ! [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)) ). % 172.48/172.44 % 172.48/172.44 fof(fact_wf__exp,axiom, % 172.48/172.44 ! [V_R_2,V_n_2,T_a] : % 172.48/172.44 ( 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)) % 172.48/172.44 => c_Wellfounded_Owf(T_a,V_R_2) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_funpow__swap1,axiom, % 172.48/172.44 ! [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)) ). % 172.48/172.44 % 172.48/172.44 fof(fact_funpow__mult,axiom, % 172.48/172.44 ! [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) ). % 172.48/172.44 % 172.48/172.44 fof(fact_single__valued__rel__comp,axiom, % 172.48/172.44 ! [V_s_2,T_c,V_r_2,T_b,T_a] : % 172.48/172.44 ( c_Relation_Osingle__valued(T_a,T_b,V_r_2) % 172.48/172.44 => ( c_Relation_Osingle__valued(T_b,T_c,V_s_2) % 172.48/172.44 => 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)) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_rel__pow__commute,axiom, % 172.48/172.44 ! [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) ). % 172.48/172.44 % 172.48/172.44 fof(fact_rel__pow__1,axiom, % 172.48/172.44 ! [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 ). % 172.48/172.44 % 172.48/172.44 fof(fact_single__valued__rel__pow,axiom, % 172.48/172.44 ! [V_n_2,V_R_2,T_a] : % 172.48/172.44 ( c_Relation_Osingle__valued(T_a,T_a,V_R_2) % 172.48/172.44 => 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)) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_single__valued__Id,axiom, % 172.48/172.44 ! [T_a] : c_Relation_Osingle__valued(T_a,T_a,c_Relation_OId(T_a)) ). % 172.48/172.44 % 172.48/172.44 fof(fact_rel__pow__imp__rtrancl,axiom, % 172.48/172.44 ! [V_R_2,V_n_2,V_p_2,T_a] : % 172.48/172.44 ( 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))) % 172.48/172.44 => hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Ortrancl(T_a,V_R_2))) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_rtrancl__power,axiom, % 172.48/172.44 ! [V_R_2,V_p_2,T_a] : % 172.48/172.44 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Ortrancl(T_a,V_R_2))) % 172.48/172.44 <=> ? [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))) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_single__valued__Id__on,axiom, % 172.48/172.44 ! [V_A_2,T_a] : c_Relation_Osingle__valued(T_a,T_a,c_Relation_OId__on(T_a,V_A_2)) ). % 172.48/172.44 % 172.48/172.44 fof(fact_relpow_Osimps_I2_J,axiom, % 172.48/172.44 ! [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) ). % 172.48/172.44 % 172.48/172.44 fof(fact_rel__pow__add,axiom, % 172.48/172.44 ! [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)) ). % 172.48/172.44 % 172.48/172.44 fof(fact_relpow_Osimps_I1_J,axiom, % 172.48/172.44 ! [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) ). % 172.48/172.44 % 172.48/172.44 fof(fact_rel__pow__0__I,axiom, % 172.48/172.44 ! [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))) ). % 172.48/172.44 % 172.48/172.44 fof(fact_rel__pow__0__E,axiom, % 172.48/172.44 ! [V_R_2,V_y_2,V_x_2,T_a] : % 172.48/172.44 ( 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))) % 172.48/172.44 => V_x_2 = V_y_2 ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_rel__pow__Suc__I,axiom, % 172.48/172.44 ! [V_z_2,V_R_2,V_n_2,V_y_2,V_x_2,T_a] : % 172.48/172.44 ( 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))) % 172.48/172.44 => ( 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)) % 172.48/172.44 => 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))) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_rel__pow__Suc__I2,axiom, % 172.48/172.44 ! [V_n_2,V_z_2,V_R_2,V_y_2,V_x_2,T_a] : % 172.48/172.44 ( 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)) % 172.48/172.44 => ( 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))) % 172.48/172.44 => 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))) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_funpow_Osimps_I2_J,axiom, % 172.48/172.44 ! [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)) ). % 172.48/172.44 % 172.48/172.44 fof(fact_funpow__add,axiom, % 172.48/172.44 ! [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)) ). % 172.48/172.44 % 172.48/172.44 fof(fact_single__valued__def,axiom, % 172.48/172.44 ! [V_r_2,T_b,T_a] : % 172.48/172.44 ( c_Relation_Osingle__valued(T_a,T_b,V_r_2) % 172.48/172.44 <=> ! [B_x,B_y] : % 172.48/172.44 ( 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)) % 172.48/172.44 => ! [B_z] : % 172.48/172.44 ( 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)) % 172.48/172.44 => B_y = B_z ) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_single__valuedD,axiom, % 172.48/172.44 ! [V_z_2,V_y_2,V_x_2,V_r_2,T_b,T_a] : % 172.48/172.44 ( c_Relation_Osingle__valued(T_a,T_b,V_r_2) % 172.48/172.44 => ( 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)) % 172.48/172.44 => ( 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)) % 172.48/172.44 => V_y_2 = V_z_2 ) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_funpow_Osimps_I1_J,axiom, % 172.48/172.44 ! [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) ). % 172.48/172.44 % 172.48/172.44 fof(fact_trancl__power,axiom, % 172.48/172.44 ! [V_R_2,V_p_2,T_a] : % 172.48/172.44 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Transitive__Closure_Otrancl(T_a,V_R_2))) % 172.48/172.44 <=> ? [B_n] : % 172.48/172.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),B_n)) % 172.48/172.44 & 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))) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_rtrancl__is__UN__rel__pow,axiom, % 172.48/172.44 ! [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)) ). % 172.48/172.44 % 172.48/172.44 fof(fact_single__valued__confluent,axiom, % 172.48/172.44 ! [V_z_2,V_y_2,V_x_2,V_r_2,T_a] : % 172.48/172.44 ( c_Relation_Osingle__valued(T_a,T_a,V_r_2) % 172.48/172.44 => ( 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))) % 172.48/172.44 => ( 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))) % 172.48/172.44 => ( 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))) % 172.48/172.44 | 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))) ) ) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_funpow__code__def,axiom, % 172.48/172.44 ! [T_a] : c_Nat_Ofunpow(T_a) = c_Nat_Ocompow(T_a,T_a) ). % 172.48/172.44 % 172.48/172.44 fof(fact_rel__pow__E,axiom, % 172.48/172.44 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_a] : % 172.48/172.44 ( 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))) % 172.48/172.44 => ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 172.48/172.44 => V_x_2 != V_z_2 ) % 172.48/172.44 => ~ ! [B_y,B_m] : % 172.48/172.44 ( V_n_2 = hAPP(c_Nat_OSuc,B_m) % 172.48/172.44 => ( 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))) % 172.48/172.44 => ~ 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)) ) ) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_rel__pow__E2,axiom, % 172.48/172.44 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_a] : % 172.48/172.44 ( 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))) % 172.48/172.44 => ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 172.48/172.44 => V_x_2 != V_z_2 ) % 172.48/172.44 => ~ ! [B_y,B_m] : % 172.48/172.44 ( V_n_2 = hAPP(c_Nat_OSuc,B_m) % 172.48/172.44 => ( 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)) % 172.48/172.44 => ~ 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))) ) ) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_rtrancl__Un__separatorE,axiom, % 172.48/172.44 ! [V_Q_2,V_P_2,V_b_2,V_a_2,T_a] : % 172.48/172.44 ( 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)))) % 172.48/172.44 => ( ! [B_x] : % 172.48/172.44 ( 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))) % 172.48/172.44 => ! [B_y] : % 172.48/172.44 ( 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)) % 172.48/172.44 => B_x = B_y ) ) % 172.48/172.44 => 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))) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_rtrancl__Un__separator__converseE,axiom, % 172.48/172.44 ! [V_Q_2,V_P_2,V_b_2,V_a_2,T_a] : % 172.48/172.44 ( 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)))) % 172.48/172.44 => ( ! [B_x] : % 172.48/172.44 ( 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))) % 172.48/172.44 => ! [B_y] : % 172.48/172.44 ( 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)) % 172.48/172.44 => B_y = B_x ) ) % 172.48/172.44 => 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))) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_rel__pow__Suc__E,axiom, % 172.48/172.44 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_a] : % 172.48/172.44 ( 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))) % 172.48/172.44 => ~ ! [B_y] : % 172.48/172.44 ( 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))) % 172.48/172.44 => ~ 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)) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_rel__pow__Suc__D2,axiom, % 172.48/172.44 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_a] : % 172.48/172.44 ( 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))) % 172.48/172.44 => ? [B_y] : % 172.48/172.44 ( 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)) % 172.48/172.44 & 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))) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_rel__pow__Suc__E2,axiom, % 172.48/172.44 ! [V_R_2,V_n_2,V_z_2,V_x_2,T_a] : % 172.48/172.44 ( 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))) % 172.48/172.44 => ~ ! [B_y] : % 172.48/172.44 ( 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)) % 172.48/172.44 => ~ 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))) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_tranclD2,axiom, % 172.48/172.44 ! [V_R_2,V_y_2,V_x_2,T_a] : % 172.48/172.44 ( 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))) % 172.48/172.44 => ? [B_z] : % 172.48/172.44 ( 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))) % 172.48/172.44 & 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)) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_tranclD,axiom, % 172.48/172.44 ! [V_R_2,V_y_2,V_x_2,T_a] : % 172.48/172.44 ( 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))) % 172.48/172.44 => ? [B_z] : % 172.48/172.44 ( 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)) % 172.48/172.44 & 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))) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_IdE,axiom, % 172.48/172.44 ! [V_p_2,T_a] : % 172.48/172.44 ( hBOOL(hAPP(hAPP(c_member(tc_prod(T_a,T_a)),V_p_2),c_Relation_OId(T_a))) % 172.48/172.44 => ~ ! [B_x] : V_p_2 != hAPP(hAPP(c_Product__Type_OPair(T_a,T_a),B_x),B_x) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_nat__intermed__int__val,axiom, % 172.48/172.44 ! [V_k_2,V_f_2,V_n_2,V_m_2] : % 172.48/172.44 ( ! [B_i] : % 172.48/172.44 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),B_i)) % 172.48/172.44 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2)) ) % 172.48/172.44 => 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))) ) % 172.48/172.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_m_2),V_n_2)) % 172.48/172.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),hAPP(V_f_2,V_m_2)),V_k_2)) % 172.48/172.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_k_2),hAPP(V_f_2,V_n_2))) % 172.48/172.44 => ? [B_i] : % 172.48/172.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),B_i)) % 172.48/172.44 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),V_n_2)) % 172.48/172.44 & hAPP(V_f_2,B_i) = V_k_2 ) ) ) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_min__max_OSup__fin_Oeq__fold_H,axiom, % 172.48/172.44 ! [V_x_2,V_A_2,T_a] : % 172.48/172.44 ( class_Orderings_Olinorder(T_a) % 172.48/172.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.44 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 172.48/172.44 => 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) ) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_mod__div__decomp,axiom, % 172.48/172.44 ! [V_b,V_a,T_a] : % 172.48/172.44 ( class_Divides_Osemiring__div(T_a) % 172.48/172.44 => 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)) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_fold__image__def,axiom, % 172.48/172.44 ! [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)) ). % 172.48/172.44 % 172.48/172.44 fof(fact_fold__empty,axiom, % 172.48/172.44 ! [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 ). % 172.48/172.44 % 172.48/172.44 fof(fact_folding_Oeq__fold,axiom, % 172.48/172.44 ! [V_s_2,V_A_2,V_F_2,V_f_2,T_b,T_a] : % 172.48/172.44 ( c_Finite__Set_Ofolding(T_a,T_b,V_f_2,V_F_2) % 172.48/172.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.44 => 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) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_fold__def,axiom, % 172.48/172.44 ! [V_A_2,V_z_2,V_f_2,T_a,T_b] : hAPP(hAPP(c_Finite__Set_Ofold(T_b,T_a,V_f_2),V_z_2),V_A_2) = c_HOL_OThe(T_a,c_Finite__Set_Ofold__graph(T_b,T_a,V_f_2,V_z_2,V_A_2)) ). % 172.48/172.44 % 172.48/172.44 fof(fact_union__fold__insert,axiom, % 172.48/172.44 ! [V_B_2,V_A_2,T_a] : % 172.48/172.44 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.44 => 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) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_fold__sup__insert,axiom, % 172.48/172.44 ! [V_a_2,V_b_2,V_A_2,T_a] : % 172.48/172.44 ( class_Lattices_Osemilattice__sup(T_a) % 172.48/172.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.44 => 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)) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_fold__inf__insert,axiom, % 172.48/172.44 ! [V_a_2,V_b_2,V_A_2,T_a] : % 172.48/172.44 ( class_Lattices_Osemilattice__inf(T_a) % 172.48/172.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.44 => 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)) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_min__max_Ofold__inf__insert,axiom, % 172.48/172.44 ! [V_a_2,V_b_2,V_A_2,T_a] : % 172.48/172.44 ( class_Orderings_Olinorder(T_a) % 172.48/172.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.44 => 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)) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_min__max_Ofold__sup__insert,axiom, % 172.48/172.44 ! [V_a_2,V_b_2,V_A_2,T_a] : % 172.48/172.44 ( class_Orderings_Olinorder(T_a) % 172.48/172.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.44 => 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)) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_fun__left__comm__idem_Ofold__insert__idem2,axiom, % 172.48/172.44 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_b,T_a] : % 172.48/172.44 ( c_Finite__Set_Ofun__left__comm__idem(T_a,T_b,V_f_2) % 172.48/172.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.44 => 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) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_fun__left__comm__idem_Ofold__insert__idem,axiom, % 172.48/172.44 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_b,T_a] : % 172.48/172.44 ( c_Finite__Set_Ofun__left__comm__idem(T_a,T_b,V_f_2) % 172.48/172.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.44 => 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)) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_sup__SUPR__fold__sup,axiom, % 172.48/172.44 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] : % 172.48/172.44 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 172.48/172.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.44 => 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) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_folding__one__idem_Oeq__fold__idem_H,axiom, % 172.48/172.44 ! [V_a_2,V_A_2,V_F_2,V_f_2,T_a] : % 172.48/172.44 ( c_Finite__Set_Ofolding__one__idem(T_a,V_f_2,V_F_2) % 172.48/172.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.44 => 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) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_sup__le__fold__sup,axiom, % 172.48/172.44 ! [V_b_2,V_a_2,V_A_2,T_a] : % 172.48/172.44 ( class_Lattices_Osemilattice__sup(T_a) % 172.48/172.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.44 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 172.48/172.44 => 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))) ) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_fold__inf__le__inf,axiom, % 172.48/172.44 ! [V_b_2,V_a_2,V_A_2,T_a] : % 172.48/172.44 ( class_Lattices_Osemilattice__inf(T_a) % 172.48/172.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.44 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 172.48/172.44 => 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))) ) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_min__max_Ofold__inf__le__inf,axiom, % 172.48/172.44 ! [V_b_2,V_a_2,V_A_2,T_a] : % 172.48/172.44 ( class_Orderings_Olinorder(T_a) % 172.48/172.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.44 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 172.48/172.44 => 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))) ) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_min__max_Osup__le__fold__sup,axiom, % 172.48/172.44 ! [V_b_2,V_a_2,V_A_2,T_a] : % 172.48/172.44 ( class_Orderings_Olinorder(T_a) % 172.48/172.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.44 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 172.48/172.44 => 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))) ) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_fold1__eq__fold__idem,axiom, % 172.48/172.44 ! [V_a_2,V_A_2,T_a] : % 172.48/172.44 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 172.48/172.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.44 => 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) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_Sup__fin_Oeq__fold__idem_H,axiom, % 172.48/172.44 ! [V_a_2,V_A_2,T_a] : % 172.48/172.44 ( class_Lattices_Olattice(T_a) % 172.48/172.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.44 => 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) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_Inf__fin_Oeq__fold__idem_H,axiom, % 172.48/172.44 ! [V_a_2,V_A_2,T_a] : % 172.48/172.44 ( class_Lattices_Olattice(T_a) % 172.48/172.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.44 => 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) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_Min_Oeq__fold__idem_H,axiom, % 172.48/172.44 ! [V_a_2,V_A_2,T_a] : % 172.48/172.44 ( class_Orderings_Olinorder(T_a) % 172.48/172.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.44 => 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) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_Max_Oeq__fold__idem_H,axiom, % 172.48/172.44 ! [V_a_2,V_A_2,T_a] : % 172.48/172.44 ( class_Orderings_Olinorder(T_a) % 172.48/172.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.44 => 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) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_min__max_OInf__fin_Oeq__fold__idem_H,axiom, % 172.48/172.44 ! [V_a_2,V_A_2,T_a] : % 172.48/172.44 ( class_Orderings_Olinorder(T_a) % 172.48/172.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.44 => 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) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_min__max_OSup__fin_Oeq__fold__idem_H,axiom, % 172.48/172.44 ! [V_a_2,V_A_2,T_a] : % 172.48/172.44 ( class_Orderings_Olinorder(T_a) % 172.48/172.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.44 => 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) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_minus__fold__remove,axiom, % 172.48/172.44 ! [V_B_2,V_A_2,T_a] : % 172.48/172.44 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.44 => 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) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_folding__one_Oeq__fold_H,axiom, % 172.48/172.44 ! [V_x_2,V_A_2,V_F_2,V_f_2,T_a] : % 172.48/172.44 ( c_Finite__Set_Ofolding__one(T_a,V_f_2,V_F_2) % 172.48/172.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.44 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 172.48/172.44 => 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) ) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_SUPR__fold__sup,axiom, % 172.48/172.44 ! [V_f_2,V_A_2,T_a,T_b] : % 172.48/172.44 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 172.48/172.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.44 => 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) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_fold1__eq__fold,axiom, % 172.48/172.44 ! [V_a_2,V_A_2,T_a] : % 172.48/172.44 ( class_Groups_Oab__semigroup__mult(T_a) % 172.48/172.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.44 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 172.48/172.44 => 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) ) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_Sup__fin_Oeq__fold_H,axiom, % 172.48/172.44 ! [V_x_2,V_A_2,T_a] : % 172.48/172.44 ( class_Lattices_Olattice(T_a) % 172.48/172.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.44 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 172.48/172.44 => 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) ) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_Inf__fin_Oeq__fold_H,axiom, % 172.48/172.44 ! [V_x_2,V_A_2,T_a] : % 172.48/172.44 ( class_Lattices_Olattice(T_a) % 172.48/172.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.44 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 172.48/172.44 => 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) ) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_Min_Oeq__fold_H,axiom, % 172.48/172.44 ! [V_x_2,V_A_2,T_a] : % 172.48/172.44 ( class_Orderings_Olinorder(T_a) % 172.48/172.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.44 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 172.48/172.44 => 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) ) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_Max_Oeq__fold_H,axiom, % 172.48/172.44 ! [V_x_2,V_A_2,T_a] : % 172.48/172.44 ( class_Orderings_Olinorder(T_a) % 172.48/172.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.44 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 172.48/172.44 => 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) ) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_min__max_OInf__fin_Oeq__fold_H,axiom, % 172.48/172.44 ! [V_x_2,V_A_2,T_a] : % 172.48/172.44 ( class_Orderings_Olinorder(T_a) % 172.48/172.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.44 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 172.48/172.44 => 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) ) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_fun__left__comm_Ofold__rec,axiom, % 172.48/172.44 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_b,T_a] : % 172.48/172.44 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 172.48/172.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.44 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 172.48/172.44 => 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)))))) ) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_fun__left__comm_Ofold__insert__remove,axiom, % 172.48/172.44 ! [V_x_2,V_z_2,V_A_2,V_f_2,T_b,T_a] : % 172.48/172.44 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 172.48/172.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.44 => 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)))))) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_fun__left__comm_Ofun__comp__comm,axiom, % 172.48/172.44 ! [V_y_2,V_x_2,V_f_2,T_b,T_a] : % 172.48/172.44 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 172.48/172.44 => 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)) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_fun__left__comm_Ofold__graph__determ,axiom, % 172.48/172.44 ! [V_y_2,V_x_2,V_A_2,V_z_2,V_f_2,T_b,T_a] : % 172.48/172.44 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 172.48/172.44 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),V_x_2)) % 172.48/172.44 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),V_y_2)) % 172.48/172.44 => V_y_2 = V_x_2 ) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_fun__left__comm,axiom, % 172.48/172.44 ! [T_a] : % 172.48/172.44 ( class_Groups_Oab__semigroup__mult(T_a) % 172.48/172.44 => c_Finite__Set_Ofun__left__comm(T_a,T_a,c_Groups_Otimes__class_Otimes(T_a)) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_fun__left__comm_Ofun__left__comm__apply,axiom, % 172.48/172.44 ! [V_g_2,T_c,V_f_2,T_b,T_a] : % 172.48/172.44 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 172.48/172.44 => 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)) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_fun__left__comm_Ofun__left__comm,axiom, % 172.48/172.44 ! [V_z_2,V_y_2,V_x_2,V_f_2,T_b,T_a] : % 172.48/172.44 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 172.48/172.44 => 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)) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_fun__left__comm_Ofold__fun__comm,axiom, % 172.48/172.44 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_b,T_a] : % 172.48/172.44 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 172.48/172.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.44 => 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) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_fun__left__comm_Ofold__equality,axiom, % 172.48/172.44 ! [V_y_2,V_A_2,V_z_2,V_f_2,T_b,T_a] : % 172.48/172.44 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 172.48/172.44 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),V_y_2)) % 172.48/172.44 => hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_z_2),V_A_2) = V_y_2 ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_fun__left__comm_Ofold__graph__fold,axiom, % 172.48/172.44 ! [V_z_2,V_A_2,V_f_2,T_b,T_a] : % 172.48/172.44 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 172.48/172.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.44 => hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_b,V_f_2),V_z_2),V_A_2))) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_fun__left__comm_Ofold__insert,axiom, % 172.48/172.44 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_b,T_a] : % 172.48/172.44 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 172.48/172.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.44 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 172.48/172.44 => 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)) ) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_fun__left__comm_Ofold__insert2,axiom, % 172.48/172.44 ! [V_z_2,V_x_2,V_A_2,V_f_2,T_b,T_a] : % 172.48/172.44 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 172.48/172.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.44 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 172.48/172.44 => 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) ) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_fun__left__comm_Ofold__graph__insertE__aux,axiom, % 172.48/172.44 ! [V_a_2,V_y_2,V_A_2,V_z_2,V_f_2,T_b,T_a] : % 172.48/172.44 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 172.48/172.44 => ( hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),V_y_2)) % 172.48/172.44 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 172.48/172.44 => ? [B_y_H] : % 172.48/172.44 ( V_y_2 = hAPP(hAPP(V_f_2,V_a_2),B_y_H) % 172.48/172.44 & hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))),B_y_H)) ) ) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_INFI__fold__inf,axiom, % 172.48/172.44 ! [V_f_2,V_A_2,T_a,T_b] : % 172.48/172.44 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 172.48/172.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.44 => 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) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_INF1__D,axiom, % 172.48/172.44 ! [V_a_2,V_b_2,V_B_2,V_A_2,T_b,T_a] : % 172.48/172.44 ( 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)) % 172.48/172.44 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 172.48/172.44 => hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2)) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_INF1__E,axiom, % 172.48/172.44 ! [V_a_2,V_b_2,V_B_2,V_A_2,T_b,T_a] : % 172.48/172.44 ( 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)) % 172.48/172.44 => ( ~ hBOOL(hAPP(hAPP(V_B_2,V_a_2),V_b_2)) % 172.48/172.44 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_INT__E,axiom, % 172.48/172.44 ! [V_a_2,V_B_2,V_A_2,T_b,V_b_2,T_a] : % 172.48/172.44 ( 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))) % 172.48/172.44 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(V_B_2,V_a_2))) % 172.48/172.44 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_INT__D,axiom, % 172.48/172.44 ! [V_a_2,V_B_2,V_A_2,T_b,V_b_2,T_a] : % 172.48/172.44 ( 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))) % 172.48/172.44 => ( hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),V_A_2)) % 172.48/172.44 => hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(V_B_2,V_a_2))) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_INF2__D,axiom, % 172.48/172.44 ! [V_a_2,V_ca_2,V_b_2,V_B_2,V_A_2,T_c,T_b,T_a] : % 172.48/172.44 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_ca_2)) % 172.48/172.44 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 172.48/172.44 => hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_ca_2)) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_INF2__E,axiom, % 172.48/172.44 ! [V_a_2,V_ca_2,V_b_2,V_B_2,V_A_2,T_c,T_b,T_a] : % 172.48/172.44 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_ca_2)) % 172.48/172.44 => ( ~ hBOOL(hAPP(hAPP(hAPP(V_B_2,V_a_2),V_b_2),V_ca_2)) % 172.48/172.44 => ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_finite__INT,axiom, % 172.48/172.44 ! [V_A_2,T_b,V_I_2,T_a] : % 172.48/172.44 ( ? [B_x] : % 172.48/172.44 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_I_2)) % 172.48/172.44 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_b),hAPP(V_A_2,B_x))) ) % 172.48/172.44 => 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))) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_Compl__INT,axiom, % 172.48/172.44 ! [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)) ). % 172.48/172.44 % 172.48/172.44 fof(fact_Compl__UN,axiom, % 172.48/172.44 ! [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)) ). % 172.48/172.44 % 172.48/172.44 fof(fact_INT__simps_I9_J,axiom, % 172.48/172.44 ! [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)) ). % 172.48/172.44 % 172.48/172.44 fof(fact_INT__extend__simps_I9_J,axiom, % 172.48/172.44 ! [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) ). % 172.48/172.44 % 172.48/172.44 fof(fact_UN__simps_I7_J,axiom, % 172.48/172.44 ! [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)) ). % 172.48/172.44 % 172.48/172.44 fof(fact_UN__extend__simps_I7_J,axiom, % 172.48/172.44 ! [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)) ). % 172.48/172.44 % 172.48/172.44 fof(fact_INT__absorb,axiom, % 172.48/172.44 ! [V_A_2,T_b,V_I_2,V_k_2,T_a] : % 172.48/172.44 ( hBOOL(hAPP(hAPP(c_member(T_a),V_k_2),V_I_2)) % 172.48/172.44 => 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) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_INT__insert__distrib,axiom, % 172.48/172.44 ! [V_B_2,V_a_2,T_b,V_A_2,V_u_2,T_a] : % 172.48/172.44 ( hBOOL(hAPP(hAPP(c_member(T_a),V_u_2),V_A_2)) % 172.48/172.44 => 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)) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_INFI__bool__eq,axiom, % 172.48/172.44 ! [T_a] : c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_HOL_Obool) = c_Set_OBall(T_a) ). % 172.48/172.44 % 172.48/172.44 fof(fact_INT__simps_I5_J,axiom, % 172.48/172.44 ! [V_B_2,V_a_2,V_C_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_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)) ). % 172.48/172.44 % 172.48/172.44 fof(fact_INT__extend__simps_I5_J,axiom, % 172.48/172.44 ! [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)) ). % 172.48/172.44 % 172.48/172.44 fof(fact_INF__INT__eq2,axiom, % 172.48/172.44 ! [V_y_2,V_x_2,V_r_2,T_c,T_b,T_a] : % 172.48/172.44 ( 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)) % 172.48/172.44 <=> 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))) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_INT__iff,axiom, % 172.48/172.44 ! [V_B_2,V_A_2,T_b,V_b_2,T_a] : % 172.48/172.44 ( 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))) % 172.48/172.44 <=> ! [B_x] : % 172.48/172.44 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 172.48/172.44 => hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),hAPP(V_B_2,B_x))) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_INF__commute,axiom, % 172.48/172.44 ! [V_f_2,V_B_2,T_c,V_A_2,T_b,T_a] : % 172.48/172.44 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 172.48/172.44 => 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))) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_INFI__apply,axiom, % 172.48/172.44 ! [V_x_2,V_f_2,V_A_2,T_c,T_b,T_a] : % 172.48/172.44 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 172.48/172.44 => 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)) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_Pow__INT__eq,axiom, % 172.48/172.44 ! [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)) ). % 172.48/172.44 % 172.48/172.44 fof(fact_INT__Int__distrib,axiom, % 172.48/172.44 ! [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)) ). % 172.48/172.44 % 172.48/172.44 fof(fact_INTER__UNIV__conv_I2_J,axiom, % 172.48/172.44 ! [V_B_2,V_A_2,T_a,T_b] : % 172.48/172.44 ( 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)) % 172.48/172.44 <=> ! [B_x] : % 172.48/172.44 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 172.48/172.44 => hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_INTER__UNIV__conv_I1_J,axiom, % 172.48/172.44 ! [V_B_2,V_A_2,T_b,T_a] : % 172.48/172.44 ( 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) % 172.48/172.44 <=> ! [B_x] : % 172.48/172.44 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 172.48/172.44 => hAPP(V_B_2,B_x) = c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_vimage__INT,axiom, % 172.48/172.44 ! [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)) ). % 172.48/172.44 % 172.48/172.44 fof(fact_INT__simps_I10_J,axiom, % 172.48/172.44 ! [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)) ). % 172.48/172.44 % 172.48/172.44 fof(fact_INT__extend__simps_I10_J,axiom, % 172.48/172.44 ! [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) ). % 172.48/172.44 % 172.48/172.44 fof(fact_INF__INT__eq,axiom, % 172.48/172.44 ! [V_x_2,V_r_2,T_b,T_a] : % 172.48/172.44 ( 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)) % 172.48/172.44 <=> 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))) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_INF__const,axiom, % 172.48/172.44 ! [V_M_2,T_a,V_A_2,T_b] : % 172.48/172.44 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 172.48/172.44 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.44 => 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 ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_INT__lower,axiom, % 172.48/172.44 ! [V_B_2,T_b,V_A_2,V_a_2,T_a] : % 172.48/172.44 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),V_A_2)) % 172.48/172.44 => 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))) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_le__INF__iff,axiom, % 172.48/172.44 ! [V_M_2,V_A_2,T_b,V_u_2,T_a] : % 172.48/172.44 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 172.48/172.44 => ( 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))) % 172.48/172.44 <=> ! [B_x] : % 172.48/172.44 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 172.48/172.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_u_2),hAPP(V_M_2,B_x))) ) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_INT__subset__iff,axiom, % 172.48/172.44 ! [V_A_2,V_I_2,T_b,V_B_2,T_a] : % 172.48/172.44 ( 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))) % 172.48/172.44 <=> ! [B_x] : % 172.48/172.44 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_I_2)) % 172.48/172.44 => 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))) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_INF__less__iff,axiom, % 172.48/172.44 ! [V_a_2,V_f_2,V_A_2,T_b,T_a] : % 172.48/172.44 ( ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 172.48/172.44 & class_Orderings_Olinorder(T_a) ) % 172.48/172.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,T_a),V_A_2),V_f_2)),V_a_2)) % 172.48/172.44 <=> ? [B_x] : % 172.48/172.44 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 172.48/172.44 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),hAPP(V_f_2,B_x)),V_a_2)) ) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_INT__Un,axiom, % 172.48/172.44 ! [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)) ). % 172.48/172.44 % 172.48/172.44 fof(fact_Collect__ball__eq,axiom, % 172.48/172.44 ! [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))) ). % 172.48/172.44 % 172.48/172.44 fof(fact_INT__insert,axiom, % 172.48/172.44 ! [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)) ). % 172.48/172.44 % 172.48/172.44 fof(fact_INT__extend__simps_I2_J,axiom, % 172.48/172.44 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 172.48/172.44 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.44 => 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 ) % 172.48/172.44 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.44 => 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)) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_INT__extend__simps_I1_J,axiom, % 172.48/172.44 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 172.48/172.44 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.44 => 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 ) % 172.48/172.44 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.44 => 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)) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_INT__constant,axiom, % 172.48/172.44 ! [V_ca_2,T_b,T_a,V_A_2] : % 172.48/172.44 ( ( V_A_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.44 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_ca_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) % 172.48/172.44 & ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.44 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(c_COMBK(tc_fun(T_b,tc_HOL_Obool),T_a),V_ca_2)) = V_ca_2 ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_INT__empty,axiom, % 172.48/172.44 ! [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)) ). % 172.48/172.44 % 172.48/172.44 fof(fact_converse__INTER,axiom, % 172.48/172.44 ! [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)) ). % 172.48/172.44 % 172.48/172.44 fof(fact_Un__INT__distrib2,axiom, % 172.48/172.44 ! [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))) ). % 172.48/172.44 % 172.48/172.44 fof(fact_INT__extend__simps_I6_J,axiom, % 172.48/172.44 ! [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)) ). % 172.48/172.44 % 172.48/172.44 fof(fact_Un__INT__distrib,axiom, % 172.48/172.44 ! [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)) ). % 172.48/172.44 % 172.48/172.44 fof(fact_INT__extend__simps_I7_J,axiom, % 172.48/172.44 ! [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)) ). % 172.48/172.44 % 172.48/172.44 fof(fact_INT__simps_I6_J,axiom, % 172.48/172.44 ! [V_B_2,V_A_2,V_C_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_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) ). % 172.48/172.44 % 172.48/172.44 fof(fact_INT__simps_I7_J,axiom, % 172.48/172.44 ! [V_B_2,V_A_2,V_C_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_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)) ). % 172.48/172.44 % 172.48/172.44 fof(fact_Image__INT__subset,axiom, % 172.48/172.44 ! [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)))) ). % 172.48/172.44 % 172.48/172.44 fof(fact_INF__subset,axiom, % 172.48/172.44 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] : % 172.48/172.44 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 172.48/172.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 172.48/172.44 => 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))) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_INTER__def,axiom, % 172.48/172.44 ! [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)))) ). % 172.48/172.44 % 172.48/172.44 fof(fact_INT__simps_I2_J,axiom, % 172.48/172.44 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 172.48/172.44 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.44 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) % 172.48/172.44 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.44 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_INT__simps_I1_J,axiom, % 172.48/172.44 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 172.48/172.44 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.44 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) % 172.48/172.44 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.44 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_Collect__all__eq,axiom, % 172.48/172.44 ! [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))) ). % 172.48/172.44 % 172.48/172.44 fof(fact_INT__extend__simps_I3_J,axiom, % 172.48/172.44 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 172.48/172.44 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.44 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))),V_B_2) ) % 172.48/172.44 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.44 => hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) = hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_INT__simps_I3_J,axiom, % 172.48/172.44 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 172.48/172.44 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.44 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) % 172.48/172.44 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.44 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_A_2)),V_B_2) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_INT__extend__simps_I4_J,axiom, % 172.48/172.44 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 172.48/172.44 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.44 => 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 ) % 172.48/172.44 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.44 => 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)) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_INF__leI,axiom, % 172.48/172.44 ! [V_M_2,V_A_2,V_i_2,T_a,T_b] : % 172.48/172.44 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 172.48/172.44 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_i_2),V_A_2)) % 172.48/172.44 => 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))) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_INT__greaterThan__UNIV,axiom, % 172.48/172.44 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)) ). % 172.48/172.44 % 172.48/172.44 fof(fact_INT__simps_I4_J,axiom, % 172.48/172.44 ! [V_B_2,V_A_2,T_b,T_a,V_C_2] : % 172.48/172.44 ( ( V_C_2 = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.44 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) = c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool)) ) % 172.48/172.44 & ( V_C_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.44 => hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool),T_a),hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2)),V_B_2)) = hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_fun(T_b,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(T_a,tc_fun(T_b,tc_HOL_Obool)),V_C_2),V_B_2)) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_Image__INT__eq,axiom, % 172.48/172.44 ! [V_B_2,T_c,V_A_2,V_r_2,T_b,T_a] : % 172.48/172.44 ( c_Relation_Osingle__valued(T_a,T_b,hAPP(c_Relation_Oconverse(T_b,T_a),V_r_2)) % 172.48/172.44 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_c,tc_HOL_Obool)) % 172.48/172.44 => 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)) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_inf__INFI__fold__inf,axiom, % 172.48/172.44 ! [V_f_2,V_B_2,V_A_2,T_a,T_b] : % 172.48/172.44 ( class_Complete__Lattice_Ocomplete__lattice(T_b) % 172.48/172.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.44 => 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) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_Inf__fold__inf,axiom, % 172.48/172.44 ! [V_A_2,T_a] : % 172.48/172.44 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 172.48/172.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.44 => 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) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_Sup__fold__sup,axiom, % 172.48/172.44 ! [V_A_2,T_a] : % 172.48/172.44 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 172.48/172.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.44 => 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) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_finite__Inter,axiom, % 172.48/172.44 ! [V_M_2,T_a] : % 172.48/172.44 ( ? [B_x] : % 172.48/172.44 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_x),V_M_2)) % 172.48/172.44 & hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),B_x)) ) % 172.48/172.44 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_M_2))) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_UnionI,axiom, % 172.48/172.44 ! [V_A_2,V_C_2,V_X_2,T_a] : % 172.48/172.44 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),V_C_2)) % 172.48/172.44 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),V_X_2)) % 172.48/172.44 => 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))) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_InterD,axiom, % 172.48/172.44 ! [V_X_2,V_C_2,V_A_2,T_a] : % 172.48/172.44 ( 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))) % 172.48/172.44 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),V_C_2)) % 172.48/172.44 => hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),V_X_2)) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_InterE,axiom, % 172.48/172.44 ! [V_X_2,V_C_2,V_A_2,T_a] : % 172.48/172.44 ( 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))) % 172.48/172.44 => ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_X_2),V_C_2)) % 172.48/172.44 => hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),V_X_2)) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_INT__extend__simps_I8_J,axiom, % 172.48/172.44 ! [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) ). % 172.48/172.44 % 172.48/172.44 fof(fact_INT__simps_I8_J,axiom, % 172.48/172.44 ! [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)) ). % 172.48/172.44 % 172.48/172.44 fof(fact_INF2__iff,axiom, % 172.48/172.44 ! [V_ca_2,V_b_2,V_B_2,V_A_2,T_c,T_b,T_a] : % 172.48/172.44 ( hBOOL(hAPP(hAPP(hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_a,tc_fun(T_b,tc_fun(T_c,tc_HOL_Obool))),V_A_2),V_B_2),V_b_2),V_ca_2)) % 172.48/172.44 <=> ! [B_x] : % 172.48/172.44 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 172.48/172.44 => hBOOL(hAPP(hAPP(hAPP(V_B_2,B_x),V_b_2),V_ca_2)) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_INF1__iff,axiom, % 172.48/172.44 ! [V_b_2,V_B_2,V_A_2,T_b,T_a] : % 172.48/172.44 ( 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)) % 172.48/172.44 <=> ! [B_x] : % 172.48/172.44 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 172.48/172.44 => hBOOL(hAPP(hAPP(V_B_2,B_x),V_b_2)) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_INTER__eq__Inter__image,axiom, % 172.48/172.44 ! [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)) ). % 172.48/172.44 % 172.48/172.44 fof(fact_Inter__image__eq,axiom, % 172.48/172.44 ! [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) ). % 172.48/172.44 % 172.48/172.44 fof(fact_Un__Inter,axiom, % 172.48/172.44 ! [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)) ). % 172.48/172.44 % 172.48/172.44 fof(fact_Inter__lower,axiom, % 172.48/172.44 ! [V_A_2,V_B_2,T_a] : % 172.48/172.44 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 172.48/172.44 => 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)) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_le__Inf__iff,axiom, % 172.48/172.44 ! [V_A_2,V_b_2,T_a] : % 172.48/172.44 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 172.48/172.44 => ( 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))) % 172.48/172.44 <=> ! [B_x] : % 172.48/172.44 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 172.48/172.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),B_x)) ) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_Sup__le__iff,axiom, % 172.48/172.44 ! [V_b_2,V_A_2,T_a] : % 172.48/172.44 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 172.48/172.44 => ( 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)) % 172.48/172.44 <=> ! [B_x] : % 172.48/172.44 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 172.48/172.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_x),V_b_2)) ) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_Inf__less__iff,axiom, % 172.48/172.44 ! [V_a_2,V_S_2,T_a] : % 172.48/172.44 ( ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 172.48/172.44 & class_Orderings_Olinorder(T_a) ) % 172.48/172.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Complete__Lattice_OInf__class_OInf(T_a,V_S_2)),V_a_2)) % 172.48/172.44 <=> ? [B_x] : % 172.48/172.44 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2)) % 172.48/172.44 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),B_x),V_a_2)) ) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_less__Sup__iff,axiom, % 172.48/172.44 ! [V_S_2,V_a_2,T_a] : % 172.48/172.44 ( ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 172.48/172.44 & class_Orderings_Olinorder(T_a) ) % 172.48/172.44 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),c_Complete__Lattice_OSup__class_OSup(T_a,V_S_2))) % 172.48/172.44 <=> ? [B_x] : % 172.48/172.44 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_S_2)) % 172.48/172.44 & hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),V_a_2),B_x)) ) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_Union__upper,axiom, % 172.48/172.44 ! [V_A_2,V_B_2,T_a] : % 172.48/172.44 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_B_2),V_A_2)) % 172.48/172.44 => 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))) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_Union__disjoint,axiom, % 172.48/172.44 ! [V_A_2,V_C_2,T_a] : % 172.48/172.44 ( 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)) % 172.48/172.44 <=> ! [B_x] : % 172.48/172.44 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_x),V_C_2)) % 172.48/172.44 => 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)) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_Field__Union,axiom, % 172.48/172.44 ! [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)) ). % 172.48/172.44 % 172.48/172.44 fof(fact_Union__Pow__eq,axiom, % 172.48/172.44 ! [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 ). % 172.48/172.44 % 172.48/172.44 fof(fact_Domain__Union,axiom, % 172.48/172.44 ! [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)) ). % 172.48/172.44 % 172.48/172.44 fof(fact_vimage__Union,axiom, % 172.48/172.44 ! [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)) ). % 172.48/172.44 % 172.48/172.44 fof(fact_Int__Union2,axiom, % 172.48/172.44 ! [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)) ). % 172.48/172.44 % 172.48/172.44 fof(fact_Int__Union,axiom, % 172.48/172.44 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),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)) ). % 172.48/172.44 % 172.48/172.44 fof(fact_UN__extend__simps_I8_J,axiom, % 172.48/172.44 ! [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) ). % 172.48/172.44 % 172.48/172.44 fof(fact_UN__simps_I8_J,axiom, % 172.48/172.44 ! [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)) ). % 172.48/172.44 % 172.48/172.44 fof(fact_Sigma__Union,axiom, % 172.48/172.44 ! [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)) ). % 172.48/172.44 % 172.48/172.44 fof(fact_image__Union,axiom, % 172.48/172.44 ! [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)) ). % 172.48/172.44 % 172.48/172.44 fof(fact_Range__Union,axiom, % 172.48/172.44 ! [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)) ). % 172.48/172.44 % 172.48/172.44 fof(fact_Inf__Sup,axiom, % 172.48/172.44 ! [V_A_2,T_a] : % 172.48/172.44 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 172.48/172.44 => 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))))) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_Sup__Inf,axiom, % 172.48/172.44 ! [V_A_2,T_a] : % 172.48/172.44 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 172.48/172.44 => 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)))))) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_Union__empty,axiom, % 172.48/172.44 ! [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)) ). % 172.48/172.44 % 172.48/172.44 fof(fact_Union__mono,axiom, % 172.48/172.44 ! [V_B_2,V_A_2,T_a] : % 172.48/172.44 ( 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)) % 172.48/172.44 => 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))) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_Union__quotient,axiom, % 172.48/172.44 ! [V_r_2,V_A_2,T_a] : % 172.48/172.44 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 172.48/172.44 => 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 ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_Union__insert,axiom, % 172.48/172.44 ! [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)) ). % 172.48/172.44 % 172.48/172.44 fof(fact_finite__UnionD,axiom, % 172.48/172.44 ! [V_A_2,T_a] : % 172.48/172.44 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_A_2))) % 172.48/172.44 => hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_a,tc_HOL_Obool)),V_A_2)) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_subset__Pow__Union,axiom, % 172.48/172.44 ! [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)))) ). % 172.48/172.44 % 172.48/172.44 fof(fact_Inter__anti__mono,axiom, % 172.48/172.44 ! [V_A_2,V_B_2,T_a] : % 172.48/172.44 ( 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)) % 172.48/172.44 => 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))) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_Inter__empty,axiom, % 172.48/172.44 ! [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)) ). % 172.48/172.44 % 172.48/172.44 fof(fact_Inter__eq,axiom, % 172.48/172.44 ! [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)))) ). % 172.48/172.44 % 172.48/172.44 fof(fact_Union__UNIV,axiom, % 172.48/172.44 ! [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)) ). % 172.48/172.44 % 172.48/172.44 fof(fact_Union__Un__distrib,axiom, % 172.48/172.44 ! [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)) ). % 172.48/172.44 % 172.48/172.44 fof(fact_Inter__insert,axiom, % 172.48/172.44 ! [V_B_2,V_a_2,T_a] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool)),V_a_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_a_2),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_B_2)) ). % 172.48/172.44 % 172.48/172.44 fof(fact_Union__image__eq,axiom, % 172.48/172.44 ! [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) ). % 172.48/172.44 % 172.48/172.44 fof(fact_UNION__eq__Union__image,axiom, % 172.48/172.44 ! [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)) ). % 172.48/172.44 % 172.48/172.44 fof(fact_Sup__upper,axiom, % 172.48/172.44 ! [V_A_2,V_x_2,T_a] : % 172.48/172.44 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 172.48/172.44 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 172.48/172.44 => 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))) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_Inter__UNIV,axiom, % 172.48/172.44 ! [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)) ). % 172.48/172.44 % 172.48/172.44 fof(fact_Inf__lower,axiom, % 172.48/172.44 ! [V_A_2,V_x_2,T_a] : % 172.48/172.44 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 172.48/172.44 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 172.48/172.44 => 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)) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_Inter__Un__distrib,axiom, % 172.48/172.44 ! [V_B_2,V_A_2,T_a] : c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)),V_A_2),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_A_2)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),V_B_2)) ). % 172.48/172.44 % 172.48/172.44 fof(fact_Sup__empty,axiom, % 172.48/172.44 ! [T_a] : % 172.48/172.44 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 172.48/172.44 => 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) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_Sup__singleton,axiom, % 172.48/172.44 ! [V_a_2,T_a] : % 172.48/172.44 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 172.48/172.44 => 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 ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_Sup__insert,axiom, % 172.48/172.44 ! [V_A_2,V_a_2,T_a] : % 172.48/172.44 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 172.48/172.44 => 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)) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_Int__Inter__image,axiom, % 172.48/172.44 ! [V_B_2,V_A_2,V_C_2,T_a,T_b] : hAPP(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OINFI(T_b,tc_fun(T_a,tc_HOL_Obool)),V_C_2),hAPP(hAPP(c_COMBS(T_b,tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool)),T_b),c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool))),V_A_2)),V_B_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_Oimage(T_b,tc_fun(T_a,tc_HOL_Obool),V_A_2),V_C_2))),c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),hAPP(c_Set_Oimage(T_b,tc_fun(T_a,tc_HOL_Obool),V_B_2),V_C_2))) ). % 172.48/172.44 % 172.48/172.44 fof(fact_Inf__singleton,axiom, % 172.48/172.44 ! [V_a_2,T_a] : % 172.48/172.44 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 172.48/172.44 => c_Complete__Lattice_OInf__class_OInf(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)))) = V_a_2 ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_Sup__UNIV,axiom, % 172.48/172.44 ! [T_a] : % 172.48/172.44 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 172.48/172.44 => 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) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_Inf__empty,axiom, % 172.48/172.44 ! [T_a] : % 172.48/172.44 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 172.48/172.44 => 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) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_Inf__UNIV,axiom, % 172.48/172.44 ! [T_a] : % 172.48/172.44 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 172.48/172.44 => 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) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_Inf__insert,axiom, % 172.48/172.44 ! [V_A_2,V_a_2,T_a] : % 172.48/172.44 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 172.48/172.44 => c_Complete__Lattice_OInf__class_OInf(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),V_A_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a_2),c_Complete__Lattice_OInf__class_OInf(T_a,V_A_2)) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_Un__eq__Union,axiom, % 172.48/172.44 ! [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))))) ). % 172.48/172.44 % 172.48/172.44 fof(fact_Un__Union__image,axiom, % 172.48/172.44 ! [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))) ). % 172.48/172.44 % 172.48/172.44 fof(fact_Union__Int__subset,axiom, % 172.48/172.44 ! [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)))) ). % 172.48/172.44 % 172.48/172.44 fof(fact_Int__eq__Inter,axiom, % 172.48/172.44 ! [V_B_2,V_A_2,T_a] : hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2) = c_Complete__Lattice_OInf__class_OInf(tc_fun(T_a,tc_HOL_Obool),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool)),V_A_2),hAPP(hAPP(c_Set_Oinsert(tc_fun(T_a,tc_HOL_Obool)),V_B_2),c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool))))) ). % 172.48/172.44 % 172.48/172.44 fof(fact_Inter__Un__subset,axiom, % 172.48/172.44 ! [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)))) ). % 172.48/172.44 % 172.48/172.44 fof(fact_Sup__binary,axiom, % 172.48/172.44 ! [V_b_2,V_a_2,T_a] : % 172.48/172.44 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 172.48/172.44 => 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) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_Inf__binary,axiom, % 172.48/172.44 ! [V_b_2,V_a_2,T_a] : % 172.48/172.44 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 172.48/172.44 => c_Complete__Lattice_OInf__class_OInf(T_a,hAPP(hAPP(c_Set_Oinsert(T_a),V_a_2),hAPP(hAPP(c_Set_Oinsert(T_a),V_b_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))))) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_a_2),V_b_2) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_sup__Sup__fold__sup,axiom, % 172.48/172.44 ! [V_B_2,V_A_2,T_a] : % 172.48/172.44 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 172.48/172.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.44 => 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) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_Sup__fin__Sup,axiom, % 172.48/172.44 ! [V_A_2,T_a] : % 172.48/172.44 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 172.48/172.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.44 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.44 => c_Big__Operators_Olattice__class_OSup__fin(T_a,V_A_2) = c_Complete__Lattice_OSup__class_OSup(T_a,V_A_2) ) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_inf__Inf__fold__inf,axiom, % 172.48/172.44 ! [V_B_2,V_A_2,T_a] : % 172.48/172.44 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 172.48/172.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.44 => hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_B_2),c_Complete__Lattice_OInf__class_OInf(T_a,V_A_2)) = hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a)),V_B_2),V_A_2) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_Inf__fin__Inf,axiom, % 172.48/172.44 ! [V_A_2,T_a] : % 172.48/172.44 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 172.48/172.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.44 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.44 => c_Big__Operators_Olattice__class_OInf__fin(T_a,V_A_2) = c_Complete__Lattice_OInf__class_OInf(T_a,V_A_2) ) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_image__INT,axiom, % 172.48/172.44 ! [V_j_2,V_B_2,V_A_2,T_c,V_C_2,V_f_2,T_b,T_a] : % 172.48/172.44 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,V_C_2) % 172.48/172.44 => ( ! [B_x] : % 172.48/172.44 ( hBOOL(hAPP(hAPP(c_member(T_c),B_x),V_A_2)) % 172.48/172.44 => 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)) ) % 172.48/172.44 => ( hBOOL(hAPP(hAPP(c_member(T_c),V_j_2),V_A_2)) % 172.48/172.44 => 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)) ) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_card__partition,axiom, % 172.48/172.44 ! [V_k_2,V_C_2,T_a] : % 172.48/172.44 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_a,tc_HOL_Obool)),V_C_2)) % 172.48/172.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_C_2))) % 172.48/172.44 => ( ! [B_c] : % 172.48/172.44 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_c),V_C_2)) % 172.48/172.44 => hAPP(c_Finite__Set_Ocard(T_a),B_c) = V_k_2 ) % 172.48/172.44 => ( ! [B_c1] : % 172.48/172.44 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_c1),V_C_2)) % 172.48/172.44 => ! [B_c2] : % 172.48/172.44 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_c2),V_C_2)) % 172.48/172.44 => ( B_c1 != B_c2 % 172.48/172.44 => 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)) ) ) ) % 172.48/172.44 => 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)) ) ) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_Inter__def,axiom, % 172.48/172.44 ! [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))) ). % 172.48/172.44 % 172.48/172.44 fof(fact_Union__def,axiom, % 172.48/172.44 ! [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))) ). % 172.48/172.44 % 172.48/172.44 fof(fact_finite__Union,axiom, % 172.48/172.44 ! [V_A_2,T_a] : % 172.48/172.44 ( hBOOL(hAPP(c_Finite__Set_Ofinite(tc_fun(T_a,tc_HOL_Obool)),V_A_2)) % 172.48/172.44 => ( ! [B_M] : % 172.48/172.44 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_M),V_A_2)) % 172.48/172.44 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),B_M)) ) % 172.48/172.44 => hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Complete__Lattice_OSup__class_OSup(tc_fun(T_a,tc_HOL_Obool),V_A_2))) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_insert__partition,axiom, % 172.48/172.44 ! [V_F_2,V_x_2,T_a] : % 172.48/172.44 ( ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),V_x_2),V_F_2)) % 172.48/172.44 => ( ! [B_x] : % 172.48/172.44 ( 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))) % 172.48/172.44 => ! [B_xa] : % 172.48/172.44 ( 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))) % 172.48/172.44 => ( B_x != B_xa % 172.48/172.44 => 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)) ) ) ) % 172.48/172.44 => 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)) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_inj__on__Inter,axiom, % 172.48/172.44 ! [V_f_2,T_b,T_a,V_S_2] : % 172.48/172.44 ( V_S_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)) % 172.48/172.44 => ( ! [B_A] : % 172.48/172.44 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_A),V_S_2)) % 172.48/172.44 => c_Fun_Oinj__on(T_a,T_b,V_f_2,B_A) ) % 172.48/172.44 => 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)) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_Inter__subset,axiom, % 172.48/172.44 ! [V_B_2,V_A_2,T_a] : % 172.48/172.44 ( ! [B_X] : % 172.48/172.44 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_X),V_A_2)) % 172.48/172.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),B_X),V_B_2)) ) % 172.48/172.44 => ( V_A_2 != c_Orderings_Obot__class_Obot(tc_fun(tc_fun(T_a,tc_HOL_Obool),tc_HOL_Obool)) % 172.48/172.44 => 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)) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_inj__on__INTER,axiom, % 172.48/172.44 ! [V_A_2,V_f_2,T_c,T_b,T_a,V_I_2] : % 172.48/172.44 ( V_I_2 != c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.44 => ( ! [B_i] : % 172.48/172.44 ( hBOOL(hAPP(hAPP(c_member(T_a),B_i),V_I_2)) % 172.48/172.44 => c_Fun_Oinj__on(T_b,T_c,V_f_2,hAPP(V_A_2,B_i)) ) % 172.48/172.44 => 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)) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_fun__left__comm_Ofold__graph__insertE,axiom, % 172.48/172.44 ! [V_v_2,V_A_2,V_x_2,V_z_2,V_f_2,T_b,T_a] : % 172.48/172.44 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 172.48/172.44 => ( 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)) % 172.48/172.44 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 172.48/172.44 => ~ ! [B_y] : % 172.48/172.44 ( V_v_2 = hAPP(hAPP(V_f_2,V_x_2),B_y) % 172.48/172.44 => ~ hBOOL(hAPP(c_Finite__Set_Ofold__graph(T_a,T_b,V_f_2,V_z_2,V_A_2),B_y)) ) ) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_min__max_Ofold__sup__le__sup,axiom, % 172.48/172.44 ! [V_ca_2,V_b_2,V_A_2,T_a] : % 172.48/172.44 ( class_Orderings_Olinorder(T_a) % 172.48/172.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.44 => ( ! [B_x] : % 172.48/172.44 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 172.48/172.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_x),V_b_2)) ) % 172.48/172.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omax(T_a)),V_ca_2),V_A_2)),hAPP(hAPP(c_Orderings_Oord__class_Omax(T_a),V_b_2),V_ca_2))) ) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_min__max_Oinf__le__fold__inf,axiom, % 172.48/172.44 ! [V_ca_2,V_b_2,V_A_2,T_a] : % 172.48/172.44 ( class_Orderings_Olinorder(T_a) % 172.48/172.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.44 => ( ! [B_x] : % 172.48/172.44 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 172.48/172.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),B_x)) ) % 172.48/172.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Orderings_Oord__class_Omin(T_a),V_b_2),V_ca_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Orderings_Oord__class_Omin(T_a)),V_ca_2),V_A_2))) ) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_InterI,axiom, % 172.48/172.44 ! [V_A_2,V_C_2,T_a] : % 172.48/172.44 ( ! [B_X] : % 172.48/172.44 ( hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_X),V_C_2)) % 172.48/172.44 => hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),B_X)) ) % 172.48/172.44 => 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))) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_inf__le__fold__inf,axiom, % 172.48/172.44 ! [V_ca_2,V_b_2,V_A_2,T_a] : % 172.48/172.44 ( class_Lattices_Osemilattice__inf(T_a) % 172.48/172.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.44 => ( ! [B_x] : % 172.48/172.44 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 172.48/172.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_b_2),B_x)) ) % 172.48/172.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(T_a),V_b_2),V_ca_2)),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__inf__class_Oinf(T_a)),V_ca_2),V_A_2))) ) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_fold__sup__le__sup,axiom, % 172.48/172.44 ! [V_ca_2,V_b_2,V_A_2,T_a] : % 172.48/172.44 ( class_Lattices_Osemilattice__sup(T_a) % 172.48/172.44 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.44 => ( ! [B_x] : % 172.48/172.44 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 172.48/172.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_x),V_b_2)) ) % 172.48/172.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),hAPP(hAPP(c_Finite__Set_Ofold(T_a,T_a,c_Lattices_Osemilattice__sup__class_Osup(T_a)),V_ca_2),V_A_2)),hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(T_a),V_b_2),V_ca_2))) ) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_wf__eq__minimal,axiom, % 172.48/172.44 ! [V_r_2,T_a] : % 172.48/172.44 ( c_Wellfounded_Owf(T_a,V_r_2) % 172.48/172.44 <=> ! [B_Q] : % 172.48/172.44 ( ? [B_x] : hBOOL(hAPP(hAPP(c_member(T_a),B_x),B_Q)) % 172.48/172.44 => ? [B_x] : % 172.48/172.44 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),B_Q)) % 172.48/172.44 & ! [B_y] : % 172.48/172.44 ( 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)) % 172.48/172.44 => ~ hBOOL(hAPP(hAPP(c_member(T_a),B_y),B_Q)) ) ) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_transfer__nat__int__set__cong,axiom, % 172.48/172.44 ! [V_P_H_2,V_P_2] : % 172.48/172.44 ( ! [B_x] : % 172.48/172.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),B_x)) % 172.48/172.44 => ( hBOOL(hAPP(V_P_2,B_x)) % 172.48/172.44 <=> hBOOL(hAPP(V_P_H_2,B_x)) ) ) % 172.48/172.44 => 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)) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_Int__Collect__mono,axiom, % 172.48/172.44 ! [V_Q_2,V_P_2,V_B_2,V_A_2,T_a] : % 172.48/172.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 172.48/172.44 => ( ! [B_x] : % 172.48/172.44 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 172.48/172.44 => ( hBOOL(hAPP(V_P_2,B_x)) % 172.48/172.44 => hBOOL(hAPP(V_Q_2,B_x)) ) ) % 172.48/172.44 => 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)))) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_UnionE,axiom, % 172.48/172.44 ! [V_C_2,V_A_2,T_a] : % 172.48/172.44 ( 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))) % 172.48/172.44 => ~ ! [B_X] : % 172.48/172.44 ( hBOOL(hAPP(hAPP(c_member(T_a),V_A_2),B_X)) % 172.48/172.44 => ~ hBOOL(hAPP(hAPP(c_member(tc_fun(T_a,tc_HOL_Obool)),B_X),V_C_2)) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_rel__compE,axiom, % 172.48/172.44 ! [V_s_2,V_r_2,T_c,V_xz_2,T_b,T_a] : % 172.48/172.44 ( 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))) % 172.48/172.44 => ~ ! [B_x,B_y,B_z] : % 172.48/172.44 ( V_xz_2 = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_x),B_z) % 172.48/172.44 => ( 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)) % 172.48/172.44 => ~ 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)) ) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_converseE,axiom, % 172.48/172.44 ! [V_r_2,V_yx_2,T_b,T_a] : % 172.48/172.44 ( 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))) % 172.48/172.44 => ~ ! [B_x,B_y] : % 172.48/172.44 ( V_yx_2 = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),B_y),B_x) % 172.48/172.44 => ~ 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)) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_Nitpick_Oplus__frac__def,axiom, % 172.48/172.44 ! [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))) ). % 172.48/172.44 % 172.48/172.44 fof(fact_Nitpick_Otimes__frac__def,axiom, % 172.48/172.44 ! [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))) ). % 172.48/172.44 % 172.48/172.44 fof(fact_Nitpick_Oof__frac__def,axiom, % 172.48/172.44 ! [V_q,T_a,T_b] : % 172.48/172.44 ( ( class_Rings_Oinverse(T_b) % 172.48/172.44 & class_Rings_Oring__1(T_b) ) % 172.48/172.44 => 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))) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_Nitpick_Oinverse__frac__def,axiom, % 172.48/172.44 ! [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)) ). % 172.48/172.44 % 172.48/172.44 fof(fact_Nitpick_Ouminus__frac__def,axiom, % 172.48/172.44 ! [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))) ). % 172.48/172.44 % 172.48/172.44 fof(fact_Nitpick_Oless__frac__def,axiom, % 172.48/172.44 ! [V_r_2,V_q_2,T_a] : % 172.48/172.44 ( c_Nitpick_Oless__frac(T_a,V_q_2,V_r_2) % 172.48/172.44 <=> 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))) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_Nitpick_Oless__eq__frac__def,axiom, % 172.48/172.44 ! [V_r_2,V_q_2,T_a] : % 172.48/172.44 ( c_Nitpick_Oless__eq__frac(T_a,V_q_2,V_r_2) % 172.48/172.44 <=> 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))) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_Nitpick_Onum__def,axiom, % 172.48/172.44 ! [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)) ). % 172.48/172.44 % 172.48/172.44 fof(fact_Nitpick_Odenom__def,axiom, % 172.48/172.44 ! [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)) ). % 172.48/172.44 % 172.48/172.44 fof(fact_setprod__pos,axiom, % 172.48/172.44 ! [V_f_2,V_A_2,T_a,T_b] : % 172.48/172.44 ( class_Rings_Olinordered__semidom(T_b) % 172.48/172.44 => ( ! [B_x] : % 172.48/172.44 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 172.48/172.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(V_f_2,B_x))) ) % 172.48/172.44 => 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))) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_internal__split__def,axiom, % 172.48/172.44 ! [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) ). % 172.48/172.44 % 172.48/172.44 fof(fact_internal__split__conv,axiom, % 172.48/172.44 ! [V_b_2,V_a_2,V_ca_2,T_a,T_c,T_b] : hAPP(hAPP(c_Product__Type_Ointernal__split(T_b,T_c,T_a),V_ca_2),hAPP(hAPP(c_Product__Type_OPair(T_b,T_c),V_a_2),V_b_2)) = hAPP(hAPP(V_ca_2,V_a_2),V_b_2) ). % 172.48/172.44 % 172.48/172.44 fof(fact_setprod__nonneg,axiom, % 172.48/172.44 ! [V_f_2,V_A_2,T_a,T_b] : % 172.48/172.44 ( class_Rings_Olinordered__semidom(T_b) % 172.48/172.44 => ( ! [B_x] : % 172.48/172.44 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) % 172.48/172.44 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),c_Groups_Ozero__class_Ozero(T_b)),hAPP(V_f_2,B_x))) ) % 172.48/172.44 => 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))) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_bool_Osize_I2_J,axiom, % 172.48/172.44 c_HOL_Obool_Obool__size(c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 172.48/172.44 % 172.48/172.44 fof(fact_bool_Osize_I1_J,axiom, % 172.48/172.44 c_HOL_Obool_Obool__size(c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 172.48/172.44 % 172.48/172.44 fof(fact_finite__less__ub,axiom, % 172.48/172.44 ! [V_u_2,V_f_2] : % 172.48/172.44 ( ! [B_n] : hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_n),hAPP(V_f_2,B_n))) % 172.48/172.44 => 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)))) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_lenlex__def,axiom, % 172.48/172.44 ! [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)))) ). % 172.48/172.44 % 172.48/172.44 fof(fact_neq__if__length__neq,axiom, % 172.48/172.44 ! [V_ys,V_xs,T_a] : % 172.48/172.44 ( 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) % 172.48/172.44 => V_xs != V_ys ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_lexn__length,axiom, % 172.48/172.44 ! [V_n_2,V_r_2,V_ys_2,V_xs_2,T_a] : % 172.48/172.44 ( 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))) % 172.48/172.44 => ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = V_n_2 % 172.48/172.44 & hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2) = V_n_2 ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_lenlex__conv,axiom, % 172.48/172.44 ! [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)))))) ). % 172.48/172.44 % 172.48/172.44 fof(fact_length__sublist,axiom, % 172.48/172.44 ! [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)))) ). % 172.48/172.44 % 172.48/172.44 fof(fact_lexn_Osimps_I2_J,axiom, % 172.48/172.44 ! [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)))))) ). % 172.48/172.44 % 172.48/172.44 fof(fact_impossible__Cons,axiom, % 172.48/172.44 ! [V_x,V_ys,V_xs,T_a] : % 172.48/172.44 ( 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))) % 172.48/172.44 => V_xs != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_ys) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_not__Cons__self,axiom, % 172.48/172.44 ! [V_x,T_a,V_xs] : V_xs != hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) ). % 172.48/172.44 % 172.48/172.44 fof(fact_not__Cons__self2,axiom, % 172.48/172.44 ! [V_xs,V_x,T_a] : hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) != V_xs ). % 172.48/172.44 % 172.48/172.44 fof(fact_list_Oinject,axiom, % 172.48/172.44 ! [V_list_H_2,V_a_H_2,V_list_2,V_a_2,T_a] : % 172.48/172.44 ( 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) % 172.48/172.44 <=> ( V_a_2 = V_a_H_2 % 172.48/172.44 & V_list_2 = V_list_H_2 ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_list_Osize_I4_J,axiom, % 172.48/172.44 ! [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))) ). % 172.48/172.44 % 172.48/172.44 fof(fact_Cons__in__lex,axiom, % 172.48/172.44 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,V_x_2,T_a] : % 172.48/172.44 ( 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))) % 172.48/172.44 <=> ( ( 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)) % 172.48/172.44 & 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) ) % 172.48/172.44 | ( V_x_2 = V_y_2 % 172.48/172.44 & 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))) ) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_set__Cons__def,axiom, % 172.48/172.44 ! [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)))))) ). % 172.48/172.44 % 172.48/172.44 fof(fact_pick_Osimps,axiom, % 172.48/172.44 ! [V_xs,V_x,T_a,V_i] : % 172.48/172.44 ( ( 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))) % 172.48/172.44 => 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) ) % 172.48/172.44 & ( ~ 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))) % 172.48/172.44 => 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))) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_select__weight__cons__zero,axiom, % 172.48/172.44 ! [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) ). % 172.48/172.44 % 172.48/172.44 fof(fact_lexord__cons__cons,axiom, % 172.48/172.44 ! [V_r_2,V_y_2,V_b_2,V_x_2,V_a_2,T_a] : % 172.48/172.44 ( 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))) % 172.48/172.44 <=> ( 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)) % 172.48/172.44 | ( V_a_2 = V_b_2 % 172.48/172.44 & 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))) ) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_lexord__lex,axiom, % 172.48/172.44 ! [V_r_2,V_y_2,V_x_2,T_a] : % 172.48/172.44 ( 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))) % 172.48/172.44 <=> ( 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))) % 172.48/172.44 & 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) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_rtrancl__listrel1__ConsI2,axiom, % 172.48/172.44 ! [V_ys_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_a] : % 172.48/172.44 ( 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))) % 172.48/172.44 => ( 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)))) % 172.48/172.44 => 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)))) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_list_Osize_I2_J,axiom, % 172.48/172.44 ! [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))) ). % 172.48/172.44 % 172.48/172.44 fof(fact_Cons__acc__listrel1I,axiom, % 172.48/172.44 ! [V_xs_2,V_r_2,V_x_2,T_a] : % 172.48/172.44 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Wellfounded_Oacc(T_a,V_r_2))) % 172.48/172.44 => ( 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)))) % 172.48/172.44 => 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)))) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_listrel1__mono,axiom, % 172.48/172.44 ! [V_s_2,V_r_2,T_a] : % 172.48/172.44 ( 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)) % 172.48/172.44 => 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))) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_listrel1__converse,axiom, % 172.48/172.44 ! [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)) ). % 172.48/172.44 % 172.48/172.44 fof(fact_listrel1__rtrancl__subset__rtrancl__listrel1,axiom, % 172.48/172.44 ! [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)))) ). % 172.48/172.44 % 172.48/172.44 fof(fact_rtrancl__listrel1__ConsI1,axiom, % 172.48/172.44 ! [V_x_2,V_r_2,V_ys_2,V_xs_2,T_a] : % 172.48/172.44 ( 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)))) % 172.48/172.44 => 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)))) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_listrel1I2,axiom, % 172.48/172.44 ! [V_x_2,V_r_2,V_ys_2,V_xs_2,T_a] : % 172.48/172.44 ( 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))) % 172.48/172.44 => 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))) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_rtrancl__listrel1__eq__len,axiom, % 172.48/172.44 ! [V_r_2,V_y_2,V_x_2,T_a] : % 172.48/172.44 ( 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)))) % 172.48/172.44 => 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) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_listrel1__eq__len,axiom, % 172.48/172.44 ! [V_r_2,V_ys_2,V_xs_2,T_a] : % 172.48/172.44 ( 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))) % 172.48/172.44 => 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) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_in__listrel1__converse,axiom, % 172.48/172.44 ! [V_r_2,V_y_2,V_x_2,T_a] : % 172.48/172.44 ( 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)))) % 172.48/172.44 <=> 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)))) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_Cons__listrel1__Cons,axiom, % 172.48/172.44 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,V_x_2,T_a] : % 172.48/172.44 ( 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))) % 172.48/172.44 <=> ( ( 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)) % 172.48/172.44 & V_xs_2 = V_ys_2 ) % 172.48/172.44 | ( V_x_2 = V_y_2 % 172.48/172.44 & 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))) ) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_listrel1I1,axiom, % 172.48/172.44 ! [V_xs_2,V_r_2,V_y_2,V_x_2,T_a] : % 172.48/172.44 ( 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)) % 172.48/172.44 => 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))) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_listrel__Cons,axiom, % 172.48/172.44 ! [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))))) ). % 172.48/172.44 % 172.48/172.44 fof(fact_lexord__linear,axiom, % 172.48/172.44 ! [V_y_2,V_x_2,V_r_2,T_a] : % 172.48/172.44 ( ! [B_a,B_b] : % 172.48/172.44 ( 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)) % 172.48/172.44 | B_a = B_b % 172.48/172.44 | 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)) ) % 172.48/172.44 => ( 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))) % 172.48/172.44 | V_x_2 = V_y_2 % 172.48/172.44 | 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))) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_listrel__rtrancl__refl,axiom, % 172.48/172.44 ! [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)))) ). % 172.48/172.44 % 172.48/172.44 fof(fact_listrel__mono,axiom, % 172.48/172.44 ! [V_s_2,V_r_2,T_a] : % 172.48/172.44 ( 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)) % 172.48/172.44 => 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))) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_listrel__subset__rtrancl__listrel1,axiom, % 172.48/172.44 ! [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)))) ). % 172.48/172.44 % 172.48/172.44 fof(fact_listrel__eq__len,axiom, % 172.48/172.44 ! [V_r_2,V_ys_2,V_xs_2,T_a] : % 172.48/172.44 ( 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))) % 172.48/172.44 => 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) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_listrel__rtrancl__trans,axiom, % 172.48/172.44 ! [V_zs_2,V_r_2,V_ys_2,V_xs_2,T_a] : % 172.48/172.44 ( 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)))) % 172.48/172.44 => ( 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)))) % 172.48/172.44 => 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)))) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_listrel__rtrancl__eq__rtrancl__listrel1,axiom, % 172.48/172.44 ! [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)) ). % 172.48/172.44 % 172.48/172.44 fof(fact_listrel__reflcl__if__listrel1,axiom, % 172.48/172.44 ! [V_r_2,V_ys_2,V_xs_2,T_a] : % 172.48/172.44 ( 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))) % 172.48/172.44 => 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)))) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_listrel1__subset__listrel,axiom, % 172.48/172.44 ! [V_r_H_2,V_r_2,T_a] : % 172.48/172.44 ( 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)) % 172.48/172.44 => ( c_Relation_Orefl__on(T_a,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)),V_r_H_2) % 172.48/172.44 => 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))) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_rtrancl__listrel1__if__listrel,axiom, % 172.48/172.44 ! [V_r_2,V_ys_2,V_xs_2,T_a] : % 172.48/172.44 ( 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))) % 172.48/172.44 => 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)))) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_listrel_OCons,axiom, % 172.48/172.44 ! [V_ys_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_a] : % 172.48/172.44 ( 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)) % 172.48/172.44 => ( 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))) % 172.48/172.44 => 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))) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_listrelp__listrel__eq,axiom, % 172.48/172.44 ! [V_xa_2,V_x_2,V_r_2,T_a] : % 172.48/172.44 ( 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) % 172.48/172.44 <=> 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))) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_listrel__Cons1,axiom, % 172.48/172.44 ! [V_r_2,V_xs_2,V_ys_2,V_y_2,T_a] : % 172.48/172.44 ( 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))) % 172.48/172.44 => ~ ! [B_y,B_ys] : % 172.48/172.44 ( V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_y),B_ys) % 172.48/172.44 => ( 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)) % 172.48/172.44 => ~ 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))) ) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_listrelp_OCons,axiom, % 172.48/172.44 ! [V_ys_2,V_xs_2,T_a,V_y_2,V_x_2,V_r_2] : % 172.48/172.44 ( hBOOL(hAPP(hAPP(V_r_2,V_x_2),V_y_2)) % 172.48/172.44 => ( c_List_Olistrelp(T_a,V_r_2,V_xs_2,V_ys_2) % 172.48/172.44 => 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)) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_listrelp_Oequations_I2_J,axiom, % 172.48/172.44 ! [V_a4_2,V_a2_2,V_a3_2,V_a1_2,V_r_2,T_a] : % 172.48/172.44 ( 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)) % 172.48/172.44 <=> ( hBOOL(hAPP(hAPP(V_r_2,V_a1_2),V_a2_2)) % 172.48/172.44 & c_List_Olistrelp(T_a,V_r_2,V_a3_2,V_a4_2) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_listrel__Cons2,axiom, % 172.48/172.44 ! [V_r_2,V_ys_2,V_y_2,V_xs_2,T_a] : % 172.48/172.44 ( 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))) % 172.48/172.44 => ~ ! [B_x,B_xs] : % 172.48/172.44 ( V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_x),B_xs) % 172.48/172.44 => ( 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)) % 172.48/172.44 => ~ 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))) ) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_listrel__subset,axiom, % 172.48/172.44 ! [V_A_2,V_r_2,T_a] : % 172.48/172.44 ( 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)))) % 172.48/172.44 => 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))))) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_lists__UNIV,axiom, % 172.48/172.44 ! [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)) ). % 172.48/172.44 % 172.48/172.44 fof(fact_lists__mono,axiom, % 172.48/172.44 ! [V_B_2,V_A_2,T_a] : % 172.48/172.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 172.48/172.44 => 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))) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_equiv__listrel,axiom, % 172.48/172.44 ! [V_r_2,V_A_2,T_a] : % 172.48/172.44 ( c_Equiv__Relations_Oequiv(T_a,V_A_2,V_r_2) % 172.48/172.44 => 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)) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_listrel__refl__on,axiom, % 172.48/172.44 ! [V_r_2,V_A_2,T_a] : % 172.48/172.44 ( c_Relation_Orefl__on(T_a,V_A_2,V_r_2) % 172.48/172.44 => 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)) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_Cons__in__lists__iff,axiom, % 172.48/172.44 ! [V_A_2,V_xs_2,V_x_2,T_a] : % 172.48/172.44 ( 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))) % 172.48/172.44 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 172.48/172.44 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_xs_2),c_List_Olists(T_a,V_A_2))) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_lists__accD,axiom, % 172.48/172.44 ! [V_r_2,V_xs_2,T_a] : % 172.48/172.44 ( 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)))) % 172.48/172.44 => 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)))) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_lists__accI,axiom, % 172.48/172.44 ! [V_r_2,V_xs_2,T_a] : % 172.48/172.44 ( 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)))) % 172.48/172.44 => 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)))) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_listrel__iff__nth,axiom, % 172.48/172.44 ! [V_r_2,V_ys_2,V_xs_2,T_a] : % 172.48/172.44 ( 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))) % 172.48/172.44 <=> ( 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) % 172.48/172.44 & ! [B_n] : % 172.48/172.44 ( 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))) % 172.48/172.44 => 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)) ) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_lexord__irreflexive,axiom, % 172.48/172.44 ! [V_y_2,V_r_2,T_a] : % 172.48/172.44 ( ! [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)) % 172.48/172.44 => ~ 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))) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_infinite__UNIV__listI,axiom, % 172.48/172.44 ! [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)))) ). % 172.48/172.44 % 172.48/172.44 fof(fact_list__eq__iff__nth__eq,axiom, % 172.48/172.44 ! [T_a,V_ys_2,V_xs_2] : % 172.48/172.44 ( V_xs_2 = V_ys_2 % 172.48/172.44 <=> ( 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) % 172.48/172.44 & ! [B_i] : % 172.48/172.44 ( 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))) % 172.48/172.44 => hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i) = hAPP(hAPP(c_List_Onth(T_a),V_ys_2),B_i) ) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_nth__Cons__Suc,axiom, % 172.48/172.44 ! [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) ). % 172.48/172.44 % 172.48/172.44 fof(fact_nth__Cons__0,axiom, % 172.48/172.44 ! [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 ). % 172.48/172.44 % 172.48/172.44 fof(fact_nth_Osimps,axiom, % 172.48/172.44 ! [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) ). % 172.48/172.44 % 172.48/172.44 fof(fact_nth__Cons_H,axiom, % 172.48/172.44 ! [V_xs,V_x,T_a,V_n] : % 172.48/172.44 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 172.48/172.44 => hAPP(hAPP(c_List_Onth(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)),V_n) = V_x ) % 172.48/172.44 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 172.48/172.44 => 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))) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_nth__Cons__number__of,axiom, % 172.48/172.44 ! [V_xs,V_x,T_a,V_v] : % 172.48/172.44 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 172.48/172.44 => 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 ) % 172.48/172.44 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 172.48/172.44 => 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))) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_lexord__take__index__conv,axiom, % 172.48/172.44 ! [V_r_2,V_y_2,V_x_2,T_a] : % 172.48/172.44 ( 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))) % 172.48/172.44 <=> ( ( 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))) % 172.48/172.44 & 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 ) % 172.48/172.44 | ? [B_i] : % 172.48/172.44 ( 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)))) % 172.48/172.44 & hAPP(hAPP(c_List_Otake(T_a),B_i),V_x_2) = hAPP(hAPP(c_List_Otake(T_a),B_i),V_y_2) % 172.48/172.44 & 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)) ) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_set__sublist,axiom, % 172.48/172.44 ! [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))))) ). % 172.48/172.44 % 172.48/172.44 fof(fact_finite__set,axiom, % 172.48/172.44 ! [V_xs_2,T_a] : hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),hAPP(c_List_Oset(T_a),V_xs_2))) ). % 172.48/172.44 % 172.48/172.44 fof(fact_set__subset__Cons,axiom, % 172.48/172.44 ! [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)))) ). % 172.48/172.44 % 172.48/172.44 fof(fact_take__all,axiom, % 172.48/172.44 ! [V_n,V_xs,T_a] : % 172.48/172.44 ( 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)) % 172.48/172.44 => hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs) = V_xs ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_set__take__subset__set__take,axiom, % 172.48/172.44 ! [V_xs_2,T_a,V_n_2,V_m_2] : % 172.48/172.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 172.48/172.44 => 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)))) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_set__take__subset,axiom, % 172.48/172.44 ! [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))) ). % 172.48/172.44 % 172.48/172.44 fof(fact_set__sublist__subset,axiom, % 172.48/172.44 ! [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))) ). % 172.48/172.44 % 172.48/172.44 fof(fact_nth__take,axiom, % 172.48/172.44 ! [V_xs,T_a,V_n,V_i] : % 172.48/172.44 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_n)) % 172.48/172.44 => 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) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_sublist__upt__eq__take,axiom, % 172.48/172.44 ! [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) ). % 172.48/172.44 % 172.48/172.44 fof(fact_take__Suc__Cons,axiom, % 172.48/172.44 ! [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)) ). % 172.48/172.44 % 172.48/172.44 fof(fact_set__ConsD,axiom, % 172.48/172.44 ! [V_xs_2,V_x_2,V_y_2,T_a] : % 172.48/172.44 ( 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)))) % 172.48/172.44 => ( V_y_2 = V_x_2 % 172.48/172.44 | hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_in__set__sublistD,axiom, % 172.48/172.44 ! [V_I_2,V_xs_2,V_x_2,T_a] : % 172.48/172.44 ( 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)))) % 172.48/172.44 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_in__set__takeD,axiom, % 172.48/172.44 ! [V_xs_2,V_n_2,V_x_2,T_a] : % 172.48/172.44 ( 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)))) % 172.48/172.44 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_notin__set__sublistI,axiom, % 172.48/172.44 ! [V_I_2,V_xs_2,V_x_2,T_a] : % 172.48/172.44 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 172.48/172.44 => ~ 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)))) ) ). % 172.48/172.44 % 172.48/172.44 fof(fact_length__take,axiom, % 172.48/172.44 ! [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) ). % 172.48/172.44 % 172.48/172.44 fof(fact_take__take,axiom, % 172.48/172.44 ! [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) ). % 172.48/172.44 % 172.48/172.44 fof(fact_List_Oset_Osimps_I2_J,axiom, % 172.48/172.44 ! [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)) ). % 172.48/172.44 % 172.48/172.44 fof(fact_card__length,axiom, % 172.48/172.44 ! [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))) ). % 172.48/172.45 % 172.48/172.45 fof(fact_all__set__conv__all__nth,axiom, % 172.48/172.45 ! [V_P_2,V_xs_2,T_a] : % 172.48/172.45 ( ! [B_x] : % 172.48/172.45 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 172.48/172.45 => hBOOL(hAPP(V_P_2,B_x)) ) % 172.48/172.45 <=> ! [B_i] : % 172.48/172.45 ( 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))) % 172.48/172.45 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i))) ) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_list__size__estimation,axiom, % 172.48/172.45 ! [V_f_2,V_y_2,V_xs_2,V_x_2,T_a] : % 172.48/172.45 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 172.48/172.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_y_2),hAPP(V_f_2,V_x_2))) % 172.48/172.45 => 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))) ) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_list__size__estimation_H,axiom, % 172.48/172.45 ! [V_f_2,V_y_2,V_xs_2,V_x_2,T_a] : % 172.48/172.45 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 172.48/172.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_y_2),hAPP(V_f_2,V_x_2))) % 172.48/172.45 => 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))) ) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_in__lists__conv__set,axiom, % 172.48/172.45 ! [V_A_2,V_xs_2,T_a] : % 172.48/172.45 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_xs_2),c_List_Olists(T_a,V_A_2))) % 172.48/172.45 <=> ! [B_x] : % 172.48/172.45 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 172.48/172.45 => hBOOL(hAPP(hAPP(c_member(T_a),B_x),V_A_2)) ) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_length__pos__if__in__set,axiom, % 172.48/172.45 ! [V_xs_2,V_x_2,T_a] : % 172.48/172.45 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 172.48/172.45 => 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))) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_nth__mem,axiom, % 172.48/172.45 ! [V_xs_2,T_a,V_n_2] : % 172.48/172.45 ( 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))) % 172.48/172.45 => 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))) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_in__set__conv__nth,axiom, % 172.48/172.45 ! [V_xs_2,V_x_2,T_a] : % 172.48/172.45 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 172.48/172.45 <=> ? [B_i] : % 172.48/172.45 ( 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))) % 172.48/172.45 & hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i) = V_x_2 ) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_lists__eq__set,axiom, % 172.48/172.45 ! [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)) ). % 172.48/172.45 % 172.48/172.45 fof(fact_set__conv__nth,axiom, % 172.48/172.45 ! [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))))) ). % 172.48/172.45 % 172.48/172.45 fof(fact_finite__lists__length__eq,axiom, % 172.48/172.45 ! [V_n_2,V_A_2,T_a] : % 172.48/172.45 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.45 => 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))))) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_finite__lists__length__le,axiom, % 172.48/172.45 ! [V_n_2,V_A_2,T_a] : % 172.48/172.45 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.45 => 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))))) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_listrel__iff__zip,axiom, % 172.48/172.45 ! [V_r_2,V_ys_2,V_xs_2,T_a] : % 172.48/172.45 ( 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))) % 172.48/172.45 <=> ( 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) % 172.48/172.45 & ! [B_x] : % 172.48/172.45 ( 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)))) % 172.48/172.45 => 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)) ) ) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_set__zip,axiom, % 172.48/172.45 ! [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)))))) ). % 172.48/172.45 % 172.48/172.45 fof(fact_take__zip,axiom, % 172.48/172.45 ! [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)) ). % 172.48/172.45 % 172.48/172.45 fof(fact_length__zip,axiom, % 172.48/172.45 ! [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)) ). % 172.48/172.45 % 172.48/172.45 fof(fact_zip__Cons__Cons,axiom, % 172.48/172.45 ! [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)) ). % 172.48/172.45 % 172.48/172.45 fof(fact_list__eq__iff__zip__eq,axiom, % 172.48/172.45 ! [T_a,V_ys_2,V_xs_2] : % 172.48/172.45 ( V_xs_2 = V_ys_2 % 172.48/172.45 <=> ( 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) % 172.48/172.45 & ! [B_x] : % 172.48/172.45 ( 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)))) % 172.48/172.45 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),c_fequal),B_x)) ) ) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_in__set__zipE,axiom, % 172.48/172.45 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_b,T_a] : % 172.48/172.45 ( 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)))) % 172.48/172.45 => ~ ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 172.48/172.45 => ~ hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),V_ys_2))) ) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_set__zip__rightD,axiom, % 172.48/172.45 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_b,T_a] : % 172.48/172.45 ( 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)))) % 172.48/172.45 => hBOOL(hAPP(hAPP(c_member(T_b),V_y_2),hAPP(c_List_Oset(T_b),V_ys_2))) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_set__zip__leftD,axiom, % 172.48/172.45 ! [V_ys_2,V_xs_2,V_y_2,V_x_2,T_b,T_a] : % 172.48/172.45 ( 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)))) % 172.48/172.45 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_zip__same,axiom, % 172.48/172.45 ! [V_xs_2,V_b_2,V_a_2,T_a] : % 172.48/172.45 ( 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)))) % 172.48/172.45 <=> ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 172.48/172.45 & V_a_2 = V_b_2 ) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_nth__zip,axiom, % 172.48/172.45 ! [V_ys,T_b,V_xs,T_a,V_i] : % 172.48/172.45 ( 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))) % 172.48/172.45 => ( 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))) % 172.48/172.45 => 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)) ) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_greaterThanLessThan__upto,axiom, % 172.48/172.45 ! [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)))) ). % 172.48/172.45 % 172.48/172.45 fof(fact_listsum__setsum__nth,axiom, % 172.48/172.45 ! [V_xs_2,T_a] : % 172.48/172.45 ( class_Groups_Ocomm__monoid__add(T_a) % 172.48/172.45 => 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))) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_listsum__eq__0__nat__iff__nat,axiom, % 172.48/172.45 ! [V_ns_2] : % 172.48/172.45 ( hAPP(c_List_Omonoid__add__class_Olistsum(tc_Nat_Onat),V_ns_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 172.48/172.45 <=> ! [B_x] : % 172.48/172.45 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2))) % 172.48/172.45 => B_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_set__upto,axiom, % 172.48/172.45 ! [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) ). % 172.48/172.45 % 172.48/172.45 fof(fact_atLeastAtMost__upto,axiom, % 172.48/172.45 ! [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)) ). % 172.48/172.45 % 172.48/172.45 fof(fact_elem__le__listsum__nat,axiom, % 172.48/172.45 ! [V_ns,V_k] : % 172.48/172.45 ( 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))) % 172.48/172.45 => 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))) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_listsum__simps_I2_J,axiom, % 172.48/172.45 ! [V_xs,V_x,T_a] : % 172.48/172.45 ( class_Groups_Omonoid__add(T_a) % 172.48/172.45 => 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)) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_atLeastLessThan__upto,axiom, % 172.48/172.45 ! [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)))) ). % 172.48/172.45 % 172.48/172.45 fof(fact_greaterThanAtMost__upto,axiom, % 172.48/172.45 ! [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)) ). % 172.48/172.45 % 172.48/172.45 fof(fact_nat__list__def,axiom, % 172.48/172.45 ! [V_l_2] : % 172.48/172.45 ( c_List_Onat__list(V_l_2) % 172.48/172.45 <=> c_Nat__Transfer_Onat__set(hAPP(c_List_Oset(tc_Int_Oint),V_l_2)) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_list__size__pointwise,axiom, % 172.48/172.45 ! [V_g_2,V_f_2,V_xs_2,T_a] : % 172.48/172.45 ( ! [B_x] : % 172.48/172.45 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 172.48/172.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) ) % 172.48/172.45 => 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))) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_listsum__update__nat,axiom, % 172.48/172.45 ! [V_n,V_ns,V_k] : % 172.48/172.45 ( 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))) % 172.48/172.45 => 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)) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_butlast__take,axiom, % 172.48/172.45 ! [V_xs,T_a,V_n] : % 172.48/172.45 ( 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))) % 172.48/172.45 => 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) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_list__update__beyond,axiom, % 172.48/172.45 ! [V_x,V_i,V_xs,T_a] : % 172.48/172.45 ( 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)) % 172.48/172.45 => hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_i),V_x) = V_xs ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_nth__list__update__neq,axiom, % 172.48/172.45 ! [V_x,V_xs,T_a,V_j,V_i] : % 172.48/172.45 ( V_i != V_j % 172.48/172.45 => 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) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_list__update__id,axiom, % 172.48/172.45 ! [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 ). % 172.48/172.45 % 172.48/172.45 fof(fact_length__list__update,axiom, % 172.48/172.45 ! [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) ). % 172.48/172.45 % 172.48/172.45 fof(fact_butlast__list__update,axiom, % 172.48/172.45 ! [V_x,V_xs,T_a,V_k] : % 172.48/172.45 ( ( 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)) % 172.48/172.45 => 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) ) % 172.48/172.45 & ( 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)) % 172.48/172.45 => 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) ) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_zip__update,axiom, % 172.48/172.45 ! [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)) ). % 172.48/172.45 % 172.48/172.45 fof(fact_update__zip,axiom, % 172.48/172.45 ! [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))) ). % 172.48/172.45 % 172.48/172.45 fof(fact_list__update__overwrite,axiom, % 172.48/172.45 ! [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) ). % 172.48/172.45 % 172.48/172.45 fof(fact_list__update__swap,axiom, % 172.48/172.45 ! [V_x_H,V_x,V_xs,T_a,V_i_H,V_i] : % 172.48/172.45 ( V_i != V_i_H % 172.48/172.45 => 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) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_list__update__code_I3_J,axiom, % 172.48/172.45 ! [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)) ). % 172.48/172.45 % 172.48/172.45 fof(fact_list__update_Osimps_I2_J,axiom, % 172.48/172.45 ! [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) ). % 172.48/172.45 % 172.48/172.45 fof(fact_list__update__code_I2_J,axiom, % 172.48/172.45 ! [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) ). % 172.48/172.45 % 172.48/172.45 fof(fact_in__set__butlastD,axiom, % 172.48/172.45 ! [V_xs_2,V_x_2,T_a] : % 172.48/172.45 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_List_Obutlast(T_a,V_xs_2)))) % 172.48/172.45 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_set__update__subsetI,axiom, % 172.48/172.45 ! [V_i_2,V_x_2,V_A_2,V_xs_2,T_a] : % 172.48/172.45 ( 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)) % 172.48/172.45 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 172.48/172.45 => 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)) ) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_set__update__subset__insert,axiom, % 172.48/172.45 ! [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)))) ). % 172.48/172.45 % 172.48/172.45 fof(fact_nth__list__update,axiom, % 172.48/172.45 ! [V_x,V_j,V_xs,T_a,V_i] : % 172.48/172.45 ( 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))) % 172.48/172.45 => ( ( V_i = V_j % 172.48/172.45 => 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 ) % 172.48/172.45 & ( V_i != V_j % 172.48/172.45 => 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) ) ) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_list__update__same__conv,axiom, % 172.48/172.45 ! [V_x_2,V_xs_2,T_a,V_i_2] : % 172.48/172.45 ( 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))) % 172.48/172.45 => ( hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),V_i_2),V_x_2) = V_xs_2 % 172.48/172.45 <=> hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_i_2) = V_x_2 ) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_nth__list__update__eq,axiom, % 172.48/172.45 ! [V_x,V_xs,T_a,V_i] : % 172.48/172.45 ( 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))) % 172.48/172.45 => 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 ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_take__butlast,axiom, % 172.48/172.45 ! [V_xs,T_a,V_n] : % 172.48/172.45 ( 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))) % 172.48/172.45 => 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) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_length__butlast,axiom, % 172.48/172.45 ! [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)) ). % 172.48/172.45 % 172.48/172.45 fof(fact_set__update__memI,axiom, % 172.48/172.45 ! [V_x_2,V_xs_2,T_a,V_n_2] : % 172.48/172.45 ( 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))) % 172.48/172.45 => 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)))) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_butlast__conv__take,axiom, % 172.48/172.45 ! [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) ). % 172.48/172.45 % 172.48/172.45 fof(fact_listrel1__iff__update,axiom, % 172.48/172.45 ! [V_r_2,V_ys_2,V_xs_2,T_a] : % 172.48/172.45 ( 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))) % 172.48/172.45 <=> ? [B_y,B_n] : % 172.48/172.45 ( 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)) % 172.48/172.45 & 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))) % 172.48/172.45 & V_ys_2 = hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),B_n),B_y) ) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_distinct__list__update,axiom, % 172.48/172.45 ! [V_i_2,V_a_2,V_xs_2,T_a] : % 172.48/172.45 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 172.48/172.45 => ( ~ 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)))))) % 172.48/172.45 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),V_i_2),V_a_2))) ) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_distinct__upto,axiom, % 172.48/172.45 ! [V_j,V_i] : hBOOL(hAPP(c_List_Odistinct(tc_Int_Oint),c_List_Oupto(V_i,V_j))) ). % 172.48/172.45 % 172.48/172.45 fof(fact_distinct__take,axiom, % 172.48/172.45 ! [V_i,V_xs,T_a] : % 172.48/172.45 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 172.48/172.45 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Otake(T_a),V_i),V_xs))) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_distinct__sublistI,axiom, % 172.48/172.45 ! [V_I_2,V_xs_2,T_a] : % 172.48/172.45 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 172.48/172.45 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Osublist(T_a,V_xs_2,V_I_2))) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_distinct__zipI1,axiom, % 172.48/172.45 ! [V_ys,T_b,V_xs,T_a] : % 172.48/172.45 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 172.48/172.45 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_a,T_b)),hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs),V_ys))) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_distinct__zipI2,axiom, % 172.48/172.45 ! [V_xs,T_b,V_ys,T_a] : % 172.48/172.45 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_ys)) % 172.48/172.45 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_b,T_a)),hAPP(hAPP(c_List_Ozip(T_b,T_a),V_xs),V_ys))) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_distinct_Osimps_I2_J,axiom, % 172.48/172.45 ! [V_xs_2,V_x_2,T_a] : % 172.48/172.45 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2))) % 172.48/172.45 <=> ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 172.48/172.45 & hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_distinct__card,axiom, % 172.48/172.45 ! [V_xs_2,T_a] : % 172.48/172.45 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 172.48/172.45 => 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) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_card__distinct,axiom, % 172.48/172.45 ! [V_xs_2,T_a] : % 172.48/172.45 ( 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) % 172.48/172.45 => hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_distinct__conv__nth,axiom, % 172.48/172.45 ! [V_xs_2,T_a] : % 172.48/172.45 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 172.48/172.45 <=> ! [B_i] : % 172.48/172.45 ( 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))) % 172.48/172.45 => ! [B_j] : % 172.48/172.45 ( 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))) % 172.48/172.45 => ( B_i != B_j % 172.48/172.45 => hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i) != hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_j) ) ) ) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_nth__eq__iff__index__eq,axiom, % 172.48/172.45 ! [V_j_2,V_i_2,V_xs_2,T_a] : % 172.48/172.45 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 172.48/172.45 => ( 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))) % 172.48/172.45 => ( 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))) % 172.48/172.45 => ( 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) % 172.48/172.45 <=> V_i_2 = V_j_2 ) ) ) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_distinct__listsum__conv__Setsum,axiom, % 172.48/172.45 ! [V_xs_2,T_a] : % 172.48/172.45 ( class_Groups_Ocomm__monoid__add(T_a) % 172.48/172.45 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 172.48/172.45 => 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)) ) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_Nitpick_Ocard_H__def,axiom, % 172.48/172.45 ! [V_A_2,T_a] : % 172.48/172.45 ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.45 => 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)))) ) % 172.48/172.45 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.45 => c_Nitpick_Ocard_H(T_a,V_A_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_dom__map__upds,axiom, % 172.48/172.45 ! [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)) ). % 172.48/172.45 % 172.48/172.45 fof(fact_map__upds__apply__nontin,axiom, % 172.48/172.45 ! [V_ys_2,V_f_2,T_b,V_xs_2,V_x_2,T_a] : % 172.48/172.45 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 172.48/172.45 => 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) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_map__upds__list__update2__drop,axiom, % 172.48/172.45 ! [V_y_2,V_m_2,V_ys_2,T_b,V_i_2,V_xs_2,T_a] : % 172.48/172.45 ( 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)) % 172.48/172.45 => ( 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))) % 172.48/172.45 => 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) ) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_nth__take__lemma,axiom, % 172.48/172.45 ! [V_ys,V_xs,T_a,V_k] : % 172.48/172.45 ( 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))) % 172.48/172.45 => ( 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))) % 172.48/172.45 => ( ! [B_i] : % 172.48/172.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_k)) % 172.48/172.45 => hAPP(hAPP(c_List_Onth(T_a),V_xs),B_i) = hAPP(hAPP(c_List_Onth(T_a),V_ys),B_i) ) % 172.48/172.45 => hAPP(hAPP(c_List_Otake(T_a),V_k),V_xs) = hAPP(hAPP(c_List_Otake(T_a),V_k),V_ys) ) ) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_restrict__map__upds,axiom, % 172.48/172.45 ! [V_m_2,V_D_2,V_ys_2,T_b,V_xs_2,T_a] : % 172.48/172.45 ( 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) % 172.48/172.45 => ( 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)) % 172.48/172.45 => 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) ) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_restrict__map__insert,axiom, % 172.48/172.45 ! [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)) ). % 172.48/172.45 % 172.48/172.45 fof(fact_restrict__restrict,axiom, % 172.48/172.45 ! [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)) ). % 172.48/172.45 % 172.48/172.45 fof(fact_restrict__in,axiom, % 172.48/172.45 ! [V_m_2,T_b,V_A_2,V_x_2,T_a] : % 172.48/172.45 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 172.48/172.45 => 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) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_dom__restrict,axiom, % 172.48/172.45 ! [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) ). % 172.48/172.45 % 172.48/172.45 fof(fact_fun__upd__restrict,axiom, % 172.48/172.45 ! [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) ). % 172.48/172.45 % 172.48/172.45 fof(fact_fun__upd__restrict__conv,axiom, % 172.48/172.45 ! [V_y_2,V_m_2,T_b,V_D_2,V_x_2,T_a] : % 172.48/172.45 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_D_2)) % 172.48/172.45 => 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) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_restrict__fun__upd,axiom, % 172.48/172.45 ! [V_y_2,V_m_2,T_b,V_D_2,V_x_2,T_a] : % 172.48/172.45 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_D_2)) % 172.48/172.45 => 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) ) % 172.48/172.45 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_D_2)) % 172.48/172.45 => 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) ) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_set__remove1__eq,axiom, % 172.48/172.45 ! [V_x_2,V_xs_2,T_a] : % 172.48/172.45 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 172.48/172.45 => 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)))) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_take__Cons__number__of,axiom, % 172.48/172.45 ! [V_xs,V_x,T_a,V_v] : % 172.48/172.45 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 172.48/172.45 => 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) ) % 172.48/172.45 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 172.48/172.45 => 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)) ) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_lists_ONil,axiom, % 172.48/172.45 ! [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))) ). % 172.48/172.45 % 172.48/172.45 fof(fact_listrel__Nil1,axiom, % 172.48/172.45 ! [V_r_2,V_xs_2,T_a] : % 172.48/172.45 ( 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))) % 172.48/172.45 => V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_listrel__Nil2,axiom, % 172.48/172.45 ! [V_r_2,V_xs_2,T_a] : % 172.48/172.45 ( 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))) % 172.48/172.45 => V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_list__update__nonempty,axiom, % 172.48/172.45 ! [V_x_2,V_k_2,V_xs_2,T_a] : % 172.48/172.45 ( hAPP(hAPP(c_List_Olist__update(T_a,V_xs_2),V_k_2),V_x_2) = c_List_Olist_ONil(T_a) % 172.48/172.45 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_list__update_Osimps_I1_J,axiom, % 172.48/172.45 ! [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) ). % 172.48/172.45 % 172.48/172.45 fof(fact_list__update__code_I1_J,axiom, % 172.48/172.45 ! [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) ). % 172.48/172.45 % 172.48/172.45 fof(fact_List_Oset_Osimps_I1_J,axiom, % 172.48/172.45 ! [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)) ). % 172.48/172.45 % 172.48/172.45 fof(fact_set__empty2,axiom, % 172.48/172.45 ! [V_xs_2,T_a] : % 172.48/172.45 ( c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) = hAPP(c_List_Oset(T_a),V_xs_2) % 172.48/172.45 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_set__empty,axiom, % 172.48/172.45 ! [V_xs_2,T_a] : % 172.48/172.45 ( hAPP(c_List_Oset(T_a),V_xs_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.48/172.45 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_list_Osize_I3_J,axiom, % 172.48/172.45 ! [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) ). % 172.48/172.45 % 172.48/172.45 fof(fact_length__0__conv,axiom, % 172.48/172.45 ! [V_xs_2,T_a] : % 172.48/172.45 ( hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs_2) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 172.48/172.45 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_listsum__simps_I1_J,axiom, % 172.48/172.45 ! [T_a] : % 172.48/172.45 ( class_Groups_Omonoid__add(T_a) % 172.48/172.45 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),c_List_Olist_ONil(T_a)) = c_Groups_Ozero__class_Ozero(T_a) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_zip_Osimps_I1_J,axiom, % 172.48/172.45 ! [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)) ). % 172.48/172.45 % 172.48/172.45 fof(fact_zip__Nil,axiom, % 172.48/172.45 ! [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)) ). % 172.48/172.45 % 172.48/172.45 fof(fact_listrelp_ONil,axiom, % 172.48/172.45 ! [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)) ). % 172.48/172.45 % 172.48/172.45 fof(fact_listrelp_Oequations_I1_J,axiom, % 172.48/172.45 ! [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)) ). % 172.48/172.45 % 172.48/172.45 fof(fact_list_Osize_I1_J,axiom, % 172.48/172.45 ! [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) ). % 172.48/172.45 % 172.48/172.45 fof(fact_remove1_Osimps_I1_J,axiom, % 172.48/172.45 ! [V_x,T_a] : c_List_Oremove1(T_a,V_x,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 172.48/172.45 % 172.48/172.45 fof(fact_remove1__commute,axiom, % 172.48/172.45 ! [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)) ). % 172.48/172.45 % 172.48/172.45 fof(fact_sublist__nil,axiom, % 172.48/172.45 ! [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) ). % 172.48/172.45 % 172.48/172.45 fof(fact_take__0,axiom, % 172.48/172.45 ! [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) ). % 172.48/172.45 % 172.48/172.45 fof(fact_take__eq__Nil,axiom, % 172.48/172.45 ! [V_xs_2,V_n_2,T_a] : % 172.48/172.45 ( hAPP(hAPP(c_List_Otake(T_a),V_n_2),V_xs_2) = c_List_Olist_ONil(T_a) % 172.48/172.45 <=> ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 172.48/172.45 | V_xs_2 = c_List_Olist_ONil(T_a) ) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_take__Nil,axiom, % 172.48/172.45 ! [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) ). % 172.48/172.45 % 172.48/172.45 fof(fact_upto__empty,axiom, % 172.48/172.45 ! [V_i,V_j] : % 172.48/172.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_j),V_i)) % 172.48/172.45 => c_List_Oupto(V_i,V_j) = c_List_Olist_ONil(tc_Int_Oint) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_remove1_Osimps_I2_J,axiom, % 172.48/172.45 ! [V_xs,T_a,V_y,V_x] : % 172.48/172.45 ( ( V_x = V_y % 172.48/172.45 => c_List_Oremove1(T_a,V_x,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_xs)) = V_xs ) % 172.48/172.45 & ( V_x != V_y % 172.48/172.45 => 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)) ) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_list_Osimps_I3_J,axiom, % 172.48/172.45 ! [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) ). % 172.48/172.45 % 172.48/172.45 fof(fact_list_Osimps_I2_J,axiom, % 172.48/172.45 ! [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) ). % 172.48/172.45 % 172.48/172.45 fof(fact_butlast_Osimps_I2_J,axiom, % 172.48/172.45 ! [V_x,T_a,V_xs] : % 172.48/172.45 ( ( V_xs = c_List_Olist_ONil(T_a) % 172.48/172.45 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olist_ONil(T_a) ) % 172.48/172.45 & ( V_xs != c_List_Olist_ONil(T_a) % 172.48/172.45 => 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)) ) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_butlast_Osimps_I1_J,axiom, % 172.48/172.45 ! [T_a] : c_List_Obutlast(T_a,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 172.48/172.45 % 172.48/172.45 fof(fact_map__upds__Nil2,axiom, % 172.48/172.45 ! [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 ). % 172.48/172.45 % 172.48/172.45 fof(fact_map__upds__Nil1,axiom, % 172.48/172.45 ! [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 ). % 172.48/172.45 % 172.48/172.45 fof(fact_distinct_Osimps_I1_J,axiom, % 172.48/172.45 ! [T_a] : hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Olist_ONil(T_a))) ). % 172.48/172.45 % 172.48/172.45 fof(fact_distinct__remove1,axiom, % 172.48/172.45 ! [V_x,V_xs,T_a] : % 172.48/172.45 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 172.48/172.45 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oremove1(T_a,V_x,V_xs))) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_distinct__butlast,axiom, % 172.48/172.45 ! [T_a,V_xs] : % 172.48/172.45 ( V_xs != c_List_Olist_ONil(T_a) % 172.48/172.45 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 172.48/172.45 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Obutlast(T_a,V_xs))) ) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_remove1__idem,axiom, % 172.48/172.45 ! [V_xs_2,V_x_2,T_a] : % 172.48/172.45 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 172.48/172.45 => c_List_Oremove1(T_a,V_x_2,V_xs_2) = V_xs_2 ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_notin__set__remove1,axiom, % 172.48/172.45 ! [V_y_2,V_xs_2,V_x_2,T_a] : % 172.48/172.45 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 172.48/172.45 => ~ 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)))) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_in__set__remove1,axiom, % 172.48/172.45 ! [V_xs_2,T_a,V_b_2,V_a_2] : % 172.48/172.45 ( V_a_2 != V_b_2 % 172.48/172.45 => ( 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)))) % 172.48/172.45 <=> hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_sublist__empty,axiom, % 172.48/172.45 ! [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) ). % 172.48/172.45 % 172.48/172.45 fof(fact_set__remove1__subset,axiom, % 172.48/172.45 ! [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))) ). % 172.48/172.45 % 172.48/172.45 fof(fact_length__greater__0__conv,axiom, % 172.48/172.45 ! [V_xs_2,T_a] : % 172.48/172.45 ( 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))) % 172.48/172.45 <=> V_xs_2 != c_List_Olist_ONil(T_a) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_take__1__Cons,axiom, % 172.48/172.45 ! [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)) ). % 172.48/172.45 % 172.48/172.45 fof(fact_not__Nil__listrel1,axiom, % 172.48/172.45 ! [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))) ). % 172.48/172.45 % 172.48/172.45 fof(fact_not__listrel1__Nil,axiom, % 172.48/172.45 ! [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))) ). % 172.48/172.45 % 172.48/172.45 fof(fact_listrel_ONil,axiom, % 172.48/172.45 ! [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))) ). % 172.48/172.45 % 172.48/172.45 fof(fact_lexord__Nil__right,axiom, % 172.48/172.45 ! [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))) ). % 172.48/172.45 % 172.48/172.45 fof(fact_Nil__notin__lex,axiom, % 172.48/172.45 ! [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))) ). % 172.48/172.45 % 172.48/172.45 fof(fact_Nil2__notin__lex,axiom, % 172.48/172.45 ! [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))) ). % 172.48/172.45 % 172.48/172.45 fof(fact_take__Cons,axiom, % 172.48/172.45 ! [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) ). % 172.48/172.45 % 172.48/172.45 fof(fact_upto_Osimps,axiom, % 172.48/172.45 ! [V_j,V_i] : % 172.48/172.45 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j)) % 172.48/172.45 => 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)) ) % 172.48/172.45 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i),V_j)) % 172.48/172.45 => c_List_Oupto(V_i,V_j) = c_List_Olist_ONil(tc_Int_Oint) ) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_sublist__singleton,axiom, % 172.48/172.45 ! [V_x_2,T_a,V_A_2] : % 172.48/172.45 ( ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2)) % 172.48/172.45 => 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)) ) % 172.48/172.45 & ( ~ hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_A_2)) % 172.48/172.45 => 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) ) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_lists__empty,axiom, % 172.48/172.45 ! [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))) ). % 172.48/172.45 % 172.48/172.45 fof(fact_take__Cons_H,axiom, % 172.48/172.45 ! [V_xs,V_x,T_a,V_n] : % 172.48/172.45 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 172.48/172.45 => 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) ) % 172.48/172.45 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 172.48/172.45 => 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)) ) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_upto__rec__number__of,axiom, % 172.48/172.45 ! [V_n,V_m] : % 172.48/172.45 ( ( 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))) % 172.48/172.45 => 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))) ) % 172.48/172.45 & ( ~ 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))) % 172.48/172.45 => 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) ) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_listrel__Nil,axiom, % 172.48/172.45 ! [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))) ). % 172.48/172.45 % 172.48/172.45 fof(fact_set__Cons__sing__Nil,axiom, % 172.48/172.45 ! [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) ). % 172.48/172.45 % 172.48/172.45 fof(fact_length__remove1,axiom, % 172.48/172.45 ! [V_xs_2,V_x_2,T_a] : % 172.48/172.45 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 172.48/172.45 => 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)) ) % 172.48/172.45 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 172.48/172.45 => 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) ) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_upto_Opsimps,axiom, % 172.48/172.45 ! [V_j_2,V_i_2] : % 172.48/172.45 ( 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))) % 172.48/172.45 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),V_j_2)) % 172.48/172.45 => 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)) ) % 172.48/172.45 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),V_i_2),V_j_2)) % 172.48/172.45 => c_List_Oupto(V_i_2,V_j_2) = c_List_Olist_ONil(tc_Int_Oint) ) ) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_select,axiom, % 172.48/172.45 ! [V_s_2,T_a,V_xs_2] : % 172.48/172.45 ( V_xs_2 != c_List_Olist_ONil(T_a) % 172.48/172.45 => 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))) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_listset_Osimps_I1_J,axiom, % 172.48/172.45 ! [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))) ). % 172.48/172.45 % 172.48/172.45 fof(fact_zip__Cons1,axiom, % 172.48/172.45 ! [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) ). % 172.48/172.45 % 172.48/172.45 fof(fact_list_Osimps_I5_J,axiom, % 172.48/172.45 ! [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) ). % 172.48/172.45 % 172.48/172.45 fof(fact_list_Osimps_I4_J,axiom, % 172.48/172.45 ! [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 ). % 172.48/172.45 % 172.48/172.45 fof(fact_listset_Osimps_I2_J,axiom, % 172.48/172.45 ! [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)) ). % 172.48/172.45 % 172.48/172.45 fof(fact_zip__Cons,axiom, % 172.48/172.45 ! [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) ). % 172.48/172.45 % 172.48/172.45 fof(fact_sorted__list__of__set__remove,axiom, % 172.48/172.45 ! [V_x_2,V_A_2,T_a] : % 172.48/172.45 ( class_Orderings_Olinorder(T_a) % 172.48/172.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.45 => 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)) ) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_upto_Opinduct,axiom, % 172.48/172.45 ! [V_P_2,V_a1_2,V_a0_2] : % 172.48/172.45 ( 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))) % 172.48/172.45 => ( ! [B_i,B_j] : % 172.48/172.45 ( 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))) % 172.48/172.45 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint),B_i),B_j)) % 172.48/172.45 => 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)) ) % 172.48/172.45 => hBOOL(hAPP(hAPP(V_P_2,B_i),B_j)) ) ) % 172.48/172.45 => hBOOL(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2)) ) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_sorted__list__of__set__empty,axiom, % 172.48/172.45 ! [T_a] : % 172.48/172.45 ( class_Orderings_Olinorder(T_a) % 172.48/172.45 => 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) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_anamorph_Osimps,axiom, % 172.48/172.45 ! [V_x_2,V_f_2,T_a,T_b,V_k_2] : % 172.48/172.45 ( ( V_k_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 172.48/172.45 => hAPP(hAPP(c_Lazy__Sequence_Oanamorph(T_b,T_a,V_f_2),V_k_2),V_x_2) = hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),T_b),c_List_Olist_ONil(T_a)),V_x_2) ) % 172.48/172.45 & ( V_k_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 172.48/172.45 => hAPP(hAPP(c_Lazy__Sequence_Oanamorph(T_b,T_a,V_f_2),V_k_2),V_x_2) = hAPP(c_Option_Ooption_Ooption__case(tc_prod(tc_List_Olist(T_a),T_b),tc_prod(T_a,T_b),hAPP(hAPP(c_Product__Type_OPair(tc_List_Olist(T_a),T_b),c_List_Olist_ONil(T_a)),V_x_2),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_prod(tc_List_Olist(T_a),T_b)),hAPP(hAPP(c_COMBC(T_a,tc_fun(T_b,tc_prod(tc_List_Olist(T_a),T_b)),tc_fun(T_b,tc_prod(tc_List_Olist(T_a),T_b))),hAPP(hAPP(c_COMBB(tc_fun(tc_prod(tc_List_Olist(T_a),T_b),tc_prod(tc_List_Olist(T_a),T_b)),tc_fun(tc_fun(T_b,tc_prod(tc_List_Olist(T_a),T_b)),tc_fun(T_b,tc_prod(tc_List_Olist(T_a),T_b))),T_a),c_COMBB(tc_prod(tc_List_Olist(T_a),T_b),tc_prod(tc_List_Olist(T_a),T_b),T_b)),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_fun(T_b,tc_prod(tc_List_Olist(T_a),T_b))),tc_fun(tc_prod(tc_List_Olist(T_a),T_b),tc_prod(tc_List_Olist(T_a),T_b)),T_a),c_Product__Type_Oprod_Oprod__case(tc_List_Olist(T_a),T_b,tc_prod(tc_List_Olist(T_a),T_b))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_fun(tc_List_Olist(T_a),tc_fun(T_b,tc_prod(tc_List_Olist(T_a),T_b))),T_a),hAPP(c_COMBB(tc_List_Olist(T_a),tc_fun(T_b,tc_prod(tc_List_Olist(T_a),T_b)),tc_List_Olist(T_a)),c_Product__Type_OPair(tc_List_Olist(T_a),T_b))),c_List_Olist_OCons(T_a))))),hAPP(c_Lazy__Sequence_Oanamorph(T_b,T_a,V_f_2),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_k_2),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))))),hAPP(V_f_2,V_x_2)) ) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_sublist__Cons,axiom, % 172.48/172.45 ! [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)))) ). % 172.48/172.45 % 172.48/172.45 fof(fact_append1__eq__conv,axiom, % 172.48/172.45 ! [V_y_2,V_ys_2,V_x_2,V_xs_2,T_a] : % 172.48/172.45 ( 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))) % 172.48/172.45 <=> ( V_xs_2 = V_ys_2 % 172.48/172.45 & V_x_2 = V_y_2 ) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_Cons__eq__append__conv,axiom, % 172.48/172.45 ! [V_zs_2,V_ys_2,V_xs_2,V_x_2,T_a] : % 172.48/172.45 ( 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) % 172.48/172.45 <=> ( ( V_ys_2 = c_List_Olist_ONil(T_a) % 172.48/172.45 & hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2) = V_zs_2 ) % 172.48/172.45 | ? [B_ys_H] : % 172.48/172.45 ( hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),B_ys_H) = V_ys_2 % 172.48/172.45 & V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),B_ys_H),V_zs_2) ) ) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_append__eq__Cons__conv,axiom, % 172.48/172.45 ! [V_xs_2,V_x_2,V_zs_2,V_ys_2,T_a] : % 172.48/172.45 ( 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) % 172.48/172.45 <=> ( ( V_ys_2 = c_List_Olist_ONil(T_a) % 172.48/172.45 & V_zs_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2) ) % 172.48/172.45 | ? [B_ys_H] : % 172.48/172.45 ( V_ys_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),B_ys_H) % 172.48/172.45 & hAPP(hAPP(c_List_Oappend(T_a),B_ys_H),V_zs_2) = V_xs_2 ) ) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_Cons__eq__appendI,axiom, % 172.48/172.45 ! [V_zs,V_xs,V_ys,V_xs1,V_x,T_a] : % 172.48/172.45 ( hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs1) = V_ys % 172.48/172.45 => ( V_xs = hAPP(hAPP(c_List_Oappend(T_a),V_xs1),V_zs) % 172.48/172.45 => hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs) = hAPP(hAPP(c_List_Oappend(T_a),V_ys),V_zs) ) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_append__Cons,axiom, % 172.48/172.45 ! [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)) ). % 172.48/172.45 % 172.48/172.45 fof(fact_set__append,axiom, % 172.48/172.45 ! [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)) ). % 172.48/172.45 % 172.48/172.45 fof(fact_zip__append,axiom, % 172.48/172.45 ! [V_vs,V_ys,V_us,T_b,V_xs,T_a] : % 172.48/172.45 ( 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) % 172.48/172.45 => ( 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) % 172.48/172.45 => 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)) ) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_length__append,axiom, % 172.48/172.45 ! [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)) ). % 172.48/172.45 % 172.48/172.45 fof(fact_listsum__append,axiom, % 172.48/172.45 ! [V_ys,V_xs,T_a] : % 172.48/172.45 ( class_Groups_Omonoid__add(T_a) % 172.48/172.45 => 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)) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_append__assoc,axiom, % 172.48/172.45 ! [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)) ). % 172.48/172.45 % 172.48/172.45 fof(fact_append__eq__append__conv2,axiom, % 172.48/172.45 ! [V_ts_2,V_zs_2,V_ys_2,V_xs_2,T_a] : % 172.48/172.45 ( 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) % 172.48/172.45 <=> ? [B_us] : % 172.48/172.45 ( ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),V_zs_2),B_us) % 172.48/172.45 & hAPP(hAPP(c_List_Oappend(T_a),B_us),V_ys_2) = V_ts_2 ) % 172.48/172.45 | ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),B_us) = V_zs_2 % 172.48/172.45 & V_ys_2 = hAPP(hAPP(c_List_Oappend(T_a),B_us),V_ts_2) ) ) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_same__append__eq,axiom, % 172.48/172.45 ! [V_zs_2,V_ys_2,V_xs_2,T_a] : % 172.48/172.45 ( 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) % 172.48/172.45 <=> V_ys_2 = V_zs_2 ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_append__same__eq,axiom, % 172.48/172.45 ! [V_zs_2,V_xs_2,V_ys_2,T_a] : % 172.48/172.45 ( 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) % 172.48/172.45 <=> V_ys_2 = V_zs_2 ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_append__eq__appendI,axiom, % 172.48/172.45 ! [V_us,V_ys,V_zs,V_xs1,V_xs,T_a] : % 172.48/172.45 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_xs1) = V_zs % 172.48/172.45 => ( V_ys = hAPP(hAPP(c_List_Oappend(T_a),V_xs1),V_us) % 172.48/172.45 => hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys) = hAPP(hAPP(c_List_Oappend(T_a),V_zs),V_us) ) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_append__in__lists__conv,axiom, % 172.48/172.45 ! [V_A_2,V_ys_2,V_xs_2,T_a] : % 172.48/172.45 ( 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))) % 172.48/172.45 <=> ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_xs_2),c_List_Olists(T_a,V_A_2))) % 172.48/172.45 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_ys_2),c_List_Olists(T_a,V_A_2))) ) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_fun__upds__append2__drop,axiom, % 172.48/172.45 ! [V_zs_2,V_m_2,V_ys_2,T_b,V_xs_2,T_a] : % 172.48/172.45 ( 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) % 172.48/172.45 => 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) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_fun__upds__append__drop,axiom, % 172.48/172.45 ! [V_zs_2,V_m_2,V_ys_2,T_b,V_xs_2,T_a] : % 172.48/172.45 ( 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) % 172.48/172.45 => 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) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_butlast__append,axiom, % 172.48/172.45 ! [V_xs,T_a,V_ys] : % 172.48/172.45 ( ( V_ys = c_List_Olist_ONil(T_a) % 172.48/172.45 => c_List_Obutlast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Obutlast(T_a,V_xs) ) % 172.48/172.45 & ( V_ys != c_List_Olist_ONil(T_a) % 172.48/172.45 => 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)) ) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_eq__Nil__appendI,axiom, % 172.48/172.45 ! [T_a,V_ys,V_xs] : % 172.48/172.45 ( V_xs = V_ys % 172.48/172.45 => V_xs = hAPP(hAPP(c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_ys) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_append__self__conv2,axiom, % 172.48/172.45 ! [V_ys_2,V_xs_2,T_a] : % 172.48/172.45 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) = V_ys_2 % 172.48/172.45 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_append__self__conv,axiom, % 172.48/172.45 ! [V_ys_2,V_xs_2,T_a] : % 172.48/172.45 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) = V_xs_2 % 172.48/172.45 <=> V_ys_2 = c_List_Olist_ONil(T_a) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_append__is__Nil__conv,axiom, % 172.48/172.45 ! [V_ys_2,V_xs_2,T_a] : % 172.48/172.45 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) = c_List_Olist_ONil(T_a) % 172.48/172.45 <=> ( V_xs_2 = c_List_Olist_ONil(T_a) % 172.48/172.45 & V_ys_2 = c_List_Olist_ONil(T_a) ) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_self__append__conv2,axiom, % 172.48/172.45 ! [V_xs_2,T_a,V_ys_2] : % 172.48/172.45 ( V_ys_2 = hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) % 172.48/172.45 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_self__append__conv,axiom, % 172.48/172.45 ! [V_ys_2,T_a,V_xs_2] : % 172.48/172.45 ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) % 172.48/172.45 <=> V_ys_2 = c_List_Olist_ONil(T_a) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_append__Nil2,axiom, % 172.48/172.45 ! [V_xs,T_a] : hAPP(hAPP(c_List_Oappend(T_a),V_xs),c_List_Olist_ONil(T_a)) = V_xs ). % 172.48/172.45 % 172.48/172.45 fof(fact_Nil__is__append__conv,axiom, % 172.48/172.45 ! [V_ys_2,V_xs_2,T_a] : % 172.48/172.45 ( c_List_Olist_ONil(T_a) = hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) % 172.48/172.45 <=> ( V_xs_2 = c_List_Olist_ONil(T_a) % 172.48/172.45 & V_ys_2 = c_List_Olist_ONil(T_a) ) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_append__Nil,axiom, % 172.48/172.45 ! [V_ys,T_a] : hAPP(hAPP(c_List_Oappend(T_a),c_List_Olist_ONil(T_a)),V_ys) = V_ys ). % 172.48/172.45 % 172.48/172.45 fof(fact_nth__append__length,axiom, % 172.48/172.45 ! [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 ). % 172.48/172.45 % 172.48/172.45 fof(fact_nth__append__length__plus,axiom, % 172.48/172.45 ! [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) ). % 172.48/172.45 % 172.48/172.45 fof(fact_take__append,axiom, % 172.48/172.45 ! [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)) ). % 172.48/172.45 % 172.48/172.45 fof(fact_list__update__append1,axiom, % 172.48/172.45 ! [V_x,V_ys,V_xs,T_a,V_i] : % 172.48/172.45 ( 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))) % 172.48/172.45 => 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) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_list__update__length,axiom, % 172.48/172.45 ! [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)) ). % 172.48/172.45 % 172.48/172.45 fof(fact_remove1__append,axiom, % 172.48/172.45 ! [V_ys_2,V_xs_2,V_x_2,T_a] : % 172.48/172.45 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 172.48/172.45 => 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) ) % 172.48/172.45 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 172.48/172.45 => 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)) ) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_in__set__butlast__appendI,axiom, % 172.48/172.45 ! [V_ys_2,V_xs_2,V_x_2,T_a] : % 172.48/172.45 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_List_Obutlast(T_a,V_xs_2)))) % 172.48/172.45 | hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_List_Obutlast(T_a,V_ys_2)))) ) % 172.48/172.45 => 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))))) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_butlast__snoc,axiom, % 172.48/172.45 ! [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 ). % 172.48/172.45 % 172.48/172.45 fof(fact_append__listrel1I,axiom, % 172.48/172.45 ! [V_vs_2,V_us_2,V_r_2,V_ys_2,V_xs_2,T_a] : % 172.48/172.45 ( ( ( 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))) % 172.48/172.45 & V_us_2 = V_vs_2 ) % 172.48/172.45 | ( V_xs_2 = V_ys_2 % 172.48/172.45 & 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))) ) ) % 172.48/172.45 => 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))) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_lexord__append__leftI,axiom, % 172.48/172.45 ! [V_x_2,V_r_2,V_v_2,V_u_2,T_a] : % 172.48/172.45 ( 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))) % 172.48/172.45 => 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))) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_distinct__append,axiom, % 172.48/172.45 ! [V_ys_2,V_xs_2,T_a] : % 172.48/172.45 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2))) % 172.48/172.45 <=> ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 172.48/172.45 & hBOOL(hAPP(c_List_Odistinct(T_a),V_ys_2)) % 172.48/172.45 & 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)) ) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_nth__append,axiom, % 172.48/172.45 ! [V_ys,V_xs,T_a,V_n] : % 172.48/172.45 ( ( 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))) % 172.48/172.45 => 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) ) % 172.48/172.45 & ( ~ 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))) % 172.48/172.45 => 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))) ) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_list__update__append,axiom, % 172.48/172.45 ! [V_x,V_ys,V_xs,T_a,V_n] : % 172.48/172.45 ( ( 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))) % 172.48/172.45 => 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) ) % 172.48/172.45 & ( ~ 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))) % 172.48/172.45 => 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)) ) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_sublist__append,axiom, % 172.48/172.45 ! [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)))) ). % 172.48/172.45 % 172.48/172.45 fof(fact_listrel1I,axiom, % 172.48/172.45 ! [V_ys_2,V_vs_2,V_us_2,V_xs_2,V_r_2,V_y_2,V_x_2,T_a] : % 172.48/172.45 ( 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)) % 172.48/172.45 => ( 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)) % 172.48/172.45 => ( 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)) % 172.48/172.45 => 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))) ) ) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_lexord__append__left__rightI,axiom, % 172.48/172.45 ! [V_y_2,V_x_2,V_u_2,V_r_2,V_b_2,V_a_2,T_a] : % 172.48/172.45 ( 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)) % 172.48/172.45 => 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))) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_take__Suc__conv__app__nth,axiom, % 172.48/172.45 ! [V_xs,T_a,V_i] : % 172.48/172.45 ( 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))) % 172.48/172.45 => 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))) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_snoc__listrel1__snoc__iff,axiom, % 172.48/172.45 ! [V_r_2,V_y_2,V_ys_2,V_x_2,V_xs_2,T_a] : % 172.48/172.45 ( 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))) % 172.48/172.45 <=> ( ( 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))) % 172.48/172.45 & V_x_2 = V_y_2 ) % 172.48/172.45 | ( V_xs_2 = V_ys_2 % 172.48/172.45 & 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)) ) ) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_listrel1E,axiom, % 172.48/172.45 ! [V_r_2,V_ys_2,V_xs_2,T_a] : % 172.48/172.45 ( 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))) % 172.48/172.45 => ~ ! [B_x,B_y] : % 172.48/172.45 ( 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)) % 172.48/172.45 => ! [B_us,B_vs] : % 172.48/172.45 ( V_xs_2 = hAPP(hAPP(c_List_Oappend(T_a),B_us),hAPP(hAPP(c_List_Olist_OCons(T_a),B_x),B_vs)) % 172.48/172.45 => V_ys_2 != hAPP(hAPP(c_List_Oappend(T_a),B_us),hAPP(hAPP(c_List_Olist_OCons(T_a),B_y),B_vs)) ) ) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_lexord__append__leftD,axiom, % 172.48/172.45 ! [V_r_2,V_v_2,V_u_2,V_x_2,T_a] : % 172.48/172.45 ( 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))) % 172.48/172.45 => ( ! [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)) % 172.48/172.45 => 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))) ) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_rotate1__def,axiom, % 172.48/172.45 ! [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) ). % 172.48/172.45 % 172.48/172.45 fof(fact_map__upds__append1,axiom, % 172.48/172.45 ! [V_x_2,V_m_2,V_ys_2,T_b,V_xs_2,T_a] : % 172.48/172.45 ( 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))) % 172.48/172.45 => 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)))) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_image__map__upd,axiom, % 172.48/172.45 ! [V_y_2,V_m_2,T_b,V_A_2,V_x_2,T_a] : % 172.48/172.45 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 172.48/172.45 => 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) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_set__rotate1,axiom, % 172.48/172.45 ! [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) ). % 172.48/172.45 % 172.48/172.45 fof(fact_length__rotate1,axiom, % 172.48/172.45 ! [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) ). % 172.48/172.45 % 172.48/172.45 fof(fact_dom__const,axiom, % 172.48/172.45 ! [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)) ). % 172.48/172.45 % 172.48/172.45 fof(fact_domI,axiom, % 172.48/172.45 ! [T_b,V_b_2,T_a,V_a_2,V_m_2] : % 172.48/172.45 ( hAPP(V_m_2,V_a_2) = hAPP(c_Option_Ooption_OSome(T_a),V_b_2) % 172.48/172.45 => hBOOL(hAPP(hAPP(c_member(T_b),V_a_2),c_Map_Odom(T_b,T_a,V_m_2))) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_insert__dom,axiom, % 172.48/172.45 ! [T_b,V_y_2,T_a,V_x_2,V_f_2] : % 172.48/172.45 ( hAPP(V_f_2,V_x_2) = hAPP(c_Option_Ooption_OSome(T_a),V_y_2) % 172.48/172.45 => 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) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_distinct1__rotate,axiom, % 172.48/172.45 ! [V_xs_2,T_a] : % 172.48/172.45 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Orotate1(T_a),V_xs_2))) % 172.48/172.45 <=> hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_map__upd__Some__unfold,axiom, % 172.48/172.45 ! [V_y_2,V_x_2,V_b_2,V_a_2,V_m_2,T_a,T_b] : % 172.48/172.45 ( 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) % 172.48/172.45 <=> ( ( V_x_2 = V_a_2 % 172.48/172.45 & V_b_2 = V_y_2 ) % 172.48/172.45 | ( V_x_2 != V_a_2 % 172.48/172.45 & hAPP(V_m_2,V_x_2) = hAPP(c_Option_Ooption_OSome(T_a),V_y_2) ) ) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_map__upd__triv,axiom, % 172.48/172.45 ! [T_b,V_x_2,T_a,V_k_2,V_t_2] : % 172.48/172.45 ( hAPP(V_t_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_x_2) % 172.48/172.45 => 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 ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_map__upd__eqD1,axiom, % 172.48/172.45 ! [V_y_2,V_n_2,V_x_2,V_a_2,V_m_2,T_b,T_a] : % 172.48/172.45 ( 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)) % 172.48/172.45 => V_x_2 = V_y_2 ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_rotate1__is__Nil__conv,axiom, % 172.48/172.45 ! [V_xs_2,T_a] : % 172.48/172.45 ( hAPP(c_List_Orotate1(T_a),V_xs_2) = c_List_Olist_ONil(T_a) % 172.48/172.45 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_map__upds__Cons,axiom, % 172.48/172.45 ! [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) ). % 172.48/172.45 % 172.48/172.45 fof(fact_finite__range__updI,axiom, % 172.48/172.45 ! [V_b_2,V_a_2,V_f_2,T_b,T_a] : % 172.48/172.45 ( 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))))) % 172.48/172.45 => 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))))) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_map__upds__twist,axiom, % 172.48/172.45 ! [V_bs_2,V_b_2,V_m_2,T_b,V_as_2,V_a_2,T_a] : % 172.48/172.45 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_List_Oset(T_a),V_as_2))) % 172.48/172.45 => 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)) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_restrict__upd__same,axiom, % 172.48/172.45 ! [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))))) ). % 172.48/172.45 % 172.48/172.45 fof(fact_rotate__simps,axiom, % 172.48/172.45 ! [V_xs,V_x,T_b,T_a] : % 172.48/172.45 ( hAPP(c_List_Orotate1(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) % 172.48/172.45 & 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))) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_rotate1__length01,axiom, % 172.48/172.45 ! [V_xs,T_a] : % 172.48/172.45 ( 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))) % 172.48/172.45 => hAPP(c_List_Orotate1(T_a),V_xs) = V_xs ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_map__upd__upds__conv__if,axiom, % 172.48/172.45 ! [V_y_2,V_f_2,V_xs_2,V_ys_2,T_b,V_x_2,T_a] : % 172.48/172.45 ( ( 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)))) % 172.48/172.45 => 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) ) % 172.48/172.45 & ( ~ 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)))) % 172.48/172.45 => 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)) ) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_option_Osize_I2_J,axiom, % 172.48/172.45 ! [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))) ). % 172.48/172.45 % 172.48/172.45 fof(fact_option_Osimps_I5_J,axiom, % 172.48/172.45 ! [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) ). % 172.48/172.45 % 172.48/172.45 fof(fact_option_Oinject,axiom, % 172.48/172.45 ! [V_a_H_2,V_a_2,T_a] : % 172.48/172.45 ( hAPP(c_Option_Ooption_OSome(T_a),V_a_2) = hAPP(c_Option_Ooption_OSome(T_a),V_a_H_2) % 172.48/172.45 <=> V_a_2 = V_a_H_2 ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_inj__Some,axiom, % 172.48/172.45 ! [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) ). % 172.48/172.45 % 172.48/172.45 fof(fact_the_Osimps,axiom, % 172.48/172.45 ! [V_x,T_a] : hAPP(c_Option_Othe(T_a),hAPP(c_Option_Ooption_OSome(T_a),V_x)) = V_x ). % 172.48/172.45 % 172.48/172.45 fof(fact_Option_Oset_Osimps_I2_J,axiom, % 172.48/172.45 ! [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))) ). % 172.48/172.45 % 172.48/172.45 fof(fact_upd__conv__take__nth__drop,axiom, % 172.48/172.45 ! [V_a,V_xs,T_a,V_i] : % 172.48/172.45 ( 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))) % 172.48/172.45 => 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))) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_append__take__drop__id,axiom, % 172.48/172.45 ! [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 ). % 172.48/172.45 % 172.48/172.45 fof(fact_nth__via__drop,axiom, % 172.48/172.45 ! [V_ys,V_y,V_xs,V_n,T_a] : % 172.48/172.45 ( hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_ys) % 172.48/172.45 => hAPP(hAPP(c_List_Onth(T_a),V_xs),V_n) = V_y ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_drop__1__Cons,axiom, % 172.48/172.45 ! [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 ). % 172.48/172.45 % 172.48/172.45 fof(fact_drop__Suc__Cons,axiom, % 172.48/172.45 ! [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) ). % 172.48/172.45 % 172.48/172.45 fof(fact_set__drop__subset,axiom, % 172.48/172.45 ! [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))) ). % 172.48/172.45 % 172.48/172.45 fof(fact_in__set__dropD,axiom, % 172.48/172.45 ! [V_xs_2,V_n_2,V_x_2,T_a] : % 172.48/172.45 ( 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)))) % 172.48/172.45 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_length__drop,axiom, % 172.48/172.45 ! [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) ). % 172.48/172.45 % 172.48/172.45 fof(fact_drop__zip,axiom, % 172.48/172.45 ! [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)) ). % 172.48/172.45 % 172.48/172.45 fof(fact_drop__drop,axiom, % 172.48/172.45 ! [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) ). % 172.48/172.45 % 172.48/172.45 fof(fact_drop__0,axiom, % 172.48/172.45 ! [V_xs,T_a] : hAPP(hAPP(c_List_Odrop(T_a),c_Groups_Ozero__class_Ozero(tc_Nat_Onat)),V_xs) = V_xs ). % 172.48/172.45 % 172.48/172.45 fof(fact_take__drop,axiom, % 172.48/172.45 ! [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)) ). % 172.48/172.45 % 172.48/172.45 fof(fact_drop__take,axiom, % 172.48/172.45 ! [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)) ). % 172.48/172.45 % 172.48/172.45 fof(fact_drop__butlast,axiom, % 172.48/172.45 ! [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)) ). % 172.48/172.45 % 172.48/172.45 fof(fact_butlast__drop,axiom, % 172.48/172.45 ! [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)) ). % 172.48/172.45 % 172.48/172.45 fof(fact_distinct__drop,axiom, % 172.48/172.45 ! [V_i,V_xs,T_a] : % 172.48/172.45 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 172.48/172.45 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Odrop(T_a),V_i),V_xs))) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_drop__Nil,axiom, % 172.48/172.45 ! [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) ). % 172.48/172.45 % 172.48/172.45 fof(fact_set__drop__subset__set__drop,axiom, % 172.48/172.45 ! [V_xs_2,T_a,V_m_2,V_n_2] : % 172.48/172.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) % 172.48/172.45 => 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)))) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_drop__all,axiom, % 172.48/172.45 ! [V_n,V_xs,T_a] : % 172.48/172.45 ( 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)) % 172.48/172.45 => hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs) = c_List_Olist_ONil(T_a) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_drop__eq__Nil,axiom, % 172.48/172.45 ! [V_xs_2,V_n_2,T_a] : % 172.48/172.45 ( hAPP(hAPP(c_List_Odrop(T_a),V_n_2),V_xs_2) = c_List_Olist_ONil(T_a) % 172.48/172.45 <=> 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)) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_drop__append,axiom, % 172.48/172.45 ! [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)) ). % 172.48/172.45 % 172.48/172.45 fof(fact_append__eq__conv__conj,axiom, % 172.48/172.45 ! [V_zs_2,V_ys_2,V_xs_2,T_a] : % 172.48/172.45 ( hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2) = V_zs_2 % 172.48/172.45 <=> ( 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) % 172.48/172.45 & 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) ) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_drop__Cons,axiom, % 172.48/172.45 ! [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) ). % 172.48/172.45 % 172.48/172.45 fof(fact_drop__Cons_H,axiom, % 172.48/172.45 ! [V_xs,V_x,T_a,V_n] : % 172.48/172.45 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 172.48/172.45 => 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) ) % 172.48/172.45 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 172.48/172.45 => 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) ) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_nth__drop,axiom, % 172.48/172.45 ! [V_xs,T_a,V_i,V_n] : % 172.48/172.45 ( 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))) % 172.48/172.45 => 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)) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_append__eq__append__conv__if,axiom, % 172.48/172.45 ! [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] : % 172.48/172.45 ( 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) % 172.48/172.45 <=> ( ( 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))) % 172.48/172.45 => ( 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) % 172.48/172.45 & 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) ) ) % 172.48/172.45 & ( ~ 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))) % 172.48/172.45 => ( 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 % 172.48/172.45 & 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 ) ) ) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_nth__drop_H,axiom, % 172.48/172.45 ! [V_xs,T_a,V_i] : % 172.48/172.45 ( 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))) % 172.48/172.45 => 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) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_drop__Cons__number__of,axiom, % 172.48/172.45 ! [V_xs,V_x,T_a,V_v] : % 172.48/172.45 ( ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 172.48/172.45 => 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) ) % 172.48/172.45 & ( hAPP(c_Int_Onumber__class_Onumber__of(tc_Nat_Onat),V_v) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 172.48/172.45 => 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) ) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_take__add,axiom, % 172.48/172.45 ! [V_xs,T_a,V_j,V_i] : % 172.48/172.45 ( 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))) % 172.48/172.45 => 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))) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_elem__set,axiom, % 172.48/172.45 ! [V_xo_2,V_x_2,T_a] : % 172.48/172.45 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),c_Option_Oset(T_a,V_xo_2))) % 172.48/172.45 <=> V_xo_2 = hAPP(c_Option_Ooption_OSome(T_a),V_x_2) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_zip__append1,axiom, % 172.48/172.45 ! [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))) ). % 172.48/172.45 % 172.48/172.45 fof(fact_zip__append2,axiom, % 172.48/172.45 ! [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)) ). % 172.48/172.45 % 172.48/172.45 fof(fact_id__take__nth__drop,axiom, % 172.48/172.45 ! [V_xs,T_a,V_i] : % 172.48/172.45 ( 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))) % 172.48/172.45 => 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))) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_take__hd__drop,axiom, % 172.48/172.45 ! [V_xs,T_a,V_n] : % 172.48/172.45 ( 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))) % 172.48/172.45 => 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) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_hd__drop__conv__nth,axiom, % 172.48/172.45 ! [V_n,T_a,V_xs] : % 172.48/172.45 ( V_xs != c_List_Olist_ONil(T_a) % 172.48/172.45 => ( 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))) % 172.48/172.45 => 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) ) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_hd_Osimps,axiom, % 172.48/172.45 ! [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 ). % 172.48/172.45 % 172.48/172.45 fof(fact_hd__append,axiom, % 172.48/172.45 ! [V_ys,T_a,V_xs] : % 172.48/172.45 ( ( V_xs = c_List_Olist_ONil(T_a) % 172.48/172.45 => 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) ) % 172.48/172.45 & ( V_xs != c_List_Olist_ONil(T_a) % 172.48/172.45 => 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) ) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_hd__append2,axiom, % 172.48/172.45 ! [V_ys,T_a,V_xs] : % 172.48/172.45 ( V_xs != c_List_Olist_ONil(T_a) % 172.48/172.45 => 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) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_hd__in__set,axiom, % 172.48/172.45 ! [T_a,V_xs_2] : % 172.48/172.45 ( V_xs_2 != c_List_Olist_ONil(T_a) % 172.48/172.45 => 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))) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_hd__conv__nth,axiom, % 172.48/172.45 ! [T_a,V_xs] : % 172.48/172.45 ( V_xs != c_List_Olist_ONil(T_a) % 172.48/172.45 => 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)) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_rotate1__hd__tl,axiom, % 172.48/172.45 ! [T_a,V_xs] : % 172.48/172.45 ( V_xs != c_List_Olist_ONil(T_a) % 172.48/172.45 => 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))) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_option_Osize_I4_J,axiom, % 172.48/172.45 ! [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) ). % 172.48/172.45 % 172.48/172.45 fof(fact_tl__drop,axiom, % 172.48/172.45 ! [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)) ). % 172.48/172.45 % 172.48/172.45 fof(fact_drop__tl,axiom, % 172.48/172.45 ! [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)) ). % 172.48/172.45 % 172.48/172.45 fof(fact_tl_Osimps_I2_J,axiom, % 172.48/172.45 ! [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 ). % 172.48/172.45 % 172.48/172.45 fof(fact_distinct__tl,axiom, % 172.48/172.45 ! [V_xs,T_a] : % 172.48/172.45 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 172.48/172.45 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Otl(T_a),V_xs))) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_tl_Osimps_I1_J,axiom, % 172.48/172.45 ! [T_a] : hAPP(c_List_Otl(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 172.48/172.45 % 172.48/172.45 fof(fact_tl__append2,axiom, % 172.48/172.45 ! [V_ys,T_a,V_xs] : % 172.48/172.45 ( V_xs != c_List_Olist_ONil(T_a) % 172.48/172.45 => 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) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_take__tl,axiom, % 172.48/172.45 ! [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)) ). % 172.48/172.45 % 172.48/172.45 fof(fact_drop__Suc,axiom, % 172.48/172.45 ! [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)) ). % 172.48/172.45 % 172.48/172.45 fof(fact_tl__append,axiom, % 172.48/172.45 ! [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) ). % 172.48/172.45 % 172.48/172.45 fof(fact_length__tl,axiom, % 172.48/172.45 ! [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)) ). % 172.48/172.45 % 172.48/172.45 fof(fact_tl__take,axiom, % 172.48/172.45 ! [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)) ). % 172.48/172.45 % 172.48/172.45 fof(fact_take__Suc,axiom, % 172.48/172.45 ! [V_n,T_a,V_xs] : % 172.48/172.45 ( V_xs != c_List_Olist_ONil(T_a) % 172.48/172.45 => 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))) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_fold1__set,axiom, % 172.48/172.45 ! [V_xs_2,T_a] : % 172.48/172.45 ( class_Lattices_Oab__semigroup__idem__mult(T_a) % 172.48/172.45 => ( V_xs_2 != c_List_Olist_ONil(T_a) % 172.48/172.45 => 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)) ) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_hd__rotate__conv__nth,axiom, % 172.48/172.45 ! [V_n,T_a,V_xs] : % 172.48/172.45 ( V_xs != c_List_Olist_ONil(T_a) % 172.48/172.45 => 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))) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_length__rotate,axiom, % 172.48/172.45 ! [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) ). % 172.48/172.45 % 172.48/172.45 fof(fact_rotate__def,axiom, % 172.48/172.45 ! [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)) ). % 172.48/172.45 % 172.48/172.45 fof(fact_rotate1__rotate__swap,axiom, % 172.48/172.45 ! [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)) ). % 172.48/172.45 % 172.48/172.45 fof(fact_rotate__is__Nil__conv,axiom, % 172.48/172.45 ! [V_xs_2,V_n_2,T_a] : % 172.48/172.45 ( hAPP(c_List_Orotate(T_a,V_n_2),V_xs_2) = c_List_Olist_ONil(T_a) % 172.48/172.45 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_foldl__Nil,axiom, % 172.48/172.45 ! [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 ). % 172.48/172.45 % 172.48/172.45 fof(fact_distinct__rotate,axiom, % 172.48/172.45 ! [V_xs_2,V_n_2,T_a] : % 172.48/172.45 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Orotate(T_a,V_n_2),V_xs_2))) % 172.48/172.45 <=> hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_rotate__add,axiom, % 172.48/172.45 ! [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)) ). % 172.48/172.45 % 172.48/172.45 fof(fact_foldl__absorb0,axiom, % 172.48/172.45 ! [V_zs_2,V_x_2,T_a] : % 172.48/172.45 ( class_Groups_Omonoid__add(T_a) % 172.48/172.45 => 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) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_rotate0,axiom, % 172.48/172.45 ! [T_a] : c_List_Orotate(T_a,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_Fun_Oid(tc_List_Olist(T_a)) ). % 172.48/172.45 % 172.48/172.45 fof(fact_rotate__rotate,axiom, % 172.48/172.45 ! [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) ). % 172.48/172.45 % 172.48/172.45 fof(fact_foldl__assoc,axiom, % 172.48/172.45 ! [V_zs_2,V_y_2,V_x_2,T_a] : % 172.48/172.45 ( class_Groups_Osemigroup__add(T_a) % 172.48/172.45 => 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)) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_start__le__sum,axiom, % 172.48/172.45 ! [V_ns_2,V_n_2,V_m_2] : % 172.48/172.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_m_2),V_n_2)) % 172.48/172.45 => 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))) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_set__rotate,axiom, % 172.48/172.45 ! [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) ). % 172.48/172.45 % 172.48/172.45 fof(fact_foldl__Cons,axiom, % 172.48/172.45 ! [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) ). % 172.48/172.45 % 172.48/172.45 fof(fact_foldl__append,axiom, % 172.48/172.45 ! [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) ). % 172.48/172.45 % 172.48/172.45 fof(fact_rotate__conv__mod,axiom, % 172.48/172.45 ! [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) ). % 172.48/172.45 % 172.48/172.45 fof(fact_rotate__Suc,axiom, % 172.48/172.45 ! [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)) ). % 172.48/172.45 % 172.48/172.45 fof(fact_listsum__foldl,axiom, % 172.48/172.45 ! [T_a] : % 172.48/172.45 ( class_Groups_Omonoid__add(T_a) % 172.48/172.45 => 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)) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_sum__eq__0__conv,axiom, % 172.48/172.45 ! [V_ns_2,V_m_2] : % 172.48/172.45 ( 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) % 172.48/172.45 <=> ( V_m_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 172.48/172.45 & ! [B_x] : % 172.48/172.45 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),B_x),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2))) % 172.48/172.45 => B_x = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_rotate__id,axiom, % 172.48/172.45 ! [V_xs,T_a,V_n] : % 172.48/172.45 ( 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) % 172.48/172.45 => hAPP(c_List_Orotate(T_a,V_n),V_xs) = V_xs ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_rotate__length01,axiom, % 172.48/172.45 ! [V_n,V_xs,T_a] : % 172.48/172.45 ( 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))) % 172.48/172.45 => hAPP(c_List_Orotate(T_a,V_n),V_xs) = V_xs ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_fun__left__comm__idem_Ofold__set,axiom, % 172.48/172.45 ! [V_xs_2,V_y_2,V_f_2,T_b,T_a] : % 172.48/172.45 ( c_Finite__Set_Ofun__left__comm__idem(T_a,T_b,V_f_2) % 172.48/172.45 => 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) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_Sup__set__fold,axiom, % 172.48/172.45 ! [V_xs_2,T_a] : % 172.48/172.45 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 172.48/172.45 => 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) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_Inf__set__fold,axiom, % 172.48/172.45 ! [V_xs_2,T_a] : % 172.48/172.45 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 172.48/172.45 => 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) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_Sup__fin__set__fold,axiom, % 172.48/172.45 ! [V_xs_2,V_x_2,T_a] : % 172.48/172.45 ( class_Lattices_Olattice(T_a) % 172.48/172.45 => 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) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_Inf__fin__set__fold,axiom, % 172.48/172.45 ! [V_xs_2,V_x_2,T_a] : % 172.48/172.45 ( class_Lattices_Olattice(T_a) % 172.48/172.45 => 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) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_Min__fin__set__fold,axiom, % 172.48/172.45 ! [V_xs_2,V_x_2,T_a] : % 172.48/172.45 ( class_Orderings_Olinorder(T_a) % 172.48/172.45 => 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) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_Max__fin__set__fold,axiom, % 172.48/172.45 ! [V_xs_2,V_x_2,T_a] : % 172.48/172.45 ( class_Orderings_Olinorder(T_a) % 172.48/172.45 => 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) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_min__max_OInf__fin__set__fold,axiom, % 172.48/172.45 ! [V_xs_2,V_x_2,T_a] : % 172.48/172.45 ( class_Orderings_Olinorder(T_a) % 172.48/172.45 => 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) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_min__max_OSup__fin__set__fold,axiom, % 172.48/172.45 ! [V_xs_2,V_x_2,T_a] : % 172.48/172.45 ( class_Orderings_Olinorder(T_a) % 172.48/172.45 => 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) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_SUPR__set__fold,axiom, % 172.48/172.45 ! [V_f_2,V_xs_2,T_b,T_a] : % 172.48/172.45 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 172.48/172.45 => 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) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_INFI__set__fold,axiom, % 172.48/172.45 ! [V_f_2,V_xs_2,T_b,T_a] : % 172.48/172.45 ( class_Complete__Lattice_Ocomplete__lattice(T_a) % 172.48/172.45 => 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) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_map__upds__fold__map__upd,axiom, % 172.48/172.45 ! [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)) ). % 172.48/172.45 % 172.48/172.45 fof(fact_elem__le__sum,axiom, % 172.48/172.45 ! [V_ns_2,V_n_2] : % 172.48/172.45 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_n_2),hAPP(c_List_Oset(tc_Nat_Onat),V_ns_2))) % 172.48/172.45 => 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))) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_rotate__drop__take,axiom, % 172.48/172.45 ! [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)) ). % 172.48/172.45 % 172.48/172.45 fof(fact_ran__def,axiom, % 172.48/172.45 ! [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)))) ). % 172.48/172.45 % 172.48/172.45 fof(fact_lexord__append__rightI,axiom, % 172.48/172.45 ! [V_r_2,V_x_2,T_a,V_y_2] : % 172.48/172.45 ( ? [B_b,B_z] : V_y_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_b),B_z) % 172.48/172.45 => 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))) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_ranI,axiom, % 172.48/172.45 ! [T_b,V_b_2,T_a,V_a_2,V_m_2] : % 172.48/172.45 ( hAPP(V_m_2,V_a_2) = hAPP(c_Option_Ooption_OSome(T_a),V_b_2) % 172.48/172.45 => hBOOL(hAPP(hAPP(c_member(T_a),V_b_2),c_Map_Oran(T_b,T_a,V_m_2))) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_sorted__list__of__set__insert,axiom, % 172.48/172.45 ! [V_x_2,V_A_2,T_a] : % 172.48/172.45 ( class_Orderings_Olinorder(T_a) % 172.48/172.45 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.48/172.45 => 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)))))) ) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_lexord__Nil__left,axiom, % 172.48/172.45 ! [V_r_2,V_y_2,T_a] : % 172.48/172.45 ( 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))) % 172.48/172.45 <=> ? [B_a,B_x] : V_y_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_a),B_x) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_length__insort,axiom, % 172.48/172.45 ! [V_xs_2,V_x_2,V_f_2,T_a,T_b] : % 172.48/172.45 ( class_Orderings_Olinorder(T_b) % 172.48/172.45 => 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)) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_insort__not__Nil,axiom, % 172.48/172.45 ! [V_xs_2,V_a_2,V_f_2,T_a,T_b] : % 172.48/172.45 ( class_Orderings_Olinorder(T_b) % 172.48/172.45 => 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) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_remove1__insort,axiom, % 172.48/172.45 ! [V_xs_2,V_x_2,T_a] : % 172.48/172.45 ( class_Orderings_Olinorder(T_a) % 172.48/172.45 => 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 ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_fun__left__comm__insort,axiom, % 172.48/172.45 ! [T_a] : % 172.48/172.45 ( class_Orderings_Olinorder(T_a) % 172.48/172.45 => 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))) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_insort__left__comm,axiom, % 172.48/172.45 ! [V_xs_2,V_y_2,V_x_2,T_a] : % 172.48/172.45 ( class_Orderings_Olinorder(T_a) % 172.48/172.45 => 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)) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_insort__key__left__comm,axiom, % 172.48/172.45 ! [V_xs_2,T_b,V_y_2,V_x_2,V_f_2,T_a] : % 172.48/172.45 ( class_Orderings_Olinorder(T_a) % 172.48/172.45 => ( hAPP(V_f_2,V_x_2) != hAPP(V_f_2,V_y_2) % 172.48/172.45 => 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)) ) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_set__insort,axiom, % 172.48/172.45 ! [V_xs_2,V_x_2,V_f_2,T_a,T_b] : % 172.48/172.45 ( class_Orderings_Olinorder(T_b) % 172.48/172.45 => 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)) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_insort__key_Osimps_I2_J,axiom, % 172.48/172.45 ! [V_ys_2,T_b,V_y_2,V_x_2,V_f_2,T_a] : % 172.48/172.45 ( class_Orderings_Olinorder(T_a) % 172.48/172.45 => ( ( 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))) % 172.48/172.45 => 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)) ) % 172.48/172.45 & ( ~ 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))) % 172.48/172.45 => 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)) ) ) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_insort__key_Osimps_I1_J,axiom, % 172.48/172.45 ! [V_x_2,V_f_2,T_a,T_b] : % 172.48/172.45 ( class_Orderings_Olinorder(T_b) % 172.48/172.45 => 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)) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_distinct__insort,axiom, % 172.48/172.45 ! [V_xs_2,V_x_2,V_f_2,T_a,T_b] : % 172.48/172.45 ( class_Orderings_Olinorder(T_b) % 172.48/172.45 => ( 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))) % 172.48/172.45 <=> ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 172.48/172.45 & hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_insort__insert__insort__key,axiom, % 172.48/172.45 ! [V_xs_2,T_b,V_x_2,V_f_2,T_a] : % 172.48/172.45 ( class_Orderings_Olinorder(T_a) % 172.48/172.45 => ( ~ 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)))) % 172.48/172.45 => 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) ) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_insort__insert__insort,axiom, % 172.48/172.45 ! [V_xs_2,V_x_2,T_a] : % 172.48/172.45 ( class_Orderings_Olinorder(T_a) % 172.48/172.45 => ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 172.48/172.45 => 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) ) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_distinct__insort__insert,axiom, % 172.48/172.45 ! [V_x_2,V_f_2,V_xs_2,T_a,T_b] : % 172.48/172.45 ( class_Orderings_Olinorder(T_b) % 172.48/172.45 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 172.48/172.45 => 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))) ) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_insort__insert__triv,axiom, % 172.48/172.45 ! [V_xs_2,V_x_2,T_a] : % 172.48/172.45 ( class_Orderings_Olinorder(T_a) % 172.48/172.45 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 172.48/172.45 => c_List_Olinorder__class_Oinsort__insert__key(T_a,T_a,c_COMBI(T_a),V_x_2,V_xs_2) = V_xs_2 ) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_set__insort__insert,axiom, % 172.48/172.45 ! [V_xs_2,V_x_2,T_a] : % 172.48/172.45 ( class_Orderings_Olinorder(T_a) % 172.48/172.45 => 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)) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_insort__insert__key__triv,axiom, % 172.48/172.45 ! [V_xs_2,T_b,V_x_2,V_f_2,T_a] : % 172.48/172.45 ( class_Orderings_Olinorder(T_a) % 172.48/172.45 => ( 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)))) % 172.48/172.45 => c_List_Olinorder__class_Oinsort__insert__key(T_b,T_a,V_f_2,V_x_2,V_xs_2) = V_xs_2 ) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_last__list__update,axiom, % 172.48/172.45 ! [V_x,V_k,T_a,V_xs] : % 172.48/172.45 ( V_xs != c_List_Olist_ONil(T_a) % 172.48/172.45 => ( ( 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)) % 172.48/172.45 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist__update(T_a,V_xs),V_k),V_x)) = V_x ) % 172.48/172.45 & ( 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)) % 172.48/172.45 => 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) ) ) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_last__conv__nth,axiom, % 172.48/172.45 ! [T_a,V_xs] : % 172.48/172.45 ( V_xs != c_List_Olist_ONil(T_a) % 172.48/172.45 => 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))) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_last__appendL,axiom, % 172.48/172.45 ! [V_xs,T_a,V_ys] : % 172.48/172.45 ( V_ys = c_List_Olist_ONil(T_a) % 172.48/172.45 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_xs) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_last__appendR,axiom, % 172.48/172.45 ! [V_xs,T_a,V_ys] : % 172.48/172.45 ( V_ys != c_List_Olist_ONil(T_a) % 172.48/172.45 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_ys) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_last__append,axiom, % 172.48/172.45 ! [V_xs,T_a,V_ys] : % 172.48/172.45 ( ( V_ys = c_List_Olist_ONil(T_a) % 172.48/172.45 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_xs) ) % 172.48/172.45 & ( V_ys != c_List_Olist_ONil(T_a) % 172.48/172.45 => c_List_Olast(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs),V_ys)) = c_List_Olast(T_a,V_ys) ) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_last__ConsL,axiom, % 172.48/172.45 ! [V_x,T_a,V_xs] : % 172.48/172.45 ( V_xs = c_List_Olist_ONil(T_a) % 172.48/172.45 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_last__ConsR,axiom, % 172.48/172.45 ! [V_x,T_a,V_xs] : % 172.48/172.45 ( V_xs != c_List_Olist_ONil(T_a) % 172.48/172.45 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olast(T_a,V_xs) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_last_Osimps,axiom, % 172.48/172.45 ! [V_x,T_a,V_xs] : % 172.48/172.45 ( ( V_xs = c_List_Olist_ONil(T_a) % 172.48/172.45 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = V_x ) % 172.48/172.45 & ( V_xs != c_List_Olist_ONil(T_a) % 172.48/172.45 => c_List_Olast(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = c_List_Olast(T_a,V_xs) ) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_last__in__set,axiom, % 172.48/172.45 ! [T_a,V_as_2] : % 172.48/172.45 ( V_as_2 != c_List_Olist_ONil(T_a) % 172.48/172.45 => hBOOL(hAPP(hAPP(c_member(T_a),c_List_Olast(T_a,V_as_2)),hAPP(c_List_Oset(T_a),V_as_2))) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_last__snoc,axiom, % 172.48/172.45 ! [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 ). % 172.48/172.45 % 172.48/172.45 fof(fact_last__drop,axiom, % 172.48/172.45 ! [V_xs,T_a,V_n] : % 172.48/172.45 ( 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))) % 172.48/172.45 => c_List_Olast(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) = c_List_Olast(T_a,V_xs) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_append__butlast__last__id,axiom, % 172.48/172.45 ! [T_a,V_xs] : % 172.48/172.45 ( V_xs != c_List_Olist_ONil(T_a) % 172.48/172.45 => 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 ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_snoc__eq__iff__butlast,axiom, % 172.48/172.45 ! [V_ys_2,V_x_2,V_xs_2,T_a] : % 172.48/172.45 ( 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 % 172.48/172.45 <=> ( V_ys_2 != c_List_Olist_ONil(T_a) % 172.48/172.45 & c_List_Obutlast(T_a,V_ys_2) = V_xs_2 % 172.48/172.45 & c_List_Olast(T_a,V_ys_2) = V_x_2 ) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_lists_Osimps,axiom, % 172.48/172.45 ! [V_A_2,V_a_2,T_a] : % 172.48/172.45 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_a_2),c_List_Olists(T_a,V_A_2))) % 172.48/172.45 <=> ( V_a_2 = c_List_Olist_ONil(T_a) % 172.48/172.45 | ? [B_a,B_l] : % 172.48/172.45 ( V_a_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_a),B_l) % 172.48/172.45 & hBOOL(hAPP(hAPP(c_member(T_a),B_a),V_A_2)) % 172.48/172.45 & hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_l),c_List_Olists(T_a,V_A_2))) ) ) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_map__of__zip__upd,axiom, % 172.48/172.45 ! [V_z_2,V_y_2,V_x_2,V_zs_2,V_xs_2,T_b,V_ys_2,T_a] : % 172.48/172.45 ( 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) % 172.48/172.45 => ( 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) % 172.48/172.45 => ( ~ hBOOL(hAPP(hAPP(c_member(T_b),V_x_2),hAPP(c_List_Oset(T_b),V_xs_2))) % 172.48/172.45 => ( 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)) % 172.48/172.45 => 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)) ) ) ) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_finite__dom__map__of,axiom, % 172.48/172.45 ! [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)))) ). % 172.48/172.45 % 172.48/172.45 fof(fact_map__of__zip__inject,axiom, % 172.48/172.45 ! [V_zs_2,V_xs_2,T_b,V_ys_2,T_a] : % 172.48/172.45 ( 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) % 172.48/172.45 => ( 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) % 172.48/172.45 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 172.48/172.45 => ( 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)) % 172.48/172.45 => V_ys_2 = V_zs_2 ) ) ) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_map__of__Cons__code_I2_J,axiom, % 172.48/172.45 ! [V_ps,V_v,T_c,T_b,V_k,V_l] : % 172.48/172.45 ( ( V_l = V_k % 172.48/172.45 => 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) ) % 172.48/172.45 & ( V_l != V_k % 172.48/172.45 => 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) ) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_map__of__eq__dom,axiom, % 172.48/172.45 ! [V_ys_2,V_xs_2,T_b,T_a] : % 172.48/172.45 ( hAPP(c_Map_Omap__of(T_a,T_b),V_xs_2) = hAPP(c_Map_Omap__of(T_a,T_b),V_ys_2) % 172.48/172.45 => 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)) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_finite__range__map__of,axiom, % 172.48/172.45 ! [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))))) ). % 172.48/172.45 % 172.48/172.45 fof(fact_map__of__is__SomeD,axiom, % 172.48/172.45 ! [V_y_2,V_x_2,V_xys_2,T_a,T_b] : % 172.48/172.45 ( 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) % 172.48/172.45 => 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))) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_map__of__SomeD,axiom, % 172.48/172.45 ! [V_y_2,V_k_2,V_xs_2,T_a,T_b] : % 172.48/172.45 ( 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) % 172.48/172.45 => 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))) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_dom__map__of__conv__image__fst,axiom, % 172.48/172.45 ! [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)) ). % 172.48/172.45 % 172.48/172.45 fof(fact_map__of__zip__is__Some,axiom, % 172.48/172.45 ! [V_x_2,V_ys_2,T_b,V_xs_2,T_a] : % 172.48/172.45 ( 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) % 172.48/172.45 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 172.48/172.45 <=> ? [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) ) ) ). % 172.48/172.45 % 172.48/172.45 fof(fact_dom__map__of__zip,axiom, % 172.78/172.45 ! [V_ys_2,T_b,V_xs_2,T_a] : % 172.78/172.45 ( 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) % 172.78/172.45 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 172.78/172.45 => 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) ) ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_map__of_Osimps_I2_J,axiom, % 172.78/172.45 ! [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))) ). % 172.78/172.45 % 172.78/172.45 fof(fact_ran__distinct,axiom, % 172.78/172.45 ! [V_al_2,T_b,T_a] : % 172.78/172.45 ( 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))) % 172.78/172.45 => 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)) ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_set__map__of__compr,axiom, % 172.78/172.45 ! [V_xs_2,T_b,T_a] : % 172.78/172.45 ( 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))) % 172.78/172.45 => 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)))) ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_inj__mapI,axiom, % 172.78/172.45 ! [V_f_2,T_b,T_a] : % 172.78/172.45 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 172.78/172.45 => 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))) ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_foldl__map,axiom, % 172.78/172.45 ! [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) ). % 172.78/172.45 % 172.78/172.45 fof(fact_list__size__map,axiom, % 172.78/172.45 ! [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) ). % 172.78/172.45 % 172.78/172.45 fof(fact_List_Omap_Oid,axiom, % 172.78/172.45 ! [T_a] : hAPP(c_List_Omap(T_a,T_a),c_Fun_Oid(T_a)) = c_Fun_Oid(tc_List_Olist(T_a)) ). % 172.78/172.45 % 172.78/172.45 fof(fact_List_Omap_Oidentity,axiom, % 172.78/172.45 ! [T_a] : hAPP(c_List_Omap(T_a,T_a),c_COMBI(T_a)) = c_Fun_Oid(tc_List_Olist(T_a)) ). % 172.78/172.45 % 172.78/172.45 fof(fact_map__map,axiom, % 172.78/172.45 ! [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) ). % 172.78/172.45 % 172.78/172.45 fof(fact_List_Omap_Ocompositionality,axiom, % 172.78/172.45 ! [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) ). % 172.78/172.45 % 172.78/172.45 fof(fact_map__comp__map,axiom, % 172.78/172.45 ! [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)) ). % 172.78/172.45 % 172.78/172.45 fof(fact_List_Omap_Ocomp,axiom, % 172.78/172.45 ! [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)) ). % 172.78/172.45 % 172.78/172.45 fof(fact_zip__map2,axiom, % 172.78/172.45 ! [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)) ). % 172.78/172.45 % 172.78/172.45 fof(fact_map__zip__map2,axiom, % 172.78/172.45 ! [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)) ). % 172.78/172.45 % 172.78/172.45 fof(fact_map__zip__map,axiom, % 172.78/172.45 ! [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)) ). % 172.78/172.45 % 172.78/172.45 fof(fact_zip__map1,axiom, % 172.78/172.45 ! [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)) ). % 172.78/172.45 % 172.78/172.45 fof(fact_zip__map__map,axiom, % 172.78/172.45 ! [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)) ). % 172.78/172.45 % 172.78/172.45 fof(fact_map__inj__on,axiom, % 172.78/172.45 ! [V_ys_2,V_xs_2,V_f_2,T_a,T_b] : % 172.78/172.45 ( 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) % 172.78/172.45 => ( 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))) % 172.78/172.45 => V_xs_2 = V_ys_2 ) ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_inj__on__map__eq__map,axiom, % 172.78/172.45 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_a] : % 172.78/172.45 ( 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))) % 172.78/172.45 => ( 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) % 172.78/172.45 <=> V_xs_2 = V_ys_2 ) ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_nth__map,axiom, % 172.78/172.45 ! [V_f_2,T_b,V_xs_2,T_a,V_n_2] : % 172.78/172.45 ( 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))) % 172.78/172.45 => 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)) ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_map__fun__upd,axiom, % 172.78/172.45 ! [V_v_2,V_f_2,T_b,V_xs_2,V_y_2,T_a] : % 172.78/172.45 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_y_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 172.78/172.45 => 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) ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_map__eq__imp__length__eq,axiom, % 172.78/172.45 ! [V_ys_2,V_g_2,T_c,V_xs_2,V_f_2,T_a,T_b] : % 172.78/172.45 ( 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) % 172.78/172.45 => 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) ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_length__map,axiom, % 172.78/172.45 ! [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) ). % 172.78/172.45 % 172.78/172.45 fof(fact_map__tl,axiom, % 172.78/172.45 ! [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)) ). % 172.78/172.45 % 172.78/172.45 fof(fact_inj__map__eq__map,axiom, % 172.78/172.45 ! [V_ys_2,V_xs_2,V_f_2,T_b,T_a] : % 172.78/172.45 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 172.78/172.45 => ( 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) % 172.78/172.45 <=> V_xs_2 = V_ys_2 ) ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_map__injective,axiom, % 172.78/172.45 ! [V_ys_2,V_xs_2,V_f_2,T_a,T_b] : % 172.78/172.45 ( 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) % 172.78/172.45 => ( c_Fun_Oinj__on(T_b,T_a,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_b,tc_HOL_Obool))) % 172.78/172.45 => V_xs_2 = V_ys_2 ) ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_Nil__is__map__conv,axiom, % 172.78/172.45 ! [V_xs_2,V_f_2,T_b,T_a] : % 172.78/172.45 ( c_List_Olist_ONil(T_a) = hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2) % 172.78/172.45 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_map_Osimps_I1_J,axiom, % 172.78/172.45 ! [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) ). % 172.78/172.45 % 172.78/172.45 fof(fact_map__is__Nil__conv,axiom, % 172.78/172.45 ! [V_xs_2,V_f_2,T_a,T_b] : % 172.78/172.45 ( hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2) = c_List_Olist_ONil(T_a) % 172.78/172.45 <=> V_xs_2 = c_List_Olist_ONil(T_b) ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_map__butlast,axiom, % 172.78/172.45 ! [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)) ). % 172.78/172.45 % 172.78/172.45 fof(fact_take__map,axiom, % 172.78/172.45 ! [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)) ). % 172.78/172.45 % 172.78/172.45 fof(fact_map__ident,axiom, % 172.78/172.45 ! [V_xs_2,T_a] : hAPP(hAPP(c_List_Omap(T_a,T_a),c_COMBI(T_a)),V_xs_2) = V_xs_2 ). % 172.78/172.45 % 172.78/172.45 fof(fact_listsum__const__mult,axiom, % 172.78/172.45 ! [V_xs_2,V_f_2,V_ca_2,T_b,T_a] : % 172.78/172.45 ( class_Rings_Osemiring__0(T_a) % 172.78/172.45 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),hAPP(hAPP(c_COMBB(T_a,T_a,T_b),hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2)),V_f_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),V_ca_2),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2))) ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_listsum__mult__const,axiom, % 172.78/172.45 ! [V_xs_2,V_ca_2,V_f_2,T_b,T_a] : % 172.78/172.45 ( class_Rings_Osemiring__0(T_a) % 172.78/172.45 => hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),hAPP(hAPP(c_COMBC(T_b,T_a,T_a),hAPP(hAPP(c_COMBB(T_a,tc_fun(T_a,T_a),T_b),c_Groups_Otimes__class_Otimes(T_a)),V_f_2)),V_ca_2)),V_xs_2)) = hAPP(hAPP(c_Groups_Otimes__class_Otimes(T_a),hAPP(c_List_Omonoid__add__class_Olistsum(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2))),V_ca_2) ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_listsum__0,axiom, % 172.78/172.45 ! [V_xs_2,T_b,T_a] : % 172.78/172.45 ( class_Groups_Omonoid__add(T_a) % 172.78/172.45 => 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) ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_listsum__subtractf,axiom, % 172.78/172.45 ! [V_xs_2,V_g_2,V_f_2,T_b,T_a] : % 172.78/172.45 ( class_Groups_Oab__group__add(T_a) % 172.78/172.45 => 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))) ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_listsum__addf,axiom, % 172.78/172.45 ! [V_xs_2,V_g_2,V_f_2,T_b,T_a] : % 172.78/172.45 ( class_Groups_Ocomm__monoid__add(T_a) % 172.78/172.45 => 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))) ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_map__eq__conv,axiom, % 172.78/172.45 ! [V_g_2,V_xs_2,V_f_2,T_a,T_b] : % 172.78/172.45 ( 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) % 172.78/172.45 <=> ! [B_x] : % 172.78/172.45 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),hAPP(c_List_Oset(T_b),V_xs_2))) % 172.78/172.45 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_map__update,axiom, % 172.78/172.45 ! [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)) ). % 172.78/172.45 % 172.78/172.45 fof(fact_map_Osimps_I2_J,axiom, % 172.78/172.45 ! [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)) ). % 172.78/172.45 % 172.78/172.45 fof(fact_map__append,axiom, % 172.78/172.45 ! [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)) ). % 172.78/172.45 % 172.78/172.45 fof(fact_set__map,axiom, % 172.78/172.45 ! [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)) ). % 172.78/172.45 % 172.78/172.45 fof(fact_hd__map,axiom, % 172.78/172.45 ! [V_f_2,T_b,T_a,V_xs_2] : % 172.78/172.45 ( V_xs_2 != c_List_Olist_ONil(T_a) % 172.78/172.45 => 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)) ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_drop__map,axiom, % 172.78/172.45 ! [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)) ). % 172.78/172.45 % 172.78/172.45 fof(fact_rotate__map,axiom, % 172.78/172.45 ! [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)) ). % 172.78/172.45 % 172.78/172.45 fof(fact_last__map,axiom, % 172.78/172.45 ! [V_f_2,T_b,T_a,V_xs_2] : % 172.78/172.45 ( V_xs_2 != c_List_Olist_ONil(T_a) % 172.78/172.45 => 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)) ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_distinct__map,axiom, % 172.78/172.45 ! [V_xs_2,V_f_2,T_b,T_a] : % 172.78/172.45 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2))) % 172.78/172.45 <=> ( hBOOL(hAPP(c_List_Odistinct(T_b),V_xs_2)) % 172.78/172.45 & c_Fun_Oinj__on(T_b,T_a,V_f_2,hAPP(c_List_Oset(T_b),V_xs_2)) ) ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_listsum__abs,axiom, % 172.78/172.45 ! [V_xs_2,T_a] : % 172.78/172.45 ( class_Groups_Oordered__ab__group__add__abs(T_a) % 172.78/172.45 => 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)))) ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_uminus__listsum__map,axiom, % 172.78/172.45 ! [V_xs_2,V_f_2,T_b,T_a] : % 172.78/172.45 ( class_Groups_Oab__group__add(T_a) % 172.78/172.45 => 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)) ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_inj__on__mapI,axiom, % 172.78/172.45 ! [V_A_2,V_f_2,T_b,T_a] : % 172.78/172.45 ( 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))) % 172.78/172.45 => 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) ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_map__fst__zip,axiom, % 172.78/172.45 ! [V_ys_2,T_b,V_xs_2,T_a] : % 172.78/172.45 ( 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) % 172.78/172.45 => 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 ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_map__snd__zip,axiom, % 172.78/172.45 ! [V_ys_2,T_b,V_xs_2,T_a] : % 172.78/172.45 ( 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) % 172.78/172.45 => 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 ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_zip__map__fst__snd,axiom, % 172.78/172.45 ! [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 ). % 172.78/172.45 % 172.78/172.45 fof(fact_inj__map,axiom, % 172.78/172.45 ! [V_f_2,T_b,T_a] : % 172.78/172.45 ( 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))) % 172.78/172.45 <=> c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_inj__mapD,axiom, % 172.78/172.45 ! [V_f_2,T_b,T_a] : % 172.78/172.45 ( 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))) % 172.78/172.45 => c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_pick__member,axiom, % 172.78/172.45 ! [V_xs_2,T_a,V_i_2] : % 172.78/172.45 ( 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)))) % 172.78/172.45 => 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)))) ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_listsum__distinct__conv__setsum__set,axiom, % 172.78/172.45 ! [V_f_2,V_xs_2,T_a,T_b] : % 172.78/172.45 ( class_Groups_Ocomm__monoid__add(T_b) % 172.78/172.45 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 172.78/172.45 => 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)) ) ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_zip__eq__conv,axiom, % 172.78/172.45 ! [V_zs_2,V_ys_2,T_b,V_xs_2,T_a] : % 172.78/172.45 ( 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) % 172.78/172.45 => ( hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2) = V_zs_2 % 172.78/172.45 <=> ( 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 % 172.78/172.45 & 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 ) ) ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_listsum__triv,axiom, % 172.78/172.45 ! [V_xs_2,V_r_2,T_b,T_a] : % 172.78/172.45 ( class_Rings_Osemiring__1(T_a) % 172.78/172.45 => 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) ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_map__of__inject__set,axiom, % 172.78/172.45 ! [V_ys_2,V_xs_2,T_b,T_a] : % 172.78/172.45 ( 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))) % 172.78/172.45 => ( 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))) % 172.78/172.45 => ( hAPP(c_Map_Omap__of(T_a,T_b),V_xs_2) = hAPP(c_Map_Omap__of(T_a,T_b),V_ys_2) % 172.78/172.45 <=> 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) ) ) ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_listsum__map__remove1,axiom, % 172.78/172.45 ! [V_f_2,V_xs_2,V_x_2,T_a,T_b] : % 172.78/172.45 ( class_Groups_Ocomm__monoid__add(T_b) % 172.78/172.45 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 172.78/172.45 => 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)))) ) ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_select__weight__member,axiom, % 172.78/172.45 ! [V_s_2,V_xs_2,T_a] : % 172.78/172.45 ( 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)))) % 172.78/172.45 => 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)))) ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_select__weight__def,axiom, % 172.78/172.45 ! [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))) ). % 172.78/172.45 % 172.78/172.45 fof(fact_map__of__mapk__SomeI,axiom, % 172.78/172.45 ! [V_x_2,V_k_2,V_t_2,T_c,V_f_2,T_b,T_a] : % 172.78/172.45 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 172.78/172.45 => ( 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) % 172.78/172.45 => 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) ) ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_Some__eq__map__of__iff,axiom, % 172.78/172.45 ! [V_x_2,V_y_2,V_xys_2,T_b,T_a] : % 172.78/172.45 ( 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))) % 172.78/172.45 => ( 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) % 172.78/172.45 <=> 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))) ) ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_map__of__eq__Some__iff,axiom, % 172.78/172.45 ! [V_y_2,V_x_2,V_xys_2,T_b,T_a] : % 172.78/172.45 ( 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))) % 172.78/172.45 => ( 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) % 172.78/172.45 <=> 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))) ) ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_map__of__is__SomeI,axiom, % 172.78/172.45 ! [V_y_2,V_x_2,V_xys_2,T_b,T_a] : % 172.78/172.45 ( 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))) % 172.78/172.45 => ( 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))) % 172.78/172.45 => 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) ) ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_Nitpick_Osetsum_H__def,axiom, % 172.78/172.45 ! [V_f_2,V_A_2,T_a,T_b] : % 172.78/172.45 ( class_Groups_Ocomm__monoid__add(T_b) % 172.78/172.45 => ( ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.78/172.45 => 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))))) ) % 172.78/172.45 & ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.78/172.45 => c_Nitpick_Osetsum_H(T_a,T_b,V_f_2,V_A_2) = c_Groups_Ozero__class_Ozero(T_b) ) ) ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_listsum__mono,axiom, % 172.78/172.45 ! [V_g_2,V_f_2,V_xs_2,T_a,T_b] : % 172.78/172.45 ( ( class_Groups_Omonoid__add(T_b) % 172.78/172.45 & class_Groups_Oordered__ab__semigroup__add(T_b) ) % 172.78/172.45 => ( ! [B_x] : % 172.78/172.45 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 172.78/172.45 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,B_x)),hAPP(V_g_2,B_x))) ) % 172.78/172.45 => 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)))) ) ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_zip__same__conv__map,axiom, % 172.78/172.45 ! [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) ). % 172.78/172.45 % 172.78/172.45 fof(fact_list__size__conv__listsum,axiom, % 172.78/172.45 ! [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)) ). % 172.78/172.45 % 172.78/172.45 fof(fact_interv__listsum__conv__setsum__set__int,axiom, % 172.78/172.45 ! [V_l_2,V_k_2,V_f_2,T_a] : % 172.78/172.45 ( class_Groups_Ocomm__monoid__add(T_a) % 172.78/172.45 => 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))) ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_setsum__set__upto__conv__listsum__int,axiom, % 172.78/172.45 ! [V_j_2,V_i_2,V_f_2,T_a] : % 172.78/172.45 ( class_Groups_Ocomm__monoid__add(T_a) % 172.78/172.45 => 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))) ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_map__of__map__restrict,axiom, % 172.78/172.45 ! [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)) ). % 172.78/172.45 % 172.78/172.45 fof(fact_map__of__map__keys,axiom, % 172.78/172.45 ! [V_m_2,T_b,V_xs_2,T_a] : % 172.78/172.45 ( hAPP(c_List_Oset(T_a),V_xs_2) = c_Map_Odom(T_a,T_b,V_m_2) % 172.78/172.45 => 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 ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_select__weigth__select,axiom, % 172.78/172.45 ! [T_a,V_xs_2] : % 172.78/172.45 ( V_xs_2 != c_List_Olist_ONil(T_a) % 172.78/172.45 => 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) ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_pick__same,axiom, % 172.78/172.45 ! [V_xs_2,T_a,V_l_2] : % 172.78/172.45 ( 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))) % 172.78/172.45 => 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) ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_map__of__map,axiom, % 172.78/172.45 ! [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)) ). % 172.78/172.45 % 172.78/172.45 fof(fact_Option_Omap_Ocomp,axiom, % 172.78/172.45 ! [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)) ). % 172.78/172.45 % 172.78/172.45 fof(fact_Option_Omap_Ocompositionality,axiom, % 172.78/172.45 ! [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) ). % 172.78/172.45 % 172.78/172.45 fof(fact_option__map__comp,axiom, % 172.78/172.45 ! [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) ). % 172.78/172.45 % 172.78/172.45 fof(fact_option__map__o__map__upd,axiom, % 172.78/172.45 ! [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))) ). % 172.78/172.45 % 172.78/172.45 fof(fact_Option_Omap_Oid,axiom, % 172.78/172.45 ! [T_a] : hAPP(c_Option_Omap(T_a,T_a),c_Fun_Oid(T_a)) = c_Fun_Oid(tc_Option_Ooption(T_a)) ). % 172.78/172.45 % 172.78/172.45 fof(fact_Option_Omap_Oidentity,axiom, % 172.78/172.45 ! [T_a] : hAPP(c_Option_Omap(T_a,T_a),c_COMBI(T_a)) = c_Fun_Oid(tc_Option_Ooption(T_a)) ). % 172.78/172.45 % 172.78/172.45 fof(fact_less__code__numeral__code,axiom, % 172.78/172.45 ! [V_m_2,V_n_2] : % 172.78/172.45 ( 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))) % 172.78/172.45 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_n_2),V_m_2)) ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_code__numeral_Oof__nat__inject,axiom, % 172.78/172.45 ! [V_y_2,V_x_2] : % 172.78/172.45 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_x_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) % 172.78/172.45 => ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) % 172.78/172.45 => ( hAPP(c_Code__Numeral_Oof__nat,V_x_2) = hAPP(c_Code__Numeral_Oof__nat,V_y_2) % 172.78/172.45 <=> V_x_2 = V_y_2 ) ) ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_Code__Numeral_Oof__nat__code,axiom, % 172.78/172.45 c_Code__Numeral_Oof__nat = c_Nat_Osemiring__1__class_Oof__nat(tc_Code__Numeral_Ocode__numeral) ). % 172.78/172.45 % 172.78/172.45 fof(fact_Code__Numeral_Oof__nat__inject,axiom, % 172.78/172.45 ! [V_m_2,V_n_2] : % 172.78/172.45 ( hAPP(c_Code__Numeral_Oof__nat,V_n_2) = hAPP(c_Code__Numeral_Oof__nat,V_m_2) % 172.78/172.45 <=> V_n_2 = V_m_2 ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_times__code__numeral__code,axiom, % 172.78/172.45 ! [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)) ). % 172.78/172.45 % 172.78/172.45 fof(fact_dom__option__map,axiom, % 172.78/172.45 ! [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) ). % 172.78/172.45 % 172.78/172.45 fof(fact_zero__code__numeral__def,axiom, % 172.78/172.45 c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) ). % 172.78/172.45 % 172.78/172.45 fof(fact_option__map__Some,axiom, % 172.78/172.45 ! [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)) ). % 172.78/172.45 % 172.78/172.45 fof(fact_option__map__eq__Some,axiom, % 172.78/172.45 ! [V_y_2,V_xo_2,V_f_2,T_a,T_b] : % 172.78/172.45 ( 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) % 172.78/172.45 <=> ? [B_z] : % 172.78/172.45 ( V_xo_2 = hAPP(c_Option_Ooption_OSome(T_b),B_z) % 172.78/172.45 & hAPP(V_f_2,B_z) = V_y_2 ) ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_one__code__numeral__def,axiom, % 172.78/172.45 c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral) = hAPP(c_Code__Numeral_Oof__nat,c_Groups_Oone__class_Oone(tc_Nat_Onat)) ). % 172.78/172.45 % 172.78/172.45 fof(fact_number__of__code__numeral__def,axiom, % 172.78/172.45 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) ). % 172.78/172.45 % 172.78/172.45 fof(fact_plus__code__numeral__code,axiom, % 172.78/172.45 ! [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)) ). % 172.78/172.45 % 172.78/172.45 fof(fact_less__eq__code__numeral__code,axiom, % 172.78/172.45 ! [V_m_2,V_n_2] : % 172.78/172.45 ( 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))) % 172.78/172.45 <=> hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_n_2),V_m_2)) ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_code__numeral__not__eq__zero,axiom, % 172.78/172.45 ! [V_i_2] : % 172.78/172.45 ( V_i_2 != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 172.78/172.45 <=> 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)) ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_select__def,axiom, % 172.78/172.45 ! [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))) ). % 172.78/172.45 % 172.78/172.45 fof(fact_subtract__code__numeral__code,axiom, % 172.78/172.45 ! [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)) ). % 172.78/172.45 % 172.78/172.45 fof(fact_nat__of__inverse,axiom, % 172.78/172.45 ! [V_x] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,V_x)) = V_x ). % 172.78/172.45 % 172.78/172.45 fof(fact_of__nat__nat__of,axiom, % 172.78/172.45 ! [V_k] : hAPP(c_Code__Numeral_Oof__nat,hAPP(c_Code__Numeral_Onat__of,V_k)) = V_k ). % 172.78/172.45 % 172.78/172.45 fof(fact_nat__of__of__nat,axiom, % 172.78/172.45 ! [V_n] : hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,V_n)) = V_n ). % 172.78/172.45 % 172.78/172.45 fof(fact_times__code__numeral__def,axiom, % 172.78/172.45 ! [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))) ). % 172.78/172.45 % 172.78/172.45 fof(fact_Code__Numeral_Onat__of__inject,axiom, % 172.78/172.45 ! [V_l_2,V_k_2] : % 172.78/172.45 ( hAPP(c_Code__Numeral_Onat__of,V_k_2) = hAPP(c_Code__Numeral_Onat__of,V_l_2) % 172.78/172.45 <=> V_k_2 = V_l_2 ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_code__numeral_Onat__of__inject,axiom, % 172.78/172.45 ! [V_y_2,V_x_2] : % 172.78/172.45 ( hAPP(c_Code__Numeral_Onat__of,V_x_2) = hAPP(c_Code__Numeral_Onat__of,V_y_2) % 172.78/172.45 <=> V_x_2 = V_y_2 ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_type__definition__code__numeral,axiom, % 172.78/172.45 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))) ). % 172.78/172.45 % 172.78/172.45 fof(fact_less__code__numeral__def,axiom, % 172.78/172.45 ! [V_m_2,V_n_2] : % 172.78/172.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Code__Numeral_Ocode__numeral),V_n_2),V_m_2)) % 172.78/172.45 <=> 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))) ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_nat__of,axiom, % 172.78/172.45 ! [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)))) ). % 172.78/172.45 % 172.78/172.45 fof(fact_nat__of__number,axiom, % 172.78/172.45 ! [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) ). % 172.78/172.45 % 172.78/172.45 fof(fact_int__of__def,axiom, % 172.78/172.45 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) ). % 172.78/172.45 % 172.78/172.45 fof(fact_less__eq__code__numeral__def,axiom, % 172.78/172.45 ! [V_m_2,V_n_2] : % 172.78/172.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Code__Numeral_Ocode__numeral),V_n_2),V_m_2)) % 172.78/172.45 <=> 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))) ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_nat__of__code,axiom, % 172.78/172.45 ! [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)) ). % 172.78/172.45 % 172.78/172.45 fof(fact_nat__of__aux__def,axiom, % 172.78/172.45 ! [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) ). % 172.78/172.45 % 172.78/172.45 fof(fact_Suc__code__numeral__def,axiom, % 172.78/172.45 ! [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))) ). % 172.78/172.45 % 172.78/172.45 fof(fact_minus__code__numeral__def,axiom, % 172.78/172.45 ! [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))) ). % 172.78/172.45 % 172.78/172.45 fof(fact_of__nat__inverse,axiom, % 172.78/172.45 ! [V_y_2] : % 172.78/172.45 ( hBOOL(hAPP(hAPP(c_member(tc_Nat_Onat),V_y_2),c_Orderings_Otop__class_Otop(tc_fun(tc_Nat_Onat,tc_HOL_Obool)))) % 172.78/172.45 => hAPP(c_Code__Numeral_Onat__of,hAPP(c_Code__Numeral_Oof__nat,V_y_2)) = V_y_2 ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_plus__code__numeral__def,axiom, % 172.78/172.45 ! [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))) ). % 172.78/172.45 % 172.78/172.45 fof(fact_div__code__numeral__def,axiom, % 172.78/172.45 ! [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))) ). % 172.78/172.45 % 172.78/172.45 fof(fact_minus__code__numeral__code,axiom, % 172.78/172.45 ! [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) ). % 172.78/172.45 % 172.78/172.45 fof(fact_subtract__code__numeral__def,axiom, % 172.78/172.45 c_Code__Numeral_Osubtract__code__numeral = c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral) ). % 172.78/172.45 % 172.78/172.45 fof(fact_mod__code__numeral__def,axiom, % 172.78/172.45 ! [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))) ). % 172.78/172.45 % 172.78/172.45 fof(fact_code__numeral__decr,axiom, % 172.78/172.45 ! [V_k] : % 172.78/172.45 ( V_k != hAPP(c_Code__Numeral_Oof__nat,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) % 172.78/172.45 => 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))) ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_New__DSequence_Opos__not__seq__def,axiom, % 172.78/172.45 ! [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))) ). % 172.78/172.45 % 172.78/172.45 fof(fact_weak__map__of__SomeI,axiom, % 172.78/172.45 ! [V_l_2,V_x_2,V_k_2,T_b,T_a] : % 172.78/172.45 ( 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))) % 172.78/172.45 => ? [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) ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_map__of__zip__map,axiom, % 172.78/172.45 ! [V_f_2,T_b,V_xs_2,V_x_2,T_a] : % 172.78/172.45 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 172.78/172.45 => 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)) ) % 172.78/172.45 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 172.78/172.45 => 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) ) ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_partition__set,axiom, % 172.78/172.45 ! [V_no_2,V_yes_2,V_xs_2,V_P_2,T_a] : % 172.78/172.45 ( 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) % 172.78/172.45 => 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) ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_option__map__is__None,axiom, % 172.78/172.45 ! [V_opt_2,V_f_2,T_a,T_b] : % 172.78/172.45 ( hAPP(hAPP(c_Option_Omap(T_b,T_a),V_f_2),V_opt_2) = c_Option_Ooption_ONone(T_a) % 172.78/172.45 <=> V_opt_2 = c_Option_Ooption_ONone(T_b) ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_option__map__None,axiom, % 172.78/172.45 ! [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) ). % 172.78/172.45 % 172.78/172.45 fof(fact_ran__empty,axiom, % 172.78/172.45 ! [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)) ). % 172.78/172.45 % 172.78/172.45 fof(fact_not__None__eq,axiom, % 172.78/172.45 ! [T_a,V_x_2] : % 172.78/172.45 ( V_x_2 != c_Option_Ooption_ONone(T_a) % 172.78/172.45 <=> ? [B_y] : V_x_2 = hAPP(c_Option_Ooption_OSome(T_a),B_y) ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_not__Some__eq,axiom, % 172.78/172.45 ! [T_a,V_x_2] : % 172.78/172.45 ( ! [B_y] : V_x_2 != hAPP(c_Option_Ooption_OSome(T_a),B_y) % 172.78/172.45 <=> V_x_2 = c_Option_Ooption_ONone(T_a) ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_option_Osimps_I3_J,axiom, % 172.78/172.45 ! [V_a_H,T_a] : hAPP(c_Option_Ooption_OSome(T_a),V_a_H) != c_Option_Ooption_ONone(T_a) ). % 172.78/172.45 % 172.78/172.45 fof(fact_option_Osimps_I2_J,axiom, % 172.78/172.45 ! [V_a_H,T_a] : c_Option_Ooption_ONone(T_a) != hAPP(c_Option_Ooption_OSome(T_a),V_a_H) ). % 172.78/172.45 % 172.78/172.45 fof(fact_option_Osimps_I4_J,axiom, % 172.78/172.45 ! [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 ). % 172.78/172.45 % 172.78/172.45 fof(fact_restrict__map__to__empty,axiom, % 172.78/172.45 ! [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) ). % 172.78/172.45 % 172.78/172.45 fof(fact_restrict__map__empty,axiom, % 172.78/172.45 ! [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) ). % 172.78/172.45 % 172.78/172.45 fof(fact_restrict__out,axiom, % 172.78/172.45 ! [V_m_2,T_b,V_A_2,V_x_2,T_a] : % 172.78/172.45 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 172.78/172.45 => hAPP(c_Map_Orestrict__map(T_a,T_b,V_m_2,V_A_2),V_x_2) = c_Option_Ooption_ONone(T_b) ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_restrict__map__def,axiom, % 172.78/172.45 ! [V_m_2,T_b,V_A_2,V_x_2,T_a] : % 172.78/172.45 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 172.78/172.45 => 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) ) % 172.78/172.45 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_A_2)) % 172.78/172.45 => hAPP(c_Map_Orestrict__map(T_a,T_b,V_m_2,V_A_2),V_x_2) = c_Option_Ooption_ONone(T_b) ) ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_dom__def,axiom, % 172.78/172.45 ! [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)))) ). % 172.78/172.45 % 172.78/172.45 fof(fact_domIff,axiom, % 172.78/172.45 ! [V_m_2,T_b,V_a_2,T_a] : % 172.78/172.45 ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),c_Map_Odom(T_a,T_b,V_m_2))) % 172.78/172.45 <=> hAPP(V_m_2,V_a_2) != c_Option_Ooption_ONone(T_b) ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_dom__eq__empty__conv,axiom, % 172.78/172.45 ! [V_f_2,T_b,T_a] : % 172.78/172.45 ( c_Map_Odom(T_a,T_b,V_f_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.78/172.45 <=> V_f_2 = hAPP(c_COMBK(tc_Option_Ooption(T_b),T_a),c_Option_Ooption_ONone(T_b)) ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_dom__empty,axiom, % 172.78/172.45 ! [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)) ). % 172.78/172.45 % 172.78/172.45 fof(fact_empty__upd__none,axiom, % 172.78/172.45 ! [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) ). % 172.78/172.45 % 172.78/172.45 fof(fact_map__upd__nonempty,axiom, % 172.78/172.45 ! [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)) ). % 172.78/172.45 % 172.78/172.45 fof(fact_Option_Oset_Osimps_I1_J,axiom, % 172.78/172.45 ! [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)) ). % 172.78/172.45 % 172.78/172.45 fof(fact_set__empty__eq,axiom, % 172.78/172.45 ! [V_xo_2,T_a] : % 172.78/172.45 ( c_Option_Oset(T_a,V_xo_2) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) % 172.78/172.45 <=> V_xo_2 = c_Option_Ooption_ONone(T_a) ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_map__of__Cons__code_I1_J,axiom, % 172.78/172.45 ! [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) ). % 172.78/172.45 % 172.78/172.45 fof(fact_map__of_Osimps_I1_J,axiom, % 172.78/172.45 ! [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) ). % 172.78/172.45 % 172.78/172.45 fof(fact_option__map__o__empty,axiom, % 172.78/172.45 ! [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) ). % 172.78/172.45 % 172.78/172.45 fof(fact_Option_Omap__def,axiom, % 172.78/172.45 ! [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)) ). % 172.78/172.45 % 172.78/172.45 fof(fact_option_Osize_I3_J,axiom, % 172.78/172.45 ! [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) ). % 172.78/172.45 % 172.78/172.45 fof(fact_option_Osize_I1_J,axiom, % 172.78/172.45 ! [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) ). % 172.78/172.45 % 172.78/172.45 fof(fact_dom__minus,axiom, % 172.78/172.45 ! [V_A_2,T_b,T_a,V_x_2,V_f_2] : % 172.78/172.45 ( hAPP(V_f_2,V_x_2) = c_Option_Ooption_ONone(T_a) % 172.78/172.45 => 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) ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_partition__P,axiom, % 172.78/172.45 ! [V_no_2,V_yes_2,V_xs_2,V_P_2,T_a] : % 172.78/172.45 ( 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) % 172.78/172.45 => ( ! [B_x] : % 172.78/172.45 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_yes_2))) % 172.78/172.45 => hBOOL(hAPP(V_P_2,B_x)) ) % 172.78/172.45 & ! [B_x] : % 172.78/172.45 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_no_2))) % 172.78/172.45 => ~ hBOOL(hAPP(V_P_2,B_x)) ) ) ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_partition_Osimps_I1_J,axiom, % 172.78/172.45 ! [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)) ). % 172.78/172.45 % 172.78/172.45 fof(fact_ran__map__upd,axiom, % 172.78/172.45 ! [V_b_2,T_b,T_a,V_a_2,V_m_2] : % 172.78/172.45 ( hAPP(V_m_2,V_a_2) = c_Option_Ooption_ONone(T_a) % 172.78/172.45 => 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)) ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_map__of__zip__is__None,axiom, % 172.78/172.45 ! [V_x_2,V_ys_2,T_b,V_xs_2,T_a] : % 172.78/172.45 ( 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) % 172.78/172.45 => ( 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) % 172.78/172.45 <=> ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) ) ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_partition_Osimps_I2_J,axiom, % 172.78/172.45 ! [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)) ). % 172.78/172.45 % 172.78/172.45 fof(fact_dom__fun__upd,axiom, % 172.78/172.45 ! [V_x_2,V_f_2,T_b,T_a,V_y_2] : % 172.78/172.45 ( ( V_y_2 = c_Option_Ooption_ONone(T_a) % 172.78/172.45 => 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)))) ) % 172.78/172.45 & ( V_y_2 != c_Option_Ooption_ONone(T_a) % 172.78/172.45 => 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)) ) ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_restrict__complement__singleton__eq,axiom, % 172.78/172.45 ! [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)) ). % 172.78/172.45 % 172.78/172.45 fof(fact_map__of__eq__None__iff,axiom, % 172.78/172.45 ! [V_x_2,V_xys_2,T_a,T_b] : % 172.78/172.45 ( hAPP(hAPP(c_Map_Omap__of(T_b,T_a),V_xys_2),V_x_2) = c_Option_Ooption_ONone(T_a) % 172.78/172.45 <=> ~ 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)))) ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_UNIV__option__conv,axiom, % 172.78/172.45 ! [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)))) ). % 172.78/172.45 % 172.78/172.45 fof(fact_dom__eq__singleton__conv,axiom, % 172.78/172.45 ! [V_x_2,V_f_2,T_b,T_a] : % 172.78/172.45 ( 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))) % 172.78/172.45 <=> ? [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)) ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_fun__upd__None__restrict,axiom, % 172.78/172.45 ! [V_m_2,T_b,V_D_2,V_x_2,T_a] : % 172.78/172.45 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_D_2)) % 172.78/172.45 => 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))))) ) % 172.78/172.45 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),V_D_2)) % 172.78/172.45 => 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) ) ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_lists__IntI,axiom, % 172.78/172.45 ! [V_B_2,V_A_2,V_l_2,T_a] : % 172.78/172.45 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_l_2),c_List_Olists(T_a,V_A_2))) % 172.78/172.45 => ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_l_2),c_List_Olists(T_a,V_B_2))) % 172.78/172.45 => 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)) ) ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_lists__Int__eq,axiom, % 172.78/172.45 ! [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))) ). % 172.78/172.45 % 172.78/172.45 fof(fact_listsp_ONil,axiom, % 172.78/172.45 ! [V_A_2,T_a] : hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),c_List_Olist_ONil(T_a))) ). % 172.78/172.45 % 172.78/172.45 fof(fact_listsp_Oequations_I1_J,axiom, % 172.78/172.45 ! [V_A_2,T_a] : hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),c_List_Olist_ONil(T_a))) ). % 172.78/172.45 % 172.78/172.45 fof(fact_listsp__infI,axiom, % 172.78/172.45 ! [V_B_2,V_l_2,V_A_2,T_a] : % 172.78/172.45 ( hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_l_2)) % 172.78/172.45 => ( hBOOL(hAPP(c_List_Olistsp(T_a,V_B_2),V_l_2)) % 172.78/172.45 => 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)) ) ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_listsp__inf__eq,axiom, % 172.78/172.45 ! [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)) ). % 172.78/172.45 % 172.78/172.45 fof(fact_listsp__conj__eq,axiom, % 172.78/172.45 ! [V_x_2,V_B_2,V_A_2,T_a] : % 172.78/172.45 ( 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)) % 172.78/172.45 <=> ( hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_x_2)) % 172.78/172.45 & hBOOL(hAPP(c_List_Olistsp(T_a,V_B_2),V_x_2)) ) ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_in__listsp__conv__set,axiom, % 172.78/172.45 ! [V_xs_2,V_A_2,T_a] : % 172.78/172.45 ( hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_xs_2)) % 172.78/172.45 <=> ! [B_x] : % 172.78/172.45 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 172.78/172.45 => hBOOL(hAPP(V_A_2,B_x)) ) ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_listsp_Oequations_I2_J,axiom, % 172.78/172.45 ! [V_a2_2,V_a1_2,V_A_2,T_a] : % 172.78/172.45 ( hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),hAPP(hAPP(c_List_Olist_OCons(T_a),V_a1_2),V_a2_2))) % 172.78/172.45 <=> ( hBOOL(hAPP(V_A_2,V_a1_2)) % 172.78/172.45 & hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_a2_2)) ) ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_append__in__listsp__conv,axiom, % 172.78/172.45 ! [V_ys_2,V_xs_2,V_A_2,T_a] : % 172.78/172.45 ( hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2))) % 172.78/172.45 <=> ( hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_xs_2)) % 172.78/172.45 & hBOOL(hAPP(c_List_Olistsp(T_a,V_A_2),V_ys_2)) ) ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_listsp__mono,axiom, % 172.78/172.45 ! [V_B_2,V_A_2,T_a] : % 172.78/172.45 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,tc_HOL_Obool)),V_A_2),V_B_2)) % 172.78/172.45 => 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))) ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_listsp__lists__eq,axiom, % 172.78/172.45 ! [V_x_2,V_A_2,T_a] : % 172.78/172.45 ( 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)) % 172.78/172.45 <=> hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),V_x_2),c_List_Olists(T_a,V_A_2))) ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_,axiom, % 172.78/172.45 ! [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) ). % 172.78/172.45 % 172.78/172.45 fof(fact_product_Osimps_I2_J,axiom, % 172.78/172.45 ! [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)) ). % 172.78/172.45 % 172.78/172.45 fof(fact_product_Osimps_I1_J,axiom, % 172.78/172.45 ! [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)) ). % 172.78/172.45 % 172.78/172.45 fof(fact_distinct__product,axiom, % 172.78/172.45 ! [V_ys,T_b,V_xs,T_a] : % 172.78/172.45 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 172.78/172.45 => ( hBOOL(hAPP(c_List_Odistinct(T_b),V_ys)) % 172.78/172.45 => hBOOL(hAPP(c_List_Odistinct(tc_prod(T_a,T_b)),c_Enum_Oproduct(T_a,T_b,V_xs,V_ys))) ) ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_product__list__set,axiom, % 172.78/172.45 ! [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))) ). % 172.78/172.45 % 172.78/172.45 fof(fact_sublists__powset,axiom, % 172.78/172.45 ! [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)) ). % 172.78/172.45 % 172.78/172.45 fof(fact_length__sublists,axiom, % 172.78/172.45 ! [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)) ). % 172.78/172.45 % 172.78/172.45 fof(fact_sublists_Osimps_I1_J,axiom, % 172.78/172.45 ! [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))) ). % 172.78/172.45 % 172.78/172.45 fof(fact_sublists_Osimps_I2_J,axiom, % 172.78/172.45 ! [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))))) ). % 172.78/172.45 % 172.78/172.45 fof(fact_distinct__set__sublists,axiom, % 172.78/172.45 ! [V_xs_2,T_a] : % 172.78/172.45 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 172.78/172.45 => 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)))) ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_set__n__lists,axiom, % 172.78/172.45 ! [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)))) ). % 172.78/172.45 % 172.78/172.45 fof(fact_enum__the__def,axiom, % 172.78/172.45 ! [V_P_2,T_a] : c_Enum_Oenum__the(T_a,V_P_2) = c_HOL_OThe(T_a,V_P_2) ). % 172.78/172.45 % 172.78/172.45 fof(fact_distinct__n__lists,axiom, % 172.78/172.45 ! [V_n,V_xs,T_a] : % 172.78/172.45 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 172.78/172.45 => hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(T_a)),c_Enum_On__lists(T_a,V_n,V_xs))) ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_n__lists_Osimps_I1_J,axiom, % 172.78/172.45 ! [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))) ). % 172.78/172.45 % 172.78/172.45 fof(fact_n__lists__Nil,axiom, % 172.78/172.45 ! [T_a,V_n] : % 172.78/172.45 ( ( V_n = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 172.78/172.45 => 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))) ) % 172.78/172.45 & ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 172.78/172.45 => c_Enum_On__lists(T_a,V_n,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(tc_List_Olist(T_a)) ) ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_length__n__lists,axiom, % 172.78/172.45 ! [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) ). % 172.78/172.45 % 172.78/172.45 fof(fact_length__n__lists__elem,axiom, % 172.78/172.45 ! [V_xs_2,V_n_2,V_ys_2,T_a] : % 172.78/172.45 ( 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)))) % 172.78/172.45 => hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys_2) = V_n_2 ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_full__small__int__def,axiom, % 172.78/172.45 ! [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))) ). % 172.78/172.45 % 172.78/172.45 fof(fact_map__of__zip__enum__inject,axiom, % 172.78/172.45 ! [V_ys_2,V_xs_2,T_a,T_b] : % 172.78/172.45 ( ( class_Enum_Oenum(T_b) % 172.78/172.45 & class_Enum_Oenum(T_a) ) % 172.78/172.45 => ( 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)) % 172.78/172.45 => ( 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)) % 172.78/172.45 => ( 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))) % 172.78/172.45 => V_xs_2 = V_ys_2 ) ) ) ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_enum__option__def,axiom, % 172.78/172.45 ! [T_a] : % 172.78/172.45 ( class_Enum_Oenum(T_a) % 172.78/172.45 => 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))) ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_enum__distinct,axiom, % 172.78/172.45 ! [T_a] : % 172.78/172.45 ( class_Enum_Oenum(T_a) % 172.78/172.45 => hBOOL(hAPP(c_List_Odistinct(T_a),c_Enum_Oenum__class_Oenum(T_a))) ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_enum__prod__def,axiom, % 172.78/172.45 ! [T_b,T_a] : % 172.78/172.45 ( ( class_Enum_Oenum(T_a) % 172.78/172.45 & class_Enum_Oenum(T_b) ) % 172.78/172.45 => 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)) ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_in__enum,axiom, % 172.78/172.45 ! [V_x_2,T_a] : % 172.78/172.45 ( class_Enum_Oenum(T_a) % 172.78/172.45 => hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_Enum_Oenum__class_Oenum(T_a)))) ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_UNIV__enum,axiom, % 172.78/172.45 ! [T_a] : % 172.78/172.45 ( class_Enum_Oenum(T_a) % 172.78/172.45 => 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)) ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_enum__UNIV,axiom, % 172.78/172.45 ! [T_a] : % 172.78/172.45 ( class_Enum_Oenum(T_a) % 172.78/172.45 => 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)) ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_enum__fun__code,axiom, % 172.78/172.45 ! [T_b,T_a] : % 172.78/172.45 ( ( class_Enum_Oenum(T_a) % 172.78/172.45 & class_HOL_Oequal(T_a) % 172.78/172.45 & class_Enum_Oenum(T_b) ) % 172.78/172.45 => 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))) ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_enum__fun__def,axiom, % 172.78/172.45 ! [T_b,T_a] : % 172.78/172.45 ( ( class_Enum_Oenum(T_a) % 172.78/172.45 & class_Enum_Oenum(T_b) ) % 172.78/172.45 => 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))) ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_all__n__lists__def,axiom, % 172.78/172.45 ! [V_n_2,V_P_2,T_a] : % 172.78/172.45 ( class_Enum_Oenum(T_a) % 172.78/172.45 => ( c_Enum_Oall__n__lists(T_a,V_P_2,V_n_2) % 172.78/172.45 <=> ! [B_x] : % 172.78/172.45 ( 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))))) % 172.78/172.45 => hBOOL(hAPP(V_P_2,B_x)) ) ) ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_ex__n__lists__def,axiom, % 172.78/172.45 ! [V_n_2,V_P_2,T_a] : % 172.78/172.45 ( class_Enum_Oenum(T_a) % 172.78/172.45 => ( c_Enum_Oex__n__lists(T_a,V_P_2,V_n_2) % 172.78/172.45 <=> ? [B_x] : % 172.78/172.45 ( 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))))) % 172.78/172.45 & hBOOL(hAPP(V_P_2,B_x)) ) ) ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_enum__ex__fun__code,axiom, % 172.78/172.45 ! [V_P_2,T_a,T_b] : % 172.78/172.45 ( ( class_Enum_Oenum(T_b) % 172.78/172.45 & class_Enum_Oenum(T_a) % 172.78/172.45 & class_HOL_Oequal(T_a) ) % 172.78/172.45 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_fun(T_a,T_b)),V_P_2)) % 172.78/172.45 <=> 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))) ) ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_enum__all__fun__code,axiom, % 172.78/172.45 ! [V_P_2,T_a,T_b] : % 172.78/172.45 ( ( class_Enum_Oenum(T_b) % 172.78/172.45 & class_Enum_Oenum(T_a) % 172.78/172.45 & class_HOL_Oequal(T_a) ) % 172.78/172.45 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_fun(T_a,T_b)),V_P_2)) % 172.78/172.45 <=> 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))) ) ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_all__code,axiom, % 172.78/172.45 ! [V_P_2,T_a] : % 172.78/172.45 ( class_Enum_Oenum(T_a) % 172.78/172.45 => ( ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) % 172.78/172.45 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_a),V_P_2)) ) ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_exists__code,axiom, % 172.78/172.45 ! [V_P_2,T_a] : % 172.78/172.45 ( class_Enum_Oenum(T_a) % 172.78/172.45 => ( ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) % 172.78/172.45 <=> hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_a),V_P_2)) ) ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_enum__all,axiom, % 172.78/172.45 ! [V_P_2,T_a] : % 172.78/172.45 ( class_Enum_Oenum(T_a) % 172.78/172.45 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(T_a),V_P_2)) % 172.78/172.45 <=> ! [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ) ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_enum__ex,axiom, % 172.78/172.45 ! [V_P_2,T_a] : % 172.78/172.45 ( class_Enum_Oenum(T_a) % 172.78/172.45 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(T_a),V_P_2)) % 172.78/172.45 <=> ? [B_x1] : hBOOL(hAPP(V_P_2,B_x1)) ) ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_enum__ex__prod__def,axiom, % 172.78/172.45 ! [V_P_2,T_a,T_b] : % 172.78/172.45 ( ( class_Enum_Oenum(T_b) % 172.78/172.45 & class_Enum_Oenum(T_a) ) % 172.78/172.45 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_prod(T_a,T_b)),V_P_2)) % 172.78/172.45 <=> 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))))) ) ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_enum__all__prod__def,axiom, % 172.78/172.45 ! [V_P_2,T_a,T_b] : % 172.78/172.45 ( ( class_Enum_Oenum(T_b) % 172.78/172.45 & class_Enum_Oenum(T_a) ) % 172.78/172.45 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_prod(T_a,T_b)),V_P_2)) % 172.78/172.45 <=> 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))))) ) ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_enum__ex__option__def,axiom, % 172.78/172.45 ! [V_P_2,T_a] : % 172.78/172.45 ( class_Enum_Oenum(T_a) % 172.78/172.45 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_Option_Ooption(T_a)),V_P_2)) % 172.78/172.45 <=> ( hBOOL(hAPP(V_P_2,c_Option_Ooption_ONone(T_a))) % 172.78/172.45 | 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)))) ) ) ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_enum__all__option__def,axiom, % 172.78/172.45 ! [V_P_2,T_a] : % 172.78/172.45 ( class_Enum_Oenum(T_a) % 172.78/172.45 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_Option_Ooption(T_a)),V_P_2)) % 172.78/172.45 <=> ( hBOOL(hAPP(V_P_2,c_Option_Ooption_ONone(T_a))) % 172.78/172.45 & 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)))) ) ) ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_order__fun_I1_J,axiom, % 172.78/172.45 ! [V_g_2,V_f_2,T_a,T_b] : % 172.78/172.45 ( ( class_Orderings_Oorder(T_b) % 172.78/172.45 & class_Enum_Oenum(T_a) ) % 172.78/172.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_f_2),V_g_2)) % 172.78/172.45 <=> 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))) ) ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_order__fun_I2_J,axiom, % 172.78/172.45 ! [V_g_2,V_f_2,T_a,T_b] : % 172.78/172.45 ( ( class_Orderings_Oorder(T_b) % 172.78/172.45 & class_Enum_Oenum(T_a) ) % 172.78/172.45 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_fun(T_a,T_b)),V_f_2),V_g_2)) % 172.78/172.45 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_fun(T_a,T_b)),V_f_2),V_g_2)) % 172.78/172.45 & 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)))) ) ) ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_enum__all__fun__def,axiom, % 172.78/172.45 ! [V_P_2,T_a,T_b] : % 172.78/172.45 ( ( class_Enum_Oenum(T_b) % 172.78/172.45 & class_Enum_Oenum(T_a) ) % 172.78/172.45 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__all(tc_fun(T_a,T_b)),V_P_2)) % 172.78/172.45 <=> 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))) ) ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_enum__ex__fun__def,axiom, % 172.78/172.45 ! [V_P_2,T_a,T_b] : % 172.78/172.45 ( ( class_Enum_Oenum(T_b) % 172.78/172.45 & class_Enum_Oenum(T_a) ) % 172.78/172.45 => ( hBOOL(hAPP(c_Enum_Oenum__class_Oenum__ex(tc_fun(T_a,T_b)),V_P_2)) % 172.78/172.45 <=> 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))) ) ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_small_H_Osimps,axiom, % 172.78/172.45 ! [V_f_2,V_i_2,V_d_2] : % 172.78/172.45 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2)) % 172.78/172.45 => c_Smallcheck_Osmall_H(V_f_2,V_d_2,V_i_2) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)) ) % 172.78/172.45 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2)) % 172.78/172.45 => 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)) ) ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_map__of__zip__enum__is__Some,axiom, % 172.78/172.45 ! [V_x,V_ys,T_b,T_a] : % 172.78/172.45 ( class_Enum_Oenum(T_a) % 172.78/172.45 => ( 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)) % 172.78/172.45 => ? [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) ) ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_small_H_Opsimps,axiom, % 172.78/172.45 ! [V_i_2,V_d_2,V_f_2] : % 172.78/172.45 ( 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)))) % 172.78/172.45 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2)) % 172.78/172.45 => c_Smallcheck_Osmall_H(V_f_2,V_d_2,V_i_2) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)) ) % 172.78/172.45 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2)) % 172.78/172.45 => 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)) ) ) ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_small__int__def,axiom, % 172.78/172.45 ! [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))) ). % 172.78/172.45 % 172.78/172.45 fof(fact_small__prod__def,axiom, % 172.78/172.45 ! [V_d_2,V_f_2,T_a,T_b] : % 172.78/172.45 ( ( class_Smallcheck_Osmall(T_b) % 172.78/172.45 & class_Smallcheck_Osmall(T_a) ) % 172.78/172.45 => 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) ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_small_H_Opinduct,axiom, % 172.78/172.45 ! [V_P_2,V_a2_2,V_a1_2,V_a0_2] : % 172.78/172.45 ( 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)))) % 172.78/172.45 => ( ! [B_f,B_d,B_i] : % 172.78/172.45 ( 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)))) % 172.78/172.45 => ( ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),B_d),B_i)) % 172.78/172.45 => ( hAPP(B_f,B_i) = c_Option_Ooption_ONone(tc_List_Olist(tc_Code__Evaluation_Oterm)) % 172.78/172.45 => 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)))) ) ) % 172.78/172.45 => hBOOL(hAPP(hAPP(hAPP(V_P_2,B_f),B_d),B_i)) ) ) % 172.78/172.45 => hBOOL(hAPP(hAPP(hAPP(V_P_2,V_a0_2),V_a1_2),V_a2_2)) ) ) ). % 172.78/172.45 % 172.78/172.45 fof(fact_list__all2__def,axiom, % 172.78/172.45 ! [V_ys_2,V_xs_2,V_P_2,T_b,T_a] : % 172.78/172.45 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) % 172.78/172.45 <=> ( 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) % 172.78/172.45 & ! [B_x] : % 172.78/172.45 ( 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)))) % 172.78/172.45 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),V_P_2),B_x)) ) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_list__all2__lengthD,axiom, % 172.78/172.46 ! [V_ys_2,V_xs_2,V_P_2,T_b,T_a] : % 172.78/172.46 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) % 172.78/172.46 => 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) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_list__all2__dropI,axiom, % 172.78/172.46 ! [V_n_2,V_bs_2,V_as_2,V_P_2,T_b,T_a] : % 172.78/172.46 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_as_2,V_bs_2) % 172.78/172.46 => 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)) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_list__all2__eq,axiom, % 172.78/172.46 ! [T_a,V_ys_2,V_xs_2] : % 172.78/172.46 ( V_xs_2 = V_ys_2 % 172.78/172.46 <=> c_List_Olist__all2(T_a,T_a,c_fequal,V_xs_2,V_ys_2) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_list__all2__takeI,axiom, % 172.78/172.46 ! [V_n_2,V_ys_2,V_xs_2,V_P_2,T_b,T_a] : % 172.78/172.46 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) % 172.78/172.46 => 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)) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_list__all2__Nil,axiom, % 172.78/172.46 ! [V_ys_2,V_P_2,T_b,T_a] : % 172.78/172.46 ( c_List_Olist__all2(T_a,T_b,V_P_2,c_List_Olist_ONil(T_a),V_ys_2) % 172.78/172.46 <=> V_ys_2 = c_List_Olist_ONil(T_b) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_list__all2__Nil2,axiom, % 172.78/172.46 ! [V_xs_2,V_P_2,T_b,T_a] : % 172.78/172.46 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,c_List_Olist_ONil(T_b)) % 172.78/172.46 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_list__all2__appendI,axiom, % 172.78/172.46 ! [V_d_2,V_ca_2,V_b_2,V_a_2,V_P_2,T_b,T_a] : % 172.78/172.46 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_a_2,V_b_2) % 172.78/172.46 => ( c_List_Olist__all2(T_a,T_b,V_P_2,V_ca_2,V_d_2) % 172.78/172.46 => c_List_Olist__all2(T_a,T_b,V_P_2,hAPP(hAPP(c_List_Oappend(T_a),V_a_2),V_ca_2),hAPP(hAPP(c_List_Oappend(T_b),V_b_2),V_d_2)) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_list__all2__append,axiom, % 172.78/172.46 ! [V_vs_2,V_us_2,V_P_2,V_ys_2,T_b,V_xs_2,T_a] : % 172.78/172.46 ( 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) % 172.78/172.46 => ( 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)) % 172.78/172.46 <=> ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) % 172.78/172.46 & c_List_Olist__all2(T_a,T_b,V_P_2,V_us_2,V_vs_2) ) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_list__all2__map2,axiom, % 172.78/172.46 ! [V_bs_2,V_f_2,T_c,V_as_2,V_P_2,T_b,T_a] : % 172.78/172.46 ( 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)) % 172.78/172.46 <=> 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) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_list__all2__map1,axiom, % 172.78/172.46 ! [V_bs_2,V_as_2,V_f_2,T_c,V_P_2,T_b,T_a] : % 172.78/172.46 ( 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) % 172.78/172.46 <=> 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) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_list__all2__Cons,axiom, % 172.78/172.46 ! [V_ys_2,V_y_2,V_xs_2,V_x_2,V_P_2,T_b,T_a] : % 172.78/172.46 ( 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)) % 172.78/172.46 <=> ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2)) % 172.78/172.46 & c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_list__all2__nthD2,axiom, % 172.78/172.46 ! [V_p_2,V_ys_2,V_xs_2,V_P_2,T_b,T_a] : % 172.78/172.46 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) % 172.78/172.46 => ( 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))) % 172.78/172.46 => 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))) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_list__all2__nthD,axiom, % 172.78/172.46 ! [V_p_2,V_ys_2,V_xs_2,V_P_2,T_b,T_a] : % 172.78/172.46 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) % 172.78/172.46 => ( 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))) % 172.78/172.46 => 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))) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_list__all2__conv__all__nth,axiom, % 172.78/172.46 ! [V_ys_2,V_xs_2,V_P_2,T_b,T_a] : % 172.78/172.46 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) % 172.78/172.46 <=> ( 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) % 172.78/172.46 & ! [B_i] : % 172.78/172.46 ( 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))) % 172.78/172.46 => 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))) ) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_list__all2__update__cong2,axiom, % 172.78/172.46 ! [V_i_2,V_y_2,V_x_2,V_ys_2,V_xs_2,V_P_2,T_b,T_a] : % 172.78/172.46 ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) % 172.78/172.46 => ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2)) % 172.78/172.46 => ( 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))) % 172.78/172.46 => 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)) ) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_list__all2__update__cong,axiom, % 172.78/172.46 ! [V_y_2,V_x_2,V_ys_2,V_P_2,T_b,V_xs_2,T_a,V_i_2] : % 172.78/172.46 ( 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))) % 172.78/172.46 => ( c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) % 172.78/172.46 => ( hBOOL(hAPP(hAPP(V_P_2,V_x_2),V_y_2)) % 172.78/172.46 => 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)) ) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_list__all2I,axiom, % 172.78/172.46 ! [V_P_2,V_b_2,V_a_2,T_b,T_a] : % 172.78/172.46 ( ! [B_x] : % 172.78/172.46 ( 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)))) % 172.78/172.46 => hBOOL(hAPP(hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_b,tc_HOL_Obool),V_P_2),B_x)) ) % 172.78/172.46 => ( 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) % 172.78/172.46 => c_List_Olist__all2(T_a,T_b,V_P_2,V_a_2,V_b_2) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_all__nth__imp__all__set,axiom, % 172.78/172.46 ! [V_x_2,V_P_2,V_xs_2,T_a] : % 172.78/172.46 ( ! [B_i] : % 172.78/172.46 ( 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))) % 172.78/172.46 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i))) ) % 172.78/172.46 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 172.78/172.46 => hBOOL(hAPP(V_P_2,V_x_2)) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_body__def,axiom, % 172.78/172.46 c_Com_Obody = hAPP(c_Map_Omap__of(tc_Com_Opname,tc_Com_Ocom),c_Com_Obodies) ). % 172.78/172.46 % 172.78/172.46 fof(fact_fun__left__comm_Ofold__set__remdups,axiom, % 172.78/172.46 ! [V_xs_2,V_y_2,V_f_2,T_b,T_a] : % 172.78/172.46 ( c_Finite__Set_Ofun__left__comm(T_a,T_b,V_f_2) % 172.78/172.46 => 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)) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_distinct__remdups,axiom, % 172.78/172.46 ! [V_xs,T_a] : hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oremdups(T_a,V_xs))) ). % 172.78/172.46 % 172.78/172.46 fof(fact_length__remdups__leq,axiom, % 172.78/172.46 ! [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))) ). % 172.78/172.46 % 172.78/172.46 fof(fact_remove1__remdups,axiom, % 172.78/172.46 ! [V_x,V_xs,T_a] : % 172.78/172.46 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 172.78/172.46 => 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)) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_remdups__id__iff__distinct,axiom, % 172.78/172.46 ! [V_xs_2,T_a] : % 172.78/172.46 ( c_List_Oremdups(T_a,V_xs_2) = V_xs_2 % 172.78/172.46 <=> hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_distinct__remdups__id,axiom, % 172.78/172.46 ! [V_xs,T_a] : % 172.78/172.46 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 172.78/172.46 => c_List_Oremdups(T_a,V_xs) = V_xs ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_length__remdups__eq,axiom, % 172.78/172.46 ! [V_xs_2,T_a] : % 172.78/172.46 ( 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) % 172.78/172.46 <=> c_List_Oremdups(T_a,V_xs_2) = V_xs_2 ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_set__remdups,axiom, % 172.78/172.46 ! [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) ). % 172.78/172.46 % 172.78/172.46 fof(fact_remdups__remdups,axiom, % 172.78/172.46 ! [V_xs,T_a] : c_List_Oremdups(T_a,c_List_Oremdups(T_a,V_xs)) = c_List_Oremdups(T_a,V_xs) ). % 172.78/172.46 % 172.78/172.46 fof(fact_remdups_Osimps_I1_J,axiom, % 172.78/172.46 ! [T_a] : c_List_Oremdups(T_a,c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 172.78/172.46 % 172.78/172.46 fof(fact_remdups__eq__nil__right__iff,axiom, % 172.78/172.46 ! [V_x_2,T_a] : % 172.78/172.46 ( c_List_Olist_ONil(T_a) = c_List_Oremdups(T_a,V_x_2) % 172.78/172.46 <=> V_x_2 = c_List_Olist_ONil(T_a) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_remdups__eq__nil__iff,axiom, % 172.78/172.46 ! [V_x_2,T_a] : % 172.78/172.46 ( c_List_Oremdups(T_a,V_x_2) = c_List_Olist_ONil(T_a) % 172.78/172.46 <=> V_x_2 = c_List_Olist_ONil(T_a) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_remdups__map__remdups,axiom, % 172.78/172.46 ! [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)) ). % 172.78/172.46 % 172.78/172.46 fof(fact_remdups_Osimps_I2_J,axiom, % 172.78/172.46 ! [V_xs_2,V_x_2,T_a] : % 172.78/172.46 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 172.78/172.46 => 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) ) % 172.78/172.46 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 172.78/172.46 => 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)) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_length__remdups__card__conv,axiom, % 172.78/172.46 ! [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)) ). % 172.78/172.46 % 172.78/172.46 fof(fact_length__remdups__concat,axiom, % 172.78/172.46 ! [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))) ). % 172.78/172.46 % 172.78/172.46 fof(fact_sorted__list__of__set__sort__remdups,axiom, % 172.78/172.46 ! [V_xs_2,T_a] : % 172.78/172.46 ( class_Orderings_Olinorder(T_a) % 172.78/172.46 => 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)) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_concat_Osimps_I2_J,axiom, % 172.78/172.46 ! [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)) ). % 172.78/172.46 % 172.78/172.46 fof(fact_map__concat,axiom, % 172.78/172.46 ! [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)) ). % 172.78/172.46 % 172.78/172.46 fof(fact_Nil__eq__concat__conv,axiom, % 172.78/172.46 ! [V_xss_2,T_a] : % 172.78/172.46 ( c_List_Olist_ONil(T_a) = c_List_Oconcat(T_a,V_xss_2) % 172.78/172.46 <=> ! [B_x] : % 172.78/172.46 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xss_2))) % 172.78/172.46 => B_x = c_List_Olist_ONil(T_a) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_concat__eq__Nil__conv,axiom, % 172.78/172.46 ! [V_xss_2,T_a] : % 172.78/172.46 ( c_List_Oconcat(T_a,V_xss_2) = c_List_Olist_ONil(T_a) % 172.78/172.46 <=> ! [B_x] : % 172.78/172.46 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xss_2))) % 172.78/172.46 => B_x = c_List_Olist_ONil(T_a) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_sort__key__simps_I1_J,axiom, % 172.78/172.46 ! [V_f_2,T_a,T_b] : % 172.78/172.46 ( class_Orderings_Olinorder(T_b) % 172.78/172.46 => 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) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_concat_Osimps_I1_J,axiom, % 172.78/172.46 ! [T_a] : c_List_Oconcat(T_a,c_List_Olist_ONil(tc_List_Olist(T_a))) = c_List_Olist_ONil(T_a) ). % 172.78/172.46 % 172.78/172.46 fof(fact_foldl__conv__concat,axiom, % 172.78/172.46 ! [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)) ). % 172.78/172.46 % 172.78/172.46 fof(fact_concat__conv__foldl,axiom, % 172.78/172.46 ! [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) ). % 172.78/172.46 % 172.78/172.46 fof(fact_set__sort,axiom, % 172.78/172.46 ! [V_xs_2,V_f_2,T_a,T_b] : % 172.78/172.46 ( class_Orderings_Olinorder(T_b) % 172.78/172.46 => 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) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_length__sort,axiom, % 172.78/172.46 ! [V_xs_2,V_f_2,T_a,T_b] : % 172.78/172.46 ( class_Orderings_Olinorder(T_b) % 172.78/172.46 => 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) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_distinct__sort,axiom, % 172.78/172.46 ! [V_xs_2,V_f_2,T_a,T_b] : % 172.78/172.46 ( class_Orderings_Olinorder(T_b) % 172.78/172.46 => ( hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Olinorder__class_Osort__key(T_a,T_b,V_f_2,V_xs_2))) % 172.78/172.46 <=> hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_length__concat,axiom, % 172.78/172.46 ! [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)) ). % 172.78/172.46 % 172.78/172.46 fof(fact_set__concat,axiom, % 172.78/172.46 ! [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)) ). % 172.78/172.46 % 172.78/172.46 fof(fact_sort__key__simps_I2_J,axiom, % 172.78/172.46 ! [V_xs_2,V_x_2,V_f_2,T_a,T_b] : % 172.78/172.46 ( class_Orderings_Olinorder(T_b) % 172.78/172.46 => 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)) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_concat__append,axiom, % 172.78/172.46 ! [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)) ). % 172.78/172.46 % 172.78/172.46 fof(fact_sort__foldl__insort,axiom, % 172.78/172.46 ! [V_xs_2,T_a] : % 172.78/172.46 ( class_Orderings_Olinorder(T_a) % 172.78/172.46 => 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) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_concat__eq__concat__iff,axiom, % 172.78/172.46 ! [V_ys_2,V_xs_2,T_a] : % 172.78/172.46 ( ! [B_x] : % 172.78/172.46 ( 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)))) % 172.78/172.46 => 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)) ) % 172.78/172.46 => ( 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) % 172.78/172.46 => ( c_List_Oconcat(T_a,V_xs_2) = c_List_Oconcat(T_a,V_ys_2) % 172.78/172.46 <=> V_xs_2 = V_ys_2 ) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_concat__injective,axiom, % 172.78/172.46 ! [V_ys_2,V_xs_2,T_a] : % 172.78/172.46 ( c_List_Oconcat(T_a,V_xs_2) = c_List_Oconcat(T_a,V_ys_2) % 172.78/172.46 => ( 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) % 172.78/172.46 => ( ! [B_x] : % 172.78/172.46 ( 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)))) % 172.78/172.46 => 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)) ) % 172.78/172.46 => V_xs_2 = V_ys_2 ) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_concat__map__singleton,axiom, % 172.78/172.46 ! [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) ). % 172.78/172.46 % 172.78/172.46 fof(fact_n__lists_Osimps_I2_J,axiom, % 172.78/172.46 ! [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))) ). % 172.78/172.46 % 172.78/172.46 fof(fact_transpose_Osimps_I3_J,axiom, % 172.78/172.46 ! [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))))) ). % 172.78/172.46 % 172.78/172.46 fof(fact_transpose__aux__filter__head,axiom, % 172.78/172.46 ! [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)) ). % 172.78/172.46 % 172.78/172.46 fof(fact_filter__concat,axiom, % 172.78/172.46 ! [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)) ). % 172.78/172.46 % 172.78/172.46 fof(fact_filter__sort,axiom, % 172.78/172.46 ! [V_xs_2,V_f_2,V_P_2,T_a,T_b] : % 172.78/172.46 ( class_Orderings_Olinorder(T_b) % 172.78/172.46 => 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)) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_transpose_Osimps_I2_J,axiom, % 172.78/172.46 ! [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) ). % 172.78/172.46 % 172.78/172.46 fof(fact_distinct__filter,axiom, % 172.78/172.46 ! [V_P_2,V_xs_2,T_a] : % 172.78/172.46 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 172.78/172.46 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2))) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_partition__filter2,axiom, % 172.78/172.46 ! [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) ). % 172.78/172.46 % 172.78/172.46 fof(fact_length__filter__le,axiom, % 172.78/172.46 ! [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))) ). % 172.78/172.46 % 172.78/172.46 fof(fact_sum__length__filter__compl,axiom, % 172.78/172.46 ! [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) ). % 172.78/172.46 % 172.78/172.46 fof(fact_filter__id__conv,axiom, % 172.78/172.46 ! [V_xs_2,V_P_2,T_a] : % 172.78/172.46 ( hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2) = V_xs_2 % 172.78/172.46 <=> ! [B_x] : % 172.78/172.46 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 172.78/172.46 => hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_filter__is__subset,axiom, % 172.78/172.46 ! [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))) ). % 172.78/172.46 % 172.78/172.46 fof(fact_filter__insort__triv,axiom, % 172.78/172.46 ! [V_xs_2,V_f_2,T_a,V_x_2,V_P_2,T_b] : % 172.78/172.46 ( class_Orderings_Olinorder(T_b) % 172.78/172.46 => ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 172.78/172.46 => 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) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_filter__filter,axiom, % 172.78/172.46 ! [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) ). % 172.78/172.46 % 172.78/172.46 fof(fact_remove1__filter__not,axiom, % 172.78/172.46 ! [V_xs_2,T_a,V_x_2,V_P_2] : % 172.78/172.46 ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 172.78/172.46 => 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) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_filter__remove1,axiom, % 172.78/172.46 ! [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)) ). % 172.78/172.46 % 172.78/172.46 fof(fact_partition__filter1,axiom, % 172.78/172.46 ! [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) ). % 172.78/172.46 % 172.78/172.46 fof(fact_transpose_Osimps_I1_J,axiom, % 172.78/172.46 ! [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)) ). % 172.78/172.46 % 172.78/172.46 fof(fact_filter_Osimps_I1_J,axiom, % 172.78/172.46 ! [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) ). % 172.78/172.46 % 172.78/172.46 fof(fact_filter__append,axiom, % 172.78/172.46 ! [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)) ). % 172.78/172.46 % 172.78/172.46 fof(fact_filter__empty__conv,axiom, % 172.78/172.46 ! [V_xs_2,V_P_2,T_a] : % 172.78/172.46 ( hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2) = c_List_Olist_ONil(T_a) % 172.78/172.46 <=> ! [B_x] : % 172.78/172.46 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 172.78/172.46 => ~ hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_filter_Osimps_I2_J,axiom, % 172.78/172.46 ! [V_xs_2,T_a,V_x_2,V_P_2] : % 172.78/172.46 ( ( hBOOL(hAPP(V_P_2,V_x_2)) % 172.78/172.46 => 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)) ) % 172.78/172.46 & ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 172.78/172.46 => 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) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_filter__map,axiom, % 172.78/172.46 ! [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)) ). % 172.78/172.46 % 172.78/172.46 fof(fact_remdups__filter,axiom, % 172.78/172.46 ! [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)) ). % 172.78/172.46 % 172.78/172.46 fof(fact_nth__transpose,axiom, % 172.78/172.46 ! [V_xs_2,T_a,V_i_2] : % 172.78/172.46 ( 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)))) % 172.78/172.46 => 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)) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_transpose__map__map,axiom, % 172.78/172.46 ! [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)) ). % 172.78/172.46 % 172.78/172.46 fof(fact_set__filter,axiom, % 172.78/172.46 ! [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)) ). % 172.78/172.46 % 172.78/172.46 fof(fact_length__filter__map,axiom, % 172.78/172.46 ! [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)) ). % 172.78/172.46 % 172.78/172.46 fof(fact_length__filter__less,axiom, % 172.78/172.46 ! [V_P_2,V_xs_2,V_x_2,T_a] : % 172.78/172.46 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 172.78/172.46 => ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 172.78/172.46 => 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))) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_partition__filter__conv,axiom, % 172.78/172.46 ! [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)) ). % 172.78/172.46 % 172.78/172.46 fof(fact_set__minus__filter__out,axiom, % 172.78/172.46 ! [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)) ). % 172.78/172.46 % 172.78/172.46 fof(fact_filter__in__sublist,axiom, % 172.78/172.46 ! [V_s_2,V_xs_2,T_a] : % 172.78/172.46 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 172.78/172.46 => 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) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_transpose__empty,axiom, % 172.78/172.46 ! [V_xs_2,T_a] : % 172.78/172.46 ( c_List_Otranspose(T_a,V_xs_2) = c_List_Olist_ONil(tc_List_Olist(T_a)) % 172.78/172.46 <=> ! [B_x] : % 172.78/172.46 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_x),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xs_2))) % 172.78/172.46 => B_x = c_List_Olist_ONil(T_a) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_length__filter__conv__card,axiom, % 172.78/172.46 ! [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))))) ). % 172.78/172.46 % 172.78/172.46 fof(fact_transpose__aux__filter__tail,axiom, % 172.78/172.46 ! [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)) ). % 172.78/172.46 % 172.78/172.46 fof(fact_transpose_Opsimps_I3_J,axiom, % 172.78/172.46 ! [V_xss_2,V_xs_2,V_x_2,T_a] : % 172.78/172.46 ( 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))) % 172.78/172.46 => 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))))) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_map__filter__def,axiom, % 172.78/172.46 ! [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)) ). % 172.78/172.46 % 172.78/172.46 fof(fact_map__filter__simps_I2_J,axiom, % 172.78/172.46 ! [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) ). % 172.78/172.46 % 172.78/172.46 fof(fact_map__of__filter__in,axiom, % 172.78/172.46 ! [V_P_2,V_z_2,V_k_2,V_xs_2,T_a,T_b] : % 172.78/172.46 ( 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) % 172.78/172.46 => ( hBOOL(hAPP(hAPP(V_P_2,V_k_2),V_z_2)) % 172.78/172.46 => 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) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_map__filter__simps_I1_J,axiom, % 172.78/172.46 ! [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)) ). % 172.78/172.46 % 172.78/172.46 fof(fact_sublist__shift__lemma__Suc,axiom, % 172.78/172.46 ! [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)))) ). % 172.78/172.46 % 172.78/172.46 fof(fact_pick__drop__zero,axiom, % 172.78/172.46 ! [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) ). % 172.78/172.46 % 172.78/172.46 fof(fact_select__weigth__drop__zero,axiom, % 172.78/172.46 ! [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) ). % 172.78/172.46 % 172.78/172.46 fof(fact_transpose_Opsimps_I1_J,axiom, % 172.78/172.46 ! [T_a] : % 172.78/172.46 ( 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)))) % 172.78/172.46 => c_List_Otranspose(T_a,c_List_Olist_ONil(tc_List_Olist(T_a))) = c_List_Olist_ONil(tc_List_Olist(T_a)) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_map__filter__map__filter,axiom, % 172.78/172.46 ! [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) ). % 172.78/172.46 % 172.78/172.46 fof(fact_transpose_Opsimps_I2_J,axiom, % 172.78/172.46 ! [V_xss_2,T_a] : % 172.78/172.46 ( 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))) % 172.78/172.46 => 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) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_transpose__max__length,axiom, % 172.78/172.46 ! [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)) ). % 172.78/172.46 % 172.78/172.46 fof(fact_transpose__aux__max,axiom, % 172.78/172.46 ! [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)))) ). % 172.78/172.46 % 172.78/172.46 fof(fact_foldr__conv__foldl,axiom, % 172.78/172.46 ! [V_a_2,V_xs_2,T_a] : % 172.78/172.46 ( class_Groups_Oab__semigroup__add(T_a) % 172.78/172.46 => 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) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_foldr_Osimps_I1_J,axiom, % 172.78/172.46 ! [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 ). % 172.78/172.46 % 172.78/172.46 fof(fact_foldr__append,axiom, % 172.78/172.46 ! [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)) ). % 172.78/172.46 % 172.78/172.46 fof(fact_foldr_Osimps_I2_J,axiom, % 172.78/172.46 ! [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)) ). % 172.78/172.46 % 172.78/172.46 fof(fact_foldr__map,axiom, % 172.78/172.46 ! [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) ). % 172.78/172.46 % 172.78/172.46 fof(fact_foldl__foldr1,axiom, % 172.78/172.46 ! [V_xs_2,T_a] : % 172.78/172.46 ( class_Groups_Omonoid__add(T_a) % 172.78/172.46 => 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)) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_foldl__foldr1__lemma,axiom, % 172.78/172.46 ! [V_xs_2,V_a_2,T_a] : % 172.78/172.46 ( class_Groups_Omonoid__add(T_a) % 172.78/172.46 => 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))) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_length__transpose,axiom, % 172.78/172.46 ! [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)) ). % 172.78/172.46 % 172.78/172.46 fof(fact_sublist__def,axiom, % 172.78/172.46 ! [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))))) ). % 172.78/172.46 % 172.78/172.46 fof(fact_sublist__shift__lemma,axiom, % 172.78/172.46 ! [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))))) ). % 172.78/172.46 % 172.78/172.46 fof(fact_atLeastLessThan__upt,axiom, % 172.78/172.46 ! [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)) ). % 172.78/172.46 % 172.78/172.46 fof(fact_set__upt,axiom, % 172.78/172.46 ! [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) ). % 172.78/172.46 % 172.78/172.46 fof(fact_upt__conv__Cons,axiom, % 172.78/172.46 ! [V_j,V_i] : % 172.78/172.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 172.78/172.46 => 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)) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_upt__rec,axiom, % 172.78/172.46 ! [V_j,V_i] : % 172.78/172.46 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 172.78/172.46 => 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)) ) % 172.78/172.46 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 172.78/172.46 => c_List_Oupt(V_i,V_j) = c_List_Olist_ONil(tc_Nat_Onat) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_upt__Suc__append,axiom, % 172.78/172.46 ! [V_j,V_i] : % 172.78/172.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 172.78/172.46 => 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))) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_upt__Suc,axiom, % 172.78/172.46 ! [V_j,V_i] : % 172.78/172.46 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 172.78/172.46 => 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))) ) % 172.78/172.46 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 172.78/172.46 => c_List_Oupt(V_i,hAPP(c_Nat_OSuc,V_j)) = c_List_Olist_ONil(tc_Nat_Onat) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_upt__add__eq__append,axiom, % 172.78/172.46 ! [V_k,V_j,V_i] : % 172.78/172.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 172.78/172.46 => 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))) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_upt__0,axiom, % 172.78/172.46 ! [V_i] : c_List_Oupt(V_i,c_Groups_Ozero__class_Ozero(tc_Nat_Onat)) = c_List_Olist_ONil(tc_Nat_Onat) ). % 172.78/172.46 % 172.78/172.46 fof(fact_upt__eq__Nil__conv,axiom, % 172.78/172.46 ! [V_j_2,V_i_2] : % 172.78/172.46 ( c_List_Oupt(V_i_2,V_j_2) = c_List_Olist_ONil(tc_Nat_Onat) % 172.78/172.46 <=> ( V_j_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 172.78/172.46 | hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j_2),V_i_2)) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_upt__conv__Nil,axiom, % 172.78/172.46 ! [V_i,V_j] : % 172.78/172.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_j),V_i)) % 172.78/172.46 => c_List_Oupt(V_i,V_j) = c_List_Olist_ONil(tc_Nat_Onat) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_take__upt,axiom, % 172.78/172.46 ! [V_n,V_m,V_i] : % 172.78/172.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_i),V_m)),V_n)) % 172.78/172.46 => 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)) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_sorted__list__of__set__range,axiom, % 172.78/172.46 ! [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) ). % 172.78/172.46 % 172.78/172.46 fof(fact_hd__upt,axiom, % 172.78/172.46 ! [V_j,V_i] : % 172.78/172.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 172.78/172.46 => hAPP(c_List_Ohd(tc_Nat_Onat),c_List_Oupt(V_i,V_j)) = V_i ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_drop__upt,axiom, % 172.78/172.46 ! [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) ). % 172.78/172.46 % 172.78/172.46 fof(fact_distinct__upt,axiom, % 172.78/172.46 ! [V_j,V_i] : hBOOL(hAPP(c_List_Odistinct(tc_Nat_Onat),c_List_Oupt(V_i,V_j))) ). % 172.78/172.46 % 172.78/172.46 fof(fact_length__upt,axiom, % 172.78/172.46 ! [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) ). % 172.78/172.46 % 172.78/172.46 fof(fact_upt__rec__number__of,axiom, % 172.78/172.46 ! [V_n,V_m] : % 172.78/172.46 ( ( 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))) % 172.78/172.46 => 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))) ) % 172.78/172.46 & ( ~ 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))) % 172.78/172.46 => 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) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_upt__eq__Cons__conv,axiom, % 172.78/172.46 ! [V_xs_2,V_x_2,V_j_2,V_i_2] : % 172.78/172.46 ( c_List_Oupt(V_i_2,V_j_2) = hAPP(hAPP(c_List_Olist_OCons(tc_Nat_Onat),V_x_2),V_xs_2) % 172.78/172.46 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i_2),V_j_2)) % 172.78/172.46 & V_i_2 = V_x_2 % 172.78/172.46 & 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 ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_last__upt,axiom, % 172.78/172.46 ! [V_j,V_i] : % 172.78/172.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_j)) % 172.78/172.46 => 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)) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_map__Suc__upt,axiom, % 172.78/172.46 ! [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)) ). % 172.78/172.46 % 172.78/172.46 fof(fact_atLeastAtMost__upt,axiom, % 172.78/172.46 ! [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))) ). % 172.78/172.46 % 172.78/172.46 fof(fact_atLeast__upt,axiom, % 172.78/172.46 ! [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)) ). % 172.78/172.46 % 172.78/172.46 fof(fact_nth__upt,axiom, % 172.78/172.46 ! [V_j,V_k,V_i] : % 172.78/172.46 ( 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)) % 172.78/172.46 => 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) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_greaterThanAtMost__upt,axiom, % 172.78/172.46 ! [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))) ). % 172.78/172.46 % 172.78/172.46 fof(fact_greaterThanLessThan__upt,axiom, % 172.78/172.46 ! [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)) ). % 172.78/172.46 % 172.78/172.46 fof(fact_atMost__upto,axiom, % 172.78/172.46 ! [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))) ). % 172.78/172.46 % 172.78/172.46 fof(fact_map__nth,axiom, % 172.78/172.46 ! [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 ). % 172.78/172.46 % 172.78/172.46 fof(fact_interv__listsum__conv__setsum__set__nat,axiom, % 172.78/172.46 ! [V_n_2,V_m_2,V_f_2,T_a] : % 172.78/172.46 ( class_Groups_Ocomm__monoid__add(T_a) % 172.78/172.46 => 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))) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_setsum__set__upt__conv__listsum__nat,axiom, % 172.78/172.46 ! [V_n_2,V_m_2,V_f_2,T_a] : % 172.78/172.46 ( class_Groups_Ocomm__monoid__add(T_a) % 172.78/172.46 => 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))) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_nth__map__upt,axiom, % 172.78/172.46 ! [V_f_2,T_a,V_m_2,V_n_2,V_i_2] : % 172.78/172.46 ( 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))) % 172.78/172.46 => 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)) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_transpose__rectangle,axiom, % 172.78/172.46 ! [V_n_2,T_a,V_xs_2] : % 172.78/172.46 ( ( V_xs_2 = c_List_Olist_ONil(tc_List_Olist(T_a)) % 172.78/172.46 => V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) % 172.78/172.46 => ( ! [B_i] : % 172.78/172.46 ( 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))) % 172.78/172.46 => 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 ) % 172.78/172.46 => 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)) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_insort__key__remove1,axiom, % 172.78/172.46 ! [V_f_2,V_xs_2,V_a_2,T_a,T_b] : % 172.78/172.46 ( class_Orderings_Olinorder(T_b) % 172.78/172.46 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 172.78/172.46 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2)) % 172.78/172.46 => ( 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 % 172.78/172.46 => 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 ) ) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_sorted_ONil,axiom, % 172.78/172.46 ! [T_a] : % 172.78/172.46 ( class_Orderings_Olinorder(T_a) % 172.78/172.46 => c_List_Olinorder__class_Osorted(T_a,c_List_Olist_ONil(T_a)) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_sorted__single,axiom, % 172.78/172.46 ! [V_x,T_a] : % 172.78/172.46 ( class_Orderings_Olinorder(T_a) % 172.78/172.46 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a))) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_sorted__upt,axiom, % 172.78/172.46 ! [V_j,V_i] : c_List_Olinorder__class_Osorted(tc_Nat_Onat,c_List_Oupt(V_i,V_j)) ). % 172.78/172.46 % 172.78/172.46 fof(fact_sorted__sort,axiom, % 172.78/172.46 ! [V_xs_2,T_a] : % 172.78/172.46 ( class_Orderings_Olinorder(T_a) % 172.78/172.46 => c_List_Olinorder__class_Osorted(T_a,c_List_Olinorder__class_Osort__key(T_a,T_a,c_COMBI(T_a),V_xs_2)) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_sorted__insort,axiom, % 172.78/172.46 ! [V_xs_2,V_x_2,T_a] : % 172.78/172.46 ( class_Orderings_Olinorder(T_a) % 172.78/172.46 => ( 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)) % 172.78/172.46 <=> c_List_Olinorder__class_Osorted(T_a,V_xs_2) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_sorted__drop,axiom, % 172.78/172.46 ! [V_n,V_xs,T_a] : % 172.78/172.46 ( class_Orderings_Olinorder(T_a) % 172.78/172.46 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 172.78/172.46 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Odrop(T_a),V_n),V_xs)) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_sorted__take,axiom, % 172.78/172.46 ! [V_n,V_xs,T_a] : % 172.78/172.46 ( class_Orderings_Olinorder(T_a) % 172.78/172.46 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 172.78/172.46 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Otake(T_a),V_n),V_xs)) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_sorted__upto,axiom, % 172.78/172.46 ! [V_j,V_i] : c_List_Olinorder__class_Osorted(tc_Int_Oint,c_List_Oupto(V_i,V_j)) ). % 172.78/172.46 % 172.78/172.46 fof(fact_sorted__remove1,axiom, % 172.78/172.46 ! [V_a,V_xs,T_a] : % 172.78/172.46 ( class_Orderings_Olinorder(T_a) % 172.78/172.46 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 172.78/172.46 => c_List_Olinorder__class_Osorted(T_a,c_List_Oremove1(T_a,V_a,V_xs)) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_sorted__tl,axiom, % 172.78/172.46 ! [V_xs,T_a] : % 172.78/172.46 ( class_Orderings_Olinorder(T_a) % 172.78/172.46 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 172.78/172.46 => c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Otl(T_a),V_xs)) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_sorted__insort__insert,axiom, % 172.78/172.46 ! [V_x_2,V_xs_2,T_a] : % 172.78/172.46 ( class_Orderings_Olinorder(T_a) % 172.78/172.46 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2) % 172.78/172.46 => 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)) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_sorted_Oequations_I1_J,axiom, % 172.78/172.46 ! [T_a] : % 172.78/172.46 ( class_Orderings_Olinorder(T_a) % 172.78/172.46 => c_List_Olinorder__class_Osorted(T_a,c_List_Olist_ONil(T_a)) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_sorted__butlast,axiom, % 172.78/172.46 ! [V_xs,T_a] : % 172.78/172.46 ( class_Orderings_Olinorder(T_a) % 172.78/172.46 => ( V_xs != c_List_Olist_ONil(T_a) % 172.78/172.46 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 172.78/172.46 => c_List_Olinorder__class_Osorted(T_a,c_List_Obutlast(T_a,V_xs)) ) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_sorted__many,axiom, % 172.78/172.46 ! [V_zs,V_y,V_x,T_a] : % 172.78/172.46 ( class_Orderings_Olinorder(T_a) % 172.78/172.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) % 172.78/172.46 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_zs)) % 172.78/172.46 => 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))) ) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_sorted__many__eq,axiom, % 172.78/172.46 ! [V_zs_2,V_y_2,V_x_2,T_a] : % 172.78/172.46 ( class_Orderings_Olinorder(T_a) % 172.78/172.46 => ( 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))) % 172.78/172.46 <=> ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),V_y_2)) % 172.78/172.46 & c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_zs_2)) ) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_sorted__remdups,axiom, % 172.78/172.46 ! [V_l,T_a] : % 172.78/172.46 ( class_Orderings_Olinorder(T_a) % 172.78/172.46 => ( c_List_Olinorder__class_Osorted(T_a,V_l) % 172.78/172.46 => c_List_Olinorder__class_Osorted(T_a,c_List_Oremdups(T_a,V_l)) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_sorted__distinct__set__unique,axiom, % 172.78/172.46 ! [V_ys_2,V_xs_2,T_a] : % 172.78/172.46 ( class_Orderings_Olinorder(T_a) % 172.78/172.46 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2) % 172.78/172.46 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 172.78/172.46 => ( c_List_Olinorder__class_Osorted(T_a,V_ys_2) % 172.78/172.46 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_ys_2)) % 172.78/172.46 => ( hAPP(c_List_Oset(T_a),V_xs_2) = hAPP(c_List_Oset(T_a),V_ys_2) % 172.78/172.46 => V_xs_2 = V_ys_2 ) ) ) ) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_sorted__sort__key,axiom, % 172.78/172.46 ! [V_xs_2,V_f_2,T_b,T_a] : % 172.78/172.46 ( class_Orderings_Olinorder(T_a) % 172.78/172.46 => 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))) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_sorted__insort__insert__key,axiom, % 172.78/172.46 ! [V_x_2,V_xs_2,V_f_2,T_b,T_a] : % 172.78/172.46 ( class_Orderings_Olinorder(T_a) % 172.78/172.46 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) % 172.78/172.46 => 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))) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_sorted__map__remove1,axiom, % 172.78/172.46 ! [V_x_2,V_xs_2,V_f_2,T_b,T_a] : % 172.78/172.46 ( class_Orderings_Olinorder(T_a) % 172.78/172.46 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) % 172.78/172.46 => 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))) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_sorted__insort__key,axiom, % 172.78/172.46 ! [V_xs_2,V_x_2,V_f_2,T_b,T_a] : % 172.78/172.46 ( class_Orderings_Olinorder(T_a) % 172.78/172.46 => ( 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))) % 172.78/172.46 <=> c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_sorted__filter,axiom, % 172.78/172.46 ! [V_P_2,V_xs_2,V_f_2,T_b,T_a] : % 172.78/172.46 ( class_Orderings_Olinorder(T_a) % 172.78/172.46 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) % 172.78/172.46 => 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))) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_sorted__map__same,axiom, % 172.78/172.46 ! [V_xs_2,V_g_2,V_f_2,T_b,T_a] : % 172.78/172.46 ( class_Orderings_Olinorder(T_a) % 172.78/172.46 => 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))) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_sorted__same,axiom, % 172.78/172.46 ! [V_xs_2,V_g_2,T_a] : % 172.78/172.46 ( class_Orderings_Olinorder(T_a) % 172.78/172.46 => 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)) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_sorted__Cons,axiom, % 172.78/172.46 ! [V_xs_2,V_x_2,T_a] : % 172.78/172.46 ( class_Orderings_Olinorder(T_a) % 172.78/172.46 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) % 172.78/172.46 <=> ( c_List_Olinorder__class_Osorted(T_a,V_xs_2) % 172.78/172.46 & ! [B_x] : % 172.78/172.46 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 172.78/172.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),B_x)) ) ) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_sorted__append,axiom, % 172.78/172.46 ! [V_ys_2,V_xs_2,T_a] : % 172.78/172.46 ( class_Orderings_Olinorder(T_a) % 172.78/172.46 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)) % 172.78/172.46 <=> ( c_List_Olinorder__class_Osorted(T_a,V_xs_2) % 172.78/172.46 & c_List_Olinorder__class_Osorted(T_a,V_ys_2) % 172.78/172.46 & ! [B_x] : % 172.78/172.46 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 172.78/172.46 => ! [B_xa] : % 172.78/172.46 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),hAPP(c_List_Oset(T_a),V_ys_2))) % 172.78/172.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_x),B_xa)) ) ) ) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_filter__insort,axiom, % 172.78/172.46 ! [V_x_2,V_P_2,V_xs_2,V_f_2,T_b,T_a] : % 172.78/172.46 ( class_Orderings_Olinorder(T_a) % 172.78/172.46 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),V_xs_2)) % 172.78/172.46 => ( hBOOL(hAPP(V_P_2,V_x_2)) % 172.78/172.46 => 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)) ) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_sorted_Oequations_I2_J,axiom, % 172.78/172.46 ! [V_a1_2,V_a2_2,T_a] : % 172.78/172.46 ( class_Orderings_Olinorder(T_a) % 172.78/172.46 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_a2_2),V_a1_2)) % 172.78/172.46 <=> ( ! [B_x] : % 172.78/172.46 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_a1_2))) % 172.78/172.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_a2_2),B_x)) ) % 172.78/172.46 & c_List_Olinorder__class_Osorted(T_a,V_a1_2) ) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_sorted__list__of__set,axiom, % 172.78/172.46 ! [V_A_2,T_a] : % 172.78/172.46 ( class_Orderings_Olinorder(T_a) % 172.78/172.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.78/172.46 => ( hAPP(c_List_Oset(T_a),c_List_Olinorder__class_Osorted__list__of__set(T_a,V_A_2)) = V_A_2 % 172.78/172.46 & c_List_Olinorder__class_Osorted(T_a,c_List_Olinorder__class_Osorted__list__of__set(T_a,V_A_2)) % 172.78/172.46 & hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Olinorder__class_Osorted__list__of__set(T_a,V_A_2))) ) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_insort__remove1,axiom, % 172.78/172.46 ! [V_xs_2,V_a_2,T_a] : % 172.78/172.46 ( class_Orderings_Olinorder(T_a) % 172.78/172.46 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_a_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 172.78/172.46 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2) % 172.78/172.46 => 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 ) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_sorted__equals__nth__mono,axiom, % 172.78/172.46 ! [V_xs_2,T_a] : % 172.78/172.46 ( class_Orderings_Olinorder(T_a) % 172.78/172.46 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2) % 172.78/172.46 <=> ! [B_j] : % 172.78/172.46 ( 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))) % 172.78/172.46 => ! [B_i] : % 172.78/172.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_j)) % 172.78/172.46 => 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))) ) ) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_sorted__nth__mono,axiom, % 172.78/172.46 ! [V_j,V_i,V_xs,T_a] : % 172.78/172.46 ( class_Orderings_Olinorder(T_a) % 172.78/172.46 => ( c_List_Olinorder__class_Osorted(T_a,V_xs) % 172.78/172.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 172.78/172.46 => ( 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))) % 172.78/172.46 => 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))) ) ) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_map__sorted__distinct__set__unique,axiom, % 172.78/172.46 ! [V_ys_2,V_xs_2,V_f_2,T_a,T_b] : % 172.78/172.46 ( class_Orderings_Olinorder(T_b) % 172.78/172.46 => ( 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))) % 172.78/172.46 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2)) % 172.78/172.46 => ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_xs_2))) % 172.78/172.46 => ( c_List_Olinorder__class_Osorted(T_b,hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_ys_2)) % 172.78/172.46 => ( hBOOL(hAPP(c_List_Odistinct(T_b),hAPP(hAPP(c_List_Omap(T_a,T_b),V_f_2),V_ys_2))) % 172.78/172.46 => ( hAPP(c_List_Oset(T_a),V_xs_2) = hAPP(c_List_Oset(T_a),V_ys_2) % 172.78/172.46 => V_xs_2 = V_ys_2 ) ) ) ) ) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_transpose__column,axiom, % 172.78/172.46 ! [V_i_2,V_xs_2,T_a] : % 172.78/172.46 ( 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))) % 172.78/172.46 => ( 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))) % 172.78/172.46 => 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) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_nth__nth__transpose__sorted,axiom, % 172.78/172.46 ! [V_j_2,V_i_2,V_xs_2,T_a] : % 172.78/172.46 ( 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))) % 172.78/172.46 => ( 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)))) % 172.78/172.46 => ( 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)))) % 172.78/172.46 => 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) ) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_inj__on__rev,axiom, % 172.78/172.46 ! [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) ). % 172.78/172.46 % 172.78/172.46 fof(fact_distinct__rev,axiom, % 172.78/172.46 ! [V_xs_2,T_a] : % 172.78/172.46 ( hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_Orev(T_a),V_xs_2))) % 172.78/172.46 <=> hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_rev_Osimps_I1_J,axiom, % 172.78/172.46 ! [T_a] : hAPP(c_List_Orev(T_a),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 172.78/172.46 % 172.78/172.46 fof(fact_Nil__is__rev__conv,axiom, % 172.78/172.46 ! [V_xs_2,T_a] : % 172.78/172.46 ( c_List_Olist_ONil(T_a) = hAPP(c_List_Orev(T_a),V_xs_2) % 172.78/172.46 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_rev__is__Nil__conv,axiom, % 172.78/172.46 ! [V_xs_2,T_a] : % 172.78/172.46 ( hAPP(c_List_Orev(T_a),V_xs_2) = c_List_Olist_ONil(T_a) % 172.78/172.46 <=> V_xs_2 = c_List_Olist_ONil(T_a) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_rev__append,axiom, % 172.78/172.46 ! [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)) ). % 172.78/172.46 % 172.78/172.46 fof(fact_singleton__rev__conv,axiom, % 172.78/172.46 ! [V_xs_2,V_x_2,T_a] : % 172.78/172.46 ( 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) % 172.78/172.46 <=> V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a)) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_rev__singleton__conv,axiom, % 172.78/172.46 ! [V_x_2,V_xs_2,T_a] : % 172.78/172.46 ( 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)) % 172.78/172.46 <=> V_xs_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),c_List_Olist_ONil(T_a)) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_rev__concat,axiom, % 172.78/172.46 ! [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))) ). % 172.78/172.46 % 172.78/172.46 fof(fact_rev__map,axiom, % 172.78/172.46 ! [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)) ). % 172.78/172.46 % 172.78/172.46 fof(fact_rev__eq__Cons__iff,axiom, % 172.78/172.46 ! [V_ys_2,V_y_2,V_xs_2,T_a] : % 172.78/172.46 ( hAPP(c_List_Orev(T_a),V_xs_2) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_y_2),V_ys_2) % 172.78/172.46 <=> 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))) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_rev_Osimps_I2_J,axiom, % 172.78/172.46 ! [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))) ). % 172.78/172.46 % 172.78/172.46 fof(fact_rev__filter,axiom, % 172.78/172.46 ! [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)) ). % 172.78/172.46 % 172.78/172.46 fof(fact_zip__rev,axiom, % 172.78/172.46 ! [V_ys,T_b,V_xs,T_a] : % 172.78/172.46 ( 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) % 172.78/172.46 => 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)) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_set__rev,axiom, % 172.78/172.46 ! [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) ). % 172.78/172.46 % 172.78/172.46 fof(fact_list__all2__rev1,axiom, % 172.78/172.46 ! [V_ys_2,V_xs_2,V_P_2,T_b,T_a] : % 172.78/172.46 ( c_List_Olist__all2(T_a,T_b,V_P_2,hAPP(c_List_Orev(T_a),V_xs_2),V_ys_2) % 172.78/172.46 <=> c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,hAPP(c_List_Orev(T_b),V_ys_2)) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_list__all2__rev,axiom, % 172.78/172.46 ! [V_ys_2,V_xs_2,V_P_2,T_b,T_a] : % 172.78/172.46 ( 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)) % 172.78/172.46 <=> c_List_Olist__all2(T_a,T_b,V_P_2,V_xs_2,V_ys_2) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_listsum__rev,axiom, % 172.78/172.46 ! [V_xs,T_a] : % 172.78/172.46 ( class_Groups_Ocomm__monoid__add(T_a) % 172.78/172.46 => 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) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_rev__is__rev__conv,axiom, % 172.78/172.46 ! [V_ys_2,V_xs_2,T_a] : % 172.78/172.46 ( hAPP(c_List_Orev(T_a),V_xs_2) = hAPP(c_List_Orev(T_a),V_ys_2) % 172.78/172.46 <=> V_xs_2 = V_ys_2 ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_rev__swap,axiom, % 172.78/172.46 ! [V_ys_2,V_xs_2,T_a] : % 172.78/172.46 ( hAPP(c_List_Orev(T_a),V_xs_2) = V_ys_2 % 172.78/172.46 <=> V_xs_2 = hAPP(c_List_Orev(T_a),V_ys_2) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_rev__rev__ident,axiom, % 172.78/172.46 ! [V_xs,T_a] : hAPP(c_List_Orev(T_a),hAPP(c_List_Orev(T_a),V_xs)) = V_xs ). % 172.78/172.46 % 172.78/172.46 fof(fact_length__rev,axiom, % 172.78/172.46 ! [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) ). % 172.78/172.46 % 172.78/172.46 fof(fact_foldl__foldr,axiom, % 172.78/172.46 ! [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) ). % 172.78/172.46 % 172.78/172.46 fof(fact_foldr__foldl,axiom, % 172.78/172.46 ! [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)) ). % 172.78/172.46 % 172.78/172.46 fof(fact_last__rev,axiom, % 172.78/172.46 ! [T_a,V_xs] : % 172.78/172.46 ( V_xs != c_List_Olist_ONil(T_a) % 172.78/172.46 => c_List_Olast(T_a,hAPP(c_List_Orev(T_a),V_xs)) = hAPP(c_List_Ohd(T_a),V_xs) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_hd__rev,axiom, % 172.78/172.46 ! [T_a,V_xs] : % 172.78/172.46 ( V_xs != c_List_Olist_ONil(T_a) % 172.78/172.46 => hAPP(c_List_Ohd(T_a),hAPP(c_List_Orev(T_a),V_xs)) = c_List_Olast(T_a,V_xs) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_sorted__transpose,axiom, % 172.78/172.46 ! [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)))) ). % 172.78/172.46 % 172.78/172.46 fof(fact_rev__foldl__cons,axiom, % 172.78/172.46 ! [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) ). % 172.78/172.46 % 172.78/172.46 fof(fact_rev__drop,axiom, % 172.78/172.46 ! [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)) ). % 172.78/172.46 % 172.78/172.46 fof(fact_rev__take,axiom, % 172.78/172.46 ! [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)) ). % 172.78/172.46 % 172.78/172.46 fof(fact_rotate__rev,axiom, % 172.78/172.46 ! [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)) ). % 172.78/172.46 % 172.78/172.46 fof(fact_rev__nth,axiom, % 172.78/172.46 ! [V_xs,T_a,V_n] : % 172.78/172.46 ( 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))) % 172.78/172.46 => 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))) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_rev__update,axiom, % 172.78/172.46 ! [V_y,V_xs,T_a,V_k] : % 172.78/172.46 ( 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))) % 172.78/172.46 => 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) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_sorted__rev__nth__mono,axiom, % 172.78/172.46 ! [V_j,V_i,V_xs,T_a] : % 172.78/172.46 ( class_Orderings_Olinorder(T_a) % 172.78/172.46 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Orev(T_a),V_xs)) % 172.78/172.46 => ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),V_i),V_j)) % 172.78/172.46 => ( 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))) % 172.78/172.46 => 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))) ) ) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_foldr__max__sorted,axiom, % 172.78/172.46 ! [V_y_2,V_xs_2,T_a] : % 172.78/172.46 ( class_Orderings_Olinorder(T_a) % 172.78/172.46 => ( c_List_Olinorder__class_Osorted(T_a,hAPP(c_List_Orev(T_a),V_xs_2)) % 172.78/172.46 => ( ( V_xs_2 = c_List_Olist_ONil(T_a) % 172.78/172.46 => c_List_Ofoldr(T_a,T_a,c_Orderings_Oord__class_Omax(T_a),V_xs_2,V_y_2) = V_y_2 ) % 172.78/172.46 & ( V_xs_2 != c_List_Olist_ONil(T_a) % 172.78/172.46 => 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) ) ) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_length__transpose__sorted,axiom, % 172.78/172.46 ! [V_xs_2,T_a] : % 172.78/172.46 ( 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))) % 172.78/172.46 => ( ( V_xs_2 = c_List_Olist_ONil(tc_List_Olist(T_a)) % 172.78/172.46 => 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) ) % 172.78/172.46 & ( V_xs_2 != c_List_Olist_ONil(tc_List_Olist(T_a)) % 172.78/172.46 => 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))) ) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_transpose__column__length,axiom, % 172.78/172.46 ! [V_i_2,V_xs_2,T_a] : % 172.78/172.46 ( 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))) % 172.78/172.46 => ( 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))) % 172.78/172.46 => 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)) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_transpose__transpose,axiom, % 172.78/172.46 ! [V_xs_2,T_a] : % 172.78/172.46 ( 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))) % 172.78/172.46 => 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) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_transfer__nat__int__list__functions_I2_J,axiom, % 172.78/172.46 c_List_Olist_ONil(tc_Nat_Onat) = c_List_Oreturn__list(c_List_Olist_ONil(tc_Int_Oint)) ). % 172.78/172.46 % 172.78/172.46 fof(fact_sorted__takeWhile,axiom, % 172.78/172.46 ! [V_P_2,V_xs_2,T_a] : % 172.78/172.46 ( class_Orderings_Olinorder(T_a) % 172.78/172.46 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2) % 172.78/172.46 => c_List_Olinorder__class_Osorted(T_a,c_List_OtakeWhile(T_a,V_P_2,V_xs_2)) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_length__takeWhile__le,axiom, % 172.78/172.46 ! [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))) ). % 172.78/172.46 % 172.78/172.46 fof(fact_set__takeWhileD,axiom, % 172.78/172.46 ! [V_xs_2,V_P_2,V_x_2,T_a] : % 172.78/172.46 ( 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)))) % 172.78/172.46 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 172.78/172.46 & hBOOL(hAPP(V_P_2,V_x_2)) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_takeWhile__eq__all__conv,axiom, % 172.78/172.46 ! [V_xs_2,V_P_2,T_a] : % 172.78/172.46 ( c_List_OtakeWhile(T_a,V_P_2,V_xs_2) = V_xs_2 % 172.78/172.46 <=> ! [B_x] : % 172.78/172.46 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 172.78/172.46 => hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_zip__takeWhile__snd,axiom, % 172.78/172.46 ! [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)) ). % 172.78/172.46 % 172.78/172.46 fof(fact_zip__takeWhile__fst,axiom, % 172.78/172.46 ! [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)) ). % 172.78/172.46 % 172.78/172.46 fof(fact_takeWhile__map,axiom, % 172.78/172.46 ! [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)) ). % 172.78/172.46 % 172.78/172.46 fof(fact_takeWhile_Osimps_I2_J,axiom, % 172.78/172.46 ! [V_xs_2,T_a,V_x_2,V_P_2] : % 172.78/172.46 ( ( hBOOL(hAPP(V_P_2,V_x_2)) % 172.78/172.46 => 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)) ) % 172.78/172.46 & ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 172.78/172.46 => 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) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_takeWhile__tail,axiom, % 172.78/172.46 ! [V_l_2,V_xs_2,T_a,V_x_2,V_P_2] : % 172.78/172.46 ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 172.78/172.46 => 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) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_takeWhile_Osimps_I1_J,axiom, % 172.78/172.46 ! [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) ). % 172.78/172.46 % 172.78/172.46 fof(fact_takeWhile__eq__take,axiom, % 172.78/172.46 ! [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) ). % 172.78/172.46 % 172.78/172.46 fof(fact_distinct__takeWhile,axiom, % 172.78/172.46 ! [V_P_2,V_xs_2,T_a] : % 172.78/172.46 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 172.78/172.46 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_OtakeWhile(T_a,V_P_2,V_xs_2))) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_return__list__def,axiom, % 172.78/172.46 ! [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) ). % 172.78/172.46 % 172.78/172.46 fof(fact_takeWhile__append1,axiom, % 172.78/172.46 ! [V_ys_2,V_P_2,V_xs_2,V_x_2,T_a] : % 172.78/172.46 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 172.78/172.46 => ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 172.78/172.46 => 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) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_nth__length__takeWhile,axiom, % 172.78/172.46 ! [V_xs_2,V_P_2,T_a] : % 172.78/172.46 ( 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))) % 172.78/172.46 => ~ 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))))) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_takeWhile__nth,axiom, % 172.78/172.46 ! [V_xs_2,V_P_2,T_a,V_j_2] : % 172.78/172.46 ( 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)))) % 172.78/172.46 => 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) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_takeWhile__not__last,axiom, % 172.78/172.46 ! [T_a,V_xs_2] : % 172.78/172.46 ( V_xs_2 != c_List_Olist_ONil(T_a) % 172.78/172.46 => ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 172.78/172.46 => 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) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_filter__equals__takeWhile__sorted__rev,axiom, % 172.78/172.46 ! [V_t_2,V_xs_2,V_f_2,T_b,T_a] : % 172.78/172.46 ( class_Orderings_Olinorder(T_a) % 172.78/172.46 => ( 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))) % 172.78/172.46 => 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) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_transfer__nat__int__list__return__embed,axiom, % 172.78/172.46 ! [V_l] : % 172.78/172.46 ( c_List_Onat__list(V_l) % 172.78/172.46 => c_List_Oembed__list(c_List_Oreturn__list(V_l)) = V_l ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_transfer__nat__int__list__functions_I1_J,axiom, % 172.78/172.46 ! [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))) ). % 172.78/172.46 % 172.78/172.46 fof(fact_embed__list__def,axiom, % 172.78/172.46 ! [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) ). % 172.78/172.46 % 172.78/172.46 fof(fact_takeWhile__neq__rev,axiom, % 172.78/172.46 ! [V_x_2,V_xs_2,T_a] : % 172.78/172.46 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 172.78/172.46 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 172.78/172.46 => 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))) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_dropWhile__neq__rev,axiom, % 172.78/172.46 ! [V_x_2,V_xs_2,T_a] : % 172.78/172.46 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 172.78/172.46 => ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 172.78/172.46 => 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))) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_takeWhile__dropWhile__id,axiom, % 172.78/172.46 ! [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 ). % 172.78/172.46 % 172.78/172.46 fof(fact_dropWhile__map,axiom, % 172.78/172.46 ! [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)) ). % 172.78/172.46 % 172.78/172.46 fof(fact_sorted__dropWhile,axiom, % 172.78/172.46 ! [V_P_2,V_xs_2,T_a] : % 172.78/172.46 ( class_Orderings_Olinorder(T_a) % 172.78/172.46 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2) % 172.78/172.46 => c_List_Olinorder__class_Osorted(T_a,c_List_OdropWhile(T_a,V_P_2,V_xs_2)) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_length__dropWhile__le,axiom, % 172.78/172.46 ! [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))) ). % 172.78/172.46 % 172.78/172.46 fof(fact_dropWhile__eq__Nil__conv,axiom, % 172.78/172.46 ! [V_xs_2,V_P_2,T_a] : % 172.78/172.46 ( c_List_OdropWhile(T_a,V_P_2,V_xs_2) = c_List_Olist_ONil(T_a) % 172.78/172.46 <=> ! [B_x] : % 172.78/172.46 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 172.78/172.46 => hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_dropWhile_Osimps_I2_J,axiom, % 172.78/172.46 ! [V_xs_2,T_a,V_x_2,V_P_2] : % 172.78/172.46 ( ( hBOOL(hAPP(V_P_2,V_x_2)) % 172.78/172.46 => 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) ) % 172.78/172.46 & ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 172.78/172.46 => 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) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_dropWhile_Osimps_I1_J,axiom, % 172.78/172.46 ! [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) ). % 172.78/172.46 % 172.78/172.46 fof(fact_distinct__dropWhile,axiom, % 172.78/172.46 ! [V_P_2,V_xs_2,T_a] : % 172.78/172.46 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs_2)) % 172.78/172.46 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_OdropWhile(T_a,V_P_2,V_xs_2))) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_hd__dropWhile,axiom, % 172.78/172.46 ! [V_xs_2,V_P_2,T_a] : % 172.78/172.46 ( c_List_OdropWhile(T_a,V_P_2,V_xs_2) != c_List_Olist_ONil(T_a) % 172.78/172.46 => ~ hBOOL(hAPP(V_P_2,hAPP(c_List_Ohd(T_a),c_List_OdropWhile(T_a,V_P_2,V_xs_2)))) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_dropWhile__append1,axiom, % 172.78/172.46 ! [V_ys_2,V_P_2,V_xs_2,V_x_2,T_a] : % 172.78/172.46 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 172.78/172.46 => ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 172.78/172.46 => 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) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_dropWhile__eq__Cons__conv,axiom, % 172.78/172.46 ! [V_ys_2,V_y_2,V_xs_2,V_P_2,T_a] : % 172.78/172.46 ( 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) % 172.78/172.46 <=> ( 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)) % 172.78/172.46 & ~ hBOOL(hAPP(V_P_2,V_y_2)) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_dropWhile__eq__drop,axiom, % 172.78/172.46 ! [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) ). % 172.78/172.46 % 172.78/172.46 fof(fact_dropWhile__nth,axiom, % 172.78/172.46 ! [V_xs_2,V_P_2,T_a,V_j_2] : % 172.78/172.46 ( 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)))) % 172.78/172.46 => 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)))) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_listsum__map__filter,axiom, % 172.78/172.46 ! [V_f_2,V_P_2,V_xs_2,T_a,T_b] : % 172.78/172.46 ( class_Groups_Omonoid__add(T_b) % 172.78/172.46 => ( ! [B_x] : % 172.78/172.46 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 172.78/172.46 => ( ~ hBOOL(hAPP(V_P_2,B_x)) % 172.78/172.46 => hAPP(V_f_2,B_x) = c_Groups_Ozero__class_Ozero(T_b) ) ) % 172.78/172.46 => 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)) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_sorted__nth__monoI,axiom, % 172.78/172.46 ! [V_xs,T_a] : % 172.78/172.46 ( class_Orderings_Olinorder(T_a) % 172.78/172.46 => ( ! [B_i,B_j] : % 172.78/172.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat),B_i),B_j)) % 172.78/172.46 => ( 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))) % 172.78/172.46 => 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))) ) ) % 172.78/172.46 => c_List_Olinorder__class_Osorted(T_a,V_xs) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_takeWhile__eq__filter,axiom, % 172.78/172.46 ! [V_xs_2,V_P_2,T_a] : % 172.78/172.46 ( ! [B_x] : % 172.78/172.46 ( 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)))) % 172.78/172.46 => ~ hBOOL(hAPP(V_P_2,B_x)) ) % 172.78/172.46 => c_List_OtakeWhile(T_a,V_P_2,V_xs_2) = hAPP(c_List_Ofilter(T_a,V_P_2),V_xs_2) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_takeWhile__eq__take__P__nth,axiom, % 172.78/172.46 ! [V_P_2,V_xs_2,T_a,V_n_2] : % 172.78/172.46 ( ! [B_i] : % 172.78/172.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_n_2)) % 172.78/172.46 => ( 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))) % 172.78/172.46 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i))) ) ) % 172.78/172.46 => ( ( 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))) % 172.78/172.46 => ~ hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_n_2))) ) % 172.78/172.46 => c_List_OtakeWhile(T_a,V_P_2,V_xs_2) = hAPP(hAPP(c_List_Otake(T_a),V_n_2),V_xs_2) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_length__takeWhile__less__P__nth,axiom, % 172.78/172.46 ! [V_xs_2,T_a,V_P_2,V_j_2] : % 172.78/172.46 ( ! [B_i] : % 172.78/172.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),B_i),V_j_2)) % 172.78/172.46 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_i))) ) % 172.78/172.46 => ( 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))) % 172.78/172.46 => 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)))) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_sorted_Osimps,axiom, % 172.78/172.46 ! [V_a_2,T_a] : % 172.78/172.46 ( class_Orderings_Olinorder(T_a) % 172.78/172.46 => ( c_List_Olinorder__class_Osorted(T_a,V_a_2) % 172.78/172.46 <=> ( V_a_2 = c_List_Olist_ONil(T_a) % 172.78/172.46 | ? [B_xs,B_x] : % 172.78/172.46 ( V_a_2 = hAPP(hAPP(c_List_Olist_OCons(T_a),B_x),B_xs) % 172.78/172.46 & ! [B_xa] : % 172.78/172.46 ( hBOOL(hAPP(hAPP(c_member(T_a),B_xa),hAPP(c_List_Oset(T_a),B_xs))) % 172.78/172.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),B_x),B_xa)) ) % 172.78/172.46 & c_List_Olinorder__class_Osorted(T_a,B_xs) ) ) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_map__upds__def,axiom, % 172.78/172.46 ! [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)))) ). % 172.78/172.46 % 172.78/172.46 fof(fact_map__removeAll__inj__on,axiom, % 172.78/172.46 ! [V_xs_2,V_x_2,V_f_2,T_b,T_a] : % 172.78/172.46 ( 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))) % 172.78/172.46 => 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)) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_map__of__append,axiom, % 172.78/172.46 ! [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)) ). % 172.78/172.46 % 172.78/172.46 fof(fact_removeAll__append,axiom, % 172.78/172.46 ! [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)) ). % 172.78/172.46 % 172.78/172.46 fof(fact_dom__map__add,axiom, % 172.78/172.46 ! [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)) ). % 172.78/172.46 % 172.78/172.46 fof(fact_map__add__dom__app__simps_I2_J,axiom, % 172.78/172.46 ! [V_l2_2,V_l1_2,T_b,V_m_2,T_a] : % 172.78/172.46 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_m_2),c_Map_Odom(T_a,T_b,V_l1_2))) % 172.78/172.46 => 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) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_map__add__dom__app__simps_I3_J,axiom, % 172.78/172.46 ! [V_l1_2,V_l2_2,T_b,V_m_2,T_a] : % 172.78/172.46 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_m_2),c_Map_Odom(T_a,T_b,V_l2_2))) % 172.78/172.46 => 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) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_map__add__dom__app__simps_I1_J,axiom, % 172.78/172.46 ! [V_l1_2,V_l2_2,T_b,V_m_2,T_a] : % 172.78/172.46 ( hBOOL(hAPP(hAPP(c_member(T_a),V_m_2),c_Map_Odom(T_a,T_b,V_l2_2))) % 172.78/172.46 => 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) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_map__add__assoc,axiom, % 172.78/172.46 ! [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) ). % 172.78/172.46 % 172.78/172.46 fof(fact_map__add__upds,axiom, % 172.78/172.46 ! [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) ). % 172.78/172.46 % 172.78/172.46 fof(fact_map__add__None,axiom, % 172.78/172.46 ! [V_k_2,V_n_2,V_m_2,T_a,T_b] : % 172.78/172.46 ( hAPP(c_Map_Omap__add(T_b,T_a,V_m_2,V_n_2),V_k_2) = c_Option_Ooption_ONone(T_a) % 172.78/172.46 <=> ( hAPP(V_n_2,V_k_2) = c_Option_Ooption_ONone(T_a) % 172.78/172.46 & hAPP(V_m_2,V_k_2) = c_Option_Ooption_ONone(T_a) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_empty__map__add,axiom, % 172.78/172.46 ! [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 ). % 172.78/172.46 % 172.78/172.46 fof(fact_map__add__empty,axiom, % 172.78/172.46 ! [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 ). % 172.78/172.46 % 172.78/172.46 fof(fact_map__add__SomeD,axiom, % 172.78/172.46 ! [V_x_2,V_k_2,V_n_2,V_m_2,T_a,T_b] : % 172.78/172.46 ( 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) % 172.78/172.46 => ( hAPP(V_n_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_x_2) % 172.78/172.46 | ( hAPP(V_n_2,V_k_2) = c_Option_Ooption_ONone(T_a) % 172.78/172.46 & hAPP(V_m_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_x_2) ) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_map__add__Some__iff,axiom, % 172.78/172.46 ! [V_x_2,V_k_2,V_n_2,V_m_2,T_a,T_b] : % 172.78/172.46 ( 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) % 172.78/172.46 <=> ( hAPP(V_n_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_x_2) % 172.78/172.46 | ( hAPP(V_n_2,V_k_2) = c_Option_Ooption_ONone(T_a) % 172.78/172.46 & hAPP(V_m_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_x_2) ) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_map__add__find__right,axiom, % 172.78/172.46 ! [V_m_2,T_b,V_xx_2,T_a,V_k_2,V_n_2] : % 172.78/172.46 ( hAPP(V_n_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_xx_2) % 172.78/172.46 => 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) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_map__add__upd,axiom, % 172.78/172.46 ! [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)) ). % 172.78/172.46 % 172.78/172.46 fof(fact_removeAll__id,axiom, % 172.78/172.46 ! [V_xs_2,V_x_2,T_a] : % 172.78/172.46 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 172.78/172.46 => hAPP(c_List_OremoveAll(T_a,V_x_2),V_xs_2) = V_xs_2 ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_removeAll__filter__not__eq,axiom, % 172.78/172.46 ! [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))) ). % 172.78/172.46 % 172.78/172.46 fof(fact_removeAll__filter__not,axiom, % 172.78/172.46 ! [V_xs_2,T_a,V_x_2,V_P_2] : % 172.78/172.46 ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 172.78/172.46 => 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) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_removeAll_Osimps_I2_J,axiom, % 172.78/172.46 ! [V_xs,T_a,V_y,V_x] : % 172.78/172.46 ( ( V_x = V_y % 172.78/172.46 => 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) ) % 172.78/172.46 & ( V_x != V_y % 172.78/172.46 => 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)) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_removeAll_Osimps_I1_J,axiom, % 172.78/172.46 ! [V_x,T_a] : hAPP(c_List_OremoveAll(T_a,V_x),c_List_Olist_ONil(T_a)) = c_List_Olist_ONil(T_a) ). % 172.78/172.46 % 172.78/172.46 fof(fact_distinct__removeAll,axiom, % 172.78/172.46 ! [V_x,V_xs,T_a] : % 172.78/172.46 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 172.78/172.46 => hBOOL(hAPP(c_List_Odistinct(T_a),hAPP(c_List_OremoveAll(T_a,V_x),V_xs))) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_inj__on__map__add__dom,axiom, % 172.78/172.46 ! [V_m_H_2,V_m_2,T_b,T_a] : % 172.78/172.46 ( 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)) % 172.78/172.46 <=> 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)) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_map__add__def,axiom, % 172.78/172.46 ! [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)) ). % 172.78/172.46 % 172.78/172.46 fof(fact_distinct__remove1__removeAll,axiom, % 172.78/172.46 ! [V_x,V_xs,T_a] : % 172.78/172.46 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 172.78/172.46 => c_List_Oremove1(T_a,V_x,V_xs) = hAPP(c_List_OremoveAll(T_a,V_x),V_xs) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_map__add__comm,axiom, % 172.78/172.46 ! [V_m2_2,V_m1_2,T_b,T_a] : % 172.78/172.46 ( 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)) % 172.78/172.46 => 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) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_map__add__map__of__foldr,axiom, % 172.78/172.46 ! [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) ). % 172.78/172.46 % 172.78/172.46 fof(fact_map__removeAll__inj,axiom, % 172.78/172.46 ! [V_xs_2,V_x_2,V_f_2,T_b,T_a] : % 172.78/172.46 ( c_Fun_Oinj__on(T_a,T_b,V_f_2,c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool))) % 172.78/172.46 => 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)) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_map__add__upd__left,axiom, % 172.78/172.46 ! [V_u1_2,V_e1_2,V_e2_2,T_b,V_m_2,T_a] : % 172.78/172.46 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_m_2),c_Map_Odom(T_a,T_b,V_e2_2))) % 172.78/172.46 => 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)) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_finite__range__map__of__map__add,axiom, % 172.78/172.46 ! [V_l_2,V_f_2,T_b,T_a] : % 172.78/172.46 ( 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))))) % 172.78/172.46 => 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))))) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_set__removeAll,axiom, % 172.78/172.46 ! [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)))) ). % 172.78/172.46 % 172.78/172.46 fof(fact_map__comp__def,axiom, % 172.78/172.46 ! [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)) ). % 172.78/172.46 % 172.78/172.46 fof(fact_not__in__set__insert,axiom, % 172.78/172.46 ! [V_xs_2,V_x_2,T_a] : % 172.78/172.46 ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 172.78/172.46 => 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) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_distinct__insert,axiom, % 172.78/172.46 ! [V_x,V_xs,T_a] : % 172.78/172.46 ( hBOOL(hAPP(c_List_Odistinct(T_a),V_xs)) % 172.78/172.46 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oinsert(T_a,V_x,V_xs))) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_map__comp__empty_I2_J,axiom, % 172.78/172.46 ! [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) ). % 172.78/172.46 % 172.78/172.46 fof(fact_map__comp__empty_I1_J,axiom, % 172.78/172.46 ! [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) ). % 172.78/172.46 % 172.78/172.46 fof(fact_insert__remdups,axiom, % 172.78/172.46 ! [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)) ). % 172.78/172.46 % 172.78/172.46 fof(fact_map__comp__simps_I2_J,axiom, % 172.78/172.46 ! [V_m1_2,T_b,T_c,V_k_H_2,T_a,V_k_2,V_m2_2] : % 172.78/172.46 ( hAPP(V_m2_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_a),V_k_H_2) % 172.78/172.46 => 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) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_map__comp__Some__iff,axiom, % 172.78/172.46 ! [V_v_2,V_k_2,V_m2_2,V_m1_2,T_c,T_a,T_b] : % 172.78/172.46 ( 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) % 172.78/172.46 <=> ? [B_k_H] : % 172.78/172.46 ( hAPP(V_m2_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),B_k_H) % 172.78/172.46 & hAPP(V_m1_2,B_k_H) = hAPP(c_Option_Ooption_OSome(T_a),V_v_2) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_map__comp__simps_I1_J,axiom, % 172.78/172.46 ! [V_m1_2,T_b,T_c,T_a,V_k_2,V_m2_2] : % 172.78/172.46 ( hAPP(V_m2_2,V_k_2) = c_Option_Ooption_ONone(T_a) % 172.78/172.46 => 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) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_in__set__insert,axiom, % 172.78/172.46 ! [V_xs_2,V_x_2,T_a] : % 172.78/172.46 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 172.78/172.46 => c_List_Oinsert(T_a,V_x_2,V_xs_2) = V_xs_2 ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_List_Oset__insert,axiom, % 172.78/172.46 ! [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)) ). % 172.78/172.46 % 172.78/172.46 fof(fact_insert__Nil,axiom, % 172.78/172.46 ! [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)) ). % 172.78/172.46 % 172.78/172.46 fof(fact_map__comp__None__iff,axiom, % 172.78/172.46 ! [V_k_2,V_m2_2,V_m1_2,T_c,T_a,T_b] : % 172.78/172.46 ( 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) % 172.78/172.46 <=> ( hAPP(V_m2_2,V_k_2) = c_Option_Ooption_ONone(T_b) % 172.78/172.46 | ? [B_k_H] : % 172.78/172.46 ( hAPP(V_m2_2,V_k_2) = hAPP(c_Option_Ooption_OSome(T_b),B_k_H) % 172.78/172.46 & hAPP(V_m1_2,B_k_H) = c_Option_Ooption_ONone(T_a) ) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_List_Oinsert__def,axiom, % 172.78/172.46 ! [V_xs_2,V_x_2,T_a] : % 172.78/172.46 ( ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 172.78/172.46 => c_List_Oinsert(T_a,V_x_2,V_xs_2) = V_xs_2 ) % 172.78/172.46 & ( ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 172.78/172.46 => 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) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_concat__map__maps,axiom, % 172.78/172.46 ! [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) ). % 172.78/172.46 % 172.78/172.46 fof(fact_maps__def,axiom, % 172.78/172.46 ! [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)) ). % 172.78/172.46 % 172.78/172.46 fof(fact_maps__simps_I2_J,axiom, % 172.78/172.46 ! [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) ). % 172.78/172.46 % 172.78/172.46 fof(fact_maps__simps_I1_J,axiom, % 172.78/172.46 ! [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)) ). % 172.78/172.46 % 172.78/172.46 fof(fact_distinct__concat,axiom, % 172.78/172.46 ! [V_xs_2,T_a] : % 172.78/172.46 ( hBOOL(hAPP(c_List_Odistinct(tc_List_Olist(T_a)),V_xs_2)) % 172.78/172.46 => ( ! [B_ys] : % 172.78/172.46 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_ys),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xs_2))) % 172.78/172.46 => hBOOL(hAPP(c_List_Odistinct(T_a),B_ys)) ) % 172.78/172.46 => ( ! [B_ys] : % 172.78/172.46 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_ys),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xs_2))) % 172.78/172.46 => ! [B_zs] : % 172.78/172.46 ( hBOOL(hAPP(hAPP(c_member(tc_List_Olist(T_a)),B_zs),hAPP(c_List_Oset(tc_List_Olist(T_a)),V_xs_2))) % 172.78/172.46 => ( B_ys != B_zs % 172.78/172.46 => 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)) ) ) ) % 172.78/172.46 => hBOOL(hAPP(c_List_Odistinct(T_a),c_List_Oconcat(T_a,V_xs_2))) ) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_ran__restrictD,axiom, % 172.78/172.46 ! [V_A_2,V_m_2,T_b,V_y_2,T_a] : % 172.78/172.46 ( 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)))) % 172.78/172.46 => ? [B_x] : % 172.78/172.46 ( hBOOL(hAPP(hAPP(c_member(T_b),B_x),V_A_2)) % 172.78/172.46 & hAPP(V_m_2,B_x) = hAPP(c_Option_Ooption_OSome(T_a),V_y_2) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_measures__lesseq,axiom, % 172.78/172.46 ! [V_fs_2,T_a,V_y_2,V_x_2,V_f_2] : % 172.78/172.46 ( 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))) % 172.78/172.46 => ( 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))) % 172.78/172.46 => 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)))) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_in__measures_I2_J,axiom, % 172.78/172.46 ! [V_fs_2,V_f_2,V_y_2,V_x_2,T_a] : % 172.78/172.46 ( 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)))) % 172.78/172.46 <=> ( 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))) % 172.78/172.46 | ( hAPP(V_f_2,V_x_2) = hAPP(V_f_2,V_y_2) % 172.78/172.46 & 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))) ) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_wf__measures,axiom, % 172.78/172.46 ! [V_fs_2,T_a] : c_Wellfounded_Owf(T_a,c_List_Omeasures(T_a,V_fs_2)) ). % 172.78/172.46 % 172.78/172.46 fof(fact_in__measures_I1_J,axiom, % 172.78/172.46 ! [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))))) ). % 172.78/172.46 % 172.78/172.46 fof(fact_measures__def,axiom, % 172.78/172.46 ! [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)) ). % 172.78/172.46 % 172.78/172.46 fof(fact_measures__less,axiom, % 172.78/172.46 ! [V_fs_2,T_a,V_y_2,V_x_2,V_f_2] : % 172.78/172.46 ( 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))) % 172.78/172.46 => 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)))) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_foldl__apply,axiom, % 172.78/172.46 ! [V_s_2,V_g_2,V_h_2,V_f_2,T_b,T_c,V_xs_2,T_a] : % 172.78/172.46 ( ! [B_x] : % 172.78/172.46 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 172.78/172.46 => 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)) ) % 172.78/172.46 => 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)) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_zip__obtain__same__length,axiom, % 172.78/172.46 ! [V_P_2,V_ys_2,T_b,V_xs_2,T_a] : % 172.78/172.46 ( ( 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)) % 172.78/172.46 => 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)))) ) % 172.78/172.46 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Ozip(T_a,T_b),V_xs_2),V_ys_2))) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_map__of__eqI,axiom, % 172.78/172.46 ! [V_ys_2,V_xs_2,T_b,T_a] : % 172.78/172.46 ( 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)) % 172.78/172.46 => ( ! [B_x] : % 172.78/172.46 ( 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)))) % 172.78/172.46 => 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) ) % 172.78/172.46 => hAPP(c_Map_Omap__of(T_a,T_b),V_xs_2) = hAPP(c_Map_Omap__of(T_a,T_b),V_ys_2) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_pos__not__random__dseq__def,axiom, % 172.78/172.46 ! [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)) ). % 172.78/172.46 % 172.78/172.46 fof(fact_dropWhile__append2,axiom, % 172.78/172.46 ! [V_ys_2,V_P_2,V_xs_2,T_a] : % 172.78/172.46 ( ! [B_x] : % 172.78/172.46 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 172.78/172.46 => hBOOL(hAPP(V_P_2,B_x)) ) % 172.78/172.46 => 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) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_list__all2__all__nthI,axiom, % 172.78/172.46 ! [V_P_2,V_b_2,T_b,V_a_2,T_a] : % 172.78/172.46 ( 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) % 172.78/172.46 => ( ! [B_n] : % 172.78/172.46 ( 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))) % 172.78/172.46 => 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))) ) % 172.78/172.46 => c_List_Olist__all2(T_a,T_b,V_P_2,V_a_2,V_b_2) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_finite__map__freshness,axiom, % 172.78/172.46 ! [V_f_2,T_b,T_a] : % 172.78/172.46 ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Map_Odom(T_a,T_b,V_f_2))) % 172.78/172.46 => ( ~ hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),c_Orderings_Otop__class_Otop(tc_fun(T_a,tc_HOL_Obool)))) % 172.78/172.46 => ? [B_x] : hAPP(V_f_2,B_x) = c_Option_Ooption_ONone(T_b) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_finite__sorted__distinct__unique,axiom, % 172.78/172.46 ! [V_A_2,T_a] : % 172.78/172.46 ( class_Orderings_Olinorder(T_a) % 172.78/172.46 => ( hBOOL(hAPP(c_Finite__Set_Ofinite(T_a),V_A_2)) % 172.78/172.46 => ? [B_x] : % 172.78/172.46 ( hAPP(c_List_Oset(T_a),B_x) = V_A_2 % 172.78/172.46 & c_List_Olinorder__class_Osorted(T_a,B_x) % 172.78/172.46 & hBOOL(hAPP(c_List_Odistinct(T_a),B_x)) % 172.78/172.46 & ! [B_y] : % 172.78/172.46 ( ( hAPP(c_List_Oset(T_a),B_y) = V_A_2 % 172.78/172.46 & c_List_Olinorder__class_Osorted(T_a,B_y) % 172.78/172.46 & hBOOL(hAPP(c_List_Odistinct(T_a),B_y)) ) % 172.78/172.46 => B_y = B_x ) ) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_takeWhile__append2,axiom, % 172.78/172.46 ! [V_ys_2,V_P_2,V_xs_2,T_a] : % 172.78/172.46 ( ! [B_x] : % 172.78/172.46 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 172.78/172.46 => hBOOL(hAPP(V_P_2,B_x)) ) % 172.78/172.46 => 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)) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_insort__is__Cons,axiom, % 172.78/172.46 ! [V_a_2,V_f_2,V_xs_2,T_a,T_b] : % 172.78/172.46 ( class_Orderings_Olinorder(T_b) % 172.78/172.46 => ( ! [B_x] : % 172.78/172.46 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 172.78/172.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_b),hAPP(V_f_2,V_a_2)),hAPP(V_f_2,B_x))) ) % 172.78/172.46 => 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) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_filter__eq__Cons__iff,axiom, % 172.78/172.46 ! [V_xs_2,V_x_2,V_ys_2,V_P_2,T_a] : % 172.78/172.46 ( 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) % 172.78/172.46 <=> ? [B_us,B_vs] : % 172.78/172.46 ( 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)) % 172.78/172.46 & ! [B_x] : % 172.78/172.46 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),B_us))) % 172.78/172.46 => ~ hBOOL(hAPP(V_P_2,B_x)) ) % 172.78/172.46 & hBOOL(hAPP(V_P_2,V_x_2)) % 172.78/172.46 & V_xs_2 = hAPP(c_List_Ofilter(T_a,V_P_2),B_vs) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_Cons__eq__filter__iff,axiom, % 172.78/172.46 ! [V_ys_2,V_P_2,V_xs_2,V_x_2,T_a] : % 172.78/172.46 ( 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) % 172.78/172.46 <=> ? [B_us,B_vs] : % 172.78/172.46 ( 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)) % 172.78/172.46 & ! [B_x] : % 172.78/172.46 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),B_us))) % 172.78/172.46 => ~ hBOOL(hAPP(V_P_2,B_x)) ) % 172.78/172.46 & hBOOL(hAPP(V_P_2,V_x_2)) % 172.78/172.46 & V_xs_2 = hAPP(c_List_Ofilter(T_a,V_P_2),B_vs) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_list__ball__nth,axiom, % 172.78/172.46 ! [V_P_2,V_xs_2,T_a,V_n_2] : % 172.78/172.46 ( 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))) % 172.78/172.46 => ( ! [B_x] : % 172.78/172.46 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 172.78/172.46 => hBOOL(hAPP(V_P_2,B_x)) ) % 172.78/172.46 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),V_n_2))) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_sorted_OCons,axiom, % 172.78/172.46 ! [V_x_2,V_xs_2,T_a] : % 172.78/172.46 ( class_Orderings_Olinorder(T_a) % 172.78/172.46 => ( ! [B_x] : % 172.78/172.46 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 172.78/172.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x_2),B_x)) ) % 172.78/172.46 => ( c_List_Olinorder__class_Osorted(T_a,V_xs_2) % 172.78/172.46 => c_List_Olinorder__class_Osorted(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) ) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_list__ex__length,axiom, % 172.78/172.46 ! [V_xs_2,V_P_2,T_a] : % 172.78/172.46 ( c_List_Olist__ex(T_a,V_P_2,V_xs_2) % 172.78/172.46 <=> ? [B_n] : % 172.78/172.46 ( 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))) % 172.78/172.46 & hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_n))) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_in__set__conv__decomp,axiom, % 172.78/172.46 ! [V_xs_2,V_x_2,T_a] : % 172.78/172.46 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 172.78/172.46 <=> ? [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)) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_list__ex__simps_I2_J,axiom, % 172.78/172.46 ! [V_P_2,T_a] : ~ c_List_Olist__ex(T_a,V_P_2,c_List_Olist_ONil(T_a)) ). % 172.78/172.46 % 172.78/172.46 fof(fact_list__ex__append,axiom, % 172.78/172.46 ! [V_ys_2,V_xs_2,V_P_2,T_a] : % 172.78/172.46 ( c_List_Olist__ex(T_a,V_P_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)) % 172.78/172.46 <=> ( c_List_Olist__ex(T_a,V_P_2,V_xs_2) % 172.78/172.46 | c_List_Olist__ex(T_a,V_P_2,V_ys_2) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_list__ex__iff,axiom, % 172.78/172.46 ! [V_xs_2,V_P_2,T_a] : % 172.78/172.46 ( c_List_Olist__ex(T_a,V_P_2,V_xs_2) % 172.78/172.46 <=> ? [B_x] : % 172.78/172.46 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 172.78/172.46 & hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_list__ex__rev,axiom, % 172.78/172.46 ! [V_xs_2,V_P_2,T_a] : % 172.78/172.46 ( c_List_Olist__ex(T_a,V_P_2,hAPP(c_List_Orev(T_a),V_xs_2)) % 172.78/172.46 <=> c_List_Olist__ex(T_a,V_P_2,V_xs_2) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_list__ex__simps_I1_J,axiom, % 172.78/172.46 ! [V_xs_2,V_x_2,V_P_2,T_a] : % 172.78/172.46 ( c_List_Olist__ex(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) % 172.78/172.46 <=> ( hBOOL(hAPP(V_P_2,V_x_2)) % 172.78/172.46 | c_List_Olist__ex(T_a,V_P_2,V_xs_2) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_in__set__conv__decomp__first,axiom, % 172.78/172.46 ! [V_xs_2,V_x_2,T_a] : % 172.78/172.46 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 172.78/172.46 <=> ? [B_ys] : % 172.78/172.46 ( ? [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)) % 172.78/172.46 & ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),B_ys))) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_in__set__conv__decomp__last,axiom, % 172.78/172.46 ! [V_xs_2,V_x_2,T_a] : % 172.78/172.46 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),V_xs_2))) % 172.78/172.46 <=> ? [B_ys,B_zs] : % 172.78/172.46 ( 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)) % 172.78/172.46 & ~ hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),B_zs))) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_option_Orecs_I2_J,axiom, % 172.78/172.46 ! [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) ). % 172.78/172.46 % 172.78/172.46 fof(fact_option_Orecs_I1_J,axiom, % 172.78/172.46 ! [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 ). % 172.78/172.46 % 172.78/172.46 fof(fact_list__all__length,axiom, % 172.78/172.46 ! [V_xs_2,V_P_2,T_a] : % 172.78/172.46 ( c_List_Olist__all(T_a,V_P_2,V_xs_2) % 172.78/172.46 <=> ! [B_n] : % 172.78/172.46 ( 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))) % 172.78/172.46 => hBOOL(hAPP(V_P_2,hAPP(hAPP(c_List_Onth(T_a),V_xs_2),B_n))) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_measure__function__int,axiom, % 172.78/172.46 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))) ). % 172.78/172.46 % 172.78/172.46 fof(fact_list__all__simps_I1_J,axiom, % 172.78/172.46 ! [V_xs_2,V_x_2,V_P_2,T_a] : % 172.78/172.46 ( c_List_Olist__all(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) % 172.78/172.46 <=> ( hBOOL(hAPP(V_P_2,V_x_2)) % 172.78/172.46 & c_List_Olist__all(T_a,V_P_2,V_xs_2) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_list__all__rev,axiom, % 172.78/172.46 ! [V_xs_2,V_P_2,T_a] : % 172.78/172.46 ( c_List_Olist__all(T_a,V_P_2,hAPP(c_List_Orev(T_a),V_xs_2)) % 172.78/172.46 <=> c_List_Olist__all(T_a,V_P_2,V_xs_2) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_measure__snd,axiom, % 172.78/172.46 ! [T_b,V_f_2,T_a] : % 172.78/172.46 ( c_FunDef_Ois__measure(T_a,V_f_2) % 172.78/172.46 => 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))) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_measure__fst,axiom, % 172.78/172.46 ! [T_b,V_f_2,T_a] : % 172.78/172.46 ( c_FunDef_Ois__measure(T_a,V_f_2) % 172.78/172.46 => 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))) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_list__all__iff,axiom, % 172.78/172.46 ! [V_xs_2,V_P_2,T_a] : % 172.78/172.46 ( c_List_Olist__all(T_a,V_P_2,V_xs_2) % 172.78/172.46 <=> ! [B_x] : % 172.78/172.46 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 172.78/172.46 => hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_is__measure_Osimps,axiom, % 172.78/172.46 ! [V_a_2,T_a] : c_FunDef_Ois__measure(T_a,V_a_2) ). % 172.78/172.46 % 172.78/172.46 fof(fact_is__measure_Oequations,axiom, % 172.78/172.46 ! [V_a_2,T_a] : c_FunDef_Ois__measure(T_a,V_a_2) ). % 172.78/172.46 % 172.78/172.46 fof(fact_is__measure_Ointros,axiom, % 172.78/172.46 ! [V_f_2,T_a] : c_FunDef_Ois__measure(T_a,V_f_2) ). % 172.78/172.46 % 172.78/172.46 fof(fact_measure__size,axiom, % 172.78/172.46 ! [T_a] : % 172.78/172.46 ( class_Nat_Osize(T_a) % 172.78/172.46 => c_FunDef_Ois__measure(T_a,c_Nat_Osize__class_Osize(T_a)) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_list__all__append,axiom, % 172.78/172.46 ! [V_ys_2,V_xs_2,V_P_2,T_a] : % 172.78/172.46 ( c_List_Olist__all(T_a,V_P_2,hAPP(hAPP(c_List_Oappend(T_a),V_xs_2),V_ys_2)) % 172.78/172.46 <=> ( c_List_Olist__all(T_a,V_P_2,V_xs_2) % 172.78/172.46 & c_List_Olist__all(T_a,V_P_2,V_ys_2) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_Ball__set__list__all,axiom, % 172.78/172.46 ! [V_P_2,V_xs_2,T_a] : % 172.78/172.46 ( ! [B_x] : % 172.78/172.46 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 172.78/172.46 => hBOOL(hAPP(V_P_2,B_x)) ) % 172.78/172.46 <=> c_List_Olist__all(T_a,V_P_2,V_xs_2) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_list__all__simps_I2_J,axiom, % 172.78/172.46 ! [V_P_2,T_a] : c_List_Olist__all(T_a,V_P_2,c_List_Olist_ONil(T_a)) ). % 172.78/172.46 % 172.78/172.46 fof(fact_list__all__iff__raw,axiom, % 172.78/172.46 ! [V_xs_2,V_P_2,T_a] : % 172.78/172.46 ( c_List_Olist__all(T_a,V_P_2,V_xs_2) % 172.78/172.46 <=> ! [B_x] : % 172.78/172.46 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 172.78/172.46 => hBOOL(hAPP(V_P_2,B_x)) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_list__ex1__simps_I2_J,axiom, % 172.78/172.46 ! [V_xs_2,V_x_2,V_P_2,T_a] : % 172.78/172.46 ( c_List_Olist__ex1(T_a,V_P_2,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x_2),V_xs_2)) % 172.78/172.46 <=> ( ( hBOOL(hAPP(V_P_2,V_x_2)) % 172.78/172.46 => 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) ) % 172.78/172.46 & ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 172.78/172.46 => c_List_Olist__ex1(T_a,V_P_2,V_xs_2) ) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_equal__fun__def,axiom, % 172.78/172.46 ! [V_g_2,V_f_2,T_a,T_b] : % 172.78/172.46 ( ( class_HOL_Oequal(T_b) % 172.78/172.46 & class_Enum_Oenum(T_a) ) % 172.78/172.46 => ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_fun(T_a,T_b)),V_f_2),V_g_2)) % 172.78/172.46 <=> ! [B_x] : % 172.78/172.46 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),c_Enum_Oenum__class_Oenum(T_a)))) % 172.78/172.46 => hAPP(V_f_2,B_x) = hAPP(V_g_2,B_x) ) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_list__ex1__simps_I1_J,axiom, % 172.78/172.46 ! [V_P_2,T_a] : ~ c_List_Olist__ex1(T_a,V_P_2,c_List_Olist_ONil(T_a)) ). % 172.78/172.46 % 172.78/172.46 fof(fact_equal,axiom, % 172.78/172.46 ! [T_a] : % 172.78/172.46 ( class_HOL_Oequal(T_a) % 172.78/172.46 => c_HOL_Oequal__class_Oequal(T_a) = c_fequal ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_equal__refl,axiom, % 172.78/172.46 ! [V_x,T_a] : % 172.78/172.46 ( class_HOL_Oequal(T_a) % 172.78/172.46 => hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(T_a),V_x),V_x)) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_equal__eq,axiom, % 172.78/172.46 ! [V_y_2,V_x_2,T_a] : % 172.78/172.46 ( class_HOL_Oequal(T_a) % 172.78/172.46 => ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(T_a),V_x_2),V_y_2)) % 172.78/172.46 <=> V_x_2 = V_y_2 ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_eq__equal,axiom, % 172.78/172.46 ! [T_a] : % 172.78/172.46 ( class_HOL_Oequal(T_a) % 172.78/172.46 => c_fequal = c_HOL_Oequal__class_Oequal(T_a) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_exists1__code,axiom, % 172.78/172.46 ! [V_P_2,T_a] : % 172.78/172.46 ( class_Enum_Oenum(T_a) % 172.78/172.46 => ( ? [B_x] : % 172.78/172.46 ( hBOOL(hAPP(V_P_2,B_x)) % 172.78/172.46 & ! [B_y] : % 172.78/172.46 ( hBOOL(hAPP(V_P_2,B_y)) % 172.78/172.46 => B_y = B_x ) ) % 172.78/172.46 <=> c_List_Olist__ex1(T_a,V_P_2,c_Enum_Oenum__class_Oenum(T_a)) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_bool_Osize_I3_J,axiom, % 172.78/172.46 hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fTrue) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 172.78/172.46 % 172.78/172.46 fof(fact_bool_Osize_I4_J,axiom, % 172.78/172.46 hAPP(c_Nat_Osize__class_Osize(tc_HOL_Obool),c_fFalse) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ). % 172.78/172.46 % 172.78/172.46 fof(fact_list__ex1__iff,axiom, % 172.78/172.46 ! [V_xs_2,V_P_2,T_a] : % 172.78/172.46 ( c_List_Olist__ex1(T_a,V_P_2,V_xs_2) % 172.78/172.46 <=> ? [B_x] : % 172.78/172.46 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),V_xs_2))) % 172.78/172.46 & hBOOL(hAPP(V_P_2,B_x)) % 172.78/172.46 & ! [B_y] : % 172.78/172.46 ( ( hBOOL(hAPP(hAPP(c_member(T_a),B_y),hAPP(c_List_Oset(T_a),V_xs_2))) % 172.78/172.46 & hBOOL(hAPP(V_P_2,B_y)) ) % 172.78/172.46 => B_y = B_x ) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_size__code,axiom, % 172.78/172.46 ! [V_xq_2,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(T_a)),V_xq_2) = hAPP(c_Option_Ooption_Ooption__case(tc_Nat_Onat,tc_prod(T_a,tc_Lazy__Sequence_Olazy__sequence(T_a)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,tc_Lazy__Sequence_Olazy__sequence(T_a),tc_Nat_Onat),hAPP(c_COMBK(tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_a),tc_Nat_Onat),T_a),hAPP(hAPP(c_COMBC(tc_Lazy__Sequence_Olazy__sequence(T_a),tc_Nat_Onat,tc_Nat_Onat),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Lazy__Sequence_Olazy__sequence(T_a)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(T_a)))),c_Groups_Oone__class_Oone(tc_Nat_Onat))))),hAPP(c_Lazy__Sequence_Oyield(T_a),V_xq_2)) ). % 172.78/172.46 % 172.78/172.46 fof(fact_transfer__morphism__int__nat,axiom, % 172.78/172.46 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)) ). % 172.78/172.46 % 172.78/172.46 fof(fact_eq__int__code_I5_J,axiom, % 172.78/172.46 ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OPls)) ). % 172.78/172.46 % 172.78/172.46 fof(fact_eq__int__code_I2_J,axiom, % 172.78/172.46 ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OMin)) ). % 172.78/172.46 % 172.78/172.46 fof(fact_eq__int__code_I8_J,axiom, % 172.78/172.46 ! [V_k2_2] : % 172.78/172.46 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OBit1(V_k2_2))) % 172.78/172.46 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),V_k2_2)) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_eq__int__code_I12_J,axiom, % 172.78/172.46 ! [V_k1_2] : % 172.78/172.46 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OMin)) % 172.78/172.46 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k1_2),c_Int_OMin)) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_eq__int__code_I7_J,axiom, % 172.78/172.46 ! [V_k2] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OBit0(V_k2))) ). % 172.78/172.46 % 172.78/172.46 fof(fact_eq__int__code_I11_J,axiom, % 172.78/172.46 ! [V_k1] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(V_k1)),c_Int_OMin)) ). % 172.78/172.46 % 172.78/172.46 fof(fact_eq__int__code_I4_J,axiom, % 172.78/172.46 ! [V_k2] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OBit1(V_k2))) ). % 172.78/172.46 % 172.78/172.46 fof(fact_eq__int__code_I10_J,axiom, % 172.78/172.46 ! [V_k1] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(V_k1)),c_Int_OPls)) ). % 172.78/172.46 % 172.78/172.46 fof(fact_eq__int__code_I3_J,axiom, % 172.78/172.46 ! [V_k2_2] : % 172.78/172.46 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OBit0(V_k2_2))) % 172.78/172.46 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),V_k2_2)) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_eq__int__code_I9_J,axiom, % 172.78/172.46 ! [V_k1_2] : % 172.78/172.46 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OPls)) % 172.78/172.46 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k1_2),c_Int_OPls)) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_eq__int__code_I14_J,axiom, % 172.78/172.46 ! [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))) ). % 172.78/172.46 % 172.78/172.46 fof(fact_eq__int__code_I15_J,axiom, % 172.78/172.46 ! [V_k2,V_k1] : ~ hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(V_k1)),c_Int_OBit0(V_k2))) ). % 172.78/172.46 % 172.78/172.46 fof(fact_equal__int__def,axiom, % 172.78/172.46 ! [V_l_2,V_k_2] : % 172.78/172.46 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k_2),V_l_2)) % 172.78/172.46 <=> hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_k_2),V_l_2) = c_Groups_Ozero__class_Ozero(tc_Int_Oint) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_eq__number__of__int__code,axiom, % 172.78/172.46 ! [V_l_2,V_k_2] : % 172.78/172.46 ( 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))) % 172.78/172.46 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k_2),V_l_2)) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_eq__int__code_I6_J,axiom, % 172.78/172.46 hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OMin),c_Int_OMin)) ). % 172.78/172.46 % 172.78/172.46 fof(fact_eq__int__code_I16_J,axiom, % 172.78/172.46 ! [V_k2_2,V_k1_2] : % 172.78/172.46 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit1(V_k1_2)),c_Int_OBit1(V_k2_2))) % 172.78/172.46 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_eq__int__code_I1_J,axiom, % 172.78/172.46 hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OPls),c_Int_OPls)) ). % 172.78/172.46 % 172.78/172.46 fof(fact_eq__int__code_I13_J,axiom, % 172.78/172.46 ! [V_k2_2,V_k1_2] : % 172.78/172.46 ( hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),c_Int_OBit0(V_k1_2)),c_Int_OBit0(V_k2_2))) % 172.78/172.46 <=> hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k1_2),V_k2_2)) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_lazy__sequence__size__code,axiom, % 172.78/172.46 ! [V_xq_2,V_s_2,T_a] : hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(T_a,V_s_2),V_xq_2) = hAPP(c_Option_Ooption_Ooption__case(tc_Nat_Onat,tc_prod(T_a,tc_Lazy__Sequence_Olazy__sequence(T_a)),c_Groups_Ozero__class_Ozero(tc_Nat_Onat),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,tc_Lazy__Sequence_Olazy__sequence(T_a),tc_Nat_Onat),hAPP(hAPP(c_COMBC(T_a,tc_Nat_Onat,tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_a),tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_a),tc_fun(tc_Nat_Onat,tc_Nat_Onat)),tc_fun(tc_Nat_Onat,tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_a),tc_Nat_Onat)),T_a),c_COMBC(tc_Lazy__Sequence_Olazy__sequence(T_a),tc_Nat_Onat,tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_a),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_a),tc_fun(tc_Nat_Onat,tc_Nat_Onat)),T_a),hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_Lazy__Sequence_Olazy__sequence(T_a)),c_Groups_Oplus__class_Oplus(tc_Nat_Onat))),hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_a),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_a),tc_Nat_Onat)),hAPP(hAPP(c_COMBB(tc_fun(tc_Nat_Onat,tc_Nat_Onat),tc_fun(tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_a),tc_Nat_Onat),tc_fun(tc_Lazy__Sequence_Olazy__sequence(T_a),tc_Nat_Onat)),T_a),c_COMBB(tc_Nat_Onat,tc_Nat_Onat,tc_Lazy__Sequence_Olazy__sequence(T_a))),hAPP(hAPP(c_COMBB(tc_Nat_Onat,tc_fun(tc_Nat_Onat,tc_Nat_Onat),T_a),c_Groups_Oplus__class_Oplus(tc_Nat_Onat)),V_s_2))),c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(T_a,V_s_2))))),c_Groups_Oone__class_Oone(tc_Nat_Onat)))),hAPP(c_Lazy__Sequence_Oyield(T_a),V_xq_2)) ). % 172.78/172.46 % 172.78/172.46 fof(fact_seq__case,axiom, % 172.78/172.46 ! [V_xq_2,V_g_2,V_f_2,T_b,T_a] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(T_a,T_b,V_f_2,V_g_2,V_xq_2) = hAPP(c_Option_Ooption_Ooption__case(T_a,tc_prod(T_b,tc_Lazy__Sequence_Olazy__sequence(T_b)),V_f_2,hAPP(c_Product__Type_Oprod_Oprod__case(T_b,tc_Lazy__Sequence_Olazy__sequence(T_b),T_a),V_g_2)),hAPP(c_Lazy__Sequence_Oyield(T_b),V_xq_2)) ). % 172.78/172.46 % 172.78/172.46 fof(fact_eq__int__refl,axiom, % 172.78/172.46 ! [V_k] : hBOOL(hAPP(hAPP(c_HOL_Oequal__class_Oequal(tc_Int_Oint),V_k),V_k)) ). % 172.78/172.46 % 172.78/172.46 fof(fact_yieldn__def,axiom, % 172.78/172.46 ! [T_a] : c_Lazy__Sequence_Oyieldn(T_a) = c_Lazy__Sequence_Oanamorph(tc_Lazy__Sequence_Olazy__sequence(T_a),T_a,c_Lazy__Sequence_Oyield(T_a)) ). % 172.78/172.46 % 172.78/172.46 fof(fact_lazy__sequence_Osize_I2_J,axiom, % 172.78/172.46 ! [V_lazy__sequence_2,V_a_2,V_fa_2,T_a] : hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(T_a,V_fa_2),c_Lazy__Sequence_Olazy__sequence_OInsert(T_a,V_a_2,V_lazy__sequence_2)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(V_fa_2,V_a_2)),hAPP(c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__size(T_a,V_fa_2),V_lazy__sequence_2))),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 172.78/172.46 % 172.78/172.46 fof(fact_lazy__sequence_Osimps_I5_J,axiom, % 172.78/172.46 ! [V_lazy__sequence_2,V_a_2,V_f2_2,V_f1_2,T_b,T_a] : c_Lazy__Sequence_Olazy__sequence_Olazy__sequence__case(T_a,T_b,V_f1_2,V_f2_2,c_Lazy__Sequence_Olazy__sequence_OInsert(T_b,V_a_2,V_lazy__sequence_2)) = hAPP(hAPP(V_f2_2,V_a_2),V_lazy__sequence_2) ). % 172.78/172.46 % 172.78/172.46 fof(fact_lazy__sequence_Oinject,axiom, % 172.78/172.46 ! [V_lazy__sequence_H_2,V_a_H_2,V_lazy__sequence_2,V_a_2,T_a] : % 172.78/172.46 ( c_Lazy__Sequence_Olazy__sequence_OInsert(T_a,V_a_2,V_lazy__sequence_2) = c_Lazy__Sequence_Olazy__sequence_OInsert(T_a,V_a_H_2,V_lazy__sequence_H_2) % 172.78/172.46 <=> ( V_a_2 = V_a_H_2 % 172.78/172.46 & V_lazy__sequence_2 = V_lazy__sequence_H_2 ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact__01,axiom, % 172.78/172.46 ! [V_xq,V_x,T_a] : hAPP(c_Lazy__Sequence_Oyield(T_a),c_Lazy__Sequence_Olazy__sequence_OInsert(T_a,V_x,V_xq)) = hAPP(c_Option_Ooption_OSome(tc_prod(T_a,tc_Lazy__Sequence_Olazy__sequence(T_a))),hAPP(hAPP(c_Product__Type_OPair(T_a,tc_Lazy__Sequence_Olazy__sequence(T_a)),V_x),V_xq)) ). % 172.78/172.46 % 172.78/172.46 fof(fact_lazy__sequence_Osize_I4_J,axiom, % 172.78/172.46 ! [V_lazy__sequence,V_a,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(T_a)),c_Lazy__Sequence_Olazy__sequence_OInsert(T_a,V_a,V_lazy__sequence)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_Lazy__Sequence_Olazy__sequence(T_a)),V_lazy__sequence)),hAPP(c_Nat_OSuc,c_Groups_Ozero__class_Ozero(tc_Nat_Onat))) ). % 172.78/172.46 % 172.78/172.46 fof(fact_New__DSequence_Opos__decr__bind__def,axiom, % 172.78/172.46 ! [V_f_2,V_x_2,T_a,T_b,V_i_2] : % 172.78/172.46 ( ( V_i_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 172.78/172.46 => hAPP(c_New__DSequence_Opos__decr__bind(T_b,T_a,V_x_2,V_f_2),V_i_2) = c_Lazy__Sequence_Oempty(T_a) ) % 172.78/172.46 & ( V_i_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 172.78/172.46 => hAPP(c_New__DSequence_Opos__decr__bind(T_b,T_a,V_x_2,V_f_2),V_i_2) = hAPP(c_Lazy__Sequence_Obind(T_b,T_a,hAPP(V_x_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_i_2),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral)))),hAPP(hAPP(c_COMBC(T_b,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_a)),V_f_2),V_i_2)) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_New__DSequence_Oneg__decr__bind__def,axiom, % 172.78/172.46 ! [V_f_2,V_x_2,T_a,T_b,V_i_2] : % 172.78/172.46 ( ( V_i_2 = c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 172.78/172.46 => hAPP(c_New__DSequence_Oneg__decr__bind(T_b,T_a,V_x_2,V_f_2),V_i_2) = c_Lazy__Sequence_Ohit__bound(T_a) ) % 172.78/172.46 & ( V_i_2 != c_Groups_Ozero__class_Ozero(tc_Code__Numeral_Ocode__numeral) % 172.78/172.46 => hAPP(c_New__DSequence_Oneg__decr__bind(T_b,T_a,V_x_2,V_f_2),V_i_2) = c_Lazy__Sequence_Ohb__bind(T_b,T_a,hAPP(V_x_2,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Code__Numeral_Ocode__numeral),V_i_2),c_Groups_Oone__class_Oone(tc_Code__Numeral_Ocode__numeral))),hAPP(hAPP(c_COMBC(T_b,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_a))),V_f_2),V_i_2)) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_New__Random__Sequence_Opos__decr__bind__def,axiom, % 172.78/172.46 ! [V_seed_2,V_size_2,V_nrandom_2,V_f_2,V_R_2,T_a,T_b] : c_New__Random__Sequence_Opos__decr__bind(T_b,T_a,V_R_2,V_f_2,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Opos__decr__bind(T_b,T_a,hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(c_COMBC(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_a))),hAPP(hAPP(c_COMBC(T_b,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_a)))),hAPP(hAPP(c_COMBC(T_b,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_a))))),V_f_2),V_nrandom_2)),V_size_2)),V_seed_2)) ). % 172.78/172.46 % 172.78/172.46 fof(fact_New__Random__Sequence_Oneg__decr__bind__def,axiom, % 172.78/172.46 ! [V_seed_2,V_size_2,V_nrandom_2,V_f_2,V_R_2,T_a,T_b] : c_New__Random__Sequence_Oneg__decr__bind(T_b,T_a,V_R_2,V_f_2,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Oneg__decr__bind(T_b,T_a,hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(c_COMBC(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_a)))),hAPP(hAPP(c_COMBC(T_b,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_a))))),hAPP(hAPP(c_COMBC(T_b,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_a)))))),V_f_2),V_nrandom_2)),V_size_2)),V_seed_2)) ). % 172.78/172.46 % 172.78/172.46 fof(fact_New__DSequence_Oneg__bind__def,axiom, % 172.78/172.46 ! [V_i_2,V_f_2,V_x_2,T_a,T_b] : hAPP(c_New__DSequence_Oneg__bind(T_b,T_a,V_x_2,V_f_2),V_i_2) = c_Lazy__Sequence_Ohb__bind(T_b,T_a,hAPP(V_x_2,V_i_2),hAPP(hAPP(c_COMBC(T_b,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_a))),V_f_2),V_i_2)) ). % 172.78/172.46 % 172.78/172.46 fof(fact_New__DSequence_Opos__empty__def,axiom, % 172.78/172.46 ! [V_i_1,T_a] : hAPP(c_New__DSequence_Opos__empty(T_a),V_i_1) = c_Lazy__Sequence_Oempty(T_a) ). % 172.78/172.46 % 172.78/172.46 fof(fact_pos__empty__def,axiom, % 172.78/172.46 ! [V_seed_2,V_size_2,V_nrandom_2,T_a] : c_New__Random__Sequence_Opos__empty(T_a,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Opos__empty(T_a) ). % 172.78/172.46 % 172.78/172.46 fof(fact_neg__bind__def,axiom, % 172.78/172.46 ! [V_seed_2,V_size_2,V_nrandom_2,V_f_2,V_R_2,T_a,T_b] : hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__bind(T_b,T_a,V_R_2,V_f_2),V_nrandom_2),V_size_2),V_seed_2) = c_New__DSequence_Oneg__bind(T_b,T_a,hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(c_COMBC(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_a)))),hAPP(hAPP(c_COMBC(T_b,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_a))))),hAPP(hAPP(c_COMBC(T_b,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_a)))))),V_f_2),V_nrandom_2)),V_size_2)),V_seed_2)) ). % 172.78/172.46 % 172.78/172.46 fof(fact_New__DSequence_Opos__bind__def,axiom, % 172.78/172.46 ! [V_i_2,V_f_2,V_x_2,T_a,T_b] : hAPP(c_New__DSequence_Opos__bind(T_b,T_a,V_x_2,V_f_2),V_i_2) = hAPP(c_Lazy__Sequence_Obind(T_b,T_a,hAPP(V_x_2,V_i_2)),hAPP(hAPP(c_COMBC(T_b,tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_a)),V_f_2),V_i_2)) ). % 172.78/172.46 % 172.78/172.46 fof(fact_neg__map__def,axiom, % 172.78/172.46 ! [V_P_2,V_f_2,T_a,T_b] : c_New__Random__Sequence_Oneg__map(T_b,T_a,V_f_2,V_P_2) = c_New__Random__Sequence_Oneg__bind(T_b,T_a,V_P_2,hAPP(c_Fun_Ocomp(T_a,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(tc_Option_Ooption(T_a)))))),T_b,c_New__Random__Sequence_Oneg__single(T_a)),V_f_2)) ). % 172.78/172.46 % 172.78/172.46 fof(fact_neg__single__def,axiom, % 172.78/172.46 ! [V_seed_2,V_size_2,V_nrandom_2,V_x_2,T_a] : hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Oneg__single(T_a),V_x_2),V_nrandom_2),V_size_2),V_seed_2) = c_New__DSequence_Oneg__single(T_a,V_x_2) ). % 172.78/172.46 % 172.78/172.46 fof(fact_pos__bind__def,axiom, % 172.78/172.46 ! [V_seed_2,V_size_2,V_nrandom_2,V_f_2,V_R_2,T_a,T_b] : hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__bind(T_b,T_a,V_R_2,V_f_2),V_nrandom_2),V_size_2),V_seed_2) = c_New__DSequence_Opos__bind(T_b,T_a,hAPP(hAPP(hAPP(V_R_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(c_COMBC(T_b,tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_a))),hAPP(hAPP(c_COMBC(T_b,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_a)))),hAPP(hAPP(c_COMBC(T_b,tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_a))))),V_f_2),V_nrandom_2)),V_size_2)),V_seed_2)) ). % 172.78/172.46 % 172.78/172.46 fof(fact_New__DSequence_Oneg__single__def,axiom, % 172.78/172.46 ! [V_i_1,V_x,T_a] : hAPP(c_New__DSequence_Oneg__single(T_a,V_x),V_i_1) = c_Lazy__Sequence_Ohb__single(T_a,V_x) ). % 172.78/172.46 % 172.78/172.46 fof(fact_pos__map__def,axiom, % 172.78/172.46 ! [V_P_2,V_f_2,T_a,T_b] : c_New__Random__Sequence_Opos__map(T_b,T_a,V_f_2,V_P_2) = c_New__Random__Sequence_Opos__bind(T_b,T_a,V_P_2,hAPP(c_Fun_Ocomp(T_a,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_Code__Numeral_Ocode__numeral,tc_fun(tc_prod(tc_Code__Numeral_Ocode__numeral,tc_Code__Numeral_Ocode__numeral),tc_fun(tc_Code__Numeral_Ocode__numeral,tc_Lazy__Sequence_Olazy__sequence(T_a))))),T_b,c_New__Random__Sequence_Opos__single(T_a)),V_f_2)) ). % 172.78/172.46 % 172.78/172.46 fof(fact_pos__single__def,axiom, % 172.78/172.46 ! [V_seed_2,V_size_2,V_nrandom_2,V_x_2,T_a] : hAPP(hAPP(hAPP(hAPP(c_New__Random__Sequence_Opos__single(T_a),V_x_2),V_nrandom_2),V_size_2),V_seed_2) = c_New__DSequence_Opos__single(T_a,V_x_2) ). % 172.78/172.46 % 172.78/172.46 fof(fact_length__splice,axiom, % 172.78/172.46 ! [V_ys,V_xs,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Osplice(T_a,V_xs,V_ys)) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_xs)),hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),V_ys)) ). % 172.78/172.46 % 172.78/172.46 fof(fact_splice_Osimps_I3_J,axiom, % 172.78/172.46 ! [V_ys,V_y,V_xs,V_x,T_a] : c_List_Osplice(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),V_ys)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Olist_OCons(T_a),V_y),c_List_Osplice(T_a,V_xs,V_ys))) ). % 172.78/172.46 % 172.78/172.46 fof(fact_splice__Nil2,axiom, % 172.78/172.46 ! [V_xs,T_a] : c_List_Osplice(T_a,V_xs,c_List_Olist_ONil(T_a)) = V_xs ). % 172.78/172.46 % 172.78/172.46 fof(fact_splice_Osimps_I1_J,axiom, % 172.78/172.46 ! [V_ys,T_a] : c_List_Osplice(T_a,c_List_Olist_ONil(T_a),V_ys) = V_ys ). % 172.78/172.46 % 172.78/172.46 fof(fact_splice_Osimps_I2_J,axiom, % 172.78/172.46 ! [V_va,V_v,T_a] : c_List_Osplice(T_a,hAPP(hAPP(c_List_Olist_OCons(T_a),V_v),V_va),c_List_Olist_ONil(T_a)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_v),V_va) ). % 172.78/172.46 % 172.78/172.46 fof(fact_New__DSequence_Opos__single__def,axiom, % 172.78/172.46 ! [V_i_1,V_x,T_a] : hAPP(c_New__DSequence_Opos__single(T_a,V_x),V_i_1) = hAPP(c_Lazy__Sequence_Osingle(T_a),V_x) ). % 172.78/172.46 % 172.78/172.46 fof(fact_acyclicP__converse,axiom, % 172.78/172.46 ! [V_r_2,T_a] : % 172.78/172.46 ( c_Wellfounded_Oacyclic(T_a,hAPP(c_Set_OCollect(tc_prod(T_a,T_a)),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,T_a,tc_HOL_Obool),c_Predicate_Oconversep(T_a,T_a,V_r_2)))) % 172.78/172.46 <=> 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))) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_converse__meet,axiom, % 172.78/172.46 ! [V_s_2,V_r_2,T_a,T_b] : c_Predicate_Oconversep(T_b,T_a,hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool))),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__inf__class_Oinf(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),c_Predicate_Oconversep(T_b,T_a,V_r_2)),c_Predicate_Oconversep(T_b,T_a,V_s_2)) ). % 172.78/172.46 % 172.78/172.46 fof(fact_converse__join,axiom, % 172.78/172.46 ! [V_s_2,V_r_2,T_a,T_b] : c_Predicate_Oconversep(T_b,T_a,hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_b,tc_fun(T_a,tc_HOL_Obool))),V_r_2),V_s_2)) = hAPP(hAPP(c_Lattices_Osemilattice__sup__class_Osup(tc_fun(T_a,tc_fun(T_b,tc_HOL_Obool))),c_Predicate_Oconversep(T_b,T_a,V_r_2)),c_Predicate_Oconversep(T_b,T_a,V_s_2)) ). % 172.78/172.46 % 172.78/172.46 fof(fact_conversep__eq,axiom, % 172.78/172.46 ! [T_a] : c_Predicate_Oconversep(T_a,T_a,c_fequal) = c_fequal ). % 172.78/172.46 % 172.78/172.46 fof(fact_conversep__conversep,axiom, % 172.78/172.46 ! [V_r_2,T_a,T_b] : c_Predicate_Oconversep(T_b,T_a,c_Predicate_Oconversep(T_a,T_b,V_r_2)) = V_r_2 ). % 172.78/172.46 % 172.78/172.46 fof(fact_conversep__iff,axiom, % 172.78/172.46 ! [V_b_2,V_a_2,V_r_2,T_b,T_a] : % 172.78/172.46 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_a,T_b,V_r_2),V_a_2),V_b_2)) % 172.78/172.46 <=> hBOOL(hAPP(hAPP(V_r_2,V_b_2),V_a_2)) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_conversep_Oequations,axiom, % 172.78/172.46 ! [V_a1_2,V_a2_2,V_r_2,T_b,T_a] : % 172.78/172.46 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_a,T_b,V_r_2),V_a2_2),V_a1_2)) % 172.78/172.46 <=> hBOOL(hAPP(hAPP(V_r_2,V_a1_2),V_a2_2)) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_conversep_Ointros,axiom, % 172.78/172.46 ! [T_b,T_a,V_b_2,V_a_2,V_r_2] : % 172.78/172.46 ( hBOOL(hAPP(hAPP(V_r_2,V_a_2),V_b_2)) % 172.78/172.46 => hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_a,T_b,V_r_2),V_b_2),V_a_2)) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_conversepD,axiom, % 172.78/172.46 ! [V_b_2,V_a_2,V_r_2,T_b,T_a] : % 172.78/172.46 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_a,T_b,V_r_2),V_a_2),V_b_2)) % 172.78/172.46 => hBOOL(hAPP(hAPP(V_r_2,V_b_2),V_a_2)) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_conversep__noteq,axiom, % 172.78/172.46 ! [V_y_2,V_x_2,T_a] : % 172.78/172.46 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_a,T_a,hAPP(hAPP(c_COMBB(tc_fun(T_a,tc_HOL_Obool),tc_fun(T_a,tc_HOL_Obool),T_a),hAPP(c_COMBB(tc_HOL_Obool,tc_HOL_Obool,T_a),c_fNot)),c_fequal)),V_x_2),V_y_2)) % 172.78/172.46 <=> V_x_2 != V_y_2 ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_converse__pred__comp,axiom, % 172.78/172.46 ! [V_s_2,V_r_2,T_c,T_a,T_b] : c_Predicate_Oconversep(T_b,T_a,c_Predicate_Opred__comp(T_b,T_c,T_a,V_r_2,V_s_2)) = c_Predicate_Opred__comp(T_a,T_c,T_b,c_Predicate_Oconversep(T_c,T_a,V_s_2),c_Predicate_Oconversep(T_b,T_c,V_r_2)) ). % 172.78/172.46 % 172.78/172.46 fof(fact_conversep__converse__eq,axiom, % 172.78/172.46 ! [V_y_2,V_x_2,V_r_2,T_b,T_a] : % 172.78/172.46 ( hBOOL(hAPP(hAPP(c_Predicate_Oconversep(T_a,T_b,hAPP(hAPP(c_COMBC(T_a,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_fun(T_b,tc_HOL_Obool)),T_a),c_COMBC(T_b,tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool)),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_fun(tc_fun(tc_prod(T_a,T_b),tc_HOL_Obool),tc_HOL_Obool),T_b),c_member(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))),V_r_2)),V_x_2),V_y_2)) % 172.78/172.46 <=> hBOOL(hAPP(hAPP(c_member(tc_prod(T_b,T_a)),hAPP(hAPP(c_Product__Type_OPair(T_b,T_a),V_x_2),V_y_2)),hAPP(c_Relation_Oconverse(T_a,T_b),V_r_2))) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact__02,axiom, % 172.78/172.46 ! [V_s2_2,V_s1_2,T_b,T_a] : c_Lazy__Sequence_Oproduct(T_a,T_b,V_s1_2,V_s2_2) = hAPP(c_Lazy__Sequence_Obind(T_a,tc_prod(T_a,T_b),V_s1_2),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_Lazy__Sequence_Olazy__sequence(tc_prod(T_a,T_b))),tc_Lazy__Sequence_Olazy__sequence(tc_prod(T_a,T_b)),T_a),c_Lazy__Sequence_Obind(T_b,tc_prod(T_a,T_b),V_s2_2)),hAPP(hAPP(c_COMBB(tc_fun(T_b,tc_prod(T_a,T_b)),tc_fun(T_b,tc_Lazy__Sequence_Olazy__sequence(tc_prod(T_a,T_b))),T_a),hAPP(c_COMBB(tc_prod(T_a,T_b),tc_Lazy__Sequence_Olazy__sequence(tc_prod(T_a,T_b)),T_b),c_Lazy__Sequence_Osingle(tc_prod(T_a,T_b)))),c_Product__Type_OPair(T_a,T_b)))) ). % 172.78/172.46 % 172.78/172.46 fof(fact_tl__replicate,axiom, % 172.78/172.46 ! [V_x,T_a,V_n] : % 172.78/172.46 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 172.78/172.46 => hAPP(c_List_Otl(T_a),c_List_Oreplicate(T_a,V_n,V_x)) = c_List_Oreplicate(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_n),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_x) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_zip__replicate,axiom, % 172.78/172.46 ! [V_y,V_j,V_x,V_i,T_b,T_a] : hAPP(hAPP(c_List_Ozip(T_a,T_b),c_List_Oreplicate(T_a,V_i,V_x)),c_List_Oreplicate(T_b,V_j,V_y)) = c_List_Oreplicate(tc_prod(T_a,T_b),hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_i),V_j),hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),V_x),V_y)) ). % 172.78/172.46 % 172.78/172.46 fof(fact_replicate__app__Cons__same,axiom, % 172.78/172.46 ! [V_xs,V_x,V_n,T_a] : hAPP(hAPP(c_List_Oappend(T_a),c_List_Oreplicate(T_a,V_n,V_x)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),V_xs)) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),hAPP(hAPP(c_List_Oappend(T_a),c_List_Oreplicate(T_a,V_n,V_x)),V_xs)) ). % 172.78/172.46 % 172.78/172.46 fof(fact_replicate__Suc,axiom, % 172.78/172.46 ! [V_x,V_n,T_a] : c_List_Oreplicate(T_a,hAPP(c_Nat_OSuc,V_n),V_x) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Oreplicate(T_a,V_n,V_x)) ). % 172.78/172.46 % 172.78/172.46 fof(fact_rev__replicate,axiom, % 172.78/172.46 ! [V_x,V_n,T_a] : hAPP(c_List_Orev(T_a),c_List_Oreplicate(T_a,V_n,V_x)) = c_List_Oreplicate(T_a,V_n,V_x) ). % 172.78/172.46 % 172.78/172.46 fof(fact_last__replicate,axiom, % 172.78/172.46 ! [V_x,T_a,V_n] : % 172.78/172.46 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 172.78/172.46 => c_List_Olast(T_a,c_List_Oreplicate(T_a,V_n,V_x)) = V_x ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_drop__replicate,axiom, % 172.78/172.46 ! [V_x,V_k,V_i,T_a] : hAPP(hAPP(c_List_Odrop(T_a),V_i),c_List_Oreplicate(T_a,V_k,V_x)) = c_List_Oreplicate(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Nat_Onat),V_k),V_i),V_x) ). % 172.78/172.46 % 172.78/172.46 fof(fact_hd__replicate,axiom, % 172.78/172.46 ! [V_x,T_a,V_n] : % 172.78/172.46 ( V_n != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 172.78/172.46 => hAPP(c_List_Ohd(T_a),c_List_Oreplicate(T_a,V_n,V_x)) = V_x ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_take__replicate,axiom, % 172.78/172.46 ! [V_x,V_k,V_i,T_a] : hAPP(hAPP(c_List_Otake(T_a),V_i),c_List_Oreplicate(T_a,V_k,V_x)) = c_List_Oreplicate(T_a,hAPP(hAPP(c_Orderings_Oord__class_Omin(tc_Nat_Onat),V_i),V_k),V_x) ). % 172.78/172.46 % 172.78/172.46 fof(fact_Ball__set__replicate,axiom, % 172.78/172.46 ! [V_P_2,V_a_2,V_n_2,T_a] : % 172.78/172.46 ( ! [B_x] : % 172.78/172.46 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),c_List_Oreplicate(T_a,V_n_2,V_a_2)))) % 172.78/172.46 => hBOOL(hAPP(V_P_2,B_x)) ) % 172.78/172.46 <=> ( hBOOL(hAPP(V_P_2,V_a_2)) % 172.78/172.46 | V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_Bex__set__replicate,axiom, % 172.78/172.46 ! [V_P_2,V_a_2,V_n_2,T_a] : % 172.78/172.46 ( ? [B_x] : % 172.78/172.46 ( hBOOL(hAPP(hAPP(c_member(T_a),B_x),hAPP(c_List_Oset(T_a),c_List_Oreplicate(T_a,V_n_2,V_a_2)))) % 172.78/172.46 & hBOOL(hAPP(V_P_2,B_x)) ) % 172.78/172.46 <=> ( hBOOL(hAPP(V_P_2,V_a_2)) % 172.78/172.46 & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_replicate__eq__replicate,axiom, % 172.78/172.46 ! [V_y_2,V_n_2,V_x_2,V_m_2,T_a] : % 172.78/172.46 ( c_List_Oreplicate(T_a,V_m_2,V_x_2) = c_List_Oreplicate(T_a,V_n_2,V_y_2) % 172.78/172.46 <=> ( V_m_2 = V_n_2 % 172.78/172.46 & ( V_m_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 172.78/172.46 => V_x_2 = V_y_2 ) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_nth__replicate,axiom, % 172.78/172.46 ! [V_x,T_a,V_n,V_i] : % 172.78/172.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Nat_Onat),V_i),V_n)) % 172.78/172.46 => hAPP(hAPP(c_List_Onth(T_a),c_List_Oreplicate(T_a,V_n,V_x)),V_i) = V_x ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_replicate__add,axiom, % 172.78/172.46 ! [V_x,V_m,V_n,T_a] : c_List_Oreplicate(T_a,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),V_n),V_m),V_x) = hAPP(hAPP(c_List_Oappend(T_a),c_List_Oreplicate(T_a,V_n,V_x)),c_List_Oreplicate(T_a,V_m,V_x)) ). % 172.78/172.46 % 172.78/172.46 fof(fact_append__replicate__commute,axiom, % 172.78/172.46 ! [V_k,V_x,V_n,T_a] : hAPP(hAPP(c_List_Oappend(T_a),c_List_Oreplicate(T_a,V_n,V_x)),c_List_Oreplicate(T_a,V_k,V_x)) = hAPP(hAPP(c_List_Oappend(T_a),c_List_Oreplicate(T_a,V_k,V_x)),c_List_Oreplicate(T_a,V_n,V_x)) ). % 172.78/172.46 % 172.78/172.46 fof(fact_in__set__replicate,axiom, % 172.78/172.46 ! [V_y_2,V_n_2,V_x_2,T_a] : % 172.78/172.46 ( hBOOL(hAPP(hAPP(c_member(T_a),V_x_2),hAPP(c_List_Oset(T_a),c_List_Oreplicate(T_a,V_n_2,V_y_2)))) % 172.78/172.46 <=> ( V_x_2 = V_y_2 % 172.78/172.46 & V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_filter__replicate,axiom, % 172.78/172.46 ! [V_n_2,T_a,V_x_2,V_P_2] : % 172.78/172.46 ( ( hBOOL(hAPP(V_P_2,V_x_2)) % 172.78/172.46 => hAPP(c_List_Ofilter(T_a,V_P_2),c_List_Oreplicate(T_a,V_n_2,V_x_2)) = c_List_Oreplicate(T_a,V_n_2,V_x_2) ) % 172.78/172.46 & ( ~ hBOOL(hAPP(V_P_2,V_x_2)) % 172.78/172.46 => hAPP(c_List_Ofilter(T_a,V_P_2),c_List_Oreplicate(T_a,V_n_2,V_x_2)) = c_List_Olist_ONil(T_a) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_concat__replicate__trivial,axiom, % 172.78/172.46 ! [V_i,T_a] : c_List_Oconcat(T_a,c_List_Oreplicate(tc_List_Olist(T_a),V_i,c_List_Olist_ONil(T_a))) = c_List_Olist_ONil(T_a) ). % 172.78/172.46 % 172.78/172.46 fof(fact_replicate__empty,axiom, % 172.78/172.46 ! [V_x_2,V_n_2,T_a] : % 172.78/172.46 ( c_List_Oreplicate(T_a,V_n_2,V_x_2) = c_List_Olist_ONil(T_a) % 172.78/172.46 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_empty__replicate,axiom, % 172.78/172.46 ! [V_x_2,V_n_2,T_a] : % 172.78/172.46 ( c_List_Olist_ONil(T_a) = c_List_Oreplicate(T_a,V_n_2,V_x_2) % 172.78/172.46 <=> V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_replicate__0,axiom, % 172.78/172.46 ! [V_x,T_a] : c_List_Oreplicate(T_a,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_x) = c_List_Olist_ONil(T_a) ). % 172.78/172.46 % 172.78/172.46 fof(fact_map__replicate,axiom, % 172.78/172.46 ! [V_x_2,V_n_2,V_f_2,T_a,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_a),V_f_2),c_List_Oreplicate(T_b,V_n_2,V_x_2)) = c_List_Oreplicate(T_a,V_n_2,hAPP(V_f_2,V_x_2)) ). % 172.78/172.46 % 172.78/172.46 fof(fact_replicate__append__same,axiom, % 172.78/172.46 ! [V_x,V_i,T_a] : hAPP(hAPP(c_List_Oappend(T_a),c_List_Oreplicate(T_a,V_i,V_x)),hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Olist_ONil(T_a))) = hAPP(hAPP(c_List_Olist_OCons(T_a),V_x),c_List_Oreplicate(T_a,V_i,V_x)) ). % 172.78/172.46 % 172.78/172.46 fof(fact_replicate__length__filter,axiom, % 172.78/172.46 ! [V_xs_2,V_x_2,T_a] : c_List_Oreplicate(T_a,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),hAPP(c_List_Ofilter(T_a,hAPP(c_fequal,V_x_2)),V_xs_2)),V_x_2) = hAPP(c_List_Ofilter(T_a,hAPP(c_fequal,V_x_2)),V_xs_2) ). % 172.78/172.46 % 172.78/172.46 fof(fact_length__replicate,axiom, % 172.78/172.46 ! [V_x,V_n,T_a] : hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_a)),c_List_Oreplicate(T_a,V_n,V_x)) = V_n ). % 172.78/172.46 % 172.78/172.46 fof(fact_map__replicate__const,axiom, % 172.78/172.46 ! [V_lst_2,V_k_2,T_a,T_b] : hAPP(hAPP(c_List_Omap(T_b,T_a),hAPP(c_COMBK(T_a,T_b),V_k_2)),V_lst_2) = c_List_Oreplicate(T_a,hAPP(c_Nat_Osize__class_Osize(tc_List_Olist(T_b)),V_lst_2),V_k_2) ). % 172.78/172.46 % 172.78/172.46 fof(fact_map__replicate__trivial,axiom, % 172.78/172.46 ! [V_i_2,V_x_2,T_a] : hAPP(hAPP(c_List_Omap(tc_Nat_Onat,T_a),hAPP(c_COMBK(T_a,tc_Nat_Onat),V_x_2)),c_List_Oupt(c_Groups_Ozero__class_Ozero(tc_Nat_Onat),V_i_2)) = c_List_Oreplicate(T_a,V_i_2,V_x_2) ). % 172.78/172.46 % 172.78/172.46 fof(fact_set__replicate__conv__if,axiom, % 172.78/172.46 ! [V_x_2,T_a,V_n_2] : % 172.78/172.46 ( ( V_n_2 = c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 172.78/172.46 => hAPP(c_List_Oset(T_a),c_List_Oreplicate(T_a,V_n_2,V_x_2)) = c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool)) ) % 172.78/172.46 & ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 172.78/172.46 => hAPP(c_List_Oset(T_a),c_List_Oreplicate(T_a,V_n_2,V_x_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_set__replicate,axiom, % 172.78/172.46 ! [V_x_2,T_a,V_n_2] : % 172.78/172.46 ( V_n_2 != c_Groups_Ozero__class_Ozero(tc_Nat_Onat) % 172.78/172.46 => hAPP(c_List_Oset(T_a),c_List_Oreplicate(T_a,V_n_2,V_x_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_set__replicate__Suc,axiom, % 172.78/172.46 ! [V_x_2,V_n_2,T_a] : hAPP(c_List_Oset(T_a),c_List_Oreplicate(T_a,hAPP(c_Nat_OSuc,V_n_2),V_x_2)) = hAPP(hAPP(c_Set_Oinsert(T_a),V_x_2),c_Orderings_Obot__class_Obot(tc_fun(T_a,tc_HOL_Obool))) ). % 172.78/172.46 % 172.78/172.46 fof(fact_small__lazy__list_Osimps,axiom, % 172.78/172.46 ! [V_d_2,T_a] : % 172.78/172.46 ( class_Lazy__Sequence_Osmall__lazy(T_a) % 172.78/172.46 => c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(T_a),V_d_2) = c_Lazy__Sequence_Oappend(tc_List_Olist(T_a),hAPP(c_Lazy__Sequence_Osingle(tc_List_Olist(T_a)),c_List_Olist_ONil(T_a)),hAPP(hAPP(hAPP(c_If(tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(T_a))),hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint)),V_d_2)),hAPP(c_Lazy__Sequence_Obind(tc_prod(T_a,tc_List_Olist(T_a)),tc_List_Olist(T_a),c_Lazy__Sequence_Oproduct(T_a,tc_List_Olist(T_a),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(T_a,hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_d_2),c_Groups_Oone__class_Oone(tc_Int_Oint))),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_List_Olist(T_a),hAPP(hAPP(c_Groups_Ominus__class_Ominus(tc_Int_Oint),V_d_2),c_Groups_Oone__class_Oone(tc_Int_Oint))))),hAPP(c_Product__Type_Oprod_Oprod__case(T_a,tc_List_Olist(T_a),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(T_a))),hAPP(hAPP(c_COMBB(tc_fun(tc_List_Olist(T_a),tc_List_Olist(T_a)),tc_fun(tc_List_Olist(T_a),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(T_a))),T_a),hAPP(c_COMBB(tc_List_Olist(T_a),tc_Lazy__Sequence_Olazy__sequence(tc_List_Olist(T_a)),tc_List_Olist(T_a)),c_Lazy__Sequence_Osingle(tc_List_Olist(T_a)))),c_List_Olist_OCons(T_a))))),c_Lazy__Sequence_Oempty(tc_List_Olist(T_a)))) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_eq__comp__r,axiom, % 172.78/172.46 ! [V_R_2,T_a] : c_Predicate_Opred__comp(T_a,T_a,T_a,c_fequal,c_Predicate_Opred__comp(T_a,T_a,T_a,V_R_2,c_fequal)) = V_R_2 ). % 172.78/172.46 % 172.78/172.46 fof(fact_small__lazy__prod__def,axiom, % 172.78/172.46 ! [V_d,T_b,T_a] : % 172.78/172.46 ( ( class_Lazy__Sequence_Osmall__lazy(T_a) % 172.78/172.46 & class_Lazy__Sequence_Osmall__lazy(T_b) ) % 172.78/172.46 => c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_prod(T_a,T_b),V_d) = c_Lazy__Sequence_Oproduct(T_a,T_b,c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(T_a,V_d),c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(T_b,V_d)) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact__03,axiom, % 172.78/172.46 ! [V_yq,V_xq,V_x,T_a] : c_Lazy__Sequence_Oappend(T_a,c_Lazy__Sequence_Olazy__sequence_OInsert(T_a,V_x,V_xq),V_yq) = c_Lazy__Sequence_Olazy__sequence_OInsert(T_a,V_x,c_Lazy__Sequence_Oappend(T_a,V_xq,V_yq)) ). % 172.78/172.46 % 172.78/172.46 fof(fact_New__DSequence_Opos__union__def,axiom, % 172.78/172.46 ! [V_i_2,V_yq_2,V_xq_2,T_a] : hAPP(c_New__DSequence_Opos__union(T_a,V_xq_2,V_yq_2),V_i_2) = c_Lazy__Sequence_Oappend(T_a,hAPP(V_xq_2,V_i_2),hAPP(V_yq_2,V_i_2)) ). % 172.78/172.46 % 172.78/172.46 fof(fact_field__le__epsilon,axiom, % 172.78/172.46 ! [V_y,V_x,T_a] : % 172.78/172.46 ( class_Fields_Olinordered__field(T_a) % 172.78/172.46 => ( ! [B_e] : % 172.78/172.46 ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(T_a),c_Groups_Ozero__class_Ozero(T_a)),B_e)) % 172.78/172.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),hAPP(hAPP(c_Groups_Oplus__class_Oplus(T_a),V_y),B_e))) ) % 172.78/172.46 => hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless__eq(T_a),V_x),V_y)) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_pos__union__def,axiom, % 172.78/172.46 ! [V_seed_2,V_size_2,V_nrandom_2,V_R2_2,V_R1_2,T_a] : c_New__Random__Sequence_Opos__union(T_a,V_R1_2,V_R2_2,V_nrandom_2,V_size_2,V_seed_2) = c_New__DSequence_Opos__union(T_a,hAPP(hAPP(hAPP(V_R1_2,V_nrandom_2),V_size_2),V_seed_2),hAPP(hAPP(hAPP(V_R2_2,V_nrandom_2),V_size_2),V_seed_2)) ). % 172.78/172.46 % 172.78/172.46 fof(fact_small__lazy_H_Osimps,axiom, % 172.78/172.46 ! [V_i,V_d] : % 172.78/172.46 ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d),V_i)) % 172.78/172.46 => c_Lazy__Sequence_Osmall__lazy_H(V_d,V_i) = c_Lazy__Sequence_Oempty(tc_Int_Oint) ) % 172.78/172.46 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d),V_i)) % 172.78/172.46 => c_Lazy__Sequence_Osmall__lazy_H(V_d,V_i) = c_Lazy__Sequence_Oappend(tc_Int_Oint,hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint),V_i),c_Lazy__Sequence_Osmall__lazy_H(V_d,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ) ). % 172.78/172.46 % 172.78/172.46 fof(fact_small__lazy__int__def,axiom, % 172.78/172.46 ! [V_d] : c_Lazy__Sequence_Osmall__lazy__class_Osmall__lazy(tc_Int_Oint,V_d) = c_Lazy__Sequence_Osmall__lazy_H(V_d,hAPP(c_Groups_Ouminus__class_Ouminus(tc_Int_Oint),V_d)) ). % 172.78/172.46 % 172.78/172.46 fof(fact_small__lazy_H_Opsimps,axiom, % 172.78/172.46 ! [V_i_2,V_d_2] : % 172.78/172.46 ( hBOOL(hAPP(c_Wellfounded_Oaccp(tc_prod(tc_Int_Oint,tc_Int_Oint),c_Lazy__Sequence_Osmall__lazy_H__rel),hAPP(hAPP(c_Product__Type_OPair(tc_Int_Oint,tc_Int_Oint),V_d_2),V_i_2))) % 172.78/172.46 => ( ( hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2)) % 172.78/172.46 => c_Lazy__Sequence_Osmall__lazy_H(V_d_2,V_i_2) = c_Lazy__Sequence_Oempty(tc_Int_Oint) ) % 172.78/172.46 & ( ~ hBOOL(hAPP(hAPP(c_Orderings_Oord__class_Oless(tc_Int_Oint),V_d_2),V_i_2)) % 172.78/172.46 => c_Lazy__Sequence_Osmall__lazy_H(V_d_2,V_i_2) = c_Lazy__Sequence_Oappend(tc_Int_Oint,hAPP(c_Lazy__Sequence_Osingle(tc_Int_Oint),V_i_2),c_Lazy__Sequence_Osmall__lazy_H(V_d_2,hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Int_Oint),V_i_2),c_Groups_Oone__class_Oone(tc_Int_Oint)))) ) ) ) ). % 172.78/172.46 % 172.78/172.46 %----Arity declarations (235) % 172.78/172.46 fof(arity_HOL__Obool__Lattices_Obounded__lattice,axiom, % 172.78/172.46 class_Lattices_Obounded__lattice(tc_HOL_Obool) ). % 172.78/172.46 % 172.78/172.46 fof(arity_fun__Lattices_Obounded__lattice,axiom, % 172.78/172.46 ! [T_2,T_1] : % 172.78/172.46 ( class_Lattices_Obounded__lattice(T_1) % 172.78/172.46 => class_Lattices_Obounded__lattice(tc_fun(T_2,T_1)) ) ). % 172.78/172.46 % 172.78/172.46 fof(arity_fun__Complete__Lattice_Ocomplete__lattice,axiom, % 172.78/172.46 ! [T_2,T_1] : % 172.78/172.46 ( class_Complete__Lattice_Ocomplete__lattice(T_1) % 172.78/172.46 => class_Complete__Lattice_Ocomplete__lattice(tc_fun(T_2,T_1)) ) ). % 172.78/172.46 % 172.78/172.46 fof(arity_fun__Lattices_Obounded__lattice__top,axiom, % 172.78/172.46 ! [T_2,T_1] : % 172.78/172.46 ( class_Lattices_Obounded__lattice(T_1) % 172.78/172.46 => class_Lattices_Obounded__lattice__top(tc_fun(T_2,T_1)) ) ). % 172.78/172.46 % 172.78/172.46 fof(arity_fun__Lattices_Obounded__lattice__bot,axiom, % 172.78/172.46 ! [T_2,T_1] : % 172.78/172.46 ( class_Lattices_Obounded__lattice(T_1) % 172.78/172.46 => class_Lattices_Obounded__lattice__bot(tc_fun(T_2,T_1)) ) ). % 172.78/172.46 % 172.78/172.46 fof(arity_fun__Lattices_Osemilattice__sup,axiom, % 172.78/172.46 ! [T_2,T_1] : % 172.78/172.46 ( class_Lattices_Olattice(T_1) % 172.78/172.46 => class_Lattices_Osemilattice__sup(tc_fun(T_2,T_1)) ) ). % 172.78/172.46 % 172.78/172.46 fof(arity_fun__Lattices_Osemilattice__inf,axiom, % 172.78/172.46 ! [T_2,T_1] : % 172.78/172.46 ( class_Lattices_Olattice(T_1) % 172.78/172.46 => class_Lattices_Osemilattice__inf(tc_fun(T_2,T_1)) ) ). % 172.78/172.46 % 172.78/172.46 fof(arity_fun__Lattices_Odistrib__lattice,axiom, % 172.78/172.46 ! [T_2,T_1] : % 172.78/172.46 ( class_Lattices_Odistrib__lattice(T_1) % 172.78/172.46 => class_Lattices_Odistrib__lattice(tc_fun(T_2,T_1)) ) ). % 172.78/172.46 % 172.78/172.46 fof(arity_fun__Lattices_Oboolean__algebra,axiom, % 172.78/172.46 ! [T_2,T_1] : % 172.78/172.46 ( class_Lattices_Oboolean__algebra(T_1) % 172.78/172.46 => class_Lattices_Oboolean__algebra(tc_fun(T_2,T_1)) ) ). % 172.78/172.46 % 172.78/172.46 fof(arity_fun__Orderings_Opreorder,axiom, % 172.78/172.46 ! [T_2,T_1] : % 172.78/172.46 ( class_Orderings_Opreorder(T_1) % 172.78/172.46 => class_Orderings_Opreorder(tc_fun(T_2,T_1)) ) ). % 172.78/172.46 % 172.78/172.46 fof(arity_fun__Finite__Set_Ofinite,axiom, % 172.78/172.46 ! [T_1,T_2] : % 172.78/172.46 ( ( class_Finite__Set_Ofinite(T_2) % 172.78/172.46 & class_Finite__Set_Ofinite(T_1) ) % 172.78/172.46 => class_Finite__Set_Ofinite(tc_fun(T_2,T_1)) ) ). % 172.78/172.46 % 172.78/172.46 fof(arity_fun__Lattices_Olattice,axiom, % 172.78/172.46 ! [T_2,T_1] : % 172.78/172.46 ( class_Lattices_Olattice(T_1) % 172.78/172.46 => class_Lattices_Olattice(tc_fun(T_2,T_1)) ) ). % 172.78/172.46 % 172.78/172.46 fof(arity_fun__Orderings_Oorder,axiom, % 172.78/172.46 ! [T_2,T_1] : % 172.78/172.46 ( class_Orderings_Oorder(T_1) % 172.78/172.46 => class_Orderings_Oorder(tc_fun(T_2,T_1)) ) ). % 172.78/172.46 % 172.78/172.46 fof(arity_fun__Orderings_Otop,axiom, % 172.78/172.46 ! [T_2,T_1] : % 172.78/172.46 ( class_Orderings_Otop(T_1) % 172.78/172.46 => class_Orderings_Otop(tc_fun(T_2,T_1)) ) ). % 172.78/172.46 % 172.78/172.46 fof(arity_fun__Orderings_Oord,axiom, % 172.78/172.46 ! [T_2,T_1] : % 172.78/172.46 ( class_Orderings_Oord(T_1) % 172.78/172.46 => class_Orderings_Oord(tc_fun(T_2,T_1)) ) ). % 172.78/172.46 % 172.78/172.46 fof(arity_fun__Orderings_Obot,axiom, % 172.78/172.46 ! [T_2,T_1] : % 172.78/172.46 ( class_Orderings_Obot(T_1) % 172.78/172.46 => class_Orderings_Obot(tc_fun(T_2,T_1)) ) ). % 172.78/172.46 % 172.78/172.46 fof(arity_fun__Groups_Ouminus,axiom, % 172.78/172.46 ! [T_2,T_1] : % 172.78/172.46 ( class_Groups_Ouminus(T_1) % 172.78/172.46 => class_Groups_Ouminus(tc_fun(T_2,T_1)) ) ). % 172.78/172.46 % 172.78/172.46 fof(arity_fun__Groups_Ominus,axiom, % 172.78/172.46 ! [T_2,T_1] : % 172.78/172.46 ( class_Groups_Ominus(T_1) % 172.78/172.46 => class_Groups_Ominus(tc_fun(T_2,T_1)) ) ). % 172.78/172.46 % 172.78/172.46 fof(arity_fun__HOL_Oequal,axiom, % 172.78/172.46 ! [T_1,T_2] : % 172.78/172.46 ( ( class_Enum_Oenum(T_2) % 172.78/172.46 & class_HOL_Oequal(T_1) ) % 172.78/172.46 => class_HOL_Oequal(tc_fun(T_2,T_1)) ) ). % 172.78/172.46 % 172.78/172.46 fof(arity_fun__Enum_Oenum,axiom, % 172.78/172.46 ! [T_1,T_2] : % 172.78/172.46 ( ( class_Enum_Oenum(T_2) % 172.78/172.46 & class_Enum_Oenum(T_1) ) % 172.78/172.46 => class_Enum_Oenum(tc_fun(T_2,T_1)) ) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Com__Ocom__HOL_Oequal,axiom, % 172.78/172.46 class_HOL_Oequal(tc_Com_Ocom) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Com__Ocom__Nat_Osize,axiom, % 172.78/172.46 class_Nat_Osize(tc_Com_Ocom) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Int__Oint__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom, % 172.78/172.46 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Int_Oint) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Int__Oint__Groups_Oordered__cancel__ab__semigroup__add,axiom, % 172.78/172.46 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Int_Oint) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add__imp__le,axiom, % 172.78/172.46 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Int_Oint) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Int__Oint__Rings_Olinordered__comm__semiring__strict,axiom, % 172.78/172.46 class_Rings_Olinordered__comm__semiring__strict(tc_Int_Oint) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Int__Oint__Rings_Olinordered__semiring__1__strict,axiom, % 172.78/172.46 class_Rings_Olinordered__semiring__1__strict(tc_Int_Oint) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Int__Oint__Groups_Olinordered__ab__semigroup__add,axiom, % 172.78/172.46 class_Groups_Olinordered__ab__semigroup__add(tc_Int_Oint) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Int__Oint__Rings_Olinordered__semiring__strict,axiom, % 172.78/172.46 class_Rings_Olinordered__semiring__strict(tc_Int_Oint) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Int__Oint__Groups_Oordered__ab__semigroup__add,axiom, % 172.78/172.46 class_Groups_Oordered__ab__semigroup__add(tc_Int_Oint) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Int__Oint__Groups_Oordered__ab__group__add__abs,axiom, % 172.78/172.46 class_Groups_Oordered__ab__group__add__abs(tc_Int_Oint) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Int__Oint__Groups_Oordered__comm__monoid__add,axiom, % 172.78/172.46 class_Groups_Oordered__comm__monoid__add(tc_Int_Oint) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Int__Oint__Groups_Olinordered__ab__group__add,axiom, % 172.78/172.46 class_Groups_Olinordered__ab__group__add(tc_Int_Oint) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Int__Oint__Groups_Ocancel__ab__semigroup__add,axiom, % 172.78/172.46 class_Groups_Ocancel__ab__semigroup__add(tc_Int_Oint) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Int__Oint__Rings_Oring__1__no__zero__divisors,axiom, % 172.78/172.46 class_Rings_Oring__1__no__zero__divisors(tc_Int_Oint) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Int__Oint__Rings_Oordered__cancel__semiring,axiom, % 172.78/172.46 class_Rings_Oordered__cancel__semiring(tc_Int_Oint) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Int__Oint__Rings_Olinordered__ring__strict,axiom, % 172.78/172.46 class_Rings_Olinordered__ring__strict(tc_Int_Oint) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Int__Oint__Rings_Oring__no__zero__divisors,axiom, % 172.78/172.46 class_Rings_Oring__no__zero__divisors(tc_Int_Oint) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Int__Oint__Rings_Oordered__comm__semiring,axiom, % 172.78/172.46 class_Rings_Oordered__comm__semiring(tc_Int_Oint) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Int__Oint__Rings_Olinordered__semiring__1,axiom, % 172.78/172.46 class_Rings_Olinordered__semiring__1(tc_Int_Oint) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Int__Oint__Groups_Oordered__ab__group__add,axiom, % 172.78/172.46 class_Groups_Oordered__ab__group__add(tc_Int_Oint) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Int__Oint__Groups_Ocancel__semigroup__add,axiom, % 172.78/172.46 class_Groups_Ocancel__semigroup__add(tc_Int_Oint) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Int__Oint__Rings_Olinordered__semiring,axiom, % 172.78/172.46 class_Rings_Olinordered__semiring(tc_Int_Oint) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Int__Oint__Rings_Olinordered__semidom,axiom, % 172.78/172.46 class_Rings_Olinordered__semidom(tc_Int_Oint) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Int__Oint__Lazy__Sequence_Osmall__lazy,axiom, % 172.78/172.46 class_Lazy__Sequence_Osmall__lazy(tc_Int_Oint) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Int__Oint__Lattices_Osemilattice__sup,axiom, % 172.78/172.46 class_Lattices_Osemilattice__sup(tc_Int_Oint) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Int__Oint__Lattices_Osemilattice__inf,axiom, % 172.78/172.46 class_Lattices_Osemilattice__inf(tc_Int_Oint) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Int__Oint__Lattices_Odistrib__lattice,axiom, % 172.78/172.46 class_Lattices_Odistrib__lattice(tc_Int_Oint) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Int__Oint__Groups_Oab__semigroup__mult,axiom, % 172.78/172.46 class_Groups_Oab__semigroup__mult(tc_Int_Oint) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Int__Oint__Groups_Ocomm__monoid__mult,axiom, % 172.78/172.46 class_Groups_Ocomm__monoid__mult(tc_Int_Oint) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Int__Oint__Groups_Oab__semigroup__add,axiom, % 172.78/172.46 class_Groups_Oab__semigroup__add(tc_Int_Oint) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Int__Oint__Rings_Oordered__semiring,axiom, % 172.78/172.46 class_Rings_Oordered__semiring(tc_Int_Oint) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Int__Oint__Rings_Oordered__ring__abs,axiom, % 172.78/172.46 class_Rings_Oordered__ring__abs(tc_Int_Oint) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Int__Oint__Rings_Ono__zero__divisors,axiom, % 172.78/172.46 class_Rings_Ono__zero__divisors(tc_Int_Oint) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Int__Oint__Groups_Ocomm__monoid__add,axiom, % 172.78/172.46 class_Groups_Ocomm__monoid__add(tc_Int_Oint) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Int__Oint__Rings_Olinordered__ring,axiom, % 172.78/172.46 class_Rings_Olinordered__ring(tc_Int_Oint) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Int__Oint__Rings_Olinordered__idom,axiom, % 172.78/172.46 class_Rings_Olinordered__idom(tc_Int_Oint) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Int__Oint__Rings_Ocomm__semiring__1,axiom, % 172.78/172.46 class_Rings_Ocomm__semiring__1(tc_Int_Oint) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Int__Oint__Groups_Osemigroup__add,axiom, % 172.78/172.46 class_Groups_Osemigroup__add(tc_Int_Oint) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Int__Oint__Divides_Osemiring__div,axiom, % 172.78/172.46 class_Divides_Osemiring__div(tc_Int_Oint) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Int__Oint__Rings_Ocomm__semiring,axiom, % 172.78/172.46 class_Rings_Ocomm__semiring(tc_Int_Oint) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Int__Oint__Nat_Osemiring__char__0,axiom, % 172.78/172.46 class_Nat_Osemiring__char__0(tc_Int_Oint) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Int__Oint__Groups_Oab__group__add,axiom, % 172.78/172.46 class_Groups_Oab__group__add(tc_Int_Oint) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Int__Oint__Rings_Ozero__neq__one,axiom, % 172.78/172.46 class_Rings_Ozero__neq__one(tc_Int_Oint) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Int__Oint__Rings_Oordered__ring,axiom, % 172.78/172.46 class_Rings_Oordered__ring(tc_Int_Oint) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Int__Oint__Orderings_Opreorder,axiom, % 172.78/172.46 class_Orderings_Opreorder(tc_Int_Oint) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Int__Oint__Orderings_Olinorder,axiom, % 172.78/172.46 class_Orderings_Olinorder(tc_Int_Oint) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Int__Oint__Groups_Omonoid__mult,axiom, % 172.78/172.46 class_Groups_Omonoid__mult(tc_Int_Oint) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Int__Oint__Rings_Ocomm__ring__1,axiom, % 172.78/172.46 class_Rings_Ocomm__ring__1(tc_Int_Oint) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Int__Oint__Groups_Omonoid__add,axiom, % 172.78/172.46 class_Groups_Omonoid__add(tc_Int_Oint) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Int__Oint__Smallcheck_Osmall,axiom, % 172.78/172.46 class_Smallcheck_Osmall(tc_Int_Oint) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Int__Oint__Rings_Osemiring__1,axiom, % 172.78/172.46 class_Rings_Osemiring__1(tc_Int_Oint) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Int__Oint__Rings_Osemiring__0,axiom, % 172.78/172.46 class_Rings_Osemiring__0(tc_Int_Oint) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Int__Oint__Lattices_Olattice,axiom, % 172.78/172.46 class_Lattices_Olattice(tc_Int_Oint) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Int__Oint__Groups_Ogroup__add,axiom, % 172.78/172.46 class_Groups_Ogroup__add(tc_Int_Oint) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Int__Oint__Divides_Oring__div,axiom, % 172.78/172.46 class_Divides_Oring__div(tc_Int_Oint) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Int__Oint__Rings_Omult__zero,axiom, % 172.78/172.46 class_Rings_Omult__zero(tc_Int_Oint) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Int__Oint__Orderings_Oorder,axiom, % 172.78/172.46 class_Orderings_Oorder(tc_Int_Oint) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Int__Oint__Int_Oring__char__0,axiom, % 172.78/172.46 class_Int_Oring__char__0(tc_Int_Oint) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Int__Oint__Int_Onumber__ring,axiom, % 172.78/172.46 class_Int_Onumber__ring(tc_Int_Oint) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Int__Oint__Rings_Osemiring,axiom, % 172.78/172.46 class_Rings_Osemiring(tc_Int_Oint) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Int__Oint__Orderings_Oord,axiom, % 172.78/172.46 class_Orderings_Oord(tc_Int_Oint) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Int__Oint__Groups_Ouminus,axiom, % 172.78/172.46 class_Groups_Ouminus(tc_Int_Oint) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Int__Oint__Groups_Osgn__if,axiom, % 172.78/172.46 class_Groups_Osgn__if(tc_Int_Oint) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Int__Oint__Groups_Oabs__if,axiom, % 172.78/172.46 class_Groups_Oabs__if(tc_Int_Oint) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Int__Oint__Rings_Oring__1,axiom, % 172.78/172.46 class_Rings_Oring__1(tc_Int_Oint) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Int__Oint__Groups_Ominus,axiom, % 172.78/172.46 class_Groups_Ominus(tc_Int_Oint) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Int__Oint__Power_Opower,axiom, % 172.78/172.46 class_Power_Opower(tc_Int_Oint) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Int__Oint__Groups_Ozero,axiom, % 172.78/172.46 class_Groups_Ozero(tc_Int_Oint) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Int__Oint__Rings_Oring,axiom, % 172.78/172.46 class_Rings_Oring(tc_Int_Oint) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Int__Oint__Rings_Oidom,axiom, % 172.78/172.46 class_Rings_Oidom(tc_Int_Oint) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Int__Oint__Int_Onumber,axiom, % 172.78/172.46 class_Int_Onumber(tc_Int_Oint) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Int__Oint__Groups_Oone,axiom, % 172.78/172.46 class_Groups_Oone(tc_Int_Oint) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Int__Oint__HOL_Oequal,axiom, % 172.78/172.46 class_HOL_Oequal(tc_Int_Oint) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Nat__Onat__Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom, % 172.78/172.46 class_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct(tc_Nat_Onat) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Nat__Onat__Groups_Oordered__cancel__ab__semigroup__add,axiom, % 172.78/172.46 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Nat_Onat) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add__imp__le,axiom, % 172.78/172.46 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Nat_Onat) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Nat__Onat__Rings_Olinordered__comm__semiring__strict,axiom, % 172.78/172.46 class_Rings_Olinordered__comm__semiring__strict(tc_Nat_Onat) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Nat__Onat__Groups_Olinordered__ab__semigroup__add,axiom, % 172.78/172.46 class_Groups_Olinordered__ab__semigroup__add(tc_Nat_Onat) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Nat__Onat__Rings_Olinordered__semiring__strict,axiom, % 172.78/172.46 class_Rings_Olinordered__semiring__strict(tc_Nat_Onat) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Nat__Onat__Groups_Oordered__ab__semigroup__add,axiom, % 172.78/172.46 class_Groups_Oordered__ab__semigroup__add(tc_Nat_Onat) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Nat__Onat__Groups_Oordered__comm__monoid__add,axiom, % 172.78/172.46 class_Groups_Oordered__comm__monoid__add(tc_Nat_Onat) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Nat__Onat__Groups_Ocancel__ab__semigroup__add,axiom, % 172.78/172.46 class_Groups_Ocancel__ab__semigroup__add(tc_Nat_Onat) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Nat__Onat__Rings_Oordered__cancel__semiring,axiom, % 172.78/172.46 class_Rings_Oordered__cancel__semiring(tc_Nat_Onat) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Nat__Onat__Rings_Oordered__comm__semiring,axiom, % 172.78/172.46 class_Rings_Oordered__comm__semiring(tc_Nat_Onat) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Nat__Onat__Groups_Ocancel__semigroup__add,axiom, % 172.78/172.46 class_Groups_Ocancel__semigroup__add(tc_Nat_Onat) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Nat__Onat__Rings_Olinordered__semiring,axiom, % 172.78/172.46 class_Rings_Olinordered__semiring(tc_Nat_Onat) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Nat__Onat__Rings_Olinordered__semidom,axiom, % 172.78/172.46 class_Rings_Olinordered__semidom(tc_Nat_Onat) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Nat__Onat__Lattices_Osemilattice__sup,axiom, % 172.78/172.46 class_Lattices_Osemilattice__sup(tc_Nat_Onat) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Nat__Onat__Lattices_Osemilattice__inf,axiom, % 172.78/172.46 class_Lattices_Osemilattice__inf(tc_Nat_Onat) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Nat__Onat__Lattices_Odistrib__lattice,axiom, % 172.78/172.46 class_Lattices_Odistrib__lattice(tc_Nat_Onat) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Nat__Onat__Groups_Oab__semigroup__mult,axiom, % 172.78/172.46 class_Groups_Oab__semigroup__mult(tc_Nat_Onat) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Nat__Onat__Groups_Ocomm__monoid__mult,axiom, % 172.78/172.46 class_Groups_Ocomm__monoid__mult(tc_Nat_Onat) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Nat__Onat__Groups_Oab__semigroup__add,axiom, % 172.78/172.46 class_Groups_Oab__semigroup__add(tc_Nat_Onat) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Nat__Onat__Rings_Oordered__semiring,axiom, % 172.78/172.46 class_Rings_Oordered__semiring(tc_Nat_Onat) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Nat__Onat__Rings_Ono__zero__divisors,axiom, % 172.78/172.46 class_Rings_Ono__zero__divisors(tc_Nat_Onat) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Nat__Onat__Groups_Ocomm__monoid__add,axiom, % 172.78/172.46 class_Groups_Ocomm__monoid__add(tc_Nat_Onat) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Nat__Onat__Rings_Ocomm__semiring__1,axiom, % 172.78/172.46 class_Rings_Ocomm__semiring__1(tc_Nat_Onat) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Nat__Onat__Groups_Osemigroup__add,axiom, % 172.78/172.46 class_Groups_Osemigroup__add(tc_Nat_Onat) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Nat__Onat__Divides_Osemiring__div,axiom, % 172.78/172.46 class_Divides_Osemiring__div(tc_Nat_Onat) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Nat__Onat__Rings_Ocomm__semiring,axiom, % 172.78/172.46 class_Rings_Ocomm__semiring(tc_Nat_Onat) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Nat__Onat__Orderings_Owellorder,axiom, % 172.78/172.46 class_Orderings_Owellorder(tc_Nat_Onat) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Nat__Onat__Nat_Osemiring__char__0,axiom, % 172.78/172.46 class_Nat_Osemiring__char__0(tc_Nat_Onat) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Nat__Onat__Rings_Ozero__neq__one,axiom, % 172.78/172.46 class_Rings_Ozero__neq__one(tc_Nat_Onat) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Nat__Onat__Orderings_Opreorder,axiom, % 172.78/172.46 class_Orderings_Opreorder(tc_Nat_Onat) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Nat__Onat__Orderings_Olinorder,axiom, % 172.78/172.46 class_Orderings_Olinorder(tc_Nat_Onat) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Nat__Onat__Groups_Omonoid__mult,axiom, % 172.78/172.46 class_Groups_Omonoid__mult(tc_Nat_Onat) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Nat__Onat__Groups_Omonoid__add,axiom, % 172.78/172.46 class_Groups_Omonoid__add(tc_Nat_Onat) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Nat__Onat__Rings_Osemiring__1,axiom, % 172.78/172.46 class_Rings_Osemiring__1(tc_Nat_Onat) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Nat__Onat__Rings_Osemiring__0,axiom, % 172.78/172.46 class_Rings_Osemiring__0(tc_Nat_Onat) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Nat__Onat__Lattices_Olattice,axiom, % 172.78/172.46 class_Lattices_Olattice(tc_Nat_Onat) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Nat__Onat__Rings_Omult__zero,axiom, % 172.78/172.46 class_Rings_Omult__zero(tc_Nat_Onat) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Nat__Onat__Orderings_Oorder,axiom, % 172.78/172.46 class_Orderings_Oorder(tc_Nat_Onat) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Nat__Onat__Rings_Osemiring,axiom, % 172.78/172.46 class_Rings_Osemiring(tc_Nat_Onat) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Nat__Onat__Orderings_Oord,axiom, % 172.78/172.46 class_Orderings_Oord(tc_Nat_Onat) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Nat__Onat__Orderings_Obot,axiom, % 172.78/172.46 class_Orderings_Obot(tc_Nat_Onat) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Nat__Onat__Groups_Ominus,axiom, % 172.78/172.46 class_Groups_Ominus(tc_Nat_Onat) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Nat__Onat__Power_Opower,axiom, % 172.78/172.46 class_Power_Opower(tc_Nat_Onat) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Nat__Onat__Groups_Ozero,axiom, % 172.78/172.46 class_Groups_Ozero(tc_Nat_Onat) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Nat__Onat__Int_Onumber,axiom, % 172.78/172.46 class_Int_Onumber(tc_Nat_Onat) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Nat__Onat__Groups_Oone,axiom, % 172.78/172.46 class_Groups_Oone(tc_Nat_Onat) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Nat__Onat__HOL_Oequal,axiom, % 172.78/172.46 class_HOL_Oequal(tc_Nat_Onat) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Nat__Onat__Nat_Osize,axiom, % 172.78/172.46 class_Nat_Osize(tc_Nat_Onat) ). % 172.78/172.46 % 172.78/172.46 fof(arity_HOL__Obool__Complete__Lattice_Ocomplete__lattice,axiom, % 172.78/172.46 class_Complete__Lattice_Ocomplete__lattice(tc_HOL_Obool) ). % 172.78/172.46 % 172.78/172.46 fof(arity_HOL__Obool__Lattices_Obounded__lattice__top,axiom, % 172.78/172.46 class_Lattices_Obounded__lattice__top(tc_HOL_Obool) ). % 172.78/172.46 % 172.78/172.46 fof(arity_HOL__Obool__Lattices_Obounded__lattice__bot,axiom, % 172.78/172.46 class_Lattices_Obounded__lattice__bot(tc_HOL_Obool) ). % 172.78/172.46 % 172.78/172.46 fof(arity_HOL__Obool__Lattices_Osemilattice__sup,axiom, % 172.78/172.46 class_Lattices_Osemilattice__sup(tc_HOL_Obool) ). % 172.78/172.46 % 172.78/172.46 fof(arity_HOL__Obool__Lattices_Osemilattice__inf,axiom, % 172.78/172.46 class_Lattices_Osemilattice__inf(tc_HOL_Obool) ). % 172.78/172.46 % 172.78/172.46 fof(arity_HOL__Obool__Lattices_Odistrib__lattice,axiom, % 172.78/172.46 class_Lattices_Odistrib__lattice(tc_HOL_Obool) ). % 172.78/172.46 % 172.78/172.46 fof(arity_HOL__Obool__Lattices_Oboolean__algebra,axiom, % 172.78/172.46 class_Lattices_Oboolean__algebra(tc_HOL_Obool) ). % 172.78/172.46 % 172.78/172.46 fof(arity_HOL__Obool__Orderings_Opreorder,axiom, % 172.78/172.46 class_Orderings_Opreorder(tc_HOL_Obool) ). % 172.78/172.46 % 172.78/172.46 fof(arity_HOL__Obool__Finite__Set_Ofinite,axiom, % 172.78/172.46 class_Finite__Set_Ofinite(tc_HOL_Obool) ). % 172.78/172.46 % 172.78/172.46 fof(arity_HOL__Obool__Lattices_Olattice,axiom, % 172.78/172.46 class_Lattices_Olattice(tc_HOL_Obool) ). % 172.78/172.46 % 172.78/172.46 fof(arity_HOL__Obool__Orderings_Oorder,axiom, % 172.78/172.46 class_Orderings_Oorder(tc_HOL_Obool) ). % 172.78/172.46 % 172.78/172.46 fof(arity_HOL__Obool__Orderings_Otop,axiom, % 172.78/172.46 class_Orderings_Otop(tc_HOL_Obool) ). % 172.78/172.46 % 172.78/172.46 fof(arity_HOL__Obool__Orderings_Oord,axiom, % 172.78/172.46 class_Orderings_Oord(tc_HOL_Obool) ). % 172.78/172.46 % 172.78/172.46 fof(arity_HOL__Obool__Orderings_Obot,axiom, % 172.78/172.46 class_Orderings_Obot(tc_HOL_Obool) ). % 172.78/172.46 % 172.78/172.46 fof(arity_HOL__Obool__Groups_Ouminus,axiom, % 172.78/172.46 class_Groups_Ouminus(tc_HOL_Obool) ). % 172.78/172.46 % 172.78/172.46 fof(arity_HOL__Obool__Groups_Ominus,axiom, % 172.78/172.46 class_Groups_Ominus(tc_HOL_Obool) ). % 172.78/172.46 % 172.78/172.46 fof(arity_HOL__Obool__HOL_Oequal,axiom, % 172.78/172.46 class_HOL_Oequal(tc_HOL_Obool) ). % 172.78/172.46 % 172.78/172.46 fof(arity_HOL__Obool__Enum_Oenum,axiom, % 172.78/172.46 class_Enum_Oenum(tc_HOL_Obool) ). % 172.78/172.46 % 172.78/172.46 fof(arity_HOL__Obool__Nat_Osize,axiom, % 172.78/172.46 class_Nat_Osize(tc_HOL_Obool) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Com__Ostate__HOL_Oequal,axiom, % 172.78/172.46 class_HOL_Oequal(tc_Com_Ostate) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Com__Ostate__Nat_Osize,axiom, % 172.78/172.46 class_Nat_Osize(tc_Com_Ostate) ). % 172.78/172.46 % 172.78/172.46 fof(arity_List__Olist__Lazy__Sequence_Osmall__lazy,axiom, % 172.78/172.46 ! [T_1] : % 172.78/172.46 ( class_Lazy__Sequence_Osmall__lazy(T_1) % 172.78/172.46 => class_Lazy__Sequence_Osmall__lazy(tc_List_Olist(T_1)) ) ). % 172.78/172.46 % 172.78/172.46 fof(arity_List__Olist__HOL_Oequal,axiom, % 172.78/172.46 ! [T_1] : class_HOL_Oequal(tc_List_Olist(T_1)) ). % 172.78/172.46 % 172.78/172.46 fof(arity_List__Olist__Nat_Osize,axiom, % 172.78/172.46 ! [T_1] : class_Nat_Osize(tc_List_Olist(T_1)) ). % 172.78/172.46 % 172.78/172.46 fof(arity_sum__Finite__Set_Ofinite,axiom, % 172.78/172.46 ! [T_1,T_2] : % 172.78/172.46 ( ( class_Finite__Set_Ofinite(T_2) % 172.78/172.46 & class_Finite__Set_Ofinite(T_1) ) % 172.78/172.46 => class_Finite__Set_Ofinite(tc_sum(T_2,T_1)) ) ). % 172.78/172.46 % 172.78/172.46 fof(arity_sum__HOL_Oequal,axiom, % 172.78/172.46 ! [T_1,T_2] : class_HOL_Oequal(tc_sum(T_2,T_1)) ). % 172.78/172.46 % 172.78/172.46 fof(arity_sum__Enum_Oenum,axiom, % 172.78/172.46 ! [T_1,T_2] : % 172.78/172.46 ( ( class_Enum_Oenum(T_2) % 172.78/172.46 & class_Enum_Oenum(T_1) ) % 172.78/172.46 => class_Enum_Oenum(tc_sum(T_2,T_1)) ) ). % 172.78/172.46 % 172.78/172.46 fof(arity_sum__Nat_Osize,axiom, % 172.78/172.46 ! [T_1,T_2] : class_Nat_Osize(tc_sum(T_2,T_1)) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Option__Ooption__Finite__Set_Ofinite,axiom, % 172.78/172.46 ! [T_1] : % 172.78/172.46 ( class_Finite__Set_Ofinite(T_1) % 172.78/172.46 => class_Finite__Set_Ofinite(tc_Option_Ooption(T_1)) ) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Option__Ooption__HOL_Oequal,axiom, % 172.78/172.46 ! [T_1] : class_HOL_Oequal(tc_Option_Ooption(T_1)) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Option__Ooption__Enum_Oenum,axiom, % 172.78/172.46 ! [T_1] : % 172.78/172.46 ( class_Enum_Oenum(T_1) % 172.78/172.46 => class_Enum_Oenum(tc_Option_Ooption(T_1)) ) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Option__Ooption__Nat_Osize,axiom, % 172.78/172.46 ! [T_1] : class_Nat_Osize(tc_Option_Ooption(T_1)) ). % 172.78/172.46 % 172.78/172.46 fof(arity_prod__Lazy__Sequence_Osmall__lazy,axiom, % 172.78/172.46 ! [T_1,T_2] : % 172.78/172.46 ( ( class_Lazy__Sequence_Osmall__lazy(T_2) % 172.78/172.46 & class_Lazy__Sequence_Osmall__lazy(T_1) ) % 172.78/172.46 => class_Lazy__Sequence_Osmall__lazy(tc_prod(T_2,T_1)) ) ). % 172.78/172.46 % 172.78/172.46 fof(arity_prod__Finite__Set_Ofinite,axiom, % 172.78/172.46 ! [T_1,T_2] : % 172.78/172.46 ( ( class_Finite__Set_Ofinite(T_2) % 172.78/172.46 & class_Finite__Set_Ofinite(T_1) ) % 172.78/172.46 => class_Finite__Set_Ofinite(tc_prod(T_2,T_1)) ) ). % 172.78/172.46 % 172.78/172.46 fof(arity_prod__Smallcheck_Osmall,axiom, % 172.78/172.46 ! [T_1,T_2] : % 172.78/172.46 ( ( class_Smallcheck_Osmall(T_2) % 172.78/172.46 & class_Smallcheck_Osmall(T_1) ) % 172.78/172.46 => class_Smallcheck_Osmall(tc_prod(T_2,T_1)) ) ). % 172.78/172.46 % 172.78/172.46 fof(arity_prod__HOL_Oequal,axiom, % 172.78/172.46 ! [T_1,T_2] : class_HOL_Oequal(tc_prod(T_2,T_1)) ). % 172.78/172.46 % 172.78/172.46 fof(arity_prod__Enum_Oenum,axiom, % 172.78/172.46 ! [T_1,T_2] : % 172.78/172.46 ( ( class_Enum_Oenum(T_2) % 172.78/172.46 & class_Enum_Oenum(T_1) ) % 172.78/172.46 => class_Enum_Oenum(tc_prod(T_2,T_1)) ) ). % 172.78/172.46 % 172.78/172.46 fof(arity_prod__Nat_Osize,axiom, % 172.78/172.46 ! [T_1,T_2] : class_Nat_Osize(tc_prod(T_2,T_1)) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Product____Type__Ounit__Lazy__Sequence_Osmall__lazy,axiom, % 172.78/172.46 class_Lazy__Sequence_Osmall__lazy(tc_Product__Type_Ounit) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Product____Type__Ounit__Finite__Set_Ofinite,axiom, % 172.78/172.46 class_Finite__Set_Ofinite(tc_Product__Type_Ounit) ). % 172.78/172.46 % 172.78/172.46 fof(arity_Product____Type__Ounit__Smallcheck_Osmall,axiom, % 172.78/172.47 class_Smallcheck_Osmall(tc_Product__Type_Ounit) ). % 172.78/172.47 % 172.78/172.47 fof(arity_Product____Type__Ounit__HOL_Oequal,axiom, % 172.78/172.47 class_HOL_Oequal(tc_Product__Type_Ounit) ). % 172.78/172.47 % 172.78/172.47 fof(arity_Product____Type__Ounit__Enum_Oenum,axiom, % 172.78/172.47 class_Enum_Oenum(tc_Product__Type_Ounit) ). % 172.78/172.47 % 172.78/172.47 fof(arity_Product____Type__Ounit__Nat_Osize,axiom, % 172.78/172.47 class_Nat_Osize(tc_Product__Type_Ounit) ). % 172.78/172.47 % 172.78/172.47 fof(arity_Code____Evaluation__Oterm__HOL_Oequal,axiom, % 172.78/172.47 class_HOL_Oequal(tc_Code__Evaluation_Oterm) ). % 172.78/172.47 % 172.78/172.47 fof(arity_Code____Evaluation__Oterm__Nat_Osize,axiom, % 172.78/172.47 class_Nat_Osize(tc_Code__Evaluation_Oterm) ). % 172.78/172.47 % 172.78/172.47 fof(arity_Hoare____Mirabelle__Otriple__HOL_Oequal,axiom, % 172.78/172.47 ! [T_1] : class_HOL_Oequal(tc_Hoare__Mirabelle_Otriple(T_1)) ). % 172.78/172.47 % 172.78/172.47 fof(arity_Hoare____Mirabelle__Otriple__Nat_Osize,axiom, % 172.78/172.47 ! [T_1] : class_Nat_Osize(tc_Hoare__Mirabelle_Otriple(T_1)) ). % 172.78/172.47 % 172.78/172.47 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__cancel__ab__semigroup__add,axiom, % 172.78/172.47 class_Groups_Oordered__cancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 172.78/172.47 % 172.78/172.47 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add__imp__le,axiom, % 172.78/172.47 class_Groups_Oordered__ab__semigroup__add__imp__le(tc_Code__Numeral_Ocode__numeral) ). % 172.78/172.47 % 172.78/172.47 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__comm__semiring__strict,axiom, % 172.78/172.47 class_Rings_Olinordered__comm__semiring__strict(tc_Code__Numeral_Ocode__numeral) ). % 172.78/172.47 % 172.78/172.47 fof(arity_Code____Numeral__Ocode____numeral__Groups_Olinordered__ab__semigroup__add,axiom, % 172.78/172.47 class_Groups_Olinordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 172.78/172.47 % 172.78/172.47 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring__strict,axiom, % 172.78/172.47 class_Rings_Olinordered__semiring__strict(tc_Code__Numeral_Ocode__numeral) ). % 172.78/172.47 % 172.78/172.47 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__ab__semigroup__add,axiom, % 172.78/172.47 class_Groups_Oordered__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 172.78/172.47 % 172.78/172.47 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oordered__comm__monoid__add,axiom, % 172.78/172.47 class_Groups_Oordered__comm__monoid__add(tc_Code__Numeral_Ocode__numeral) ). % 172.78/172.47 % 172.78/172.47 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__ab__semigroup__add,axiom, % 172.78/172.47 class_Groups_Ocancel__ab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 172.78/172.47 % 172.78/172.47 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__cancel__semiring,axiom, % 172.78/172.47 class_Rings_Oordered__cancel__semiring(tc_Code__Numeral_Ocode__numeral) ). % 172.78/172.47 % 172.78/172.47 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__comm__semiring,axiom, % 172.78/172.47 class_Rings_Oordered__comm__semiring(tc_Code__Numeral_Ocode__numeral) ). % 172.78/172.47 % 172.78/172.47 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocancel__semigroup__add,axiom, % 172.78/172.47 class_Groups_Ocancel__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 172.78/172.47 % 172.78/172.47 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semiring,axiom, % 172.78/172.47 class_Rings_Olinordered__semiring(tc_Code__Numeral_Ocode__numeral) ). % 172.78/172.47 % 172.78/172.47 fof(arity_Code____Numeral__Ocode____numeral__Rings_Olinordered__semidom,axiom, % 172.78/172.47 class_Rings_Olinordered__semidom(tc_Code__Numeral_Ocode__numeral) ). % 172.78/172.47 % 172.78/172.47 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__mult,axiom, % 172.78/172.47 class_Groups_Oab__semigroup__mult(tc_Code__Numeral_Ocode__numeral) ). % 172.78/172.47 % 172.78/172.47 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__mult,axiom, % 172.78/172.47 class_Groups_Ocomm__monoid__mult(tc_Code__Numeral_Ocode__numeral) ). % 172.78/172.47 % 172.78/172.47 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oab__semigroup__add,axiom, % 172.78/172.47 class_Groups_Oab__semigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 172.78/172.47 % 172.78/172.47 fof(arity_Code____Numeral__Ocode____numeral__Rings_Oordered__semiring,axiom, % 172.78/172.47 class_Rings_Oordered__semiring(tc_Code__Numeral_Ocode__numeral) ). % 172.78/172.47 % 172.78/172.47 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ono__zero__divisors,axiom, % 172.78/172.47 class_Rings_Ono__zero__divisors(tc_Code__Numeral_Ocode__numeral) ). % 172.78/172.47 % 172.78/172.47 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ocomm__monoid__add,axiom, % 172.78/172.47 class_Groups_Ocomm__monoid__add(tc_Code__Numeral_Ocode__numeral) ). % 172.78/172.47 % 172.78/172.47 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring__1,axiom, % 172.78/172.47 class_Rings_Ocomm__semiring__1(tc_Code__Numeral_Ocode__numeral) ). % 172.78/172.47 % 172.78/172.47 fof(arity_Code____Numeral__Ocode____numeral__Groups_Osemigroup__add,axiom, % 172.78/172.47 class_Groups_Osemigroup__add(tc_Code__Numeral_Ocode__numeral) ). % 172.78/172.47 % 172.78/172.47 fof(arity_Code____Numeral__Ocode____numeral__Divides_Osemiring__div,axiom, % 172.78/172.47 class_Divides_Osemiring__div(tc_Code__Numeral_Ocode__numeral) ). % 172.78/172.47 % 172.78/172.47 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ocomm__semiring,axiom, % 172.78/172.47 class_Rings_Ocomm__semiring(tc_Code__Numeral_Ocode__numeral) ). % 172.78/172.47 % 172.78/172.47 fof(arity_Code____Numeral__Ocode____numeral__Nat_Osemiring__char__0,axiom, % 172.78/172.47 class_Nat_Osemiring__char__0(tc_Code__Numeral_Ocode__numeral) ). % 172.78/172.47 % 172.78/172.47 fof(arity_Code____Numeral__Ocode____numeral__Rings_Ozero__neq__one,axiom, % 172.78/172.47 class_Rings_Ozero__neq__one(tc_Code__Numeral_Ocode__numeral) ). % 172.78/172.47 % 172.78/172.47 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Opreorder,axiom, % 172.78/172.47 class_Orderings_Opreorder(tc_Code__Numeral_Ocode__numeral) ). % 172.78/172.47 % 172.78/172.47 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Olinorder,axiom, % 172.78/172.47 class_Orderings_Olinorder(tc_Code__Numeral_Ocode__numeral) ). % 172.78/172.47 % 172.78/172.47 fof(arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__mult,axiom, % 172.78/172.47 class_Groups_Omonoid__mult(tc_Code__Numeral_Ocode__numeral) ). % 172.78/172.47 % 172.78/172.47 fof(arity_Code____Numeral__Ocode____numeral__Groups_Omonoid__add,axiom, % 172.78/172.47 class_Groups_Omonoid__add(tc_Code__Numeral_Ocode__numeral) ). % 172.78/172.47 % 172.78/172.47 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__1,axiom, % 172.78/172.47 class_Rings_Osemiring__1(tc_Code__Numeral_Ocode__numeral) ). % 172.78/172.47 % 172.78/172.47 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring__0,axiom, % 172.78/172.47 class_Rings_Osemiring__0(tc_Code__Numeral_Ocode__numeral) ). % 172.78/172.47 % 172.78/172.47 fof(arity_Code____Numeral__Ocode____numeral__Rings_Omult__zero,axiom, % 172.78/172.47 class_Rings_Omult__zero(tc_Code__Numeral_Ocode__numeral) ). % 172.78/172.47 % 172.78/172.47 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Oorder,axiom, % 172.78/172.47 class_Orderings_Oorder(tc_Code__Numeral_Ocode__numeral) ). % 172.78/172.47 % 172.78/172.47 fof(arity_Code____Numeral__Ocode____numeral__Rings_Osemiring,axiom, % 172.78/172.47 class_Rings_Osemiring(tc_Code__Numeral_Ocode__numeral) ). % 172.78/172.47 % 172.78/172.47 fof(arity_Code____Numeral__Ocode____numeral__Orderings_Oord,axiom, % 172.78/172.47 class_Orderings_Oord(tc_Code__Numeral_Ocode__numeral) ). % 172.78/172.47 % 172.78/172.47 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ominus,axiom, % 172.78/172.47 class_Groups_Ominus(tc_Code__Numeral_Ocode__numeral) ). % 172.78/172.47 % 172.78/172.47 fof(arity_Code____Numeral__Ocode____numeral__Power_Opower,axiom, % 172.78/172.47 class_Power_Opower(tc_Code__Numeral_Ocode__numeral) ). % 172.78/172.47 % 172.78/172.47 fof(arity_Code____Numeral__Ocode____numeral__Groups_Ozero,axiom, % 172.78/172.47 class_Groups_Ozero(tc_Code__Numeral_Ocode__numeral) ). % 172.78/172.47 % 172.78/172.47 fof(arity_Code____Numeral__Ocode____numeral__Int_Onumber,axiom, % 172.78/172.47 class_Int_Onumber(tc_Code__Numeral_Ocode__numeral) ). % 172.78/172.47 % 172.78/172.47 fof(arity_Code____Numeral__Ocode____numeral__Groups_Oone,axiom, % 172.78/172.47 class_Groups_Oone(tc_Code__Numeral_Ocode__numeral) ). % 172.78/172.47 % 172.78/172.47 fof(arity_Code____Numeral__Ocode____numeral__HOL_Oequal,axiom, % 172.78/172.47 class_HOL_Oequal(tc_Code__Numeral_Ocode__numeral) ). % 172.78/172.47 % 172.78/172.47 fof(arity_Code____Numeral__Ocode____numeral__Nat_Osize,axiom, % 172.78/172.47 class_Nat_Osize(tc_Code__Numeral_Ocode__numeral) ). % 172.78/172.47 % 172.78/172.47 fof(arity_Lazy____Sequence__Olazy____sequence__HOL_Oequal,axiom, % 172.78/172.47 ! [T_1] : class_HOL_Oequal(tc_Lazy__Sequence_Olazy__sequence(T_1)) ). % 172.78/172.47 % 172.78/172.47 fof(arity_Lazy____Sequence__Olazy____sequence__Nat_Osize,axiom, % 172.78/172.47 ! [T_1] : class_Nat_Osize(tc_Lazy__Sequence_Olazy__sequence(T_1)) ). % 172.78/172.47 % 172.78/172.47 %----Helper facts (20) % 172.78/172.47 fof(help_c__COMBI__1,axiom, % 172.78/172.47 ! [V_P,T_a] : hAPP(c_COMBI(T_a),V_P) = V_P ). % 172.78/172.47 % 172.78/172.47 fof(help_c__COMBK__1,axiom, % 172.78/172.47 ! [V_Q,V_P,T_b,T_a] : hAPP(hAPP(c_COMBK(T_a,T_b),V_P),V_Q) = V_P ). % 172.78/172.47 % 172.78/172.47 fof(help_c__COMBB__1,axiom, % 172.78/172.47 ! [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)) ). % 172.78/172.47 % 172.78/172.47 fof(help_c__COMBC__1,axiom, % 172.78/172.47 ! [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) ). % 172.78/172.47 % 172.78/172.47 fof(help_c__COMBS__1,axiom, % 172.78/172.47 ! [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)) ). % 172.78/172.47 % 172.78/172.47 fof(help_c__fequal__1,axiom, % 172.78/172.47 ! [V_y_2,V_x_2] : % 172.78/172.47 ( ~ hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2)) % 172.78/172.47 | V_x_2 = V_y_2 ) ). % 172.78/172.47 % 172.78/172.47 fof(help_c__fequal__2,axiom, % 172.78/172.47 ! [V_y_2,V_x_2] : % 172.78/172.47 ( V_x_2 != V_y_2 % 172.78/172.47 | hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2)) ) ). % 172.78/172.47 % 172.78/172.47 fof(help_c__fFalse__1,axiom, % 172.78/172.47 ~ hBOOL(c_fFalse) ). % 172.78/172.47 % 172.78/172.47 fof(help_c__fTrue__1,axiom, % 172.78/172.47 hBOOL(c_fTrue) ). % 172.78/172.47 % 172.78/172.47 fof(help_c__fNot__1,axiom, % 172.78/172.47 ! [V_P_2] : % 172.78/172.47 ( ~ hBOOL(hAPP(c_fNot,V_P_2)) % 172.78/172.47 | ~ hBOOL(V_P_2) ) ). % 172.78/172.47 % 172.78/172.47 fof(help_c__fNot__2,axiom, % 172.78/172.47 ! [V_P_2] : % 172.78/172.47 ( ~ ~ hBOOL(V_P_2) % 172.78/172.47 | hBOOL(hAPP(c_fNot,V_P_2)) ) ). % 172.78/172.47 % 172.78/172.47 fof(help_c__fconj__1,axiom, % 172.78/172.47 ! [V_Q_2,V_P_2] : % 172.78/172.47 ( ~ hBOOL(V_P_2) % 172.78/172.47 | ~ hBOOL(V_Q_2) % 172.78/172.47 | hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2)) ) ). % 172.78/172.47 % 172.78/172.47 fof(help_c__fconj__2,axiom, % 172.78/172.47 ! [V_Q_2,V_P_2] : % 172.78/172.47 ( ~ hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2)) % 172.78/172.47 | hBOOL(V_P_2) ) ). % 172.78/172.47 % 172.78/172.47 fof(help_c__fconj__3,axiom, % 172.78/172.47 ! [V_Q_2,V_P_2] : % 172.78/172.47 ( ~ hBOOL(hAPP(hAPP(c_fconj,V_P_2),V_Q_2)) % 172.78/172.47 | hBOOL(V_Q_2) ) ). % 172.78/172.47 % 172.78/172.47 fof(help_c__fdisj__1,axiom, % 172.78/172.47 ! [V_Q_2,V_P_2] : % 172.78/172.47 ( ~ hBOOL(V_P_2) % 172.78/172.47 | hBOOL(hAPP(hAPP(c_fdisj,V_P_2),V_Q_2)) ) ). % 172.78/172.47 % 172.78/172.47 fof(help_c__fdisj__2,axiom, % 172.78/172.47 ! [V_P_2,V_Q_2] : % 172.78/172.47 ( ~ hBOOL(V_Q_2) % 172.78/172.47 | hBOOL(hAPP(hAPP(c_fdisj,V_P_2),V_Q_2)) ) ). % 172.78/172.47 % 172.78/172.47 fof(help_c__fdisj__3,axiom, % 172.78/172.47 ! [V_Q_2,V_P_2] : % 172.78/172.47 ( ~ hBOOL(hAPP(hAPP(c_fdisj,V_P_2),V_Q_2)) % 172.78/172.47 | hBOOL(V_P_2) % 172.78/172.47 | hBOOL(V_Q_2) ) ). % 172.78/172.47 % 172.78/172.47 fof(help_c__fimplies__1,axiom, % 172.78/172.47 ! [V_Q_2,V_P_2] : % 172.78/172.47 ( hBOOL(V_P_2) % 172.78/172.47 | hBOOL(hAPP(hAPP(c_fimplies,V_P_2),V_Q_2)) ) ). % 172.78/172.47 % 172.78/172.47 fof(help_c__fimplies__2,axiom, % 172.78/172.47 ! [V_P_2,V_Q_2] : % 172.78/172.47 ( ~ hBOOL(V_Q_2) % 172.78/172.47 | hBOOL(hAPP(hAPP(c_fimplies,V_P_2),V_Q_2)) ) ). % 172.78/172.47 % 172.78/172.47 fof(help_c__fimplies__3,axiom, % 172.78/172.47 ! [V_Q_2,V_P_2] : % 172.78/172.47 ( ~ hBOOL(hAPP(hAPP(c_fimplies,V_P_2),V_Q_2)) % 172.78/172.47 | ~ hBOOL(V_P_2) % 172.78/172.47 | hBOOL(V_Q_2) ) ). % 172.78/172.47 % 172.78/172.47 %----Conjectures (3) % 172.78/172.47 fof(conj_0,hypothesis, % 172.78/172.47 c_Hoare__Mirabelle_Ostate__not__singleton ). % 172.78/172.47 % 172.78/172.47 fof(conj_1,hypothesis, % 172.78/172.47 ! [B_x] : % 172.78/172.47 ( hBOOL(hAPP(hAPP(c_member(tc_Com_Opname),B_x),c_Map_Odom(tc_Com_Opname,tc_Com_Ocom,c_Com_Obody))) % 172.78/172.47 => c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,v_G,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)))) ) ). % 172.78/172.47 % 172.78/172.47 fof(conj_2,conjecture, % 172.78/172.47 c_Hoare__Mirabelle_Ohoare__derivs(tc_Com_Ostate,v_G,hAPP(hAPP(c_Set_Oinsert(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate)),c_Hoare__Mirabelle_OMGT(c_Com_Ocom_OSKIP)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(tc_Com_Ostate),tc_HOL_Obool)))) ). % 172.78/172.47 % 172.78/172.47 %------------------------------------------------------------------------------ % 172.78/172.47 %------------------------------------------- % 172.78/172.47 % Proof found % 172.78/172.47 % SZS status Theorem for theBenchmark % 172.78/172.47 % SZS output start Proof % 172.78/172.47 %ClaNum:10213(EqnAxiom:2877) % 172.78/172.47 %VarNum:70360(SingletonVarNum:20506) % 172.78/172.47 %MaxLitNum:8 % 172.78/172.47 %MaxfuncDepth:15 % 172.78/172.47 %SharedTerms:1074 % 172.78/172.47 %goalClause: 4572 % 172.78/172.47 %singleGoalClaCount:1 % 172.78/172.47 [2878]P1(a5000) % 172.78/172.47 [2882]P23(a871) % 172.78/172.47 [2883]P23(a876) % 172.78/172.47 [2884]P102(a194) % 172.78/172.47 [2885]P24(a871) % 172.78/172.47 [2886]P24(a879) % 172.78/172.47 [2887]P61(a871) % 172.78/172.47 [2888]P61(a876) % 172.78/172.47 [2889]P61(a1) % 172.78/172.47 [2890]P62(a871) % 172.78/172.47 [2891]P97(a871) % 172.78/172.47 [2892]P97(a876) % 172.78/172.47 [2893]P97(a1) % 172.78/172.47 [2894]P63(a871) % 172.78/172.47 [2895]P63(a876) % 172.78/172.47 [2896]P63(a1) % 172.78/172.47 [2897]P63(a102) % 172.78/172.47 [2898]P64(a876) % 172.78/172.47 [2899]P64(a1) % 172.78/172.47 [2900]P64(a102) % 172.78/172.47 [2901]P98(a871) % 172.78/172.47 [2902]P98(a876) % 172.78/172.47 [2903]P98(a1) % 172.78/172.47 [2904]P95(a871) % 172.78/172.47 [2905]P95(a876) % 172.78/172.47 [2906]P95(a1) % 172.78/172.47 [2907]P103(a871) % 172.78/172.47 [2908]P103(a876) % 172.78/172.47 [2909]P103(a1) % 172.78/172.47 [2910]P103(a102) % 172.78/172.47 [2911]P104(a876) % 172.78/172.47 [2912]P104(a1) % 172.78/172.47 [2913]P104(a102) % 172.78/172.47 [2914]P105(a871) % 172.78/172.47 [2915]P105(a876) % 172.78/172.47 [2916]P105(a1) % 172.78/172.47 [2917]P105(a102) % 172.78/172.47 [2918]P106(a871) % 172.78/172.47 [2919]P106(a876) % 172.78/172.47 [2920]P106(a1) % 172.78/172.47 [2921]P106(a102) % 172.78/172.47 [2922]P67(a876) % 172.78/172.47 [2923]P67(a1) % 172.78/172.47 [2924]P67(a102) % 172.78/172.47 [2925]P107(a876) % 172.78/172.47 [2926]P107(a1) % 172.78/172.47 [2927]P107(a102) % 172.78/172.47 [2928]P108(a876) % 172.78/172.47 [2929]P108(a1) % 172.78/172.47 [2930]P108(a102) % 172.78/172.47 [2931]P122(a876) % 172.78/172.47 [2932]P122(a1) % 172.78/172.47 [2933]P122(a102) % 172.78/172.47 [2934]P123(a1) % 172.78/172.47 [2935]P124(a1) % 172.78/172.47 [2936]P113(a1) % 172.78/172.47 [2937]P114(a876) % 172.78/172.47 [2938]P114(a1) % 172.78/172.47 [2939]P114(a102) % 172.78/172.47 [2940]P75(a876) % 172.78/172.47 [2941]P75(a1) % 172.78/172.47 [2942]P75(a102) % 172.78/172.47 [2943]P68(a876) % 172.78/172.47 [2944]P68(a1) % 172.78/172.47 [2945]P68(a102) % 172.78/172.47 [2946]P69(a876) % 172.78/172.47 [2947]P69(a1) % 172.78/172.47 [2948]P69(a102) % 172.78/172.47 [2949]P65(a876) % 172.78/172.47 [2950]P65(a1) % 172.78/172.47 [2951]P65(a102) % 172.78/172.47 [2952]P66(a1) % 172.78/172.47 [2953]P77(a876) % 172.78/172.47 [2954]P77(a1) % 172.78/172.47 [2955]P77(a102) % 172.78/172.47 [2956]P78(a876) % 172.78/172.47 [2957]P78(a1) % 172.78/172.47 [2958]P78(a102) % 172.78/172.47 [2959]P82(a876) % 172.78/172.47 [2960]P82(a1) % 172.78/172.47 [2961]P82(a102) % 172.78/172.47 [2962]P79(a1) % 172.78/172.47 [2963]P138(a876) % 172.78/172.47 [2964]P138(a1) % 172.78/172.47 [2965]P72(a1) % 172.78/172.47 [2966]P71(a876) % 172.78/172.47 [2967]P71(a1) % 172.78/172.47 [2968]P71(a102) % 172.78/172.47 [2969]P139(a876) % 172.78/172.47 [2970]P139(a1) % 172.78/172.47 [2971]P139(a102) % 172.78/172.47 [2972]P80(a876) % 172.78/172.47 [2973]P80(a1) % 172.78/172.47 [2974]P80(a102) % 172.78/172.47 [2975]P83(a876) % 172.78/172.47 [2976]P83(a1) % 172.78/172.47 [2977]P83(a102) % 172.78/172.47 [2978]P76(a876) % 172.78/172.47 [2979]P76(a1) % 172.78/172.47 [2980]P76(a102) % 172.78/172.47 [2981]P73(a1) % 172.78/172.47 [2982]P125(a876) % 172.78/172.47 [2983]P125(a1) % 172.78/172.47 [2984]P125(a102) % 172.78/172.47 [2985]P135(a1) % 172.78/172.47 [2986]P130(a876) % 172.78/172.47 [2987]P130(a1) % 172.78/172.47 [2988]P130(a102) % 172.78/172.47 [2989]P140(a876) % 172.78/172.47 [2990]P140(a1) % 172.78/172.47 [2991]P140(a102) % 172.78/172.47 [2992]P84(a876) % 172.78/172.47 [2993]P84(a1) % 172.78/172.47 [2994]P84(a102) % 172.78/172.47 [2995]P131(a876) % 172.78/172.47 [2996]P131(a1) % 172.78/172.47 [2997]P131(a102) % 172.78/172.47 [2998]P133(a876) % 172.78/172.47 [2999]P133(a1) % 172.78/172.47 [3000]P133(a102) % 172.78/172.47 [3001]P132(a876) % 172.78/172.47 [3002]P132(a1) % 172.78/172.47 [3003]P132(a102) % 172.78/172.47 [3004]P120(a1) % 172.78/172.47 [3005]P121(a1) % 172.78/172.47 [3006]P115(a876) % 172.78/172.47 [3007]P115(a1) % 172.78/172.47 [3008]P115(a102) % 172.78/172.47 [3009]P126(a876) % 172.78/172.47 [3010]P126(a1) % 172.78/172.47 [3011]P126(a102) % 172.78/172.47 [3012]P127(a876) % 172.78/172.47 [3013]P127(a1) % 172.78/172.47 [3014]P127(a102) % 172.78/172.47 [3015]P128(a1) % 172.78/172.47 [3016]P129(a1) % 172.78/172.47 [3017]P136(a1) % 172.78/172.47 [3018]P109(a876) % 172.78/172.47 [3019]P109(a1) % 172.78/172.47 [3020]P109(a102) % 172.78/172.47 [3021]P137(a1) % 172.78/172.47 [3022]P88(a1) % 172.78/172.47 [3023]P25(a876) % 172.78/172.47 [3024]P25(a1) % 172.78/172.47 [3025]P25(a102) % 172.78/172.47 [3026]P26(a1) % 172.78/172.47 [3027]P99(a876) % 172.78/172.47 [3028]P99(a1) % 172.78/172.47 [3029]P99(a102) % 172.78/172.47 [3030]P141(a876) % 172.78/172.47 [3031]P141(a1) % 172.78/172.47 [3032]P141(a102) % 172.78/172.47 [3033]P81(a1) % 172.78/172.47 [3034]P134(a1) % 172.78/172.47 [3035]P74(a876) % 172.78/172.47 [3036]P74(a1) % 172.78/172.47 [3037]P74(a102) % 172.78/172.47 [3038]P110(a871) % 172.78/172.47 [3039]P96(a871) % 172.78/172.47 [3040]P27(a871) % 172.78/172.47 [3041]P92(a871) % 172.78/172.47 [3042]P116(a1) % 172.78/172.47 [3043]P85(a871) % 172.78/172.47 [3044]P85(a1) % 172.78/172.47 [3045]P112(a1) % 172.78/172.47 [3046]P70(a1) % 172.78/172.47 [3047]P86(a1) % 172.78/172.47 [3048]P89(a1) % 172.78/172.47 [3049]P90(a876) % 172.78/172.47 [3050]P90(a1) % 172.78/172.47 [3051]P90(a102) % 172.78/172.47 [3052]P111(a876) % 172.78/172.47 [3053]P87(a876) % 172.78/172.47 [3054]P87(a1) % 172.78/172.47 [3055]P87(a102) % 172.78/172.47 [3056]P56(a871) % 172.78/172.47 [3057]P56(a879) % 172.78/172.47 [3058]P91(a871) % 172.78/172.47 [3059]P91(a872) % 172.78/172.47 [3060]P91(a873) % 172.78/172.47 [3061]P91(a876) % 172.78/172.47 [3062]P91(a1) % 172.78/172.47 [3063]P91(a879) % 172.78/172.47 [3064]P91(a102) % 172.78/172.47 [3065]P91(a328) % 172.78/172.47 [3066]P142(a1) % 172.78/172.47 [3067]P142(a879) % 172.78/172.47 [3068]P101(a871) % 172.78/172.47 [3069]P101(a872) % 172.78/172.47 [3070]P101(a873) % 172.78/172.47 [3071]P101(a876) % 172.78/172.47 [3072]P101(a879) % 172.78/172.47 [3073]P101(a102) % 172.78/172.47 [3074]P101(a328) % 172.78/172.47 [3075]P100(a1) % 172.78/172.47 [3076]P100(a879) % 172.78/172.47 [3077]P94(a871) % 172.78/172.47 [3097]P38(a876,a251) % 172.78/172.47 [3098]P38(a876,a322) % 172.78/172.47 [4474]~E(a100,a82) % 172.78/172.47 [4475]~P102(a250) % 172.78/172.47 [2879]E(f2(a1),a82) % 172.78/172.47 [2880]E(f103(a102),a3) % 172.78/172.47 [2881]E(f22(a102),a23) % 172.78/172.47 [3078]E(f195(a876),f2(a876)) % 172.78/172.47 [3079]E(f30(a24),f2(a876)) % 172.78/172.47 [3080]E(f104(a876),f244(a876)) % 172.78/172.47 [3081]E(f113(a876),f245(a876)) % 172.78/172.47 [3082]E(f105(a1),f33(a1)) % 172.78/172.47 [3083]E(f83(a250),f2(a876)) % 172.78/172.47 [3084]E(f83(a194),f2(a876)) % 172.78/172.47 [3085]P28(f77(a1)) % 172.78/172.47 [3086]P28(f2(a1)) % 172.78/172.47 [3146]P38(f882(a876,a876),a34) % 172.78/172.47 [3502]E(f325(a876,a876,a251,a251),a34) % 172.78/172.47 [4476]~E(f77(a1),f2(a1)) % 172.78/172.47 [3087]E(f4(f2(a102)),f2(a876)) % 172.78/172.47 [3088]E(f114(f2(a876)),f2(a876)) % 172.78/172.47 [3100]E(f332(f78(a1),a82),a82) % 172.78/172.47 [3103]E(f332(a115,f2(a876)),f77(a876)) % 172.78/172.47 [3104]E(f332(a107,f77(a1)),f77(a876)) % 172.78/172.47 [3105]E(f332(a3,f77(a876)),f77(a102)) % 172.78/172.47 [3107]E(f332(a3,f2(a876)),f2(a102)) % 172.78/172.47 [3109]E(f332(f106(a1),a82),f2(a1)) % 172.78/172.47 [3110]E(f332(f106(a102),a82),f2(a102)) % 172.78/172.47 [3111]E(f332(a107,f2(a1)),f2(a876)) % 172.78/172.47 [3112]E(f332(f196(a871),a250),f2(a876)) % 172.78/172.47 [3113]E(f332(f196(a871),a194),f2(a876)) % 172.78/172.47 [3114]E(f332(f196(a873),a24),f2(a876)) % 172.78/172.47 [3115]E(f332(f106(a876),a82),f2(a876)) % 172.78/172.47 [3119]E(f332(f78(a1),f77(a1)),a100) % 172.78/172.47 [3127]E(f332(f196(a102),f2(a102)),f2(a876)) % 172.78/172.47 [3128]E(f332(f103(a1),f77(a876)),f77(a1)) % 172.78/172.47 [3129]E(f332(f103(a1),f2(a876)),f2(a1)) % 172.78/172.47 [3130]E(f332(f78(a1),f2(a1)),f2(a1)) % 172.78/172.47 [3142]E(f332(a107,f77(a1)),f332(a115,f2(a876))) % 172.78/172.47 [3143]E(f332(f179(a874,a873),a26),a27) % 172.78/172.47 [3144]E(f323(f882(a876,a876),a34),a35) % 172.78/172.47 [3145]E(f324(f882(a876,a876),a34),a36) % 172.78/172.47 [3167]E(f332(f253(a876),f2(a876)),f195(f883(a876,a871))) % 172.78/172.47 [3168]E(f332(f254(a876),f2(a876)),f255(f883(a876,a871))) % 172.78/172.47 [3176]P39(f195(f883(a1,a871))) % 172.78/172.47 [3212]E(f332(f332(f22(a102),f2(a102)),f77(a102)),f2(a102)) % 172.78/172.47 [3293]P102(f332(f332(f247(a1),a100),f2(a1))) % 172.78/172.47 [3318]P102(f332(f332(f247(a1),f2(a1)),f77(a1))) % 172.78/172.47 [3319]P102(f332(f332(f246(a1),f2(a1)),f77(a1))) % 172.78/172.47 [3494]P102(f332(f61(a874),f185(a874,a873,a27))) % 172.78/172.47 [3532]E(f332(f332(f289(a876,a876,a876),a322),f308(a876,a322)),a251) % 172.78/172.47 [3572]P41(a1,a876,a107,f332(f246(a1),f2(a1))) % 172.78/172.47 [3576]E(f332(f332(f41(a876,f883(a876,a871)),f255(f883(a876,a871))),f253(a876)),f255(f883(a876,a871))) % 172.78/172.47 [3577]E(f332(f332(f41(a876,f883(a876,a871)),f255(f883(a876,a871))),f301(a876)),f255(f883(a876,a871))) % 172.78/172.47 [3578]E(f332(f332(f41(a876,f883(a876,a871)),f255(f883(a876,a871))),f254(a876)),f255(f883(a876,a871))) % 172.78/172.47 [3579]E(f332(f332(f42(a876,f883(a876,a871)),f255(f883(a876,a871))),f304(a876)),f195(f883(a876,a871))) % 172.78/172.47 [3595]P20(a876,a1,f103(a1),f255(f883(a876,a871))) % 172.78/172.47 [3608]P41(a876,a1,f103(a1),f332(f16(a871,a876),a194)) % 172.78/172.47 [3746]E(f332(f72(a876,a102,a1,a3),a107),f106(a102)) % 172.78/172.47 [3974]P52(a102,a876,a19,a3,f255(f883(a876,a871))) % 172.78/172.47 [3983]P52(a1,f883(f882(a876,a876),a871),a110,a88,a101) % 172.78/172.47 [4249]E(f272(a1,a1,a1,a1,f33(a1),f78(a1)),a50) % 172.78/172.47 [4499]~E(f332(f106(a1),a100),f332(f106(a1),a82)) % 172.78/172.47 [4500]~P102(f332(a200,f77(a1))) % 172.78/172.47 [4501]~P102(f332(a200,f2(a1))) % 172.78/172.47 [4542]~P102(f332(f332(f247(a1),a82),f2(a1))) % 172.78/172.47 [3159]E(f332(f332(f22(a1),a100),a100),a82) % 172.78/172.47 [3174]E(f332(f103(a1),f332(a115,f2(a876))),f77(a1)) % 172.78/172.47 [3242]E(f332(f37(a879),f255(f883(a879,a871))),f77(a876)) % 172.78/172.47 [3263]P102(f332(a200,f332(f106(a1),a100))) % 172.78/172.47 [3264]P102(f332(f332(f247(a1),a100),a82)) % 172.78/172.47 [3266]P102(f332(f332(f246(a1),a100),a82)) % 172.78/172.47 [3329]E(f332(f332(f310(a876),f2(a876)),f195(f883(a876,a871))),f332(f301(a876),f2(a876))) % 172.78/172.47 [3385]P102(f332(f332(f246(a1),f2(a1)),f332(f106(a1),a82))) % 172.78/172.47 [3397]E(f332(f311(a876,a876,a115),f255(f883(a876,a871))),f332(f304(a876),f2(a876))) % 172.78/172.47 [3437]P3(f882(a876,a876),f255(f883(f882(a876,a876),a871)),a111) % 172.78/172.47 [3754]E(f332(f72(a876,a1,a102,f103(a1)),a19),a20) % 172.78/172.47 [3816]P38(a876,f332(f252(f882(a876,a876)),f332(f271(a876,a876,a871),f247(a876)))) % 172.78/172.47 [4531]~P102(f332(a200,f332(f106(a1),a82))) % 172.78/172.47 [4532]~P102(f332(f332(f247(a1),a82),a82)) % 172.78/172.47 [4533]~P102(f332(f332(f247(a1),a82),a100)) % 172.78/172.47 [4534]~P102(f332(f332(f247(a1),a100),a100)) % 172.78/172.47 [4535]~P102(f332(f332(f246(a1),a82),a100)) % 172.78/172.47 [4536]~P102(f332(f332(f90(a1),a82),a100)) % 172.78/172.47 [4537]~P102(f332(f332(f90(a1),a100),a82)) % 172.78/172.47 [4548]~P102(f332(f61(a876),f255(f883(a876,a871)))) % 172.78/172.47 [4549]~P102(f332(f61(a1),f255(f883(a1,a871)))) % 172.78/172.47 [4420]E(f332(f271(a1,a1,a871),f332(f332(f8(f883(a1,a871),f883(a1,a871),a1),f332(f18(a1,a871,a871),f332(f332(f8(a871,f883(a871,a871),a1),a330),f332(f247(a1),f2(a1))))),f332(f332(f7(a1,a1,f883(a1,a871)),f332(f332(f8(f883(a1,f883(a1,a871)),f883(a1,f883(a1,a871)),a1),f7(a1,a1,a871)),f332(f332(f8(f883(a1,a1),f883(a1,f883(a1,a871)),a1),f332(f8(a1,f883(a1,a871),a1),a329)),a228))),f77(a1)))),a224) % 172.78/172.47 [4572]~P19(a872,a884,f332(f332(f310(f875(a872)),f332(f332(f332(f91(a872),a329),a24),f201(a24))),f195(f883(f875(a872),a871)))) % 172.78/172.47 [3475]E(f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100),f332(f78(a1),a100)) % 172.78/172.47 [3515]E(f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100),f332(f332(f22(a1),a82),a100)) % 172.78/172.47 [3679]E(f332(f332(f60(f882(a876,a876)),f255(f883(f882(a876,a876),a871))),a111),a101) % 172.78/172.47 [3708]E(f332(f106(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f77(a1)) % 172.78/172.47 [3709]E(f332(f106(a102),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f77(a102)) % 172.78/172.47 [3710]E(f332(f106(a876),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f77(a876)) % 172.78/172.47 [3714]E(f332(f106(a876),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(a115,f2(a876))) % 172.78/172.47 [4108]E(f332(f332(f113(f883(f882(f882(a876,a876),f882(a876,a876)),a871)),a34),f308(f882(a876,a876),f195(f883(f882(f882(a876,a876),f882(a876,a876)),a871)))),a69) % 172.78/172.47 [4179]E(f332(a88,f332(f286(f882(a876,a876),f882(a876,a876),a111),f332(f332(f310(f882(a876,a876)),f332(f332(f267(a876,a876),f77(a876)),f2(a876))),f195(f883(f882(a876,a876),a871))))),f77(a1)) % 172.78/172.47 [4180]E(f332(a88,f332(f286(f882(a876,a876),f882(a876,a876),a111),f332(f332(f310(f882(a876,a876)),f332(f332(f267(a876,a876),f2(a876)),f2(a876))),f195(f883(f882(a876,a876),a871))))),f2(a1)) % 172.78/172.47 [4195]E(f332(f252(f882(a876,a876)),f332(f271(a876,a876,a871),f332(f332(f8(a876,f883(a876,a871),a876),f332(f7(a876,a876,a871),a329)),a115))),a322) % 172.78/172.47 [4165]E(f332(f106(a876),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100))),f332(a115,f332(a115,f2(a876)))) % 172.78/172.47 [4168]E(f332(f106(a876),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100))),f332(f332(f79(a876),f77(a876)),f77(a876))) % 172.78/172.47 [4169]E(f332(f106(a876),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100))),f332(f37(a871),f255(f883(a871,a871)))) % 172.78/172.47 [4235]P28(f332(f106(a1),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)))) % 172.78/172.47 [4307]P21(f883(f882(a876,a876),a871),f332(f332(f267(f883(f882(f883(f882(a876,a876),a871),f883(f882(a876,a876),a871)),a871),f883(f882(f883(f882(a876,a876),a871),f883(f882(a876,a876),a871)),a871)),a35),a70)) % 172.78/172.47 [4308]P21(f883(f882(a876,a876),a871),f332(f332(f267(f883(f882(f883(f882(a876,a876),a871),f883(f882(a876,a876),a871)),a871),f883(f882(f883(f882(a876,a876),a871),f883(f882(a876,a876),a871)),a871)),a36),a68)) % 172.78/172.47 [4348]E(f332(f332(f113(f883(f882(f883(f882(a876,a876),a871),f883(f882(a876,a876),a871)),a871)),f324(f882(a876,a876),a69)),f332(f332(f310(f882(f883(f882(a876,a876),a871),f883(f882(a876,a876),a871))),f332(f332(f267(f883(f882(a876,a876),a871),f883(f882(a876,a876),a871)),f195(f883(f882(a876,a876),a871))),f195(f883(f882(a876,a876),a871)))),f195(f883(f882(f883(f882(a876,a876),a871),f883(f882(a876,a876),a871)),a871)))),a68) % 172.78/172.47 [4349]E(f332(f332(f113(f883(f882(f883(f882(a876,a876),a871),f883(f882(a876,a876),a871)),a871)),f323(f882(a876,a876),a69)),f332(f332(f310(f882(f883(f882(a876,a876),a871),f883(f882(a876,a876),a871))),f332(f332(f267(f883(f882(a876,a876),a871),f883(f882(a876,a876),a871)),f195(f883(f882(a876,a876),a871))),f195(f883(f882(a876,a876),a871)))),f195(f883(f882(f883(f882(a876,a876),a871),f883(f882(a876,a876),a871)),a871)))),a70) % 172.78/172.47 [4237]E(f332(a107,f332(f106(a1),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)))),f332(a115,f332(a115,f2(a876)))) % 172.78/172.47 [4284]E(f332(f103(a1),f332(f106(a876),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)))),f332(f106(a1),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)))) % 172.78/172.47 [4319]P102(f332(f332(f246(a1),f2(a1)),f332(f106(a1),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100))))) % 172.78/172.47 [4320]E(f332(f106(a876),f332(f332(f22(a1),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100))),a100)),f332(a115,f332(a115,f332(a115,f2(a876))))) % 172.78/172.47 [4362]P28(f332(f106(a1),f332(f332(f22(a1),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100))),a100))) % 172.78/172.47 [4390]E(f332(f103(a1),f332(f106(a876),f332(f332(f22(a1),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100))),a100))),f332(f106(a1),f332(f332(f22(a1),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100))),a100))) % 172.78/172.47 [4405]P102(f332(f332(f246(a1),f2(a1)),f332(f106(a1),f332(f332(f22(a1),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100))),a100)))) % 172.78/172.47 [3099]P2(x30991,a329) % 172.78/172.47 [3503]P20(a876,a876,a115,x35031) % 172.78/172.47 [3089]P91(f875(x30891)) % 172.78/172.47 [3090]P91(f880(x30901)) % 172.78/172.47 [3091]P91(f877(x30911)) % 172.78/172.47 [3092]P91(f878(x30921)) % 172.78/172.47 [3093]P101(f875(x30931)) % 172.78/172.47 [3094]P101(f880(x30941)) % 172.78/172.47 [3095]P101(f877(x30951)) % 172.78/172.47 [3096]P101(f878(x30961)) % 172.78/172.47 [3116]P38(a1,f108(x31161)) % 172.78/172.47 [3117]P38(a1,f109(x31171)) % 172.78/172.47 [3164]P38(f883(x31641,a871),f307(x31641)) % 172.78/172.47 [3188]E(f256(x31881,x31881,a329),a329) % 172.78/172.47 [3203]E(f44(a1,x32031,x32031),f2(a1)) % 172.78/172.47 [3260]P10(x32601,f883(x32601,a871),f310(x32601)) % 172.78/172.47 [4478]~E(f332(a25,x44781),a24) % 172.78/172.47 [4480]~E(f332(a115,x44801),x44801) % 172.78/172.47 [4490]~E(f332(a115,x44901),f2(a876)) % 172.78/172.47 [3101]E(f332(f196(a876),x31011),x31011) % 172.78/172.47 [3102]E(f332(f106(a1),x31021),x31021) % 172.78/172.47 [3118]E(f332(a88,f333(x31181)),x31181) % 172.78/172.47 [3131]E(f117(x31311,f116(x31311)),f116(x31311)) % 172.78/172.47 [3132]E(f152(x31321,f116(x31321)),f116(x31321)) % 172.78/172.47 [3134]E(f30(f332(a25,x31341)),f2(a876)) % 172.78/172.47 [3139]E(f332(f168(x31391),f116(x31391)),f116(x31391)) % 172.78/172.47 [3140]E(f332(f172(x31401),f116(x31401)),f116(x31401)) % 172.78/172.47 [3141]E(f332(f169(x31411),f116(x31411)),f116(x31411)) % 172.78/172.47 [3147]E(f332(f106(a1),x31471),f332(f105(a1),x31471)) % 172.78/172.47 [3148]E(f332(a88,f332(a110,x31481)),x31481) % 172.78/172.47 [3150]E(f332(a3,f332(a19,x31501)),x31501) % 172.78/172.47 [3151]E(f332(a19,f332(a3,x31511)),x31511) % 172.78/172.47 [3152]P28(f332(f103(a1),x31521)) % 172.78/172.47 [3157]E(f332(f196(f880(x31571)),f208(x31571)),f2(a876)) % 172.78/172.47 [3158]E(f332(f196(f877(x31581)),f116(x31581)),f2(a876)) % 172.78/172.47 [3163]E(f332(f196(a873),f332(a25,x31631)),f2(a876)) % 172.78/172.47 [3172]E(f238(x31721,f208(x31721)),f195(f883(x31721,a871))) % 172.78/172.47 [3179]E(f332(f332(f22(a876),x31791),f2(a876)),x31791) % 172.78/172.47 [3180]E(f332(f332(f80(a876),x31801),f77(a876)),x31801) % 172.78/172.47 [3181]E(f332(f332(f80(a1),x31811),f77(a1)),x31811) % 172.78/172.47 [3182]E(f332(f332(f79(a876),x31821),f2(a876)),x31821) % 172.78/172.47 [3183]E(f332(f332(f79(a1),x31831),f2(a1)),x31831) % 172.78/172.47 [3184]E(f332(f332(f245(a876),x31841),f2(a876)),x31841) % 172.78/172.47 [3185]E(f332(f332(f80(a876),x31851),f2(a876)),f2(a876)) % 172.78/172.47 [3186]E(f332(f332(f38(a1),x31861),f2(a1)),f2(a1)) % 172.78/172.47 [3187]E(f332(f332(f244(a876),x31871),f2(a876)),f2(a876)) % 172.78/172.47 [3194]E(f332(f173(x31941),f116(x31941)),f195(f883(x31941,a871))) % 172.78/172.47 [3198]P102(f332(f137(x31981),f116(x31981))) % 172.78/172.47 [3204]E(f332(f154(x32041,x32041),f5(x32041)),f33(f877(x32041))) % 172.78/172.47 [3205]E(f332(f154(x32051,x32051),f33(x32051)),f33(f877(x32051))) % 172.78/172.47 [3206]E(f332(f209(x32061,x32061),f5(x32061)),f33(f880(x32061))) % 172.78/172.47 [3207]E(f332(f209(x32071,x32071),f33(x32071)),f33(f880(x32071))) % 172.78/172.47 [3208]E(f44(a1,x32081,f2(a1)),x32081) % 172.78/172.47 [3209]E(f332(f246(a876),f332(a115,x32091)),f332(f247(a876),x32091)) % 172.78/172.47 [3210]E(f332(f253(a876),f332(a115,x32101)),f332(f301(a876),x32101)) % 172.78/172.47 [3211]E(f332(f254(a876),f332(a115,x32111)),f332(f304(a876),x32111)) % 172.78/172.47 [3213]E(f44(a1,f2(a1),x32131),f2(a1)) % 172.78/172.47 [3226]E(f332(f332(f79(a876),x32261),f77(a876)),f332(a115,x32261)) % 172.78/172.47 [3236]E(f332(f302(a876,x32361),f2(a876)),f195(f883(a876,a871))) % 172.78/172.47 [3248]E(f303(a876,f2(a876),x32481),f332(f301(a876),x32481)) % 172.78/172.47 [3296]E(f332(f332(f22(a876),f332(a115,x32961)),f77(a876)),x32961) % 172.78/172.47 [3309]E(f46(f2(a1),x33091),f332(f332(f267(a1,a1),f2(a1)),f2(a1))) % 172.78/172.47 [3359]P102(f332(f332(f247(a876),x33591),f332(a115,x33591))) % 172.78/172.47 [3371]P102(f332(f332(f247(a876),f2(a876)),f332(a115,x33711))) % 172.78/172.47 [3665]E(f332(f332(f22(a102),f332(a3,f332(a115,f332(a19,x36651)))),f77(a102)),x36651) % 172.78/172.47 [3738]P102(f332(f332(f246(a1),f332(f78(a1),f332(f103(a1),x37381))),f2(a1))) % 172.78/172.47 [3890]P102(f332(f332(f247(a1),f332(f78(a1),f332(f103(a1),f332(a115,x38901)))),f2(a1))) % 172.78/172.47 [4506]~E(f255(f883(x45061,a871)),f195(f883(x45061,a871))) % 172.78/172.47 [4545]~P102(f332(f332(f247(a876),x45451),f2(a876))) % 172.78/172.47 [4557]~P102(f332(f332(f247(a1),f332(f103(a1),x45571)),f2(a1))) % 172.78/172.47 [3162]E(f181(x31621,f116(f877(x31621))),f116(f877(x31621))) % 172.78/172.47 [3165]E(f332(f332(f80(a1),a82),x31651),a82) % 172.78/172.47 [3166]E(f332(f332(f79(a1),a82),x31661),x31661) % 172.78/172.47 [3169]E(f332(a107,f332(f103(a1),x31691)),x31691) % 172.78/172.47 [3170]E(f332(f332(f22(a1),x31701),a82),x31701) % 172.78/172.47 [3171]E(f332(f332(f79(a1),x31711),a82),x31711) % 172.78/172.47 [3173]E(f332(f332(f22(a876),x31731),x31731),f2(a876)) % 172.78/172.47 [3177]E(f332(f37(a876),f332(f253(a876),x31771)),x31771) % 172.78/172.47 [3178]E(f332(f78(a1),f332(f78(a1),x31781)),x31781) % 172.78/172.47 [3189]E(f332(f332(f80(a876),f77(a876)),x31891),x31891) % 172.78/172.47 [3190]E(f332(f332(f80(a1),f77(a1)),x31901),x31901) % 172.78/172.47 [3191]E(f332(f332(f79(a876),f2(a876)),x31911),x31911) % 172.78/172.47 [3192]E(f332(f332(f79(a1),f2(a1)),x31921),x31921) % 172.78/172.47 [3193]E(f332(f332(f245(a876),f2(a876)),x31931),x31931) % 172.78/172.47 [3199]E(f332(f332(f22(a876),f2(a876)),x31991),f2(a876)) % 172.78/172.47 [3200]E(f332(f332(f80(a876),f2(a876)),x32001),f2(a876)) % 172.78/172.47 [3201]E(f332(f332(f38(a1),f2(a1)),x32011),f2(a1)) % 172.78/172.47 [3202]E(f332(f332(f244(a876),f2(a876)),x32021),f2(a876)) % 172.78/172.47 [3214]E(f125(x32141,f332(f78(a1),x32141)),f132(a1,x32141)) % 172.78/172.47 [3220]E(f332(f302(a876,f2(a876)),x32201),f332(f253(a876),x32201)) % 172.78/172.47 [3221]E(f332(f332(f80(a1),a100),x32211),f332(f78(a1),x32211)) % 172.78/172.47 [3228]E(f332(a107,f332(f106(a1),x32281)),f332(f106(a876),x32281)) % 172.78/172.47 [3229]E(f332(a19,f332(f106(a102),x32291)),f332(f106(a876),x32291)) % 172.78/172.47 [3230]E(f332(f37(a876),f332(f301(a876),x32301)),f332(a115,x32301)) % 172.78/172.47 [3240]E(f332(f332(f79(a876),f77(a876)),x32401),f332(a115,x32401)) % 172.78/172.47 [3244]E(f332(f74(a1),f332(f103(a1),x32441)),f332(f103(a1),x32441)) % 172.78/172.47 [3245]E(f332(f105(a1),f332(f103(a1),x32451)),f332(f103(a1),x32451)) % 172.78/172.47 [3250]E(f332(f37(x32501),f195(f883(x32501,a871))),f2(a876)) % 172.78/172.47 [3252]E(f332(f332(f38(a876),x32521),f332(a115,f2(a876))),x32521) % 172.78/172.47 [3261]E(f44(a876,x32611,f332(a115,f2(a876))),f2(a876)) % 172.78/172.47 [3262]E(f44(a1,x32621,f332(f106(a1),a100)),f2(a1)) % 172.78/172.47 [3278]E(f332(f332(f38(a1),x32781),f332(f106(a1),a100)),f332(f78(a1),x32781)) % 172.78/172.47 [3282]E(f139(a876,f332(f302(a876,x32821),f2(a876))),f116(a876)) % 172.78/172.47 [3283]E(f332(f332(f79(a1),x32831),f77(a1)),f332(f332(f22(a1),x32831),a100)) % 172.78/172.47 [3284]E(f332(f332(f22(a1),x32841),f77(a1)),f332(f332(f79(a1),x32841),a100)) % 172.78/172.47 [3289]P102(f332(f332(f201(a24),x32891),x32891)) % 172.78/172.47 [3290]P102(f332(f332(f246(a876),x32901),x32901)) % 172.78/172.47 [3291]P102(f332(f332(f246(a1),x32911),x32911)) % 172.78/172.47 [3292]P102(f332(f332(f90(a1),x32921),x32921)) % 172.78/172.47 [3297]E(f332(f78(a1),f332(f106(a1),x32971)),f332(f106(a1),f332(f78(a1),x32971))) % 172.78/172.47 [3298]P102(f332(f61(a876),f332(f253(a876),x32981))) % 172.78/172.47 [3299]P102(f332(f61(a876),f332(f301(a876),x32991))) % 172.78/172.47 [3307]E(f161(x33071,f255(f883(x33071,a871))),f255(f883(f877(x33071),a871))) % 172.78/172.47 [3312]P102(f332(f332(f246(a876),f2(a876)),x33121)) % 172.78/172.47 [3322]E(f332(f332(f79(a876),f114(x33221)),f332(a115,f2(a876))),f114(f332(a115,x33221))) % 172.78/172.47 [3323]E(f332(f252(x33231),f332(f16(a871,x33231),a250)),f195(f883(x33231,a871))) % 172.78/172.47 [3324]E(f332(f252(x33241),f332(f16(a871,x33241),a194)),f255(f883(x33241,a871))) % 172.78/172.47 [3328]E(f332(f332(f310(a876),x33281),f332(f253(a876),x33281)),f332(f253(a876),f332(a115,x33281))) % 172.78/172.47 [3340]E(f332(f332(f79(a1),f77(a1)),f332(f103(a1),x33401)),f332(f103(a1),f332(a115,x33401))) % 172.78/172.47 [3342]E(f332(f332(f151(f877(x33421)),f116(x33421)),f116(f877(x33421))),f53(x33421,f116(x33421))) % 172.78/172.47 [3362]E(f195(f883(f882(x33621,x33621),a871)),f264(x33621,f195(f883(x33621,a871)))) % 172.78/172.47 [3363]E(f332(f309(x33631),f255(f883(x33631,a871))),f255(f883(f883(x33631,a871),a871))) % 172.78/172.47 [3364]E(f332(f78(f883(x33641,a871)),f195(f883(x33641,a871))),f255(f883(x33641,a871))) % 172.78/172.47 [3365]E(f332(f78(f883(x33651,a871)),f255(f883(x33651,a871))),f195(f883(x33651,a871))) % 172.78/172.47 [3367]P102(f332(f61(x33671),f195(f883(x33671,a871)))) % 172.78/172.47 [3369]E(f332(f302(a876,x33691),f332(a115,x33691)),f332(f332(f310(a876),x33691),f195(f883(a876,a871)))) % 172.78/172.47 [3370]E(f84(f882(a876,a876),f47(x33701,f2(a876))),f332(f332(f267(a876,a876),f2(a876)),x33701)) % 172.78/172.47 [3384]E(f332(f332(f310(a876),f332(a115,x33841)),f332(f301(a876),x33841)),f332(f301(a876),f332(a115,x33841))) % 172.78/172.47 [3388]P38(x33881,f195(f883(f882(x33881,x33881),a871))) % 172.78/172.47 [3391]P102(f332(f332(f246(a1),f2(a1)),f332(f103(a1),x33911))) % 172.78/172.47 [3399]E(f332(f332(f79(a876),f332(f196(a876),x33991)),f332(a115,f2(a876))),f332(f196(a876),f332(a115,x33991))) % 172.78/172.47 [3510]P39(f332(f311(a876,a1,f103(a1)),x35101)) % 172.78/172.47 [3548]P40(x35481,f195(f883(x35481,a871)),f195(f883(f882(x35481,x35481),a871))) % 172.78/172.47 [3568]E(f332(f332(f267(a1,a1),f332(f106(a1),a100)),f332(f332(f22(a1),x35681),f77(a1))),f49(f332(f106(a1),a100),x35681)) % 172.78/172.47 [3620]P55(x36201,f332(f16(f883(x36201,a871),x36201),f332(f16(a871,x36201),a250))) % 172.78/172.47 [3828]P102(f332(f332(f334(f883(f882(a876,a876),a871)),f333(x38281)),a101)) % 172.78/172.47 [3854]P102(f332(f332(f334(f883(f882(a876,a876),a871)),f332(a110,x38541)),a101)) % 172.78/172.47 [3992]P20(x39921,f883(x39921,a871),f332(f332(f7(x39921,f883(x39921,a871),f883(x39921,a871)),f310(x39921)),f195(f883(x39921,a871))),f255(f883(x39921,a871))) % 172.78/172.47 [4503]~E(f332(f332(f79(a1),x45031),x45031),a100) % 172.78/172.47 [4530]~E(f332(a3,f332(a115,f332(a19,x45301))),f2(a102)) % 172.78/172.47 [4538]~P102(f332(a200,f332(f103(a1),x45381))) % 172.78/172.47 [4541]~P102(f332(f332(f247(a876),x45411),x45411)) % 172.78/172.47 [4550]~P102(f332(f332(f246(a876),f332(a115,x45501)),x45501)) % 172.78/172.47 [3314]E(f332(a107,f332(f78(a1),f332(f103(a1),x33141))),f2(a876)) % 172.78/172.47 [3317]E(f332(f332(f79(a1),f332(f78(a1),x33171)),x33171),f2(a1)) % 172.78/172.47 [3321]E(f332(f37(a1),f332(f302(a1,f2(a1)),x33211)),f332(a107,x33211)) % 172.78/172.47 [3333]E(f332(f332(f257(a876),f332(a115,f2(a876))),x33331),f332(a115,f2(a876))) % 172.78/172.47 [3434]E(f332(f285(x34341),f195(f883(f882(x34341,x34341),a871))),f195(f883(x34341,a871))) % 172.78/172.47 [3442]E(f40(f883(x34421,a871),f195(f883(f883(x34421,a871),a871))),f255(f883(x34421,a871))) % 172.78/172.47 [3443]E(f40(f883(x34431,a871),f255(f883(f883(x34431,a871),a871))),f195(f883(x34431,a871))) % 172.78/172.47 [3444]E(f39(f883(x34441,a871),f195(f883(f883(x34441,a871),a871))),f195(f883(x34441,a871))) % 172.78/172.47 [3445]E(f39(f883(x34451,a871),f255(f883(f883(x34451,a871),a871))),f255(f883(x34451,a871))) % 172.78/172.47 [3492]E(f332(f332(f310(f877(x34921)),f116(x34921)),f195(f883(f877(x34921),a871))),f161(x34921,f195(f883(x34921,a871)))) % 172.78/172.47 [3493]E(f332(f332(f310(f877(x34931)),f116(x34931)),f195(f883(f877(x34931),a871))),f162(x34931,f116(f883(x34931,a871)))) % 172.78/172.47 [3531]E(f332(f332(f79(a876),f4(x35311)),f332(a115,f2(a876))),f4(f332(a3,f332(a115,f332(a19,x35311))))) % 172.78/172.47 [3559]E(f332(f37(a1),f332(f311(a876,a1,f103(a1)),x35591)),f332(f37(a876),x35591)) % 172.78/172.47 [3560]P102(f332(f332(f246(a876),x35601),f332(f332(f80(a876),x35601),x35601))) % 172.78/172.47 [3599]E(f332(f311(a1,a876,a107),f303(a1,f2(a1),f332(f103(a1),x35991))),f332(f301(a876),x35991)) % 172.78/172.47 [3615]E(f332(f332(f38(a876),f332(a115,f2(a876))),f332(f106(a876),x36151)),f332(a107,f332(f332(f38(a1),f77(a1)),f332(f106(a1),x36151)))) % 172.78/172.47 [3617]E(f332(f173(a876),f139(a876,f332(f302(a876,f2(a876)),f332(a115,x36171)))),f332(f301(a876),x36171)) % 172.78/172.47 [3618]E(f332(f332(f79(a876),f332(f196(a102),x36181)),f332(a115,f2(a876))),f332(f196(a102),f332(a3,f332(a115,f332(a19,x36181))))) % 172.78/172.47 [3638]E(f332(f311(a1,a876,a107),f332(f311(a876,a1,f103(a1)),x36381)),x36381) % 172.78/172.47 [3671]E(f332(f332(f310(a876),f2(a876)),f332(f311(a876,a876,a115),f332(f253(a876),x36711))),f332(f253(a876),f332(a115,x36711))) % 172.78/172.47 [3678]P50(x36781,x36781,f308(x36781,f195(f883(f882(x36781,x36781),a871)))) % 172.78/172.47 [3684]P102(f332(a200,f332(f78(a1),f332(f103(a1),f332(a115,x36841))))) % 172.78/172.47 [3695]E(f332(f332(f22(f883(a876,a871)),f332(f254(a876),x36951)),f332(f332(f310(a876),x36951),f195(f883(a876,a871)))),f332(f254(a876),f332(a115,x36951))) % 172.78/172.47 [3711]E(f332(f332(f79(a1),f332(f332(f22(a1),a82),x37111)),f332(f332(f22(a1),a82),x37111)),f332(f332(f22(a1),a82),f332(f332(f79(a1),x37111),x37111))) % 172.78/172.47 [3727]E(f332(f332(f310(f883(x37271,a871)),f195(f883(x37271,a871))),f195(f883(f883(x37271,a871),a871))),f332(f309(x37271),f195(f883(x37271,a871)))) % 172.78/172.47 [3755]E(f332(f332(f22(f883(a876,a871)),f332(f304(a876),x37551)),f332(f332(f310(a876),f332(a115,x37551)),f195(f883(a876,a871)))),f332(f304(a876),f332(a115,x37551))) % 172.78/172.47 [3764]E(f332(f332(f310(f880(x37641)),f208(x37641)),f332(f311(x37641,f880(x37641),f239(x37641)),f255(f883(x37641,a871)))),f255(f883(f880(x37641),a871))) % 172.78/172.47 [3866]E(f332(f106(a876),f332(f332(f79(a1),x38661),x38661)),f332(f332(f85(a876,a876),f332(f106(a876),x38661)),f332(f332(f18(a876,a876,a876),f79(a876)),f5(a876)))) % 172.78/172.47 [4258]P10(x42581,f883(x42581,a871),f332(f332(f8(f883(x42581,a871),f883(f883(x42581,a871),f883(x42581,a871)),x42581),f332(f7(f883(x42581,a871),f883(x42581,a871),f883(x42581,a871)),f22(f883(x42581,a871)))),f332(f332(f7(x42581,f883(x42581,a871),f883(x42581,a871)),f310(x42581)),f195(f883(x42581,a871))))) % 172.78/172.47 [4347]E(f332(f252(f882(a1,a1)),f332(f271(a1,a1,a871),f332(f332(f8(f883(a1,a871),f883(a1,a871),a1),f332(f18(a1,a871,a871),f332(f332(f8(a871,f883(a871,a871),a1),a330),f332(f246(a1),x43471)))),f247(a1)))),f108(x43471)) % 172.78/172.47 [4380]E(f332(f252(f882(a1,a1)),f332(f271(a1,a1,a871),f332(f332(f18(a1,f883(a1,a871),f883(a1,a871)),f332(f332(f8(f883(a871,a871),f883(f883(a1,a871),f883(a1,a871)),a1),f8(a871,a871,a1)),f332(f332(f8(a871,f883(a871,a871),a1),a330),f332(f246(a1),x43801)))),f247(a1)))),f109(x43801)) % 172.78/172.47 [4435]E(f332(f252(f882(f883(x44351,a871),f883(x44351,a871))),f332(f271(f883(x44351,a871),f883(x44351,a871),a871),f332(f332(f7(f883(x44351,a871),f883(f883(x44351,a871),a871),f883(f883(x44351,a871),a871)),f332(f332(f8(f883(f883(x44351,a871),f883(a871,a871)),f883(f883(f883(x44351,a871),a871),f883(f883(x44351,a871),a871)),f883(x44351,a871)),f18(f883(x44351,a871),a871,a871)),f332(f332(f8(f883(f883(x44351,a871),a871),f883(f883(x44351,a871),f883(a871,a871)),f883(x44351,a871)),f332(f8(a871,f883(a871,a871),f883(x44351,a871)),a330)),f247(f883(x44351,a871))))),f61(x44351)))),f307(x44351)) % 172.78/172.47 [4554]~P102(f332(f61(f877(x45541)),f255(f883(f877(x45541),a871)))) % 172.78/172.47 [4559]~P102(f332(f332(f90(a1),a100),f332(f332(f79(a1),x45591),x45591))) % 172.78/172.47 [4569]~P102(f332(f332(f246(a1),f2(a1)),f332(f78(a1),f332(f103(a1),f332(a115,x45691))))) % 172.78/172.47 [3469]E(f332(f332(f22(a1),f332(f332(f79(a1),x34691),a100)),a100),x34691) % 172.78/172.47 [3485]E(f332(f173(a876),f139(a876,f332(f302(a876,f2(a876)),x34851))),f332(f253(a876),x34851)) % 172.78/172.47 [3734]E(f332(f332(f79(a1),f332(f332(f79(a1),f77(a1)),x37341)),x37341),f332(f332(f22(a1),f332(f332(f79(a1),x37341),x37341)),a100)) % 172.78/172.47 [3783]E(f332(f287(x37831,x37831),f308(x37831,f195(f883(f882(x37831,x37831),a871)))),f308(x37831,f195(f883(f882(x37831,x37831),a871)))) % 172.78/172.47 [3831]P102(f332(f332(f246(a876),x38311),f332(f332(f80(a876),x38311),f332(f332(f80(a876),x38311),x38311)))) % 172.78/172.47 [4112]P102(f332(f61(a876),f332(f252(a876),f332(f332(f7(a876,a876,a871),f247(a876)),x41121)))) % 172.78/172.47 [4113]P102(f332(f61(a876),f332(f252(a876),f332(f332(f7(a876,a876,a871),f246(a876)),x41131)))) % 172.78/172.47 [4400]E(f332(f252(f882(x44001,x44001)),f332(f332(f8(f883(x44001,a871),a871,f882(x44001,x44001)),f86(x44001)),f332(f332(f7(f882(x44001,x44001),f883(x44001,f882(x44001,x44001)),f883(x44001,a871)),f332(f332(f8(f883(f882(x44001,x44001),a871),f883(f883(x44001,f882(x44001,x44001)),f883(x44001,a871)),f882(x44001,x44001)),f8(f882(x44001,x44001),a871,x44001)),a329)),f332(f332(f18(x44001,x44001,f882(x44001,x44001)),f267(x44001,x44001)),f5(x44001))))),f308(x44001,f195(f883(f882(x44001,x44001),a871)))) % 172.78/172.47 [4556]~E(f332(f332(f22(a1),f332(f332(f79(a1),x45561),x45561)),a100),a82) % 172.78/172.47 [4558]~E(f332(f332(f79(a1),f332(f332(f79(a1),f77(a1)),x45581)),x45581),f2(a1)) % 172.78/172.47 [4566]~P102(f332(f332(f90(a1),f332(f332(f79(a1),x45661),x45661)),a100)) % 172.78/172.47 [3879]E(f332(f332(f79(a1),f332(f332(f22(a1),a100),x38791)),f332(f332(f22(a1),a100),x38791)),f332(f332(f22(a1),a100),f332(f332(f22(a1),f332(f332(f79(a1),x38791),x38791)),a100))) % 172.78/172.47 [4001]E(f332(f332(f22(a1),f332(f332(f79(a1),f332(f332(f22(a1),a100),x40011)),f332(f332(f22(a1),a100),x40011))),a100),f332(f332(f22(a1),a100),f332(f332(f79(a1),x40011),x40011))) % 172.78/172.47 [4036]E(f332(f332(f22(a1),f332(f332(f79(a1),f332(f332(f79(a1),x40361),a100)),f332(f332(f79(a1),x40361),a100))),a100),f332(f332(f79(a1),f332(f332(f79(a1),x40361),x40361)),a100)) % 172.78/172.47 [4074]E(f332(f332(f22(a1),f332(f332(f79(a1),f332(f332(f22(a1),a100),x40741)),f332(f332(f22(a1),a100),x40741))),a100),f332(f332(f22(a1),a82),f332(f332(f22(a1),f332(f332(f79(a1),x40741),x40741)),a100))) % 172.78/172.47 [4175]E(f332(a88,f332(f286(f882(a876,a876),f882(a876,a876),a111),f332(f332(f310(f882(a876,a876)),f332(f332(f267(a876,a876),x41751),f2(a876))),f195(f883(f882(a876,a876),a871))))),f332(f103(a1),x41751)) % 172.78/172.47 [4185]E(f332(a88,f332(f286(f882(a876,a876),f882(a876,a876),a111),f332(f332(f310(f882(a876,a876)),f332(f332(f267(a876,a876),f337(x41851)),f501(x41851))),f195(f883(f882(a876,a876),a871))))),x41851) % 172.78/172.47 [4220]E(f332(f252(a1),f332(f332(f18(a1,a871,a871),f332(f332(f8(a871,f883(a871,a871),a1),a330),f332(f246(a1),f2(a1)))),x42201)),f332(f311(a876,a1,f103(a1)),f332(f252(a876),f332(f332(f8(a1,a871,a876),x42201),f103(a1))))) % 172.78/172.47 [4266]P39(f332(f252(a1),f332(f332(f18(a1,a871,a871),f332(f332(f8(a871,f883(a871,a871),a1),a330),f332(f246(a1),f2(a1)))),x42661))) % 172.78/172.47 [4287]P102(f332(f332(f334(f882(f883(f882(a876,a876),a871),f883(f882(a876,a876),a871))),f332(f332(f267(f883(f882(a876,a876),a871),f883(f882(a876,a876),a871)),x42871),f195(f883(f882(a876,a876),a871)))),a70)) % 172.78/172.47 [4293]E(f332(f311(a1,a876,a107),f332(f252(a1),f332(f332(f18(a1,a871,a871),f332(f332(f8(a871,f883(a871,a871),a1),a330),f332(f246(a1),f2(a1)))),f332(f332(f8(a876,a871,a1),x42931),a107)))),f332(f252(a876),x42931)) % 172.78/172.47 [4449]E(f313(a876,f332(f332(f41(f882(a876,a876),f883(a876,a871)),f332(a110,x44491)),f332(f271(a876,a876,f883(a876,a871)),f332(f332(f7(a876,f883(a876,a871),f883(a876,f883(a876,a871))),f332(f332(f8(f883(a876,f883(f883(a876,a871),f883(a876,a871))),f883(f883(a876,a871),f883(a876,f883(a876,a871))),a876),f7(a876,f883(a876,a871),f883(a876,a871))),f332(f332(f8(f883(a876,a876),f883(a876,f883(f883(a876,a871),f883(a876,a871))),a876),f332(f8(a876,f883(f883(a876,a871),f883(a876,a871)),a876),f310(a876))),f22(a876)))),f195(f883(a876,a871)))))),f332(a107,x44491)) % 172.78/172.47 [4571]~P102(f332(f332(f90(a1),a82),f332(f332(f22(a1),f332(f332(f79(a1),x45711),x45711)),a100))) % 172.78/172.47 [3924]E(f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),x39241),x39241)),a100)),a100),f332(f332(f79(a1),x39241),x39241)) % 172.78/172.47 [3975]E(f332(f332(f22(a1),f332(f332(f22(a1),f332(f332(f79(a1),x39751),x39751)),a100)),a100),f332(f332(f79(a1),f332(f332(f22(a1),x39751),a100)),f332(f332(f22(a1),x39751),a100))) % 172.78/172.47 [4193]E(f332(f332(f22(a1),f332(f332(f79(a1),f332(f332(f79(a1),f332(f78(a1),x41931)),a100)),f332(f332(f79(a1),f332(f78(a1),x41931)),a100))),a100),f332(f78(a1),f332(f332(f22(a1),f332(f332(f79(a1),x41931),x41931)),a100))) % 172.78/172.47 [4580]~P102(f332(f332(f90(a1),f332(f332(f22(a1),f332(f332(f79(a1),x45801),x45801)),a100)),a82)) % 172.78/172.47 [4238]E(f332(f332(f79(a876),x42381),f332(f106(a876),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)))),f332(a115,f332(a115,x42381))) % 172.78/172.47 [4239]E(f332(f332(f80(a876),x42391),f332(f106(a876),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)))),f332(f332(f79(a876),x42391),x42391)) % 172.78/172.47 [4240]E(f332(f332(f38(a876),f332(f332(f79(a876),x42401),x42401)),f332(f106(a876),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)))),x42401) % 172.78/172.47 [4322]E(f44(a876,f332(a115,f332(a115,x43221)),f332(f106(a876),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)))),f44(a876,x43221,f332(f106(a876),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100))))) % 172.78/172.47 [4464]E(f332(a88,f332(f332(f41(f882(a876,a876),f883(f882(a876,a876),a871)),f332(a110,x44641)),f332(f271(a876,a876,f883(f882(a876,a876),a871)),f332(f332(f8(f883(a876,f883(f882(a876,a876),a871)),f883(a876,f883(f882(a876,a876),a871)),a876),f332(f8(f883(f882(a876,a876),a871),f883(f882(a876,a876),a871),a876),f286(f882(a876,a876),f882(a876,a876),a111))),f332(f332(f7(a876,f883(f882(a876,a876),a871),f883(a876,f883(f882(a876,a876),a871))),f332(f332(f8(f883(a876,f883(f883(f882(a876,a876),a871),f883(f882(a876,a876),a871))),f883(f883(f882(a876,a876),a871),f883(a876,f883(f882(a876,a876),a871))),a876),f7(a876,f883(f882(a876,a876),a871),f883(f882(a876,a876),a871))),f332(f332(f8(f883(a876,f882(a876,a876)),f883(a876,f883(f883(f882(a876,a876),a871),f883(f882(a876,a876),a871))),a876),f332(f8(f882(a876,a876),f883(f883(f882(a876,a876),a871),f883(f882(a876,a876),a871)),a876),f310(f882(a876,a876)))),f332(f7(a876,a876,f882(a876,a876)),f267(a876,a876))))),f195(f883(f882(a876,a876),a871))))))),f332(f78(a1),x44641)) % 172.78/172.47 [4317]E(f332(f332(f79(a876),f332(f106(a876),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)))),x43171),f332(a115,f332(a115,x43171))) % 172.78/172.47 [4318]E(f332(f332(f80(a876),f332(f106(a876),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)))),x43181),f332(f332(f79(a876),x43181),x43181)) % 172.78/172.47 [4352]E(f332(f332(f38(a876),f332(a115,f332(a115,x43521))),f332(f106(a876),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)))),f332(a115,f332(f332(f38(a876),x43521),f332(f106(a876),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)))))) % 172.78/172.47 [4406]E(f332(f332(f79(a876),f332(f106(a876),f332(f332(f22(a1),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100))),a100))),x44061),f332(a115,f332(a115,f332(a115,x44061)))) % 172.78/172.47 [4472]E(f332(f271(a1,a1,f882(a1,a1)),f332(f332(f18(a1,f883(a1,f882(a1,a1)),f883(a1,f882(a1,a1))),f332(f332(f8(f883(a1,f883(f882(a1,a1),f882(a1,a1))),f883(f883(a1,f882(a1,a1)),f883(a1,f882(a1,a1))),a1),f18(a1,f882(a1,a1),f882(a1,a1))),f332(f332(f8(f883(a1,f882(a1,a1)),f883(a1,f883(f882(a1,a1),f882(a1,a1))),a1),f332(f18(a1,f882(a1,a1),f883(f882(a1,a1),f882(a1,a1))),f332(f332(f8(a871,f883(f882(a1,a1),f883(f882(a1,a1),f882(a1,a1))),a1),f99(f882(a1,a1))),f332(f332(f8(a1,a871,a1),f332(f246(a1),f2(a1))),f332(f332(f7(a1,a1,a1),f22(a1)),x44721))))),f332(f332(f7(a1,f883(a1,a1),f883(a1,f882(a1,a1))),f332(f332(f8(f883(a1,f882(a1,a1)),f883(f883(a1,a1),f883(a1,f882(a1,a1))),a1),f8(a1,f882(a1,a1),a1)),f332(f332(f8(a1,f883(a1,f882(a1,a1)),a1),f267(a1,a1)),f332(f332(f7(a1,a1,a1),f332(f332(f8(a1,f883(a1,a1),a1),f79(a1)),f332(f80(a1),f332(f106(a1),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)))))),f77(a1))))),f332(f332(f7(a1,a1,a1),f22(a1)),x44721))))),f332(f332(f8(a1,f883(a1,f882(a1,a1)),a1),f267(a1,a1)),f332(f80(a1),f332(f106(a1),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100))))))),f43(x44721)) % 172.78/172.47 [3135]P91(f881(x31351,x31352)) % 172.78/172.47 [3136]P91(f882(x31361,x31362)) % 172.78/172.47 [3137]P101(f881(x31371,x31372)) % 172.78/172.47 [3138]P101(f882(x31381,x31382)) % 172.78/172.47 [3155]P29(a1,f180(x31551,x31552)) % 172.78/172.47 [3156]P38(x31561,f153(x31561,x31562)) % 172.78/172.47 [3222]P32(x32221,x32222,f116(x32221)) % 172.78/172.47 [3256]P40(x32561,x32562,f264(x32561,x32562)) % 172.78/172.47 [3257]P50(x32571,x32571,f264(x32571,x32572)) % 172.78/172.47 [3534]P20(x35341,x35341,f5(x35341),x35342) % 172.78/172.47 [3535]P20(x35351,x35351,f33(x35351),x35352) % 172.78/172.47 [3543]P33(x35431,x35432,f116(x35431),f116(x35431)) % 172.78/172.47 [3544]P20(x35441,f880(x35441),f239(x35441),x35442) % 172.78/172.47 [3553]P20(f877(x35531),f877(x35531),f169(x35531),x35532) % 172.78/172.47 [4483]~E(f32(x44831,x44832),a24) % 172.78/172.47 [4484]~E(f31(x44841,x44842),a24) % 172.78/172.47 [4513]~P34(x45131,x45132,f116(x45131)) % 172.78/172.47 [4514]~P36(x45141,x45142,f116(x45141)) % 172.78/172.47 [3120]E(f332(f5(x31201),x31202),x31202) % 172.78/172.47 [3121]E(f332(f252(x31211),x31212),x31212) % 172.78/172.47 [3123]E(f332(f33(x31231),x31232),x31232) % 172.78/172.47 [3133]E(f332(f198(x31331),x31332),f118(x31331)) % 172.78/172.47 [3153]E(f84(x31531,f332(a329,x31532)),x31532) % 172.78/172.47 [3154]E(f89(x31541,f332(a329,x31542)),x31542) % 172.78/172.47 [3175]E(f332(f136(x31751,x31752),f116(x31751)),f116(x31751)) % 172.78/172.47 [3195]E(f308(x31951,f308(x31951,x31952)),f308(x31951,x31952)) % 172.78/172.47 [3196]E(f152(x31961,f152(x31961,x31962)),f152(x31961,x31962)) % 172.78/172.47 [3217]E(f332(f332(f134(x32171),x32172),f116(x32171)),x32172) % 172.78/172.47 [3223]E(f174(x32231,x32232,f116(x32231)),x32232) % 172.78/172.47 [3224]E(f174(x32241,f116(x32241),x32242),x32242) % 172.78/172.47 [3225]E(f170(x32251,f2(a876),x32252),f116(x32251)) % 172.78/172.47 [3231]E(f332(f332(f176(x32311),x32312),f116(x32311)),f116(x32311)) % 172.78/172.47 [3232]E(f332(f332(f138(x32321),x32322),f116(x32321)),f116(x32321)) % 172.78/172.47 [3234]E(f155(x32341,x32342,f116(x32341)),f2(a876)) % 172.78/172.47 [3235]E(f240(x32351,x32352,f208(x32351)),f2(a876)) % 172.78/172.47 [3237]E(f171(x32371,x32372,f116(x32371)),f116(x32371)) % 172.78/172.47 [3238]E(f178(x32381,x32382,f116(x32381)),f116(x32381)) % 172.78/172.47 [3239]E(f177(x32391,f116(x32391),x32392),f116(x32391)) % 172.78/172.47 [3243]E(f332(f173(x32431),f152(x32431,x32432)),f332(f173(x32431),x32432)) % 172.78/172.47 [3246]E(f332(f263(x32461,x32461),f264(x32461,x32462)),x32462) % 172.78/172.47 [3247]E(f332(f265(x32471,x32471),f264(x32471,x32472)),x32472) % 172.78/172.47 [3255]E(f332(f287(x32551,x32551),f264(x32551,x32552)),f264(x32551,x32552)) % 172.78/172.47 [3270]E(f308(f877(x32701),f157(x32701,x32702)),f158(x32701,f308(x32701,x32702))) % 172.78/172.47 [3272]P102(f332(f137(a1),f180(x32721,x32722))) % 172.78/172.47 [3280]E(f332(f263(x32801,x32801),f308(x32801,x32802)),f255(f883(x32801,a871))) % 172.78/172.47 [3281]E(f332(f265(x32811,x32811),f308(x32811,x32812)),f255(f883(x32811,a871))) % 172.78/172.47 [3285]P102(f332(f137(x32851),f152(x32851,x32852))) % 172.78/172.47 [3287]P102(f332(f160(x32871,x32872),f116(x32871))) % 172.78/172.47 [3295]E(f332(f173(a1),f180(x32951,x32952)),f303(a1,x32951,x32952)) % 172.78/172.47 [3310]P51(x33101,f195(f883(x33101,a871)),x33102) % 172.78/172.47 [3315]E(f332(f270(a1,a1),f45(x33151,x33152)),f44(a1,x33151,x33152)) % 172.78/172.47 [3316]E(f332(f302(a876,x33161),f332(a115,x33162)),f303(a876,x33161,x33162)) % 172.78/172.47 [3332]E(f332(f332(f151(x33321),x33322),f116(x33321)),f140(x33321,x33322,f116(x33321))) % 172.78/172.47 [3344]E(f303(a876,f332(a115,x33441),x33442),f305(a876,x33441,x33442)) % 172.78/172.47 [3347]P40(x33471,f255(f883(x33471,a871)),f308(x33471,x33472)) % 172.78/172.47 [3411]E(f332(f332(f22(a876),x34111),f332(a115,x34112)),f332(f37(a876),f306(a876,x34112,x34111))) % 172.78/172.47 [3470]E(f167(x34701,x34702,f116(x34701)),f332(f332(f267(f877(x34701),f877(x34701)),f116(x34701)),f116(x34701))) % 172.78/172.47 [3490]E(f332(f271(x34901,x34902,f882(x34901,x34902)),f267(x34901,x34902)),f33(f882(x34901,x34902))) % 172.78/172.47 [3495]P102(f332(f332(f334(f877(x34951)),f116(x34951)),f161(x34951,x34952))) % 172.78/172.47 [3496]E(f332(f196(f877(x34961)),f117(x34961,x34962)),f332(f332(f22(a876),f332(f196(f877(x34961)),x34962)),f77(a876))) % 172.78/172.47 [3504]P102(f332(f61(a876),f303(a876,x35041,x35042))) % 172.78/172.47 [3505]P102(f332(f61(a876),f306(a876,x35051,x35052))) % 172.78/172.47 [3506]P102(f332(f61(a876),f305(a876,x35061,x35062))) % 172.78/172.47 [3507]P102(f332(f61(a1),f303(a1,x35071,x35072))) % 172.78/172.47 [3508]P102(f332(f61(a1),f306(a1,x35081,x35082))) % 172.78/172.47 [3509]P102(f332(f61(a1),f305(a1,x35091,x35092))) % 172.78/172.47 [3614]E(f332(f311(a876,a876,a115),f303(a876,x36141,x36142)),f303(a876,f332(a115,x36141),f332(a115,x36142))) % 172.78/172.47 [3635]E(f332(f332(f289(x36351,x36351,x36351),f308(x36351,x36352)),f308(x36351,x36352)),f308(x36351,x36352)) % 172.78/172.47 [3669]E(f332(f332(f267(a1,a1),f332(f332(f38(a1),x36691),x36692)),f44(a1,x36691,x36692)),f45(x36691,x36692)) % 172.78/172.47 [3670]E(f332(f332(f267(a102,a102),f332(f332(f38(a102),x36701),x36702)),f44(a102,x36701,x36702)),f21(x36701,x36702)) % 172.78/172.47 [3699]E(f332(f332(f267(a876,a876),f332(f332(f38(a876),x36991),x36992)),f44(a876,x36991,x36992)),f84(f882(a876,a876),f47(x36991,x36992))) % 172.78/172.47 [3751]P102(f332(f332(f247(a876),f332(f332(f22(a876),x37511),x37512)),f332(a115,x37511))) % 172.78/172.47 [3853]E(f332(f332(f79(a1),f332(f332(f80(a1),x38531),f332(f332(f38(a1),x38532),x38531))),f44(a1,x38532,x38531)),x38532) % 172.78/172.47 [3857]E(f332(f332(f41(a876,f883(f882(f877(x38571),f877(x38571)),a871)),f255(f883(a876,a871))),f143(x38571,x38572)),f145(x38571,x38572)) % 172.78/172.47 [4087]P102(f332(f332(f334(f882(f877(x40871),f877(x40871))),f332(f332(f267(f877(x40871),f877(x40871)),f116(x40871)),f116(x40871))),f158(x40871,x40872))) % 172.78/172.47 [4205]E(f268(x42051,x42051,x42051,a329,f268(x42051,x42051,x42051,x42052,a329)),x42052) % 172.78/172.47 [4251]E(f272(x42511,x42511,x42512,x42512,f5(x42511),f5(x42512)),f33(f882(x42511,x42512))) % 172.78/172.47 [4253]E(f272(x42531,x42531,x42532,x42532,f33(x42531),f33(x42532)),f33(f882(x42531,x42532))) % 172.78/172.47 [4492]~E(f332(f239(x44921),x44922),f208(x44921)) % 172.78/172.47 [3215]E(f332(f243(x32151),f332(f239(x32151),x32152)),x32152) % 172.78/172.47 [3216]E(f332(f169(x32161),f332(f169(x32161),x32162)),x32162) % 172.78/172.47 [3218]E(f332(f332(f138(x32181),f2(a876)),x32182),x32182) % 172.78/172.47 [3233]E(f332(f332(f176(x32331),f2(a876)),x32332),f116(x32331)) % 172.78/172.47 [3241]E(f332(f332(f134(x32411),f116(x32411)),x32412),x32412) % 172.78/172.47 [3249]E(f332(f196(f880(x32491)),f332(f239(x32491),x32492)),f2(a876)) % 172.78/172.47 [3251]E(f39(f883(x32511,a871),f332(f309(x32511),x32512)),x32512) % 172.78/172.47 [3253]E(f332(f173(x32531),f332(f168(x32531),x32532)),f332(f173(x32531),x32532)) % 172.78/172.47 [3254]E(f332(f173(x32541),f332(f169(x32541),x32542)),f332(f173(x32541),x32542)) % 172.78/172.47 [3259]E(f332(f332(f22(a102),x32591),x32592),f332(f332(a23,x32591),x32592)) % 172.78/172.47 [3274]E(f332(f332(f80(a876),x32741),x32742),f332(f332(f80(a876),x32742),x32741)) % 172.78/172.47 [3275]E(f332(f332(f80(a1),x32751),x32752),f332(f332(f80(a1),x32752),x32751)) % 172.78/172.47 [3276]E(f332(f332(f79(a876),x32761),x32762),f332(f332(f79(a876),x32762),x32761)) % 172.78/172.47 [3277]E(f332(f332(f79(a1),x32771),x32772),f332(f332(f79(a1),x32772),x32771)) % 172.78/172.47 [3302]E(f332(f332(f190(x33021,x33021),f2(a876)),x33022),f33(x33021)) % 172.78/172.47 [3303]E(f332(f196(f877(x33031)),f332(f168(x33031),x33032)),f332(f196(f877(x33031)),x33032)) % 172.78/172.47 [3304]E(f332(f196(f877(x33041)),f332(f169(x33041),x33042)),f332(f196(f877(x33041)),x33042)) % 172.78/172.47 [3305]E(f177(x33051,x33052,f195(f883(a876,a871))),f116(x33051)) % 172.78/172.47 [3306]E(f332(f332(f154(x33061,x33061),f5(x33061)),x33062),x33062) % 172.78/172.47 [3308]E(f332(f266(a1,a1),f45(x33081,x33082)),f332(f332(f38(a1),x33081),x33082)) % 172.78/172.47 [3325]E(f332(f196(f877(x33251)),f152(x33251,x33252)),f332(f37(x33251),f332(f173(x33251),x33252))) % 172.78/172.47 [3326]E(f30(f31(x33261,x33262)),f332(f332(f79(a876),f30(x33262)),f332(a115,f2(a876)))) % 172.78/172.47 [3327]E(f332(f285(x33271),f332(f287(x33271,x33271),x33272)),f332(f285(x33271),x33272)) % 172.78/172.47 [3331]P102(f332(f61(x33311),f332(f173(x33311),x33312))) % 172.78/172.47 [3339]E(f332(f332(f79(a1),x33391),f332(f78(a1),x33392)),f332(f332(f22(a1),x33391),x33392)) % 172.78/172.47 [3346]P19(x33461,x33462,f195(f883(f875(x33461),a871))) % 172.78/172.47 [3348]E(f332(f311(x33481,x33481,f5(x33481)),x33482),x33482) % 172.78/172.47 [3349]E(f332(f311(x33491,x33491,f33(x33491)),x33492),x33492) % 172.78/172.47 [3350]E(f332(f312(x33501,x33501,f5(x33501)),x33502),x33502) % 172.78/172.47 [3351]E(f332(f312(x33511,x33511,f33(x33511)),x33512),x33512) % 172.78/172.47 [3352]P102(f332(f255(f883(x33521,a871)),x33522)) % 172.78/172.47 [3354]E(f332(f37(a876),f332(f302(a876,x33541),x33542)),f332(f332(f22(a876),x33542),x33541)) % 172.78/172.47 [3355]E(f332(f302(a876,f332(a115,x33551)),x33552),f306(a876,x33551,x33552)) % 172.78/172.47 [3368]E(f332(f332(f310(x33681),x33682),f195(f883(x33681,a871))),f332(f252(x33681),f332(a329,x33682))) % 172.78/172.47 [3372]E(f332(f332(f310(x33721),x33722),f195(f883(x33721,a871))),f238(x33721,f332(f239(x33721),x33722))) % 172.78/172.47 [3374]E(f308(x33741,f332(f287(x33741,x33741),x33742)),f332(f287(x33741,x33741),f308(x33741,x33742))) % 172.78/172.47 [3379]E(f332(f332(f79(a876),f332(a115,x33791)),x33792),f332(f332(f79(a876),x33791),f332(a115,x33792))) % 172.78/172.47 [3380]E(f332(f332(f22(a876),f332(a115,x33801)),f332(a115,x33802)),f332(f332(f22(a876),x33801),x33802)) % 172.78/172.47 [3386]E(f54(x33861,f2(a876),x33862),f332(f332(f151(f877(x33861)),f116(x33861)),f116(f877(x33861)))) % 172.78/172.47 [3387]E(f332(f37(a876),f305(a876,x33871,x33872)),f332(f332(f22(a876),x33872),x33871)) % 172.78/172.47 [3396]P38(x33961,f332(f332(f288(a876,x33961),a251),x33962)) % 172.78/172.47 [3398]P29(a876,f139(a876,f332(f302(a876,x33981),x33982))) % 172.78/172.47 [3400]P102(f332(f61(a876),f332(f302(a876,x34001),x34002))) % 172.78/172.47 [3401]P102(f332(f61(a1),f332(f302(a1,x34011),x34012))) % 172.78/172.47 [3404]E(f332(f287(f877(x34041),f877(x34041)),f157(x34041,x34042)),f157(x34041,f332(f287(x34041,x34041),x34042))) % 172.78/172.47 [3405]E(f332(f196(a873),f31(x34051,x34052)),f332(f332(f79(a876),f332(f196(a873),x34052)),f332(a115,f2(a876)))) % 172.78/172.47 [3407]E(f332(f302(a1,x34071),f332(f332(f79(a1),x34072),f77(a1))),f303(a1,x34071,x34072)) % 172.78/172.47 [3410]E(f332(f332(f38(a1),f332(f78(a1),x34101)),f332(f78(a1),x34102)),f332(f332(f38(a1),x34101),x34102)) % 172.78/172.47 [3418]E(f185(x34181,x34182,f332(f16(f880(x34182),x34181),f208(x34182))),f195(f883(x34181,a871))) % 172.78/172.47 [3419]E(f187(x34191,x34192,f332(f16(f880(x34192),x34191),f208(x34192))),f195(f883(x34192,a871))) % 172.78/172.47 [3420]E(f332(f332(f190(f882(x34201,x34201),a871),f77(a876)),x34202),x34202) % 172.78/172.47 [3422]E(f332(f332(f113(f883(x34221,a871)),x34222),f195(f883(x34221,a871))),x34222) % 172.78/172.47 [3423]E(f332(f332(f22(f883(x34231,a871)),x34232),f195(f883(x34231,a871))),x34232) % 172.78/172.47 [3424]E(f332(f332(f104(f883(x34241,a871)),x34242),f255(f883(x34241,a871))),x34242) % 172.78/172.47 [3425]E(f332(f266(a876,a876),f84(f882(a876,a876),f47(x34251,x34252))),f332(f332(f38(a876),x34251),x34252)) % 172.78/172.47 [3432]E(f314(x34321,f332(a20,x34322),f332(f78(a1),f332(a20,x34322))),f332(f332(f317(a1),x34321),x34322)) % 172.78/172.47 [3433]E(f303(a1,f332(f332(f79(a1),x34331),f77(a1)),x34332),f305(a1,x34331,x34332)) % 172.78/172.47 [3438]E(f332(f270(a876,a876),f84(f882(a876,a876),f47(x34381,x34382))),f44(a876,x34381,x34382)) % 172.78/172.47 [3446]E(f315(x34461,f332(a20,x34462),f332(f78(a1),f332(a20,x34462))),f316(a1,x34461,x34462)) % 172.78/172.47 [3449]P102(f332(f332(f334(x34491),x34492),f255(f883(x34491,a871)))) % 172.78/172.47 [3454]E(f332(f332(f22(a876),f332(a115,x34541)),x34542),f332(f37(a876),f303(a876,x34542,x34541))) % 172.78/172.47 [3481]E(f332(f332(f113(f883(x34811,a871)),x34812),f255(f883(x34811,a871))),f255(f883(x34811,a871))) % 172.78/172.47 [3482]E(f332(f332(f22(f883(x34821,a871)),x34822),f255(f883(x34821,a871))),f195(f883(x34821,a871))) % 172.78/172.47 [3483]E(f332(f332(f104(f883(x34831,a871)),x34832),f195(f883(x34831,a871))),f195(f883(x34831,a871))) % 172.78/172.47 [3499]E(f44(a1,f332(f103(a1),x34991),f332(f103(a1),x34992)),f332(f103(a1),f44(a876,x34991,x34992))) % 172.78/172.47 [3500]E(f44(a1,f332(f78(a1),x35001),f332(f78(a1),x35002)),f332(f78(a1),f44(a1,x35001,x35002))) % 172.78/172.47 [3511]E(f332(f196(f877(x35111)),f332(f172(x35111),x35112)),f332(f332(f22(a876),f332(f196(f877(x35111)),x35112)),f77(a876))) % 172.78/172.47 [3536]E(f332(f332(f38(a1),f44(a1,x35361,x35362)),x35362),f2(a1)) % 172.78/172.47 [3546]E(f332(a3,f44(a876,f332(a19,x35461),f332(a19,x35462))),f44(a102,x35461,x35462)) % 172.78/172.47 [3581]E(f332(a3,f332(f332(f22(a876),f332(a19,x35811)),f332(a19,x35812))),f332(f332(f22(a102),x35811),x35812)) % 172.78/172.47 [3582]E(f332(a3,f332(f332(f80(a876),f332(a19,x35821)),f332(a19,x35822))),f332(f332(f80(a102),x35821),x35822)) % 172.78/172.47 [3583]E(f332(a3,f332(f332(f79(a876),f332(a19,x35831)),f332(a19,x35832))),f332(f332(f79(a102),x35831),x35832)) % 172.78/172.47 [3584]E(f332(a3,f332(f332(f38(a876),f332(a19,x35841)),f332(a19,x35842))),f332(f332(f38(a102),x35841),x35842)) % 172.78/172.47 [3593]E(f332(f311(a876,a876,a115),f332(f302(a876,x35931),x35932)),f332(f302(a876,f332(a115,x35931)),f332(a115,x35932))) % 172.78/172.47 [3619]P102(f332(f47(x36191,x36192),f84(f882(a876,a876),f47(x36191,x36192)))) % 172.78/172.47 [3641]E(f332(f332(f79(a876),f332(f332(f79(a876),f30(x36411)),f30(x36412))),f332(a115,f2(a876))),f30(f32(x36411,x36412))) % 172.78/172.47 [3642]E(f44(a876,f332(a115,f44(a876,x36421,x36422)),x36422),f44(a876,f332(a115,x36421),x36422)) % 172.78/172.47 [3656]E(f332(f332(f42(f883(x36561,a871),f883(x36561,a871)),x36562),f5(f883(x36561,a871))),f40(f883(x36561,a871),x36562)) % 172.78/172.47 [3657]E(f332(f332(f41(f883(x36571,a871),f883(x36571,a871)),x36572),f5(f883(x36571,a871))),f39(f883(x36571,a871),x36572)) % 172.78/172.47 [3658]E(f332(f311(f877(x36581),f883(x36581,a871),f173(x36581)),f332(f173(f877(x36581)),f53(x36581,x36582))),f332(f309(x36581),f332(f173(x36581),x36582))) % 172.78/172.47 [3662]P102(f332(f332(f334(f883(x36621,a871)),x36622),f332(f309(x36621),x36622))) % 172.78/172.47 [3668]E(f44(a1,f332(f78(a1),f44(a1,x36681,x36682)),x36682),f44(a1,f332(f78(a1),x36681),x36682)) % 172.78/172.47 [3680]P102(f332(f332(f246(f883(x36801,a871)),x36802),f255(f883(x36801,a871)))) % 172.78/172.47 [3682]E(f332(f332(f289(x36821,x36821,x36821),f308(x36821,x36822)),f308(x36821,f308(x36821,x36822))),f308(x36821,x36822)) % 172.78/172.47 [3683]E(f332(f332(f113(f883(x36831,a871)),f332(f265(x36831,x36831),x36832)),f332(f263(x36831,x36831),x36832)),f332(f285(x36831),x36832)) % 172.78/172.47 [3704]E(f319(x37041,x37042,f255(f883(x37041,a871)),f255(f883(x37042,a871))),f255(f883(f881(x37041,x37042),a871))) % 172.78/172.47 [3756]P102(f332(f332(f246(a876),f44(a876,x37561,x37562)),x37561)) % 172.78/172.47 [3781]P102(f332(f332(f246(a1),f332(f78(a1),f332(f103(a1),x37811))),f332(f103(a1),x37812))) % 172.78/172.47 [3807]P102(f332(f332(f334(f883(x38071,a871)),f195(f883(x38071,a871))),f332(f309(x38071),x38072))) % 172.78/172.47 [3812]E(f308(x38121,f332(f332(f289(x38121,x38121,x38121),x38122),f308(x38121,x38122))),f308(x38121,x38122)) % 172.78/172.47 [3815]E(f332(f332(f289(x38151,x38151,x38151),f308(x38151,x38152)),x38152),f332(f332(f289(x38151,x38151,x38151),x38152),f308(x38151,x38152))) % 172.78/172.47 [3817]E(f332(a107,f332(f332(f79(a1),f332(f332(f22(a1),x38171),x38172)),f77(a1))),f332(f37(a1),f303(a1,x38172,x38171))) % 172.78/172.47 [3832]E(f332(f263(x38321,x38321),f332(f332(f289(x38321,x38321,x38321),x38322),f308(x38321,x38322))),f332(f263(x38321,x38321),x38322)) % 172.78/172.47 [3833]E(f332(f265(x38331,x38331),f332(f332(f289(x38331,x38331,x38331),x38332),f308(x38331,x38332))),f332(f265(x38331,x38331),x38332)) % 172.78/172.47 [3849]E(f332(f332(f79(a876),f332(f332(f79(a876),f332(f196(a873),x38491)),f332(f196(a873),x38492))),f332(a115,f2(a876))),f332(f196(a873),f32(x38491,x38492))) % 172.78/172.47 [3852]E(f332(f142(f877(x38521),f877(x38521),f134(x38521),f116(x38521)),f170(f877(x38521),x38522,f116(x38521))),f116(x38521)) % 172.78/172.47 [3861]P20(a876,a876,f332(f332(f7(a876,a876,a876),f79(a876)),x38611),x38612) % 172.78/172.47 [3863]P29(a876,f332(f169(a876),f332(f332(f154(f877(x38631),a876),f196(f877(x38631))),f181(x38631,x38632)))) % 172.78/172.47 [3910]P102(f332(f332(f247(a1),f332(f78(a1),f332(f103(a1),f332(a115,x39101)))),f332(f103(a1),x39102))) % 172.78/172.47 [3956]E(f332(f142(f877(x39561),x39561,f332(f7(x39561,f877(x39561),f877(x39561)),f151(x39561)),f116(x39561)),x39562),f332(f169(x39561),x39562)) % 172.78/172.47 [4008]P102(f332(f332(f246(f883(f882(f877(x40081),f877(x40081)),a871)),f158(x40081,x40082)),f308(f877(x40081),f157(x40081,x40082)))) % 172.78/172.47 [4040]P102(f332(f47(x40401,x40402),f332(f332(f267(a876,a876),f332(f332(f38(a876),x40401),x40402)),f44(a876,x40401,x40402)))) % 172.78/172.47 [4051]P102(f332(f332(f246(f883(f882(f877(x40511),f877(x40511)),a871)),f157(x40511,f308(x40511,x40512))),f308(f877(x40511),f157(x40511,x40512)))) % 172.78/172.47 [4277]E(f332(f332(f273(f882(a102,a102),a102,f882(a102,a102),f882(x42771,f882(a102,a102))),f277(f332(f166(a102),f332(f332(f154(f882(a102,x42771),a102),f266(a102,x42771)),x42772)))),f332(f332(f8(x42771,f883(f882(a102,a102),f882(x42771,f882(a102,a102))),a102),f267(x42771,f882(a102,a102))),f278(x42771,x42772))),f276(x42771,x42772)) % 172.78/172.47 [4388]E(f332(f241(a876,f882(x43881,f878(x43881)),f2(a876),f332(f271(x43881,f878(x43881),a876),f332(f16(f883(f878(x43881),a876),x43881),f332(f332(f7(f878(x43881),a876,a876),f332(f332(f8(a876,f883(a876,a876),f878(x43881)),f79(a876)),f196(f878(x43881)))),f77(a876))))),f332(f135(x43881),x43882)),f332(f196(f878(x43881)),x43882)) % 172.78/172.47 [4463]E(f332(f271(f883(f882(x44631,x44631),a871),f883(f882(x44631,x44631),a871),f883(f883(x44632,x44631),f882(f883(f882(x44632,x44632),a871),f883(f882(x44632,x44632),a871)))),f332(f332(f7(f883(f882(x44631,x44631),a871),f883(f883(f882(x44631,x44631),a871),f883(f883(x44632,x44631),f883(f882(x44632,x44632),a871))),f883(f883(f882(x44631,x44631),a871),f883(f883(x44632,x44631),f882(f883(f882(x44632,x44632),a871),f883(f882(x44632,x44632),a871))))),f332(f332(f8(f883(f883(f883(x44632,x44631),f883(f882(x44632,x44632),a871)),f883(f883(x44632,x44631),f882(f883(f882(x44632,x44632),a871),f883(f882(x44632,x44632),a871)))),f883(f883(f883(f882(x44631,x44631),a871),f883(f883(x44632,x44631),f883(f882(x44632,x44632),a871))),f883(f883(f882(x44631,x44631),a871),f883(f883(x44632,x44631),f882(f883(f882(x44632,x44632),a871),f883(f882(x44632,x44632),a871))))),f883(f882(x44631,x44631),a871)),f8(f883(f883(x44632,x44631),f883(f882(x44632,x44632),a871)),f883(f883(x44632,x44631),f882(f883(f882(x44632,x44632),a871),f883(f882(x44632,x44632),a871))),f883(f882(x44631,x44631),a871))),f332(f332(f8(f883(f883(x44632,x44631),f883(f883(f882(x44632,x44632),a871),f882(f883(f882(x44632,x44632),a871),f883(f882(x44632,x44632),a871)))),f883(f883(f883(x44632,x44631),f883(f882(x44632,x44632),a871)),f883(f883(x44632,x44631),f882(f883(f882(x44632,x44632),a871),f883(f882(x44632,x44632),a871)))),f883(f882(x44631,x44631),a871)),f18(f883(x44632,x44631),f883(f882(x44632,x44632),a871),f882(f883(f882(x44632,x44632),a871),f883(f882(x44632,x44632),a871)))),f332(f332(f8(f883(f883(x44632,x44631),f883(f882(x44632,x44632),a871)),f883(f883(x44632,x44631),f883(f883(f882(x44632,x44632),a871),f882(f883(f882(x44632,x44632),a871),f883(f882(x44632,x44632),a871)))),f883(f882(x44631,x44631),a871)),f332(f8(f883(f882(x44632,x44632),a871),f883(f883(f882(x44632,x44632),a871),f882(f883(f882(x44632,x44632),a871),f883(f882(x44632,x44632),a871))),f883(x44632,x44631)),f267(f883(f882(x44632,x44632),a871),f883(f882(x44632,x44632),a871)))),f288(x44631,x44632))))),f288(x44631,x44632))),f73(x44631,x44632)) % 172.78/172.47 [4539]~E(f332(f309(x45391),x45392),f195(f883(f883(x45391,a871),a871))) % 172.78/172.47 [4553]~P102(f332(f332(f334(x45531),x45532),f195(f883(x45531,a871)))) % 172.78/172.47 [4563]~P102(f332(f332(f247(f883(x45631,a871)),x45632),f195(f883(x45631,a871)))) % 172.78/172.47 [3357]E(f332(f332(f22(a876),x33571),f332(f332(f79(a876),x33571),x33572)),f2(a876)) % 172.78/172.47 [3360]E(f332(f332(f113(f883(x33601,a871)),x33602),x33602),x33602) % 172.78/172.47 [3361]E(f332(f332(f104(f883(x33611,a871)),x33612),x33612),x33612) % 172.78/172.47 [3389]E(f332(f332(f22(f883(x33891,a871)),x33892),x33892),f195(f883(x33891,a871))) % 172.78/172.47 [3392]E(f332(f143(x33921,x33922),f2(a876)),f195(f883(f882(f877(x33921),f877(x33921)),a871))) % 172.78/172.47 [3393]E(f332(f332(f79(a876),x33931),f332(a115,x33932)),f332(a115,f332(f332(f79(a876),x33931),x33932))) % 172.78/172.47 [3406]E(f202(f332(f103(a1),x34061),f332(f103(a1),x34062)),f332(f103(a1),f332(f332(f22(a876),x34061),x34062))) % 172.78/172.47 [3409]E(f332(f332(f38(a1),f332(f78(a1),x34091)),x34092),f332(f332(f38(a1),x34091),f332(f78(a1),x34092))) % 172.78/172.47 [3413]E(f332(f37(a1),f332(f302(a1,x34131),x34132)),f332(a107,f332(f332(f22(a1),x34132),x34131))) % 172.78/172.47 [3416]E(f332(f332(f79(a876),f332(a115,x34161)),x34162),f332(a115,f332(f332(f79(a876),x34161),x34162))) % 172.78/172.47 [3421]E(f332(f78(f883(x34211,a871)),f332(f78(f883(x34211,a871)),x34212)),x34212) % 172.78/172.47 [3435]E(f181(x34351,f332(f332(f151(f877(x34351)),f116(x34351)),x34352)),f181(x34351,x34352)) % 172.78/172.47 [3439]E(f332(f332(f79(a876),x34391),f332(f332(f80(a876),x34391),x34392)),f332(f332(f80(a876),x34391),f332(a115,x34392))) % 172.78/172.47 [3447]E(f332(f332(a23,f332(a3,x34471)),f332(a3,x34472)),f332(a3,f332(f332(f22(a876),x34471),x34472))) % 172.78/172.47 [3461]E(f332(f332(f80(a1),f332(f78(a1),x34611)),x34612),f332(f78(a1),f332(f332(f80(a1),x34611),x34612))) % 172.78/172.47 [3463]E(f332(f332(f257(a1),f332(f103(a1),x34631)),x34632),f332(f103(a1),f332(f332(f257(a876),x34631),x34632))) % 172.78/172.47 [3464]E(f332(f332(f80(a102),f332(a3,x34641)),f332(a3,x34642)),f332(a3,f332(f332(f80(a876),x34641),x34642))) % 172.78/172.47 [3465]E(f332(f332(f79(a102),f332(a3,x34651)),f332(a3,x34652)),f332(a3,f332(f332(f79(a876),x34651),x34652))) % 172.78/172.47 [3466]E(f332(f332(f244(a876),f332(a115,x34661)),f332(a115,x34662)),f332(a115,f332(f332(f244(a876),x34661),x34662))) % 172.78/172.47 [3467]E(f332(f332(f245(a876),f332(a115,x34671)),f332(a115,x34672)),f332(a115,f332(f332(f245(a876),x34671),x34672))) % 172.78/172.47 [3473]E(f332(f173(a876),f139(a876,f332(f302(a876,x34731),x34732))),f332(f302(a876,x34731),x34732)) % 172.78/172.47 [3474]E(f313(x34741,f332(f332(f310(x34741),x34742),f195(f883(x34741,a871)))),x34742) % 172.78/172.47 [3479]E(f332(f263(x34791,x34792),f195(f883(f882(x34791,x34792),a871))),f195(f883(x34792,a871))) % 172.78/172.47 [3480]E(f332(f265(x34801,x34802),f195(f883(f882(x34801,x34802),a871))),f195(f883(x34801,a871))) % 172.78/172.47 [3484]E(f332(a107,f332(f332(f22(a1),x34841),x34842)),f332(f37(a1),f305(a1,x34842,x34841))) % 172.78/172.47 [3489]E(f332(f332(f79(a876),x34891),f332(f332(f80(a876),x34892),x34891)),f332(f332(f80(a876),f332(a115,x34892)),x34891)) % 172.78/172.47 [3491]E(f332(f332(f60(x34911),f195(f883(x34911,a871))),x34912),f195(f883(f883(x34911,a871),a871))) % 172.78/172.47 [3501]E(f332(f196(f877(a876)),f139(a876,f332(f302(a876,x35011),x35012))),f332(f332(f22(a876),x35012),x35011)) % 172.78/172.47 [3516]E(f332(f332(f113(f883(x35161,a871)),f195(f883(x35161,a871))),x35162),x35162) % 172.78/172.47 [3517]E(f332(f332(f104(f883(x35171,a871)),f255(f883(x35171,a871))),x35172),x35172) % 172.78/172.47 [3520]E(f332(f332(f79(a1),f332(f78(a1),x35201)),f332(f78(a1),x35202)),f332(f78(a1),f332(f332(f79(a1),x35201),x35202))) % 172.78/172.47 [3523]E(f332(f332(f80(a1),f332(f103(a1),x35231)),f332(f103(a1),x35232)),f332(f103(a1),f332(f332(f80(a876),x35231),x35232))) % 172.78/172.47 [3524]E(f332(f332(f80(a1),f332(f106(a1),x35241)),f332(f106(a1),x35242)),f332(f106(a1),f332(f332(f80(a1),x35241),x35242))) % 172.78/172.47 [3526]E(f332(f332(f79(a1),f332(f103(a1),x35261)),f332(f103(a1),x35262)),f332(f103(a1),f332(f332(f79(a876),x35261),x35262))) % 172.78/172.47 [3527]E(f332(f332(f79(a1),f332(f106(a1),x35271)),f332(f106(a1),x35272)),f332(f106(a1),f332(f332(f79(a1),x35271),x35272))) % 172.78/172.47 [3528]E(f332(f332(f38(a1),f332(f103(a1),x35281)),f332(f103(a1),x35282)),f332(f103(a1),f332(f332(f38(a876),x35281),x35282))) % 172.78/172.47 [3547]E(f332(f332(f6(x35471,a876),f332(f16(a876,x35471),f77(a876))),x35472),f332(f37(x35471),x35472)) % 172.78/172.47 [3554]E(f332(f78(a1),f44(a1,f332(f78(a1),x35541),x35542)),f44(a1,x35541,f332(f78(a1),x35542))) % 172.78/172.47 [3556]E(f332(f173(a1),f180(x35561,f332(f332(f22(a1),x35562),f77(a1)))),f332(f302(a1,x35561),x35562)) % 172.78/172.47 [3561]P102(f332(f332(f246(a876),x35611),f332(f332(f79(a876),x35612),x35611))) % 172.78/172.47 [3562]P102(f332(f332(f246(a876),x35621),f332(f332(f79(a876),x35621),x35622))) % 172.78/172.47 [3564]E(f332(f332(f113(f883(x35641,a871)),f255(f883(x35641,a871))),x35642),f255(f883(x35641,a871))) % 172.78/172.47 [3565]E(f332(f332(f22(f883(x35651,a871)),f195(f883(x35651,a871))),x35652),f195(f883(x35651,a871))) % 172.78/172.47 [3566]E(f332(f332(f104(f883(x35661,a871)),f195(f883(x35661,a871))),x35662),f195(f883(x35661,a871))) % 172.78/172.47 [3573]E(f332(f332(f267(a1,a1),x35731),f332(f78(a1),x35732)),f332(a50,f332(f332(f267(a1,a1),x35731),x35732))) % 172.78/172.47 [3574]E(f332(f302(a1,f332(f332(f79(a1),x35741),f77(a1))),x35742),f306(a1,x35741,x35742)) % 172.78/172.47 [3585]E(f332(f332(f80(a876),x35851),f332(f332(f38(a876),x35852),x35851)),f332(f332(f22(a876),x35852),f44(a876,x35852,x35851))) % 172.78/172.47 [3586]E(f332(f332(f80(a1),x35861),f332(f332(f38(a1),x35862),x35861)),f332(f332(f22(a1),x35862),f44(a1,x35862,x35861))) % 172.78/172.47 [3590]E(f332(f173(a1),f180(f332(f332(f79(a1),x35901),f77(a1)),x35902)),f305(a1,x35901,x35902)) % 172.78/172.47 [3594]P102(f332(f332(f246(f883(x35941,a871)),x35942),x35942)) % 172.78/172.47 [3597]E(f332(f332(f113(f883(x35971,a871)),x35972),f332(f78(f883(x35971,a871)),x35972)),f255(f883(x35971,a871))) % 172.78/172.47 [3598]E(f332(f332(f104(f883(x35981,a871)),x35982),f332(f78(f883(x35981,a871)),x35982)),f195(f883(x35981,a871))) % 172.78/172.47 [3606]E(f332(f332(f22(a876),f332(f332(f22(a876),x36061),f77(a876))),x36062),f332(f332(f22(a876),x36061),f332(a115,x36062))) % 172.78/172.47 [3611]E(f332(f332(f22(f883(x36111,a871)),f255(f883(x36111,a871))),x36112),f332(f78(f883(x36111,a871)),x36112)) % 172.78/172.47 [3612]E(f332(f332(f22(a1),f332(f106(a1),x36121)),f332(f106(a1),x36122)),f332(f106(a1),f332(f332(f79(a1),x36121),f332(f78(a1),x36122)))) % 172.78/172.47 [3625]E(f332(f173(a876),f139(a876,f332(f302(a876,x36251),f332(a115,x36252)))),f303(a876,x36251,x36252)) % 172.78/172.47 [3633]P102(f332(f332(f332(f332(a203,a24),x36331),x36332),x36331)) % 172.78/172.47 [3639]E(f332(f196(f877(f877(x36391))),f53(x36391,x36392)),f332(f332(f257(a876),f332(a115,f332(a115,f2(a876)))),f332(f196(f877(x36391)),x36392))) % 172.78/172.47 [3660]E(f332(f332(f190(f882(x36601,x36601),a871),f2(a876)),x36602),f308(x36601,f195(f883(f882(x36601,x36601),a871)))) % 172.78/172.47 [3664]P102(f332(f137(a876),f139(a876,f332(f302(a876,x36641),x36642)))) % 172.78/172.47 [3681]E(f332(f311(a1,a876,a107),f303(a1,f332(f103(a1),x36811),f332(f103(a1),x36812))),f303(a876,x36811,x36812)) % 172.78/172.47 [3691]E(f192(a876,f2(a876),f5(a876),f332(f332(f22(a876),x36911),x36912)),f332(f332(f22(a876),x36911),f332(a115,x36912))) % 172.78/172.47 [3692]E(f332(a107,f332(f332(f22(a1),x36921),f332(f332(f79(a1),x36922),f77(a1)))),f332(f37(a1),f306(a1,x36922,x36921))) % 172.78/172.47 [3728]E(f332(f332(f154(a876,a876),a115),f139(a876,f332(f302(a876,x37281),x37282))),f139(a876,f332(f302(a876,f332(a115,x37281)),f332(a115,x37282)))) % 172.78/172.47 [3736]E(f332(f173(a1),f180(f332(f332(f79(a1),x37361),f77(a1)),f332(f332(f22(a1),x37362),f77(a1)))),f306(a1,x37361,x37362)) % 172.78/172.47 [3747]P102(f332(f332(f246(f883(x37471,a871)),f195(f883(x37471,a871))),x37472)) % 172.78/172.47 [3752]E(f84(x37521,f332(f332(f7(x37521,x37521,a871),a329),x37522)),x37522) % 172.78/172.47 [3753]E(f89(x37531,f332(f332(f7(x37531,x37531,a871),a329),x37532)),x37532) % 172.78/172.47 [3757]E(f332(f173(a876),f139(a876,f332(f302(a876,f332(a115,x37571)),f332(a115,x37572)))),f305(a876,x37571,x37572)) % 172.78/172.47 [3784]E(f332(f332(f269(x37841,x37842),f255(f883(x37841,a871))),f332(f16(f883(x37842,a871),x37841),f255(f883(x37842,a871)))),f255(f883(f882(x37841,x37842),a871))) % 172.78/172.47 [3819]E(f332(f252(x38191),f332(f332(f8(a871,a871,x38191),a327),x38192)),f332(f78(f883(x38191,a871)),f332(f252(x38191),x38192))) % 172.78/172.47 [3822]E(f332(f252(x38221),f332(f332(f7(x38221,x38221,a871),a329),x38222)),f332(f332(f310(x38221),x38222),f195(f883(x38221,a871)))) % 172.78/172.47 [3829]E(f332(f332(f79(a1),f332(f332(f22(a1),x38291),x38292)),f332(f332(f22(a1),x38291),x38292)),f332(f332(f22(a1),f332(f332(f79(a1),x38291),x38291)),f332(f332(f79(a1),x38292),x38292))) % 172.78/172.47 [3830]E(f332(f332(f79(a1),f332(f332(f79(a1),x38301),x38301)),f332(f332(f79(a1),x38302),x38302)),f332(f332(f79(a1),f332(f332(f79(a1),x38301),x38302)),f332(f332(f79(a1),x38301),x38302))) % 172.78/172.47 [3846]P102(f332(f332(f246(a876),f332(f37(x38461),f332(f173(x38461),x38462))),f332(f196(f877(x38461)),x38462))) % 172.78/172.47 [3847]P102(f332(f332(f246(a876),f332(f196(f877(x38471)),f152(x38471,x38472))),f332(f196(f877(x38471)),x38472))) % 172.78/172.47 [3858]E(f332(f252(x38581),f332(f332(f7(x38581,f883(x38581,a871),a871),f334(x38581)),x38582)),x38582) % 172.78/172.47 [3874]E(f332(f332(f176(x38741),f332(f332(f22(a876),f332(f196(f877(x38741)),x38742)),f77(a876))),x38742),f117(x38741,x38742)) % 172.78/172.47 [3897]E(f192(a876,f2(a876),f332(f332(f8(a876,a876,a876),a115),f332(f244(a876),x38971)),x38972),f332(f332(f244(a876),f332(a115,x38971)),x38972)) % 172.78/172.47 [3901]E(f39(f883(x39011,a871),f332(f311(f883(f882(x39011,x39011),a871),f883(x39011,a871),f285(x39011)),x39012)),f332(f285(x39011),f39(f883(f882(x39011,x39011),a871),x39012))) % 172.78/172.47 [3902]E(f192(a876,f332(a115,x39021),f332(f332(f8(a876,a876,a876),a115),f332(f245(a876),x39021)),x39022),f332(f332(f245(a876),f332(a115,x39021)),x39022)) % 172.78/172.47 [3904]E(f332(f332(f267(a1,a1),f332(f332(f38(a1),f332(f74(a1),x39041)),f332(f74(a1),x39042))),f44(a1,f332(f74(a1),x39041),f332(f74(a1),x39042))),f52(x39041,x39042)) % 172.78/172.47 [3927]P102(f332(f332(f246(f883(f883(x39271,a871),a871)),x39272),f332(f309(x39271),f39(f883(x39271,a871),x39272)))) % 172.78/172.47 [3961]E(f332(f332(f41(x39611,f883(x39611,a871)),x39612),f332(f332(f7(x39611,f883(x39611,a871),f883(x39611,a871)),f310(x39611)),f195(f883(x39611,a871)))),x39612) % 172.78/172.47 [3962]E(f332(f332(f289(x39621,x39621,x39621),f332(f287(x39621,x39621),x39622)),f308(x39621,f332(f287(x39621,x39621),x39622))),f332(f287(x39621,x39621),f332(f332(f289(x39621,x39621,x39621),x39622),f308(x39621,x39622)))) % 172.78/172.47 [4031]E(f332(f173(x40311),f332(f142(f877(x40311),f877(x40311),f134(x40311),f116(x40311)),x40312)),f332(f332(f41(f877(x40311),f883(x40311,a871)),f332(f173(f877(x40311)),x40312)),f173(x40311))) % 172.78/172.47 [4063]E(f332(f332(f113(f883(f882(x40631,x40631),a871)),f308(x40631,f195(f883(f882(x40631,x40631),a871)))),f332(f332(f289(x40631,x40631,x40631),f308(x40631,x40632)),x40632)),f308(x40631,x40632)) % 172.78/172.47 [4097]E(f332(f332(f183(x40971,x40971),x40972),x40972),f332(f332(f154(x40971,f882(x40971,x40971)),f332(f332(f18(x40971,x40971,f882(x40971,x40971)),f267(x40971,x40971)),f5(x40971))),x40972)) % 172.78/172.47 [4214]E(f332(f142(a876,f877(x42141),f332(f7(f877(x42141),a876,a876),f332(f332(f8(a876,f883(a876,a876),f877(x42141)),f245(a876)),f196(f877(x42141)))),f2(a876)),f332(f169(f877(x42141)),x42142)),f332(f196(f877(f877(x42141))),f181(x42141,x42142))) % 172.78/172.47 [4292]E(f332(f332(f288(f882(a876,f877(x42921)),f877(x42921)),f325(a876,f877(x42921),a251,f145(x42921,x42922))),f332(f332(f18(f877(x42921),f877(x42921),f882(a876,f877(x42921))),f332(f332(f8(a876,f883(f877(x42921),f882(a876,f877(x42921))),f877(x42921)),f267(a876,f877(x42921))),f196(f877(x42921)))),f5(f877(x42921)))),f146(x42921,x42922)) % 172.78/172.47 [4422]E(f332(f252(x44221),f332(f332(f8(f883(f883(x44221,a871),a871),a871,x44221),f87(f883(x44221,a871))),f332(f332(f8(f883(f883(x44221,a871),a871),f883(f883(x44221,a871),a871),x44221),f332(f18(f883(x44221,a871),a871,a871),f332(f332(f8(a871,f883(a871,a871),f883(x44221,a871)),a335),f332(f332(f7(f883(x44221,a871),f883(f883(x44221,a871),a871),a871),f334(f883(x44221,a871))),x44222)))),f334(x44221)))),f40(f883(x44221,a871),x44222)) % 172.78/172.47 [4564]~P102(f332(f332(f247(a1),f332(f103(a1),x45641)),f332(f78(a1),f332(f103(a1),x45642)))) % 172.78/172.47 [4581]~P102(f332(f332(f90(a1),f332(f332(f22(a1),f332(f332(f79(a1),x45811),x45811)),a100)),f332(f332(f79(a1),x45812),x45812))) % 172.78/172.47 [3487]E(f332(f332(f22(a876),f332(f332(f79(a876),x34871),x34872)),x34872),x34871) % 172.78/172.47 [3488]E(f332(f332(f22(a876),f332(f332(f79(a876),x34881),x34882)),x34881),x34882) % 172.78/172.47 [3555]E(f332(f332(f79(a876),f332(f332(f22(a876),x35551),x35552)),x35552),f332(f332(f245(a876),x35551),x35552)) % 172.78/172.47 [3667]E(f332(f332(f80(a876),f332(f332(f38(a876),x36671),x36672)),x36672),f332(f332(f22(a876),x36671),f44(a876,x36671,x36672))) % 172.78/172.47 [3696]E(f332(f173(a876),f139(a876,f332(f302(a876,f332(a115,x36961)),x36962))),f306(a876,x36961,x36962)) % 172.78/172.47 [3703]E(f332(f103(a1),f227(f332(a107,f332(f74(a1),x37031)),f332(a107,f332(f74(a1),x37032)))),f332(f332(a228,x37031),x37032)) % 172.78/172.47 [3705]E(f332(f332(f113(f883(x37051,a871)),f332(f78(f883(x37051,a871)),x37052)),x37052),f255(f883(x37051,a871))) % 172.78/172.47 [3706]E(f332(f332(f104(f883(x37061,a871)),f332(f78(f883(x37061,a871)),x37062)),x37062),f195(f883(x37061,a871))) % 172.78/172.47 [3724]P102(f332(f332(f246(a876),f332(f332(f22(a876),x37241),x37242)),x37241)) % 172.78/172.47 [3725]P102(f332(f332(f246(a876),f332(f332(f38(a876),x37251),x37252)),x37251)) % 172.78/172.47 [3749]P102(f332(f332(f247(a876),x37491),f332(a115,f332(f332(f79(a876),x37492),x37491)))) % 172.78/172.47 [3750]P102(f332(f332(f247(a876),x37501),f332(a115,f332(f332(f79(a876),x37501),x37502)))) % 172.78/172.47 [3768]E(f332(f332(f80(a876),f332(a107,f332(f74(a1),x37681))),f332(a107,f332(f74(a1),x37682))),f332(a107,f332(f74(a1),f332(f332(f80(a1),x37681),x37682)))) % 172.78/172.47 [3780]P102(f332(f332(f246(a1),f2(a1)),f332(f332(f257(a1),f332(f74(a1),x37801)),x37802))) % 172.78/172.47 [3851]E(f332(f286(f877(x38511),f877(x38511),f158(x38511,x38512)),f332(f332(f310(f877(x38511)),f116(x38511)),f195(f883(f877(x38511),a871)))),f332(f332(f310(f877(x38511)),f116(x38511)),f195(f883(f877(x38511),a871)))) % 172.78/172.47 [3872]E(f332(f332(f113(f883(f882(x38721,x38721),a871)),f308(x38721,x38722)),f308(x38721,f195(f883(f882(x38721,x38721),a871)))),f308(x38721,x38722)) % 172.78/172.47 [3887]E(f332(f332(f38(a1),f332(f106(a1),f332(f332(f79(a1),x38871),x38871))),f332(f106(a1),f332(f332(f79(a1),x38872),x38872))),f332(f332(f38(a1),f332(f106(a1),x38871)),f332(f106(a1),x38872))) % 172.78/172.47 [3951]E(f332(f332(f257(a1),x39511),f332(f106(a876),f332(f332(f79(a1),x39512),x39512))),f332(f332(f85(a1,a1),f332(f332(f257(a1),x39511),f332(f106(a876),x39512))),f332(f332(f18(a1,a1,a1),f80(a1)),f5(a1)))) % 172.78/172.47 [3957]E(f332(f252(f883(x39571,a871)),f332(f332(f7(f883(x39571,a871),f883(x39571,a871),a871),f246(f883(x39571,a871))),x39572)),f332(f309(x39571),x39572)) % 172.78/172.47 [3972]E(f332(f332(f154(a1,a876),a107),f332(f332(f134(a1),f332(f332(f154(a876,a1),f103(a1)),x39721)),f332(f332(f154(a876,a1),f103(a1)),x39722))),f332(f332(f134(a876),x39721),x39722)) % 172.78/172.47 [4007]E(f332(f311(a1,a1,f332(f332(f7(a1,a1,a1),f79(a1)),x40071)),f332(f302(a1,f2(a1)),f332(f332(f22(a1),x40072),x40071))),f332(f302(a1,x40071),x40072)) % 172.78/172.47 [4009]P42(x40091,f332(f332(f22(f883(f882(x40091,x40091),a871)),x40092),f308(x40091,f195(f883(f882(x40091,x40091),a871))))) % 172.78/172.47 [4029]E(f332(f196(f877(x40291)),f332(f142(f877(x40291),f877(x40291),f134(x40291),f116(x40291)),x40292)),f332(f166(a876),f332(f332(f154(f877(x40291),a876),f196(f877(x40291))),x40292))) % 172.78/172.47 [4034]P40(x40341,f255(f883(x40341,a871)),f332(f332(f113(f883(f882(x40341,x40341),a871)),x40342),f308(x40341,f195(f883(f882(x40341,x40341),a871))))) % 172.78/172.47 [4077]E(f192(a876,f2(a876),f332(f332(f8(a876,a876,a876),a115),f332(f332(f7(a876,a876,a876),f244(a876)),x40771)),x40772),f332(f332(f244(a876),x40772),f332(a115,x40771))) % 172.78/172.47 [4080]E(f192(a876,f332(a115,x40801),f332(f332(f8(a876,a876,a876),a115),f332(f332(f7(a876,a876,a876),f245(a876)),x40801)),x40802),f332(f332(f245(a876),x40802),f332(a115,x40801))) % 172.78/172.47 [4083]E(f332(f311(x40831,f877(x40831),f332(f332(f7(x40831,f877(x40831),f877(x40831)),f151(x40831)),f116(x40831))),x40832),f175(x40831,x40832,f332(f332(f310(f877(x40831)),f116(x40831)),f195(f883(f877(x40831),a871))))) % 172.78/172.47 [4084]E(f332(f332(f113(f883(f882(x40841,x40841),a871)),f332(f332(f289(x40841,x40841,x40841),x40842),f308(x40841,x40842))),f308(x40841,f195(f883(f882(x40841,x40841),a871)))),f308(x40841,x40842)) % 172.78/172.47 [4092]P102(f332(f332(f246(f883(f882(x40921,x40921),a871)),f264(x40921,x40922)),f332(f332(f269(x40921,x40921),x40922),f332(f16(f883(x40921,a871),x40921),x40922)))) % 172.78/172.47 [4095]E(f332(f311(a1,a876,a107),f332(f332(f113(f883(a1,a871)),f332(f311(a876,a1,f103(a1)),x40951)),f332(f311(a876,a1,f103(a1)),x40952))),f332(f332(f113(f883(a876,a871)),x40951),x40952)) % 172.78/172.47 [4096]E(f332(f311(a1,a876,a107),f332(f332(f104(f883(a1,a871)),f332(f311(a876,a1,f103(a1)),x40961)),f332(f311(a876,a1,f103(a1)),x40962))),f332(f332(f104(f883(a876,a871)),x40961),x40962)) % 172.78/172.47 [4100]E(f332(f252(x41001),f332(f332(f8(a871,a871,x41001),a327),f332(f332(f7(x41001,f883(x41001,a871),a871),f334(x41001)),x41002))),f332(f78(f883(x41001,a871)),x41002)) % 172.78/172.47 [4127]E(f332(f142(f877(x41271),f877(x41271),f134(x41271),f116(x41271)),f332(f332(f154(f877(x41271),f877(x41271)),f169(x41271)),f332(f169(f877(x41271)),x41272))),f332(f169(x41271),f332(f142(f877(x41271),f877(x41271),f134(x41271),f116(x41271)),x41272))) % 172.78/172.47 [4156]E(f332(f332(f41(a876,f883(f882(x41561,x41561),a871)),f255(f883(a876,a871))),f332(f332(f7(a876,f883(f882(x41561,x41561),a871),f883(f882(x41561,x41561),a871)),f190(f882(x41561,x41561),a871)),x41562)),f308(x41561,x41562)) % 172.78/172.47 [4176]E(f84(x41761,f332(f332(f8(f883(x41761,a871),a871,x41761),f332(a329,x41762)),f332(f332(f7(x41761,f883(x41761,a871),f883(x41761,a871)),f310(x41761)),f195(f883(x41761,a871))))),f313(x41761,x41762)) % 172.78/172.47 [4184]E(f332(f196(f877(x41841)),f152(x41841,f332(f142(f877(x41841),f877(x41841),f134(x41841),f116(x41841)),x41842))),f332(f37(x41841),f332(f332(f41(f877(x41841),f883(x41841,a871)),f332(f173(f877(x41841)),x41842)),f173(x41841)))) % 172.78/172.47 [4200]E(f332(f332(f113(f883(f882(x42001,x42001),a871)),x42002),f332(f332(f289(x42001,x42001,x42001),f332(f332(f289(x42001,x42001,x42001),x42002),f308(x42001,x42002))),x42002)),f332(f332(f289(x42001,x42001,x42001),x42002),f308(x42001,x42002))) % 172.78/172.47 [4224]P102(f332(f332(f246(f883(f882(x42241,x42241),a871)),f332(f332(f289(x42241,x42241,x42241),x42242),f308(x42241,x42242))),f332(f332(f269(x42241,x42241),f332(f285(x42241),x42242)),f332(f16(f883(x42241,a871),x42241),f332(f285(x42241),x42242))))) % 172.78/172.47 [4267]E(f332(f252(f877(x42671)),f332(f332(f7(f877(x42671),f883(x42671,a871),a871),f332(f332(f8(f883(x42671,a871),f883(f883(x42671,a871),a871),f877(x42671)),f246(f883(x42671,a871))),f173(x42671))),x42672)),f161(x42671,x42672)) % 172.78/172.47 [4279]E(f332(f156(f877(x42791),x42791,f116(x42791),f332(f332(f8(f877(x42791),f883(f877(x42791),f877(x42791)),x42791),f332(f7(f877(x42791),f877(x42791),f877(x42791)),f134(x42791))),f332(f332(f7(x42791,f877(x42791),f877(x42791)),f151(x42791)),f116(x42791)))),x42792),f332(f168(x42791),x42792)) % 172.78/172.47 [4321]P20(f883(x43211,x43212),f883(f882(x43211,x43212),a871),f332(f332(f8(f883(f882(x43211,x43212),a871),f883(f882(x43211,x43212),a871),f883(x43211,x43212)),f252(f882(x43211,x43212))),f332(f332(f8(f883(x43211,f883(x43212,a871)),f883(f882(x43211,x43212),a871),f883(x43211,x43212)),f271(x43211,x43212,a871)),f332(f8(x43212,f883(x43212,a871),x43211),f332(f7(x43212,x43212,a871),a329)))),f255(f883(f883(x43211,x43212),a871))) % 172.78/172.47 [4326]E(f44(a1,f332(f106(a1),f332(f332(f79(a1),x43261),x43261)),f332(f106(a1),f332(f332(f79(a1),x43262),x43262))),f332(f332(f80(a1),f332(f106(a1),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)))),f44(a1,f332(f106(a1),x43261),f332(f106(a1),x43262)))) % 172.78/172.47 [4369]E(f332(f332(f41(x43691,f883(f882(x43691,x43691),a871)),x43692),f332(f332(f7(x43691,f883(f882(x43691,x43691),a871),f883(f882(x43691,x43691),a871)),f332(f332(f8(f882(x43691,x43691),f883(f883(f882(x43691,x43691),a871),f883(f882(x43691,x43691),a871)),x43691),f310(f882(x43691,x43691))),f332(f332(f18(x43691,x43691,f882(x43691,x43691)),f267(x43691,x43691)),f5(x43691)))),f195(f883(f882(x43691,x43691),a871)))),f264(x43691,x43692)) % 172.78/172.47 [4377]E(f213(x43771,f332(f332(f267(a1,a1),f332(f78(a1),f332(f332(f72(f882(a1,a1),a1,x43771,f266(a1,a1)),f223(x43771)),x43772))),f332(f332(f72(f882(a1,a1),a1,x43771,f270(a1,a1)),f223(x43771)),x43772))),f231(x43771,x43772)) % 172.78/172.47 [4458]E(f332(f252(f883(x44581,a871)),f332(f332(f8(f883(f883(x44581,a871),a871),a871,f883(x44581,a871)),f86(f883(x44581,a871))),f332(f332(f7(f883(x44581,a871),f883(f883(x44581,a871),a871),f883(f883(x44581,a871),a871)),f332(f332(f8(f883(f883(x44581,a871),f883(a871,a871)),f883(f883(f883(x44581,a871),a871),f883(f883(x44581,a871),a871)),f883(x44581,a871)),f18(f883(x44581,a871),a871,a871)),f332(f332(f8(f883(f883(x44581,a871),a871),f883(f883(x44581,a871),f883(a871,a871)),f883(x44581,a871)),f332(f8(a871,f883(a871,a871),f883(x44581,a871)),a330)),f332(f332(f7(f883(x44581,a871),f883(f883(x44581,a871),f883(x44581,a871)),f883(f883(x44581,a871),a871)),f332(f332(f8(f883(f883(x44581,a871),a871),f883(f883(f883(x44581,a871),f883(x44581,a871)),f883(f883(x44581,a871),a871)),f883(x44581,a871)),f8(f883(x44581,a871),a871,f883(x44581,a871))),a329)),f78(f883(x44581,a871)))))),f332(f332(f8(f883(f883(x44581,a871),a871),a871,f883(x44581,a871)),f332(f334(f883(x44581,a871)),x44582)),f309(x44581))))),f332(f309(x44581),f332(f78(f883(x44581,a871)),x44582))) % 172.78/172.47 [4561]~E(f332(f332(f79(a1),x45611),x45611),f332(f332(f22(a1),f332(f332(f79(a1),x45612),x45612)),a100)) % 172.78/172.47 [4567]~P102(f332(f332(f247(a876),f332(f332(f79(a876),x45671),x45672)),x45672)) % 172.78/172.47 [4568]~P102(f332(f332(f247(a876),f332(f332(f79(a876),x45681),x45682)),x45681)) % 172.78/172.47 [3785]E(f332(f332(f22(a876),x37851),f332(f332(f80(a876),f332(f332(f38(a876),x37851),x37852)),x37852)),f44(a876,x37851,x37852)) % 172.78/172.47 [3786]E(f332(f332(f22(a1),x37861),f332(f332(f80(a1),f332(f332(f38(a1),x37861),x37862)),x37862)),f44(a1,x37861,x37862)) % 172.78/172.47 [3820]E(f332(f332(f154(a876,x38201),f332(f165(x38201),x38202)),f139(a876,f332(f302(a876,f2(a876)),f332(f196(f877(x38201)),x38202)))),x38202) % 172.78/172.47 [3883]E(f332(f286(x38831,x38831,f308(x38831,f195(f883(f882(x38831,x38831),a871)))),x38832),x38832) % 172.78/172.47 [4012]E(f308(x40121,f332(f332(f113(f883(f882(x40121,x40121),a871)),x40122),f308(x40121,f195(f883(f882(x40121,x40121),a871))))),f308(x40121,x40122)) % 172.78/172.47 [4013]E(f308(x40131,f332(f332(f22(f883(f882(x40131,x40131),a871)),x40132),f308(x40131,f195(f883(f882(x40131,x40131),a871))))),f308(x40131,x40132)) % 172.78/172.47 [4066]E(f332(f332(f22(a1),f332(f332(f22(a1),f332(f332(f79(a1),x40661),x40661)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),x40662),x40662)),a100)),f332(f332(f79(a1),f332(f332(f22(a1),x40661),x40662)),f332(f332(f22(a1),x40661),x40662))) % 172.78/172.47 [4105]E(f332(f332(f22(a1),f332(f332(f79(a1),f332(f332(f79(a1),x41051),x41052)),f332(f332(f79(a1),x41051),x41052))),a100),f332(f332(f79(a1),f332(f332(f79(a1),x41051),x41051)),f332(f332(f22(a1),f332(f332(f79(a1),x41052),x41052)),a100))) % 172.78/172.47 [4131]E(f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),x41311),x41311)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),x41312),x41312)),a100)),f332(f332(f79(a1),f332(f332(f79(a1),x41311),f332(f332(f22(a1),x41312),a100))),f332(f332(f79(a1),x41311),f332(f332(f22(a1),x41312),a100)))) % 172.78/172.47 [4141]E(f332(f332(f22(a1),f332(f332(f79(a1),f332(f332(f22(a1),x41411),x41412)),f332(f332(f22(a1),x41411),x41412))),a100),f332(f332(f22(a1),f332(f332(f22(a1),f332(f332(f79(a1),x41411),x41411)),a100)),f332(f332(f79(a1),x41412),x41412))) % 172.78/172.47 [4142]E(f332(f332(f22(a1),f332(f332(f79(a1),f332(f332(f79(a1),x41421),x41422)),f332(f332(f79(a1),x41421),x41422))),a100),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),x41421),x41421)),a100)),f332(f332(f79(a1),x41422),x41422))) % 172.78/172.47 [4197]E(f332(f103(a1),f332(f332(f38(a876),f332(f332(f80(a876),f332(a107,f332(f74(a1),x41971))),f332(a107,f332(f74(a1),x41972)))),f227(f332(a107,f332(f74(a1),x41971)),f332(a107,f332(f74(a1),x41972))))),f229(x41971,x41972)) % 172.78/172.47 [4244]E(f332(f332(f273(f882(a102,a102),a102,f882(a102,a102),f882(x42441,f882(a102,a102))),f277(f332(a3,f332(f196(f877(x42441)),x42442)))),f332(f332(f8(x42441,f883(f882(a102,a102),f882(x42441,f882(a102,a102))),a102),f267(x42441,f882(a102,a102))),f332(f332(f8(a876,x42441,a102),f332(f165(x42441),x42442)),a19))),f283(x42441,x42442)) % 172.78/172.47 [4327]E(f332(f142(a876,f877(x43271),f332(f7(f877(x43271),a876,a876),f332(f332(f8(a876,f883(a876,a876),f877(x43271)),f245(a876)),f196(f877(x43271)))),f2(a876)),f332(f169(f877(x43271)),f181(x43271,x43272))),f332(f196(f877(f877(x43271))),f332(f136(f877(x43271),f332(f332(f8(a871,a871,f877(x43271)),a327),f332(f332(f7(f877(x43271),f877(x43271),a871),a329),f116(x43271)))),x43272))) % 172.78/172.47 [4333]E(f332(f332(f41(a876,f883(x43331,a871)),f255(f883(a876,a871))),f332(f332(f7(a876,f883(a876,f883(x43331,a871)),f883(x43331,a871)),f332(f332(f8(f883(a876,a871),f883(f883(a876,f883(x43331,a871)),f883(x43331,a871)),a876),f41(a876,f883(x43331,a871))),f302(a876,f2(a876)))),x43332)),f332(f332(f41(a876,f883(x43331,a871)),f255(f883(a876,a871))),x43332)) % 172.78/172.47 [4353]P102(f332(f61(a876),f332(f252(a876),f332(f332(f18(a876,a871,a871),f332(f332(f8(a871,f883(a871,a871),a876),a330),x43531)),f332(f332(f7(a876,a876,a871),f247(a876)),x43532))))) % 172.78/172.47 [4469]E(f332(f252(f882(f877(x44691),f877(x44691))),f332(f271(f877(x44691),f877(x44691),a871),f332(f332(f18(f877(x44691),f883(f877(x44691),a871),f883(f877(x44691),a871)),f332(f332(f8(f883(f877(x44691),f883(a871,a871)),f883(f883(f877(x44691),a871),f883(f877(x44691),a871)),f877(x44691)),f18(f877(x44691),a871,a871)),f332(f332(f8(f883(f877(x44691),a871),f883(f877(x44691),f883(a871,a871)),f877(x44691)),f332(f8(a871,f883(a871,a871),f877(x44691)),a331)),f332(f332(f7(f877(x44691),f883(f877(x44691),a876),f883(f877(x44691),a871)),f332(f332(f8(f883(a876,a871),f883(f883(f877(x44691),a876),f883(f877(x44691),a871)),f877(x44691)),f8(a876,a871,f877(x44691))),f332(f332(f8(a876,f883(a876,a871),f877(x44691)),f247(a876)),f196(f877(x44691))))),f196(f877(x44691)))))),f332(f332(f18(f877(x44691),f883(f877(x44691),a871),f883(f877(x44691),a871)),f332(f332(f8(f883(f877(x44691),f883(a871,a871)),f883(f883(f877(x44691),a871),f883(f877(x44691),a871)),f877(x44691)),f18(f877(x44691),a871,a871)),f332(f332(f8(f883(f877(x44691),a871),f883(f877(x44691),f883(a871,a871)),f877(x44691)),f332(f8(a871,f883(a871,a871),f877(x44691)),a330)),f332(f332(f7(f877(x44691),f883(f877(x44691),a876),f883(f877(x44691),a871)),f332(f332(f8(f883(a876,a871),f883(f883(f877(x44691),a876),f883(f877(x44691),a871)),f877(x44691)),f8(a876,a871,f877(x44691))),f332(f332(f8(a876,f883(a876,a871),f877(x44691)),a329),f196(f877(x44691))))),f196(f877(x44691)))))),f332(f332(f7(f877(x44691),f883(f882(f877(x44691),f877(x44691)),a871),f883(f877(x44691),a871)),f332(f332(f8(f883(f877(x44691),f883(f883(f882(f877(x44691),f877(x44691)),a871),a871)),f883(f883(f882(f877(x44691),f877(x44691)),a871),f883(f877(x44691),a871)),f877(x44691)),f7(f877(x44691),f883(f882(f877(x44691),f877(x44691)),a871),a871)),f332(f332(f8(f883(f877(x44691),f882(f877(x44691),f877(x44691))),f883(f877(x44691),f883(f883(f882(f877(x44691),f877(x44691)),a871),a871)),f877(x44691)),f332(f8(f882(f877(x44691),f877(x44691)),f883(f883(f882(f877(x44691),f877(x44691)),a871),a871),f877(x44691)),f334(f882(f877(x44691),f877(x44691))))),f267(f877(x44691),f877(x44691))))),f145(x44691,x44692)))))),f146(x44691,x44692)) % 172.78/172.47 [4574]~P102(f332(f332(f90(a1),f332(f332(f79(a1),x45741),x45741)),f332(f332(f22(a1),f332(f332(f79(a1),x45742),x45742)),a100))) % 172.78/172.47 [4134]E(f332(f332(f79(a1),f332(f332(f79(a1),f332(f332(f80(a1),x41341),x41342)),f332(f332(f80(a1),x41341),x41342))),x41342),f332(f332(f80(a1),f332(f332(f22(a1),f332(f332(f79(a1),x41341),x41341)),a100)),x41342)) % 172.78/172.47 [4242]E(f332(a107,f332(a88,f332(f286(f882(a876,a876),f882(a876,a876),a111),f332(f332(f310(f882(a876,a876)),f332(f332(f267(a876,a876),x42421),x42422)),f195(f883(f882(a876,a876),a871)))))),f332(f332(f22(a876),x42421),x42422)) % 172.78/172.47 [4247]E(f332(f332(f289(x42471,x42471,x42471),f332(f332(f113(f883(f882(x42471,x42471),a871)),x42472),f308(x42471,f195(f883(f882(x42471,x42471),a871))))),f308(x42471,f332(f332(f113(f883(f882(x42471,x42471),a871)),x42472),f308(x42471,f195(f883(f882(x42471,x42471),a871)))))),f308(x42471,x42472)) % 172.78/172.47 [4285]E(f278(x42851,f332(f136(f882(a102,x42851),f332(f271(a102,x42851,a871),f332(f332(f8(a871,f883(x42851,a871),a102),f16(a871,x42851)),f332(f247(a102),f2(a102))))),x42852)),f278(x42851,x42852)) % 172.78/172.47 [4286]E(f276(x42861,f332(f136(f882(a102,x42861),f332(f271(a102,x42861,a871),f332(f332(f8(a871,f883(x42861,a871),a102),f16(a871,x42861)),f332(f247(a102),f2(a102))))),x42862)),f276(x42861,x42862)) % 172.78/172.47 [4288]E(f332(f78(a1),f332(a88,f332(f286(f882(a876,a876),f882(a876,a876),a111),f332(f332(f310(f882(a876,a876)),f332(f332(f267(a876,a876),x42881),x42882)),f195(f883(f882(a876,a876),a871)))))),f332(a88,f332(f286(f882(a876,a876),f882(a876,a876),a111),f332(f332(f310(f882(a876,a876)),f332(f332(f267(a876,a876),x42882),x42881)),f195(f883(f882(a876,a876),a871)))))) % 172.78/172.47 [4345]E(f332(f332(f288(f877(a876),x43451),f145(a876,a251)),f332(f332(f7(x43451,f877(f883(x43451,a876)),f877(a876)),f332(f332(f8(f883(f883(x43451,a876),a876),f883(f877(f883(x43451,a876)),f877(a876)),x43451),f154(f883(x43451,a876),a876)),f332(f7(f883(x43451,a876),x43451,a876),f5(f883(x43451,a876))))),x43452)),f153(x43451,x43452)) % 172.78/172.47 [4366]E(f332(f332(f85(a1,a876),f332(f106(a1),f332(f332(f79(a1),x43661),a100))),f332(f332(f18(a1,a876,a876),f332(f332(f7(a1,a876,f883(a876,a876)),f332(f332(f8(a871,f883(a876,f883(a876,a876)),a1),f99(a876)),a200)),f2(a876))),f332(f332(f8(a876,a876,a1),a115),f332(f332(f8(a876,a876,a1),f332(f244(a876),x43662)),a107)))),f332(f332(f244(a876),f332(a115,x43662)),f332(f106(a876),x43661))) % 172.78/172.47 [4367]E(f332(f332(f85(a1,a876),f332(f106(a1),f332(f332(f79(a1),x43671),a100))),f332(f332(f18(a1,a876,a876),f332(f332(f7(a1,a876,f883(a876,a876)),f332(f332(f8(a871,f883(a876,f883(a876,a876)),a1),f99(a876)),a200)),f332(a115,x43672))),f332(f332(f8(a876,a876,a1),a115),f332(f332(f8(a876,a876,a1),f332(f245(a876),x43672)),a107)))),f332(f332(f245(a876),f332(a115,x43672)),f332(f106(a876),x43671))) % 172.78/172.47 [4387]E(f332(f142(f877(x43871),f877(x43871),f134(x43871),f116(x43871)),f332(f332(f154(f877(x43871),f877(x43871)),f156(f877(x43871),x43871,f116(x43871),f332(f332(f8(f877(x43871),f883(f877(x43871),f877(x43871)),x43871),f16(f877(x43871),f877(x43871))),f332(f332(f7(x43871,f877(x43871),f877(x43871)),f151(x43871)),f116(x43871))))),x43872)),f332(f332(f154(f877(x43871),x43871),f141(x43871)),f332(f136(f877(x43871),f332(f332(f8(a871,a871,f877(x43871)),a327),f332(f332(f7(f877(x43871),f877(x43871),a871),a329),f116(x43871)))),x43872))) % 172.78/172.47 [4450]E(f332(f271(a1,a1,a871),f332(f332(f7(a1,f883(a1,a871),f883(a1,a871)),f332(f332(f8(f883(a1,f883(a871,a871)),f883(f883(a1,a871),f883(a1,a871)),a1),f18(a1,a871,a871)),f332(f332(f8(f883(a1,a871),f883(a1,f883(a871,a871)),a1),f332(f8(a871,f883(a871,a871),a1),a330)),f332(f332(f8(f883(a1,a1),f883(a1,a871),a1),f332(f8(a1,a871,a1),f332(a329,x44501))),f332(f332(f8(a1,f883(a1,a1),a1),f79(a1)),f332(f80(a1),x44502)))))),f332(f332(f18(a1,a871,a871),f332(f332(f8(a871,f883(a871,a871),a1),a330),f332(f332(f8(a871,a871,a1),f332(a335,f332(f332(f247(a1),f2(a1)),x44502))),f332(f332(f18(a1,a871,a871),f332(f332(f8(a871,f883(a871,a871),a1),a330),f332(f246(a1),f2(a1)))),f332(f332(f7(a1,a1,a871),f247(a1)),x44502))))),f332(f332(f8(a871,a871,a1),f332(a335,f332(a327,f332(f332(f247(a1),f2(a1)),x44502)))),f332(f332(f18(a1,a871,a871),f332(f332(f8(a871,f883(a871,a871),a1),a330),f332(f247(a1),x44502))),f332(f332(f7(a1,a1,a871),f246(a1)),f2(a1))))))),f48(x44501,x44502)) % 172.78/172.47 [4452]E(f332(f252(x44521),f332(f332(f8(f883(a876,a871),a871,x44521),f86(a876)),f332(f332(f7(x44521,f883(a876,a871),f883(a876,a871)),f332(f332(f8(f883(a876,f883(a871,a871)),f883(f883(a876,a871),f883(a876,a871)),x44521),f18(a876,a871,a871)),f332(f332(f8(f883(a876,a871),f883(a876,f883(a871,a871)),x44521),f332(f8(a871,f883(a871,a871),a876),a330)),f332(f332(f7(x44521,f883(a876,x44521),f883(a876,a871)),f332(f332(f8(f883(x44521,a871),f883(f883(a876,x44521),f883(a876,a871)),x44521),f8(x44521,a871,a876)),a329)),f332(f165(x44521),x44522))))),f332(f332(f7(a876,a876,a871),f247(a876)),f332(f196(f877(x44521)),x44522))))),f332(f173(x44521),x44522)) % 172.78/172.47 [4257]E(f332(f332(f22(a1),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),x42571),a100)),x42572)),f332(f332(f22(a1),f332(f332(f79(a1),x42571),a100)),x42572))),a100),f332(f332(f22(a1),f332(f332(f79(a1),x42571),x42571)),f332(f332(f22(a1),f332(f332(f79(a1),x42572),x42572)),a100))) % 172.78/172.47 [4382]E(f332(f142(f877(f877(x43821)),f877(f877(x43821)),f134(f877(x43821)),f116(f877(x43821))),f332(f332(f154(f877(x43821),f877(f877(x43821))),f156(f877(f877(x43821)),x43821,f116(f877(x43821)),f332(f16(f883(f877(x43821),f877(f877(x43821))),x43821),f332(f332(f7(f877(x43821),f877(f877(x43821)),f877(f877(x43821))),f151(f877(x43821))),f116(f877(x43821)))))),x43822)),f332(f332(f154(f877(x43821),f877(x43821)),f172(x43821)),f332(f136(f877(x43821),f332(f332(f8(a871,a871,f877(x43821)),a327),f332(f332(f7(f877(x43821),f877(x43821),a871),a329),f116(x43821)))),x43822))) % 172.78/172.47 [4393]E(f332(f332(f85(a1,a876),f332(f106(a1),f332(f332(f79(a1),x43931),a100))),f332(f332(f18(a1,a876,a876),f332(f332(f7(a1,a876,f883(a876,a876)),f332(f332(f8(a871,f883(a876,f883(a876,a876)),a1),f99(a876)),a200)),f2(a876))),f332(f332(f8(a876,a876,a1),a115),f332(f332(f7(a1,a876,a876),f332(f332(f8(a876,f883(a876,a876),a1),f244(a876)),a107)),x43932)))),f332(f332(f244(a876),f332(f106(a876),x43931)),f332(a115,x43932))) % 172.78/172.47 [4394]E(f332(f332(f85(a1,a876),f332(f106(a1),f332(f332(f79(a1),x43941),a100))),f332(f332(f18(a1,a876,a876),f332(f332(f7(a1,a876,f883(a876,a876)),f332(f332(f8(a871,f883(a876,f883(a876,a876)),a1),f99(a876)),a200)),f332(a115,x43942))),f332(f332(f8(a876,a876,a1),a115),f332(f332(f7(a1,a876,a876),f332(f332(f8(a876,f883(a876,a876),a1),f245(a876)),a107)),x43942)))),f332(f332(f245(a876),f332(f106(a876),x43941)),f332(a115,x43942))) % 172.78/172.47 [4381]E(f332(f271(x43811,x43811,a871),f332(f332(f18(x43811,a871,f883(x43811,a871)),f332(f332(f8(f883(x43811,f883(a871,a871)),f883(a871,f883(x43811,a871)),x43811),f7(x43811,a871,a871)),f332(f332(f8(f883(x43811,a871),f883(x43811,f883(a871,a871)),x43811),f332(f8(a871,f883(a871,a871),x43811),a330)),a329))),x43812)),f264(x43811,x43812)) % 172.78/172.47 [4428]E(f332(f332(f38(a876),x44281),f332(f332(f79(a876),f332(f106(a876),f332(f332(f22(a1),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100))),a100))),x44282)),f332(f332(f38(a876),x44281),f332(a115,f332(a115,f332(a115,x44282))))) % 172.78/172.47 [4429]E(f44(a876,x44291,f332(f332(f79(a876),f332(f106(a876),f332(f332(f22(a1),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100))),a100))),x44292)),f44(a876,x44291,f332(a115,f332(a115,f332(a115,x44292))))) % 172.78/172.47 [4430]E(f44(a876,f332(f332(f79(a876),f332(f106(a876),f332(f332(f22(a1),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100))),a100))),x44301),x44302),f44(a876,f332(a115,f332(a115,f332(a115,x44301))),x44302)) % 172.78/172.47 [4443]E(f124(f332(x44431,f332(f332(f80(a102),f332(f106(a102),f332(f332(f22(a1),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100))),a100))),x44432))),f332(f211(x44431),x44432)) % 172.78/172.47 [4444]E(f332(f332(f38(a876),f332(f332(f79(a876),f332(f106(a876),f332(f332(f22(a1),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100))),a100))),x44441)),x44442),f332(f332(f38(a876),f332(a115,f332(a115,f332(a115,x44441)))),x44442)) % 172.78/172.47 [4493]~E(f32(x44931,x44932),f332(a25,x44933)) % 172.78/172.47 [4494]~E(f31(x44941,x44942),f332(a25,x44943)) % 172.78/172.47 [4495]~E(f332(a25,x44951),f32(x44952,x44953)) % 172.78/172.47 [4496]~E(f332(a25,x44961),f31(x44962,x44963)) % 172.78/172.47 [4509]~E(f29(x45091,x45092,x45093),a24) % 172.78/172.47 [4510]~E(f28(x45101,x45102,x45103),a24) % 172.78/172.47 [3197]E(f332(f199(x31971,x31972),x31973),f122(x31971,x31972)) % 172.78/172.47 [3219]E(f332(f210(x32191,x32192),x32193),f332(f126(x32191),x32192)) % 172.78/172.47 [3300]E(f332(f332(f154(x33001,x33002),x33003),f116(x33001)),f116(x33002)) % 172.78/172.47 [3301]E(f332(f332(f209(x33011,x33012),x33013),f208(x33011)),f208(x33012)) % 172.78/172.47 [3341]E(f332(f191(x33411,x33412,x33413),f2(a876)),x33412) % 172.78/172.47 [3343]E(f332(f332(f183(x33431,x33432),x33433),f116(x33432)),f116(f882(x33431,x33432))) % 172.78/172.47 [3358]E(f332(f196(f877(x33581)),f170(x33581,x33582,x33583)),x33582) % 172.78/172.47 [3378]E(f84(x33781,f62(x33781,x33782,x33783)),f332(f63(x33781,x33782),x33783)) % 172.78/172.47 [3382]E(f256(x33821,x33822,f256(x33822,x33821,x33823)),x33823) % 172.78/172.47 [3402]E(f332(f169(x34021),f170(x34021,x34022,x34023)),f170(x34021,x34022,x34023)) % 172.78/172.47 [3431]E(f140(x34311,x34312,f152(x34311,x34313)),f152(x34311,f140(x34311,x34312,x34313))) % 172.78/172.47 [3450]E(f332(f266(f877(x34501),f877(x34501)),f167(x34501,x34502,x34503)),f332(f136(x34501,x34502),x34503)) % 172.78/172.47 [3497]E(f332(f332(f151(x34971),x34972),f170(x34971,x34973,x34972)),f170(x34971,f332(a115,x34973),x34972)) % 172.78/172.47 [3529]E(f192(x35291,x35292,x35293,f2(a876)),x35292) % 172.78/172.47 [3530]E(f17(x35301,x35302,x35303,f2(a102)),x35302) % 172.78/172.47 [3537]E(f163(x35371,x35372,x35373,f116(x35371)),f116(x35372)) % 172.78/172.47 [3538]E(f164(x35381,x35382,x35383,f116(x35381)),f116(x35382)) % 172.78/172.47 [3545]E(f332(f332(f165(x35451),f332(f332(f151(x35451),x35452),x35453)),f2(a876)),x35452) % 172.78/172.47 [3575]E(f59(x35751,x35752,f116(x35751),x35753),f116(f882(x35751,x35752))) % 172.78/172.47 [3596]P20(x35961,x35962,x35963,f195(f883(x35961,a871))) % 172.78/172.47 [3758]E(f332(f72(x37581,x37582,x37581,x37583),f33(x37581)),x37583) % 172.78/172.47 [3942]P102(f332(f332(f334(f882(x39421,x39421)),f332(f332(f267(x39421,x39421),x39422),x39422)),f308(x39421,x39423))) % 172.78/172.47 [4575]~P102(f332(f332(f334(f882(f877(x45751),f877(x45751))),f332(f332(f267(f877(x45751),f877(x45751)),x45752),f116(x45751))),f145(x45751,x45753))) % 172.78/172.47 [4576]~P102(f332(f332(f334(f882(f877(x45761),f877(x45761))),f332(f332(f267(f877(x45761),f877(x45761)),x45762),f116(x45761))),f147(x45761,x45763))) % 172.78/172.47 [4577]~P102(f332(f332(f334(f882(f877(x45771),f877(x45771))),f332(f332(f267(f877(x45771),f877(x45771)),x45772),f116(x45771))),f157(x45771,x45773))) % 172.78/172.47 [4578]~P102(f332(f332(f334(f882(f877(x45781),f877(x45781))),f332(f332(f267(f877(x45781),f877(x45781)),f116(x45781)),x45782)),f145(x45781,x45783))) % 172.78/172.47 [4579]~P102(f332(f332(f334(f882(f877(x45791),f877(x45791))),f332(f332(f267(f877(x45791),f877(x45791)),f116(x45791)),x45792)),f157(x45791,x45793))) % 172.78/172.47 [3273]E(f332(f332(f212(x32731),x32732),x32733),f213(x32731,f226(x32732,x32733))) % 172.78/172.47 [3330]E(f332(f287(x33301,x33302),f332(f287(x33302,x33301),x33303)),x33303) % 172.78/172.47 [3353]E(f332(f332(f183(x33531,x33532),f116(x33531)),x33533),f116(f882(x33531,x33532))) % 172.78/172.47 [3356]E(f177(x33561,x33562,f332(f253(a876),x33563)),f332(f332(f176(x33561),x33563),x33562)) % 172.78/172.47 [3375]E(f152(x33751,f332(f136(x33751,x33752),x33753)),f332(f136(x33751,x33752),f152(x33751,x33753))) % 172.78/172.47 [3376]E(f332(f263(x33761,x33762),f332(f287(x33762,x33761),x33763)),f332(f265(x33762,x33761),x33763)) % 172.78/172.47 [3377]E(f332(f265(x33771,x33772),f332(f287(x33772,x33771),x33773)),f332(f263(x33772,x33771),x33773)) % 172.78/172.47 [3394]E(f332(f136(x33941,x33942),f332(f169(x33941),x33943)),f332(f169(x33941),f332(f136(x33941,x33942),x33943))) % 172.78/172.47 [3408]E(f332(f332(f138(x34081),x34082),f332(f172(x34081),x34083)),f332(f332(f138(x34081),f332(a115,x34082)),x34083)) % 172.78/172.47 [3426]E(f30(f28(x34261,x34262,x34263)),f332(f332(f79(a876),f30(x34263)),f332(a115,f2(a876)))) % 172.78/172.47 [3427]E(f332(f311(x34271,x34272,x34273),f195(f883(x34271,a871))),f195(f883(x34272,a871))) % 172.78/172.47 [3428]E(f332(f286(x34281,x34282,x34283),f195(f883(x34281,a871))),f195(f883(x34282,a871))) % 172.78/172.47 [3429]E(f332(f312(x34291,x34292,x34293),f195(f883(x34292,a871))),f195(f883(x34291,a871))) % 172.78/172.47 [3430]E(f332(f312(x34301,x34302,x34303),f255(f883(x34302,a871))),f255(f883(x34301,a871))) % 172.78/172.47 [3459]E(f332(f332(f310(x34591),x34592),f332(f173(x34591),x34593)),f332(f173(x34591),f140(x34591,x34592,x34593))) % 172.78/172.47 [3471]E(f240(x34711,x34712,f332(f239(x34711),x34713)),f332(f332(f79(a876),f332(x34712,x34713)),f332(a115,f2(a876)))) % 172.78/172.47 [3549]E(f332(f196(a873),f28(x35491,x35492,x35493)),f332(f332(f79(a876),f332(f196(a873),x35493)),f332(a115,f2(a876)))) % 172.78/172.47 [3550]E(f332(f311(f882(x35501,x35502),x35502,f270(x35501,x35502)),x35503),f332(f263(x35501,x35502),x35503)) % 172.78/172.47 [3551]E(f332(f311(f882(x35511,x35512),x35511,f266(x35511,x35512)),x35513),f332(f265(x35511,x35512),x35513)) % 172.78/172.47 [3567]E(f332(f173(x35671),f170(x35671,f332(a115,x35672),x35673)),f332(f332(f310(x35671),x35673),f195(f883(x35671,a871)))) % 172.78/172.47 [3624]E(f332(f332(f267(x36241,x36242),f332(f266(x36241,x36242),x36243)),f332(f270(x36241,x36242),x36243)),x36243) % 172.78/172.47 [3631]E(f332(f196(f878(x36311)),f127(x36311,x36312,x36313)),f332(f332(f79(a876),f332(f196(f878(x36311)),x36313)),f332(a115,f2(a876)))) % 172.78/172.47 [3634]E(f332(f332(f271(x36341,x36342,x36341),f16(x36341,x36342)),x36343),f332(f266(x36341,x36342),x36343)) % 172.78/172.47 [3654]E(f186(x36541,x36542,x36543,f332(f16(f880(x36542),x36541),f208(x36542))),x36543) % 172.78/172.47 [3655]E(f186(x36551,x36552,f332(f16(f880(x36552),x36551),f208(x36552)),x36553),x36553) % 172.78/172.47 [3712]E(f30(f29(x37121,x37122,x37123)),f332(f332(f79(a876),f332(f332(f79(a876),f30(x37122)),f30(x37123))),f332(a115,f2(a876)))) % 172.78/172.47 [3763]E(f332(f72(x37631,x37631,x37632,f33(x37631)),x37633),x37633) % 172.78/172.47 [3771]E(f332(f332(f134(x37711),f170(x37711,x37712,x37713)),f332(f332(f151(x37711),x37713),f116(x37711))),f332(f332(f151(x37711),x37713),f170(x37711,x37712,x37713))) % 172.78/172.47 [3875]E(f332(f196(a873),f29(x38751,x38752,x38753)),f332(f332(f79(a876),f332(f332(f79(a876),f332(f196(a873),x38752)),f332(f196(a873),x38753))),f332(a115,f2(a876)))) % 172.78/172.47 [3952]P102(f332(f332(f246(f883(x39521,a871)),f332(f173(x39521),f332(f136(x39521,x39522),x39523))),f332(f173(x39521),x39523))) % 172.78/172.47 [3997]P102(f332(f332(f246(f883(x39971,a871)),f332(f173(x39971),f332(f332(f176(x39971),x39972),x39973))),f332(f173(x39971),x39973))) % 172.78/172.47 [3998]P102(f332(f332(f246(f883(x39981,a871)),f332(f173(x39981),f332(f332(f138(x39981),x39982),x39983))),f332(f173(x39981),x39983))) % 172.78/172.47 [4003]P102(f332(f332(f246(f883(x40031,a871)),f332(f173(x40031),f177(x40031,x40032,x40033))),f332(f173(x40031),x40032))) % 172.78/172.47 [4004]P102(f332(f332(f246(f883(x40041,a871)),f332(f173(x40041),f171(x40041,x40042,x40043))),f332(f173(x40041),x40043))) % 172.78/172.47 [4027]P20(f882(x40271,x40272),f882(x40272,x40271),f332(f271(x40271,x40272,f882(x40272,x40271)),f332(f7(x40272,x40271,f882(x40272,x40271)),f267(x40272,x40271))),x40273) % 172.78/172.47 [4039]E(f332(f332(f332(f190(f877(x40391),f877(x40391)),f44(a876,x40392,f332(f196(f877(x40391)),x40393))),f168(x40391)),x40393),f332(f332(f332(f190(f877(x40391),f877(x40391)),x40392),f168(x40391)),x40393)) % 172.78/172.47 [4081]P102(f332(f332(f334(f882(f877(x40811),f877(x40811))),f332(f332(f267(f877(x40811),f877(x40811)),x40812),x40812)),f158(x40811,f308(x40811,x40813)))) % 172.78/172.47 [4227]E(f84(f882(x42271,x42272),f332(f332(f18(f882(x42271,x42272),x42272,a871),f332(f332(f8(x42271,f883(x42272,a871),f882(x42271,x42272)),x42273),f266(x42271,x42272))),f270(x42271,x42272))),f84(f882(x42271,x42272),f332(f271(x42271,x42272,a871),x42273))) % 172.78/172.47 [4228]E(f89(f882(x42281,x42282),f332(f332(f18(f882(x42281,x42282),x42282,a871),f332(f332(f8(x42281,f883(x42282,a871),f882(x42281,x42282)),x42283),f266(x42281,x42282))),f270(x42281,x42282))),f89(f882(x42281,x42282),f332(f271(x42281,x42282,a871),x42283))) % 172.78/172.47 [4264]E(f332(f332(f288(f882(a876,x42641),x42641),f325(a876,x42641,a251,x42642)),f332(f332(f18(x42641,x42641,f882(a876,x42641)),f332(f332(f8(a876,f883(x42641,f882(a876,x42641)),x42641),f267(a876,x42641)),x42643)),f5(x42641))),f326(x42641,x42643,x42642)) % 172.78/172.47 [4329]E(f332(f272(x43291,x43291,x43292,x43292,f5(x43291),f5(x43292)),x43293),x43293) % 172.78/172.47 [4404]E(f332(f142(f877(f877(x44041)),f877(f877(x44041)),f134(f877(x44041)),f116(f877(x44041))),f332(f332(f154(f877(x44041),f877(f877(x44041))),f332(f332(f7(f877(x44041),f877(x44041),f877(f877(x44041))),f332(f332(f8(f883(x44041,f877(x44041)),f883(f877(x44041),f877(f877(x44041))),f877(x44041)),f154(x44041,f877(x44041))),f332(f7(x44041,f877(x44041),f877(x44041)),f151(x44041)))),x44042)),f54(x44041,x44043,x44042))),f54(x44041,f332(a115,x44043),x44042)) % 172.78/172.47 [4465]E(f332(f241(a876,f882(x44651,f878(x44651)),f2(a876),f332(f271(x44651,f878(x44651),a876),f332(f332(f7(x44651,a876,f883(f878(x44651),a876)),f332(f332(f8(f883(f878(x44651),f883(a876,a876)),f883(a876,f883(f878(x44651),a876)),x44651),f7(f878(x44651),a876,a876)),f332(f332(f8(f883(f878(x44651),a876),f883(f878(x44651),f883(a876,a876)),x44651),f332(f8(a876,f883(a876,a876),f878(x44651)),f79(a876))),f332(f332(f7(x44651,f883(f878(x44651),a876),f883(f878(x44651),a876)),f332(f332(f8(f883(a876,a876),f883(f883(f878(x44651),a876),f883(f878(x44651),a876)),x44651),f8(a876,a876,f878(x44651))),f332(f332(f8(a876,f883(a876,a876),x44651),f79(a876)),x44652))),f129(x44651,x44652))))),f77(a876)))),f332(f135(x44651),x44653)),f332(f129(x44651,x44652),x44653)) % 172.78/172.47 [4468]E(f332(f332(f85(a1,x44681),f229(f332(f332(f72(f882(a1,a1),a1,x44681,f270(a1,a1)),f223(x44681)),x44682),f332(f332(f72(f882(a1,a1),a1,x44681,f270(a1,a1)),f223(x44681)),x44683))),f332(f332(f18(a1,a1,x44681),f332(f332(f8(a1,f883(a1,x44681),a1),f212(x44681)),f332(f332(f18(a1,a1,a1),f332(f332(f8(a1,f883(a1,a1),a1),f79(a1)),f332(f332(f8(a1,a1,a1),f332(f80(a1),f332(f332(f72(f882(a1,a1),a1,x44681,f266(a1,a1)),f223(x44681)),x44682))),f332(f332(f7(a1,a1,a1),f38(a1)),f332(f332(f72(f882(a1,a1),a1,x44681,f270(a1,a1)),f223(x44681)),x44682))))),f332(f332(f8(a1,a1,a1),f332(f80(a1),f332(f332(f72(f882(a1,a1),a1,x44681,f266(a1,a1)),f223(x44681)),x44683))),f332(f332(f7(a1,a1,a1),f38(a1)),f332(f332(f72(f882(a1,a1),a1,x44681,f270(a1,a1)),f223(x44681)),x44683)))))),f5(a1))),f234(x44681,x44682,x44683)) % 172.78/172.47 [4505]~E(f332(f332(f151(x45051),x45052),x45053),x45053) % 172.78/172.47 [4512]~E(f332(f332(f151(x45121),x45122),x45123),f116(x45121)) % 172.78/172.47 [4528]~E(f332(f332(f310(x45281),x45282),x45283),f195(f883(x45281,a871))) % 172.78/172.47 [4551]~E(f332(f311(x45511,f883(x45511,a871),x45512),x45513),f332(f309(x45511),x45513)) % 172.78/172.47 [3335]E(f332(f332(f159(x33351,f116(x33351)),x33352),x33353),f116(x33351)) % 172.78/172.47 [3336]E(f332(f141(x33361),f332(f332(f151(x33361),x33362),x33363)),x33362) % 172.78/172.47 [3337]E(f332(f172(x33371),f332(f332(f151(x33371),x33372),x33373)),x33373) % 172.78/172.47 [3381]E(f332(f332(f138(x33811),f77(a876)),f332(f332(f151(x33811),x33812),x33813)),x33813) % 172.78/172.47 [3415]E(f117(x34151,f332(f332(f138(x34151),x34152),x34153)),f332(f332(f138(x34151),x34152),f117(x34151,x34153))) % 172.78/172.47 [3417]E(f332(f332(f159(x34171,x34172),x34173),f332(f332(f165(x34171),x34172),x34173)),x34172) % 172.78/172.47 [3441]E(f332(f332(f310(x34411),x34412),f332(f332(f310(x34411),x34412),x34413)),f332(f332(f310(x34411),x34412),x34413)) % 172.78/172.47 [3452]E(f332(f332(f179(x34521,x34522),f116(f882(x34521,x34522))),x34523),f208(x34522)) % 172.78/172.47 [3455]E(f332(f332(f310(x34551),x34552),f332(f173(x34551),x34553)),f332(f173(x34551),f332(f332(f151(x34551),x34552),x34553))) % 172.78/172.47 [3457]E(f332(f332(f138(x34571),x34572),f332(f172(x34571),x34573)),f332(f172(x34571),f332(f332(f138(x34571),x34572),x34573))) % 172.78/172.47 [3468]E(f332(f332(f176(x34681),f77(a876)),f332(f332(f151(x34681),x34682),x34683)),f332(f332(f151(x34681),x34682),f116(x34681))) % 172.78/172.47 [3514]E(f332(f63(x35141,x35142),f332(f332(f310(x35141),x35143),f195(f883(x35141,a871)))),x35143) % 172.78/172.47 [3557]E(f332(f332(f79(a876),x35571),f332(f332(f79(a876),x35572),x35573)),f332(f332(f79(a876),x35572),f332(f332(f79(a876),x35571),x35573))) % 172.78/172.47 [3558]E(f332(f332(f79(a1),x35581),f332(f332(f79(a1),x35582),x35583)),f332(f332(f79(a1),x35582),f332(f332(f79(a1),x35581),x35583))) % 172.78/172.47 [3563]E(f332(f332(f269(x35631,x35632),f195(f883(x35631,a871))),x35633),f195(f883(f882(x35631,x35632),a871))) % 172.78/172.47 [3588]E(f332(f332(f113(f883(x35881,a871)),x35882),x35883),f332(f332(f113(f883(x35881,a871)),x35883),x35882)) % 172.78/172.47 [3589]E(f332(f332(f104(f883(x35891,a871)),x35892),x35893),f332(f332(f104(f883(x35891,a871)),x35893),x35892)) % 172.78/172.47 [3591]E(f332(f332(f134(x35911),x35912),f332(f332(f151(x35911),x35913),f116(x35911))),f332(f168(x35911),f332(f332(f151(x35911),x35913),x35912))) % 172.78/172.47 [3592]E(f332(f332(f134(x35921),f332(f169(x35921),x35922)),f332(f169(x35921),x35923)),f332(f169(x35921),f332(f332(f134(x35921),x35923),x35922))) % 172.78/172.47 [3602]E(f332(f172(x36021),f332(f332(f176(x36021),f332(a115,x36022)),x36023)),f332(f332(f176(x36021),x36022),f332(f172(x36021),x36023))) % 172.78/172.47 [3609]P102(f332(f332(f334(x36091),x36092),f332(f332(f310(x36091),x36092),x36093))) % 172.78/172.47 [3613]E(f332(f332(f42(x36131,f883(x36132,a871)),f195(f883(x36131,a871))),x36133),f255(f883(x36132,a871))) % 172.78/172.47 [3616]E(f332(f286(x36161,x36161,f264(x36161,x36162)),x36163),f332(f332(f104(f883(x36161,a871)),x36162),x36163)) % 172.78/172.47 [3630]E(f332(f196(f877(x36301)),f332(f332(f151(x36301),x36302),x36303)),f332(f332(f79(a876),f332(f196(f877(x36301)),x36303)),f332(a115,f2(a876)))) % 172.78/172.47 [3636]E(f117(x36361,f332(f332(f134(x36361),x36362),f332(f332(f151(x36361),x36363),f116(x36361)))),x36362) % 172.78/172.47 [3637]E(f144(x36371,f332(f332(f134(x36371),x36372),f332(f332(f151(x36371),x36373),f116(x36371)))),x36373) % 172.78/172.47 [3643]E(f332(f332(f134(x36431),f332(f332(f176(x36431),x36432),x36433)),f332(f332(f138(x36431),x36432),x36433)),x36433) % 172.78/172.47 [3652]E(f332(f332(f22(a876),f332(f332(f79(a876),x36521),x36522)),f332(f332(f79(a876),x36523),x36522)),f332(f332(f22(a876),x36521),x36523)) % 172.78/172.47 [3653]E(f332(f332(f22(a876),f332(f332(f79(a876),x36531),x36532)),f332(f332(f79(a876),x36531),x36533)),f332(f332(f22(a876),x36532),x36533)) % 172.78/172.47 [3661]E(f332(f332(f134(x36611),f332(f169(x36611),x36612)),f332(f332(f151(x36611),x36613),f116(x36611))),f332(f169(x36611),f332(f332(f151(x36611),x36613),x36612))) % 172.78/172.47 [3663]E(f332(f332(f79(a876),f332(f196(f877(x36631)),x36632)),f332(f196(f877(x36631)),x36633)),f332(f196(f877(x36631)),f332(f332(f134(x36631),x36632),x36633))) % 172.78/172.47 [3666]E(f332(f332(f79(a876),f332(f196(f877(x36661)),x36662)),f332(f196(f877(x36661)),x36663)),f332(f196(f877(x36661)),f174(x36661,x36662,x36663))) % 172.78/172.47 [3674]E(f332(f332(f113(f883(x36741,a871)),f332(f173(x36741),x36742)),f332(f173(x36741),x36743)),f332(f173(x36741),f332(f332(f134(x36741),x36742),x36743))) % 172.78/172.47 [3675]E(f44(a876,f332(f332(f80(a876),x36751),x36752),f332(f332(f80(a876),x36751),x36753)),f332(f332(f80(a876),x36751),f44(a876,x36752,x36753))) % 172.78/172.47 [3688]E(f332(f332(f176(x36881),f332(f332(f22(a876),x36882),f77(a876))),f332(f172(x36881),x36883)),f332(f172(x36881),f332(f332(f176(x36881),x36882),x36883))) % 172.78/172.47 [3693]E(f332(f332(f104(f883(x36931,a871)),x36932),f332(f78(f883(x36931,a871)),x36933)),f332(f332(f22(f883(x36931,a871)),x36932),x36933)) % 172.78/172.47 [3694]E(f332(f332(f22(f883(x36941,a871)),x36942),f332(f78(f883(x36941,a871)),x36943)),f332(f332(f104(f883(x36941,a871)),x36942),x36943)) % 172.78/172.47 [3716]E(f332(f332(f269(x37161,x37162),x37163),f332(f16(f883(x37162,a871),x37161),f195(f883(x37162,a871)))),f195(f883(f882(x37161,x37162),a871))) % 172.78/172.47 [3718]E(f332(f332(f22(a876),f332(f332(f80(a876),x37181),x37182)),f332(f332(f80(a876),x37181),x37183)),f332(f332(f80(a876),x37181),f332(f332(f22(a876),x37182),x37183))) % 172.78/172.47 [3719]E(f332(f332(f79(a876),f332(f332(f80(a876),x37191),x37192)),f332(f332(f80(a876),x37191),x37193)),f332(f332(f80(a876),x37191),f332(f332(f79(a876),x37192),x37193))) % 172.78/172.47 [3720]E(f332(f332(f22(a1),f332(f332(f80(a1),x37201),x37202)),f332(f332(f80(a1),x37201),x37203)),f332(f332(f80(a1),x37201),f332(f332(f22(a1),x37202),x37203))) % 172.78/172.47 [3721]E(f332(f332(f79(a1),f332(f332(f80(a1),x37211),x37212)),f332(f332(f80(a1),x37211),x37213)),f332(f332(f80(a1),x37211),f332(f332(f79(a1),x37212),x37213))) % 172.78/172.47 [3722]E(f332(f332(f80(a1),f332(f332(f257(a1),x37221),x37222)),f332(f332(f257(a1),x37221),x37223)),f332(f332(f257(a1),x37221),f332(f332(f79(a876),x37222),x37223))) % 172.78/172.47 [3737]E(f332(f332(f41(x37371,f883(x37372,a871)),x37373),f332(f16(f883(x37372,a871),x37371),f195(f883(x37372,a871)))),f195(f883(x37372,a871))) % 172.78/172.47 [3739]E(f44(a876,f332(f332(f80(a876),x37391),x37392),f332(f332(f80(a876),x37393),x37392)),f332(f332(f80(a876),f44(a876,x37391,x37393)),x37392)) % 172.78/172.47 [3743]E(f44(a1,f332(f332(f22(a1),x37431),f44(a1,x37432,x37433)),x37433),f44(a1,f332(f332(f22(a1),x37431),x37432),x37433)) % 172.78/172.47 [3744]E(f44(a1,f332(f332(f80(a1),x37441),f44(a1,x37442,x37443)),x37443),f44(a1,f332(f332(f80(a1),x37441),x37442),x37443)) % 172.78/172.47 [3745]P102(f332(f332(f246(f883(x37451,a871)),x37452),f332(f332(f310(x37451),x37453),x37452))) % 172.78/172.47 [3748]E(f332(f311(f882(x37481,x37482),x37481,f266(x37481,x37482)),f332(f173(f882(x37481,x37482)),x37483)),f185(x37481,x37482,f332(f179(x37481,x37482),x37483))) % 172.78/172.47 [3799]P102(f332(f61(x37991),f185(x37991,x37992,f332(f179(x37991,x37992),x37993)))) % 172.78/172.47 [3824]E(f332(f332(f42(f883(x38241,a871),f883(x38241,a871)),x38242),f332(f113(f883(x38241,a871)),x38243)),f332(f332(f113(f883(x38241,a871)),x38243),f40(f883(x38241,a871),x38242))) % 172.78/172.47 [3825]E(f332(f332(f41(f883(x38251,a871),f883(x38251,a871)),x38252),f332(f104(f883(x38251,a871)),x38253)),f332(f332(f104(f883(x38251,a871)),x38253),f39(f883(x38251,a871),x38252))) % 172.78/172.47 [3836]E(f332(f173(x38361),f332(f332(f332(f190(f877(x38361),f877(x38361)),x38362),f168(x38361)),x38363)),f332(f173(x38361),x38363)) % 172.78/172.47 [3840]E(f332(f332(f176(x38401),f332(f196(f877(x38401)),f178(x38401,x38402,x38403))),x38403),f178(x38401,x38402,x38403)) % 172.78/172.47 [3841]E(f185(x38411,x38412,f332(f332(f8(x38412,f880(x38412),x38411),f239(x38412)),x38413)),f255(f883(x38411,a871))) % 172.78/172.47 [3845]E(f332(f196(f877(x38451)),f332(f332(f332(f190(f877(x38451),f877(x38451)),x38452),f168(x38451)),x38453)),f332(f196(f877(x38451)),x38453)) % 172.78/172.47 [3848]E(f332(f332(f271(x38481,x38482,x38482),f332(f16(f883(x38482,x38482),x38481),f5(x38482))),x38483),f332(f270(x38481,x38482),x38483)) % 172.78/172.47 [3855]E(f44(a1,f332(f332(f22(a1),f44(a1,x38551,x38552)),x38553),x38552),f44(a1,f332(f332(f22(a1),x38551),x38553),x38552)) % 172.78/172.47 [3856]E(f44(a1,f332(f332(f257(a1),f44(a1,x38561,x38562)),x38563),x38562),f44(a1,f332(f332(f257(a1),x38561),x38563),x38562)) % 172.78/172.47 [3859]E(f332(f332(f41(f883(f882(x38591,x38592),a871),f883(x38592,a871)),x38593),f263(x38591,x38592)),f332(f263(x38591,x38592),f39(f883(f882(x38591,x38592),a871),x38593))) % 172.78/172.47 [3860]E(f332(f332(f41(f883(f882(x38601,x38602),a871),f883(x38601,a871)),x38603),f265(x38601,x38602)),f332(f265(x38601,x38602),f39(f883(f882(x38601,x38602),a871),x38603))) % 172.78/172.47 [3888]E(f332(f72(x38881,x38881,x38881,x38882),f332(f332(f190(x38881,x38881),x38883),x38882)),f332(f332(f190(x38881,x38881),f332(a115,x38883)),x38882)) % 172.78/172.47 [3898]E(f241(f880(x38981),x38982,f208(x38981),f332(f332(f8(x38981,f880(x38981),x38982),f239(x38981)),x38983)),f332(f209(x38982,x38981),x38983)) % 172.78/172.47 [3905]E(f332(f332(f138(x39051),f332(f332(f22(a876),f332(f196(f877(x39051)),x39052)),x39053)),f332(f169(x39051),x39052)),f332(f169(x39051),f332(f332(f176(x39051),x39053),x39052))) % 172.78/172.47 [3906]E(f332(f332(f176(x39061),f332(f332(f22(a876),f332(f196(f877(x39061)),x39062)),x39063)),f332(f169(x39061),x39062)),f332(f169(x39061),f332(f332(f138(x39061),x39063),x39062))) % 172.78/172.47 [3909]E(f332(f332(f79(a876),f332(f166(a876),f332(f332(f154(x39091,a876),x39092),x39093))),f332(f196(f877(x39091)),x39093)),f155(x39091,x39092,x39093)) % 172.78/172.47 [3928]E(f332(f168(x39281),f332(f332(f332(f190(f877(x39281),f877(x39281)),x39282),f168(x39281)),x39283)),f332(f332(f332(f190(f877(x39281),f877(x39281)),f332(a115,x39282)),f168(x39281)),x39283)) % 172.78/172.47 [3943]P102(f332(f332(f246(a876),f332(f196(f877(x39431)),f332(f136(x39431,x39432),x39433))),f332(f196(f877(x39431)),x39433))) % 172.78/172.47 [3960]E(f332(f332(f113(f883(f883(x39601,a871),a871)),f332(f309(x39601),x39602)),f332(f311(f883(x39601,a871),f883(x39601,a871),f332(f310(x39601),x39603)),f332(f309(x39601),x39602))),f332(f309(x39601),f332(f332(f310(x39601),x39603),x39602))) % 172.78/172.47 [3979]P19(x39791,x39792,f332(f332(f310(f875(x39791)),f332(f332(f332(f91(x39791),x39793),a24),x39793)),f195(f883(f875(x39791),a871)))) % 172.78/172.47 [3994]P102(f332(f332(f246(a876),f332(f196(f877(x39941)),f178(x39941,x39942,x39943))),f332(f196(f877(x39941)),x39943))) % 172.78/172.47 [4002]E(f332(f265(x40021,x40022),f332(f252(f882(x40021,x40022)),f332(f271(x40021,x40022,a871),x40023))),f332(f252(x40021),f332(f332(f8(f883(x40022,a871),a871,x40021),f86(x40022)),x40023))) % 172.78/172.47 [4014]E(f332(f311(a876,a876,f332(f332(f7(a876,a876,a876),f79(a876)),x40141)),f303(a876,x40142,x40143)),f303(a876,f332(f332(f79(a876),x40142),x40141),f332(f332(f79(a876),x40143),x40141))) % 172.78/172.47 [4017]P102(f332(f61(f880(x40171)),f332(f311(x40172,f880(x40171),f332(f179(x40172,x40171),x40173)),f255(f883(x40172,a871))))) % 172.78/172.47 [4030]E(f332(f311(a876,a876,f332(f332(f7(a876,a876,a876),f79(a876)),x40301)),f332(f302(a876,x40302),x40303)),f332(f302(a876,f332(f332(f79(a876),x40302),x40301)),f332(f332(f79(a876),x40303),x40301))) % 172.78/172.47 [4048]E(f332(f332(f183(x40481,x40482),f332(f332(f154(f882(x40481,x40482),x40481),f266(x40481,x40482)),x40483)),f332(f332(f154(f882(x40481,x40482),x40482),f270(x40481,x40482)),x40483)),x40483) % 172.78/172.47 [4053]E(f332(f332(f79(a876),f332(f332(f80(a876),x40531),f44(a876,f332(f332(f38(a876),x40532),x40531),x40533))),f44(a876,x40532,x40531)),f44(a876,x40532,f332(f332(f80(a876),x40531),x40533))) % 172.78/172.47 [4067]E(f332(f332(f134(x40671),x40672),f332(f142(f877(x40671),f877(x40671),f134(x40671),f116(x40671)),x40673)),f332(f142(f877(x40671),f877(x40671),f134(x40671),x40672),x40673)) % 172.78/172.47 [4085]P102(f332(f332(f334(f882(x40851,x40851)),f332(f332(f267(x40851,x40851),x40852),x40852)),f332(f332(f190(f882(x40851,x40851),a871),f2(a876)),x40853))) % 172.78/172.47 [4091]E(f332(f252(x40911),f332(f332(f8(f883(x40912,a871),a871,x40911),f86(x40912)),f332(f7(x40912,x40911,a871),x40913))),f332(f263(x40912,x40911),f332(f252(f882(x40912,x40911)),f332(f271(x40912,x40911,a871),x40913)))) % 172.78/172.47 [4109]E(f332(f332(f113(f883(x41091,a871)),f332(f332(f41(a876,f883(x41091,a871)),f303(a876,f77(a876),x41092)),x41093)),f332(x41093,f2(a876))),f332(f332(f41(a876,f883(x41091,a871)),f332(f301(a876),x41092)),x41093)) % 172.78/172.47 [4124]E(f332(f142(f877(x41241),f877(x41241),f134(x41241),f116(x41241)),f332(f332(f154(f877(x41241),f877(x41241)),f136(x41241,x41242)),x41243)),f332(f136(x41241,x41242),f332(f142(f877(x41241),f877(x41241),f134(x41241),f116(x41241)),x41243))) % 172.78/172.47 [4129]E(f332(f270(f877(x41291),f877(x41291)),f167(x41291,x41292,x41293)),f332(f136(x41291,f332(f72(a871,a871,x41291,a327),x41292)),x41293)) % 172.78/172.47 [4147]E(f332(f332(f42(x41471,f883(x41472,a871)),f255(f883(x41471,a871))),f332(f332(f8(f883(x41472,a871),f883(x41472,a871),x41471),f252(x41472)),f332(f7(x41472,x41471,a871),x41473))),f332(f252(x41472),f332(f332(f8(f883(x41471,a871),a871,x41472),f87(x41471)),x41473))) % 172.78/172.47 [4178]E(f332(f332(f79(a1),f332(f332(f79(a1),f332(f332(f80(a1),x41781),f332(f332(f38(a1),x41782),x41781))),f44(a1,x41782,x41781))),x41783),f332(f332(f79(a1),x41782),x41783)) % 172.78/172.47 [4216]E(f332(f332(f79(a1),f332(f332(f79(a1),f332(f332(f80(a1),f332(f332(f38(a1),x42161),x42162)),x42162)),f44(a1,x42161,x42162))),x42163),f332(f332(f79(a1),x42161),x42163)) % 172.78/172.47 [4245]E(f84(f882(x42451,x42452),f332(f271(x42451,x42452,a871),f332(f332(f8(f883(x42452,f882(x42451,x42452)),f883(x42452,a871),x42451),f332(f8(f882(x42451,x42452),a871,x42452),x42453)),f267(x42451,x42452)))),f84(f882(x42451,x42452),x42453)) % 172.78/172.47 [4246]E(f89(f882(x42461,x42462),f332(f271(x42461,x42462,a871),f332(f332(f8(f883(x42462,f882(x42461,x42462)),f883(x42462,a871),x42461),f332(f8(f882(x42461,x42462),a871,x42462),x42463)),f267(x42461,x42462)))),f89(f882(x42461,x42462),x42463)) % 172.78/172.47 [4274]P102(f332(f332(f246(f883(x42741,a871)),f39(f883(x42741,a871),f332(f332(f104(f883(f883(x42741,a871),a871)),x42742),x42743))),f332(f332(f104(f883(x42741,a871)),f39(f883(x42741,a871),x42742)),f39(f883(x42741,a871),x42743)))) % 172.78/172.47 [4275]E(f332(f169(x42751),f332(f332(f332(f190(f877(x42751),f877(x42751)),f332(f332(f22(a876),f332(f196(f877(x42751)),x42752)),f44(a876,x42753,f332(f196(f877(x42751)),x42752)))),f168(x42751)),x42752)),f332(f332(f332(f190(f877(x42751),f877(x42751)),x42753),f168(x42751)),f332(f169(x42751),x42752))) % 172.78/172.47 [4289]E(f332(f252(x42891),f332(f332(f8(a871,a871,x42891),a327),f332(f332(f7(x42891,f880(x42892),a871),f332(f332(f8(f880(x42892),f883(f880(x42892),a871),x42891),a329),x42893)),f208(x42892)))),f185(x42891,x42892,x42893)) % 172.78/172.47 [4314]P102(f332(f332(f246(a876),f332(f196(f877(x43141)),f332(f332(f138(x43141),f332(f196(f877(x43141)),f178(x43141,x43142,x43143))),x43143))),f332(f196(f877(x43141)),x43143))) % 172.78/172.47 [4355]E(f332(f252(x43551),f332(f332(f8(f883(x43552,a871),a871,x43551),f86(x43552)),f332(f332(f8(f880(x43551),f883(x43552,a871),x43551),f332(f7(x43552,f880(x43551),a871),f332(f332(f8(f880(x43551),f883(f880(x43551),a871),x43552),a329),x43553))),f239(x43551)))),f187(x43552,x43551,x43553)) % 172.78/172.47 [4565]~P102(f332(f62(x45651,x45652,f195(f883(x45651,a871))),x45653)) % 172.78/172.47 [4573]~P102(f332(f332(f334(f882(x45731,x45731)),f332(f332(f267(x45731,x45731),x45732),x45733)),f153(x45731,f116(f883(x45731,a876))))) % 172.78/172.47 [3603]E(f332(f196(f877(x36031)),f332(f332(f176(x36031),x36032),x36033)),f332(f332(f244(a876),f332(f196(f877(x36031)),x36033)),x36032)) % 172.78/172.47 [3604]E(f332(f196(f877(x36041)),f332(f332(f138(x36041),x36042),x36043)),f332(f332(f22(a876),f332(f196(f877(x36041)),x36043)),x36042)) % 172.78/172.47 [3629]E(f332(f196(f877(f877(x36291))),f54(x36291,x36292,x36293)),f332(f332(f257(a876),f332(f196(f877(x36291)),x36293)),x36292)) % 172.78/172.47 [3645]E(f332(f332(f38(a876),f332(f332(f38(a876),x36451),x36452)),x36453),f332(f332(f38(a876),x36451),f332(f332(f80(a876),x36452),x36453))) % 172.78/172.47 [3646]E(f332(f332(f22(a876),f332(f332(f22(a876),x36461),x36462)),x36463),f332(f332(f22(a876),x36461),f332(f332(f79(a876),x36462),x36463))) % 172.78/172.47 [3647]E(f332(f332(f80(a876),f332(f332(f80(a876),x36471),x36472)),x36473),f332(f332(f80(a876),x36471),f332(f332(f80(a876),x36472),x36473))) % 172.78/172.47 [3648]E(f332(f332(f80(a1),f332(f332(f80(a1),x36481),x36482)),x36483),f332(f332(f80(a1),x36481),f332(f332(f80(a1),x36482),x36483))) % 172.78/172.47 [3649]E(f332(f332(f79(a876),f332(f332(f79(a876),x36491),x36492)),x36493),f332(f332(f79(a876),x36491),f332(f332(f79(a876),x36492),x36493))) % 172.78/172.47 [3650]E(f332(f332(f79(a1),f332(f332(f79(a1),x36501),x36502)),x36503),f332(f332(f79(a1),x36501),f332(f332(f79(a1),x36502),x36503))) % 172.78/172.47 [3651]E(f332(f332(f257(a1),f332(f332(f257(a1),x36511),x36512)),x36513),f332(f332(f257(a1),x36511),f332(f332(f80(a876),x36512),x36513))) % 172.78/172.47 [3672]E(f162(x36721,f332(f332(f151(f883(x36721,a871)),x36722),x36723)),f175(x36721,x36722,f162(x36721,x36723))) % 172.78/172.47 [3717]E(f332(f332(f22(a876),f332(f332(f22(a876),x37171),x37172)),x37173),f332(f332(f22(a876),f332(f332(f22(a876),x37171),x37173)),x37172)) % 172.78/172.47 [3723]E(f332(f239(f882(x37231,f878(x37231))),f332(f332(f267(x37231,f878(x37231)),x37232),x37233)),f332(f135(x37231),f127(x37231,x37232,x37233))) % 172.78/172.47 [3726]E(f332(f332(f104(f883(x37261,a871)),x37262),f332(f332(f22(f883(x37261,a871)),x37263),x37262)),f195(f883(x37261,a871))) % 172.78/172.47 [3730]E(f332(f332(f154(a876,x37301),f332(f16(x37301,a876),x37302)),f139(a876,f332(f302(a876,f2(a876)),x37303))),f170(x37301,x37303,x37302)) % 172.78/172.47 [3769]E(f40(f883(x37691,a871),f332(f332(f310(f883(x37691,a871)),x37692),x37693)),f332(f332(f104(f883(x37691,a871)),x37692),f40(f883(x37691,a871),x37693))) % 172.78/172.47 [3770]E(f39(f883(x37701,a871),f332(f332(f310(f883(x37701,a871)),x37702),x37703)),f332(f332(f113(f883(x37701,a871)),x37702),f39(f883(x37701,a871),x37703))) % 172.78/172.47 [3772]E(f170(x37721,f332(f196(f877(x37721)),f332(f136(x37721,f332(a329,x37722)),x37723)),x37722),f332(f136(x37721,f332(a329,x37722)),x37723)) % 172.78/172.47 [3774]E(f332(f332(f22(a876),f332(f332(f80(a876),x37741),x37742)),f332(f332(f80(a876),x37743),x37742)),f332(f332(f80(a876),f332(f332(f22(a876),x37741),x37743)),x37742)) % 172.78/172.47 [3775]E(f332(f332(f79(a876),f332(f332(f80(a876),x37751),x37752)),f332(f332(f80(a876),x37753),x37752)),f332(f332(f80(a876),f332(f332(f79(a876),x37751),x37753)),x37752)) % 172.78/172.47 [3776]E(f332(f332(f22(a1),f332(f332(f80(a1),x37761),x37762)),f332(f332(f80(a1),x37763),x37762)),f332(f332(f80(a1),f332(f332(f22(a1),x37761),x37763)),x37762)) % 172.78/172.47 [3777]E(f332(f332(f79(a1),f332(f332(f80(a1),x37771),x37772)),f332(f332(f80(a1),x37773),x37772)),f332(f332(f80(a1),f332(f332(f79(a1),x37771),x37773)),x37772)) % 172.78/172.47 [3779]E(f332(f332(f244(a876),f332(f332(f22(a876),x37791),x37792)),f332(f332(f22(a876),x37793),x37792)),f332(f332(f22(a876),f332(f332(f244(a876),x37791),x37793)),x37792)) % 172.78/172.47 [3802]E(f332(f332(f104(f883(f877(x38021),a871)),f160(x38021,x38022)),f160(x38021,x38023)),f160(x38021,f332(f332(f104(f883(x38021,a871)),x38022),x38023))) % 172.78/172.47 [3804]E(f332(f332(f113(f883(x38041,a871)),x38042),f332(f332(f113(f883(x38041,a871)),x38042),x38043)),f332(f332(f113(f883(x38041,a871)),x38042),x38043)) % 172.78/172.47 [3805]E(f332(f332(f113(f883(x38051,a871)),x38052),f332(f332(f22(f883(x38051,a871)),x38053),x38052)),f332(f332(f113(f883(x38051,a871)),x38052),x38053)) % 172.78/172.47 [3806]E(f332(f332(f104(f883(x38061,a871)),x38062),f332(f332(f104(f883(x38061,a871)),x38062),x38063)),f332(f332(f104(f883(x38061,a871)),x38062),x38063)) % 172.78/172.47 [3818]E(f332(f332(f289(x38181,x38182,x38182),x38183),f308(x38182,f195(f883(f882(x38182,x38182),a871)))),x38183) % 172.78/172.47 [3821]E(f332(f332(f113(f883(x38211,a871)),f332(f332(f310(x38211),x38212),f195(f883(x38211,a871)))),x38213),f332(f332(f310(x38211),x38212),x38213)) % 172.78/172.47 [3839]E(f332(f332(f22(a876),f332(f332(f22(a876),f332(a115,x38391)),x38392)),f332(a115,x38393)),f332(f332(f22(a876),f332(f332(f22(a876),x38391),x38392)),x38393)) % 172.78/172.47 [3869]E(f332(f332(f104(f883(f883(x38691,a871),a871)),f332(f309(x38691),x38692)),f332(f309(x38691),x38693)),f332(f309(x38691),f332(f332(f104(f883(x38691,a871)),x38692),x38693))) % 172.78/172.47 [3873]E(f332(f332(f113(f883(x38731,a871)),f332(f78(f883(x38731,a871)),x38732)),x38733),f332(f78(f883(x38731,a871)),f332(f332(f22(f883(x38731,a871)),x38732),x38733))) % 172.78/172.47 [3885]E(f332(f332(f310(x38851),x38852),f332(f332(f22(f883(x38851,a871)),x38853),f332(f332(f310(x38851),x38852),f195(f883(x38851,a871))))),f332(f332(f310(x38851),x38852),x38853)) % 172.78/172.47 [3895]P102(f332(f332(f246(f883(x38951,a871)),x38952),f332(f332(f113(f883(x38951,a871)),x38953),x38952))) % 172.78/172.47 [3896]P102(f332(f332(f246(f883(x38961,a871)),x38962),f332(f332(f113(f883(x38961,a871)),x38962),x38963))) % 172.78/172.47 [3899]E(f332(f332(f104(f883(x38991,a871)),f332(f78(f883(x38991,a871)),x38992)),f332(f78(f883(x38991,a871)),x38993)),f332(f78(f883(x38991,a871)),f332(f332(f113(f883(x38991,a871)),x38992),x38993))) % 172.78/172.47 [3900]E(f332(f332(f113(f883(x39001,a871)),f332(f78(f883(x39001,a871)),x39002)),f332(f78(f883(x39001,a871)),x39003)),f332(f78(f883(x39001,a871)),f332(f332(f104(f883(x39001,a871)),x39002),x39003))) % 172.78/172.47 [3914]P102(f332(f332(f246(f883(x39141,a871)),f332(f173(x39141),x39142)),f332(f173(x39141),f332(f332(f151(x39141),x39143),x39142)))) % 172.78/172.47 [3925]E(f332(f332(f113(f883(x39251,a871)),f332(f332(f22(f883(x39251,a871)),x39252),x39253)),f332(f332(f104(f883(x39251,a871)),x39252),x39253)),x39252) % 172.78/172.47 [3981]E(f332(f332(f6(x39811,a1),f332(f332(f8(a876,a1,x39811),f103(a1)),x39812)),x39813),f332(f103(a1),f332(f332(f6(x39811,a876),x39812),x39813))) % 172.78/172.47 [3982]E(f332(f332(f9(x39821,a1),f332(f332(f8(a876,a1,x39821),f103(a1)),x39822)),x39823),f332(f103(a1),f332(f332(f9(x39821,a876),x39822),x39823))) % 172.78/172.47 [4032]E(f332(f332(f134(x40321),f178(x40321,x40322,x40323)),f332(f332(f138(x40321),f332(f196(f877(x40321)),f178(x40321,x40322,x40323))),x40323)),x40323) % 172.78/172.47 [4037]E(f332(f78(f883(f882(x40371,x40372),a871)),f332(f332(f269(x40371,x40372),x40373),f332(f16(f883(x40372,a871),x40371),f255(f883(x40372,a871))))),f332(f332(f269(x40371,x40372),f332(f78(f883(x40371,a871)),x40373)),f332(f16(f883(x40372,a871),x40371),f255(f883(x40372,a871))))) % 172.78/172.47 [4038]E(f332(f78(f883(f882(x40381,x40382),a871)),f332(f332(f269(x40381,x40382),f255(f883(x40381,a871))),f332(f16(f883(x40382,a871),x40381),x40383))),f332(f332(f269(x40381,x40382),f255(f883(x40381,a871))),f332(f16(f883(x40382,a871),x40381),f332(f78(f883(x40382,a871)),x40383)))) % 172.78/172.47 [4086]E(f332(f332(f41(f883(x40861,a871),f883(x40861,a871)),x40862),f332(f332(f7(f883(x40861,a871),f883(x40861,a871),f883(x40861,a871)),f104(f883(x40861,a871))),x40863)),f332(f332(f104(f883(x40861,a871)),f39(f883(x40861,a871),x40862)),x40863)) % 172.78/172.47 [4093]E(f332(f142(f877(x40931),f877(x40931),f134(x40931),f116(x40931)),f332(f332(f151(f877(x40931)),x40932),x40933)),f332(f332(f134(x40931),x40932),f332(f142(f877(x40931),f877(x40931),f134(x40931),f116(x40931)),x40933))) % 172.78/172.47 [4115]E(f332(f332(f310(f883(x41151,a871)),f332(f286(x41151,x41151,x41152),f332(f332(f310(x41151),x41153),f195(f883(x41151,a871))))),f195(f883(f883(x41151,a871),a871))),f332(f332(f60(x41151),f332(f332(f310(x41151),x41153),f195(f883(x41151,a871)))),x41152)) % 172.78/172.47 [4125]E(f332(f332(f79(a876),f332(f332(f80(a876),x41251),f332(f332(f38(a876),x41252),x41253))),f332(f332(f38(a876),f332(f332(f80(a876),x41251),f44(a876,x41252,x41253))),x41253)),f332(f332(f38(a876),f332(f332(f80(a876),x41251),x41252)),x41253)) % 172.78/172.47 [4126]E(f332(f332(f79(a1),f332(f332(f80(a1),x41261),f332(f332(f38(a1),x41262),x41263))),f332(f332(f38(a1),f332(f332(f80(a1),x41261),f44(a1,x41262,x41263))),x41263)),f332(f332(f38(a1),f332(f332(f80(a1),x41261),x41262)),x41263)) % 172.78/172.47 [4163]E(f332(f332(f22(f883(x41631,a871)),f332(f173(x41631),x41632)),f332(f332(f310(x41631),x41633),f195(f883(x41631,a871)))),f332(f173(x41631),f332(f136(x41631,f332(f332(f8(a871,a871,x41631),a327),f332(a329,x41633))),x41632))) % 172.78/172.47 [4213]E(f332(f332(f134(x42131),f332(f142(f877(x42131),f877(x42131),f134(x42131),f116(x42131)),x42132)),f332(f142(f877(x42131),f877(x42131),f134(x42131),f116(x42131)),x42133)),f332(f142(f877(x42131),f877(x42131),f134(x42131),f116(x42131)),f332(f332(f134(f877(x42131)),x42132),x42133))) % 172.78/172.47 [4218]E(f332(f332(f267(f877(x42181),f877(x42181)),f332(f136(x42181,x42182),x42183)),f332(f136(x42181,f332(f72(a871,a871,x42181,a327),x42182)),x42183)),f167(x42181,x42182,x42183)) % 172.78/172.47 [4221]E(f332(f332(f79(a876),f332(f332(f79(a876),f332(f332(f38(a876),x42211),x42212)),f332(f332(f38(a876),x42213),x42212))),f332(f332(f38(a876),f332(f332(f79(a876),f44(a876,x42211,x42212)),f44(a876,x42213,x42212))),x42212)),f332(f332(f38(a876),f332(f332(f79(a876),x42211),x42213)),x42212)) % 172.78/172.47 [4222]E(f332(f332(f79(a1),f332(f332(f79(a1),f332(f332(f38(a1),x42221),x42222)),f332(f332(f38(a1),x42223),x42222))),f332(f332(f38(a1),f332(f332(f79(a1),f44(a1,x42221,x42222)),f44(a1,x42223,x42222))),x42222)),f332(f332(f38(a1),f332(f332(f79(a1),x42221),x42223)),x42222)) % 172.78/172.47 [4278]E(f332(f332(f104(f883(f877(x42781),a871)),f332(f332(f7(f877(x42781),f883(f877(x42781),a871),a871),f334(f877(x42781))),f161(x42781,x42782))),f332(f332(f7(f877(x42781),f883(f877(x42781),a871),a871),f334(f877(x42781))),f161(x42781,x42783))),f160(x42781,f332(f332(f104(f883(x42781,a871)),f332(f332(f7(x42781,f883(x42781,a871),a871),f334(x42781)),x42782)),f332(f332(f7(x42781,f883(x42781,a871),a871),f334(x42781)),x42783)))) % 172.78/172.47 [4291]E(f332(f252(x42911),f332(f332(f18(x42911,a871,a871),f332(f332(f8(a871,f883(a871,a871),x42911),a331),f332(f332(f7(x42911,x42911,a871),a329),x42912))),f332(f332(f7(x42911,f883(x42911,a871),a871),f334(x42911)),x42913))),f332(f332(f310(x42911),x42912),x42913)) % 172.78/172.47 [4311]E(f332(f332(f85(f877(f877(x43111)),f877(f877(x43111))),f53(x43111,x43112)),f332(f332(f18(f877(f877(x43111)),f877(f877(x43111)),f877(f877(x43111))),f332(f332(f8(f877(f877(x43111)),f883(f877(f877(x43111)),f877(f877(x43111))),f877(f877(x43111))),f134(f877(x43111))),f332(f154(f877(x43111),f877(x43111)),f332(f151(x43111),x43113)))),f5(f877(f877(x43111))))),f53(x43111,f332(f332(f151(x43111),x43113),x43112))) % 172.78/172.47 [4315]E(f332(f252(x43151),f332(f332(f18(x43151,a871,a871),f332(f332(f8(a871,f883(a871,a871),x43151),a331),f332(f332(f7(x43151,f883(x43151,a871),a871),f334(x43151)),x43152))),f332(f332(f7(x43151,f883(x43151,a871),a871),f334(x43151)),x43153))),f332(f332(f113(f883(x43151,a871)),x43152),x43153)) % 172.78/172.47 [4316]E(f332(f252(x43161),f332(f332(f18(x43161,a871,a871),f332(f332(f8(a871,f883(a871,a871),x43161),a330),f332(f332(f7(x43161,f883(x43161,a871),a871),f334(x43161)),x43162))),f332(f332(f7(x43161,f883(x43161,a871),a871),f334(x43161)),x43163))),f332(f332(f104(f883(x43161,a871)),x43162),x43163)) % 172.78/172.47 [4407]E(f332(f332(f41(x44071,f883(f883(x44071,a871),a871)),x44072),f332(f332(f7(x44071,f883(f883(x44071,a871),a871),f883(f883(x44071,a871),a871)),f332(f332(f8(f883(x44071,a871),f883(f883(f883(x44071,a871),a871),f883(f883(x44071,a871),a871)),x44071),f310(f883(x44071,a871))),f332(f332(f8(f883(x44071,a871),f883(x44071,a871),x44071),f286(x44071,x44071,x44073)),f332(f332(f7(x44071,f883(x44071,a871),f883(x44071,a871)),f310(x44071)),f195(f883(x44071,a871)))))),f195(f883(f883(x44071,a871),a871)))),f332(f332(f60(x44071),x44072),x44073)) % 172.78/172.47 [4409]E(f332(f332(f212(x44091),f332(f332(f80(a1),f332(f332(f72(f882(a1,a1),a1,x44091,f266(a1,a1)),f223(x44091)),x44092)),f332(f332(f72(f882(a1,a1),a1,x44091,f266(a1,a1)),f223(x44091)),x44093))),f332(f332(f80(a1),f332(f332(f72(f882(a1,a1),a1,x44091,f270(a1,a1)),f223(x44091)),x44092)),f332(f332(f72(f882(a1,a1),a1,x44091,f270(a1,a1)),f223(x44091)),x44093))),f232(x44091,x44092,x44093)) % 172.78/172.47 [4412]E(f332(f252(f877(x44121)),f332(f332(f18(f877(x44121),a871,a871),f332(f332(f8(a871,f883(a871,a871),f877(x44121)),a330),f332(f332(f7(f877(x44121),a876,a871),f332(f332(f8(a876,f883(a876,a871),f877(x44121)),a329),f196(f877(x44121)))),x44122))),f332(f332(f7(f877(x44121),f883(x44121,a871),a871),f332(f332(f8(f883(x44121,a871),f883(f883(x44121,a871),a871),f877(x44121)),f246(f883(x44121,a871))),f173(x44121))),f332(f173(x44121),x44123)))),f332(f173(f877(x44121)),f54(x44121,x44122,x44123))) % 172.78/172.47 [3792]E(f44(a876,f332(f332(f79(a876),f332(f332(f80(a876),x37921),x37922)),x37923),x37922),f44(a876,x37923,x37922)) % 172.78/172.47 [3838]E(f139(a876,f332(f302(a876,f332(f332(f79(a876),x38381),x38382)),x38383)),f332(f332(f138(a876),x38382),f139(a876,f332(f302(a876,x38381),x38383)))) % 172.78/172.47 [3884]E(f332(f332(f79(a1),f332(f103(a1),x38841)),f332(f332(f79(a1),f332(f103(a1),x38842)),x38843)),f332(f332(f79(a1),f332(f103(a1),f332(f332(f79(a876),x38841),x38842))),x38843)) % 172.78/172.47 [3891]E(f332(f332(f113(f883(x38911,a871)),f332(f332(f22(f883(x38911,a871)),x38912),x38913)),x38913),f332(f332(f113(f883(x38911,a871)),x38912),x38913)) % 172.78/172.47 [3892]E(f332(f332(f22(f883(x38921,a871)),f332(f332(f22(f883(x38921,a871)),x38922),x38923)),x38923),f332(f332(f22(f883(x38921,a871)),x38922),x38923)) % 172.78/172.47 [3915]E(f332(f332(f289(x39151,x39151,x39152),f308(x39151,f195(f883(f882(x39151,x39151),a871)))),x39153),x39153) % 172.78/172.47 [3922]E(f332(f332(f113(f883(x39221,a871)),f332(f285(x39221),x39222)),f332(f285(x39221),x39223)),f332(f285(x39221),f332(f332(f113(f883(f882(x39221,x39221),a871)),x39222),x39223))) % 172.78/172.47 [3933]E(f276(x39331,f332(f332(f151(f882(a102,x39331)),f332(f332(f267(a102,x39331),f2(a102)),x39332)),x39333)),f276(x39331,x39333)) % 172.78/172.47 [3936]E(f332(f332(f104(f883(x39361,a871)),f40(f883(x39361,a871),x39362)),f40(f883(x39361,a871),x39363)),f40(f883(x39361,a871),f332(f332(f113(f883(f883(x39361,a871),a871)),x39362),x39363))) % 172.78/172.47 [3937]E(f332(f332(f113(f883(x39371,a871)),f39(f883(x39371,a871),x39372)),f39(f883(x39371,a871),x39373)),f39(f883(x39371,a871),f332(f332(f113(f883(f883(x39371,a871),a871)),x39372),x39373))) % 172.78/172.47 [3973]E(f332(f332(f289(x39731,x39731,x39731),f332(f332(f190(f882(x39731,x39731),a871),x39732),x39733)),x39733),f332(f332(f190(f882(x39731,x39731),a871),f332(a115,x39732)),x39733)) % 172.78/172.47 [4023]P102(f332(f332(f246(f883(x40231,a871)),f332(f332(f22(f883(x40231,a871)),x40232),x40233)),x40232)) % 172.78/172.47 [4024]P102(f332(f332(f246(f883(x40241,a871)),f332(f332(f104(f883(x40241,a871)),x40242),x40243)),x40243)) % 172.78/172.47 [4025]P102(f332(f332(f246(f883(x40251,a871)),f332(f332(f104(f883(x40251,a871)),x40252),x40253)),x40252)) % 172.78/172.47 [4050]E(f308(x40501,f332(f332(f113(f883(f882(x40501,x40501),a871)),f308(x40501,x40502)),f308(x40501,x40503))),f308(x40501,f332(f332(f113(f883(f882(x40501,x40501),a871)),x40502),x40503))) % 172.78/172.47 [4054]E(f39(f883(x40541,a871),f332(f332(f310(f883(x40541,a871)),x40542),f332(f332(f310(f883(x40541,a871)),x40543),f195(f883(f883(x40541,a871),a871))))),f332(f332(f113(f883(x40541,a871)),x40542),x40543)) % 172.78/172.47 [4055]E(f40(f883(x40551,a871),f332(f332(f310(f883(x40551,a871)),x40552),f332(f332(f310(f883(x40551,a871)),x40553),f195(f883(f883(x40551,a871),a871))))),f332(f332(f104(f883(x40551,a871)),x40552),x40553)) % 172.78/172.47 [4061]E(f332(f332(f289(x40611,x40611,x40611),f332(f332(f190(f882(x40611,x40611),a871),x40612),x40613)),x40613),f332(f332(f289(x40611,x40611,x40611),x40613),f332(f332(f190(f882(x40611,x40611),a871),x40612),x40613))) % 172.78/172.47 [4130]E(f332(f332(f113(f883(x41301,a871)),f332(f252(x41301),f332(f332(f7(x41301,x41301,a871),a329),x41302))),x41303),f332(f332(f310(x41301),x41302),x41303)) % 172.78/172.47 [4132]E(f332(a107,f332(f332(f6(x41321,a1),f332(f332(f8(a876,a1,x41321),f103(a1)),x41322)),x41323)),f332(f332(f6(x41321,a876),x41322),x41323)) % 172.78/172.47 [4133]E(f332(a107,f332(f332(f9(x41331,a1),f332(f332(f8(a876,a1,x41331),f103(a1)),x41332)),x41333)),f332(f332(f9(x41331,a876),x41332),x41333)) % 172.78/172.47 [4210]E(f332(f156(f877(x42101),x42101,f332(f172(x42101),x42102),f332(f16(f883(f877(x42101),f877(x42101)),x42101),f332(f332(f7(f877(x42101),f877(x42101),f877(x42101)),f134(x42101)),x42102))),x42103),f332(f172(x42101),f332(f332(f134(x42101),x42103),x42102))) % 172.78/172.47 [4241]P102(f332(f332(f246(f883(f883(x42411,a871),a871)),f332(f332(f113(f883(f883(x42411,a871),a871)),f332(f309(x42411),x42412)),f332(f309(x42411),x42413))),f332(f309(x42411),f332(f332(f113(f883(x42411,a871)),x42412),x42413)))) % 172.78/172.47 [4334]E(f332(f252(x43341),f332(f332(f18(x43341,a871,a871),f332(f332(f8(a871,f883(a871,a871),x43341),a330),f332(f332(f7(x43341,f883(x43341,a871),a871),f334(x43341)),x43342))),f332(f332(f8(a871,a871,x43341),a327),f332(f332(f7(x43341,f883(x43341,a871),a871),f334(x43341)),x43343)))),f332(f332(f22(f883(x43341,a871)),x43342),x43343)) % 172.78/172.47 [4356]E(f332(f37(a876),f332(f252(a876),f332(f332(f18(a876,a871,a871),f332(f332(f8(a871,f883(a871,a871),a876),a330),f332(f332(f7(a876,a876,a871),f247(a876)),f332(f196(f877(x43561)),x43562)))),f332(f332(f8(x43561,a871,a876),x43563),f332(f165(x43561),x43562))))),f332(f196(f877(x43561)),f332(f136(x43561,x43563),x43562))) % 172.78/172.47 [4358]E(f332(f196(f877(x43581)),f177(x43581,x43582,x43583)),f332(f37(a876),f332(f252(a876),f332(f332(f18(a876,a871,a871),f332(f332(f8(a871,f883(a871,a871),a876),a330),f332(f332(f7(a876,a876,a871),f247(a876)),f332(f196(f877(x43581)),x43582)))),f332(f332(f7(a876,f883(a876,a871),a871),f334(a876)),x43583))))) % 172.78/172.47 [4455]E(f332(f332(f104(f883(f882(f877(x44551),f877(x44551)),a871)),f332(f311(f882(f882(x44551,f877(x44551)),f882(x44551,f877(x44551))),f882(f877(x44551),f877(x44551)),f272(f882(x44551,f877(x44551)),f877(x44551),f882(x44551,f877(x44551)),f877(x44551),f332(f271(x44551,f877(x44551),f877(x44551)),f151(x44551)),f332(f271(x44551,f877(x44551),f877(x44551)),f151(x44551)))),f325(x44551,f877(x44551),x44552,f332(f143(x44551,x44552),x44553)))),f332(f252(f882(f877(x44551),f877(x44551))),f332(f271(f877(x44551),f877(x44551),a871),f332(f332(f7(f877(x44551),f883(f877(x44551),a871),f883(f877(x44551),a871)),f332(f332(f8(f883(a871,a871),f883(f883(f877(x44551),a871),f883(f877(x44551),a871)),f877(x44551)),f8(a871,a871,f877(x44551))),f332(f332(f8(a871,f883(a871,a871),f877(x44551)),a330),f332(f332(f7(f877(x44551),a876,a871),f332(f332(f8(a876,f883(a876,a871),f877(x44551)),a329),f196(f877(x44551)))),f332(a115,x44553))))),f332(f332(f7(f877(x44551),a876,a871),f332(f332(f8(a876,f883(a876,a871),f877(x44551)),a329),f196(f877(x44551)))),f332(a115,x44553)))))),f332(f143(x44551,x44552),f332(a115,x44553))) % 172.78/172.47 [3938]E(f44(a876,f332(a115,f332(f332(f79(a876),f332(f332(f80(a876),x39381),x39382)),x39383)),x39382),f44(a876,f332(a115,x39383),x39382)) % 172.78/172.47 [4198]E(f332(f252(x41981),f332(f332(f18(x41981,a871,a871),f332(f332(f8(a871,f883(a871,a871),x41981),a330),x41982)),x41983)),f332(f332(f104(f883(x41981,a871)),f332(f252(x41981),x41982)),f332(f252(x41981),x41983))) % 172.78/172.47 [4199]E(f332(f252(x41991),f332(f332(f18(x41991,a871,a871),f332(f332(f8(a871,f883(a871,a871),x41991),a331),x41992)),x41993)),f332(f332(f113(f883(x41991,a871)),f332(f252(x41991),x41992)),f332(f252(x41991),x41993))) % 172.78/172.47 [4201]E(f332(f332(f134(x42011),f332(f332(f138(x42011),f44(a876,x42012,f332(f196(f877(x42011)),x42013))),x42013)),f332(f332(f176(x42011),f44(a876,x42012,f332(f196(f877(x42011)),x42013))),x42013)),f332(f332(f332(f190(f877(x42011),f877(x42011)),x42012),f168(x42011)),x42013)) % 172.78/172.47 [4207]E(f332(f252(x42071),f332(f332(f18(x42071,a871,a871),f332(f332(f8(a871,f883(a871,a871),x42071),a335),x42072)),x42073)),f332(f332(f113(f883(x42071,a871)),f332(f78(f883(x42071,a871)),f332(f252(x42071),x42072))),f332(f252(x42071),x42073))) % 172.78/172.47 [4223]E(f332(f332(f79(a876),f332(f196(f877(x42231)),f332(f136(x42231,x42232),x42233))),f332(f196(f877(x42231)),f332(f136(x42231,f332(f332(f8(a871,a871,x42231),a327),x42232)),x42233))),f332(f196(f877(x42231)),x42233)) % 172.78/172.47 [4248]P102(f332(f332(f246(f883(x42481,a871)),f332(f332(f113(f883(x42481,a871)),f40(f883(x42481,a871),x42482)),f40(f883(x42481,a871),x42483))),f40(f883(x42481,a871),f332(f332(f104(f883(f883(x42481,a871),a871)),x42482),x42483)))) % 172.78/172.47 [4262]E(f332(f173(x42621),f332(f136(x42621,f332(f332(f8(a871,a871,x42621),a327),f332(f332(f7(x42621,x42621,a871),a329),x42622))),x42623)),f332(f332(f22(f883(x42621,a871)),f332(f173(x42621),x42623)),f332(f332(f310(x42621),x42622),f195(f883(x42621,a871))))) % 172.78/172.47 [4271]P102(f332(f332(f246(f883(f882(x42711,x42711),a871)),f332(f332(f113(f883(f882(x42711,x42711),a871)),f308(x42711,x42712)),f308(x42711,x42713))),f308(x42711,f332(f332(f113(f883(f882(x42711,x42711),a871)),x42712),x42713)))) % 172.78/172.47 [4296]E(f332(f332(f80(a876),f332(a115,f332(a115,f2(a876)))),f332(f332(f6(a876,a876),f332(f332(f8(a876,a876,a876),f332(f79(a876),x42961)),f332(f332(f7(a876,a876,a876),f80(a876)),x42962))),f332(f253(a876),x42963))),f332(f332(f80(a876),x42963),f332(f332(f79(a876),x42961),f332(f332(f79(a876),x42961),f332(f332(f80(a876),f332(f332(f22(a876),x42963),f77(a876))),x42962))))) % 172.78/172.47 [4306]E(f332(f252(x43061),f332(f332(f18(x43061,a871,a871),f332(f332(f8(a871,f883(a871,a871),x43061),a330),f332(f332(f7(x43061,f883(x43061,a871),a871),f334(x43061)),f332(f173(x43061),x43062)))),x43063)),f332(f173(x43061),f332(f136(x43061,x43063),x43062))) % 172.78/172.47 [4454]E(f332(f252(x44541),f332(f332(f8(f883(a876,a871),a871,x44541),f86(a876)),f332(f332(f7(x44541,f883(a876,a871),f883(a876,a871)),f332(f332(f8(f883(a876,f883(a871,a871)),f883(f883(a876,a871),f883(a876,a871)),x44541),f18(a876,a871,a871)),f332(f332(f8(f883(a876,a871),f883(a876,f883(a871,a871)),x44541),f332(f8(a871,f883(a871,a871),a876),a330)),f332(f332(f7(x44541,f883(a876,x44541),f883(a876,a871)),f332(f332(f8(f883(x44541,a871),f883(f883(a876,x44541),f883(a876,a871)),x44541),f8(x44541,a871,a876)),a329)),f332(f165(x44541),x44542))))),f332(f332(f18(a876,a871,a871),f332(f332(f8(a871,f883(a871,a871),a876),a330),f332(f332(f7(a876,a876,a871),f247(a876)),f332(f196(f877(x44541)),x44542)))),f332(f332(f7(a876,f883(a876,a871),a871),f334(a876)),x44543))))),f332(f173(x44541),f177(x44541,x44542,x44543))) % 172.78/172.47 [4346]E(f332(f252(x43461),f332(f332(f18(x43461,a871,a871),f332(f332(f8(a871,f883(a871,a871),x43461),a335),f332(f332(f8(a871,a871,x43461),a327),f332(f332(f7(x43461,x43461,a871),a329),x43462)))),x43463)),f332(f332(f310(x43461),x43462),f332(f252(x43461),x43463))) % 172.78/172.47 [4378]E(f332(f332(f154(f882(x43781,a876),x43781),f266(x43781,a876)),f332(f136(f882(x43781,a876),f332(f332(f7(f882(x43781,a876),f883(a876,a871),a871),f332(f332(f8(a876,f883(f883(a876,a871),a871),f882(x43781,a876)),f334(a876)),f270(x43781,a876))),x43782)),f332(f332(f183(x43781,a876),x43783),f139(a876,f332(f302(a876,f2(a876)),f332(f196(f877(x43781)),x43783)))))),f177(x43781,x43783,x43782)) % 172.78/172.47 [4408]E(f332(f332(f80(a1),f332(f106(a1),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)))),f332(f332(f6(a876,a1),f332(f332(f8(a1,a1,a876),f332(f79(a1),x44081)),f332(f332(f7(a876,a1,a1),f332(f332(f8(a1,f883(a1,a1),a876),f80(a1)),f103(a1))),x44082))),f332(f253(a876),x44083))),f332(f332(f80(a1),f332(f103(a1),x44083)),f332(f332(f79(a1),x44081),f332(f332(f79(a1),x44081),f332(f332(f80(a1),f332(f103(a1),f332(f332(f22(a876),x44083),f77(a876)))),x44082))))) % 172.78/172.47 [4448]E(f332(f252(f882(x44481,x44482)),f332(f271(x44481,x44482,a871),f332(f332(f7(x44481,f883(f882(x44482,x44481),a871),f883(x44482,a871)),f332(f332(f8(f883(x44482,f883(f883(f882(x44482,x44481),a871),a871)),f883(f883(f882(x44482,x44481),a871),f883(x44482,a871)),x44481),f7(x44482,f883(f882(x44482,x44481),a871),a871)),f332(f332(f8(f883(x44482,f882(x44482,x44481)),f883(x44482,f883(f883(f882(x44482,x44481),a871),a871)),x44481),f332(f8(f882(x44482,x44481),f883(f883(f882(x44482,x44481),a871),a871),x44482),f334(f882(x44482,x44481)))),f332(f7(x44482,x44481,f882(x44482,x44481)),f267(x44482,x44481))))),x44483))),f332(f287(x44482,x44481),x44483)) % 172.78/172.47 [4470]E(f332(f252(f877(x44701)),f332(f332(f8(f883(x44701,a871),a871,f877(x44701)),f86(x44701)),f332(f332(f8(f883(x44701,f883(f877(x44701),a871)),f883(x44701,a871),f877(x44701)),f332(f8(f883(f877(x44701),a871),a871,x44701),f86(f877(x44701)))),f332(f332(f7(f877(x44701),f883(x44701,f883(f877(x44701),a871)),f883(x44701,f883(f877(x44701),a871))),f332(f332(f8(f883(x44701,f883(f883(f877(x44701),a871),f883(f877(x44701),a871))),f883(f883(x44701,f883(f877(x44701),a871)),f883(x44701,f883(f877(x44701),a871))),f877(x44701)),f18(x44701,f883(f877(x44701),a871),f883(f877(x44701),a871))),f332(f332(f8(f883(x44701,f883(f877(x44701),f883(a871,a871))),f883(x44701,f883(f883(f877(x44701),a871),f883(f877(x44701),a871))),f877(x44701)),f332(f8(f883(f877(x44701),f883(a871,a871)),f883(f883(f877(x44701),a871),f883(f877(x44701),a871)),x44701),f18(f877(x44701),a871,a871))),f332(f332(f8(f883(x44701,f883(f877(x44701),a871)),f883(x44701,f883(f877(x44701),f883(a871,a871))),f877(x44701)),f332(f8(f883(f877(x44701),a871),f883(f877(x44701),f883(a871,a871)),x44701),f332(f8(a871,f883(a871,a871),f877(x44701)),a330))),f332(f332(f7(f877(x44701),f883(x44701,f883(f877(x44701),f877(x44701))),f883(x44701,f883(f877(x44701),a871))),f332(f332(f8(f883(f883(f877(x44701),f877(x44701)),f883(f877(x44701),a871)),f883(f883(x44701,f883(f877(x44701),f877(x44701))),f883(x44701,f883(f877(x44701),a871))),f877(x44701)),f8(f883(f877(x44701),f877(x44701)),f883(f877(x44701),a871),x44701)),f332(f332(f8(f883(f877(x44701),a871),f883(f883(f877(x44701),f877(x44701)),f883(f877(x44701),a871)),f877(x44701)),f8(f877(x44701),a871,f877(x44701))),a329))),f151(x44701)))))),f332(f332(f7(x44701,f883(f877(x44701),a871),f883(f877(x44701),a871)),f332(f332(f8(f883(a871,a871),f883(f883(f877(x44701),a871),f883(f877(x44701),a871)),x44701),f8(a871,a871,f877(x44701))),f332(f332(f8(a871,f883(a871,a871),x44701),a330),f332(f332(f7(x44701,f883(x44701,a871),a871),f334(x44701)),x44702)))),f332(f332(f7(f877(x44701),f883(f877(x44701),a871),a871),f334(f877(x44701))),x44703)))))),f175(x44701,x44702,x44703)) % 172.78/172.47 [4467]E(f332(f332(f85(a1,f882(a1,a1)),f332(f332(f22(a1),x44671),x44672)),f332(f332(f7(a1,f882(a1,a1),f882(a1,a1)),f332(f332(f18(a1,f882(a1,a1),f883(f882(a1,a1),f882(a1,a1))),f332(f332(f8(a871,f883(f882(a1,a1),f883(f882(a1,a1),f882(a1,a1))),a1),f99(f882(a1,a1))),f332(f246(a1),f2(a1)))),f332(f267(a1,a1),f332(f332(f79(a1),f332(f332(f80(a1),f332(f106(a1),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)))),x44673)),f77(a1))))),f332(f332(f267(a1,a1),f332(f332(f80(a1),f332(f106(a1),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)))),x44673)),x44671))),f332(f43(x44672),f332(f332(f267(a1,a1),x44673),x44671))) % 172.78/172.47 [4498]~E(f31(x44981,x44982),f32(x44983,x44984)) % 172.78/172.47 [4515]~E(f332(a25,x45151),f29(x45152,x45153,x45154)) % 172.78/172.47 [4516]~E(f332(a25,x45161),f28(x45162,x45163,x45164)) % 172.78/172.47 [4517]~E(f29(x45171,x45172,x45173),f332(a25,x45174)) % 172.78/172.47 [4518]~E(f28(x45181,x45182,x45183),f332(a25,x45184)) % 172.78/172.47 [3478]E(f332(f332(f332(f71(x34781,x34782),x34783),x34784),f332(x34783,x34784)),x34783) % 172.78/172.47 [3486]E(f119(x34861,f332(x34862,x34863),f332(x34864,x34863)),f332(f214(x34861,x34862,x34864),x34863)) % 172.78/172.47 [3539]E(f332(f332(f258(x35391,x35392,x35393),x35394),f2(a876)),x35392) % 172.78/172.47 [3580]E(f192(x35801,x35802,x35803,f332(a115,x35804)),f332(x35803,x35804)) % 172.78/172.47 [3621]E(f171(x36211,x36212,f171(x36211,x36213,x36214)),f171(x36211,x36213,f171(x36211,x36212,x36214))) % 172.78/172.47 [3622]E(f119(x36221,f127(x36221,x36222,x36223),x36224),f127(x36221,x36222,f119(x36221,x36223,x36224))) % 172.78/172.47 [3759]E(f332(f156(x37591,x37592,x37593,x37594),f116(x37592)),x37593) % 172.78/172.47 [3760]E(f332(f241(x37601,x37602,x37603,x37604),f208(x37602)),x37603) % 172.78/172.47 [3761]E(f332(f142(x37611,x37612,x37613,x37614),f116(x37612)),x37614) % 172.78/172.47 [3868]E(f332(f332(f134(x38681),f170(x38681,x38682,x38683)),f170(x38681,x38684,x38683)),f332(f332(f134(x38681),f170(x38681,x38684,x38683)),f170(x38681,x38682,x38683))) % 172.78/172.47 [3881]E(f332(f241(f880(x38811),x38812,f208(x38811),f332(f16(f880(x38811),x38812),f208(x38811))),f332(x38813,x38814)),f208(x38811)) % 172.78/172.47 [3926]E(f332(f332(f113(f883(x39261,a871)),f185(x39261,x39262,x39263)),f185(x39261,x39262,x39264)),f185(x39261,x39262,f186(x39261,x39262,x39264,x39263))) % 172.78/172.47 [3958]E(f332(f332(f273(x39581,x39582,x39583,f882(x39582,x39583)),x39584),f267(x39582,x39583)),x39584) % 172.78/172.47 [3967]E(f188(x39671,x39672,x39673,x39674,f116(x39672)),x39673) % 172.78/172.47 [3968]E(f242(x39681,x39682,x39683,x39684,f208(x39682)),x39683) % 172.78/172.47 [3969]E(f188(x39691,x39692,x39693,f116(x39691),x39694),x39693) % 172.78/172.47 [4255]P43(x42551,x42552,x42553,x42554,f195(f883(x42551,a871)),x42554) % 172.78/172.47 [3279]E(f332(f332(f16(x32791,x32792),x32793),x32794),x32793) % 172.78/172.47 [3395]E(f332(f332(f209(x33951,x33952),x33953),f332(f239(x33951),x33954)),f332(f239(x33952),f332(x33953,x33954))) % 172.78/172.47 [3570]E(f171(x35701,x35702,f332(f136(x35701,x35703),x35704)),f332(f136(x35701,x35703),f171(x35701,x35702,x35704))) % 172.78/172.47 [3605]E(f332(f332(f64(x36051,x36052,x36053),x36054),f195(f883(x36051,a871))),x36054) % 172.78/172.47 [3628]E(f332(f332(f165(x36281),f332(f332(f151(x36281),x36282),x36283)),f332(a115,x36284)),f332(f332(f165(x36281),x36283),x36284)) % 172.78/172.47 [3673]P30(x36731,f2(a876),f332(f332(f332(f91(x36731),x36732),f332(a25,x36733)),x36734)) % 172.78/172.47 [3698]E(f332(f332(x36981,x36982),f332(f191(x36983,x36984,x36981),x36982)),f332(f191(x36983,x36984,x36981),f332(a115,x36982))) % 172.78/172.47 [3797]E(f332(f332(f159(x37971,f332(f332(f151(x37971),x37972),x37973)),f2(a876)),x37974),f332(f332(f151(x37971),x37974),x37973)) % 172.78/172.47 [3808]E(f332(f332(f41(f883(x38081,a871),f883(x38082,a871)),x38083),f311(x38081,x38082,x38084)),f332(f311(x38081,x38082,x38084),f39(f883(x38081,a871),x38083))) % 172.78/172.47 [3809]E(f332(f332(f41(f883(x38091,a871),f883(x38092,a871)),x38093),f312(x38092,x38091,x38094)),f332(f312(x38092,x38091,x38094),f39(f883(x38091,a871),x38093))) % 172.78/172.47 [3908]E(f185(x39081,x39082,f189(x39081,x39082,x39083,x39084)),f332(f332(f104(f883(x39081,a871)),f185(x39081,x39082,x39083)),x39084)) % 172.78/172.47 [3912]E(f332(f129(x39121,x39122),f127(x39121,x39123,x39124)),f332(f332(f79(a876),f332(f332(f79(a876),f332(x39122,x39123)),f332(f129(x39121,x39122),x39124))),f332(a115,f2(a876)))) % 172.78/172.47 [3932]E(f332(f142(x39321,x39322,f332(f7(x39322,x39321,x39321),x39323),x39324),f332(f169(x39322),f116(x39322))),x39324) % 172.78/172.47 [3980]E(f75(x39801,x39802,x39803,x39804,f195(f883(x39801,a871))),x39803) % 172.78/172.47 [4026]E(f332(f332(f332(f332(f71(x40261,f880(x40262)),f332(f16(f880(x40262),x40261),f208(x40262))),x40263),f208(x40262)),x40264),f208(x40262)) % 172.78/172.47 [4181]E(f332(f271(x41811,x41812,x41813),f332(f332(f8(f883(x41812,f882(x41811,x41812)),f883(x41812,x41813),x41811),f332(f8(f882(x41811,x41812),x41813,x41812),x41814)),f267(x41811,x41812))),x41814) % 172.78/172.47 [3476]E(f332(f270(x34761,x34762),f332(f332(f267(x34761,x34762),x34763),x34764)),x34764) % 172.78/172.47 [3477]E(f332(f266(x34771,x34772),f332(f332(f267(x34771,x34772),x34773),x34774)),x34773) % 172.78/172.47 [3512]E(f332(f196(f877(x35121)),f332(f332(f159(x35121,x35122),x35123),x35124)),f332(f196(f877(x35121)),x35122)) % 172.78/172.47 [3513]E(f332(f196(f877(x35131)),f332(f332(f154(x35132,x35131),x35133),x35134)),f332(f196(f877(x35132)),x35134)) % 172.78/172.47 [3533]E(f332(f332(f138(x35331),f332(a115,x35332)),f332(f332(f151(x35331),x35333),x35334)),f332(f332(f138(x35331),x35332),x35334)) % 172.78/172.47 [3600]E(f332(f332(f176(x36001),x36002),f170(x36001,x36003,x36004)),f170(x36001,f332(f332(f244(a876),x36002),x36003),x36004)) % 172.78/172.47 [3601]E(f332(f332(f138(x36011),x36012),f170(x36011,x36013,x36014)),f170(x36011,f332(f332(f22(a876),x36013),x36012),x36014)) % 172.78/172.47 [3607]E(f332(f332(f310(x36071),x36072),f332(f332(f310(x36071),x36073),x36074)),f332(f332(f310(x36071),x36073),f332(f332(f310(x36071),x36072),x36074))) % 172.78/172.47 [3610]E(f332(f332(f154(x36101,x36102),x36103),f117(x36101,x36104)),f117(x36102,f332(f332(f154(x36101,x36102),x36103),x36104))) % 172.78/172.47 [3626]E(f332(f169(x36261),f332(f332(f154(x36262,x36261),x36263),x36264)),f332(f332(f154(x36262,x36261),x36263),f332(f169(x36262),x36264))) % 172.78/172.47 [3627]E(f332(f332(f154(x36271,x36272),x36273),f332(f172(x36271),x36274)),f332(f172(x36272),f332(f332(f154(x36271,x36272),x36273),x36274))) % 172.78/172.47 [3640]E(f332(f332(f176(x36401),f332(a115,x36402)),f332(f332(f151(x36401),x36403),x36404)),f332(f332(f151(x36401),x36403),f332(f332(f176(x36401),x36402),x36404))) % 172.78/172.47 [3644]E(f332(f173(x36441),f332(f332(f154(x36442,x36441),x36443),x36444)),f332(f311(x36442,x36441,x36443),f332(f173(x36442),x36444))) % 172.78/172.47 [3659]E(f332(f332(f154(x36591,x36592),f332(f16(x36592,x36591),x36593)),x36594),f170(x36592,f332(f196(f877(x36591)),x36594),x36593)) % 172.78/172.47 [3697]E(f17(x36971,x36972,x36973,f332(a3,f332(a115,f332(a19,x36974)))),f332(x36973,x36974)) % 172.78/172.47 [3700]E(f332(f332(f134(x37001),f332(f136(x37001,x37002),x37003)),f332(f136(x37001,x37002),x37004)),f332(f136(x37001,x37002),f332(f332(f134(x37001),x37003),x37004))) % 172.78/172.47 [3713]E(f152(x37131,f332(f332(f154(x37132,x37131),x37133),f152(x37132,x37134))),f152(x37131,f332(f332(f154(x37132,x37131),x37133),x37134))) % 172.78/172.47 [3729]E(f332(f287(x37291,x37291),f332(f332(f288(x37292,x37291),x37293),x37294)),f332(f332(f288(x37292,x37291),f332(f287(x37292,x37292),x37293)),x37294)) % 172.78/172.47 [3740]E(f332(f332(f289(x37401,x37402,x37403),x37404),f195(f883(f882(x37402,x37403),a871))),f195(f883(f882(x37401,x37403),a871))) % 172.78/172.47 [3741]E(f332(f332(f176(x37411),f332(f332(f22(a876),x37412),x37413)),f332(f332(f138(x37411),x37413),x37414)),f332(f332(f138(x37411),x37413),f332(f332(f176(x37411),x37412),x37414))) % 172.78/172.47 [3762]E(f332(f332(f134(x37621),f170(x37621,x37622,x37623)),f170(x37621,x37624,x37623)),f170(x37621,f332(f332(f79(a876),x37622),x37624),x37623)) % 172.78/172.47 [3789]E(f40(f883(x37891,a871),f332(f311(x37892,f883(x37891,a871),x37893),x37894)),f332(f332(f42(x37892,f883(x37891,a871)),x37894),x37893)) % 172.78/172.47 [3790]E(f39(f883(x37901,a871),f332(f311(x37902,f883(x37901,a871),x37903),x37904)),f332(f332(f41(x37902,f883(x37901,a871)),x37904),x37903)) % 172.78/172.47 [3791]E(f332(f196(f877(f882(x37911,x37912))),f332(f332(f183(x37911,x37912),x37913),x37914)),f332(f332(f244(a876),f332(f196(f877(x37911)),x37913)),f332(f196(f877(x37912)),x37914))) % 172.78/172.47 [3793]E(f332(f312(x37931,x37932,x37933),f332(f78(f883(x37932,a871)),x37934)),f332(f78(f883(x37931,a871)),f332(f312(x37931,x37932,x37933),x37934))) % 172.78/172.47 [3823]E(f332(f189(x38231,x38232,x38233,f195(f883(x38231,a871))),x38234),f208(x38232)) % 172.78/172.47 [3844]E(f332(f312(x38441,x38442,x38443),f332(f252(x38442),x38444)),f332(f252(x38441),f332(f332(f8(x38442,a871,x38441),x38444),x38443))) % 172.78/172.47 [3862]E(f332(f332(f165(x38621),f332(f332(f134(x38621),x38622),f332(f332(f151(x38621),x38623),x38624))),f332(f196(f877(x38621)),x38622)),x38623) % 172.78/172.47 [3867]E(f332(f189(x38671,x38672,f332(f16(f880(x38672),x38671),f208(x38672)),x38673),x38674),f208(x38672)) % 172.78/172.47 [3889]E(f332(f311(x38891,x38892,x38893),f332(f312(x38891,x38892,x38893),x38894)),f332(f332(f104(f883(x38892,a871)),x38894),f332(f311(x38891,x38892,x38893),f255(f883(x38891,a871))))) % 172.78/172.47 [3907]P102(f332(f332(f334(x39071),f332(x39072,x39073)),f332(f311(x39074,x39071,x39072),f255(f883(x39074,a871))))) % 172.78/172.47 [3919]E(f332(f332(f134(x39191),f170(x39191,x39192,x39193)),f332(f332(f151(x39191),x39193),x39194)),f332(f332(f151(x39191),x39193),f332(f332(f134(x39191),f170(x39191,x39192,x39193)),x39194))) % 172.78/172.47 [3921]E(f332(f332(f269(x39211,x39212),f332(f173(x39211),x39213)),f332(f16(f883(x39212,a871),x39211),f332(f173(x39212),x39214))),f332(f173(f882(x39211,x39212)),f59(x39211,x39212,x39213,x39214))) % 172.78/172.47 [3935]E(f155(x39351,x39352,f332(f332(f151(x39351),x39353),x39354)),f332(f332(f79(a876),f332(f332(f79(a876),f332(x39352,x39353)),f155(x39351,x39352,x39354))),f332(a115,f2(a876)))) % 172.78/172.47 [3949]E(f192(f877(x39491),f332(f332(f151(x39491),x39492),x39493),f332(f332(f7(a876,f877(x39491),f877(x39491)),f138(x39491)),x39493),x39494),f332(f332(f138(x39491),x39494),f332(f332(f151(x39491),x39492),x39493))) % 172.78/172.47 [3950]P20(x39501,f882(x39502,x39501),f336(x39503,x39504,x39502,x39501),f332(f332(f41(x39502,f883(x39501,a871)),x39504),x39503)) % 172.78/172.47 [3959]E(f332(f332(f22(f883(x39591,a871)),f332(f332(f22(f883(x39591,a871)),x39592),x39593)),f332(f332(f310(x39591),x39594),f195(f883(x39591,a871)))),f332(f332(f22(f883(x39591,a871)),x39592),f332(f332(f310(x39591),x39594),x39593))) % 172.78/172.47 [3971]E(f332(f332(f190(f883(x39711,x39712),f883(x39711,x39712)),x39713),f72(x39712,x39712,x39711,x39714)),f72(x39712,x39712,x39711,f332(f332(f190(x39712,x39712),x39713),x39714))) % 172.78/172.47 [4049]E(f332(f332(f332(f190(f877(x40491),f877(x40491)),x40492),f168(x40491)),f332(f332(f332(f190(f877(x40491),f877(x40491)),x40493),f168(x40491)),x40494)),f332(f332(f332(f190(f877(x40491),f877(x40491)),f332(f332(f79(a876),x40492),x40493)),f168(x40491)),x40494)) % 172.78/172.47 [4135]P102(f332(f332(f246(f883(x41351,a871)),f332(f173(x41351),f332(f332(f159(x41351,x41352),x41353),x41354))),f332(f332(f310(x41351),x41354),f332(f173(x41351),x41352)))) % 172.78/172.47 [4171]E(f332(f332(f41(f883(x41711,a871),f883(f882(x41711,x41712),a871)),x41713),f332(f332(f7(f883(x41711,a871),f883(x41711,f883(x41712,a871)),f883(f882(x41711,x41712),a871)),f269(x41711,x41712)),x41714)),f332(f332(f269(x41711,x41712),f39(f883(x41711,a871),x41713)),x41714)) % 172.78/172.47 [4209]E(f220(x42091,x42092,x42093,f332(f72(x42092,f883(a102,f883(a102,f883(f882(a102,a102),f883(a102,f878(x42092))))),x42091,f219(x42092)),x42094)),f221(x42091,x42092,x42094,x42093)) % 172.78/172.47 [4226]E(f216(x42261,x42262,x42263,f332(f72(x42262,f883(a102,f883(a102,f883(f882(a102,a102),f883(a102,f878(f880(x42262)))))),x42261,f215(x42262)),x42264)),f217(x42261,x42262,x42264,x42263)) % 172.78/172.47 [4231]P102(f332(f66(x42311,x42312,x42313,x42314,f195(f883(x42311,a871))),x42314)) % 172.78/172.47 [4273]E(f332(f332(f41(x42731,f883(x42732,a871)),x42733),f332(f332(f7(x42731,f883(x42732,a871),f883(x42732,a871)),f332(f332(f8(x42732,f883(f883(x42732,a871),f883(x42732,a871)),x42731),f310(x42732)),x42734)),f195(f883(x42732,a871)))),f332(f311(x42731,x42732,x42734),x42733)) % 172.78/172.47 [4280]P102(f332(f332(f246(f883(x42801,a871)),f332(f263(x42802,x42801),f332(f332(f104(f883(f882(x42802,x42801),a871)),x42803),x42804))),f332(f332(f104(f883(x42801,a871)),f332(f263(x42802,x42801),x42803)),f332(f263(x42802,x42801),x42804)))) % 172.78/172.47 [4281]P102(f332(f332(f246(f883(x42811,a871)),f332(f265(x42811,x42812),f332(f332(f104(f883(f882(x42811,x42812),a871)),x42813),x42814))),f332(f332(f104(f883(x42811,a871)),f332(f265(x42811,x42812),x42813)),f332(f265(x42811,x42812),x42814)))) % 172.78/172.47 [4343]P102(f332(f332(f246(f883(f882(x43431,x43432),a871)),f332(f311(x43432,f882(x43431,x43432),f336(x43433,x43434,x43431,x43432)),f332(f332(f41(x43431,f883(x43432,a871)),x43434),x43433))),f332(f332(f269(x43431,x43432),x43434),x43433))) % 172.78/172.47 [4344]E(f332(f121(x43441,f882(x43441,x43442),x43443),f332(f332(f8(f883(x43442,f878(f882(x43441,x43442))),f878(f882(x43441,x43442)),x43441),f121(x43442,f882(x43441,x43442),x43444)),f332(f332(f8(f883(x43442,f882(x43441,x43442)),f883(x43442,f878(f882(x43441,x43442))),x43441),f332(f8(f882(x43441,x43442),f878(f882(x43441,x43442)),x43442),f126(f882(x43441,x43442)))),f267(x43441,x43442)))),f131(x43441,x43442,x43443,x43444)) % 172.78/172.47 [4384]E(f84(f882(x43841,x43842),f332(f271(x43841,x43842,a871),f332(f332(f7(x43841,f883(x43842,a871),f883(x43842,a871)),f332(f332(f8(f883(a871,a871),f883(f883(x43842,a871),f883(x43842,a871)),x43841),f8(a871,a871,x43842)),f332(f332(f8(a871,f883(a871,a871),x43841),a330),f332(a329,x43843)))),f332(a329,x43844)))),f332(f332(f267(x43841,x43842),x43843),x43844)) % 172.78/172.47 [4385]E(f89(f882(x43851,x43852),f332(f271(x43851,x43852,a871),f332(f332(f7(x43851,f883(x43852,a871),f883(x43852,a871)),f332(f332(f8(f883(a871,a871),f883(f883(x43852,a871),f883(x43852,a871)),x43851),f8(a871,a871,x43852)),f332(f332(f8(a871,f883(a871,a871),x43851),a330),f332(a329,x43853)))),f332(a329,x43854)))),f332(f332(f267(x43851,x43852),x43853),x43854)) % 172.78/172.47 [4456]E(f332(f332(f271(f877(x44561),f877(x44561),f882(f877(x44561),f877(x44561))),f332(f332(f18(f877(x44561),f883(f877(x44561),f882(f877(x44561),f877(x44561))),f883(f877(x44561),f882(f877(x44561),f877(x44561)))),f332(f332(f8(f883(f877(x44561),f883(f882(f877(x44561),f877(x44561)),f882(f877(x44561),f877(x44561)))),f883(f883(f877(x44561),f882(f877(x44561),f877(x44561))),f883(f877(x44561),f882(f877(x44561),f877(x44561)))),f877(x44561)),f18(f877(x44561),f882(f877(x44561),f877(x44561)),f882(f877(x44561),f877(x44561)))),f332(f332(f8(f883(f877(x44561),f882(f877(x44561),f877(x44561))),f883(f877(x44561),f883(f882(f877(x44561),f877(x44561)),f882(f877(x44561),f877(x44561)))),f877(x44561)),f332(f8(f882(f877(x44561),f877(x44561)),f883(f882(f877(x44561),f877(x44561)),f882(f877(x44561),f877(x44561))),f877(x44561)),f332(f99(f882(f877(x44561),f877(x44561))),f332(x44562,x44563)))),f332(f332(f8(f877(x44561),f883(f877(x44561),f882(f877(x44561),f877(x44561))),f877(x44561)),f267(f877(x44561),f877(x44561))),f332(f151(x44561),x44563))))),f332(f332(f7(f877(x44561),f883(f877(x44561),f877(x44561)),f883(f877(x44561),f882(f877(x44561),f877(x44561)))),f332(f332(f8(f883(f877(x44561),f882(f877(x44561),f877(x44561))),f883(f883(f877(x44561),f877(x44561)),f883(f877(x44561),f882(f877(x44561),f877(x44561)))),f877(x44561)),f8(f877(x44561),f882(f877(x44561),f877(x44561)),f877(x44561))),f267(f877(x44561),f877(x44561)))),f332(f151(x44561),x44563)))),f167(x44561,x44562,x44564)),f167(x44561,x44562,f332(f332(f151(x44561),x44563),x44564))) % 172.78/172.47 [4462]E(f332(f142(f883(x44621,f880(x44622)),f882(x44621,x44622),f332(f7(f882(x44621,x44622),f883(x44621,f880(x44622)),f883(x44621,f880(x44622))),f332(f271(x44621,x44622,f883(f883(x44621,f880(x44622)),f883(x44621,f880(x44622)))),f332(f332(f7(x44621,f883(x44622,f880(x44622)),f883(x44622,f883(f883(x44621,f880(x44622)),f883(x44621,f880(x44622))))),f332(f332(f8(f883(f880(x44622),f883(f883(x44621,f880(x44622)),f883(x44621,f880(x44622)))),f883(f883(x44622,f880(x44622)),f883(x44622,f883(f883(x44621,f880(x44622)),f883(x44621,f880(x44622))))),x44621),f8(f880(x44622),f883(f883(x44621,f880(x44622)),f883(x44621,f880(x44622))),x44622)),f332(f332(f8(f883(f883(x44621,f880(x44622)),f883(f880(x44622),f883(x44621,f880(x44622)))),f883(f880(x44622),f883(f883(x44621,f880(x44622)),f883(x44621,f880(x44622)))),x44621),f7(f883(x44621,f880(x44622)),f880(x44622),f883(x44621,f880(x44622)))),f332(f7(f883(x44621,f880(x44622)),x44621,f883(f880(x44622),f883(x44621,f880(x44622)))),f71(x44621,f880(x44622)))))),f239(x44622)))),x44623),f332(f169(f882(x44621,x44622)),x44624)),f186(x44621,x44622,x44623,f332(f179(x44621,x44622),x44624))) % 172.78/172.47 [3552]E(f332(f196(f875(x35521)),f332(f332(f332(f91(x35521),x35522),x35523),x35524)),f2(a876)) % 172.78/172.47 [3676]E(f332(f332(f176(x36761),x36762),f332(f332(f176(x36761),x36763),x36764)),f332(f332(f176(x36761),f332(f332(f244(a876),x36762),x36763)),x36764)) % 172.78/172.47 [3677]E(f332(f332(f138(x36771),x36772),f332(f332(f138(x36771),x36773),x36774)),f332(f332(f138(x36771),f332(f332(f79(a876),x36772),x36773)),x36774)) % 172.78/172.47 [3689]E(f332(f332(f134(x36891),f332(f332(f151(x36891),x36892),x36893)),x36894),f332(f332(f151(x36891),x36892),f332(f332(f134(x36891),x36893),x36894))) % 172.78/172.47 [3690]E(f332(f332(f134(x36901),f332(f332(f134(x36901),x36902),x36903)),x36904),f332(f332(f134(x36901),x36902),f332(f332(f134(x36901),x36903),x36904))) % 172.78/172.47 [3773]E(f332(f332(f165(x37731),f332(f332(f151(x37731),x37732),x37733)),x37734),f192(x37731,x37732,f332(f165(x37731),x37733),x37734)) % 172.78/172.47 [3782]E(f332(f332(f190(x37821,x37821),x37822),f332(f332(f190(x37821,x37821),x37823),x37824)),f332(f332(f190(x37821,x37821),f332(f332(f80(a876),x37823),x37822)),x37824)) % 172.78/172.47 [3811]E(f332(f332(f113(f883(x38111,a871)),x38112),f332(f332(f310(x38111),x38113),x38114)),f332(f332(f310(x38111),x38113),f332(f332(f113(f883(x38111,a871)),x38112),x38114))) % 172.78/172.47 [3826]E(f332(f332(f332(f190(x38261,x38261),x38262),x38263),f332(x38263,x38264)),f332(x38263,f332(f332(f332(f190(x38261,x38261),x38262),x38263),x38264))) % 172.78/172.47 [3834]E(f332(f332(f289(x38341,x38342,x38343),f195(f883(f882(x38341,x38342),a871))),x38344),f195(f883(f882(x38341,x38343),a871))) % 172.78/172.47 [3850]E(f332(f332(f113(f883(x38501,a871)),f332(f332(f310(x38501),x38502),x38503)),x38504),f332(f332(f310(x38501),x38502),f332(f332(f113(f883(x38501,a871)),x38503),x38504))) % 172.78/172.47 [3870]E(f186(x38701,x38702,f332(f179(x38701,x38702),x38703),f332(f179(x38701,x38702),x38704)),f332(f179(x38701,x38702),f332(f332(f134(f882(x38701,x38702)),x38704),x38703))) % 172.78/172.47 [3871]E(f332(f37(f882(x38711,x38712)),f332(f332(f269(x38711,x38712),x38713),f332(f16(f883(x38712,a871),x38711),x38714))),f332(f332(f80(a876),f332(f37(x38711),x38713)),f332(f37(x38712),x38714))) % 172.78/172.47 [3878]E(f332(f332(f104(f883(x38781,a871)),f332(f332(f310(x38781),x38782),x38783)),f332(f332(f310(x38781),x38782),x38784)),f332(f332(f310(x38781),x38782),f332(f332(f104(f883(x38781,a871)),x38783),x38784))) % 172.78/172.47 [3893]E(f332(f332(f113(f883(x38931,a871)),x38932),f332(f332(f113(f883(x38931,a871)),x38933),x38934)),f332(f332(f113(f883(x38931,a871)),x38933),f332(f332(f113(f883(x38931,a871)),x38932),x38934))) % 172.78/172.47 [3894]E(f332(f332(f104(f883(x38941,a871)),x38942),f332(f332(f104(f883(x38941,a871)),x38943),x38944)),f332(f332(f104(f883(x38941,a871)),x38943),f332(f332(f104(f883(x38941,a871)),x38942),x38944))) % 172.78/172.47 [3903]E(f64(x39031,x39032,f332(f332(f8(x39032,f883(x39032,x39032),x39031),x39033),x39034)),f332(f65(x39032,x39031,x39033),x39034)) % 172.78/172.47 [3913]E(f181(x39131,f332(f332(f154(f877(x39132),f877(x39131)),f332(f154(x39132,x39131),x39133)),x39134)),f332(f332(f154(f877(x39132),f877(x39131)),f332(f154(x39132,x39131),x39133)),f181(x39132,x39134))) % 172.78/172.47 [3931]E(f332(f142(f877(x39311),f877(x39311),f134(x39311),f116(x39311)),f332(f332(f154(x39312,f877(x39311)),x39313),x39314)),f164(x39312,x39311,x39313,x39314)) % 172.78/172.47 [3934]E(f189(x39341,x39342,x39343,f332(f78(f883(x39341,a871)),f332(f332(f310(x39341),x39344),f195(f883(x39341,a871))))),f332(f332(f332(f71(x39341,f880(x39342)),x39343),x39344),f208(x39342))) % 172.78/172.47 [3976]E(f332(f332(f332(f71(x39761,f880(x39762)),f332(f179(x39761,x39762),x39763)),f332(f266(x39761,x39762),x39764)),f332(f239(x39762),f332(f270(x39761,x39762),x39764))),f332(f179(x39761,x39762),f332(f332(f151(f882(x39761,x39762)),x39764),x39763))) % 172.78/172.47 [3993]E(f332(f72(x39931,x39931,x39931,f332(f332(f190(x39931,x39931),x39932),x39933)),f332(f332(f190(x39931,x39931),x39934),x39933)),f332(f332(f190(x39931,x39931),f332(f332(f79(a876),x39932),x39934)),x39933)) % 172.78/172.47 [4018]E(f332(f332(f104(f883(x40181,a871)),f332(f332(f113(f883(x40181,a871)),x40182),x40183)),f332(f332(f113(f883(x40181,a871)),x40182),x40184)),f332(f332(f113(f883(x40181,a871)),x40182),f332(f332(f104(f883(x40181,a871)),x40183),x40184))) % 172.78/172.47 [4019]E(f332(f332(f104(f883(x40191,a871)),f332(f332(f22(f883(x40191,a871)),x40192),x40193)),f332(f332(f22(f883(x40191,a871)),x40192),x40194)),f332(f332(f22(f883(x40191,a871)),x40192),f332(f332(f113(f883(x40191,a871)),x40193),x40194))) % 172.78/172.47 [4020]E(f332(f332(f113(f883(x40201,a871)),f332(f332(f22(f883(x40201,a871)),x40202),x40203)),f332(f332(f22(f883(x40201,a871)),x40202),x40204)),f332(f332(f22(f883(x40201,a871)),x40202),f332(f332(f104(f883(x40201,a871)),x40203),x40204))) % 172.78/172.47 [4021]E(f332(f332(f113(f883(x40211,a871)),f332(f332(f104(f883(x40211,a871)),x40212),x40213)),f332(f332(f104(f883(x40211,a871)),x40212),x40214)),f332(f332(f104(f883(x40211,a871)),x40212),f332(f332(f113(f883(x40211,a871)),x40213),x40214))) % 172.78/172.47 [4022]E(f332(f332(f22(f883(x40221,a871)),f332(f332(f104(f883(x40221,a871)),x40222),x40223)),f332(f332(f104(f883(x40221,a871)),x40222),x40224)),f332(f332(f104(f883(x40221,a871)),x40222),f332(f332(f22(f883(x40221,a871)),x40223),x40224))) % 172.78/172.47 [4028]E(f332(f37(f882(x40281,x40282)),f332(f332(f269(x40281,x40282),f332(f332(f310(x40281),x40283),f195(f883(x40281,a871)))),f332(f16(f883(x40282,a871),x40281),x40284))),f332(f37(x40282),x40284)) % 172.78/172.47 [4064]E(f332(f332(f42(x40641,f883(x40642,a871)),x40643),f332(f332(f8(f883(x40642,a871),f883(x40642,a871),x40641),f78(f883(x40642,a871))),x40644)),f332(f78(f883(x40642,a871)),f332(f332(f41(x40641,f883(x40642,a871)),x40643),x40644))) % 172.78/172.47 [4065]E(f332(f332(f41(x40651,f883(x40652,a871)),x40653),f332(f332(f8(f883(x40652,a871),f883(x40652,a871),x40651),f78(f883(x40652,a871))),x40654)),f332(f78(f883(x40652,a871)),f332(f332(f42(x40651,f883(x40652,a871)),x40653),x40654))) % 172.78/172.47 [4079]E(f332(f332(f289(x40791,x40791,x40791),f332(f332(f190(f882(x40791,x40791),a871),x40792),x40793)),f332(f332(f190(f882(x40791,x40791),a871),x40794),x40793)),f332(f332(f190(f882(x40791,x40791),a871),f332(f332(f79(a876),x40792),x40794)),x40793)) % 172.78/172.47 [4110]E(f332(f332(f42(x41101,f883(f883(x41102,a871),a871)),x41103),f332(f332(f8(f883(x41102,a871),f883(f883(x41102,a871),a871),x41101),f309(x41102)),x41104)),f332(f309(x41102),f332(f332(f42(x41101,f883(x41102,a871)),x41103),x41104))) % 172.78/172.47 [4139]E(f332(f332(f41(f883(x41391,a871),f883(x41392,a871)),x41393),f332(f332(f7(f883(x41391,a871),f883(x41391,f883(x41392,a871)),f883(x41392,a871)),f41(x41391,f883(x41392,a871))),x41394)),f332(f332(f41(x41391,f883(x41392,a871)),f39(f883(x41391,a871),x41393)),x41394)) % 172.78/172.47 [4140]E(f332(f332(f42(f883(x41401,a871),f883(x41402,a871)),x41403),f332(f332(f7(f883(x41401,a871),f883(x41401,f883(x41402,a871)),f883(x41402,a871)),f42(x41401,f883(x41402,a871))),x41404)),f332(f332(f42(x41401,f883(x41402,a871)),f39(f883(x41401,a871),x41403)),x41404)) % 172.78/172.47 [4145]E(f332(f332(f154(x41451,x41452),x41453),f332(f142(f877(x41451),f877(x41451),f134(x41451),f116(x41451)),x41454)),f332(f142(f877(x41452),f877(x41452),f134(x41452),f116(x41452)),f332(f332(f154(f877(x41451),f877(x41452)),f332(f154(x41451,x41452),x41453)),x41454))) % 172.78/172.47 [4149]E(f192(f877(x41491),f116(x41491),f332(f332(f8(f877(x41491),f877(x41491),a876),f332(f151(x41491),x41492)),f332(f332(f7(a876,f877(x41491),f877(x41491)),f176(x41491)),x41493)),x41494),f332(f332(f176(x41491),x41494),f332(f332(f151(x41491),x41492),x41493))) % 172.78/172.47 [4191]P102(f332(f332(f246(f883(x41911,a871)),f332(f311(x41912,x41911,x41913),f332(f312(x41912,x41911,x41913),x41914))),x41914)) % 172.78/172.47 [4194]E(f332(f311(f882(x41941,x41942),f882(x41942,x41941),f332(f271(x41941,x41942,f882(x41942,x41941)),f332(f7(x41942,x41941,f882(x41942,x41941)),f267(x41942,x41941)))),f332(f332(f269(x41941,x41942),x41943),f332(f16(f883(x41942,a871),x41941),x41944))),f332(f332(f269(x41942,x41941),x41944),f332(f16(f883(x41941,a871),x41942),x41943))) % 172.78/172.47 [4203]E(f332(f332(f41(x42031,f883(x42032,a871)),x42033),f332(f332(f8(f883(x42031,a871),f883(x42032,a871),x42031),f286(x42031,x42032,x42034)),f332(f332(f7(x42031,f883(x42031,a871),f883(x42031,a871)),f310(x42031)),f195(f883(x42031,a871))))),f332(f286(x42031,x42032,x42034),x42033)) % 172.78/172.47 [4204]E(f332(f332(f41(x42041,f883(x42042,a871)),x42043),f332(f332(f8(f883(x42041,a871),f883(x42042,a871),x42041),f312(x42042,x42041,x42044)),f332(f332(f7(x42041,f883(x42041,a871),f883(x42041,a871)),f310(x42041)),f195(f883(x42041,a871))))),f332(f312(x42042,x42041,x42044),x42043)) % 172.78/172.47 [4295]E(f332(f332(f113(f883(x42951,a871)),f332(f332(f113(f883(x42951,a871)),f332(f332(f104(f883(x42951,a871)),x42952),x42953)),f332(f332(f104(f883(x42951,a871)),x42953),x42954))),f332(f332(f104(f883(x42951,a871)),x42954),x42952)),f332(f332(f104(f883(x42951,a871)),f332(f332(f104(f883(x42951,a871)),f332(f332(f113(f883(x42951,a871)),x42952),x42953)),f332(f332(f113(f883(x42951,a871)),x42953),x42954))),f332(f332(f113(f883(x42951,a871)),x42954),x42952))) % 172.78/172.47 [4357]E(f332(f142(f877(x43571),f877(x43571),f134(x43571),f116(x43571)),f332(f332(f154(x43572,f877(x43571)),f332(f332(f7(x43572,f877(x43571),f877(x43571)),f332(f332(f8(x43571,f883(f877(x43571),f877(x43571)),x43572),f151(x43571)),x43573)),f116(x43571))),x43574)),f332(f332(f154(x43572,x43571),x43573),x43574)) % 172.78/172.47 [4368]E(f332(f332(f85(a1,x43681),f332(f106(a1),f332(f332(f79(a1),x43682),a100))),f332(f332(f18(a1,x43681,x43681),f332(f332(f7(a1,x43681,f883(x43681,x43681)),f332(f332(f8(a871,f883(x43681,f883(x43681,x43681)),a1),f99(x43681)),a200)),x43683)),f332(f332(f8(a876,x43681,a1),x43684),a107))),f192(x43681,x43683,x43684,f332(f106(a876),x43682))) % 172.78/172.47 [4570]~P102(f332(f332(f195(f883(x45701,f883(x45702,a871))),x45703),x45704)) % 172.78/172.47 [3837]E(f332(f332(f165(x38371),f332(f332(f134(x38371),x38372),x38373)),f332(f332(f79(a876),f332(f196(f877(x38371)),x38372)),x38374)),f332(f332(f165(x38371),x38373),x38374)) % 172.78/172.47 [3843]E(f332(f332(f138(x38431),x38432),f332(f332(f176(x38431),f332(f332(f79(a876),x38433),x38432)),x38434)),f332(f332(f176(x38431),x38433),f332(f332(f138(x38431),x38432),x38434))) % 172.78/172.47 [3947]E(f332(f332(f113(f883(x39471,a871)),f332(f263(x39472,x39471),x39473)),f332(f263(x39472,x39471),x39474)),f332(f263(x39472,x39471),f332(f332(f113(f883(f882(x39472,x39471),a871)),x39473),x39474))) % 172.78/172.47 [3948]E(f332(f332(f113(f883(x39481,a871)),f332(f265(x39481,x39482),x39483)),f332(f265(x39481,x39482),x39484)),f332(f265(x39481,x39482),f332(f332(f113(f883(f882(x39481,x39482),a871)),x39483),x39484))) % 172.78/172.47 [3953]E(f332(f332(f113(f883(x39531,a871)),f332(f332(f113(f883(x39531,a871)),x39532),x39533)),x39534),f332(f332(f113(f883(x39531,a871)),x39532),f332(f332(f113(f883(x39531,a871)),x39533),x39534))) % 172.78/172.47 [3954]E(f332(f332(f22(f883(x39541,a871)),f332(f332(f104(f883(x39541,a871)),x39542),x39543)),x39544),f332(f332(f104(f883(x39541,a871)),x39542),f332(f332(f22(f883(x39541,a871)),x39543),x39544))) % 172.78/172.47 [3955]E(f332(f332(f104(f883(x39551,a871)),f332(f332(f104(f883(x39551,a871)),x39552),x39553)),x39554),f332(f332(f104(f883(x39551,a871)),x39552),f332(f332(f104(f883(x39551,a871)),x39553),x39554))) % 172.78/172.47 [3995]E(f332(f332(f113(f883(f882(x39951,x39952),a871)),f332(f287(x39952,x39951),x39953)),f332(f287(x39952,x39951),x39954)),f332(f287(x39952,x39951),f332(f332(f113(f883(f882(x39952,x39951),a871)),x39953),x39954))) % 172.78/172.47 [3996]E(f332(f332(f104(f883(f882(x39961,x39962),a871)),f332(f287(x39962,x39961),x39963)),f332(f287(x39962,x39961),x39964)),f332(f287(x39962,x39961),f332(f332(f104(f883(f882(x39962,x39961),a871)),x39963),x39964))) % 172.78/172.47 [4010]E(f332(f332(f113(f883(x40101,f883(x40102,a871))),f256(x40102,x40101,x40103)),f256(x40102,x40101,x40104)),f256(x40102,x40101,f332(f332(f113(f883(x40102,f883(x40101,a871))),x40103),x40104))) % 172.78/172.47 [4011]E(f332(f332(f104(f883(x40111,f883(x40112,a871))),f256(x40112,x40111,x40113)),f256(x40112,x40111,x40114)),f256(x40112,x40111,f332(f332(f104(f883(x40112,f883(x40111,a871))),x40113),x40114))) % 172.78/172.47 [4068]E(f332(f332(f104(f883(x40681,a871)),f332(f332(f113(f883(x40681,a871)),x40682),x40683)),f332(f332(f113(f883(x40681,a871)),x40684),x40683)),f332(f332(f113(f883(x40681,a871)),f332(f332(f104(f883(x40681,a871)),x40682),x40684)),x40683)) % 172.78/172.47 [4069]E(f332(f332(f113(f883(x40691,a871)),f332(f332(f22(f883(x40691,a871)),x40692),x40693)),f332(f332(f22(f883(x40691,a871)),x40694),x40693)),f332(f332(f22(f883(x40691,a871)),f332(f332(f113(f883(x40691,a871)),x40692),x40694)),x40693)) % 172.78/172.47 [4070]E(f332(f332(f113(f883(x40701,a871)),f332(f332(f104(f883(x40701,a871)),x40702),x40703)),f332(f332(f104(f883(x40701,a871)),x40704),x40703)),f332(f332(f104(f883(x40701,a871)),f332(f332(f113(f883(x40701,a871)),x40702),x40704)),x40703)) % 172.78/172.47 [4071]E(f332(f332(f22(f883(x40711,a871)),f332(f332(f104(f883(x40711,a871)),x40712),x40713)),f332(f332(f104(f883(x40711,a871)),x40714),x40713)),f332(f332(f104(f883(x40711,a871)),f332(f332(f22(f883(x40711,a871)),x40712),x40714)),x40713)) % 172.78/172.47 [4072]E(f332(f332(f22(f883(x40721,a871)),f332(f332(f104(f883(x40721,a871)),x40722),x40723)),f332(f332(f104(f883(x40721,a871)),x40724),x40723)),f332(f332(f22(f883(x40721,a871)),f332(f332(f104(f883(x40721,a871)),x40722),x40723)),x40724)) % 172.78/172.47 [4082]E(f332(f332(f22(f883(x40821,a871)),f332(f332(f22(f883(x40821,a871)),x40822),f332(f332(f310(x40821),x40823),f195(f883(x40821,a871))))),x40824),f332(f332(f22(f883(x40821,a871)),x40822),f332(f332(f310(x40821),x40823),x40824))) % 172.78/172.47 [4136]E(f332(f332(f113(f883(x41361,a871)),f332(f332(f310(x41361),x41362),f332(f332(f310(x41361),x41363),f195(f883(x41361,a871))))),f332(f285(x41361),x41364)),f332(f285(x41361),f332(f332(f310(f882(x41361,x41361)),f332(f332(f267(x41361,x41361),x41362),x41363)),x41364))) % 172.78/172.47 [4166]E(f332(f332(f41(a876,f883(x41661,a871)),f332(f301(a876),x41662)),f332(f332(f8(a876,f883(x41661,a871),a876),x41663),f332(f332(f7(a876,a876,a876),f79(a876)),x41664))),f332(f332(f41(a876,f883(x41661,a871)),f303(a876,x41664,f332(f332(f79(a876),x41662),x41664))),x41663)) % 172.78/172.47 [4167]E(f175(x41671,f332(f286(x41671,x41671,x41672),f332(f332(f310(x41671),x41673),f195(f883(x41671,a871)))),f332(f286(f877(x41671),f877(x41671),f158(x41671,x41672)),f332(f332(f310(f877(x41671)),x41674),f195(f883(f877(x41671),a871))))),f332(f286(f877(x41671),f877(x41671),f158(x41671,x41672)),f332(f332(f310(f877(x41671)),f332(f332(f151(x41671),x41673),x41674)),f195(f883(f877(x41671),a871))))) % 172.78/172.47 [4229]E(f332(f179(x42291,x42292),f332(f332(f154(x42291,f882(x42291,x42292)),f332(f332(f18(x42291,x42292,f882(x42291,x42292)),f267(x42291,x42292)),x42293)),x42294)),f189(x42291,x42292,f332(f72(x42292,f880(x42292),x42291,f239(x42292)),x42293),f332(f173(x42291),x42294))) % 172.78/172.47 [4234]E(f332(f252(x42341),f332(f332(f7(x42341,f883(x42342,a871),a871),f332(f332(f8(x42342,f883(f883(x42342,a871),a871),x42341),f334(x42342)),x42343)),x42344)),f332(f312(x42341,x42342,x42343),x42344)) % 172.78/172.47 [4328]E(f332(f252(x43281),f332(f332(f7(x43281,f883(f882(x43282,x43281),a871),a871),f332(f332(f8(f882(x43282,x43281),f883(f883(f882(x43282,x43281),a871),a871),x43281),f334(f882(x43282,x43281))),f332(f267(x43282,x43281),x43283))),x43284)),f332(f286(x43282,x43281,x43284),f332(f332(f310(x43282),x43283),f195(f883(x43282,a871))))) % 172.78/172.47 [4342]E(f332(f332(f154(f882(x43421,a876),x43421),f266(x43421,a876)),f332(f136(f882(x43421,a876),f332(f332(f8(a876,a871,f882(x43421,a876)),x43422),f332(f332(f8(a876,a876,f882(x43421,a876)),a115),f270(x43421,a876)))),f332(f332(f183(x43421,a876),x43423),x43424))),f332(f332(f154(f882(x43421,a876),x43421),f266(x43421,a876)),f332(f136(f882(x43421,a876),f332(f332(f8(a876,a871,f882(x43421,a876)),x43422),f270(x43421,a876))),f332(f332(f183(x43421,a876),x43423),f332(f332(f154(a876,a876),a115),x43424))))) % 172.78/172.47 [4350]P102(f332(f332(f246(f883(f883(x43501,a871),a871)),f332(f332(f41(x43502,f883(f883(x43501,a871),a871)),x43503),f332(f332(f8(f883(x43501,a871),f883(f883(x43501,a871),a871),x43502),f309(x43501)),x43504))),f332(f309(x43501),f332(f332(f41(x43502,f883(x43501,a871)),x43503),x43504)))) % 172.78/172.47 [4392]E(f332(f332(f85(a1,x43921),f332(f106(a1),f332(f332(f79(a1),x43922),a100))),f332(f332(f18(a1,x43921,x43921),f332(f332(f7(a1,x43921,f883(x43921,x43921)),f332(f332(f8(a871,f883(x43921,f883(x43921,x43921)),a1),f99(x43921)),a200)),x43923)),f332(f332(f18(a1,x43921,x43921),f332(f332(f8(a876,f883(x43921,x43921),a1),x43924),a107)),f332(f332(f8(a876,x43921,a1),f191(x43921,x43923,x43924)),a107)))),f332(f191(x43921,x43923,x43924),f332(f106(a876),x43922))) % 172.78/172.47 [4395]E(f332(f332(f154(x43951,x43952),f332(f72(f880(x43952),x43952,x43951,f243(x43952)),x43953)),f332(f136(x43951,f332(f332(f8(a871,a871,x43951),a327),f332(f332(f7(x43951,f880(x43952),a871),f332(f332(f8(f880(x43952),f883(f880(x43952),a871),x43951),a329),x43953)),f208(x43952)))),x43954)),f163(x43951,x43952,x43953,x43954)) % 172.78/172.47 [4418]E(f332(f252(f882(x44181,x44182)),f332(f271(x44181,x44182,a871),f332(f332(f7(x44181,f883(x44182,a871),f883(x44182,a871)),f332(f332(f8(f883(a871,a871),f883(f883(x44182,a871),f883(x44182,a871)),x44181),f8(a871,a871,x44182)),f332(f332(f8(a871,f883(a871,a871),x44181),a330),f332(f332(f7(x44181,f883(x44181,a871),a871),f334(x44181)),x44183)))),f332(f332(f7(x44182,f883(x44182,a871),a871),f334(x44182)),x44184)))),f233(x44181,x44182,x44183,x44184)) % 172.78/172.47 [4451]E(f332(f332(f41(x44511,f883(f882(x44511,x44512),a871)),x44513),f332(f332(f18(x44511,f883(x44512,f883(f882(x44511,x44512),a871)),f883(f882(x44511,x44512),a871)),f332(f332(f8(f883(x44512,a871),f883(f883(x44512,f883(f882(x44511,x44512),a871)),f883(f882(x44511,x44512),a871)),x44511),f41(x44512,f883(f882(x44511,x44512),a871))),x44514)),f332(f332(f7(x44511,f883(f882(x44511,x44512),a871),f883(x44512,f883(f882(x44511,x44512),a871))),f332(f332(f8(f883(x44512,f883(f883(f882(x44511,x44512),a871),f883(f882(x44511,x44512),a871))),f883(f883(f882(x44511,x44512),a871),f883(x44512,f883(f882(x44511,x44512),a871))),x44511),f7(x44512,f883(f882(x44511,x44512),a871),f883(f882(x44511,x44512),a871))),f332(f332(f8(f883(x44512,f882(x44511,x44512)),f883(x44512,f883(f883(f882(x44511,x44512),a871),f883(f882(x44511,x44512),a871))),x44511),f332(f8(f882(x44511,x44512),f883(f883(f882(x44511,x44512),a871),f883(f882(x44511,x44512),a871)),x44512),f310(f882(x44511,x44512)))),f267(x44511,x44512)))),f195(f883(f882(x44511,x44512),a871))))),f332(f332(f269(x44511,x44512),x44513),x44514)) % 172.78/172.47 [4005]E(f332(f332(f134(x40051),f332(f332(f176(x40051),x40052),x40053)),f332(f332(f176(x40051),f332(f332(f22(a876),x40052),f332(f196(f877(x40051)),x40053))),x40054)),f332(f332(f176(x40051),x40052),f332(f332(f134(x40051),x40053),x40054))) % 172.78/172.47 [4006]E(f332(f332(f134(x40061),f332(f332(f138(x40061),x40062),x40063)),f332(f332(f138(x40061),f332(f332(f22(a876),x40062),f332(f196(f877(x40061)),x40063))),x40064)),f332(f332(f138(x40061),x40062),f332(f332(f134(x40061),x40063),x40064))) % 172.78/172.47 [4058]E(f332(f332(f79(a876),f332(f332(f80(a876),x40581),x40582)),f332(f332(f79(a876),f332(f332(f80(a876),x40583),x40582)),x40584)),f332(f332(f79(a876),f332(f332(f80(a876),f332(f332(f79(a876),x40581),x40583)),x40582)),x40584)) % 172.78/172.47 [4259]P102(f332(f332(f246(f883(x42591,a871)),f332(f332(f22(f883(x42591,a871)),f332(f263(x42592,x42591),x42593)),f332(f263(x42592,x42591),x42594))),f332(f263(x42592,x42591),f332(f332(f22(f883(f882(x42592,x42591),a871)),x42593),x42594)))) % 172.78/172.47 [4260]P102(f332(f332(f246(f883(x42601,a871)),f332(f332(f22(f883(x42601,a871)),f332(f265(x42601,x42602),x42603)),f332(f265(x42601,x42602),x42604))),f332(f265(x42601,x42602),f332(f332(f22(f883(f882(x42601,x42602),a871)),x42603),x42604)))) % 172.78/172.47 [4370]E(f332(f332(f79(a1),f332(a88,f332(f286(f882(a876,a876),f882(a876,a876),a111),f332(f332(f310(f882(a876,a876)),f332(f332(f267(a876,a876),x43701),x43702)),f195(f883(f882(a876,a876),a871)))))),f332(a88,f332(f286(f882(a876,a876),f882(a876,a876),a111),f332(f332(f310(f882(a876,a876)),f332(f332(f267(a876,a876),x43703),x43704)),f195(f883(f882(a876,a876),a871)))))),f332(a88,f332(f286(f882(a876,a876),f882(a876,a876),a111),f332(f332(f310(f882(a876,a876)),f332(f332(f267(a876,a876),f332(f332(f79(a876),x43701),x43703)),f332(f332(f79(a876),x43702),x43704))),f195(f883(f882(a876,a876),a871)))))) % 172.78/172.47 [4413]E(f332(f332(f80(a1),f332(a88,f332(f286(f882(a876,a876),f882(a876,a876),a111),f332(f332(f310(f882(a876,a876)),f332(f332(f267(a876,a876),x44131),x44132)),f195(f883(f882(a876,a876),a871)))))),f332(a88,f332(f286(f882(a876,a876),f882(a876,a876),a111),f332(f332(f310(f882(a876,a876)),f332(f332(f267(a876,a876),x44133),x44134)),f195(f883(f882(a876,a876),a871)))))),f332(a88,f332(f286(f882(a876,a876),f882(a876,a876),a111),f332(f332(f310(f882(a876,a876)),f332(f332(f267(a876,a876),f332(f332(f79(a876),f332(f332(f80(a876),x44131),x44133)),f332(f332(f80(a876),x44132),x44134))),f332(f332(f79(a876),f332(f332(f80(a876),x44131),x44134)),f332(f332(f80(a876),x44132),x44133)))),f195(f883(f882(a876,a876),a871)))))) % 172.78/172.47 [4433]E(f332(f252(x44331),f332(f332(f8(f883(x44332,a871),a871,x44331),f87(x44332)),f332(f332(f8(f883(x44332,a871),f883(x44332,a871),x44331),f332(f18(x44332,a871,a871),f332(f332(f8(a871,f883(a871,a871),x44332),a335),f332(f332(f7(x44332,f883(x44332,a871),a871),f334(x44332)),x44333)))),f332(f332(f7(x44331,f883(x44332,f883(x44331,a871)),f883(x44332,a871)),f332(f332(f8(f883(f883(x44331,a871),a871),f883(f883(x44332,f883(x44331,a871)),f883(x44332,a871)),x44331),f8(f883(x44331,a871),a871,x44332)),f334(x44331))),x44334)))),f332(f332(f42(x44332,f883(x44331,a871)),x44333),x44334)) % 172.78/172.47 [4466]E(f332(f332(f289(x44661,x44661,x44661),f332(f332(f310(f882(x44661,x44661)),f332(f332(f267(x44661,x44661),x44662),x44663)),x44664)),f308(x44661,f332(f332(f310(f882(x44661,x44661)),f332(f332(f267(x44661,x44661),x44662),x44663)),x44664))),f332(f332(f113(f883(f882(x44661,x44661),a871)),f332(f332(f289(x44661,x44661,x44661),x44664),f308(x44661,x44664))),f332(f252(f882(x44661,x44661)),f332(f271(x44661,x44661,a871),f332(f332(f7(x44661,f883(x44661,a871),f883(x44661,a871)),f332(f332(f8(f883(a871,a871),f883(f883(x44661,a871),f883(x44661,a871)),x44661),f8(a871,a871,x44661)),f332(f332(f8(a871,f883(a871,a871),x44661),a330),f332(f332(f7(x44661,f883(f882(x44661,x44661),a871),a871),f332(f332(f8(f882(x44661,x44661),f883(f883(f882(x44661,x44661),a871),a871),x44661),f334(f882(x44661,x44661))),f332(f332(f7(x44661,x44661,f882(x44661,x44661)),f267(x44661,x44661)),x44662))),f308(x44661,x44664))))),f332(f332(f7(x44661,f883(f882(x44661,x44661),a871),a871),f332(f332(f8(f882(x44661,x44661),f883(f883(f882(x44661,x44661),a871),a871),x44661),f334(f882(x44661,x44661))),f332(f267(x44661,x44661),x44663))),f308(x44661,x44664))))))) % 172.78/172.47 [4261]E(f332(f136(x42611,f332(f332(f18(x42611,a871,a871),f332(f332(f8(a871,f883(a871,a871),x42611),a330),x42612)),x42613)),x42614),f332(f136(x42611,x42613),f332(f136(x42611,x42612),x42614))) % 172.78/172.47 [4364]E(f332(f332(f134(x43641),f332(f332(f332(f99(f877(x43641)),f332(f332(f334(a876),f2(a876)),x43642)),f332(f332(f151(x43641),x43643),f116(x43641))),f116(x43641))),f177(x43641,x43644,f332(f252(a876),f332(f332(f7(a876,f883(a876,a871),a871),f332(f332(f8(a876,f883(f883(a876,a871),a871),a876),f334(a876)),a115)),x43642)))),f177(x43641,f332(f332(f151(x43641),x43643),x43644),x43642)) % 172.78/172.47 [4460]E(f332(f252(f882(x44601,x44602)),f332(f332(f8(f883(a876,a871),a871,f882(x44601,x44602)),f86(a876)),f332(f332(f7(f882(x44601,x44602),f883(a876,a871),f883(a876,a871)),f332(f332(f8(f883(a876,f883(a871,a871)),f883(f883(a876,a871),f883(a876,a871)),f882(x44601,x44602)),f18(a876,a871,a871)),f332(f332(f8(f883(a876,a871),f883(a876,f883(a871,a871)),f882(x44601,x44602)),f332(f8(a871,f883(a871,a871),a876),a330)),f332(f332(f7(f882(x44601,x44602),f883(a876,f882(x44601,x44602)),f883(a876,a871)),f332(f332(f8(f883(f882(x44601,x44602),a871),f883(f883(a876,f882(x44601,x44602)),f883(a876,a871)),f882(x44601,x44602)),f8(f882(x44601,x44602),a871,a876)),a329)),f332(f332(f18(a876,x44602,f882(x44601,x44602)),f332(f332(f8(x44601,f883(x44602,f882(x44601,x44602)),a876),f267(x44601,x44602)),f332(f165(x44601),x44603))),f332(f165(x44602),x44604)))))),f332(f332(f7(a876,a876,a871),f247(a876)),f332(f332(f244(a876),f332(f196(f877(x44601)),x44603)),f332(f196(f877(x44602)),x44604)))))),f332(f173(f882(x44601,x44602)),f332(f332(f183(x44601,x44602),x44603),x44604))) % 172.78/172.47 [4383]E(f332(f252(f882(x43831,x43832)),f332(f271(x43831,x43832,a871),f332(f332(f7(x43831,f883(x43832,a871),f883(x43832,a871)),f332(f332(f8(f883(a871,a871),f883(f883(x43832,a871),f883(x43832,a871)),x43831),f8(a871,a871,x43832)),f332(f332(f8(a871,f883(a871,a871),x43831),a330),x43833))),x43834))),f332(f332(f269(x43831,x43832),f332(f252(x43831),x43833)),f332(f16(f883(x43832,a871),x43831),f332(f252(x43832),x43834)))) % 172.78/172.47 [4386]E(f332(f252(f882(x43861,x43862)),f332(f271(x43861,x43862,a871),f332(f332(f18(x43861,f883(x43862,a871),f883(x43862,a871)),f332(f332(f8(f883(a871,a871),f883(f883(x43862,a871),f883(x43862,a871)),x43861),f8(a871,a871,x43862)),f332(f332(f8(a871,f883(a871,a871),x43861),a330),x43863))),x43864))),f332(f332(f269(x43861,x43862),f332(f252(x43861),x43863)),f332(f332(f8(f883(x43862,a871),f883(x43862,a871),x43861),f252(x43862)),x43864))) % 172.78/172.47 [4402]E(f332(f252(x44021),f332(f332(f8(f883(x44022,a871),a871,x44021),f87(x44022)),f332(f332(f8(f883(x44022,a871),f883(x44022,a871),x44021),f332(f18(x44022,a871,a871),f332(f332(f8(a871,f883(a871,a871),x44022),a335),f332(f332(f7(x44022,f883(x44022,a871),a871),f334(x44022)),x44023)))),x44024))),f332(f332(f42(x44022,f883(x44021,a871)),x44023),f332(f332(f8(f883(x44021,a871),f883(x44021,a871),x44022),f252(x44021)),f332(f7(x44021,x44022,a871),x44024)))) % 172.78/172.47 [4446]E(f332(f332(f154(f882(x44461,a876),x44461),f266(x44461,a876)),f332(f136(f882(x44461,a876),f332(f332(f7(f882(x44461,a876),f883(a876,a871),a871),f332(f332(f8(a876,f883(f883(a876,a871),a871),f882(x44461,a876)),f334(a876)),f270(x44461,a876))),x44462)),f332(f332(f183(x44461,a876),x44463),f139(a876,f332(f302(a876,x44464),f332(f332(f79(a876),x44464),f332(f196(f877(x44461)),x44463))))))),f332(f332(f154(f882(x44461,a876),x44461),f266(x44461,a876)),f332(f136(f882(x44461,a876),f332(f332(f7(f882(x44461,a876),f883(a876,a871),a871),f332(f332(f8(a876,f883(f883(a876,a871),a871),f882(x44461,a876)),f334(a876)),f332(f332(f7(f882(x44461,a876),a876,a876),f332(f332(f8(a876,f883(a876,a876),f882(x44461,a876)),f79(a876)),f270(x44461,a876))),x44464))),x44462)),f332(f332(f183(x44461,a876),x44463),f139(a876,f332(f302(a876,f2(a876)),f332(f196(f877(x44461)),x44463))))))) % 172.78/172.47 [4447]E(f332(a115,f332(f332(f245(a876),f332(f196(f877(x44471)),x44472)),f332(f142(a876,f877(x44473),f332(f7(f877(x44473),a876,a876),f332(f332(f8(a876,f883(a876,a876),f877(x44473)),f245(a876)),f332(f332(f7(f877(x44473),a876,a876),f332(f332(f8(a876,f883(a876,a876),f877(x44473)),f22(a876)),f196(f877(x44473)))),f332(a115,f2(a876))))),f2(a876)),f332(f169(f877(x44473)),f332(f136(f877(x44473),f332(f332(f8(a871,a871,f877(x44473)),a327),f332(f332(f7(f877(x44473),f877(x44473),a871),a329),f116(x44473)))),x44474))))),f332(f332(f245(a876),f332(a115,f332(f196(f877(x44471)),x44472))),f332(f142(a876,f877(x44473),f332(f7(f877(x44473),a876,a876),f332(f332(f8(a876,f883(a876,a876),f877(x44473)),f245(a876)),f196(f877(x44473)))),f2(a876)),f332(f169(f877(x44473)),x44474)))) % 172.78/172.47 [4401]E(f332(f332(f134(x44011),f177(x44011,x44012,x44013)),f177(x44011,x44014,f332(f252(a876),f332(f332(f7(a876,f883(a876,a871),a871),f332(f332(f8(a876,f883(f883(a876,a871),a871),a876),f334(a876)),f332(f332(f7(a876,a876,a876),f79(a876)),f332(f196(f877(x44011)),x44012)))),x44013)))),f177(x44011,f332(f332(f134(x44011),x44012),x44014),x44013)) % 172.78/172.47 [4453]E(f332(f332(f151(f877(x44531)),f332(f332(f151(x44531),x44532),f332(f142(f877(x44531),f877(x44531),f134(x44531),f116(x44531)),f332(f332(f154(f877(x44531),f877(x44531)),f156(f877(x44531),x44531,f116(x44531),f332(f332(f8(f877(x44531),f883(f877(x44531),f877(x44531)),x44531),f16(f877(x44531),f877(x44531))),f332(f332(f7(x44531,f877(x44531),f877(x44531)),f151(x44531)),f116(x44531))))),x44533)))),f181(x44531,f332(f332(f151(f877(x44531)),x44534),f332(f142(f877(f877(x44531)),f877(f877(x44531)),f134(f877(x44531)),f116(f877(x44531))),f332(f332(f154(f877(x44531),f877(f877(x44531))),f156(f877(f877(x44531)),x44531,f116(f877(x44531)),f332(f16(f883(f877(x44531),f877(f877(x44531))),x44531),f332(f332(f7(f877(x44531),f877(f877(x44531)),f877(f877(x44531))),f151(f877(x44531))),f116(f877(x44531)))))),x44533))))),f181(x44531,f332(f332(f151(f877(x44531)),f332(f332(f151(x44531),x44532),x44534)),x44533))) % 172.78/172.47 [4461]E(f332(f252(f882(x44611,x44611)),f332(f271(x44611,x44611,a871),f332(f332(f7(x44611,f883(f882(x44612,x44612),a871),f883(x44611,a871)),f332(f332(f8(f883(x44611,f883(f883(f882(x44612,x44612),a871),a871)),f883(f883(f882(x44612,x44612),a871),f883(x44611,a871)),x44611),f7(x44611,f883(f882(x44612,x44612),a871),a871)),f332(f332(f8(f883(x44611,f882(x44612,x44612)),f883(x44611,f883(f883(f882(x44612,x44612),a871),a871)),x44611),f332(f8(f882(x44612,x44612),f883(f883(f882(x44612,x44612),a871),a871),x44611),f334(f882(x44612,x44612)))),f332(f332(f7(x44611,f883(x44611,x44612),f883(x44611,f882(x44612,x44612))),f332(f332(f8(f883(x44612,f882(x44612,x44612)),f883(f883(x44611,x44612),f883(x44611,f882(x44612,x44612))),x44611),f8(x44612,f882(x44612,x44612),x44611)),f332(f332(f8(x44612,f883(x44612,f882(x44612,x44612)),x44611),f267(x44612,x44612)),x44613))),x44613)))),x44614))),f332(f332(f288(x44612,x44611),x44614),x44613)) % 172.78/172.47 [4519]~E(f32(x45191,x45192),f29(x45193,x45194,x45195)) % 172.78/172.47 [4520]~E(f32(x45201,x45202),f28(x45203,x45204,x45205)) % 172.78/172.47 [4521]~E(f31(x45211,x45212),f29(x45213,x45214,x45215)) % 172.78/172.47 [4522]~E(f31(x45221,x45222),f28(x45223,x45224,x45225)) % 172.78/172.47 [4523]~E(f29(x45231,x45232,x45233),f32(x45234,x45235)) % 172.78/172.47 [4524]~E(f29(x45241,x45242,x45243),f31(x45244,x45245)) % 172.78/172.47 [4525]~E(f28(x45251,x45252,x45253),f32(x45254,x45255)) % 172.78/172.47 [4526]~E(f28(x45261,x45262,x45263),f31(x45264,x45265)) % 172.78/172.47 [3571]E(f332(f332(f154(x35711,x35712),x35713),f170(x35711,x35714,x35715)),f170(x35712,x35714,f332(x35713,x35715))) % 172.78/172.47 [3945]E(f332(f186(x39451,x39452,x39453,x39454),x39455),f332(f241(f880(x39452),x39452,f332(x39453,x39455),f239(x39452)),f332(x39454,x39455))) % 172.78/172.47 [4033]E(f186(x40331,x40332,f186(x40331,x40332,x40333,x40334),x40335),f186(x40331,x40332,x40333,f186(x40331,x40332,x40334,x40335))) % 172.78/172.47 [4208]E(f268(x42081,x42082,x42083,f256(x42082,x42081,x42084),f256(x42083,x42082,x42085)),f256(x42083,x42081,f268(x42083,x42082,x42081,x42085,x42084))) % 172.78/172.47 [4215]E(f332(f332(f113(f883(x42151,a871)),f332(f173(x42151),f332(f332(f176(x42151),f332(f196(f877(x42152)),x42153)),x42154))),f185(x42151,x42152,x42155)),f185(x42151,x42152,f188(x42151,x42152,x42155,x42154,x42153))) % 172.78/172.47 [3767]E(f332(f332(f271(x37671,x37672,x37673),x37674),x37675),f332(f332(x37674,f332(f266(x37671,x37672),x37675)),f332(f270(x37671,x37672),x37675))) % 172.78/172.47 [3794]E(f332(f241(x37941,x37942,x37943,x37944),f332(f239(x37942),x37945)),f332(x37944,x37945)) % 172.78/172.47 [3803]E(f332(f332(f332(f65(x38031,x38032,x38033),x38034),x38035),f195(f883(x38032,a871))),x38035) % 172.78/172.47 [3977]E(f242(x39771,x39772,x39773,x39774,f332(f239(x39772),x39775)),f332(x39774,x39775)) % 172.78/172.47 [4088]E(f332(f72(f880(x40881),f880(x40882),f880(x40883),f332(f209(x40881,x40882),x40884)),f332(f209(x40883,x40881),x40885)),f332(f209(x40883,x40882),f332(f72(x40881,x40882,x40883,x40884),x40885))) % 172.78/172.47 [4090]E(f332(f72(f877(x40901),f877(x40902),f877(x40903),f332(f154(x40901,x40902),x40904)),f332(f154(x40903,x40901),x40905)),f332(f154(x40903,x40902),f332(f72(x40901,x40902,x40903,x40904),x40905))) % 172.78/172.47 [4146]E(f332(f241(x41461,f882(x41462,f878(x41462)),x41463,f332(f271(x41462,f878(x41462),x41461),x41464)),f332(f135(x41462),x41465)),f130(x41461,x41462,x41463,x41464,x41465)) % 172.78/172.47 [4170]E(f84(x41701,f66(x41702,x41701,x41703,x41704,x41705)),f332(f332(f64(x41702,x41701,x41703),x41704),x41705)) % 172.78/172.47 [4206]E(f332(f332(f79(a876),f332(f332(f79(a876),f332(x42061,f332(f266(x42062,x42063),x42064))),f332(x42065,f332(f270(x42062,x42063),x42064)))),f332(a115,f2(a876))),f275(x42062,x42063,x42061,x42065,x42064)) % 172.78/172.47 [4397]E(f163(x43971,x43972,f332(f332(f7(x43971,f880(x43972),f880(x43972)),f332(f332(f18(x43971,f880(x43972),f883(f880(x43972),f880(x43972))),f332(f332(f8(a871,f883(f880(x43972),f883(f880(x43972),f880(x43972))),x43971),f99(f880(x43972))),x43973)),f332(f332(f8(x43972,f880(x43972),x43971),f239(x43972)),x43974))),f208(x43972)),x43975),f332(f332(f154(x43971,x43972),x43974),f332(f136(x43971,x43973),x43975))) % 172.78/172.47 [4562]~E(f332(f332(f332(f71(x45621,f880(x45622)),x45623),x45624),f332(f239(x45622),x45625)),f332(f16(f880(x45622),x45621),f208(x45622))) % 172.78/172.47 [3701]E(f332(f332(f176(x37011),x37012),f332(f332(f154(x37013,x37011),x37014),x37015)),f332(f332(f154(x37013,x37011),x37014),f332(f332(f176(x37013),x37012),x37015))) % 172.78/172.47 [3702]E(f332(f332(f138(x37021),x37022),f332(f332(f154(x37023,x37021),x37024),x37025)),f332(f332(f154(x37023,x37021),x37024),f332(f332(f138(x37023),x37022),x37025))) % 172.78/172.47 [3735]E(f332(f332(f154(x37351,x37352),x37353),f332(f332(f151(x37351),x37354),x37355)),f332(f332(f151(x37352),f332(x37353,x37354)),f332(f332(f154(x37351,x37352),x37353),x37355))) % 172.78/172.47 [3798]E(f332(f311(x37981,x37982,x37983),f332(f332(f310(x37981),x37984),x37985)),f332(f332(f310(x37982),f332(x37983,x37984)),f332(f311(x37981,x37982,x37983),x37985))) % 172.78/172.47 [3827]E(f174(x38271,f332(f332(f151(x38271),x38272),x38273),f332(f332(f151(x38271),x38274),x38275)),f332(f332(f151(x38271),x38272),f332(f332(f151(x38271),x38274),f174(x38271,x38273,x38275)))) % 172.78/172.47 [3864]E(f332(f332(f183(x38641,x38642),f332(f332(f176(x38641),x38643),x38644)),f332(f332(f176(x38642),x38643),x38645)),f332(f332(f176(f882(x38641,x38642)),x38643),f332(f332(f183(x38641,x38642),x38644),x38645))) % 172.78/172.47 [3865]E(f332(f332(f183(x38651,x38652),f332(f332(f138(x38651),x38653),x38654)),f332(f332(f138(x38652),x38653),x38655)),f332(f332(f138(f882(x38651,x38652)),x38653),f332(f332(f183(x38651,x38652),x38654),x38655))) % 172.78/172.47 [3877]E(f332(f332(f159(x38771,f332(f332(f151(x38771),x38772),x38773)),f332(a115,x38774)),x38775),f332(f332(f151(x38771),x38772),f332(f332(f159(x38771,x38773),x38774),x38775))) % 172.78/172.47 [3880]E(f332(f241(f880(x38801),x38802,f208(x38801),x38803),f332(f332(f16(f880(x38802),x38804),f208(x38802)),x38805)),f208(x38801)) % 172.78/172.47 [3882]E(f332(f332(f134(x38821),f332(f332(f154(x38822,x38821),x38823),x38824)),f332(f332(f154(x38822,x38821),x38823),x38825)),f332(f332(f154(x38822,x38821),x38823),f332(f332(f134(x38822),x38824),x38825))) % 172.78/172.47 [3886]E(f332(f332(x38861,x38862),f332(f332(f258(x38863,x38864,x38861),x38862),x38865)),f332(f332(f258(x38863,x38864,x38861),x38862),f332(a115,x38865))) % 172.78/172.47 [3916]E(f164(x39161,x39162,x39163,f332(f332(f151(x39161),x39164),x39165)),f332(f332(f134(x39162),f332(x39163,x39164)),f164(x39161,x39162,x39163,x39165))) % 172.78/172.47 [3929]E(f332(f332(f289(x39291,x39292,x39293),f332(f287(x39292,x39291),x39294)),f332(f287(x39293,x39292),x39295)),f332(f287(x39293,x39291),f332(f332(f289(x39293,x39292,x39291),x39295),x39294))) % 172.78/172.47 [3963]E(f332(f332(f332(f190(f877(x39631),f877(x39631)),x39632),f168(x39631)),f332(f332(f154(x39633,x39631),x39634),x39635)),f332(f332(f154(x39633,x39631),x39634),f332(f332(f332(f190(f877(x39633),f877(x39633)),x39632),f168(x39633)),x39635))) % 172.78/172.47 [3964]E(f332(f332(f273(x39641,x39642,x39641,x39643),f332(f267(x39642,x39641),x39644)),x39645),f332(x39645,x39644)) % 172.78/172.47 [3991]E(f155(x39911,x39912,f332(f332(f154(x39913,x39911),x39914),x39915)),f155(x39913,f332(f72(x39911,a876,x39913,x39912),x39914),x39915)) % 172.78/172.47 [4056]E(f332(f332(f72(f880(x40561),f880(x40562),x40563,f332(f209(x40561,x40562),x40564)),f332(f16(f880(x40561),x40563),f208(x40561))),x40565),f208(x40562)) % 172.78/172.47 [4057]E(f178(f882(x40571,x40572),f332(f72(x40572,a871,f882(x40571,x40572),x40573),f270(x40571,x40572)),f332(f332(f183(x40571,x40572),x40574),x40575)),f332(f332(f183(x40571,x40572),x40574),f178(x40572,x40573,x40575))) % 172.78/172.47 [4062]E(f332(f311(x40621,x40622,f332(f332(f8(x40623,x40622,x40621),x40624),x40625)),f255(f883(x40621,a871))),f332(f311(x40623,x40622,x40624),f332(f311(x40621,x40623,x40625),f255(f883(x40621,a871))))) % 172.78/172.47 [4075]E(f178(f882(x40751,x40752),f332(f72(x40751,a871,f882(x40751,x40752),x40753),f266(x40751,x40752)),f332(f332(f183(x40751,x40752),x40754),x40755)),f332(f332(f183(x40751,x40752),f178(x40751,x40753,x40754)),x40755)) % 172.78/172.47 [4094]E(f332(f332(f113(f883(x40941,a871)),f332(f312(x40941,x40942,x40943),f332(f332(f310(x40942),x40944),f195(f883(x40942,a871))))),f332(f312(x40941,x40942,x40943),x40945)),f332(f312(x40941,x40942,x40943),f332(f332(f310(x40942),x40944),x40945))) % 172.78/172.47 [4154]E(f332(f332(f134(f882(x41541,x41542)),f332(f332(f154(x41542,f882(x41541,x41542)),f332(f267(x41541,x41542),x41543)),x41544)),f59(x41541,x41542,x41545,x41544)),f59(x41541,x41542,f332(f332(f151(x41541),x41543),x41545),x41544)) % 172.78/172.47 [4155]E(f332(f332(f154(x41551,x41552),x41553),f178(x41551,f332(f72(x41552,a871,x41551,x41554),x41553),x41555)),f178(x41552,x41554,f332(f332(f154(x41551,x41552),x41553),x41555))) % 172.78/172.47 [4161]E(f332(f142(x41611,x41612,f332(f7(x41612,x41611,x41611),f332(f7(x41611,x41612,x41611),x41613)),x41614),f332(f169(x41612),f332(f169(x41612),x41615))),f332(f142(x41611,x41612,x41613,x41614),x41615)) % 172.78/172.47 [4162]E(f332(f332(f332(f71(x41621,f880(x41622)),f189(x41621,x41622,x41623,x41624)),x41625),f332(x41623,x41625)),f189(x41621,x41622,x41623,f332(f332(f310(x41621),x41625),x41624))) % 172.78/172.47 [4232]E(f332(f241(f877(x42321),x42321,f163(x42322,x42321,x42323,x42324),f332(f332(f7(x42321,f877(x42321),f877(x42321)),f151(x42321)),f163(x42322,x42321,x42323,x42324))),f332(x42323,x42325)),f163(x42322,x42321,x42323,f332(f332(f151(x42322),x42325),x42324))) % 172.78/172.47 [4269]P102(f332(f332(f246(f883(x42691,a871)),f332(f311(x42692,x42691,x42693),f332(f332(f104(f883(x42692,a871)),x42694),x42695))),f332(f332(f104(f883(x42691,a871)),f332(f311(x42692,x42691,x42693),x42694)),f332(f311(x42692,x42691,x42693),x42695)))) % 172.78/172.47 [4270]P102(f332(f332(f246(f883(x42701,a871)),f332(f286(x42702,x42701,x42703),f332(f332(f104(f883(x42702,a871)),x42704),x42705))),f332(f332(f104(f883(x42701,a871)),f332(f286(x42702,x42701,x42703),x42704)),f332(f286(x42702,x42701,x42703),x42705)))) % 172.78/172.47 [4371]E(f332(f270(x43711,x43712),f332(f272(x43713,x43711,x43712,x43712,x43714,f33(x43712)),x43715)),f332(f270(x43713,x43712),x43715)) % 172.78/172.47 [4372]E(f332(f266(x43721,x43722),f332(f272(x43721,x43721,x43723,x43722,f33(x43721),x43724),x43725)),f332(f266(x43721,x43723),x43725)) % 172.78/172.47 [4457]E(f332(f142(f883(x44571,f880(x44572)),f882(x44571,x44572),f332(f332(f8(f883(x44571,f883(x44572,f883(x44571,f880(x44572)))),f883(f882(x44571,x44572),f883(x44571,f880(x44572))),f883(x44571,f880(x44572))),f271(x44571,x44572,f883(x44571,f880(x44572)))),f332(f332(f7(f883(x44571,f880(x44572)),f883(x44572,f880(x44572)),f883(x44571,f883(x44572,f883(x44571,f880(x44572))))),f332(f332(f8(f883(x44571,f883(f883(x44572,f880(x44572)),f883(x44572,f883(x44571,f880(x44572))))),f883(f883(x44572,f880(x44572)),f883(x44571,f883(x44572,f883(x44571,f880(x44572))))),f883(x44571,f880(x44572))),f7(x44571,f883(x44572,f880(x44572)),f883(x44572,f883(x44571,f880(x44572))))),f332(f332(f8(f883(x44571,f883(f880(x44572),f883(x44571,f880(x44572)))),f883(x44571,f883(f883(x44572,f880(x44572)),f883(x44572,f883(x44571,f880(x44572))))),f883(x44571,f880(x44572))),f332(f8(f883(f880(x44572),f883(x44571,f880(x44572))),f883(f883(x44572,f880(x44572)),f883(x44572,f883(x44571,f880(x44572)))),x44571),f8(f880(x44572),f883(x44571,f880(x44572)),x44572))),f71(x44571,f880(x44572))))),f239(x44572))),x44573),f332(f332(f183(x44571,x44572),x44574),x44575)),f188(x44571,x44572,x44573,x44574,x44575)) % 172.78/172.47 [4459]P19(x44591,x44592,f332(f332(f310(f875(x44591)),f332(f332(f332(f91(x44591),f332(f332(f7(x44591,f883(a872,a871),f883(a872,a871)),f332(f332(f8(f883(a872,f883(a871,a871)),f883(f883(a872,a871),f883(a872,a871)),x44591),f18(a872,a871,a871)),f332(f332(f8(f883(a872,a871),f883(a872,f883(a871,a871)),x44591),f332(f8(a871,f883(a871,a871),a872),a330)),x44593))),f332(f332(f8(a871,a871,a872),a327),x44594))),f31(x44594,x44595)),x44593)),f195(f883(f875(x44591),a871)))) % 172.78/172.47 [3540]E(f332(f332(f332(f332(f215(x35401),x35402),x35403),x35404),x35405),f199(x35401,x35402)) % 172.78/172.47 [3541]E(f332(f332(f332(f332(f219(x35411),x35412),x35413),x35414),x35415),f210(x35411,x35412)) % 172.78/172.47 [3587]E(f96(x35871,x35872,f332(f332(f332(f91(x35871),x35873),x35874),x35875)),f2(a876)) % 172.78/172.47 [3685]E(f332(f332(f332(f332(f71(x36851,x36852),x36853),x36854),x36855),x36854),x36855) % 172.78/172.47 [3917]E(f332(f332(f41(x39171,f883(x39172,a871)),f332(f332(f310(x39171),x39173),x39174)),x39175),f332(f332(f113(f883(x39172,a871)),f332(x39175,x39173)),f332(f332(f41(x39171,f883(x39172,a871)),x39174),x39175))) % 172.78/172.47 [3918]E(f332(f332(f42(x39181,f883(x39182,a871)),f332(f332(f310(x39181),x39183),x39184)),x39185),f332(f332(f104(f883(x39182,a871)),f332(x39185,x39183)),f332(f332(f42(x39181,f883(x39182,a871)),x39184),x39185))) % 172.78/172.47 [3970]E(f332(f121(x39701,x39702,f332(x39703,x39704)),f332(f332(f7(x39701,a102,f878(x39702)),x39705),x39704)),f332(f206(x39701,x39702,x39703,x39705),x39704)) % 172.78/172.47 [3984]E(f332(f332(f113(f883(x39841,a871)),f332(f311(x39842,x39841,x39843),x39844)),f332(f311(x39842,x39841,x39843),x39845)),f332(f311(x39842,x39841,x39843),f332(f332(f113(f883(x39842,a871)),x39844),x39845))) % 172.78/172.47 [3985]E(f332(f332(f113(f883(x39851,a871)),f332(f286(x39852,x39851,x39853),x39854)),f332(f286(x39852,x39851,x39853),x39855)),f332(f286(x39852,x39851,x39853),f332(f332(f113(f883(x39852,a871)),x39854),x39855))) % 172.78/172.47 [3986]E(f332(f332(f113(f883(x39861,a871)),f332(f312(x39861,x39862,x39863),x39864)),f332(f312(x39861,x39862,x39863),x39865)),f332(f312(x39861,x39862,x39863),f332(f332(f113(f883(x39862,a871)),x39864),x39865))) % 172.78/172.47 [3987]E(f332(f332(f22(f883(x39871,a871)),f332(f312(x39871,x39872,x39873),x39874)),f332(f312(x39871,x39872,x39873),x39875)),f332(f312(x39871,x39872,x39873),f332(f332(f22(f883(x39872,a871)),x39874),x39875))) % 172.78/172.47 [3988]E(f332(f332(f104(f883(x39881,a871)),f332(f312(x39881,x39882,x39883),x39884)),f332(f312(x39881,x39882,x39883),x39885)),f332(f312(x39881,x39882,x39883),f332(f332(f104(f883(x39882,a871)),x39884),x39885))) % 172.78/172.47 [3990]E(f189(x39901,x39902,f189(x39901,x39902,x39903,x39904),x39905),f189(x39901,x39902,x39903,f332(f332(f104(f883(x39901,a871)),x39904),x39905))) % 172.78/172.47 [4052]E(f332(f332(f159(x40521,f332(f332(f134(x40521),x40522),f332(f332(f151(x40521),x40523),x40524))),f332(f196(f877(x40521)),x40522)),x40525),f332(f332(f134(x40521),x40522),f332(f332(f151(x40521),x40525),x40524))) % 172.78/172.47 [4060]E(f332(f332(f42(x40601,f883(x40602,a871)),x40603),f332(f332(f8(f883(x40602,a871),f883(x40602,a871),x40601),f332(f310(x40602),x40604)),x40605)),f332(f332(f310(x40602),x40604),f332(f332(f42(x40601,f883(x40602,a871)),x40603),x40605))) % 172.78/172.47 [4128]E(f189(x41281,x41282,f332(f332(f332(f71(x41281,f880(x41282)),x41283),x41284),f332(f239(x41282),x41285)),f332(f78(f883(x41281,a871)),f332(f332(f310(x41281),x41284),f195(f883(x41281,a871))))),f189(x41281,x41282,x41283,f332(f78(f883(x41281,a871)),f332(f332(f310(x41281),x41284),f195(f883(x41281,a871)))))) % 172.78/172.47 [4219]E(f332(f332(f154(x42191,x42192),x42193),f332(f136(x42191,f332(f72(x42192,a871,x42191,x42194),x42193)),x42195)),f332(f136(x42192,x42194),f332(f332(f154(x42191,x42192),x42193),x42195))) % 172.78/172.47 [4225]E(f332(f196(f877(x42251)),f332(f136(x42251,x42252),f332(f332(f154(x42253,x42251),x42254),x42255))),f332(f196(f877(x42253)),f332(f136(x42253,f332(f72(x42251,a871,x42253,x42252),x42254)),x42255))) % 172.78/172.47 [4363]E(f332(f332(f113(f883(x43631,a871)),f332(f332(f22(f883(x43631,a871)),f185(x43631,x43632,x43633)),f332(f252(x43631),f332(f332(f7(x43631,f883(x43631,a871),a871),f334(x43631)),f332(f332(f22(f883(x43631,a871)),x43634),f185(x43631,x43632,x43635)))))),f332(f252(x43631),f332(f332(f7(x43631,f883(x43631,a871),a871),f334(x43631)),f332(f332(f104(f883(x43631,a871)),x43634),f185(x43631,x43632,x43635))))),f185(x43631,x43632,f75(x43631,f880(x43632),x43633,x43635,x43634))) % 172.78/172.47 [4438]E(f332(f156(f877(f882(x44381,x44382)),x44382,f116(f882(x44381,x44382)),f332(f332(f7(x44382,f883(f877(x44382),f877(f882(x44381,x44382))),f883(f877(x44382),f877(f882(x44381,x44382)))),f332(f332(f8(f883(f877(f882(x44381,x44382)),f877(f882(x44381,x44382))),f883(f883(f877(x44382),f877(f882(x44381,x44382))),f883(f877(x44382),f877(f882(x44381,x44382)))),x44382),f8(f877(f882(x44381,x44382)),f877(f882(x44381,x44382)),f877(x44382))),f332(f332(f8(f882(x44381,x44382),f883(f877(f882(x44381,x44382)),f877(f882(x44381,x44382))),x44382),f151(f882(x44381,x44382))),f332(f267(x44381,x44382),x44383)))),f332(f183(x44381,x44382),x44384))),x44385),f332(f332(f183(x44381,x44382),f332(f332(f151(x44381),x44383),x44384)),x44385)) % 172.78/172.47 [3911]E(f332(f332(f159(x39111,f332(f332(f159(x39111,x39112),x39113),x39114)),x39113),x39115),f332(f332(f159(x39111,x39112),x39113),x39115)) % 172.78/172.47 [3965]E(f332(f263(x39651,x39652),f332(f332(f310(f882(x39651,x39652)),f332(f332(f267(x39651,x39652),x39653),x39654)),x39655)),f332(f332(f310(x39652),x39654),f332(f263(x39651,x39652),x39655))) % 172.78/172.47 [3966]E(f332(f265(x39661,x39662),f332(f332(f310(f882(x39661,x39662)),f332(f332(f267(x39661,x39662),x39663),x39664)),x39665)),f332(f332(f310(x39661),x39663),f332(f265(x39661,x39662),x39665))) % 172.78/172.47 [4015]E(f123(x40151,x40152,f332(x40153,x40154),f332(f332(f7(x40151,a102,f878(f880(x40152))),x40155),x40154)),f332(f204(x40151,x40152,x40153,x40155),x40154)) % 172.78/172.47 [4045]E(f332(f332(f113(f883(f882(x40451,x40452),a871)),f332(f332(f269(x40451,x40452),x40453),x40454)),f332(f332(f269(x40451,x40452),x40455),x40454)),f332(f332(f269(x40451,x40452),f332(f332(f113(f883(x40451,a871)),x40453),x40455)),x40454)) % 172.78/172.47 [4046]E(f332(f332(f22(f883(f882(x40461,x40462),a871)),f332(f332(f269(x40461,x40462),x40463),x40464)),f332(f332(f269(x40461,x40462),x40465),x40464)),f332(f332(f269(x40461,x40462),f332(f332(f22(f883(x40461,a871)),x40463),x40465)),x40464)) % 172.78/172.47 [4047]E(f332(f332(f104(f883(f882(x40471,x40472),a871)),f332(f332(f269(x40471,x40472),x40473),x40474)),f332(f332(f269(x40471,x40472),x40475),x40474)),f332(f332(f269(x40471,x40472),f332(f332(f104(f883(x40471,a871)),x40473),x40475)),x40474)) % 172.78/172.47 [4106]E(f332(f332(f113(f883(x41061,a871)),f332(f332(f41(x41062,f883(x41061,a871)),x41063),x41064)),f332(f332(f41(x41062,f883(x41061,a871)),x41065),x41064)),f332(f332(f41(x41062,f883(x41061,a871)),f332(f332(f113(f883(x41062,a871)),x41063),x41065)),x41064)) % 172.78/172.47 [4107]E(f332(f332(f104(f883(x41071,a871)),f332(f332(f42(x41072,f883(x41071,a871)),x41073),x41074)),f332(f332(f42(x41072,f883(x41071,a871)),x41075),x41074)),f332(f332(f42(x41072,f883(x41071,a871)),f332(f332(f113(f883(x41072,a871)),x41073),x41075)),x41074)) % 172.78/172.47 [4121]E(f332(f332(f41(x41211,f883(x41212,a871)),x41213),f332(f332(f8(f883(x41212,a871),f883(x41212,a871),x41211),f332(f22(f883(x41212,a871)),x41214)),x41215)),f332(f332(f22(f883(x41212,a871)),x41214),f332(f332(f42(x41211,f883(x41212,a871)),x41213),x41215))) % 172.78/172.47 [4122]E(f332(f332(f41(x41221,f883(x41222,a871)),x41223),f332(f332(f8(f883(x41222,a871),f883(x41222,a871),x41221),f332(f104(f883(x41222,a871)),x41224)),x41225)),f332(f332(f104(f883(x41222,a871)),x41224),f332(f332(f41(x41221,f883(x41222,a871)),x41223),x41225))) % 172.78/172.47 [4123]E(f332(f332(f42(x41231,f883(x41232,a871)),x41233),f332(f332(f8(f883(x41232,a871),f883(x41232,a871),x41231),f332(f113(f883(x41232,a871)),x41234)),x41235)),f332(f332(f113(f883(x41232,a871)),x41234),f332(f332(f42(x41231,f883(x41232,a871)),x41233),x41235))) % 172.78/172.47 [4160]E(f186(x41601,x41602,x41603,f332(f179(x41601,x41602),f332(f169(f882(x41601,x41602)),f332(f332(f183(x41601,x41602),x41604),x41605)))),f188(x41601,x41602,x41603,x41604,x41605)) % 172.78/172.47 [4182]E(f192(f877(x41821),f332(f332(f151(x41821),x41822),x41823),f332(f332(f8(f877(x41821),f877(x41821),a876),f332(f151(x41821),x41824)),f332(f332(f7(a876,x41821,f877(x41821)),f159(x41821,x41823)),x41822)),x41825),f332(f332(f159(x41821,f332(f332(f151(x41821),x41824),x41823)),x41825),x41822)) % 172.78/172.47 [4186]E(f332(f332(f41(x41861,f883(f882(x41862,x41863),a871)),x41864),f332(f332(f8(f883(f882(x41863,x41862),a871),f883(f882(x41862,x41863),a871),x41861),f287(x41863,x41862)),x41865)),f332(f287(x41863,x41862),f332(f332(f41(x41861,f883(f882(x41863,x41862),a871)),x41864),x41865))) % 172.78/172.47 [4187]E(f332(f332(f42(x41871,f883(f882(x41872,x41873),a871)),x41874),f332(f332(f8(f883(f882(x41873,x41872),a871),f883(f882(x41872,x41873),a871),x41871),f287(x41873,x41872)),x41875)),f332(f287(x41873,x41872),f332(f332(f42(x41871,f883(f882(x41873,x41872),a871)),x41874),x41875))) % 172.78/172.47 [4243]E(f185(x42431,x42432,f332(f332(f18(x42431,f880(x42433),f880(x42432)),f332(f332(f8(f883(x42433,x42432),f883(f880(x42433),f880(x42432)),x42431),f209(x42433,x42432)),x42434)),x42435)),f185(x42431,x42433,x42435)) % 172.78/172.47 [4294]P102(f332(f332(f246(f883(x42941,a871)),f332(f332(f22(f883(x42941,a871)),f332(f311(x42942,x42941,x42943),x42944)),f332(f311(x42942,x42941,x42943),x42945))),f332(f311(x42942,x42941,x42943),f332(f332(f22(f883(x42942,a871)),x42944),x42945)))) % 172.78/172.47 [4442]E(f332(f156(f877(f882(x44421,x44422)),x44421,f116(f882(x44421,x44422)),f332(f332(f7(x44421,f883(f877(x44421),f877(f882(x44421,x44422))),f883(f877(x44421),f877(f882(x44421,x44422)))),f332(f332(f8(f883(f877(f882(x44421,x44422)),f877(f882(x44421,x44422))),f883(f883(f877(x44421),f877(f882(x44421,x44422))),f883(f877(x44421),f877(f882(x44421,x44422)))),x44421),f8(f877(f882(x44421,x44422)),f877(f882(x44421,x44422)),f877(x44421))),f332(f332(f8(f882(x44421,x44422),f883(f877(f882(x44421,x44422)),f877(f882(x44421,x44422))),x44421),f151(f882(x44421,x44422))),f332(f332(f7(x44421,x44422,f882(x44421,x44422)),f267(x44421,x44422)),x44423)))),f332(f332(f7(f877(x44421),f877(x44422),f877(f882(x44421,x44422))),f183(x44421,x44422)),x44424))),x44425),f332(f332(f183(x44421,x44422),x44425),f332(f332(f151(x44422),x44423),x44424))) % 172.78/172.47 [4148]E(f332(f332(f113(f883(x41481,a871)),f332(f286(x41482,x41481,x41483),x41484)),f332(f286(x41482,x41481,x41485),x41484)),f332(f286(x41482,x41481,f332(f332(f113(f883(f882(x41482,x41481),a871)),x41483),x41485)),x41484)) % 172.78/172.47 [4189]E(f332(f332(f134(f882(x41891,x41892)),f332(f332(f183(x41891,x41892),x41893),f332(f332(f176(x41892),f332(f196(f877(x41891)),x41893)),x41894))),f332(f332(f183(x41891,x41892),x41895),f332(f332(f138(x41892),f332(f196(f877(x41891)),x41893)),x41894))),f332(f332(f183(x41891,x41892),f332(f332(f134(x41891),x41893),x41895)),x41894)) % 172.78/172.47 [4297]E(f332(f332(f269(x42971,x42972),x42973),f332(f332(f18(x42971,f883(x42972,a871),f883(x42972,a871)),f332(f332(f8(f883(x42972,a871),f883(f883(x42972,a871),f883(x42972,a871)),x42971),f113(f883(x42972,a871))),x42974)),x42975)),f332(f332(f113(f883(f882(x42971,x42972),a871)),f332(f332(f269(x42971,x42972),x42973),x42974)),f332(f332(f269(x42971,x42972),x42973),x42975))) % 172.78/172.47 [4298]E(f332(f332(f269(x42981,x42982),x42983),f332(f332(f18(x42981,f883(x42982,a871),f883(x42982,a871)),f332(f332(f8(f883(x42982,a871),f883(f883(x42982,a871),f883(x42982,a871)),x42981),f22(f883(x42982,a871))),x42984)),x42985)),f332(f332(f22(f883(f882(x42981,x42982),a871)),f332(f332(f269(x42981,x42982),x42983),x42984)),f332(f332(f269(x42981,x42982),x42983),x42985))) % 172.78/172.47 [4299]E(f332(f332(f269(x42991,x42992),x42993),f332(f332(f18(x42991,f883(x42992,a871),f883(x42992,a871)),f332(f332(f8(f883(x42992,a871),f883(f883(x42992,a871),f883(x42992,a871)),x42991),f104(f883(x42992,a871))),x42994)),x42995)),f332(f332(f104(f883(f882(x42991,x42992),a871)),f332(f332(f269(x42991,x42992),x42993),x42994)),f332(f332(f269(x42991,x42992),x42993),x42995))) % 172.78/172.47 [4303]E(f332(f332(f41(x43031,f883(x43032,a871)),x43033),f332(f332(f7(x43031,f883(x43032,a871),f883(x43032,a871)),f332(f332(f8(f883(x43032,a871),f883(f883(x43032,a871),f883(x43032,a871)),x43031),f22(f883(x43032,a871))),x43034)),x43035)),f332(f332(f22(f883(x43032,a871)),f332(f332(f41(x43031,f883(x43032,a871)),x43033),x43034)),x43035)) % 172.78/172.47 [4304]E(f332(f332(f41(x43041,f883(x43042,a871)),x43043),f332(f332(f7(x43041,f883(x43042,a871),f883(x43042,a871)),f332(f332(f8(f883(x43042,a871),f883(f883(x43042,a871),f883(x43042,a871)),x43041),f104(f883(x43042,a871))),x43044)),x43045)),f332(f332(f104(f883(x43042,a871)),f332(f332(f41(x43041,f883(x43042,a871)),x43043),x43044)),x43045)) % 172.78/172.47 [4305]E(f332(f332(f42(x43051,f883(x43052,a871)),x43053),f332(f332(f7(x43051,f883(x43052,a871),f883(x43052,a871)),f332(f332(f8(f883(x43052,a871),f883(f883(x43052,a871),f883(x43052,a871)),x43051),f113(f883(x43052,a871))),x43054)),x43055)),f332(f332(f113(f883(x43052,a871)),f332(f332(f42(x43051,f883(x43052,a871)),x43053),x43054)),x43055)) % 172.78/172.47 [4309]E(f332(f332(f41(x43091,f883(x43092,a871)),x43093),f332(f332(f18(x43091,f883(x43092,a871),f883(x43092,a871)),f332(f332(f8(f883(x43092,a871),f883(f883(x43092,a871),f883(x43092,a871)),x43091),f113(f883(x43092,a871))),x43094)),x43095)),f332(f332(f113(f883(x43092,a871)),f332(f332(f41(x43091,f883(x43092,a871)),x43093),x43094)),f332(f332(f41(x43091,f883(x43092,a871)),x43093),x43095))) % 172.78/172.47 [4310]E(f332(f332(f42(x43101,f883(x43102,a871)),x43103),f332(f332(f18(x43101,f883(x43102,a871),f883(x43102,a871)),f332(f332(f8(f883(x43102,a871),f883(f883(x43102,a871),f883(x43102,a871)),x43101),f104(f883(x43102,a871))),x43104)),x43105)),f332(f332(f104(f883(x43102,a871)),f332(f332(f42(x43101,f883(x43102,a871)),x43103),x43104)),f332(f332(f42(x43101,f883(x43102,a871)),x43103),x43105))) % 172.78/172.47 [4324]E(f332(f332(f41(x43241,f883(x43242,a871)),x43243),f332(f332(f18(x43241,f883(x43242,a871),f883(x43242,a871)),f332(f332(f8(f883(x43242,a871),f883(f883(x43242,a871),f883(x43242,a871)),x43241),f113(f883(x43242,a871))),x43244)),x43245)),f332(f332(f113(f883(x43242,a871)),f39(f883(x43242,a871),f332(f311(x43241,f883(x43242,a871),x43244),x43243))),f39(f883(x43242,a871),f332(f311(x43241,f883(x43242,a871),x43245),x43243)))) % 172.78/172.47 [4325]E(f332(f332(f42(x43251,f883(x43252,a871)),x43253),f332(f332(f18(x43251,f883(x43252,a871),f883(x43252,a871)),f332(f332(f8(f883(x43252,a871),f883(f883(x43252,a871),f883(x43252,a871)),x43251),f104(f883(x43252,a871))),x43254)),x43255)),f332(f332(f104(f883(x43252,a871)),f40(f883(x43252,a871),f332(f311(x43251,f883(x43252,a871),x43254),x43253))),f40(f883(x43252,a871),f332(f311(x43251,f883(x43252,a871),x43255),x43253)))) % 172.78/172.47 [4359]E(f332(f332(f138(x43591),f332(f196(f877(x43591)),f178(x43591,x43592,f332(f332(f154(x43593,x43591),x43594),x43595)))),f332(f332(f154(x43593,x43591),x43594),x43595)),f332(f332(f154(x43593,x43591),x43594),f332(f332(f138(x43593),f332(f196(f877(x43593)),f178(x43593,f332(f72(x43591,a871,x43593,x43592),x43594),x43595))),x43595))) % 172.78/172.47 [4233]E(f332(f332(f134(f882(x42331,x42332)),f332(f332(f183(x42331,x42332),f332(f332(f176(x42331),f332(f196(f877(x42332)),x42333)),x42334)),x42333)),f332(f332(f183(x42331,x42332),f332(f332(f138(x42331),f332(f196(f877(x42332)),x42333)),x42334)),x42335)),f332(f332(f183(x42331,x42332),x42334),f332(f332(f134(x42332),x42333),x42335))) % 172.78/172.47 [4351]E(f84(x43511,f332(f332(f18(x43511,a871,a871),f332(f332(f8(a871,f883(a871,a871),x43511),a330),f332(f332(f7(x43511,f883(x43511,a871),a871),f334(x43511)),x43512))),f332(f332(f7(x43511,x43513,a871),f332(f332(f8(x43513,f883(x43513,a871),x43511),a329),x43514)),x43515))),f332(f76(x43511,x43513,x43512,x43514),x43515)) % 172.78/172.47 [4403]E(f332(f332(f85(a1,x44031),f332(f106(a1),f332(f332(f79(a1),x44032),a100))),f332(f332(f18(a1,x44031,x44031),f332(f332(f7(a1,x44031,f883(x44031,x44031)),f332(f332(f8(a871,f883(x44031,f883(x44031,x44031)),a1),f99(x44031)),a200)),f192(x44031,x44033,x44034,x44035))),f332(f332(f8(a876,x44031,a1),x44034),f332(f332(f7(a1,a876,a876),f332(f332(f8(a876,f883(a876,a876),a1),f79(a876)),a107)),x44035)))),f192(x44031,x44033,x44034,f332(f332(f79(a876),f332(f106(a876),x44032)),x44035))) % 172.78/172.47 [4439]E(f332(f179(x44391,x44392),f332(f332(f154(f882(x44391,x44393),f882(x44391,x44392)),f332(f271(x44391,x44393,f882(x44391,x44392)),f332(f332(f7(x44391,f883(x44393,x44392),f883(x44393,f882(x44391,x44392))),f332(f332(f8(f883(x44392,f882(x44391,x44392)),f883(f883(x44393,x44392),f883(x44393,f882(x44391,x44392))),x44391),f8(x44392,f882(x44391,x44392),x44393)),f267(x44391,x44392))),x44394))),x44395)),f332(f72(f880(x44393),f880(x44392),x44391,f332(f209(x44393,x44392),x44394)),f332(f179(x44391,x44393),x44395))) % 172.78/172.47 [4396]E(f185(x43961,x43962,f332(f332(f18(x43961,f880(x43962),f880(x43962)),f332(f332(f18(x43961,f880(x43962),f883(f880(x43962),f880(x43962))),f332(f332(f8(a871,f883(f880(x43962),f883(f880(x43962),f880(x43962))),x43961),f99(f880(x43962))),x43963)),x43964)),x43965)),f332(f332(f113(f883(x43961,a871)),f332(f332(f104(f883(x43961,a871)),f185(x43961,x43962,x43964)),f332(f252(x43961),x43963))),f332(f332(f104(f883(x43961,a871)),f185(x43961,x43962,x43965)),f332(f252(x43961),f332(f332(f8(a871,a871,x43961),a327),x43963))))) % 172.78/172.47 [4437]E(f332(f332(f85(a1,x44371),f332(f106(a1),f332(f332(f79(a1),x44372),a100))),f332(f332(f18(a1,x44371,x44371),f332(f332(f7(a1,x44371,f883(x44371,x44371)),f332(f332(f8(a871,f883(x44371,f883(x44371,x44371)),a1),f99(x44371)),a200)),f332(f191(x44371,x44373,x44374),x44375))),f332(f332(f18(a1,x44371,x44371),f332(f332(f8(a876,f883(x44371,x44371),a1),x44374),f332(f332(f7(a1,a876,a876),f332(f332(f8(a876,f883(a876,a876),a1),f79(a876)),a107)),x44375))),f332(f332(f8(a876,x44371,a1),f191(x44371,x44373,x44374)),f332(f332(f7(a1,a876,a876),f332(f332(f8(a876,f883(a876,a876),a1),f79(a876)),a107)),x44375))))),f332(f191(x44371,x44373,x44374),f332(f332(f79(a876),f332(f106(a876),x44372)),x44375))) % 172.78/172.47 [4471]E(f332(f252(f882(x44711,x44712)),f332(f271(x44711,x44712,a871),f332(f332(f8(f883(x44712,f883(x44713,a871)),f883(x44712,a871),x44711),f332(f8(f883(x44713,a871),a871,x44712),f86(x44713))),f332(f332(f7(x44711,f883(x44712,f883(x44713,a871)),f883(x44712,f883(x44713,a871))),f332(f332(f8(f883(f883(x44713,a871),f883(x44713,a871)),f883(f883(x44712,f883(x44713,a871)),f883(x44712,f883(x44713,a871))),x44711),f8(f883(x44713,a871),f883(x44713,a871),x44712)),f332(f332(f8(f883(x44713,f883(a871,a871)),f883(f883(x44713,a871),f883(x44713,a871)),x44711),f18(x44713,a871,a871)),f332(f332(f8(f883(x44713,a871),f883(x44713,f883(a871,a871)),x44711),f332(f8(a871,f883(a871,a871),x44713),a330)),f332(f332(f7(x44711,f883(f882(x44711,x44713),a871),f883(x44713,a871)),f332(f332(f8(f883(x44713,f883(f883(f882(x44711,x44713),a871),a871)),f883(f883(f882(x44711,x44713),a871),f883(x44713,a871)),x44711),f7(x44713,f883(f882(x44711,x44713),a871),a871)),f332(f332(f8(f883(x44713,f882(x44711,x44713)),f883(x44713,f883(f883(f882(x44711,x44713),a871),a871)),x44711),f332(f8(f882(x44711,x44713),f883(f883(f882(x44711,x44713),a871),a871),x44713),f334(f882(x44711,x44713)))),f267(x44711,x44713)))),x44714))))),f332(f332(f7(x44712,f883(f882(x44713,x44712),a871),f883(x44713,a871)),f332(f332(f8(f883(x44713,f883(f883(f882(x44713,x44712),a871),a871)),f883(f883(f882(x44713,x44712),a871),f883(x44713,a871)),x44712),f7(x44713,f883(f882(x44713,x44712),a871),a871)),f332(f332(f8(f883(x44713,f882(x44713,x44712)),f883(x44713,f883(f883(f882(x44713,x44712),a871),a871)),x44712),f332(f8(f882(x44713,x44712),f883(f883(f882(x44713,x44712),a871),a871),x44713),f334(f882(x44713,x44712)))),f332(f7(x44713,x44712,f882(x44713,x44712)),f267(x44713,x44712))))),x44715))))),f332(f332(f289(x44711,x44713,x44712),x44714),x44715)) % 172.78/172.47 [4547]~E(f28(x45471,x45472,x45473),f29(x45474,x45475,x45476)) % 172.78/172.47 [4000]E(f130(x40001,x40002,x40003,x40004,f127(x40002,x40005,x40006)),f332(f332(x40004,x40005),x40006)) % 172.78/172.47 [4217]E(f188(x42171,x42172,f186(x42171,x42172,x42173,x42174),x42175,x42176),f186(x42171,x42172,x42173,f188(x42171,x42172,x42174,x42175,x42176))) % 172.78/172.47 [4340]E(f332(f72(f882(x43401,x43402),x43402,f882(x43403,x43404),f270(x43401,x43402)),f272(x43403,x43401,x43404,x43402,x43405,x43406)),f332(f72(x43404,x43402,f882(x43403,x43404),x43406),f270(x43403,x43404))) % 172.78/172.47 [4341]E(f332(f72(f882(x43411,x43412),x43411,f882(x43413,x43414),f266(x43411,x43412)),f272(x43413,x43411,x43414,x43412,x43415,x43416)),f332(f72(x43413,x43411,f882(x43413,x43414),x43415),f266(x43413,x43414))) % 172.78/172.47 [3940]E(f332(f332(f72(x39401,x39402,x39403,x39404),x39405),x39406),f332(x39404,f332(x39405,x39406))) % 172.78/172.47 [3733]E(f332(f332(f271(x37331,x37332,x37333),x37334),f332(f332(f267(x37331,x37332),x37335),x37336)),f332(f332(x37334,x37335),x37336)) % 172.78/172.47 [3795]E(f332(f332(f332(f8(x37951,x37952,x37953),x37954),x37955),x37956),f332(x37954,f332(x37955,x37956))) % 172.78/172.47 [3796]E(f332(f332(f332(f7(x37961,x37962,x37963),x37964),x37965),x37966),f332(f332(x37964,x37966),x37965)) % 172.78/172.47 [3813]E(f332(f332(f332(f18(x38131,x38132,x38133),x38134),x38135),x38136),f332(f332(x38134,x38136),f332(x38135,x38136))) % 172.78/172.47 [3835]E(f332(f156(x38351,x38352,x38353,x38354),f332(f332(f151(x38352),x38355),x38356)),f332(f332(x38354,x38355),x38356)) % 172.78/172.47 [3876]E(f170(f882(x38761,x38762),f332(f332(f244(a876),x38763),x38764),f332(f332(f267(x38761,x38762),x38765),x38766)),f332(f332(f183(x38761,x38762),f170(x38761,x38763,x38765)),f170(x38762,x38764,x38766))) % 172.78/172.47 [3944]E(f332(f332(f151(f882(x39441,x39442)),f332(f332(f267(x39441,x39442),x39443),x39444)),f332(f332(f183(x39441,x39442),x39445),x39446)),f332(f332(f183(x39441,x39442),f332(f332(f151(x39441),x39443),x39445)),f332(f332(f151(x39442),x39444),x39446))) % 172.78/172.47 [3946]E(f332(f332(f154(x39461,x39462),x39463),f332(f332(f159(x39461,x39464),x39465),x39466)),f332(f332(f159(x39462,f332(f332(f154(x39461,x39462),x39463),x39464)),x39465),f332(x39463,x39466))) % 172.78/172.47 [3989]E(f332(f142(x39891,x39892,x39893,x39894),f332(f332(f151(x39892),x39895),x39896)),f332(f142(x39891,x39892,x39893,f332(f332(x39893,x39894),x39895)),x39896)) % 172.78/172.47 [4016]E(f274(x40161,x40162,x40163,x40164,f332(f332(f267(x40161,x40162),x40165),x40166)),f332(f332(x40164,x40165),x40166)) % 172.78/172.47 [4099]E(f332(f332(f41(x40991,f883(x40992,a871)),x40993),f332(f72(x40994,f883(x40992,a871),x40991,x40995),x40996)),f332(f332(f41(x40994,f883(x40992,a871)),f332(f311(x40991,x40994,x40996),x40993)),x40995)) % 172.78/172.47 [4151]E(f332(f332(f154(x41511,x41512),x41513),f332(f332(f154(x41514,x41511),x41515),x41516)),f332(f332(f154(x41514,x41512),f332(f72(x41511,x41512,x41514,x41513),x41515)),x41516)) % 172.78/172.47 [4153]E(f332(f332(f209(x41531,x41532),x41533),f332(f332(f209(x41534,x41531),x41535),x41536)),f332(f332(f209(x41534,x41532),f332(f72(x41531,x41532,x41534,x41533),x41535)),x41536)) % 172.78/172.47 [4158]E(f332(f311(x41581,x41582,f332(f72(x41583,x41582,x41581,x41584),x41585)),x41586),f332(f311(x41583,x41582,x41584),f332(f311(x41581,x41583,x41585),x41586))) % 172.78/172.47 [4159]E(f332(f312(x41591,x41592,f332(f72(x41593,x41592,x41591,x41594),x41595)),x41596),f332(f312(x41591,x41593,x41595),f332(f312(x41593,x41592,x41594),x41596))) % 172.78/172.47 [4188]E(f186(x41881,x41882,x41883,f332(f332(f332(f71(x41881,f880(x41882)),x41884),x41885),f332(f239(x41882),x41886))),f332(f332(f332(f71(x41881,f880(x41882)),f186(x41881,x41882,x41883,x41884)),x41885),f332(f239(x41882),x41886))) % 172.78/172.47 [4190]E(f332(f142(x41901,x41902,x41903,f332(f142(x41901,x41902,x41903,x41904),x41905)),x41906),f332(f142(x41901,x41902,x41903,x41904),f332(f332(f134(x41902),x41905),x41906))) % 172.78/172.47 [4330]E(f332(f272(x43301,x43301,x43302,x43303,f33(x43301),x43304),f332(f332(f267(x43301,x43302),x43305),x43306)),f332(f332(f267(x43301,x43303),x43305),f332(x43304,x43306))) % 172.78/172.47 [4331]E(f332(f272(x43311,x43312,x43313,x43313,x43314,f33(x43313)),f332(f332(f267(x43311,x43313),x43315),x43316)),f332(f332(f267(x43312,x43313),f332(x43314,x43315)),x43316)) % 172.78/172.47 [4421]E(f332(f332(f154(f882(x44211,x44212),f882(x44211,x44213)),f332(f271(x44211,x44212,f882(x44211,x44213)),f332(f332(f7(x44211,f883(x44212,x44213),f883(x44212,f882(x44211,x44213))),f332(f332(f8(f883(x44213,f882(x44211,x44213)),f883(f883(x44212,x44213),f883(x44212,f882(x44211,x44213))),x44211),f8(x44213,f882(x44211,x44213),x44212)),f267(x44211,x44213))),x44214))),f332(f332(f183(x44211,x44212),x44215),x44216)),f332(f332(f183(x44211,x44213),x44215),f332(f332(f154(x44212,x44213),x44214),x44216))) % 172.78/172.47 [3800]E(f97(x38001,x38002,x38003,f332(f332(f332(f91(x38001),x38004),x38005),x38006)),f332(f332(f332(x38003,x38004),x38005),x38006)) % 172.78/172.47 [3801]E(f98(x38011,x38012,x38013,f332(f332(f332(f91(x38011),x38014),x38015),x38016)),f332(f332(f332(x38013,x38014),x38015),x38016)) % 172.78/172.47 [3999]E(f332(f332(f72(x39991,x39992,x39993,f332(f16(x39992,x39991),x39994)),x39995),x39996),x39994) % 172.78/172.47 [4035]E(f332(f311(x40351,x40352,x40353),f332(f311(x40354,x40351,x40355),x40356)),f332(f311(x40354,x40352,f332(f332(f8(x40351,x40352,x40354),x40353),x40355)),x40356)) % 172.78/172.47 [4041]E(f332(f332(f41(x40411,f883(x40412,a871)),f332(f311(x40413,x40411,x40414),x40415)),x40416),f332(f332(f41(x40413,f883(x40412,a871)),x40415),f332(f332(f8(x40411,f883(x40412,a871),x40413),x40416),x40414))) % 172.78/172.47 [4042]E(f332(f332(f42(x40421,f883(x40422,a871)),f332(f311(x40423,x40421,x40424),x40425)),x40426),f332(f332(f42(x40423,f883(x40422,a871)),x40425),f332(f332(f8(x40421,f883(x40422,a871),x40423),x40426),x40424))) % 172.78/172.47 [4043]E(f332(f332(f41(x40431,f883(x40432,a871)),x40433),f332(f332(f8(x40434,f883(x40432,a871),x40431),x40435),x40436)),f332(f332(f41(x40434,f883(x40432,a871)),f332(f311(x40431,x40434,x40436),x40433)),x40435)) % 172.78/172.47 [4044]E(f332(f332(f42(x40441,f883(x40442,a871)),x40443),f332(f332(f8(x40444,f883(x40442,a871),x40441),x40445),x40446)),f332(f332(f42(x40444,f883(x40442,a871)),f332(f311(x40441,x40444,x40446),x40443)),x40445)) % 172.78/172.47 [4101]E(f332(f332(f41(x41011,f883(x41012,a871)),x41013),f332(f332(f8(f883(x41014,a871),f883(x41012,a871),x41011),f311(x41014,x41012,x41015)),x41016)),f332(f311(x41014,x41012,x41015),f332(f332(f41(x41011,f883(x41014,a871)),x41013),x41016))) % 172.78/172.47 [4102]E(f332(f332(f41(x41021,f883(x41022,a871)),x41023),f332(f332(f8(f883(x41024,a871),f883(x41022,a871),x41021),f286(x41024,x41022,x41025)),x41026)),f332(f286(x41024,x41022,x41025),f332(f332(f41(x41021,f883(x41024,a871)),x41023),x41026))) % 172.78/172.47 [4103]E(f332(f332(f41(x41031,f883(x41032,a871)),x41033),f332(f332(f8(f883(x41034,a871),f883(x41032,a871),x41031),f312(x41032,x41034,x41035)),x41036)),f332(f312(x41032,x41034,x41035),f332(f332(f41(x41031,f883(x41034,a871)),x41033),x41036))) % 172.78/172.47 [4104]E(f332(f332(f42(x41041,f883(x41042,a871)),x41043),f332(f332(f8(f883(x41044,a871),f883(x41042,a871),x41041),f312(x41042,x41044,x41045)),x41046)),f332(f312(x41042,x41044,x41045),f332(f332(f42(x41041,f883(x41044,a871)),x41043),x41046))) % 172.78/172.47 [4196]E(f332(f142(x41961,x41962,f332(f7(x41962,x41961,x41961),x41963),x41964),f332(f169(x41962),f332(f332(f151(x41962),x41965),x41966))),f332(f332(x41963,x41965),f332(f142(x41961,x41962,f332(f7(x41962,x41961,x41961),x41963),x41964),f332(f169(x41962),x41966)))) % 172.78/172.47 [4256]E(f332(f332(f18(f882(x42561,x42562),x42562,x42563),f332(f332(f8(x42564,f883(x42562,x42563),f882(x42561,x42562)),x42565),f332(f332(f8(x42561,x42564,f882(x42561,x42562)),x42566),f266(x42561,x42562)))),f270(x42561,x42562)),f332(f271(x42561,x42562,x42563),f332(f332(f8(x42564,f883(x42562,x42563),x42561),x42565),x42566))) % 172.78/172.47 [4263]E(f332(f142(x42631,x42632,f332(f7(x42632,x42631,x42631),x42633),f332(f142(x42631,x42632,f332(f7(x42632,x42631,x42631),x42633),x42634),f332(f169(x42632),x42635))),f332(f169(x42632),x42636)),f332(f142(x42631,x42632,f332(f7(x42632,x42631,x42631),x42633),x42634),f332(f169(x42632),f332(f332(f134(x42632),x42636),x42635)))) % 172.78/172.47 [4265]E(f332(f332(f154(f882(x42651,x42652),f882(x42653,x42652)),f332(f271(x42651,x42652,f882(x42653,x42652)),f332(f332(f8(x42653,f883(x42652,f882(x42653,x42652)),x42651),f267(x42653,x42652)),x42654))),f332(f332(f183(x42651,x42652),x42655),x42656)),f332(f332(f183(x42653,x42652),f332(f332(f154(x42651,x42653),x42654),x42655)),x42656)) % 172.78/172.47 [4313]P102(f332(f332(f246(f883(x43131,a871)),f332(f286(x43132,x43131,x43133),f332(f332(f42(x43134,f883(x43132,a871)),x43135),x43136))),f332(f332(f42(x43134,f883(x43131,a871)),x43135),f332(f332(f8(f883(x43132,a871),f883(x43131,a871),x43134),f286(x43132,x43131,x43133)),x43136)))) % 172.78/172.47 [4114]E(f332(f332(f183(x41141,x41142),f332(f332(f159(x41141,x41143),x41144),f332(f266(x41141,x41142),x41145))),f332(f332(f159(x41142,x41146),x41144),f332(f270(x41141,x41142),x41145))),f332(f332(f159(f882(x41141,x41142),f332(f332(f183(x41141,x41142),x41143),x41146)),x41144),x41145)) % 172.78/172.47 [4177]E(f332(f332(f113(f883(f882(x41771,x41772),a871)),f332(f332(f289(x41771,x41773,x41772),x41774),x41775)),f332(f332(f289(x41771,x41773,x41772),x41774),x41776)),f332(f332(f289(x41771,x41773,x41772),x41774),f332(f332(f113(f883(f882(x41773,x41772),a871)),x41775),x41776))) % 172.78/172.47 [4276]E(f332(f332(f310(f882(x42761,x42762)),f332(f332(f267(x42761,x42762),x42763),x42764)),f332(f332(f113(f883(f882(x42761,x42762),a871)),f332(f332(f269(x42761,x42762),x42765),f332(f16(f883(x42762,a871),x42761),f332(f332(f310(x42762),x42764),x42766)))),f332(f332(f269(x42761,x42762),f332(f332(f310(x42761),x42763),x42765)),f332(f16(f883(x42762,a871),x42761),x42766)))),f332(f332(f269(x42761,x42762),f332(f332(f310(x42761),x42763),x42765)),f332(f16(f883(x42762,a871),x42761),f332(f332(f310(x42762),x42764),x42766)))) % 172.78/172.47 [4354]E(f332(f332(f104(f883(x43541,a871)),f332(f312(x43541,x43542,f332(f72(f882(x43542,x43543),x43542,x43541,f266(x43542,x43543)),x43544)),x43545)),f332(f312(x43541,x43543,f332(f72(f882(x43542,x43543),x43543,x43541,f270(x43542,x43543)),x43544)),x43546)),f332(f312(x43541,f882(x43542,x43543),x43544),f332(f332(f269(x43542,x43543),x43545),f332(f16(f883(x43543,a871),x43542),x43546)))) % 172.78/172.47 [4098]E(f332(f332(f332(f71(x40981,x40982),f332(f332(f332(f71(x40981,x40982),x40983),x40984),x40985)),x40984),x40986),f332(f332(f332(f71(x40981,x40982),x40983),x40984),x40986)) % 172.78/172.47 [4202]E(f332(f332(f113(f883(f882(x42021,x42022),a871)),f332(f332(f289(x42021,x42023,x42022),x42024),x42025)),f332(f332(f289(x42021,x42023,x42022),x42026),x42025)),f332(f332(f289(x42021,x42023,x42022),f332(f332(f113(f883(f882(x42021,x42023),a871)),x42024),x42026)),x42025)) % 172.78/172.47 [4338]E(f332(f332(f41(x43381,f883(x43382,a871)),x43383),f332(f332(f7(x43381,f883(x43384,f883(x43382,a871)),f883(x43382,a871)),f332(f332(f8(f883(x43384,a871),f883(f883(x43384,f883(x43382,a871)),f883(x43382,a871)),x43381),f41(x43384,f883(x43382,a871))),x43385)),x43386)),f332(f332(f41(x43384,f883(x43382,a871)),f332(f332(f41(x43381,f883(x43384,a871)),x43383),x43385)),x43386)) % 172.78/172.47 [4339]E(f332(f332(f42(x43391,f883(x43392,a871)),x43393),f332(f332(f7(x43391,f883(x43394,f883(x43392,a871)),f883(x43392,a871)),f332(f332(f8(f883(x43394,a871),f883(f883(x43394,f883(x43392,a871)),f883(x43392,a871)),x43391),f42(x43394,f883(x43392,a871))),x43395)),x43396)),f332(f332(f42(x43394,f883(x43392,a871)),f332(f332(f41(x43391,f883(x43394,a871)),x43393),x43395)),x43396)) % 172.78/172.47 [4391]E(f332(f271(x43911,x43912,f882(x43913,x43914)),f332(f332(f7(x43911,f883(x43912,x43914),f883(x43912,f882(x43913,x43914))),f332(f332(f8(f883(x43914,f882(x43913,x43914)),f883(f883(x43912,x43914),f883(x43912,f882(x43913,x43914))),x43911),f8(x43914,f882(x43913,x43914),x43912)),f332(f332(f8(x43913,f883(x43914,f882(x43913,x43914)),x43911),f267(x43913,x43914)),x43915))),x43916)),f272(x43911,x43913,x43912,x43914,x43915,x43916)) % 172.78/172.47 [4312]E(f332(f332(f332(f71(x43121,f880(x43122)),f189(x43121,x43122,x43123,f332(f332(f22(f883(x43121,a871)),x43124),f332(f332(f310(x43121),x43125),f195(f883(x43121,a871)))))),x43125),x43126),f332(f332(f332(f71(x43121,f880(x43122)),f189(x43121,x43122,x43123,x43124)),x43125),x43126)) % 172.78/172.47 [4416]E(f332(f311(x44161,x44162,f332(f332(f18(x44161,x44162,x44162),f332(f332(f18(x44161,x44162,f883(x44162,x44162)),f332(f332(f8(a871,f883(x44162,f883(x44162,x44162)),x44161),f99(x44162)),x44163)),x44164)),x44165)),x44166),f332(f332(f113(f883(x44162,a871)),f332(f311(x44161,x44162,x44164),f332(f332(f104(f883(x44161,a871)),x44166),f332(f252(x44161),x44163)))),f332(f311(x44161,x44162,x44165),f332(f332(f104(f883(x44161,a871)),x44166),f332(f252(x44161),f332(f332(f8(a871,a871,x44161),a327),x44163)))))) % 172.78/172.47 [4427]E(f332(f311(x44271,f882(x44272,x44273),f332(f332(f18(x44271,x44273,f882(x44272,x44273)),f332(f332(f8(x44272,f883(x44273,f882(x44272,x44273)),x44271),f267(x44272,x44273)),x44274)),x44275)),x44276),f332(f332(f269(x44272,x44273),f332(f311(x44271,x44272,x44274),x44276)),f332(f332(f8(f883(x44271,a871),f883(x44273,a871),x44272),f311(x44271,x44273,x44275)),f332(f332(f7(x44272,f883(x44271,a871),f883(x44271,a871)),f332(f332(f8(f883(x44271,a871),f883(f883(x44271,a871),f883(x44271,a871)),x44272),f104(f883(x44271,a871))),f332(f332(f8(f883(x44272,a871),f883(x44271,a871),x44272),f312(x44271,x44272,x44274)),f332(f332(f7(x44272,f883(x44272,a871),f883(x44272,a871)),f310(x44272)),f195(f883(x44272,a871)))))),x44276)))) % 172.78/172.47 [4373]E(f332(f270(x43731,x43732),f332(f272(x43733,x43731,x43734,x43732,x43735,x43736),x43737)),f332(x43736,f332(f270(x43733,x43734),x43737))) % 172.78/172.47 [4374]E(f332(f266(x43741,x43742),f332(f272(x43743,x43741,x43744,x43742,x43745,x43746),x43747)),f332(x43745,f332(f266(x43743,x43744),x43747))) % 172.78/172.47 [4076]E(f332(f332(f183(x40761,x40762),f332(f332(f159(x40761,x40763),x40764),x40765)),f332(f332(f159(x40762,x40766),x40764),x40767)),f332(f332(f159(f882(x40761,x40762),f332(f332(f183(x40761,x40762),x40763),x40766)),x40764),f332(f332(f267(x40761,x40762),x40765),x40767))) % 172.78/172.47 [4144]E(f332(f332(f332(f273(x41441,x41442,x41443,x41444),x41445),x41446),x41447),f332(f332(f271(x41442,x41443,x41444),x41446),f332(x41445,x41447))) % 172.78/172.47 [4157]E(f332(f332(f332(f273(x41571,x41572,x41573,x41574),x41575),x41576),x41577),f332(f332(x41576,f332(f266(x41572,x41573),f332(x41575,x41577))),f332(f270(x41572,x41573),f332(x41575,x41577)))) % 172.78/172.47 [4192]E(f188(x41921,x41922,f332(f332(f332(f71(x41921,f880(x41922)),x41923),x41924),f332(f239(x41922),x41925)),x41926,x41927),f188(x41921,x41922,x41923,f332(f332(f151(x41921),x41924),x41926),f332(f332(f151(x41922),x41925),x41927))) % 172.78/172.47 [4211]E(f332(f72(x42111,x42112,x42113,x42114),f332(f72(x42115,x42111,x42113,x42116),x42117)),f332(f72(x42115,x42112,x42113,f332(f72(x42111,x42112,x42115,x42114),x42116)),x42117)) % 172.78/172.47 [4272]E(f332(f72(f880(x42721),f880(x42722),x42723,f332(f209(x42721,x42722),x42724)),f332(f332(f332(f71(x42723,f880(x42721)),x42725),x42726),f332(f239(x42721),x42727))),f332(f332(f332(f71(x42723,f880(x42722)),f332(f72(f880(x42721),f880(x42722),x42723,f332(f209(x42721,x42722),x42724)),x42725)),x42726),f332(f239(x42722),f332(x42724,x42727)))) % 172.78/172.47 [4398]E(f332(f272(x43981,x43982,x43983,x43983,x43984,f33(x43983)),f332(f272(x43981,x43981,x43985,x43983,f33(x43981),x43986),x43987)),f332(f332(f267(x43982,x43983),f332(x43984,f332(f266(x43981,x43985),x43987))),f332(x43986,f332(f270(x43981,x43985),x43987)))) % 172.78/172.47 [4399]E(f332(f272(x43991,x43991,x43992,x43993,f33(x43991),x43994),f332(f272(x43995,x43991,x43992,x43992,x43996,f33(x43992)),x43997)),f332(f332(f267(x43991,x43993),f332(x43996,f332(f266(x43995,x43992),x43997))),f332(x43994,f332(f270(x43995,x43992),x43997)))) % 172.78/172.47 [4414]E(f332(f272(x44141,x44142,x44143,x44143,x44144,f33(x44143)),f332(f272(x44145,x44141,x44143,x44143,x44146,f33(x44143)),x44147)),f332(f272(x44145,x44142,x44143,x44143,f332(f72(x44141,x44142,x44145,x44144),x44146),f33(x44143)),x44147)) % 172.78/172.47 [4415]E(f332(f272(x44151,x44151,x44152,x44153,f33(x44151),x44154),f332(f272(x44151,x44151,x44155,x44152,f33(x44151),x44156),x44157)),f332(f272(x44151,x44151,x44155,x44153,f33(x44151),f332(f72(x44152,x44153,x44155,x44154),x44156)),x44157)) % 172.78/172.47 [4424]E(f332(f272(x44241,x44242,x44243,x44243,x44244,f33(x44243)),f332(f272(x44241,x44241,x44245,x44243,f33(x44241),x44246),x44247)),f332(f272(x44242,x44242,x44245,x44243,f33(x44242),x44246),f332(f272(x44241,x44242,x44245,x44245,x44244,f33(x44245)),x44247))) % 172.78/172.47 [4111]E(f332(f332(f289(x41111,x41112,x41113),f332(f332(f289(x41111,x41114,x41112),x41115),x41116)),x41117),f332(f332(f289(x41111,x41114,x41113),x41115),f332(f332(f289(x41114,x41112,x41113),x41116),x41117))) % 172.78/172.47 [4183]E(f332(f332(f271(x41831,x41832,x41833),f332(f72(x41834,f883(x41832,x41833),x41831,x41835),x41836)),x41837),f332(f332(x41835,f332(x41836,f332(f266(x41831,x41832),x41837))),f332(f270(x41831,x41832),x41837))) % 172.78/172.47 [4236]E(f332(f72(x42361,x42362,x42363,x42364),f332(f332(f332(f71(x42363,x42361),x42365),x42366),x42367)),f332(f332(f332(f71(x42363,x42362),f332(f72(x42361,x42362,x42363,x42364),x42365)),x42366),f332(x42364,x42367))) % 172.78/172.47 [4268]E(f332(f142(x42681,x42682,f332(f7(x42682,x42681,x42681),x42683),x42684),f332(f169(x42682),f332(f332(f154(x42685,x42682),x42686),x42687))),f332(f142(x42681,x42685,f332(f7(x42685,x42681,x42681),f332(f72(x42682,f883(x42681,x42681),x42685,x42683),x42686)),x42684),f332(f169(x42685),x42687))) % 172.78/172.47 [4212]E(f332(f332(f41(x42121,f883(f882(x42122,x42123),a871)),x42124),f332(f332(f8(f883(f882(x42125,x42123),a871),f883(f882(x42122,x42123),a871),x42121),f332(f289(x42122,x42125,x42123),x42126)),x42127)),f332(f332(f289(x42122,x42125,x42123),x42126),f332(f332(f41(x42121,f883(f882(x42125,x42123),a871)),x42124),x42127))) % 172.78/172.47 [4360]E(f332(f332(f41(x43601,f883(f882(x43602,x43603),a871)),x43604),f332(f332(f7(x43601,f883(f882(x43605,x43603),a871),f883(f882(x43602,x43603),a871)),f332(f332(f8(f883(f882(x43602,x43605),a871),f883(f883(f882(x43605,x43603),a871),f883(f882(x43602,x43603),a871)),x43601),f289(x43602,x43605,x43603)),x43606)),x43607)),f332(f332(f289(x43602,x43605,x43603),f332(f332(f41(x43601,f883(f882(x43602,x43605),a871)),x43604),x43606)),x43607)) % 172.78/172.47 [4361]E(f332(f142(x43611,x43612,f332(f332(f7(x43611,f883(x43612,x43613),f883(x43612,x43611)),f332(f332(f8(f883(x43613,x43611),f883(f883(x43612,x43613),f883(x43612,x43611)),x43611),f8(x43613,x43611,x43612)),x43614)),x43615),x43616),x43617),f332(f142(x43611,x43613,x43614,x43616),f332(f332(f154(x43612,x43613),x43615),x43617))) % 172.78/172.47 [4425]E(f332(f332(f42(x44251,f883(x44252,a871)),x44253),f332(f332(f8(f883(x44254,f883(x44252,a871)),f883(x44252,a871),x44251),f332(f42(x44254,f883(x44252,a871)),x44255)),f332(f332(f7(x44251,f883(x44254,f883(x44252,a871)),f883(x44254,f883(x44252,a871))),f332(f332(f8(f883(f883(x44252,a871),f883(x44252,a871)),f883(f883(x44254,f883(x44252,a871)),f883(x44254,f883(x44252,a871))),x44251),f8(f883(x44252,a871),f883(x44252,a871),x44254)),f332(f332(f8(f883(x44252,a871),f883(f883(x44252,a871),f883(x44252,a871)),x44251),f113(f883(x44252,a871))),x44256))),x44257))),f332(f332(f113(f883(x44252,a871)),f332(f332(f42(x44251,f883(x44252,a871)),x44253),x44256)),f332(f332(f42(x44254,f883(x44252,a871)),x44255),x44257))) % 172.78/172.47 [4426]E(f332(f332(f41(x44261,f883(x44262,a871)),x44263),f332(f332(f8(f883(x44264,f883(x44262,a871)),f883(x44262,a871),x44261),f332(f41(x44264,f883(x44262,a871)),x44265)),f332(f332(f7(x44261,f883(x44264,f883(x44262,a871)),f883(x44264,f883(x44262,a871))),f332(f332(f8(f883(f883(x44262,a871),f883(x44262,a871)),f883(f883(x44264,f883(x44262,a871)),f883(x44264,f883(x44262,a871))),x44261),f8(f883(x44262,a871),f883(x44262,a871),x44264)),f332(f332(f8(f883(x44262,a871),f883(f883(x44262,a871),f883(x44262,a871)),x44261),f104(f883(x44262,a871))),x44266))),x44267))),f332(f332(f104(f883(x44262,a871)),f332(f332(f41(x44261,f883(x44262,a871)),x44263),x44266)),f332(f332(f41(x44264,f883(x44262,a871)),x44265),x44267))) % 172.78/172.47 [4419]E(f206(x44191,x44192,f332(f332(f332(x44193,x44194),x44195),x44196),f332(f332(f7(x44191,f882(a102,a102),f883(a102,f878(x44192))),f332(f332(f7(x44191,a102,f883(f882(a102,a102),f883(a102,f878(x44192)))),f332(f332(f7(x44191,a102,f883(a102,f883(f882(a102,a102),f883(a102,f878(x44192))))),x44197),x44194)),x44195)),x44196)),f332(f332(f332(f220(x44191,x44192,x44193,x44197),x44194),x44195),x44196)) % 172.78/172.47 [4432]E(f207(x44321,x44322,f332(f332(f332(x44323,x44324),x44325),x44326),f332(f332(f7(x44321,f882(a102,a102),f883(a102,f878(x44322))),f332(f332(f7(x44321,a102,f883(f882(a102,a102),f883(a102,f878(x44322)))),f332(f332(f7(x44321,a102,f883(a102,f883(f882(a102,a102),f883(a102,f878(x44322))))),x44327),x44324)),x44325)),x44326)),f222(x44321,x44322,x44323,x44327,x44324,x44325,x44326)) % 172.78/172.47 [4423]E(f204(x44231,x44232,f332(f332(f332(x44233,x44234),x44235),x44236),f332(f332(f7(x44231,f882(a102,a102),f883(a102,f878(f880(x44232)))),f332(f332(f7(x44231,a102,f883(f882(a102,a102),f883(a102,f878(f880(x44232))))),f332(f332(f7(x44231,a102,f883(a102,f883(f882(a102,a102),f883(a102,f878(f880(x44232)))))),x44237),x44234)),x44235)),x44236)),f332(f332(f332(f216(x44231,x44232,x44233,x44237),x44234),x44235),x44236)) % 172.78/172.47 [4434]E(f205(x44341,x44342,f332(f332(f332(x44343,x44344),x44345),x44346),f332(f332(f7(x44341,f882(a102,a102),f883(a102,f878(f880(x44342)))),f332(f332(f7(x44341,a102,f883(f882(a102,a102),f883(a102,f878(f880(x44342))))),f332(f332(f7(x44341,a102,f883(a102,f883(f882(a102,a102),f883(a102,f878(f880(x44342)))))),x44347),x44344)),x44345)),x44346)),f218(x44341,x44342,x44343,x44347,x44344,x44345,x44346)) % 172.78/172.47 [4332]E(f332(f272(x43321,x43322,x43323,x43324,x43325,x43326),f332(f332(f267(x43321,x43323),x43327),x43328)),f332(f332(f267(x43322,x43324),f332(x43325,x43327)),f332(x43326,x43328))) % 172.78/172.47 [4436]E(f332(f332(f154(f882(x44361,x44362),f882(x44363,x44364)),f332(f271(x44361,x44362,f882(x44363,x44364)),f332(f332(f7(x44361,f883(x44362,x44364),f883(x44362,f882(x44363,x44364))),f332(f332(f8(f883(x44364,f882(x44363,x44364)),f883(f883(x44362,x44364),f883(x44362,f882(x44363,x44364))),x44361),f8(x44364,f882(x44363,x44364),x44362)),f332(f332(f8(x44363,f883(x44364,f882(x44363,x44364)),x44361),f267(x44363,x44364)),x44365))),x44366))),f332(f332(f183(x44361,x44362),x44367),x44368)),f332(f332(f183(x44363,x44364),f332(f332(f154(x44361,x44363),x44365),x44367)),f332(f332(f154(x44362,x44364),x44366),x44368))) % 172.78/172.47 [4440]E(f332(f332(f154(f882(x44401,x44402),x44403),f332(f271(x44401,x44402,x44403),f332(f332(f8(f883(x44402,f882(x44401,x44404)),f883(x44402,x44403),x44401),f332(f8(f882(x44401,x44404),x44403,x44402),x44405)),f332(f332(f7(x44401,f883(x44402,x44404),f883(x44402,f882(x44401,x44404))),f332(f332(f8(f883(x44404,f882(x44401,x44404)),f883(f883(x44402,x44404),f883(x44402,f882(x44401,x44404))),x44401),f8(x44404,f882(x44401,x44404),x44402)),f267(x44401,x44404))),x44406)))),f332(f332(f183(x44401,x44402),x44407),x44408)),f332(f332(f154(f882(x44401,x44404),x44403),x44405),f332(f332(f183(x44401,x44404),x44407),f332(f332(f154(x44402,x44404),x44406),x44408)))) % 172.78/172.47 [4365]E(f332(f332(f154(f882(x43651,x43652),x43653),f332(f271(x43651,x43652,x43653),f332(f332(f8(f883(x43652,f882(x43654,x43652)),f883(x43652,x43653),x43651),f332(f8(f882(x43654,x43652),x43653,x43652),x43655)),f332(f332(f8(x43654,f883(x43652,f882(x43654,x43652)),x43651),f267(x43654,x43652)),x43656)))),f332(f332(f183(x43651,x43652),x43657),x43658)),f332(f332(f154(f882(x43654,x43652),x43653),x43655),f332(f332(f183(x43654,x43652),f332(f332(f154(x43651,x43654),x43656),x43657)),x43658))) % 172.78/172.47 [4323]E(f332(f332(f271(x43231,x43232,x43233),f332(f332(f8(f883(x43232,f882(x43234,x43235)),f883(x43232,x43233),x43231),f332(f8(f882(x43234,x43235),x43233,x43232),f332(f271(x43234,x43235,x43233),x43236))),x43237)),x43238),f332(f332(f271(x43234,x43235,x43233),x43236),f332(f332(f271(x43231,x43232,f882(x43234,x43235)),x43237),x43238))) % 172.78/172.47 [4441]E(f332(f332(f41(f882(x44411,x44412),f883(f882(x44413,x44414),a871)),f332(f332(f269(x44411,x44412),x44415),f332(f16(f883(x44412,a871),x44411),x44416))),f332(f271(x44411,x44412,f883(f882(x44413,x44414),a871)),f332(f332(f7(x44411,f883(x44412,f883(x44413,f883(x44414,a871))),f883(x44412,f883(f882(x44413,x44414),a871))),f332(f332(f8(f883(f883(x44413,f883(x44414,a871)),f883(f882(x44413,x44414),a871)),f883(f883(x44412,f883(x44413,f883(x44414,a871))),f883(x44412,f883(f882(x44413,x44414),a871))),x44411),f8(f883(x44413,f883(x44414,a871)),f883(f882(x44413,x44414),a871),x44412)),f332(f332(f8(f883(x44413,a871),f883(f883(x44413,f883(x44414,a871)),f883(f882(x44413,x44414),a871)),x44411),f269(x44413,x44414)),x44417))),f332(f332(f8(f883(x44414,a871),f883(x44413,f883(x44414,a871)),x44412),f16(f883(x44414,a871),x44413)),x44418)))),f332(f332(f269(x44413,x44414),f332(f332(f41(x44411,f883(x44413,a871)),x44415),x44417)),f332(f16(f883(x44414,a871),x44413),f332(f332(f41(x44412,f883(x44414,a871)),x44416),x44418)))) % 172.78/172.47 [4379]E(f332(f332(f273(x43791,x43792,x43793,x43794),f332(f332(f273(x43791,x43795,x43796,f882(x43792,x43793)),x43797),x43798)),x43799),f332(f332(f273(x43791,x43795,x43796,x43794),x43797),f332(f332(f7(x43795,f883(x43792,f883(x43793,x43794)),f883(x43796,x43794)),f332(f332(f8(f883(x43796,f882(x43792,x43793)),f883(f883(x43792,f883(x43793,x43794)),f883(x43796,x43794)),x43795),f273(x43796,x43792,x43793,x43794)),x43798)),x43799))) % 172.78/172.47 [4411]E(f332(f72(f882(x44111,x44112),f882(x44113,x44114),f882(x44115,x44116),f272(x44111,x44113,x44112,x44114,x44117,x44118)),f272(x44115,x44111,x44116,x44112,x44119,x441110)),f272(x44115,x44113,x44116,x44114,f332(f72(x44111,x44113,x44115,x44117),x44119),f332(f72(x44112,x44114,x44116,x44118),x441110))) % 172.78/172.47 [4417]E(f332(f272(x44171,x44172,x44173,x44174,x44175,x44176),f332(f272(x44177,x44171,x44178,x44173,x44179,x441710),x441711)),f332(f272(x44177,x44172,x44178,x44174,f332(f72(x44171,x44172,x44177,x44175),x44179),f332(f72(x44173,x44174,x44178,x44176),x441710)),x441711)) % 172.78/172.47 [4583]~P91(x45831)+E(f90(x45831),a329) % 172.78/172.47 [4584]~P24(x45841)+P24(f880(x45841)) % 172.78/172.47 [4585]~P56(x45851)+P56(f880(x45851)) % 172.78/172.47 [4586]~P100(x45861)+P100(f877(x45861)) % 172.78/172.47 [4589]~P140(x45891)+~E(f77(x45891),f2(x45891)) % 172.78/172.47 [4591]~E(x45911,f2(a102))+E(f332(a20,x45911),f2(a1)) % 172.78/172.47 [4592]~E(x45921,f2(a1))+E(f81(a1,x45921),f2(a1)) % 172.78/172.47 [4598]~P141(x45981)+P31(x45981,f2(x45981)) % 172.78/172.47 [4600]~P104(x46001)+P29(x46001,f116(x46001)) % 172.78/172.47 [4609]P102(x46091)+P102(f332(a327,x46091)) % 172.78/172.47 [4652]~P141(x46521)+~P31(x46521,f77(x46521)) % 172.78/172.47 [4699]~P102(x46991)+~P102(f332(a327,x46991)) % 172.78/172.47 [4722]E(f332(a107,x47221),f2(a876))+~P102(f332(a200,x47221)) % 172.78/172.47 [4788]~P97(x47881)+P10(x47881,x47881,f113(x47881)) % 172.78/172.47 [4789]~P98(x47891)+P10(x47891,x47891,f104(x47891)) % 172.78/172.47 [4790]~P93(x47901)+P10(x47901,x47901,f80(x47901)) % 172.78/172.47 [4791]~P104(x47911)+P10(x47911,x47911,f244(x47911)) % 172.78/172.47 [4792]~P104(x47921)+P10(x47921,x47921,f245(x47921)) % 172.78/172.47 [4793]~P64(x47931)+P11(x47931,x47931,f80(x47931)) % 172.78/172.47 [4595]~E(x45951,f2(a876))+E(f332(f103(a1),x45951),f2(a1)) % 172.78/172.47 [4602]~P89(x46021)+E(f332(f106(x46021),a82),f2(x46021)) % 172.78/172.47 [4605]~E(f564(x46051),f2(a876))+E(f332(f166(a876),x46051),f2(a876)) % 172.78/172.47 [4606]~P106(x46061)+E(f248(x46061,f246(x46061)),f244(x46061)) % 172.78/172.47 [4607]~P106(x46071)+E(f249(x46071,f246(x46071)),f245(x46071)) % 172.78/172.47 [4608]~P86(x46081)+E(f81(x46081,f2(x46081)),f2(x46081)) % 172.78/172.47 [4617]~P141(x46171)+E(f332(f103(x46171),f77(a876)),f77(x46171)) % 172.78/172.47 [4618]~P141(x46181)+E(f332(f103(x46181),f2(a876)),f2(x46181)) % 172.78/172.47 [4619]~P137(x46191)+E(f332(f105(x46191),f77(a1)),f77(x46191)) % 172.78/172.47 [4620]~P137(x46201)+E(f332(f105(x46201),f2(a1)),f2(x46201)) % 172.78/172.47 [4621]E(x46211,f2(a876))+~E(f332(f103(a1),x46211),f2(a1)) % 172.78/172.47 [4646]~P113(x46461)+E(f332(f74(x46461),f77(x46461)),f77(x46461)) % 172.78/172.47 [4647]~P81(x46471)+E(f332(f74(x46471),f2(x46471)),f2(x46471)) % 172.78/172.47 [4648]~P92(x46481)+E(f332(f78(x46481),f195(x46481)),f255(x46481)) % 172.78/172.47 [4649]~P72(x46491)+E(f332(f78(x46491),f2(x46491)),f2(x46491)) % 172.78/172.47 [4650]~P92(x46501)+E(f332(f78(x46501),f255(x46501)),f195(x46501)) % 172.78/172.47 [4651]~P76(x46511)+E(f332(f166(x46511),f116(x46511)),f2(x46511)) % 172.78/172.47 [4672]~P37(x46721)+P39(f332(f173(a1),x46721)) % 172.78/172.47 [4704]~P89(x47041)+E(f332(f78(x47041),f77(x47041)),f332(f106(x47041),a100)) % 172.78/172.47 [4721]~P89(x47211)+P31(x47211,f332(f106(x47211),a82)) % 172.78/172.47 [4738]~P56(x47381)+E(f332(f173(x47381),f55(x47381)),f255(f883(x47381,a871))) % 172.78/172.47 [4748]P37(x47481)+~P39(f332(f173(a1),x47481)) % 172.78/172.47 [4749]~P56(x47491)+P102(f332(f137(x47491),f55(x47491))) % 172.78/172.47 [4794]E(f332(f103(a1),f332(a107,x47941)),x47941)+P102(f332(a200,x47941)) % 172.78/172.47 [4811]~P106(x48111)+E(f92(x48111,x48111,f5(x48111)),f93(x48111)) % 172.78/172.47 [4863]~P109(x48631)+E(f258(x48631,f77(x48631),f80(x48631)),f257(x48631)) % 172.78/172.47 [4893]~P89(x48931)+~P31(x48931,f332(f106(x48931),a100)) % 172.78/172.47 [5036]E(f332(f74(a1),x50361),x50361)+P102(f332(f332(f247(a1),x50361),f2(a1))) % 172.78/172.47 [5054]~E(f332(a107,x50541),f2(a876))+P102(f332(f332(f246(a1),x50541),f2(a1))) % 172.78/172.47 [5116]~P102(f332(a200,x51161))+P102(f332(f332(f247(a1),x51161),f2(a1))) % 172.78/172.47 [5156]~P137(x51561)+P102(f332(f332(f334(x51561),f77(x51561)),f112(x51561))) % 172.78/172.47 [5157]~P141(x51571)+P102(f332(f332(f334(x51571),f77(x51571)),f193(x51571))) % 172.78/172.47 [5158]~P137(x51581)+P102(f332(f332(f334(x51581),f2(x51581)),f112(x51581))) % 172.78/172.47 [5159]~P141(x51591)+P102(f332(f332(f334(x51591),f2(x51591)),f193(x51591))) % 172.78/172.47 [5160]~P107(x51601)+P102(f332(f332(f247(x51601),f2(x51601)),f77(x51601))) % 172.78/172.47 [5161]~P107(x51611)+P102(f332(f332(f246(x51611),f2(x51611)),f77(x51611))) % 172.78/172.47 [5213]E(x52131,f2(a876))+~P102(f332(f332(f246(a876),x52131),f2(a876))) % 172.78/172.47 [5256]E(f332(a107,x52561),f2(a876))+~P102(f332(f332(f246(a1),x52561),f2(a1))) % 172.78/172.47 [5319]P102(f332(a200,x53191))+~P102(f332(f332(f247(a1),x53191),f2(a1))) % 172.78/172.47 [5324]~P104(x53241)+P11(x53241,f877(x53241),f148(x53241,x53241,f5(x53241))) % 172.78/172.47 [5342]P39(x53421)+~P102(f332(f332(f246(a1),f2(a1)),f339(x53421))) % 172.78/172.47 [5348]E(f332(f74(a1),x53481),f332(f78(a1),x53481))+~P102(f332(f332(f247(a1),x53481),f2(a1))) % 172.78/172.47 [5522]~P107(x55221)+~P102(f332(f332(f247(x55221),f77(x55221)),f2(x55221))) % 172.78/172.47 [5523]~P107(x55231)+~P102(f332(f332(f246(x55231),f77(x55231)),f2(x55231))) % 172.78/172.47 [5533]~E(x55331,f2(a1))+P102(f332(f332(f247(a1),f332(f74(a1),x55331)),f77(a1))) % 172.78/172.47 [5534]~E(x55341,f2(a876))+P102(f332(f332(f246(a1),f332(f103(a1),x55341)),f2(a1))) % 172.78/172.47 [5655]~P76(x56551)+E(f142(x56551,x56551,f79(x56551),f2(x56551)),f166(x56551)) % 172.78/172.47 [5825]~P99(x58251)+P20(a876,x58251,f103(x58251),f255(f883(a876,a871))) % 172.78/172.47 [6020]E(x60201,f2(a876))+~P102(f332(f332(f246(a1),f332(f103(a1),x60201)),f2(a1))) % 172.78/172.47 [6021]E(x60211,f2(a1))+~P102(f332(f332(f247(a1),f332(f74(a1),x60211)),f77(a1))) % 172.78/172.47 [6812]~P102(f332(f332(f247(a1),x68121),f2(a1)))+P102(f332(f332(f247(a1),f332(f332(f79(a1),x68121),x68121)),f2(a1))) % 172.78/172.47 [7361]P102(f332(f332(f247(a1),x73611),f2(a1)))+~P102(f332(f332(f247(a1),f332(f332(f79(a1),x73611),x73611)),f2(a1))) % 172.78/172.47 [7923]E(x79231,f332(a3,f2(a876)))+P102(f332(f332(f247(a876),f332(f332(f22(a876),f332(a19,x79231)),f332(a115,f2(a876)))),f332(a19,x79231))) % 172.78/172.47 [8693]~P102(f332(f332(f247(a1),x86931),f2(a1)))+P102(f332(f332(f247(a1),f332(f332(f22(a1),f332(f332(f79(a1),x86931),x86931)),a100)),f2(a1))) % 172.78/172.47 [8779]~P102(f332(f332(f247(a1),x87791),f2(a1)))+P102(f332(f332(f247(a1),f332(f332(f79(a1),f332(f332(f79(a1),f77(a1)),x87791)),x87791)),f2(a1))) % 172.78/172.47 [9105]P102(f332(f332(f247(a1),x91051),f2(a1)))+~P102(f332(f332(f247(a1),f332(f332(f22(a1),f332(f332(f79(a1),x91051),x91051)),a100)),f2(a1))) % 172.78/172.47 [9168]P102(f332(f332(f247(a1),x91681),f2(a1)))+~P102(f332(f332(f247(a1),f332(f332(f79(a1),f332(f332(f79(a1),f77(a1)),x91681)),x91681)),f2(a1))) % 172.78/172.47 [4692]~E(a82,x46921)+E(f332(f332(f79(a1),x46921),x46921),a82) % 172.78/172.47 [4693]~E(x46931,a82)+E(f332(f332(f79(a1),x46931),x46931),a82) % 172.78/172.47 [4707]E(x47071,f2(a1))+E(f332(f332(f38(a1),x47071),x47071),f77(a1)) % 172.78/172.47 [4840]E(x48401,a82)+~E(f332(f332(f79(a1),x48401),x48401),a82) % 172.78/172.47 [4841]E(a82,x48411)+~E(f332(f332(f79(a1),x48411),x48411),a82) % 172.78/172.47 [4853]~P27(x48531)+E(f40(x48531,f195(f883(x48531,a871))),f255(x48531)) % 172.78/172.47 [4854]~P27(x48541)+E(f40(x48541,f255(f883(x48541,a871))),f195(x48541)) % 172.78/172.47 [4855]~P27(x48551)+E(f39(x48551,f195(f883(x48551,a871))),f195(x48551)) % 172.78/172.47 [4856]~P27(x48561)+E(f39(x48561,f255(f883(x48561,a871))),f255(x48561)) % 172.78/172.47 [4857]~P104(x48571)+E(f139(x48571,f195(f883(x48571,a871))),f116(x48571)) % 172.78/172.47 [4994]E(x49941,f2(a876))+P102(f332(f332(f247(a876),f2(a876)),x49941)) % 172.78/172.47 [5013]~P28(x50131)+P102(f332(f332(f246(a1),f2(a1)),x50131)) % 172.78/172.47 [5045]~E(f332(f106(a876),x50451),f2(a876))+P102(f332(f332(f246(a1),x50451),a82)) % 172.78/172.47 [5050]P39(x50501)+P102(f332(f332(f334(a1),f339(x50501)),x50501)) % 172.78/172.47 [5051]E(x50511,f332(a3,f2(a876)))+P102(f332(f332(f246(a102),f77(a102)),x50511)) % 172.78/172.47 [5090]P102(f332(a200,x50901))+P102(f332(f332(f246(a1),f2(a1)),x50901)) % 172.78/172.47 [5138]E(f332(f103(a1),f332(a107,x51381)),f2(a1))+P102(f332(f332(f246(a1),f2(a1)),x51381)) % 172.78/172.47 [5198]E(f332(f103(a1),f332(f106(a876),x51981)),f332(f106(a1),x51981))+P102(f332(a200,f332(f106(a1),x51981))) % 172.78/172.47 [5219]E(f332(f106(a876),x52191),f2(a876))+~P102(f332(a200,f332(f106(a1),x52191))) % 172.78/172.47 [5220]E(f332(f106(a876),x52201),f2(a876))+~P102(f332(f332(f246(a1),x52201),a82)) % 172.78/172.47 [5253]P28(x52531)+~P102(f332(f332(f246(a1),f2(a1)),x52531)) % 172.78/172.47 [5327]E(f332(a115,f806(x53271)),x53271)+~P102(f332(f332(f247(a876),f2(a876)),x53271)) % 172.78/172.47 [5336]E(f332(a115,f332(f106(a876),x53361)),f77(a876))+~P102(f332(a200,f332(f106(a1),x53361))) % 172.78/172.47 [5344]E(f332(f103(a1),f375(x53441)),x53441)+~P102(f332(f332(f247(a1),f2(a1)),x53441)) % 172.78/172.47 [5352]~E(x53521,f332(a3,f2(a876)))+~P102(f332(f332(f246(a102),f77(a102)),x53521)) % 172.78/172.47 [5359]E(f332(f103(a1),f332(f106(a876),x53591)),f2(a1))+~P102(f332(a200,f332(f106(a1),x53591))) % 172.78/172.47 [5385]E(f332(f166(a876),x53851),f2(a876))+P102(f332(f332(f334(a876),f564(x53851)),f332(f173(a876),x53851))) % 172.78/172.47 [5406]E(f332(f103(a1),f332(a107,x54061)),x54061)+~P102(f332(f332(f246(a1),f2(a1)),x54061)) % 172.78/172.47 [5415]~P102(f332(a200,x54151))+~P102(f332(f332(f246(a1),f2(a1)),x54151)) % 172.78/172.47 [5515]E(f332(f332(f79(a876),f77(a876)),f332(f106(a876),x55151)),f77(a876))+~P102(f332(f332(f247(a1),x55151),a82)) % 172.78/172.47 [5575]E(x55751,f2(a876))+~P102(f332(f332(f247(a876),x55751),f332(a115,f2(a876)))) % 172.78/172.47 [5614]E(f332(f332(f22(a876),f332(f106(a876),x56141)),f77(a876)),f2(a876))+~P102(f332(f332(f246(a1),x56141),a82)) % 172.78/172.47 [5615]E(f332(f332(f79(a876),f332(f106(a876),x56151)),f77(a876)),f77(a876))+~P102(f332(f332(f247(a1),x56151),a82)) % 172.78/172.47 [5625]~P39(x56251)+E(f332(f37(a876),f332(f311(a1,a876,a107),x56251)),f332(f37(a1),x56251)) % 172.78/172.47 [5656]~P104(x56561)+E(f248(x56561,f332(f7(x56561,x56561,a871),f246(x56561))),f245(x56561)) % 172.78/172.47 [5657]~P104(x56571)+E(f249(x56571,f332(f7(x56571,x56571,a871),f246(x56571))),f244(x56571)) % 172.78/172.47 [5667]E(f44(a876,f332(a115,f2(a876)),f332(f106(a876),x56671)),f332(a115,f2(a876)))+~P102(f332(a200,f332(f106(a1),x56671))) % 172.78/172.47 [5676]P102(f332(f332(f247(a1),f2(a1)),x56761))+~P102(f332(f332(f246(a1),f77(a1)),x56761)) % 172.78/172.47 [5677]~P102(f332(f332(f247(a1),f2(a1)),x56771))+P102(f332(f332(f246(a1),f77(a1)),x56771)) % 172.78/172.47 [5688]E(f332(a115,f332(f332(f22(a876),x56881),f77(a876))),x56881)+~P102(f332(f332(f247(a876),f2(a876)),x56881)) % 172.78/172.47 [5744]P102(f332(f332(f247(a876),f2(a876)),f375(x57441)))+~P102(f332(f332(f247(a1),f2(a1)),x57441)) % 172.78/172.47 [5803]E(f44(a1,f332(f106(a1),a100),x58031),f332(f332(f22(a1),x58031),f77(a1)))+~P102(f332(f332(f247(a1),f2(a1)),x58031)) % 172.78/172.47 [5837]~P102(f332(f332(f247(a1),a82),x58371))+P102(f332(f332(f247(a876),f2(a876)),f332(f106(a876),x58371))) % 172.78/172.47 [5887]P102(f332(f332(f247(a876),f2(a876)),f332(a107,x58871)))+~P102(f332(f332(f247(a1),f2(a1)),x58871)) % 172.78/172.47 [5937]~P102(f332(f332(f247(a876),f2(a876)),x59371))+P102(f332(f332(f247(a1),f2(a1)),f332(f103(a1),x59371))) % 172.78/172.47 [5975]~P102(f332(f332(f247(a876),f2(a876)),f332(a107,x59751)))+P102(f332(f332(f247(a1),f2(a1)),x59751)) % 172.78/172.47 [5990]~P39(x59901)+E(f332(f311(a876,a1,f103(a1)),f332(f311(a1,a876,a107),x59901)),x59901) % 172.78/172.47 [6001]P102(f332(f332(f247(a1),a82),x60011))+~P102(f332(f332(f247(a876),f2(a876)),f332(f106(a876),x60011))) % 172.78/172.47 [6049]~P56(x60491)+E(f332(f332(f151(f880(x60491)),f208(x60491)),f332(f332(f154(x60491,f880(x60491)),f239(x60491)),f55(x60491))),f55(f880(x60491))) % 172.78/172.47 [6060]P102(f332(f332(f247(a876),f2(a876)),x60601))+~P102(f332(f332(f247(a1),f2(a1)),f332(f103(a1),x60601))) % 172.78/172.47 [6169]E(f332(f311(a876,a1,f103(a1)),f332(f253(a876),f332(a107,x61691))),f332(f302(a1,f2(a1)),x61691))+~P102(f332(f332(f246(a1),f2(a1)),x61691)) % 172.78/172.47 [6185]~P107(x61851)+P102(f332(f332(f247(x61851),f2(x61851)),f332(f332(f79(x61851),f77(x61851)),f77(x61851)))) % 172.78/172.47 [6236]P102(f332(f332(f247(a876),f332(a115,f2(a876))),f332(a107,x62361)))+~P102(f332(f332(f247(a1),f77(a1)),x62361)) % 172.78/172.47 [6331]E(x63311,f2(a1))+P102(f332(f48(f2(a1),x63311),f332(f332(f267(a1,a1),f2(a1)),f2(a1)))) % 172.78/172.47 [6495]~P102(f332(f332(f247(a876),f332(a115,f2(a876))),f332(a107,x64951)))+P102(f332(f332(f247(a1),f77(a1)),x64951)) % 172.78/172.47 [6924]~P111(x69241)+P38(x69241,f332(f252(f882(x69241,x69241)),f332(f271(x69241,x69241,a871),f247(x69241)))) % 172.78/172.47 [5562]E(f332(f106(a876),f332(f332(f22(a1),x55621),a100)),f332(a115,f332(f106(a876),x55621)))+P102(f332(a200,f332(f106(a1),x55621))) % 172.78/172.47 [5578]~P37(x55781)+E(f332(f332(f154(a876,a1),f103(a1)),f332(f332(f154(a1,a876),a107),x55781)),x55781) % 172.78/172.47 [5694]E(f332(f78(a1),f332(f103(a1),f332(a115,f472(x56941)))),x56941)+~P102(f332(f332(f247(a1),x56941),f2(a1))) % 172.78/172.47 [5704]E(f332(f332(f79(a876),f77(a876)),f332(f106(a876),x57041)),f332(f106(a876),f332(f332(f22(a1),x57041),a100)))+P102(f332(f332(f247(a1),x57041),a82)) % 172.78/172.47 [5746]E(f332(f332(f38(a1),f332(f106(a1),a100)),x57461),f332(f106(a1),a100))+~P102(f332(f332(f247(a1),f2(a1)),x57461)) % 172.78/172.47 [5833]E(f332(f332(f22(a876),f332(f106(a876),x58331)),f77(a876)),f332(f106(a876),f332(f332(f79(a1),x58331),a100)))+P102(f332(f332(f246(a1),x58331),a82)) % 172.78/172.47 [5834]E(f332(f332(f79(a876),f332(f106(a876),x58341)),f77(a876)),f332(f106(a876),f332(f332(f22(a1),x58341),a100)))+P102(f332(f332(f247(a1),x58341),a82)) % 172.78/172.47 [5875]E(f332(a107,f332(f332(f79(a1),f77(a1)),x58751)),f332(a115,f332(a107,x58751)))+~P102(f332(f332(f246(a1),f2(a1)),x58751)) % 172.78/172.47 [5909]E(f332(a115,f332(f332(f22(a876),x59091),f332(a115,f2(a876)))),x59091)+~P102(f332(f332(f247(a876),f2(a876)),x59091)) % 172.78/172.47 [6120]E(f44(a876,f332(a115,f2(a876)),f332(f106(a876),x61201)),f332(a107,f44(a1,f77(a1),f332(f106(a1),x61201))))+P102(f332(a200,f332(f106(a1),x61201))) % 172.78/172.47 [6159]~P102(f332(f332(f247(a1),a82),x61591))+P102(f332(f332(f247(a1),a82),f332(f332(f79(a1),x61591),x61591))) % 172.78/172.47 [6160]~P102(f332(f332(f247(a1),a100),x61601))+P102(f332(f332(f247(a1),a100),f332(f332(f79(a1),x61601),x61601))) % 172.78/172.47 [6161]~P102(f332(f332(f246(a1),a82),x61611))+P102(f332(f332(f246(a1),a82),f332(f332(f79(a1),x61611),x61611))) % 172.78/172.47 [6162]~P102(f332(f332(f247(a1),a100),x61621))+P102(f332(f332(f246(a1),a100),f332(f332(f79(a1),x61621),x61621))) % 172.78/172.47 [6163]~P102(f332(f332(f90(a1),a82),x61631))+P102(f332(f332(f90(a1),a82),f332(f332(f79(a1),x61631),x61631))) % 172.78/172.47 [6344]~P102(f332(f61(x63441),f255(f883(x63441,a871))))+P102(f332(f61(f880(x63441)),f255(f883(f880(x63441),a871)))) % 172.78/172.47 [6429]~P102(f332(f332(f246(a1),f2(a1)),x64291))+P102(f332(f332(f247(a1),f2(a1)),f332(f332(f79(a1),f77(a1)),x64291))) % 172.78/172.47 [6436]E(f332(f266(a1,a1),f46(f77(a1),f332(f106(a1),x64361))),f332(f332(f38(a1),f77(a1)),f332(f106(a1),x64361)))+~P102(f332(f332(f246(a1),f2(a1)),f332(f106(a1),x64361))) % 172.78/172.47 [6456]E(f332(f270(a1,a1),f46(f77(a1),f332(f106(a1),x64561))),f44(a1,f77(a1),f332(f106(a1),x64561)))+~P102(f332(f332(f246(a1),f2(a1)),f332(f106(a1),x64561))) % 172.78/172.47 [6467]P102(f332(f61(x64671),f255(f883(x64671,a871))))+~P102(f332(f61(f880(x64671)),f255(f883(f880(x64671),a871)))) % 172.78/172.47 [6496]P102(f332(f332(f247(a1),a82),x64961))+~P102(f332(f332(f247(a1),a82),f332(f332(f79(a1),x64961),x64961))) % 172.78/172.47 [6497]P102(f332(f332(f247(a1),a100),x64971))+~P102(f332(f332(f247(a1),a100),f332(f332(f79(a1),x64971),x64971))) % 172.78/172.47 [6498]P102(f332(f332(f247(a1),a100),x64981))+~P102(f332(f332(f246(a1),a100),f332(f332(f79(a1),x64981),x64981))) % 172.78/172.47 [6499]P102(f332(f332(f246(a1),a82),x64991))+~P102(f332(f332(f246(a1),a82),f332(f332(f79(a1),x64991),x64991))) % 172.78/172.47 [6500]P102(f332(f332(f90(a1),a82),x65001))+~P102(f332(f332(f90(a1),a82),f332(f332(f79(a1),x65001),x65001))) % 172.78/172.47 [6816]~P102(f332(f61(x68161),f255(f883(x68161,a871))))+P102(f332(f332(f247(a876),f2(a876)),f332(f37(x68161),f255(f883(x68161,a871))))) % 172.78/172.47 [7403]P102(f332(f61(a876),x74031))+~P102(f332(f61(a1),f332(f311(a876,a1,f103(a1)),x74031))) % 172.78/172.47 [8812]P19(a872,a884,f332(f332(f310(f875(a872)),f332(f332(f332(f91(a872),a329),f332(a25,x88121)),f201(f332(a25,x88121)))),f195(f883(f875(a872),a871))))+~P102(f332(f332(f334(a874),x88121),f185(a874,a873,a27))) % 172.78/172.47 [5490]~E(a100,x54901)+E(f332(f332(f22(a1),f332(f332(f79(a1),x54901),x54901)),a100),a100) % 172.78/172.47 [5491]~E(x54911,a100)+E(f332(f332(f22(a1),f332(f332(f79(a1),x54911),x54911)),a100),a100) % 172.78/172.47 [5996]E(x59961,a100)+~E(f332(f332(f22(a1),f332(f332(f79(a1),x59961),x59961)),a100),a100) % 172.78/172.47 [5997]E(a100,x59971)+~E(f332(f332(f22(a1),f332(f332(f79(a1),x59971),x59971)),a100),a100) % 172.78/172.47 [6398]~E(f332(f106(a876),x63981),f2(a876))+P102(f332(a200,f332(f106(a1),f332(f332(f79(a1),x63981),a100)))) % 172.78/172.47 [6742]~P102(f332(a200,f332(f106(a1),x67421)))+P102(f332(a200,f332(f106(a1),f332(f332(f79(a1),x67421),x67421)))) % 172.78/172.47 [6743]~P102(f332(f332(f247(a1),x67431),a82))+P102(f332(f332(f247(a1),f332(f332(f79(a1),x67431),x67431)),a82)) % 172.78/172.47 [6744]~P102(f332(f332(f246(a1),x67441),a100))+P102(f332(f332(f247(a1),f332(f332(f79(a1),x67441),x67441)),a100)) % 172.78/172.47 [6745]~P102(f332(f332(f246(a1),x67451),a82))+P102(f332(f332(f246(a1),f332(f332(f79(a1),x67451),x67451)),a82)) % 172.78/172.47 [6746]~P102(f332(f332(f246(a1),x67461),a100))+P102(f332(f332(f246(a1),f332(f332(f79(a1),x67461),x67461)),a100)) % 172.78/172.47 [6747]~P102(f332(f332(f90(a1),x67471),a82))+P102(f332(f332(f90(a1),f332(f332(f79(a1),x67471),x67471)),a82)) % 172.78/172.47 [7071]E(f332(f106(a876),x70711),f2(a876))+~P102(f332(a200,f332(f106(a1),f332(f332(f79(a1),x70711),a100)))) % 172.78/172.47 [7310]~P102(f332(f332(f246(a1),f2(a1)),f332(f106(a1),x73101)))+P102(f332(f332(f246(a1),f2(a1)),f332(f106(a1),f332(f332(f79(a1),x73101),x73101)))) % 172.78/172.47 [7311]P102(f332(a200,f332(f106(a1),x73111)))+~P102(f332(a200,f332(f106(a1),f332(f332(f79(a1),x73111),x73111)))) % 172.78/172.47 [7312]P102(f332(f332(f247(a1),x73121),a82))+~P102(f332(f332(f247(a1),f332(f332(f79(a1),x73121),x73121)),a82)) % 172.78/172.47 [7313]P102(f332(f332(f246(a1),x73131),a82))+~P102(f332(f332(f246(a1),f332(f332(f79(a1),x73131),x73131)),a82)) % 172.78/172.47 [7314]P102(f332(f332(f246(a1),x73141),a100))+~P102(f332(f332(f247(a1),f332(f332(f79(a1),x73141),x73141)),a100)) % 172.78/172.47 [7315]P102(f332(f332(f246(a1),x73151),a100))+~P102(f332(f332(f246(a1),f332(f332(f79(a1),x73151),x73151)),a100)) % 172.78/172.47 [7316]P102(f332(f332(f90(a1),x73161),a82))+~P102(f332(f332(f90(a1),f332(f332(f79(a1),x73161),x73161)),a82)) % 172.78/172.47 [7687]E(f332(a110,f556(x76871)),x76871)+~P102(f332(f332(f334(f883(f882(a876,a876),a871)),x76871),a101)) % 172.78/172.47 [6317]~P89(x63171)+E(f332(f106(x63171),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f77(x63171)) % 172.78/172.47 [6794]~P102(f332(a200,f332(f106(a1),x67941)))+E(f332(f106(a876),f332(f332(f22(a1),f332(f332(f79(a1),x67941),x67941)),a100)),f2(a876)) % 172.78/172.47 [7868]~P102(f332(f332(f247(a1),f332(f106(a1),x78681)),f2(a1)))+E(f332(f266(a1,a1),f332(a50,f49(f332(f78(a1),f77(a1)),f332(f78(a1),f332(f106(a1),x78681))))),f332(f332(f38(a1),f77(a1)),f332(f106(a1),x78681))) % 172.78/172.47 [7881]~P102(f332(f332(f247(a1),f332(f106(a1),x78811)),f2(a1)))+E(f332(f270(a1,a1),f332(a50,f49(f332(f78(a1),f77(a1)),f332(f78(a1),f332(f106(a1),x78811))))),f44(a1,f77(a1),f332(f106(a1),x78811))) % 172.78/172.47 [7929]~P102(f332(f332(f246(a1),a82),x79291))+P102(f332(f332(f247(a1),a82),f332(f332(f22(a1),f332(f332(f79(a1),x79291),x79291)),a100))) % 172.78/172.47 [7930]~P102(f332(f332(f247(a1),a100),x79301))+P102(f332(f332(f247(a1),a100),f332(f332(f22(a1),f332(f332(f79(a1),x79301),x79301)),a100))) % 172.78/172.47 [7931]~P102(f332(f332(f246(a1),a82),x79311))+P102(f332(f332(f246(a1),a82),f332(f332(f22(a1),f332(f332(f79(a1),x79311),x79311)),a100))) % 172.78/172.47 [7932]~P102(f332(f332(f246(a1),a100),x79321))+P102(f332(f332(f246(a1),a100),f332(f332(f22(a1),f332(f332(f79(a1),x79321),x79321)),a100))) % 172.78/172.47 [7933]~P102(f332(f332(f90(a1),a100),x79331))+P102(f332(f332(f90(a1),a100),f332(f332(f22(a1),f332(f332(f79(a1),x79331),x79331)),a100))) % 172.78/172.47 [8243]~P89(x82431)+~P31(x82431,f332(f106(x82431),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100))) % 172.78/172.47 [8424]P102(f332(f332(f247(a1),a100),x84241))+~P102(f332(f332(f247(a1),a100),f332(f332(f22(a1),f332(f332(f79(a1),x84241),x84241)),a100))) % 172.78/172.47 [8425]P102(f332(f332(f246(a1),a82),x84251))+~P102(f332(f332(f247(a1),a82),f332(f332(f22(a1),f332(f332(f79(a1),x84251),x84251)),a100))) % 172.78/172.47 [8426]P102(f332(f332(f246(a1),a82),x84261))+~P102(f332(f332(f246(a1),a82),f332(f332(f22(a1),f332(f332(f79(a1),x84261),x84261)),a100))) % 172.78/172.47 [8427]P102(f332(f332(f246(a1),a100),x84271))+~P102(f332(f332(f246(a1),a100),f332(f332(f22(a1),f332(f332(f79(a1),x84271),x84271)),a100))) % 172.78/172.47 [8428]P102(f332(f332(f90(a1),a100),x84281))+~P102(f332(f332(f90(a1),a100),f332(f332(f22(a1),f332(f332(f79(a1),x84281),x84281)),a100))) % 172.78/172.47 [8737]E(f332(f106(a876),f332(f332(f22(a1),f332(f332(f79(a1),x87371),x87371)),a100)),f332(f332(f85(a876,a876),f332(f106(a876),x87371)),f332(f332(f8(a876,a876,a876),a115),f332(f332(f18(a876,a876,a876),f79(a876)),f5(a876)))))+P102(f332(a200,f332(f106(a1),x87371))) % 172.78/172.47 [9583]E(x95831,f195(f883(f882(a876,a876),a871)))+P102(f332(f332(f334(f882(f883(f882(a876,a876),a871),f883(f882(a876,a876),a871))),f332(f332(f267(f883(f882(a876,a876),a871),f883(f882(a876,a876),a871)),x95831),f195(f883(f882(a876,a876),a871)))),a35)) % 172.78/172.47 [8668]~P102(f332(a200,f332(f106(a1),x86681)))+P102(f332(a200,f332(f106(a1),f332(f332(f22(a1),f332(f332(f79(a1),x86681),x86681)),a100)))) % 172.78/172.47 [8669]~P102(f332(f332(f247(a1),x86691),a82))+P102(f332(f332(f247(a1),f332(f332(f22(a1),f332(f332(f79(a1),x86691),x86691)),a100)),a82)) % 172.78/172.47 [8670]~P102(f332(f332(f247(a1),x86701),a100))+P102(f332(f332(f247(a1),f332(f332(f22(a1),f332(f332(f79(a1),x86701),x86701)),a100)),a100)) % 172.78/172.47 [8671]~P102(f332(f332(f247(a1),x86711),a82))+P102(f332(f332(f246(a1),f332(f332(f22(a1),f332(f332(f79(a1),x86711),x86711)),a100)),a82)) % 172.78/172.47 [8672]~P102(f332(f332(f246(a1),x86721),a100))+P102(f332(f332(f246(a1),f332(f332(f22(a1),f332(f332(f79(a1),x86721),x86721)),a100)),a100)) % 172.78/172.47 [8673]~P102(f332(f332(f90(a1),x86731),a100))+P102(f332(f332(f90(a1),f332(f332(f22(a1),f332(f332(f79(a1),x86731),x86731)),a100)),a100)) % 172.78/172.47 [8772]~P102(f332(f332(f246(a1),f2(a1)),f332(f106(a1),x87721)))+P102(f332(f332(f246(a1),f2(a1)),f332(f106(a1),f332(f332(f22(a1),f332(f332(f79(a1),x87721),x87721)),a100)))) % 172.78/172.47 [8934]~P89(x89341)+E(f332(f332(f79(x89341),f77(x89341)),f77(x89341)),f332(f106(x89341),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)))) % 172.78/172.47 [9089]P102(f332(a200,f332(f106(a1),x90891)))+~P102(f332(a200,f332(f106(a1),f332(f332(f22(a1),f332(f332(f79(a1),x90891),x90891)),a100)))) % 172.78/172.47 [9090]P102(f332(f332(f247(a1),x90901),a82))+~P102(f332(f332(f247(a1),f332(f332(f22(a1),f332(f332(f79(a1),x90901),x90901)),a100)),a82)) % 172.78/172.47 [9091]P102(f332(f332(f247(a1),x90911),a82))+~P102(f332(f332(f246(a1),f332(f332(f22(a1),f332(f332(f79(a1),x90911),x90911)),a100)),a82)) % 172.78/172.47 [9092]P102(f332(f332(f247(a1),x90921),a100))+~P102(f332(f332(f247(a1),f332(f332(f22(a1),f332(f332(f79(a1),x90921),x90921)),a100)),a100)) % 172.78/172.47 [9093]P102(f332(f332(f246(a1),x90931),a100))+~P102(f332(f332(f246(a1),f332(f332(f22(a1),f332(f332(f79(a1),x90931),x90931)),a100)),a100)) % 172.78/172.47 [9094]P102(f332(f332(f90(a1),x90941),a100))+~P102(f332(f332(f90(a1),f332(f332(f22(a1),f332(f332(f79(a1),x90941),x90941)),a100)),a100)) % 172.78/172.47 [9629]~P102(f332(f61(f882(a876,a876)),x96291))+P102(f332(f332(f334(f882(f883(f882(a876,a876),a871),f883(f882(a876,a876),a871))),f332(f332(f267(f883(f882(a876,a876),a871),f883(f882(a876,a876),a871)),f195(f883(f882(a876,a876),a871))),x96291)),a68)) % 172.78/172.47 [9416]~P141(x94161)+E(f332(f332(f257(x94161),f77(x94161)),f332(f106(a876),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)))),f77(x94161)) % 172.78/172.47 [9417]~P141(x94171)+E(f332(f332(f257(x94171),f2(x94171)),f332(f106(a876),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)))),f2(x94171)) % 172.78/172.47 [9856]~P102(f332(f332(f247(a876),f77(a876)),x98561))+P102(f332(f332(f247(a876),f2(a876)),f332(f332(f38(a876),x98561),f332(f106(a876),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)))))) % 172.78/172.47 [9868]~P102(f332(f332(f247(a876),f2(a876)),x98681))+P102(f332(f332(f247(a876),f2(a876)),f332(f332(f38(a876),f332(f332(f79(a876),x98681),f77(a876))),f332(f106(a876),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)))))) % 172.78/172.47 [9910]~E(f44(a876,x99101,f332(f106(a876),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)))),f77(a876))+P102(f332(f332(f247(a876),f2(a876)),f44(a876,x99101,f332(f106(a876),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)))))) % 172.78/172.47 [9929]E(f44(a876,x99291,f332(f106(a876),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)))),f77(a876))+~P102(f332(f332(f247(a876),f2(a876)),f44(a876,x99291,f332(f106(a876),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)))))) % 172.78/172.47 [4625]~P38(x46251,x46252)+P53(x46251,x46252) % 172.78/172.47 [4626]~P44(x46261,x46262)+P53(x46261,x46262) % 172.78/172.47 [4587]~E(x45871,x45872)+E(f279(x45871,x45872),f77(a102)) % 172.78/172.47 [4590]E(f227(x45901,x45902),x45901)+~E(x45902,f2(a876)) % 172.78/172.47 [4597]~E(x45972,f116(x45971))+E(f152(x45971,x45972),f116(x45971)) % 172.78/172.47 [4616]~E(f152(x46162,x46161),f116(x46162))+E(x46161,f116(x46162)) % 172.78/172.47 [4630]~P23(x46302)+P23(f883(x46301,x46302)) % 172.78/172.47 [4631]~P61(x46312)+P61(f883(x46311,x46312)) % 172.78/172.47 [4632]~P94(x46322)+P62(f883(x46321,x46322)) % 172.78/172.47 [4633]~P61(x46332)+P97(f883(x46331,x46332)) % 172.78/172.47 [4634]~P63(x46342)+P63(f883(x46341,x46342)) % 172.78/172.47 [4635]~P61(x46352)+P98(f883(x46351,x46352)) % 172.78/172.47 [4636]~P95(x46362)+P95(f883(x46361,x46362)) % 172.78/172.47 [4637]~P103(x46372)+P103(f883(x46371,x46372)) % 172.78/172.47 [4638]~P105(x46382)+P105(f883(x46381,x46382)) % 172.78/172.47 [4639]~P106(x46392)+P106(f883(x46391,x46392)) % 172.78/172.47 [4640]~P110(x46402)+P110(f883(x46401,x46402)) % 172.78/172.47 [4641]~P94(x46412)+P96(f883(x46411,x46412)) % 172.78/172.47 [4642]~P27(x46422)+P27(f883(x46421,x46422)) % 172.78/172.47 [4643]~P92(x46432)+P92(f883(x46431,x46432)) % 172.78/172.47 [4644]~P85(x46442)+P85(f883(x46441,x46442)) % 172.78/172.47 [4645]~P94(x46452)+P94(f883(x46451,x46452)) % 172.78/172.47 [4657]E(x46571,x46572)+~E(f332(a25,x46571),f332(a25,x46572)) % 172.78/172.47 [4659]E(x46591,x46592)+~E(f332(a115,x46591),f332(a115,x46592)) % 172.78/172.47 [4660]E(x46601,x46602)+~E(f332(a110,x46601),f332(a110,x46602)) % 172.78/172.47 [4661]E(x46611,x46612)+~E(f332(a3,x46611),f332(a3,x46612)) % 172.78/172.47 [4663]E(x46631,x46632)+~E(f332(a19,x46631),f332(a19,x46632)) % 172.78/172.47 [4767]~P25(x47671)+E(f44(x47671,x47672,x47672),f2(x47671)) % 172.78/172.47 [4801]~P38(x48011,x48012)+P38(f877(x48011),f146(x48011,x48012)) % 172.78/172.47 [4802]~P38(x48021,x48022)+P38(f877(x48021),f145(x48021,x48022)) % 172.78/172.47 [4898]~P38(x48981,x48982)+P38(f883(x48981,a871),f324(x48981,x48982)) % 172.78/172.47 [4899]~P38(x48991,x48992)+P38(f883(x48991,a871),f323(x48991,x48992)) % 172.78/172.47 [5019]~P28(x50191)+P39(f303(a1,x50191,x50192)) % 172.78/172.47 [5119]~P38(x51191,x51192)+P55(x51191,f67(x51191,x51191,x51192)) % 172.78/172.47 [5619]~P79(x56191)+P20(x56191,x56191,f78(x56191),x56192) % 172.78/172.47 [4611]~E(x46112,f116(x46111))+E(f332(f168(x46111),x46112),f116(x46111)) % 172.78/172.47 [4612]~E(x46122,f116(x46121))+E(f332(f169(x46121),x46122),f116(x46121)) % 172.78/172.47 [4667]E(x46671,f332(a107,x46672))+~E(f332(f103(a1),x46671),x46672) % 172.78/172.47 [4670]E(x46701,f116(x46702))+~E(f332(f168(x46702),x46701),f116(x46702)) % 172.78/172.47 [4671]E(x46711,f116(x46712))+~E(f332(f169(x46712),x46711),f116(x46712)) % 172.78/172.47 [4689]~P89(x46891)+E(f332(f106(x46891),x46892),f332(f105(x46891),x46892)) % 172.78/172.47 [4696]~E(x46962,f208(x46961))+E(f238(x46961,x46962),f195(f883(x46961,a871))) % 172.78/172.47 [4698]~P24(x46981)+P102(f332(f61(x46981),x46982)) % 172.78/172.47 [4705]E(x47051,f208(x47052))+E(f332(f239(x47052),f686(x47052,x47051)),x47051) % 172.78/172.47 [4706]E(x47061,f208(x47062))+E(f332(f239(x47062),f717(x47062,x47061)),x47061) % 172.78/172.47 [4708]~E(f718(x47082,x47081),f116(x47081))+E(f181(x47081,x47082),f116(f877(x47081))) % 172.78/172.47 [4717]~E(x47172,f116(x47171))+E(f332(f173(x47171),x47172),f195(f883(x47171,a871))) % 172.78/172.47 [4718]~E(x47182,f116(x47181))+E(f195(f883(x47181,a871)),f332(f173(x47181),x47182)) % 172.78/172.47 [4720]E(x47201,x47202)+~E(f332(f103(a1),x47201),f332(f103(a1),x47202)) % 172.78/172.47 [4723]E(f225(x47231,x47232),f2(a876))+P102(f332(f61(x47231),x47232)) % 172.78/172.47 [4743]~P113(x47431)+E(f81(x47431,f81(x47431,x47432)),f81(x47431,x47432)) % 172.78/172.47 [4756]~P114(x47561)+E(f332(f332(f257(x47561),x47562),f77(a876)),x47562) % 172.78/172.47 [4757]~P75(x47571)+E(f332(f332(f257(x47571),x47572),f77(a876)),x47572) % 172.78/172.47 [4761]E(x47611,x47612)+E(f279(x47611,x47612),f332(f332(f79(a102),x47612),f77(a102))) % 172.78/172.47 [4764]E(f332(f37(x47641),x47642),f2(a876))+P102(f332(f61(x47641),x47642)) % 172.78/172.47 [4768]~E(f152(x47681,x47682),x47682)+P102(f332(f137(x47681),x47682)) % 172.78/172.47 [4771]~P62(x47711)+E(f332(f332(f113(x47711),x47712),f195(x47711)),x47712) % 172.78/172.47 [4772]~P72(x47721)+E(f332(f332(f22(x47721),x47722),f2(x47721)),x47722) % 172.78/172.47 [4773]~P96(x47731)+E(f332(f332(f104(x47731),x47732),f255(x47731)),x47732) % 172.78/172.47 [4774]~P67(x47741)+E(f332(f332(f80(x47741),x47742),f77(x47741)),x47742) % 172.78/172.47 [4775]~P114(x47751)+E(f332(f332(f80(x47751),x47752),f77(x47751)),x47752) % 172.78/172.47 [4776]~P75(x47761)+E(f332(f332(f80(x47761),x47762),f77(x47761)),x47762) % 172.78/172.47 [4777]~P114(x47771)+E(f332(f332(f79(x47771),x47772),f2(x47771)),x47772) % 172.78/172.47 [4778]~P71(x47781)+E(f332(f332(f79(x47781),x47782),f2(x47781)),x47782) % 172.78/172.47 [4779]~P76(x47791)+E(f332(f332(f79(x47791),x47792),f2(x47791)),x47792) % 172.78/172.47 [4780]~P117(x47801)+E(f332(f332(f290(x47801),x47802),f77(x47801)),x47802) % 172.78/172.47 [4781]~P25(x47811)+E(f332(f332(f38(x47811),x47812),f77(x47811)),x47812) % 172.78/172.47 [4782]~P114(x47821)+E(f332(f332(f257(x47821),x47822),f2(a876)),f77(x47821)) % 172.78/172.47 [4783]~P109(x47831)+E(f332(f332(f257(x47831),x47832),f2(a876)),f77(x47831)) % 172.78/172.47 [4784]~E(x47842,f195(f883(x47841,a871)))+E(f332(f37(x47841),x47842),f2(a876)) % 172.78/172.47 [4795]~P25(x47951)+E(f44(x47951,x47952,f2(x47951)),x47952) % 172.78/172.47 [4803]~P96(x48031)+E(f332(f332(f113(x48031),x48032),f255(x48031)),f255(x48031)) % 172.78/172.47 [4804]~P62(x48041)+E(f332(f332(f104(x48041),x48042),f195(x48041)),f195(x48041)) % 172.78/172.47 [4805]~P114(x48051)+E(f332(f332(f80(x48051),x48052),f2(x48051)),f2(x48051)) % 172.78/172.47 [4806]~P125(x48061)+E(f332(f332(f80(x48061),x48062),f2(x48061)),f2(x48061)) % 172.78/172.47 [4807]~P118(x48071)+E(f332(f332(f290(x48071),x48072),f2(x48071)),f2(x48071)) % 172.78/172.47 [4808]~P25(x48081)+E(f332(f332(f38(x48081),x48082),f2(x48081)),f2(x48081)) % 172.78/172.47 [4809]E(x48091,f208(x48092))+~E(f238(x48092,x48091),f195(f883(x48092,a871))) % 172.78/172.47 [4812]~P25(x48121)+E(f44(x48121,x48122,f77(x48121)),f2(x48121)) % 172.78/172.47 [4813]~P25(x48131)+E(f44(x48131,f2(x48131),x48132),f2(x48131)) % 172.78/172.47 [4842]E(x48421,f2(a876))+E(f54(x48422,x48421,f116(x48422)),f116(f877(x48422))) % 172.78/172.47 [4865]P38(x48651,x48652)+~E(f565(x48652,x48651),f195(f883(x48651,a871))) % 172.78/172.47 [4866]E(x48661,f116(x48662))+~E(f332(f173(x48662),x48661),f195(f883(x48662,a871))) % 172.78/172.47 [4867]E(x48671,f116(x48672))+~E(f195(f883(x48672,a871)),f332(f173(x48672),x48671)) % 172.78/172.47 [4870]~E(x48701,x48702)+P102(f332(f332(a329,x48701),x48702)) % 172.78/172.47 [4880]P102(x48801)+P102(f332(f332(a335,x48801),x48802)) % 172.78/172.47 [4881]E(x48811,f116(x48812))+E(f332(f332(f165(x48812),x48811),f2(a876)),f332(f141(x48812),x48811)) % 172.78/172.47 [4884]E(f152(x48841,x48842),x48842)+~P102(f332(f137(x48841),x48842)) % 172.78/172.47 [4889]~P102(x48892)+P102(f332(f332(a335,x48891),x48892)) % 172.78/172.47 [4890]~P102(x48902)+P102(f332(f332(a331,x48901),x48902)) % 172.78/172.47 [4891]~P102(x48911)+P102(f332(f332(a331,x48911),x48912)) % 172.78/172.47 [4901]~E(x49012,f195(f883(x49011,a871)))+P102(f332(f61(x49011),x49012)) % 172.78/172.47 [4902]~E(f687(x49022,x49021),f692(x49022,x49021))+P102(f332(f137(x49021),x49022)) % 172.78/172.47 [4909]E(f332(f252(x49091),x49092),f195(f883(x49091,a871)))+P102(f332(x49092,f338(x49092))) % 172.78/172.47 [4910]E(f195(f883(x49101,a871)),f332(f252(x49101),x49102))+P102(f332(x49102,f428(x49102))) % 172.78/172.47 [4976]~P113(x49761)+E(f332(f332(f80(x49761),x49762),f81(x49761,x49762)),f332(f74(x49761),x49762)) % 172.78/172.47 [4987]~E(x49871,f2(a1))+E(f45(x49871,x49872),f332(f332(f267(a1,a1),f2(a1)),f2(a1))) % 172.78/172.47 [5018]~P53(x50181,x50182)+P53(x50181,f332(f287(x50181,x50181),x50182)) % 172.78/172.47 [5041]E(x50411,x50412)+~P102(f332(f332(a329,x50411),x50412)) % 172.78/172.47 [5052]P102(x50521)+~P102(f332(f332(a330,x50522),x50521)) % 172.78/172.47 [5053]P102(x50531)+~P102(f332(f332(a330,x50531),x50532)) % 172.78/172.47 [5058]~P110(x50581)+P102(f332(f332(f246(x50581),x50582),f255(x50581))) % 172.78/172.47 [5062]E(x50621,x50622)+~E(f332(x50621,f429(x50622,x50621)),f332(x50622,f429(x50622,x50621))) % 172.78/172.47 [5092]E(x50921,f2(a876))+E(f227(x50921,f44(a876,x50922,x50921)),f227(x50922,x50921)) % 172.78/172.47 [5097]~P104(x50971)+P29(x50971,f332(f332(f151(x50971),x50972),f116(x50971))) % 172.78/172.47 [5099]E(x50991,f2(a1))+P102(f332(f48(x50992,x50991),f45(x50992,x50991))) % 172.78/172.47 [5117]~E(x51171,x51172)+P102(f332(f332(f247(a876),x51171),f332(a115,x51172))) % 172.78/172.47 [5127]~E(x51271,f2(a876))+P102(f332(f332(f247(a876),x51271),f332(a115,x51272))) % 172.78/172.47 [5137]P102(f332(x51371,x51372))+P102(f332(f332(f246(a1),f2(a1)),f341(x51371))) % 172.78/172.47 [5202]P53(x52021,x52022)+~P53(x52021,f332(f287(x52021,x52021),x52022)) % 172.78/172.47 [5206]~E(f44(a876,x52062,x52061),f2(a876))+E(f332(f332(f80(a876),x52061),f342(x52061,x52062)),x52062) % 172.78/172.47 [5207]~E(f44(a1,x52072,x52071),f2(a1))+E(f332(f332(f80(a1),x52071),f343(x52071,x52072)),x52072) % 172.78/172.47 [5232]~P102(f332(x52321,x52322))+P102(f332(f332(f246(a1),f2(a1)),f340(x52321))) % 172.78/172.47 [5244]E(f332(f332(f22(a876),f332(a107,x52441)),f332(a107,x52442)),f332(a107,x52441))+~P102(f332(a200,x52442)) % 172.78/172.47 [5274]E(f280(x52741,x52742),f77(a102))+~P102(f332(f332(f246(a102),x52741),f77(a102))) % 172.78/172.47 [5371]E(f332(f332(f165(x53711),x53712),f687(x53712,x53711)),f332(f332(f165(x53711),x53712),f692(x53712,x53711)))+P102(f332(f137(x53711),x53712)) % 172.78/172.47 [5416]~P102(f332(x54161,f89(x54162,x54161)))+P102(f332(x54161,f579(x54162,x54161))) % 172.78/172.47 [5479]P55(x54791,x54792)+~P102(f332(f320(x54791,x54792),f535(x54792,x54791))) % 172.78/172.47 [5626]~E(f332(a115,f44(a876,x56261,x56262)),x56262)+E(f44(a876,f332(a115,x56261),x56262),f2(a876)) % 172.78/172.47 [5683]P38(x56831,x56832)+P102(f332(f332(f334(x56831),f599(x56832,x56831)),f600(x56832,x56831))) % 172.78/172.47 [5690]~P137(x56901)+P102(f332(f332(f334(x56901),f332(f103(x56901),x56902)),f112(x56901))) % 172.78/172.47 [5691]~P141(x56911)+P102(f332(f332(f334(x56911),f332(f103(x56911),x56912)),f193(x56911))) % 172.78/172.47 [5692]~P137(x56921)+P102(f332(f332(f334(x56921),f332(f105(x56921),x56922)),f112(x56921))) % 172.78/172.47 [5693]~P89(x56931)+P102(f332(f332(f334(x56931),f332(f106(x56931),x56932)),f112(x56931))) % 172.78/172.47 [5836]E(f332(a115,f44(a876,x58361,x58362)),x58362)+E(f44(a876,f332(a115,x58361),x58362),f332(a115,f44(a876,x58361,x58362))) % 172.78/172.47 [6248]P38(x62481,x62482)+~P102(f332(f332(f334(x62481),f507(x62482,x62481)),f321(x62481,x62482))) % 172.78/172.47 [6283]~P107(x62831)+~P102(f332(f332(f247(x62831),f332(f103(x62831),x62832)),f2(x62831))) % 172.78/172.47 [6284]~P81(x62841)+~P102(f332(f332(f247(x62841),f332(f74(x62841),x62842)),f2(x62841))) % 172.78/172.47 [6371]P102(f332(f332(f247(a1),x63711),f44(a1,x63712,x63711)))+~P102(f332(f332(f247(a1),x63711),f2(a1))) % 172.78/172.47 [6469]E(f332(f332(f310(a876),f332(a115,x64691)),f303(a876,x64692,x64691)),f303(a876,x64692,f332(a115,x64691)))+~P102(f332(f332(f246(a876),x64692),f332(a115,x64691))) % 172.78/172.47 [6556]~P104(x65561)+P29(x65561,f150(x65561,x65561,f5(x65561),x65562)) % 172.78/172.47 [6686]E(f332(f168(x66861),x66862),x66862)+~P102(f332(f332(f246(a876),f332(f196(f877(x66861)),x66862)),f77(a876))) % 172.78/172.47 [6706]~P81(x67061)+P102(f332(f332(f246(x67061),f332(f78(x67061),f332(f74(x67061),x67062))),f2(x67061))) % 172.78/172.47 [6739]~P38(x67391,x67392)+P38(x67391,f332(f332(f289(x67391,x67391,x67391),x67392),f308(x67391,x67392))) % 172.78/172.47 [6962]~P102(f332(f332(f247(a1),x69622),f2(a1)))+P102(f332(f332(f246(a1),f44(a1,x69621,x69622)),f2(a1))) % 172.78/172.47 [7358]~P141(x73581)+E(f197(x73581,f332(f332(f7(x73581,x73581,x73581),f79(x73581)),f77(x73581)),x73582,f2(x73581)),f332(f103(x73581),x73582)) % 172.78/172.47 [7386]~P121(x73861)+~P102(f332(f332(f247(x73861),f332(f332(f80(x73861),x73862),x73862)),f2(x73861))) % 172.78/172.47 [10019]~P113(x100191)+~P102(f332(f332(f247(x100191),f332(f332(f257(x100191),x100192),f332(f106(a876),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100))))),f2(x100191))) % 172.78/172.47 [4668]~E(x46682,f116(x46681))+E(f332(f196(f877(x46681)),x46682),f2(a876)) % 172.78/172.47 [4709]~E(x47091,f2(a876))+E(f332(f332(f79(a876),x47091),x47092),x47092) % 172.78/172.47 [4710]~E(x47102,f2(a876))+E(f332(f332(f80(a876),x47101),x47102),f2(a876)) % 172.78/172.47 [4712]~E(x47121,f2(a876))+E(f332(f332(f80(a876),x47121),x47122),f2(a876)) % 172.78/172.47 [4713]~E(x47132,f2(a876))+E(f332(f332(f257(a876),x47131),x47132),f77(a876)) % 172.78/172.47 [4714]~E(x47142,f2(a1))+E(f332(f332(f38(a1),x47141),x47142),f2(a1)) % 172.78/172.47 [4724]E(x47241,f116(x47242))+~E(f332(f196(f877(x47242)),x47241),f2(a876)) % 172.78/172.47 [4725]~P61(x47251)+E(f332(f332(f113(x47251),x47252),x47252),x47252) % 172.78/172.47 [4727]~P97(x47271)+E(f332(f332(f113(x47271),x47272),x47272),x47272) % 172.78/172.47 [4728]~P61(x47281)+E(f332(f332(f104(x47281),x47282),x47282),x47282) % 172.78/172.47 [4730]~P98(x47301)+E(f332(f332(f104(x47301),x47302),x47302),x47302) % 172.78/172.47 [4732]~P93(x47321)+E(f332(f332(f80(x47321),x47322),x47322),x47322) % 172.78/172.47 [4734]~P104(x47341)+E(f332(f332(f244(x47341),x47342),x47342),x47342) % 172.78/172.47 [4736]~P104(x47361)+E(f332(f332(f245(x47361),x47362),x47362),x47362) % 172.78/172.47 [4755]~P72(x47551)+E(f332(f332(f22(x47551),x47552),x47552),f2(x47551)) % 172.78/172.47 [4769]~P72(x47691)+E(f332(f78(x47691),f332(f78(x47691),x47692)),x47692) % 172.78/172.47 [4770]~P92(x47701)+E(f332(f78(x47701),f332(f78(x47701),x47702)),x47702) % 172.78/172.47 [4787]~E(x47872,f2(a876))+E(f332(f332(f257(a876),x47871),x47872),f332(a115,f2(a876))) % 172.78/172.47 [4821]~P62(x48211)+E(f332(f332(f113(x48211),f195(x48211)),x48212),x48212) % 172.78/172.47 [4822]~P96(x48221)+E(f332(f332(f104(x48221),f255(x48221)),x48222),x48222) % 172.78/172.47 [4823]~P67(x48231)+E(f332(f332(f80(x48231),f77(x48231)),x48232),x48232) % 172.78/172.47 [4824]~P114(x48241)+E(f332(f332(f80(x48241),f77(x48241)),x48242),x48242) % 172.78/172.47 [4825]~P75(x48251)+E(f332(f332(f80(x48251),f77(x48251)),x48252),x48252) % 172.78/172.47 [4826]~P114(x48261)+E(f332(f332(f79(x48261),f2(x48261)),x48262),x48262) % 172.78/172.47 [4827]~P71(x48271)+E(f332(f332(f79(x48271),f2(x48271)),x48272),x48272) % 172.78/172.47 [4828]~P76(x48281)+E(f332(f332(f79(x48281),f2(x48281)),x48282),x48282) % 172.78/172.47 [4846]~P96(x48461)+E(f332(f332(f113(x48461),f255(x48461)),x48462),f255(x48461)) % 172.78/172.47 [4847]~P62(x48471)+E(f332(f332(f104(x48471),f195(x48471)),x48472),f195(x48471)) % 172.78/172.47 [4848]~P114(x48481)+E(f332(f332(f80(x48481),f2(x48481)),x48482),f2(x48481)) % 172.78/172.47 [4849]~P125(x48491)+E(f332(f332(f80(x48491),f2(x48491)),x48492),f2(x48491)) % 172.78/172.47 [4850]~P75(x48501)+E(f332(f332(f257(x48501),f77(x48501)),x48502),f77(x48501)) % 172.78/172.47 [4851]~P117(x48511)+E(f332(f332(f290(x48511),f2(x48511)),x48512),f2(x48511)) % 172.78/172.47 [4852]~P25(x48521)+E(f332(f332(f38(x48521),f2(x48521)),x48522),f2(x48521)) % 172.78/172.47 [4860]E(x48601,f116(x48602))+E(f144(x48602,f332(f169(x48602),x48601)),f332(f141(x48602),x48601)) % 172.78/172.47 [4861]E(x48611,f116(x48612))+E(f332(f141(x48612),f332(f169(x48612),x48611)),f144(x48612,x48611)) % 172.78/172.47 [4862]E(x48621,f2(a876))+~E(f332(f332(f79(a876),x48622),x48621),x48622) % 172.78/172.47 [4868]~P137(x48681)+E(f332(f105(x48681),f332(f103(a1),x48682)),f332(f103(x48681),x48682)) % 172.78/172.47 [4869]~P89(x48691)+E(f332(f105(x48691),f332(f106(a1),x48692)),f332(f106(x48691),x48692)) % 172.78/172.47 [4876]E(x48761,f77(a876))+~E(f332(f332(f80(a876),x48762),x48761),f77(a876)) % 172.78/172.47 [4877]E(x48771,f77(a876))+~E(f332(f332(f80(a876),x48771),x48772),f77(a876)) % 172.78/172.47 [4878]E(x48781,f2(a876))+~E(f332(f332(f79(a876),x48782),x48781),f2(a876)) % 172.78/172.47 [4879]E(x48791,f2(a876))+~E(f332(f332(f79(a876),x48791),x48792),f2(a876)) % 172.78/172.47 [4894]~P113(x48941)+E(f332(f74(x48941),f332(f103(x48941),x48942)),f332(f103(x48941),x48942)) % 172.78/172.47 [4895]~P81(x48951)+E(f332(f74(x48951),f332(f74(x48951),x48952)),f332(f74(x48951),x48952)) % 172.78/172.47 [4896]~P81(x48961)+E(f332(f74(x48961),f332(f78(x48961),x48962)),f332(f74(x48961),x48962)) % 172.78/172.47 [4897]~P71(x48971)+E(f332(f166(x48971),f332(f169(x48971),x48972)),f332(f166(x48971),x48972)) % 172.78/172.47 [4903]~E(x49031,f332(a115,f2(a876)))+E(f332(f332(f257(a876),x49031),x49032),f332(a115,f2(a876))) % 172.78/172.47 [4912]~P72(x49121)+E(f332(f332(f22(x49121),f2(x49121)),x49122),f332(f78(x49121),x49122)) % 172.78/172.47 [4913]~E(x49132,f2(a876))+E(f139(a876,f332(f302(a876,x49131),x49132)),f116(a876)) % 172.78/172.47 [4922]~P89(x49221)+E(f332(f332(f79(x49221),x49222),f332(f106(x49221),a82)),x49222) % 172.78/172.47 [4923]E(x49231,f2(a1))+E(f46(f332(f74(a1),x49232),f332(f74(a1),x49231)),f52(x49232,x49231)) % 172.78/172.47 [4939]~E(x49391,x49392)+P102(f332(f332(f246(a876),x49391),x49392)) % 172.78/172.47 [4946]~E(x49461,f2(a102))+E(f332(f332(f79(a876),f332(a19,x49461)),x49462),x49462) % 172.78/172.47 [4947]~E(f332(f106(a1),x49472),f332(f103(a1),x49471))+E(x49471,f332(a107,f332(f106(a1),x49472))) % 172.78/172.47 [4956]~P28(x49561)+P28(f332(f332(f257(a1),x49561),x49562)) % 172.78/172.47 [4957]~P92(x49571)+E(f332(f332(f113(x49571),x49572),f332(f78(x49571),x49572)),f255(x49571)) % 172.78/172.47 [4958]~P92(x49581)+E(f332(f332(f104(x49581),x49582),f332(f78(x49581),x49582)),f195(x49581)) % 172.78/172.47 [4959]~P72(x49591)+E(f332(f332(f79(x49591),x49592),f332(f78(x49591),x49592)),f2(x49591)) % 172.78/172.47 [4984]E(x49841,f2(a876))+~E(f332(f78(a1),f332(f103(a1),x49842)),f332(f103(a1),x49841)) % 172.78/172.47 [4985]E(x49851,f2(a876))+~E(f332(f78(a1),f332(f103(a1),x49851)),f332(f103(a1),x49852)) % 172.78/172.47 [4995]E(f202(x49951,x49952),f2(a1))+P102(f332(f332(f246(a1),x49952),x49951)) % 172.78/172.47 [4996]E(f180(x49961,x49962),f116(a1))+P102(f332(f332(f246(a1),x49961),x49962)) % 172.78/172.47 [5009]E(x50091,f332(a115,f2(a876)))+~E(f332(f332(f80(a876),x50092),x50091),f332(a115,f2(a876))) % 172.78/172.47 [5010]E(x50101,f332(a115,f2(a876)))+~E(f332(f332(f80(a876),x50101),x50102),f332(a115,f2(a876))) % 172.78/172.47 [5011]~P103(x50111)+P102(f332(f332(f246(x50111),x50112),x50112)) % 172.78/172.47 [5012]~P91(x50121)+P102(f332(f332(f90(x50121),x50122),x50122)) % 172.78/172.47 [5015]~P89(x50151)+E(f332(f332(f80(x50151),x50152),f332(f106(x50151),a100)),f332(f78(x50151),x50152)) % 172.78/172.47 [5033]~P137(x50331)+E(f332(f78(x50331),f332(f105(x50331),x50332)),f332(f105(x50331),f332(f78(a1),x50332))) % 172.78/172.47 [5034]~P89(x50341)+E(f332(f78(x50341),f332(f106(x50341),x50342)),f332(f106(x50341),f332(f78(a1),x50342))) % 172.78/172.47 [5063]~E(x50631,f332(a115,x50632))+P102(f332(f332(f247(a876),f2(a876)),x50631)) % 172.78/172.47 [5080]~P104(x50801)+E(f332(f78(f883(x50801,a871)),f332(f253(x50801),x50802)),f332(f254(x50801),x50802)) % 172.78/172.47 [5081]~P104(x50811)+E(f332(f78(f883(x50811,a871)),f332(f301(x50811),x50812)),f332(f304(x50811),x50812)) % 172.78/172.47 [5082]~P104(x50821)+E(f332(f78(f883(x50821,a871)),f332(f254(x50821),x50822)),f332(f253(x50821),x50822)) % 172.78/172.47 [5083]~P104(x50831)+E(f332(f78(f883(x50831,a871)),f332(f304(x50831),x50832)),f332(f301(x50831),x50832)) % 172.78/172.47 [5091]~E(f332(f103(a1),x50912),x50911)+P102(f332(f332(f246(a1),f2(a1)),x50911)) % 172.78/172.47 [5098]~E(x50982,f2(a1))+E(f52(x50981,x50982),f332(f332(f267(a1,a1),f2(a1)),f332(f74(a1),x50981))) % 172.78/172.47 [5100]~P23(x51001)+P102(f332(f332(f246(x51001),f195(x51001)),x51002)) % 172.78/172.47 [5132]E(x51321,x51322)+~E(f332(f332(f79(a1),x51321),x51321),f332(f332(f79(a1),x51322),x51322)) % 172.78/172.47 [5136]~P102(f332(x51361,x51362))+P102(f332(x51361,f332(a107,f340(x51361)))) % 172.78/172.47 [5162]~P113(x51621)+E(f332(f332(f80(x51621),f81(x51621,x51622)),f332(f74(x51621),x51622)),x51622) % 172.78/172.47 [5163]E(x51631,x51632)+~P102(f332(f332(f201(a24),x51631),x51632)) % 172.78/172.47 [5170]~E(x51702,f2(a876))+E(f84(f882(a876,a876),f47(x51701,x51702)),f332(f332(f267(a876,a876),f2(a876)),x51701)) % 172.78/172.47 [5175]~E(x51751,x51752)+~P102(f332(f332(f247(a876),x51751),x51752)) % 172.78/172.47 [5176]~E(x51761,x51762)+~P102(f332(f332(f247(a1),x51761),x51762)) % 172.78/172.47 [5179]~P141(x51791)+E(f332(f332(f79(x51791),f77(x51791)),f332(f103(x51791),x51792)),f332(f103(x51791),f332(a115,x51792))) % 172.78/172.47 [5183]~E(x51831,f2(a876))+~P102(f332(f332(f247(a876),x51832),x51831)) % 172.78/172.47 [5199]E(f152(x51991,x51992),x51992)+~E(f332(f196(f877(x51991)),f152(x51991,x51992)),f332(f196(f877(x51991)),x51992)) % 172.78/172.47 [5200]E(f332(f37(x52001),f332(f173(x52001),x52002)),f332(f196(f877(x52001)),x52002))+~P102(f332(f137(x52001),x52002)) % 172.78/172.47 [5211]~P102(f332(x52111,f357(x52111)))+P102(f332(x52111,f332(f103(a1),x52112))) % 172.78/172.47 [5222]E(f280(x52221,x52222),f77(a102))+~P102(f332(f332(f247(a102),x52222),x52221)) % 172.78/172.47 [5223]E(f180(x52231,x52232),f116(a1))+~P102(f332(f332(f247(a1),x52232),x52231)) % 172.78/172.47 [5224]E(f125(x52241,x52242),f118(a1))+~P102(f332(f332(f247(a1),x52241),x52242)) % 172.78/172.47 [5225]~P105(x52251)+E(f303(x52251,x52252,x52252),f332(f332(f310(x52251),x52252),f195(f883(x52251,a871)))) % 172.78/172.47 [5247]~E(f332(f332(f22(a876),x52471),x52472),f2(a876))+P102(f332(f332(f246(a876),x52471),x52472)) % 172.78/172.47 [5248]~E(f332(f332(f22(a1),x52481),x52482),f2(a1))+P102(f332(f332(f90(a1),x52481),x52482)) % 172.78/172.47 [5271]~E(x52712,f2(a876))+E(f54(x52711,x52712,f116(x52711)),f332(f332(f151(f877(x52711)),f116(x52711)),f116(f877(x52711)))) % 172.78/172.47 [5275]~P103(x52751)+~P102(f332(f332(f247(x52751),x52752),x52752)) % 172.78/172.47 [5278]~E(f44(a1,x52781,x52782),f2(a1))+E(f44(a1,x52781,f332(f78(a1),x52782)),f2(a1)) % 172.78/172.47 [5280]~E(f44(a1,x52801,x52802),f2(a1))+E(f44(a1,f332(f78(a1),x52801),x52802),f2(a1)) % 172.78/172.47 [5289]E(f332(f302(a876,x52891),f332(a115,x52892)),f195(f883(a876,a871)))+P102(f332(f332(f246(a876),x52891),x52892)) % 172.78/172.47 [5310]E(f139(a876,f332(f302(a876,x53101),x53102)),f116(a876))+P102(f332(f332(f247(a876),x53101),x53102)) % 172.78/172.47 [5315]~E(f332(f37(x53151),f332(f173(x53151),x53152)),f332(f196(f877(x53151)),x53152))+P102(f332(f137(x53151),x53152)) % 172.78/172.47 [5320]~P102(f332(f137(x53201),x53202))+P102(f332(f137(x53201),f332(f168(x53201),x53202))) % 172.78/172.47 [5321]~P102(f332(f137(x53211),x53212))+P102(f332(f137(x53211),f332(f172(x53211),x53212))) % 172.78/172.47 [5322]~P102(f332(f137(x53221),x53222))+P102(f332(f137(x53221),f332(f169(x53221),x53222))) % 172.78/172.47 [5329]P102(f332(x53291,x53292))+~P102(f332(x53291,f332(a107,f341(x53291)))) % 172.78/172.47 [5330]P102(f332(f332(f246(a876),x53302),x53301))+P102(f332(f332(f246(a876),x53301),x53302)) % 172.78/172.47 [5331]P102(f332(f332(f246(a1),x53312),x53311))+P102(f332(f332(f246(a1),x53311),x53312)) % 172.78/172.47 [5334]~P81(x53341)+P102(f332(f332(f246(x53341),x53342),f332(f74(x53341),x53342))) % 172.78/172.47 [5337]P102(f332(x53371,f366(x53371)))+~P102(f332(x53371,f332(f103(a1),x53372))) % 172.78/172.47 [5363]E(f332(f332(f22(a876),x53631),x53632),f2(a876))+~P102(f332(f332(f246(a876),x53631),x53632)) % 172.78/172.47 [5364]E(f332(f332(f22(a1),x53641),x53642),f2(a1))+~P102(f332(f332(f90(a1),x53641),x53642)) % 172.78/172.47 [5365]E(f332(f332(f38(a876),x53651),x53652),f2(a876))+~P102(f332(f332(f247(a876),x53651),x53652)) % 172.78/172.47 [5383]E(f44(a876,x53831,x53832),x53831)+~P102(f332(f332(f247(a876),x53831),x53832)) % 172.78/172.47 [5392]E(f44(a1,x53921,f332(f78(a1),x53922)),f291(x53921,x53922))+P102(f332(f332(f246(a1),f2(a1)),x53922)) % 172.78/172.47 [5404]E(f332(f332(f22(a1),x54041),x54042),f202(x54041,x54042))+~P102(f332(f332(f246(a1),x54042),x54041)) % 172.78/172.47 [5423]P102(f332(f332(f246(a1),f2(a1)),f357(x54231)))+P102(f332(x54231,f332(f103(a1),x54232))) % 172.78/172.47 [5435]~P56(x54351)+P102(f332(f332(f334(x54351),x54352),f332(f173(x54351),f55(x54351)))) % 172.78/172.47 [5437]~P107(x54371)+P102(f332(f332(f246(x54371),f2(x54371)),f332(f103(x54371),x54372))) % 172.78/172.47 [5438]~P81(x54381)+P102(f332(f332(f246(x54381),f2(x54381)),f332(f74(x54381),x54382))) % 172.78/172.47 [5465]E(f332(f332(f79(a876),x54651),f807(x54652,x54651)),x54652)+~P102(f332(f332(f246(a876),x54651),x54652)) % 172.78/172.47 [5477]~E(f332(f106(a1),x54771),f332(f103(a1),x54772))+P102(f332(f332(f246(a1),f2(a1)),f332(f106(a1),x54771))) % 172.78/172.47 [5480]E(f303(a1,x54801,x54802),f195(f883(a1,a871)))+~P102(f332(f332(f247(a1),x54802),x54801)) % 172.78/172.47 [5482]~P113(x54821)+E(f332(f332(f80(x54821),f332(f74(x54821),x54822)),f332(f74(x54821),x54822)),f332(f332(f80(x54821),x54822),x54822)) % 172.78/172.47 [5489]E(f139(a876,f332(f302(a876,x54891),f332(a115,x54892))),f116(a876))+P102(f332(f332(f246(a876),x54891),x54892)) % 172.78/172.47 [5493]E(f332(f332(f38(a1),x54931),x54932),f292(x54931,x54932))+~P102(f332(f332(f246(a1),f2(a1)),x54932)) % 172.78/172.47 [5513]P102(f332(f137(x55131),x55132))+~P102(f332(f137(x55131),f332(f168(x55131),x55132))) % 172.78/172.47 [5514]P102(f332(f137(x55141),x55142))+~P102(f332(f137(x55141),f332(f169(x55141),x55142))) % 172.78/172.47 [5535]P102(f332(f61(a876),x55351))+P102(f332(f332(f334(a876),f358(x55351,x55352)),x55351)) % 172.78/172.47 [5536]P102(f332(f61(a876),x55361))+P102(f332(f332(f334(a876),f360(x55361,x55362)),x55361)) % 172.78/172.47 [5539]P102(f332(f332(f247(a876),x55392),f332(a115,x55391)))+P102(f332(f332(f247(a876),x55391),x55392)) % 172.78/172.47 [5540]E(f44(a1,x55401,x55402),f291(x55401,x55402))+~P102(f332(f332(f246(a1),f2(a1)),x55402)) % 172.78/172.47 [5543]E(f139(a876,f332(f302(a876,x55431),x55432)),f116(a876))+~P102(f332(f332(f246(a876),x55432),x55431)) % 172.78/172.47 [5544]~P79(x55441)+E(f332(f311(x55441,x55441,f78(x55441)),f332(f253(x55441),x55442)),f332(f304(x55441),f332(f78(x55441),x55442))) % 172.78/172.47 [5545]~P79(x55451)+E(f332(f311(x55451,x55451,f78(x55451)),f332(f301(x55451),x55452)),f332(f254(x55451),f332(f78(x55451),x55452))) % 172.78/172.47 [5546]~P79(x55461)+E(f332(f311(x55461,x55461,f78(x55461)),f332(f254(x55461),x55462)),f332(f301(x55461),f332(f78(x55461),x55462))) % 172.78/172.47 [5547]~P79(x55471)+E(f332(f311(x55471,x55471,f78(x55471)),f332(f304(x55471),x55472)),f332(f253(x55471),f332(f78(x55471),x55472))) % 172.78/172.47 [5558]E(x55581,f195(f883(x55582,a871)))+P102(f332(f332(f334(x55582),f449(x55581,x55582)),x55581)) % 172.78/172.47 [5559]E(x55591,f195(f883(x55592,a871)))+P102(f332(f332(f334(x55592),f450(x55591,x55592)),x55591)) % 172.78/172.47 [5570]~P102(f332(f332(f247(a876),x55701),x55702))+P102(f332(f332(f246(a876),x55701),x55702)) % 172.78/172.47 [5571]~P102(f332(f332(f247(a1),x55711),x55712))+P102(f332(f332(f246(a1),x55711),x55712)) % 172.78/172.47 [5587]E(f46(x55871,x55872),f332(f332(f267(a1,a1),f2(a1)),x55871))+~P102(f332(f332(f247(a1),x55871),x55872)) % 172.78/172.47 [5589]E(f226(f332(f78(a1),x55891),f332(f78(a1),x55892)),f226(x55891,x55892))+~P102(f332(f332(f247(a1),x55892),f2(a1))) % 172.78/172.47 [5600]E(x56001,x56002)+~E(f332(a3,f332(a115,f332(a19,x56001))),f332(a3,f332(a115,f332(a19,x56002)))) % 172.78/172.47 [5605]E(f46(x56051,x56052),f332(f332(f267(a1,a1),f2(a1)),x56051))+~P102(f332(f332(f246(a1),x56052),f2(a1))) % 172.78/172.47 [5632]E(f44(a876,f332(f106(a876),x56321),f332(f106(a876),x56322)),f2(a876))+~P102(f332(a200,f332(f106(a1),x56321))) % 172.78/172.47 [5647]P102(f332(f332(f246(a1),f2(a1)),f366(x56471)))+~P102(f332(x56471,f332(f103(a1),x56472))) % 172.78/172.47 [5681]P39(f303(a1,x56811,x56812))+~P102(f332(f332(f246(a1),f2(a1)),x56811)) % 172.78/172.47 [5686]~P102(f332(f61(x56861),x56862))+P102(f332(f61(f883(x56861,a871)),f332(f309(x56861),x56862))) % 172.78/172.47 [5699]E(f332(f332(f79(a1),x56991),f332(f103(a1),f369(x56992,x56991))),x56992)+~P102(f332(f332(f246(a1),x56991),x56992)) % 172.78/172.47 [5707]P102(f332(f332(f246(a876),x57071),x57072))+P102(f332(f332(f246(a876),f332(a115,x57072)),x57071)) % 172.78/172.47 [5750]E(f332(f332(f38(a876),f332(f106(a876),x57501)),f332(f106(a876),x57502)),f2(a876))+~P102(f332(a200,f332(f106(a1),x57501))) % 172.78/172.47 [5751]E(f332(f332(f80(a876),f332(f106(a876),x57511)),f332(f106(a876),x57512)),f2(a876))+~P102(f332(f332(f247(a1),x57511),a82)) % 172.78/172.47 [5753]P102(f332(f332(f247(a876),x57531),f332(a115,x57532)))+~P102(f332(f332(f247(a876),x57531),x57532)) % 172.78/172.47 [5755]P102(f332(f332(f247(a876),x57551),f332(a115,x57552)))+~P102(f332(f332(f246(a876),x57551),x57552)) % 172.78/172.47 [5757]P102(f332(f332(f246(a876),x57571),f332(a115,x57572)))+~P102(f332(f332(f246(a876),x57571),x57572)) % 172.78/172.47 [5760]~E(x57601,x57602)+P102(f332(f332(f247(a1),x57601),f332(f332(f79(a1),x57602),f77(a1)))) % 172.78/172.47 [5763]E(f44(a1,x57631,x57632),f2(a1))+E(f332(f332(f22(a1),x57632),f44(a1,x57631,x57632)),f44(a1,f332(f78(a1),x57631),x57632)) % 172.78/172.47 [5772]E(x57721,f116(x57722))+P102(f332(f332(f334(x57722),f144(x57722,x57721)),f332(f173(x57722),x57721))) % 172.78/172.47 [5784]E(f84(f882(a876,a876),f47(x57841,x57842)),f332(f332(f267(a876,a876),f2(a876)),x57841))+~P102(f332(f332(f247(a876),x57841),x57842)) % 172.78/172.47 [5817]E(f332(f332(f22(a876),f332(f106(a876),x58171)),f332(f106(a876),x58172)),f332(f106(a876),x58171))+~P102(f332(f332(f247(a1),x58172),a82)) % 172.78/172.47 [5818]E(f332(f332(f79(a876),f332(f106(a876),x58181)),f332(f106(a876),x58182)),f332(f106(a876),x58182))+~P102(f332(f332(f247(a1),x58181),a82)) % 172.78/172.47 [5823]E(f332(a115,f332(f332(f79(a876),x58231),f808(x58232,x58231))),x58232)+~P102(f332(f332(f247(a876),x58231),x58232)) % 172.78/172.47 [5846]P102(f332(x58461,x58462))+~P102(f332(x58461,f332(a88,f561(x58462,x58461)))) % 172.78/172.47 [5854]~P102(f332(f332(f247(a876),x58541),f332(a115,x58542)))+P102(f332(f332(f246(a876),x58541),x58542)) % 172.78/172.47 [5900]E(f332(f332(f310(a876),x59001),f332(f302(a876,x59002),x59001)),f332(f302(a876,x59002),f332(a115,x59001)))+~P102(f332(f332(f246(a876),x59002),x59001)) % 172.78/172.47 [5902]E(x59021,f116(x59022))+E(f332(f332(f134(x59022),f117(x59022,x59021)),f332(f332(f151(x59022),f144(x59022,x59021)),f116(x59022))),x59021) % 172.78/172.47 [5916]P102(f332(f61(x59161),x59162))+~P102(f332(f332(f247(a876),f2(a876)),f332(f37(x59161),x59162))) % 172.78/172.47 [5918]~E(x59181,f195(f883(x59182,a871)))+~P102(f332(f332(f247(a876),f2(a876)),f332(f37(x59182),x59181))) % 172.78/172.47 [5930]~P102(f332(f332(f247(a876),x59301),x59302))+P102(f332(f332(f246(a876),f332(a115,x59301)),x59302)) % 172.78/172.47 [5938]~P104(x59381)+E(f150(x59381,x59381,f5(x59381),f152(x59381,x59382)),f139(x59381,f332(f173(x59381),x59382))) % 172.78/172.47 [5941]E(x59411,f116(x59412))+P102(f332(f332(f334(x59412),f332(f141(x59412),x59411)),f332(f173(x59412),x59411))) % 172.78/172.47 [5947]~P107(x59471)+P102(f332(f332(f247(x59471),x59472),f332(f332(f79(x59471),x59472),f77(x59471)))) % 172.78/172.47 [5949]~P81(x59491)+P102(f332(f332(f246(x59491),f332(f78(x59491),x59492)),f332(f74(x59491),x59492))) % 172.78/172.47 [5982]P102(f332(f61(a876),x59821))+~P102(f332(f332(f247(a876),f358(x59821,x59822)),x59822)) % 172.78/172.47 [5983]P102(f332(f61(a876),x59831))+~P102(f332(f332(f246(a876),f360(x59831,x59832)),x59832)) % 172.78/172.47 [5987]~P102(f332(f61(f882(x59871,x59871)),x59872))+P102(f332(f61(x59871),f332(f285(x59871),x59872))) % 172.78/172.47 [6041]~P102(f332(f332(f247(a876),x60412),f332(a115,x60411)))+~P102(f332(f332(f247(a876),x60411),x60412)) % 172.78/172.47 [6042]~P105(x60421)+E(f332(f332(f104(f883(x60421,a871)),f332(f301(x60421),x60422)),f332(f254(x60421),x60422)),f332(f332(f310(x60421),x60422),f195(f883(x60421,a871)))) % 172.78/172.47 [6055]P102(f332(f61(x60551),x60552))+~P102(f332(f61(f883(x60551,a871)),f332(f309(x60551),x60552))) % 172.78/172.47 [6080]P102(f332(f332(f247(a876),f332(a115,x60801)),f332(a115,x60802)))+~P102(f332(f332(f247(a876),x60801),x60802)) % 172.78/172.47 [6081]P102(f332(f332(f247(a876),f332(a19,x60811)),f332(a19,x60812)))+~P102(f332(f332(f247(a102),x60811),x60812)) % 172.78/172.47 [6082]P102(f332(f332(f247(a102),f332(a3,x60821)),f332(a3,x60822)))+~P102(f332(f332(f247(a876),x60821),x60822)) % 172.78/172.47 [6083]P102(f332(f332(f246(a876),f332(a115,x60831)),f332(a115,x60832)))+~P102(f332(f332(f246(a876),x60831),x60832)) % 172.78/172.47 [6084]P102(f332(f332(f246(a876),f332(a19,x60841)),f332(a19,x60842)))+~P102(f332(f332(f246(a102),x60841),x60842)) % 172.78/172.47 [6085]P102(f332(f332(f246(a102),f332(a3,x60851)),f332(a3,x60852)))+~P102(f332(f332(f246(a876),x60851),x60852)) % 172.78/172.47 [6088]E(x60881,x60882)+~E(f332(f311(a876,a1,f103(a1)),x60881),f332(f311(a876,a1,f103(a1)),x60882)) % 172.78/172.47 [6104]P102(f332(f332(f247(a876),x61041),x61042))+~P102(f332(f332(f247(a876),f332(a115,x61041)),x61042)) % 172.78/172.47 [6107]P102(f332(f332(f247(a876),x61071),x61072))+~P102(f332(f332(f246(a876),f332(a115,x61071)),x61072)) % 172.78/172.47 [6108]P102(f332(f332(f246(a876),x61081),x61082))+~P102(f332(f332(f246(a876),f332(a115,x61081)),x61082)) % 172.78/172.47 [6123]E(f44(a1,x61231,x61232),f2(a1))+E(f332(f332(f22(a1),f44(a1,x61231,x61232)),x61232),f44(a1,x61231,f332(f78(a1),x61232))) % 172.78/172.47 [6188]E(f332(f37(f883(x61881,a871)),f332(f309(x61881),x61882)),f332(f332(f257(a876),f332(a115,f332(a115,f2(a876)))),f332(f37(x61881),x61882)))+~P102(f332(f61(x61881),x61882)) % 172.78/172.47 [6191]E(x61911,f116(x61912))+E(f332(f332(f165(x61912),x61911),f332(f332(f22(a876),f332(f196(f877(x61912)),x61911)),f77(a876))),f144(x61912,x61911)) % 172.78/172.47 [6216]E(x62161,f116(x62162))+E(f332(f332(f134(x62162),f332(f172(x62162),x62161)),f332(f332(f151(x62162),f332(f141(x62162),x62161)),f116(x62162))),f332(f168(x62162),x62161)) % 172.78/172.47 [6245]~P102(f332(f61(x62451),f39(f883(x62451,a871),x62452)))+P102(f332(f61(f883(x62451,a871)),x62452)) % 172.78/172.47 [6268]P102(f332(f332(f246(a876),f332(f106(a876),x62681)),f332(f106(a876),x62682)))+~P102(f332(f332(f246(a1),x62681),a82)) % 172.78/172.47 [6285]~P102(f332(f332(f247(a1),x62851),x62852))+P102(f332(f332(f247(a1),x62851),f332(f332(f79(a1),x62852),f77(a1)))) % 172.78/172.47 [6286]~P102(f332(f332(f246(a1),x62861),x62862))+P102(f332(f332(f247(a1),x62861),f332(f332(f79(a1),x62862),f77(a1)))) % 172.78/172.47 [6287]~P102(f332(f332(f247(a1),x62871),x62872))+P102(f332(f332(f246(a1),x62871),f332(f332(f22(a1),x62872),f77(a1)))) % 172.78/172.47 [6290]~P102(f332(f332(f247(a876),x62901),x62902))+P102(f332(f332(f247(a1),f332(f103(a1),x62901)),f332(f103(a1),x62902))) % 172.78/172.47 [6291]~P102(f332(f332(f247(a1),x62911),x62912))+P102(f332(f332(f247(a1),f332(f106(a1),x62911)),f332(f106(a1),x62912))) % 172.78/172.47 [6292]~P102(f332(f332(f246(a1),x62921),x62922))+P102(f332(f332(f246(a876),f332(f106(a876),x62921)),f332(f106(a876),x62922))) % 172.78/172.47 [6294]~P102(f332(f332(f246(a876),x62941),x62942))+P102(f332(f332(f246(a1),f332(f103(a1),x62941)),f332(f103(a1),x62942))) % 172.78/172.47 [6295]~P102(f332(f332(f246(a1),x62951),x62952))+P102(f332(f332(f246(a1),f332(f106(a1),x62951)),f332(f106(a1),x62952))) % 172.78/172.47 [6296]~P102(f332(f332(f90(a1),x62961),x62962))+P102(f332(f332(f90(a1),f332(f106(a1),x62961)),f332(f106(a1),x62962))) % 172.78/172.47 [6314]~P102(f332(f332(f246(a876),x63141),x63142))+~P102(f332(f332(f246(a876),f332(a115,x63142)),x63141)) % 172.78/172.47 [6358]~P102(f332(f332(f247(a876),f332(a115,x63581)),f332(a115,x63582)))+P102(f332(f332(f247(a876),x63581),x63582)) % 172.78/172.47 [6359]~P102(f332(f332(f247(a102),f332(a3,x63591)),f332(a3,x63592)))+P102(f332(f332(f247(a876),x63591),x63592)) % 172.78/172.47 [6360]~P102(f332(f332(f247(a876),f332(a107,x63601)),f332(a107,x63602)))+P102(f332(f332(f247(a1),x63601),x63602)) % 172.78/172.47 [6361]~P102(f332(f332(f247(a876),f332(a19,x63611)),f332(a19,x63612)))+P102(f332(f332(f247(a102),x63611),x63612)) % 172.78/172.47 [6362]~P102(f332(f332(f246(a876),f332(a115,x63621)),f332(a115,x63622)))+P102(f332(f332(f246(a876),x63621),x63622)) % 172.78/172.47 [6363]~P102(f332(f332(f246(a102),f332(a3,x63631)),f332(a3,x63632)))+P102(f332(f332(f246(a876),x63631),x63632)) % 172.78/172.47 [6364]~P102(f332(f332(f246(a876),f332(a19,x63641)),f332(a19,x63642)))+P102(f332(f332(f246(a102),x63641),x63642)) % 172.78/172.47 [6404]~P102(f332(f332(f247(a876),f332(a107,x64042)),f332(a107,x64041)))+P102(f332(f332(f247(a1),f2(a1)),x64041)) % 172.78/172.47 [6435]P102(f332(f332(f246(a1),f2(a1)),f44(a1,x64351,x64352)))+~P102(f332(f332(f247(a1),f2(a1)),x64352)) % 172.78/172.47 [6592]P38(x65921,x65922)+~E(f332(f332(f289(x65921,x65921,x65921),x65922),x65922),f195(f883(f882(x65921,x65921),a871))) % 172.78/172.47 [6604]~P38(x66041,x66042)+P38(x66041,f332(f332(f289(x66041,x66041,x66041),x66042),x66042)) % 172.78/172.47 [6616]P102(f332(f332(f247(a1),x66161),x66162))+~P102(f332(f332(f246(a1),x66161),f332(f332(f22(a1),x66162),f77(a1)))) % 172.78/172.47 [6617]P102(f332(f332(f246(a1),x66171),x66172))+~P102(f332(f332(f247(a1),x66171),f332(f332(f79(a1),x66172),f77(a1)))) % 172.78/172.47 [6620]P102(f332(f332(f247(a876),x66201),x66202))+~P102(f332(f332(f247(a1),f332(f103(a1),x66201)),f332(f103(a1),x66202))) % 172.78/172.47 [6621]P102(f332(f332(f247(a1),x66211),x66212))+~P102(f332(f332(f247(a876),f332(f106(a876),x66211)),f332(f106(a876),x66212))) % 172.78/172.47 [6622]P102(f332(f332(f247(a1),x66221),x66222))+~P102(f332(f332(f247(a1),f332(f106(a1),x66221)),f332(f106(a1),x66222))) % 172.78/172.47 [6624]P102(f332(f332(f246(a876),x66241),x66242))+~P102(f332(f332(f246(a1),f332(f103(a1),x66241)),f332(f103(a1),x66242))) % 172.78/172.47 [6625]P102(f332(f332(f246(a1),x66251),x66252))+~P102(f332(f332(f246(a1),f332(f106(a1),x66251)),f332(f106(a1),x66252))) % 172.78/172.47 [6626]P102(f332(f332(f90(a1),x66261),x66262))+~P102(f332(f332(f90(a1),f332(f106(a1),x66261)),f332(f106(a1),x66262))) % 172.78/172.47 [6719]~E(f737(x67192,x67191),f116(x67191))+E(f332(f142(f877(x67191),f877(x67191),f134(x67191),f116(x67191)),x67192),f116(x67191)) % 172.78/172.47 [6720]~E(f740(x67202,x67201),f116(x67201))+E(f332(f142(f877(x67201),f877(x67201),f134(x67201),f116(x67201)),x67202),f116(x67201)) % 172.78/172.47 [6727]~P27(x67271)+E(f332(f142(x67271,x67271,f104(x67271),f255(x67271)),x67272),f40(x67271,f332(f173(x67271),x67272))) % 172.78/172.47 [6728]~P27(x67281)+E(f332(f142(x67281,x67281,f113(x67281),f195(x67281)),x67282),f39(x67281,f332(f173(x67281),x67282))) % 172.78/172.47 [6740]E(x67401,f2(a102))+E(f332(f332(f79(a876),f332(a19,f332(f332(f22(a102),x67401),f77(a102)))),f332(a115,x67402)),f332(f332(f79(a876),f332(a19,x67401)),x67402)) % 172.78/172.47 [6790]P102(f332(f332(f247(a1),f332(f332(f22(a1),x67901),x67902)),f2(a1)))+~P102(f332(f332(f247(a1),x67901),x67902)) % 172.78/172.47 [6818]~P104(x68181)+E(f332(f332(f113(f883(x68181,a871)),f332(f332(f310(x68181),x68182),f195(f883(x68181,a871)))),f332(f304(x68181),x68182)),f332(f254(x68181),x68182)) % 172.78/172.47 [6893]~P55(x68931,x68932)+P38(x68931,f332(f252(f882(x68931,x68931)),f332(f271(x68931,x68931,a871),x68932))) % 172.78/172.47 [6894]~P55(x68941,x68942)+P53(x68941,f332(f252(f882(x68941,x68941)),f332(f271(x68941,x68941,a871),x68942))) % 172.78/172.47 [6895]E(x68951,f195(f883(x68952,a871)))+~P102(f332(f332(f246(f883(x68952,a871)),x68951),f195(f883(x68952,a871)))) % 172.78/172.47 [6978]~P102(f332(f332(f247(a876),f2(a876)),x69782))+P102(f332(f332(f247(a876),f44(a876,x69781,x69782)),x69782)) % 172.78/172.47 [6980]~P102(f332(f332(f247(a1),f2(a1)),x69802))+P102(f332(f332(f247(a1),f44(a1,x69801,x69802)),x69802)) % 172.78/172.47 [6981]~P102(f332(f332(f247(a876),f2(a876)),x69812))+P102(f332(f332(f246(a876),f44(a876,x69811,x69812)),x69812)) % 172.78/172.47 [6982]~P102(f332(f332(f246(a1),f2(a1)),x69821))+P102(f332(f332(f246(a1),f44(a1,x69821,x69822)),x69821)) % 172.78/172.47 [7060]~P105(x70601)+E(f332(f332(f22(f883(x70601,a871)),f332(f332(f310(x70601),x70602),f195(f883(x70601,a871)))),f332(f253(x70601),x70602)),f332(f332(f310(x70601),x70602),f195(f883(x70601,a871)))) % 172.78/172.47 [7133]~P49(x71331,x71332)+P40(x71331,f255(f883(x71331,a871)),f332(f252(f882(x71331,x71331)),f332(f271(x71331,x71331,a871),x71332))) % 172.78/172.47 [7134]P102(f332(x71341,x71342))+P102(f332(f332(f334(f883(f882(a876,a876),a871)),f561(x71342,x71341)),a101)) % 172.78/172.47 [7179]E(f332(f332(f134(a876),f139(a876,f332(f302(a876,x71791),x71792))),f332(f332(f151(a876),x71792),f116(a876))),f139(a876,f332(f302(a876,x71791),f332(a115,x71792))))+~P102(f332(f332(f246(a876),x71791),x71792)) % 172.78/172.47 [7320]E(x73201,f2(a876))+~E(f332(f142(a876,a876,f79(a876),x73201),x73202),f2(a876)) % 172.78/172.47 [7348]~P102(f332(f332(f247(a1),f332(f332(f22(a1),x73481),x73482)),f2(a1)))+P102(f332(f332(f247(a1),x73481),x73482)) % 172.78/172.47 [7377]P38(x73771,x73772)+~P38(x73771,f332(f332(f289(x73771,x73771,x73771),x73772),x73772)) % 172.78/172.47 [7406]~P102(f332(f332(f246(a876),f332(a115,x74061)),x74062))+P102(f192(a871,a250,f332(f246(a876),x74061),x74062)) % 172.78/172.47 [7565]P20(a876,a876,f332(f332(f7(a876,a876,a876),f22(a876)),x75651),x75652)+P102(f332(f332(f334(a876),f568(x75651,x75652)),x75652)) % 172.78/172.47 [7621]E(f332(f332(f332(f65(a876,x76211,f79(a876)),f332(f16(a876,x76211),f77(a876))),f2(a876)),x76212),f332(f37(x76211),x76212))+~P102(f332(f61(x76211),x76212)) % 172.78/172.47 [7663]P20(a876,a876,f332(f332(f7(a876,a876,a876),f22(a876)),x76631),x76632)+~P102(f332(f332(f246(a876),x76631),f568(x76631,x76632))) % 172.78/172.47 [7723]P38(x77231,x77232)+P102(f332(f332(f246(f883(x77231,a871)),f565(x77232,x77231)),f332(f286(x77231,x77231,x77232),f565(x77232,x77231)))) % 172.78/172.47 [7728]P55(x77281,x77282)+~P38(x77281,f332(f252(f882(x77281,x77281)),f332(f271(x77281,x77281,a871),x77282))) % 172.78/172.47 [7801]P102(f332(f332(f246(a876),f332(a115,x78011)),x78012))+~P102(f192(a871,a250,f332(f246(a876),x78011),x78012)) % 172.78/172.47 [7856]P102(f332(f332(f334(f882(a876,a876)),f332(f332(f267(a876,a876),x78561),x78562)),f308(a876,a322)))+~P102(f332(f332(f246(a876),x78561),x78562)) % 172.78/172.47 [7953]P49(x79531,x79532)+~P40(x79531,f255(f883(x79531,a871)),f332(f252(f882(x79531,x79531)),f332(f271(x79531,x79531,a871),x79532))) % 172.78/172.47 [8014]~P102(f332(f137(x80141),x80142))+P102(f332(f137(f883(x80141,a871)),f332(f332(f154(f877(x80141),f883(x80141,a871)),f173(x80141)),f53(x80141,x80142)))) % 172.78/172.47 [8220]~P38(x82201,f332(f287(x82201,x82201),x82202))+P38(x82201,f332(f287(x82201,x82201),f332(f332(f289(x82201,x82201,x82201),x82202),f308(x82201,x82202)))) % 172.78/172.47 [8341]P102(f332(f61(f882(x83411,x83411)),f332(f332(f289(x83411,x83411,x83411),x83412),f308(x83411,x83412))))+~P102(f332(f61(f882(x83411,x83411)),x83412)) % 172.78/172.47 [8372]E(x83721,f2(a1))+P102(f332(f48(x83722,x83721),f332(f332(f267(a1,a1),f332(f332(f38(a1),x83722),x83721)),f44(a1,x83722,x83721)))) % 172.78/172.47 [8383]~P102(f332(f332(f334(f882(a876,a876)),f332(f332(f267(a876,a876),x83831),x83832)),f308(a876,a322)))+P102(f332(f332(f246(a876),x83831),x83832)) % 172.78/172.47 [8401]~P76(x84011)+E(f332(f142(x84011,x84011,f332(f7(x84011,x84011,x84011),f79(x84011)),f2(x84011)),f332(f169(x84011),x84012)),f332(f142(x84011,x84011,f79(x84011),f2(x84011)),x84012)) % 172.78/172.47 [8577]~P104(x85771)+E(f332(f142(f877(x85771),x85771,f332(f7(x85771,f877(x85771),f877(x85771)),f148(x85771,x85771,f5(x85771))),f116(x85771)),x85772),f150(x85771,x85771,f5(x85771),x85772)) % 172.78/172.47 [8678]~P53(x86781,f332(f252(f882(x86781,x86781)),f332(f271(x86781,x86781,a871),x86782)))+P53(x86781,f332(f252(f882(x86781,x86781)),f332(f271(x86781,x86781,a871),f256(x86781,x86781,x86782)))) % 172.78/172.47 [8692]P102(f332(f332(f334(f882(a876,a876)),f332(f332(f267(a876,a876),x86921),x86922)),f332(f332(f289(a876,a876,a876),a322),f308(a876,a322))))+~P102(f332(f332(f247(a876),x86921),x86922)) % 172.78/172.47 [8735]~P102(f332(f61(f882(x87351,x87351)),f332(f332(f289(x87351,x87351,x87351),x87352),f308(x87351,x87352))))+P102(f332(f61(f882(x87351,x87351)),x87352)) % 172.78/172.47 [8786]~P53(x87861,f332(f252(f882(x87861,x87861)),f332(f271(x87861,x87861,a871),f256(x87861,x87861,x87862))))+P53(x87861,f332(f252(f882(x87861,x87861)),f332(f271(x87861,x87861,a871),x87862))) % 172.78/172.47 [8991]P53(x89911,x89912)+P102(f332(f332(f334(f882(x89911,x89911)),f332(f332(f267(x89911,x89911),f587(x89912,x89911)),f587(x89912,x89911))),f332(f332(f289(x89911,x89911,x89911),x89912),f308(x89911,x89912)))) % 172.78/172.47 [8992]P53(x89921,x89922)+P102(f332(f332(f334(f882(x89921,x89921)),f332(f332(f267(x89921,x89921),f597(x89922,x89921)),f597(x89922,x89921))),f332(f332(f289(x89921,x89921,x89921),x89922),f308(x89921,x89922)))) % 172.78/172.47 [9108]~P102(f332(f332(f334(f882(a876,a876)),f332(f332(f267(a876,a876),x91081),x91082)),f332(f332(f289(a876,a876,a876),a322),f308(a876,a322))))+P102(f332(f332(f247(a876),x91081),x91082)) % 172.78/172.47 [5076]~P89(x50761)+E(f332(f332(f79(x50761),f332(f106(x50761),a82)),x50762),x50762) % 172.78/172.47 [5105]~P92(x51051)+E(f332(f332(f113(x51051),f332(f78(x51051),x51052)),x51052),f255(x51051)) % 172.78/172.47 [5106]~P92(x51061)+E(f332(f332(f104(x51061),f332(f78(x51061),x51062)),x51062),f195(x51061)) % 172.78/172.47 [5107]~P66(x51071)+E(f332(f332(f79(x51071),f332(f78(x51071),x51072)),x51072),f2(x51071)) % 172.78/172.47 [5108]~P72(x51081)+E(f332(f332(f79(x51081),f332(f78(x51081),x51082)),x51082),f2(x51081)) % 172.78/172.47 [5140]~P89(x51401)+E(f332(f332(f80(x51401),f332(f106(x51401),a100)),x51402),f332(f78(x51401),x51402)) % 172.78/172.47 [5303]~P112(x53031)+E(f332(f332(f80(x53031),f332(f78(x53031),f77(x53031))),x53032),f332(f78(x53031),x53032)) % 172.78/172.47 [5347]E(f332(f74(a1),x53471),f77(a1))+~E(f332(f74(a1),f332(f332(f80(a1),x53471),x53472)),f77(a1)) % 172.78/172.47 [5440]~P89(x54401)+E(f332(f332(f79(x54401),f77(x54401)),f332(f106(x54401),x54402)),f332(f106(x54401),f332(f332(f22(a1),x54402),a100))) % 172.78/172.47 [5494]~P61(x54941)+E(f13(x54941,f332(f332(f310(x54941),x54942),f195(f883(x54941,a871)))),x54942) % 172.78/172.47 [5495]~P61(x54951)+E(f10(x54951,f332(f332(f310(x54951),x54952),f195(f883(x54951,a871)))),x54952) % 172.78/172.47 [5496]~P104(x54961)+E(f14(x54961,f332(f332(f310(x54961),x54962),f195(f883(x54961,a871)))),x54962) % 172.78/172.47 [5497]~P104(x54971)+E(f15(x54971,f332(f332(f310(x54971),x54972),f195(f883(x54971,a871)))),x54972) % 172.78/172.47 [5498]~P27(x54981)+E(f40(x54981,f332(f332(f310(x54981),x54982),f195(f883(x54981,a871)))),x54982) % 172.78/172.47 [5499]~P27(x54991)+E(f39(x54991,f332(f332(f310(x54991),x54992),f195(f883(x54991,a871)))),x54992) % 172.78/172.47 [5521]E(f332(f332(f79(a876),x55211),f332(f332(f22(a876),x55212),x55211)),x55212)+P102(f332(f332(f247(a876),x55212),x55211)) % 172.78/172.47 [5553]E(x55531,f116(x55532))+P102(f332(f332(f247(a876),f2(a876)),f332(f196(f877(x55532)),x55531))) % 172.78/172.47 [5678]~P104(x56781)+E(f11(x56781,f245(x56781),f332(f332(f310(x56781),x56782),f195(f883(x56781,a871)))),x56782) % 172.78/172.47 [5679]~P104(x56791)+E(f12(x56791,f244(x56791),f332(f332(f310(x56791),x56792),f195(f883(x56791,a871)))),x56792) % 172.78/172.47 [5740]E(f332(f332(f22(a876),x57401),f332(f332(f22(a876),x57401),x57402)),x57402)+~P102(f332(f332(f246(a876),x57402),x57401)) % 172.78/172.47 [5741]E(f332(f332(f79(a876),x57411),f332(f332(f22(a876),x57412),x57411)),x57412)+~P102(f332(f332(f246(a876),x57411),x57412)) % 172.78/172.47 [5762]E(f44(a876,f332(f332(f22(a876),x57621),x57622),x57622),f44(a876,x57621,x57622))+P102(f332(f332(f247(a876),x57621),x57622)) % 172.78/172.47 [5773]E(f332(f78(a1),f332(f332(f38(a1),x57731),f332(f78(a1),x57732))),f292(x57731,x57732))+P102(f332(f332(f246(a1),f2(a1)),x57732)) % 172.78/172.47 [5775]~E(x57752,f2(a876))+P102(f332(f332(f247(a876),f2(a876)),f332(f332(f257(a876),x57751),x57752))) % 172.78/172.47 [5826]~P89(x58261)+E(f332(f332(f79(x58261),f332(f78(x58261),f77(x58261))),f332(f106(x58261),x58262)),f332(f106(x58261),f332(f332(f79(a1),x58262),a100))) % 172.78/172.47 [5827]E(f332(f332(f257(a876),f332(f106(a876),x58271)),x58272),f332(f332(f257(a876),f2(a876)),x58272))+~P102(f332(a200,f332(f106(a1),x58271))) % 172.78/172.47 [5922]E(f332(f141(a876),f139(a876,f332(f302(a876,x59221),x59222))),x59221)+~P102(f332(f332(f247(a876),x59221),x59222)) % 172.78/172.47 [5942]E(f332(f332(f80(a876),f332(f106(a876),x59421)),f332(f106(a876),x59422)),f332(f106(a876),f332(f332(f80(a1),x59421),x59422)))+P102(f332(f332(f247(a1),x59421),a82)) % 172.78/172.47 [5948]~P121(x59481)+P102(f332(f332(f246(x59481),f2(x59481)),f332(f332(f80(x59481),x59482),x59482))) % 172.78/172.47 [5960]E(f332(f332(f22(a876),f332(a115,x59601)),x59602),f332(a115,f332(f332(f22(a876),x59601),x59602)))+~P102(f332(f332(f246(a876),x59602),x59601)) % 172.78/172.47 [5963]E(f44(a876,f332(f332(f22(a876),x59631),x59632),x59632),f44(a876,x59631,x59632))+~P102(f332(f332(f246(a876),x59632),x59631)) % 172.78/172.47 [6016]E(f332(f332(f257(a876),f332(a107,x60161)),x60162),f332(a107,f332(f332(f257(a1),x60161),x60162)))+~P102(f332(f332(f246(a1),f2(a1)),x60161)) % 172.78/172.47 [6032]P102(f332(f137(x60321),x60322))+P102(f332(f332(f247(a876),f687(x60322,x60321)),f332(f196(f877(x60321)),x60322))) % 172.78/172.47 [6033]P102(f332(f137(x60331),x60332))+P102(f332(f332(f247(a876),f692(x60332,x60331)),f332(f196(f877(x60331)),x60332))) % 172.78/172.47 [6048]~E(x60481,f116(x60482))+~P102(f332(f332(f247(a876),f2(a876)),f332(f196(f877(x60482)),x60481))) % 172.78/172.47 [6062]E(f144(a876,f139(a876,f332(f302(a876,x60621),x60622))),f332(f332(f22(a876),x60622),f77(a876)))+~P102(f332(f332(f247(a876),x60621),x60622)) % 172.78/172.47 [6065]E(f332(f332(f79(a1),x60651),f332(f103(a1),f332(a115,f370(x60652,x60651)))),x60652)+~P102(f332(f332(f247(a1),x60651),x60652)) % 172.78/172.47 [6072]E(x60721,f2(a876))+E(f332(f332(f80(a876),x60722),f332(f332(f257(a876),x60722),f332(f332(f22(a876),x60721),f77(a876)))),f332(f332(f257(a876),x60722),x60721)) % 172.78/172.47 [6098]E(f332(f332(f80(a876),f332(a107,x60981)),f332(a107,x60982)),f332(a107,f332(f332(f80(a1),x60981),x60982)))+~P102(f332(f332(f246(a1),f2(a1)),x60981)) % 172.78/172.47 [6099]E(f332(f332(f38(a876),f332(a107,x60991)),f332(a107,x60992)),f332(a107,f332(f332(f38(a1),x60991),x60992)))+~P102(f332(f332(f246(a1),f2(a1)),x60991)) % 172.78/172.47 [6113]~P114(x61131)+E(f332(f332(f79(x61131),x61132),x61132),f332(f332(f80(x61131),f332(f332(f79(x61131),f77(x61131)),f77(x61131))),x61132)) % 172.78/172.47 [6130]E(f332(f332(f22(a1),f332(f103(a1),x61301)),f332(f103(a1),x61302)),f332(f103(a1),f332(f332(f22(a876),x61301),x61302)))+~P102(f332(f332(f246(a876),x61302),x61301)) % 172.78/172.47 [6132]E(f332(f332(f267(a1,a1),f332(f106(a1),a100)),f332(f332(f79(a1),x61321),x61322)),f49(x61321,x61322))+~P102(f332(f332(f246(a1),x61322),f2(a1))) % 172.78/172.47 [6166]E(f181(x61661,x61662),f116(f877(x61661)))+P102(f332(f332(f334(f877(x61661)),f718(x61662,x61661)),f332(f173(f877(x61661)),x61662))) % 172.78/172.47 [6175]E(f119(a1,f332(f126(a1),x61751),f125(x61752,f332(f332(f79(a1),x61751),f77(a1)))),f125(x61752,x61751))+P102(f332(f332(f247(a1),x61752),x61751)) % 172.78/172.47 [6251]E(f332(f332(f151(a1),x62511),f180(f332(f332(f79(a1),x62511),f77(a1)),x62512)),f180(x62511,x62512))+~P102(f332(f332(f246(a1),x62511),x62512)) % 172.78/172.47 [6288]~P102(f332(f332(f247(a876),x62882),x62881))+P102(f332(f332(f247(a876),f2(a876)),f332(f332(f22(a876),x62881),x62882))) % 172.78/172.48 [6319]~P102(f332(f332(f247(a876),x63191),f332(a107,x63192)))+P102(f332(f332(f247(a1),f332(f103(a1),x63191)),x63192)) % 172.78/172.48 [6348]~P104(x63481)+E(f332(f332(f113(f883(x63481,a871)),f332(f253(x63481),x63482)),f332(f332(f310(x63481),x63482),f195(f883(x63481,a871)))),f332(f301(x63481),x63482)) % 172.78/172.48 [6351]~P102(f332(f332(f247(a876),f2(a876)),x63511))+P102(f332(f332(f247(a876),f2(a876)),f332(f332(f257(a876),x63511),x63512))) % 172.78/172.48 [6352]~P102(f332(f332(f246(a1),f2(a1)),x63521))+P102(f332(f332(f246(a1),f2(a1)),f332(f332(f257(a1),x63521),x63522))) % 172.78/172.48 [6380]~E(f332(x63801,f2(a876)),f2(a876))+E(f332(f332(f6(a876,a876),x63801),f303(a876,f332(a115,f2(a876)),x63802)),f332(f332(f6(a876,a876),x63801),f303(a876,f2(a876),x63802))) % 172.78/172.48 [6443]~P89(x64431)+E(f332(f332(f80(x64431),f332(f332(f79(x64431),f77(x64431)),f77(x64431))),f332(f106(x64431),x64432)),f332(f106(x64431),f332(f332(f79(a1),x64432),x64432))) % 172.78/172.48 [6458]E(f332(f332(f310(a1),x64581),f303(a1,f332(f332(f79(a1),x64581),f77(a1)),x64582)),f303(a1,x64581,x64582))+P102(f332(f332(f247(a1),x64582),x64581)) % 172.78/172.48 [6459]P102(f332(f332(f247(a876),x64591),f332(a107,x64592)))+~P102(f332(f332(f247(a1),f332(f103(a1),x64591)),x64592)) % 172.78/172.48 [6560]E(f332(a107,f332(f332(f38(a1),f332(f106(a1),x65601)),f332(f106(a1),x65602))),f332(f332(f38(a876),f332(f106(a876),x65601)),f332(f106(a876),x65602)))+P102(f332(a200,f332(f106(a1),x65601))) % 172.78/172.48 [6618]P102(f332(f332(f247(a876),x66181),x66182))+~P102(f332(f332(f247(a876),f2(a876)),f332(f332(f22(a876),x66182),x66181))) % 172.78/172.48 [6662]P102(f332(f332(f247(a876),f2(a876)),x66621))+~P102(f332(f332(f247(a876),f2(a876)),f332(f332(f80(a876),x66622),x66621))) % 172.78/172.48 [6663]P102(f332(f332(f247(a876),f2(a876)),x66631))+~P102(f332(f332(f247(a876),f2(a876)),f332(f332(f80(a876),x66631),x66632))) % 172.78/172.48 [6680]~P102(f332(f332(f246(a1),x66801),f2(a1)))+E(f332(f332(f80(a876),f332(a107,f332(f78(a1),x66801))),f332(a107,f332(f78(a1),x66802))),f332(a107,f332(f332(f80(a1),x66801),x66802))) % 172.78/172.48 [6738]~E(x67382,f195(f883(x67381,a871)))+P102(f332(f332(f246(f883(x67381,a871)),x67382),f332(f78(f883(x67381,a871)),x67382))) % 172.78/172.48 [6801]~P89(x68011)+E(f332(f332(f79(x68011),f332(f332(f79(x68011),f2(x68011)),f332(f106(x68011),x68012))),f332(f106(x68011),x68012)),f332(f106(x68011),f332(f332(f79(a1),x68012),x68012))) % 172.78/172.48 [6858]~P102(f332(f332(f247(a1),x68581),x68582))+P102(f332(f332(f246(a1),f332(f332(f79(a1),x68581),f77(a1))),x68582)) % 172.78/172.48 [6925]E(x69251,f2(a876))+~P102(f332(f332(f246(a1),f332(f103(a1),x69252)),f332(f78(a1),f332(f103(a1),x69251)))) % 172.78/172.48 [6926]E(x69261,f2(a876))+~P102(f332(f332(f246(a1),f332(f103(a1),x69261)),f332(f78(a1),f332(f103(a1),x69262)))) % 172.78/172.48 [7031]E(f332(f332(f267(a1,a1),f332(f106(a1),a100)),f332(f332(f79(a1),x70311),x70312)),f49(x70311,x70312))+~P102(f332(f332(f246(a1),f2(a1)),f332(f332(f79(a1),x70311),x70312))) % 172.78/172.48 [7073]~P21(x70731,x70732)+P38(x70731,f332(f266(f883(f882(x70731,x70731),a871),f883(f882(x70731,x70731),a871)),x70732)) % 172.78/172.48 [7091]~P102(f332(f332(f246(a876),f332(a115,f2(a876))),x70911))+P102(f332(f332(f246(a876),f332(a115,f2(a876))),f332(f332(f257(a876),x70911),x70912))) % 172.78/172.48 [7254]~P102(f332(f332(f247(a1),x72541),x72542))+P102(f332(f332(f247(a1),f332(f332(f79(a1),x72541),x72541)),f332(f332(f79(a1),x72542),x72542))) % 172.78/172.48 [7266]~P102(f332(f332(f246(a1),x72661),x72662))+P102(f332(f332(f246(a1),f332(f332(f79(a1),x72661),x72661)),f332(f332(f79(a1),x72662),x72662))) % 172.78/172.48 [7267]~P102(f332(f332(f90(a1),x72671),x72672))+P102(f332(f332(f90(a1),f332(f332(f79(a1),x72671),x72671)),f332(f332(f79(a1),x72672),x72672))) % 172.78/172.48 [7322]~P102(f332(f332(f247(a876),f2(a876)),x73221))+P102(f332(f332(f247(a876),f332(f332(f22(a876),x73221),f332(a115,x73222))),x73221)) % 172.78/172.48 [7359]P102(f332(f332(f246(a876),f332(a115,f2(a876))),x73591))+~P102(f332(f332(f246(a876),f332(a115,f2(a876))),f332(f332(f80(a876),x73592),x73591))) % 172.78/172.48 [7360]P102(f332(f332(f246(a876),f332(a115,f2(a876))),x73601))+~P102(f332(f332(f246(a876),f332(a115,f2(a876))),f332(f332(f80(a876),x73601),x73602))) % 172.78/172.48 [7364]P102(f332(f332(f246(a876),f332(f332(f165(a876),x73641),x73642)),f332(f166(a876),x73641)))+~P102(f332(f332(f247(a876),x73642),f332(f196(f877(a876)),x73641))) % 172.78/172.48 [7405]P102(f332(f332(f247(a1),x74051),x74052))+~P102(f332(f332(f246(a1),f332(f332(f79(a1),x74051),f77(a1))),x74052)) % 172.78/172.48 [7450]P102(f332(f61(x74501),f255(f883(x74501,a871))))+~P102(f332(f61(f883(x74502,x74501)),f255(f883(f883(x74502,x74501),a871)))) % 172.78/172.48 [7451]P102(f332(f61(x74511),f255(f883(x74511,a871))))+~P102(f332(f61(f881(x74512,x74511)),f255(f883(f881(x74512,x74511),a871)))) % 172.78/172.48 [7452]P102(f332(f61(x74521),f255(f883(x74521,a871))))+~P102(f332(f61(f881(x74521,x74522)),f255(f883(f881(x74521,x74522),a871)))) % 172.78/172.48 [7494]E(x74941,f195(f883(x74942,a871)))+~P102(f332(f332(f246(f883(x74942,a871)),x74941),f332(f78(f883(x74942,a871)),x74941))) % 172.78/172.48 [7631]E(f332(f142(f877(x76311),f877(x76311),f134(x76311),f116(x76311)),x76312),f116(x76311))+P102(f332(f332(f334(f877(x76311)),f737(x76312,x76311)),f332(f173(f877(x76311)),x76312))) % 172.78/172.48 [7632]E(f332(f142(f877(x76321),f877(x76321),f134(x76321),f116(x76321)),x76322),f116(x76321))+P102(f332(f332(f334(f877(x76321)),f740(x76322,x76321)),f332(f173(f877(x76321)),x76322))) % 172.78/172.48 [7875]P102(f332(f332(f247(a1),x78751),x78752))+~P102(f332(f332(f247(a1),f332(f332(f79(a1),x78751),x78751)),f332(f332(f79(a1),x78752),x78752))) % 172.78/172.48 [7878]P102(f332(f332(f246(a1),x78781),x78782))+~P102(f332(f332(f246(a1),f332(f332(f79(a1),x78781),x78781)),f332(f332(f79(a1),x78782),x78782))) % 172.78/172.48 [7879]P102(f332(f332(f90(a1),x78791),x78792))+~P102(f332(f332(f90(a1),f332(f332(f79(a1),x78791),x78791)),f332(f332(f79(a1),x78792),x78792))) % 172.78/172.48 [7973]~P114(x79731)+E(f332(f332(f80(x79731),f332(f332(f79(x79731),f77(x79731)),f77(x79731))),f332(f332(f6(a876,x79731),f103(x79731)),f303(a876,f77(a876),x79732))),f332(f332(f80(x79731),f332(f103(x79731),x79732)),f332(f332(f79(x79731),f332(f103(x79731),x79732)),f77(x79731)))) % 172.78/172.48 [8030]P102(f332(f332(f334(a876),x80301),x80302))+~P102(f332(f332(f334(a1),f332(f103(a1),x80301)),f332(f311(a876,a1,f103(a1)),x80302))) % 172.78/172.48 [8191]~P102(f332(f61(x81911),x81912))+E(f332(f311(a876,x81911,f431(x81912,x81911)),f332(f252(a876),f332(f332(f7(a876,a876,a871),f247(a876)),f432(x81912,x81911)))),x81912) % 172.78/172.48 [8480]P42(x84801,x84802)+P102(f332(f332(f334(f882(x84801,x84801)),f332(f332(f267(x84801,x84801),f497(x84802,x84801)),f497(x84802,x84801))),x84802)) % 172.78/172.48 [8618]~P89(x86181)+E(f332(f332(f22(x86181),f77(x86181)),f332(f106(x86181),x86182)),f332(f106(x86181),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f78(a1),x86182)))) % 172.78/172.48 [8731]~P102(f332(f332(f247(f883(a876,a871)),x87311),x87312))+P102(f332(f332(f247(f883(a1,a871)),f332(f311(a876,a1,f103(a1)),x87311)),f332(f311(a876,a1,f103(a1)),x87312))) % 172.78/172.48 [8760]~P102(f332(f332(f247(a1),x87601),x87602))+P102(f332(f332(f247(a1),f332(f332(f22(a1),f332(f332(f79(a1),x87601),x87601)),a100)),f332(f332(f79(a1),x87602),x87602))) % 172.78/172.48 [8762]~P102(f332(f332(f247(a1),x87621),x87622))+P102(f332(f332(f246(a1),f332(f332(f22(a1),f332(f332(f79(a1),x87621),x87621)),a100)),f332(f332(f79(a1),x87622),x87622))) % 172.78/172.48 [8833]~P102(f332(f332(f334(a876),x88331),f332(f173(a876),x88332)))+P102(f332(f332(f246(a876),x88331),f332(f142(a876,a876,f79(a876),f2(a876)),x88332))) % 172.78/172.48 [8927]P46(x89271,x89272)+~P102(f332(f332(f334(f882(x89271,x89271)),f332(f332(f267(x89271,x89271),f488(x89272,x89271)),f488(x89272,x89271))),x89272)) % 172.78/172.48 [9074]~P102(f332(f332(f247(f883(a1,a871)),f332(f311(a876,a1,f103(a1)),x90741)),f332(f311(a876,a1,f103(a1)),x90742)))+P102(f332(f332(f247(f883(a876,a871)),x90741),x90742)) % 172.78/172.48 [9075]~P102(f332(f332(f246(f883(a1,a871)),f332(f311(a876,a1,f103(a1)),x90751)),f332(f311(a876,a1,f103(a1)),x90752)))+P102(f332(f332(f246(f883(a876,a871)),x90751),x90752)) % 172.78/172.48 [9155]P102(f332(f332(f247(a1),x91551),x91552))+~P102(f332(f332(f247(a1),f332(f332(f22(a1),f332(f332(f79(a1),x91551),x91551)),a100)),f332(f332(f79(a1),x91552),x91552))) % 172.78/172.48 [9157]P102(f332(f332(f247(a1),x91571),x91572))+~P102(f332(f332(f246(a1),f332(f332(f22(a1),f332(f332(f79(a1),x91571),x91571)),a100)),f332(f332(f79(a1),x91572),x91572))) % 172.78/172.48 [10039]~P100(x100391)+E(f119(f877(x100391),f332(f126(f877(x100391)),f116(x100391)),f332(f332(f332(f99(f878(f877(x100391))),f332(f332(f247(a1),f2(a1)),x100392)),f332(f121(f882(x100391,f877(x100391)),f877(x100391),f131(x100391,f877(x100391),f132(x100391,f332(f332(f22(a1),x100392),f77(a1))),f132(f877(x100391),f332(f332(f22(a1),x100392),f77(a1))))),f332(f271(x100391,f877(x100391),f878(f877(x100391))),f332(f332(f8(f883(f877(x100391),f877(x100391)),f883(f877(x100391),f878(f877(x100391))),x100391),f332(f8(f877(x100391),f878(f877(x100391)),f877(x100391)),f126(f877(x100391)))),f151(x100391))))),f118(f877(x100391)))),f132(f877(x100391),x100392)) % 172.78/172.48 [10061]~P102(f332(f61(x100611),x100612))+E(f332(f196(f877(x100611)),f89(f877(x100611),f332(f332(f18(f877(x100611),a871,a871),f332(f332(f8(a871,f883(a871,a871),f877(x100611)),a330),f332(f332(f7(f877(x100611),f883(x100611,a871),a871),f332(f332(f8(f883(x100611,a871),f883(f883(x100611,a871),a871),f877(x100611)),a329),f173(x100611))),x100612))),f137(x100611)))),f225(x100611,x100612)) % 172.78/172.48 [10197]~P19(a872,x101971,f332(f332(f310(f875(a872)),f332(f332(f332(f91(a872),a329),x101972),f201(x101972))),f195(f883(f875(a872),a871))))+P19(a872,x101971,f332(f332(f310(f875(a872)),f332(f332(f332(f91(a872),f332(f332(f8(f883(a872,f883(a872,a871)),f883(a872,a871),a872),f332(f8(f883(a872,a871),a871,a872),f87(a872))),f332(f332(f8(f883(a872,a871),f883(a872,f883(a872,a871)),a872),f332(f7(a872,f883(a872,a871),f883(a872,a871)),f332(f332(f8(f883(a872,f883(a871,a871)),f883(f883(a872,a871),f883(a872,a871)),a872),f18(a872,a871,a871)),f332(f332(f8(f883(a872,a871),f883(a872,f883(a871,a871)),a872),f332(f8(a871,f883(a871,a871),a872),a335)),f201(x101972))))),a329))),x101972),a329)),f195(f883(f875(a872),a871)))) % 172.78/172.48 [6061]E(f332(f332(f79(a876),f332(f332(f22(a876),x60611),x60612)),x60612),x60611)+~P102(f332(f332(f246(a876),x60612),x60611)) % 172.78/172.48 [6126]E(f332(f332(f38(a876),f332(f332(f80(a876),x61261),x61262)),x61262),x61261)+~P102(f332(f332(f247(a876),f2(a876)),x61262)) % 172.78/172.48 [6127]E(f332(f332(f38(a876),f332(f332(f80(a876),x61271),x61272)),x61271),x61272)+~P102(f332(f332(f247(a876),f2(a876)),x61271)) % 172.78/172.48 [6131]~P71(x61311)+E(f332(f332(f6(a876,x61311),f332(f165(x61311),x61312)),f332(f302(a876,f2(a876)),f332(f196(f877(x61311)),x61312))),f332(f166(x61311),x61312)) % 172.78/172.48 [6243]E(f44(a876,f332(a115,f332(f332(f80(a876),x62431),x62432)),x62431),f77(a876))+~P102(f332(f332(f247(a876),f77(a876)),x62431)) % 172.78/172.48 [6249]E(f332(a115,f332(f332(f79(a876),f332(f106(a876),x62491)),x62492)),f332(f332(f79(a876),f77(a876)),x62492))+~P102(f332(a200,f332(f106(a1),x62491))) % 172.78/172.48 [6277]E(f332(a107,f332(f332(f257(a1),f332(f106(a1),x62771)),x62772)),f332(f332(f257(a876),f332(f106(a876),x62771)),x62772))+P102(f332(a200,f332(f106(a1),x62771))) % 172.78/172.48 [6512]E(f332(f332(f22(a876),x65121),f332(f106(a876),f332(f332(f79(a1),x65122),a100))),f332(f332(f22(a876),f332(a115,x65121)),f332(f106(a876),x65122)))+~P102(f332(f332(f247(a1),a82),x65122)) % 172.78/172.48 [6591]E(x65911,f2(a876))+E(f332(a115,f332(f332(f79(a876),f332(f332(f22(a876),x65911),f77(a876))),x65912)),f332(f332(f79(a876),x65911),x65912)) % 172.78/172.48 [6632]E(x66321,f2(a1))+P102(f332(f332(f247(a1),f2(a1)),f332(f332(f257(a1),f332(f74(a1),x66321)),x66322))) % 172.78/172.48 [6647]~E(x66472,f2(a876))+P102(f332(f332(f247(a1),f2(a1)),f332(f332(f257(a1),f332(f74(a1),x66471)),x66472))) % 172.78/172.48 [6684]E(x66841,f2(a876))+E(f332(f332(f79(a876),x66842),f332(f332(f80(a876),f332(f332(f22(a876),x66841),f77(a876))),x66842)),f332(f332(f80(a876),x66841),x66842)) % 172.78/172.48 [6732]~P102(f332(f332(f246(a1),x67321),x67322))+P102(f332(f332(f247(a1),f332(f332(f79(a1),x67321),a100)),x67322)) % 172.78/172.48 [6861]E(f332(f332(f151(a876),x68611),f139(a876,f332(f302(a876,f332(a115,x68611)),x68612))),f139(a876,f332(f302(a876,x68611),x68612)))+~P102(f332(f332(f247(a876),x68611),x68612)) % 172.78/172.48 [7064]E(x70641,x70642)+~E(f332(f332(f22(a1),f332(f332(f79(a1),x70641),x70641)),a100),f332(f332(f22(a1),f332(f332(f79(a1),x70642),x70642)),a100)) % 172.78/172.48 [7067]E(x70671,f116(x70672))+E(f276(x70672,f332(f332(f154(x70672,f882(a102,x70672)),f332(f267(a102,x70672),f77(a102))),x70671)),f283(x70672,x70671)) % 172.78/172.48 [7291]P102(f332(f332(f246(a1),x72911),x72912))+~P102(f332(f332(f247(a1),f332(f332(f79(a1),x72911),a100)),x72912)) % 172.78/172.48 [7778]~P102(f332(f332(f247(a876),x77781),x77782))+P102(f332(f332(f334(f882(a876,a876)),f332(f332(f267(a876,a876),x77781),x77782)),a251)) % 172.78/172.48 [8002]~P102(f332(f332(f247(a102),f2(a102)),x80021))+P102(f332(f332(f247(a102),f332(f266(a102,f882(a102,a102)),f332(f277(x80021),x80022))),x80021)) % 172.78/172.48 [8319]~P81(x83191)+P102(f332(f332(f246(x83191),f332(f74(x83191),f332(f166(x83191),x83192))),f332(f166(x83191),f332(f332(f154(x83191,x83191),f74(x83191)),x83192)))) % 172.78/172.48 [8343]P102(f332(f332(f247(a876),x83431),x83432))+~P102(f332(f332(f334(f882(a876,a876)),f332(f332(f267(a876,a876),x83431),x83432)),a251)) % 172.78/172.48 [8503]E(f332(f332(f267(x85031,x85031),f606(x85032,x85031)),f606(x85032,x85031)),x85032)+~P102(f332(f332(f334(f882(x85031,x85031)),x85032),f308(x85031,f195(f883(f882(x85031,x85031),a871))))) % 172.78/172.48 [8544]E(f332(f302(a876,x85441),f332(f332(f79(a876),x85441),f332(f37(a876),x85442))),x85442)+~P102(f332(f332(f246(f883(a876,a871)),x85442),f332(f302(a876,x85441),f332(f332(f79(a876),x85441),f332(f37(a876),x85442))))) % 172.78/172.48 [8872]E(f332(f332(f38(a1),f332(f106(a1),f332(f332(f22(a1),f332(f332(f79(a1),x88721),x88721)),a100))),f332(f106(a1),f332(f332(f79(a1),x88722),x88722))),f332(f332(f38(a1),f332(f106(a1),x88721)),f332(f106(a1),x88722)))+~P102(f332(f332(f246(a1),f2(a1)),f332(f106(a1),x88722))) % 172.78/172.48 [9002]E(f178(f877(x90021),f332(f332(f8(a871,a871,f877(x90021)),a327),f332(f332(f7(f877(x90021),f877(x90021),a871),a329),f116(x90021))),x90022),f181(x90021,f181(x90021,x90022)))+~P29(a876,f332(f169(a876),f332(f332(f154(f877(x90021),a876),f196(f877(x90021))),x90022))) % 172.78/172.48 [9005]E(f332(f332(f38(a1),f332(f106(a1),f332(f332(f22(a1),f332(f332(f79(a1),x90051),x90051)),a100))),f332(f106(a1),f332(f332(f79(a1),x90052),x90052))),f332(f332(f38(a1),f332(f332(f79(a1),f332(f106(a1),x90051)),f77(a1))),f332(f106(a1),x90052)))+P102(f332(f332(f246(a1),f2(a1)),f332(f106(a1),x90052))) % 172.78/172.48 [9836]P102(f332(a200,x98362))+E(f332(f332(f85(a1,a876),f332(f332(f22(a1),x98361),x98362)),f332(f332(f18(a1,a876,a876),f332(f332(f7(a1,a876,f883(a876,a876)),f332(f332(f8(a871,f883(a876,f883(a876,a876)),a1),f99(a876)),a200)),f2(a876))),a107)),f332(f332(f22(a876),f332(a107,x98361)),f332(a107,x98362))) % 172.78/172.48 [9844]E(f332(f332(f85(a1,a876),f332(f106(a1),f332(f332(f79(a1),x98441),f332(f78(a1),x98442)))),f332(f332(f18(a1,a876,a876),f332(f332(f7(a1,a876,f883(a876,a876)),f332(f332(f8(a871,f883(a876,f883(a876,a876)),a1),f99(a876)),a200)),f2(a876))),a107)),f332(f332(f22(a876),f332(f106(a876),x98441)),f332(f106(a876),x98442)))+P102(f332(f332(f247(a1),x98442),a82)) % 172.78/172.48 [9845]~P21(x98451,x98452)+P102(f332(f332(f246(f883(f882(x98451,x98451),a871)),f332(f332(f289(x98451,x98451,x98451),f332(f266(f883(f882(x98451,x98451),a871),f883(f882(x98451,x98451),a871)),x98452)),f332(f270(f883(f882(x98451,x98451),a871),f883(f882(x98451,x98451),a871)),x98452))),f332(f266(f883(f882(x98451,x98451),a871),f883(f882(x98451,x98451),a871)),x98452))) % 172.78/172.48 [9911]~E(f332(f37(a876),f332(f252(a876),f332(f332(f18(a876,a871,a871),f332(f332(f8(a871,f883(a871,a871),a876),a330),f332(f332(f7(a876,f883(a876,a871),a871),f334(a876)),x99111))),f332(f332(f7(a876,a876,a871),f247(a876)),f332(a115,x99112))))),f2(a876))+~P102(f332(f332(f334(a876),f2(a876)),x99111)) % 172.78/172.48 [9967]E(f44(a1,f332(f106(a1),f332(f332(f22(a1),f332(f332(f79(a1),x99671),x99671)),a100)),f332(f106(a1),f332(f332(f79(a1),x99672),x99672))),f332(f332(f79(a1),f332(f332(f80(a1),f332(f106(a1),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)))),f44(a1,f332(f106(a1),x99671),f332(f106(a1),x99672)))),f77(a1)))+~P102(f332(f332(f246(a1),f2(a1)),f332(f106(a1),x99672))) % 172.78/172.48 [9976]E(f44(a1,f332(f106(a1),f332(f332(f22(a1),f332(f332(f79(a1),x99761),x99761)),a100)),f332(f106(a1),f332(f332(f79(a1),x99762),x99762))),f332(f332(f22(a1),f332(f332(f80(a1),f332(f106(a1),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)))),f44(a1,f332(f332(f79(a1),f332(f106(a1),x99761)),f77(a1)),f332(f106(a1),x99762)))),f77(a1)))+P102(f332(f332(f246(a1),f2(a1)),f332(f106(a1),x99762))) % 172.78/172.48 [10028]~P27(x100281)+E(f39(x100281,f332(f252(x100281),f332(f332(f8(f883(x100281,a871),a871,x100281),f87(x100281)),f332(f332(f8(f883(x100281,a871),f883(x100281,a871),x100281),f332(f18(x100281,a871,a871),f332(f332(f8(a871,f883(a871,a871),x100281),a335),f332(f332(f7(x100281,f883(x100281,a871),a871),f334(x100281)),x100282)))),f246(x100281))))),f40(x100281,x100282)) % 172.78/172.48 [10054]~P38(x100541,x100542)+P55(x100541,f332(f332(f7(x100541,f883(f882(x100541,x100541),a871),f883(x100541,a871)),f332(f332(f8(f883(x100541,f883(f883(f882(x100541,x100541),a871),a871)),f883(f883(f882(x100541,x100541),a871),f883(x100541,a871)),x100541),f7(x100541,f883(f882(x100541,x100541),a871),a871)),f332(f332(f8(f883(x100541,f882(x100541,x100541)),f883(x100541,f883(f883(f882(x100541,x100541),a871),a871)),x100541),f332(f8(f882(x100541,x100541),f883(f883(f882(x100541,x100541),a871),a871),x100541),f334(f882(x100541,x100541)))),f267(x100541,x100541)))),x100542)) % 172.78/172.48 [10055]~P3(x100551,f255(f883(x100551,a871)),x100552)+P2(x100551,f332(f332(f7(x100551,f883(f882(x100551,x100551),a871),f883(x100551,a871)),f332(f332(f8(f883(x100551,f883(f883(f882(x100551,x100551),a871),a871)),f883(f883(f882(x100551,x100551),a871),f883(x100551,a871)),x100551),f7(x100551,f883(f882(x100551,x100551),a871),a871)),f332(f332(f8(f883(x100551,f882(x100551,x100551)),f883(x100551,f883(f883(f882(x100551,x100551),a871),a871)),x100551),f332(f8(f882(x100551,x100551),f883(f883(f882(x100551,x100551),a871),a871),x100551),f334(f882(x100551,x100551)))),f267(x100551,x100551)))),x100552)) % 172.78/172.48 [10092]P38(x100921,x100922)+~P55(x100921,f332(f332(f7(x100921,f883(f882(x100921,x100921),a871),f883(x100921,a871)),f332(f332(f8(f883(x100921,f883(f883(f882(x100921,x100921),a871),a871)),f883(f883(f882(x100921,x100921),a871),f883(x100921,a871)),x100921),f7(x100921,f883(f882(x100921,x100921),a871),a871)),f332(f332(f8(f883(x100921,f882(x100921,x100921)),f883(x100921,f883(f883(f882(x100921,x100921),a871),a871)),x100921),f332(f8(f882(x100921,x100921),f883(f883(f882(x100921,x100921),a871),a871),x100921),f334(f882(x100921,x100921)))),f267(x100921,x100921)))),x100922)) % 172.78/172.48 [10093]P3(x100931,f255(f883(x100931,a871)),x100932)+~P2(x100931,f332(f332(f7(x100931,f883(f882(x100931,x100931),a871),f883(x100931,a871)),f332(f332(f8(f883(x100931,f883(f883(f882(x100931,x100931),a871),a871)),f883(f883(f882(x100931,x100931),a871),f883(x100931,a871)),x100931),f7(x100931,f883(f882(x100931,x100931),a871),a871)),f332(f332(f8(f883(x100931,f882(x100931,x100931)),f883(x100931,f883(f883(f882(x100931,x100931),a871),a871)),x100931),f332(f8(f882(x100931,x100931),f883(f883(f882(x100931,x100931),a871),a871),x100931),f334(f882(x100931,x100931)))),f267(x100931,x100931)))),x100932)) % 172.78/172.48 [7242]E(f332(f332(f79(a876),f332(f106(a876),f332(f332(f22(a1),x72421),a100))),x72422),f332(a115,f332(f332(f79(a876),f332(f106(a876),x72421)),x72422)))+P102(f332(a200,f332(f106(a1),x72421))) % 172.78/172.48 [7691]~P89(x76911)+E(f332(f332(f79(x76911),f332(f332(f79(x76911),f77(x76911)),f332(f106(x76911),x76912))),f332(f106(x76911),x76912)),f332(f106(x76911),f332(f332(f22(a1),f332(f332(f79(a1),x76912),x76912)),a100))) % 172.78/172.48 [8345]~P102(f332(f332(f246(a1),x83451),x83452))+P102(f332(f332(f247(a1),f332(f332(f79(a1),x83451),x83451)),f332(f332(f22(a1),f332(f332(f79(a1),x83452),x83452)),a100))) % 172.78/172.48 [8347]~P102(f332(f332(f246(a1),x83471),x83472))+P102(f332(f332(f246(a1),f332(f332(f79(a1),x83471),x83471)),f332(f332(f22(a1),f332(f332(f79(a1),x83472),x83472)),a100))) % 172.78/172.48 [8764]P102(f332(f332(f246(a1),x87641),x87642))+~P102(f332(f332(f247(a1),f332(f332(f79(a1),x87641),x87641)),f332(f332(f22(a1),f332(f332(f79(a1),x87642),x87642)),a100))) % 172.78/172.48 [8766]P102(f332(f332(f246(a1),x87661),x87662))+~P102(f332(f332(f246(a1),f332(f332(f79(a1),x87661),x87661)),f332(f332(f22(a1),f332(f332(f79(a1),x87662),x87662)),a100))) % 172.78/172.48 [9062]~P102(f332(f332(f247(a1),x90621),x90622))+P102(f332(f332(f247(a1),f332(f332(f22(a1),f332(f332(f79(a1),x90621),x90621)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),x90622),x90622)),a100))) % 172.78/172.48 [9064]~P102(f332(f332(f246(a1),x90641),x90642))+P102(f332(f332(f246(a1),f332(f332(f22(a1),f332(f332(f79(a1),x90641),x90641)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),x90642),x90642)),a100))) % 172.78/172.48 [9065]~P102(f332(f332(f90(a1),x90651),x90652))+P102(f332(f332(f90(a1),f332(f332(f22(a1),f332(f332(f79(a1),x90651),x90651)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),x90652),x90652)),a100))) % 172.78/172.48 [9328]P102(f332(f332(f247(a1),x93281),x93282))+~P102(f332(f332(f247(a1),f332(f332(f22(a1),f332(f332(f79(a1),x93281),x93281)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),x93282),x93282)),a100))) % 172.78/172.48 [9330]P102(f332(f332(f246(a1),x93301),x93302))+~P102(f332(f332(f246(a1),f332(f332(f22(a1),f332(f332(f79(a1),x93301),x93301)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),x93302),x93302)),a100))) % 172.78/172.48 [9331]P102(f332(f332(f90(a1),x93311),x93312))+~P102(f332(f332(f90(a1),f332(f332(f22(a1),f332(f332(f79(a1),x93311),x93311)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),x93312),x93312)),a100))) % 172.78/172.48 [9363]~P102(f332(f61(x93631),x93632))+P102(f332(f61(f883(x93631,a871)),f332(f252(f883(x93631,a871)),f332(f332(f7(f883(x93631,a871),f883(x93631,a871),a871),f246(f883(x93631,a871))),x93632)))) % 172.78/172.48 [9411]~E(f332(f286(f882(a876,a876),f882(a876,a876),a111),f332(f332(f310(f882(a876,a876)),x94111),f195(f883(f882(a876,a876),a871)))),f332(f286(f882(a876,a876),f882(a876,a876),a111),f332(f332(f310(f882(a876,a876)),x94112),f195(f883(f882(a876,a876),a871)))))+P102(f332(f332(f334(f882(f882(a876,a876),f882(a876,a876))),f332(f332(f267(f882(a876,a876),f882(a876,a876)),x94111),x94112)),a111)) % 172.78/172.48 [9495]E(f332(f286(f882(a876,a876),f882(a876,a876),a111),f332(f332(f310(f882(a876,a876)),x94951),f195(f883(f882(a876,a876),a871)))),f332(f286(f882(a876,a876),f882(a876,a876),a111),f332(f332(f310(f882(a876,a876)),x94952),f195(f883(f882(a876,a876),a871)))))+~P102(f332(f332(f334(f882(f882(a876,a876),f882(a876,a876))),f332(f332(f267(f882(a876,a876),f882(a876,a876)),x94951),x94952)),a111)) % 172.78/172.48 [9531]P102(f332(f332(f246(a1),f2(a1)),f659(x95311,x95312)))+E(f332(f252(a1),f332(f332(f18(a1,a871,a871),f332(f332(f8(a871,f883(a871,a871),a1),a330),f332(f246(a1),f2(a1)))),x95311)),f332(f252(a1),f332(f332(f18(a1,a871,a871),f332(f332(f8(a871,f883(a871,a871),a1),a330),f332(f246(a1),f2(a1)))),x95312))) % 172.78/172.48 [10038]~P27(x100381)+E(f40(x100381,f332(f252(x100381),f332(f332(f8(f883(x100381,a871),a871,x100381),f87(x100381)),f332(f332(f8(f883(x100381,a871),f883(x100381,a871),x100381),f332(f18(x100381,a871,a871),f332(f332(f8(a871,f883(a871,a871),x100381),a335),f332(f332(f7(x100381,f883(x100381,a871),a871),f334(x100381)),x100382)))),f332(f7(x100381,x100381,a871),f246(x100381)))))),f39(x100381,x100382)) % 172.78/172.48 [10060]P102(f332(f332(f334(a876),f2(a876)),x100601))+E(f332(f37(a876),f332(f252(a876),f332(f332(f18(a876,a871,a871),f332(f332(f8(a871,f883(a871,a871),a876),a330),f332(f332(f7(a876,f883(a876,a871),a871),f332(f332(f8(a876,f883(f883(a876,a871),a871),a876),f334(a876)),a115)),x100601))),f332(f332(f7(a876,a876,a871),f247(a876)),x100602)))),f332(f37(a876),f332(f252(a876),f332(f332(f18(a876,a871,a871),f332(f332(f8(a871,f883(a871,a871),a876),a330),f332(f332(f7(a876,f883(a876,a871),a871),f334(a876)),x100601))),f332(f332(f7(a876,a876,a871),f247(a876)),f332(a115,x100602)))))) % 172.78/172.48 [7559]~P89(x75591)+E(f332(f332(f80(x75591),x75592),f332(f106(x75591),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100))),x75592) % 172.78/172.48 [7826]~P89(x78261)+E(f332(f332(f79(x78261),f332(f106(x78261),x78262)),f77(x78261)),f332(f106(x78261),f332(f332(f79(a1),x78262),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)))) % 172.78/172.48 [7971]P102(f332(f332(f246(a1),f2(a1)),f332(f106(a1),x79712)))+E(f332(f332(f257(a1),x79711),f332(f106(a876),f332(f332(f22(a1),f332(f332(f79(a1),x79712),x79712)),a100))),f77(a1)) % 172.78/172.48 [9389]~P102(f332(f332(f246(a1),f2(a1)),f332(f106(a1),x93892)))+E(f332(f332(f257(a1),x93891),f332(f106(a876),f332(f332(f22(a1),f332(f332(f79(a1),x93892),x93892)),a100))),f332(f332(f85(a1,a1),f332(f332(f257(a1),x93891),f332(f106(a876),x93892))),f332(f332(f18(a1,a1,a1),f332(f332(f8(a1,f883(a1,a1),a1),f80(a1)),f332(f80(a1),x93891))),f5(a1)))) % 172.78/172.48 [9751]~P102(f332(f332(f246(a876),f668(x97512,x97511)),f332(x97511,f668(x97512,x97511))))+P102(f332(f61(a876),f332(f252(a876),f332(f332(f7(a876,a876,a871),f332(f332(f8(a876,f883(a876,a871),a876),f246(a876)),x97511)),x97512)))) % 172.78/172.48 [9901]~P102(f332(f332(f247(a876),f332(f106(a876),x99011)),f332(a115,x99012)))+P102(f332(f332(f85(a1,a871),f332(f106(a1),f332(f332(f79(a1),x99011),a100))),f332(f332(f18(a1,a871,a871),f332(f332(f8(a871,f883(a871,a871),a1),a335),f332(f332(f8(a871,a871,a1),a327),a200))),f332(f332(f7(a1,a876,a871),f332(f332(f8(a876,f883(a876,a871),a1),f247(a876)),a107)),x99012)))) % 172.78/172.48 [9902]~P102(f332(f332(f246(a876),f332(f106(a876),x99021)),f332(a115,x99022)))+P102(f332(f332(f85(a1,a871),f332(f106(a1),f332(f332(f79(a1),x99021),a100))),f332(f332(f18(a1,a871,a871),f332(f332(f8(a871,f883(a871,a871),a1),a335),f332(f332(f8(a871,a871,a1),a327),a200))),f332(f332(f7(a1,a876,a871),f332(f332(f8(a876,f883(a876,a871),a1),f246(a876)),a107)),x99022)))) % 172.78/172.48 [9951]P102(f332(f332(f247(a876),f332(f106(a876),x99511)),f332(a115,x99512)))+~P102(f332(f332(f85(a1,a871),f332(f106(a1),f332(f332(f79(a1),x99511),a100))),f332(f332(f18(a1,a871,a871),f332(f332(f8(a871,f883(a871,a871),a1),a335),f332(f332(f8(a871,a871,a1),a327),a200))),f332(f332(f7(a1,a876,a871),f332(f332(f8(a876,f883(a876,a871),a1),f247(a876)),a107)),x99512)))) % 172.78/172.48 [9952]P102(f332(f332(f246(a876),f332(f106(a876),x99521)),f332(a115,x99522)))+~P102(f332(f332(f85(a1,a871),f332(f106(a1),f332(f332(f79(a1),x99521),a100))),f332(f332(f18(a1,a871,a871),f332(f332(f8(a871,f883(a871,a871),a1),a335),f332(f332(f8(a871,a871,a1),a327),a200))),f332(f332(f7(a1,a876,a871),f332(f332(f8(a876,f883(a876,a871),a1),f246(a876)),a107)),x99522)))) % 172.78/172.48 [9982]~P102(f332(f332(f247(a876),f332(a115,x99822)),f332(f106(a876),x99821)))+P102(f332(f332(f85(a1,a871),f332(f106(a1),f332(f332(f79(a1),x99821),a100))),f332(f332(f18(a1,a871,a871),f332(f332(f8(a871,f883(a871,a871),a1),a330),f332(f332(f8(a871,a871,a1),a327),a200))),f332(f332(f18(a1,a871,a871),f332(f332(f8(a871,f883(a871,a871),a1),a335),f332(f332(f8(a871,a871,a1),a327),a200))),f332(f332(f8(a876,a871,a1),f332(f247(a876),x99822)),a107))))) % 172.78/172.48 [9983]~P102(f332(f332(f246(a876),f332(a115,x99832)),f332(f106(a876),x99831)))+P102(f332(f332(f85(a1,a871),f332(f106(a1),f332(f332(f79(a1),x99831),a100))),f332(f332(f18(a1,a871,a871),f332(f332(f8(a871,f883(a871,a871),a1),a330),f332(f332(f8(a871,a871,a1),a327),a200))),f332(f332(f18(a1,a871,a871),f332(f332(f8(a871,f883(a871,a871),a1),a335),f332(f332(f8(a871,a871,a1),a327),a200))),f332(f332(f8(a876,a871,a1),f332(f246(a876),x99832)),a107))))) % 172.78/172.48 [10026]P102(f332(f332(f247(a876),f332(a115,x100261)),f332(f106(a876),x100262)))+~P102(f332(f332(f85(a1,a871),f332(f106(a1),f332(f332(f79(a1),x100262),a100))),f332(f332(f18(a1,a871,a871),f332(f332(f8(a871,f883(a871,a871),a1),a330),f332(f332(f8(a871,a871,a1),a327),a200))),f332(f332(f18(a1,a871,a871),f332(f332(f8(a871,f883(a871,a871),a1),a335),f332(f332(f8(a871,a871,a1),a327),a200))),f332(f332(f8(a876,a871,a1),f332(f247(a876),x100261)),a107))))) % 172.78/172.48 [10027]P102(f332(f332(f246(a876),f332(a115,x100271)),f332(f106(a876),x100272)))+~P102(f332(f332(f85(a1,a871),f332(f106(a1),f332(f332(f79(a1),x100272),a100))),f332(f332(f18(a1,a871,a871),f332(f332(f8(a871,f883(a871,a871),a1),a330),f332(f332(f8(a871,a871,a1),a327),a200))),f332(f332(f18(a1,a871,a871),f332(f332(f8(a871,f883(a871,a871),a1),a335),f332(f332(f8(a871,a871,a1),a327),a200))),f332(f332(f8(a876,a871,a1),f332(f246(a876),x100271)),a107))))) % 172.78/172.48 [10100]~P102(f332(f332(f334(a876),f2(a876)),x101001))+E(f332(a115,f332(f37(a876),f332(f252(a876),f332(f332(f18(a876,a871,a871),f332(f332(f8(a871,f883(a871,a871),a876),a330),f332(f332(f7(a876,f883(a876,a871),a871),f332(f332(f8(a876,f883(f883(a876,a871),a871),a876),f334(a876)),a115)),x101001))),f332(f332(f7(a876,a876,a871),f247(a876)),x101002))))),f332(f37(a876),f332(f252(a876),f332(f332(f18(a876,a871,a871),f332(f332(f8(a871,f883(a871,a871),a876),a330),f332(f332(f7(a876,f883(a876,a871),a871),f334(a876)),x101001))),f332(f332(f7(a876,a876,a871),f247(a876)),f332(a115,x101002)))))) % 172.78/172.48 [8528]~P89(x85281)+E(f332(f332(f80(x85281),f332(f106(x85281),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100))),x85282),x85282) % 172.78/172.48 [8586]~P89(x85861)+E(f332(f332(f79(x85861),f77(x85861)),f332(f106(x85861),x85862)),f332(f106(x85861),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),x85862))) % 172.78/172.48 [8644]~P89(x86441)+E(f332(f332(f22(x86441),f332(f106(x86441),x86442)),f77(x86441)),f332(f106(x86441),f332(f332(f79(a1),x86442),f332(f78(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100))))) % 172.78/172.48 [8782]~P102(f332(f332(f247(a876),f332(f106(a876),a82)),x87822))+E(f332(f332(f22(a876),x87821),f332(f332(f22(a876),x87822),f332(f106(a876),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)))),f332(f332(f22(a876),f332(a115,x87821)),x87822)) % 172.78/172.48 [9427]~P114(x94271)+E(f332(f332(f80(x94271),x94272),x94272),f332(f332(f257(x94271),x94272),f332(f106(a876),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100))))) % 172.78/172.48 [9428]~P75(x94281)+E(f332(f332(f257(x94281),x94282),f332(f106(a876),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)))),f332(f332(f80(x94281),x94282),x94282)) % 172.78/172.48 [9430]~P89(x94301)+E(f332(f332(f80(x94301),x94302),f332(f106(x94301),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)))),f332(f332(f79(x94301),x94302),x94302)) % 172.78/172.48 [9670]~P113(x96701)+E(f332(f332(f257(x96701),f332(f74(x96701),x96702)),f332(f106(a876),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)))),f332(f332(f257(x96701),x96702),f332(f106(a876),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100))))) % 172.78/172.48 [9671]~P137(x96711)+E(f332(f332(f257(x96711),f332(f78(x96711),x96712)),f332(f106(a876),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)))),f332(f332(f257(x96711),x96712),f332(f106(a876),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100))))) % 172.78/172.48 [9667]~P89(x96671)+E(f332(f332(f80(x96671),f332(f106(x96671),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)))),x96672),f332(f332(f79(x96671),x96672),x96672)) % 172.78/172.48 [9791]~P113(x97911)+E(f332(f74(x97911),f332(f332(f257(x97911),x97912),f332(f106(a876),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100))))),f332(f332(f257(x97911),x97912),f332(f106(a876),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100))))) % 172.78/172.48 [9853]~P113(x98531)+P102(f332(f332(f246(x98531),f2(x98531)),f332(f332(f257(x98531),x98532),f332(f106(a876),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)))))) % 172.78/172.48 [10017]~E(f332(a115,x100172),f332(f106(a876),x100171))+P102(f332(f332(f85(a1,a871),f332(f106(a1),f332(f332(f79(a1),x100171),a100))),f332(f332(f18(a1,a871,a871),f332(f332(f8(a871,f883(a871,a871),a1),a330),f332(f332(f8(a871,a871,a1),a327),a200))),f332(f332(f18(a1,a871,a871),f332(f332(f8(a871,f883(a871,a871),a1),a335),f332(f332(f8(a871,a871,a1),a327),a200))),f332(f332(f7(a1,a876,a871),f332(f332(f8(a876,f883(a876,a871),a1),a329),a107)),x100172))))) % 172.78/172.48 [10018]~E(f332(f106(a876),x100181),f332(a115,x100182))+P102(f332(f332(f85(a1,a871),f332(f106(a1),f332(f332(f79(a1),x100181),a100))),f332(f332(f18(a1,a871,a871),f332(f332(f8(a871,f883(a871,a871),a1),a330),f332(f332(f8(a871,a871,a1),a327),a200))),f332(f332(f18(a1,a871,a871),f332(f332(f8(a871,f883(a871,a871),a1),a335),f332(f332(f8(a871,a871,a1),a327),a200))),f332(f332(f7(a1,a876,a871),f332(f332(f8(a876,f883(a876,a871),a1),a329),a107)),x100182))))) % 172.78/172.48 [10063]E(f332(a115,x100631),f332(f106(a876),x100632))+~P102(f332(f332(f85(a1,a871),f332(f106(a1),f332(f332(f79(a1),x100632),a100))),f332(f332(f18(a1,a871,a871),f332(f332(f8(a871,f883(a871,a871),a1),a330),f332(f332(f8(a871,a871,a1),a327),a200))),f332(f332(f18(a1,a871,a871),f332(f332(f8(a871,f883(a871,a871),a1),a335),f332(f332(f8(a871,a871,a1),a327),a200))),f332(f332(f7(a1,a876,a871),f332(f332(f8(a876,f883(a876,a871),a1),a329),a107)),x100631))))) % 172.78/172.48 [10064]E(f332(f106(a876),x100641),f332(a115,x100642))+~P102(f332(f332(f85(a1,a871),f332(f106(a1),f332(f332(f79(a1),x100641),a100))),f332(f332(f18(a1,a871,a871),f332(f332(f8(a871,f883(a871,a871),a1),a330),f332(f332(f8(a871,a871,a1),a327),a200))),f332(f332(f18(a1,a871,a871),f332(f332(f8(a871,f883(a871,a871),a1),a335),f332(f332(f8(a871,a871,a1),a327),a200))),f332(f332(f7(a1,a876,a871),f332(f332(f8(a876,f883(a876,a871),a1),a329),a107)),x100642))))) % 172.78/172.48 [9850]~P89(x98501)+E(f332(f332(f257(x98501),f332(f106(x98501),a100)),f332(f332(f80(a876),f332(f106(a876),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)))),x98502)),f77(x98501)) % 172.78/172.48 [9851]~P137(x98511)+E(f332(f332(f257(x98511),f332(f78(x98511),f77(x98511))),f332(f332(f80(a876),f332(f106(a876),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)))),x98512)),f77(x98511)) % 172.78/172.48 [9855]~P75(x98551)+E(f332(f332(f257(x98551),x98552),f332(f106(a876),f332(f332(f22(a1),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100))),a100))),f332(f332(f80(x98551),f332(f332(f80(x98551),x98552),x98552)),x98552)) % 172.78/172.48 [10042]~P102(f332(f332(f246(a1),f2(a1)),x100422))+E(f44(a1,f332(f332(f79(a1),f77(a1)),f332(f332(f80(a1),f332(f106(a1),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)))),x100421)),f332(f332(f80(a1),f332(f106(a1),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)))),x100422)),f332(f332(f79(a1),f77(a1)),f332(f332(f80(a1),f332(f106(a1),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)))),f44(a1,x100421,x100422)))) % 172.78/172.48 [10066]~P102(f332(f332(f246(a1),f2(a1)),x100662))+E(f332(f332(f38(a1),f332(f332(f79(a1),f77(a1)),f332(f332(f80(a1),f332(f106(a1),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)))),x100661))),f332(f332(f80(a1),f332(f106(a1),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)))),x100662)),f332(f332(f38(a1),x100661),x100662)) % 172.78/172.48 [10068]~P102(f332(f332(f246(a1),x100682),f2(a1)))+E(f332(f332(f38(a1),f332(f332(f79(a1),f77(a1)),f332(f332(f80(a1),f332(f106(a1),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)))),x100681))),f332(f332(f80(a1),f332(f106(a1),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)))),x100682)),f332(f332(f38(a1),f332(f332(f79(a1),x100681),f77(a1))),x100682)) % 172.78/172.48 [10069]~P102(f332(f332(f246(a1),x100692),f2(a1)))+E(f44(a1,f332(f332(f79(a1),f77(a1)),f332(f332(f80(a1),f332(f106(a1),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)))),x100691)),f332(f332(f80(a1),f332(f106(a1),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)))),x100692)),f332(f332(f22(a1),f332(f332(f80(a1),f332(f106(a1),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)))),f44(a1,f332(f332(f79(a1),x100691),f77(a1)),x100692))),f77(a1))) % 172.78/172.48 [9942]~P89(x99421)+E(f332(f332(f257(x99421),f332(f106(x99421),a100)),f332(a115,f332(f332(f80(a876),f332(f106(a876),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)))),x99422))),f332(f106(x99421),a100)) % 172.78/172.48 [9944]~P137(x99441)+E(f332(f332(f257(x99441),f332(f78(x99441),f77(x99441))),f332(a115,f332(f332(f80(a876),f332(f106(a876),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)))),x99442))),f332(f78(x99441),f77(x99441))) % 172.78/172.48 [5113]~P19(x51131,x51132,x51133)+P22(x51131,x51132,x51133) % 172.78/172.48 [8045]~E(x80452,x80453)+P35(x80451,x80451,a329,x80452,x80453) % 172.78/172.48 [8599]E(x85991,x85992)+~P35(x85993,x85993,a329,x85991,x85992) % 172.78/172.48 [4759]E(f170(x47591,x47592,x47593),f116(x47591))+~E(x47592,f2(a876)) % 172.78/172.48 [4925]~E(f170(x49252,x49251,x49253),f116(x49252))+E(x49251,f2(a876)) % 172.78/172.48 [5118]~P38(x51181,x51183)+P38(x51181,f326(x51181,x51182,x51183)) % 172.78/172.48 [5283]P30(x52831,x52832,x52833)+~P30(x52831,f332(a115,x52832),x52833) % 172.78/172.48 [5372]~P3(x53721,x53722,x53723)+P3(f877(x53721),f161(x53721,x53722),f158(x53721,x53723)) % 172.78/172.48 [5373]~P40(x53731,x53732,x53733)+P40(f877(x53731),f161(x53731,x53732),f158(x53731,x53733)) % 172.78/172.48 [5485]P51(x54851,x54852,x54853)+~E(f582(x54853,x54852,x54851),f583(x54853,x54852,x54851)) % 172.78/172.48 [5486]P50(x54861,x54862,x54863)+~E(f594(x54863,x54862,x54861),f595(x54863,x54862,x54861)) % 172.78/172.48 [6418]P22(x64181,x64182,x64183)+~P30(x64181,f566(x64183,x64182,x64181),f571(x64183,x64182,x64181)) % 172.78/172.48 [4665]~E(x46651,f208(x46652))+~E(x46651,f332(f239(x46652),x46653)) % 172.78/172.48 [4715]~E(f332(f169(x47152),x47151),x47153)+E(x47151,f332(f169(x47152),x47153)) % 172.78/172.48 [4716]~E(x47162,f332(f169(x47161),x47163))+E(f332(f169(x47161),x47162),x47163) % 172.78/172.48 [4765]E(x47651,x47652)+~E(f332(f239(x47653),x47651),f332(f239(x47653),x47652)) % 172.78/172.48 [4766]E(x47661,x47662)+~E(f332(f169(x47663),x47661),f332(f169(x47663),x47662)) % 172.78/172.48 [4972]~P2(x49723,x49721)+P102(f332(f332(x49721,x49722),x49722)) % 172.78/172.48 [4973]~P49(x49733,x49731)+P102(f332(f332(x49731,x49732),x49732)) % 172.78/172.48 [4975]~P55(x49751,x49752)+P102(f332(f320(x49751,x49752),x49753)) % 172.78/172.48 [5037]~P38(x50371,x50372)+P38(f877(x50371),f332(f143(x50371,x50372),x50373)) % 172.78/172.48 [5042]~P102(f332(x50422,x50423))+~E(f332(f252(x50421),x50422),f195(f883(x50421,a871))) % 172.78/172.48 [5043]~P102(f332(x50432,x50433))+~E(f195(f883(x50431,a871)),f332(f252(x50431),x50432)) % 172.78/172.48 [5055]E(x50551,f2(a876))+E(f144(x50552,f170(x50552,x50551,x50553)),x50553) % 172.78/172.48 [5073]~P102(f332(x50731,x50733))+P102(f332(x50731,f89(x50732,x50731))) % 172.78/172.48 [5085]E(x50851,f2(a876))+E(f332(f141(x50852),f170(x50852,x50851,x50853)),x50853) % 172.78/172.48 [5191]~E(x51912,x51913)+P102(f332(f332(f334(x51911),x51912),f332(a329,x51913))) % 172.78/172.48 [5203]P102(f332(x52031,x52032))+~P102(f332(x52031,f534(x52031,x52033))) % 172.78/172.48 [5204]~E(x52042,f2(a876))+E(f332(f173(x52041),f170(x52041,x52042,x52043)),f195(f883(x52041,a871))) % 172.78/172.48 [5249]E(f332(f169(x52491),x52492),f332(f332(f151(x52491),x52493),f116(x52491)))+~E(x52492,f332(f332(f151(x52491),x52493),f116(x52491))) % 172.78/172.48 [5250]~E(x52503,f332(f332(f151(x52501),x52502),f116(x52501)))+E(f332(f332(f151(x52501),x52502),f116(x52501)),f332(f169(x52501),x52503)) % 172.78/172.48 [5276]~E(x52763,f332(f16(f880(x52762),x52761),f208(x52762)))+E(f185(x52761,x52762,x52763),f195(f883(x52761,a871))) % 172.78/172.48 [5298]~P34(x52981,x52982,x52983)+P34(x52981,x52982,f332(f169(x52981),x52983)) % 172.78/172.48 [5299]~P32(x52991,x52992,x52993)+P32(x52991,x52992,f332(f169(x52991),x52993)) % 172.78/172.48 [5302]E(f332(f37(x53021),f776(x53022,x53023,x53021)),x53022)+~E(f332(f37(x53021),x53023),f332(a115,x53022)) % 172.78/172.48 [5308]~P38(x53081,x53083)+P102(f332(f332(f334(x53081),x53082),f321(x53081,x53083))) % 172.78/172.48 [5312]~E(f332(f169(x53122),x53121),f332(f332(f151(x53122),x53123),f116(x53122)))+E(x53121,f332(f332(f151(x53122),x53123),f116(x53122))) % 172.78/172.48 [5313]~E(f332(f332(f151(x53132),x53133),f116(x53132)),f332(f169(x53132),x53131))+E(x53131,f332(f332(f151(x53132),x53133),f116(x53132))) % 172.78/172.48 [5328]E(x53281,f332(f16(f880(x53282),x53283),f208(x53282)))+~E(f185(x53283,x53282,x53281),f195(f883(x53283,a871))) % 172.78/172.48 [5335]E(f84(f882(a876,a876),f47(x53351,x53352)),x53353)+~P102(f332(f47(x53351,x53352),x53353)) % 172.78/172.48 [5343]~E(x53433,f332(f239(x53431),x53432))+P102(f332(f332(f334(x53431),x53432),f238(x53431,x53433))) % 172.78/172.48 [5376]P34(x53761,x53762,x53763)+~P34(x53761,x53762,f332(f169(x53761),x53763)) % 172.78/172.48 [5377]P32(x53771,x53772,x53773)+~P32(x53771,x53772,f332(f169(x53771),x53773)) % 172.78/172.48 [5439]~E(x54392,f116(x54391))+P102(f332(f332(f334(f877(x54391)),x54392),f161(x54391,x54393))) % 172.78/172.48 [5446]~P40(x54461,x54462,x54463)+P40(x54461,x54462,f332(f287(x54461,x54461),x54463)) % 172.78/172.48 [5447]~P51(x54471,x54472,x54473)+P51(x54471,x54472,f332(f287(x54471,x54471),x54473)) % 172.78/172.48 [5466]~P25(x54661)+E(f44(x54661,f44(x54661,x54662,x54663),x54663),f44(x54661,x54662,x54663)) % 172.78/172.48 [5564]E(x55641,x55642)+~P102(f332(f332(f334(x55643),x55641),f332(a329,x55642))) % 172.78/172.48 [5610]~P141(x56101)+E(f197(x56101,x56102,f2(a876),x56103),x56103) % 172.78/172.48 [5630]P40(x56301,x56302,x56303)+~P40(x56301,x56302,f332(f287(x56301,x56301),x56303)) % 172.78/172.48 [5631]P51(x56311,x56312,x56313)+~P51(x56311,x56312,f332(f287(x56311,x56311),x56313)) % 172.78/172.48 [5635]~P104(x56352)+E(f150(x56351,x56352,x56353,f116(x56351)),f116(x56351)) % 172.78/172.48 [5648]E(f171(x56481,x56482,f152(x56481,x56483)),f152(x56481,f171(x56481,x56482,x56483)))+~P102(f332(f137(x56481),x56483)) % 172.78/172.48 [5654]E(x56541,f332(f239(x56542),x56543))+~P102(f332(f332(f334(x56542),x56543),f238(x56542,x56541))) % 172.78/172.48 [5749]E(f332(f136(x57491,x57492),x57493),f116(x57491))+P102(f332(x57492,f735(x57493,x57492,x57491))) % 172.78/172.48 [5892]~P102(f332(f137(x58921),x58922))+P102(f332(f137(x58921),f177(x58921,x58922,x58923))) % 172.78/172.48 [5893]~P102(f332(f137(x58931),x58933))+P102(f332(f137(x58931),f171(x58931,x58932,x58933))) % 172.78/172.48 [5894]~P102(f332(f137(x58941),x58943))+P102(f332(f137(x58941),f178(x58941,x58942,x58943))) % 172.78/172.48 [5895]~P102(f332(f137(x58951),x58953))+P102(f332(f137(x58951),f140(x58951,x58952,x58953))) % 172.78/172.48 [5896]~P143(x58961,x58962,x58963)+P102(f332(x58961,f44(a1,x58962,x58963))) % 172.78/172.48 [5913]~P34(x59133,x59131,x59132)+P102(f332(x59131,f779(x59132,x59131,x59133))) % 172.78/172.48 [5914]~P36(x59143,x59141,x59142)+P102(f332(x59141,f809(x59142,x59141,x59143))) % 172.78/172.48 [5936]E(f332(f136(x59361,x59362),x59363),f178(x59361,x59362,x59363))+P102(f332(x59362,f758(x59363,x59362,x59361))) % 172.78/172.48 [5978]~P102(f332(f137(x59781),x59783))+P102(f332(f137(f877(x59781)),f54(x59781,x59782,x59783))) % 172.78/172.48 [6011]~P105(x60111)+E(f332(f332(f104(f883(x60111,a871)),f332(f253(x60111),x60112)),f303(x60111,x60112,x60113)),f195(f883(x60111,a871))) % 172.78/172.48 [6012]~P105(x60121)+E(f332(f332(f104(f883(x60121,a871)),f332(f301(x60121),x60122)),f306(x60121,x60122,x60123)),f195(f883(x60121,a871))) % 172.78/172.48 [6013]~P105(x60131)+E(f332(f332(f104(f883(x60131,a871)),f332(f301(x60131),x60132)),f305(x60131,x60132,x60133)),f195(f883(x60131,a871))) % 172.78/172.48 [6239]E(f332(f136(x62391,x62392),x62393),x62393)+~P102(f332(x62392,f736(x62393,x62392,x62391))) % 172.78/172.48 [6241]E(f332(f332(f310(x62411),f856(x62412,x62413,x62411)),f776(x62412,x62413,x62411)),x62413)+~E(f332(f37(x62411),x62413),f332(a115,x62412)) % 172.78/172.48 [6257]P143(x62571,x62572,x62573)+~P102(f332(x62571,f44(a1,x62572,x62573))) % 172.78/172.48 [6304]P32(x63041,x63042,x63043)+~P102(f332(x63042,f796(x63043,x63042,x63041))) % 172.78/172.48 [6305]P32(x63051,x63052,x63053)+~P102(f332(x63052,f802(x63052,x63053,x63051))) % 172.78/172.48 [6306]P32(x63061,x63062,x63063)+~P102(f332(x63062,f803(x63063,x63062,x63061))) % 172.78/172.48 [6308]E(f178(x63081,x63082,x63083),x63083)+~P102(f332(x63082,f753(x63083,x63082,x63081))) % 172.78/172.48 [6387]~P102(f332(x63872,f554(x63873,x63872,x63871)))+P102(f332(f260(x63871,x63872),x63873)) % 172.78/172.48 [6388]~P102(f332(x63882,f724(x63883,x63882,x63881)))+P102(f332(f160(x63881,x63882),x63883)) % 172.78/172.48 [6633]~P102(f332(f320(x66331,x66332),f482(x66333,x66332,x66331)))+P102(f332(f320(x66331,x66332),x66333)) % 172.78/172.48 [6634]~P102(f332(f320(x66341,x66342),f496(x66343,x66342,x66341)))+P102(f332(f320(x66341,x66342),x66343)) % 172.78/172.48 [7243]~P25(x72431)+E(f332(f332(f79(x72431),f332(f332(f80(x72431),x72432),f332(f332(f38(x72431),x72433),x72432))),f44(x72431,x72433,x72432)),x72433) % 172.78/172.48 [7715]E(f332(f332(f267(x77151,x77151),f509(x77152,x77153,x77151)),f509(x77152,x77153,x77151)),x77153)+~P102(f332(f332(f334(f882(x77151,x77151)),x77153),f264(x77151,x77152))) % 172.78/172.48 [7834]~P102(f332(f332(f334(x78341),f521(x78343,x78342,x78341)),f321(x78341,x78343)))+P102(f332(f332(f334(x78341),x78342),f321(x78341,x78343))) % 172.78/172.48 [7835]~P102(f332(f332(f334(x78351),f584(x78353,x78352,x78351)),f321(x78351,x78353)))+P102(f332(f332(f334(x78351),x78352),f321(x78351,x78353))) % 172.78/172.48 [7836]~P102(f332(f332(f334(x78361),f585(x78363,x78362,x78361)),f321(x78361,x78363)))+P102(f332(f332(f334(x78361),x78362),f321(x78361,x78363))) % 172.78/172.48 [8026]~P25(x80261)+E(f332(f332(f79(x80261),f332(f332(f80(x80261),f332(f332(f38(x80261),x80262),x80263)),x80263)),f44(x80261,x80262,x80263)),x80262) % 172.78/172.48 [8071]~E(f332(f37(x80711),x80712),f332(a115,x80713))+~P102(f332(f332(f334(x80711),f856(x80713,x80712,x80711)),f776(x80713,x80712,x80711))) % 172.78/172.48 [8694]P102(f332(f332(f246(f883(f882(x86941,x86941),a871)),f308(x86941,x86942)),f308(x86941,x86943)))+~P102(f332(f332(f246(f883(f882(x86941,x86941),a871)),x86942),f308(x86941,x86943))) % 172.78/172.48 [8971]E(x89711,f116(x89712))+~P102(f332(f332(f334(f882(f877(x89712),f877(x89712))),f332(f332(f267(f877(x89712),f877(x89712)),x89711),f116(x89712))),f158(x89712,x89713))) % 172.78/172.48 [8996]E(x89961,f116(x89962))+~P102(f332(f332(f334(f882(f877(x89962),f877(x89962))),f332(f332(f267(f877(x89962),f877(x89962)),f116(x89962)),x89961)),f158(x89962,x89963))) % 172.78/172.48 [9119]E(f332(f332(f151(x91191),f708(x91192,x91193,x91191)),f709(x91192,x91193,x91191)),x91193)+~P102(f332(f332(f334(f882(f877(x91191),f877(x91191))),f332(f332(f267(f877(x91191),f877(x91191)),f116(x91191)),x91193)),f147(x91191,x91192))) % 172.78/172.48 [9356]~P121(x93561)+~P102(f332(f332(f247(x93561),f332(f332(f79(x93561),f332(f332(f80(x93561),x93562),x93562)),f332(f332(f80(x93561),x93563),x93563))),f2(x93561))) % 172.78/172.48 [9406]P102(f332(f61(x94061),x94062))+~P102(f332(f332(f334(f882(f883(x94061,a871),f883(x94061,a871))),f332(f332(f267(f883(x94061,a871),f883(x94061,a871)),x94063),x94062)),f307(x94061))) % 172.78/172.48 [9692]~P47(x96921,x96922,x96923)+P102(f332(f332(f247(a1),f332(f332(f72(f882(a1,a1),a1,x96921,f266(a1,a1)),f223(x96921)),f234(x96921,x96922,f231(x96921,x96923)))),f2(a1))) % 172.78/172.48 [9693]~P48(x96931,x96932,x96933)+P102(f332(f332(f246(a1),f332(f332(f72(f882(a1,a1),a1,x96931,f266(a1,a1)),f223(x96931)),f234(x96931,x96932,f231(x96931,x96933)))),f2(a1))) % 172.78/172.48 [9820]P47(x98201,x98202,x98203)+~P102(f332(f332(f247(a1),f332(f332(f72(f882(a1,a1),a1,x98201,f266(a1,a1)),f223(x98201)),f234(x98201,x98202,f231(x98201,x98203)))),f2(a1))) % 172.78/172.48 [9821]P48(x98211,x98212,x98213)+~P102(f332(f332(f246(a1),f332(f332(f72(f882(a1,a1),a1,x98211,f266(a1,a1)),f223(x98211)),f234(x98211,x98212,f231(x98211,x98213)))),f2(a1))) % 172.78/172.48 [10143]~P113(x101431)+~P102(f332(f332(f247(x101431),f332(f332(f79(x101431),f332(f332(f257(x101431),x101432),f332(f106(a876),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100))))),f332(f332(f257(x101431),x101433),f332(f106(a876),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)))))),f2(x101431))) % 172.78/172.48 [4746]~E(x47463,f116(x47461))+E(f332(f332(f134(x47461),x47462),x47463),x47462) % 172.78/172.48 [4747]~E(x47472,f116(x47471))+E(f332(f332(f134(x47471),x47472),x47473),x47473) % 172.78/172.48 [4754]~E(x47542,f2(a876))+E(f332(f332(f176(x47541),x47542),x47543),f116(x47541)) % 172.78/172.48 [4760]~E(x47603,f116(x47601))+E(f332(f332(f176(x47601),x47602),x47603),f116(x47601)) % 172.78/172.48 [4800]~E(x48001,x48003)+E(x48001,f332(f332(f134(x48002),f116(x48002)),x48003)) % 172.78/172.48 [4887]~P23(x48872)+E(f332(f195(f883(x48871,x48872)),x48873),f195(x48872)) % 172.78/172.48 [4888]~P110(x48882)+E(f332(f255(f883(x48881,x48882)),x48883),f255(x48882)) % 172.78/172.48 [4907]E(x49071,f116(x49072))+~E(f332(f332(f134(x49072),x49073),x49071),x49073) % 172.78/172.48 [4908]E(x49081,f116(x49082))+~E(f332(f332(f134(x49082),x49081),x49083),x49083) % 172.78/172.48 [4916]E(x49161,f116(x49162))+~E(f332(f332(f134(x49162),x49163),x49161),f116(x49162)) % 172.78/172.48 [4917]E(x49171,f116(x49172))+~E(f332(f332(f134(x49172),x49171),x49173),f116(x49172)) % 172.78/172.48 [4942]~E(x49422,f2(a876))+E(f332(f332(f80(a876),x49421),x49422),f332(f332(f80(a876),x49423),x49422)) % 172.78/172.48 [4944]~E(x49441,f2(a876))+E(f332(f332(f80(a876),x49441),x49442),f332(f332(f80(a876),x49441),x49443)) % 172.78/172.48 [4997]~P61(x49971)+E(f332(f332(f113(x49971),x49972),x49973),f332(f332(f113(x49971),x49973),x49972)) % 172.78/172.48 [4999]~P97(x49991)+E(f332(f332(f113(x49991),x49992),x49993),f332(f332(f113(x49991),x49993),x49992)) % 172.78/172.48 [5000]~P61(x50001)+E(f332(f332(f104(x50001),x50002),x50003),f332(f332(f104(x50001),x50003),x50002)) % 172.78/172.48 [5002]~P98(x50021)+E(f332(f332(f104(x50021),x50022),x50023),f332(f332(f104(x50021),x50023),x50022)) % 172.78/172.48 [5003]~P114(x50031)+E(f332(f332(f80(x50031),x50032),x50033),f332(f332(f80(x50031),x50033),x50032)) % 172.78/172.48 [5004]~P114(x50041)+E(f332(f332(f79(x50041),x50042),x50043),f332(f332(f79(x50041),x50043),x50042)) % 172.78/172.48 [5006]~P104(x50061)+E(f332(f332(f244(x50061),x50062),x50063),f332(f332(f244(x50061),x50063),x50062)) % 172.78/172.48 [5008]~P104(x50081)+E(f332(f332(f245(x50081),x50082),x50083),f332(f332(f245(x50081),x50083),x50082)) % 172.78/172.48 [5068]E(f44(a876,x50681,x50682),f2(a876))+~E(x50681,f332(f332(f80(a876),x50682),x50683)) % 172.78/172.48 [5069]E(f44(a1,x50691,x50692),f2(a1))+~E(x50691,f332(f332(f80(a1),x50692),x50693)) % 172.78/172.48 [5130]E(x51301,x51302)+~E(f332(f332(f79(a876),x51303),x51301),f332(f332(f79(a876),x51303),x51302)) % 172.78/172.48 [5131]E(x51311,x51312)+~E(f332(f332(f79(a876),x51311),x51313),f332(f332(f79(a876),x51312),x51313)) % 172.78/172.48 [5141]~P92(x51411)+E(f332(f332(f104(x51411),x51412),f332(f78(x51411),x51413)),f332(f332(f22(x51411),x51412),x51413)) % 172.78/172.48 [5142]~P66(x51421)+E(f332(f332(f79(x51421),x51422),f332(f78(x51421),x51423)),f332(f332(f22(x51421),x51422),x51423)) % 172.78/172.48 [5143]~P72(x51431)+E(f332(f332(f79(x51431),x51432),f332(f78(x51431),x51433)),f332(f332(f22(x51431),x51432),x51433)) % 172.78/172.48 [5144]~P112(x51441)+E(f332(f332(f79(x51441),x51442),f332(f78(x51441),x51443)),f332(f332(f22(x51441),x51442),x51443)) % 172.78/172.48 [5145]~P72(x51451)+E(f332(f332(f22(x51451),x51452),f332(f78(x51451),x51453)),f332(f332(f79(x51451),x51452),x51453)) % 172.78/172.48 [5184]~P102(f332(x51843,x51842))+P102(f332(f332(f334(x51841),x51842),x51843)) % 172.78/172.48 [5186]~P71(x51862)+E(f332(f332(f6(x51861,x51862),x51863),f195(f883(x51861,a871))),f2(x51862)) % 172.78/172.48 [5188]~P67(x51882)+E(f332(f332(f9(x51881,x51882),x51883),f195(f883(x51881,a871))),f77(x51882)) % 172.78/172.48 [5237]~E(x52372,f332(f332(f79(a876),x52371),x52373))+P102(f332(f332(f246(a876),x52371),x52372)) % 172.78/172.48 [5240]~E(x52402,f195(f883(x52401,a871)))+E(f332(f332(f60(x52401),x52402),x52403),f195(f883(f883(x52401,a871),a871))) % 172.78/172.48 [5241]~E(x52412,f195(f883(x52411,a871)))+E(f195(f883(f883(x52411,a871),a871)),f332(f332(f60(x52411),x52412),x52413)) % 172.78/172.48 [5317]~E(f332(f263(x53172,x53173),x53171),f195(f883(x53173,a871)))+E(x53171,f195(f883(f882(x53172,x53173),a871))) % 172.78/172.48 [5318]~E(f332(f265(x53182,x53183),x53181),f195(f883(x53182,a871)))+E(x53181,f195(f883(f882(x53182,x53183),a871))) % 172.78/172.48 [5349]E(f332(f263(x53491,x53492),x53493),f195(f883(x53492,a871)))+~E(x53493,f195(f883(f882(x53491,x53492),a871))) % 172.78/172.48 [5350]E(f332(f265(x53501,x53502),x53503),f195(f883(x53501,a871)))+~E(x53503,f195(f883(f882(x53501,x53502),a871))) % 172.78/172.48 [5354]E(f282(x53541,x53542,x53543),f332(f332(f22(a102),x53542),x53543))+P102(f332(f332(f247(a102),x53542),x53543)) % 172.78/172.48 [5370]P102(f332(x53701,x53702))+~P102(f332(f332(f334(x53703),x53702),x53701)) % 172.78/172.48 [5409]E(x54091,x54092)+~E(f332(f78(f883(x54093,a871)),x54091),f332(f78(f883(x54093,a871)),x54092)) % 172.78/172.48 [5414]E(f314(x54141,x54142,x54143),f208(f877(a328)))+~P102(f332(f332(f247(a1),x54142),x54143)) % 172.78/172.48 [5419]~E(x54191,f195(f883(x54192,a871)))+~P102(f332(f332(f334(x54192),x54193),x54191)) % 172.78/172.48 [5448]~E(x54482,f332(f332(f79(a1),x54481),f332(f103(a1),x54483)))+P102(f332(f332(f246(a1),x54481),x54482)) % 172.78/172.48 [5464]E(f332(f332(f310(x54641),x54642),x54643),x54643)+~P102(f332(f332(f334(x54641),x54642),x54643)) % 172.78/172.48 [5475]E(x54751,f195(f883(x54752,a871)))+~E(f332(f332(f60(x54752),x54751),x54753),f195(f883(f883(x54752,a871),a871))) % 172.78/172.48 [5476]E(x54761,f195(f883(x54762,a871)))+~E(f195(f883(f883(x54762,a871),a871)),f332(f332(f60(x54762),x54761),x54763)) % 172.78/172.48 [5483]~P123(x54831)+E(f332(f332(f80(x54831),f332(f78(x54831),x54832)),f332(f78(x54831),x54833)),f332(f332(f80(x54831),x54832),x54833)) % 172.78/172.48 [5484]~P57(x54841)+E(f332(f332(f290(x54841),f332(f78(x54841),x54842)),f332(f78(x54841),x54843)),f332(f332(f290(x54841),x54842),x54843)) % 172.78/172.48 [5517]~P102(f332(x55173,x55172))+P102(f332(f332(f334(x55171),x55172),f332(f252(x55171),x55173))) % 172.78/172.48 [5538]E(x55381,f2(a876))+E(f332(f173(x55382),f170(x55382,x55381,x55383)),f332(f332(f310(x55382),x55383),f195(f883(x55382,a871)))) % 172.78/172.48 [5557]E(f171(x55571,x55572,x55573),x55573)+P102(f332(f332(f334(x55571),x55572),f332(f173(x55571),x55573))) % 172.78/172.48 [5639]~P102(f332(f137(x56391),x56393))+P102(f332(f137(x56391),f332(f136(x56391,x56392),x56393))) % 172.78/172.48 [5684]~P25(x56841)+E(f332(f332(f38(x56841),f44(x56841,x56842,x56843)),x56843),f2(x56841)) % 172.78/172.48 [5703]E(f177(x57031,f332(f332(f151(x57031),x57032),f116(x57031)),x57033),f116(x57031))+P102(f332(f332(f334(a876),f2(a876)),x57033)) % 172.78/172.48 [5709]E(x57091,f2(a876))+E(f332(f172(x57092),f170(x57092,x57091,x57093)),f170(x57092,f332(f332(f22(a876),x57091),f77(a876)),x57093)) % 172.78/172.48 [5759]E(f332(f332(f151(x57591),x57592),x57593),f140(x57591,x57592,x57593))+P102(f332(f332(f334(x57591),x57592),f332(f173(x57591),x57593))) % 172.78/172.48 [5768]E(x57681,x57682)+~E(f332(f332(f80(a876),f332(a115,x57683)),x57681),f332(f332(f80(a876),f332(a115,x57683)),x57682)) % 172.78/172.48 [5769]~E(x57692,f332(f332(f79(a1),x57691),f332(f103(a1),f332(a115,x57693))))+P102(f332(f332(f247(a1),x57691),x57692)) % 172.78/172.48 [5874]~E(x58743,f116(x58741))+E(f332(f332(f332(f190(f877(x58741),f877(x58741)),x58742),f168(x58741)),x58743),f116(x58741)) % 172.78/172.48 [5878]P102(f332(x58781,x58782))+~P102(f332(f332(f334(x58783),x58782),f332(f252(x58783),x58781))) % 172.78/172.48 [5908]E(x59081,x59082)+~E(f332(f332(f310(x59083),x59081),f195(f883(x59083,a871))),f332(f332(f310(x59083),x59082),f195(f883(x59083,a871)))) % 172.78/172.48 [5919]~P105(x59191)+E(f332(f332(f104(f883(x59191,a871)),f332(f253(x59191),x59192)),f332(f302(x59191,x59192),x59193)),f195(f883(x59191,a871))) % 172.78/172.48 [5962]E(f140(x59621,x59622,x59623),x59623)+~P102(f332(f332(f334(x59621),x59622),f332(f173(x59621),x59623))) % 172.78/172.48 [5986]~P79(x59861)+E(f332(f311(x59861,x59861,f78(x59861)),f332(f302(x59861,x59862),x59863)),f305(x59861,f332(f78(x59861),x59863),f332(f78(x59861),x59862))) % 172.78/172.48 [5995]E(f332(f196(f877(x59951)),f171(x59951,x59952,x59953)),f332(f196(f877(x59951)),x59953))+P102(f332(f332(f334(x59951),x59952),f332(f173(x59951),x59953))) % 172.78/172.48 [6047]~P105(x60471)+E(f332(f332(f104(f883(x60471,a871)),f332(f302(x60471,x60472),x60473)),f332(f254(x60471),x60473)),f195(f883(x60471,a871))) % 172.78/172.48 [6070]~P79(x60701)+E(f332(f311(x60701,x60701,f78(x60701)),f303(x60701,x60702,x60703)),f303(x60701,f332(f78(x60701),x60703),f332(f78(x60701),x60702))) % 172.78/172.48 [6071]~P79(x60711)+E(f332(f311(x60711,x60711,f78(x60711)),f306(x60711,x60712,x60713)),f306(x60711,f332(f78(x60711),x60713),f332(f78(x60711),x60712))) % 172.78/172.48 [6128]E(f177(x61281,f332(f332(f151(x61281),x61282),f116(x61281)),x61283),f332(f332(f151(x61281),x61282),f116(x61281)))+~P102(f332(f332(f334(a876),f2(a876)),x61283)) % 172.78/172.48 [6135]~P79(x61351)+E(f332(f311(x61351,x61351,f78(x61351)),f305(x61351,x61352,x61353)),f332(f302(x61351,f332(f78(x61351),x61353)),f332(f78(x61351),x61352))) % 172.78/172.48 [6155]~P26(x61551)+E(f44(x61551,f332(f78(x61551),f44(x61551,x61552,x61553)),x61553),f44(x61551,f332(f78(x61551),x61552),x61553)) % 172.78/172.48 [6254]~P102(f332(f61(f882(x62542,x62541)),x62543))+P102(f332(f61(x62541),f332(f263(x62542,x62541),x62543))) % 172.78/172.48 [6255]~P102(f332(f61(f882(x62551,x62552)),x62553))+P102(f332(f61(x62551),f332(f265(x62551,x62552),x62553))) % 172.78/172.48 [6261]~P105(x62611)+E(f332(f332(f104(f883(x62611,a871)),f303(x62611,x62612,x62613)),f332(f304(x62611),x62613)),f195(f883(x62611,a871))) % 172.78/172.48 [6262]~P105(x62621)+E(f332(f332(f104(f883(x62621,a871)),f306(x62621,x62622,x62623)),f332(f254(x62621),x62623)),f195(f883(x62621,a871))) % 172.78/172.48 [6263]~P105(x62631)+E(f332(f332(f104(f883(x62631,a871)),f305(x62631,x62632,x62633)),f332(f304(x62631),x62633)),f195(f883(x62631,a871))) % 172.78/172.48 [6329]E(f332(f332(f165(x63291),x63292),f654(x63292,x63293,x63291)),x63293)+~P102(f332(f332(f334(x63291),x63293),f332(f173(x63291),x63292))) % 172.78/172.48 [6468]E(x64681,f116(x64682))+~E(f332(f332(f332(f190(f877(x64682),f877(x64682)),x64683),f168(x64682)),x64681),f116(x64682)) % 172.78/172.48 [6570]~P102(f332(f61(f882(x65702,x65701)),x65703))+P102(f332(f61(f882(x65701,x65702)),f332(f287(x65702,x65701),x65703))) % 172.78/172.48 [6721]P51(x67211,x67212,x67213)+P102(f332(f332(f334(x67211),f583(x67213,x67212,x67211)),x67212)) % 172.78/172.48 [6722]P51(x67221,x67222,x67223)+P102(f332(f332(f334(x67221),f582(x67223,x67222,x67221)),x67222)) % 172.78/172.48 [6734]P102(f332(f320(x67341,x67342),x67343))+P102(f332(f332(x67342,f482(x67343,x67342,x67341)),x67343)) % 172.78/172.48 [6735]P102(f332(f320(x67351,x67352),x67353))+P102(f332(f332(x67352,f496(x67353,x67352,x67351)),x67353)) % 172.78/172.48 [6766]E(f332(f196(f877(x67661)),f171(x67661,x67662,x67663)),f332(f332(f22(a876),f332(f196(f877(x67661)),x67663)),f77(a876)))+~P102(f332(f332(f334(x67661),x67662),f332(f173(x67661),x67663))) % 172.78/172.48 [6806]P102(f332(f260(x68061,x68062),x68063))+P102(f332(f332(f334(x68061),f554(x68063,x68062,x68061)),x68063)) % 172.78/172.48 [6817]~P102(f332(f61(f882(x68172,x68171)),f332(f287(x68171,x68172),x68173)))+P102(f332(f61(f882(x68171,x68172)),x68173)) % 172.78/172.48 [6873]~P102(f332(f332(f334(x68731),x68732),f332(f173(x68731),f117(x68731,x68733))))+P102(f332(f332(f334(x68731),x68732),f332(f173(x68731),x68733))) % 172.78/172.48 [6878]P22(x68781,x68782,x68783)+P102(f332(f332(f334(f875(x68781)),f571(x68783,x68782,x68781)),x68783)) % 172.78/172.48 [6908]E(f332(f136(x69081,x69082),x69083),x69083)+P102(f332(f332(f334(x69081),f736(x69083,x69082,x69081)),f332(f173(x69081),x69083))) % 172.78/172.48 [6923]E(f332(f136(x69231,x69232),x69233),f116(x69231))+P102(f332(f332(f334(x69231),f735(x69233,x69232,x69231)),f332(f173(x69231),x69233))) % 172.78/172.48 [6946]P32(x69461,x69462,x69463)+P102(f332(f332(f334(x69461),f796(x69463,x69462,x69461)),f332(f173(x69461),x69463))) % 172.78/172.48 [6947]P32(x69471,x69472,x69473)+P102(f332(f332(f334(x69471),f803(x69473,x69472,x69471)),f332(f173(x69471),x69473))) % 172.78/172.48 [6948]P32(x69481,x69482,x69483)+P102(f332(f332(f334(x69481),f802(x69482,x69483,x69481)),f332(f173(x69481),x69483))) % 172.78/172.48 [6951]E(f178(x69511,x69512,x69513),x69513)+P102(f332(f332(f334(x69511),f753(x69513,x69512,x69511)),f332(f173(x69511),x69513))) % 172.78/172.48 [7032]P102(f332(f160(x70321,x70322),x70323))+P102(f332(f332(f334(x70321),f724(x70323,x70322,x70321)),f332(f173(x70321),x70323))) % 172.78/172.48 [7041]~P34(x70411,x70413,x70412)+P102(f332(f332(f334(x70411),f779(x70412,x70413,x70411)),f332(f173(x70411),x70412))) % 172.78/172.48 [7042]~P36(x70421,x70423,x70422)+P102(f332(f332(f334(x70421),f809(x70422,x70423,x70421)),f332(f173(x70421),x70422))) % 172.78/172.48 [7077]P102(f332(f332(f334(x70771),x70772),f656(x70773,x70772,x70771)))+~P102(f332(f332(f334(x70771),x70772),f39(f883(x70771,a871),x70773))) % 172.78/172.48 [7078]~P71(x70781)+E(f332(f332(f79(x70781),f332(f332(f6(a876,x70781),x70782),f332(f253(a876),x70783))),f332(x70782,x70783)),f332(f332(f6(a876,x70781),x70782),f332(f253(a876),f332(a115,x70783)))) % 172.78/172.48 [7167]~P34(x71672,x71671,x71673)+P102(f332(x71671,f332(f332(f165(x71672),x71673),f792(x71673,x71671,x71672)))) % 172.78/172.48 [7180]~P102(f332(f332(f334(x71801),x71802),f644(x71802,x71803,x71801)))+P102(f332(f332(f334(x71801),x71802),f40(f883(x71801,a871),x71803))) % 172.78/172.48 [7210]~P71(x72101)+E(f332(f332(f79(x72101),f332(f332(f6(a876,x72101),x72102),f332(f301(a876),x72103))),f332(x72102,f332(a115,x72103))),f332(f332(f6(a876,x72101),x72102),f332(f301(a876),f332(a115,x72103)))) % 172.78/172.48 [7345]P102(f332(f332(f334(f877(x73451)),x73452),f161(x73451,x73453)))+P102(f332(f332(f334(x73451),f679(x73453,x73452,x73451)),f332(f173(x73451),x73452))) % 172.78/172.48 [7362]~P102(f332(f332(f334(f877(x73621)),x73622),f161(x73621,f321(x73621,x73623))))+P102(f332(f332(f334(f877(x73621)),x73622),f321(f877(x73621),f157(x73621,x73623)))) % 172.78/172.48 [7387]~P102(f332(f332(f334(f877(x73871)),x73872),f321(f877(x73871),f157(x73871,x73873))))+P102(f332(f332(f334(f877(x73871)),x73872),f161(x73871,f321(x73871,x73873)))) % 172.78/172.48 [7423]E(f332(f332(f332(f190(f877(x74231),f877(x74231)),x74232),f168(x74231)),x74233),x74233)+~P102(f332(f332(f246(a876),f332(f196(f877(x74231)),x74233)),f77(a876))) % 172.78/172.48 [7459]E(f332(f332(f134(x74591),f793(x74592,x74593,x74591)),f332(f332(f151(x74591),x74593),f795(x74592,x74593,x74591))),x74592)+~P102(f332(f332(f334(x74591),x74593),f332(f173(x74591),x74592))) % 172.78/172.48 [7460]E(f332(f332(f134(x74601),f798(x74602,x74603,x74601)),f332(f332(f151(x74601),x74603),f799(x74602,x74603,x74601))),x74602)+~P102(f332(f332(f334(x74601),x74603),f332(f173(x74601),x74602))) % 172.78/172.48 [7461]E(f332(f332(f134(x74611),f800(x74612,x74613,x74611)),f332(f332(f151(x74611),x74613),f801(x74612,x74613,x74611))),x74612)+~P102(f332(f332(f334(x74611),x74613),f332(f173(x74611),x74612))) % 172.78/172.48 [7485]~P20(x74851,x74852,x74853,f255(f883(x74851,a871)))+P20(f877(x74851),f877(x74852),f332(f154(x74851,x74852),x74853),f255(f883(f877(x74851),a871))) % 172.78/172.48 [7634]E(x76341,f332(f332(f79(a876),f332(f332(f80(a876),f332(f266(a876,a876),x76342)),x76343)),f332(f270(a876,a876),x76342)))+~P102(f332(f47(x76341,x76343),x76342)) % 172.78/172.48 [7642]P20(x76421,x76422,x76423,f255(f883(x76421,a871)))+~P20(f877(x76421),f877(x76422),f332(f154(x76421,x76422),x76423),f255(f883(f877(x76421),a871))) % 172.78/172.48 [7681]~P102(f332(f332(f201(x76811),x76812),x76813))+P102(f332(f332(f332(f332(a203,x76811),x76812),f569(x76813,x76812,x76811)),x76813)) % 172.78/172.48 [7686]P102(f332(f332(f334(f883(x76861,a871)),f644(x76862,x76863,x76861)),x76863))+P102(f332(f332(f334(x76861),x76862),f40(f883(x76861,a871),x76863))) % 172.78/172.48 [7782]P102(f332(f332(f334(f877(x77821)),x77822),f161(x77821,x77823)))+~P102(f332(f332(f334(x77821),f679(x77823,x77822,x77821)),x77823)) % 172.78/172.48 [7883]P32(x78831,x78832,x78833)+~P102(f332(x78832,f332(f332(f165(x78831),x78833),f797(x78833,x78832,x78831)))) % 172.78/172.48 [7908]E(x79081,x79082)+~E(f332(f332(f7(x79083,f883(x79083,a871),a871),f334(x79083)),x79081),f332(f332(f7(x79083,f883(x79083,a871),a871),f334(x79083)),x79082)) % 172.78/172.48 [7914]~P102(f332(f332(f334(f882(x79141,x79141)),x79143),f264(x79141,x79142)))+P102(f332(f332(f334(x79141),f509(x79142,x79143,x79141)),x79142)) % 172.78/172.48 [7916]~P102(f332(f332(f334(x79161),x79163),f39(f883(x79161,a871),x79162)))+P102(f332(f332(f334(f883(x79161,a871)),f656(x79162,x79163,x79161)),x79162)) % 172.78/172.48 [8099]~P102(f332(f332(f334(x80991),x80992),f332(f173(x80991),f798(x80993,x80992,x80991))))+~P102(f332(f332(f334(x80991),x80992),f332(f173(x80991),x80993))) % 172.78/172.48 [8100]~P102(f332(f332(f334(x81001),x81002),f332(f173(x81001),f801(x81003,x81002,x81001))))+~P102(f332(f332(f334(x81001),x81002),f332(f173(x81001),x81003))) % 172.78/172.48 [8190]E(f332(f241(f880(f877(a328)),f877(a328),f314(x81901,x81902,f332(f332(f79(a1),x81903),f77(a1))),f239(f877(a328))),f332(x81901,x81903)),f314(x81901,x81902,x81903))+P102(f332(f332(f247(a1),x81902),x81903)) % 172.78/172.48 [8292]E(x82921,f116(x82922))+P102(f332(f332(f334(x82922),f332(f266(x82922,f882(a102,a102)),f332(f283(x82922,x82921),x82923))),f332(f173(x82922),x82921))) % 172.78/172.48 [8388]~P65(x83881)+E(f332(f142(x83881,x83881,f332(f7(x83881,x83881,x83881),f79(x83881)),x83882),f332(f169(x83881),x83883)),f332(f142(x83881,x83881,f79(x83881),x83882),x83883)) % 172.78/172.48 [8878]~P104(x88781)+E(f332(f173(x88781),f149(x88781,x88781,f5(x88781),x88782,x88783)),f332(f332(f310(x88781),x88782),f332(f173(x88781),x88783))) % 172.78/172.48 [8889]P102(f332(f332(f247(a876),f2(a876)),f607(x88891,x88892,x88893)))+~P102(f332(f332(f334(f882(x88893,x88893)),x88892),f332(f332(f289(x88893,x88893,x88893),x88891),f308(x88893,x88891)))) % 172.78/172.48 [9179]~P53(x91791,x91792)+~P102(f332(f332(f334(f882(x91791,x91791)),f332(f332(f267(x91791,x91791),x91793),x91793)),f332(f332(f289(x91791,x91791,x91791),x91792),f308(x91791,x91792)))) % 172.78/172.48 [9311]~E(f332(f332(f104(f883(f882(x93111,x93111),a871)),f332(f287(x93111,x93111),x93112)),f308(x93111,x93112)),f195(f883(f882(x93111,x93111),a871)))+~P102(f332(f332(f334(f882(x93111,x93111)),f332(f332(f267(x93111,x93111),x93113),x93113)),f332(f332(f289(x93111,x93111,x93111),x93112),f308(x93111,x93112)))) % 172.78/172.48 [9490]~P102(f332(f61(x94901),x94902))+P102(f332(f332(f246(a876),f332(f37(x94901),f332(f332(f22(f883(x94901,a871)),x94902),f332(f332(f310(x94901),x94903),f195(f883(x94901,a871)))))),f332(f37(x94901),x94902))) % 172.78/172.48 [5057]~E(x50573,f116(x50571))+E(f144(x50571,f332(f332(f151(x50571),x50572),x50573)),x50572) % 172.78/172.48 [5065]~E(x50653,f116(x50651))+E(f117(x50651,f332(f332(f151(x50651),x50652),x50653)),f116(x50651)) % 172.78/172.48 [5094]E(x50941,f116(x50942))+E(f144(x50942,f332(f332(f151(x50942),x50943),x50941)),f144(x50942,x50941)) % 172.78/172.48 [5096]E(x50961,f116(x50962))+E(f144(x50962,f332(f332(f134(x50962),x50963),x50961)),f144(x50962,x50961)) % 172.78/172.48 [5101]~E(x51013,f116(x51011))+E(f117(x51011,f332(f332(f134(x51011),x51012),x51013)),f117(x51011,x51012)) % 172.78/172.48 [5103]~E(x51033,f116(x51031))+E(f144(x51031,f332(f332(f134(x51031),x51032),x51033)),f144(x51031,x51032)) % 172.78/172.48 [5135]E(x51351,f116(x51352))+E(f332(f141(x51352),f332(f332(f134(x51352),x51351),x51353)),f332(f141(x51352),x51351)) % 172.78/172.48 [5164]~E(x51642,f116(x51641))+E(f332(f141(x51641),f332(f332(f134(x51641),x51642),x51643)),f332(f141(x51641),x51643)) % 172.78/172.48 [5214]~P61(x52141)+E(f332(f332(f113(x52141),x52142),f332(f332(f104(x52141),x52142),x52143)),x52142) % 172.78/172.48 [5215]~P61(x52151)+E(f332(f332(f104(x52151),x52152),f332(f332(f113(x52151),x52152),x52153)),x52152) % 172.78/172.48 [5216]~P104(x52161)+E(f332(f332(f244(x52161),x52162),f332(f332(f245(x52161),x52162),x52163)),x52162) % 172.78/172.48 [5217]~P104(x52171)+E(f332(f332(f245(x52171),x52172),f332(f332(f244(x52171),x52172),x52173)),x52172) % 172.78/172.48 [5235]~P25(x52351)+E(f44(x52351,f332(f332(f80(x52351),x52352),x52353),x52353),f2(x52351)) % 172.78/172.48 [5236]~P25(x52361)+E(f44(x52361,f332(f332(f80(x52361),x52362),x52363),x52362),f2(x52361)) % 172.78/172.48 [5311]~P66(x53111)+E(f332(f78(x53111),f332(f332(f22(x53111),x53112),x53113)),f332(f332(f22(x53111),x53113),x53112)) % 172.78/172.48 [5374]E(x53741,f116(x53742))+E(f117(x53742,f332(f332(f151(x53742),x53743),x53741)),f332(f332(f151(x53742),x53743),f117(x53742,x53741))) % 172.78/172.48 [5375]E(x53751,f116(x53752))+E(f117(x53752,f332(f332(f134(x53752),x53753),x53751)),f332(f332(f134(x53752),x53753),f117(x53752,x53751))) % 172.78/172.48 [5378]~P27(x53781)+E(f40(x53781,f332(f332(f310(x53781),x53782),x53783)),f332(f332(f104(x53781),x53782),f40(x53781,x53783))) % 172.78/172.48 [5379]~P27(x53791)+E(f39(x53791,f332(f332(f310(x53791),x53792),x53793)),f332(f332(f113(x53791),x53792),f39(x53791,x53793))) % 172.78/172.48 [5424]~P61(x54241)+E(f332(f332(f113(x54241),x54242),f332(f332(f113(x54241),x54242),x54243)),f332(f332(f113(x54241),x54242),x54243)) % 172.78/172.48 [5426]~P97(x54261)+E(f332(f332(f113(x54261),x54262),f332(f332(f113(x54261),x54262),x54263)),f332(f332(f113(x54261),x54262),x54263)) % 172.78/172.48 [5427]~P61(x54271)+E(f332(f332(f104(x54271),x54272),f332(f332(f104(x54271),x54272),x54273)),f332(f332(f104(x54271),x54272),x54273)) % 172.78/172.48 [5429]~P98(x54291)+E(f332(f332(f104(x54291),x54292),f332(f332(f104(x54291),x54292),x54293)),f332(f332(f104(x54291),x54292),x54293)) % 172.78/172.48 [5430]~P93(x54301)+E(f332(f332(f80(x54301),x54302),f332(f332(f80(x54301),x54302),x54303)),f332(f332(f80(x54301),x54302),x54303)) % 172.78/172.48 [5432]~P104(x54321)+E(f332(f332(f244(x54321),x54322),f332(f332(f244(x54321),x54322),x54323)),f332(f332(f244(x54321),x54322),x54323)) % 172.78/172.48 [5434]~P104(x54341)+E(f332(f332(f245(x54341),x54342),f332(f332(f245(x54341),x54342),x54343)),f332(f332(f245(x54341),x54342),x54343)) % 172.78/172.48 [5442]~P25(x54421)+E(f44(x54421,f332(f332(f79(x54421),x54422),x54423),x54423),f44(x54421,x54422,x54423)) % 172.78/172.48 [5443]~P25(x54431)+E(f44(x54431,f332(f332(f79(x54431),x54432),x54433),x54432),f44(x54431,x54433,x54432)) % 172.78/172.48 [5449]~P123(x54491)+E(f332(f332(f80(x54491),x54492),f332(f78(x54491),x54493)),f332(f78(x54491),f332(f332(f80(x54491),x54492),x54493))) % 172.78/172.48 [5450]~P57(x54501)+E(f332(f332(f290(x54501),x54502),f332(f78(x54501),x54503)),f332(f78(x54501),f332(f332(f290(x54501),x54502),x54503))) % 172.78/172.48 [5451]~P76(x54511)+E(f332(f332(f79(x54511),x54512),f332(f166(x54511),x54513)),f332(f166(x54511),f332(f332(f151(x54511),x54512),x54513))) % 172.78/172.48 [5481]~P123(x54811)+E(f332(f332(f80(x54811),f332(f78(x54811),x54812)),x54813),f332(f332(f80(x54811),x54812),f332(f78(x54811),x54813))) % 172.78/172.48 [5488]~P3(x54881,x54882,x54883)+E(f39(f883(x54881,a871),f332(f332(f60(x54881),x54882),x54883)),x54882) % 172.78/172.48 [5549]~P109(x55491)+E(f332(f332(f80(x55491),x55492),f332(f332(f257(x55491),x55492),x55493)),f332(f332(f257(x55491),x55492),f332(a115,x55493))) % 172.78/172.48 [5550]~P114(x55501)+E(f332(f332(f80(x55501),x55502),f332(f332(f257(x55501),x55502),x55503)),f332(f332(f257(x55501),x55502),f332(a115,x55503))) % 172.78/172.48 [5560]~P72(x55601)+E(f332(f332(f79(x55601),f332(f78(x55601),x55602)),f332(f332(f79(x55601),x55602),x55603)),x55603) % 172.78/172.48 [5583]~P141(x55831)+E(f332(f332(f257(x55831),f332(f103(x55831),x55832)),x55833),f332(f103(x55831),f332(f332(f257(a876),x55832),x55833))) % 172.78/172.48 [5584]~P137(x55841)+E(f332(f332(f257(x55841),f332(f105(x55841),x55842)),x55843),f332(f105(x55841),f332(f332(f257(a1),x55842),x55843))) % 172.78/172.48 [5590]~P81(x55901)+E(f332(f74(x55901),f332(f332(f22(x55901),x55902),x55903)),f332(f74(x55901),f332(f332(f22(x55901),x55903),x55902))) % 172.78/172.48 [5592]~P113(x55921)+E(f332(f332(f80(x55921),f81(x55921,x55922)),f81(x55921,x55923)),f81(x55921,f332(f332(f80(x55921),x55922),x55923))) % 172.78/172.48 [5596]E(x55961,f116(x55962))+E(f332(f332(f134(x55962),f332(f172(x55962),x55961)),x55963),f332(f172(x55962),f332(f332(f134(x55962),x55961),x55963))) % 172.78/172.48 [5601]~E(x56012,f332(a115,f332(f332(f79(a876),x56011),x56013)))+P102(f332(f332(f247(a876),x56011),x56012)) % 172.78/172.48 [5602]~P113(x56021)+E(f332(f332(f257(x56021),f332(f74(x56021),x56022)),x56023),f332(f74(x56021),f332(f332(f257(x56021),x56022),x56023))) % 172.78/172.48 [5603]~P123(x56031)+E(f332(f332(f80(x56031),f332(f78(x56031),x56032)),x56033),f332(f78(x56031),f332(f332(f80(x56031),x56032),x56033))) % 172.78/172.48 [5604]~P117(x56041)+E(f332(f332(f290(x56041),f332(f78(x56041),x56042)),x56043),f332(f78(x56041),f332(f332(f290(x56041),x56042),x56043))) % 172.78/172.48 [5702]E(f721(x57021,x57022,x57023),f728(x57021,x57022,x57023))+E(f332(f332(f104(f883(x57023,a871)),x57022),x57021),f195(f883(x57023,a871))) % 172.78/172.48 [5717]~P71(x57172)+E(f332(f332(f6(x57171,x57172),f332(f16(x57172,x57171),f2(x57172))),x57173),f2(x57172)) % 172.78/172.48 [5718]~P67(x57182)+E(f332(f332(f9(x57181,x57182),f332(f16(x57182,x57181),f77(x57182))),x57183),f77(x57182)) % 172.78/172.48 [5720]~P141(x57201)+E(f332(f332(f80(x57201),f332(f103(x57201),x57202)),f332(f103(x57201),x57203)),f332(f103(x57201),f332(f332(f80(a876),x57202),x57203))) % 172.78/172.48 [5721]~P141(x57211)+E(f332(f332(f79(x57211),f332(f103(x57211),x57212)),f332(f103(x57211),x57213)),f332(f103(x57211),f332(f332(f79(a876),x57212),x57213))) % 172.78/172.48 [5722]~P137(x57221)+E(f332(f332(f22(x57221),f332(f105(x57221),x57222)),f332(f105(x57221),x57223)),f332(f105(x57221),f332(f332(f22(a1),x57222),x57223))) % 172.78/172.48 [5723]~P137(x57231)+E(f332(f332(f80(x57231),f332(f105(x57231),x57232)),f332(f105(x57231),x57233)),f332(f105(x57231),f332(f332(f80(a1),x57232),x57233))) % 172.78/172.48 [5724]~P137(x57241)+E(f332(f332(f79(x57241),f332(f105(x57241),x57242)),f332(f105(x57241),x57243)),f332(f105(x57241),f332(f332(f79(a1),x57242),x57243))) % 172.78/172.48 [5725]~P89(x57251)+E(f332(f332(f22(x57251),f332(f106(x57251),x57252)),f332(f106(x57251),x57253)),f332(f106(x57251),f332(f332(f22(a1),x57252),x57253))) % 172.78/172.48 [5728]~P89(x57281)+E(f332(f332(f80(x57281),f332(f106(x57281),x57282)),f332(f106(x57281),x57283)),f332(f106(x57281),f332(f332(f80(a1),x57282),x57283))) % 172.78/172.48 [5729]~P89(x57291)+E(f332(f332(f79(x57291),f332(f106(x57291),x57292)),f332(f106(x57291),x57293)),f332(f106(x57291),f332(f332(f79(a1),x57292),x57293))) % 172.78/172.48 [5776]~E(x57763,x57762)+P102(f332(f332(f246(f883(x57761,a871)),x57762),x57763)) % 172.78/172.48 [5782]~E(x57822,x57823)+P102(f332(f332(f246(f883(x57821,a871)),x57822),x57823)) % 172.78/172.48 [5787]~P113(x57871)+E(f332(f332(f80(x57871),f332(f74(x57871),x57872)),f332(f74(x57871),x57873)),f332(f74(x57871),f332(f332(f80(x57871),x57872),x57873))) % 172.78/172.48 [5788]~P59(x57881)+E(f332(f332(f290(x57881),f332(f74(x57881),x57882)),f332(f74(x57881),x57883)),f332(f74(x57881),f332(f332(f290(x57881),x57882),x57883))) % 172.78/172.48 [5789]~P92(x57891)+E(f332(f332(f104(x57891),f332(f78(x57891),x57892)),f332(f78(x57891),x57893)),f332(f78(x57891),f332(f332(f113(x57891),x57892),x57893))) % 172.78/172.48 [5790]~P92(x57901)+E(f332(f332(f113(x57901),f332(f78(x57901),x57902)),f332(f78(x57901),x57903)),f332(f78(x57901),f332(f332(f104(x57901),x57902),x57903))) % 172.78/172.48 [5791]~P72(x57911)+E(f332(f332(f79(x57911),f332(f78(x57911),x57912)),f332(f78(x57911),x57913)),f332(f78(x57911),f332(f332(f79(x57911),x57913),x57912))) % 172.78/172.48 [5792]~P66(x57921)+E(f332(f332(f79(x57921),f332(f78(x57921),x57922)),f332(f78(x57921),x57923)),f332(f78(x57921),f332(f332(f79(x57921),x57922),x57923))) % 172.78/172.48 [5793]~P73(x57931)+E(f332(f332(f245(x57931),f332(f78(x57931),x57932)),f332(f78(x57931),x57933)),f332(f78(x57931),f332(f332(f244(x57931),x57932),x57933))) % 172.78/172.48 [5794]~P73(x57941)+E(f332(f332(f244(x57941),f332(f78(x57941),x57942)),f332(f78(x57941),x57943)),f332(f78(x57941),f332(f332(f245(x57941),x57942),x57943))) % 172.78/172.48 [5795]~P76(x57951)+E(f332(f332(f79(x57951),f332(f166(x57951),x57952)),f332(f166(x57951),x57953)),f332(f166(x57951),f332(f332(f134(x57951),x57952),x57953))) % 172.78/172.48 [5796]E(x57961,f195(f883(x57962,a871)))+~E(f332(f332(f113(f883(x57962,a871)),x57963),x57961),f195(f883(x57962,a871))) % 172.78/172.48 [5797]E(x57971,f195(f883(x57972,a871)))+~E(f332(f332(f113(f883(x57972,a871)),x57971),x57973),f195(f883(x57972,a871))) % 172.78/172.48 [5798]~P144(x57981,x57982,x57983)+P102(f332(x57981,f332(f332(f38(a1),x57982),x57983))) % 172.78/172.48 [5848]~P102(f332(f61(x58481),x58483))+P102(f332(f61(x58481),f332(f332(f310(x58481),x58482),x58483))) % 172.78/172.48 [5849]~P102(f332(f137(x58491),x58493))+P102(f332(f137(x58491),f332(f332(f176(x58491),x58492),x58493))) % 172.78/172.48 [5850]~P102(f332(f137(x58501),x58503))+P102(f332(f137(x58501),f332(f332(f138(x58501),x58502),x58503))) % 172.78/172.48 [5879]~P61(x58791)+P102(f332(f332(f246(x58791),x58792),f332(f332(f113(x58791),x58793),x58792))) % 172.78/172.48 [5880]~P97(x58801)+P102(f332(f332(f246(x58801),x58802),f332(f332(f113(x58801),x58803),x58802))) % 172.78/172.48 [5881]~P61(x58811)+P102(f332(f332(f246(x58811),x58812),f332(f332(f113(x58811),x58812),x58813))) % 172.78/172.48 [5882]~P97(x58821)+P102(f332(f332(f246(x58821),x58822),f332(f332(f113(x58821),x58822),x58823))) % 172.78/172.48 [5883]~P104(x58831)+P102(f332(f332(f246(x58831),x58832),f332(f332(f245(x58831),x58833),x58832))) % 172.78/172.48 [5884]~P104(x58841)+P102(f332(f332(f246(x58841),x58842),f332(f332(f245(x58841),x58842),x58843))) % 172.78/172.48 [5898]~E(x58981,f2(a876))+E(f332(f332(f38(a876),f332(f332(f80(a876),x58981),x58982)),f332(f332(f80(a876),x58981),x58983)),f2(a876)) % 172.78/172.48 [5965]P102(f332(x59651,x59652))+P102(f332(f332(f201(f31(x59651,x59653)),x59652),x59652)) % 172.78/172.48 [5980]~P89(x59801)+E(f332(f332(f22(x59801),f332(f106(x59801),x59802)),f332(f106(x59801),x59803)),f332(f106(x59801),f332(f332(f79(a1),x59802),f332(f78(a1),x59803)))) % 172.78/172.48 [6034]E(x60341,f2(a876))+E(f332(f332(f38(a876),f332(f332(f80(a876),x60341),x60342)),f332(f332(f80(a876),x60341),x60343)),f332(f332(f38(a876),x60342),x60343)) % 172.78/172.48 [6068]E(f152(x60681,f332(f332(f151(x60681),x60682),x60683)),f332(f332(f151(x60681),x60682),f152(x60681,x60683)))+P102(f332(f332(f334(x60681),x60682),f332(f173(x60681),x60683))) % 172.78/172.48 [6102]P144(x61021,x61022,x61023)+~P102(f332(x61021,f332(f332(f38(a1),x61022),x61023))) % 172.78/172.48 [6171]E(x61711,f116(x61712))+E(f332(f332(f151(x61712),f332(f141(x61712),x61711)),f332(f332(f176(x61712),x61713),f332(f172(x61712),x61711))),f332(f332(f176(x61712),f332(a115,x61713)),x61711)) % 172.78/172.48 [6178]E(f332(f332(f22(f883(x61781,a871)),x61782),x61783),x61782)+~E(f332(f332(f104(f883(x61781,a871)),x61782),x61783),f195(f883(x61781,a871))) % 172.78/172.48 [6192]E(f152(x61921,f332(f332(f151(x61921),x61922),x61923)),f152(x61921,x61923))+~P102(f332(f332(f334(x61921),x61922),f332(f173(x61921),x61923))) % 172.78/172.48 [6224]~P102(f332(f332(f247(a876),x62241),x62243))+P102(f332(f332(f247(a876),x62241),f332(f332(f79(a876),x62242),x62243))) % 172.78/172.48 [6226]~P102(f332(f332(f247(a876),x62261),x62262))+P102(f332(f332(f247(a876),x62261),f332(f332(f79(a876),x62262),x62263))) % 172.78/172.48 [6228]~P102(f332(f332(f246(a876),x62281),x62283))+P102(f332(f332(f246(a876),x62281),f332(f332(f79(a876),x62282),x62283))) % 172.78/172.48 [6230]~P102(f332(f332(f246(a876),x62301),x62302))+P102(f332(f332(f246(a876),x62301),f332(f332(f79(a876),x62302),x62303))) % 172.78/172.48 [6269]P102(f332(f61(x62691),x62692))+~P102(f332(f61(x62691),f332(f332(f310(x62691),x62693),x62692))) % 172.78/172.48 [6270]P102(f332(f137(x62701),x62702))+~P102(f332(f137(x62701),f332(f332(f151(x62701),x62703),x62702))) % 172.78/172.48 [6271]P102(f332(f137(x62711),x62712))+~P102(f332(f137(x62711),f332(f332(f134(x62711),x62713),x62712))) % 172.78/172.48 [6272]P102(f332(f137(x62721),x62722))+~P102(f332(f137(x62721),f332(f332(f134(x62721),x62722),x62723))) % 172.78/172.48 [6318]~P114(x63181)+E(f332(f332(f79(x63181),x63182),f332(f332(f80(x63181),x63183),x63182)),f332(f332(f80(x63181),f332(f332(f79(x63181),x63183),f77(x63181))),x63182)) % 172.78/172.48 [6365]~E(x63651,x63652)+~P102(f332(f332(f247(f883(x63653,a871)),x63651),x63652)) % 172.78/172.48 [6409]P102(f332(f332(f334(x64091),x64092),x64093))+P102(f332(f332(f334(x64091),x64092),f332(f78(f883(x64091,a871)),x64093))) % 172.78/172.48 [6415]E(f144(x64151,f332(f332(f138(x64151),x64152),x64153)),f144(x64151,x64153))+~P102(f332(f332(f247(a876),x64152),f332(f196(f877(x64151)),x64153))) % 172.78/172.48 [6416]E(f332(f332(f176(x64161),x64162),f117(x64161,x64163)),f332(f332(f176(x64161),x64162),x64163))+~P102(f332(f332(f247(a876),x64162),f332(f196(f877(x64161)),x64163))) % 172.78/172.48 [6470]E(f332(f332(f332(f190(f877(x64701),f877(x64701)),x64702),f168(x64701)),x64703),x64703)+~E(f44(a876,x64702,f332(f196(f877(x64701)),x64703)),f2(a876)) % 172.78/172.48 [6477]~P3(x64771,x64773,x64772)+E(f332(f332(f289(x64771,x64771,x64771),f332(f287(x64771,x64771),x64772)),x64772),x64772) % 172.78/172.48 [6519]~E(f332(f332(f113(f883(x65191,a871)),x65192),x65193),x65193)+P102(f332(f332(f246(f883(x65191,a871)),x65192),x65193)) % 172.78/172.48 [6524]~P50(x65241,x65241,x65243)+P50(x65241,x65241,f332(f332(f190(f882(x65241,x65241),a871),x65242),x65243)) % 172.78/172.48 [6526]~P102(f332(f332(f334(x65261),x65263),f332(f173(x65261),x65262)))+P102(f332(f332(f247(a876),f2(a876)),f332(f196(f877(x65261)),x65262))) % 172.78/172.48 [6552]~P81(x65521)+E(f332(f74(x65521),f332(f332(f79(x65521),f332(f74(x65521),x65522)),f332(f74(x65521),x65523))),f332(f332(f79(x65521),f332(f74(x65521),x65522)),f332(f74(x65521),x65523))) % 172.78/172.48 [6563]E(f332(f332(f38(a876),f332(f332(f80(a876),x65631),x65632)),f332(f332(f80(a876),x65631),x65633)),f332(f332(f38(a876),x65632),x65633))+~P102(f332(f332(f247(a876),f2(a876)),x65631)) % 172.78/172.48 [6611]E(x66111,x66112)+~P102(f332(f332(f332(f332(a203,a24),x66111),x66113),x66112)) % 172.78/172.48 [6700]~P102(f332(f61(x67001),x67003))+E(f332(f332(f64(x67001,f883(x67001,a871),f310(x67001)),x67002),x67003),f332(f332(f113(f883(x67001,a871)),x67003),x67002)) % 172.78/172.48 [6759]E(f332(f332(f113(f883(x67591,a871)),x67592),x67593),x67592)+~P102(f332(f332(f246(f883(x67591,a871)),x67593),x67592)) % 172.78/172.48 [6761]E(f332(f332(f113(f883(x67611,a871)),x67612),x67613),x67613)+~P102(f332(f332(f246(f883(x67611,a871)),x67612),x67613)) % 172.78/172.48 [6762]E(f332(f332(f104(f883(x67621,a871)),x67622),x67623),x67623)+~P102(f332(f332(f246(f883(x67621,a871)),x67623),x67622)) % 172.78/172.48 [6763]E(f332(f332(f104(f883(x67631,a871)),x67632),x67633),x67632)+~P102(f332(f332(f246(f883(x67631,a871)),x67632),x67633)) % 172.78/172.48 [6815]~P102(f332(f137(x68151),x68152))+E(f332(f332(f22(f883(x68151,a871)),f332(f173(x68151),x68152)),f332(f332(f310(x68151),x68153),f195(f883(x68151,a871)))),f332(f173(x68151),f171(x68151,x68153,x68152))) % 172.78/172.48 [6868]P38(x68681,x68682)+~P38(x68681,f332(f332(f190(f882(x68681,x68681),a871),x68683),x68682)) % 172.78/172.48 [6934]P102(f332(f48(x69341,x69342),f332(a50,x69343)))+~P102(f332(f48(f332(f78(a1),x69341),f332(f78(a1),x69342)),x69343)) % 172.78/172.48 [6939]E(f332(f332(f22(f883(x69391,a871)),f332(f332(f310(x69391),x69392),x69393)),f332(f332(f310(x69391),x69392),f195(f883(x69391,a871)))),x69393)+P102(f332(f332(f334(x69391),x69392),x69393)) % 172.78/172.48 [6960]E(f332(f332(f104(f883(x69601,a871)),f332(f173(x69601),x69602)),f332(f173(x69601),x69603)),f195(f883(x69601,a871)))+~P102(f332(f137(x69601),f332(f332(f134(x69601),x69602),x69603))) % 172.78/172.48 [6976]~P102(f332(f332(f334(x69761),x69762),f332(f173(x69761),x69763)))+~P102(f332(f137(x69761),f332(f332(f151(x69761),x69762),x69763))) % 172.78/172.48 [7048]P32(x70481,x70482,x70483)+P102(f332(f332(f247(a876),f797(x70483,x70482,x70481)),f332(f196(f877(x70481)),x70483))) % 172.78/172.48 [7058]E(f332(f332(f104(f883(x70581,a871)),x70582),x70583),f195(f883(x70581,a871)))+P102(f332(f332(f334(x70581),f721(x70583,x70582,x70581)),x70582)) % 172.78/172.48 [7059]E(f332(f332(f104(f883(x70591,a871)),x70592),x70593),f195(f883(x70591,a871)))+P102(f332(f332(f334(x70591),f728(x70593,x70592,x70591)),x70593)) % 172.78/172.48 [7063]E(f117(x70631,f332(f332(f176(x70631),x70632),x70633)),f332(f332(f176(x70631),f332(f332(f22(a876),x70632),f77(a876))),x70633))+~P102(f332(f332(f246(a876),x70632),f332(f196(f877(x70631)),x70633))) % 172.78/172.48 [7122]~P34(x71223,x71222,x71221)+P102(f332(f332(f247(a876),f792(x71221,x71222,x71223)),f332(f196(f877(x71223)),x71221))) % 172.78/172.48 [7140]P102(f332(f332(f247(a876),f2(a876)),x71401))+P102(f332(f332(f246(a876),f332(f332(f80(a876),x71402),x71401)),f332(f332(f80(a876),x71403),x71401))) % 172.78/172.48 [7141]P102(f332(f332(f247(a876),f2(a876)),x71411))+P102(f332(f332(f246(a876),f332(f332(f80(a876),x71411),x71412)),f332(f332(f80(a876),x71411),x71413))) % 172.78/172.48 [7144]~P102(f332(f332(f334(x71441),x71442),x71443))+~P102(f332(f332(f334(x71441),x71442),f332(f78(f883(x71441,a871)),x71443))) % 172.78/172.48 [7151]~P102(f332(f332(f247(f883(x71511,a871)),x71512),x71513))+P102(f332(f332(f246(f883(x71511,a871)),x71512),x71513)) % 172.78/172.48 [7250]~P102(f332(f332(f247(a876),x72502),x72503))+P102(f332(f332(f247(a876),f332(f332(f79(a876),x72501),x72502)),f332(f332(f79(a876),x72501),x72503))) % 172.78/172.48 [7251]~P102(f332(f332(f247(a876),x72511),x72513))+P102(f332(f332(f247(a876),f332(f332(f79(a876),x72511),x72512)),f332(f332(f79(a876),x72513),x72512))) % 172.78/172.48 [7252]~P102(f332(f332(f247(a1),x72521),x72523))+P102(f332(f332(f247(a1),f332(f332(f79(a1),x72521),x72522)),f332(f332(f79(a1),x72523),x72522))) % 172.78/172.48 [7255]~P102(f332(f332(f246(a876),x72553),x72552))+P102(f332(f332(f246(a876),f332(f332(f22(a876),x72551),x72552)),f332(f332(f22(a876),x72551),x72553))) % 172.78/172.48 [7256]~P102(f332(f332(f246(a876),x72561),x72563))+P102(f332(f332(f246(a876),f332(f332(f22(a876),x72561),x72562)),f332(f332(f22(a876),x72563),x72562))) % 172.78/172.48 [7258]~P102(f332(f332(f246(a876),x72582),x72583))+P102(f332(f332(f246(a876),f332(f332(f80(a876),x72581),x72582)),f332(f332(f80(a876),x72581),x72583))) % 172.78/172.48 [7260]~P102(f332(f332(f246(a876),x72601),x72603))+P102(f332(f332(f246(a876),f332(f332(f80(a876),x72601),x72602)),f332(f332(f80(a876),x72603),x72602))) % 172.78/172.48 [7261]~P102(f332(f332(f246(a876),x72612),x72613))+P102(f332(f332(f246(a876),f332(f332(f79(a876),x72611),x72612)),f332(f332(f79(a876),x72611),x72613))) % 172.78/172.48 [7262]~P102(f332(f332(f246(a876),x72621),x72623))+P102(f332(f332(f246(a876),f332(f332(f79(a876),x72621),x72622)),f332(f332(f79(a876),x72623),x72622))) % 172.78/172.48 [7263]~P102(f332(f332(f246(a876),x72631),x72633))+P102(f332(f332(f246(a876),f332(f332(f38(a876),x72631),x72632)),f332(f332(f38(a876),x72633),x72632))) % 172.78/172.48 [7264]~P102(f332(f332(f246(a1),x72642),x72643))+P102(f332(f332(f246(a1),f332(f332(f79(a1),x72641),x72642)),f332(f332(f79(a1),x72641),x72643))) % 172.78/172.48 [7344]E(x73441,x73442)+~P102(f332(f332(f334(x73443),x73441),f332(f332(f310(x73443),x73442),f195(f883(x73443,a871))))) % 172.78/172.48 [7346]~E(f332(f332(f104(f883(x73461,a871)),x73462),x73463),f195(f883(x73461,a871)))+P102(f332(f332(f246(f883(x73461,a871)),x73462),f332(f78(f883(x73461,a871)),x73463))) % 172.78/172.48 [7354]P102(f332(f332(f334(f883(x73541,a871)),x73542),f332(f309(x73541),x73543)))+~P102(f332(f332(f246(f883(x73541,a871)),x73542),x73543)) % 172.78/172.48 [7407]E(f332(f332(f151(x74071),f332(f332(f165(x74071),x74072),x74073)),f332(f332(f138(x74071),f332(a115,x74073)),x74072)),f332(f332(f138(x74071),x74073),x74072))+~P102(f332(f332(f247(a876),x74073),f332(f196(f877(x74071)),x74072))) % 172.78/172.48 [7434]P102(f332(f332(f334(f882(x74341,x74341)),x74342),f308(x74341,x74343)))+~P102(f332(f332(f334(f882(x74341,x74341)),x74342),x74343)) % 172.78/172.48 [7445]~P102(f332(f332(f334(f883(x74451,a871)),x74452),f332(f309(x74451),x74453)))+P102(f332(f332(f246(f883(x74451,a871)),x74452),x74453)) % 172.78/172.48 [7491]P102(f332(f332(f246(f883(x74911,a871)),x74912),f39(f883(x74911,a871),x74913)))+~P102(f332(f332(f334(f883(x74911,a871)),x74912),x74913)) % 172.78/172.48 [7516]~P137(x75161)+E(f332(f332(f80(x75161),f332(f332(f257(x75161),f332(f78(x75161),f77(x75161))),x75162)),f332(f332(f257(x75161),x75163),x75162)),f332(f332(f257(x75161),f332(f78(x75161),x75163)),x75162)) % 172.78/172.48 [7538]E(f332(f332(f165(x75381),x75382),f332(f332(f22(a876),f332(f196(f877(x75381)),x75382)),f332(a115,x75383))),f332(f332(f165(x75381),f332(f169(x75381),x75382)),x75383))+~P102(f332(f332(f247(a876),x75383),f332(f196(f877(x75381)),x75382))) % 172.78/172.48 [7555]~E(f332(f332(f104(f883(x75551,a871)),f635(x75553,x75552,x75551)),x75553),f195(f883(x75551,a871)))+E(f332(f332(f104(f883(x75551,a871)),f39(f883(x75551,a871),x75552)),x75553),f195(f883(x75551,a871))) % 172.78/172.48 [7616]~P102(f332(f332(f334(x76163),x76162),f332(f173(x76163),x76161)))+P102(f332(f332(f247(a876),f654(x76161,x76162,x76163)),f332(f196(f877(x76163)),x76161))) % 172.78/172.48 [7624]P102(f332(f332(f334(x76241),f332(f332(f165(x76241),x76242),x76243)),f332(f173(x76241),x76242)))+~P102(f332(f332(f247(a876),x76243),f332(f196(f877(x76241)),x76242))) % 172.78/172.48 [7726]~P102(f332(x77262,f754(x77263,x77262,x77261)))+E(f332(f332(f138(x77261),f332(f196(f877(x77261)),f178(x77261,x77262,x77263))),x77263),f116(x77261)) % 172.78/172.48 [7737]P102(f332(f332(f246(f883(f877(x77371),a871)),f161(x77371,x77372)),f161(x77371,x77373)))+~P102(f332(f332(f246(f883(x77371,a871)),x77372),x77373)) % 172.78/172.48 [7738]P102(f332(f332(f246(f883(f877(x77381),a871)),f160(x77381,x77382)),f160(x77381,x77383)))+~P102(f332(f332(f246(f883(x77381,a871)),x77382),x77383)) % 172.78/172.48 [7767]E(f332(f332(f104(f883(x77671,a871)),f39(f883(x77671,a871),x77672)),x77673),f195(f883(x77671,a871)))+P102(f332(f332(f334(f883(x77671,a871)),f635(x77673,x77672,x77671)),x77672)) % 172.78/172.48 [7770]~P102(f332(f332(f334(f883(x77701,a871)),x77703),x77702))+P102(f332(f332(f246(f883(x77701,a871)),f40(f883(x77701,a871),x77702)),x77703)) % 172.78/172.48 [7772]E(f332(f332(f104(f883(x77721,a871)),x77722),x77723),f195(f883(x77721,a871)))+~P102(f332(f332(f246(f883(x77721,a871)),x77722),f332(f78(f883(x77721,a871)),x77723))) % 172.78/172.48 [7821]E(f332(f332(f22(a876),f332(f332(f79(a876),f332(f166(a876),x78211)),x78212)),f332(f332(f165(a876),x78211),x78213)),f332(f166(a876),f332(f332(f159(a876,x78211),x78213),x78212)))+~P102(f332(f332(f247(a876),x78213),f332(f196(f877(a876)),x78211))) % 172.78/172.48 [7871]P102(f332(f332(f247(a876),x78711),x78712))+~P102(f332(f332(f247(a876),f332(f332(f79(a876),x78713),x78711)),f332(f332(f79(a876),x78713),x78712))) % 172.78/172.48 [7872]P102(f332(f332(f247(a876),x78721),x78722))+~P102(f332(f332(f247(a876),f332(f332(f80(a876),x78723),x78721)),f332(f332(f80(a876),x78723),x78722))) % 172.78/172.48 [7873]P102(f332(f332(f247(a876),x78731),x78732))+~P102(f332(f332(f247(a876),f332(f332(f80(a876),x78731),x78733)),f332(f332(f80(a876),x78732),x78733))) % 172.78/172.48 [7876]P102(f332(f332(f246(a876),x78761),x78762))+~P102(f332(f332(f246(a876),f332(f332(f79(a876),x78763),x78761)),f332(f332(f79(a876),x78763),x78762))) % 172.78/172.48 [7906]P102(f332(f332(f247(a876),f2(a876)),x79061))+~P102(f332(f332(f247(a876),f332(f332(f80(a876),x79062),x79061)),f332(f332(f80(a876),x79063),x79061))) % 172.78/172.48 [7907]P102(f332(f332(f247(a876),f2(a876)),x79071))+~P102(f332(f332(f247(a876),f332(f332(f80(a876),x79071),x79072)),f332(f332(f80(a876),x79071),x79073))) % 172.78/172.48 [7981]E(f259(x79811,x79812,x79813),x79812)+~P102(f332(f332(f246(f883(x79811,a871)),x79813),f332(f332(f310(x79811),x79812),f195(f883(x79811,a871))))) % 172.78/172.48 [8039]~P102(f332(f137(x80391),x80393))+E(f332(f136(x80391,f332(f332(f8(a871,a871,x80391),a327),f332(a329,x80392))),x80393),f171(x80391,x80392,x80393)) % 172.78/172.48 [8062]E(f332(f332(f138(x80621),f332(f196(f877(x80621)),f178(x80621,x80622,x80623))),x80623),f116(x80621))+P102(f332(f332(f334(x80621),f754(x80623,x80622,x80621)),f332(f173(x80621),x80623))) % 172.78/172.48 [8066]E(f332(f332(f134(x80661),f332(f332(f176(x80661),x80662),x80663)),f332(f332(f151(x80661),f332(f332(f165(x80661),x80663),x80662)),f116(x80661))),f332(f332(f176(x80661),f332(a115,x80662)),x80663))+~P102(f332(f332(f247(a876),x80662),f332(f196(f877(x80661)),x80663))) % 172.78/172.48 [8128]E(f332(f136(x81281,f332(f332(f8(a871,a871,x81281),a327),f332(a329,x81282))),x81283),x81283)+P102(f332(f332(f334(x81281),x81282),f332(f173(x81281),x81283))) % 172.78/172.48 [8136]P102(f332(f332(f246(f883(f883(x81361,a871),a871)),f260(x81361,x81362)),f260(x81361,x81363)))+~P102(f332(f332(f246(f883(x81361,a871)),x81362),x81363)) % 172.78/172.48 [8181]~P102(f332(f137(x81811),x81813))+P102(f332(f137(x81811),f332(f332(f332(f190(f877(x81811),f877(x81811)),x81812),f168(x81811)),x81813))) % 172.78/172.48 [8186]~P102(f332(f332(f247(a876),x81862),x81863))+P102(f332(f332(f247(a876),f332(f332(f80(a876),f332(a115,x81861)),x81862)),f332(f332(f80(a876),f332(a115,x81861)),x81863))) % 172.78/172.48 [8209]P102(f332(f332(f246(f883(f883(x82091,a871),a871)),f332(f309(x82091),x82092)),f332(f309(x82091),x82093)))+~P102(f332(f332(f246(f883(x82091,a871)),x82092),x82093)) % 172.78/172.48 [8371]~P102(f332(f332(f246(f883(x83711,a871)),x83713),x83712))+P102(f332(f332(f246(f883(x83711,a871)),f332(f78(f883(x83711,a871)),x83712)),f332(f78(f883(x83711,a871)),x83713))) % 172.78/172.48 [8404]E(f332(f311(a876,a876,f332(f332(f7(a876,a876,a876),f22(a876)),x84041)),f332(f302(a876,x84042),x84043)),f332(f302(a876,f332(f332(f22(a876),x84042),x84041)),f332(f332(f22(a876),x84043),x84041)))+~P102(f332(f332(f247(a876),x84041),x84043)) % 172.78/172.48 [8433]~P76(x84331)+E(f332(f332(f79(x84331),x84332),f332(f142(x84331,x84331,f79(x84331),f2(x84331)),x84333)),f332(f142(x84331,x84331,f79(x84331),x84332),x84333)) % 172.78/172.48 [8515]~P81(x85151)+P102(f332(f332(f246(x85151),f332(f74(x85151),f332(f332(f22(x85151),x85152),x85153))),f332(f332(f79(x85151),f332(f74(x85151),x85152)),f332(f74(x85151),x85153)))) % 172.78/172.48 [8516]~P81(x85161)+P102(f332(f332(f246(x85161),f332(f74(x85161),f332(f332(f79(x85161),x85162),x85163))),f332(f332(f79(x85161),f332(f74(x85161),x85162)),f332(f74(x85161),x85163)))) % 172.78/172.48 [8526]E(f332(f332(f79(a1),f332(f332(f80(a1),x85261),f44(a1,f332(f332(f38(a1),x85262),x85261),x85263))),f44(a1,x85262,x85261)),f44(a1,x85262,f332(f332(f80(a1),x85261),x85263)))+~P102(f332(f332(f247(a1),f2(a1)),x85263)) % 172.78/172.48 [8532]E(f332(f332(f134(x85321),f332(f332(f176(x85321),x85322),x85323)),f332(f332(f151(x85321),f332(f141(x85321),f332(f332(f138(x85321),x85322),x85323))),f116(x85321))),f332(f332(f176(x85321),f332(a115,x85322)),x85323))+~P102(f332(f332(f247(a876),x85322),f332(f196(f877(x85321)),x85323))) % 172.78/172.48 [8551]E(f332(f278(x85511,f332(f332(f154(x85511,f882(a102,x85511)),f332(f267(a102,x85511),f77(a102))),x85512)),f332(a3,x85513)),f332(f332(f165(x85511),x85512),x85513))+~P102(f332(f332(f247(a876),x85513),f332(f196(f877(x85511)),x85512))) % 172.78/172.48 [8615]P102(f332(f332(f334(f882(x86151,x86151)),x86152),f332(f332(f289(x86151,x86151,x86151),x86153),f308(x86151,x86153))))+~P102(f332(f332(f334(f882(x86151,x86151)),x86152),x86153)) % 172.78/172.48 [8635]P102(f332(f332(f246(a876),x86351),x86352))+~P102(f332(f332(f246(a876),f332(f332(f80(a876),f332(a115,x86353)),x86351)),f332(f332(f80(a876),f332(a115,x86353)),x86352))) % 172.78/172.48 [8649]P102(f332(f332(f246(f883(x86491,a871)),x86492),x86493))+~P102(f332(f332(f246(f883(x86491,a871)),f332(f78(f883(x86491,a871)),x86493)),f332(f78(f883(x86491,a871)),x86492))) % 172.78/172.48 [8667]P102(f332(f137(x86671),x86672))+~P102(f332(f137(x86671),f332(f332(f332(f190(f877(x86671),f877(x86671)),x86673),f168(x86671)),x86672))) % 172.78/172.48 [8727]E(f332(f311(f882(x87271,x87272),x87272,f270(x87271,x87272)),f332(f173(f882(x87271,x87272)),x87273)),f187(x87271,x87272,f332(f179(x87271,x87272),x87273)))+~P102(f332(f137(x87271),f332(f332(f154(f882(x87271,x87272),x87271),f266(x87271,x87272)),x87273))) % 172.78/172.48 [8736]E(f332(f286(x87361,x87361,f308(x87361,x87362)),x87363),x87363)+~P102(f332(f332(f246(f883(x87361,a871)),f332(f286(x87361,x87361,x87362),x87363)),x87363)) % 172.78/172.48 [8778]~P104(x87781)+P29(x87781,f332(f136(x87781,f332(f332(f7(x87781,x87781,a871),a329),f332(x87782,x87783))),x87783)) % 172.78/172.48 [8784]~P102(f332(f332(f246(a876),x87841),x87842))+P102(f332(f332(f246(a876),x87841),f332(f142(a876,a876,f79(a876),x87842),x87843))) % 172.78/172.48 [8862]~P102(f332(f332(f334(f882(x88621,x88621)),x88622),f308(x88621,x88623)))+P102(f332(f332(f334(f882(x88621,x88621)),x88622),f332(f332(f190(f882(x88621,x88621),a871),f596(x88623,x88622,x88621)),x88623))) % 172.78/172.48 [8957]~P76(x89571)+E(f332(f332(f79(x89571),x89572),f332(f142(x89571,x89571,f332(f7(x89571,x89571,x89571),f79(x89571)),f2(x89571)),f332(f169(x89571),x89573))),f332(f142(x89571,x89571,f79(x89571),x89572),x89573)) % 172.78/172.48 [9225]P50(x92251,x92252,x92253)+P102(f332(f332(f334(f882(x92251,x92252)),f332(f332(f267(x92251,x92252),f598(x92253,x92252,x92251)),f595(x92253,x92252,x92251))),x92253)) % 172.78/172.48 [9226]P50(x92261,x92262,x92263)+P102(f332(f332(f334(f882(x92261,x92262)),f332(f332(f267(x92261,x92262),f598(x92263,x92262,x92261)),f594(x92263,x92262,x92261))),x92263)) % 172.78/172.48 [9296]~P102(f332(f332(f334(f882(x92961,x92961)),x92962),f332(f332(f289(x92961,x92961,x92961),x92963),f308(x92961,x92963))))+P102(f332(f332(f334(f882(x92961,x92961)),x92962),f332(f332(f190(f882(x92961,x92961),a871),f607(x92963,x92962,x92961)),x92963))) % 172.78/172.48 [9297]~P102(f332(x92971,f332(f332(f165(x92972),x92973),f332(f196(f877(x92972)),f178(x92972,x92971,x92973)))))+~P102(f332(f332(f247(a876),f332(f196(f877(x92972)),f178(x92972,x92971,x92973))),f332(f196(f877(x92972)),x92973))) % 172.78/172.48 [9386]~P102(f332(f332(f246(f883(x93861,a871)),x93862),x93863))+P102(f332(f332(f246(f883(x93861,a871)),f332(f332(f7(x93861,f883(x93861,a871),a871),f334(x93861)),x93862)),f332(f332(f7(x93861,f883(x93861,a871),a871),f334(x93861)),x93863))) % 172.78/172.48 [9439]~P102(f332(f332(f334(f882(f883(x94391,a871),f883(x94391,a871))),f332(f332(f267(f883(x94391,a871),f883(x94391,a871)),x94392),x94393)),f307(x94391)))+P102(f332(f332(f247(f883(x94391,a871)),x94392),x94393)) % 172.78/172.48 [9464]P51(x94641,x94642,x94643)+~P102(f332(f332(f334(f882(x94641,x94641)),f332(f332(f267(x94641,x94641),f583(x94643,x94642,x94641)),f582(x94643,x94642,x94641))),x94643)) % 172.78/172.48 [9465]P51(x94651,x94652,x94653)+~P102(f332(f332(f334(f882(x94651,x94651)),f332(f332(f267(x94651,x94651),f582(x94653,x94652,x94651)),f583(x94653,x94652,x94651))),x94653)) % 172.78/172.48 [9501]~P102(f332(f332(f334(f882(f877(x95011),f877(x95011))),f332(f332(f267(f877(x95011),f877(x95011)),x95012),x95012)),f147(x95011,x95013)))+P102(f332(f332(f334(f882(x95011,x95011)),f332(f332(f267(x95011,x95011),f678(x95012,x95013,x95011)),f678(x95012,x95013,x95011))),x95013)) % 172.78/172.48 [9552]P102(f332(f332(f246(f883(x95521,a871)),x95522),x95523))+~P102(f332(f332(f246(f883(x95521,a871)),f332(f332(f7(x95521,f883(x95521,a871),a871),f334(x95521)),x95522)),f332(f332(f7(x95521,f883(x95521,a871),a871),f334(x95521)),x95523))) % 172.78/172.48 [9633]E(f332(f332(f22(a876),f332(f332(f6(a876,a876),x96331),f332(f253(a876),x96332))),f332(f332(f6(a876,a876),x96333),f332(f253(a876),x96332))),f332(f332(f6(a876,a876),f332(f332(f18(a876,a876,a876),f332(f332(f8(a876,f883(a876,a876),a876),f22(a876)),x96331)),x96333)),f332(f253(a876),x96332)))+~P102(f332(f332(f246(a876),f332(x96333,f372(x96332,x96331,x96333))),f332(x96331,f372(x96332,x96331,x96333)))) % 172.78/172.48 [9936]E(f332(f252(f882(x99361,x99362)),f332(f271(x99361,x99362,a871),f332(f332(f7(x99361,f883(x99362,f880(x99362)),f883(x99362,a871)),f332(f332(f8(f883(f880(x99362),a871),f883(f883(x99362,f880(x99362)),f883(x99362,a871)),x99361),f8(f880(x99362),a871,x99362)),f332(f332(f8(f880(x99362),f883(f880(x99362),a871),x99361),a329),f332(f179(x99361,x99362),x99363)))),f239(x99362)))),f332(f173(f882(x99361,x99362)),x99363))+~P102(f332(f137(x99361),f332(f332(f154(f882(x99361,x99362),x99361),f266(x99361,x99362)),x99363))) % 172.78/172.48 [5636]~P72(x56361)+E(f332(f332(f22(x56361),f332(f332(f79(x56361),x56362),x56363)),x56363),x56362) % 172.78/172.48 [5637]~P72(x56371)+E(f332(f332(f79(x56371),f332(f332(f22(x56371),x56372),x56373)),x56373),x56372) % 172.78/172.48 [5856]~P72(x58561)+E(f332(f332(f79(x58561),x58562),f332(f332(f79(x58561),f332(f78(x58561),x58562)),x58563)),x58563) % 172.78/172.48 [5939]~P75(x59391)+E(f332(f332(f80(x59391),f332(f332(f257(x59391),x59392),x59393)),x59392),f332(f332(f257(x59391),x59392),f332(a115,x59393))) % 172.78/172.48 [5940]~P114(x59401)+E(f332(f332(f80(x59401),f332(f332(f257(x59401),x59402),x59403)),x59402),f332(f332(f257(x59401),x59402),f332(a115,x59403))) % 172.78/172.48 [6152]~P113(x61521)+E(f332(f74(x61521),f332(f332(f257(x61521),f332(f78(x61521),x61522)),x61523)),f332(f74(x61521),f332(f332(f257(x61521),x61522),x61523))) % 172.78/172.48 [6204]~P75(x62041)+E(f332(f332(f80(x62041),f332(f332(f257(x62041),x62042),x62043)),x62042),f332(f332(f80(x62041),x62042),f332(f332(f257(x62041),x62042),x62043))) % 172.78/172.48 [6260]E(f332(f332(f22(a102),f332(f332(f79(a102),x62601),x62602)),x62603),f282(x62601,x62602,x62603))+~P102(f332(f332(f247(a102),x62602),x62603)) % 172.78/172.48 [6281]~E(f332(f332(f138(x62811),x62813),x62812),f116(x62811))+P102(f332(f332(f246(a876),f332(f196(f877(x62811)),x62812)),x62813)) % 172.78/172.48 [6414]E(f332(f332(f80(a876),f332(f106(a876),x64141)),f332(f332(f80(a876),f332(f106(a876),x64142)),x64143)),f2(a876))+~P102(f332(f332(f247(a1),x64141),a82)) % 172.78/172.48 [6430]~P57(x64301)+E(f332(f332(f257(x64301),f332(f332(f290(x64301),f77(x64301)),x64302)),x64303),f332(f332(f290(x64301),f77(x64301)),f332(f332(f257(x64301),x64302),x64303))) % 172.78/172.48 [6506]E(f332(f332(f22(a876),f332(f332(f79(a876),x65061),x65062)),x65063),f332(f332(f22(a876),x65061),f332(f332(f22(a876),x65063),x65062)))+~P102(f332(f332(f246(a876),x65062),x65063)) % 172.78/172.48 [6508]E(f332(f332(f22(a876),f332(f332(f79(a876),x65081),x65082)),x65083),f332(f332(f79(a876),x65081),f332(f332(f22(a876),x65082),x65083)))+~P102(f332(f332(f246(a876),x65083),x65082)) % 172.78/172.48 [6543]~P61(x65431)+P102(f332(f332(f246(x65431),f332(f332(f104(x65431),x65432),x65433)),x65433)) % 172.78/172.48 [6544]~P98(x65441)+P102(f332(f332(f246(x65441),f332(f332(f104(x65441),x65442),x65443)),x65443)) % 172.78/172.48 [6545]~P61(x65451)+P102(f332(f332(f246(x65451),f332(f332(f104(x65451),x65452),x65453)),x65452)) % 172.78/172.48 [6546]~P98(x65461)+P102(f332(f332(f246(x65461),f332(f332(f104(x65461),x65462),x65463)),x65462)) % 172.78/172.48 [6547]~P104(x65471)+P102(f332(f332(f246(x65471),f332(f332(f244(x65471),x65472),x65473)),x65473)) % 172.78/172.48 [6548]~P104(x65481)+P102(f332(f332(f246(x65481),f332(f332(f244(x65481),x65482),x65483)),x65482)) % 172.78/172.48 [6562]E(f332(f332(f38(a1),f332(f332(f38(a1),x65621),x65622)),x65623),f332(f332(f38(a1),x65621),f332(f332(f80(a1),x65622),x65623)))+~P102(f332(f332(f247(a1),f2(a1)),x65623)) % 172.78/172.48 [6614]~P114(x66141)+E(f332(f332(f79(x66141),f332(f332(f80(x66141),x66142),x66143)),x66143),f332(f332(f80(x66141),f332(f332(f79(x66141),x66142),f77(x66141))),x66143)) % 172.78/172.48 [6615]~P89(x66151)+E(f332(f332(f80(x66151),f332(f78(x66151),f332(f106(x66151),x66152))),x66153),f332(f332(f80(x66151),f332(f106(x66151),f332(f78(a1),x66152))),x66153)) % 172.78/172.48 [6687]~P76(x66871)+E(f332(f166(x66871),f332(f332(f154(x66872,x66871),f332(f16(x66871,x66872),f2(x66871))),x66873)),f2(x66871)) % 172.78/172.48 [6703]E(f332(f332(f79(a876),f332(f106(a876),x67031)),f332(f332(f79(a876),f332(f106(a876),x67032)),x67033)),f332(f332(f79(a876),f332(f106(a876),x67032)),x67033))+~P102(f332(a200,f332(f106(a1),x67031))) % 172.78/172.48 [6717]~P27(x67171)+E(f40(x67171,f332(f332(f310(x67171),x67172),f332(f332(f310(x67171),x67173),f195(f883(x67171,a871))))),f332(f332(f104(x67171),x67172),x67173)) % 172.78/172.48 [6718]~P27(x67181)+E(f39(x67181,f332(f332(f310(x67181),x67182),f332(f332(f310(x67181),x67183),f195(f883(x67181,a871))))),f332(f332(f113(x67181),x67182),x67183)) % 172.78/172.48 [6741]E(f332(f332(f176(x67411),x67412),x67413),x67413)+~P102(f332(f332(f246(a876),f332(f196(f877(x67411)),x67413)),x67412)) % 172.78/172.48 [6754]E(f332(f332(f138(x67541),x67542),x67543),f116(x67541))+~P102(f332(f332(f246(a876),f332(f196(f877(x67541)),x67543)),x67542)) % 172.78/172.48 [6765]E(f332(f332(f79(a876),f332(f332(f22(a876),x67651),x67652)),x67653),f332(f332(f22(a876),f332(f332(f79(a876),x67651),x67653)),x67652))+~P102(f332(f332(f246(a876),x67652),x67651)) % 172.78/172.48 [6779]~P102(f332(f332(f247(a876),x67791),x67793))+P102(f332(f332(f247(a876),f332(f332(f22(a876),x67791),x67792)),x67793)) % 172.78/172.48 [6807]~P104(x68071)+E(f171(x68071,x68072,f332(f332(f148(x68071,x68071,f5(x68071)),x68072),x68073)),x68073) % 172.78/172.48 [6896]E(f332(f332(f22(a876),f332(f332(f79(a876),x68961),x68962)),f332(a115,x68963)),f332(f332(f22(a876),x68961),f332(a115,f332(f332(f22(a876),x68963),x68962))))+~P102(f332(f332(f246(a876),x68962),x68963)) % 172.78/172.48 [6897]~P113(x68971)+P102(f332(f332(f246(x68971),f2(x68971)),f332(f332(f257(x68971),f332(f74(x68971),x68972)),x68973))) % 172.78/172.48 [6944]P19(x69441,x69442,x69443)+~P102(f332(f332(f246(f883(f875(x69441),a871)),x69443),x69442)) % 172.78/172.48 [6987]~P102(f332(f61(x69871),x69872))+P102(f332(f61(x69871),f332(f332(f22(f883(x69871,a871)),x69872),x69873))) % 172.78/172.48 [6988]~P102(f332(f61(x69881),x69883))+P102(f332(f61(x69881),f332(f332(f104(f883(x69881,a871)),x69882),x69883))) % 172.78/172.48 [6989]~P102(f332(f61(x69891),x69892))+P102(f332(f61(x69891),f332(f332(f104(f883(x69891,a871)),x69892),x69893))) % 172.78/172.48 [7130]~P38(x71301,x71303)+P38(x71301,f332(f332(f104(f883(f882(x71301,x71301),a871)),x71302),x71303)) % 172.78/172.48 [7131]~P38(x71311,x71312)+P38(x71311,f332(f332(f104(f883(f882(x71311,x71311),a871)),x71312),x71313)) % 172.78/172.48 [7246]~P61(x72461)+E(f13(x72461,f332(f173(x72461),f332(f332(f151(x72461),x72462),x72463))),f332(f142(x72461,x72461,f113(x72461),x72462),x72463)) % 172.78/172.48 [7247]~P61(x72471)+E(f10(x72471,f332(f173(x72471),f332(f332(f151(x72471),x72472),x72473))),f332(f142(x72471,x72471,f104(x72471),x72472),x72473)) % 172.78/172.48 [7248]~P104(x72481)+E(f14(x72481,f332(f173(x72481),f332(f332(f151(x72481),x72482),x72483))),f332(f142(x72481,x72481,f245(x72481),x72482),x72483)) % 172.78/172.48 [7249]~P104(x72491)+E(f15(x72491,f332(f173(x72491),f332(f332(f151(x72491),x72492),x72493))),f332(f142(x72491,x72491,f244(x72491),x72492),x72493)) % 172.78/172.48 [7309]~P102(f332(f61(x73091),x73092))+P102(f332(f332(f246(a876),f332(f37(x73091),x73092)),f332(f37(x73091),f332(f332(f310(x73091),x73093),x73092)))) % 172.78/172.48 [7317]E(f332(f332(f113(f883(a876,a871)),f332(f302(a876,x73171),x73172)),f332(f302(a876,x73172),f332(f332(f79(a876),x73172),x73173))),f332(f302(a876,x73171),f332(f332(f79(a876),x73172),x73173)))+~P102(f332(f332(f246(a876),x73171),x73172)) % 172.78/172.48 [7325]P102(f332(f332(f247(a876),x73251),x73252))+~P102(f332(f332(f247(a876),f332(f332(f79(a876),x73251),x73253)),x73252)) % 172.78/172.48 [7328]P102(f332(f332(f246(a876),x73281),x73282))+~P102(f332(f332(f246(a876),f332(f332(f79(a876),x73283),x73281)),x73282)) % 172.78/172.48 [7329]P102(f332(f332(f246(a876),x73291),x73292))+~P102(f332(f332(f246(a876),f332(f332(f79(a876),x73291),x73293)),x73292)) % 172.78/172.48 [7371]~P104(x73711)+E(f11(x73711,f245(x73711),f332(f173(x73711),f332(f332(f151(x73711),x73712),x73713))),f332(f142(x73711,x73711,f245(x73711),x73712),x73713)) % 172.78/172.48 [7372]~P104(x73721)+E(f12(x73721,f244(x73721),f332(f173(x73721),f332(f332(f151(x73721),x73722),x73723))),f332(f142(x73721,x73721,f244(x73721),x73722),x73723)) % 172.78/172.48 [7376]~E(x73762,f195(f883(f882(x73761,x73761),a871)))+P102(f332(f332(f246(f883(f882(x73761,x73761),a871)),x73762),x73763)) % 172.78/172.48 [7486]E(f332(f332(f113(f883(x74861,a871)),x74862),f332(f332(f22(f883(x74861,a871)),x74863),x74862)),x74863)+~P102(f332(f332(f246(f883(x74861,a871)),x74862),x74863)) % 172.78/172.48 [7487]~P102(f332(f332(f247(a876),x74871),f332(f332(f22(a876),x74873),x74872)))+P102(f332(f332(f247(a876),f332(f332(f79(a876),x74871),x74872)),x74873)) % 172.78/172.48 [7488]~P102(f332(f332(f246(a876),x74881),f332(f332(f79(a876),x74883),x74882)))+P102(f332(f332(f246(a876),f332(f332(f22(a876),x74881),x74882)),x74883)) % 172.78/172.48 [7545]E(x75451,f116(x75452))+E(f332(f141(x75452),f332(f332(f332(f190(f877(x75452),f877(x75452)),x75453),f168(x75452)),x75451)),f332(f332(f165(x75452),x75451),f44(a876,x75453,f332(f196(f877(x75452)),x75451)))) % 172.78/172.48 [7554]E(f332(f332(f310(x75541),x75542),f332(f332(f22(f883(x75541,a871)),x75543),f332(f332(f310(x75541),x75542),f195(f883(x75541,a871))))),x75543)+~P102(f332(f332(f334(x75541),x75542),x75543)) % 172.78/172.48 [7717]P102(f332(f332(f247(a876),x77171),f332(f332(f22(a876),x77172),x77173)))+~P102(f332(f332(f247(a876),f332(f332(f79(a876),x77171),x77173)),x77172)) % 172.78/172.48 [7718]P102(f332(f332(f246(a876),x77181),f332(f332(f79(a876),x77182),x77183)))+~P102(f332(f332(f246(a876),f332(f332(f22(a876),x77181),x77183)),x77182)) % 172.78/172.48 [7741]P102(f332(f61(x77411),x77412))+~P102(f332(f61(x77411),f332(f332(f113(f883(x77411,a871)),x77413),x77412))) % 172.78/172.48 [7742]P102(f332(f61(x77421),x77422))+~P102(f332(f61(x77421),f332(f332(f113(f883(x77421,a871)),x77422),x77423))) % 172.78/172.48 [7820]~P46(x78201,x78203)+P102(f332(f332(f334(f882(x78201,x78201)),f332(f332(f267(x78201,x78201),x78202),x78202)),x78203)) % 172.78/172.48 [7954]E(f332(f332(f165(a876),f139(a876,f332(f302(a876,x79541),x79542))),x79543),f332(f332(f79(a876),x79541),x79543))+~P102(f332(f332(f247(a876),f332(f332(f79(a876),x79541),x79543)),x79542)) % 172.78/172.48 [8023]~P102(f332(f332(f201(f332(a25,x80231)),x80232),x80233))+P102(f332(f332(f201(f332(f243(a873),f332(a27,x80231))),x80232),x80233)) % 172.78/172.48 [8028]E(f332(f332(f176(a876),x80281),f139(a876,f332(f302(a876,x80282),x80283))),f139(a876,f332(f302(a876,x80282),f332(f332(f79(a876),x80282),x80281))))+~P102(f332(f332(f246(a876),f332(f332(f79(a876),x80282),x80281)),x80283)) % 172.78/172.48 [8081]~P89(x80811)+E(f332(f332(f257(x80811),x80812),f332(f106(a876),f332(f332(f79(a1),x80813),x80813))),f332(f332(f85(x80811,x80811),f332(f332(f257(x80811),x80812),f332(f106(a876),x80813))),f332(f332(f18(x80811,x80811,x80811),f80(x80811)),f5(x80811)))) % 172.78/172.48 [8291]P102(f332(f332(f201(f332(a25,x82911)),x82912),x82913))+~P102(f332(f332(f201(f332(f243(a873),f332(a27,x82911))),x82912),x82913)) % 172.78/172.48 [8351]E(f332(f332(f134(x83511),f332(f332(f176(x83511),x83512),x83513)),f332(f332(f151(x83511),f332(f332(f165(x83511),x83513),x83512)),f332(f332(f138(x83511),f332(a115,x83512)),x83513))),x83513)+~P102(f332(f332(f247(a876),x83512),f332(f196(f877(x83511)),x83513))) % 172.78/172.48 [8358]P102(f332(f332(f246(f883(x83581,a871)),f320(x83581,x83582)),f320(x83581,x83583)))+~P102(f332(f332(f246(f883(x83581,f883(x83581,a871))),x83583),x83582)) % 172.78/172.48 [8360]~P51(x83601,x83602,x83603)+P51(x83601,x83602,f332(f332(f22(f883(f882(x83601,x83601),a871)),x83603),f308(x83601,f195(f883(f882(x83601,x83601),a871))))) % 172.78/172.48 [8377]P102(f332(f332(f246(f883(x83771,a871)),f321(x83771,x83772)),f321(x83771,x83773)))+~P102(f332(f332(f246(f883(f882(x83771,x83771),a871)),x83773),x83772)) % 172.78/172.48 [8384]~P121(x83841)+P102(f332(f332(f246(x83841),f2(x83841)),f332(f332(f79(x83841),f332(f332(f80(x83841),x83842),x83842)),f332(f332(f80(x83841),x83843),x83843)))) % 172.78/172.48 [8420]P102(f332(f332(f246(f883(x84201,a871)),f332(f285(x84201),x84202)),f332(f285(x84201),x84203)))+~P102(f332(f332(f246(f883(f882(x84201,x84201),a871)),x84202),x84203)) % 172.78/172.48 [8454]~P42(x84541,x84542)+~P102(f332(f332(f334(f882(x84541,x84541)),f332(f332(f267(x84541,x84541),x84543),x84543)),x84542)) % 172.78/172.48 [8456]~P38(x84561,x84562)+~P102(f332(f332(f334(f882(x84561,x84561)),f332(f332(f267(x84561,x84561),x84563),x84563)),x84562)) % 172.78/172.48 [8517]P102(f332(f332(f246(f883(x85171,a871)),f40(f883(x85171,a871),x85172)),f40(f883(x85171,a871),x85173)))+~P102(f332(f332(f246(f883(f883(x85171,a871),a871)),x85173),x85172)) % 172.78/172.48 [8518]P102(f332(f332(f246(f883(x85181,a871)),f39(f883(x85181,a871),x85182)),f39(f883(x85181,a871),x85183)))+~P102(f332(f332(f246(f883(f883(x85181,a871),a871)),x85182),x85183)) % 172.78/172.48 [8570]~P3(x85701,x85703,x85702)+P102(f332(f332(f246(f883(f882(x85701,x85701),a871)),x85702),f332(f332(f269(x85701,x85701),x85703),f332(f16(f883(x85701,a871),x85701),x85703)))) % 172.78/172.48 [8571]~P40(x85711,x85713,x85712)+P102(f332(f332(f246(f883(f882(x85711,x85711),a871)),x85712),f332(f332(f269(x85711,x85711),x85713),f332(f16(f883(x85711,a871),x85711),x85713)))) % 172.78/172.48 [8616]~P81(x86161)+P102(f332(f332(f246(x86161),f332(f332(f22(x86161),f332(f74(x86161),x86162)),f332(f74(x86161),x86163))),f332(f74(x86161),f332(f332(f22(x86161),x86163),x86162)))) % 172.78/172.48 [8617]~P81(x86171)+P102(f332(f332(f246(x86171),f332(f332(f22(x86171),f332(f74(x86171),x86172)),f332(f74(x86171),x86173))),f332(f74(x86171),f332(f332(f22(x86171),x86172),x86173)))) % 172.78/172.48 [8647]P102(f332(f332(f246(f883(f882(x86471,x86471),a871)),f308(x86471,x86472)),f308(x86471,x86473)))+~P102(f332(f332(f246(f883(f882(x86471,x86471),a871)),x86472),x86473)) % 172.78/172.48 [8802]P51(x88021,x88022,x88023)+~P51(x88021,x88022,f332(f332(f22(f883(f882(x88021,x88021),a871)),x88023),f308(x88021,f195(f883(f882(x88021,x88021),a871))))) % 172.78/172.48 [8821]P102(f332(f332(f246(f883(f882(f877(x88211),f877(x88211)),a871)),f157(x88211,x88212)),f157(x88211,x88213)))+~P102(f332(f332(f246(f883(f882(x88211,x88211),a871)),x88212),x88213)) % 172.78/172.48 [8822]P102(f332(f332(f246(f883(f882(f877(x88221),f877(x88221)),a871)),f158(x88221,x88222)),f158(x88221,x88223)))+~P102(f332(f332(f246(f883(f882(x88221,x88221),a871)),x88222),x88223)) % 172.78/172.48 [8841]~P40(x88411,x88413,x88412)+P102(f332(f332(f246(f883(f882(x88411,x88411),a871)),x88412),f332(f332(f289(x88411,x88411,x88411),f332(f287(x88411,x88411),x88412)),x88412))) % 172.78/172.48 [8890]~P102(f332(f137(x88901),x88902))+E(f332(f136(x88901,f332(f332(f7(x88901,f883(x88901,a871),a871),f334(x88901)),f332(f173(x88901),f177(x88901,x88902,x88903)))),x88902),f177(x88901,x88902,x88903)) % 172.78/172.48 [8955]E(x89551,x89552)+~P102(f332(f332(f334(f882(x89553,x89553)),f332(f332(f267(x89553,x89553),x89551),x89552)),f308(x89553,f195(f883(f882(x89553,x89553),a871))))) % 172.78/172.48 [9040]P102(f332(f332(f334(x90401),x90402),f321(x90401,x90403)))+P102(f332(f332(f334(f882(x90401,x90401)),f332(f332(f267(x90401,x90401),f521(x90403,x90402,x90401)),x90402)),x90403)) % 172.78/172.48 [9041]P102(f332(f332(f334(x90411),x90412),f321(x90411,x90413)))+P102(f332(f332(f334(f882(x90411,x90411)),f332(f332(f267(x90411,x90411),f584(x90413,x90412,x90411)),x90412)),x90413)) % 172.78/172.48 [9042]P102(f332(f332(f334(x90421),x90422),f321(x90421,x90423)))+P102(f332(f332(f334(f882(x90421,x90421)),f332(f332(f267(x90421,x90421),f585(x90423,x90422,x90421)),x90422)),x90423)) % 172.78/172.48 [9128]~P102(f332(f332(f334(f877(x91281)),x91283),f161(x91281,x91282)))+P102(f332(f160(x91281,f332(f332(f7(x91281,f883(x91281,a871),a871),f334(x91281)),x91282)),x91283)) % 172.78/172.48 [9149]P102(f332(x91493,x91492))+E(f332(f252(x91491),f332(f332(f18(x91491,a871,a871),f332(f332(f8(a871,f883(a871,a871),x91491),a330),f332(a329,x91492))),x91493)),f195(f883(x91491,a871))) % 172.78/172.48 [9170]~P81(x91701)+P102(f332(f332(f246(x91701),f332(f74(x91701),f332(f332(f22(x91701),f332(f74(x91701),x91702)),f332(f74(x91701),x91703)))),f332(f74(x91701),f332(f332(f22(x91701),x91702),x91703)))) % 172.78/172.48 [9184]~P102(f332(x91843,x91842))+E(f332(f252(x91841),f332(f332(f18(x91841,a871,a871),f332(f332(f8(a871,f883(a871,a871),x91841),a330),f332(a329,x91842))),x91843)),f332(f332(f310(x91841),x91842),f195(f883(x91841,a871)))) % 172.78/172.48 [9191]~P102(f332(f332(f334(f883(x91911,a871)),x91913),f332(f309(x91911),x91912)))+P102(f332(f260(x91911,f332(f332(f7(x91911,f883(x91911,a871),a871),f334(x91911)),x91912)),x91913)) % 172.78/172.48 [9224]P38(x92241,x92242)+P102(f332(f332(f334(f882(x92241,x92241)),f332(f332(f267(x92241,x92241),f332(f530(x92242,x92241),f332(a115,x92243))),f332(f530(x92242,x92241),x92243))),x92242)) % 172.78/172.48 [9365]P102(f332(f332(f334(f877(x93651)),x93652),f161(x93651,x93653)))+~P102(f332(f160(x93651,f332(f332(f7(x93651,f883(x93651,a871),a871),f334(x93651)),x93653)),x93652)) % 172.78/172.48 [9378]P102(f332(f332(f334(f883(x93781,a871)),x93782),f332(f309(x93781),x93783)))+~P102(f332(f260(x93781,f332(f332(f7(x93781,f883(x93781,a871),a871),f334(x93781)),x93783)),x93782)) % 172.78/172.48 [9435]P102(f332(f332(f334(x94351),f332(f278(x94351,x94352),x94353)),f332(f173(x94351),f332(f332(f154(f882(a102,x94351),x94351),f270(a102,x94351)),x94352))))+~P102(f332(f332(f247(a102),x94353),f332(f166(a102),f332(f332(f154(f882(a102,x94351),a102),f266(a102,x94351)),x94352)))) % 172.78/172.48 [9483]P102(f332(f332(f246(f883(f882(f877(x94831),f877(x94831)),a871)),f158(x94831,x94832)),f332(f332(f269(f877(x94831),f877(x94831)),f161(x94831,x94833)),f332(f16(f883(f877(x94831),a871),f877(x94831)),f161(x94831,x94833)))))+~P102(f332(f332(f246(f883(f882(x94831,x94831),a871)),x94832),f332(f332(f269(x94831,x94831),x94833),f332(f16(f883(x94831,a871),x94831),x94833)))) % 172.78/172.48 [9504]P102(f332(f332(f334(x95041),f332(f266(x95041,f882(a102,a102)),f332(f276(x95041,x95042),x95043))),f332(f173(x95041),f332(f332(f154(f882(a102,x95041),x95041),f270(a102,x95041)),x95042))))+~P102(f332(f332(f247(a102),f2(a102)),f332(f166(a102),f332(f332(f154(f882(a102,x95041),a102),f266(a102,x95041)),x95042)))) % 172.78/172.48 [9521]~P102(f332(f332(f246(f883(f882(x95211,x95211),a871)),x95212),f332(f332(f269(x95211,x95211),x95213),f332(f16(f883(x95211,a871),x95211),x95213))))+P102(f332(f332(f246(f883(f882(x95211,x95211),a871)),f332(f332(f289(x95211,x95211,x95211),x95212),f308(x95211,x95212))),f332(f332(f269(x95211,x95211),x95213),f332(f16(f883(x95211,a871),x95211),x95213)))) % 172.78/172.48 [9823]~P38(x98231,x98232)+~P102(f332(f332(f334(f882(x98231,x98231)),f332(f332(f267(x98231,x98231),f332(x98233,f332(a115,f531(x98232,x98231,x98233)))),f332(x98233,f531(x98232,x98231,x98233)))),x98232)) % 172.78/172.48 [9824]~P38(x98241,x98242)+~P102(f332(f332(f334(f882(x98241,x98241)),f332(f332(f267(x98241,x98241),f332(x98243,f332(a115,f590(x98243,x98242,x98241)))),f332(x98243,f590(x98243,x98242,x98241)))),x98242)) % 172.78/172.48 [10077]P102(f332(f332(f246(f883(f882(f883(x100771,a871),f883(x100771,a871)),a871)),f332(f332(f289(f883(x100771,a871),f883(x100771,a871),f883(x100771,a871)),f324(x100771,x100772)),f332(f332(f113(f883(f882(f883(x100771,a871),f883(x100771,a871)),a871)),f324(x100771,x100773)),f332(f332(f310(f882(f883(x100771,a871),f883(x100771,a871))),f332(f332(f267(f883(x100771,a871),f883(x100771,a871)),f195(f883(x100771,a871))),f195(f883(x100771,a871)))),f195(f883(f882(f883(x100771,a871),f883(x100771,a871)),a871)))))),f324(x100771,x100772)))+~P102(f332(f332(f246(f883(f882(x100771,x100771),a871)),f332(f332(f289(x100771,x100771,x100771),x100772),x100773)),x100772)) % 172.78/172.48 [10078]P102(f332(f332(f246(f883(f882(f883(x100781,a871),f883(x100781,a871)),a871)),f332(f332(f289(f883(x100781,a871),f883(x100781,a871),f883(x100781,a871)),f323(x100781,x100782)),f332(f332(f113(f883(f882(f883(x100781,a871),f883(x100781,a871)),a871)),f323(x100781,x100783)),f332(f332(f310(f882(f883(x100781,a871),f883(x100781,a871))),f332(f332(f267(f883(x100781,a871),f883(x100781,a871)),f195(f883(x100781,a871))),f195(f883(x100781,a871)))),f195(f883(f882(f883(x100781,a871),f883(x100781,a871)),a871)))))),f323(x100781,x100782)))+~P102(f332(f332(f246(f883(f882(x100781,x100781),a871)),f332(f332(f289(x100781,x100781,x100781),x100782),x100783)),x100782)) % 172.78/172.48 [7245]~P102(f332(f332(f246(a876),x72452),x72451))+E(f332(f332(f22(a876),f332(a115,f332(f332(f22(a876),x72451),x72452))),x72453),f332(f332(f22(a876),f332(a115,x72451)),f332(f332(f79(a876),x72452),x72453))) % 172.78/172.48 [7284]~P25(x72841)+E(f332(f332(f79(x72841),f44(x72841,x72842,x72843)),f332(f332(f80(x72841),f332(f332(f38(x72841),x72842),x72843)),x72843)),x72842) % 172.78/172.48 [7492]E(f332(f332(f80(a876),f332(f106(a876),x74921)),f332(f332(f80(a876),f332(f106(a876),x74922)),x74923)),f332(f332(f80(a876),f332(f106(a876),f332(f332(f80(a1),x74921),x74922))),x74923))+P102(f332(f332(f247(a1),x74921),a82)) % 172.78/172.48 [7963]~P102(f332(f332(f246(a876),x79633),x79632))+P102(f332(f332(f246(a876),x79631),f332(f332(f22(a876),f332(f332(f79(a876),x79632),x79631)),x79633))) % 172.78/172.48 [8171]~P102(f332(f332(f246(a876),x81711),x81712))+E(f332(f332(f134(a876),f139(a876,f332(f302(a876,x81711),x81712))),f139(a876,f332(f302(a876,x81712),f332(f332(f79(a876),x81712),x81713)))),f139(a876,f332(f302(a876,x81711),f332(f332(f79(a876),x81712),x81713)))) % 172.78/172.48 [8430]~P102(f332(f61(x84301),x84302))+E(f332(a115,f332(f37(x84301),f332(f332(f22(f883(x84301,a871)),x84302),f332(f332(f310(x84301),x84303),f195(f883(x84301,a871)))))),f332(f37(x84301),f332(f332(f310(x84301),x84303),x84302))) % 172.78/172.48 [8477]~P102(f332(f61(x84771),x84772))+E(f332(f332(f79(a876),f77(a876)),f332(f37(x84771),f332(f332(f22(f883(x84771,a871)),x84772),f332(f332(f310(x84771),x84773),f195(f883(x84771,a871)))))),f332(f37(x84771),f332(f332(f310(x84771),x84773),x84772))) % 172.78/172.48 [8656]E(f332(f332(f22(a876),f332(f37(x86561),x86562)),f332(f37(x86561),f332(f332(f104(f883(x86561,a871)),x86562),x86563))),f332(f37(x86561),f332(f332(f22(f883(x86561,a871)),x86562),x86563)))+~P102(f332(f61(x86561),f332(f332(f104(f883(x86561,a871)),x86562),x86563))) % 172.78/172.48 [8886]~P28(f332(x88862,f421(x88862,x88863,x88861)))+E(f332(f103(a1),f332(f332(f6(x88861,a876),f332(f332(f8(a1,a876,x88861),a107),x88862)),x88863)),f332(f332(f6(x88861,a1),x88862),x88863)) % 172.78/172.48 [8887]~P28(f332(x88872,f422(x88872,x88873,x88871)))+E(f332(f103(a1),f332(f332(f9(x88871,a876),f332(f332(f8(a1,a876,x88871),a107),x88872)),x88873)),f332(f332(f9(x88871,a1),x88872),x88873)) % 172.78/172.48 [8937]~P102(f332(f61(x89371),x89373))+P102(f332(f332(f246(a876),f332(f332(f22(a876),f332(f37(x89371),x89372)),f332(f37(x89371),x89373))),f332(f37(x89371),f332(f332(f22(f883(x89371,a871)),x89372),x89373)))) % 172.78/172.48 [8963]P102(f332(f332(f334(x89631),f421(x89632,x89633,x89631)),x89633))+E(f332(f103(a1),f332(f332(f6(x89631,a876),f332(f332(f8(a1,a876,x89631),a107),x89632)),x89633)),f332(f332(f6(x89631,a1),x89632),x89633)) % 172.78/172.48 [8964]P102(f332(f332(f334(x89641),f422(x89642,x89643,x89641)),x89643))+E(f332(f103(a1),f332(f332(f9(x89641,a876),f332(f332(f8(a1,a876,x89641),a107),x89642)),x89643)),f332(f332(f9(x89641,a1),x89642),x89643)) % 172.78/172.48 [9032]E(f84(x90321,f332(f332(f7(x90321,f883(x90321,a871),a871),f334(x90321)),f332(f332(f22(f883(x90321,a871)),x90322),f332(f332(f310(x90321),x90323),f195(f883(x90321,a871)))))),f259(x90321,x90323,x90322))+P102(f332(f332(f246(f883(x90321,a871)),x90322),f332(f332(f310(x90321),x90323),f195(f883(x90321,a871))))) % 172.78/172.48 [9379]E(f332(f332(f154(f877(x93791),x93791),f332(f332(f7(f877(x93791),a876,x93791),f165(x93791)),x93792)),f332(f136(f877(x93791),f332(f332(f8(a876,a871,f877(x93791)),f332(f247(a876),x93792)),f196(f877(x93791)))),x93793)),f332(f332(f165(f877(x93791)),f181(x93791,x93793)),x93792))+~P102(f332(f332(f247(a876),x93792),f332(f196(f877(f877(x93791))),f181(x93791,x93793)))) % 172.78/172.48 [9452]E(f332(f136(x94521,x94522),x94523),f178(x94521,x94522,x94523))+P102(f332(f332(f334(x94521),f758(x94523,x94522,x94521)),f332(f173(x94521),f332(f332(f138(x94521),f332(f196(f877(x94521)),f178(x94521,x94522,x94523))),x94523)))) % 172.78/172.48 [9592]E(f332(f332(f138(x95921),f332(f196(f877(x95921)),f178(x95921,x95922,x95923))),x95923),f116(x95921))+~P102(f332(x95922,f332(f141(x95921),f332(f332(f138(x95921),f332(f196(f877(x95921)),f178(x95921,x95922,x95923))),x95923)))) % 172.78/172.48 [9685]~P102(f332(f332(f334(f882(x96851,x96851)),x96852),f308(x96851,x96853)))+P102(f332(f332(f334(f882(x96851,x96851)),x96852),f332(f332(f41(a876,f883(f882(x96851,x96851),a871)),f255(f883(a876,a871))),f332(f332(f7(a876,f883(f882(x96851,x96851),a871),f883(f882(x96851,x96851),a871)),f190(f882(x96851,x96851),a871)),x96853)))) % 172.78/172.48 [9741]~P102(f332(f332(f246(f883(x97411,a871)),f332(f332(f41(a876,f883(x97411,a871)),f332(f302(a876,f2(a876)),f453(x97413,x97412,x97411))),x97412)),x97413))+P102(f332(f332(f246(f883(x97411,a871)),f332(f332(f41(a876,f883(x97411,a871)),f255(f883(a876,a871))),x97412)),x97413)) % 172.78/172.48 [9799]~P102(f332(f332(f247(a1),f2(a1)),x97993))+P102(f332(f332(f247(a1),x97991),f332(f332(f79(a1),x97992),f332(f332(f80(a1),f332(f332(f79(a1),f332(f74(a1),f332(f332(f22(a1),x97992),x97991))),f77(a1))),x97993)))) % 172.78/172.48 [9810]~P38(x98101,f332(f332(f113(f883(f882(x98101,x98101),a871)),x98102),x98103))+P38(x98101,f332(f332(f113(f883(f882(x98101,x98101),a871)),f332(f332(f113(f883(f882(x98101,x98101),a871)),f332(f332(f289(x98101,x98101,x98101),x98102),x98102)),f332(f332(f289(x98101,x98101,x98101),x98103),x98102))),x98103)) % 172.78/172.48 [9892]P38(x98921,f332(f332(f113(f883(f882(x98921,x98921),a871)),x98922),x98923))+~P38(x98921,f332(f332(f113(f883(f882(x98921,x98921),a871)),f332(f332(f113(f883(f882(x98921,x98921),a871)),f332(f332(f289(x98921,x98921,x98921),x98922),x98922)),f332(f332(f289(x98921,x98921,x98921),x98923),x98922))),x98923)) % 172.78/172.48 [9456]~P137(x94561)+E(f332(f105(x94561),f332(a88,f332(f286(f882(a876,a876),f882(a876,a876),a111),f332(f332(f310(f882(a876,a876)),f332(f332(f267(a876,a876),x94562),x94563)),f195(f883(f882(a876,a876),a871)))))),f332(f332(f22(x94561),f332(f103(x94561),x94562)),f332(f103(x94561),x94563))) % 172.78/172.48 [9539]P102(f332(x95393,x95392))+E(f332(f252(x95391),f332(f332(f18(x95391,a871,a871),f332(f332(f8(a871,f883(a871,a871),x95391),a330),f332(f332(f7(x95391,x95391,a871),a329),x95392))),x95393)),f195(f883(x95391,a871))) % 172.78/172.48 [9541]~P102(f332(x95413,x95412))+E(f332(f252(x95411),f332(f332(f18(x95411,a871,a871),f332(f332(f8(a871,f883(a871,a871),x95411),a330),f332(f332(f7(x95411,x95411,a871),a329),x95412))),x95413)),f332(f332(f310(x95411),x95412),f195(f883(x95411,a871)))) % 172.78/172.48 [9777]E(x97771,x97772)+P102(f332(f332(f256(x97773,x97773,f332(f332(f8(f883(x97773,a871),f883(x97773,a871),x97773),f332(f8(a871,a871,x97773),a327)),a329)),x97771),x97772)) % 172.78/172.48 [9870]~E(x98701,x98702)+~P102(f332(f332(f256(x98703,x98703,f332(f332(f8(f883(x98703,a871),f883(x98703,a871),x98703),f332(f8(a871,a871,x98703),a327)),a329)),x98701),x98702)) % 172.78/172.48 [9884]~P102(f332(f61(x98841),x98843))+E(f332(f332(f64(x98841,f883(x98841,a871),f332(f332(f8(f883(x98841,a871),f883(f883(x98841,a871),f883(x98841,a871)),x98841),f332(f7(f883(x98841,a871),f883(x98841,a871),f883(x98841,a871)),f22(f883(x98841,a871)))),f332(f332(f7(x98841,f883(x98841,a871),f883(x98841,a871)),f310(x98841)),f195(f883(x98841,a871))))),x98842),x98843),f332(f332(f22(f883(x98841,a871)),x98842),x98843)) % 172.78/172.48 [9916]~P102(f332(f332(f247(a1),f2(a1)),x99163))+P102(f332(f332(f247(a1),f332(f332(f22(a1),x99161),f332(f332(f80(a1),f332(f332(f79(a1),f332(f74(a1),f332(f332(f22(a1),x99161),x99162))),f77(a1))),x99163))),x99162)) % 172.78/172.48 [10139]~P102(f332(f332(f334(x101391),x101393),f321(x101391,x101392)))+P102(f332(f320(x101391,f332(f332(f7(x101391,f883(f882(x101391,x101391),a871),f883(x101391,a871)),f332(f332(f8(f883(x101391,f883(f883(f882(x101391,x101391),a871),a871)),f883(f883(f882(x101391,x101391),a871),f883(x101391,a871)),x101391),f7(x101391,f883(f882(x101391,x101391),a871),a871)),f332(f332(f8(f883(x101391,f882(x101391,x101391)),f883(x101391,f883(f883(f882(x101391,x101391),a871),a871)),x101391),f332(f8(f882(x101391,x101391),f883(f883(f882(x101391,x101391),a871),a871),x101391),f334(f882(x101391,x101391)))),f267(x101391,x101391)))),x101392)),x101393)) % 172.78/172.48 [10151]P102(f332(f332(f334(x101511),x101512),f321(x101511,x101513)))+~P102(f332(f320(x101511,f332(f332(f7(x101511,f883(f882(x101511,x101511),a871),f883(x101511,a871)),f332(f332(f8(f883(x101511,f883(f883(f882(x101511,x101511),a871),a871)),f883(f883(f882(x101511,x101511),a871),f883(x101511,a871)),x101511),f7(x101511,f883(f882(x101511,x101511),a871),a871)),f332(f332(f8(f883(x101511,f882(x101511,x101511)),f883(x101511,f883(f883(f882(x101511,x101511),a871),a871)),x101511),f332(f8(f882(x101511,x101511),f883(f883(f882(x101511,x101511),a871),a871),x101511),f334(f882(x101511,x101511)))),f267(x101511,x101511)))),x101513)),x101512)) % 172.78/172.48 [9739]~P102(f332(f61(x97391),f332(f252(x97391),x97393)))+P102(f332(f61(x97391),f332(f252(x97391),f332(f332(f18(x97391,a871,a871),f332(f332(f8(a871,f883(a871,a871),x97391),a330),x97392)),x97393)))) % 172.78/172.48 [9740]~P102(f332(f61(x97401),f332(f252(x97401),x97402)))+P102(f332(f61(x97401),f332(f252(x97401),f332(f332(f18(x97401,a871,a871),f332(f332(f8(a871,f883(a871,a871),x97401),a330),x97402)),x97403)))) % 172.78/172.48 [9842]P102(f332(f61(x98421),f332(f252(x98421),x98422)))+~P102(f332(f61(x98421),f332(f252(x98421),f332(f332(f18(x98421,a871,a871),f332(f332(f8(a871,f883(a871,a871),x98421),a331),x98423)),x98422)))) % 172.78/172.48 [9843]P102(f332(f61(x98431),f332(f252(x98431),x98432)))+~P102(f332(f61(x98431),f332(f252(x98431),f332(f332(f18(x98431,a871,a871),f332(f332(f8(a871,f883(a871,a871),x98431),a331),x98432)),x98433)))) % 172.78/172.48 [10126]~P102(f332(f61(x101261),x101262))+P102(f332(f61(f877(x101261)),f332(f252(f877(x101261)),f332(f332(f18(f877(x101261),a871,a871),f332(f332(f8(a871,f883(a871,a871),f877(x101261)),a330),f332(f332(f7(f877(x101261),f883(x101261,a871),a871),f332(f332(f8(f883(x101261,a871),f883(f883(x101261,a871),a871),f877(x101261)),f246(f883(x101261,a871))),f173(x101261))),x101262))),f332(f332(f7(f877(x101261),a876,a871),f332(f332(f8(a876,f883(a876,a871),f877(x101261)),a329),f196(f877(x101261)))),x101263))))) % 172.78/172.48 [10127]~P102(f332(f61(x101271),x101272))+P102(f332(f61(f877(x101271)),f332(f252(f877(x101271)),f332(f332(f18(f877(x101271),a871,a871),f332(f332(f8(a871,f883(a871,a871),f877(x101271)),a330),f332(f332(f7(f877(x101271),f883(x101271,a871),a871),f332(f332(f8(f883(x101271,a871),f883(f883(x101271,a871),a871),f877(x101271)),f246(f883(x101271,a871))),f173(x101271))),x101272))),f332(f332(f7(f877(x101271),a876,a871),f332(f332(f8(a876,f883(a876,a871),f877(x101271)),f246(a876)),f196(f877(x101271)))),x101273))))) % 172.78/172.48 [9857]~P114(x98571)+E(f332(f332(f257(x98571),x98572),f332(f332(f80(a876),f332(f106(a876),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)))),x98573)),f332(f332(f80(x98571),f332(f332(f257(x98571),x98572),x98573)),f332(f332(f257(x98571),x98572),x98573))) % 172.78/172.48 [9897]~P75(x98971)+E(f332(f332(f257(x98971),f332(f332(f257(x98971),x98972),x98973)),f332(f106(a876),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)))),f332(f332(f257(x98971),x98972),f332(f332(f80(a876),f332(f106(a876),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)))),x98973))) % 172.78/172.48 [9943]~P137(x99431)+E(f332(f332(f257(x99431),f332(f78(x99431),x99432)),f332(f332(f80(a876),f332(f106(a876),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)))),x99433)),f332(f332(f257(x99431),x99432),f332(f332(f80(a876),f332(f106(a876),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)))),x99433))) % 172.78/172.48 [10084]~P113(x100841)+P102(f332(f332(f246(x100841),f2(x100841)),f332(f332(f79(x100841),f332(f332(f257(x100841),x100842),f332(f106(a876),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100))))),f332(f332(f257(x100841),x100843),f332(f106(a876),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100))))))) % 172.78/172.48 [9953]~P114(x99531)+E(f332(f332(f257(x99531),x99532),f332(a115,f332(f332(f80(a876),f332(f106(a876),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)))),x99533))),f332(f332(f80(x99531),x99532),f332(f332(f80(x99531),f332(f332(f257(x99531),x99532),x99533)),f332(f332(f257(x99531),x99532),x99533)))) % 172.78/172.48 [10002]~P75(x100021)+E(f332(f332(f80(x100021),x100022),f332(f332(f257(x100021),f332(f332(f257(x100021),x100022),x100023)),f332(f106(a876),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100))))),f332(f332(f257(x100021),x100022),f332(a115,f332(f332(f80(a876),f332(f106(a876),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)))),x100023)))) % 172.78/172.48 [10041]~P113(x100411)+P102(f332(f332(f246(x100411),f2(x100411)),f332(f332(f257(x100411),x100412),f332(f332(f80(a876),f332(f106(a876),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)))),x100413)))) % 172.78/172.48 [10107]~P89(x101071)+E(f332(f332(f22(x101071),f332(f332(f79(x101071),f332(f332(f257(x101071),x101072),f332(f106(a876),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100))))),f332(f332(f257(x101071),x101073),f332(f106(a876),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)))))),f332(f332(f80(x101071),f332(f332(f80(x101071),f332(f106(x101071),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)))),x101072)),x101073)),f332(f332(f257(x101071),f332(f332(f22(x101071),x101072),x101073)),f332(f106(a876),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100))))) % 172.78/172.48 [10108]~P89(x101081)+E(f332(f332(f79(x101081),f332(f332(f79(x101081),f332(f332(f257(x101081),x101082),f332(f106(a876),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100))))),f332(f332(f257(x101081),x101083),f332(f106(a876),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)))))),f332(f332(f80(x101081),f332(f332(f80(x101081),f332(f106(x101081),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)))),x101082)),x101083)),f332(f332(f257(x101081),f332(f332(f79(x101081),x101082),x101083)),f332(f106(a876),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100))))) % 172.78/172.48 [10206]~P30(x102061,x102062,x102063)+P102(f98(x102061,a871,f332(f332(f8(f883(a873,f883(f883(x102061,f883(a872,a871)),f883(x102061,a871))),f883(a873,f883(f883(x102061,f883(a872,a871)),a871)),f883(x102061,f883(a872,a871))),f332(f8(f883(f883(x102061,f883(a872,a871)),f883(x102061,a871)),f883(f883(x102061,f883(a872,a871)),a871),a873),f332(f8(f883(x102061,a871),a871,f883(x102061,f883(a872,a871))),f87(x102061)))),f332(f332(f8(f883(a873,f883(f883(x102061,f883(a872,a871)),f883(x102061,f883(a872,a871)))),f883(a873,f883(f883(x102061,f883(a872,a871)),f883(x102061,a871))),f883(x102061,f883(a872,a871))),f332(f8(f883(f883(x102061,f883(a872,a871)),f883(x102061,f883(a872,a871))),f883(f883(x102061,f883(a872,a871)),f883(x102061,a871)),a873),f332(f8(f883(x102061,f883(a872,a871)),f883(x102061,a871),f883(x102061,f883(a872,a871))),f332(f8(f883(a872,a871),a871,x102061),f87(a872))))),f332(f332(f7(f883(x102061,f883(a872,a871)),f883(a873,f883(f883(x102061,f883(a872,a871)),f883(x102061,f883(a872,a871)))),f883(a873,f883(f883(x102061,f883(a872,a871)),f883(x102061,f883(a872,a871))))),f332(f332(f8(f883(f883(f883(x102061,f883(a872,a871)),f883(x102061,f883(a872,a871))),f883(f883(x102061,f883(a872,a871)),f883(x102061,f883(a872,a871)))),f883(f883(a873,f883(f883(x102061,f883(a872,a871)),f883(x102061,f883(a872,a871)))),f883(a873,f883(f883(x102061,f883(a872,a871)),f883(x102061,f883(a872,a871))))),f883(x102061,f883(a872,a871))),f8(f883(f883(x102061,f883(a872,a871)),f883(x102061,f883(a872,a871))),f883(f883(x102061,f883(a872,a871)),f883(x102061,f883(a872,a871))),a873)),f332(f332(f8(f883(f883(x102061,f883(a872,a871)),f883(x102061,f883(a872,a871))),f883(f883(f883(x102061,f883(a872,a871)),f883(x102061,f883(a872,a871))),f883(f883(x102061,f883(a872,a871)),f883(x102061,f883(a872,a871)))),f883(x102061,f883(a872,a871))),f8(f883(x102061,f883(a872,a871)),f883(x102061,f883(a872,a871)),f883(x102061,f883(a872,a871)))),f332(f332(f8(f883(x102061,f883(f883(a872,a871),f883(a872,a871))),f883(f883(x102061,f883(a872,a871)),f883(x102061,f883(a872,a871))),f883(x102061,f883(a872,a871))),f18(x102061,f883(a872,a871),f883(a872,a871))),f332(f332(f8(f883(x102061,f883(a872,f883(a871,a871))),f883(x102061,f883(f883(a872,a871),f883(a872,a871))),f883(x102061,f883(a872,a871))),f332(f8(f883(a872,f883(a871,a871)),f883(f883(a872,a871),f883(a872,a871)),x102061),f18(a872,a871,a871))),f332(f8(f883(a872,a871),f883(a872,f883(a871,a871)),x102061),f332(f8(a871,f883(a871,a871),a872),a335))))))),f332(f332(f8(f883(f883(x102061,f883(a872,a871)),f883(x102061,f883(a872,f883(a872,a871)))),f883(f883(x102061,f883(a872,a871)),f883(x102061,f883(a872,a871))),a873),f332(f8(f883(x102061,f883(a872,f883(a872,a871))),f883(x102061,f883(a872,a871)),f883(x102061,f883(a872,a871))),f332(f8(f883(a872,f883(a872,a871)),f883(a872,a871),x102061),f332(f8(f883(a872,a871),a871,a872),f87(a872))))),f332(f332(f8(f883(f883(a872,a871),f883(a872,f883(a872,a871))),f883(f883(x102061,f883(a872,a871)),f883(x102061,f883(a872,f883(a872,a871)))),a873),f8(f883(a872,a871),f883(a872,f883(a872,a871)),x102061)),f332(f332(f8(f883(a872,f883(f883(a872,a871),f883(a872,a871))),f883(f883(a872,a871),f883(a872,f883(a872,a871))),a873),f7(a872,f883(a872,a871),f883(a872,a871))),f332(f332(f8(f883(a872,f883(a872,f883(a871,a871))),f883(a872,f883(f883(a872,a871),f883(a872,a871))),a873),f332(f8(f883(a872,f883(a871,a871)),f883(f883(a872,a871),f883(a872,a871)),a872),f18(a872,a871,a871))),f332(f332(f8(f883(a872,f883(a872,a871)),f883(a872,f883(a872,f883(a871,a871))),a873),f332(f8(f883(a872,a871),f883(a872,f883(a871,a871)),a872),f332(f8(a871,f883(a871,a871),a872),a335))),f332(f332(f7(a873,a876,f883(a872,f883(a872,a871))),f332(f332(f8(f883(a872,f883(a876,f883(a872,a871))),f883(a876,f883(a872,f883(a872,a871))),a873),f7(a872,a876,f883(a872,a871))),a203)),x102062))))))))),x102063)) % 172.78/172.48 [10208]P30(x102081,x102082,x102083)+~P102(f98(x102081,a871,f332(f332(f8(f883(a873,f883(f883(x102081,f883(a872,a871)),f883(x102081,a871))),f883(a873,f883(f883(x102081,f883(a872,a871)),a871)),f883(x102081,f883(a872,a871))),f332(f8(f883(f883(x102081,f883(a872,a871)),f883(x102081,a871)),f883(f883(x102081,f883(a872,a871)),a871),a873),f332(f8(f883(x102081,a871),a871,f883(x102081,f883(a872,a871))),f87(x102081)))),f332(f332(f8(f883(a873,f883(f883(x102081,f883(a872,a871)),f883(x102081,f883(a872,a871)))),f883(a873,f883(f883(x102081,f883(a872,a871)),f883(x102081,a871))),f883(x102081,f883(a872,a871))),f332(f8(f883(f883(x102081,f883(a872,a871)),f883(x102081,f883(a872,a871))),f883(f883(x102081,f883(a872,a871)),f883(x102081,a871)),a873),f332(f8(f883(x102081,f883(a872,a871)),f883(x102081,a871),f883(x102081,f883(a872,a871))),f332(f8(f883(a872,a871),a871,x102081),f87(a872))))),f332(f332(f7(f883(x102081,f883(a872,a871)),f883(a873,f883(f883(x102081,f883(a872,a871)),f883(x102081,f883(a872,a871)))),f883(a873,f883(f883(x102081,f883(a872,a871)),f883(x102081,f883(a872,a871))))),f332(f332(f8(f883(f883(f883(x102081,f883(a872,a871)),f883(x102081,f883(a872,a871))),f883(f883(x102081,f883(a872,a871)),f883(x102081,f883(a872,a871)))),f883(f883(a873,f883(f883(x102081,f883(a872,a871)),f883(x102081,f883(a872,a871)))),f883(a873,f883(f883(x102081,f883(a872,a871)),f883(x102081,f883(a872,a871))))),f883(x102081,f883(a872,a871))),f8(f883(f883(x102081,f883(a872,a871)),f883(x102081,f883(a872,a871))),f883(f883(x102081,f883(a872,a871)),f883(x102081,f883(a872,a871))),a873)),f332(f332(f8(f883(f883(x102081,f883(a872,a871)),f883(x102081,f883(a872,a871))),f883(f883(f883(x102081,f883(a872,a871)),f883(x102081,f883(a872,a871))),f883(f883(x102081,f883(a872,a871)),f883(x102081,f883(a872,a871)))),f883(x102081,f883(a872,a871))),f8(f883(x102081,f883(a872,a871)),f883(x102081,f883(a872,a871)),f883(x102081,f883(a872,a871)))),f332(f332(f8(f883(x102081,f883(f883(a872,a871),f883(a872,a871))),f883(f883(x102081,f883(a872,a871)),f883(x102081,f883(a872,a871))),f883(x102081,f883(a872,a871))),f18(x102081,f883(a872,a871),f883(a872,a871))),f332(f332(f8(f883(x102081,f883(a872,f883(a871,a871))),f883(x102081,f883(f883(a872,a871),f883(a872,a871))),f883(x102081,f883(a872,a871))),f332(f8(f883(a872,f883(a871,a871)),f883(f883(a872,a871),f883(a872,a871)),x102081),f18(a872,a871,a871))),f332(f8(f883(a872,a871),f883(a872,f883(a871,a871)),x102081),f332(f8(a871,f883(a871,a871),a872),a335))))))),f332(f332(f8(f883(f883(x102081,f883(a872,a871)),f883(x102081,f883(a872,f883(a872,a871)))),f883(f883(x102081,f883(a872,a871)),f883(x102081,f883(a872,a871))),a873),f332(f8(f883(x102081,f883(a872,f883(a872,a871))),f883(x102081,f883(a872,a871)),f883(x102081,f883(a872,a871))),f332(f8(f883(a872,f883(a872,a871)),f883(a872,a871),x102081),f332(f8(f883(a872,a871),a871,a872),f87(a872))))),f332(f332(f8(f883(f883(a872,a871),f883(a872,f883(a872,a871))),f883(f883(x102081,f883(a872,a871)),f883(x102081,f883(a872,f883(a872,a871)))),a873),f8(f883(a872,a871),f883(a872,f883(a872,a871)),x102081)),f332(f332(f8(f883(a872,f883(f883(a872,a871),f883(a872,a871))),f883(f883(a872,a871),f883(a872,f883(a872,a871))),a873),f7(a872,f883(a872,a871),f883(a872,a871))),f332(f332(f8(f883(a872,f883(a872,f883(a871,a871))),f883(a872,f883(f883(a872,a871),f883(a872,a871))),a873),f332(f8(f883(a872,f883(a871,a871)),f883(f883(a872,a871),f883(a872,a871)),a872),f18(a872,a871,a871))),f332(f332(f8(f883(a872,f883(a872,a871)),f883(a872,f883(a872,f883(a871,a871))),a873),f332(f8(f883(a872,a871),f883(a872,f883(a871,a871)),a872),f332(f8(a871,f883(a871,a871),a872),a335))),f332(f332(f7(a873,a876,f883(a872,f883(a872,a871))),f332(f332(f8(f883(a872,f883(a876,f883(a872,a871))),f883(a876,f883(a872,f883(a872,a871))),a873),f7(a872,a876,f883(a872,a871))),a203)),x102082))))))))),x102083)) % 172.78/172.48 [4685]E(x46851,x46852)+~E(f32(x46853,x46851),f32(x46854,x46852)) % 172.78/172.48 [4686]E(x46861,x46862)+~E(f32(x46861,x46863),f32(x46862,x46864)) % 172.78/172.48 [4687]E(x46871,x46872)+~E(f31(x46873,x46871),f31(x46874,x46872)) % 172.78/172.48 [4688]E(x46881,x46882)+~E(f31(x46881,x46883),f31(x46882,x46884)) % 172.78/172.48 [7761]P20(x77611,x77612,x77613,x77614)+~E(f515(x77614,x77613,x77612,x77611),f517(x77614,x77613,x77612,x77611)) % 172.78/172.48 [8060]P35(x80601,x80602,x80603,x80604,f116(x80602))+~E(x80604,f116(x80601)) % 172.78/172.48 [8061]P35(x80611,x80612,x80613,f116(x80611),x80614)+~E(x80614,f116(x80612)) % 172.78/172.48 [8276]~P20(x82761,f880(x82762),x82764,f185(x82761,x82762,x82764))+P20(x82761,f880(x82762),f186(x82761,x82762,x82763,x82764),f185(x82761,x82762,x82764)) % 172.78/172.48 [8491]~P20(x84911,f880(x84912),f186(x84911,x84912,x84914,x84913),f185(x84911,x84912,x84913))+P20(x84911,f880(x84912),x84913,f185(x84911,x84912,x84913)) % 172.78/172.48 [8606]~P35(x86062,x86063,x86064,x86061,f116(x86063))+E(x86061,f116(x86062)) % 172.78/172.48 [8607]~P35(x86073,x86072,x86074,f116(x86073),x86071)+E(x86071,f116(x86072)) % 172.78/172.48 [5061]~P12(x50613,x50611,x50614)+E(f332(f332(x50611,x50612),x50612),x50612) % 172.78/172.48 [5309]P102(f332(x53092,x53094))+E(f332(f136(x53091,x53092),f170(x53091,x53093,x53094)),f116(x53091)) % 172.78/172.48 [5346]~E(x53464,f195(f883(x53461,a871)))+E(f332(f311(x53461,x53462,x53463),x53464),f195(f883(x53462,a871))) % 172.78/172.48 [5588]~P102(f332(x55882,x55884))+E(f332(f136(x55881,x55882),f170(x55881,x55883,x55884)),f170(x55881,x55883,x55884)) % 172.78/172.48 [5617]~E(f332(f311(x56172,x56173,x56174),x56171),f195(f883(x56173,a871)))+E(x56171,f195(f883(x56172,a871))) % 172.78/172.48 [5899]~P104(x58992)+E(f332(f332(f148(x58991,x58992,x58993),x58994),f116(x58991)),f332(f332(f151(x58991),x58994),f116(x58991))) % 172.78/172.48 [5935]E(f332(x59351,x59352),f208(x59353))+P102(f332(f332(f334(x59354),x59352),f185(x59354,x59353,x59351))) % 172.78/172.48 [6253]~E(x62531,f195(f883(x62532,a871)))+~P102(f332(f62(x62532,x62533,x62531),x62534)) % 172.78/172.48 [6275]~P54(x62751,x62753,x62754,x62752)+P102(f332(f61(x62751),x62752)) % 172.78/172.48 [6276]~P54(x62761,x62763,x62762,x62764)+P102(f332(f61(x62761),x62762)) % 172.78/172.48 [6282]~P54(x62822,x62823,x62824,x62821)+~E(x62821,f195(f883(x62822,a871))) % 172.78/172.48 [6313]~P105(x63131)+E(f332(f332(f104(f883(x63131,a871)),f332(f302(x63131,x63132),x63133)),f303(x63131,x63133,x63134)),f195(f883(x63131,a871))) % 172.78/172.48 [6340]~P102(f332(f332(x63403,x63404),x63402))+P102(f332(f332(f334(x63401),x63402),f293(x63401,x63403,x63404))) % 172.78/172.48 [6341]~P102(f332(f332(x63413,x63414),x63412))+P102(f332(f332(f334(x63411),x63412),f294(x63411,x63413,x63414))) % 172.78/172.48 [6342]~P102(f332(f332(x63423,x63422),x63424))+P102(f332(f332(f334(x63421),x63422),f295(x63421,x63423,x63424))) % 172.78/172.48 [6343]~P102(f332(f332(x63433,x63432),x63434))+P102(f332(f332(f334(x63431),x63432),f298(x63431,x63433,x63434))) % 172.78/172.48 [6481]~P105(x64811)+E(f332(f332(f104(f883(x64811,a871)),f303(x64811,x64812,x64813)),f306(x64811,x64813,x64814)),f195(f883(x64811,a871))) % 172.78/172.48 [6482]~P105(x64821)+E(f332(f332(f104(f883(x64821,a871)),f303(x64821,x64822,x64823)),f305(x64821,x64823,x64824)),f195(f883(x64821,a871))) % 172.78/172.48 [6483]~P105(x64831)+E(f332(f332(f104(f883(x64831,a871)),f306(x64831,x64832,x64833)),f303(x64831,x64833,x64834)),f195(f883(x64831,a871))) % 172.78/172.48 [6484]~P105(x64841)+E(f332(f332(f104(f883(x64841,a871)),f305(x64841,x64842,x64843)),f306(x64841,x64843,x64844)),f195(f883(x64841,a871))) % 172.78/172.48 [6485]~P105(x64851)+E(f332(f332(f104(f883(x64851,a871)),f305(x64851,x64852,x64853)),f305(x64851,x64853,x64854)),f195(f883(x64851,a871))) % 172.78/172.48 [6522]P102(f332(f332(x65221,x65222),f536(x65222,x65221)))+~P102(f332(f261(x65223,x65224,x65221),x65222)) % 172.78/172.48 [6571]~E(f332(x65711,x65712),f208(x65713))+~P102(f332(f332(f334(x65714),x65712),f185(x65714,x65713,x65711))) % 172.78/172.48 [6600]~P104(x66002)+E(f332(f173(x66001),f150(x66001,x66002,x66003,x66004)),f332(f173(x66001),x66004)) % 172.78/172.48 [6652]~P141(x66521)+E(f197(x66521,x66522,f332(a115,x66523),x66524),f197(x66521,x66522,x66523,f332(x66522,x66524))) % 172.78/172.48 [6712]~P102(f332(f332(f334(x67124),x67123),f293(x67124,x67121,x67122)))+P102(f332(f332(x67121,x67122),x67123)) % 172.78/172.48 [6713]~P102(f332(f332(f334(x67134),x67133),f294(x67134,x67131,x67132)))+P102(f332(f332(x67131,x67132),x67133)) % 172.78/172.48 [6714]~P102(f332(f332(f334(x67144),x67142),f295(x67144,x67141,x67143)))+P102(f332(f332(x67141,x67142),x67143)) % 172.78/172.48 [6715]~P102(f332(f332(f334(x67154),x67152),f298(x67154,x67151,x67153)))+P102(f332(f332(x67151,x67152),x67153)) % 172.78/172.48 [6792]E(f332(f37(f881(x67921,x67922)),f319(x67921,x67922,x67923,x67924)),f2(a876))+P102(f332(f61(x67922),x67924)) % 172.78/172.48 [6793]E(f332(f37(f881(x67931,x67932)),f319(x67931,x67932,x67933,x67934)),f2(a876))+P102(f332(f61(x67931),x67933)) % 172.78/172.48 [6996]~P10(x69964,x69961,x69962)+E(f332(f72(x69961,x69961,x69961,f332(x69962,x69963)),f332(x69962,x69963)),f332(x69962,x69963)) % 172.78/172.48 [7800]~P102(f332(x78001,x78004))+P102(f332(x78001,f95(x78002,a876,x78003,x78001))) % 172.78/172.48 [7884]~E(x78842,x78843)+P102(f332(f332(f334(f882(x78841,x78841)),f332(f332(f267(x78841,x78841),x78842),x78843)),f308(x78841,x78844))) % 172.78/172.48 [7913]~P20(x79131,x79132,x79133,f255(f883(x79131,a871)))+E(f332(f76(x79131,x79132,f255(f883(x79131,a871)),x79133),f332(x79133,x79134)),x79134) % 172.78/172.48 [8006]~P102(f332(f332(f334(f877(x80061)),f332(f332(f151(x80061),x80064),x80062)),f161(x80061,x80063)))+P102(f332(f332(f334(f877(x80061)),x80062),f161(x80061,x80063))) % 172.78/172.48 [8007]~P102(f332(f332(f334(f877(x80071)),f332(f332(f134(x80071),x80074),x80072)),f161(x80071,x80073)))+P102(f332(f332(f334(f877(x80071)),x80072),f161(x80071,x80073))) % 172.78/172.48 [8008]~P102(f332(f332(f334(f877(x80081)),f332(f332(f134(x80081),x80082),x80084)),f161(x80081,x80083)))+P102(f332(f332(f334(f877(x80081)),x80082),f161(x80081,x80083))) % 172.78/172.48 [8024]~P104(x80241)+P29(x80241,f332(f332(f154(x80242,x80241),x80243),f150(x80242,x80241,x80243,x80244))) % 172.78/172.48 [8122]P20(x81224,x81223,x81221,x81222)+E(f332(x81221,f515(x81222,x81221,x81223,x81224)),f332(x81221,f517(x81222,x81221,x81223,x81224))) % 172.78/172.48 [8135]E(f186(x81351,x81352,x81353,x81354),f186(x81351,x81352,x81354,x81353))+~E(f332(f332(f104(f883(x81351,a871)),f185(x81351,x81352,x81353)),f185(x81351,x81352,x81354)),f195(f883(x81351,a871))) % 172.78/172.48 [8239]~P20(x82392,x82391,x82394,x82393)+P20(x82391,x82392,f76(x82392,x82391,x82393,x82394),f332(f311(x82392,x82391,x82394),x82393)) % 172.78/172.48 [8375]P38(f882(x83752,x83754),f284(x83752,x83754,x83751,x83753))+P102(f332(x83751,f529(x83752,x83753,x83754,x83751))) % 172.78/172.48 [8498]E(x84981,x84982)+~P102(f332(f332(f334(f882(x84983,x84983)),f332(f332(f267(x84983,x84983),x84981),x84982)),f264(x84983,x84984))) % 172.78/172.48 [8562]~P102(f332(f61(f881(x85623,x85621)),f319(x85623,x85621,x85624,x85622)))+P102(f332(f61(x85621),x85622)) % 172.78/172.48 [8563]~P102(f332(f61(f881(x85631,x85633)),f319(x85631,x85633,x85632,x85634)))+P102(f332(f61(x85631),x85632)) % 172.78/172.48 [8739]P38(f882(x87391,x87392),f284(x87391,x87392,x87393,x87394))+~P38(x87392,f332(x87394,f529(x87391,x87394,x87392,x87393))) % 172.78/172.48 [9301]E(f332(f332(f159(x93011,x93012),f689(x93013,x93014,x93012,x93011)),f690(x93013,x93014,x93012,x93011)),x93014)+~P102(f332(f332(f334(f882(f877(x93011),f877(x93011))),f332(f332(f267(f877(x93011),f877(x93011)),x93012),x93014)),f157(x93011,x93013))) % 172.78/172.48 [9302]~P102(f332(x93023,x93024))+P102(f332(f332(f246(a876),f332(x93021,f95(x93022,a876,x93021,x93023))),f332(x93021,x93024))) % 172.78/172.48 [9308]~P102(f332(f332(f334(f882(f877(x93081),f877(x93081))),f332(f332(f267(f877(x93081),f877(x93081)),x93082),x93083)),f145(x93081,x93084)))+P102(f332(f332(f334(f882(f877(x93081),f877(x93081))),f332(f332(f267(f877(x93081),f877(x93081)),x93082),x93083)),f147(x93081,x93084))) % 172.78/172.48 [9414]P102(f332(f61(x94141),x94142))+~P102(f332(f332(f334(f882(f883(x94141,a871),f883(x94141,a871))),f332(f332(f267(f883(x94141,a871),f883(x94141,a871)),x94143),x94142)),f324(x94141,x94144))) % 172.78/172.48 [9415]P102(f332(f61(x94151),x94152))+~P102(f332(f332(f334(f882(f883(x94151,a871),f883(x94151,a871))),f332(f332(f267(f883(x94151,a871),f883(x94151,a871)),x94152),x94153)),f324(x94151,x94154))) % 172.78/172.48 [9418]~E(x94181,f195(f883(x94182,a871)))+~P102(f332(f332(f334(f882(f883(x94182,a871),f883(x94182,a871))),f332(f332(f267(f883(x94182,a871),f883(x94182,a871)),x94183),x94181)),f324(x94182,x94184))) % 172.78/172.48 [10053]P8(x100531,x100532,x100533,x100534)+~P102(f332(f332(f271(x100531,x100531,a871),f332(f332(f7(x100531,f883(x100531,x100532),f883(x100531,a871)),f332(f332(f8(f883(x100532,a871),f883(f883(x100531,x100532),f883(x100531,a871)),x100531),f8(x100532,a871,x100531)),f332(f332(f8(x100532,f883(x100532,a871),x100531),a329),x100534))),x100534)),f563(x100534,x100533,x100532,x100531))) % 172.78/172.48 [4963]~E(x49632,f116(x49631))+E(f332(f332(f159(x49631,x49632),x49633),x49634),f116(x49631)) % 172.78/172.48 [4964]~E(x49644,f116(x49641))+E(f332(f332(f154(x49641,x49642),x49643),x49644),f116(x49642)) % 172.78/172.48 [4965]~E(x49654,f208(x49651))+E(f332(f332(f209(x49651,x49652),x49653),x49654),f208(x49652)) % 172.78/172.48 [5193]E(x51931,f116(x51932))+~E(f332(f332(f154(x51932,x51933),x51934),x51931),f116(x51933)) % 172.78/172.48 [5194]E(x51941,f208(x51942))+~E(f332(f332(f209(x51942,x51943),x51944),x51941),f208(x51943)) % 172.78/172.48 [5195]E(x51951,f116(x51952))+~E(f332(f332(f159(x51952,x51951),x51953),x51954),f116(x51952)) % 172.78/172.48 [5227]E(x52271,x52272)+~E(f332(f332(f134(x52273),x52274),x52271),f332(f332(f134(x52273),x52274),x52272)) % 172.78/172.48 [5228]E(x52281,x52282)+~E(f332(f332(f134(x52283),x52281),x52284),f332(f332(f134(x52283),x52282),x52284)) % 172.78/172.48 [5384]P102(f332(x53843,x53842))+E(f171(x53841,x53842,f332(f136(x53841,x53843),x53844)),f332(f136(x53841,x53843),x53844)) % 172.78/172.48 [5387]~P102(f332(x53872,x53873))+P34(x53871,x53872,f332(f332(f151(x53871),x53873),x53874)) % 172.78/172.48 [5396]E(x53961,x53962)+~E(f139(a876,f332(f302(a876,x53961),x53963)),f332(f332(f151(a876),x53962),x53964)) % 172.78/172.48 [5444]~P21(x54442,x54443)+P21(x54441,f332(f332(f73(x54442,x54441),x54443),x54444)) % 172.78/172.48 [5445]~P38(x54452,x54453)+P38(x54451,f332(f332(f288(x54452,x54451),x54453),x54454)) % 172.78/172.48 [5572]~P34(x55721,x55722,x55724)+P34(x55721,x55722,f332(f332(f151(x55721),x55723),x55724)) % 172.78/172.48 [5573]~P34(x55731,x55732,x55734)+P34(x55731,x55732,f332(f332(f134(x55731),x55733),x55734)) % 172.78/172.48 [5574]~P34(x55741,x55742,x55743)+P34(x55741,x55742,f332(f332(f134(x55741),x55743),x55744)) % 172.78/172.48 [5660]~E(x56601,f116(x56602))+~E(f332(f332(f134(x56602),x56603),f332(f332(f151(x56602),x56604),f116(x56602))),x56601) % 172.78/172.48 [5685]~P32(x56853,x56851,f332(f332(f151(x56853),x56852),x56854))+P102(f332(x56851,x56852)) % 172.78/172.48 [5695]E(f117(x56951,x56952),x56953)+~E(f332(f332(f134(x56951),x56953),f332(f332(f151(x56951),x56954),f116(x56951))),x56952) % 172.78/172.48 [5696]E(f144(x56961,x56962),x56963)+~E(f332(f332(f134(x56961),x56964),f332(f332(f151(x56961),x56963),f116(x56961))),x56962) % 172.78/172.48 [5804]~E(f139(a876,f332(f302(a876,x58041),x58042)),f332(f332(f151(a876),x58043),x58044))+P102(f332(f332(f247(a876),x58041),x58042)) % 172.78/172.48 [5812]P32(x58121,x58122,x58123)+~P32(x58121,x58122,f332(f332(f151(x58121),x58124),x58123)) % 172.78/172.48 [5813]P32(x58131,x58132,x58133)+~P32(x58131,x58132,f332(f332(f134(x58131),x58134),x58133)) % 172.78/172.48 [5814]P32(x58141,x58142,x58143)+~P32(x58141,x58142,f332(f332(f134(x58141),x58143),x58144)) % 172.78/172.48 [6002]E(x60021,f332(f332(f134(x60022),f332(f169(x60022),x60023)),f332(f332(f151(x60022),x60024),f116(x60022))))+~E(f332(f169(x60022),x60021),f332(f332(f151(x60022),x60024),x60023)) % 172.78/172.48 [6173]~P105(x61731)+E(f332(f332(f104(f883(x61731,a871)),f332(f302(x61731,x61732),x61733)),f332(f302(x61731,x61733),x61734)),f195(f883(x61731,a871))) % 172.78/172.48 [6184]E(f332(f332(f165(x61841),f170(x61841,x61842,x61843)),x61844),x61843)+~P102(f332(f332(f247(a876),x61844),x61842)) % 172.78/172.48 [6211]~P71(x62111)+E(f332(f166(x62111),f332(f332(f154(a1,x62111),x62112),f180(x62113,x62114))),f332(f332(f6(a1,x62111),x62112),f332(f173(a1),f180(x62113,x62114)))) % 172.78/172.48 [6212]~P71(x62121)+E(f332(f332(f6(a1,x62121),x62122),f332(f173(a1),f180(x62123,x62124))),f332(f166(x62121),f332(f332(f154(a1,x62121),x62122),f180(x62123,x62124)))) % 172.78/172.48 [6353]~E(x63532,f332(f332(f134(x63531),f332(f169(x63531),x63534)),f332(f332(f151(x63531),x63533),f116(x63531))))+E(f332(f169(x63531),x63532),f332(f332(f151(x63531),x63533),x63534)) % 172.78/172.48 [6369]~P14(x63692,x63693,x63694,x63691)+E(f332(x63691,f195(f883(x63692,a871))),f33(x63693)) % 172.78/172.48 [6395]~P105(x63951)+E(f332(f332(f104(f883(x63951,a871)),f306(x63951,x63952,x63953)),f332(f302(x63951,x63953),x63954)),f195(f883(x63951,a871))) % 172.78/172.48 [6601]E(x66011,f195(f883(x66012,a871)))+~E(f319(x66013,x66012,x66014,x66011),f195(f883(f881(x66013,x66012),a871))) % 172.78/172.48 [6602]E(x66021,f195(f883(x66022,a871)))+~E(f319(x66022,x66023,x66021,x66024),f195(f883(f881(x66022,x66023),a871))) % 172.78/172.48 [6671]~P104(x66712)+E(f332(f196(f877(x66711)),f150(x66711,x66712,x66713,x66714)),f332(f196(f877(x66711)),x66714)) % 172.78/172.48 [6683]~P102(f332(f262(x66833,x66834,x66831),x66832))+P102(f332(f332(x66831,f537(x66832,x66831)),x66832)) % 172.78/172.48 [6723]~P102(f332(f61(x67232),x67234))+P102(f332(f61(x67231),f332(f311(x67232,x67231,x67233),x67234))) % 172.78/172.48 [6956]~P20(x69562,x69561,x69563,x69564)+E(f332(f37(x69561),f332(f311(x69562,x69561,x69563),x69564)),f332(f37(x69562),x69564)) % 172.78/172.48 [6975]E(f332(f311(x69751,x69752,x69753),f332(f312(x69751,x69752,x69753),x69754)),x69754)+~E(f332(f311(x69751,x69752,x69753),f255(f883(x69751,a871))),f255(f883(x69752,a871))) % 172.78/172.48 [7385]~P20(x73851,x73852,x73853,f255(f883(x73851,a871)))+E(f332(f312(x73851,x73852,x73853),f332(f311(x73851,x73852,x73853),x73854)),x73854) % 172.78/172.48 [7673]E(x76731,x76732)+~P102(f332(f332(f334(x76733),x76731),f332(f173(x76733),f170(x76733,x76734,x76732)))) % 172.78/172.48 [7683]~E(x76831,f2(a876))+~P102(f332(f332(f334(x76832),x76833),f332(f173(x76832),f170(x76832,x76831,x76834)))) % 172.78/172.48 [7720]P102(f332(x77201,x77202))+~P102(f332(f332(f334(x77203),x77202),f332(f173(x77203),f178(x77203,x77201,x77204)))) % 172.78/172.48 [7831]~P102(f332(f332(f334(f877(x78311)),f332(f332(f151(x78311),x78312),x78314)),f161(x78311,x78313)))+P102(f332(f332(f334(x78311),x78312),x78313)) % 172.78/172.48 [7960]~P102(f332(f332(f334(x79601),x79602),f332(f173(x79601),f177(x79601,x79603,x79604))))+P102(f332(f332(f334(x79601),x79602),f332(f173(x79601),x79603))) % 172.78/172.48 [7961]~P102(f332(f332(f334(x79611),x79612),f332(f173(x79611),f171(x79611,x79614,x79613))))+P102(f332(f332(f334(x79611),x79612),f332(f173(x79611),x79613))) % 172.78/172.48 [7962]~P102(f332(f332(f334(x79621),x79622),f332(f173(x79621),f178(x79621,x79624,x79623))))+P102(f332(f332(f334(x79621),x79622),f332(f173(x79621),x79623))) % 172.78/172.48 [7972]E(f332(f196(f877(x79721)),x79722),x79723)+~P102(f332(f332(f334(f877(x79721)),x79722),f332(f173(f877(x79721)),f54(x79721,x79723,x79724)))) % 172.78/172.48 [8072]P102(f332(x80723,x80722))+E(f332(f136(x80721,f332(f332(f8(a871,a871,x80721),a327),f332(a329,x80722))),f332(f136(x80721,x80723),x80724)),f332(f136(x80721,x80723),x80724)) % 172.78/172.48 [8188]E(f332(f332(f165(x81881),f178(x81881,x81882,x81883)),x81884),f332(f332(f165(x81881),x81883),x81884))+~P102(f332(f332(f247(a876),x81884),f332(f196(f877(x81881)),f178(x81881,x81882,x81883)))) % 172.78/172.48 [8274]~P71(x82741)+E(f332(f332(f6(a876,x82741),f332(f332(f8(a876,x82741,a876),x82742),a115)),f332(f302(a876,x82743),x82744)),f332(f332(f6(a876,x82741),x82742),f332(f302(a876,f332(a115,x82743)),f332(a115,x82744)))) % 172.78/172.48 [8283]~P71(x82831)+E(f332(f332(f6(a876,x82831),f332(f332(f8(a876,x82831,a876),x82832),a115)),f303(a876,x82833,x82834)),f332(f332(f6(a876,x82831),x82832),f303(a876,f332(a115,x82833),f332(a115,x82834)))) % 172.78/172.48 [8413]~P20(x84131,x84133,x84134,f255(f883(x84131,a871)))+P20(x84131,f883(x84132,x84133),f332(f332(f8(x84133,f883(x84132,x84133),x84131),f16(x84133,x84132)),x84134),f255(f883(x84131,a871))) % 172.78/172.48 [8506]~P20(x85062,x85061,x85064,x85063)+E(f332(f311(x85061,x85062,f76(x85062,x85061,x85063,x85064)),f332(f311(x85062,x85061,x85064),x85063)),x85063) % 172.78/172.48 [8564]~P102(f332(f332(f334(f882(x85641,x85641)),f332(f332(f267(x85641,x85641),x85642),x85644)),f264(x85641,x85643)))+P102(f332(f332(f334(x85641),x85642),x85643)) % 172.78/172.48 [8652]E(f332(f332(f332(f71(x86521,f880(x86522)),f332(f16(f880(x86522),x86521),f208(x86522))),x86523),f332(f239(x86522),f725(x86523,x86524,x86522,x86521))),x86524)+~E(f185(x86521,x86522,x86524),f332(f332(f310(x86521),x86523),f195(f883(x86521,a871)))) % 172.78/172.48 [8774]~E(f332(f332(f6(x87741,a876),x87744),x87743),f332(a115,x87742))+P102(f332(f332(f334(x87741),f356(x87742,x87743,x87744,x87741)),x87743)) % 172.78/172.48 [8794]~E(f332(f332(f6(x87944,a876),x87941),x87943),f332(a115,x87942))+P102(f332(f332(f247(a876),f2(a876)),f332(x87941,f356(x87942,x87943,x87941,x87944)))) % 172.78/172.48 [8805]~P102(f332(f61(x88052),x88054))+P102(f332(f332(f246(a876),f332(f37(x88051),f332(f311(x88052,x88051,x88053),x88054))),f332(f37(x88052),x88054))) % 172.78/172.48 [8806]E(f332(f332(f267(x88061,x88062),f661(x88063,x88064,x88062,x88061)),f662(x88063,x88064,x88062,x88061)),x88064)+~P102(f332(f332(f334(f882(x88061,x88062)),x88064),f332(f287(x88062,x88061),x88063))) % 172.78/172.48 [8815]P20(x88151,x88152,x88153,x88154)+P102(f332(f332(f334(x88151),f515(x88154,x88153,x88152,x88151)),x88154)) % 172.78/172.48 [8816]P20(x88161,x88162,x88163,x88164)+P102(f332(f332(f334(x88161),f517(x88164,x88163,x88162,x88161)),x88164)) % 172.78/172.48 [8877]P8(x88771,x88772,x88773,x88774)+P102(f332(f332(f334(f882(x88771,x88771)),f563(x88774,x88773,x88772,x88771)),x88773)) % 172.78/172.48 [8941]P102(f332(x89411,x89412))+~P102(f332(x89411,f332(f332(f267(x89413,x89414),f489(x89414,x89413,x89411)),f490(x89414,x89413,x89411)))) % 172.78/172.48 [8958]E(f332(f196(f877(x89581)),x89582),f332(f196(f877(x89581)),x89583))+~P102(f332(f332(f334(f882(f877(x89581),f877(x89581))),f332(f332(f267(f877(x89581),f877(x89581)),x89582),x89583)),f145(x89581,x89584))) % 172.78/172.48 [8959]E(f332(f196(f877(x89591)),x89592),f332(f196(f877(x89591)),x89593))+~P102(f332(f332(f334(f882(f877(x89591),f877(x89591))),f332(f332(f267(f877(x89591),f877(x89591)),x89592),x89593)),f157(x89591,x89594))) % 172.78/172.48 [8962]E(f332(f196(f877(x89621)),x89622),f332(f196(f877(x89621)),x89623))+~P102(f332(f332(f334(f882(f877(x89621),f877(x89621))),f332(f332(f267(f877(x89621),f877(x89621)),x89622),x89623)),f158(x89621,x89624))) % 172.78/172.48 [9036]P102(f332(f332(f246(a876),f155(x90361,x90362,x90363)),f155(x90361,x90364,x90363)))+P102(f332(f332(f334(x90361),f688(x90364,x90362,x90363,x90361)),f332(f173(x90361),x90363))) % 172.78/172.48 [9039]E(f332(f196(f877(x90391)),x90392),f332(f196(f877(x90391)),x90393))+~P102(f332(f332(f334(f882(f877(x90391),f877(x90391))),f332(f332(f267(f877(x90391),f877(x90391)),x90392),x90393)),f308(f877(x90391),f157(x90391,x90394)))) % 172.78/172.48 [9273]~P20(x92731,x92732,x92733,x92734)+~P102(f332(f332(f247(a876),f332(f37(x92732),f332(f311(x92731,x92732,x92733),x92734))),f332(f37(x92731),x92734))) % 172.78/172.48 [9319]~P102(f332(f332(f334(f882(f877(x93191),f877(x93191))),f332(f332(f267(f877(x93191),f877(x93191)),x93192),x93193)),f157(x93191,x93194)))+P102(f332(f332(f334(f882(f877(x93191),f877(x93191))),f332(f332(f267(f877(x93191),f877(x93191)),x93192),x93193)),f158(x93191,f308(x93191,x93194)))) % 172.78/172.48 [9323]~P102(f332(f332(f334(f882(f877(x93231),f877(x93231))),f332(f332(f267(f877(x93231),f877(x93231)),x93232),x93233)),f158(x93231,x93234)))+P102(f332(f332(f334(f882(f877(x93231),f877(x93231))),f332(f332(f267(f877(x93231),f877(x93231)),x93232),x93233)),f308(f877(x93231),f157(x93231,x93234)))) % 172.78/172.48 [9340]P102(f332(f332(f334(f882(x93401,x93401)),f332(f332(f267(x93401,x93401),x93402),x93403)),f308(x93401,x93404)))+~P102(f332(f332(f334(f882(x93401,x93401)),f332(f332(f267(x93401,x93401),x93402),x93403)),f332(f332(f289(x93401,x93401,x93401),x93404),f308(x93401,x93404)))) % 172.78/172.48 [9522]E(f332(f332(f134(x95221),f701(x95222,x95223,x95224,x95221)),f332(f332(f151(x95221),f702(x95222,x95223,x95224,x95221)),f705(x95222,x95223,x95224,x95221))),x95224)+~P102(f332(f332(f334(f882(f877(x95221),f877(x95221))),f332(f332(f267(f877(x95221),f877(x95221)),x95224),x95223)),f157(x95221,x95222))) % 172.78/172.48 [9523]E(f332(f332(f134(x95231),f701(x95232,x95233,x95234,x95231)),f332(f332(f151(x95231),f703(x95232,x95233,x95234,x95231)),f705(x95232,x95233,x95234,x95231))),x95233)+~P102(f332(f332(f334(f882(f877(x95231),f877(x95231))),f332(f332(f267(f877(x95231),f877(x95231)),x95234),x95233)),f157(x95231,x95232))) % 172.78/172.48 [9599]P102(f332(f332(f334(f882(x95991,x95991)),f332(f332(f267(x95991,x95991),x95992),f622(x95993,x95994,x95992,x95991))),f308(x95991,x95993)))+~P102(f332(f332(f334(f882(x95991,x95991)),f332(f332(f267(x95991,x95991),x95992),x95994)),f332(f332(f289(x95991,x95991,x95991),x95993),f308(x95991,x95993)))) % 172.78/172.48 [9668]P102(f332(f332(f246(a876),f155(x96681,x96682,x96683)),f155(x96681,x96684,x96683)))+~P102(f332(f332(f247(a876),f332(x96682,f688(x96684,x96682,x96683,x96681))),f332(x96684,f688(x96684,x96682,x96683,x96681)))) % 172.78/172.48 [9735]P102(f332(f332(f334(f882(x97351,x97351)),f332(f332(f267(x97351,x97351),f621(x97352,x97353,x97354,x97351)),x97353)),f308(x97351,x97352)))+~P102(f332(f332(f334(f882(x97351,x97351)),f332(f332(f267(x97351,x97351),x97354),x97353)),f332(f332(f289(x97351,x97351,x97351),x97352),f308(x97351,x97352)))) % 172.78/172.48 [5210]~E(x52102,x52103)+E(f171(x52101,x52102,f332(f332(f151(x52101),x52103),x52104)),x52104) % 172.78/172.48 [5338]P102(f332(x53382,x53383))+E(f178(x53381,x53382,f332(f332(f151(x53381),x53383),x53384)),f116(x53381)) % 172.78/172.48 [5408]~P85(x54082)+E(f332(f332(f78(f883(x54081,x54082)),x54083),x54084),f332(f78(x54082),f332(x54083,x54084))) % 172.78/172.48 [5420]~E(x54202,f2(a876))+E(f332(f332(f138(x54201),x54202),f332(f332(f151(x54201),x54203),x54204)),f332(f332(f151(x54201),x54203),x54204)) % 172.78/172.48 [5421]P102(f332(x54212,x54213))+E(f332(f136(x54211,x54212),f332(f332(f151(x54211),x54213),x54214)),f332(f136(x54211,x54212),x54214)) % 172.78/172.48 [5555]~E(x55552,x55554)+P102(f332(f332(f332(f310(x55551),x55552),x55553),x55554)) % 172.78/172.48 [5563]E(x55631,f116(x55632))+E(f144(x55633,f332(f332(f154(x55632,x55633),x55634),x55631)),f332(x55634,f144(x55632,x55631))) % 172.78/172.48 [5577]~E(x55771,f63(x55772,x55774))+E(f332(x55771,f332(f332(f310(x55772),x55773),f195(f883(x55772,a871)))),x55773) % 172.78/172.48 [5612]E(x56121,f116(x56122))+E(f332(f141(x56123),f332(f332(f154(x56122,x56123),x56124),x56121)),f332(x56124,f332(f141(x56122),x56121))) % 172.78/172.48 [5715]~P102(f332(x57153,x57154))+P102(f332(f332(f332(f310(x57151),x57152),x57153),x57154)) % 172.78/172.48 [5829]~P13(x58292,x58294,x58291)+E(f332(x58291,f332(f332(f310(x58292),x58293),f195(f883(x58292,a871)))),x58293) % 172.78/172.48 [5853]~E(x58532,x58533)+P102(f332(f332(f334(x58531),x58532),f332(f332(f310(x58531),x58533),x58534))) % 172.78/172.48 [5857]~P61(x58571)+E(f332(f332(f113(x58571),x58572),f332(f332(f113(x58571),x58573),x58574)),f332(f332(f113(x58571),x58573),f332(f332(f113(x58571),x58572),x58574))) % 172.78/172.48 [5859]~P97(x58591)+E(f332(f332(f113(x58591),x58592),f332(f332(f113(x58591),x58593),x58594)),f332(f332(f113(x58591),x58593),f332(f332(f113(x58591),x58592),x58594))) % 172.78/172.48 [5860]~P61(x58601)+E(f332(f332(f104(x58601),x58602),f332(f332(f104(x58601),x58603),x58604)),f332(f332(f104(x58601),x58603),f332(f332(f104(x58601),x58602),x58604))) % 172.78/172.48 [5862]~P98(x58621)+E(f332(f332(f104(x58621),x58622),f332(f332(f104(x58621),x58623),x58624)),f332(f332(f104(x58621),x58623),f332(f332(f104(x58621),x58622),x58624))) % 172.78/172.48 [5863]~P114(x58631)+E(f332(f332(f80(x58631),x58632),f332(f332(f80(x58631),x58633),x58634)),f332(f332(f80(x58631),x58633),f332(f332(f80(x58631),x58632),x58634))) % 172.78/172.48 [5864]~P114(x58641)+E(f332(f332(f79(x58641),x58642),f332(f332(f79(x58641),x58643),x58644)),f332(f332(f79(x58641),x58643),f332(f332(f79(x58641),x58642),x58644))) % 172.78/172.48 [5866]~P104(x58661)+E(f332(f332(f244(x58661),x58662),f332(f332(f244(x58661),x58663),x58664)),f332(f332(f244(x58661),x58663),f332(f332(f244(x58661),x58662),x58664))) % 172.78/172.48 [5868]~P104(x58681)+E(f332(f332(f245(x58681),x58682),f332(f332(f245(x58681),x58683),x58684)),f332(f332(f245(x58681),x58683),f332(f332(f245(x58681),x58682),x58684))) % 172.78/172.48 [5873]E(x58731,x58732)+E(f171(x58733,x58731,f332(f332(f151(x58733),x58732),x58734)),f332(f332(f151(x58733),x58732),f171(x58733,x58731,x58734))) % 172.78/172.48 [5886]~P102(f332(x58862,x58863))+E(f332(f136(x58861,x58862),f332(f332(f151(x58861),x58863),x58864)),f332(f332(f151(x58861),x58863),f332(f136(x58861,x58862),x58864))) % 172.78/172.48 [6022]~P102(f332(x60222,x60223))+E(f178(x60221,x60222,f332(f332(f151(x60221),x60223),x60224)),f332(f332(f151(x60221),x60223),f178(x60221,x60222,x60224))) % 172.78/172.48 [6073]P19(x60731,x60732,x60733)+~P19(x60731,x60732,f332(f332(f310(f875(x60731)),x60734),x60733)) % 172.78/172.48 [6086]E(x60861,f195(f883(x60862,a871)))+E(f332(f332(f41(x60862,f883(x60863,a871)),x60861),f332(f16(f883(x60863,a871),x60862),x60864)),x60864) % 172.78/172.48 [6087]E(x60871,f195(f883(x60872,a871)))+E(f332(f332(f42(x60872,f883(x60873,a871)),x60871),f332(f16(f883(x60873,a871),x60872),x60874)),x60874) % 172.78/172.48 [6096]~E(x60964,f195(f883(x60962,a871)))+E(f332(f332(f269(x60961,x60962),x60963),f332(f16(f883(x60962,a871),x60961),x60964)),f195(f883(f882(x60961,x60962),a871))) % 172.78/172.48 [6097]~E(x60973,f195(f883(x60971,a871)))+E(f332(f332(f269(x60971,x60972),x60973),f332(f16(f883(x60972,a871),x60971),x60974)),f195(f883(f882(x60971,x60972),a871))) % 172.78/172.48 [6143]E(x61431,f2(a876))+E(f332(f332(f138(x61432),x61431),f332(f332(f151(x61432),x61433),x61434)),f332(f332(f138(x61432),f332(f332(f22(a876),x61431),f77(a876))),x61434)) % 172.78/172.48 [6167]E(x61671,f195(f883(x61672,a871)))+E(f332(f311(x61672,x61673,f332(f16(x61673,x61672),x61674)),x61671),f332(f332(f310(x61673),x61674),f195(f883(x61673,a871)))) % 172.78/172.48 [6170]E(f332(f312(x61701,x61702,f332(f16(x61702,x61701),x61703)),x61704),f195(f883(x61701,a871)))+P102(f332(f332(f334(x61702),x61703),x61704)) % 172.78/172.48 [6237]~E(x62373,f195(f883(x62371,a871)))+E(f332(f332(f41(x62371,f883(x62372,a871)),x62373),f332(f16(f883(x62372,a871),x62371),x62374)),f195(f883(x62372,a871))) % 172.78/172.48 [6238]~E(x62383,f195(f883(x62381,a871)))+E(f332(f332(f42(x62381,f883(x62382,a871)),x62383),f332(f16(f883(x62382,a871),x62381),x62384)),f255(f883(x62382,a871))) % 172.78/172.48 [6240]~P25(x62401)+E(f44(x62401,f332(f332(f80(x62401),x62402),x62403),f332(f332(f80(x62401),x62402),x62404)),f332(f332(f80(x62401),x62402),f44(x62401,x62403,x62404))) % 172.78/172.48 [6405]E(f332(f312(x64051,x64052,f332(f16(x64052,x64051),x64053)),x64054),f255(f883(x64051,a871)))+~P102(f332(f332(f334(x64052),x64053),x64054)) % 172.78/172.48 [6428]~P102(f332(f332(f334(x64281),x64282),x64284))+P102(f332(f332(f334(x64281),x64282),f332(f332(f310(x64281),x64283),x64284))) % 172.78/172.48 [6433]P102(f332(x64331,x64332))+~P102(f332(f160(x64333,x64331),f332(f332(f151(x64333),x64332),x64334))) % 172.78/172.48 [6442]~E(x64423,f332(f332(f22(a876),f332(f196(f877(x64421)),x64422)),f77(a876)))+E(f117(x64421,f332(f332(f159(x64421,x64422),x64423),x64424)),f117(x64421,x64422)) % 172.78/172.48 [6460]~P104(x64601)+E(f332(f332(f104(f883(x64601,a871)),f332(f301(x64601),x64602)),f303(x64601,x64603,x64604)),f303(x64601,x64603,f332(f332(f244(x64601),x64602),x64604))) % 172.78/172.48 [6461]~P104(x64611)+E(f332(f332(f104(f883(x64611,a871)),f332(f254(x64611),x64612)),f303(x64611,x64613,x64614)),f303(x64611,f332(f332(f245(x64611),x64612),x64613),x64614)) % 172.78/172.48 [6476]E(f332(f332(f104(f883(x64761,a871)),x64762),f332(f332(f310(x64761),x64763),x64764)),f332(f332(f104(f883(x64761,a871)),x64762),x64764))+P102(f332(f332(f334(x64761),x64763),x64762)) % 172.78/172.48 [6488]E(f171(x64881,x64882,f332(f332(f134(x64881),x64883),x64884)),f332(f332(f134(x64881),x64883),f171(x64881,x64882,x64884)))+P102(f332(f332(f334(x64881),x64882),f332(f173(x64881),x64883))) % 172.78/172.48 [6492]~P75(x64921)+E(f332(f332(f80(x64921),f332(f332(f257(x64921),x64922),x64923)),f332(f332(f257(x64921),x64922),x64924)),f332(f332(f257(x64921),x64922),f332(f332(f79(a876),x64923),x64924))) % 172.78/172.48 [6493]~P114(x64931)+E(f332(f332(f80(x64931),f332(f332(f257(x64931),x64932),x64933)),f332(f332(f257(x64931),x64932),x64934)),f332(f332(f257(x64931),x64932),f332(f332(f79(a876),x64933),x64934))) % 172.78/172.48 [6529]~P95(x65291)+E(f332(f332(f104(x65291),f332(f332(f113(x65291),x65292),x65293)),f332(f332(f113(x65291),x65292),x65294)),f332(f332(f113(x65291),x65292),f332(f332(f104(x65291),x65293),x65294))) % 172.78/172.48 [6530]~P95(x65301)+E(f332(f332(f113(x65301),f332(f332(f104(x65301),x65302),x65303)),f332(f332(f104(x65301),x65302),x65304)),f332(f332(f104(x65301),x65302),f332(f332(f113(x65301),x65303),x65304))) % 172.78/172.48 [6531]~P114(x65311)+E(f332(f332(f79(x65311),f332(f332(f80(x65311),x65312),x65313)),f332(f332(f80(x65311),x65312),x65314)),f332(f332(f80(x65311),x65312),f332(f332(f79(x65311),x65313),x65314))) % 172.78/172.48 [6532]~P104(x65321)+E(f332(f332(f245(x65321),f332(f332(f244(x65321),x65322),x65323)),f332(f332(f244(x65321),x65322),x65324)),f332(f332(f244(x65321),x65322),f332(f332(f245(x65321),x65323),x65324))) % 172.78/172.48 [6533]~P104(x65331)+E(f332(f332(f244(x65331),f332(f332(f245(x65331),x65332),x65333)),f332(f332(f245(x65331),x65332),x65334)),f332(f332(f245(x65331),x65332),f332(f332(f244(x65331),x65333),x65334))) % 172.78/172.48 [6565]~P25(x65651)+E(f44(x65651,f332(f332(f80(x65651),x65652),x65653),f332(f332(f80(x65651),x65654),x65653)),f332(f332(f80(x65651),f44(x65651,x65652,x65654)),x65653)) % 172.78/172.48 [6568]~E(f332(f196(f877(x65681)),x65683),f332(f196(f877(x65682)),x65684))+E(f332(f332(f154(f882(x65681,x65682),x65682),f270(x65681,x65682)),f332(f332(f183(x65681,x65682),x65683),x65684)),x65684) % 172.78/172.48 [6569]~E(f332(f196(f877(x65691)),x65693),f332(f196(f877(x65692)),x65694))+E(f332(f332(f154(f882(x65691,x65692),x65691),f266(x65691,x65692)),f332(f332(f183(x65691,x65692),x65693),x65694)),x65693) % 172.78/172.48 [6575]P102(f332(f160(x65751,x65752),x65753))+~P102(f332(f160(x65751,x65752),f332(f332(f151(x65751),x65754),x65753))) % 172.78/172.48 [6576]P102(f332(f160(x65761,x65762),x65763))+~P102(f332(f160(x65761,x65762),f332(f332(f134(x65761),x65764),x65763))) % 172.78/172.48 [6577]P102(f332(f160(x65771,x65772),x65773))+~P102(f332(f160(x65771,x65772),f332(f332(f134(x65771),x65773),x65774))) % 172.78/172.48 [6582]~P26(x65821)+E(f44(x65821,f332(f332(f22(x65821),x65822),f44(x65821,x65823,x65824)),x65824),f44(x65821,f332(f332(f22(x65821),x65822),x65823),x65824)) % 172.78/172.48 [6583]~P25(x65831)+E(f44(x65831,f332(f332(f80(x65831),x65832),f44(x65831,x65833,x65834)),x65834),f44(x65831,f332(f332(f80(x65831),x65832),x65833),x65834)) % 172.78/172.48 [6585]~P25(x65851)+E(f44(x65851,f332(f332(f79(x65851),x65852),f44(x65851,x65853,x65854)),x65854),f44(x65851,f332(f332(f79(x65851),x65852),x65853),x65854)) % 172.78/172.48 [6665]~P104(x66651)+E(f332(f332(f104(f883(x66651,a871)),f303(x66651,x66652,x66653)),f332(f301(x66651),x66654)),f303(x66651,x66652,f332(f332(f244(x66651),x66653),x66654))) % 172.78/172.48 [6666]~P104(x66661)+E(f332(f332(f104(f883(x66661,a871)),f303(x66661,x66662,x66663)),f332(f254(x66661),x66664)),f303(x66661,f332(f332(f245(x66661),x66662),x66664),x66663)) % 172.78/172.48 [6669]~E(f332(f196(f877(x66691)),x66693),f332(f196(f877(x66692)),x66694))+E(f332(f332(f183(x66691,x66692),f332(f169(x66691),x66693)),f332(f169(x66692),x66694)),f332(f169(f882(x66691,x66692)),f332(f332(f183(x66691,x66692),x66693),x66694))) % 172.78/172.48 [6679]E(x66791,f332(f332(f22(a876),f332(f196(f877(x66792)),x66793)),f77(a876)))+E(f117(x66792,f332(f332(f159(x66792,x66793),x66791),x66794)),f332(f332(f159(x66792,f117(x66792,x66793)),x66791),x66794)) % 172.78/172.48 [6694]~P102(f332(f137(x66942),x66944))+P102(f332(f137(f882(x66941,x66942)),f332(f332(f183(x66941,x66942),x66943),x66944))) % 172.78/172.48 [6695]~P102(f332(f137(x66951),x66953))+P102(f332(f137(f882(x66951,x66952)),f332(f332(f183(x66951,x66952),x66953),x66954))) % 172.78/172.48 [6959]E(f332(f332(f38(a876),x69591),x69592),x69593)+~P102(f332(f47(x69591,x69592),f332(f332(f267(a876,a876),x69593),x69594))) % 172.78/172.48 [6983]E(f44(a876,x69831,x69832),x69833)+~P102(f332(f47(x69831,x69832),f332(f332(f267(a876,a876),x69834),x69833))) % 172.78/172.48 [6986]P102(f332(f137(x69861),x69862))+~P102(f332(f137(x69863),f332(f332(f154(x69861,x69863),x69864),x69862))) % 172.78/172.48 [6994]~P19(x69941,x69942,f332(f332(f310(f875(x69941)),x69943),x69944))+P19(x69941,x69942,f332(f332(f310(f875(x69941)),x69943),f195(f883(f875(x69941),a871)))) % 172.78/172.48 [7000]P102(f332(f332(f201(x70001),x70002),x70003))+~P102(f332(f332(f332(f332(a203,x70001),x70002),x70004),x70003)) % 172.78/172.48 [7072]E(f171(x70721,x70722,f332(f332(f134(x70721),x70723),x70724)),f332(f332(f134(x70721),f171(x70721,x70722,x70723)),x70724))+~P102(f332(f332(f334(x70721),x70722),f332(f173(x70721),x70723))) % 172.78/172.48 [7162]~P26(x71621)+E(f44(x71621,f332(f332(f22(x71621),f44(x71621,x71622,x71623)),x71624),x71623),f44(x71621,f332(f332(f22(x71621),x71622),x71624),x71623)) % 172.78/172.48 [7165]~P25(x71651)+E(f44(x71651,f332(f332(f80(x71651),f44(x71651,x71652,x71653)),x71654),x71653),f44(x71651,f332(f332(f80(x71651),x71652),x71654),x71653)) % 172.78/172.48 [7166]~P25(x71661)+E(f44(x71661,f332(f332(f79(x71661),f44(x71661,x71662,x71663)),x71664),x71663),f44(x71661,f332(f332(f79(x71661),x71662),x71664),x71663)) % 172.78/172.48 [7356]~E(x73561,f332(f332(f151(x73562),x73563),x73564))+~P102(f332(f332(f246(a876),f332(f196(f877(x73562)),x73561)),f332(f196(f877(x73562)),x73564))) % 172.78/172.48 [7431]~E(f332(f179(x74311,x74312),x74313),f332(f179(x74311,x74312),x74314))+E(f332(f311(f882(x74311,x74312),x74311,f266(x74311,x74312)),f332(f173(f882(x74311,x74312)),x74313)),f332(f311(f882(x74311,x74312),x74311,f266(x74311,x74312)),f332(f173(f882(x74311,x74312)),x74314))) % 172.78/172.48 [7566]P20(x75661,x75662,x75663,f332(f173(x75661),x75664))+~P102(f332(f137(x75662),f332(f332(f154(x75661,x75662),x75663),x75664))) % 172.78/172.48 [7640]~P102(f332(f332(f246(f883(x76401,a871)),x76402),x76404))+P102(f332(f332(f246(f883(x76401,a871)),x76402),f332(f332(f310(x76401),x76403),x76404))) % 172.78/172.48 [7674]~P26(x76741)+E(f44(x76741,f332(f332(f22(x76741),f44(x76741,x76742,x76743)),f44(x76741,x76744,x76743)),x76743),f44(x76741,f332(f332(f22(x76741),x76742),x76744),x76743)) % 172.78/172.48 [7675]~P25(x76751)+E(f44(x76751,f332(f332(f80(x76751),f44(x76751,x76752,x76753)),f44(x76751,x76754,x76753)),x76753),f44(x76751,f332(f332(f80(x76751),x76752),x76754),x76753)) % 172.78/172.48 [7676]~P25(x76761)+E(f44(x76761,f332(f332(f79(x76761),f44(x76761,x76762,x76763)),f44(x76761,x76764,x76763)),x76763),f44(x76761,f332(f332(f79(x76761),x76762),x76764),x76763)) % 172.78/172.48 [7779]P102(f332(f332(f332(f332(a203,x77791),x77792),f332(a115,x77793)),x77794))+~P102(f332(f332(f332(f332(a203,x77791),x77792),x77793),x77794)) % 172.78/172.48 [7786]~E(f332(x77864,f430(x77864,x77863,x77861,x77862)),f195(f883(x77862,a871)))+E(f332(f332(f41(x77861,f883(x77862,a871)),x77863),x77864),f195(f883(x77862,a871))) % 172.78/172.48 [7787]~E(f332(x77874,f604(x77874,x77873,x77871,x77872)),f255(f883(x77872,a871)))+E(f332(f332(f42(x77871,f883(x77872,a871)),x77873),x77874),f255(f883(x77872,a871))) % 172.78/172.48 [7788]~E(f332(x77884,f446(x77884,x77883,x77882,x77881)),f195(f883(x77882,a871)))+E(f332(f332(f41(x77881,f883(x77882,a871)),x77883),x77884),f195(f883(x77882,a871))) % 172.78/172.48 [7789]~E(f332(x77894,f605(x77894,x77893,x77892,x77891)),f255(f883(x77892,a871)))+E(f332(f332(f42(x77891,f883(x77892,a871)),x77893),x77894),f255(f883(x77892,a871))) % 172.78/172.48 [8189]P102(f332(x81891,x81892))+~P102(f332(f332(f334(x81893),x81892),f332(f332(f104(f883(x81893,a871)),x81894),f332(f252(x81893),x81891)))) % 172.78/172.48 [8228]~P102(f332(f332(f246(f883(x82281,a871)),x82283),x82284))+P102(f332(f332(f246(f883(x82281,a871)),f332(f332(f310(x82281),x82282),x82283)),f332(f332(f310(x82281),x82282),x82284))) % 172.78/172.48 [8395]P102(f332(f332(f201(x83951),x83952),f858(x83953,x83952,x83954,x83951)))+~P102(f332(f332(f201(f32(x83951,x83954)),x83952),x83953)) % 172.78/172.48 [8396]P102(f332(f332(f201(x83961),x83962),f364(x83963,x83962,x83964,x83961)))+~P102(f332(f332(f201(f32(x83961,x83964)),x83962),x83963)) % 172.78/172.48 [8405]P102(f332(x84052,x84053))+E(f332(f332(f138(x84051),f332(f196(f877(x84051)),f178(x84051,x84052,f332(f332(f151(x84051),x84053),x84054)))),f332(f332(f151(x84051),x84053),x84054)),f332(f332(f151(x84051),x84053),x84054)) % 172.78/172.48 [8520]~P102(f332(f332(f247(a876),f332(x85204,x85202)),f332(x85204,x85203)))+P102(f332(f332(f334(f882(x85201,x85201)),f332(f332(f267(x85201,x85201),x85202),x85203)),f332(f332(f288(a876,x85201),a251),x85204))) % 172.78/172.48 [8609]~P102(f332(x86092,f781(x86094,x86092,x86093,x86091)))+E(f178(x86091,x86092,f332(f332(f134(x86091),x86093),x86094)),f332(f332(f134(x86091),x86093),f178(x86091,x86092,x86094))) % 172.78/172.48 [8679]P20(f877(x86791),f877(x86792),f332(f154(x86791,x86792),x86793),x86794)+~P20(x86791,x86792,x86793,f39(f883(x86791,a871),f332(f311(f877(x86791),f883(x86791,a871),f173(x86791)),x86794))) % 172.78/172.48 [8746]~P102(f332(x87462,x87463))+E(f332(f332(f138(x87461),f332(f196(f877(x87461)),f178(x87461,x87462,f332(f332(f151(x87461),x87463),x87464)))),f332(f332(f151(x87461),x87463),x87464)),f332(f332(f138(x87461),f332(f196(f877(x87461)),f178(x87461,x87462,x87464))),x87464)) % 172.78/172.48 [8785]~E(x87852,x87853)+E(f332(f136(x87851,f332(f332(f8(a871,a871,x87851),a327),f332(a329,x87852))),f332(f332(f151(x87851),x87853),x87854)),f332(f136(x87851,f332(f332(f8(a871,a871,x87851),a327),f332(a329,x87852))),x87854)) % 172.78/172.48 [8795]E(f332(f332(f41(x87951,f883(x87952,a871)),x87953),x87954),f195(f883(x87952,a871)))+P102(f332(f332(f334(x87951),f430(x87954,x87953,x87951,x87952)),x87953)) % 172.78/172.48 [8796]E(f332(f332(f42(x87961,f883(x87962,a871)),x87963),x87964),f255(f883(x87962,a871)))+P102(f332(f332(f334(x87961),f604(x87964,x87963,x87961,x87962)),x87963)) % 172.78/172.48 [8797]E(f332(f332(f41(x87971,f883(x87972,a871)),x87973),x87974),f195(f883(x87972,a871)))+P102(f332(f332(f334(x87971),f446(x87974,x87973,x87972,x87971)),x87973)) % 172.78/172.48 [8798]E(f332(f332(f42(x87981,f883(x87982,a871)),x87983),x87984),f255(f883(x87982,a871)))+P102(f332(f332(f334(x87981),f605(x87984,x87983,x87982,x87981)),x87983)) % 172.78/172.48 [8835]P102(f332(f332(f247(a876),f332(x88351,x88352)),f332(x88351,x88353)))+~P102(f332(f332(f334(f882(x88354,x88354)),f332(f332(f267(x88354,x88354),x88352),x88353)),f332(f332(f288(a876,x88354),a251),x88351))) % 172.78/172.48 [8856]E(f178(x88561,x88562,f332(f332(f134(x88561),x88563),x88564)),f332(f332(f134(x88561),x88563),f178(x88561,x88562,x88564)))+P102(f332(f332(f334(x88561),f781(x88564,x88562,x88563,x88561)),f332(f173(x88561),x88563))) % 172.78/172.48 [8893]P102(f332(f332(f201(x88931),f858(x88932,x88933,x88931,x88934)),x88932))+~P102(f332(f332(f201(f32(x88934,x88931)),x88933),x88932)) % 172.78/172.48 [8894]P102(f332(f332(f201(x88941),f364(x88942,x88943,x88941,x88944)),x88942))+~P102(f332(f332(f201(f32(x88944,x88941)),x88943),x88942)) % 172.78/172.48 [9025]P102(f332(f332(f334(x90251),f503(x90252,x90253,x90254,x90251)),x90253))+~P102(f332(f332(f334(f883(x90251,a871)),x90254),f332(f332(f60(x90251),x90253),x90252))) % 172.78/172.48 [9028]E(x90281,x90282)+~P102(f332(f332(f334(f882(x90283,x90283)),f332(f332(f267(x90283,x90283),x90281),x90282)),f332(f332(f190(f882(x90283,x90283),a871),f2(a876)),x90284))) % 172.78/172.48 [9107]E(f332(f286(x91071,x91071,x91072),f332(f332(f310(x91071),f503(x91072,x91073,x91074,x91071)),f195(f883(x91071,a871)))),x91074)+~P102(f332(f332(f334(f883(x91071,a871)),x91074),f332(f332(f60(x91071),x91073),x91072))) % 172.78/172.48 [9112]~P102(f332(f332(f334(f882(x91121,x91121)),f332(f332(f267(x91121,x91121),x91123),x91122)),f308(x91121,x91124)))+P102(f332(f332(f334(f882(x91121,x91121)),f332(f332(f267(x91121,x91121),x91122),x91123)),f308(x91121,f332(f287(x91121,x91121),x91124)))) % 172.78/172.48 [9124]~P25(x91241)+E(f332(f332(f79(x91241),f332(f332(f79(x91241),f332(f332(f80(x91241),x91242),f332(f332(f38(x91241),x91243),x91242))),f44(x91241,x91243,x91242))),x91244),f332(f332(f79(x91241),x91243),x91244)) % 172.78/172.48 [9134]~P102(f332(f332(f334(x91341),x91343),x91344))+P102(f332(f332(f334(f883(x91341,a871)),f332(f286(x91341,x91341,x91342),f332(f332(f310(x91341),x91343),f195(f883(x91341,a871))))),f332(f332(f60(x91341),x91344),x91342))) % 172.78/172.48 [9145]P102(f332(f332(f334(f882(x91451,x91451)),f332(f332(f267(x91451,x91451),x91452),x91453)),f308(x91451,x91454)))+~P102(f332(f332(f334(f882(x91451,x91451)),f332(f332(f267(x91451,x91451),x91453),x91452)),f308(x91451,f332(f287(x91451,x91451),x91454)))) % 172.78/172.48 [9237]E(f332(f332(f159(x92371,f332(f169(x92371),x92372)),f332(f332(f22(a876),f332(f332(f22(a876),f332(f196(f877(x92371)),x92372)),x92373)),f77(a876))),x92374),f332(f169(x92371),f332(f332(f159(x92371,x92372),x92373),x92374)))+~P102(f332(f332(f247(a876),x92373),f332(f196(f877(x92371)),x92372))) % 172.78/172.48 [9240]~P102(f332(x92402,f774(x92404,x92402,x92403,x92401)))+E(f332(f332(f138(x92401),f332(f196(f877(x92401)),f178(x92401,x92402,f332(f332(f134(x92401),x92403),x92404)))),f332(f332(f134(x92401),x92403),x92404)),f332(f332(f138(x92401),f332(f196(f877(x92401)),f178(x92401,x92402,x92404))),x92404)) % 172.78/172.48 [9279]~P20(x92792,x92791,x92793,f255(f883(x92792,a871)))+P102(f332(f332(f246(f883(x92791,a871)),f332(f311(x92792,x92791,x92793),f332(f78(f883(x92792,a871)),x92794))),f332(f78(f883(x92791,a871)),f332(f311(x92792,x92791,x92793),x92794)))) % 172.78/172.48 [9292]~P27(x92921)+E(f332(f142(x92921,x92922,f332(f7(x92922,x92921,x92921),f332(f332(f8(x92921,f883(x92921,x92921),x92922),f113(x92921)),x92923)),f195(x92921)),x92924),f332(f332(f41(x92922,x92921),f332(f173(x92922),x92924)),x92923)) % 172.78/172.48 [9293]~P27(x92931)+E(f332(f142(x92931,x92932,f332(f7(x92932,x92931,x92931),f332(f332(f8(x92931,f883(x92931,x92931),x92932),f104(x92931)),x92933)),f255(x92931)),x92934),f332(f332(f42(x92932,x92931),f332(f173(x92932),x92934)),x92933)) % 172.78/172.48 [9305]E(f332(f332(f138(x93051),f332(f196(f877(x93051)),f178(x93051,x93052,f332(f332(f134(x93051),x93053),x93054)))),f332(f332(f134(x93051),x93053),x93054)),f332(f332(f138(x93051),f332(f196(f877(x93051)),f178(x93051,x93052,x93054))),x93054))+P102(f332(f332(f334(x93051),f774(x93054,x93052,x93053,x93051)),f332(f173(x93051),x93053))) % 172.78/172.48 [9373]~P102(f332(f332(f334(f882(f877(x93734),f877(x93734))),f332(f332(f267(f877(x93734),f877(x93734)),x93733),x93732)),f157(x93734,x93731)))+P102(f332(f332(f247(a876),f689(x93731,x93732,x93733,x93734)),f332(f196(f877(x93734)),x93733))) % 172.78/172.48 [9374]~P25(x93741)+E(f332(f332(f79(x93741),f332(f332(f79(x93741),f332(f332(f80(x93741),f332(f332(f38(x93741),x93742),x93743)),x93743)),f44(x93741,x93742,x93743))),x93744),f332(f332(f79(x93741),x93742),x93744)) % 172.78/172.48 [9402]~P102(f332(f332(f334(f882(f877(x94021),f877(x94021))),f332(f332(f267(f877(x94021),f877(x94021)),x94022),x94023)),f332(f287(f877(x94021),f877(x94021)),f157(x94021,x94024))))+P102(f332(f332(f334(f882(f877(x94021),f877(x94021))),f332(f332(f267(f877(x94021),f877(x94021)),x94022),x94023)),f157(x94021,f332(f287(x94021,x94021),x94024)))) % 172.78/172.48 [9403]P102(f332(f332(f334(f882(f877(x94031),f877(x94031))),f332(f332(f267(f877(x94031),f877(x94031)),x94032),x94033)),f332(f287(f877(x94031),f877(x94031)),f157(x94031,x94034))))+~P102(f332(f332(f334(f882(f877(x94031),f877(x94031))),f332(f332(f267(f877(x94031),f877(x94031)),x94032),x94033)),f157(x94031,f332(f287(x94031,x94031),x94034)))) % 172.78/172.48 [9437]~P102(f332(f332(f334(x94371),x94373),f332(f265(x94371,x94372),x94374)))+P102(f332(f332(f334(f882(x94371,x94372)),f332(f332(f267(x94371,x94372),x94373),f545(x94374,x94372,x94373,x94371))),x94374)) % 172.78/172.48 [9438]~P102(f332(f332(f334(x94381),x94383),f332(f265(x94381,x94382),x94384)))+P102(f332(f332(f334(f882(x94381,x94382)),f332(f332(f267(x94381,x94382),x94383),f549(x94384,x94382,x94383,x94381))),x94384)) % 172.78/172.48 [9547]~P102(f332(f61(f880(x95471)),f332(f311(x95472,f880(x95471),x95473),f255(f883(x95472,a871)))))+P102(f332(f61(f880(x95471)),f332(f311(x95472,f880(x95471),f186(x95472,x95471,x95473,f332(f179(x95472,x95471),x95474))),f255(f883(x95472,a871))))) % 172.78/172.48 [9594]~P102(f332(f332(f334(f882(x95941,x95941)),f332(f332(f267(x95941,x95941),x95942),x95944)),f332(f332(f289(x95941,x95941,x95941),x95943),f308(x95941,x95943))))+P102(f332(f332(f334(f882(x95941,x95941)),f332(f332(f267(x95941,x95941),x95942),f621(x95943,x95944,x95942,x95941))),x95943)) % 172.78/172.48 [9762]~P102(f332(f332(f334(f882(x97622,x97621)),x97624),f332(f287(x97621,x97622),x97623)))+P102(f332(f332(f334(f882(x97621,x97622)),f332(f332(f267(x97621,x97622),f662(x97623,x97624,x97621,x97622)),f661(x97623,x97624,x97621,x97622))),x97623)) % 172.78/172.48 [9790]~P102(f332(f332(f334(f882(f877(x97901),f877(x97901))),f332(f332(f267(f877(x97901),f877(x97901)),x97904),x97903)),f157(x97901,x97902)))+P102(f332(f332(f334(f882(x97901,x97901)),f332(f332(f267(x97901,x97901),f702(x97902,x97903,x97904,x97901)),f703(x97902,x97903,x97904,x97901))),x97902)) % 172.78/172.48 [9886]~P102(f332(f332(f334(f882(f877(x98861),f877(x98861))),f332(f332(f267(f877(x98861),f877(x98861)),x98862),x98864)),f157(x98861,x98863)))+P102(f332(f332(f334(f882(x98861,x98861)),f332(f332(f267(x98861,x98861),f332(f332(f165(x98861),x98862),f689(x98863,x98864,x98862,x98861))),f690(x98863,x98864,x98862,x98861))),x98863)) % 172.78/172.48 [9908]~P102(f332(f61(x99082),x99084))+E(f332(f332(f332(f65(f883(x99081,a871),x99082,f113(f883(x99081,a871))),f332(f332(f7(x99082,f883(x99081,a871),f883(x99081,a871)),f332(f332(f8(x99081,f883(f883(x99081,a871),f883(x99081,a871)),x99082),f310(x99081)),x99083)),f195(f883(x99081,a871)))),f195(f883(x99081,a871))),x99084),f332(f311(x99082,x99081,x99083),x99084)) % 172.78/172.48 [10003]~P20(x100031,x100032,x100033,f255(f883(x100031,a871)))+P102(f332(f332(f246(f883(x100031,a871)),f332(f312(x100031,x100032,x100033),f332(f332(f310(x100032),x100034),f195(f883(x100032,a871))))),f332(f332(f310(x100031),f84(x100031,f332(f332(f7(x100031,x100032,a871),f332(f332(f8(x100032,f883(x100032,a871),x100031),a329),x100033)),x100034))),f195(f883(x100031,a871))))) % 172.78/172.48 [5621]~E(f332(f332(f134(x56211),x56212),x56214),x56213)+E(f332(f332(f176(x56211),f332(f196(f877(x56211)),x56212)),x56213),x56212) % 172.78/172.48 [5622]~E(f332(f332(f134(x56222),x56223),x56221),x56224)+E(x56221,f332(f332(f138(x56222),f332(f196(f877(x56222)),x56223)),x56224)) % 172.78/172.48 [5633]~E(x56334,f2(a876))+E(f332(f332(f165(x56331),f332(f332(f151(x56331),x56332),x56333)),x56334),x56332) % 172.78/172.48 [6156]~P114(x61561)+E(f332(f332(f257(x61561),f332(f332(f257(x61561),x61562),x61563)),x61564),f332(f332(f257(x61561),x61562),f332(f332(f80(a876),x61563),x61564))) % 172.78/172.48 [6157]~P75(x61571)+E(f332(f332(f257(x61571),f332(f332(f257(x61571),x61572),x61573)),x61574),f332(f332(f257(x61571),x61572),f332(f332(f80(a876),x61573),x61574))) % 172.78/172.48 [6168]E(x61681,f2(a876))+E(f332(f332(f165(x61682),f332(f332(f151(x61682),x61683),x61684)),x61681),f332(f332(f165(x61682),x61684),f332(f332(f22(a876),x61681),f77(a876)))) % 172.78/172.48 [6194]~P117(x61941)+E(f332(f332(f290(x61941),f332(f332(f80(x61941),x61942),x61943)),x61944),f332(f332(f80(x61941),x61942),f332(f332(f290(x61941),x61943),x61944))) % 172.78/172.48 [6196]~P61(x61961)+E(f332(f332(f113(x61961),f332(f332(f113(x61961),x61962),x61963)),x61964),f332(f332(f113(x61961),x61962),f332(f332(f113(x61961),x61963),x61964))) % 172.78/172.48 [6198]~P97(x61981)+E(f332(f332(f113(x61981),f332(f332(f113(x61981),x61982),x61983)),x61984),f332(f332(f113(x61981),x61982),f332(f332(f113(x61981),x61983),x61984))) % 172.78/172.48 [6199]~P61(x61991)+E(f332(f332(f104(x61991),f332(f332(f104(x61991),x61992),x61993)),x61994),f332(f332(f104(x61991),x61992),f332(f332(f104(x61991),x61993),x61994))) % 172.78/172.48 [6201]~P98(x62011)+E(f332(f332(f104(x62011),f332(f332(f104(x62011),x62012),x62013)),x62014),f332(f332(f104(x62011),x62012),f332(f332(f104(x62011),x62013),x62014))) % 172.78/172.48 [6202]~P64(x62021)+E(f332(f332(f80(x62021),f332(f332(f80(x62021),x62022),x62023)),x62024),f332(f332(f80(x62021),x62022),f332(f332(f80(x62021),x62023),x62024))) % 172.78/172.48 [6203]~P114(x62031)+E(f332(f332(f80(x62031),f332(f332(f80(x62031),x62032),x62033)),x62034),f332(f332(f80(x62031),x62032),f332(f332(f80(x62031),x62033),x62034))) % 172.78/172.48 [6205]~P114(x62051)+E(f332(f332(f79(x62051),f332(f332(f79(x62051),x62052),x62053)),x62054),f332(f332(f79(x62051),x62052),f332(f332(f79(x62051),x62053),x62054))) % 172.78/172.48 [6206]~P65(x62061)+E(f332(f332(f79(x62061),f332(f332(f79(x62061),x62062),x62063)),x62064),f332(f332(f79(x62061),x62062),f332(f332(f79(x62061),x62063),x62064))) % 172.78/172.48 [6208]~P104(x62081)+E(f332(f332(f244(x62081),f332(f332(f244(x62081),x62082),x62083)),x62084),f332(f332(f244(x62081),x62082),f332(f332(f244(x62081),x62083),x62084))) % 172.78/172.48 [6210]~P104(x62101)+E(f332(f332(f245(x62101),f332(f332(f245(x62101),x62102),x62103)),x62104),f332(f332(f245(x62101),x62102),f332(f332(f245(x62101),x62103),x62104))) % 172.78/172.48 [6221]~P25(x62211)+E(f44(x62211,f332(f332(f79(x62211),x62212),f332(f332(f80(x62211),x62213),x62214)),x62214),f44(x62211,x62212,x62214)) % 172.78/172.48 [6222]~P25(x62221)+E(f44(x62221,f332(f332(f79(x62221),x62222),f332(f332(f80(x62221),x62223),x62224)),x62223),f44(x62221,x62222,x62223)) % 172.78/172.48 [6354]E(f332(f332(f165(x63541),f332(f332(f176(x63541),x63542),x63543)),x63544),f332(f332(f165(x63541),x63543),x63544))+~P102(f332(f332(f247(a876),x63544),x63542)) % 172.78/172.48 [6527]~P114(x65271)+E(f332(f332(f80(x65271),f332(f332(f80(x65271),x65272),x65273)),x65274),f332(f332(f80(x65271),f332(f332(f80(x65271),x65272),x65274)),x65273)) % 172.78/172.48 [6528]~P114(x65281)+E(f332(f332(f79(x65281),f332(f332(f79(x65281),x65282),x65283)),x65284),f332(f332(f79(x65281),f332(f332(f79(x65281),x65282),x65284)),x65283)) % 172.78/172.48 [6588]~P141(x65882)+E(f332(f332(f6(x65881,x65882),f332(f16(x65882,x65881),x65883)),x65884),f332(f332(f80(x65882),f332(f103(x65882),f332(f37(x65881),x65884))),x65883)) % 172.78/172.48 [6757]E(f332(f332(f104(f883(x67571,a871)),f332(f332(f310(x67571),x67572),x67573)),x67574),f332(f332(f104(f883(x67571,a871)),x67573),x67574))+P102(f332(f332(f334(x67571),x67572),x67574)) % 172.78/172.48 [6827]~P95(x68271)+E(f332(f332(f104(x68271),f332(f332(f113(x68271),x68272),x68273)),f332(f332(f113(x68271),x68274),x68273)),f332(f332(f113(x68271),f332(f332(f104(x68271),x68272),x68274)),x68273)) % 172.78/172.48 [6828]~P79(x68281)+E(f332(f332(f244(x68281),f332(f332(f22(x68281),x68282),x68283)),f332(f332(f22(x68281),x68284),x68283)),f332(f332(f22(x68281),f332(f332(f244(x68281),x68282),x68284)),x68283)) % 172.78/172.48 [6829]~P79(x68291)+E(f332(f332(f245(x68291),f332(f332(f22(x68291),x68292),x68293)),f332(f332(f22(x68291),x68294),x68293)),f332(f332(f22(x68291),f332(f332(f245(x68291),x68292),x68294)),x68293)) % 172.78/172.48 [6830]~P95(x68301)+E(f332(f332(f113(x68301),f332(f332(f104(x68301),x68302),x68303)),f332(f332(f104(x68301),x68304),x68303)),f332(f332(f104(x68301),f332(f332(f113(x68301),x68302),x68304)),x68303)) % 172.78/172.48 [6831]~P108(x68311)+E(f332(f332(f79(x68311),f332(f332(f80(x68311),x68312),x68313)),f332(f332(f80(x68311),x68314),x68313)),f332(f332(f80(x68311),f332(f332(f79(x68311),x68312),x68314)),x68313)) % 172.78/172.48 [6833]~P78(x68331)+E(f332(f332(f244(x68331),f332(f332(f79(x68331),x68332),x68333)),f332(f332(f79(x68331),x68334),x68333)),f332(f332(f79(x68331),f332(f332(f244(x68331),x68332),x68334)),x68333)) % 172.78/172.48 [6834]~P78(x68341)+E(f332(f332(f245(x68341),f332(f332(f79(x68341),x68342),x68343)),f332(f332(f79(x68341),x68344),x68343)),f332(f332(f79(x68341),f332(f332(f245(x68341),x68342),x68344)),x68343)) % 172.78/172.48 [6835]~P67(x68351)+E(f332(f332(f80(x68351),f332(f332(f257(x68351),x68352),x68353)),f332(f332(f257(x68351),x68354),x68353)),f332(f332(f257(x68351),f332(f332(f80(x68351),x68352),x68354)),x68353)) % 172.78/172.48 [6836]~P114(x68361)+E(f332(f332(f80(x68361),f332(f332(f257(x68361),x68362),x68363)),f332(f332(f257(x68361),x68364),x68363)),f332(f332(f257(x68361),f332(f332(f80(x68361),x68362),x68364)),x68363)) % 172.78/172.48 [6837]~P57(x68371)+E(f332(f332(f290(x68371),f332(f332(f257(x68371),x68372),x68373)),f332(f332(f257(x68371),x68374),x68373)),f332(f332(f257(x68371),f332(f332(f290(x68371),x68372),x68374)),x68373)) % 172.78/172.48 [6838]~P117(x68381)+E(f332(f332(f22(x68381),f332(f332(f290(x68381),x68382),x68383)),f332(f332(f290(x68381),x68384),x68383)),f332(f332(f290(x68381),f332(f332(f22(x68381),x68382),x68384)),x68383)) % 172.78/172.48 [6839]~P117(x68391)+E(f332(f332(f79(x68391),f332(f332(f290(x68391),x68392),x68393)),f332(f332(f290(x68391),x68394),x68393)),f332(f332(f290(x68391),f332(f332(f79(x68391),x68392),x68394)),x68393)) % 172.78/172.48 [6840]~P104(x68401)+E(f332(f332(f245(x68401),f332(f332(f244(x68401),x68402),x68403)),f332(f332(f244(x68401),x68404),x68403)),f332(f332(f244(x68401),f332(f332(f245(x68401),x68402),x68404)),x68403)) % 172.78/172.48 [6841]~P104(x68411)+E(f332(f332(f244(x68411),f332(f332(f245(x68411),x68412),x68413)),f332(f332(f245(x68411),x68414),x68413)),f332(f332(f245(x68411),f332(f332(f244(x68411),x68412),x68414)),x68413)) % 172.78/172.48 [6842]~P114(x68421)+E(f332(f332(f79(x68421),f332(f332(f80(x68421),x68422),x68423)),f332(f332(f80(x68421),x68424),x68423)),f332(f332(f80(x68421),f332(f332(f79(x68421),x68422),x68424)),x68423)) % 172.78/172.48 [6874]E(f332(f332(f159(x68741,x68742),x68743),x68744),x68742)+~P102(f332(f332(f246(a876),f332(f196(f877(x68741)),x68742)),x68743)) % 172.78/172.48 [6899]~P102(f332(x68993,x68994))+P102(f332(f332(f332(f113(f883(x68991,a871)),x68992),x68993),x68994)) % 172.78/172.48 [6901]~P102(f332(x69012,x69014))+P102(f332(f332(f332(f113(f883(x69011,a871)),x69012),x69013),x69014)) % 172.78/172.48 [6922]E(f332(f332(f165(x69221),f332(f332(f134(x69221),x69222),x69223)),x69224),f332(f332(f165(x69221),x69222),x69224))+~P102(f332(f332(f247(a876),x69224),f332(f196(f877(x69221)),x69222))) % 172.78/172.48 [6932]E(f332(f332(f22(f883(x69321,a871)),f332(f332(f310(x69321),x69322),x69323)),x69324),f332(f332(f22(f883(x69321,a871)),x69323),x69324))+~P102(f332(f332(f334(x69321),x69322),x69324)) % 172.78/172.48 [6973]~E(f139(a876,f332(f302(a876,x69731),x69732)),f332(f332(f151(a876),x69734),x69733))+E(f139(a876,f332(f302(a876,f332(f332(f79(a876),x69731),f77(a876))),x69732)),x69733) % 172.78/172.48 [7046]E(x70461,f2(a876))+E(f332(f332(f151(x70462),x70463),f332(f332(f176(x70462),f332(f332(f22(a876),x70461),f77(a876))),x70464)),f332(f332(f176(x70462),x70461),f332(f332(f151(x70462),x70463),x70464))) % 172.78/172.48 [7146]E(f332(f332(f165(x71461),x71462),f332(f332(f22(a876),x71463),f332(f196(f877(x71461)),x71464))),f332(f332(f165(x71461),f332(f332(f134(x71461),x71464),x71462)),x71463))+P102(f332(f332(f247(a876),x71463),f332(f196(f877(x71461)),x71464))) % 172.78/172.48 [7176]E(f332(f332(f104(f883(x71761,a871)),x71762),f332(f332(f310(x71761),x71763),x71764)),f332(f332(f310(x71761),x71763),f332(f332(f104(f883(x71761,a871)),x71762),x71764)))+~P102(f332(f332(f334(x71761),x71763),x71762)) % 172.78/172.48 [7211]E(f332(f332(f165(x72111),f332(f332(f159(x72111,x72112),x72113),x72114)),x72113),x72114)+~P102(f332(f332(f247(a876),x72113),f332(f196(f877(x72111)),x72112))) % 172.78/172.48 [7232]E(x72321,f195(f883(x72322,a871)))+E(f332(f311(f882(x72323,x72322),x72323,f266(x72323,x72322)),f332(f332(f269(x72323,x72322),x72324),f332(f16(f883(x72322,a871),x72323),x72321))),x72324) % 172.78/172.48 [7233]E(x72331,f195(f883(x72332,a871)))+E(f332(f311(f882(x72332,x72333),x72333,f270(x72332,x72333)),f332(f332(f269(x72332,x72333),x72331),f332(f16(f883(x72333,a871),x72332),x72334))),x72334) % 172.78/172.48 [7300]E(f332(f332(f22(f883(x73001,a871)),f332(f332(f310(x73001),x73002),x73003)),x73004),f332(f332(f310(x73001),x73002),f332(f332(f22(f883(x73001,a871)),x73003),x73004)))+P102(f332(f332(f334(x73001),x73002),x73004)) % 172.78/172.48 [7332]P102(f332(x73321,x73322))+P102(f332(f332(f332(f332(a203,f31(x73321,x73323)),x73322),x73324),x73322)) % 172.78/172.48 [7339]~E(x73394,f195(f883(x73392,a871)))+E(f332(f311(f882(x73391,x73392),x73391,f266(x73391,x73392)),f332(f332(f269(x73391,x73392),x73393),f332(f16(f883(x73392,a871),x73391),x73394))),f195(f883(x73391,a871))) % 172.78/172.48 [7340]~E(x73403,f195(f883(x73401,a871)))+E(f332(f311(f882(x73401,x73402),x73402,f270(x73401,x73402)),f332(f332(f269(x73401,x73402),x73403),f332(f16(f883(x73402,a871),x73401),x73404))),f195(f883(x73402,a871))) % 172.78/172.48 [7396]~P102(f332(f332(f334(x73961),x73962),x73964))+P102(f332(f332(f334(x73961),x73962),f332(f332(f113(f883(x73961,a871)),x73963),x73964))) % 172.78/172.48 [7399]~P102(f332(f332(f334(x73991),x73992),x73993))+P102(f332(f332(f334(x73991),x73992),f332(f332(f113(f883(x73991,a871)),x73993),x73994))) % 172.78/172.48 [7418]E(f332(f332(f104(f883(x74181,a871)),f332(f332(f310(x74181),x74182),x74183)),x74184),f332(f332(f310(x74181),x74182),f332(f332(f104(f883(x74181,a871)),x74183),x74184)))+~P102(f332(f332(f334(x74181),x74182),x74184)) % 172.78/172.48 [7698]P102(f332(x76981,x76982))+~P102(f332(f332(f332(f104(f883(x76983,a871)),x76984),x76981),x76982)) % 172.78/172.48 [7699]P102(f332(x76991,x76992))+~P102(f332(f332(f332(f104(f883(x76993,a871)),x76991),x76994),x76992)) % 172.78/172.48 [7702]E(f332(f332(f6(x77021,a876),x77022),f332(f332(f22(f883(x77021,a871)),x77023),f332(f332(f310(x77021),x77024),f195(f883(x77021,a871))))),f332(f332(f6(x77021,a876),x77022),x77023))+P102(f332(f332(f334(x77021),x77024),x77023)) % 172.78/172.48 [7708]~P71(x77081)+E(f332(f166(x77081),f332(f332(f154(a876,x77081),x77082),f139(a876,f332(f302(a876,x77083),x77084)))),f332(f332(f6(a876,x77081),x77082),f332(f173(a876),f139(a876,f332(f302(a876,x77083),x77084))))) % 172.78/172.48 [7709]~P71(x77091)+E(f332(f332(f6(a876,x77091),x77092),f332(f173(a876),f139(a876,f332(f302(a876,x77093),x77094)))),f332(f166(x77091),f332(f332(f154(a876,x77091),x77092),f139(a876,f332(f302(a876,x77093),x77094))))) % 172.78/172.48 [7824]~E(x78243,x78244)+P102(f332(f62(x78241,x78242,f332(f332(f310(x78241),x78243),f195(f883(x78241,a871)))),x78244)) % 172.78/172.48 [7921]P102(f332(f332(f334(x79211),x79212),f332(f173(x79211),x79213)))+~P102(f332(f332(f334(x79211),x79212),f332(f173(x79211),f332(f332(f176(x79211),x79214),x79213)))) % 172.78/172.48 [7922]P102(f332(f332(f334(x79221),x79222),f332(f173(x79221),x79223)))+~P102(f332(f332(f334(x79221),x79222),f332(f173(x79221),f332(f332(f138(x79221),x79224),x79223)))) % 172.78/172.48 [7996]P102(f332(f332(f334(x79961),x79962),x79963))+~P102(f332(f332(f334(x79961),x79962),f332(f332(f22(f883(x79961,a871)),x79963),x79964))) % 172.78/172.48 [7998]P102(f332(f332(f334(x79981),x79982),x79983))+~P102(f332(f332(f334(x79981),x79982),f332(f332(f104(f883(x79981,a871)),x79984),x79983))) % 172.78/172.48 [8001]P102(f332(f332(f334(x80011),x80012),x80013))+~P102(f332(f332(f334(x80011),x80012),f332(f332(f104(f883(x80011,a871)),x80013),x80014))) % 172.78/172.48 [8019]E(f332(f332(f134(x80191),f332(f332(f176(x80191),x80192),x80193)),f332(f332(f151(x80191),x80194),f332(f332(f138(x80191),f332(a115,x80192)),x80193))),f332(f332(f159(x80191,x80193),x80192),x80194))+~P102(f332(f332(f247(a876),x80192),f332(f196(f877(x80191)),x80193))) % 172.78/172.48 [8044]P102(f332(f332(f334(x80441),x80442),x80443))+~P102(f332(f332(f246(f883(x80441,a871)),f332(f332(f310(x80441),x80442),x80444)),x80443)) % 172.78/172.48 [8077]~P102(f332(f332(f334(x80771),x80772),x80773))+~P102(f332(f332(f334(x80771),x80772),f332(f332(f22(f883(x80771,a871)),x80774),x80773))) % 172.78/172.48 [8110]~P102(f332(f332(f247(a876),x81104),f332(f196(f877(x81101)),x81103)))+P102(f332(f332(f334(x81101),x81102),f332(f173(x81101),f332(f332(f159(x81101,x81103),x81104),x81102)))) % 172.78/172.48 [8166]E(f332(f332(f165(x81661),f332(f332(f138(x81661),x81662),x81663)),x81664),f332(f332(f165(x81661),x81663),f332(f332(f79(a876),x81662),x81664)))+~P102(f332(f332(f246(a876),f332(f332(f79(a876),x81662),x81664)),f332(f196(f877(x81661)),x81663))) % 172.78/172.48 [8176]~P141(x81762)+E(f332(f332(f6(x81761,x81762),f332(f332(f8(a876,x81762,x81761),f103(x81762)),x81763)),x81764),f332(f103(x81762),f332(f332(f6(x81761,a876),x81763),x81764))) % 172.78/172.48 [8177]~P137(x81772)+E(f332(f332(f6(x81771,x81772),f332(f332(f8(a1,x81772,x81771),f105(x81772)),x81773)),x81774),f332(f105(x81772),f332(f332(f6(x81771,a1),x81773),x81774))) % 172.78/172.48 [8230]~P60(x82302)+E(f332(f332(f9(x82301,x82302),f332(f332(f8(x82302,x82302,x82301),f74(x82302)),x82303)),x82304),f332(f74(x82302),f332(f332(f9(x82301,x82302),x82303),x82304))) % 172.78/172.48 [8231]~P66(x82312)+E(f332(f332(f6(x82311,x82312),f332(f332(f8(x82312,x82312,x82311),f78(x82312)),x82313)),x82314),f332(f78(x82312),f332(f332(f6(x82311,x82312),x82313),x82314))) % 172.78/172.48 [8233]E(f332(f332(f6(x82331,a876),x82332),f332(f332(f22(f883(x82331,a871)),x82333),f332(f332(f310(x82331),x82334),f195(f883(x82331,a871))))),f332(f332(f22(a876),f332(f332(f6(x82331,a876),x82332),x82333)),f332(x82332,x82334)))+~P102(f332(f332(f334(x82331),x82334),x82333)) % 172.78/172.48 [8253]P102(f332(f332(f246(f883(x82531,a871)),x82532),x82533))+~P102(f332(f332(f246(f883(x82531,a871)),f332(f332(f310(x82531),x82534),x82532)),x82533)) % 172.78/172.48 [8462]E(f332(a115,f647(x84621,x84622,x84623,x84624)),x84622)+~P102(f332(f332(f332(f332(a203,f332(a25,x84624)),x84623),x84622),x84621)) % 172.78/172.48 [8464]E(f332(f332(f179(x84641,x84642),x84643),x84644),f208(x84642))+P102(f332(f332(f334(x84641),x84644),f332(f311(f882(x84641,x84642),x84641,f266(x84641,x84642)),f332(f173(f882(x84641,x84642)),x84643)))) % 172.78/172.48 [8465]P38(x84651,x84652)+~P38(x84651,f332(f332(f310(f882(x84651,x84651)),f332(f332(f267(x84651,x84651),x84653),x84654)),x84652)) % 172.78/172.48 [8466]P53(x84661,x84662)+~P53(x84661,f332(f332(f310(f882(x84661,x84661)),f332(f332(f267(x84661,x84661),x84663),x84664)),x84662)) % 172.78/172.48 [8474]~P104(x84741)+E(f332(f332(f148(x84741,x84741,f5(x84741)),x84742),f332(f332(f148(x84741,x84741,f5(x84741)),x84743),x84744)),f332(f332(f148(x84741,x84741,f5(x84741)),x84743),f332(f332(f148(x84741,x84741,f5(x84741)),x84742),x84744))) % 172.78/172.48 [8484]E(x84841,x84842)+~P102(f332(f62(x84843,x84844,f332(f332(f310(x84843),x84841),f195(f883(x84843,a871)))),x84842)) % 172.78/172.48 [8494]E(f332(f332(f134(x84941),f332(f332(f176(x84941),x84942),x84943)),f332(f332(f176(x84941),x84944),f332(f332(f138(x84941),x84942),x84943))),f332(f332(f176(x84941),f332(f332(f79(a876),x84942),x84944)),x84943))+~P102(f332(f332(f246(a876),f332(f332(f79(a876),x84942),x84944)),f332(f196(f877(x84941)),x84943))) % 172.78/172.48 [8534]P102(f332(f61(x85341),x85342))+~E(x85342,f332(f311(a876,x85341,x85343),f332(f252(a876),f332(f332(f7(a876,a876,a871),f247(a876)),x85344)))) % 172.78/172.48 [8554]~P87(x85541)+E(f332(f142(x85541,x85541,f79(x85541),f332(f332(f79(x85541),x85542),x85543)),x85544),f332(f332(f79(x85541),x85542),f332(f142(x85541,x85541,f79(x85541),x85543),x85544))) % 172.78/172.48 [8587]P102(f332(f332(f246(f883(x85871,a871)),f332(f265(x85871,x85872),x85873)),f332(f265(x85871,x85872),x85874)))+~P102(f332(f332(f246(f883(f882(x85871,x85872),a871)),x85873),x85874)) % 172.78/172.48 [8600]~P102(f332(f332(f246(a876),x86002),x86004))+P102(f332(f332(f246(f883(x86001,a871)),f332(f173(x86001),f332(f332(f176(x86001),x86002),x86003))),f332(f173(x86001),f332(f332(f176(x86001),x86004),x86003)))) % 172.78/172.48 [8601]~P102(f332(f332(f246(a876),x86014),x86012))+P102(f332(f332(f246(f883(x86011,a871)),f332(f173(x86011),f332(f332(f138(x86011),x86012),x86013))),f332(f173(x86011),f332(f332(f138(x86011),x86014),x86013)))) % 172.78/172.48 [8654]~P102(f332(f61(x86541),f332(f332(f22(f883(x86541,a871)),x86542),x86544)))+P102(f332(f61(x86541),f332(f332(f22(f883(x86541,a871)),x86542),f332(f332(f310(x86541),x86543),x86544)))) % 172.78/172.48 [8690]P102(f332(f332(f334(f882(x86901,x86901)),x86902),f308(x86901,x86903)))+~P102(f332(f332(f334(f882(x86901,x86901)),x86902),f332(f332(f190(f882(x86901,x86901),a871),x86904),x86903))) % 172.78/172.48 [8767]~P102(f332(f61(x87671),f332(f332(f22(f883(x87671,a871)),x87672),f332(f332(f310(x87671),x87674),x87673))))+P102(f332(f61(x87671),f332(f332(f22(f883(x87671,a871)),x87672),x87673))) % 172.78/172.48 [8916]~E(f332(f332(f179(x89161,x89162),x89163),x89164),f208(x89162))+~P102(f332(f332(f334(x89161),x89164),f332(f311(f882(x89161,x89162),x89161,f266(x89161,x89162)),f332(f173(f882(x89161,x89162)),x89163)))) % 172.78/172.48 [8984]~P61(x89841)+P102(f332(f332(f246(x89841),f332(f332(f113(x89841),x89842),f332(f332(f104(x89841),x89843),x89844))),f332(f332(f104(x89841),f332(f332(f113(x89841),x89842),x89843)),f332(f332(f113(x89841),x89842),x89844)))) % 172.78/172.48 [8985]~P104(x89851)+P102(f332(f332(f246(x89851),f332(f332(f245(x89851),x89852),f332(f332(f244(x89851),x89853),x89854))),f332(f332(f244(x89851),f332(f332(f245(x89851),x89852),x89853)),f332(f332(f245(x89851),x89852),x89854)))) % 172.78/172.48 [9130]E(x91301,x91302)+~P102(f332(f332(f334(f882(x91303,x91303)),f332(f332(f267(x91303,x91303),x91301),x91302)),f332(f173(f882(x91303,x91303)),f332(f332(f183(x91303,x91303),x91304),x91304)))) % 172.78/172.48 [9163]~P102(f332(f332(f334(f882(x91631,x91631)),f332(f332(f267(x91631,x91631),x91633),x91632)),f308(x91631,x91634)))+~P38(x91631,f332(f332(f310(f882(x91631,x91631)),f332(f332(f267(x91631,x91631),x91632),x91633)),x91634)) % 172.78/172.48 [9164]~P102(f332(f332(f334(f882(x91641,x91641)),f332(f332(f267(x91641,x91641),x91643),x91642)),f308(x91641,x91644)))+~P53(x91641,f332(f332(f310(f882(x91641,x91641)),f332(f332(f267(x91641,x91641),x91642),x91643)),x91644)) % 172.78/172.48 [9169]E(x91691,x91692)+E(f332(f136(x91693,f332(f332(f8(a871,a871,x91693),a327),f332(a329,x91691))),f332(f332(f151(x91693),x91692),x91694)),f332(f332(f151(x91693),x91692),f332(f136(x91693,f332(f332(f8(a871,a871,x91693),a327),f332(a329,x91691))),x91694))) % 172.78/172.48 [9213]~P61(x92131)+P102(f332(f332(f246(x92131),f332(f332(f113(x92131),f332(f332(f104(x92131),x92132),x92133)),f332(f332(f104(x92131),x92132),x92134))),f332(f332(f104(x92131),x92132),f332(f332(f113(x92131),x92133),x92134)))) % 172.78/172.48 [9214]~P104(x92141)+P102(f332(f332(f246(x92141),f332(f332(f245(x92141),f332(f332(f244(x92141),x92142),x92143)),f332(f332(f244(x92141),x92142),x92144))),f332(f332(f244(x92141),x92142),f332(f332(f245(x92141),x92143),x92144)))) % 172.78/172.48 [9288]~E(f332(f311(x92882,x92881,x92883),f255(f883(x92882,a871))),f255(f883(x92881,a871)))+P102(f332(f332(f246(f883(x92881,a871)),f332(f78(f883(x92881,a871)),f332(f311(x92882,x92881,x92883),x92884))),f332(f311(x92882,x92881,x92883),f332(f78(f883(x92882,a871)),x92884)))) % 172.78/172.48 [9366]P102(f332(f332(f332(f332(a203,f332(f243(a873),f332(a27,x93661))),x93662),f647(x93663,x93664,x93662,x93661)),x93663))+~P102(f332(f332(f332(f332(a203,f332(a25,x93661)),x93662),x93664),x93663)) % 172.78/172.48 [9608]P102(f332(f332(f334(f882(x96081,x96081)),f332(f332(f267(x96081,x96081),x96082),x96083)),f332(f287(x96081,x96081),f332(f332(f289(x96081,x96081,x96081),x96084),f308(x96081,x96084)))))+~P102(f332(f332(f334(f882(x96081,x96081)),f332(f332(f267(x96081,x96081),x96082),x96083)),f332(f332(f289(x96081,x96081,x96081),f332(f287(x96081,x96081),x96084)),f308(x96081,f332(f287(x96081,x96081),x96084))))) % 172.78/172.48 [9609]~P102(f332(f332(f334(f882(x96091,x96091)),f332(f332(f267(x96091,x96091),x96092),x96093)),f332(f287(x96091,x96091),f332(f332(f289(x96091,x96091,x96091),x96094),f308(x96091,x96094)))))+P102(f332(f332(f334(f882(x96091,x96091)),f332(f332(f267(x96091,x96091),x96092),x96093)),f332(f332(f289(x96091,x96091,x96091),f332(f287(x96091,x96091),x96094)),f308(x96091,f332(f287(x96091,x96091),x96094))))) % 172.78/172.48 [9630]~P102(f332(f332(f334(x96302),x96304),f332(f263(x96301,x96302),x96303)))+P102(f332(f332(f334(f882(x96301,x96302)),f332(f332(f267(x96301,x96302),f533(x96303,x96301,x96304,x96302)),x96304)),x96303)) % 172.78/172.48 [9631]~P102(f332(f332(f334(x96312),x96314),f332(f263(x96311,x96312),x96313)))+P102(f332(f332(f334(f882(x96311,x96312)),f332(f332(f267(x96311,x96312),f547(x96313,x96311,x96314,x96312)),x96314)),x96313)) % 172.78/172.48 [9656]~P102(f332(f332(f334(x96561),x96564),f332(f332(f113(f883(x96561,a871)),x96562),x96563)))+P102(f332(f332(f332(f113(f883(x96561,a871)),f332(f332(f7(x96561,f883(x96561,a871),a871),f334(x96561)),x96562)),f332(f332(f7(x96561,f883(x96561,a871),a871),f334(x96561)),x96563)),x96564)) % 172.78/172.48 [9657]~P102(f332(f332(f334(x96571),x96574),f332(f332(f104(f883(x96571,a871)),x96572),x96573)))+P102(f332(f332(f332(f104(f883(x96571,a871)),f332(f332(f7(x96571,f883(x96571,a871),a871),f334(x96571)),x96572)),f332(f332(f7(x96571,f883(x96571,a871),a871),f334(x96571)),x96573)),x96574)) % 172.78/172.48 [9733]~P102(f332(f332(f334(f882(x97331,x97331)),f332(f332(f267(x97331,x97331),x97334),x97333)),f332(f332(f289(x97331,x97331,x97331),x97332),f308(x97331,x97332))))+P102(f332(f332(f334(f882(x97331,x97331)),f332(f332(f267(x97331,x97331),f622(x97332,x97333,x97334,x97331)),x97333)),x97332)) % 172.78/172.48 [9778]P102(f332(f332(f334(x97781),x97782),f332(f332(f113(f883(x97781,a871)),x97783),x97784)))+~P102(f332(f332(f332(f113(f883(x97781,a871)),f332(f332(f7(x97781,f883(x97781,a871),a871),f334(x97781)),x97783)),f332(f332(f7(x97781,f883(x97781,a871),a871),f334(x97781)),x97784)),x97782)) % 172.78/172.48 [9779]P102(f332(f332(f334(x97791),x97792),f332(f332(f104(f883(x97791,a871)),x97793),x97794)))+~P102(f332(f332(f332(f104(f883(x97791,a871)),f332(f332(f7(x97791,f883(x97791,a871),a871),f334(x97791)),x97793)),f332(f332(f7(x97791,f883(x97791,a871),a871),f334(x97791)),x97794)),x97792)) % 172.78/172.48 [10058]P33(x100581,f332(f332(f7(x100581,f883(f882(x100581,x100581),a871),f883(x100581,a871)),f332(f332(f8(f883(x100581,f883(f883(f882(x100581,x100581),a871),a871)),f883(f883(f882(x100581,x100581),a871),f883(x100581,a871)),x100581),f7(x100581,f883(f882(x100581,x100581),a871),a871)),f332(f332(f8(f883(x100581,f882(x100581,x100581)),f883(x100581,f883(f883(f882(x100581,x100581),a871),a871)),x100581),f332(f8(f882(x100581,x100581),f883(f883(f882(x100581,x100581),a871),a871),x100581),f334(f882(x100581,x100581)))),f267(x100581,x100581)))),x100582),x100583,x100584)+~P102(f332(f332(f334(f882(f877(x100581),f877(x100581))),f332(f332(f267(f877(x100581),f877(x100581)),x100583),x100584)),f158(x100581,x100582))) % 172.78/172.48 [10062]P54(x100621,f332(f332(f7(x100621,f883(f882(x100621,x100621),a871),f883(x100621,a871)),f332(f332(f8(f883(x100621,f883(f883(f882(x100621,x100621),a871),a871)),f883(f883(f882(x100621,x100621),a871),f883(x100621,a871)),x100621),f7(x100621,f883(f882(x100621,x100621),a871),a871)),f332(f332(f8(f883(x100621,f882(x100621,x100621)),f883(x100621,f883(f883(f882(x100621,x100621),a871),a871)),x100621),f332(f8(f882(x100621,x100621),f883(f883(f882(x100621,x100621),a871),a871),x100621),f334(f882(x100621,x100621)))),f267(x100621,x100621)))),x100622),x100623,x100624)+~P102(f332(f332(f334(f882(f883(x100621,a871),f883(x100621,a871))),f332(f332(f267(f883(x100621,a871),f883(x100621,a871)),x100623),x100624)),f324(x100621,x100622))) % 172.78/172.48 [10091]E(x100911,x100912)+~E(f332(f332(f7(x100913,f883(f882(x100913,x100914),a871),f883(x100914,a871)),f332(f332(f8(f883(x100914,f883(f883(f882(x100913,x100914),a871),a871)),f883(f883(f882(x100913,x100914),a871),f883(x100914,a871)),x100913),f7(x100914,f883(f882(x100913,x100914),a871),a871)),f332(f332(f8(f883(x100914,f882(x100913,x100914)),f883(x100914,f883(f883(f882(x100913,x100914),a871),a871)),x100913),f332(f8(f882(x100913,x100914),f883(f883(f882(x100913,x100914),a871),a871),x100914),f334(f882(x100913,x100914)))),f267(x100913,x100914)))),x100911),f332(f332(f7(x100913,f883(f882(x100913,x100914),a871),f883(x100914,a871)),f332(f332(f8(f883(x100914,f883(f883(f882(x100913,x100914),a871),a871)),f883(f883(f882(x100913,x100914),a871),f883(x100914,a871)),x100913),f7(x100914,f883(f882(x100913,x100914),a871),a871)),f332(f332(f8(f883(x100914,f882(x100913,x100914)),f883(x100914,f883(f883(f882(x100913,x100914),a871),a871)),x100913),f332(f8(f882(x100913,x100914),f883(f883(f882(x100913,x100914),a871),a871),x100914),f334(f882(x100913,x100914)))),f267(x100913,x100914)))),x100912)) % 172.78/172.48 [10095]~P33(x100951,f332(f332(f7(x100951,f883(f882(x100951,x100951),a871),f883(x100951,a871)),f332(f332(f8(f883(x100951,f883(f883(f882(x100951,x100951),a871),a871)),f883(f883(f882(x100951,x100951),a871),f883(x100951,a871)),x100951),f7(x100951,f883(f882(x100951,x100951),a871),a871)),f332(f332(f8(f883(x100951,f882(x100951,x100951)),f883(x100951,f883(f883(f882(x100951,x100951),a871),a871)),x100951),f332(f8(f882(x100951,x100951),f883(f883(f882(x100951,x100951),a871),a871),x100951),f334(f882(x100951,x100951)))),f267(x100951,x100951)))),x100954),x100952,x100953)+P102(f332(f332(f334(f882(f877(x100951),f877(x100951))),f332(f332(f267(f877(x100951),f877(x100951)),x100952),x100953)),f158(x100951,x100954))) % 172.78/172.48 [10096]~P54(x100961,f332(f332(f7(x100961,f883(f882(x100961,x100961),a871),f883(x100961,a871)),f332(f332(f8(f883(x100961,f883(f883(f882(x100961,x100961),a871),a871)),f883(f883(f882(x100961,x100961),a871),f883(x100961,a871)),x100961),f7(x100961,f883(f882(x100961,x100961),a871),a871)),f332(f332(f8(f883(x100961,f882(x100961,x100961)),f883(x100961,f883(f883(f882(x100961,x100961),a871),a871)),x100961),f332(f8(f882(x100961,x100961),f883(f883(f882(x100961,x100961),a871),a871),x100961),f334(f882(x100961,x100961)))),f267(x100961,x100961)))),x100964),x100962,x100963)+P102(f332(f332(f334(f882(f883(x100961,a871),f883(x100961,a871))),f332(f332(f267(f883(x100961,a871),f883(x100961,a871)),x100962),x100963)),f324(x100961,x100964))) % 172.78/172.48 [7470]~P89(x74701)+E(f332(f332(f80(x74701),f332(f106(x74701),x74702)),f332(f332(f80(x74701),f332(f106(x74701),x74703)),x74704)),f332(f332(f80(x74701),f332(f106(x74701),f332(f332(f80(a1),x74702),x74703))),x74704)) % 172.78/172.48 [7471]~P89(x74711)+E(f332(f332(f79(x74711),f332(f106(x74711),x74712)),f332(f332(f22(x74711),f332(f106(x74711),x74713)),x74714)),f332(f332(f22(x74711),f332(f106(x74711),f332(f332(f79(a1),x74712),x74713))),x74714)) % 172.78/172.48 [7472]~P89(x74721)+E(f332(f332(f79(x74721),f332(f106(x74721),x74722)),f332(f332(f79(x74721),f332(f106(x74721),x74723)),x74724)),f332(f332(f79(x74721),f332(f106(x74721),f332(f332(f79(a1),x74722),x74723))),x74724)) % 172.78/172.48 [7517]~P141(x75171)+E(f332(f166(x75171),f332(f332(f154(x75172,x75171),f332(f16(x75171,x75172),x75173)),x75174)),f332(f332(f80(x75171),f332(f103(x75171),f332(f196(f877(x75172)),x75174))),x75173)) % 172.78/172.48 [7755]E(f332(f278(x77551,f332(f332(f151(f882(a102,x77551)),x77552),x77553)),x77554),f332(f270(a102,x77551),x77552))+~P102(f332(f332(f247(a102),x77554),f332(f266(a102,x77551),x77552))) % 172.78/172.48 [7802]~P89(x78021)+E(f332(f332(f79(x78021),f332(f106(x78021),x78022)),f332(f332(f22(x78021),x78023),f332(f106(x78021),x78024))),f332(f332(f79(x78021),f332(f106(x78021),f332(f332(f79(a1),x78022),f332(f78(a1),x78024)))),x78023)) % 172.78/172.48 [7934]E(f332(f278(x79341,x79342),f332(f332(f22(a102),x79343),f332(f266(a102,x79341),x79344))),f332(f278(x79341,f332(f332(f151(f882(a102,x79341)),x79344),x79342)),x79343))+P102(f332(f332(f247(a102),x79343),f332(f266(a102,x79341),x79344))) % 172.78/172.48 [8379]~P102(f332(f332(f334(x83791),x83792),f332(f173(x83791),f117(x83791,x83794))))+P102(f332(f332(f334(x83791),x83792),f332(f173(x83791),f117(x83791,f332(f332(f134(x83791),x83793),x83794))))) % 172.78/172.48 [8380]~P102(f332(f332(f334(x83801),x83802),f332(f173(x83801),f117(x83801,x83803))))+P102(f332(f332(f334(x83801),x83802),f332(f173(x83801),f117(x83801,f332(f332(f134(x83801),x83803),x83804))))) % 172.78/172.48 [8400]E(f332(f332(f113(f883(x84001,a871)),f332(f332(f104(f883(x84001,a871)),x84002),x84003)),x84004),f332(f332(f104(f883(x84001,a871)),x84002),f332(f332(f113(f883(x84001,a871)),x84003),x84004)))+~P102(f332(f332(f246(f883(x84001,a871)),x84004),x84002)) % 172.78/172.48 [8703]~E(f332(f332(f113(f883(x87031,a871)),f332(f332(f104(f883(x87031,a871)),x87033),x87034)),x87032),f332(f332(f104(f883(x87031,a871)),x87033),f332(f332(f113(f883(x87031,a871)),x87034),x87032)))+P102(f332(f332(f246(f883(x87031,a871)),x87032),x87033)) % 172.78/172.48 [8990]~P102(f332(f332(f246(f883(x89901,a871)),x89902),f332(f332(f113(f883(x89901,a871)),x89903),x89904)))+P102(f332(f332(f246(f883(x89901,a871)),f332(f332(f22(f883(x89901,a871)),x89902),x89903)),x89904)) % 172.78/172.48 [9049]~P102(f332(f332(f332(f332(a203,f332(a25,x90491)),x90492),f332(a115,x90493)),x90494))+P102(f332(f332(f332(f332(a203,f332(f243(a873),f332(a27,x90491))),x90492),x90493),x90494)) % 172.78/172.48 [9109]P102(f332(f332(f246(f883(x91091,a871)),x91092),f332(f332(f113(f883(x91091,a871)),x91093),x91094)))+~P102(f332(f332(f246(f883(x91091,a871)),f332(f332(f22(f883(x91091,a871)),x91092),x91093)),x91094)) % 172.78/172.48 [9162]P102(f332(f332(f332(f332(a203,f332(a25,x91621)),x91622),f332(a115,x91623)),x91624))+~P102(f332(f332(f332(f332(a203,f332(f243(a873),f332(a27,x91621))),x91622),x91623),x91624)) % 172.78/172.48 [9194]~P81(x91941)+E(f332(f74(x91941),f332(f332(f6(x91942,x91941),f332(f332(f8(x91941,x91941,x91942),f74(x91941)),x91943)),x91944)),f332(f332(f6(x91942,x91941),f332(f332(f8(x91941,x91941,x91942),f74(x91941)),x91943)),x91944)) % 172.78/172.48 [9364]~P81(x93641)+P102(f332(f332(f246(x93641),f2(x93641)),f332(f332(f6(x93642,x93641),f332(f332(f8(x93641,x93641,x93642),f74(x93641)),x93643)),x93644))) % 172.78/172.48 [9369]~P66(x93691)+E(f332(f166(x93691),f332(f332(f154(x93692,x93691),f332(f72(x93691,x93691,x93692,f78(x93691)),x93693)),x93694)),f332(f78(x93691),f332(f166(x93691),f332(f332(f154(x93692,x93691),x93693),x93694)))) % 172.78/172.48 [9503]~P81(x95031)+P102(f332(f332(f246(x95031),f332(f74(x95031),f332(f332(f6(x95032,x95031),x95033),x95034))),f332(f332(f6(x95032,x95031),f332(f332(f8(x95031,x95031,x95032),f74(x95031)),x95033)),x95034))) % 172.78/172.48 [9533]~E(f332(f332(f79(a876),x95331),x95334),f332(f332(f79(a876),x95333),x95332))+P102(f332(f332(f334(f882(f882(a876,a876),f882(a876,a876))),f332(f332(f267(f882(a876,a876),f882(a876,a876)),f332(f332(f267(a876,a876),x95331),x95332)),f332(f332(f267(a876,a876),x95333),x95334))),a111)) % 172.78/172.48 [9534]~P102(f332(f332(f247(a876),x95341),x95343))+P102(f332(f332(f334(f882(f882(a876,a876),f882(a876,a876))),f332(f332(f267(f882(a876,a876),f882(a876,a876)),f332(f332(f267(a876,a876),x95341),x95342)),f332(f332(f267(a876,a876),x95343),x95344))),a34)) % 172.78/172.48 [9535]~P102(f332(f332(f247(a876),x95351),x95353))+P102(f332(f332(f334(f882(f882(a876,a876),f882(a876,a876))),f332(f332(f267(f882(a876,a876),f882(a876,a876)),f332(f332(f267(a876,a876),x95351),x95352)),f332(f332(f267(a876,a876),x95353),x95354))),a69)) % 172.78/172.48 [9681]E(f332(f332(f79(a876),x96811),x96812),f332(f332(f79(a876),x96813),x96814))+~P102(f332(f332(f334(f882(f882(a876,a876),f882(a876,a876))),f332(f332(f267(f882(a876,a876),f882(a876,a876)),f332(f332(f267(a876,a876),x96811),x96814)),f332(f332(f267(a876,a876),x96813),x96812))),a111)) % 172.78/172.48 [9707]E(f332(f332(f165(x97071),f332(f332(f138(x97071),f332(f196(f877(x97071)),f178(x97071,x97072,x97073))),x97073)),x97074),f332(f332(f165(x97071),x97073),f332(f332(f79(a876),x97074),f332(f196(f877(x97071)),f178(x97071,x97072,x97073)))))+~P102(f332(f332(f247(a876),x97074),f332(f196(f877(x97071)),f332(f332(f138(x97071),f332(f196(f877(x97071)),f178(x97071,x97072,x97073))),x97073)))) % 172.78/172.48 [9724]~P102(f332(f332(f334(x97242),x97244),f332(f332(f41(x97241,f883(x97242,a871)),f255(f883(x97241,a871))),x97243)))+P102(f332(f332(f332(f41(x97241,f883(x97242,a871)),f255(f883(x97241,a871))),f332(f332(f8(f883(x97242,a871),f883(x97242,a871),x97241),f332(f7(x97242,f883(x97242,a871),a871),f334(x97242))),x97243)),x97244)) % 172.78/172.48 [9725]~P102(f332(f332(f334(x97252),x97254),f332(f332(f42(x97251,f883(x97252,a871)),f255(f883(x97251,a871))),x97253)))+P102(f332(f332(f332(f42(x97251,f883(x97252,a871)),f255(f883(x97251,a871))),f332(f332(f8(f883(x97252,a871),f883(x97252,a871),x97251),f332(f7(x97252,f883(x97252,a871),a871),f334(x97252))),x97253)),x97254)) % 172.78/172.48 [9806]~P102(f332(f48(x98061,x98062),f332(f332(f267(a1,a1),x98064),x98063)))+P102(f332(f48(f332(f78(a1),x98061),x98062),f332(f332(f267(a1,a1),f332(f332(f332(f99(a1),f332(f332(a329,x98063),f2(a1))),f332(f78(a1),x98064)),f332(f332(f22(a1),f332(f78(a1),x98064)),f77(a1)))),f332(f332(f332(f99(a1),f332(f332(a329,x98063),f2(a1))),f2(a1)),f332(f332(f22(a1),x98062),x98063))))) % 172.78/172.48 [9815]P102(f332(f332(f334(x98151),x98152),f332(f332(f41(x98153,f883(x98151,a871)),f255(f883(x98153,a871))),x98154)))+~P102(f332(f332(f332(f41(x98153,f883(x98151,a871)),f255(f883(x98153,a871))),f332(f332(f8(f883(x98151,a871),f883(x98151,a871),x98153),f332(f7(x98151,f883(x98151,a871),a871),f334(x98151))),x98154)),x98152)) % 172.78/172.48 [9816]P102(f332(f332(f334(x98161),x98162),f332(f332(f42(x98163,f883(x98161,a871)),f255(f883(x98163,a871))),x98164)))+~P102(f332(f332(f332(f42(x98163,f883(x98161,a871)),f255(f883(x98163,a871))),f332(f332(f8(f883(x98161,a871),f883(x98161,a871),x98163),f332(f7(x98161,f883(x98161,a871),a871),f334(x98161))),x98164)),x98162)) % 172.78/172.48 [9828]E(f332(f332(f41(a876,f883(x98281,a871)),f255(f883(a876,a871))),x98282),f332(f332(f41(a876,f883(x98281,a871)),f255(f883(a876,a871))),x98283))+~E(f332(f332(f41(a876,f883(x98281,a871)),f332(f302(a876,f2(a876)),f454(x98282,x98284,x98283,x98281))),x98283),f332(f332(f41(a876,f883(x98281,a871)),f332(f302(a876,f2(a876)),f332(f332(f79(a876),f454(x98282,x98284,x98283,x98281)),x98284))),x98282)) % 172.78/172.48 [10149]~P102(f332(f332(f246(f883(f882(x101491,x101492),a871)),x101493),x101494))+P102(f332(f332(f246(f883(x101491,f883(x101492,a871))),f332(f332(f7(x101491,f883(f882(x101491,x101492),a871),f883(x101492,a871)),f332(f332(f8(f883(x101492,f883(f883(f882(x101491,x101492),a871),a871)),f883(f883(f882(x101491,x101492),a871),f883(x101492,a871)),x101491),f7(x101492,f883(f882(x101491,x101492),a871),a871)),f332(f332(f8(f883(x101492,f882(x101491,x101492)),f883(x101492,f883(f883(f882(x101491,x101492),a871),a871)),x101491),f332(f8(f882(x101491,x101492),f883(f883(f882(x101491,x101492),a871),a871),x101492),f334(f882(x101491,x101492)))),f267(x101491,x101492)))),x101493)),f332(f332(f7(x101491,f883(f882(x101491,x101492),a871),f883(x101492,a871)),f332(f332(f8(f883(x101492,f883(f883(f882(x101491,x101492),a871),a871)),f883(f883(f882(x101491,x101492),a871),f883(x101492,a871)),x101491),f7(x101492,f883(f882(x101491,x101492),a871),a871)),f332(f332(f8(f883(x101492,f882(x101491,x101492)),f883(x101492,f883(f883(f882(x101491,x101492),a871),a871)),x101491),f332(f8(f882(x101491,x101492),f883(f883(f882(x101491,x101492),a871),a871),x101492),f334(f882(x101491,x101492)))),f267(x101491,x101492)))),x101494))) % 172.78/172.48 [10166]P102(f332(f332(f246(f883(f882(x101661,x101662),a871)),x101663),x101664))+~P102(f332(f332(f246(f883(x101661,f883(x101662,a871))),f332(f332(f7(x101661,f883(f882(x101661,x101662),a871),f883(x101662,a871)),f332(f332(f8(f883(x101662,f883(f883(f882(x101661,x101662),a871),a871)),f883(f883(f882(x101661,x101662),a871),f883(x101662,a871)),x101661),f7(x101662,f883(f882(x101661,x101662),a871),a871)),f332(f332(f8(f883(x101662,f882(x101661,x101662)),f883(x101662,f883(f883(f882(x101661,x101662),a871),a871)),x101661),f332(f8(f882(x101661,x101662),f883(f883(f882(x101661,x101662),a871),a871),x101662),f334(f882(x101661,x101662)))),f267(x101661,x101662)))),x101663)),f332(f332(f7(x101661,f883(f882(x101661,x101662),a871),f883(x101662,a871)),f332(f332(f8(f883(x101662,f883(f883(f882(x101661,x101662),a871),a871)),f883(f883(f882(x101661,x101662),a871),f883(x101662,a871)),x101661),f7(x101662,f883(f882(x101661,x101662),a871),a871)),f332(f332(f8(f883(x101662,f882(x101661,x101662)),f883(x101662,f883(f883(f882(x101661,x101662),a871),a871)),x101661),f332(f8(f882(x101661,x101662),f883(f883(f882(x101661,x101662),a871),a871),x101662),f334(f882(x101661,x101662)))),f267(x101661,x101662)))),x101664))) % 172.78/172.48 [9243]~P102(f332(f332(f334(f882(x92431,x92431)),x92432),f308(x92431,x92434)))+P102(f332(f332(f334(f882(x92431,x92431)),x92432),f308(x92431,f332(f332(f113(f883(f882(x92431,x92431),a871)),x92433),x92434)))) % 172.78/172.48 [9244]~P102(f332(f332(f334(f882(x92441,x92441)),x92442),f308(x92441,x92443)))+P102(f332(f332(f334(f882(x92441,x92441)),x92442),f308(x92441,f332(f332(f113(f883(f882(x92441,x92441),a871)),x92443),x92444)))) % 172.78/172.48 [9600]~E(f332(f173(x96001),x96004),f185(x96001,x96002,x96003))+E(f332(f179(x96001,x96002),f332(f332(f154(x96001,f882(x96001,x96002)),f332(f332(f18(x96001,x96002,f882(x96001,x96002)),f267(x96001,x96002)),f332(f332(f8(f880(x96002),x96002,x96001),f243(x96002)),x96003))),x96004)),x96003) % 172.78/172.48 [9922]~P102(f332(f332(f247(a876),f332(f332(f79(a876),x99221),x99224)),f332(f332(f79(a876),x99223),x99222)))+P102(f332(f332(f247(a1),f332(a88,f332(f286(f882(a876,a876),f882(a876,a876),a111),f332(f332(f310(f882(a876,a876)),f332(f332(f267(a876,a876),x99221),x99222)),f195(f883(f882(a876,a876),a871)))))),f332(a88,f332(f286(f882(a876,a876),f882(a876,a876),a111),f332(f332(f310(f882(a876,a876)),f332(f332(f267(a876,a876),x99223),x99224)),f195(f883(f882(a876,a876),a871))))))) % 172.78/172.48 [9923]~P102(f332(f332(f246(a876),f332(f332(f79(a876),x99231),x99234)),f332(f332(f79(a876),x99233),x99232)))+P102(f332(f332(f246(a1),f332(a88,f332(f286(f882(a876,a876),f882(a876,a876),a111),f332(f332(f310(f882(a876,a876)),f332(f332(f267(a876,a876),x99231),x99232)),f195(f883(f882(a876,a876),a871)))))),f332(a88,f332(f286(f882(a876,a876),f882(a876,a876),a111),f332(f332(f310(f882(a876,a876)),f332(f332(f267(a876,a876),x99233),x99234)),f195(f883(f882(a876,a876),a871))))))) % 172.78/172.48 [10000]P102(f332(f332(f247(a876),f332(f332(f79(a876),x100001),x100002)),f332(f332(f79(a876),x100003),x100004)))+~P102(f332(f332(f247(a1),f332(a88,f332(f286(f882(a876,a876),f882(a876,a876),a111),f332(f332(f310(f882(a876,a876)),f332(f332(f267(a876,a876),x100001),x100004)),f195(f883(f882(a876,a876),a871)))))),f332(a88,f332(f286(f882(a876,a876),f882(a876,a876),a111),f332(f332(f310(f882(a876,a876)),f332(f332(f267(a876,a876),x100003),x100002)),f195(f883(f882(a876,a876),a871))))))) % 172.78/172.48 [10001]P102(f332(f332(f246(a876),f332(f332(f79(a876),x100011),x100012)),f332(f332(f79(a876),x100013),x100014)))+~P102(f332(f332(f246(a1),f332(a88,f332(f286(f882(a876,a876),f882(a876,a876),a111),f332(f332(f310(f882(a876,a876)),f332(f332(f267(a876,a876),x100011),x100014)),f195(f883(f882(a876,a876),a871)))))),f332(a88,f332(f286(f882(a876,a876),f882(a876,a876),a111),f332(f332(f310(f882(a876,a876)),f332(f332(f267(a876,a876),x100013),x100012)),f195(f883(f882(a876,a876),a871))))))) % 172.78/172.48 [10043]P102(f332(f332(f246(f883(x100431,a871)),f332(f332(f41(a876,f883(x100431,a871)),f255(f883(a876,a871))),x100432)),f332(f332(f41(a876,f883(x100431,a871)),f255(f883(a876,a871))),x100433)))+~P102(f332(f332(f246(f883(x100431,a871)),f332(f332(f41(a876,f883(x100431,a871)),f332(f302(a876,f2(a876)),f455(x100433,x100434,x100432,x100431))),x100432)),f332(f332(f41(a876,f883(x100431,a871)),f332(f302(a876,f2(a876)),f332(f332(f79(a876),f455(x100433,x100434,x100432,x100431)),x100434))),x100433))) % 172.78/172.48 [10140]~P102(f332(f332(f334(x101402),x101404),f332(f263(x101401,x101402),x101403)))+P102(f332(f262(x101401,x101402,f332(f332(f7(x101401,f883(f882(x101401,x101402),a871),f883(x101402,a871)),f332(f332(f8(f883(x101402,f883(f883(f882(x101401,x101402),a871),a871)),f883(f883(f882(x101401,x101402),a871),f883(x101402,a871)),x101401),f7(x101402,f883(f882(x101401,x101402),a871),a871)),f332(f332(f8(f883(x101402,f882(x101401,x101402)),f883(x101402,f883(f883(f882(x101401,x101402),a871),a871)),x101401),f332(f8(f882(x101401,x101402),f883(f883(f882(x101401,x101402),a871),a871),x101402),f334(f882(x101401,x101402)))),f267(x101401,x101402)))),x101403)),x101404)) % 172.78/172.48 [10141]~P102(f332(f332(f334(x101411),x101414),f332(f265(x101411,x101412),x101413)))+P102(f332(f261(x101411,x101412,f332(f332(f7(x101411,f883(f882(x101411,x101412),a871),f883(x101412,a871)),f332(f332(f8(f883(x101412,f883(f883(f882(x101411,x101412),a871),a871)),f883(f883(f882(x101411,x101412),a871),f883(x101412,a871)),x101411),f7(x101412,f883(f882(x101411,x101412),a871),a871)),f332(f332(f8(f883(x101412,f882(x101411,x101412)),f883(x101412,f883(f883(f882(x101411,x101412),a871),a871)),x101411),f332(f8(f882(x101411,x101412),f883(f883(f882(x101411,x101412),a871),a871),x101412),f334(f882(x101411,x101412)))),f267(x101411,x101412)))),x101413)),x101414)) % 172.78/172.48 [10152]P102(f332(f332(f334(x101521),x101522),f332(f263(x101523,x101521),x101524)))+~P102(f332(f262(x101523,x101521,f332(f332(f7(x101523,f883(f882(x101523,x101521),a871),f883(x101521,a871)),f332(f332(f8(f883(x101521,f883(f883(f882(x101523,x101521),a871),a871)),f883(f883(f882(x101523,x101521),a871),f883(x101521,a871)),x101523),f7(x101521,f883(f882(x101523,x101521),a871),a871)),f332(f332(f8(f883(x101521,f882(x101523,x101521)),f883(x101521,f883(f883(f882(x101523,x101521),a871),a871)),x101523),f332(f8(f882(x101523,x101521),f883(f883(f882(x101523,x101521),a871),a871),x101521),f334(f882(x101523,x101521)))),f267(x101523,x101521)))),x101524)),x101522)) % 172.78/172.48 [10153]P102(f332(f332(f334(x101531),x101532),f332(f265(x101531,x101533),x101534)))+~P102(f332(f261(x101531,x101533,f332(f332(f7(x101531,f883(f882(x101531,x101533),a871),f883(x101533,a871)),f332(f332(f8(f883(x101533,f883(f883(f882(x101531,x101533),a871),a871)),f883(f883(f882(x101531,x101533),a871),f883(x101533,a871)),x101531),f7(x101533,f883(f882(x101531,x101533),a871),a871)),f332(f332(f8(f883(x101533,f882(x101531,x101533)),f883(x101533,f883(f883(f882(x101531,x101533),a871),a871)),x101531),f332(f8(f882(x101531,x101533),f883(f883(f882(x101531,x101533),a871),a871),x101533),f334(f882(x101531,x101533)))),f267(x101531,x101533)))),x101534)),x101532)) % 172.78/172.48 [9838]P102(f332(f160(x98381,x98382),x98383))+~P102(f332(f160(x98381,f332(f332(f18(x98381,a871,a871),f332(f332(f8(a871,f883(a871,a871),x98381),a330),x98384)),x98382)),x98383)) % 172.78/172.48 [9839]P102(f332(f160(x98391,x98392),x98393))+~P102(f332(f160(x98391,f332(f332(f18(x98391,a871,a871),f332(f332(f8(a871,f883(a871,a871),x98391),a330),x98392)),x98394)),x98393)) % 172.78/172.48 [9924]~P114(x99241)+E(f332(f332(f80(x99241),f332(f332(f79(x99241),f77(x99241)),f77(x99241))),f332(f332(f6(a876,x99241),f332(f332(f8(x99241,x99241,a876),f332(f79(x99241),x99242)),f332(f332(f7(a876,x99241,x99241),f332(f332(f8(x99241,f883(x99241,x99241),a876),f80(x99241)),f103(x99241))),x99243))),f332(f253(a876),x99244))),f332(f332(f80(x99241),f332(f103(x99241),x99244)),f332(f332(f79(x99241),x99242),f332(f332(f79(x99241),x99242),f332(f332(f80(x99241),f332(f103(x99241),f332(f332(f22(a876),x99244),f77(a876)))),x99243))))) % 172.78/172.48 [10065]P102(f332(x100651,f532(x100652,x100653,x100654,x100651)))+P38(x100652,f332(f252(f882(x100652,x100652)),f332(f271(x100652,x100652,a871),f332(f332(f8(f883(x100652,a871),f883(x100652,a871),x100652),f332(f18(x100652,a871,a871),f332(f332(f8(a871,f883(a871,a871),x100652),a330),x100651))),f332(f332(f7(x100652,f883(x100652,x100652),f883(x100652,a871)),f332(f332(f8(f883(x100652,a871),f883(f883(x100652,x100652),f883(x100652,a871)),x100652),f8(x100652,a871,x100652)),a329)),x100653))))) % 172.78/172.48 [10079]~P102(f332(f332(f247(a876),f332(x100794,f332(x100793,f532(x100791,x100793,x100794,x100792)))),f332(x100794,f532(x100791,x100793,x100794,x100792))))+P38(x100791,f332(f252(f882(x100791,x100791)),f332(f271(x100791,x100791,a871),f332(f332(f8(f883(x100791,a871),f883(x100791,a871),x100791),f332(f18(x100791,a871,a871),f332(f332(f8(a871,f883(a871,a871),x100791),a330),x100792))),f332(f332(f7(x100791,f883(x100791,x100791),f883(x100791,a871)),f332(f332(f8(f883(x100791,a871),f883(f883(x100791,x100791),f883(x100791,a871)),x100791),f8(x100791,a871,x100791)),a329)),x100793))))) % 172.78/172.48 [10179]~P102(f332(f332(f334(f882(x101791,x101791)),f332(f332(f267(x101791,x101791),x101793),x101794)),f332(f332(f113(f883(f882(x101791,x101791),a871)),x101792),f308(x101791,f195(f883(f882(x101791,x101791),a871))))))+P102(f332(f332(f332(f332(f113(f883(x101791,f883(x101791,a871))),f332(f332(f7(x101791,f883(f882(x101791,x101791),a871),f883(x101791,a871)),f332(f332(f8(f883(x101791,f883(f883(f882(x101791,x101791),a871),a871)),f883(f883(f882(x101791,x101791),a871),f883(x101791,a871)),x101791),f7(x101791,f883(f882(x101791,x101791),a871),a871)),f332(f332(f8(f883(x101791,f882(x101791,x101791)),f883(x101791,f883(f883(f882(x101791,x101791),a871),a871)),x101791),f332(f8(f882(x101791,x101791),f883(f883(f882(x101791,x101791),a871),a871),x101791),f334(f882(x101791,x101791)))),f267(x101791,x101791)))),x101792)),a329),x101793),x101794)) % 172.78/172.48 [10189]P102(f332(f332(f334(f882(x101891,x101891)),f332(f332(f267(x101891,x101891),x101892),x101893)),f332(f332(f113(f883(f882(x101891,x101891),a871)),x101894),f308(x101891,f195(f883(f882(x101891,x101891),a871))))))+~P102(f332(f332(f332(f332(f113(f883(x101891,f883(x101891,a871))),f332(f332(f7(x101891,f883(f882(x101891,x101891),a871),f883(x101891,a871)),f332(f332(f8(f883(x101891,f883(f883(f882(x101891,x101891),a871),a871)),f883(f883(f882(x101891,x101891),a871),f883(x101891,a871)),x101891),f7(x101891,f883(f882(x101891,x101891),a871),a871)),f332(f332(f8(f883(x101891,f882(x101891,x101891)),f883(x101891,f883(f883(f882(x101891,x101891),a871),a871)),x101891),f332(f8(f882(x101891,x101891),f883(f883(f882(x101891,x101891),a871),a871),x101891),f334(f882(x101891,x101891)))),f267(x101891,x101891)))),x101894)),a329),x101892),x101893)) % 172.78/172.48 [10051]~P106(x100513)+E(f89(x100511,f332(f332(f18(x100511,a871,a871),f332(f332(f8(a871,f883(a871,a871),x100511),a330),x100512)),f332(f332(f8(f883(x100511,a871),a871,x100511),f87(x100511)),f332(f332(f8(f883(x100511,a871),f883(x100511,a871),x100511),f332(f18(x100511,a871,a871),f332(f332(f8(a871,f883(a871,a871),x100511),a335),x100512))),f332(f332(f8(x100513,f883(x100511,a871),x100511),f332(f7(x100511,x100513,a871),f332(f332(f8(x100513,f883(x100513,a871),x100511),f246(x100513)),x100514))),x100514))))),f332(f92(x100511,x100513,x100514),x100512)) % 172.78/172.48 [10094]~P106(x100943)+E(f89(x100941,f332(f332(f18(x100941,a871,a871),f332(f332(f8(a871,f883(a871,a871),x100941),a330),x100942)),f332(f332(f8(f883(x100941,a871),a871,x100941),f87(x100941)),f332(f332(f8(f883(x100941,a871),f883(x100941,a871),x100941),f332(f18(x100941,a871,a871),f332(f332(f8(a871,f883(a871,a871),x100941),a335),x100942))),f332(f332(f7(x100941,f883(x100941,x100943),f883(x100941,a871)),f332(f332(f8(f883(x100943,a871),f883(f883(x100941,x100943),f883(x100941,a871)),x100941),f8(x100943,a871,x100941)),f332(f332(f8(x100943,f883(x100943,a871),x100941),f246(x100943)),x100944))),x100944))))),f95(x100941,x100943,x100944,x100942)) % 172.78/172.48 [10138]E(f332(f332(f151(f877(x101381)),f332(f332(f151(x101381),x101382),f332(f142(f877(x101381),f877(x101381),f134(x101381),f116(x101381)),f332(f332(f154(f877(x101381),f877(x101381)),f156(f877(x101381),x101381,f116(x101381),f332(f332(f8(f877(x101381),f883(f877(x101381),f877(x101381)),x101381),f16(f877(x101381),f877(x101381))),f332(f332(f7(x101381,f877(x101381),f877(x101381)),f151(x101381)),f116(x101381))))),x101383)))),f181(x101381,f332(f332(f151(f877(x101381)),x101384),f332(f142(f877(f877(x101381)),f877(f877(x101381)),f134(f877(x101381)),f116(f877(x101381))),f332(f332(f154(f877(x101381),f877(f877(x101381))),f156(f877(f877(x101381)),x101381,f116(f877(x101381)),f332(f16(f883(f877(x101381),f877(f877(x101381))),x101381),f332(f332(f7(f877(x101381),f877(f877(x101381)),f877(f877(x101381))),f151(f877(x101381))),f116(f877(x101381)))))),x101383))))),f181(x101381,f332(f332(f151(f877(x101381)),f332(f332(f151(x101381),x101382),x101384)),x101383)))+~P102(f332(f320(f877(f877(x101381)),f182(x101381)),f332(f332(f151(f877(x101381)),f332(f332(f151(x101381),x101382),x101384)),x101383))) % 172.78/172.48 [10178]~P102(f332(f61(x101782),f332(f252(x101782),x101784)))+P102(f332(f61(x101781),f332(f252(x101781),f332(f332(f8(f883(x101782,a871),a871,x101781),f86(x101782)),f332(f332(f7(x101781,f883(x101782,a871),f883(x101782,a871)),f332(f332(f8(f883(x101782,f883(a871,a871)),f883(f883(x101782,a871),f883(x101782,a871)),x101781),f18(x101782,a871,a871)),f332(f332(f8(f883(x101782,a871),f883(x101782,f883(a871,a871)),x101781),f332(f8(a871,f883(a871,a871),x101782),a330)),f332(f332(f7(x101781,f883(x101782,x101781),f883(x101782,a871)),f332(f332(f8(f883(x101781,a871),f883(f883(x101782,x101781),f883(x101782,a871)),x101781),f8(x101781,a871,x101782)),a329)),x101783)))),x101784))))) % 172.78/172.48 [5263]E(x52631,x52632)+~E(f127(x52633,x52634,x52631),f127(x52633,x52635,x52632)) % 172.78/172.48 [5264]E(x52641,x52642)+~E(f127(x52643,x52641,x52644),f127(x52643,x52642,x52645)) % 172.78/172.48 [5265]E(x52651,x52652)+~E(f170(x52653,x52651,x52654),f170(x52653,x52652,x52655)) % 172.78/172.48 [5646]E(f332(f332(f310(x56461),x56462),f185(x56461,x56463,x56464)),f185(x56461,x56463,x56464))+~E(f332(x56464,x56462),f332(f239(x56463),x56465)) % 172.78/172.48 [6052]P102(f332(f262(x60521,x60522,x60523),x60524))+~P102(f332(f332(x60523,x60525),x60524)) % 172.78/172.48 [6054]P102(f332(f261(x60541,x60542,x60543),x60544))+~P102(f332(f332(x60543,x60544),x60545)) % 172.78/172.48 [6057]~E(f332(x60574,x60572),f332(f239(x60573),x60575))+P102(f332(f332(f334(x60571),x60572),f185(x60571,x60573,x60574))) % 172.78/172.48 [6058]~E(f332(x60584,x60585),f332(f239(x60581),x60582))+P102(f332(f332(f334(x60581),x60582),f187(x60583,x60581,x60584))) % 172.78/172.48 [6517]~E(x65175,f2(a102))+E(f332(f207(x65171,x65172,x65173,x65174),x65175),f118(x65172)) % 172.78/172.48 [6518]~E(x65185,f2(a102))+E(f332(f205(x65181,x65182,x65183,x65184),x65185),f128(x65182)) % 172.78/172.48 [6654]~E(x66543,f2(a102))+E(f332(f281(x66541,x66542,x66543,x66544),x66545),f332(f267(x66541,x66542),x66545)) % 172.78/172.48 [6726]~E(f332(x67264,x67265),f208(x67262))+E(f332(f241(f880(x67261),x67262,f208(x67261),x67263),f332(x67264,x67265)),f208(x67261)) % 172.78/172.48 [7351]E(f332(x73511,x73512),f208(x73513))+~E(f332(f186(x73514,x73513,x73515,x73511),x73512),f208(x73513)) % 172.78/172.48 [7352]E(f332(x73521,x73522),f208(x73523))+~E(f332(f186(x73524,x73523,x73521,x73525),x73522),f208(x73523)) % 172.78/172.48 [7388]E(f332(f186(x73881,x73882,x73883,x73884),x73885),f332(x73883,x73885))+P102(f332(f332(f334(x73881),x73885),f185(x73881,x73882,x73884))) % 172.78/172.48 [7389]E(f332(f186(x73891,x73892,x73893,x73894),x73895),f332(x73894,x73895))+P102(f332(f332(f334(x73891),x73895),f185(x73891,x73892,x73893))) % 172.78/172.48 [7713]~P15(x77134,x77131,x77132,x77135)+E(f332(f72(x77131,x77131,x77131,f332(x77132,x77133)),f332(x77132,x77133)),f332(x77132,x77133)) % 172.78/172.48 [7759]E(f332(f186(x77591,x77592,x77593,x77594),x77595),f332(x77594,x77595))+~P102(f332(f332(f334(x77591),x77595),f185(x77591,x77592,x77594))) % 172.78/172.48 [8111]~P11(x81115,x81111,x81112)+E(f332(f72(x81111,x81111,x81111,f332(x81112,x81113)),f332(x81112,x81114)),f332(f72(x81111,x81111,x81111,f332(x81112,x81114)),f332(x81112,x81113))) % 172.78/172.48 [8443]P102(f332(f332(f334(f882(x84431,x84431)),f332(f332(f267(x84431,x84431),x84432),x84433)),f326(x84431,x84434,x84435)))+~P102(f332(f332(f247(a876),f332(x84434,x84432)),f332(x84434,x84433))) % 172.78/172.48 [8540]~P102(f332(f332(f334(x85404),x85403),f296(x85404,x85401,x85402,x85405)))+P102(f332(f332(x85401,x85402),x85403)) % 172.78/172.48 [8541]~P102(f332(f332(f334(x85414),x85413),f299(x85414,x85411,x85412,x85415)))+P102(f332(f332(x85411,x85412),x85413)) % 172.78/172.48 [8542]~P102(f332(f332(f334(x85424),x85422),f296(x85424,x85421,x85425,x85423)))+P102(f332(f332(x85421,x85422),x85423)) % 172.78/172.48 [8543]~P102(f332(f332(f334(x85434),x85432),f299(x85434,x85431,x85435,x85433)))+P102(f332(f332(x85431,x85432),x85433)) % 172.78/172.48 [8680]~P52(x86802,x86801,x86805,x86803,x86804)+E(f332(f311(x86801,x86802,x86803),x86804),f255(f883(x86802,a871))) % 172.78/172.48 [9120]~P35(x91201,x91202,x91203,x91204,x91205)+P35(x91201,x91202,x91203,f332(f169(x91201),x91204),f332(f169(x91202),x91205)) % 172.78/172.48 [9122]~P35(x91221,x91222,x91223,f332(f169(x91221),x91224),x91225)+P35(x91221,x91222,x91223,x91224,f332(f169(x91222),x91225)) % 172.78/172.48 [9123]~P35(x91231,x91232,x91233,x91234,f332(f169(x91232),x91235))+P35(x91231,x91232,x91233,f332(f169(x91231),x91234),x91235) % 172.78/172.48 [9129]P35(x91291,x91292,x91293,x91294,x91295)+~P35(x91291,x91292,x91293,f332(f169(x91291),x91294),f332(f169(x91292),x91295)) % 172.78/172.48 [9524]P102(f332(f332(f334(f882(f877(x95241),f877(x95241))),f332(f332(f267(f877(x95241),f877(x95241)),f332(f332(f151(x95241),x95242),x95243)),f332(f332(f151(x95241),x95242),x95244))),f157(x95241,x95245)))+~P102(f332(f332(f334(f882(f877(x95241),f877(x95241))),f332(f332(f267(f877(x95241),f877(x95241)),x95243),x95244)),f157(x95241,x95245))) % 172.78/172.48 [9525]P102(f332(f332(f334(f882(f877(x95251),f877(x95251))),f332(f332(f267(f877(x95251),f877(x95251)),f332(f332(f134(x95251),x95252),x95253)),f332(f332(f134(x95251),x95252),x95254))),f147(x95251,x95255)))+~P102(f332(f332(f334(f882(f877(x95251),f877(x95251))),f332(f332(f267(f877(x95251),f877(x95251)),x95253),x95254)),f147(x95251,x95255))) % 172.78/172.48 [9714]E(f332(f332(f151(x97141),f674(x97142,x97143,x97144,x97145,x97141)),f677(x97142,x97143,x97144,x97145,x97141)),x97145)+~P102(f332(f332(f334(f882(f877(x97141),f877(x97141))),f332(f332(f267(f877(x97141),f877(x97141)),x97145),f332(f332(f151(x97141),x97144),x97143))),f158(x97141,x97142))) % 172.78/172.48 [9736]E(f332(f332(f151(x97361),f675(x97362,x97363,x97364,x97365,x97361)),f676(x97362,x97363,x97364,x97365,x97361)),x97363)+~P102(f332(f332(f334(f882(f877(x97361),f877(x97361))),f332(f332(f267(f877(x97361),f877(x97361)),f332(f332(f151(x97361),x97365),x97364)),x97363)),f158(x97361,x97362))) % 172.78/172.48 [9898]~P102(f332(f332(f334(f882(f877(x98981),f877(x98981))),f332(f332(f267(f877(x98981),f877(x98981)),f332(f332(f151(x98981),x98985),x98982)),x98984)),f158(x98981,x98983)))+P102(f332(f332(f334(f882(f877(x98981),f877(x98981))),f332(f332(f267(f877(x98981),f877(x98981)),x98982),f676(x98983,x98984,x98982,x98985,x98981))),f158(x98981,x98983))) % 172.78/172.48 [9968]~P102(f332(f332(f334(f882(f877(x99681),f877(x99681))),f332(f332(f267(f877(x99681),f877(x99681)),x99685),f332(f332(f151(x99681),x99684),x99683))),f158(x99681,x99682)))+P102(f332(f332(f334(f882(f877(x99681),f877(x99681))),f332(f332(f267(f877(x99681),f877(x99681)),f677(x99682,x99683,x99684,x99685,x99681)),x99683)),f158(x99681,x99682))) % 172.78/172.48 [10133]P102(f332(f332(f334(f882(x101331,x101331)),f332(f332(f267(x101331,x101331),f332(x101332,f332(f332(f79(a876),x101333),x101334))),f332(x101332,x101333))),f308(x101331,x101335)))+~P102(f332(f332(f334(f882(x101331,x101331)),f332(f332(f267(x101331,x101331),f332(x101332,f332(a115,f593(x101334,x101333,x101335,x101332,x101331)))),f332(x101332,f593(x101334,x101333,x101335,x101332,x101331)))),f308(x101331,x101335))) % 172.78/172.48 [5229]E(x52291,x52292)+~E(f332(f332(f151(x52293),x52294),x52291),f332(f332(f151(x52293),x52295),x52292)) % 172.78/172.48 [5230]E(x52301,x52302)+~E(f332(f332(f151(x52303),x52301),x52304),f332(f332(f151(x52303),x52302),x52305)) % 172.78/172.48 [5281]P102(f332(x52811,x52812))+~E(f332(f136(x52813,x52811),x52814),f332(f332(f151(x52813),x52812),x52815)) % 172.78/172.48 [5282]P102(f332(x52821,x52822))+~E(f332(f332(f151(x52823),x52822),x52824),f332(f136(x52823,x52821),x52825)) % 172.78/172.48 [5441]~E(f332(f332(f138(x54411),x54413),x54412),f332(f332(f151(x54411),x54414),x54415))+E(f332(f332(f165(x54411),x54412),x54413),x54414) % 172.78/172.48 [5576]~P10(x55764,x55765,x55761)+E(f332(f332(x55761,x55762),f332(f332(x55761,x55762),x55763)),f332(f332(x55761,x55762),x55763)) % 172.78/172.48 [6110]~E(x61104,f2(a102))+E(f332(f332(f120(x61101,x61102,x61103),x61104),x61105),f332(f332(f267(f877(x61102),x61101),f116(x61102)),x61105)) % 172.78/172.48 [6177]~P104(x61772)+~E(f332(f332(f148(x61771,x61772,x61773),x61774),x61775),f116(x61771)) % 172.78/172.48 [6554]E(x65541,x65542)+~E(f332(f332(f134(x65543),x65544),f332(f332(f151(x65543),x65541),f116(x65543))),f332(f332(f134(x65543),x65545),f332(f332(f151(x65543),x65542),f116(x65543)))) % 172.78/172.48 [6555]E(x65551,x65552)+~E(f332(f332(f134(x65553),x65551),f332(f332(f151(x65553),x65554),f116(x65553))),f332(f332(f134(x65553),x65552),f332(f332(f151(x65553),x65555),f116(x65553)))) % 172.78/172.48 [6810]E(f332(f189(x68101,x68102,x68103,x68104),x68105),f208(x68102))+P102(f332(f332(f334(x68101),x68105),x68104)) % 172.78/172.48 [6872]E(f332(f332(f310(x68721),f332(x68722,x68723)),f332(f311(x68724,x68721,x68722),x68725)),f332(f311(x68724,x68721,x68722),x68725))+~P102(f332(f332(f334(x68724),x68723),x68725)) % 172.78/172.48 [6879]~P102(f332(x68794,f332(x68793,x68795)))+P102(f332(f332(f312(x68791,x68792,x68793),x68794),x68795)) % 172.78/172.48 [6882]~P102(f332(f332(x68823,x68825),x68824))+P102(f332(f332(f256(x68821,x68822,x68823),x68824),x68825)) % 172.78/172.48 [6977]~E(f332(f311(x69771,x69772,x69773),x69774),x69775)+E(f332(f311(f883(x69771,a871),f883(x69772,a871),f311(x69771,x69772,x69773)),f332(f309(x69771),x69774)),f332(f309(x69772),x69775)) % 172.78/172.48 [7009]E(f332(f189(x70091,x70092,x70093,x70094),x70095),f332(x70093,x70095))+~P102(f332(f332(f334(x70091),x70095),x70094)) % 172.78/172.48 [7308]P20(x73081,x73082,x73083,x73084)+~P20(x73081,x73082,x73083,f332(f332(f310(x73081),x73085),x73084)) % 172.78/172.48 [7378]P102(f332(x73781,x73782))+~P102(f332(f332(f94(x73783,x73784,x73781),x73785),x73782)) % 172.78/172.48 [7422]~P102(f332(f332(f334(x74224),x74223),x74225))+P102(f332(f332(f334(x74221),f332(x74222,x74223)),f332(f311(x74224,x74221,x74222),x74225))) % 172.78/172.48 [7446]~P104(x74462)+E(f150(x74461,x74462,x74463,f332(f136(x74461,x74464),x74465)),f332(f136(x74461,x74464),f150(x74461,x74462,x74463,x74465))) % 172.78/172.48 [7479]P102(f332(x74791,f332(x74792,x74793)))+~P102(f332(f332(f312(x74794,x74795,x74792),x74791),x74793)) % 172.78/172.48 [7482]P102(f332(f332(x74821,x74822),x74823))+~P102(f332(f332(f256(x74824,x74825,x74821),x74823),x74822)) % 172.78/172.48 [7483]P102(f332(f332(x74831,x74832),x74833))+~P102(f332(f332(f94(x74834,x74831,x74835),x74832),x74833)) % 172.78/172.48 [7547]~P102(f332(f332(f334(x75473),f332(x75474,x75472)),x75475))+P102(f332(f332(f334(x75471),x75472),f332(f312(x75471,x75473,x75474),x75475))) % 172.78/172.48 [7948]~P102(f332(f332(f334(x79485),x79483),f332(f312(x79485,x79481,x79482),x79484)))+P102(f332(f332(f334(x79481),f332(x79482,x79483)),x79484)) % 172.78/172.48 [8178]~E(x81783,f332(f332(f332(f71(x81781,f880(x81782)),f332(f16(f880(x81782),x81781),f208(x81782))),x81784),f332(f239(x81782),x81785)))+E(f185(x81781,x81782,x81783),f332(f332(f310(x81781),x81784),f195(f883(x81781,a871)))) % 172.78/172.48 [8258]~P11(x82582,x82581,x82583)+E(f332(f142(x82581,x82582,f332(f7(x82582,x82581,x82581),x82583),x82584),f152(x82582,x82585)),f332(f332(f64(x82582,x82581,x82583),x82584),f332(f173(x82582),x82585))) % 172.78/172.48 [8277]E(f332(x82771,f486(x82772,x82771,x82773,x82774)),x82774)+~P102(f332(f332(f334(x82775),x82774),f332(f311(x82773,x82775,x82771),x82772))) % 172.78/172.48 [8585]~E(x85852,f332(f332(f151(x85851),x85854),x85855))+P102(f332(f332(f334(f882(f877(x85851),f877(x85851))),f332(f332(f267(f877(x85851),f877(x85851)),f116(x85851)),x85852)),f147(x85851,x85853))) % 172.78/172.48 [8638]~P35(x86381,x86383,x86385,x86382,x86384)+E(f332(f196(f877(x86381)),x86382),f332(f196(f877(x86383)),x86384)) % 172.78/172.48 [8648]P102(f332(f332(f246(f883(x86481,a871)),f332(f332(f42(x86482,f883(x86481,a871)),x86483),x86484)),f332(x86484,x86485)))+~P102(f332(f332(f334(x86482),x86485),x86483)) % 172.78/172.48 [8696]~P52(x86961,x86962,x86963,x86965,x86964)+E(f332(f311(x86961,x86962,x86963),f255(f883(x86961,a871))),x86964) % 172.78/172.48 [8902]E(f332(f332(f332(f71(x89021,f880(x89022)),f189(x89021,x89022,x89023,x89024)),x89025),f208(x89022)),f189(x89021,x89022,x89023,x89024))+P102(f332(f332(f334(x89021),x89025),x89024)) % 172.78/172.48 [8907]E(f332(f136(x89071,x89072),f783(x89073,x89074,x89075,x89072,x89071)),x89073)+~E(f332(f136(x89071,x89072),x89075),f332(f332(f151(x89071),x89074),x89073)) % 172.78/172.48 [8908]E(f332(f136(x89081,x89082),f788(x89083,x89082,x89084,x89085,x89081)),x89084)+~E(f332(f332(f151(x89081),x89085),x89084),f332(f136(x89081,x89082),x89083)) % 172.78/172.48 [8909]E(f332(x89091,f711(x89092,x89093,x89091,x89094,x89095)),x89092)+~E(f332(f332(f209(x89095,x89094),x89091),x89093),f332(f239(x89094),x89092)) % 172.78/172.48 [8913]E(f332(f239(x89131),f711(x89132,x89133,x89134,x89135,x89131)),x89133)+~E(f332(f332(f209(x89131,x89135),x89134),x89133),f332(f239(x89135),x89132)) % 172.78/172.48 [9012]E(f332(f196(f877(x90121)),x90122),x90123)+~P102(f332(f332(f334(f882(f877(x90121),f877(x90121))),f332(f332(f267(f877(x90121),f877(x90121)),x90124),x90122)),f332(f143(x90121,x90125),x90123))) % 172.78/172.48 [9013]E(f332(f196(f877(x90131)),x90132),x90133)+~P102(f332(f332(f334(f882(f877(x90131),f877(x90131))),f332(f332(f267(f877(x90131),f877(x90131)),x90132),x90134)),f332(f143(x90131,x90135),x90133))) % 172.78/172.48 [9080]P102(f332(f332(f334(x90801),f486(x90802,x90803,x90801,x90804)),x90802))+~P102(f332(f332(f334(x90805),x90804),f332(f311(x90801,x90805,x90803),x90802))) % 172.78/172.48 [9241]E(f332(f311(x92411,x92412,x92413),f835(x92414,x92413,x92411,x92415,x92412)),x92415)+~P102(f332(f332(f246(f883(x92412,a871)),x92415),f332(f311(x92411,x92412,x92413),x92414))) % 172.78/172.48 [9494]E(f332(x94941,f772(x94942,x94941,x94943,x94944,x94945)),f332(f239(x94945),x94944))+~P102(f332(f332(f334(x94945),x94944),f187(x94943,x94945,f189(x94943,x94945,x94941,x94942)))) % 172.78/172.48 [9540]P102(f332(f332(f334(f882(f877(x95401),f877(x95401))),f332(f332(f267(f877(x95401),f877(x95401)),f332(f332(f151(x95401),x95402),x95403)),f332(f332(f151(x95401),x95402),x95404))),f308(f877(x95401),f157(x95401,x95405))))+~P102(f332(f332(f334(f882(f877(x95401),f877(x95401))),f332(f332(f267(f877(x95401),f877(x95401)),x95403),x95404)),f308(f877(x95401),f157(x95401,x95405)))) % 172.78/172.48 [9571]~E(f332(x95713,f713(x95715,x95714,x95713,x95712,x95711)),f332(x95715,f713(x95715,x95714,x95713,x95712,x95711)))+E(f332(f332(f154(x95711,x95712),x95713),x95714),f332(f332(f154(x95711,x95712),x95715),x95714)) % 172.78/172.48 [9647]~E(f332(f136(x96471,x96475),x96474),f332(f332(f151(x96471),x96473),x96472))+E(f332(f332(f134(x96471),f784(x96472,x96473,x96474,x96475,x96471)),f332(f332(f151(x96471),x96473),f783(x96472,x96473,x96474,x96475,x96471))),x96474) % 172.78/172.48 [9648]~E(f332(f332(f151(x96481),x96485),x96484),f332(f136(x96481,x96483),x96482))+E(f332(f332(f134(x96481),f789(x96482,x96483,x96484,x96485,x96481)),f332(f332(f151(x96481),x96485),f788(x96482,x96483,x96484,x96485,x96481))),x96482) % 172.78/172.48 [9652]E(f332(f332(f154(x96521,x96522),x96523),x96524),f332(f332(f154(x96521,x96522),x96525),x96524))+P102(f332(f332(f334(x96521),f713(x96523,x96524,x96525,x96522,x96521)),f332(f173(x96521),x96524))) % 172.78/172.48 [9682]~P102(f332(f332(f334(x96825),x96824),f332(f286(x96821,x96825,x96823),x96822)))+P102(f332(f332(f334(x96821),f500(x96822,x96823,x96821,x96824,x96825)),x96822)) % 172.78/172.48 [9683]~P102(f332(f332(f334(x96835),x96834),f332(f286(x96831,x96835,x96833),x96832)))+P102(f332(f332(f334(x96831),f504(x96832,x96833,x96831,x96834,x96835)),x96832)) % 172.78/172.48 [9708]~P102(f332(f332(f246(f883(x97085,a871)),x97084),f332(f311(x97081,x97085,x97083),x97082)))+P102(f332(f332(f246(f883(x97081,a871)),f835(x97082,x97083,x97081,x97084,x97085)),x97082)) % 172.78/172.48 [9759]~P102(f332(f332(f334(x97595),x97594),f187(x97591,x97595,f189(x97591,x97595,x97593,x97592))))+P102(f332(f332(f334(x97591),f772(x97592,x97593,x97591,x97594,x97595)),x97592)) % 172.78/172.48 [10155]E(x101551,f2(a102))+E(f332(f241(f882(f877(x101552),x101553),f882(x101552,x101553),f332(f332(f267(f877(x101552),x101553),f116(x101552)),x101554),f332(f271(x101552,x101553,f882(f877(x101552),x101553)),f332(f332(f7(x101552,f883(x101553,f882(f877(x101552),x101553)),f883(x101553,f882(f877(x101552),x101553))),f332(f332(f8(f883(f882(f877(x101552),x101553),f882(f877(x101552),x101553)),f883(f883(x101553,f882(f877(x101552),x101553)),f883(x101553,f882(f877(x101552),x101553))),x101552),f8(f882(f877(x101552),x101553),f882(f877(x101552),x101553),x101553)),f332(f332(f8(f883(f877(x101552),f883(x101553,f882(f877(x101552),x101553))),f883(f882(f877(x101552),x101553),f882(f877(x101552),x101553)),x101552),f271(f877(x101552),x101553,f882(f877(x101552),x101553))),f332(f332(f8(f883(f877(x101552),f877(x101552)),f883(f877(x101552),f883(x101553,f882(f877(x101552),x101553))),x101552),f332(f8(f877(x101552),f883(x101553,f882(f877(x101552),x101553)),f877(x101552)),f267(f877(x101552),x101553))),f151(x101552))))),f332(f120(x101553,x101552,x101555),f332(f332(f22(a102),x101551),f77(a102)))))),f332(x101555,x101554)),f332(f332(f120(x101553,x101552,x101555),x101551),x101554)) % 172.78/172.48 [5454]~E(f332(x54543,x54544),x54545)+E(f332(f332(f332(f71(x54541,x54542),x54543),x54544),x54545),x54543) % 172.78/172.48 [5897]E(f332(x58971,x58972),x58973)+~E(f332(f332(f332(f71(x58974,x58975),x58971),x58972),x58973),x58971) % 172.78/172.48 [5991]E(x59911,x59912)+~E(f332(f270(x59913,x59914),f332(f332(f267(x59913,x59914),x59915),x59911)),x59912) % 172.78/172.48 [5992]E(x59921,x59922)+~E(f332(f266(x59923,x59924),f332(f332(f267(x59923,x59924),x59921),x59925)),x59922) % 172.78/172.48 [6252]~E(x62523,f332(f332(f134(x62521),x62524),f332(f332(f151(x62521),x62522),x62525)))+P102(f332(f332(f334(x62521),x62522),f332(f173(x62521),x62523))) % 172.78/172.48 [6641]E(f332(f311(x66411,x66412,f332(f16(x66412,x66411),x66413)),x66414),f332(f332(f310(x66412),x66413),f195(f883(x66412,a871))))+~P102(f332(f332(f334(x66411),x66415),x66414)) % 172.78/172.48 [6711]E(f332(f332(f113(f883(x67111,a871)),f332(f173(x67111),x67112)),f332(f173(x67111),x67113)),f332(f173(x67111),x67114))+~E(f167(x67111,x67115,x67114),f332(f332(f267(f877(x67111),f877(x67111)),x67112),x67113)) % 172.78/172.48 [6814]~P104(x68142)+E(f332(f196(f877(x68141)),f332(f332(f148(x68141,x68142,x68143),x68144),x68145)),f332(a115,f332(f196(f877(x68141)),x68145))) % 172.78/172.48 [6826]~P104(x68262)+E(f332(f173(x68261),f332(f332(f148(x68261,x68262,x68263),x68264),x68265)),f332(f332(f310(x68261),x68264),f332(f173(x68261),x68265))) % 172.78/172.48 [7100]~P114(x71001)+E(f332(f332(f80(x71001),f332(f332(f80(x71001),x71002),x71003)),f332(f332(f80(x71001),x71004),x71005)),f332(f332(f80(x71001),f332(f332(f80(x71001),x71002),x71004)),f332(f332(f80(x71001),x71003),x71005))) % 172.78/172.48 [7101]~P114(x71011)+E(f332(f332(f79(x71011),f332(f332(f79(x71011),x71012),x71013)),f332(f332(f79(x71011),x71014),x71015)),f332(f332(f79(x71011),f332(f332(f79(x71011),x71012),x71014)),f332(f332(f79(x71011),x71013),x71015))) % 172.78/172.48 [7102]~P57(x71021)+E(f332(f332(f290(x71021),f332(f332(f80(x71021),x71022),x71023)),f332(f332(f80(x71021),x71024),x71025)),f332(f332(f80(x71021),f332(f332(f290(x71021),x71022),x71024)),f332(f332(f290(x71021),x71023),x71025))) % 172.78/172.48 [7116]~P104(x71161)+E(f303(x71161,f332(f332(f245(x71161),x71162),x71163),f332(f332(f244(x71161),x71164),x71165)),f332(f332(f104(f883(x71161,a871)),f303(x71161,x71162,x71164)),f303(x71161,x71163,x71165))) % 172.78/172.48 [7117]~P104(x71171)+E(f306(x71171,f332(f332(f245(x71171),x71172),x71173),f332(f332(f244(x71171),x71174),x71175)),f332(f332(f104(f883(x71171,a871)),f306(x71171,x71172,x71174)),f306(x71171,x71173,x71175))) % 172.78/172.48 [7118]~P104(x71181)+E(f305(x71181,f332(f332(f245(x71181),x71182),x71183),f332(f332(f244(x71181),x71184),x71185)),f332(f332(f104(f883(x71181,a871)),f305(x71181,x71182,x71184)),f305(x71181,x71183,x71185))) % 172.78/172.48 [7119]~P104(x71191)+E(f332(f332(f104(f883(x71191,a871)),f332(f302(x71191,x71192),x71193)),f332(f302(x71191,x71194),x71195)),f332(f302(x71191,f332(f332(f245(x71191),x71192),x71194)),f332(f332(f244(x71191),x71193),x71195))) % 172.78/172.48 [7234]~P102(f332(x72341,f485(x72343,x72342,x72341)))+P102(f332(x72341,f332(f332(f267(x72342,x72343),x72344),x72345))) % 172.78/172.48 [7321]~E(f332(x73213,x73214),f208(x73212))+E(f187(x73211,x73212,f332(f332(f332(f71(x73211,f880(x73212)),x73213),x73214),f332(f239(x73212),x73215))),f332(f332(f310(x73212),x73215),f187(x73211,x73212,x73213))) % 172.78/172.48 [7342]~E(x73422,f332(x73424,x73425))+P102(f332(f332(f334(x73421),x73422),f332(f311(x73423,x73421,x73424),f255(f883(x73423,a871))))) % 172.78/172.48 [7400]~E(f332(x74003,x74004),f208(x74002))+E(f332(f332(f22(f883(x74001,a871)),f185(x74001,x74002,x74003)),f332(f332(f310(x74001),x74004),x74005)),f332(f332(f22(f883(x74001,a871)),f185(x74001,x74002,x74003)),x74005)) % 172.78/172.48 [7419]~P10(x74193,x74192,x74194)+P10(x74191,x74192,f332(f332(f8(x74193,f883(x74192,x74192),x74191),x74194),x74195)) % 172.78/172.48 [7420]~P11(x74203,x74202,x74204)+P11(x74201,x74202,f332(f332(f8(x74203,f883(x74202,x74202),x74201),x74204),x74205)) % 172.78/172.48 [7563]~P20(x75631,x75632,x75633,x75634)+P20(x75631,x75632,x75633,f332(f332(f22(f883(x75631,a871)),x75634),x75635)) % 172.78/172.48 [7722]~P102(f332(f332(x77223,x77224),x77225))+P102(f332(f332(f271(x77221,x77222,a871),x77223),f332(f332(f267(x77221,x77222),x77224),x77225))) % 172.78/172.48 [7837]~P102(f332(x78372,x78374))+~E(f332(f332(f138(x78371),f332(f196(f877(x78371)),f178(x78371,x78372,x78373))),x78373),f332(f332(f151(x78371),x78374),x78375)) % 172.78/172.48 [7857]P20(x78571,x78572,x78573,x78574)+~P20(x78571,x78572,x78573,f332(f332(f113(f883(x78571,a871)),x78575),x78574)) % 172.78/172.48 [7858]P20(x78581,x78582,x78583,x78584)+~P20(x78581,x78582,x78583,f332(f332(f113(f883(x78581,a871)),x78584),x78585)) % 172.78/172.48 [7905]~P104(x79052)+E(f332(f332(f148(x79051,x79052,x79053),x79054),f150(x79051,x79052,x79053,x79055)),f150(x79051,x79052,x79053,f332(f332(f151(x79051),x79054),x79055))) % 172.78/172.48 [8070]~P30(x80701,f332(a115,x80702),f332(f332(f332(f91(x80701),x80703),f332(a25,x80704)),x80705))+P30(x80701,x80702,f332(f332(f332(f91(x80701),x80703),f332(f243(a873),f332(a27,x80704))),x80705)) % 172.78/172.48 [8205]P30(x82051,f332(a115,x82052),f332(f332(f332(f91(x82051),x82053),f332(a25,x82054)),x82055))+~P30(x82051,x82052,f332(f332(f332(f91(x82051),x82053),f332(f243(a873),f332(a27,x82054))),x82055)) % 172.78/172.48 [8234]~P10(x82342,x82341,x82343)+E(f332(f142(x82341,x82342,f332(f7(x82342,x82341,x82341),x82343),x82344),x82345),f332(f332(f64(x82342,x82341,x82343),x82344),f332(f173(x82342),x82345))) % 172.78/172.48 [8263]~E(f332(f332(f138(x82631),f332(f196(f877(x82631)),f178(x82631,x82632,x82633))),x82633),f332(f332(f151(x82631),x82634),x82635))+E(f332(f332(f134(x82631),f178(x82631,x82632,x82633)),f332(f332(f151(x82631),x82634),x82635)),x82633) % 172.78/172.48 [8287]P102(f332(f332(x82871,x82872),x82873))+~P102(f332(f332(f271(x82874,x82875,a871),x82871),f332(f332(f267(x82874,x82875),x82872),x82873))) % 172.78/172.48 [8350]~E(f332(f332(f179(x83501,x83502),x83505),x83503),f332(f239(x83502),x83504))+P102(f332(f332(f334(f882(x83501,x83502)),f332(f332(f267(x83501,x83502),x83503),x83504)),f332(f173(f882(x83501,x83502)),x83505))) % 172.78/172.48 [8751]P102(f332(f332(f246(f883(x87511,a871)),f332(f311(x87512,x87511,x87513),x87514)),f332(f311(x87512,x87511,x87513),x87515)))+~P102(f332(f332(f246(f883(x87512,a871)),x87514),x87515)) % 172.78/172.48 [8752]P102(f332(f332(f246(f883(x87521,a871)),f332(f312(x87521,x87522,x87523),x87524)),f332(f312(x87521,x87522,x87523),x87525)))+~P102(f332(f332(f246(f883(x87522,a871)),x87524),x87525)) % 172.78/172.48 [8828]E(x88281,f2(a102))+E(f332(f332(f273(x88282,x88283,x88282,f882(x88283,x88282)),f332(x88284,x88285)),f281(x88283,x88282,f332(f332(f22(a102),x88281),f77(a102)),x88284)),f332(f281(x88283,x88282,x88281,x88284),x88285)) % 172.78/172.48 [9150]P30(x91501,x91502,f332(f332(f332(f91(x91501),x91503),x91504),x91505))+P102(f332(f332(x91503,f608(x91505,x91504,x91503,x91502)),f627(x91505,x91504,x91503,x91502))) % 172.78/172.48 [9350]E(f332(f239(x93501),f716(x93502,x93503,x93504,x93501,x93505)),f332(f332(f179(x93505,x93501),x93502),x93504))+~P102(f332(f332(f334(f882(x93505,x93501)),f332(f332(f267(x93505,x93501),x93504),x93503)),f332(f173(f882(x93505,x93501)),x93502))) % 172.78/172.48 [9395]P30(x93951,x93952,f332(f332(f332(f91(x93951),x93953),x93954),x93955))+~P102(f332(f332(x93955,f608(x93955,x93954,x93953,x93952)),f639(x93955,x93954,x93953,x93952))) % 172.78/172.48 [9454]P30(x94541,x94542,f332(f332(f332(f91(x94541),x94543),x94544),x94545))+P102(f332(f332(f332(f332(a203,x94544),f627(x94545,x94544,x94543,x94542)),x94542),f639(x94545,x94544,x94543,x94542))) % 172.78/172.48 [9457]~P19(x94571,x94572,f332(f332(f310(f875(x94571)),f332(f332(f332(f91(x94571),x94573),f332(f243(a873),f332(a27,x94574))),x94575)),f195(f883(f875(x94571),a871))))+P19(x94571,x94572,f332(f332(f310(f875(x94571)),f332(f332(f332(f91(x94571),x94573),f332(a25,x94574)),x94575)),f195(f883(f875(x94571),a871)))) % 172.78/172.48 [9485]~P102(f332(f61(x94853),f332(f311(x94852,x94853,x94855),f255(f883(x94852,a871)))))+P102(f332(f61(x94851),f332(f311(x94852,x94851,f332(f332(f8(x94853,x94851,x94852),x94854),x94855)),f255(f883(x94852,a871))))) % 172.78/172.48 [9507]P102(f332(f332(f246(f883(f883(x95071,a871),a871)),f332(f311(f883(x95072,a871),f883(x95071,a871),f311(x95072,x95071,x95073)),f332(f309(x95072),x95074))),f332(f309(x95071),x95075)))+~P102(f332(f332(f246(f883(x95071,a871)),f332(f311(x95072,x95071,x95073),x95074)),x95075)) % 172.78/172.48 [9520]~P102(f332(f61(f880(x95201)),f332(f311(x95202,f880(x95201),x95203),f255(f883(x95202,a871)))))+P102(f332(f61(f880(x95201)),f332(f311(x95202,f880(x95201),f332(f332(f332(f71(x95202,f880(x95201)),x95203),x95204),f332(f239(x95201),x95205))),f255(f883(x95202,a871))))) % 172.78/172.48 [9580]E(x95801,x95802)+~P102(f332(f66(x95803,x95804,x95805,x95801,f195(f883(x95803,a871))),x95802)) % 172.78/172.48 [9595]E(f332(f332(f267(x95951,x95952),f546(x95953,x95954,x95955,x95952,x95951)),f548(x95953,x95954,x95955,x95952,x95951)),x95955)+~P102(f332(f332(f334(f882(x95951,x95952)),x95955),f332(f332(f269(x95951,x95952),x95954),x95953))) % 172.78/172.48 [9687]P102(f332(f332(f334(x96871),f546(x96872,x96873,x96874,x96875,x96871)),x96873))+~P102(f332(f332(f334(f882(x96871,x96875)),x96874),f332(f332(f269(x96871,x96875),x96873),x96872))) % 172.78/172.48 [9795]P19(x97955,x97954,f332(f332(f310(f875(x97955)),f332(f332(f332(f91(x97955),x97951),x97953),x97952)),f195(f883(f875(x97955),a871))))+P102(f332(f332(x97951,f560(x97952,x97953,x97954,x97955,x97951)),f672(x97952,x97953,x97954,x97955,x97951))) % 172.78/172.48 [9846]P102(f332(f332(f334(x98461),f548(x98462,x98463,x98464,x98461,x98465)),f332(x98462,f546(x98462,x98463,x98464,x98461,x98465))))+~P102(f332(f332(f334(f882(x98465,x98461)),x98464),f332(f332(f269(x98465,x98461),x98463),x98462))) % 172.78/172.48 [9874]P102(f332(f332(f334(f882(x98741,x98741)),f332(f332(f267(x98741,x98741),x98742),f618(x98743,x98744,x98745,x98742,x98741))),x98743))+~P102(f332(f332(f334(f882(x98741,x98741)),f332(f332(f267(x98741,x98741),x98742),x98745)),f332(f332(f190(f882(x98741,x98741),a871),f332(a115,x98744)),x98743))) % 172.78/172.48 [9875]P102(f332(f332(f334(f882(x98751,x98751)),f332(f332(f267(x98751,x98751),x98752),f620(x98753,x98754,x98755,x98752,x98751))),x98753))+~P102(f332(f332(f334(f882(x98751,x98751)),f332(f332(f267(x98751,x98751),x98752),x98755)),f332(f332(f190(f882(x98751,x98751),a871),f332(a115,x98754)),x98753))) % 172.78/172.48 [9893]~P102(f332(f332(f334(f882(f877(x98931),f877(x98931))),f332(f332(f267(f877(x98931),f877(x98931)),f332(f332(f151(x98931),x98932),x98935)),x98934)),f158(x98931,x98933)))+P102(f332(f332(f334(f882(x98931,x98931)),f332(f332(f267(x98931,x98931),x98932),f675(x98933,x98934,x98935,x98932,x98931))),x98933)) % 172.78/172.48 [9895]~P19(x98951,x98952,f332(f332(f310(f875(x98951)),f332(f332(f332(f91(x98951),f94(x98951,x98953,x98954)),x98955),x98953)),f195(f883(f875(x98951),a871))))+P19(x98951,x98952,f332(f332(f310(f875(x98951)),f332(f332(f332(f91(x98951),x98953),f31(x98954,x98955)),f94(x98951,x98953,f332(f72(a871,a871,a872,a327),x98954)))),f195(f883(f875(x98951),a871)))) % 172.78/172.48 [9896]~P22(x98961,x98962,f332(f332(f310(f875(x98961)),f332(f332(f332(f91(x98961),f94(x98961,x98963,x98964)),x98965),x98963)),f195(f883(f875(x98961),a871))))+P22(x98961,x98962,f332(f332(f310(f875(x98961)),f332(f332(f332(f91(x98961),x98963),f31(x98964,x98965)),f94(x98961,x98963,f332(f72(a871,a871,a872,a327),x98964)))),f195(f883(f875(x98961),a871)))) % 172.78/172.48 [10156]P19(x101561,x101562,f332(f332(f310(f875(x101561)),f332(f332(f332(f91(x101561),x101563),x101564),x101565)),f195(f883(f875(x101561),a871))))+~P19(x101561,x101562,f332(f332(f310(f875(x101561)),f332(f332(f332(f91(x101561),f332(f16(f883(a872,a871),x101561),f332(f332(f7(a872,a872,a871),a329),f672(x101565,x101564,x101562,x101561,x101563)))),x101564),f332(f16(f883(a872,a871),x101561),f332(x101565,f560(x101565,x101564,x101562,x101561,x101563))))),f195(f883(f875(x101561),a871)))) % 172.78/172.48 [6326]P102(f332(x63262,x63264))+E(f178(x63261,x63262,f332(f332(f134(x63261),x63263),f332(f332(f151(x63261),x63264),x63265))),f178(x63261,x63262,x63263)) % 172.78/172.48 [6374]~P61(x63742)+E(f332(f332(f332(f113(f883(x63741,x63742)),x63743),x63744),x63745),f332(f332(f113(x63742),f332(x63743,x63745)),f332(x63744,x63745))) % 172.78/172.48 [6376]~P63(x63762)+E(f332(f332(f332(f22(f883(x63761,x63762)),x63763),x63764),x63765),f332(f332(f22(x63762),f332(x63763,x63765)),f332(x63764,x63765))) % 172.78/172.48 [6378]~P61(x63782)+E(f332(f332(f332(f104(f883(x63781,x63782)),x63783),x63784),x63785),f332(f332(f104(x63782),f332(x63783,x63785)),f332(x63784,x63785))) % 172.78/172.48 [6396]E(x63961,x63962)+E(f332(f332(f165(x63963),f332(f332(f159(x63963,x63964),x63961),x63965)),x63962),f332(f332(f165(x63963),x63964),x63962)) % 172.78/172.48 [6659]~E(x66594,f195(f883(x66593,a871)))+E(f332(f332(f113(f883(x66591,a871)),x66592),f332(f332(f41(x66593,f883(x66591,a871)),x66594),x66595)),x66592) % 172.78/172.48 [6660]~E(x66604,f195(f883(x66603,a871)))+E(f332(f332(f22(f883(x66601,a871)),x66602),f332(f332(f41(x66603,f883(x66601,a871)),x66604),x66605)),x66602) % 172.78/172.48 [6661]~E(x66614,f195(f883(x66613,a871)))+E(f332(f332(f104(f883(x66611,a871)),x66612),f332(f332(f42(x66613,f883(x66611,a871)),x66614),x66615)),x66612) % 172.78/172.48 [6675]~E(x66754,f195(f883(x66753,a871)))+E(f332(f332(f310(x66751),x66752),f332(f332(f41(x66753,f883(x66751,a871)),x66754),x66755)),f332(f332(f310(x66751),x66752),f195(f883(x66751,a871)))) % 172.78/172.48 [7468]E(f332(f332(f165(x74681),f332(f332(f154(x74682,x74681),x74683),x74684)),x74685),f332(x74683,f332(f332(f165(x74682),x74684),x74685)))+~P102(f332(f332(f247(a876),x74685),f332(f196(f877(x74682)),x74684))) % 172.78/172.48 [7535]E(f332(f332(f113(f883(x75351,a871)),f332(x75352,x75353)),f332(f332(f41(x75354,f883(x75351,a871)),x75355),x75352)),f332(f332(f41(x75354,f883(x75351,a871)),x75355),x75352))+~P102(f332(f332(f334(x75354),x75353),x75355)) % 172.78/172.48 [7536]E(f332(f332(f104(f883(x75361,a871)),f332(x75362,x75363)),f332(f332(f42(x75364,f883(x75361,a871)),x75365),x75362)),f332(f332(f42(x75364,f883(x75361,a871)),x75365),x75362))+~P102(f332(f332(f334(x75364),x75363),x75365)) % 172.78/172.48 [8150]~E(x81503,f195(f883(x81501,a871)))+E(f332(f332(f41(x81501,f883(x81502,a871)),x81503),f332(f332(f8(f883(x81502,a871),f883(x81502,a871),x81501),f332(f310(x81502),x81504)),x81505)),f195(f883(x81502,a871))) % 172.78/172.48 [8156]~P102(f332(f332(f334(x81564),x81563),x81565))+P102(f332(f332(f246(f883(x81561,a871)),f332(x81562,x81563)),f332(f332(f41(x81564,f883(x81561,a871)),x81565),x81562))) % 172.78/172.48 [8286]~E(f332(x82864,x82862),x82865)+P102(f332(f332(f334(x82861),x82862),f332(f312(x82861,x82863,x82864),f332(f332(f310(x82863),x82865),f195(f883(x82863,a871)))))) % 172.78/172.48 [8332]~P50(x83321,x83322,f332(f287(x83322,x83321),x83323))+E(f332(f332(f104(f883(x83321,a871)),f332(f286(x83322,x83321,x83323),x83324)),f332(f286(x83322,x83321,x83323),x83325)),f332(f286(x83322,x83321,x83323),f332(f332(f104(f883(x83322,a871)),x83324),x83325))) % 172.78/172.48 [8409]E(x84091,f2(a102))+E(f332(f121(x84092,x84093,f332(x84094,f332(f332(f22(a102),x84091),f77(a102)))),f332(f332(f7(x84092,a102,f878(x84093)),x84095),x84091)),f332(f207(x84092,x84093,x84094,x84095),x84091)) % 172.78/172.48 [8453]E(x84531,f195(f883(x84532,a871)))+E(f332(f332(f41(x84532,f883(x84533,a871)),x84531),f332(f332(f8(f883(x84533,a871),f883(x84533,a871),x84532),f332(f310(x84533),x84534)),x84535)),f332(f332(f310(x84533),x84534),f332(f332(f41(x84532,f883(x84533,a871)),x84531),x84535))) % 172.78/172.48 [8507]~P20(x85072,x85071,x85073,f255(f883(x85072,a871)))+E(f332(f332(f22(f883(x85071,a871)),f332(f311(x85072,x85071,x85073),x85074)),f332(f311(x85072,x85071,x85073),x85075)),f332(f311(x85072,x85071,x85073),f332(f332(f22(f883(x85072,a871)),x85074),x85075))) % 172.78/172.48 [8508]~P20(x85082,x85081,x85083,f255(f883(x85082,a871)))+E(f332(f332(f104(f883(x85081,a871)),f332(f311(x85082,x85081,x85083),x85084)),f332(f311(x85082,x85081,x85083),x85085)),f332(f311(x85082,x85081,x85083),f332(f332(f104(f883(x85082,a871)),x85084),x85085))) % 172.78/172.48 [8572]~P102(f332(f332(f67(x85721,x85722,x85725),x85723),x85724))+P102(f332(f332(f334(f882(x85721,x85722)),f332(f332(f267(x85721,x85722),x85723),x85724)),x85725)) % 172.78/172.48 [8603]P102(f332(f332(f334(x86031),x86032),f332(f263(x86033,x86031),x86034)))+~P102(f332(f332(f334(f882(x86033,x86031)),f332(f332(f267(x86033,x86031),x86035),x86032)),x86034)) % 172.78/172.48 [8605]P102(f332(f332(f334(x86051),x86052),f332(f265(x86051,x86053),x86054)))+~P102(f332(f332(f334(f882(x86051,x86053)),f332(f332(f267(x86051,x86053),x86052),x86055)),x86054)) % 172.78/172.48 [8738]P102(f332(f332(f67(x87381,x87382,x87383),x87384),x87385))+~P102(f332(f332(f334(f882(x87381,x87382)),f332(f332(f267(x87381,x87382),x87384),x87385)),x87383)) % 172.78/172.48 [8773]E(f332(x87731,x87732),x87733)+~P102(f332(f332(f334(x87734),x87732),f332(f312(x87734,x87735,x87731),f332(f332(f310(x87735),x87733),f195(f883(x87735,a871)))))) % 172.78/172.48 [9009]P102(f332(f332(f334(f882(x90091,x90092)),f332(f332(f267(x90091,x90092),x90093),x90094)),f332(f287(x90092,x90091),x90095)))+~P102(f332(f332(f334(f882(x90092,x90091)),f332(f332(f267(x90092,x90091),x90094),x90093)),x90095)) % 172.78/172.48 [9027]~P102(f332(f332(x90271,x90275),x90274))+P102(f332(f332(x90271,f332(f270(x90272,x90273),f332(f332(f267(x90272,x90273),x90274),x90275))),f332(f266(x90272,x90273),f332(f332(f267(x90272,x90273),x90274),x90275)))) % 172.78/172.48 [9057]~P102(f332(f332(f334(f882(x90572,x90571)),f332(f332(f267(x90572,x90571),x90574),x90573)),f332(f287(x90571,x90572),x90575)))+P102(f332(f332(f334(f882(x90571,x90572)),f332(f332(f267(x90571,x90572),x90573),x90574)),x90575)) % 172.78/172.48 [9087]~P102(f332(f332(f334(f882(x90873,x90871)),f332(f332(f267(x90873,x90871),x90875),x90872)),x90874))+P102(f332(f332(f334(x90871),x90872),f332(f286(x90873,x90871,x90874),f332(f332(f310(x90873),x90875),f195(f883(x90873,a871)))))) % 172.78/172.48 [9132]P102(f332(f332(f334(f882(x91321,x91322)),f332(f332(f267(x91321,x91322),x91323),x91324)),x91325))+~P102(f332(f332(f334(x91322),x91324),f332(f286(x91321,x91322,x91325),f332(f332(f310(x91321),x91323),f195(f883(x91321,a871)))))) % 172.78/172.48 [9153]E(f332(f332(f332(f71(x91531,f880(x91532)),f189(x91531,x91532,x91533,x91534)),x91535),f208(x91532)),f189(x91531,x91532,x91533,f332(f332(f22(f883(x91531,a871)),x91534),f332(f332(f310(x91531),x91535),f195(f883(x91531,a871))))))+~P102(f332(f332(f334(x91531),x91535),x91534)) % 172.78/172.48 [9221]~P71(x92211)+E(f332(f332(f6(a876,x92211),x92212),f303(a876,f332(f332(f79(a876),x92213),x92214),f332(f332(f79(a876),x92215),x92214))),f332(f332(f6(a876,x92211),f332(f332(f8(a876,x92211,a876),x92212),f332(f332(f7(a876,a876,a876),f79(a876)),x92214))),f303(a876,x92213,x92215))) % 172.78/172.48 [9245]~P71(x92451)+E(f332(f332(f6(a876,x92451),x92452),f332(f302(a876,f332(f332(f79(a876),x92453),x92454)),f332(f332(f79(a876),x92455),x92454))),f332(f332(f6(a876,x92451),f332(f332(f8(a876,x92451,a876),x92452),f332(f332(f7(a876,a876,a876),f79(a876)),x92454))),f332(f302(a876,x92453),x92455))) % 172.78/172.48 [9298]~P20(x92981,x92982,x92983,f255(f883(x92981,a871)))+E(f332(f332(f154(x92981,x92982),x92983),f332(f136(x92981,f332(f332(f8(a871,a871,x92981),a327),f332(a329,x92984))),x92985)),f332(f136(x92982,f332(f332(f8(a871,a871,x92982),a327),f332(a329,f332(x92983,x92984)))),f332(f332(f154(x92981,x92982),x92983),x92985))) % 172.78/172.48 [9316]~P20(x93161,x93162,x93163,f332(f332(f310(x93161),x93164),f332(f173(x93161),x93165)))+E(f332(f332(f154(x93161,x93162),x93163),f332(f136(x93161,f332(f332(f8(a871,a871,x93161),a327),f332(a329,x93164))),x93165)),f332(f136(x93162,f332(f332(f8(a871,a871,x93162),a327),f332(a329,f332(x93163,x93164)))),f332(f332(f154(x93161,x93162),x93163),x93165))) % 172.78/172.48 [9472]P102(f332(f332(f334(f882(f877(x94721),f877(x94721))),f332(f332(f267(f877(x94721),f877(x94721)),f332(f332(f151(x94721),x94722),x94723)),f332(f332(f151(x94721),x94724),x94723))),f157(x94721,x94725)))+~P102(f332(f332(f334(f882(x94721,x94721)),f332(f332(f267(x94721,x94721),x94722),x94724)),x94725)) % 172.78/172.48 [9508]P102(f332(f332(f332(f332(a203,x95081),x95082),x95083),f610(x95084,x95083,x95082,x95085,x95081)))+~P102(f332(f332(f332(f332(a203,f32(x95081,x95085)),x95082),x95083),x95084)) % 172.78/172.48 [9578]P19(x95781,x95782,f332(f332(f310(f875(x95781)),f332(f332(f332(f91(x95781),x95783),f332(a25,x95784)),x95785)),f195(f883(f875(x95781),a871))))+~P19(x95781,f332(f332(f310(f875(x95781)),f332(f332(f332(f91(x95781),x95783),f332(a25,x95784)),x95785)),x95782),f332(f332(f310(f875(x95781)),f332(f332(f332(f91(x95781),x95783),f332(f243(a873),f332(a27,x95784))),x95785)),f195(f883(f875(x95781),a871)))) % 172.78/172.48 [9590]E(f332(f332(f310(x95901),f682(x95902,x95903,x95904,x95905,x95901)),f691(x95902,x95903,x95904,x95905,x95901)),f332(f332(f310(x95901),x95904),x95903))+~P102(f332(f62(x95901,x95905,f332(f332(f310(x95901),x95904),x95903)),x95902)) % 172.78/172.48 [9591]E(f332(f332(f310(x95911),f704(x95912,x95913,x95914,x95915,x95911)),f714(x95912,x95913,x95914,x95915,x95911)),f332(f332(f310(x95911),x95914),x95913))+~P102(f332(f62(x95911,x95915,f332(f332(f310(x95911),x95914),x95913)),x95912)) % 172.78/172.48 [9673]P102(f332(f332(f334(x96731),f629(x96732,x96733,x96734,x96735,x96731)),x96734))+P102(f332(f332(f332(f42(x96731,f883(x96735,a871)),x96734),x96733),x96732)) % 172.78/172.48 [9678]P102(f332(f332(f334(x96781),f625(x96782,x96783,x96781,x96784,x96785)),x96783))+P102(f332(f332(f334(x96785),x96784),f332(f332(f42(x96781,f883(x96785,a871)),x96783),x96782))) % 172.78/172.48 [9686]P102(f332(f332(f334(x96861),f630(x96862,x96863,x96861,x96864,x96865)),x96863))+P102(f332(f332(f246(f883(x96865,a871)),x96864),f332(f332(f42(x96861,f883(x96865,a871)),x96863),x96862))) % 172.78/172.48 [9688]P102(f332(f332(x96881,f438(x96882,x96881,x96883,x96884,x96885)),x96882))+~P102(f332(f332(f332(f41(x96885,f883(x96884,a871)),x96883),x96881),x96882)) % 172.78/172.48 [9691]P102(f332(f332(f334(x96911),f438(x96912,x96913,x96914,x96915,x96911)),x96914))+~P102(f332(f332(f332(f41(x96911,f883(x96915,a871)),x96914),x96913),x96912)) % 172.78/172.48 [9701]P102(f332(f332(f334(x97011),f445(x97012,x97013,x97011,x97014,x97015)),x97013))+~P102(f332(f332(f334(x97015),x97014),f332(f332(f41(x97011,f883(x97015,a871)),x97013),x97012))) % 172.78/172.48 [9706]P102(f332(f332(f334(x97061),x97062),f332(x97063,f445(x97063,x97064,x97065,x97062,x97061))))+~P102(f332(f332(f334(x97061),x97062),f332(f332(f41(x97065,f883(x97061,a871)),x97064),x97063))) % 172.78/172.48 [9800]~P102(f332(f332(x98004,f629(x98005,x98004,x98003,x98002,x98001)),x98005))+P102(f332(f332(f332(f42(x98001,f883(x98002,a871)),x98003),x98004),x98005)) % 172.78/172.48 [9803]~P102(f332(f332(f334(x98031),x98032),f332(x98035,f625(x98035,x98034,x98033,x98032,x98031))))+P102(f332(f332(f334(x98031),x98032),f332(f332(f42(x98033,f883(x98031,a871)),x98034),x98035))) % 172.78/172.48 [9807]~P102(f332(f332(f246(f883(x98071,a871)),x98072),f332(x98075,f630(x98075,x98074,x98073,x98072,x98071))))+P102(f332(f332(f246(f883(x98071,a871)),x98072),f332(f332(f42(x98073,f883(x98071,a871)),x98074),x98075))) % 172.78/172.48 [9852]P102(f332(f332(f332(f332(a203,x98521),f610(x98522,x98523,x98524,x98521,x98525)),x98523),x98522))+~P102(f332(f332(f332(f332(a203,f32(x98525,x98521)),x98524),x98523),x98522)) % 172.78/172.48 [9878]~P102(f332(f332(f334(x98781),f682(x98785,x98784,x98783,x98782,x98781)),f691(x98785,x98784,x98783,x98782,x98781)))+~P102(f332(f62(x98781,x98782,f332(f332(f310(x98781),x98783),x98784)),x98785)) % 172.78/172.48 [9879]~P102(f332(f332(f334(x98791),f704(x98795,x98794,x98793,x98792,x98791)),f714(x98795,x98794,x98793,x98792,x98791)))+~P102(f332(f62(x98791,x98792,f332(f332(f310(x98791),x98793),x98794)),x98795)) % 172.78/172.48 [9880]~P102(f332(f332(f334(f882(x98801,x98801)),f332(f332(f267(x98801,x98801),x98802),x98805)),f332(f332(f190(f882(x98801,x98801),a871),f332(a115,x98804)),x98803)))+P102(f332(f332(f334(f882(x98801,x98801)),f332(f332(f267(x98801,x98801),x98802),f619(x98803,x98804,x98805,x98802,x98801))),f332(f332(f190(f882(x98801,x98801),a871),x98804),x98803))) % 172.78/172.48 [9887]P102(f332(f66(x98871,x98871,x98872,f682(x98873,x98874,x98875,x98872,x98871),f691(x98873,x98874,x98875,x98872,x98871)),x98873))+~P102(f332(f62(x98871,x98872,f332(f332(f310(x98871),x98875),x98874)),x98873)) % 172.78/172.48 [9888]P102(f332(f66(x98881,x98881,x98882,f704(x98883,x98884,x98885,x98882,x98881),f714(x98883,x98884,x98885,x98882,x98881)),x98883))+~P102(f332(f62(x98881,x98882,f332(f332(f310(x98881),x98885),x98884)),x98883)) % 172.78/172.48 [9900]~P104(x99001)+P29(x99001,f332(f332(f154(x99002,x99001),x99003),f332(f136(x99002,f332(f332(f7(x99002,x99001,a871),f332(f332(f8(x99001,f883(x99001,a871),x99002),a329),x99003)),f332(x99004,x99005))),x99005))) % 172.78/172.48 [9940]~P102(f332(f332(f334(x99402),x99405),f332(f286(x99401,x99402,x99404),x99403)))+P102(f332(f332(f334(f882(x99401,x99402)),f332(f332(f267(x99401,x99402),f500(x99403,x99404,x99401,x99405,x99402)),x99405)),x99404)) % 172.78/172.48 [9941]~P102(f332(f332(f334(x99412),x99415),f332(f286(x99411,x99412,x99414),x99413)))+P102(f332(f332(f334(f882(x99411,x99412)),f332(f332(f267(x99411,x99412),f504(x99413,x99414,x99411,x99415,x99412)),x99415)),x99414)) % 172.78/172.48 [9961]~P102(f332(f332(f334(f882(x99611,x99611)),f332(f332(f267(x99611,x99611),x99615),x99614)),f332(f332(f190(f882(x99611,x99611),a871),f332(a115,x99613)),x99612)))+P102(f332(f332(f334(f882(x99611,x99611)),f332(f332(f267(x99611,x99611),f619(x99612,x99613,x99614,x99615,x99611)),x99614)),x99612)) % 172.78/172.48 [9964]~P102(f332(f332(f334(f882(x99641,x99641)),f332(f332(f267(x99641,x99641),x99645),x99644)),f332(f332(f190(f882(x99641,x99641),a871),f332(a115,x99643)),x99642)))+P102(f332(f332(f334(f882(x99641,x99641)),f332(f332(f267(x99641,x99641),f618(x99642,x99643,x99644,x99645,x99641)),x99644)),f332(f332(f190(f882(x99641,x99641),a871),x99643),x99642))) % 172.78/172.48 [9965]~P102(f332(f332(f334(f882(x99651,x99651)),f332(f332(f267(x99651,x99651),x99655),x99654)),f332(f332(f190(f882(x99651,x99651),a871),f332(a115,x99653)),x99652)))+P102(f332(f332(f334(f882(x99651,x99651)),f332(f332(f267(x99651,x99651),f620(x99652,x99653,x99654,x99655,x99651)),x99654)),f332(f332(f190(f882(x99651,x99651),a871),x99653),x99652))) % 172.78/172.48 [9966]~P102(f332(f332(f334(f882(f877(x99661),f877(x99661))),f332(f332(f267(f877(x99661),f877(x99661)),x99665),f332(f332(f151(x99661),x99664),x99663))),f158(x99661,x99662)))+P102(f332(f332(f334(f882(x99661,x99661)),f332(f332(f267(x99661,x99661),f674(x99662,x99663,x99664,x99665,x99661)),x99664)),x99662)) % 172.78/172.48 [7062]E(x70621,f208(x70622))+E(f185(x70623,x70622,f332(f332(f332(f71(x70623,f880(x70622)),x70624),x70625),x70621)),f332(f332(f310(x70623),x70625),f185(x70623,x70622,x70624))) % 172.78/172.48 [7556]~E(x75563,f195(f883(x75562,a871)))+E(f332(f332(f113(f883(x75561,a871)),f332(f332(f41(x75562,f883(x75561,a871)),x75563),x75564)),x75565),x75565) % 172.78/172.48 [7557]~E(x75573,f195(f883(x75572,a871)))+E(f332(f332(f104(f883(x75571,a871)),f332(f332(f42(x75572,f883(x75571,a871)),x75573),x75574)),x75575),x75575) % 172.78/172.48 [7920]~E(x79205,f208(x79202))+E(f185(x79201,x79202,f332(f332(f332(f71(x79201,f880(x79202)),x79203),x79204),x79205)),f332(f332(f22(f883(x79201,a871)),f185(x79201,x79202,x79203)),f332(f332(f310(x79201),x79204),f195(f883(x79201,a871))))) % 172.78/172.48 [7990]~E(x79903,f195(f883(x79902,a871)))+E(f332(f332(f22(f883(x79901,a871)),f332(f332(f42(x79902,f883(x79901,a871)),x79903),x79904)),x79905),f332(f332(f22(f883(x79901,a871)),f255(f883(x79901,a871))),x79905)) % 172.78/172.48 [8121]E(f332(f332(f159(x81211,f332(f332(f134(x81211),x81212),x81213)),x81214),x81215),f332(f332(f134(x81211),f332(f332(f159(x81211,x81212),x81214),x81215)),x81213))+~P102(f332(f332(f247(a876),x81214),f332(f196(f877(x81211)),x81212))) % 172.78/172.48 [8238]P102(f332(f332(f334(x82381),x82385),f332(f173(x82381),x82383)))+E(f332(f332(f179(x82381,x82382),f332(f332(f183(x82381,x82382),x82383),f332(f332(f154(x82381,x82382),x82384),x82383))),x82385),f208(x82382)) % 172.78/172.48 [8359]~P102(f332(f332(f334(x83591),x83595),f332(f173(x83591),x83593)))+E(f332(f332(f179(x83591,x83592),f332(f332(f183(x83591,x83592),x83593),f332(f332(f154(x83591,x83592),x83594),x83593))),x83595),f332(f239(x83592),f332(x83594,x83595))) % 172.78/172.48 [8399]E(f332(f332(f165(x83991),f332(f332(f154(a876,x83991),x83992),f139(a876,f332(f302(a876,x83993),x83994)))),x83995),f332(x83992,f332(f332(f79(a876),x83993),x83995)))+~P102(f332(f332(f247(a876),x83995),f332(f332(f22(a876),x83994),x83993))) % 172.78/172.48 [8414]E(x84141,f2(a102))+E(f123(x84142,x84143,f332(x84144,f332(f332(f22(a102),x84141),f77(a102))),f332(f332(f7(x84142,a102,f878(f880(x84143))),x84145),x84141)),f332(f205(x84142,x84143,x84144,x84145),x84141)) % 172.78/172.48 [8440]~E(x84403,f195(f883(x84401,a871)))+E(f332(f332(f41(x84401,f883(x84402,a871)),x84403),f332(f332(f8(f883(x84402,a871),f883(x84402,a871),x84401),f332(f113(f883(x84402,a871)),x84404)),x84405)),f195(f883(x84402,a871))) % 172.78/172.48 [8441]~E(x84413,f195(f883(x84411,a871)))+E(f332(f332(f42(x84411,f883(x84412,a871)),x84413),f332(f332(f8(f883(x84412,a871),f883(x84412,a871),x84411),f332(f22(f883(x84412,a871)),x84414)),x84415)),f255(f883(x84412,a871))) % 172.78/172.48 [8442]~E(x84423,f195(f883(x84421,a871)))+E(f332(f332(f42(x84421,f883(x84422,a871)),x84423),f332(f332(f8(f883(x84422,a871),f883(x84422,a871),x84421),f332(f104(f883(x84422,a871)),x84424)),x84425)),f255(f883(x84422,a871))) % 172.78/172.48 [8447]~P139(x84472)+E(f332(f332(f6(x84471,x84472),f332(f332(f8(x84472,x84472,x84471),f332(f80(x84472),x84473)),x84474)),x84475),f332(f332(f80(x84472),x84473),f332(f332(f6(x84471,x84472),x84474),x84475))) % 172.78/172.48 [8723]E(x87231,f195(f883(x87232,a871)))+E(f332(f332(f41(x87232,f883(x87233,a871)),x87231),f332(f332(f8(f883(x87233,a871),f883(x87233,a871),x87232),f332(f113(f883(x87233,a871)),x87234)),x87235)),f332(f332(f113(f883(x87233,a871)),x87234),f332(f332(f41(x87232,f883(x87233,a871)),x87231),x87235))) % 172.78/172.48 [8724]E(x87241,f195(f883(x87242,a871)))+E(f332(f332(f42(x87242,f883(x87243,a871)),x87241),f332(f332(f8(f883(x87243,a871),f883(x87243,a871),x87242),f332(f22(f883(x87243,a871)),x87244)),x87245)),f332(f332(f22(f883(x87243,a871)),x87244),f332(f332(f41(x87242,f883(x87243,a871)),x87241),x87245))) % 172.78/172.48 [8725]E(x87251,f195(f883(x87252,a871)))+E(f332(f332(f42(x87252,f883(x87253,a871)),x87251),f332(f332(f8(f883(x87253,a871),f883(x87253,a871),x87252),f332(f104(f883(x87253,a871)),x87254)),x87255)),f332(f332(f104(f883(x87253,a871)),x87254),f332(f332(f42(x87252,f883(x87253,a871)),x87251),x87255))) % 172.78/172.48 [8922]~P102(f332(f332(f247(a876),f332(x89224,x89222)),f332(x89224,x89223)))+P102(f332(f332(f334(f882(x89221,x89221)),f332(f332(f267(x89221,x89221),x89222),x89223)),f153(x89221,f332(f332(f151(f883(x89221,a876)),x89224),x89225)))) % 172.78/172.48 [9188]~P20(x91882,x91881,x91883,f332(f332(f113(f883(x91882,a871)),x91884),x91885))+E(f332(f332(f104(f883(x91881,a871)),f332(f311(x91882,x91881,x91883),f332(f332(f22(f883(x91882,a871)),x91884),x91885))),f332(f311(x91882,x91881,x91883),f332(f332(f22(f883(x91882,a871)),x91885),x91884))),f195(f883(x91881,a871))) % 172.78/172.48 [9468]~P102(f332(f332(f246(f883(x94683,a871)),f332(f286(x94681,x94683,x94684),x94682)),x94685))+P102(f332(f332(f246(f883(x94681,a871)),x94682),f332(f78(f883(x94681,a871)),f332(f286(x94683,x94681,f332(f287(x94681,x94683),x94684)),f332(f78(f883(x94683,a871)),x94685))))) % 172.78/172.48 [9493]~P20(x94931,x94932,x94933,f332(f332(f310(x94931),x94934),x94935))+~P102(f332(f332(f334(x94932),f332(x94933,x94934)),f332(f311(x94931,x94932,x94933),f332(f332(f22(f883(x94931,a871)),x94935),f332(f332(f310(x94931),x94934),f195(f883(x94931,a871))))))) % 172.78/172.48 [9544]P102(f332(f332(f246(f883(x95441,a871)),f332(f286(x95442,x95441,x95443),x95444)),x95445))+~P102(f332(f332(f246(f883(x95442,a871)),x95444),f332(f78(f883(x95442,a871)),f332(f286(x95441,x95442,f332(f287(x95442,x95441),x95443)),f332(f78(f883(x95441,a871)),x95445))))) % 172.78/172.48 [9618]~P81(x96181)+P102(f332(f332(f246(x96181),f332(f74(x96181),f332(f332(f22(x96181),f332(f332(f79(x96181),x96182),x96183)),f332(f332(f79(x96181),x96184),x96185)))),f332(f332(f79(x96181),f332(f74(x96181),f332(f332(f22(x96181),x96182),x96184))),f332(f74(x96181),f332(f332(f22(x96181),x96183),x96185))))) % 172.78/172.48 [9721]P102(f332(f332(f334(x97211),f448(x97212,x97213,x97214,x97211,x97215)),x97214))+P102(f332(f332(f246(f883(x97215,a871)),f332(f332(f41(x97211,f883(x97215,a871)),x97214),x97213)),x97212)) % 172.78/172.48 [9918]~P102(f332(f332(f246(f883(x99181,a871)),f332(x99184,f448(x99185,x99184,x99183,x99182,x99181))),x99185))+P102(f332(f332(f246(f883(x99181,a871)),f332(f332(f41(x99182,f883(x99181,a871)),x99183),x99184)),x99185)) % 172.78/172.48 [8553]E(f332(f332(f134(x85531),x85532),f332(f332(f159(x85531,x85533),f332(f332(f22(a876),x85534),f332(f196(f877(x85531)),x85532))),x85535)),f332(f332(f159(x85531,f332(f332(f134(x85531),x85532),x85533)),x85534),x85535))+P102(f332(f332(f247(a876),x85534),f332(f196(f877(x85531)),x85532))) % 172.78/172.48 [8579]~P122(x85791)+E(f332(f332(f79(x85791),f332(f332(f80(x85791),x85792),x85793)),f332(f332(f79(x85791),f332(f332(f80(x85791),x85794),x85793)),x85795)),f332(f332(f79(x85791),f332(f332(f80(x85791),f332(f332(f79(x85791),x85792),x85794)),x85793)),x85795)) % 172.78/172.48 [9142]~P139(x91421)+E(f332(f166(x91421),f332(f332(f154(x91422,x91421),f332(f332(f8(x91421,x91421,x91422),f332(f80(x91421),x91423)),x91424)),x91425)),f332(f332(f80(x91421),x91423),f332(f166(x91421),f332(f332(f154(x91422,x91421),x91424),x91425)))) % 172.78/172.48 [9315]E(f332(f196(f877(x93151)),f332(f332(f176(x93151),f332(f332(f244(a876),f332(f196(f877(x93151)),x93152)),f332(f196(f877(x93153)),x93154))),x93152)),f332(f196(f877(x93153)),f332(f332(f176(x93153),f332(f332(f244(a876),f332(f196(f877(x93151)),x93152)),f332(f196(f877(x93153)),x93154))),x93154)))+P102(f332(x93155,f332(f332(f183(x93151,x93153),x93152),x93154))) % 172.78/172.48 [9555]~P139(x95552)+E(f332(f332(f6(x95551,x95552),f332(f332(f7(x95551,x95552,x95552),f332(f332(f8(x95552,f883(x95552,x95552),x95551),f80(x95552)),x95553)),x95554)),x95555),f332(f332(f80(x95552),f332(f332(f6(x95551,x95552),x95553),x95555)),x95554)) % 172.78/172.48 [9556]~P58(x95562)+E(f332(f332(f6(x95561,x95562),f332(f332(f7(x95561,x95562,x95562),f332(f332(f8(x95562,f883(x95562,x95562),x95561),f290(x95562)),x95563)),x95564)),x95565),f332(f332(f290(x95562),f332(f332(f6(x95561,x95562),x95563),x95565)),x95564)) % 172.78/172.48 [9563]~P66(x95632)+E(f332(f332(f6(x95631,x95632),f332(f332(f18(x95631,x95632,x95632),f332(f332(f8(x95632,f883(x95632,x95632),x95631),f22(x95632)),x95633)),x95634)),x95635),f332(f332(f22(x95632),f332(f332(f6(x95631,x95632),x95633),x95635)),f332(f332(f6(x95631,x95632),x95634),x95635))) % 172.78/172.48 [9564]~P71(x95642)+E(f332(f332(f6(x95641,x95642),f332(f332(f18(x95641,x95642,x95642),f332(f332(f8(x95642,f883(x95642,x95642),x95641),f79(x95642)),x95643)),x95644)),x95645),f332(f332(f79(x95642),f332(f332(f6(x95641,x95642),x95643),x95645)),f332(f332(f6(x95641,x95642),x95644),x95645))) % 172.78/172.48 [9565]~P67(x95652)+E(f332(f332(f9(x95651,x95652),f332(f332(f18(x95651,x95652,x95652),f332(f332(f8(x95652,f883(x95652,x95652),x95651),f80(x95652)),x95653)),x95654)),x95655),f332(f332(f80(x95652),f332(f332(f9(x95651,x95652),x95653),x95655)),f332(f332(f9(x95651,x95652),x95654),x95655))) % 172.78/172.48 [9603]~E(x96033,f195(f883(x96031,a871)))+E(f332(f332(f41(x96031,f883(x96032,a871)),x96033),f332(f332(f7(x96031,f883(x96032,a871),f883(x96032,a871)),f332(f332(f8(f883(x96032,a871),f883(f883(x96032,a871),f883(x96032,a871)),x96031),f113(f883(x96032,a871))),x96034)),x96035)),f195(f883(x96032,a871))) % 172.78/172.48 [9604]~E(x96043,f195(f883(x96041,a871)))+E(f332(f332(f42(x96041,f883(x96042,a871)),x96043),f332(f332(f7(x96041,f883(x96042,a871),f883(x96042,a871)),f332(f332(f8(f883(x96042,a871),f883(f883(x96042,a871),f883(x96042,a871)),x96041),f22(f883(x96042,a871))),x96044)),x96045)),f255(f883(x96042,a871))) % 172.78/172.48 [9605]~E(x96053,f195(f883(x96051,a871)))+E(f332(f332(f42(x96051,f883(x96052,a871)),x96053),f332(f332(f7(x96051,f883(x96052,a871),f883(x96052,a871)),f332(f332(f8(f883(x96052,a871),f883(f883(x96052,a871),f883(x96052,a871)),x96051),f104(f883(x96052,a871))),x96054)),x96055)),f255(f883(x96052,a871))) % 172.78/172.48 [9626]E(x96261,f195(f883(x96262,a871)))+E(f332(f332(f41(x96262,f883(x96263,a871)),x96261),f332(f332(f7(x96262,f883(x96263,a871),f883(x96263,a871)),f332(f332(f8(f883(x96263,a871),f883(f883(x96263,a871),f883(x96263,a871)),x96262),f113(f883(x96263,a871))),x96264)),x96265)),f332(f332(f113(f883(x96263,a871)),f332(f332(f41(x96262,f883(x96263,a871)),x96261),x96264)),x96265)) % 172.78/172.48 [9627]E(x96271,f195(f883(x96272,a871)))+E(f332(f332(f42(x96272,f883(x96273,a871)),x96271),f332(f332(f7(x96272,f883(x96273,a871),f883(x96273,a871)),f332(f332(f8(f883(x96273,a871),f883(f883(x96273,a871),f883(x96273,a871)),x96272),f22(f883(x96273,a871))),x96274)),x96275)),f332(f332(f22(f883(x96273,a871)),f332(f332(f42(x96272,f883(x96273,a871)),x96271),x96274)),x96275)) % 172.78/172.48 [9628]E(x96281,f195(f883(x96282,a871)))+E(f332(f332(f42(x96282,f883(x96283,a871)),x96281),f332(f332(f7(x96282,f883(x96283,a871),f883(x96283,a871)),f332(f332(f8(f883(x96283,a871),f883(f883(x96283,a871),f883(x96283,a871)),x96282),f104(f883(x96283,a871))),x96284)),x96285)),f332(f332(f104(f883(x96283,a871)),f332(f332(f42(x96282,f883(x96283,a871)),x96281),x96284)),x96285)) % 172.78/172.48 [9195]~P102(f332(f332(f246(a876),x91951),x91954))+E(f332(f332(f22(a876),f332(f332(f79(a876),f332(f332(f80(a876),x91951),x91952)),x91953)),f332(f332(f79(a876),f332(f332(f80(a876),x91954),x91952)),x91955)),f332(f332(f22(a876),x91953),f332(f332(f79(a876),f332(f332(f80(a876),f332(f332(f22(a876),x91954),x91951)),x91952)),x91955))) % 172.78/172.48 [9781]~P139(x97811)+E(f332(f166(x97811),f332(f332(f154(x97812,x97811),f332(f332(f7(x97812,x97811,x97811),f332(f332(f8(x97811,f883(x97811,x97811),x97812),f80(x97811)),x97813)),x97814)),x97815)),f332(f332(f80(x97811),f332(f166(x97811),f332(f332(f154(x97812,x97811),x97813),x97815))),x97814)) % 172.78/172.48 [9787]~P66(x97871)+E(f332(f166(x97871),f332(f332(f154(x97872,x97871),f332(f332(f18(x97872,x97871,x97871),f332(f332(f8(x97871,f883(x97871,x97871),x97872),f22(x97871)),x97873)),x97874)),x97875)),f332(f332(f22(x97871),f332(f166(x97871),f332(f332(f154(x97872,x97871),x97873),x97875))),f332(f166(x97871),f332(f332(f154(x97872,x97871),x97874),x97875)))) % 172.78/172.48 [9788]~P71(x97881)+E(f332(f166(x97881),f332(f332(f154(x97882,x97881),f332(f332(f18(x97882,x97881,x97881),f332(f332(f8(x97881,f883(x97881,x97881),x97882),f79(x97881)),x97883)),x97884)),x97885)),f332(f332(f79(x97881),f332(f166(x97881),f332(f332(f154(x97882,x97881),x97883),x97885))),f332(f166(x97881),f332(f332(f154(x97882,x97881),x97884),x97885)))) % 172.78/172.48 [9931]P102(f332(x99311,f332(f332(f183(x99312,x99313),x99314),x99315)))+~P102(f332(x99311,f332(f332(f183(x99312,x99313),f332(f332(f176(x99312),f332(f332(f244(a876),f332(f196(f877(x99312)),x99314)),f332(f196(f877(x99313)),x99315))),x99314)),f332(f332(f176(x99313),f332(f332(f244(a876),f332(f196(f877(x99312)),x99314)),f332(f196(f877(x99313)),x99315))),x99315)))) % 172.78/172.48 [10165]~P102(f332(f332(f334(f882(x101652,x101651)),f332(f332(f267(x101652,x101651),x101654),x101655)),f332(f287(x101651,x101652),x101653)))+P102(f332(f332(f256(x101651,x101652,f332(f332(f7(x101651,f883(f882(x101651,x101652),a871),f883(x101652,a871)),f332(f332(f8(f883(x101652,f883(f883(f882(x101651,x101652),a871),a871)),f883(f883(f882(x101651,x101652),a871),f883(x101652,a871)),x101651),f7(x101652,f883(f882(x101651,x101652),a871),a871)),f332(f332(f8(f883(x101652,f882(x101651,x101652)),f883(x101652,f883(f883(f882(x101651,x101652),a871),a871)),x101651),f332(f8(f882(x101651,x101652),f883(f883(f882(x101651,x101652),a871),a871),x101652),f334(f882(x101651,x101652)))),f267(x101651,x101652)))),x101653)),x101654),x101655)) % 172.78/172.48 [10174]P102(f332(f332(f334(f882(x101741,x101742)),f332(f332(f267(x101741,x101742),x101743),x101744)),f332(f287(x101742,x101741),x101745)))+~P102(f332(f332(f256(x101742,x101741,f332(f332(f7(x101742,f883(f882(x101742,x101741),a871),f883(x101741,a871)),f332(f332(f8(f883(x101741,f883(f883(f882(x101742,x101741),a871),a871)),f883(f883(f882(x101742,x101741),a871),f883(x101741,a871)),x101742),f7(x101741,f883(f882(x101742,x101741),a871),a871)),f332(f332(f8(f883(x101741,f882(x101742,x101741)),f883(x101741,f883(f883(f882(x101742,x101741),a871),a871)),x101742),f332(f8(f882(x101742,x101741),f883(f883(f882(x101742,x101741),a871),a871),x101741),f334(f882(x101742,x101741)))),f267(x101742,x101741)))),x101745)),x101743),x101744)) % 172.78/172.48 [9436]~P102(f332(f332(f246(a876),x94364),x94361))+E(f332(f332(f22(a876),f332(f332(f79(a876),f332(f332(f80(a876),x94361),x94362)),x94363)),f332(f332(f79(a876),f332(f332(f80(a876),x94364),x94362)),x94365)),f332(f332(f22(a876),f332(f332(f79(a876),f332(f332(f80(a876),f332(f332(f22(a876),x94361),x94364)),x94362)),x94363)),x94365)) % 172.78/172.48 [10183]P19(x101831,x101832,f332(f311(a874,f875(x101831),f332(f332(f18(a874,f883(x101831,f883(a872,a871)),f875(x101831)),f332(f332(f18(a874,a873,f883(f883(x101831,f883(a872,a871)),f875(x101831))),f332(f332(f8(f883(x101831,f883(a872,a871)),f883(a873,f883(f883(x101831,f883(a872,a871)),f875(x101831))),a874),f91(x101831)),x101833)),a25)),x101834)),x101835))+~P19(x101831,f332(f332(f113(f883(f875(x101831),a871)),x101832),f332(f311(a874,f875(x101831),f332(f332(f18(a874,f883(x101831,f883(a872,a871)),f875(x101831)),f332(f332(f18(a874,a873,f883(f883(x101831,f883(a872,a871)),f875(x101831))),f332(f332(f8(f883(x101831,f883(a872,a871)),f883(a873,f883(f883(x101831,f883(a872,a871)),f875(x101831))),a874),f91(x101831)),x101833)),a25)),x101834)),x101835)),f332(f311(a874,f875(x101831),f332(f332(f18(a874,f883(x101831,f883(a872,a871)),f875(x101831)),f332(f332(f18(a874,a873,f883(f883(x101831,f883(a872,a871)),f875(x101831))),f332(f332(f8(f883(x101831,f883(a872,a871)),f883(a873,f883(f883(x101831,f883(a872,a871)),f875(x101831))),a874),f91(x101831)),x101833)),f332(f332(f8(f880(a873),a873,a874),f243(a873)),a27))),x101834)),x101835)) % 172.78/172.48 [10184]P22(x101841,x101842,f332(f311(a874,f875(x101841),f332(f332(f18(a874,f883(x101841,f883(a872,a871)),f875(x101841)),f332(f332(f18(a874,a873,f883(f883(x101841,f883(a872,a871)),f875(x101841))),f332(f332(f8(f883(x101841,f883(a872,a871)),f883(a873,f883(f883(x101841,f883(a872,a871)),f875(x101841))),a874),f91(x101841)),x101843)),a25)),x101844)),x101845))+~P22(x101841,f332(f332(f113(f883(f875(x101841),a871)),x101842),f332(f311(a874,f875(x101841),f332(f332(f18(a874,f883(x101841,f883(a872,a871)),f875(x101841)),f332(f332(f18(a874,a873,f883(f883(x101841,f883(a872,a871)),f875(x101841))),f332(f332(f8(f883(x101841,f883(a872,a871)),f883(a873,f883(f883(x101841,f883(a872,a871)),f875(x101841))),a874),f91(x101841)),x101843)),a25)),x101844)),x101845)),f332(f311(a874,f875(x101841),f332(f332(f18(a874,f883(x101841,f883(a872,a871)),f875(x101841)),f332(f332(f18(a874,a873,f883(f883(x101841,f883(a872,a871)),f875(x101841))),f332(f332(f8(f883(x101841,f883(a872,a871)),f883(a873,f883(f883(x101841,f883(a872,a871)),f875(x101841))),a874),f91(x101841)),x101843)),f332(f332(f8(f880(a873),a873,a874),f243(a873)),a27))),x101844)),x101845)) % 172.78/172.48 [5257]E(x52571,x52572)+~E(f29(x52573,x52574,x52571),f29(x52575,x52576,x52572)) % 172.78/172.48 [5258]E(x52581,x52582)+~E(f29(x52583,x52581,x52584),f29(x52585,x52582,x52586)) % 172.78/172.48 [5259]E(x52591,x52592)+~E(f29(x52591,x52593,x52594),f29(x52592,x52595,x52596)) % 172.78/172.48 [5260]E(x52601,x52602)+~E(f28(x52603,x52604,x52601),f28(x52605,x52606,x52602)) % 172.78/172.48 [5261]E(x52611,x52612)+~E(f28(x52613,x52611,x52614),f28(x52615,x52612,x52616)) % 172.78/172.48 [5262]E(x52621,x52622)+~E(f28(x52621,x52623,x52624),f28(x52622,x52625,x52626)) % 172.78/172.48 [6702]E(f332(f186(x67021,x67022,x67023,x67024),x67025),f332(f239(x67022),x67026))+~E(f332(x67024,x67025),f332(f239(x67022),x67026)) % 172.78/172.48 [6846]E(f332(f241(f880(x68461),x68462,f208(x68461),x68463),f332(x68464,x68465)),f332(x68463,x68466))+~E(f332(x68464,x68465),f332(f239(x68462),x68466)) % 172.78/172.48 [8382]~P14(x83825,x83821,x83822,x83826)+E(f332(f72(x83821,x83821,x83821,f332(x83822,x83823)),f332(x83822,x83824)),f332(f72(x83821,x83821,x83821,f332(x83822,x83824)),f332(x83822,x83823))) % 172.78/172.48 [8620]~P52(x86204,x86205,x86202,x86201,x86206)+E(f332(x86201,f332(x86202,x86203)),x86203) % 172.78/172.48 [8771]P20(x87711,x87712,x87713,x87714)+~P20(x87711,x87715,f332(f72(x87712,x87715,x87711,x87716),x87713),x87714) % 172.78/172.48 [8855]~P20(x88554,x88552,f332(f72(x88551,x88552,x88554,x88553),x88555),x88556)+P20(x88551,x88552,x88553,f332(f311(x88554,x88551,x88555),x88556)) % 172.78/172.48 [9566]P102(f332(f61(x95661),x95662))+~P102(f332(f66(x95661,x95663,x95664,x95665,x95662),x95666)) % 172.78/172.48 [9574]~P102(f332(f332(f334(x95744),x95743),f300(x95744,x95745,x95741,x95742,x95746)))+P102(f332(f332(x95741,x95742),x95743)) % 172.78/172.48 [9575]~P102(f332(f332(f334(x95754),x95753),f297(x95754,x95751,x95755,x95752,x95756)))+P102(f332(f332(x95751,x95752),x95753)) % 172.78/172.48 [9576]~P102(f332(f332(f334(x95764),x95762),f300(x95764,x95761,x95765,x95766,x95763)))+P102(f332(f332(x95761,x95762),x95763)) % 172.78/172.48 [9577]~P102(f332(f332(f334(x95774),x95772),f297(x95774,x95775,x95771,x95776,x95773)))+P102(f332(f332(x95771,x95772),x95773)) % 172.78/172.48 [5765]E(x57651,x57652)+~E(f332(f332(f267(x57653,x57654),x57655),x57651),f332(f332(f267(x57653,x57654),x57656),x57652)) % 172.78/172.48 [5767]E(x57671,x57672)+~E(f332(f332(f267(x57673,x57674),x57671),x57675),f332(f332(f267(x57673,x57674),x57672),x57676)) % 172.78/172.48 [5891]~P11(x58915,x58916,x58911)+E(f332(f332(x58911,x58912),f332(f332(x58911,x58913),x58914)),f332(f332(x58911,x58913),f332(f332(x58911,x58912),x58914))) % 172.78/172.48 [7302]~P33(x73024,x73021,f332(f332(f151(x73024),x73022),x73025),f332(f332(f151(x73024),x73023),x73026))+P102(f332(f332(x73021,x73022),x73023)) % 172.78/172.48 [7670]P33(x76701,x76702,x76703,x76704)+~P33(x76701,x76702,f332(f332(f151(x76701),x76705),x76703),f332(f332(f151(x76701),x76706),x76704)) % 172.78/172.48 [8714]~P52(x87145,x87141,x87142,x87146,x87144)+P102(f332(f332(f334(x87141),f332(x87142,x87143)),x87144)) % 172.78/172.48 [8883]E(f332(f75(x88831,x88832,x88833,x88834,x88835),x88836),f332(x88833,x88836))+P102(f332(f332(f334(x88831),x88836),x88835)) % 172.78/172.48 [8905]~E(x89053,f332(f332(f151(x89051),x89055),x89056))+P102(f332(f332(f334(f882(f877(x89051),f877(x89051))),f332(f332(f267(f877(x89051),f877(x89051)),x89052),f332(f332(f134(x89051),x89052),x89053))),f147(x89051,x89054))) % 172.78/172.48 [8912]E(f332(f75(x89121,x89122,x89123,x89124,x89125),x89126),f332(x89124,x89126))+~P102(f332(f332(f334(x89121),x89126),x89125)) % 172.78/172.48 [8917]E(f332(f188(x89171,x89172,x89173,x89174,x89175),x89176),f332(x89173,x89176))+P102(f332(f332(f334(x89171),x89176),f332(f173(x89171),x89174))) % 172.78/172.48 [9146]~P35(x91461,x91462,x91463,x91465,x91466)+P35(x91461,x91462,x91463,f332(f332(f176(x91461),x91464),x91465),f332(f332(f176(x91462),x91464),x91466)) % 172.78/172.48 [9147]~P35(x91471,x91472,x91473,x91475,x91476)+P35(x91471,x91472,x91473,f332(f332(f138(x91471),x91474),x91475),f332(f332(f138(x91472),x91474),x91476)) % 172.78/172.48 [9638]~P18(x96384,x96382,x96385,x96383,x96386,x96381)+E(f332(x96381,f195(f883(x96382,a871))),x96383) % 172.78/172.48 [9881]~E(f332(x98814,f332(f266(x98811,x98813),x98815)),f332(x98816,f332(f266(x98811,x98813),x98815)))+E(f332(f272(x98811,x98812,x98813,x98813,x98814,f33(x98813)),x98815),f332(f272(x98811,x98812,x98813,x98813,x98816,f33(x98813)),x98815)) % 172.78/172.48 [9882]~E(f332(x98824,f332(f270(x98821,x98822),x98825)),f332(x98826,f332(f270(x98821,x98822),x98825)))+E(f332(f272(x98821,x98821,x98822,x98823,f33(x98821),x98824),x98825),f332(f272(x98821,x98821,x98822,x98823,f33(x98821),x98826),x98825)) % 172.78/172.48 [9927]~E(f332(f272(x99272,x99276,x99273,x99273,x99271,f33(x99273)),x99274),f332(f272(x99272,x99276,x99273,x99273,x99275,f33(x99273)),x99274))+E(f332(x99271,f332(f266(x99272,x99273),x99274)),f332(x99275,f332(f266(x99272,x99273),x99274))) % 172.78/172.48 [9928]~E(f332(f272(x99282,x99282,x99283,x99286,f33(x99282),x99281),x99284),f332(f272(x99282,x99282,x99283,x99286,f33(x99282),x99285),x99284))+E(f332(x99281,f332(f270(x99282,x99283),x99284)),f332(x99285,f332(f270(x99282,x99283),x99284))) % 172.78/172.48 [8810]P102(f332(f332(f334(x88101),x88102),x88103))+~P102(f332(f332(f334(f882(x88101,x88104)),f332(f332(f267(x88101,x88104),x88102),x88105)),f332(f332(f269(x88101,x88104),x88103),x88106))) % 172.78/172.48 [8825]P102(f332(f332(f334(x88251),x88252),f332(x88253,x88254)))+~P102(f332(f332(f334(f882(x88255,x88251)),f332(f332(f267(x88255,x88251),x88254),x88252)),f332(f332(f269(x88255,x88251),x88256),x88253))) % 172.78/172.48 [8914]~E(f332(f196(f877(x89141)),x89144),f332(f196(f877(x89142)),x89145))+E(f188(x89141,x89142,x89143,x89144,f332(f332(f134(x89142),x89145),x89146)),f188(x89141,x89142,x89143,x89144,x89145)) % 172.78/172.48 [8915]~E(f332(f196(f877(x89151)),x89154),f332(f196(f877(x89152)),x89156))+E(f188(x89151,x89152,x89153,f332(f332(f134(x89151),x89154),x89155),x89156),f188(x89151,x89152,x89153,x89154,x89156)) % 172.78/172.48 [9167]P102(f332(f332(f334(x91671),x91674),f185(x91671,x91672,x91676)))+E(f186(x91671,x91672,f332(f332(f332(f71(x91671,f880(x91672)),x91673),x91674),f332(f239(x91672),x91675)),x91676),f332(f332(f332(f71(x91671,f880(x91672)),f186(x91671,x91672,x91673,x91676)),x91674),f332(f239(x91672),x91675))) % 172.78/172.48 [9266]P102(f332(f332(f334(f882(x92661,x92661)),f332(f332(f267(x92661,x92661),f332(x92662,x92663)),f332(x92662,x92664))),x92665))+~P102(f332(f332(f334(f882(x92666,x92666)),f332(f332(f267(x92666,x92666),x92663),x92664)),f332(f332(f288(x92661,x92666),x92665),x92662))) % 172.78/172.48 [9286]~P102(f332(f332(f334(f882(x92864,x92864)),f332(f332(f267(x92864,x92864),f332(x92866,x92862)),f332(x92866,x92863))),x92865))+P102(f332(f332(f334(f882(x92861,x92861)),f332(f332(f267(x92861,x92861),x92862),x92863)),f332(f332(f288(x92864,x92861),x92865),x92866))) % 172.78/172.48 [9930]E(f332(f332(f267(x99301,x99302),f663(x99303,x99304,x99305,x99306,x99302,x99301)),f664(x99303,x99304,x99305,x99306,x99302,x99301)),x99306)+~P102(f332(f332(f334(f882(x99301,x99302)),x99306),f332(f332(f289(x99301,x99305,x99302),x99304),x99303))) % 172.78/172.48 [10131]~P102(f332(f332(f334(f882(x101311,x101316)),x101315),f332(f332(f289(x101311,x101312,x101316),x101314),x101313)))+P102(f332(f332(f334(f882(x101311,x101312)),f332(f332(f267(x101311,x101312),f663(x101313,x101314,x101312,x101315,x101316,x101311)),f665(x101313,x101314,x101312,x101315,x101316,x101311))),x101314)) % 172.78/172.48 [10132]~P102(f332(f332(f334(f882(x101326,x101322)),x101325),f332(f332(f289(x101326,x101321,x101322),x101324),x101323)))+P102(f332(f332(f334(f882(x101321,x101322)),f332(f332(f267(x101321,x101322),f665(x101323,x101324,x101321,x101325,x101322,x101326)),f664(x101323,x101324,x101321,x101325,x101322,x101326))),x101323)) % 172.78/172.48 [6165]~E(x61656,x61654)+E(f332(f332(f332(f332(f71(x61651,x61652),x61653),x61654),x61655),x61656),x61655) % 172.78/172.48 [6215]E(x62151,x62152)+E(f332(f332(f332(f332(f71(x62153,x62154),x62155),x62152),x62156),x62151),f332(x62155,x62151)) % 172.78/172.48 [7743]~P27(x77432)+E(f332(f332(f41(x77431,x77432),x77433),f332(f332(f7(x77431,x77434,x77432),x77435),x77436)),f332(f332(f332(f41(x77431,f883(x77434,x77432)),x77433),x77435),x77436)) % 172.78/172.48 [7744]~P27(x77442)+E(f332(f332(f42(x77441,x77442),x77443),f332(f332(f7(x77441,x77444,x77442),x77445),x77446)),f332(f332(f332(f42(x77441,f883(x77444,x77442)),x77443),x77445),x77446)) % 172.78/172.48 [8535]E(f332(f332(f41(x85351,f883(x85352,a871)),x85353),f332(f332(f8(f883(x85352,a871),f883(x85352,a871),x85351),f332(f310(x85352),x85354)),x85355)),f332(f332(f310(x85352),x85354),f332(f332(f41(x85351,f883(x85352,a871)),x85353),x85355)))+~P102(f332(f332(f334(x85351),x85356),x85353)) % 172.78/172.48 [8969]~P27(x89692)+E(f332(f332(f41(x89691,x89692),x89693),f332(f332(f8(f883(x89694,x89692),x89692,x89691),f332(f41(x89694,x89692),x89695)),f332(f7(x89694,x89691,x89692),x89696))),f332(f332(f41(x89694,x89692),x89695),f332(f332(f8(f883(x89691,x89692),x89692,x89694),f332(f41(x89691,x89692),x89693)),x89696))) % 172.78/172.48 [8970]~P27(x89702)+E(f332(f332(f42(x89701,x89702),x89703),f332(f332(f8(f883(x89704,x89702),x89702,x89701),f332(f42(x89704,x89702),x89705)),f332(f7(x89704,x89701,x89702),x89706))),f332(f332(f42(x89704,x89702),x89705),f332(f332(f8(f883(x89701,x89702),x89702,x89704),f332(f42(x89701,x89702),x89703)),x89706))) % 172.78/172.48 [9176]P102(f332(f332(f334(x91761),x91762),f332(f173(x91761),x91763)))+~P102(f332(f332(f334(f882(x91764,x91761)),f332(f332(f267(x91764,x91761),x91765),x91762)),f332(f173(f882(x91764,x91761)),f332(f332(f183(x91764,x91761),x91766),x91763)))) % 172.78/172.48 [9177]P102(f332(f332(f334(x91771),x91772),f332(f173(x91771),x91773)))+~P102(f332(f332(f334(f882(x91771,x91774)),f332(f332(f267(x91771,x91774),x91772),x91775)),f332(f173(f882(x91771,x91774)),f332(f332(f183(x91771,x91774),x91773),x91776)))) % 172.78/172.48 [9280]P102(f332(f332(f246(f883(x92801,a871)),f332(f286(x92802,x92801,x92803),x92804)),x92805))+~P102(f332(f332(f246(f883(f882(x92802,x92801),a871)),x92803),f332(f332(f269(x92802,x92801),x92806),f332(f16(f883(x92801,a871),x92802),x92805)))) % 172.78/172.48 [9471]P102(f332(f332(f334(f882(f877(x94711),f877(x94711))),f332(f332(f267(f877(x94711),f877(x94711)),f332(f332(f151(x94711),x94712),x94713)),f332(f332(f151(x94711),x94714),x94715))),f147(x94711,x94716)))+~P102(f332(f332(f334(f882(x94711,x94711)),f332(f332(f267(x94711,x94711),x94712),x94714)),x94716)) % 172.78/172.48 [9926]E(f332(f332(f267(x99261,x99262),f575(x99263,x99264,x99265,x99262,x99261,x99266)),f576(x99263,x99264,x99265,x99262,x99261,x99266)),x99266)+P102(f332(f332(f334(x99265),x99264),f332(f332(f271(x99261,x99262,f883(x99265,a871)),x99263),x99266))) % 172.78/172.48 [9932]E(f332(f332(f267(x99321,x99322),f577(x99323,x99324,x99322,x99321,x99325,x99326)),f578(x99323,x99324,x99322,x99321,x99325,x99326)),x99323)+~P102(f332(f332(f334(x99326),x99325),f332(f332(f271(x99321,x99322,f883(x99326,a871)),x99324),x99323))) % 172.78/172.48 [10090]P102(f332(f332(f334(x100901),x100902),f332(f332(x100903,f577(x100904,x100903,x100905,x100906,x100902,x100901)),f578(x100904,x100903,x100905,x100906,x100902,x100901))))+~P102(f332(f332(f334(x100901),x100902),f332(f332(f271(x100906,x100905,f883(x100901,a871)),x100903),x100904))) % 172.78/172.48 [10109]~P102(f332(f332(f334(x101091),x101092),f332(f332(x101095,f575(x101095,x101092,x101091,x101094,x101093,x101096)),f576(x101095,x101092,x101091,x101094,x101093,x101096))))+P102(f332(f332(f334(x101091),x101092),f332(f332(f271(x101093,x101094,f883(x101091,a871)),x101095),x101096))) % 172.78/172.48 [7866]P102(f332(f332(f334(x78661),x78664),x78666))+E(f189(x78661,x78662,f332(f332(f332(f71(x78661,f880(x78662)),x78663),x78664),x78665),x78666),f189(x78661,x78662,x78663,x78666)) % 172.78/172.48 [7943]P102(f332(f332(f334(x79431),x79434),x79436))+E(f332(f311(x79431,x79432,f332(f332(f332(f71(x79431,x79432),x79433),x79434),x79435)),x79436),f332(f311(x79431,x79432,x79433),x79436)) % 172.78/172.48 [7970]P102(f332(f332(f334(x79701),x79704),f332(f173(x79701),x79706)))+E(f332(f332(f154(x79701,x79702),f332(f332(f332(f71(x79701,x79702),x79703),x79704),x79705)),x79706),f332(f332(f154(x79701,x79702),x79703),x79706)) % 172.78/172.48 [8432]E(x84321,x84322)+E(f332(f332(f159(x84323,f332(f332(f159(x84323,x84324),x84321),x84325)),x84322),x84326),f332(f332(f159(x84323,f332(f332(f159(x84323,x84324),x84322),x84326)),x84321),x84325)) % 172.78/172.48 [8975]~P102(f332(f332(f334(x89753),x89756),x89755))+E(f332(f332(f310(x89751),x89752),f332(f311(x89753,x89751,x89754),f332(f332(f22(f883(x89753,a871)),x89755),f332(f332(f310(x89753),x89756),f195(f883(x89753,a871)))))),f332(f311(x89753,x89751,f332(f332(f332(f71(x89753,x89751),x89754),x89756),x89752)),x89755)) % 172.78/172.48 [9743]E(f188(x97431,x97432,x97433,f332(f332(f134(x97431),x97434),f332(f332(f151(x97431),x97435),f116(x97431))),x97436),f332(f332(f332(f71(x97431,f880(x97432)),f188(x97431,x97432,x97433,x97434,x97436)),x97435),f332(f239(x97432),f332(f332(f165(x97432),x97436),f332(f196(f877(x97431)),x97434)))))+~P102(f332(f332(f247(a876),f332(f196(f877(x97431)),x97434)),f332(f196(f877(x97432)),x97436))) % 172.78/172.48 [8753]~E(x87533,x87536)+E(f332(f332(f179(x87531,x87532),f332(f332(f151(f882(x87531,x87532)),f332(f332(f267(x87531,x87532),x87533),x87534)),x87535)),x87536),f332(f239(x87532),x87534)) % 172.78/172.48 [8780]E(x87801,x87802)+E(f332(f332(f179(x87803,x87804),f332(f332(f151(f882(x87803,x87804)),f332(f332(f267(x87803,x87804),x87801),x87805)),x87806)),x87802),f332(f332(f179(x87803,x87804),x87806),x87802)) % 172.78/172.48 [9051]~P102(f332(f332(x90514,x90515),x90516))+P102(f332(f332(f332(f332(f113(f883(x90511,f883(x90512,a871))),x90513),x90514),x90515),x90516)) % 172.78/172.48 [9053]~P102(f332(f332(x90533,x90535),x90536))+P102(f332(f332(f332(f332(f113(f883(x90531,f883(x90532,a871))),x90533),x90534),x90535),x90536)) % 172.78/172.48 [9337]P102(f332(f332(x93371,x93372),x93373))+~P102(f332(f332(f332(f332(f104(f883(x93374,f883(x93375,a871))),x93376),x93371),x93372),x93373)) % 172.78/172.48 [9338]P102(f332(f332(x93381,x93382),x93383))+~P102(f332(f332(f332(f332(f104(f883(x93384,f883(x93385,a871))),x93381),x93386),x93382),x93383)) % 172.78/172.48 [9765]~P71(x97652)+E(f332(f332(f6(x97651,x97652),f332(f332(f7(x97651,f883(x97653,a871),x97652),f332(f332(f8(f883(x97653,x97652),f883(f883(x97653,a871),x97652),x97651),f6(x97653,x97652)),x97654)),x97655)),x97656),f332(f332(f6(f882(x97651,x97653),x97652),f332(f271(x97651,x97653,x97652),x97654)),f332(f332(f269(x97651,x97653),x97656),f332(f16(f883(x97653,a871),x97651),x97655)))) % 172.78/172.48 [9766]~P67(x97662)+E(f332(f332(f9(x97661,x97662),f332(f332(f7(x97661,f883(x97663,a871),x97662),f332(f332(f8(f883(x97663,x97662),f883(f883(x97663,a871),x97662),x97661),f9(x97663,x97662)),x97664)),x97665)),x97666),f332(f332(f9(f882(x97661,x97663),x97662),f332(f271(x97661,x97663,x97662),x97664)),f332(f332(f269(x97661,x97663),x97666),f332(f16(f883(x97663,a871),x97661),x97665)))) % 172.78/172.48 [9909]~P71(x99092)+E(f332(f332(f6(x99091,x99092),f332(f332(f7(x99091,f883(x99093,a871),x99092),f332(f332(f8(f883(x99093,x99092),f883(f883(x99093,a871),x99092),x99091),f6(x99093,x99092)),f332(f7(x99093,x99091,x99092),x99094))),x99095)),x99096),f332(f332(f6(x99093,x99092),f332(f332(f7(x99093,f883(x99091,a871),x99092),f332(f332(f8(f883(x99091,x99092),f883(f883(x99091,a871),x99092),x99093),f6(x99091,x99092)),x99094)),x99096)),x99095)) % 172.78/172.48 [9607]~P102(f332(f332(f334(x96071),x96075),x96074))+E(f332(f332(f332(f71(x96071,f880(x96072)),f189(x96071,x96072,x96073,f332(f332(f22(f883(x96071,a871)),x96074),f332(f332(f310(x96071),x96075),f195(f883(x96071,a871)))))),x96075),x96076),f189(x96071,x96072,f332(f332(f332(f71(x96071,f880(x96072)),x96073),x96075),x96076),x96074)) % 172.78/172.48 [10187]~P102(f332(f332(f334(f882(x101871,x101872)),f332(f332(f267(x101871,x101872),x101875),x101876)),f332(f332(f113(f883(f882(x101871,x101872),a871)),x101873),x101874)))+P102(f332(f332(f332(f332(f113(f883(x101871,f883(x101872,a871))),f332(f332(f7(x101871,f883(f882(x101871,x101872),a871),f883(x101872,a871)),f332(f332(f8(f883(x101872,f883(f883(f882(x101871,x101872),a871),a871)),f883(f883(f882(x101871,x101872),a871),f883(x101872,a871)),x101871),f7(x101872,f883(f882(x101871,x101872),a871),a871)),f332(f332(f8(f883(x101872,f882(x101871,x101872)),f883(x101872,f883(f883(f882(x101871,x101872),a871),a871)),x101871),f332(f8(f882(x101871,x101872),f883(f883(f882(x101871,x101872),a871),a871),x101872),f334(f882(x101871,x101872)))),f267(x101871,x101872)))),x101873)),f332(f332(f7(x101871,f883(f882(x101871,x101872),a871),f883(x101872,a871)),f332(f332(f8(f883(x101872,f883(f883(f882(x101871,x101872),a871),a871)),f883(f883(f882(x101871,x101872),a871),f883(x101872,a871)),x101871),f7(x101872,f883(f882(x101871,x101872),a871),a871)),f332(f332(f8(f883(x101872,f882(x101871,x101872)),f883(x101872,f883(f883(f882(x101871,x101872),a871),a871)),x101871),f332(f8(f882(x101871,x101872),f883(f883(f882(x101871,x101872),a871),a871),x101872),f334(f882(x101871,x101872)))),f267(x101871,x101872)))),x101874)),x101875),x101876)) % 172.78/172.48 [10188]~P102(f332(f332(f334(f882(x101881,x101882)),f332(f332(f267(x101881,x101882),x101885),x101886)),f332(f332(f104(f883(f882(x101881,x101882),a871)),x101883),x101884)))+P102(f332(f332(f332(f332(f104(f883(x101881,f883(x101882,a871))),f332(f332(f7(x101881,f883(f882(x101881,x101882),a871),f883(x101882,a871)),f332(f332(f8(f883(x101882,f883(f883(f882(x101881,x101882),a871),a871)),f883(f883(f882(x101881,x101882),a871),f883(x101882,a871)),x101881),f7(x101882,f883(f882(x101881,x101882),a871),a871)),f332(f332(f8(f883(x101882,f882(x101881,x101882)),f883(x101882,f883(f883(f882(x101881,x101882),a871),a871)),x101881),f332(f8(f882(x101881,x101882),f883(f883(f882(x101881,x101882),a871),a871),x101882),f334(f882(x101881,x101882)))),f267(x101881,x101882)))),x101883)),f332(f332(f7(x101881,f883(f882(x101881,x101882),a871),f883(x101882,a871)),f332(f332(f8(f883(x101882,f883(f883(f882(x101881,x101882),a871),a871)),f883(f883(f882(x101881,x101882),a871),f883(x101882,a871)),x101881),f7(x101882,f883(f882(x101881,x101882),a871),a871)),f332(f332(f8(f883(x101882,f882(x101881,x101882)),f883(x101882,f883(f883(f882(x101881,x101882),a871),a871)),x101881),f332(f8(f882(x101881,x101882),f883(f883(f882(x101881,x101882),a871),a871),x101882),f334(f882(x101881,x101882)))),f267(x101881,x101882)))),x101884)),x101885),x101886)) % 172.78/172.48 [10194]P102(f332(f332(f334(f882(x101941,x101942)),f332(f332(f267(x101941,x101942),x101943),x101944)),f332(f332(f113(f883(f882(x101941,x101942),a871)),x101945),x101946)))+~P102(f332(f332(f332(f332(f113(f883(x101941,f883(x101942,a871))),f332(f332(f7(x101941,f883(f882(x101941,x101942),a871),f883(x101942,a871)),f332(f332(f8(f883(x101942,f883(f883(f882(x101941,x101942),a871),a871)),f883(f883(f882(x101941,x101942),a871),f883(x101942,a871)),x101941),f7(x101942,f883(f882(x101941,x101942),a871),a871)),f332(f332(f8(f883(x101942,f882(x101941,x101942)),f883(x101942,f883(f883(f882(x101941,x101942),a871),a871)),x101941),f332(f8(f882(x101941,x101942),f883(f883(f882(x101941,x101942),a871),a871),x101942),f334(f882(x101941,x101942)))),f267(x101941,x101942)))),x101945)),f332(f332(f7(x101941,f883(f882(x101941,x101942),a871),f883(x101942,a871)),f332(f332(f8(f883(x101942,f883(f883(f882(x101941,x101942),a871),a871)),f883(f883(f882(x101941,x101942),a871),f883(x101942,a871)),x101941),f7(x101942,f883(f882(x101941,x101942),a871),a871)),f332(f332(f8(f883(x101942,f882(x101941,x101942)),f883(x101942,f883(f883(f882(x101941,x101942),a871),a871)),x101941),f332(f8(f882(x101941,x101942),f883(f883(f882(x101941,x101942),a871),a871),x101942),f334(f882(x101941,x101942)))),f267(x101941,x101942)))),x101946)),x101943),x101944)) % 172.78/172.48 [10195]P102(f332(f332(f334(f882(x101951,x101952)),f332(f332(f267(x101951,x101952),x101953),x101954)),f332(f332(f104(f883(f882(x101951,x101952),a871)),x101955),x101956)))+~P102(f332(f332(f332(f332(f104(f883(x101951,f883(x101952,a871))),f332(f332(f7(x101951,f883(f882(x101951,x101952),a871),f883(x101952,a871)),f332(f332(f8(f883(x101952,f883(f883(f882(x101951,x101952),a871),a871)),f883(f883(f882(x101951,x101952),a871),f883(x101952,a871)),x101951),f7(x101952,f883(f882(x101951,x101952),a871),a871)),f332(f332(f8(f883(x101952,f882(x101951,x101952)),f883(x101952,f883(f883(f882(x101951,x101952),a871),a871)),x101951),f332(f8(f882(x101951,x101952),f883(f883(f882(x101951,x101952),a871),a871),x101952),f334(f882(x101951,x101952)))),f267(x101951,x101952)))),x101955)),f332(f332(f7(x101951,f883(f882(x101951,x101952),a871),f883(x101952,a871)),f332(f332(f8(f883(x101952,f883(f883(f882(x101951,x101952),a871),a871)),f883(f883(f882(x101951,x101952),a871),f883(x101952,a871)),x101951),f7(x101952,f883(f882(x101951,x101952),a871),a871)),f332(f332(f8(f883(x101952,f882(x101951,x101952)),f883(x101952,f883(f883(f882(x101951,x101952),a871),a871)),x101951),f332(f8(f882(x101951,x101952),f883(f883(f882(x101951,x101952),a871),a871),x101952),f334(f882(x101951,x101952)))),f267(x101951,x101952)))),x101956)),x101953),x101954)) % 172.78/172.48 [10181]~P102(f332(f332(f334(f882(x101812,x101813)),f332(f332(f267(x101812,x101813),x101815),x101816)),f332(f332(f41(x101811,f883(f882(x101812,x101813),a871)),f255(f883(x101811,a871))),x101814)))+P102(f332(f332(f332(f332(f41(x101811,f883(x101812,f883(x101813,a871))),f255(f883(x101811,a871))),f332(f332(f8(f883(f882(x101812,x101813),a871),f883(x101812,f883(x101813,a871)),x101811),f332(f7(x101812,f883(f882(x101812,x101813),a871),f883(x101813,a871)),f332(f332(f8(f883(x101813,f883(f883(f882(x101812,x101813),a871),a871)),f883(f883(f882(x101812,x101813),a871),f883(x101813,a871)),x101812),f7(x101813,f883(f882(x101812,x101813),a871),a871)),f332(f332(f8(f883(x101813,f882(x101812,x101813)),f883(x101813,f883(f883(f882(x101812,x101813),a871),a871)),x101812),f332(f8(f882(x101812,x101813),f883(f883(f882(x101812,x101813),a871),a871),x101813),f334(f882(x101812,x101813)))),f267(x101812,x101813))))),x101814)),x101815),x101816)) % 172.78/172.48 [10182]~P102(f332(f332(f334(f882(x101822,x101823)),f332(f332(f267(x101822,x101823),x101825),x101826)),f332(f332(f42(x101821,f883(f882(x101822,x101823),a871)),f255(f883(x101821,a871))),x101824)))+P102(f332(f332(f332(f332(f42(x101821,f883(x101822,f883(x101823,a871))),f255(f883(x101821,a871))),f332(f332(f8(f883(f882(x101822,x101823),a871),f883(x101822,f883(x101823,a871)),x101821),f332(f7(x101822,f883(f882(x101822,x101823),a871),f883(x101823,a871)),f332(f332(f8(f883(x101823,f883(f883(f882(x101822,x101823),a871),a871)),f883(f883(f882(x101822,x101823),a871),f883(x101823,a871)),x101822),f7(x101823,f883(f882(x101822,x101823),a871),a871)),f332(f332(f8(f883(x101823,f882(x101822,x101823)),f883(x101823,f883(f883(f882(x101822,x101823),a871),a871)),x101822),f332(f8(f882(x101822,x101823),f883(f883(f882(x101822,x101823),a871),a871),x101823),f334(f882(x101822,x101823)))),f267(x101822,x101823))))),x101824)),x101825),x101826)) % 172.78/172.48 [10191]P102(f332(f332(f334(f882(x101911,x101912)),f332(f332(f267(x101911,x101912),x101913),x101914)),f332(f332(f41(x101915,f883(f882(x101911,x101912),a871)),f255(f883(x101915,a871))),x101916)))+~P102(f332(f332(f332(f332(f41(x101915,f883(x101911,f883(x101912,a871))),f255(f883(x101915,a871))),f332(f332(f8(f883(f882(x101911,x101912),a871),f883(x101911,f883(x101912,a871)),x101915),f332(f7(x101911,f883(f882(x101911,x101912),a871),f883(x101912,a871)),f332(f332(f8(f883(x101912,f883(f883(f882(x101911,x101912),a871),a871)),f883(f883(f882(x101911,x101912),a871),f883(x101912,a871)),x101911),f7(x101912,f883(f882(x101911,x101912),a871),a871)),f332(f332(f8(f883(x101912,f882(x101911,x101912)),f883(x101912,f883(f883(f882(x101911,x101912),a871),a871)),x101911),f332(f8(f882(x101911,x101912),f883(f883(f882(x101911,x101912),a871),a871),x101912),f334(f882(x101911,x101912)))),f267(x101911,x101912))))),x101916)),x101913),x101914)) % 172.78/172.48 [10192]P102(f332(f332(f334(f882(x101921,x101922)),f332(f332(f267(x101921,x101922),x101923),x101924)),f332(f332(f42(x101925,f883(f882(x101921,x101922),a871)),f255(f883(x101925,a871))),x101926)))+~P102(f332(f332(f332(f332(f42(x101925,f883(x101921,f883(x101922,a871))),f255(f883(x101925,a871))),f332(f332(f8(f883(f882(x101921,x101922),a871),f883(x101921,f883(x101922,a871)),x101925),f332(f7(x101921,f883(f882(x101921,x101922),a871),f883(x101922,a871)),f332(f332(f8(f883(x101922,f883(f883(f882(x101921,x101922),a871),a871)),f883(f883(f882(x101921,x101922),a871),f883(x101922,a871)),x101921),f7(x101922,f883(f882(x101921,x101922),a871),a871)),f332(f332(f8(f883(x101922,f882(x101921,x101922)),f883(x101922,f883(f883(f882(x101921,x101922),a871),a871)),x101921),f332(f8(f882(x101921,x101922),f883(f883(f882(x101921,x101922),a871),a871),x101922),f334(f882(x101921,x101922)))),f267(x101921,x101922))))),x101926)),x101923),x101924)) % 172.78/172.48 [7415]E(f332(x74151,f332(x74152,x74153)),f332(x74154,x74153))+~E(f332(f72(x74155,x74156,x74157,x74151),x74152),x74154) % 172.78/172.48 [9637]~P17(x96373,x96374,x96371,x96375,x96376,x96377)+E(f332(f332(x96371,x96372),x96372),x96372) % 172.78/172.48 [10006]~E(f332(f241(f880(x100067),x100061,f208(x100067),x100065),f332(x100064,x100063)),f332(f239(x100067),x100062))+E(f332(f239(x100061),f769(x100062,x100063,x100064,x100065,x100066,x100067,x100061)),f332(x100064,x100063)) % 172.78/172.48 [10007]~E(f332(f241(f880(x100076),x100077,f208(x100076),x100071),f332(x100074,x100073)),f332(f239(x100076),x100072))+E(f332(x100071,f769(x100072,x100073,x100074,x100071,x100075,x100076,x100077)),f332(f239(x100076),x100072)) % 172.78/172.48 [5993]~E(f332(f332(f154(x59931,x59935),x59936),x59932),f332(f332(f154(x59933,x59935),x59937),x59934))+E(f332(f196(f877(x59931)),x59932),f332(f196(f877(x59933)),x59934)) % 172.78/172.48 [7493]E(x74931,x74932)+~E(f332(f332(f332(f71(x74933,f880(x74934)),x74935),x74936),f332(f239(x74934),x74931)),f332(f332(f332(f71(x74933,f880(x74934)),x74937),x74936),f332(f239(x74934),x74932))) % 172.78/172.48 [8471]E(f332(x84711,f332(x84712,x84713)),f332(x84714,x84713))+~E(f332(f72(x84715,x84716,x84717,x84711),x84712),f332(f72(x84716,x84716,x84717,f33(x84716)),x84714)) % 172.78/172.48 [8799]~P35(x87994,x87995,x87991,f332(f332(f151(x87994),x87992),x87996),f332(f332(f151(x87995),x87993),x87997))+P102(f332(f332(x87991,x87992),x87993)) % 172.78/172.48 [9183]P35(x91831,x91832,x91833,x91834,x91835)+~P35(x91831,x91832,x91833,f332(f332(f151(x91831),x91836),x91834),f332(f332(f151(x91832),x91837),x91835)) % 172.78/172.48 [9804]P102(f332(f332(x98041,x98042),f528(x98043,x98042,x98044,x98041)))+~P102(f332(f332(f268(x98045,x98046,x98047,x98041,x98044),x98042),x98043)) % 172.78/172.48 [9825]P102(f332(f332(x98251,f528(x98252,x98253,x98251,x98254)),x98252))+~P102(f332(f332(f268(x98255,x98256,x98257,x98254,x98251),x98253),x98252)) % 172.78/172.48 [6037]E(x60371,x60372)+~E(f332(f332(f332(f91(x60373),x60374),x60375),x60371),f332(f332(f332(f91(x60373),x60376),x60377),x60372)) % 172.78/172.48 [6038]E(x60381,x60382)+~E(f332(f332(f332(f91(x60383),x60384),x60381),x60385),f332(f332(f332(f91(x60383),x60386),x60382),x60387)) % 172.78/172.48 [6039]E(x60391,x60392)+~E(f332(f332(f332(f91(x60393),x60391),x60394),x60395),f332(f332(f332(f91(x60393),x60392),x60396),x60397)) % 172.78/172.48 [8920]~P15(x89206,x89201,x89203,x89207)+E(f332(f72(x89201,x89201,x89202,f332(x89203,x89204)),f332(f72(x89201,x89201,x89202,f332(x89203,x89204)),x89205)),f332(f72(x89201,x89201,x89202,f332(x89203,x89204)),x89205)) % 172.78/172.48 [9289]~P35(x92893,x92892,x92894,f332(f332(f154(x92891,x92893),x92895),x92896),x92897)+P35(x92891,x92892,f332(f332(f8(x92893,f883(x92892,a871),x92891),x92894),x92895),x92896,x92897) % 172.78/172.48 [9312]P35(x93121,x93122,x93123,f332(f332(f154(x93124,x93121),x93125),x93126),x93127)+~P35(x93124,x93122,f332(f332(f8(x93121,f883(x93122,a871),x93124),x93123),x93125),x93126,x93127) % 172.78/172.48 [9723]E(f188(x97231,x97232,f332(f332(f332(f71(x97231,f880(x97232)),x97233),x97234),f332(f239(x97232),x97235)),x97236,x97237),f332(f332(f332(f71(x97231,f880(x97232)),f188(x97231,x97232,x97233,x97236,x97237)),x97234),f332(f239(x97232),x97235)))+P102(f332(f332(f334(x97231),x97234),f332(f173(x97231),x97236))) % 172.78/172.48 [8919]~P102(f332(f332(f334(x89191),x89192),f332(f332(x89195,x89196),x89197)))+P102(f332(f332(f334(x89191),x89192),f332(f332(f271(x89193,x89194,f883(x89191,a871)),x89195),f332(f332(f267(x89193,x89194),x89196),x89197)))) % 172.78/172.48 [9209]P102(f332(f332(f332(x92091,x92092),x92093),x92094))+~P102(f332(f332(f332(f271(x92095,x92096,f883(x92097,a871)),x92091),f332(f332(f267(x92095,x92096),x92092),x92093)),x92094)) % 172.78/172.48 [9351]P102(f332(f332(f334(x93511),f332(f332(x93512,x93513),x93514)),f332(f311(f882(x93515,x93516),x93511,f332(f271(x93515,x93516,x93511),x93512)),x93517)))+~P102(f332(f332(f334(f882(x93515,x93516)),f332(f332(f267(x93515,x93516),x93513),x93514)),x93517)) % 172.78/172.48 [9684]P102(f332(f332(f334(f882(f877(x96841),f877(x96841))),f332(f332(f267(f877(x96841),f877(x96841)),f332(f332(f134(x96841),x96842),f332(f332(f151(x96841),x96843),x96844))),f332(f332(f134(x96841),x96842),f332(f332(f151(x96841),x96845),x96846)))),f147(x96841,x96847)))+~P102(f332(f332(f334(f882(x96841,x96841)),f332(f332(f267(x96841,x96841),x96843),x96845)),x96847)) % 172.78/172.48 [9745]~P35(x97451,x97453,x97454,x97456,f332(f332(f154(x97452,x97453),x97455),x97457))+P35(x97451,x97452,f332(f332(f7(x97451,f883(x97452,x97453),f883(x97452,a871)),f332(f332(f8(f883(x97453,a871),f883(f883(x97452,x97453),f883(x97452,a871)),x97451),f8(x97453,a871,x97452)),x97454)),x97455),x97456,x97457) % 172.78/172.48 [9829]P35(x98291,x98292,x98293,x98294,f332(f332(f154(x98295,x98292),x98296),x98297))+~P35(x98291,x98295,f332(f332(f7(x98291,f883(x98295,x98292),f883(x98295,a871)),f332(f332(f8(f883(x98292,a871),f883(f883(x98295,x98292),f883(x98295,a871)),x98291),f8(x98292,a871,x98295)),x98293)),x98296),x98294,x98297) % 172.78/172.48 [9201]E(x92011,x92012)+E(f332(f332(f332(f71(x92013,x92014),f332(f332(f332(f71(x92013,x92014),x92015),x92011),x92016)),x92012),x92017),f332(f332(f332(f71(x92013,x92014),f332(f332(f332(f71(x92013,x92014),x92015),x92012),x92017)),x92011),x92016)) % 172.78/172.48 [9445]E(f188(x94451,x94452,f332(f332(f332(f71(x94451,f880(x94452)),x94453),x94454),f332(f239(x94452),x94455)),x94456,x94457),f188(x94451,x94452,x94453,x94456,x94457))+~P102(f332(f332(f334(x94451),x94454),f332(f173(x94451),f332(f332(f176(x94451),f332(f196(f877(x94452)),x94457)),x94456)))) % 172.78/172.48 [9756]E(f188(x97561,x97562,f332(f332(f332(f71(x97561,f880(x97562)),x97563),x97564),f332(f239(x97562),x97565)),x97566,x97567),f332(f332(f332(f71(x97561,f880(x97562)),f188(x97561,x97562,x97563,x97566,x97567)),x97564),f332(f239(x97562),x97565)))+P102(f332(f332(f334(x97561),x97564),f332(f173(x97561),f332(f332(f176(x97561),f332(f196(f877(x97562)),x97567)),x97566)))) % 172.78/172.48 [10120]P102(f332(f332(f334(x101201),f632(x101202,x101203,x101204,x101205,x101206,x101207,x101201)),x101205))+P102(f332(f332(f332(f332(f42(x101201,f883(x101207,f883(x101206,a871))),x101205),x101204),x101203),x101202)) % 172.78/172.48 [10121]P102(f332(f332(f334(x101211),f461(x101212,x101213,x101214,x101215,x101216,x101217,x101211)),x101215))+~P102(f332(f332(f332(f332(f41(x101211,f883(x101217,f883(x101216,a871))),x101215),x101214),x101213),x101212)) % 172.78/172.48 [10146]P102(f332(f332(f332(x101461,f461(x101462,x101463,x101461,x101464,x101465,x101466,x101467)),x101463),x101462))+~P102(f332(f332(f332(f332(f41(x101467,f883(x101466,f883(x101465,a871))),x101464),x101461),x101463),x101462)) % 172.78/172.48 [10163]~P102(f332(f332(f332(x101635,f632(x101637,x101636,x101635,x101634,x101633,x101632,x101631)),x101636),x101637))+P102(f332(f332(f332(f332(f42(x101631,f883(x101632,f883(x101633,a871))),x101634),x101635),x101636),x101637)) % 172.78/172.48 [10180]~P102(f332(f332(f334(f882(x101801,x101803)),f332(f332(f267(x101801,x101803),x101806),x101807)),f332(f332(f289(x101801,x101802,x101803),x101804),x101805)))+P102(f332(f332(f268(x101801,x101802,x101803,f332(f332(f7(x101801,f883(f882(x101801,x101802),a871),f883(x101802,a871)),f332(f332(f8(f883(x101802,f883(f883(f882(x101801,x101802),a871),a871)),f883(f883(f882(x101801,x101802),a871),f883(x101802,a871)),x101801),f7(x101802,f883(f882(x101801,x101802),a871),a871)),f332(f332(f8(f883(x101802,f882(x101801,x101802)),f883(x101802,f883(f883(f882(x101801,x101802),a871),a871)),x101801),f332(f8(f882(x101801,x101802),f883(f883(f882(x101801,x101802),a871),a871),x101802),f334(f882(x101801,x101802)))),f267(x101801,x101802)))),x101804),f332(f332(f7(x101802,f883(f882(x101802,x101803),a871),f883(x101803,a871)),f332(f332(f8(f883(x101803,f883(f883(f882(x101802,x101803),a871),a871)),f883(f883(f882(x101802,x101803),a871),f883(x101803,a871)),x101802),f7(x101803,f883(f882(x101802,x101803),a871),a871)),f332(f332(f8(f883(x101803,f882(x101802,x101803)),f883(x101803,f883(f883(f882(x101802,x101803),a871),a871)),x101802),f332(f8(f882(x101802,x101803),f883(f883(f882(x101802,x101803),a871),a871),x101803),f334(f882(x101802,x101803)))),f267(x101802,x101803)))),x101805)),x101806),x101807)) % 172.78/172.48 [10190]P102(f332(f332(f334(f882(x101901,x101902)),f332(f332(f267(x101901,x101902),x101903),x101904)),f332(f332(f289(x101901,x101905,x101902),x101906),x101907)))+~P102(f332(f332(f268(x101901,x101905,x101902,f332(f332(f7(x101901,f883(f882(x101901,x101905),a871),f883(x101905,a871)),f332(f332(f8(f883(x101905,f883(f883(f882(x101901,x101905),a871),a871)),f883(f883(f882(x101901,x101905),a871),f883(x101905,a871)),x101901),f7(x101905,f883(f882(x101901,x101905),a871),a871)),f332(f332(f8(f883(x101905,f882(x101901,x101905)),f883(x101905,f883(f883(f882(x101901,x101905),a871),a871)),x101901),f332(f8(f882(x101901,x101905),f883(f883(f882(x101901,x101905),a871),a871),x101905),f334(f882(x101901,x101905)))),f267(x101901,x101905)))),x101906),f332(f332(f7(x101905,f883(f882(x101905,x101902),a871),f883(x101902,a871)),f332(f332(f8(f883(x101902,f883(f883(f882(x101905,x101902),a871),a871)),f883(f883(f882(x101905,x101902),a871),f883(x101902,a871)),x101905),f7(x101902,f883(f882(x101905,x101902),a871),a871)),f332(f332(f8(f883(x101902,f882(x101905,x101902)),f883(x101902,f883(f883(f882(x101905,x101902),a871),a871)),x101905),f332(f8(f882(x101905,x101902),f883(f883(f882(x101905,x101902),a871),a871),x101902),f334(f882(x101905,x101902)))),f267(x101905,x101902)))),x101907)),x101903),x101904)) % 172.78/172.48 [10130]~P139(x101302)+E(f332(f332(f6(x101301,x101302),f332(f332(f7(x101301,f883(x101303,a871),x101302),f332(f332(f8(f883(x101303,x101302),f883(f883(x101303,a871),x101302),x101301),f6(x101303,x101302)),f332(f332(f7(x101301,f883(x101303,x101302),f883(x101303,x101302)),f332(f332(f8(f883(x101302,x101302),f883(f883(x101303,x101302),f883(x101303,x101302)),x101301),f8(x101302,x101302,x101303)),f332(f332(f8(x101302,f883(x101302,x101302),x101301),f80(x101302)),x101304))),x101305))),x101306)),x101307),f332(f332(f80(x101302),f332(f332(f6(x101301,x101302),x101304),x101307)),f332(f332(f6(x101303,x101302),x101305),x101306))) % 172.78/172.48 [9242]~P14(x92427,x92421,x92423,x92428)+E(f332(f72(x92421,x92421,x92422,f332(x92423,x92424)),f332(f72(x92421,x92421,x92422,f332(x92423,x92425)),x92426)),f332(f72(x92421,x92421,x92422,f332(x92423,x92425)),f332(f72(x92421,x92421,x92422,f332(x92423,x92424)),x92426))) % 172.78/172.48 [10185]E(f332(f332(f267(x101851,x101852),f332(x101853,f550(x101854,x101855,x101853,x101856,x101857,x101858,x101852,x101851))),f332(x101855,f551(x101854,x101855,x101853,x101856,x101857,x101858,x101852,x101851))),x101858)+~P102(f332(f332(f334(f882(x101851,x101852)),x101858),f332(f311(f882(x101857,x101856),f882(x101851,x101852),f272(x101857,x101851,x101856,x101852,x101853,x101855)),x101854))) % 172.78/172.48 [10201]~P102(f332(f332(f334(f882(x102018,x102017)),x102016),f332(f311(f882(x102011,x102012),f882(x102018,x102017),f272(x102011,x102018,x102012,x102017,x102015,x102014)),x102013)))+P102(f332(f332(f334(f882(x102011,x102012)),f332(f332(f267(x102011,x102012),f550(x102013,x102014,x102015,x102012,x102011,x102016,x102017,x102018)),f551(x102013,x102014,x102015,x102012,x102011,x102016,x102017,x102018))),x102013)) % 172.78/172.48 [9674]P102(f332(f332(f334(f882(f882(x96741,x96742),f882(x96741,x96742))),f332(f332(f267(f882(x96741,x96742),f882(x96741,x96742)),f332(f332(f267(x96741,x96742),x96743),x96744)),f332(f332(f267(x96741,x96742),x96745),x96746))),f325(x96741,x96742,x96747,x96748)))+~P102(f332(f332(f334(f882(x96741,x96741)),f332(f332(f267(x96741,x96741),x96743),x96745)),x96747)) % 172.78/172.48 [10173]E(f332(f142(x101731,x101732,f332(f7(x101732,x101731,x101731),x101733),f332(x101734,x101735)),x101736),f332(x101734,f332(f142(x101737,x101732,f332(f7(x101732,x101737,x101737),x101738),x101735),x101736)))+P102(f332(f332(f334(x101732),f773(x101735,x101738,x101734,x101733,x101737,x101731,x101736,x101732)),f332(f173(x101732),x101736))) % 172.78/172.48 [10193]~E(f332(f72(x101931,x101931,x101937,f332(x101933,f773(x101935,x101938,x101934,x101933,x101937,x101931,x101936,x101932))),x101934),f332(f72(x101937,x101931,x101937,x101934),f332(x101938,f773(x101935,x101938,x101934,x101933,x101937,x101931,x101936,x101932))))+E(f332(f142(x101931,x101932,f332(f7(x101932,x101931,x101931),x101933),f332(x101934,x101935)),x101936),f332(x101934,f332(f142(x101937,x101932,f332(f7(x101932,x101937,x101937),x101938),x101935),x101936))) % 172.78/172.48 [8476]E(f332(x84761,f332(x84762,x84763)),f332(x84764,f332(x84765,x84763)))+~E(f332(f72(x84766,x84767,x84768,x84761),x84762),f332(f72(x84769,x84767,x84768,x84764),x84765)) % 172.78/172.48 [10059]P102(f332(f332(f334(f882(x100591,x100592)),f332(f332(f267(x100591,x100592),f332(x100593,x100594)),f332(x100595,x100596))),f332(f311(f882(x100597,x100598),f882(x100591,x100592),f272(x100597,x100591,x100598,x100592,x100593,x100595)),x100599)))+~P102(f332(f332(f334(f882(x100597,x100598)),f332(f332(f267(x100597,x100598),x100594),x100596)),x100599)) % 172.78/172.48 [8747]~E(f332(x87474,f332(x87475,x87476)),f332(x87479,f332(x874710,x874711)))+E(f332(f332(f72(x87471,x87472,x87473,x87474),x87475),x87476),f332(f332(f72(x87477,x87472,x87478,x87479),x874710),x874711)) % 172.78/172.48 [4593]~P98(x45931)+~P104(x45931)+E(f104(x45931),f244(x45931)) % 172.78/172.48 [4594]~P97(x45941)+~P104(x45941)+E(f113(x45941),f245(x45941)) % 172.78/172.48 [4839]~P113(x48391)+~P89(x48391)+E(f332(f74(x48391),f332(f106(x48391),a100)),f77(x48391)) % 172.78/172.48 [5115]E(x51151,f2(a1))+E(f81(a1,x51151),f332(f78(a1),f77(a1)))+P102(f332(f332(f247(a1),f2(a1)),x51151)) % 172.78/172.48 [5323]E(x53231,f2(a1))+E(f81(a1,x53231),f77(a1))+~P102(f332(f332(f247(a1),f2(a1)),x53231)) % 172.78/172.48 [7306]~P39(x73061)+P102(f332(f61(a1),x73061))+~P102(f332(f61(a876),f332(f311(a1,a876,a107),x73061))) % 172.78/172.48 [9636]E(x96361,f195(f883(f882(a876,a876),a871)))+~P102(f332(f61(f882(a876,a876)),x96361))+P102(f332(f332(f334(f882(f883(f882(a876,a876),a871),f883(f882(a876,a876),a871))),f332(f332(f267(f883(f882(a876,a876),a871),f883(f882(a876,a876),a871)),f195(f883(f882(a876,a876),a871))),x96361)),a36)) % 172.78/172.48 [9805]E(x98051,f2(a876))+E(x98051,f332(a115,f2(a876)))+~P102(f332(f332(f247(a876),x98051),f332(f106(a876),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100))))) % 172.78/172.48 [10087]E(x100871,f2(a102))+E(f332(f332(f79(a1),f332(f332(f80(a1),f332(f106(a1),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)))),f332(a20,f332(f332(f38(a102),x100871),f332(f106(a102),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100))))))),f77(a1)),f332(a20,x100871))+E(f44(a102,x100871,f332(f106(a102),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)))),f2(a102)) % 172.78/172.48 [9937]E(x99371,f2(a102))+~E(f44(a102,x99371,f332(f106(a102),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)))),f2(a102))+E(f332(f332(f80(a1),f332(f106(a1),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)))),f332(a20,f332(f332(f38(a102),x99371),f332(f106(a102),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)))))),f332(a20,x99371)) % 172.78/172.48 [4666]~P53(x46661,x46662)+P44(x46661,x46662)+~P45(a871) % 172.78/172.48 [4603]~P141(x46031)+P31(x46031,x46032)+~E(x46032,f2(x46031)) % 172.78/172.48 [4604]~P104(x46041)+P29(x46041,x46042)+~E(x46042,f116(x46041)) % 172.78/172.48 [4613]~P113(x46131)+~E(x46132,f2(x46131))+E(f81(x46131,x46132),f2(x46131)) % 172.78/172.48 [4614]~P86(x46141)+~E(x46142,f2(x46141))+E(f81(x46141,x46142),f2(x46141)) % 172.78/172.48 [4622]~P141(x46222)+~P31(x46222,x46221)+E(x46221,f2(x46222)) % 172.78/172.48 [4656]~P113(x46562)+~E(f81(x46562,x46561),f2(x46562))+E(x46561,f2(x46562)) % 172.78/172.48 [4673]~P24(x46732)+~P24(x46731)+P24(f883(x46731,x46732)) % 172.78/172.48 [4674]~P24(x46742)+~P24(x46741)+P24(f881(x46741,x46742)) % 172.78/172.48 [4675]~P24(x46752)+~P24(x46751)+P24(f882(x46751,x46752)) % 172.78/172.48 [4676]~P28(x46762)+~P28(x46761)+P28(f202(x46761,x46762)) % 172.78/172.48 [4677]~P56(x46772)+~P56(x46771)+P56(f883(x46771,x46772)) % 172.78/172.48 [4678]~P56(x46782)+~P56(x46781)+P56(f881(x46781,x46782)) % 172.78/172.48 [4679]~P56(x46792)+~P56(x46791)+P56(f882(x46791,x46792)) % 172.78/172.48 [4680]~P56(x46801)+~P91(x46802)+P91(f883(x46801,x46802)) % 172.78/172.48 [4681]~P142(x46812)+~P142(x46811)+P142(f882(x46811,x46812)) % 172.78/172.48 [4682]~P100(x46822)+~P100(x46821)+P100(f882(x46821,x46822)) % 172.78/172.48 [4810]~P104(x48101)+~P29(x48101,x48102)+P29(x48101,f152(x48101,x48102)) % 172.78/172.48 [5046]~P28(x50462)+~P28(x50461)+P28(f44(a1,x50461,x50462)) % 172.78/172.48 [4624]~P73(x46241)+~E(x46242,f2(x46241))+E(f332(f78(x46241),x46242),x46242) % 172.78/172.48 [4628]~P137(x46281)+~E(x46282,f2(a1))+E(f332(f105(x46281),x46282),f2(x46281)) % 172.78/172.48 [4629]~P88(x46291)+~E(x46292,f2(a1))+E(f332(f105(x46291),x46292),f2(x46291)) % 172.78/172.48 [4653]~P72(x46531)+~E(f2(x46531),x46532)+E(f332(f78(x46531),x46532),f2(x46531)) % 172.78/172.48 [4654]~P81(x46541)+~E(x46542,f2(x46541))+E(f332(f74(x46541),x46542),f2(x46541)) % 172.78/172.48 [4655]~P72(x46551)+~E(x46552,f2(x46551))+E(f332(f78(x46551),x46552),f2(x46551)) % 172.78/172.48 [4684]~P73(x46842)+E(x46841,f2(x46842))+~E(f332(f78(x46842),x46841),x46841) % 172.78/172.48 [4690]E(x46901,f332(a107,x46902))+~E(x46901,f2(a876))+~E(x46902,f332(f103(a1),x46901)) % 172.78/172.48 [4691]E(f332(a107,x46911),x46912)+~E(x46912,f2(a876))+~E(x46911,f332(f103(a1),x46912)) % 172.78/172.48 [4695]~P88(x46952)+E(x46951,f2(a1))+~E(f332(f105(x46952),x46951),f2(x46952)) % 172.78/172.48 [4700]~P81(x47002)+E(x47001,f2(x47002))+~E(f332(f74(x47002),x47001),f2(x47002)) % 172.78/172.48 [4701]~P72(x47012)+E(x47011,f2(x47012))+~E(f332(f78(x47012),x47011),f2(x47012)) % 172.78/172.48 [4702]~P72(x47021)+E(f2(x47021),x47022)+~E(f332(f78(x47021),x47022),f2(x47021)) % 172.78/172.48 [4885]~P104(x48851)+~P29(x48851,x48852)+P29(x48851,f332(f172(x48851),x48852)) % 172.78/172.48 [4911]~P102(x49112)+~P102(x49111)+P102(f332(f332(a330,x49111),x49112)) % 172.78/172.48 [4945]~E(f77(a876),f2(a876))+E(f332(f37(x49451),x49452),f2(a876))+~P102(f332(f61(x49451),x49452)) % 172.78/172.48 [4978]~P139(x49781)+~P109(x49781)+E(f332(f332(f257(x49781),f2(x49781)),f332(a115,x49782)),f2(x49781)) % 172.78/172.48 [5016]~P104(x50161)+P29(x50161,f139(x50161,x50162))+~P102(f332(f61(x50161),x50162)) % 172.78/172.48 [5017]~P104(x50171)+P29(x50171,f761(x50172,x50171))+~P102(f332(f61(x50171),x50172)) % 172.78/172.48 [5038]~P104(x50381)+E(f332(f173(x50381),f139(x50381,x50382)),x50382)+~P102(f332(f61(x50381),x50382)) % 172.78/172.48 [5039]~P104(x50391)+E(f332(f173(x50391),f761(x50392,x50391)),x50392)+~P102(f332(f61(x50391),x50392)) % 172.78/172.48 [5067]P102(x50671)+P102(x50672)+~P102(f332(f332(a331,x50672),x50671)) % 172.78/172.48 [5079]E(x50791,f195(f883(x50792,a871)))+~E(f332(f37(x50792),x50791),f2(a876))+~P102(f332(f61(x50792),x50791)) % 172.78/172.48 [5084]P102(x50841)+~P102(x50842)+~P102(f332(f332(a335,x50842),x50841)) % 172.78/172.48 [5133]~P70(x51331)+E(f332(f74(x51331),x51332),x51332)+P102(f332(f332(f247(x51331),x51332),f2(x51331))) % 172.78/172.48 [5196]~P56(x51962)+~P102(f332(f57(x51962),x51961))+P102(f332(x51961,f719(x51961,x51962))) % 172.78/172.48 [5197]~P56(x51972)+~P102(f332(f57(x51972),x51971))+P102(f332(x51971,f726(x51971,x51972))) % 172.78/172.48 [5233]E(x52331,f116(x52332))+P102(f332(f137(x52332),f117(x52332,x52331)))+~P102(f332(f137(x52332),x52331)) % 172.78/172.48 [5238]~P104(x52381)+~P102(f332(f61(x52381),x52382))+P102(f332(f137(x52381),f139(x52381,x52382))) % 172.78/172.48 [5239]~P104(x52391)+~P102(f332(f61(x52391),x52392))+P102(f332(f137(x52391),f761(x52392,x52391))) % 172.78/172.48 [5245]~P137(x52451)+E(f332(f103(x52451),f332(a107,x52452)),f332(f105(x52451),x52452))+P102(f332(f332(f247(a1),x52452),f2(a1))) % 172.78/172.48 [5273]P2(x52732,x52731)+E(f332(x52731,f502(x52731)),f332(x52731,f506(x52731)))+P102(f332(f332(x52731,f502(x52731)),f506(x52731))) % 172.78/172.48 [5288]E(f332(f103(a1),f416(x52881,x52882)),x52881)+P102(f332(x52882,f332(a107,x52881)))+~P102(f332(x52882,f2(a876))) % 172.78/172.48 [5300]~P56(x53001)+~P102(f332(x53002,f720(x53002,x53001)))+P102(f332(f58(x53001),x53002)) % 172.78/172.48 [5301]~P56(x53011)+~P102(f332(x53012,f727(x53012,x53011)))+P102(f332(f58(x53011),x53012)) % 172.78/172.48 [5316]~P56(x53162)+~P36(x53162,x53161,f55(x53162))+P102(f332(x53161,f777(x53161,x53162))) % 172.78/172.48 [5332]~P113(x53321)+~E(f81(x53321,x53322),f332(f78(x53321),f77(x53321)))+P102(f332(f332(f247(x53321),x53322),f2(x53321))) % 172.78/172.48 [5333]E(x53331,f195(f883(x53332,a871)))+P102(f332(f61(x53332),f365(x53331,x53332)))+~P102(f332(f61(x53332),x53331)) % 172.78/172.48 [5410]~E(x54102,f2(a1))+E(f226(x54101,x54102),f332(f332(f267(a1,a1),f2(a1)),f77(a1)))+P102(f332(f332(f247(a1),x54102),f2(a1))) % 172.78/172.48 [5411]~E(x54111,f2(a1))+E(f226(x54111,x54112),f332(f332(f267(a1,a1),f2(a1)),f77(a1)))+P102(f332(f332(f247(a1),x54112),f2(a1))) % 172.78/172.48 [5463]E(f332(f103(a1),f416(x54631,x54632)),x54631)+P102(f332(x54632,f332(a107,x54631)))+P102(f332(f332(f247(a1),x54631),f2(a1))) % 172.78/172.48 [5487]E(f332(f332(f310(x54872),f376(x54871,x54872)),f365(x54871,x54872)),x54871)+E(x54871,f195(f883(x54872,a871)))+~P102(f332(f61(x54872),x54871)) % 172.78/172.48 [5527]~P113(x55271)+E(f81(x55271,x55272),f332(f78(x55271),f77(x55271)))+~P102(f332(f332(f247(x55271),x55272),f2(x55271))) % 172.78/172.48 [5528]~P81(x55281)+E(f332(f74(x55281),x55282),f332(f78(x55281),x55282))+~P102(f332(f332(f247(x55281),x55282),f2(x55281))) % 172.78/172.48 [5529]~P81(x55291)+E(f332(f74(x55291),x55292),f332(f78(x55291),x55292))+~P102(f332(f332(f246(x55291),x55292),f2(x55291))) % 172.78/172.48 [5530]~P70(x55301)+E(f332(f74(x55301),x55302),f332(f78(x55301),x55302))+~P102(f332(f332(f247(x55301),x55302),f2(x55301))) % 172.78/172.48 [5627]~P102(f332(x56271,f416(x56272,x56271)))+P102(f332(x56271,f332(a107,x56272)))+~P102(f332(x56271,f2(a876))) % 172.78/172.48 [5634]E(x56341,f2(a876))+E(f332(a115,f837(x56342,x56341)),x56341)+~P102(f332(f332(f247(a876),x56341),f332(a115,x56342))) % 172.78/172.48 [5638]P2(x56381,x56382)+~E(f332(x56382,f502(x56382)),f332(x56382,f506(x56382)))+~P102(f332(f332(x56382,f502(x56382)),f506(x56382))) % 172.78/172.48 [5658]~P104(x56581)+P29(x56581,x56582)+P102(f332(f332(f246(a876),f744(x56582,x56581)),f745(x56582,x56581))) % 172.78/172.48 [5659]~P104(x56591)+P29(x56591,x56592)+P102(f332(f332(f246(a876),f752(x56592,x56591)),f756(x56592,x56591))) % 172.78/172.48 [5745]~P81(x57451)+~E(x57452,f2(x57451))+P102(f332(f332(f246(x57451),f332(f74(x57451),x57452)),f2(x57451))) % 172.78/172.48 [5824]~P56(x58242)+~P56(x58241)+E(f59(x58241,x58242,f55(x58241),f55(x58242)),f55(f882(x58241,x58242))) % 172.78/172.48 [5828]~P102(f332(x58281,f416(x58282,x58281)))+P102(f332(x58281,f332(a107,x58282)))+P102(f332(f332(f247(a1),x58282),f2(a1))) % 172.78/172.48 [5851]~P102(f332(x58511,f332(a107,x58512)))+P102(f332(x58511,f2(a876)))+~P102(f332(f332(f247(a1),x58512),f2(a1))) % 172.78/172.48 [6187]~P113(x61871)+~P102(f332(f332(f247(x61871),x61872),f2(x61871)))+P102(f332(f332(f247(x61871),f81(x61871,x61872)),f2(x61871))) % 172.78/172.48 [6301]~P113(x63011)+P102(f332(f332(f247(x63011),f332(f105(x63011),x63012)),f2(x63011)))+~P102(f332(f332(f247(a1),x63012),f2(a1))) % 172.78/172.48 [6302]~P113(x63021)+P102(f332(f332(f246(x63021),f332(f105(x63021),x63022)),f2(x63021)))+~P102(f332(f332(f246(a1),x63022),f2(a1))) % 172.78/172.48 [6309]~P81(x63092)+E(x63091,f2(x63092))+~P102(f332(f332(f246(x63092),f332(f74(x63092),x63091)),f2(x63092))) % 172.78/172.48 [6385]~P137(x63851)+~P102(f332(f332(f334(x63851),x63852),f112(x63851)))+P102(f332(f332(f334(x63851),f332(f78(x63851),x63852)),f112(x63851))) % 172.78/172.48 [6417]~P113(x64171)+~P102(f332(f332(f247(x64171),f81(x64171,x64172)),f2(x64171)))+P102(f332(f332(f247(x64171),x64172),f2(x64171))) % 172.78/172.48 [6586]~P113(x65862)+~P102(f332(f332(f247(x65862),f332(f105(x65862),x65861)),f2(x65862)))+P102(f332(f332(f247(a1),x65861),f2(a1))) % 172.78/172.48 [6587]~P113(x65872)+~P102(f332(f332(f246(x65872),f332(f105(x65872),x65871)),f2(x65872)))+P102(f332(f332(f246(a1),x65871),f2(a1))) % 172.78/172.48 [7093]~P113(x70931)+~P102(f332(f332(f247(x70931),x70932),f2(x70931)))+P102(f332(f332(f247(x70931),f332(f332(f79(x70931),x70932),x70932)),f2(x70931))) % 172.78/172.48 [7094]~P73(x70941)+~P102(f332(f332(f247(x70941),x70942),f2(x70941)))+P102(f332(f332(f247(x70941),f332(f332(f79(x70941),x70942),x70942)),f2(x70941))) % 172.78/172.48 [7095]~P73(x70951)+~P102(f332(f332(f246(x70951),x70952),f2(x70951)))+P102(f332(f332(f246(x70951),f332(f332(f79(x70951),x70952),x70952)),f2(x70951))) % 172.78/172.48 [7664]~P113(x76641)+~P102(f332(f332(f247(x76641),f332(f332(f79(x76641),x76642),x76642)),f2(x76641)))+P102(f332(f332(f247(x76641),x76642),f2(x76641))) % 172.78/172.48 [7665]~P73(x76651)+~P102(f332(f332(f247(x76651),f332(f332(f79(x76651),x76652),x76652)),f2(x76651)))+P102(f332(f332(f247(x76651),x76652),f2(x76651))) % 172.78/172.48 [7666]~P73(x76661)+~P102(f332(f332(f246(x76661),f332(f332(f79(x76661),x76662),x76662)),f2(x76661)))+P102(f332(f332(f246(x76661),x76662),f2(x76661))) % 172.78/172.48 [4740]~E(x47402,f77(a876))+~E(x47401,f77(a876))+E(f332(f332(f80(a876),x47401),x47402),f77(a876)) % 172.78/172.48 [4741]~E(x47412,f77(a1))+~E(x47411,f77(a1))+E(f332(f332(f80(a1),x47411),x47412),f77(a1)) % 172.78/172.48 [4742]~E(x47422,f2(a876))+~E(x47421,f2(a876))+E(f332(f332(f79(a876),x47421),x47422),f2(a876)) % 172.78/172.48 [4796]~P117(x47962)+E(x47961,f2(x47962))+E(f332(f332(f290(x47962),x47961),x47961),f77(x47962)) % 172.78/172.48 [4797]~P25(x47972)+E(x47971,f2(x47972))+E(f332(f332(f38(x47972),x47971),x47971),f77(x47972)) % 172.78/172.48 [4798]~P118(x47982)+E(x47981,f2(x47982))+E(f332(f332(f290(x47982),x47981),x47981),f77(x47982)) % 172.78/172.48 [4817]~P136(x48171)+~E(x48172,f77(x48171))+E(f332(f332(f80(x48171),x48172),x48172),f77(x48171)) % 172.78/172.48 [4818]~P73(x48181)+~E(x48182,f2(x48181))+E(f332(f332(f79(x48181),x48182),x48182),f2(x48181)) % 172.78/172.48 [4819]~P118(x48191)+~E(x48192,f2(x48191))+E(f332(f332(f290(x48191),x48192),x48192),f2(x48191)) % 172.78/172.48 [4864]~E(x48642,f2(a876))+~E(x48641,f2(a876))+E(f332(f78(a1),f332(f103(a1),x48641)),f332(f103(a1),x48642)) % 172.78/172.48 [4882]E(x48821,f77(a876))+E(x48822,f2(a876))+~E(f332(f332(f80(a876),x48822),x48821),x48822) % 172.78/172.48 [4892]E(x48921,f2(a876))+E(x48922,f2(a876))+~E(f332(f332(f80(a876),x48922),x48921),f2(a876)) % 172.78/172.48 [4920]~E(x49202,f2(a876))+~E(x49201,f332(a115,f2(a876)))+E(f332(f332(f79(a876),x49201),x49202),f332(a115,f2(a876))) % 172.78/172.48 [4921]~E(x49211,f2(a876))+~E(x49212,f332(a115,f2(a876)))+E(f332(f332(f79(a876),x49211),x49212),f332(a115,f2(a876))) % 172.78/172.48 [4928]E(x49281,f77(a1))+E(x49282,f332(f106(a1),a100))+~E(f332(f332(f80(a1),x49281),x49282),f77(a1)) % 172.78/172.48 [4929]E(x49291,f77(a1))+E(x49292,f332(f106(a1),a100))+~E(f332(f332(f80(a1),x49292),x49291),f77(a1)) % 172.78/172.48 [4930]E(x49301,f77(a1))+E(x49301,f332(f106(a1),a100))+~E(f332(f332(f80(a1),x49302),x49301),f77(a1)) % 172.78/172.48 [4932]E(x49321,f77(a1))+E(x49321,f332(f106(a1),a100))+~E(f332(f332(f80(a1),x49321),x49322),f77(a1)) % 172.78/172.48 [4949]~P73(x49492)+E(x49491,f2(x49492))+~E(f332(f332(f79(x49492),x49491),x49491),f2(x49492)) % 172.78/172.48 [4955]~E(x49551,f332(f106(a1),a100))+~E(x49552,f332(f106(a1),a100))+E(f332(f332(f80(a1),x49551),x49552),f77(a1)) % 172.78/172.48 [4967]E(x49671,f2(a876))+E(x49672,f2(a876))+~E(f332(f332(f79(a876),x49672),x49671),f332(a115,f2(a876))) % 172.78/172.48 [4977]~P57(x49771)+~P89(x49771)+E(f332(f332(f290(x49771),x49772),f332(f106(x49771),a82)),f2(x49771)) % 172.78/172.48 [4983]~P136(x49831)+~E(x49832,f332(f78(x49831),f77(x49831)))+E(f332(f332(f80(x49831),x49832),x49832),f77(x49831)) % 172.78/172.48 [4988]~P28(x49882)+~P28(x49881)+P28(f332(f332(f80(a1),x49881),x49882)) % 172.78/172.48 [4989]~P28(x49892)+~P28(x49891)+P28(f332(f332(f79(a1),x49891),x49892)) % 172.78/172.48 [4990]~P28(x49902)+~P28(x49901)+P28(f332(f332(f38(a1),x49901),x49902)) % 172.78/172.48 [4992]~E(x49922,f2(a1))+E(x49921,f2(a1))+E(f45(x49921,x49922),f332(f332(f267(a1,a1),f2(a1)),x49921)) % 172.78/172.48 [5014]~E(x50142,f332(a115,f2(a876)))+~E(x50141,f332(a115,f2(a876)))+E(f332(f332(f80(a876),x50141),x50142),f332(a115,f2(a876))) % 172.78/172.48 [5029]E(x50291,f2(a876))+E(x50292,f332(a115,f2(a876)))+~E(f332(f332(f257(a876),x50292),x50291),f332(a115,f2(a876))) % 172.78/172.48 [5030]E(x50301,f2(a876))+E(x50301,f332(a115,f2(a876)))+~E(f332(f332(f79(a876),x50302),x50301),f332(a115,f2(a876))) % 172.78/172.48 [5031]E(x50311,f2(a876))+E(x50311,f332(a115,f2(a876)))+~E(f332(f332(f79(a876),x50311),x50312),f332(a115,f2(a876))) % 172.78/172.48 [5040]~P57(x50401)+~P89(x50401)+E(f332(f332(f290(x50401),x50402),f332(f106(x50401),a100)),f332(f78(x50401),x50402)) % 172.78/172.48 [5059]E(x50591,f332(a107,x50592))+~E(x50591,f2(a876))+P102(f332(f332(f246(a1),f2(a1)),x50592)) % 172.78/172.48 [5060]E(f332(a107,x50601),x50602)+~E(x50602,f2(a876))+P102(f332(f332(f246(a1),f2(a1)),x50601)) % 172.78/172.48 [5075]E(x50751,f332(a115,f2(a876)))+E(x50752,f332(a115,f2(a876)))+~E(f332(f332(f79(a876),x50751),x50752),f332(a115,f2(a876))) % 172.78/172.48 [5086]~E(x50861,f332(a107,x50862))+E(x50861,f2(a876))+P102(f332(f332(f246(a1),f2(a1)),x50862)) % 172.78/172.48 [5087]~E(f332(a107,x50872),x50871)+E(x50871,f2(a876))+P102(f332(f332(f246(a1),f2(a1)),x50872)) % 172.78/172.48 [5109]~P61(x51091)+E(f332(f63(x51091,f113(x51091)),x51092),f13(x51091,x51092))+~P102(f332(f61(x51091),x51092)) % 172.78/172.48 [5110]~P61(x51101)+E(f332(f63(x51101,f104(x51101)),x51102),f10(x51101,x51102))+~P102(f332(f61(x51101),x51102)) % 172.78/172.48 [5111]~P104(x51111)+E(f332(f63(x51111,f245(x51111)),x51112),f14(x51111,x51112))+~P102(f332(f61(x51111),x51112)) % 172.78/172.48 [5112]~P104(x51121)+E(f332(f63(x51121,f244(x51121)),x51122),f15(x51121,x51122))+~P102(f332(f61(x51121),x51122)) % 172.78/172.48 [5114]~P56(x51141)+~P102(f332(x51142,f208(x51141)))+P102(f332(f57(f880(x51141)),x51142)) % 172.78/172.48 [5189]~P56(x51892)+P102(f332(x51891,f208(x51892)))+~P102(f332(f58(f880(x51892)),x51891)) % 172.78/172.48 [5190]E(x51901,x51902)+~E(f332(f332(f22(a876),x51902),x51901),f2(a876))+~E(f332(f332(f22(a876),x51901),x51902),f2(a876)) % 172.78/172.48 [5205]P28(x52051)+~P39(x52052)+~P102(f332(f332(f334(a1),x52051),x52052)) % 172.78/172.48 [5234]~P113(x52341)+~E(f81(x52341,x52342),f77(x52341))+P102(f332(f332(f247(x52341),f2(x52341)),x52342)) % 172.78/172.48 [5246]~P89(x52461)+E(f332(f103(x52461),f332(f106(a876),x52462)),f332(f106(x52461),x52462))+P102(f332(a200,f332(f106(a1),x52462))) % 172.78/172.48 [5252]~P44(x52521,x52522)+P45(a871)+P102(f332(f61(f882(x52521,x52521)),x52522)) % 172.78/172.48 [5325]~P104(x53251)+E(f332(f63(x53251,f245(x53251)),x53252),f11(x53251,f245(x53251),x53252))+~P102(f332(f61(x53251),x53252)) % 172.78/172.48 [5326]~P104(x53261)+E(f332(f63(x53261,f244(x53261)),x53262),f12(x53261,f244(x53261),x53262))+~P102(f332(f61(x53261),x53262)) % 172.78/172.48 [5340]E(x53401,x53402)+P102(f332(f332(f247(a876),x53402),x53401))+P102(f332(f332(f247(a876),x53401),x53402)) % 172.78/172.48 [5341]E(x53411,x53412)+P102(f332(f332(f247(a1),x53412),x53411))+P102(f332(f332(f247(a1),x53411),x53412)) % 172.78/172.48 [5397]~P89(x53971)+E(f332(f103(x53971),f332(f106(a876),x53972)),f2(x53971))+~P102(f332(a200,f332(f106(a1),x53972))) % 172.78/172.48 [5400]~E(x54002,f332(a107,x54001))+E(x54001,f332(f103(a1),x54002))+~P102(f332(f332(f246(a1),f2(a1)),x54001)) % 172.78/172.48 [5401]~E(f332(a107,x54011),x54012)+E(x54011,f332(f103(a1),x54012))+~P102(f332(f332(f246(a1),f2(a1)),x54011)) % 172.78/172.48 [5402]~E(x54021,f332(a107,x54022))+E(f332(f103(a1),x54021),x54022)+~P102(f332(f332(f246(a1),f2(a1)),x54022)) % 172.78/172.48 [5412]E(x54121,f332(a107,x54122))+~E(x54122,f332(f103(a1),x54121))+~P102(f332(f332(f246(a1),f2(a1)),x54122)) % 172.78/172.48 [5413]E(f332(a107,x54131),x54132)+~E(x54131,f332(f103(a1),x54132))+~P102(f332(f332(f246(a1),f2(a1)),x54131)) % 172.78/172.48 [5452]~P81(x54522)+E(x54521,f2(x54522))+P102(f332(f332(f247(x54522),f2(x54522)),f332(f74(x54522),x54521))) % 172.78/172.48 [5520]~P113(x55201)+E(f81(x55201,x55202),f77(x55201))+~P102(f332(f332(f247(x55201),f2(x55201)),x55202)) % 172.78/172.48 [5524]~P89(x55241)+E(f332(f103(x55241),f332(f106(a876),x55242)),f2(x55241))+P102(f332(f332(f246(a1),f2(a1)),f332(f106(a1),x55242))) % 172.78/172.48 [5531]~P81(x55311)+E(f332(f74(x55311),x55312),x55312)+~P102(f332(f332(f247(x55311),f2(x55311)),x55312)) % 172.78/172.48 [5532]~P81(x55321)+E(f332(f74(x55321),x55322),x55322)+~P102(f332(f332(f246(x55321),f2(x55321)),x55322)) % 172.78/172.48 [5541]E(x55411,f2(a876))+~E(f139(a876,f332(f302(a876,x55412),x55411)),f116(a876))+P102(f332(f332(f246(a876),x55411),x55412)) % 172.78/172.48 [5551]~P71(x55511)+E(f332(f332(f6(x55511,x55511),f5(x55511)),f332(f173(x55511),x55512)),f332(f166(x55511),x55512))+~P102(f332(f137(x55511),x55512)) % 172.78/172.48 [5554]~P137(x55541)+E(f332(f103(x55541),f332(a107,x55542)),f332(f105(x55541),x55542))+~P102(f332(f332(f246(a1),f2(a1)),x55542)) % 172.78/172.48 [5581]E(x55811,x55812)+P102(f332(f332(f247(a876),x55811),x55812))+~P102(f332(f332(f246(a876),x55811),x55812)) % 172.78/172.48 [5582]E(x55821,x55822)+P102(f332(f332(f247(a1),x55821),x55822))+~P102(f332(f332(f246(a1),x55821),x55822)) % 172.78/172.48 [5585]E(x55851,f77(a1))+~E(f332(f332(f80(a1),x55852),x55851),f77(a1))+~P102(f332(f332(f247(a1),f2(a1)),x55852)) % 172.78/172.48 [5586]E(x55861,f77(a1))+~E(f332(f332(f80(a1),x55861),x55862),f77(a1))+~P102(f332(f332(f247(a1),f2(a1)),x55861)) % 172.78/172.48 [5624]~P39(x56242)+P102(f332(f332(f246(a1),f2(a1)),x56241))+~P102(f332(f332(f334(a1),x56241),x56242)) % 172.78/172.48 [5643]~P53(x56431,x56432)+P38(x56431,x56432)+~P102(f332(f61(f882(x56431,x56431)),x56432)) % 172.78/172.48 [5645]~P53(x56451,x56452)+P44(x56451,x56452)+~P102(f332(f61(f882(x56451,x56451)),x56452)) % 172.78/172.48 [5689]E(x56891,f195(f883(x56892,a871)))+~P102(f332(f61(x56892),x56891))+P102(f332(f332(f247(a876),f2(a876)),f332(f37(x56892),x56891))) % 172.78/172.48 [5716]~P102(f332(x57161,x57162))+P102(f332(x57161,f2(a876)))+P102(f332(f332(f247(a876),f863(x57162,x57161)),x57162)) % 172.78/172.48 [5739]E(x57391,f2(a876))+~E(f332(f166(a876),x57392),f2(a876))+~P102(f332(f332(f334(a876),x57391),f332(f173(a876),x57392))) % 172.78/172.48 [5805]E(x58051,x58052)+~P102(f332(f332(f246(a876),x58052),x58051))+~P102(f332(f332(f246(a876),x58051),x58052)) % 172.78/172.48 [5806]E(x58061,x58062)+~P102(f332(f332(f246(a1),x58062),x58061))+~P102(f332(f332(f246(a1),x58061),x58062)) % 172.78/172.48 [5807]E(f332(f37(x58071),x58072),f2(a876))+~P102(f332(f61(x58071),x58072))+P102(f332(f332(f334(x58071),f479(x58072,x58071)),x58072)) % 172.78/172.48 [5816]E(f49(x58161,x58162),f45(x58161,x58162))+P102(f332(f332(f246(a1),f2(a1)),x58161))+~P102(f332(f332(f247(a1),f2(a1)),x58162)) % 172.78/172.48 [5840]~P102(f332(x58401,f415(x58401)))+P102(f332(x58401,f332(a107,x58402)))+~P102(f332(f332(f246(a1),f2(a1)),x58402)) % 172.78/172.48 [5842]P102(f332(f332(f247(a876),x58421),f359(x58422)))+~P102(f332(f61(a876),x58422))+~P102(f332(f332(f334(a876),x58421),x58422)) % 172.78/172.48 [5843]P102(f332(f332(f246(a876),x58431),f361(x58432)))+~P102(f332(f61(a876),x58432))+~P102(f332(f332(f334(a876),x58431),x58432)) % 172.78/172.48 [5872]E(x58721,x58722)+~P102(f332(f332(f247(a876),x58721),f332(a115,x58722)))+P102(f332(f332(f247(a876),x58721),x58722)) % 172.78/172.48 [5904]E(x59041,f332(a115,x59042))+~P102(f332(f332(f246(a876),x59041),f332(a115,x59042)))+P102(f332(f332(f246(a876),x59041),x59042)) % 172.78/172.48 [5917]P102(f332(x59171,f417(x59171)))+~P102(f332(x59171,f332(a107,x59172)))+~P102(f332(f332(f246(a1),f2(a1)),x59172)) % 172.78/172.48 [5931]~P102(f332(x59311,x59312))+~P102(f332(f332(f246(a1),f2(a1)),x59312))+P102(f332(x59311,f332(f103(a1),f367(x59311)))) % 172.78/172.48 [5946]~P81(x59462)+~E(x59461,f2(x59462))+~P102(f332(f332(f247(x59462),f2(x59462)),f332(f74(x59462),x59461))) % 172.78/172.48 [5973]~P53(x59731,x59732)+P38(x59731,f332(f287(x59731,x59731),x59732))+~P102(f332(f61(f882(x59731,x59731)),x59732)) % 172.78/172.48 [5981]~P89(x59811)+E(f332(f103(x59811),f332(f106(a876),x59812)),f332(f106(x59811),x59812))+~P102(f332(f332(f246(a1),f2(a1)),f332(f106(a1),x59812))) % 172.78/172.48 [5985]E(f332(a115,x59851),x59852)+~P102(f332(f332(f247(a876),x59851),x59852))+P102(f332(f332(f247(a876),f332(a115,x59851)),x59852)) % 172.78/172.48 [5999]E(f332(f332(f38(a1),x59991),x59992),f2(a1))+~P102(f332(f332(f246(a1),x59991),f2(a1)))+~P102(f332(f332(f247(a1),x59992),x59991)) % 172.78/172.48 [6010]E(f44(a1,x60101,x60102),x60101)+~P102(f332(f332(f246(a1),x60101),f2(a1)))+~P102(f332(f332(f247(a1),x60102),x60101)) % 172.78/172.48 [6023]E(f46(x60231,x60232),f45(x60231,x60232))+~P102(f332(f332(f246(a1),f2(a1)),x60231))+~P102(f332(f332(f246(a1),f2(a1)),x60232)) % 172.78/172.48 [6031]E(f332(f332(f38(a1),x60311),x60312),f2(a1))+~P102(f332(f332(f246(a1),f2(a1)),x60311))+~P102(f332(f332(f247(a1),x60311),x60312)) % 172.78/172.48 [6043]E(f44(a876,f332(f106(a876),x60431),f332(f106(a876),x60432)),f332(f106(a876),x60431))+P102(f332(a200,f332(f106(a1),x60431)))+~P102(f332(a200,f332(f106(a1),x60432))) % 172.78/172.48 [6045]E(f44(a1,x60451,x60452),x60451)+~P102(f332(f332(f246(a1),f2(a1)),x60451))+~P102(f332(f332(f247(a1),x60451),x60452)) % 172.78/172.48 [6046]E(x60461,x60462)+~P102(f332(f332(f247(a876),x60461),f332(a115,x60462)))+~P102(f332(f332(f246(a876),x60462),x60461)) % 172.78/172.48 [6063]~P113(x60631)+~P102(f332(f332(f247(x60631),x60632),f2(x60631)))+P102(f332(f332(f247(x60631),x60632),f332(f78(x60631),x60632))) % 172.78/172.48 [6064]~P73(x60641)+~P102(f332(f332(f246(x60641),x60642),f2(x60641)))+P102(f332(f332(f246(x60641),x60642),f332(f78(x60641),x60642))) % 172.78/172.48 [6074]~P27(x60741)+E(f332(f332(f64(x60741,x60741,f104(x60741)),f255(x60741)),x60742),f40(x60741,x60742))+~P102(f332(f61(x60741),x60742)) % 172.78/172.48 [6075]~P27(x60751)+E(f332(f332(f64(x60751,x60751,f113(x60751)),f195(x60751)),x60752),f39(x60751,x60752))+~P102(f332(f61(x60751),x60752)) % 172.78/172.48 [6089]~P107(x60891)+~P102(f332(f332(f247(a876),f2(a876)),x60892))+P102(f332(f332(f247(x60891),f2(x60891)),f332(f103(x60891),x60892))) % 172.78/172.48 [6090]~P113(x60901)+~P102(f332(f332(f247(a1),f2(a1)),x60902))+P102(f332(f332(f247(x60901),f2(x60901)),f332(f105(x60901),x60902))) % 172.78/172.48 [6091]~P113(x60911)+~P102(f332(f332(f246(a1),f2(a1)),x60912))+P102(f332(f332(f246(x60911),f2(x60911)),f332(f105(x60911),x60912))) % 172.78/172.48 [6094]~P28(x60942)+~P28(x60941)+E(f332(f311(a876,a1,f103(a1)),f303(a876,f332(a107,x60941),f332(a107,x60942))),f303(a1,x60941,x60942)) % 172.78/172.48 [6100]P102(f332(x61001,x61002))+~P102(f332(f332(f246(a1),f2(a1)),x61002))+~P102(f332(x61001,f332(f103(a1),f368(x61001)))) % 172.78/172.48 [6125]E(f332(f332(f79(a876),f332(f106(a876),x61251)),f332(f106(a876),x61252)),f332(f106(a876),x61251))+P102(f332(f332(f247(a1),x61251),a82))+~P102(f332(f332(f247(a1),x61252),a82)) % 172.78/172.48 [6129]~P113(x61291)+P102(f332(f332(f247(x61291),f2(x61291)),f81(x61291,x61292)))+~P102(f332(f332(f247(x61291),f2(x61291)),x61292)) % 172.78/172.48 [6140]~P79(x61401)+~P102(f332(f332(f247(x61401),x61402),f2(x61401)))+P102(f332(f332(f247(x61401),f2(x61401)),f332(f78(x61401),x61402))) % 172.78/172.48 [6141]~P79(x61411)+~P102(f332(f332(f246(x61411),x61412),f2(x61411)))+P102(f332(f332(f246(x61411),f2(x61411)),f332(f78(x61411),x61412))) % 172.78/172.48 [6144]E(x61441,f255(f883(x61442,a871)))+~E(f332(f37(x61442),x61441),f332(f37(x61442),f255(f883(x61442,a871))))+~P102(f332(f61(x61442),f255(f883(x61442,a871)))) % 172.78/172.48 [6179]~P113(x61791)+P102(f332(f332(f247(x61791),x61792),f2(x61791)))+~P102(f332(f332(f247(x61791),x61792),f332(f78(x61791),x61792))) % 172.78/172.48 [6180]~P73(x61801)+P102(f332(f332(f246(x61801),x61802),f2(x61801)))+~P102(f332(f332(f246(x61801),x61802),f332(f78(x61801),x61802))) % 172.78/172.48 [6189]~P89(x61891)+P102(f332(f332(f334(x61891),f332(f106(x61891),x61892)),f193(x61891)))+~P102(f332(f332(f246(a1),a82),x61892)) % 172.78/172.48 [6220]E(x62201,f2(a876))+~P102(f332(f332(f247(a876),x62201),f332(a115,x62202)))+P102(f332(f332(f247(a876),f837(x62202,x62201)),x62202)) % 172.78/172.48 [6242]~P113(x62421)+~P102(f332(f332(f247(x62421),f2(x62421)),f81(x62421,x62422)))+P102(f332(f332(f247(x62421),f2(x62421)),x62422)) % 172.78/172.48 [6244]~E(f332(f106(a876),x62442),f332(f106(a876),x62441))+P102(f332(f332(f246(a1),f332(f106(a1),x62441)),f2(a1)))+~P102(f332(a200,f332(f106(a1),x62442))) % 172.78/172.48 [6274]E(f332(f266(a1,a1),f49(x62741,x62742)),f332(f332(f38(a1),x62741),x62742))+~P102(f332(f332(f247(a1),x62741),f2(a1)))+~P102(f332(f332(f247(a1),f2(a1)),x62742)) % 172.78/172.48 [6307]E(f332(f270(a1,a1),f49(x63071,x63072)),f44(a1,x63071,x63072))+~P102(f332(f332(f247(a1),x63071),f2(a1)))+~P102(f332(f332(f247(a1),f2(a1)),x63072)) % 172.78/172.48 [6310]~P107(x63102)+~P102(f332(f332(f247(x63102),f2(x63102)),f332(f103(x63102),x63101)))+P102(f332(f332(f247(a876),f2(a876)),x63101)) % 172.78/172.48 [6311]~P113(x63112)+~P102(f332(f332(f247(x63112),f2(x63112)),f332(f105(x63112),x63111)))+P102(f332(f332(f247(a1),f2(a1)),x63111)) % 172.78/172.48 [6312]~P113(x63122)+~P102(f332(f332(f246(x63122),f2(x63122)),f332(f105(x63122),x63121)))+P102(f332(f332(f246(a1),f2(a1)),x63121)) % 172.78/172.48 [6315]E(f332(f266(a1,a1),f46(x63151,x63152)),f332(f332(f38(a1),x63151),x63152))+~P102(f332(f332(f247(a1),f2(a1)),x63151))+~P102(f332(f332(f246(a1),f2(a1)),x63152)) % 172.78/172.48 [6330]E(f332(f270(a1,a1),f46(x63301,x63302)),f44(a1,x63301,x63302))+~P102(f332(f332(f247(a1),f2(a1)),x63301))+~P102(f332(f332(f246(a1),f2(a1)),x63302)) % 172.78/172.48 [6345]~P79(x63451)+P102(f332(f332(f247(x63451),x63452),f2(x63451)))+~P102(f332(f332(f247(x63451),f2(x63451)),f332(f78(x63451),x63452))) % 172.78/172.48 [6346]~P79(x63461)+P102(f332(f332(f246(x63461),x63462),f2(x63461)))+~P102(f332(f332(f246(x63461),f2(x63461)),f332(f78(x63461),x63462))) % 172.78/172.48 [6372]P102(f332(f48(x63721,x63722),f49(x63721,x63722)))+~P102(f332(f332(f247(a1),x63721),f2(a1)))+~P102(f332(f332(f247(a1),f2(a1)),x63722)) % 172.78/172.48 [6397]P102(f332(f48(x63971,x63972),f46(x63971,x63972)))+~P102(f332(f332(f247(a1),f2(a1)),x63972))+~P102(f332(f332(f246(a1),f2(a1)),x63971)) % 172.78/172.48 [6440]~P79(x64401)+P102(f332(f332(f247(x64401),f332(f78(x64401),x64402)),f2(x64401)))+~P102(f332(f332(f247(x64401),f2(x64401)),x64402)) % 172.78/172.48 [6441]~P79(x64411)+P102(f332(f332(f246(x64411),f332(f78(x64411),x64412)),f2(x64411)))+~P102(f332(f332(f246(x64411),f2(x64411)),x64412)) % 172.78/172.48 [6457]E(f332(f332(f22(a876),f332(a107,x64571)),f332(a107,x64572)),f332(a107,f202(x64571,x64572)))+~P102(f332(f332(f246(a1),f2(a1)),x64572))+~P102(f332(f332(f246(a1),f2(a1)),x64571)) % 172.78/172.48 [6474]P102(f332(f332(f246(a1),f2(a1)),f202(x64741,x64742)))+~P102(f332(f332(f246(a1),f2(a1)),x64742))+~P102(f332(f332(f246(a1),f2(a1)),x64741)) % 172.78/172.48 [6511]~P102(f332(x65111,x65112))+P102(f332(x65111,f2(a876)))+P102(f332(x65111,f332(f332(f79(a876),f863(x65112,x65111)),f77(a876)))) % 172.78/172.48 [6593]E(f332(f106(a876),x65931),f332(f106(a876),x65932))+~P102(f332(f332(f246(a1),f332(f106(a1),x65932)),f2(a1)))+~P102(f332(a200,f332(f106(a1),x65931))) % 172.78/172.48 [6603]~E(x66031,f2(a876))+~E(f693(x66032,x66031),f2(a876))+E(f332(f142(a876,a876,f79(a876),x66031),x66032),f2(a876)) % 172.78/172.48 [6629]~P102(f332(f61(x66291),f601(x66292,x66291)))+~P102(f332(f61(f883(x66291,a871)),x66292))+P102(f332(f61(x66291),f39(f883(x66291,a871),x66292))) % 172.78/172.48 [6635]E(x66351,x66352)+P102(f332(f332(f247(a1),x66351),x66352))+~P102(f332(f332(f247(a1),x66351),f332(f332(f79(a1),x66352),f77(a1)))) % 172.78/172.48 [6637]P102(f332(f332(f247(a876),f332(a107,x66371)),f332(a107,x66372)))+~P102(f332(f332(f247(a1),f2(a1)),x66372))+~P102(f332(f332(f247(a1),x66371),x66372)) % 172.78/172.48 [6638]P102(f332(f332(f247(a876),f332(a107,x66381)),f332(a107,x66382)))+~P102(f332(f332(f246(a1),f2(a1)),x66381))+~P102(f332(f332(f247(a1),x66381),x66382)) % 172.78/172.48 [6639]P102(f332(f332(f246(a876),f332(a107,x66391)),f332(a107,x66392)))+~P102(f332(f332(f247(a1),f2(a1)),x66391))+~P102(f332(f332(f246(a1),x66391),x66392)) % 172.78/172.48 [6640]P102(f332(f332(f246(a876),f332(a107,x66401)),f332(a107,x66402)))+~P102(f332(f332(f246(a1),f2(a1)),x66402))+~P102(f332(f332(f246(a1),x66401),x66402)) % 172.78/172.48 [6651]E(f44(a876,f332(a107,x66511),f332(a107,x66512)),f332(a107,f44(a1,x66511,x66512)))+~P102(f332(f332(f246(a1),f2(a1)),x66512))+~P102(f332(f332(f246(a1),f2(a1)),x66511)) % 172.78/172.48 [6673]~P79(x66731)+~P102(f332(f332(f247(x66731),f332(f78(x66731),x66732)),f2(x66731)))+P102(f332(f332(f247(x66731),f2(x66731)),x66732)) % 172.78/172.48 [6674]~P79(x66741)+~P102(f332(f332(f246(x66741),f332(f78(x66741),x66742)),f2(x66741)))+P102(f332(f332(f246(x66741),f2(x66741)),x66742)) % 172.78/172.48 [6689]~P102(f332(f332(f247(a1),a82),x66892))+~P102(f332(f332(f247(a1),x66891),x66892))+P102(f332(f332(f247(a876),f332(f106(a876),x66891)),f332(f106(a876),x66892))) % 172.78/172.48 [6780]~P102(f332(f332(f246(a1),f2(a1)),x67801))+P102(f332(f332(f247(a876),f332(a107,x67801)),x67802))+~P102(f332(f332(f247(a1),x67801),f332(f103(a1),x67802))) % 172.78/172.48 [6797]E(x67971,f2(a1))+E(f44(a1,x67972,x67971),f2(a1))+E(f332(f332(f22(a1),f332(f78(a1),f332(f332(f38(a1),x67972),x67971))),f77(a1)),f332(f332(f38(a1),x67972),f332(f78(a1),x67971))) % 172.78/172.48 [6813]~P102(f332(f332(f246(a1),f2(a1)),x68131))+~P102(f332(f332(f247(a876),f332(a107,x68131)),x68132))+P102(f332(f332(f247(a1),x68131),f332(f103(a1),x68132))) % 172.78/172.48 [6850]~P102(f332(f332(f246(a876),f332(a107,x68501)),f332(a107,x68502)))+~P102(f332(f332(f247(a1),f2(a1)),x68501))+P102(f332(f332(f246(a1),x68501),x68502)) % 172.78/172.48 [6851]~P102(f332(f332(f246(a876),f332(a107,x68511)),f332(a107,x68512)))+~P102(f332(f332(f246(a1),f2(a1)),x68512))+P102(f332(f332(f246(a1),x68511),x68512)) % 172.78/172.48 [6877]P102(f332(f332(f246(a1),x68771),x68772))+~P102(f332(f332(f246(a876),f332(f106(a876),x68771)),f332(f106(a876),x68772)))+P102(f332(f332(f246(a1),x68771),a82)) % 172.78/172.48 [6904]P102(f332(f332(f246(a1),f2(a1)),f44(a1,x69041,x69042)))+~P102(f332(f332(f246(a1),f2(a1)),x69042))+~P102(f332(f332(f246(a1),f2(a1)),x69041)) % 172.78/172.48 [7004]P102(f332(f332(f247(a1),a82),x70041))+~P102(f332(f332(f247(a1),x70042),x70041))+~P102(f332(f332(f247(a876),f332(f106(a876),x70042)),f332(f106(a876),x70041))) % 172.78/172.48 [7055]E(f332(f332(f267(a1,a1),f332(f332(f38(a1),x70551),x70552)),f44(a1,x70551,x70552)),f49(x70551,x70552))+~P102(f332(f332(f247(a1),x70551),f2(a1)))+~P102(f332(f332(f247(a1),f2(a1)),x70552)) % 172.78/172.48 [7076]E(f332(f332(f267(a1,a1),f332(f332(f38(a1),x70761),x70762)),f44(a1,x70761,x70762)),f46(x70761,x70762))+~P102(f332(f332(f246(a1),f2(a1)),x70762))+~P102(f332(f332(f246(a1),f2(a1)),x70761)) % 172.78/172.48 [7127]~P93(x71272)+E(x71271,f116(x71272))+E(f332(f142(x71272,x71272,f80(x71272),f332(f141(x71272),x71271)),f332(f172(x71272),x71271)),f332(f63(x71272,f80(x71272)),f332(f173(x71272),x71271))) % 172.78/172.48 [7239]~E(x72391,f2(a876))+E(f332(f142(a876,a876,f79(a876),x72391),x72392),f2(a876))+P102(f332(f332(f334(a876),f693(x72392,x72391)),f332(f173(a876),x72392))) % 172.78/172.48 [7286]~P102(f332(f332(f247(a1),x72862),f2(a1)))+P102(f332(f332(f247(a1),f332(f332(f38(a1),x72861),x72862)),f2(a1)))+~P102(f332(f332(f247(a1),f2(a1)),x72861)) % 172.78/172.48 [7288]~P102(f332(f332(f247(a1),x72881),f2(a1)))+P102(f332(f332(f247(a1),f332(f332(f38(a1),x72881),x72882)),f2(a1)))+~P102(f332(f332(f247(a1),f2(a1)),x72882)) % 172.78/172.48 [7289]~P102(f332(f332(f247(a1),x72892),f2(a1)))+P102(f332(f332(f246(a1),f332(f332(f38(a1),x72891),x72892)),f2(a1)))+~P102(f332(f332(f246(a1),f2(a1)),x72891)) % 172.78/172.48 [7290]~P102(f332(f332(f246(a1),x72901),f2(a1)))+P102(f332(f332(f246(a1),f332(f332(f38(a1),x72901),x72902)),f2(a1)))+~P102(f332(f332(f247(a1),f2(a1)),x72902)) % 172.78/172.48 [7296]P102(f332(f332(f334(f883(x72961,a871)),f601(x72962,x72961)),x72962))+~P102(f332(f61(f883(x72961,a871)),x72962))+P102(f332(f61(x72961),f39(f883(x72961,a871),x72962))) % 172.78/172.48 [7393]P20(x73931,x73931,x73932,f255(f883(x73931,a871)))+~E(f332(f311(x73931,x73931,x73932),f255(f883(x73931,a871))),f255(f883(x73931,a871)))+~P102(f332(f61(x73931),f255(f883(x73931,a871)))) % 172.78/172.48 [7521]~P20(x75211,x75211,x75212,f255(f883(x75211,a871)))+E(f332(f311(x75211,x75211,x75212),f255(f883(x75211,a871))),f255(f883(x75211,a871)))+~P102(f332(f61(x75211),f255(f883(x75211,a871)))) % 172.78/172.48 [7658]E(f332(f332(f38(a1),x76581),x76582),f332(f106(a1),a100))+~P102(f332(f332(f246(a1),f332(f332(f79(a1),x76581),x76582)),f2(a1)))+~P102(f332(f332(f247(a1),f2(a1)),x76581)) % 172.78/172.48 [7719]~P102(f332(f332(f247(a1),x77192),f2(a1)))+~P102(f332(f332(f247(a1),f332(f332(f38(a1),x77191),x77192)),f2(a1)))+P102(f332(f332(f247(a1),f2(a1)),x77191)) % 172.78/172.48 [7724]E(f332(f332(f79(a1),x77241),x77242),f44(a1,x77241,x77242))+~P102(f332(f332(f246(a1),f332(f332(f79(a1),x77241),x77242)),f2(a1)))+~P102(f332(f332(f247(a1),f2(a1)),x77241)) % 172.78/172.48 [7727]P102(f332(f332(f247(a1),x77271),f2(a1)))+~P102(f332(f332(f247(a1),f332(f332(f38(a1),x77271),x77272)),f2(a1)))+~P102(f332(f332(f247(a1),f2(a1)),x77272)) % 172.78/172.48 [8124]~P56(x81241)+~P102(f332(f58(f880(x81241)),x81242))+P102(f332(f58(x81241),f332(f332(f8(f880(x81241),a871,x81241),x81242),f239(x81241)))) % 172.78/172.48 [8437]~P104(x84371)+P29(x84371,x84372)+~P102(f332(f332(f246(x84371),f332(f332(f165(x84371),x84372),f744(x84372,x84371))),f332(f332(f165(x84371),x84372),f745(x84372,x84371)))) % 172.78/172.48 [8438]~P104(x84381)+P29(x84381,x84382)+~P102(f332(f332(f246(x84381),f332(f332(f165(x84381),x84382),f752(x84382,x84381))),f332(f332(f165(x84381),x84382),f756(x84382,x84381)))) % 172.78/172.48 [8590]~P56(x85901)+P102(f332(f57(f880(x85901)),x85902))+~P102(f332(f57(x85901),f332(f332(f8(f880(x85901),a871,x85901),x85902),f239(x85901)))) % 172.78/172.48 [9753]~P56(x97531)+~P56(x97532)+E(f332(f332(f154(f877(x97531),f883(x97532,x97531)),f332(f332(f8(f883(x97532,f880(x97531)),f883(x97532,x97531),f877(x97531)),f72(f880(x97531),x97531,x97532,f243(x97531))),f332(f332(f8(f877(f882(x97532,x97531)),f883(x97532,f880(x97531)),f877(x97531)),f179(x97532,x97531)),f332(f183(x97532,x97531),f55(x97532))))),f54(x97531,f332(f196(f877(x97532)),f55(x97532)),f55(x97531))),f55(f883(x97532,x97531))) % 172.78/172.48 [5682]E(x56821,f2(a1))+~E(f44(a1,x56822,x56821),f2(a1))+E(f332(f332(f38(a1),x56822),f332(f78(a1),x56821)),f332(f78(a1),f332(f332(f38(a1),x56822),x56821))) % 172.78/172.48 [5700]~P39(x57002)+~P39(x57001)+P39(f332(f332(f113(f883(a1,a871)),x57001),x57002)) % 172.78/172.48 [5701]~P39(x57012)+~P39(x57011)+P39(f332(f332(f104(f883(a1,a871)),x57011),x57012)) % 172.78/172.48 [5719]~P57(x57191)+~P89(x57191)+E(f332(f78(x57191),f332(f332(f290(x57191),f77(x57191)),x57192)),f332(f332(f290(x57191),f332(f106(x57191),a100)),x57192)) % 172.78/172.48 [5832]E(x58321,f2(a1))+~E(f44(a1,x58322,x58321),f2(a1))+E(f332(f332(f38(a1),f332(f78(a1),x58322)),x58321),f332(f78(a1),f332(f332(f38(a1),x58322),x58321))) % 172.78/172.48 [5967]~P104(x59671)+P29(x59671,x59672)+P102(f332(f332(f247(a876),f745(x59672,x59671)),f332(f196(f877(x59671)),x59672))) % 172.78/172.48 [5968]~P104(x59681)+P29(x59681,x59682)+P102(f332(f332(f247(a876),f756(x59682,x59681)),f332(f196(f877(x59681)),x59682))) % 172.78/172.48 [6121]~P89(x61211)+~E(f332(f106(x61211),x61212),f2(x61211))+P31(x61211,f332(f106(x61211),f332(f332(f79(a1),x61212),f332(f78(a1),a82)))) % 172.78/172.48 [6122]~P89(x61221)+~E(f332(f106(x61221),x61222),f2(x61221))+P31(x61221,f332(f106(x61221),f332(f332(f79(a1),a82),f332(f78(a1),x61222)))) % 172.78/172.48 [6124]E(f332(a50,f46(f332(f78(a1),x61241),f332(f78(a1),x61242))),f45(x61241,x61242))+P102(f332(f332(f247(a1),f2(a1)),x61242))+P102(f332(f332(f246(a1),f2(a1)),x61241)) % 172.78/172.48 [6250]~E(x62502,f2(a876))+~E(x62501,f2(a876))+P102(f332(f332(f246(a1),f332(f103(a1),x62501)),f332(f78(a1),f332(f103(a1),x62502)))) % 172.78/172.48 [6278]E(f332(f332(f79(a876),f332(f106(a876),x62781)),f332(f106(a876),x62782)),f332(f106(a876),f332(f332(f79(a1),x62781),x62782)))+P102(f332(f332(f247(a1),x62781),a82))+P102(f332(f332(f247(a1),x62782),a82)) % 172.78/172.48 [6406]~P73(x64061)+~P102(f332(f332(f247(x64061),f2(x64061)),x64062))+P102(f332(f332(f247(x64061),f332(f78(x64061),x64062)),x64062)) % 172.78/172.48 [6407]~P73(x64071)+~P102(f332(f332(f246(x64071),f2(x64071)),x64072))+P102(f332(f332(f246(x64071),f332(f78(x64071),x64072)),x64072)) % 172.78/172.48 [6579]E(f332(f332(f22(a876),f332(a107,x65791)),f332(a107,x65792)),f332(a107,f332(f332(f22(a1),x65791),x65792)))+~P102(f332(f332(f246(a1),f2(a1)),x65792))+~P102(f332(f332(f246(a1),x65792),x65791)) % 172.78/172.48 [6612]E(f332(a107,f44(a1,f332(f106(a1),x66121),f332(f106(a1),x66122))),f44(a876,f332(f106(a876),x66121),f332(f106(a876),x66122)))+P102(f332(a200,f332(f106(a1),x66121)))+P102(f332(a200,f332(f106(a1),x66122))) % 172.78/172.48 [6630]~P73(x66301)+P102(f332(f332(f247(x66301),f2(x66301)),x66302))+~P102(f332(f332(f247(x66301),f332(f78(x66301),x66302)),x66302)) % 172.78/172.48 [6631]~P73(x66311)+P102(f332(f332(f246(x66311),f2(x66311)),x66312))+~P102(f332(f332(f246(x66311),f332(f78(x66311),x66312)),x66312)) % 172.78/172.48 [6642]~P73(x66421)+~P102(f332(f332(f247(x66421),f2(x66421)),x66422))+P102(f332(f332(f247(x66421),f2(x66421)),f332(f332(f79(x66421),x66422),x66422))) % 172.78/172.48 [6645]~P73(x66451)+~P102(f332(f332(f246(x66451),f2(x66451)),x66452))+P102(f332(f332(f246(x66451),f2(x66451)),f332(f332(f79(x66451),x66452),x66452))) % 172.78/172.48 [6657]E(f332(f332(f79(a876),f332(a107,x66571)),f332(a107,x66572)),f332(a107,f332(f332(f79(a1),x66571),x66572)))+~P102(f332(f332(f246(a1),f2(a1)),x66572))+~P102(f332(f332(f246(a1),f2(a1)),x66571)) % 172.78/172.48 [6668]E(x66681,f2(a876))+P102(f332(f332(f247(a876),f2(a876)),x66682))+~P102(f332(f332(f247(a876),f2(a876)),f332(f332(f257(a876),x66682),x66681))) % 172.78/172.48 [6698]~P89(x66981)+E(f332(f106(x66981),x66982),f2(x66981))+~P31(x66981,f332(f106(x66981),f332(f332(f79(a1),a82),f332(f78(a1),x66982)))) % 172.78/172.48 [6699]~P89(x66991)+E(f332(f106(x66991),x66992),f2(x66991))+~P31(x66991,f332(f106(x66991),f332(f332(f79(a1),x66992),f332(f78(a1),a82)))) % 172.78/172.48 [6758]~P102(f332(f61(x67581),x67582))+~P102(f332(f61(x67581),f255(f883(x67581,a871))))+P102(f332(f61(x67581),f332(f78(f883(x67581,a871)),x67582))) % 172.78/172.48 [6781]~P102(f332(f332(f247(a1),f2(a1)),x67812))+~P102(f332(f332(f246(a1),x67812),x67811))+P102(f332(f332(f247(a1),f2(a1)),f332(f332(f38(a1),x67811),x67812))) % 172.78/172.48 [6782]~P102(f332(f332(f247(a1),x67822),f2(a1)))+~P102(f332(f332(f246(a1),x67821),f2(a1)))+P102(f332(f332(f246(a1),f2(a1)),f332(f332(f38(a1),x67821),x67822))) % 172.78/172.48 [6821]~P102(f332(f332(f247(a876),f2(a876)),x68212))+~P102(f332(f332(f247(a876),f2(a876)),x68211))+P102(f332(f332(f247(a876),f2(a876)),f332(f332(f80(a876),x68211),x68212))) % 172.78/172.48 [6822]~P102(f332(f332(f246(a1),f2(a1)),x68222))+~P102(f332(f332(f246(a1),f2(a1)),x68221))+P102(f332(f332(f246(a1),f2(a1)),f332(f332(f80(a1),x68221),x68222))) % 172.78/172.48 [6823]~P102(f332(f332(f246(a1),f2(a1)),x68232))+~P102(f332(f332(f246(a1),f2(a1)),x68231))+P102(f332(f332(f246(a1),f2(a1)),f332(f332(f79(a1),x68231),x68232))) % 172.78/172.48 [6824]~P102(f332(f332(f247(a1),f2(a1)),x68242))+~P102(f332(f332(f246(a1),f2(a1)),x68241))+P102(f332(f332(f246(a1),f2(a1)),f332(f332(f38(a1),x68241),x68242))) % 172.78/172.48 [6825]~P102(f332(f332(f246(a1),f2(a1)),x68252))+~P102(f332(f332(f246(a1),f2(a1)),x68251))+P102(f332(f332(f246(a1),f2(a1)),f332(f332(f38(a1),x68251),x68252))) % 172.78/172.48 [6890]E(x68901,f2(a1))+E(f44(a1,x68902,x68901),f2(a1))+E(f332(f332(f22(a1),f332(f78(a1),f332(f332(f38(a1),x68902),x68901))),f77(a1)),f332(f332(f38(a1),f332(f78(a1),x68902)),x68901)) % 172.78/172.48 [6945]P102(f332(f332(f247(a876),f2(a876)),x69451))+P102(f332(f332(f247(a876),f2(a876)),x69452))+~P102(f332(f332(f247(a876),f2(a876)),f332(f332(f79(a876),x69452),x69451))) % 172.78/172.48 [6949]~P73(x69491)+P102(f332(f332(f247(x69491),f2(x69491)),x69492))+~P102(f332(f332(f247(x69491),f2(x69491)),f332(f332(f79(x69491),x69492),x69492))) % 172.78/172.48 [6950]~P73(x69501)+P102(f332(f332(f246(x69501),f2(x69501)),x69502))+~P102(f332(f332(f246(x69501),f2(x69501)),f332(f332(f79(x69501),x69502),x69502))) % 172.78/172.48 [7005]~P102(f332(f61(x70051),x70052))+P102(f332(f61(x70051),f255(f883(x70051,a871))))+~P102(f332(f61(x70051),f332(f78(f883(x70051,a871)),x70052))) % 172.78/172.48 [7068]P102(f332(f332(f246(a1),x70681),f2(a1)))+~P102(f332(f332(f247(a1),x70682),f2(a1)))+~P102(f332(f332(f246(a1),f2(a1)),f332(f332(f38(a1),x70681),x70682))) % 172.78/172.48 [7074]~P102(f332(f332(f247(a1),f2(a1)),x70741))+P102(f332(f332(f246(a1),x70741),x70742))+~P102(f332(f332(f247(a1),f2(a1)),f332(f332(f38(a1),x70742),x70741))) % 172.78/172.49 [7075]~P102(f332(f332(f246(a1),f2(a1)),x70752))+P102(f332(f332(f246(a1),x70751),x70752))+~P102(f332(f332(f247(a1),f2(a1)),f332(f332(f38(a1),x70752),x70751))) % 172.78/172.49 [7104]P102(f332(f332(f247(a1),f2(a1)),x71041))+~P102(f332(f332(f246(a1),f2(a1)),x71042))+~P102(f332(f332(f247(a1),f2(a1)),f332(f332(f38(a1),x71042),x71041))) % 172.78/172.49 [7105]P102(f332(f332(f246(a1),f2(a1)),x71051))+~P102(f332(f332(f247(a1),f2(a1)),x71052))+~P102(f332(f332(f246(a1),f2(a1)),f332(f332(f38(a1),x71051),x71052))) % 172.78/172.49 [7552]~P102(f332(f61(x75522),f255(f883(x75522,a871))))+~P102(f332(f61(x75521),f255(f883(x75521,a871))))+P102(f332(f61(f881(x75521,x75522)),f255(f883(f881(x75521,x75522),a871)))) % 172.78/172.49 [7553]~P102(f332(f61(x75532),f255(f883(x75532,a871))))+~P102(f332(f61(x75531),f255(f883(x75531,a871))))+P102(f332(f61(f882(x75531,x75532)),f255(f883(f882(x75531,x75532),a871)))) % 172.78/172.49 [7622]~P102(f332(f332(f247(a876),f332(a115,f2(a876))),x76221))+~P102(f332(f332(f247(a876),f332(a115,f2(a876))),x76222))+P102(f332(f332(f247(a876),x76221),f332(f332(f80(a876),x76222),x76221))) % 172.78/172.49 [7623]~P102(f332(f332(f247(a876),f332(a115,f2(a876))),x76231))+~P102(f332(f332(f247(a876),f332(a115,f2(a876))),x76232))+P102(f332(f332(f247(a876),x76231),f332(f332(f80(a876),x76231),x76232))) % 172.78/172.49 [7657]E(f332(f37(x76571),f255(f883(x76571,a871))),f332(a115,f2(a876)))+P102(f332(f61(x76572),f255(f883(x76572,a871))))+~P102(f332(f61(f883(x76572,x76571)),f255(f883(f883(x76572,x76571),a871)))) % 172.78/172.49 [7790]~P102(f332(f332(f247(a876),f332(a115,f2(a876))),x77902))+~P102(f332(f332(f247(a876),f332(a115,f2(a876))),x77901))+P102(f332(f332(f247(a876),f332(a115,f2(a876))),f332(f332(f80(a876),x77901),x77902))) % 172.78/172.49 [7791]~P102(f332(f332(f246(a876),f332(a115,f2(a876))),x77911))+~P102(f332(f332(f246(a876),f332(a115,f2(a876))),x77912))+P102(f332(f332(f246(a876),f332(a115,f2(a876))),f332(f332(f80(a876),x77911),x77912))) % 172.78/172.49 [8487]E(x84871,f116(x84872))+~P102(f332(f137(x84872),x84871))+E(f178(x84872,f332(f332(f8(a871,a871,x84872),a327),f332(f332(f7(x84872,x84872,a871),a329),f144(x84872,x84871))),x84871),f117(x84872,x84871)) % 172.78/172.49 [8581]~P39(x85812)+~P39(x85811)+E(f332(f311(a876,a1,f103(a1)),f332(f332(f113(f883(a876,a871)),f332(f311(a1,a876,a107),x85811)),f332(f311(a1,a876,a107),x85812))),f332(f332(f113(f883(a1,a871)),x85811),x85812)) % 172.78/172.49 [8582]~P39(x85822)+~P39(x85821)+E(f332(f311(a876,a1,f103(a1)),f332(f332(f104(f883(a876,a871)),f332(f311(a1,a876,a107),x85821)),f332(f311(a1,a876,a107),x85822))),f332(f332(f104(f883(a1,a871)),x85821),x85822)) % 172.78/172.49 [9236]~P89(x92361)+~E(f332(f106(x92361),x92362),f77(x92361))+P31(x92361,f332(f106(x92361),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f78(a1),x92362)))) % 172.78/172.49 [9469]~P89(x94691)+E(f332(f106(x94691),x94692),f77(x94691))+~P31(x94691,f332(f106(x94691),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f78(a1),x94692)))) % 172.78/172.49 [10198]E(x101981,f2(a1))+E(x101982,f2(a1))+E(f332(f272(a1,a1,a1,a1,f33(a1),f332(f80(a1),f81(a1,x101982))),f332(f332(f332(f99(f882(a1,a1)),f332(f332(a329,f81(a1,x101981)),f81(a1,x101982))),f52(x101981,x101982)),f332(f332(f271(a1,a1,f882(a1,a1)),f332(f332(f18(a1,f883(a1,f882(a1,a1)),f883(a1,f882(a1,a1))),f332(f332(f8(f883(a1,f883(f882(a1,a1),f882(a1,a1))),f883(f883(a1,f882(a1,a1)),f883(a1,f882(a1,a1))),a1),f18(a1,f882(a1,a1),f882(a1,a1))),f332(f332(f8(f882(a1,a1),f883(a1,f883(f882(a1,a1),f882(a1,a1))),a1),f332(f7(a1,f882(a1,a1),f883(f882(a1,a1),f882(a1,a1))),f332(f332(f8(a871,f883(f882(a1,a1),f883(f882(a1,a1),f882(a1,a1))),a1),f99(f882(a1,a1))),f332(f332(f7(a1,a1,a871),a329),f2(a1))))),f332(f332(f7(a1,a1,f882(a1,a1)),f332(f332(f8(a1,f883(a1,f882(a1,a1)),a1),f267(a1,a1)),f78(a1))),f2(a1))))),f332(f332(f7(a1,f883(a1,a1),f883(a1,f882(a1,a1))),f332(f332(f8(f883(a1,f882(a1,a1)),f883(f883(a1,a1),f883(a1,f882(a1,a1))),a1),f8(a1,f882(a1,a1),a1)),f332(f332(f8(a1,f883(a1,f882(a1,a1)),a1),f267(a1,a1)),f332(f332(f7(a1,a1,a1),f332(f332(f8(a1,f883(a1,a1),a1),f22(a1)),f78(a1))),f77(a1))))),f332(f22(a1),f332(f74(a1),x101982))))),f52(x101981,x101982)))),f45(x101981,x101982)) % 172.78/172.49 [10199]E(x101991,f2(a1))+E(x101992,f2(a1))+E(f332(f272(a1,a1,a1,a1,f33(a1),f332(f80(a1),f81(a1,x101992))),f332(f332(f332(f99(f882(a1,a1)),f332(f332(a331,f332(f332(a330,f332(f332(f247(a1),f2(a1)),x101992)),f332(f332(f246(a1),f2(a1)),x101991))),f332(f332(a330,f332(f332(f247(a1),x101992),f2(a1))),f332(f332(f247(a1),x101991),f2(a1))))),f52(x101991,x101992)),f332(f332(f271(a1,a1,f882(a1,a1)),f332(f332(f18(a1,f883(a1,f882(a1,a1)),f883(a1,f882(a1,a1))),f332(f332(f8(f883(a1,f883(f882(a1,a1),f882(a1,a1))),f883(f883(a1,f882(a1,a1)),f883(a1,f882(a1,a1))),a1),f18(a1,f882(a1,a1),f882(a1,a1))),f332(f332(f8(f882(a1,a1),f883(a1,f883(f882(a1,a1),f882(a1,a1))),a1),f332(f7(a1,f882(a1,a1),f883(f882(a1,a1),f882(a1,a1))),f332(f332(f8(a871,f883(f882(a1,a1),f883(f882(a1,a1),f882(a1,a1))),a1),f99(f882(a1,a1))),f332(f332(f7(a1,a1,a871),a329),f2(a1))))),f332(f332(f7(a1,a1,f882(a1,a1)),f332(f332(f8(a1,f883(a1,f882(a1,a1)),a1),f267(a1,a1)),f78(a1))),f2(a1))))),f332(f332(f7(a1,f883(a1,a1),f883(a1,f882(a1,a1))),f332(f332(f8(f883(a1,f882(a1,a1)),f883(f883(a1,a1),f883(a1,f882(a1,a1))),a1),f8(a1,f882(a1,a1),a1)),f332(f332(f8(a1,f883(a1,f882(a1,a1)),a1),f267(a1,a1)),f332(f332(f7(a1,a1,a1),f332(f332(f8(a1,f883(a1,a1),a1),f22(a1)),f78(a1))),f77(a1))))),f332(f22(a1),f332(f74(a1),x101992))))),f52(x101991,x101992)))),f45(x101991,x101992)) % 172.78/172.49 [10200]~P1(a5000)+P19(a872,x102001,f332(f332(f310(f875(a872)),f332(f332(f332(f91(a872),a329),x102002),f201(x102002))),f195(f883(f875(a872),a871))))+~P19(a872,x102001,f332(f332(f310(f875(a872)),f332(f332(f332(f91(a872),f332(f332(f8(f883(a872,f883(a872,a871)),f883(a872,a871),a872),f332(f8(f883(a872,a871),a871,a872),f87(a872))),f332(f332(f8(f883(a872,a871),f883(a872,f883(a872,a871)),a872),f332(f7(a872,f883(a872,a871),f883(a872,a871)),f332(f332(f8(f883(a872,f883(a871,a871)),f883(f883(a872,a871),f883(a872,a871)),a872),f18(a872,a871,a871)),f332(f332(f8(f883(a872,a871),f883(a872,f883(a871,a871)),a872),f332(f8(a871,f883(a871,a871),a872),a335)),f201(x102002))))),a329))),x102002),a329)),f195(f883(f875(a872),a871)))) % 172.78/172.49 [5708]~P113(x57081)+~P89(x57081)+E(f332(f74(x57081),f332(f332(f257(x57081),f332(f106(x57081),a100)),x57082)),f77(x57081)) % 172.78/172.49 [6190]~P137(x61901)+~P102(f332(f332(f247(a1),x61902),f2(a1)))+E(f332(f78(x61901),f332(f103(x61901),f332(a107,f332(f78(a1),x61902)))),f332(f105(x61901),x61902)) % 172.78/172.49 [6390]P102(f332(f332(f246(a102),x63901),f77(a102)))+E(f332(f332(f79(a102),f77(a102)),f280(x63901,f332(f332(f38(a102),x63902),x63901))),f280(x63901,x63902))+P102(f332(f332(f247(a102),x63902),x63901)) % 172.78/172.49 [6990]~P88(x69901)+~P102(f332(f332(f334(x69901),x69902),f112(x69901)))+~E(f332(f332(f79(x69901),f332(f332(f79(x69901),f77(x69901)),x69902)),x69902),f2(x69901)) % 172.78/172.49 [7106]~P102(f332(f332(f247(a1),x71061),f2(a1)))+~P102(f332(f332(f246(a1),x71062),f2(a1)))+E(f332(f266(a1,a1),f332(a50,f46(f332(f78(a1),x71061),f332(f78(a1),x71062)))),f332(f332(f38(a1),x71061),x71062)) % 172.78/172.49 [7123]~P102(f332(f332(f247(a1),x71231),f2(a1)))+~P102(f332(f332(f246(a1),x71232),f2(a1)))+E(f332(f270(a1,a1),f332(a50,f46(f332(f78(a1),x71231),f332(f78(a1),x71232)))),f44(a1,x71231,x71232)) % 172.78/172.49 [7129]~P102(f332(f332(f247(a1),x71292),f2(a1)))+E(f332(f266(a1,a1),f332(a50,f49(f332(f78(a1),x71291),f332(f78(a1),x71292)))),f332(f332(f38(a1),x71291),x71292))+~P102(f332(f332(f247(a1),f2(a1)),x71291)) % 172.78/172.49 [7147]~P102(f332(f332(f247(a1),x71472),f2(a1)))+E(f332(f270(a1,a1),f332(a50,f49(f332(f78(a1),x71471),f332(f78(a1),x71472)))),f44(a1,x71471,x71472))+~P102(f332(f332(f247(a1),f2(a1)),x71471)) % 172.78/172.49 [7200]E(f332(f332(f38(a1),f332(f332(f257(a1),x72001),x72002)),x72001),f332(f332(f257(a1),x72001),f332(f332(f22(a876),x72002),f332(a115,f2(a876)))))+~P102(f332(f332(f247(a876),f2(a876)),x72002))+~P102(f332(f332(f247(a1),f2(a1)),x72001)) % 172.78/172.49 [7293]~P102(f332(f332(f247(a876),f2(a876)),x72931))+~P102(f332(f332(f247(a876),f2(a876)),x72932))+P102(f332(f332(f247(a876),f332(f332(f22(a876),x72931),x72932)),x72931)) % 172.78/172.49 [7294]~P102(f332(f332(f247(a876),f2(a876)),x72941))+~P102(f332(f332(f247(a876),f77(a876)),x72942))+P102(f332(f332(f247(a876),f332(f332(f38(a876),x72941),x72942)),x72941)) % 172.78/172.49 [7295]~P102(f332(f332(f247(a1),f2(a1)),x72951))+~P102(f332(f332(f247(a1),f77(a1)),x72952))+P102(f332(f332(f247(a1),f332(f332(f38(a1),x72951),x72952)),x72951)) % 172.78/172.49 [7443]E(x74431,f2(a876))+~E(x74432,f2(a1))+~P102(f332(f332(f247(a1),f2(a1)),f332(f332(f257(a1),f332(f74(a1),x74432)),x74431))) % 172.78/172.49 [7869]~E(x78692,f116(f877(x78691)))+E(f332(f196(f877(f877(x78691))),f181(x78691,x78692)),f2(a876))+~P29(a876,f332(f169(a876),f332(f332(f154(f877(x78691),a876),f196(f877(x78691))),x78692))) % 172.78/172.49 [8123]P102(f332(x81231,x81232))+~P102(f332(x81231,f332(a110,f552(x81231,x81232))))+~P102(f332(f332(f334(f883(f882(a876,a876),a871)),x81232),a101)) % 172.78/172.49 [8142]E(x81421,f116(f877(x81422)))+E(f332(f196(f877(x81422)),f332(f332(f165(f877(x81422)),x81421),f2(a876))),f332(f196(f877(f877(x81422))),f181(x81422,x81421)))+~P29(a876,f332(f169(a876),f332(f332(f154(f877(x81422),a876),f196(f877(x81422))),x81421))) % 172.78/172.49 [8843]~P102(f332(f61(x88431),f332(f252(x88431),x88432)))+~P102(f332(f61(x88431),f255(f883(x88431,a871))))+P102(f332(f61(x88431),f332(f252(x88431),f332(f332(f8(a871,a871,x88431),a327),x88432)))) % 172.78/172.49 [8906]E(f332(f332(f267(a876,a876),f332(a115,f332(f332(f38(a876),f332(f332(f22(a876),x89061),x89062)),x89062))),f44(a876,f332(f332(f22(a876),x89061),x89062),x89062)),f84(f882(a876,a876),f47(x89061,x89062)))+~P102(f332(f332(f247(a876),f2(a876)),x89062))+~P102(f332(f332(f246(a876),x89062),x89061)) % 172.78/172.49 [9199]~P102(f332(f61(x91991),f332(f252(x91991),x91992)))+P102(f332(f61(x91991),f255(f883(x91991,a871))))+~P102(f332(f61(x91991),f332(f252(x91991),f332(f332(f8(a871,a871,x91991),a327),x91992)))) % 172.78/172.49 [9920]P21(x99201,x99202)+~P38(x99201,f332(f266(f883(f882(x99201,x99201),a871),f883(f882(x99201,x99201),a871)),x99202))+~P102(f332(f332(f246(f883(f882(x99201,x99201),a871)),f332(f332(f289(x99201,x99201,x99201),f332(f266(f883(f882(x99201,x99201),a871),f883(f882(x99201,x99201),a871)),x99202)),f332(f270(f883(f882(x99201,x99201),a871),f883(f882(x99201,x99201),a871)),x99202))),f332(f266(f883(f882(x99201,x99201),a871),f883(f882(x99201,x99201),a871)),x99202))) % 172.78/172.49 [7226]~P102(f332(f332(f247(a876),f2(a876)),x72262))+P102(f332(f332(f247(a876),x72261),x72262))+E(f332(a115,f332(f332(f38(a876),f332(f332(f22(a876),x72261),x72262)),x72262)),f332(f332(f38(a876),x72261),x72262)) % 172.78/172.49 [7363]~P102(f332(f332(f247(a876),f2(a876)),x73632))+~P102(f332(f332(f246(a876),x73632),x73631))+E(f332(a115,f332(f332(f38(a876),f332(f332(f22(a876),x73631),x73632)),x73632)),f332(f332(f38(a876),x73631),x73632)) % 172.78/172.49 [8352]~P89(x83521)+~P88(x83521)+~P31(x83521,f332(f106(x83521),f332(f332(f22(a1),f332(f332(f79(a1),x83522),x83522)),a100))) % 172.78/172.49 [9106]E(x91061,f2(a876))+E(f332(f332(f271(a876,a876,f882(a876,a876)),f332(f332(f8(a876,f883(a876,f882(a876,a876)),a876),f267(a876,a876)),a115)),f84(f882(a876,a876),f47(f332(f332(f22(a876),x91062),x91061),x91061))),f84(f882(a876,a876),f47(x91062,x91061)))+P102(f332(f332(f247(a876),x91062),x91061)) % 172.78/172.49 [9532]P102(f332(x95322,f659(x95322,x95321)))+P102(f332(x95321,f659(x95322,x95321)))+E(f332(f252(a1),f332(f332(f18(a1,a871,a871),f332(f332(f8(a871,f883(a871,a871),a1),a330),f332(f246(a1),f2(a1)))),x95321)),f332(f252(a1),f332(f332(f18(a1,a871,a871),f332(f332(f8(a871,f883(a871,a871),a1),a330),f332(f246(a1),f2(a1)))),x95322))) % 172.78/172.49 [9536]~P102(f332(x95362,f659(x95362,x95361)))+~P102(f332(x95361,f659(x95362,x95361)))+E(f332(f252(a1),f332(f332(f18(a1,a871,a871),f332(f332(f8(a871,f883(a871,a871),a1),a330),f332(f246(a1),f2(a1)))),x95361)),f332(f252(a1),f332(f332(f18(a1,a871,a871),f332(f332(f8(a871,f883(a871,a871),a1),a330),f332(f246(a1),f2(a1)))),x95362))) % 172.78/172.49 [7580]~P58(x75801)+~P89(x75801)+E(f332(f332(f290(x75801),x75802),f332(f106(x75801),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100))),x75802) % 172.78/172.49 [9235]~P89(x92351)+~E(f332(f106(x92351),x92352),f77(x92351))+P31(x92351,f332(f106(x92351),f332(f332(f79(a1),x92352),f332(f78(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100))))) % 172.78/172.49 [9412]~P136(x94121)+~E(x94122,f77(x94121))+E(f332(f332(f257(x94121),x94122),f332(f106(a876),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)))),f77(x94121)) % 172.78/172.49 [9413]~P136(x94131)+~E(x94132,f2(x94131))+E(f332(f332(f257(x94131),x94132),f332(f106(a876),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)))),f2(x94131)) % 172.78/172.49 [9426]~P136(x94261)+~E(x94262,f332(f78(x94261),f77(x94261)))+E(f332(f332(f257(x94261),x94262),f332(f106(a876),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)))),f77(x94261)) % 172.78/172.49 [9470]~P89(x94701)+E(f332(f106(x94701),x94702),f77(x94701))+~P31(x94701,f332(f106(x94701),f332(f332(f79(a1),x94702),f332(f78(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100))))) % 172.78/172.49 [9854]~P113(x98542)+E(x98541,f2(x98542))+P102(f332(f332(f247(x98542),f2(x98542)),f332(f332(f257(x98542),x98541),f332(f106(a876),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)))))) % 172.78/172.49 [9919]~P113(x99192)+~E(x99191,f2(x99192))+~P102(f332(f332(f247(x99192),f2(x99192)),f332(f332(f257(x99192),x99191),f332(f106(a876),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)))))) % 172.78/172.49 [9945]P102(f332(f332(f246(a1),x99451),f2(a1)))+P102(f332(f332(f247(a1),x99452),x99451))+E(f332(f43(x99451),f46(x99452,f332(f332(f80(a1),f332(f106(a1),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)))),x99451))),f46(x99452,x99451)) % 172.78/172.49 [9946]~P102(f332(f332(f247(a1),f2(a1)),x99461))+P102(f332(f332(f247(a1),x99462),x99461))+E(f332(f43(x99461),f46(x99462,f332(f332(f80(a1),f332(f106(a1),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)))),x99461))),f46(x99462,x99461)) % 172.78/172.49 [9947]P102(f332(f332(f246(a1),x99471),f2(a1)))+P102(f332(f332(f246(a1),f2(a1)),f332(f332(f79(a1),x99472),x99471)))+E(f332(f43(x99471),f49(x99472,f332(f332(f80(a1),f332(f106(a1),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)))),x99471))),f49(x99472,x99471)) % 172.78/172.49 [9948]~P102(f332(f332(f247(a1),f2(a1)),x99481))+P102(f332(f332(f246(a1),f2(a1)),f332(f332(f79(a1),x99482),x99481)))+E(f332(f43(x99481),f49(x99482,f332(f332(f80(a1),f332(f106(a1),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)))),x99481))),f49(x99482,x99481)) % 172.78/172.49 [9949]~P141(x99491)+~P102(f332(f332(f246(a1),f2(a1)),x99492))+E(f332(f103(x99491),f332(a107,f332(f332(f80(a1),f332(f106(a1),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)))),x99492))),f332(f332(f79(x99491),f332(f103(x99491),f332(a107,x99492))),f332(f103(x99491),f332(a107,x99492)))) % 172.78/172.49 [5047]~P143(x50471,x50472,x50473)+~E(x50473,f2(a1))+P102(f332(x50471,x50472)) % 172.78/172.49 [5168]~P104(x51681)+~P29(x51681,x51683)+P29(x51681,f171(x51681,x51682,x51683)) % 172.78/172.49 [5169]~P104(x51691)+~P29(x51691,x51693)+P29(x51691,f178(x51691,x51692,x51693)) % 172.78/172.49 [4751]~P72(x47512)+~E(x47513,f332(f78(x47512),x47511))+E(x47511,f332(f78(x47512),x47513)) % 172.78/172.49 [4753]~P72(x47531)+~E(f332(f78(x47531),x47533),x47532)+E(f332(f78(x47531),x47532),x47533) % 172.78/172.49 [4829]~P104(x48293)+E(x48291,x48292)+~E(f332(f253(x48293),x48291),f332(f253(x48293),x48292)) % 172.78/172.49 [4830]~P99(x48303)+E(x48301,x48302)+~E(f332(f103(x48303),x48301),f332(f103(x48303),x48302)) % 172.78/172.49 [4831]~P104(x48313)+E(x48311,x48312)+~E(f332(f301(x48313),x48311),f332(f301(x48313),x48312)) % 172.78/172.49 [4832]~P104(x48323)+E(x48321,x48322)+~E(f332(f254(x48323),x48321),f332(f254(x48323),x48322)) % 172.78/172.49 [4833]~P104(x48333)+E(x48331,x48332)+~E(f332(f304(x48333),x48331),f332(f304(x48333),x48332)) % 172.78/172.49 [4834]~P72(x48343)+E(x48341,x48342)+~E(f332(f78(x48343),x48341),f332(f78(x48343),x48342)) % 172.78/172.49 [4835]~P92(x48353)+E(x48351,x48352)+~E(f332(f78(x48353),x48351),f332(f78(x48353),x48352)) % 172.78/172.49 [4836]~P88(x48363)+E(x48361,x48362)+~E(f332(f105(x48363),x48361),f332(f105(x48363),x48362)) % 172.78/172.49 [4936]~P56(x49361)+~P102(f332(x49362,x49363))+P102(f332(f57(x49361),x49362)) % 172.78/172.49 [4969]~P56(x49693)+P102(f332(x49691,x49692))+~P102(f332(f58(x49693),x49691)) % 172.78/172.49 [5066]~P144(x50661,x50663,x50662)+~E(x50662,f2(a1))+P102(f332(x50661,f2(a1))) % 172.78/172.49 [5104]~E(x51041,f2(a876))+E(f776(x51041,x51042,x51043),f195(f883(x51043,a871)))+~E(f332(f37(x51043),x51042),f332(a115,x51041)) % 172.78/172.49 [5251]~E(x52512,f2(a876))+E(f332(f266(a876,a876),x52511),f2(a876))+~P102(f332(f47(x52513,x52512),x52511)) % 172.78/172.49 [5297]P102(f332(x52971,x52972))+~E(x52973,f332(f103(a1),x52972))+~P102(f332(x52971,f332(a107,x52973))) % 172.78/172.49 [5771]~E(x57713,f2(a876))+~P102(f332(x57711,x57712))+P102(f332(x57711,f44(a876,x57712,x57713))) % 172.78/172.49 [5932]~P56(x59323)+~P6(x59323,x59321,x59322)+P102(f332(x59321,f722(x59322,x59321,x59323))) % 172.78/172.49 [5994]~P100(x59942)+~P100(x59941)+E(f131(x59941,x59942,f132(x59941,x59943),f132(x59942,x59943)),f132(f882(x59941,x59942),x59943)) % 172.78/172.49 [6172]~E(x61723,f2(a876))+P102(f332(x61721,x61722))+~P102(f332(x61721,f44(a876,x61722,x61723))) % 172.78/172.49 [6321]~P56(x63211)+P7(x63211,x63212,x63213)+~P102(f332(x63212,f723(x63213,x63212,x63211))) % 172.78/172.49 [6847]E(x68471,f2(a876))+~P102(f332(x68472,f362(x68471,x68473,x68472)))+P102(f332(x68472,f44(a876,x68473,x68471))) % 172.78/172.49 [6955]~P27(x69551)+~P102(f332(f332(f246(x69551),x69552),f603(x69553,x69552,x69551)))+P102(f332(f332(f246(x69551),x69552),f40(x69551,x69553))) % 172.78/172.49 [6957]~P102(f332(x69571,x69572))+~P102(f332(x69571,f362(x69573,x69572,x69571)))+P102(f332(x69571,f44(a876,x69572,x69573))) % 172.78/172.49 [7061]E(x70611,f116(x70612))+E(f332(f332(f151(x70612),f707(x70613,x70611,x70612)),f710(x70613,x70611,x70612)),x70611)+~P102(f332(f332(f334(f877(x70612)),x70611),f161(x70612,x70613))) % 172.78/172.49 [7092]~P137(x70921)+~P102(f332(f332(f334(x70921),x70922),f112(x70921)))+P102(f332(f332(f334(x70921),f332(f332(f257(x70921),x70922),x70923)),f112(x70921))) % 172.78/172.49 [7412]P38(x74121,x74122)+~P102(f332(f332(f334(x74121),x74123),f600(x74122,x74121)))+P102(f332(f332(f334(x74121),f657(x74122,x74121,x74123)),f600(x74122,x74121))) % 172.78/172.49 [7685]E(x76851,f116(x76852))+~P102(f332(f332(f334(f877(x76852)),x76851),f161(x76852,x76853)))+P102(f332(f332(f334(f877(x76852)),f710(x76853,x76851,x76852)),f161(x76852,x76853))) % 172.78/172.49 [7739]E(x77391,f2(a876))+E(f332(f332(f79(a876),f332(f332(f80(a876),x77391),f363(x77391,x77392,x77393))),f362(x77391,x77392,x77393)),x77392)+P102(f332(x77393,f44(a876,x77392,x77391))) % 172.78/172.49 [7785]~P102(f332(x77853,x77852))+E(f332(f332(f79(a876),f332(f332(f80(a876),x77851),f363(x77851,x77852,x77853))),f362(x77851,x77852,x77853)),x77852)+P102(f332(x77853,f44(a876,x77852,x77851))) % 172.78/172.49 [7925]P102(f332(f332(f247(a1),x79251),f347(x79252,x79253,x79251)))+P102(f332(f332(x79253,f332(f332(f38(a1),x79252),x79251)),f44(a1,x79252,x79251)))+~P102(f332(f332(f247(a1),x79251),f2(a1))) % 172.78/172.49 [8204]P102(f332(f332(x82042,f332(f332(f38(a1),x82041),x82043)),f44(a1,x82041,x82043)))+~P102(f332(f332(f247(a1),x82043),f2(a1)))+P102(f332(f332(f246(a1),f347(x82041,x82042,x82043)),f2(a1))) % 172.78/172.49 [8385]E(f332(f332(f79(a1),f332(f332(f80(a1),x83851),f350(x83852,x83853,x83851))),f347(x83852,x83853,x83851)),x83852)+P102(f332(f332(x83853,f332(f332(f38(a1),x83852),x83851)),f44(a1,x83852,x83851)))+~P102(f332(f332(f247(a1),x83851),f2(a1))) % 172.78/172.49 [8627]~P102(f332(f332(x86271,f350(x86272,x86271,x86273)),f347(x86272,x86271,x86273)))+P102(f332(f332(x86271,f332(f332(f38(a1),x86272),x86273)),f44(a1,x86272,x86273)))+~P102(f332(f332(f247(a1),x86273),f2(a1))) % 172.78/172.49 [8853]~P104(x88531)+~P29(x88531,x88533)+P29(x88531,f149(x88531,x88531,f5(x88531),x88532,x88533)) % 172.78/172.49 [9361]~P120(x93612)+E(x93611,f2(x93612))+~P102(f332(f332(f246(x93612),f332(f332(f79(x93612),f332(f332(f80(x93612),x93613),x93613)),f332(f332(f80(x93612),x93611),x93611))),f2(x93612))) % 172.78/172.49 [9362]~P120(x93622)+E(x93621,f2(x93622))+~P102(f332(f332(f246(x93622),f332(f332(f79(x93622),f332(f332(f80(x93622),x93621),x93621)),f332(f332(f80(x93622),x93623),x93623))),f2(x93622))) % 172.78/172.49 [10136]~P113(x101361)+~P102(f332(f332(f247(x101361),x101362),f2(x101361)))+P102(f332(f332(f247(x101361),f332(f332(f257(x101361),x101362),f332(a115,f332(f332(f80(a876),f332(f106(a876),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)))),x101363)))),f2(x101361))) % 172.78/172.49 [10144]~P113(x101442)+E(x101441,f2(x101442))+~P102(f332(f332(f246(x101442),f332(f332(f79(x101442),f332(f332(f257(x101442),x101443),f332(f106(a876),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100))))),f332(f332(f257(x101442),x101441),f332(f106(a876),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)))))),f2(x101442))) % 172.78/172.49 [10145]~P113(x101452)+E(x101451,f2(x101452))+~P102(f332(f332(f246(x101452),f332(f332(f79(x101452),f332(f332(f257(x101452),x101451),f332(f106(a876),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100))))),f332(f332(f257(x101452),x101453),f332(f106(a876),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)))))),f2(x101452))) % 172.78/172.49 [4785]~E(x47852,x47853)+~P66(x47851)+E(f332(f332(f22(x47851),x47852),x47853),f2(x47851)) % 172.78/172.49 [4786]~E(x47862,x47863)+~P72(x47861)+E(f332(f332(f22(x47861),x47862),x47863),f2(x47861)) % 172.78/172.49 [4799]~P138(x47991)+~E(x47993,f2(x47991))+E(f332(f332(f79(x47991),x47992),x47993),x47992) % 172.78/172.49 [4815]~P135(x48151)+~E(x48153,f2(x48151))+E(f332(f332(f80(x48151),x48152),x48153),f2(x48151)) % 172.78/172.49 [4816]~P135(x48161)+~E(x48162,f2(x48161))+E(f332(f332(f80(x48161),x48162),x48163),f2(x48161)) % 172.78/172.49 [4838]~E(x48383,f116(x48381))+~E(x48382,f116(x48381))+E(f332(f332(f134(x48381),x48382),x48383),f116(x48381)) % 172.78/172.49 [4926]~P138(x49262)+E(x49261,f2(x49262))+~E(f332(f332(f79(x49262),x49263),x49261),x49263) % 172.78/172.49 [4927]~P72(x49271)+~E(x49272,f332(f78(x49271),x49273))+E(f332(f332(f79(x49271),x49272),x49273),f2(x49271)) % 172.78/172.49 [4934]E(x49341,f116(x49342))+E(x49343,f2(a876))+~E(f332(f332(f176(x49342),x49343),x49341),f116(x49342)) % 172.78/172.49 [4940]~P66(x49403)+E(x49401,x49402)+~E(f332(f332(f22(x49403),x49401),x49402),f2(x49403)) % 172.78/172.49 [4941]~P72(x49413)+E(x49411,x49412)+~E(f332(f332(f22(x49413),x49411),x49412),f2(x49413)) % 172.78/172.49 [4950]~P136(x49502)+E(x49501,f2(x49502))+~E(f332(f332(f257(x49502),x49501),x49503),f2(x49502)) % 172.78/172.49 [4951]~P62(x49512)+E(x49511,f195(x49512))+~E(f332(f332(f113(x49512),x49513),x49511),f195(x49512)) % 172.78/172.49 [4952]~P62(x49522)+E(x49521,f195(x49522))+~E(f332(f332(f113(x49522),x49521),x49523),f195(x49522)) % 172.78/172.49 [4953]~P96(x49532)+E(x49531,f255(x49532))+~E(f332(f332(f104(x49532),x49533),x49531),f255(x49532)) % 172.78/172.49 [4954]~P96(x49542)+E(x49541,f255(x49542))+~E(f332(f332(f104(x49542),x49541),x49543),f255(x49542)) % 172.78/172.49 [5020]~P72(x50202)+E(x50201,f332(f78(x50202),x50203))+~E(f332(f332(f79(x50202),x50201),x50203),f2(x50202)) % 172.78/172.49 [5021]~P72(x50211)+E(f332(f78(x50211),x50212),x50213)+~E(f332(f332(f79(x50211),x50212),x50213),f2(x50211)) % 172.78/172.49 [5023]~E(x50232,x50233)+~P103(x50231)+P102(f332(f332(f246(x50231),x50232),x50233)) % 172.78/172.49 [5025]~E(x50252,x50253)+~P105(x50251)+P102(f332(f332(f246(x50251),x50252),x50253)) % 172.78/172.49 [5026]~E(x50262,x50263)+~P91(x50261)+P102(f332(f332(f90(x50261),x50262),x50263)) % 172.78/172.49 [5120]~P116(x51201)+~E(x51202,f332(f78(x51201),x51203))+E(f332(f332(f80(x51201),x51202),x51202),f332(f332(f80(x51201),x51203),x51203)) % 172.78/172.49 [5128]~P104(x51281)+~P29(x51281,x51283)+P29(x51281,f332(f332(f176(x51281),x51282),x51283)) % 172.78/172.49 [5129]~P104(x51291)+~P29(x51291,x51293)+P29(x51291,f332(f332(f138(x51291),x51292),x51293)) % 172.78/172.49 [5166]E(x51661,x51662)+E(x51663,f2(a876))+~E(f332(f332(f80(a876),x51663),x51661),f332(f332(f80(a876),x51663),x51662)) % 172.78/172.49 [5167]E(x51671,x51672)+E(x51673,f2(a876))+~E(f332(f332(f80(a876),x51671),x51673),f332(f332(f80(a876),x51672),x51673)) % 172.78/172.49 [5242]~E(x52422,x52423)+~P105(x52421)+E(f303(x52421,x52422,x52423),f332(f332(f310(x52421),x52422),f195(f883(x52421,a871)))) % 172.78/172.49 [5284]E(x52841,x52842)+~P91(x52843)+~P102(f332(f332(f90(x52843),x52841),x52842)) % 172.78/172.49 [5295]~E(x52951,x52952)+~P104(x52953)+~P102(f332(f332(f247(x52953),x52951),x52952)) % 172.78/172.49 [5296]~E(x52961,x52962)+~P105(x52963)+~P102(f332(f332(f247(x52963),x52961),x52962)) % 172.78/172.49 [5306]~P105(x53061)+E(f332(f302(x53061,x53062),x53063),f195(f883(x53061,a871)))+P102(f332(f332(f247(x53061),x53062),x53063)) % 172.78/172.49 [5355]~P105(x53551)+E(f303(x53551,x53552,x53553),f195(f883(x53551,a871)))+P102(f332(f332(f246(x53551),x53552),x53553)) % 172.78/172.49 [5356]~P105(x53561)+E(f305(x53561,x53562,x53563),f195(f883(x53561,a871)))+P102(f332(f332(f247(x53561),x53562),x53563)) % 172.78/172.49 [5357]~P105(x53571)+E(f195(f883(x53571,a871)),f303(x53571,x53572,x53573))+P102(f332(f332(f246(x53571),x53572),x53573)) % 172.78/172.49 [5358]~P105(x53581)+E(f195(f883(x53581,a871)),f305(x53581,x53582,x53583))+P102(f332(f332(f247(x53581),x53582),x53583)) % 172.78/172.49 [5366]~P97(x53661)+~E(f332(f332(f113(x53661),x53662),x53663),x53663)+P102(f332(f332(f246(x53661),x53662),x53663)) % 172.78/172.49 [5367]~P98(x53671)+~E(f332(f332(f104(x53671),x53672),x53673),x53672)+P102(f332(f332(f246(x53671),x53672),x53673)) % 172.78/172.49 [5368]~P104(x53681)+~E(f332(f332(f244(x53681),x53682),x53683),x53682)+P102(f332(f332(f246(x53681),x53682),x53683)) % 172.78/172.49 [5369]~P104(x53691)+~E(f332(f332(f245(x53691),x53692),x53693),x53693)+P102(f332(f332(f246(x53691),x53692),x53693)) % 172.78/172.49 [5389]~P104(x53891)+P29(x53891,x53892)+~P29(x53891,f332(f332(f151(x53891),x53893),x53892)) % 172.78/172.49 [5390]~P104(x53901)+P29(x53901,x53902)+~P29(x53901,f332(f332(f134(x53901),x53903),x53902)) % 172.78/172.49 [5391]~P104(x53911)+P29(x53911,x53912)+~P29(x53911,f332(f332(f134(x53911),x53912),x53913)) % 172.78/172.49 [5459]~P104(x54591)+P102(f332(f332(f246(x54591),x54593),x54592))+P102(f332(f332(f247(x54591),x54592),x54593)) % 172.78/172.49 [5461]~P104(x54611)+P102(f332(f332(f246(x54611),x54613),x54612))+P102(f332(f332(f246(x54611),x54612),x54613)) % 172.78/172.49 [5500]~P97(x55001)+E(f332(f332(f113(x55001),x55002),x55003),x55002)+~P102(f332(f332(f246(x55001),x55003),x55002)) % 172.78/172.49 [5502]~P97(x55021)+E(f332(f332(f113(x55021),x55022),x55023),x55023)+~P102(f332(f332(f246(x55021),x55022),x55023)) % 172.78/172.49 [5503]~P98(x55031)+E(f332(f332(f104(x55031),x55032),x55033),x55033)+~P102(f332(f332(f246(x55031),x55033),x55032)) % 172.78/172.49 [5505]~P98(x55051)+E(f332(f332(f104(x55051),x55052),x55053),x55052)+~P102(f332(f332(f246(x55051),x55052),x55053)) % 172.78/172.49 [5506]~P104(x55061)+E(f332(f332(f244(x55061),x55062),x55063),x55063)+~P102(f332(f332(f246(x55061),x55063),x55062)) % 172.78/172.49 [5508]~P104(x55081)+E(f332(f332(f244(x55081),x55082),x55083),x55082)+~P102(f332(f332(f246(x55081),x55082),x55083)) % 172.78/172.49 [5509]~P104(x55091)+E(f332(f332(f245(x55091),x55092),x55093),x55092)+~P102(f332(f332(f246(x55091),x55093),x55092)) % 172.78/172.49 [5511]~P104(x55111)+E(f332(f332(f245(x55111),x55112),x55113),x55113)+~P102(f332(f332(f246(x55111),x55112),x55113)) % 172.78/172.49 [5518]~P117(x55182)+E(x55181,f2(x55182))+E(f332(f332(f290(x55182),f332(f78(x55182),x55183)),f332(f78(x55182),x55181)),f332(f332(f290(x55182),x55183),x55181)) % 172.78/172.49 [5565]~P105(x55651)+E(f332(f302(x55651,x55652),x55653),f195(f883(x55651,a871)))+~P102(f332(f332(f246(x55651),x55653),x55652)) % 172.78/172.49 [5597]~P105(x55971)+E(f303(x55971,x55972,x55973),f195(f883(x55971,a871)))+~P102(f332(f332(f247(x55971),x55973),x55972)) % 172.78/172.49 [5598]~P105(x55981)+E(f306(x55981,x55982,x55983),f195(f883(x55981,a871)))+~P102(f332(f332(f246(x55981),x55983),x55982)) % 172.78/172.49 [5599]~P105(x55991)+E(f305(x55991,x55992,x55993),f195(f883(x55991,a871)))+~P102(f332(f332(f246(x55991),x55993),x55992)) % 172.78/172.49 [5650]~E(f332(f332(f22(a876),x56501),x56503),x56502)+E(x56501,f332(f332(f79(a876),x56502),x56503))+~P102(f332(f332(f246(a876),x56503),x56501)) % 172.78/172.49 [5651]~E(x56511,f332(f332(f79(a876),x56513),x56512))+E(f332(f332(f22(a876),x56511),x56512),x56513)+~P102(f332(f332(f246(a876),x56512),x56511)) % 172.78/172.49 [5697]~P102(f332(x56971,x56973))+P102(f332(x56971,f377(x56971,x56972)))+~P102(f332(f332(f246(a876),x56973),x56972)) % 172.78/172.49 [5698]~P102(f332(x56981,x56983))+P102(f332(x56981,f378(x56981,x56982)))+~P102(f332(f332(f247(a876),x56983),x56982)) % 172.78/172.49 [5706]~P105(x57061)+~E(f332(f302(x57061,x57062),x57063),f195(f883(x57061,a871)))+~P102(f332(f332(f247(x57061),x57062),x57063)) % 172.78/172.49 [5711]~P103(x57111)+~P102(f332(f332(f247(x57111),x57112),x57113))+P102(f332(f332(f246(x57111),x57112),x57113)) % 172.78/172.49 [5713]~P105(x57131)+~P102(f332(f332(f247(x57131),x57132),x57133))+P102(f332(f332(f246(x57131),x57132),x57133)) % 172.78/172.49 [5819]~P105(x58191)+~E(f303(x58191,x58192,x58193),f195(f883(x58191,a871)))+~P102(f332(f332(f246(x58191),x58192),x58193)) % 172.78/172.49 [5820]~P105(x58201)+~E(f305(x58201,x58202,x58203),f195(f883(x58201,a871)))+~P102(f332(f332(f247(x58201),x58202),x58203)) % 172.78/172.49 [5821]~P105(x58211)+~E(f195(f883(x58211,a871)),f303(x58211,x58212,x58213))+~P102(f332(f332(f246(x58211),x58212),x58213)) % 172.78/172.49 [5822]~P105(x58221)+~E(f195(f883(x58221,a871)),f305(x58221,x58222,x58223))+~P102(f332(f332(f247(x58221),x58222),x58223)) % 172.78/172.49 [5830]P102(f332(x58301,x58302))+~P102(f332(x58301,f379(x58301,x58303)))+~P102(f332(f332(f246(a876),x58302),x58303)) % 172.78/172.49 [5831]P102(f332(x58311,x58312))+~P102(f332(x58311,f382(x58311,x58313)))+~P102(f332(f332(f247(a876),x58312),x58313)) % 172.78/172.49 [5839]~E(x58391,f332(a115,x58393))+P102(f332(f332(f247(a876),x58391),f332(a115,x58392)))+~P102(f332(f332(f247(a876),x58393),x58392)) % 172.78/172.49 [5855]E(x58551,x58552)+~E(f332(f332(f80(a876),x58553),x58551),f332(f332(f80(a876),x58553),x58552))+~P102(f332(f332(f247(a876),f2(a876)),x58553)) % 172.78/172.49 [5911]E(f332(x59111,f849(x59111,x59112,x59113)),f77(a876))+~E(f332(f332(f6(x59113,a876),x59111),x59112),f77(a876))+~P102(f332(f61(x59113),x59112)) % 172.78/172.49 [5923]~P27(x59231)+P102(f332(f332(f246(x59231),x59232),f39(x59231,x59233)))+~P102(f332(f332(f334(x59231),x59232),x59233)) % 172.78/172.49 [5953]~P103(x59531)+~P102(f332(f332(f247(x59531),x59533),x59532))+~P102(f332(f332(f247(x59531),x59532),x59533)) % 172.78/172.49 [5954]~P103(x59541)+~P102(f332(f332(f246(x59541),x59543),x59542))+~P102(f332(f332(f247(x59541),x59542),x59543)) % 172.78/172.49 [5955]~P104(x59551)+~P102(f332(f332(f247(x59551),x59553),x59552))+~P102(f332(f332(f247(x59551),x59552),x59553)) % 172.78/172.49 [5958]~P104(x59581)+~P102(f332(f332(f246(x59581),x59583),x59582))+~P102(f332(f332(f247(x59581),x59582),x59583)) % 172.78/172.49 [5959]~P105(x59591)+~P102(f332(f332(f247(x59591),x59593),x59592))+~P102(f332(f332(f247(x59591),x59592),x59593)) % 172.78/172.49 [5988]~E(f332(x59882,f850(x59882,x59883,x59881)),f2(a876))+E(f332(f332(f6(x59881,a876),x59882),x59883),f2(a876))+~P102(f332(f61(x59881),x59883)) % 172.78/172.49 [5989]~E(f332(x59892,f838(x59892,x59893,x59891)),f77(a876))+E(f332(f332(f9(x59891,a876),x59892),x59893),f77(a876))+~P102(f332(f61(x59891),x59893)) % 172.78/172.49 [6003]~P106(x60031)+~P102(f332(f332(f246(x60031),x60033),x60032))+P102(f332(f332(f334(x60031),x60032),f332(f254(x60031),x60033))) % 172.78/172.49 [6004]~P106(x60041)+~P102(f332(f332(f247(x60041),x60043),x60042))+P102(f332(f332(f334(x60041),x60042),f332(f304(x60041),x60043))) % 172.78/172.49 [6005]~P106(x60051)+~P102(f332(f332(f247(x60051),x60052),x60053))+P102(f332(f332(f334(x60051),x60052),f332(f253(x60051),x60053))) % 172.78/172.49 [6006]~P106(x60061)+~P102(f332(f332(f246(x60061),x60062),x60063))+P102(f332(f332(f334(x60061),x60062),f332(f301(x60061),x60063))) % 172.78/172.49 [6018]E(f332(x60181,f852(x60181,x60182,x60183)),f332(a115,f2(a876)))+~E(f332(f332(f6(x60183,a876),x60181),x60182),f332(a115,f2(a876)))+~P102(f332(f61(x60183),x60182)) % 172.78/172.49 [6101]~P27(x61011)+~P102(f332(f332(f334(x61011),x61013),x61012))+P102(f332(f332(f246(x61011),f40(x61011,x61012)),x61013)) % 172.78/172.49 [6118]~P102(f332(f332(f246(a876),x61181),x61183))+P102(f332(f332(f246(a876),x61181),x61182))+~P102(f332(f332(f246(a876),x61183),x61182)) % 172.78/172.49 [6119]~P102(f332(f332(f246(a1),x61191),x61193))+P102(f332(f332(f246(a1),x61191),x61192))+~P102(f332(f332(f246(a1),x61193),x61192)) % 172.78/172.49 [6136]~P106(x61361)+~P102(f332(f332(f334(x61361),x61363),f332(f304(x61361),x61362)))+P102(f332(f332(f247(x61361),x61362),x61363)) % 172.78/172.49 [6137]~P106(x61371)+~P102(f332(f332(f334(x61371),x61372),f332(f253(x61371),x61373)))+P102(f332(f332(f247(x61371),x61372),x61373)) % 172.78/172.49 [6138]~P106(x61381)+~P102(f332(f332(f334(x61381),x61383),f332(f254(x61381),x61382)))+P102(f332(f332(f246(x61381),x61382),x61383)) % 172.78/172.49 [6139]~P106(x61391)+~P102(f332(f332(f334(x61391),x61392),f332(f301(x61391),x61393)))+P102(f332(f332(f246(x61391),x61392),x61393)) % 172.78/172.49 [6256]P102(f332(x62561,x62562))+~P102(f332(x62561,f562(x62561)))+~P102(f332(f332(f334(x62563),x62562),f255(f883(x62563,a871)))) % 172.78/172.49 [6355]~P59(x63551)+P102(f332(f332(f247(x63551),f2(x63551)),f344(x63553,x63552,x63551)))+P102(f332(f332(f246(x63551),x63552),x63553)) % 172.78/172.49 [6356]~P60(x63561)+P102(f332(f332(f247(x63561),f2(x63561)),f810(x63563,x63562,x63561)))+P102(f332(f332(f246(x63561),x63562),x63563)) % 172.78/172.49 [6423]~P79(x64231)+~P102(f332(f332(f247(x64231),x64233),f332(f78(x64231),x64232)))+P102(f332(f332(f247(x64231),x64232),f332(f78(x64231),x64233))) % 172.78/172.49 [6425]~P79(x64251)+~P102(f332(f332(f246(x64251),x64253),f332(f78(x64251),x64252)))+P102(f332(f332(f246(x64251),x64252),f332(f78(x64251),x64253))) % 172.78/172.49 [6437]~P102(f332(f332(f247(a876),x64371),x64373))+~P102(f332(f332(f247(a876),x64373),x64372))+P102(f332(f332(f247(a876),f332(a115,x64371)),x64372)) % 172.78/172.49 [6463]~P113(x64631)+P102(f332(f332(f247(x64631),f332(f105(x64631),x64632)),f332(f105(x64631),x64633)))+~P102(f332(f332(f247(a1),x64632),x64633)) % 172.78/172.49 [6464]~P107(x64641)+P102(f332(f332(f247(x64641),f332(f103(x64641),x64642)),f332(f103(x64641),x64643)))+~P102(f332(f332(f247(a876),x64642),x64643)) % 172.78/172.49 [6465]~P107(x64651)+P102(f332(f332(f246(x64651),f332(f103(x64651),x64652)),f332(f103(x64651),x64653)))+~P102(f332(f332(f246(a876),x64652),x64653)) % 172.78/172.49 [6466]~P113(x64661)+P102(f332(f332(f246(x64661),f332(f105(x64661),x64662)),f332(f105(x64661),x64663)))+~P102(f332(f332(f246(a1),x64662),x64663)) % 172.78/172.49 [6472]~P104(x64721)+E(f332(f332(f113(f883(x64721,a871)),f332(f253(x64721),x64722)),f332(f302(x64721,x64722),x64723)),f332(f253(x64721),x64723))+~P102(f332(f332(f246(x64721),x64722),x64723)) % 172.78/172.49 [6501]~P79(x65011)+~P102(f332(f332(f247(x65011),x65013),x65012))+P102(f332(f332(f247(x65011),f332(f78(x65011),x65012)),f332(f78(x65011),x65013))) % 172.78/172.49 [6503]~P79(x65031)+~P102(f332(f332(f246(x65031),x65033),x65032))+P102(f332(f332(f246(x65031),f332(f78(x65031),x65032)),f332(f78(x65031),x65033))) % 172.78/172.49 [6505]~P92(x65051)+~P102(f332(f332(f246(x65051),x65053),x65052))+P102(f332(f332(f246(x65051),f332(f78(x65051),x65052)),f332(f78(x65051),x65053))) % 172.78/172.49 [6537]~P104(x65371)+E(f332(f332(f113(f883(x65371,a871)),f332(f253(x65371),x65372)),f303(x65371,x65372,x65373)),f332(f301(x65371),x65373))+~P102(f332(f332(f246(x65371),x65372),x65373)) % 172.78/172.49 [6538]~P104(x65381)+E(f332(f332(f113(f883(x65381,a871)),f332(f301(x65381),x65382)),f306(x65381,x65382,x65383)),f332(f253(x65381),x65383))+~P102(f332(f332(f247(x65381),x65382),x65383)) % 172.78/172.49 [6539]~P104(x65391)+E(f332(f332(f113(f883(x65391,a871)),f332(f301(x65391),x65392)),f305(x65391,x65392,x65393)),f332(f301(x65391),x65393))+~P102(f332(f332(f246(x65391),x65392),x65393)) % 172.78/172.49 [6574]~P104(x65741)+E(f332(f332(f113(f883(x65741,a871)),f332(f302(x65741,x65742),x65743)),f332(f254(x65741),x65743)),f332(f254(x65741),x65742))+~P102(f332(f332(f246(x65741),x65742),x65743)) % 172.78/172.49 [6729]~P104(x67291)+E(f332(f332(f113(f883(x67291,a871)),f303(x67291,x67292,x67293)),f332(f304(x67291),x67293)),f332(f254(x67291),x67292))+~P102(f332(f332(f246(x67291),x67292),x67293)) % 172.78/172.49 [6730]~P104(x67301)+E(f332(f332(f113(f883(x67301,a871)),f306(x67301,x67302,x67303)),f332(f254(x67301),x67303)),f332(f304(x67301),x67302))+~P102(f332(f332(f247(x67301),x67302),x67303)) % 172.78/172.49 [6731]~P104(x67311)+E(f332(f332(f113(f883(x67311,a871)),f305(x67311,x67312,x67313)),f332(f304(x67311),x67313)),f332(f304(x67311),x67312))+~P102(f332(f332(f246(x67311),x67312),x67313)) % 172.78/172.49 [6749]P102(f332(x67491,x67492))+~P102(f332(f332(f246(a876),x67492),x67493))+P102(f332(f332(f334(a876),f379(x67491,x67493)),f303(a876,f2(a876),x67493))) % 172.78/172.49 [6783]E(x67831,x67832)+~E(f332(f332(f165(x67833),x67831),f669(x67833,x67832,x67831)),f332(f332(f165(x67833),x67832),f669(x67833,x67832,x67831)))+~E(f332(f196(f877(x67833)),x67831),f332(f196(f877(x67833)),x67832)) % 172.78/172.49 [6788]~E(x67883,f332(f332(f38(a876),x67881),x67882))+~P102(f332(f332(f247(a876),f2(a876)),x67882))+P102(f332(f332(f247(a876),x67881),f332(f332(f80(a876),x67882),f332(a115,x67883)))) % 172.78/172.49 [6805]~P102(f332(x68051,x68053))+~P102(f332(f332(f246(a876),x68053),x68052))+P102(f332(f332(f334(a876),f377(x68051,x68052)),f303(a876,f2(a876),x68052))) % 172.78/172.49 [6844]~P102(f332(x68441,x68443))+P102(f332(x68441,f380(x68441,x68442)))+~P102(f332(f332(f334(a876),x68443),f303(a876,f2(a876),x68442))) % 172.78/172.49 [6864]~P107(x68643)+~P102(f332(f332(f247(x68643),f332(f103(x68643),x68641)),f332(f103(x68643),x68642)))+P102(f332(f332(f247(a876),x68641),x68642)) % 172.78/172.49 [6865]~P113(x68653)+~P102(f332(f332(f247(x68653),f332(f105(x68653),x68651)),f332(f105(x68653),x68652)))+P102(f332(f332(f247(a1),x68651),x68652)) % 172.78/172.49 [6866]~P107(x68663)+~P102(f332(f332(f246(x68663),f332(f103(x68663),x68661)),f332(f103(x68663),x68662)))+P102(f332(f332(f246(a876),x68661),x68662)) % 172.78/172.49 [6867]~P113(x68673)+~P102(f332(f332(f246(x68673),f332(f105(x68673),x68671)),f332(f105(x68673),x68672)))+P102(f332(f332(f246(a1),x68671),x68672)) % 172.78/172.49 [6884]~P107(x68841)+~P102(f332(f332(f247(x68841),f77(x68841)),x68842))+P102(f332(f332(f247(x68841),f77(x68841)),f332(f332(f257(x68841),x68842),f332(a115,x68843)))) % 172.78/172.49 [6886]~P79(x68861)+~P102(f332(f332(f247(x68861),f332(f78(x68861),x68863)),f332(f78(x68861),x68862)))+P102(f332(f332(f247(x68861),x68862),x68863)) % 172.78/172.49 [6887]~P79(x68871)+~P102(f332(f332(f246(x68871),f332(f78(x68871),x68873)),f332(f78(x68871),x68872)))+P102(f332(f332(f246(x68871),x68872),x68873)) % 172.78/172.49 [6888]~P92(x68881)+~P102(f332(f332(f246(x68881),f332(f78(x68881),x68883)),f332(f78(x68881),x68882)))+P102(f332(f332(f246(x68881),x68882),x68883)) % 172.78/172.49 [6914]P102(f332(x69141,x69142))+~P102(f332(x69141,f381(x69141,x69143)))+~P102(f332(f332(f334(a876),x69142),f303(a876,f2(a876),x69143))) % 172.78/172.49 [6933]~P59(x69331)+P102(f332(f332(f247(x69331),f344(x69333,x69332,x69331)),f77(x69331)))+P102(f332(f332(f246(x69331),x69332),x69333)) % 172.78/172.49 [6952]~E(f44(a876,x69523,x69522),f44(a876,x69521,x69522))+E(f332(f332(f79(a876),x69521),f332(f332(f80(a876),x69522),f473(x69521,x69522,x69523))),x69523)+~P102(f332(f332(f246(a876),x69521),x69523)) % 172.78/172.49 [6971]E(f332(x69711,f763(x69711,x69712,x69713)),f208(x69712))+~P102(f332(f61(x69713),f185(x69713,x69712,x69711)))+P102(f332(f61(x69713),f255(f883(x69713,a871)))) % 172.78/172.49 [7012]E(f332(f332(f6(x70121,a876),x70122),x70123),f2(a876))+~P102(f332(f61(x70121),x70123))+P102(f332(f332(f334(x70121),f850(x70122,x70123,x70121)),x70123)) % 172.78/172.49 [7013]E(f332(f332(f9(x70131,a876),x70132),x70133),f77(a876))+~P102(f332(f61(x70131),x70133))+P102(f332(f332(f334(x70131),f838(x70132,x70133,x70131)),x70133)) % 172.78/172.49 [7035]~P104(x70351)+~P102(f332(f332(f247(x70351),x70352),x70353))+P102(f332(f332(f247(f883(x70351,a871)),f332(f253(x70351),x70352)),f332(f253(x70351),x70353))) % 172.78/172.49 [7036]~P104(x70361)+~P102(f332(f332(f246(x70361),x70362),x70363))+P102(f332(f332(f246(f883(x70361,a871)),f332(f253(x70361),x70362)),f332(f253(x70361),x70363))) % 172.78/172.49 [7037]~P105(x70371)+~P102(f332(f332(f246(x70371),x70372),x70373))+P102(f332(f332(f246(f883(x70371,a871)),f332(f301(x70371),x70372)),f332(f301(x70371),x70373))) % 172.78/172.49 [7038]~P105(x70381)+~P102(f332(f332(f246(x70381),x70383),x70382))+P102(f332(f332(f246(f883(x70381,a871)),f332(f254(x70381),x70382)),f332(f254(x70381),x70383))) % 172.78/172.49 [7039]~P104(x70391)+~P102(f332(f332(f246(x70391),x70393),x70392))+P102(f332(f332(f246(f883(x70391,a871)),f332(f304(x70391),x70392)),f332(f304(x70391),x70393))) % 172.78/172.49 [7047]~P27(x70471)+P102(f332(f332(f246(x70471),x70472),f40(x70471,x70473)))+P102(f332(f332(f334(x70471),f603(x70473,x70472,x70471)),x70473)) % 172.78/172.49 [7053]~P79(x70531)+P102(f332(f332(f247(x70531),f332(f332(f22(x70531),x70532),x70533)),f2(x70531)))+~P102(f332(f332(f247(x70531),x70532),x70533)) % 172.78/172.49 [7054]~P79(x70541)+P102(f332(f332(f246(x70541),f332(f332(f22(x70541),x70542),x70543)),f2(x70541)))+~P102(f332(f332(f246(x70541),x70542),x70543)) % 172.78/172.49 [7096]P102(f332(x70961,x70962))+P102(f332(f332(f246(a876),f381(x70961,x70963)),x70963))+~P102(f332(f332(f334(a876),x70962),f303(a876,f2(a876),x70963))) % 172.78/172.49 [7136]~E(f332(f332(f6(x71361,a876),x71362),x71363),f77(a876))+~P102(f332(f61(x71361),x71363))+P102(f332(f332(f334(x71361),f849(x71362,x71363,x71361)),x71363)) % 172.78/172.49 [7137]~P102(f332(x71371,x71373))+P102(f332(f332(f246(a876),f380(x71371,x71372)),x71372))+~P102(f332(f332(f334(a876),x71373),f303(a876,f2(a876),x71372))) % 172.78/172.49 [7177]~P27(x71771)+P102(f332(f332(f334(x71771),f633(x71773,x71772,x71771)),x71772))+P102(f332(f332(f246(x71771),f39(x71771,x71772)),x71773)) % 172.78/172.49 [7208]~E(f332(f332(f6(x72081,a876),x72082),x72083),f332(a115,f2(a876)))+~P102(f332(f61(x72081),x72083))+P102(f332(f332(f334(x72081),f852(x72082,x72083,x72081)),x72083)) % 172.78/172.49 [7219]E(x72191,f2(a876))+P102(f332(x72192,f44(a876,x72193,x72191)))+P102(f332(f332(f247(a876),f362(x72191,x72193,x72192)),x72191)) % 172.78/172.49 [7324]~P102(f332(x73241,x73242))+P102(f332(x73241,f44(a876,x73242,x73243)))+P102(f332(f332(f247(a876),f362(x73243,x73242,x73241)),x73243)) % 172.78/172.49 [7447]E(x74471,f116(x74472))+~P102(f332(f332(f334(f877(x74472)),x74471),f161(x74472,x74473)))+P102(f332(f332(f334(x74472),f707(x74473,x74471,x74472)),x74473)) % 172.78/172.49 [7469]~P104(x74691)+E(f332(f332(f113(f883(x74691,a871)),f332(f332(f310(x74691),x74692),f195(f883(x74691,a871)))),f306(x74691,x74692,x74693)),f332(f302(x74691,x74692),x74693))+~P102(f332(f332(f247(x74691),x74692),x74693)) % 172.78/172.49 [7495]~P104(x74951)+E(f332(f332(f113(f883(x74951,a871)),f332(f332(f310(x74951),x74952),f195(f883(x74951,a871)))),f305(x74951,x74952,x74953)),f303(x74951,x74952,x74953))+~P102(f332(f332(f246(x74951),x74952),x74953)) % 172.78/172.49 [7602]~P104(x76021)+P102(f332(f332(f247(x76021),x76022),x76023))+~P102(f332(f332(f247(f883(x76021,a871)),f332(f253(x76021),x76022)),f332(f253(x76021),x76023))) % 172.78/172.49 [7603]~P104(x76031)+P102(f332(f332(f246(x76031),x76032),x76033))+~P102(f332(f332(f246(f883(x76031,a871)),f332(f304(x76031),x76033)),f332(f304(x76031),x76032))) % 172.78/172.49 [7604]~P105(x76041)+P102(f332(f332(f246(x76041),x76042),x76043))+~P102(f332(f332(f246(f883(x76041,a871)),f332(f254(x76041),x76043)),f332(f254(x76041),x76042))) % 172.78/172.49 [7605]~P104(x76051)+P102(f332(f332(f246(x76051),x76052),x76053))+~P102(f332(f332(f246(f883(x76051,a871)),f332(f253(x76051),x76052)),f332(f253(x76051),x76053))) % 172.78/172.49 [7606]~P105(x76061)+P102(f332(f332(f246(x76061),x76062),x76063))+~P102(f332(f332(f246(f883(x76061,a871)),f332(f301(x76061),x76062)),f332(f301(x76061),x76063))) % 172.78/172.49 [7629]~P79(x76291)+~P102(f332(f332(f247(x76291),f332(f332(f22(x76291),x76292),x76293)),f2(x76291)))+P102(f332(f332(f247(x76291),x76292),x76293)) % 172.78/172.49 [7630]~P79(x76301)+~P102(f332(f332(f246(x76301),f332(f332(f22(x76301),x76302),x76303)),f2(x76301)))+P102(f332(f332(f246(x76301),x76302),x76303)) % 172.78/172.49 [7792]E(x77921,f2(a876))+~E(f332(f142(a876,a876,f79(a876),x77922),x77923),f2(a876))+~P102(f332(f332(f334(a876),x77921),f332(f173(a876),x77923))) % 172.78/172.49 [7796]~P27(x77961)+~P102(f332(f332(f246(x77961),f633(x77963,x77962,x77961)),x77963))+P102(f332(f332(f246(x77961),f39(x77961,x77962)),x77963)) % 172.78/172.49 [7951]P102(f332(f332(f246(a1),f2(a1)),f348(x79511,x79512,x79513)))+P102(f332(f332(x79512,f332(f332(f38(a1),x79511),x79513)),f44(a1,x79511,x79513)))+~P102(f332(f332(f247(a1),f2(a1)),x79513)) % 172.78/172.49 [8046]E(x80461,x80462)+~E(f332(f196(f877(x80463)),x80461),f332(f196(f877(x80463)),x80462))+~P102(f332(f332(f271(x80463,x80463,a871),a329),f684(x80463,x80461,x80462))) % 172.78/172.49 [8114]~P38(x81142,x81143)+E(x81141,f195(f883(x81142,a871)))+~P102(f332(f332(f246(f883(x81142,a871)),x81141),f332(f286(x81142,x81142,x81143),x81141))) % 172.78/172.49 [8144]~P60(x81441)+~P102(f332(f332(f246(x81441),x81442),f332(f332(f79(x81441),x81443),f810(x81443,x81442,x81441))))+P102(f332(f332(f246(x81441),x81442),x81443)) % 172.78/172.49 [8185]P40(x81851,x81852,x81853)+P102(f332(f332(f334(x81851),f559(x81853,x81852,x81851)),x81852))+P102(f332(f332(f334(f882(x81851,x81851)),f558(x81853,x81852,x81851)),x81853)) % 172.78/172.49 [8208]P102(f332(f332(x82082,f332(f332(f38(a1),x82081),x82083)),f44(a1,x82081,x82083)))+~P102(f332(f332(f247(a1),f2(a1)),x82083))+P102(f332(f332(f247(a1),f348(x82081,x82082,x82083)),x82083)) % 172.78/172.49 [8232]E(f332(f311(a876,a876,f332(f332(f7(a876,a876,a876),f22(a876)),x82321)),f332(f302(a876,x82322),x82323)),f195(f883(a876,a871)))+P102(f332(f332(f247(a876),x82321),x82323))+P102(f332(f332(f247(a876),x82322),x82323)) % 172.78/172.49 [8338]E(f332(f311(a876,a876,f332(f332(f7(a876,a876,a876),f22(a876)),x83381)),f332(f302(a876,x83382),x83383)),f332(f332(f310(a876),f2(a876)),f195(f883(a876,a871))))+P102(f332(f332(f247(a876),x83381),x83383))+~P102(f332(f332(f247(a876),x83382),x83383)) % 172.78/172.49 [8355]~P104(x83551)+E(f149(x83551,x83551,f5(x83551),x83552,x83553),x83553)+~P102(f332(f332(f334(x83551),x83552),f332(f173(x83551),x83553))) % 172.78/172.49 [8369]P20(x83691,x83691,x83692,x83693)+~P102(f332(f61(x83691),x83693))+~P102(f332(f332(f246(f883(x83691,a871)),x83693),f332(f311(x83691,x83691,x83692),x83693))) % 172.78/172.49 [8392]E(f332(f332(f79(a1),f332(f332(f80(a1),x83921),f349(x83922,x83923,x83921))),f348(x83922,x83923,x83921)),x83922)+P102(f332(f332(x83923,f332(f332(f38(a1),x83922),x83921)),f44(a1,x83922,x83921)))+~P102(f332(f332(f247(a1),f2(a1)),x83921)) % 172.78/172.49 [8633]~P102(f332(f332(x86331,f349(x86332,x86331,x86333)),f348(x86332,x86331,x86333)))+P102(f332(f332(x86331,f332(f332(f38(a1),x86332),x86333)),f44(a1,x86332,x86333)))+~P102(f332(f332(f247(a1),f2(a1)),x86333)) % 172.78/172.49 [9499]~P102(f332(f61(x94991),x94992))+~P102(f332(f332(f334(x94991),x94993),x94992))+P102(f332(f332(f247(a876),f332(f37(x94991),f332(f332(f22(f883(x94991,a871)),x94992),f332(f332(f310(x94991),x94993),f195(f883(x94991,a871)))))),f332(f37(x94991),x94992))) % 172.78/172.49 [10097]P40(x100971,x100972,x100973)+~P102(f332(f332(f271(x100971,x100971,a871),f332(f332(f7(x100971,f883(x100971,a871),f883(x100971,a871)),f332(f332(f8(f883(a871,a871),f883(f883(x100971,a871),f883(x100971,a871)),x100971),f8(a871,a871,x100971)),f332(f332(f8(a871,f883(a871,a871),x100971),a330),f332(f332(f7(x100971,f883(x100971,a871),a871),f334(x100971)),x100972)))),f332(f332(f7(x100971,f883(x100971,a871),a871),f334(x100971)),x100972))),f558(x100973,x100972,x100971)))+P102(f332(f332(f334(x100971),f559(x100973,x100972,x100971)),x100972)) % 172.78/172.49 [5478]~P117(x54782)+E(x54781,f2(x54782))+E(f332(f332(f290(x54782),x54783),f332(f78(x54782),x54781)),f332(f78(x54782),f332(f332(f290(x54782),x54783),x54781))) % 172.78/172.49 [5613]~E(x56133,f195(f883(x56131,a871)))+~E(x56132,f195(f883(x56131,a871)))+E(f332(f332(f113(f883(x56131,a871)),x56132),x56133),f195(f883(x56131,a871))) % 172.78/172.49 [5671]~E(x56713,f2(a876))+~P102(f332(x56711,f2(a876)))+P102(f332(x56711,f332(f332(f38(a876),x56712),x56713))) % 172.78/172.49 [5811]~P60(x58112)+E(x58111,f2(x58112))+E(f332(f332(f290(x58112),f332(f74(x58112),x58113)),f332(f74(x58112),x58111)),f332(f74(x58112),f332(f332(f290(x58112),x58113),x58111))) % 172.78/172.49 [5977]~P102(f332(f61(x59771),x59773))+E(f332(f37(x59771),f332(f332(f310(x59771),x59772),x59773)),f332(a115,f332(f37(x59771),x59773)))+P102(f332(f332(f334(x59771),x59772),x59773)) % 172.78/172.49 [6050]~E(x60502,f2(a876))+P102(f332(x60501,f2(a876)))+~P102(f332(x60501,f332(f332(f38(a876),x60503),x60502))) % 172.78/172.49 [6069]~P102(f332(f61(x60691),x60693))+E(f332(f37(x60691),f332(f332(f310(x60691),x60692),x60693)),f332(f37(x60691),x60693))+~P102(f332(f332(f334(x60691),x60692),x60693)) % 172.78/172.49 [6103]~P102(f332(f61(x61031),x61033))+E(f332(f37(x61031),f332(f332(f310(x61031),x61032),x61033)),f332(f332(f79(a876),f77(a876)),f332(f37(x61031),x61033)))+P102(f332(f332(f334(x61031),x61032),x61033)) % 172.78/172.49 [6218]E(f332(f332(f79(a876),x62181),f853(x62181,x62182,x62183)),x62182)+~P102(f332(x62183,f2(a876)))+P102(f332(x62183,f332(f332(f22(a876),x62182),x62181))) % 172.78/172.49 [6219]E(f332(f332(f79(a876),x62191),f854(x62191,x62192,x62193)),x62192)+~P102(f332(x62193,f2(a876)))+P102(f332(x62193,f332(f332(f22(a876),x62192),x62191))) % 172.78/172.49 [6266]~P27(x62661)+~P102(f332(f61(x62661),x62663))+E(f332(f332(f64(x62661,x62661,f113(x62661)),x62662),x62663),f332(f332(f113(x62661),x62662),f39(x62661,x62663))) % 172.78/172.49 [6267]~P27(x62671)+~P102(f332(f61(x62671),x62673))+E(f332(f332(f64(x62671,x62671,f104(x62671)),x62672),x62673),f332(f332(f104(x62671),x62672),f40(x62671,x62673))) % 172.78/172.49 [6273]~P89(x62731)+~E(f332(f106(x62731),x62732),f332(f106(x62731),x62733))+P31(x62731,f332(f106(x62731),f332(f332(f79(a1),x62732),f332(f78(a1),x62733)))) % 172.78/172.49 [6280]~P137(x62801)+E(f332(f332(f22(x62801),f332(f103(x62801),x62802)),f332(f103(x62801),x62803)),f332(f103(x62801),f332(f332(f22(a876),x62802),x62803)))+~P102(f332(f332(f246(a876),x62803),x62802)) % 172.78/172.49 [6366]E(f332(f332(f79(a876),x63661),f853(x63661,x63662,x63663)),x63662)+P102(f332(f332(f247(a876),x63662),x63661))+P102(f332(x63663,f332(f332(f22(a876),x63662),x63661))) % 172.78/172.49 [6367]E(f332(f332(f79(a876),x63671),f854(x63671,x63672,x63673)),x63672)+P102(f332(f332(f247(a876),x63672),x63671))+P102(f332(x63673,f332(f332(f22(a876),x63672),x63671))) % 172.78/172.49 [6382]~P113(x63821)+E(f332(f332(f80(x63821),f332(f74(x63821),x63822)),x63823),f332(f74(x63821),f332(f332(f80(x63821),x63822),x63823)))+~P102(f332(f332(f246(x63821),f2(x63821)),x63823)) % 172.78/172.49 [6383]~P59(x63831)+E(f332(f332(f290(x63831),f332(f74(x63831),x63832)),x63833),f332(f74(x63831),f332(f332(f290(x63831),x63832),x63833)))+~P102(f332(f332(f247(x63831),f2(x63831)),x63833)) % 172.78/172.49 [6391]~P61(x63911)+~P102(f332(f61(x63911),x63913))+E(f332(f332(f64(x63911,x63911,f113(x63911)),x63912),x63913),f13(x63911,f332(f332(f310(x63911),x63912),x63913))) % 172.78/172.49 [6392]~P61(x63921)+~P102(f332(f61(x63921),x63923))+E(f332(f332(f64(x63921,x63921,f104(x63921)),x63922),x63923),f10(x63921,f332(f332(f310(x63921),x63922),x63923))) % 172.78/172.49 [6393]~P104(x63931)+~P102(f332(f61(x63931),x63933))+E(f332(f332(f64(x63931,x63931,f245(x63931)),x63932),x63933),f14(x63931,f332(f332(f310(x63931),x63932),x63933))) % 172.78/172.49 [6394]~P104(x63941)+~P102(f332(f61(x63941),x63943))+E(f332(f332(f64(x63941,x63941,f244(x63941)),x63942),x63943),f15(x63941,f332(f332(f310(x63941),x63942),x63943))) % 172.78/172.49 [6439]E(x64391,f116(x64392))+~E(f181(x64392,x64393),f116(f877(x64392)))+~P102(f332(f332(f334(f877(x64392)),x64391),f332(f173(f877(x64392)),x64393))) % 172.78/172.49 [6480]~P102(f332(f137(x64801),x64803))+P102(f332(f332(f334(x64801),x64802),f332(f173(x64801),x64803)))+P102(f332(f137(x64801),f332(f332(f151(x64801),x64802),x64803))) % 172.78/172.49 [6491]~P93(x64911)+~P102(f332(f61(x64911),x64913))+E(f332(f63(x64911,f80(x64911)),f332(f332(f310(x64911),x64912),x64913)),f332(f332(f64(x64911,x64911,f80(x64911)),x64912),x64913)) % 172.78/172.49 [6513]~P104(x65131)+~P102(f332(f61(x65131),x65133))+E(f11(x65131,f245(x65131),f332(f332(f310(x65131),x65132),x65133)),f332(f332(f64(x65131,x65131,f245(x65131)),x65132),x65133)) % 172.78/172.49 [6514]~P104(x65141)+~P102(f332(f61(x65141),x65143))+E(f12(x65141,f244(x65141),f332(f332(f310(x65141),x65142),x65143)),f332(f332(f64(x65141,x65141,f244(x65141)),x65142),x65143)) % 172.78/172.49 [6516]P102(f332(x65161,f2(a876)))+~P102(f332(f332(f247(a876),x65162),x65163))+~P102(f332(x65161,f332(f332(f22(a876),x65162),x65163))) % 172.78/172.49 [6534]~P113(x65341)+P102(f332(f332(f247(x65341),x65342),x65343))+~P102(f332(f332(f247(x65341),f332(f74(x65341),x65342)),x65343)) % 172.78/172.49 [6536]~P81(x65361)+P102(f332(f332(f246(x65361),x65362),x65363))+~P102(f332(f332(f246(x65361),f332(f74(x65361),x65362)),x65363)) % 172.78/172.49 [6553]E(x65531,f116(x65532))+E(f332(f141(x65532),f332(f332(f138(x65532),x65533),x65531)),f332(f332(f165(x65532),x65531),x65533))+~P102(f332(f332(f247(a876),x65533),f332(f196(f877(x65532)),x65531))) % 172.78/172.49 [6605]~P102(f332(x66051,x66053))+P102(f332(x66051,f383(x66051,x66052)))+~P102(f332(f332(f334(a876),x66053),f332(f302(a876,f2(a876)),x66052))) % 172.78/172.49 [6627]P102(f332(x66271,x66272))+~P102(f332(f332(f247(a876),x66272),x66273))+P102(f332(f332(f334(a876),f382(x66271,x66273)),f332(f302(a876,f2(a876)),x66273))) % 172.78/172.49 [6643]~P107(x66431)+~P102(f332(f332(f247(x66431),f2(x66431)),x66432))+P102(f332(f332(f247(x66431),f2(x66431)),f332(f332(f257(x66431),x66432),x66433))) % 172.78/172.49 [6644]~P107(x66441)+~P102(f332(f332(f246(x66441),f77(x66441)),x66442))+P102(f332(f332(f246(x66441),f77(x66441)),f332(f332(f257(x66441),x66442),x66443))) % 172.78/172.49 [6646]~P107(x66461)+~P102(f332(f332(f246(x66461),f2(x66461)),x66462))+P102(f332(f332(f246(x66461),f2(x66461)),f332(f332(f257(x66461),x66462),x66463))) % 172.78/172.49 [6670]~P102(f332(x66701,x66703))+~P102(f332(f332(f247(a876),x66703),x66702))+P102(f332(f332(f334(a876),f378(x66701,x66702)),f332(f302(a876,f2(a876)),x66702))) % 172.78/172.49 [6677]P102(f332(f61(x66771),x66772))+~P102(f332(f61(x66771),x66773))+~P102(f332(f332(f246(f883(x66771,a871)),x66772),x66773)) % 172.78/172.49 [6685]P102(f332(x66851,x66852))+~P102(f332(x66851,f384(x66851,x66853)))+~P102(f332(f332(f334(a876),x66852),f332(f302(a876,f2(a876)),x66853))) % 172.78/172.49 [6696]E(x66961,f2(a876))+P102(f332(x66962,f351(x66961,x66963,x66962)))+~P102(f332(x66962,f332(f332(f38(a876),x66963),x66961))) % 172.78/172.49 [6704]~P120(x67042)+E(x67041,f2(x67042))+~E(f332(f332(f79(x67042),f332(f332(f80(x67042),x67043),x67043)),f332(f332(f80(x67042),x67041),x67041)),f2(x67042)) % 172.78/172.49 [6705]~P120(x67052)+E(x67051,f2(x67052))+~E(f332(f332(f79(x67052),f332(f332(f80(x67052),x67051),x67051)),f332(f332(f80(x67052),x67053),x67053)),f2(x67052)) % 172.78/172.49 [6750]E(x67501,f2(a876))+~P102(f332(x67502,f352(x67501,x67503,x67502)))+P102(f332(x67502,f332(f332(f38(a876),x67503),x67501))) % 172.78/172.49 [6755]~P104(x67551)+~P29(x67551,x67553)+P29(x67551,f332(f332(f148(x67551,x67551,f5(x67551)),x67552),x67553)) % 172.78/172.49 [6798]P102(f332(x67981,f351(x67982,x67983,x67981)))+P102(f332(x67981,f2(a876)))+~P102(f332(x67981,f332(f332(f38(a876),x67983),x67982))) % 172.78/172.49 [6804]~P89(x68041)+E(f332(f106(x68041),x68042),f332(f106(x68041),x68043))+~P31(x68041,f332(f106(x68041),f332(f332(f79(a1),x68042),f332(f78(a1),x68043)))) % 172.78/172.49 [6870]E(x68701,f2(a1))+E(x68702,f2(a1))+~P102(f332(f48(x68702,x68702),f332(f332(f267(a1,a1),x68703),x68701))) % 172.78/172.49 [6871]E(x68711,f77(a1))+E(x68712,f2(a1))+~P102(f332(f48(x68712,x68712),f332(f332(f267(a1,a1),x68711),x68713))) % 172.78/172.49 [6885]P102(f332(x68851,x68852))+P102(f332(f332(f247(a876),f384(x68851,x68853)),x68853))+~P102(f332(f332(f334(a876),x68852),f332(f302(a876,f2(a876)),x68853))) % 172.78/172.49 [6909]~P102(f332(x69091,f853(x69093,x69092,x69091)))+~P102(f332(x69091,f2(a876)))+P102(f332(x69091,f332(f332(f22(a876),x69092),x69093))) % 172.78/172.49 [6910]~P102(f332(x69101,f854(x69103,x69102,x69101)))+~P102(f332(x69101,f2(a876)))+P102(f332(x69101,f332(f332(f22(a876),x69102),x69103))) % 172.78/172.49 [6911]~P102(f332(x69111,f352(x69113,x69112,x69111)))+~P102(f332(x69111,f2(a876)))+P102(f332(x69111,f332(f332(f38(a876),x69112),x69113))) % 172.78/172.49 [6929]~P102(f332(x69291,x69293))+P102(f332(f332(f247(a876),f383(x69291,x69292)),x69292))+~P102(f332(f332(f334(a876),x69293),f332(f302(a876,f2(a876)),x69292))) % 172.78/172.49 [6930]E(f332(f332(f22(a876),f332(f332(f22(a876),x69301),x69302)),f332(f332(f22(a876),x69303),x69302)),f332(f332(f22(a876),x69301),x69303))+~P102(f332(f332(f246(a876),x69302),x69301))+~P102(f332(f332(f246(a876),x69302),x69303)) % 172.78/172.49 [6965]~P79(x69651)+~P102(f332(f332(f247(x69651),f332(f78(x69651),x69653)),x69652))+P102(f332(f332(f247(x69651),f332(f78(x69651),x69652)),x69653)) % 172.78/172.49 [6966]~P113(x69661)+~P102(f332(f332(f247(x69661),f332(f74(x69661),x69662)),x69663))+P102(f332(f332(f247(x69661),f332(f78(x69661),x69662)),x69663)) % 172.78/172.49 [6968]~P79(x69681)+~P102(f332(f332(f246(x69681),f332(f78(x69681),x69683)),x69682))+P102(f332(f332(f246(x69681),f332(f78(x69681),x69682)),x69683)) % 172.78/172.49 [6970]~P81(x69701)+~P102(f332(f332(f246(x69701),f332(f74(x69701),x69702)),x69703))+P102(f332(f332(f246(x69701),f332(f78(x69701),x69702)),x69703)) % 172.78/172.49 [7006]~P102(f332(x70063,f853(x70062,x70061,x70063)))+P102(f332(f332(f247(a876),x70061),x70062))+P102(f332(x70063,f332(f332(f22(a876),x70061),x70062))) % 172.78/172.49 [7007]~P102(f332(x70073,f854(x70072,x70071,x70073)))+P102(f332(f332(f247(a876),x70071),x70072))+P102(f332(x70073,f332(f332(f22(a876),x70071),x70072))) % 172.78/172.49 [7057]~E(f641(x70573,x70572,x70571),f642(x70573,x70572,x70571))+E(f332(f332(f104(f883(x70571,a871)),x70572),f39(f883(x70571,a871),x70573)),f195(f883(x70571,a871)))+P102(f332(f332(f334(f883(x70571,a871)),x70572),x70573)) % 172.78/172.49 [7066]~P102(f332(f61(x70661),x70663))+P102(f332(f61(x70661),f40(f883(x70661,a871),x70662)))+~P102(f332(f332(f334(f883(x70661,a871)),x70663),x70662)) % 172.78/172.49 [7125]~P104(x71251)+E(f332(f332(f113(f883(x71251,a871)),f332(f302(x71251,x71252),x71253)),f332(f332(f310(x71251),x71253),f195(f883(x71251,a871)))),f303(x71251,x71252,x71253))+~P102(f332(f332(f246(x71251),x71252),x71253)) % 172.78/172.49 [7126]E(x71261,f2(a876))+P102(f332(f332(f247(a876),f353(x71261,x71263,x71262)),x71261))+P102(f332(x71262,f332(f332(f38(a876),x71263),x71261))) % 172.78/172.49 [7161]E(x71611,x71612)+~P102(f332(f332(f246(f883(x71613,a871)),x71611),x71612))+P102(f332(f332(f247(f883(x71613,a871)),x71611),x71612)) % 172.78/172.49 [7174]E(x71741,x71742)+~E(f332(f196(f877(x71743)),x71741),f332(f196(f877(x71743)),x71742))+P102(f332(f332(f247(a876),f669(x71743,x71741,x71742)),f332(f196(f877(x71743)),x71742))) % 172.78/172.49 [7220]P3(x72201,x72202,x72203)+~E(f332(f265(x72201,x72201),x72203),x72202)+~E(f332(f332(f289(x72201,x72201,x72201),f332(f287(x72201,x72201),x72203)),x72203),x72203) % 172.78/172.49 [7292]~P102(f332(x72921,f2(a876)))+P102(f332(f332(f247(a876),f353(x72923,x72922,x72921)),x72923))+P102(f332(x72921,f332(f332(f38(a876),x72922),x72923))) % 172.78/172.49 [7301]~P104(x73011)+E(f332(f332(f113(f883(x73011,a871)),f306(x73011,x73012,x73013)),f332(f332(f310(x73011),x73013),f195(f883(x73011,a871)))),f305(x73011,x73012,x73013))+~P102(f332(f332(f247(x73011),x73012),x73013)) % 172.78/172.49 [7401]~P102(f332(f61(x74011),x74013))+P102(f332(f332(f247(a876),f332(f37(x74011),x74012)),f332(f37(x74011),x74013)))+~P102(f332(f332(f247(f883(x74011,a871)),x74012),x74013)) % 172.78/172.49 [7402]~P102(f332(f61(x74021),x74023))+P102(f332(f332(f246(a876),f332(f37(x74021),x74022)),f332(f37(x74021),x74023)))+~P102(f332(f332(f246(f883(x74021,a871)),x74022),x74023)) % 172.78/172.49 [7440]~P102(f332(x74403,x74402))+P102(f332(f332(f201(x74401),x74402),f869(x74402,x74401,x74403)))+~P102(f332(f332(f201(f31(x74403,x74401)),x74402),x74402)) % 172.78/172.49 [7540]E(x75401,x75402)+~P102(f332(f332(f246(f883(x75403,a871)),x75402),x75401))+~P102(f332(f332(f246(f883(x75403,a871)),x75401),x75402)) % 172.78/172.49 [7543]~P104(x75431)+P29(x75431,x75432)+~P29(x75431,f332(f332(f148(x75431,x75431,f5(x75431)),x75433),x75432)) % 172.78/172.49 [7609]~P102(f332(f332(f247(a876),x76093),x76092))+~P102(f332(f332(f247(a876),x76093),x76091))+P102(f332(f332(f247(a876),f332(f332(f22(a876),x76091),x76092)),f332(f332(f22(a876),x76091),x76093))) % 172.78/172.49 [7610]~P102(f332(f332(f247(a876),x76101),x76103))+~P102(f332(f332(f246(a876),x76102),x76101))+P102(f332(f332(f247(a876),f332(f332(f22(a876),x76101),x76102)),f332(f332(f22(a876),x76103),x76102))) % 172.78/172.49 [7627]~P102(f332(f332(f247(a1),x76272),f2(a1)))+~P102(f332(f332(f246(a1),x76273),x76271))+P102(f332(f332(f246(a1),f332(f332(f38(a1),x76271),x76272)),f332(f332(f38(a1),x76273),x76272))) % 172.78/172.49 [7647]~P102(f332(f332(f247(a876),f2(a876)),x76472))+~P102(f332(f332(f247(a876),x76471),x76473))+P102(f332(f332(f247(a876),f332(f332(f80(a876),x76471),x76472)),f332(f332(f80(a876),x76473),x76472))) % 172.78/172.49 [7648]~P102(f332(f332(f247(a876),f2(a876)),x76481))+~P102(f332(f332(f247(a876),x76482),x76483))+P102(f332(f332(f247(a876),f332(f332(f80(a876),x76481),x76482)),f332(f332(f80(a876),x76481),x76483))) % 172.78/172.49 [7649]~P102(f332(f332(f247(a1),f2(a1)),x76491))+~P102(f332(f332(f247(a1),x76492),x76493))+P102(f332(f332(f247(a1),f332(f332(f80(a1),x76491),x76492)),f332(f332(f80(a1),x76491),x76493))) % 172.78/172.49 [7651]~P102(f332(f332(f247(a876),f2(a876)),x76513))+~P102(f332(f332(f246(a876),x76513),x76512))+P102(f332(f332(f246(a876),f332(f332(f38(a876),x76511),x76512)),f332(f332(f38(a876),x76511),x76513))) % 172.78/172.49 [7652]~P102(f332(f332(f247(a1),f2(a1)),x76522))+~P102(f332(f332(f246(a1),x76521),x76523))+P102(f332(f332(f246(a1),f332(f332(f38(a1),x76521),x76522)),f332(f332(f38(a1),x76523),x76522))) % 172.78/172.49 [7703]E(x77031,f2(a876))+E(f332(f332(f79(a876),f332(f332(f80(a876),x77031),f352(x77031,x77032,x77033))),f353(x77031,x77032,x77033)),x77032)+P102(f332(x77033,f332(f332(f38(a876),x77032),x77031))) % 172.78/172.49 [7764]E(f332(f332(f79(a876),f332(f332(f80(a876),x77641),f352(x77641,x77642,x77643))),f353(x77641,x77642,x77643)),x77642)+~P102(f332(x77643,f2(a876)))+P102(f332(x77643,f332(f332(f38(a876),x77642),x77641))) % 172.78/172.49 [7783]~P102(f332(f61(x77831),x77833))+P102(f332(f332(f334(x77831),f841(x77832,x77833,x77831)),x77833))+P102(f332(f332(f247(a876),f2(a876)),f332(f332(f9(x77831,a876),x77832),x77833))) % 172.78/172.49 [7784]~P102(f332(f61(x77841),x77843))+P102(f332(f332(f334(x77841),f355(x77842,x77843,x77841)),x77843))+P102(f332(f332(f247(a876),f2(a876)),f332(f332(f9(x77841,a876),x77842),x77843))) % 172.78/172.49 [8079]E(x80791,f195(f883(x80792,a871)))+E(x80791,f332(f332(f310(x80792),x80793),f195(f883(x80792,a871))))+~P102(f332(f332(f246(f883(x80792,a871)),x80791),f332(f332(f310(x80792),x80793),f195(f883(x80792,a871))))) % 172.78/172.49 [8097]~P56(x80971)+P7(x80971,x80972,x80973)+P102(f332(f332(f334(f877(x80971)),f723(x80973,x80972,x80971)),f332(f173(f877(x80971)),f54(x80971,x80973,f55(x80971))))) % 172.78/172.49 [8116]~P102(f332(f332(f247(a876),f2(a876)),x81163))+P102(f332(f332(f247(a876),x81161),x81162))+~P102(f332(f332(f247(a876),f332(f332(f257(a876),x81163),x81161)),f332(f332(f257(a876),x81163),x81162))) % 172.78/172.49 [8118]~P102(f332(f332(f247(a876),f2(a876)),x81183))+P102(f332(f332(f246(a876),x81181),x81182))+~P102(f332(f332(f246(a876),f332(f332(f80(a876),x81183),x81181)),f332(f332(f80(a876),x81183),x81182))) % 172.78/172.49 [8119]~P102(f332(f332(f247(a876),f2(a876)),x81193))+P102(f332(f332(f246(a876),x81191),x81192))+~P102(f332(f332(f246(a876),f332(f332(f80(a876),x81191),x81193)),f332(f332(f80(a876),x81192),x81193))) % 172.78/172.49 [8146]~P56(x81461)+~P6(x81461,x81463,x81462)+P102(f332(f332(f334(f877(x81461)),f722(x81462,x81463,x81461)),f332(f173(f877(x81461)),f54(x81461,x81462,f55(x81461))))) % 172.78/172.49 [8154]~P102(f332(x81541,x81543))+P102(f332(f332(f201(f31(x81541,x81542)),f869(x81543,x81542,x81541)),x81543))+~P102(f332(f332(f201(f31(x81541,x81542)),x81543),x81543)) % 172.78/172.49 [8163]~E(f332(f332(f104(f883(x81631,a871)),f642(x81633,x81632,x81631)),f641(x81633,x81632,x81631)),f195(f883(x81631,a871)))+E(f332(f332(f104(f883(x81631,a871)),x81632),f39(f883(x81631,a871),x81633)),f195(f883(x81631,a871)))+P102(f332(f332(f334(f883(x81631,a871)),x81632),x81633)) % 172.78/172.49 [8180]E(x81801,f116(x81802))+~E(f332(f142(f877(x81802),f877(x81802),f134(x81802),f116(x81802)),x81803),f116(x81802))+~P102(f332(f332(f334(f877(x81802)),x81801),f332(f173(f877(x81802)),x81803))) % 172.78/172.49 [8237]E(x82371,f195(f883(f883(x82372,a871),a871)))+P102(f332(f332(f334(f883(x82372,a871)),f645(x82373,x82371,x82372)),x82371))+P102(f332(f332(f246(f883(x82372,a871)),f40(f883(x82372,a871),x82371)),x82373)) % 172.78/172.49 [8244]~P67(x82441)+~P71(x82441)+E(f332(f332(f6(a1,x82441),f332(f332(f8(a876,x82441,a1),x82442),a107)),f332(f311(a876,a1,f103(a1)),x82443)),f332(f332(f6(a876,x82441),x82442),x82443)) % 172.78/172.49 [8245]~P67(x82451)+~P71(x82451)+E(f332(f332(f9(a1,x82451),f332(f332(f8(a876,x82451,a1),x82452),a107)),f332(f311(a876,a1,f103(a1)),x82453)),f332(f332(f9(a876,x82451),x82452),x82453)) % 172.78/172.49 [8284]~P102(f332(f61(x82841),x82843))+~P102(f332(f332(f247(a876),f2(a876)),f332(x82842,f841(x82842,x82843,x82841))))+P102(f332(f332(f247(a876),f2(a876)),f332(f332(f9(x82841,a876),x82842),x82843))) % 172.78/172.49 [8285]~P102(f332(f61(x82851),x82853))+~P102(f332(f332(f247(a876),f2(a876)),f332(x82852,f355(x82852,x82853,x82851))))+P102(f332(f332(f247(a876),f2(a876)),f332(f332(f9(x82851,a876),x82852),x82853))) % 172.78/172.49 [8320]~P58(x83202)+E(x83201,f77(x83202))+E(f332(f332(f290(x83202),f332(f332(f22(x83202),f332(f332(f257(x83202),x83201),x83203)),f77(x83202))),f332(f332(f22(x83202),x83201),f77(x83202))),f332(f332(f6(a876,x83202),f332(f257(x83202),x83201)),f332(f302(a876,f2(a876)),x83203))) % 172.78/172.49 [8378]E(x83781,f2(a876))+~P102(f332(x83783,f332(f332(f38(a876),x83782),x83781)))+P102(f332(f332(f247(a876),x83782),f332(f332(f80(a876),x83781),f332(a115,f351(x83781,x83782,x83783))))) % 172.78/172.49 [8397]P102(f332(x83971,f2(a876)))+~P102(f332(x83971,f332(f332(f38(a876),x83972),x83973)))+P102(f332(f332(f247(a876),x83972),f332(f332(f80(a876),x83973),f332(a115,f351(x83973,x83972,x83971))))) % 172.78/172.49 [8439]E(x84391,f2(a876))+~P102(f332(x84393,f332(f332(f38(a876),x84392),x84391)))+P102(f332(f332(f246(a876),f332(f332(f80(a876),x84391),f351(x84391,x84392,x84393))),x84392)) % 172.78/172.49 [8478]P102(f332(x84781,f2(a876)))+~P102(f332(x84781,f332(f332(f38(a876),x84783),x84782)))+P102(f332(f332(f246(a876),f332(f332(f80(a876),x84782),f351(x84782,x84783,x84781))),x84783)) % 172.78/172.49 [8481]~P104(x84811)+E(f332(f332(f148(x84811,x84811,f5(x84811)),x84812),x84813),f149(x84811,x84811,f5(x84811),x84812,x84813))+P102(f332(f332(f334(x84811),x84812),f332(f173(x84811),x84813))) % 172.78/172.49 [8519]~E(f332(x85193,f572(x85192,x85193,x85191)),f332(x85193,f574(x85192,x85193,x85191)))+~P55(x85191,f332(x85193,f573(x85192,x85193,x85191)))+P55(x85191,f332(f332(f41(x85192,f883(x85191,f883(x85191,a871))),f255(f883(x85192,a871))),x85193)) % 172.78/172.49 [8527]E(x85271,f195(f883(f883(x85272,a871),a871)))+~P102(f332(f332(f246(f883(x85272,a871)),f645(x85273,x85271,x85272)),x85273))+P102(f332(f332(f246(f883(x85272,a871)),f40(f883(x85272,a871),x85271)),x85273)) % 172.78/172.49 [8584]~P60(x85841)+~P102(f332(f332(f247(x85841),x85842),x85843))+P102(f332(f332(f247(x85841),x85842),f332(f332(f290(x85841),f332(f332(f79(x85841),x85842),x85843)),f332(f332(f79(x85841),f77(x85841)),f77(x85841))))) % 172.78/172.49 [8639]~P102(f332(f332(x86391,f487(x86391,x86393,x86392)),f491(x86391,x86393,x86392)))+P102(f332(f332(x86391,x86392),x86393))+~P102(f332(f320(f882(a1,a1),a51),f332(f332(f267(a1,a1),x86392),x86393))) % 172.78/172.49 [8640]~P102(f332(f332(x86401,f492(x86401,x86403,x86402)),f493(x86401,x86403,x86402)))+P102(f332(f332(x86401,x86402),x86403))+~P102(f332(f320(f882(a1,a1),a56),f332(f332(f267(a1,a1),x86402),x86403))) % 172.78/172.49 [8641]~P102(f332(f332(x86411,f494(x86411,x86413,x86412)),f495(x86411,x86413,x86412)))+P102(f332(f332(x86411,x86412),x86413))+~P102(f332(f320(f882(a1,a1),a235),f332(f332(f267(a1,a1),x86412),x86413))) % 172.78/172.49 [8642]~P102(f332(f332(x86421,f498(x86421,x86423,x86422)),f499(x86421,x86423,x86422)))+P102(f332(f332(x86421,x86422),x86423))+~P102(f332(f320(f882(a876,a876),a230),f332(f332(f267(a876,a876),x86422),x86423))) % 172.78/172.49 [8643]~P102(f332(f332(x86431,f694(x86431,x86433,x86432)),f696(x86431,x86433,x86432)))+P102(f332(f332(x86431,x86432),x86433))+~P102(f332(f320(f882(a1,a1),a184),f332(f332(f267(a1,a1),x86432),x86433))) % 172.78/172.49 [8896]P102(f332(f332(x88961,x88962),x88963))+P102(f332(f320(f882(a876,a876),a230),f332(f332(f267(a876,a876),f498(x88961,x88963,x88962)),f499(x88961,x88963,x88962))))+~P102(f332(f320(f882(a876,a876),a230),f332(f332(f267(a876,a876),x88962),x88963))) % 172.78/172.49 [8897]P102(f332(f332(x88971,x88972),x88973))+P102(f332(f320(f882(a1,a1),a51),f332(f332(f267(a1,a1),f487(x88971,x88973,x88972)),f491(x88971,x88973,x88972))))+~P102(f332(f320(f882(a1,a1),a51),f332(f332(f267(a1,a1),x88972),x88973))) % 172.78/172.49 [8898]P102(f332(f332(x88981,x88982),x88983))+P102(f332(f320(f882(a1,a1),a56),f332(f332(f267(a1,a1),f492(x88981,x88983,x88982)),f493(x88981,x88983,x88982))))+~P102(f332(f320(f882(a1,a1),a56),f332(f332(f267(a1,a1),x88982),x88983))) % 172.78/172.49 [8899]P102(f332(f332(x88991,x88992),x88993))+P102(f332(f320(f882(a1,a1),a235),f332(f332(f267(a1,a1),f494(x88991,x88993,x88992)),f495(x88991,x88993,x88992))))+~P102(f332(f320(f882(a1,a1),a235),f332(f332(f267(a1,a1),x88992),x88993))) % 172.78/172.49 [8900]P102(f332(f332(x89001,x89002),x89003))+P102(f332(f320(f882(a1,a1),a184),f332(f332(f267(a1,a1),f694(x89001,x89003,x89002)),f696(x89001,x89003,x89002))))+~P102(f332(f320(f882(a1,a1),a184),f332(f332(f267(a1,a1),x89002),x89003))) % 172.78/172.49 [9246]~P102(f332(f61(x92461),x92463))+P102(f332(f332(f334(f882(f883(x92461,a871),f883(x92461,a871))),f332(f332(f267(f883(x92461,a871),f883(x92461,a871)),x92462),x92463)),f307(x92461)))+~P102(f332(f332(f247(f883(x92461,a871)),x92462),x92463)) % 172.78/172.49 [9317]~P55(x93171,f332(x93173,f573(x93172,x93173,x93171)))+P55(x93171,f332(f332(f41(x93172,f883(x93171,f883(x93171,a871))),f255(f883(x93172,a871))),x93173))+~E(f332(f332(f104(f883(x93171,a871)),f261(x93171,x93171,f332(x93173,f572(x93172,x93173,x93171)))),f262(x93171,x93171,f332(x93173,f574(x93172,x93173,x93171)))),f195(f883(x93171,a871))) % 172.78/172.49 [9388]~P22(a872,f195(f883(f875(a872),a871)),f332(f332(f310(f875(a872)),f332(f332(f332(f91(a872),x93881),x93882),x93883)),f195(f883(f875(a872),a871))))+~P19(a872,f195(f883(f875(a872),a871)),f332(f332(f310(f875(a872)),f332(f332(f332(f91(a872),a329),x93882),f201(x93882))),f195(f883(f875(a872),a871))))+P19(a872,f195(f883(f875(a872),a871)),f332(f332(f310(f875(a872)),f332(f332(f332(f91(a872),x93881),x93882),x93883)),f195(f883(f875(a872),a871)))) % 172.78/172.49 [9514]P40(x95141,x95142,x95143)+P102(f332(f332(f334(f882(x95141,x95141)),f558(x95143,x95142,x95141)),x95143))+~P102(f332(f332(f334(f882(x95141,x95141)),f332(f332(f267(x95141,x95141),f559(x95143,x95142,x95141)),f559(x95143,x95142,x95141))),x95143)) % 172.78/172.49 [10098]P40(x100981,x100982,x100983)+~P102(f332(f332(f271(x100981,x100981,a871),f332(f332(f7(x100981,f883(x100981,a871),f883(x100981,a871)),f332(f332(f8(f883(a871,a871),f883(f883(x100981,a871),f883(x100981,a871)),x100981),f8(a871,a871,x100981)),f332(f332(f8(a871,f883(a871,a871),x100981),a330),f332(f332(f7(x100981,f883(x100981,a871),a871),f334(x100981)),x100982)))),f332(f332(f7(x100981,f883(x100981,a871),a871),f334(x100981)),x100982))),f558(x100983,x100982,x100981)))+~P102(f332(f332(f334(f882(x100981,x100981)),f332(f332(f267(x100981,x100981),f559(x100983,x100982,x100981)),f559(x100983,x100982,x100981))),x100983)) % 172.78/172.49 [5652]~P25(x56522)+E(x56521,f2(x56522))+E(f332(f332(f38(x56522),f332(f332(f80(x56522),x56523),x56521)),x56521),x56523) % 172.78/172.49 [5653]~P25(x56532)+E(x56531,f2(x56532))+E(f332(f332(f38(x56532),f332(f332(f80(x56532),x56531),x56533)),x56531),x56533) % 172.78/172.49 [6438]~P71(x64381)+~E(f332(x64382,f2(a876)),f2(x64381))+E(f332(f332(f6(a876,x64381),x64382),f332(f302(a876,f332(a115,f2(a876))),x64383)),f332(f332(f6(a876,x64381),x64382),f332(f302(a876,f2(a876)),x64383))) % 172.78/172.49 [6566]~P25(x65662)+E(x65661,f2(x65662))+E(f332(f332(f38(x65662),f332(f332(f79(x65662),x65663),x65661)),x65661),f332(f332(f79(x65662),f332(f332(f38(x65662),x65663),x65661)),f77(x65662))) % 172.78/172.49 [6567]~P25(x65672)+E(x65671,f2(x65672))+E(f332(f332(f38(x65672),f332(f332(f79(x65672),x65671),x65673)),x65671),f332(f332(f79(x65672),f332(f332(f38(x65672),x65673),x65671)),f77(x65672))) % 172.78/172.49 [6786]~P102(f332(x67863,f2(a1)))+P102(f332(f332(f246(a876),x67861),x67862))+P102(f332(x67863,f332(f103(a1),f332(f332(f22(a876),x67862),x67861)))) % 172.78/172.49 [6891]P102(f332(f332(f246(a876),x68912),x68911))+P102(f332(f332(f247(a876),x68911),x68912))+P102(f332(x68913,f332(f103(a1),f332(f332(f22(a876),x68911),x68912)))) % 172.78/172.49 [6963]E(f332(f332(f79(a876),f332(f106(a876),x69631)),f332(f332(f79(a876),f332(f106(a876),x69632)),x69633)),f332(f332(f79(a876),f332(f106(a876),x69631)),x69633))+P102(f332(a200,f332(f106(a1),x69631)))+~P102(f332(a200,f332(f106(a1),x69632))) % 172.78/172.49 [7044]~E(x70442,f332(f332(f38(a876),x70443),x70441))+~P102(f332(f332(f247(a876),f2(a876)),x70441))+P102(f332(f332(f246(a876),f332(f332(f80(a876),x70441),x70442)),x70443)) % 172.78/172.49 [7158]~P102(f332(f61(x71581),x71583))+~P102(f332(f61(x71581),x71582))+P102(f332(f61(x71581),f332(f332(f113(f883(x71581,a871)),x71582),x71583))) % 172.78/172.49 [7453]~P104(x74531)+~P102(f332(f61(x74531),x74532))+E(f139(x74531,f332(f332(f22(f883(x74531,a871)),x74532),f332(f332(f310(x74531),x74533),f195(f883(x74531,a871))))),f171(x74531,x74533,f139(x74531,x74532))) % 172.78/172.49 [7519]P102(f332(x75191,f2(a1)))+~P102(f332(f332(f247(a876),x75192),x75193))+~P102(f332(x75191,f332(f103(a1),f332(f332(f22(a876),x75192),x75193)))) % 172.78/172.49 [7537]~P102(f332(f61(x75371),x75372))+E(f332(f37(x75371),f332(f332(f22(f883(x75371,a871)),x75372),f332(f332(f310(x75371),x75373),f195(f883(x75371,a871))))),f332(f37(x75371),x75372))+P102(f332(f332(f334(x75371),x75373),x75372)) % 172.78/172.49 [7667]~P107(x76671)+~P102(f332(f332(f247(x76671),f77(x76671)),x76672))+P102(f332(f332(f247(x76671),f77(x76671)),f332(f332(f80(x76671),x76672),f332(f332(f257(x76671),x76672),x76673)))) % 172.78/172.49 [7714]~P102(f332(f61(x77141),x77143))+E(f332(f332(f22(a876),f332(f37(x77141),x77142)),f332(f37(x77141),x77143)),f332(f37(x77141),f332(f332(f22(f883(x77141,a871)),x77142),x77143)))+~P102(f332(f332(f246(f883(x77141,a871)),x77143),x77142)) % 172.78/172.49 [7773]~P102(f332(f332(f246(a876),x77732),x77733))+~P102(f332(f332(f246(a876),x77731),f332(f332(f22(a876),x77733),x77732)))+P102(f332(f332(f246(a876),f332(f332(f79(a876),x77731),x77732)),x77733)) % 172.78/172.49 [7827]P102(f332(f61(x78271),x78272))+~P102(f332(f61(x78271),x78273))+~P102(f332(f61(x78271),f332(f332(f22(f883(x78271,a871)),x78272),x78273))) % 172.78/172.49 [7833]~P102(f332(f61(x78331),x78332))+E(f332(f37(x78331),f332(f332(f22(f883(x78331,a871)),x78332),f332(f332(f310(x78331),x78333),f195(f883(x78331,a871))))),f332(f332(f22(a876),f332(f37(x78331),x78332)),f77(a876)))+~P102(f332(f332(f334(x78331),x78333),x78332)) % 172.78/172.49 [7909]P55(x79091,x79092)+~P55(x79091,x79093)+~P102(f332(f332(f246(f883(x79091,f883(x79091,a871))),x79092),x79093)) % 172.78/172.49 [7950]~P102(f332(f332(f246(a876),x79503),x79502))+P102(f332(f332(f246(a876),x79501),f332(f332(f22(a876),x79502),x79503)))+~P102(f332(f332(f246(a876),f332(f332(f79(a876),x79501),x79503)),x79502)) % 172.78/172.49 [7968]P38(x79681,x79682)+~P38(x79681,x79683)+~P102(f332(f332(f246(f883(f882(x79681,x79681),a871)),x79682),x79683)) % 172.78/172.49 [7969]P53(x79691,x79692)+~P53(x79691,x79693)+~P102(f332(f332(f246(f883(f882(x79691,x79691),a871)),x79692),x79693)) % 172.78/172.49 [8215]~P107(x82151)+~P102(f332(f332(f247(x82151),f77(x82151)),x82152))+P102(f332(f332(f247(x82151),f332(f332(f257(x82151),x82152),x82153)),f332(f332(f80(x82151),x82152),f332(f332(f257(x82151),x82152),x82153)))) % 172.78/172.49 [8304]~P102(f332(x83041,f2(a1)))+~P102(f332(x83041,f332(f332(f22(a1),f332(f103(a1),x83042)),f332(f103(a1),x83043))))+P102(f332(x83041,f332(f103(a1),f332(f332(f22(a876),x83042),x83043)))) % 172.78/172.49 [8317]~P102(f332(f332(f246(a876),x83173),x83172))+P102(f332(x83171,f332(f332(f22(a1),f332(f103(a1),x83172)),f332(f103(a1),x83173))))+~P102(f332(x83171,f332(f103(a1),f332(f332(f22(a876),x83172),x83173)))) % 172.78/172.49 [8335]P102(f332(f332(f247(a876),x83351),x83352))+~P102(f332(x83353,f332(f332(f22(a1),f332(f103(a1),x83351)),f332(f103(a1),x83352))))+P102(f332(x83353,f332(f103(a1),f332(f332(f22(a876),x83351),x83352)))) % 172.78/172.49 [8389]~P120(x83892)+E(x83891,f2(x83892))+P102(f332(f332(f247(x83892),f2(x83892)),f332(f332(f79(x83892),f332(f332(f80(x83892),x83893),x83893)),f332(f332(f80(x83892),x83891),x83891)))) % 172.78/172.49 [8390]~P120(x83902)+E(x83901,f2(x83902))+P102(f332(f332(f247(x83902),f2(x83902)),f332(f332(f79(x83902),f332(f332(f80(x83902),x83901),x83901)),f332(f332(f80(x83902),x83903),x83903)))) % 172.78/172.49 [8499]~P102(f332(f332(f247(a876),f2(a876)),x84991))+~P102(f332(f332(f247(a1),x84992),x84993))+P102(f332(f332(f247(a1),f332(f332(f80(a1),f332(f103(a1),x84991)),x84992)),f332(f332(f80(a1),f332(f103(a1),x84991)),x84993))) % 172.78/172.49 [8555]E(f332(f332(f104(f883(x85551,a871)),x85552),f39(f883(x85551,a871),x85553)),f195(f883(x85551,a871)))+P102(f332(f332(f334(f883(x85551,a871)),x85552),x85553))+P102(f332(f332(f334(f883(x85551,a871)),f642(x85553,x85552,x85551)),f332(f332(f310(f883(x85551,a871)),x85552),x85553))) % 172.78/172.49 [8556]E(f332(f332(f104(f883(x85561,a871)),x85562),f39(f883(x85561,a871),x85563)),f195(f883(x85561,a871)))+P102(f332(f332(f334(f883(x85561,a871)),x85562),x85563))+P102(f332(f332(f334(f883(x85561,a871)),f641(x85563,x85562,x85561)),f332(f332(f310(f883(x85561,a871)),x85562),x85563))) % 172.78/172.49 [8583]E(x85831,x85832)+~E(f332(f196(f877(x85833)),x85831),f332(f196(f877(x85833)),x85832))+P102(f332(f332(f334(f882(x85833,x85833)),f684(x85833,x85831,x85832)),f332(f173(f882(x85833,x85833)),f332(f332(f183(x85833,x85833),x85832),x85831)))) % 172.78/172.49 [8814]E(f308(x88141,x88142),f308(x88141,x88143))+~P102(f332(f332(f246(f883(f882(x88141,x88141),a871)),x88143),f308(x88141,x88142)))+~P102(f332(f332(f246(f883(f882(x88141,x88141),a871)),x88142),x88143)) % 172.78/172.49 [8874]~P40(x88741,f255(f883(x88741,a871)),x88743)+P102(f332(f332(f246(f883(f882(f877(x88741),f877(x88741)),a871)),f157(x88741,x88742)),f158(x88741,x88743)))+~P102(f332(f332(f246(f883(f882(x88741,x88741),a871)),x88742),x88743)) % 172.78/172.49 [9082]P38(x90821,x90822)+~P102(f332(f332(f334(x90821),x90823),f600(x90822,x90821)))+P102(f332(f332(f334(f882(x90821,x90821)),f332(f332(f267(x90821,x90821),f657(x90822,x90821,x90823)),x90823)),x90822)) % 172.78/172.49 [9116]~P102(f332(f61(x91161),x91162))+P102(f332(f61(f883(x91161,a871)),f332(f332(f60(x91161),x91162),x91163)))+~P102(f332(f332(f246(f883(f882(x91161,x91161),a871)),x91163),f332(f332(f269(x91161,x91161),x91162),f332(f16(f883(x91161,a871),x91161),x91162)))) % 172.78/172.49 [9151]P40(x91511,x91512,x91513)+P102(f332(f332(f334(x91511),f553(x91513,x91512,x91511)),x91512))+~P102(f332(f332(f246(f883(f882(x91511,x91511),a871)),x91513),f332(f332(f269(x91511,x91511),x91512),f332(f16(f883(x91511,a871),x91511),x91512)))) % 172.78/172.49 [9152]P40(x91521,x91522,x91523)+P102(f332(f332(f334(x91521),f557(x91522,x91523,x91521)),x91522))+~P102(f332(f332(f246(f883(f882(x91521,x91521),a871)),x91523),f332(f332(f269(x91521,x91521),x91522),f332(f16(f883(x91521,a871),x91521),x91522)))) % 172.78/172.49 [9187]~P60(x91871)+~P102(f332(f332(f247(x91871),x91872),x91873))+P102(f332(f332(f247(x91871),f332(f332(f290(x91871),f332(f332(f79(x91871),x91872),x91873)),f332(f332(f79(x91871),f77(x91871)),f77(x91871)))),x91873)) % 172.78/172.49 [9216]~P59(x92161)+P102(f332(f332(f246(x92161),x92162),x92163))+~P102(f332(f332(f246(x92161),f332(f332(f80(x92161),f344(x92163,x92162,x92161)),x92162)),x92163)) % 172.78/172.49 [9352]E(f332(f196(f877(f877(x93521))),f332(f136(f877(x93521),f332(f332(f8(a876,a871,f877(x93521)),f332(f247(a876),x93522)),f196(f877(x93521)))),f181(x93521,x93523))),f332(f196(f877(x93521)),f332(f332(f165(f877(x93521)),x93523),x93522)))+~P29(a876,f332(f169(a876),f332(f332(f154(f877(x93521),a876),f196(f877(x93521))),x93523)))+~P102(f332(f332(f247(a876),x93522),f332(f196(f877(f877(x93521))),x93523))) % 172.78/172.49 [9460]~P38(x94601,x94602)+P21(x94601,f332(f332(f267(f883(f882(x94601,x94601),a871),f883(f882(x94601,x94601),a871)),x94602),x94603))+~P102(f332(f332(f246(f883(f882(x94601,x94601),a871)),f332(f332(f289(x94601,x94601,x94601),x94602),x94603)),x94602)) % 172.78/172.49 [9467]E(f332(f332(f154(f877(x94671),x94671),f332(f332(f7(f877(x94671),a876,x94671),f165(x94671)),x94672)),f332(f136(f877(x94671),f332(f332(f8(a876,a871,f877(x94671)),f332(f247(a876),x94672)),f196(f877(x94671)))),f181(x94671,x94673))),f332(f332(f165(f877(x94671)),x94673),x94672))+~P29(a876,f332(f169(a876),f332(f332(f154(f877(x94671),a876),f196(f877(x94671))),x94673)))+~P102(f332(f332(f247(a876),x94672),f332(f196(f877(f877(x94671))),x94673))) % 172.78/172.49 [9601]P40(x96011,x96012,x96013)+~P102(f332(f332(f334(f882(x96011,x96011)),f332(f332(f267(x96011,x96011),f553(x96013,x96012,x96011)),f553(x96013,x96012,x96011))),x96013))+~P102(f332(f332(f246(f883(f882(x96011,x96011),a871)),x96013),f332(f332(f269(x96011,x96011),x96012),f332(f16(f883(x96011,a871),x96011),x96012)))) % 172.78/172.49 [9602]P40(x96021,x96022,x96023)+~P102(f332(f332(f334(f882(x96021,x96021)),f332(f332(f267(x96021,x96021),f557(x96022,x96023,x96021)),f557(x96022,x96023,x96021))),x96023))+~P102(f332(f332(f246(f883(f882(x96021,x96021),a871)),x96023),f332(f332(f269(x96021,x96021),x96022),f332(f16(f883(x96021,a871),x96021),x96022)))) % 172.78/172.49 [9776]~P137(x97761)+~P119(x97761)+E(f332(f332(f290(x97761),f332(f105(x97761),f332(f332(f72(f882(a1,a1),a1,x97762,f266(a1,a1)),f223(x97762)),x97763))),f332(f105(x97761),f332(f332(f72(f882(a1,a1),a1,x97762,f270(a1,a1)),f223(x97762)),x97763))),f236(x97762,x97761,x97763)) % 172.78/172.49 [9977]~E(x99773,f2(a876))+~E(f332(f196(f877(x99771)),f332(f332(f165(f877(x99771)),x99772),f748(x99773,x99771,x99772))),x99773)+E(f332(f332(f154(a876,f877(x99771)),f332(f332(f7(a876,f877(a876),f877(x99771)),f332(f332(f8(f883(a876,x99771),f883(f877(a876),f877(x99771)),a876),f154(a876,x99771)),f332(f7(a876,a876,x99771),f332(f332(f8(f877(x99771),f883(a876,x99771),a876),f165(x99771)),f332(f165(f877(x99771)),x99772))))),f139(a876,f332(f302(a876,f2(a876)),f332(f196(f877(f877(x99771))),x99772))))),f139(a876,f332(f302(a876,f2(a876)),x99773))),f181(x99771,x99772)) % 172.78/172.49 [9978]E(x99781,f116(f877(x99782)))+~E(f332(f196(f877(x99782)),f332(f332(f165(f877(x99782)),x99781),f748(x99783,x99782,x99781))),x99783)+E(f332(f332(f154(a876,f877(x99782)),f332(f332(f7(a876,f877(a876),f877(x99782)),f332(f332(f8(f883(a876,x99782),f883(f877(a876),f877(x99782)),a876),f154(a876,x99782)),f332(f7(a876,a876,x99782),f332(f332(f8(f877(x99782),f883(a876,x99782),a876),f165(x99782)),f332(f165(f877(x99782)),x99781))))),f139(a876,f332(f302(a876,f2(a876)),f332(f196(f877(f877(x99782))),x99781))))),f139(a876,f332(f302(a876,f2(a876)),x99783))),f181(x99782,x99781)) % 172.78/172.49 [9979]~E(x99793,f2(a876))+E(f332(f332(f154(a876,f877(x99791)),f332(f332(f7(a876,f877(a876),f877(x99791)),f332(f332(f8(f883(a876,x99791),f883(f877(a876),f877(x99791)),a876),f154(a876,x99791)),f332(f7(a876,a876,x99791),f332(f332(f8(f877(x99791),f883(a876,x99791),a876),f165(x99791)),f332(f165(f877(x99791)),x99792))))),f139(a876,f332(f302(a876,f2(a876)),f332(f196(f877(f877(x99791))),x99792))))),f139(a876,f332(f302(a876,f2(a876)),x99793))),f181(x99791,x99792))+P102(f332(f332(f247(a876),f748(x99793,x99791,x99792)),f332(f196(f877(f877(x99791))),x99792))) % 172.78/172.49 [9980]E(x99801,f116(f877(x99802)))+E(f332(f332(f154(a876,f877(x99802)),f332(f332(f7(a876,f877(a876),f877(x99802)),f332(f332(f8(f883(a876,x99802),f883(f877(a876),f877(x99802)),a876),f154(a876,x99802)),f332(f7(a876,a876,x99802),f332(f332(f8(f877(x99802),f883(a876,x99802),a876),f165(x99802)),f332(f165(f877(x99802)),x99801))))),f139(a876,f332(f302(a876,f2(a876)),f332(f196(f877(f877(x99802))),x99801))))),f139(a876,f332(f302(a876,f2(a876)),x99803))),f181(x99802,x99801))+P102(f332(f332(f247(a876),f748(x99803,x99802,x99801)),f332(f196(f877(f877(x99802))),x99801))) % 172.78/172.49 [7711]E(f332(f332(f79(a876),f332(f106(a876),x77111)),f332(f332(f79(a876),f332(f106(a876),x77112)),x77113)),f332(f332(f79(a876),f332(f106(a876),f332(f332(f79(a1),x77111),x77112))),x77113))+P102(f332(a200,f332(f106(a1),x77111)))+P102(f332(a200,f332(f106(a1),x77112))) % 172.78/172.49 [8490]~P102(f332(f61(x84901),x84902))+~P102(f332(f332(f334(x84901),x84903),x84902))+E(f332(a115,f332(f37(x84901),f332(f332(f22(f883(x84901,a871)),x84902),f332(f332(f310(x84901),x84903),f195(f883(x84901,a871)))))),f332(f37(x84901),x84902)) % 172.78/172.49 [8509]~P102(f332(f61(x85091),x85092))+~P102(f332(f332(f334(x85091),x85093),x85092))+E(f332(f332(f79(a876),f77(a876)),f332(f37(x85091),f332(f332(f22(f883(x85091,a871)),x85092),f332(f332(f310(x85091),x85093),f195(f883(x85091,a871)))))),f332(f37(x85091),x85092)) % 172.78/172.49 [8592]~P104(x85921)+~P102(f332(f61(x85921),x85923))+E(f332(f332(f148(x85921,x85921,f5(x85921)),x85922),f139(x85921,f332(f332(f22(f883(x85921,a871)),x85923),f332(f332(f310(x85921),x85922),f195(f883(x85921,a871)))))),f139(x85921,f332(f332(f310(x85921),x85922),x85923))) % 172.78/172.49 [8743]~P102(f332(f61(x87431),x87433))+~P102(f332(f61(x87431),x87432))+E(f332(f332(f79(a876),f332(f37(x87431),f332(f332(f113(f883(x87431,a871)),x87432),x87433))),f332(f37(x87431),f332(f332(f104(f883(x87431,a871)),x87432),x87433))),f332(f332(f79(a876),f332(f37(x87431),x87432)),f332(f37(x87431),x87433))) % 172.78/172.49 [9925]~P20(x99251,f883(f883(x99251,a871),a871),f332(f332(f7(x99251,f883(f882(x99251,x99251),a871),f883(f883(x99251,a871),a871)),f332(f332(f8(f883(x99251,a871),f883(f883(f882(x99251,x99251),a871),f883(f883(x99251,a871),a871)),x99251),f60(x99251)),f332(f332(f7(x99251,f883(x99251,a871),f883(x99251,a871)),f310(x99251)),f195(f883(x99251,a871))))),x99253),x99252)+~P102(f332(f61(x99251),x99252))+E(f332(f37(f883(x99251,a871)),f332(f332(f60(x99251),x99252),x99253)),f332(f37(x99251),x99252)) % 172.78/172.49 [7985]~P89(x79851)+P102(f332(f332(f246(a1),f2(a1)),f332(f106(a1),x79853)))+E(f332(f332(f257(x79851),x79852),f332(f106(a876),f332(f332(f22(a1),f332(f332(f79(a1),x79853),x79853)),a100))),f77(x79851)) % 172.78/172.49 [9443]~P89(x94431)+~P102(f332(f332(f246(a1),f2(a1)),f332(f106(a1),x94433)))+E(f332(f332(f257(x94431),x94432),f332(f106(a876),f332(f332(f22(a1),f332(f332(f79(a1),x94433),x94433)),a100))),f332(f332(f85(x94431,x94431),f332(f332(f257(x94431),x94432),f332(f106(a876),x94433))),f332(f332(f18(x94431,x94431,x94431),f332(f332(f8(x94431,f883(x94431,x94431),x94431),f80(x94431)),f332(f80(x94431),x94432))),f5(x94431)))) % 172.78/172.49 [9835]~P102(f332(f137(x98351),x98353))+~P102(f332(f332(f334(x98351),x98352),f332(f173(x98351),x98353)))+E(f332(f332(f138(x98351),f332(f196(f877(x98351)),f178(x98351,f332(f332(f8(a871,a871,x98351),a327),f332(f332(f7(x98351,x98351,a871),a329),x98352)),f332(f169(x98351),x98353)))),f332(f169(x98351),x98353)),f332(f332(f151(x98351),x98352),f332(f169(x98351),f178(x98351,f332(f332(f8(a871,a871,x98351),a327),f332(f332(f7(x98351,x98351,a871),a329),x98352)),x98353)))) % 172.78/172.49 [9906]P102(f332(f332(f246(f883(f882(x99061,x99061),a871)),f308(x99061,x99062)),x99063))+~P102(f332(f332(f246(f883(f882(x99061,x99061),a871)),f308(x99061,f195(f883(f882(x99061,x99061),a871)))),x99063))+~P102(f332(f332(f246(f883(f882(x99061,x99061),a871)),f332(f332(f289(x99061,x99061,x99061),f332(f332(f104(f883(f882(x99061,x99061),a871)),f308(x99061,x99062)),x99063)),x99062)),x99063)) % 172.78/172.49 [9747]~P102(f332(f61(x97471),f332(f252(x97471),x97473)))+~P102(f332(f61(x97471),f332(f252(x97471),x97472)))+P102(f332(f61(x97471),f332(f252(x97471),f332(f332(f18(x97471,a871,a871),f332(f332(f8(a871,f883(a871,a871),x97471),a331),x97472)),x97473)))) % 172.78/172.49 [10040]P102(f332(f332(f246(f883(f882(x100401,x100401),a871)),f332(f332(f289(x100401,x100401,x100401),x100402),f308(x100401,x100402))),x100403))+~P102(f332(f332(f246(f883(f882(x100401,x100401),a871)),x100402),x100403))+~P102(f332(f332(f246(f883(f882(x100401,x100401),a871)),f332(f332(f289(x100401,x100401,x100401),f332(f332(f104(f883(f882(x100401,x100401),a871)),f332(f332(f289(x100401,x100401,x100401),x100402),f308(x100401,x100402))),x100403)),x100402)),x100403)) % 172.78/172.49 [9993]~P113(x99932)+E(x99931,f2(x99932))+~E(f332(f332(f79(x99932),f332(f332(f257(x99932),x99933),f332(f106(a876),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100))))),f332(f332(f257(x99932),x99931),f332(f106(a876),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100))))),f2(x99932)) % 172.78/172.49 [9994]~P113(x99942)+E(x99941,f2(x99942))+~E(f332(f332(f79(x99942),f332(f332(f257(x99942),x99941),f332(f106(a876),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100))))),f332(f332(f257(x99942),x99943),f332(f106(a876),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100))))),f2(x99942)) % 172.78/172.49 [9999]~P102(f332(f137(x99991),x99993))+~P102(f332(f332(f334(x99991),x99992),f332(f173(x99991),x99993)))+E(f332(f169(x99991),f332(f172(x99991),f332(f332(f138(x99991),f332(f196(f877(x99991)),f178(x99991,f332(f332(f8(a871,a871,x99991),a327),f332(f332(f7(x99991,x99991,a871),a329),x99992)),x99993))),x99993))),f178(x99991,f332(f332(f8(a871,a871,x99991),a327),f332(f332(f7(x99991,x99991,a871),a329),x99992)),f332(f169(x99991),x99993))) % 172.78/172.49 [10085]~P113(x100852)+E(x100851,f2(x100852))+P102(f332(f332(f247(x100852),f2(x100852)),f332(f332(f79(x100852),f332(f332(f257(x100852),x100853),f332(f106(a876),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100))))),f332(f332(f257(x100852),x100851),f332(f106(a876),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100))))))) % 172.78/172.49 [10086]~P113(x100862)+E(x100861,f2(x100862))+P102(f332(f332(f247(x100862),f2(x100862)),f332(f332(f79(x100862),f332(f332(f257(x100862),x100861),f332(f106(a876),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100))))),f332(f332(f257(x100862),x100863),f332(f106(a876),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100))))))) % 172.78/172.49 [10128]~P113(x101281)+P102(f332(f332(f246(x101281),f2(x101281)),x101282))+~P102(f332(f332(f246(x101281),f2(x101281)),f332(f332(f257(x101281),x101282),f332(a115,f332(f332(f80(a876),f332(f106(a876),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)))),x101283))))) % 172.78/172.49 [5492]~P19(x54921,x54924,x54923)+P19(x54921,x54922,x54923)+~P19(x54921,x54922,x54924) % 172.78/172.49 [4960]~E(x49602,f89(x49603,x49601))+P102(f332(x49601,x49602))+~P102(f332(x49601,x49604)) % 172.78/172.49 [6697]~P38(x66972,x66974)+~P38(x66971,x66973)+P38(f882(x66971,x66972),f325(x66971,x66972,x66973,x66974)) % 172.78/172.49 [5139]~P2(x51394,x51391)+~E(f332(x51391,x51392),f332(x51391,x51393))+P102(f332(f332(x51391,x51392),x51393)) % 172.78/172.49 [5304]~P2(x53044,x53041)+E(f332(x53041,x53042),f332(x53041,x53043))+~P102(f332(f332(x53041,x53042),x53043)) % 172.78/172.49 [5398]~P13(x53983,x53984,x53981)+E(f332(x53981,x53982),f332(f63(x53983,x53984),x53982))+~P102(f332(f61(x53983),x53982)) % 172.78/172.49 [5399]~P4(x53993,x53994,x53991)+E(f332(x53991,x53992),f332(f63(x53993,x53994),x53992))+~P102(f332(f61(x53993),x53992)) % 172.78/172.49 [5525]~P2(x55254,x55251)+~P102(f332(f332(x55251,x55253),x55252))+P102(f332(f332(x55251,x55252),x55253)) % 172.78/172.49 [5595]E(x55951,x55952)+~E(f332(f266(x55953,x55954),x55951),f332(f266(x55953,x55954),x55952))+~E(f332(f270(x55953,x55954),x55951),f332(f270(x55953,x55954),x55952)) % 172.78/172.49 [5620]E(x56201,x56202)+~P102(f332(f47(x56203,x56204),x56202))+~P102(f332(f47(x56203,x56204),x56201)) % 172.78/172.49 [5810]~P71(x58102)+E(f237(x58101,x58102,x58103,x58104),f2(x58102))+P102(f332(f61(x58101),x58104)) % 172.78/172.49 [5945]~P102(f332(f320(x59451,x59452),x59454))+P102(f332(f320(x59451,x59452),x59453))+~P102(f332(f332(x59452,x59453),x59454)) % 172.78/172.49 [7822]E(x78221,f2(a876))+~P102(f332(x78222,x78223))+P102(f332(x78222,f812(x78222,x78223,x78221,x78224))) % 172.78/172.49 [7904]~P104(x79042)+~P102(f332(f137(x79041),x79044))+P102(f332(f137(x79041),f150(x79041,x79042,x79043,x79044))) % 172.78/172.49 [8133]~P102(f332(f61(x81332),x81334))+~P102(f332(f61(x81331),x81333))+P102(f332(f61(f881(x81331,x81332)),f319(x81331,x81332,x81333,x81334))) % 172.78/172.49 [8134]~P102(f332(f137(x81342),x81344))+~P102(f332(f137(x81341),x81343))+P102(f332(f137(f882(x81341,x81342)),f59(x81341,x81342,x81343,x81344))) % 172.78/172.49 [8138]P102(f332(f332(f334(f877(x81381)),f332(f332(f134(x81381),x81382),x81383)),f161(x81381,x81384)))+~P102(f332(f332(f334(f877(x81381)),x81383),f161(x81381,x81384)))+~P102(f332(f332(f334(f877(x81381)),x81382),f161(x81381,x81384))) % 172.78/172.49 [8423]E(x84231,f2(a876))+P102(f332(x84232,x84233))+~P102(f332(x84232,f813(x84232,x84233,x84231,x84234))) % 172.78/172.49 [8470]~P104(x84703)+~P102(f332(f137(x84701),f150(x84701,x84703,x84704,x84702)))+P102(f332(f137(x84701),x84702)) % 172.78/172.49 [8734]~P102(f332(f332(f334(f882(x87341,x87341)),f332(f332(f267(x87341,x87341),x87342),x87344)),f308(x87341,x87343)))+P102(f332(f332(f334(x87341),x87342),f321(x87341,x87343)))+~P102(f332(f332(f334(x87341),x87344),f321(x87341,x87343))) % 172.78/172.49 [5123]~P71(x51232)+E(f332(f332(f6(x51231,x51232),x51233),x51234),f2(x51232))+P102(f332(f61(x51231),x51234)) % 172.78/172.49 [5126]~P67(x51262)+E(f332(f332(f9(x51261,x51262),x51263),x51264),f77(x51262))+P102(f332(f61(x51261),x51264)) % 172.78/172.49 [5267]~P68(x52673)+E(x52671,x52672)+~E(f332(f332(f79(x52673),x52674),x52671),f332(f332(f79(x52673),x52674),x52672)) % 172.78/172.49 [5268]~P69(x52683)+E(x52681,x52682)+~E(f332(f332(f79(x52683),x52684),x52681),f332(f332(f79(x52683),x52684),x52682)) % 172.78/172.49 [5270]~P68(x52703)+E(x52701,x52702)+~E(f332(f332(f79(x52703),x52701),x52704),f332(f332(f79(x52703),x52702),x52704)) % 172.78/172.49 [5351]~E(x53512,f332(f332(f310(x53511),x53513),x53514))+~P102(f332(f61(x53511),x53514))+P102(f332(f61(x53511),x53512)) % 172.78/172.49 [5394]~P27(x53943)+E(x53941,f195(f883(x53942,a871)))+E(f332(f332(f41(x53942,x53943),x53941),f332(f16(x53943,x53942),x53944)),x53944) % 172.78/172.49 [5395]~P27(x53953)+E(x53951,f195(f883(x53952,a871)))+E(f332(f332(f42(x53952,x53953),x53951),f332(f16(x53953,x53952),x53954)),x53954) % 172.78/172.49 [5608]~P105(x56083)+E(x56081,x56082)+~E(f303(x56083,x56084,x56081),f332(f332(f310(x56083),x56082),f195(f883(x56083,a871)))) % 172.78/172.49 [5609]~P105(x56093)+E(x56091,x56092)+~E(f303(x56093,x56091,x56092),f332(f332(f310(x56093),x56094),f195(f883(x56093,a871)))) % 172.78/172.49 [5669]~P36(x56693,x56691,x56694)+P36(x56693,x56691,f332(f332(f151(x56693),x56692),x56694))+P102(f332(x56691,x56692)) % 172.78/172.49 [5770]~P32(x57701,x57702,x57704)+~P102(f332(x57702,x57703))+P32(x57701,x57702,f332(f332(f151(x57701),x57703),x57704)) % 172.78/172.49 [5901]P102(f332(x59011,x59012))+~P102(f332(f260(x59013,x59011),x59014))+~P102(f332(f332(f334(x59013),x59012),x59014)) % 172.78/172.49 [5910]~P32(x59101,x59102,x59104)+~P32(x59101,x59102,x59103)+P32(x59101,x59102,f332(f332(f134(x59101),x59103),x59104)) % 172.78/172.49 [5920]P34(x59201,x59202,x59203)+~P34(x59201,x59202,f332(f332(f151(x59201),x59204),x59203))+P102(f332(x59202,x59204)) % 172.78/172.49 [5921]P36(x59211,x59212,x59213)+~P36(x59211,x59212,f332(f332(f151(x59211),x59214),x59213))+P102(f332(x59212,x59214)) % 172.78/172.49 [5934]E(x59341,x59342)+~P102(f332(f332(f201(x59343),x59344),x59342))+~P102(f332(f332(f201(x59343),x59344),x59341)) % 172.78/172.49 [6000]P34(x60001,x60002,x60003)+P34(x60001,x60002,x60004)+~P34(x60001,x60002,f332(f332(f134(x60001),x60004),x60003)) % 172.78/172.49 [6019]~P71(x60191)+E(f332(f332(f6(a876,x60191),x60192),f332(f302(a876,x60193),f332(a115,x60194))),f2(x60191))+~P102(f332(f332(f247(a876),x60194),x60193)) % 172.78/172.49 [6024]~P26(x60241)+~E(f44(x60241,x60242,x60243),f44(x60241,x60244,x60243))+E(f44(x60241,f332(f78(x60241),x60242),x60243),f44(x60241,f332(f78(x60241),x60244),x60243)) % 172.78/172.49 [6092]P102(f332(x60921,x60922))+~E(f332(f136(x60923,x60921),x60924),x60924)+~P102(f332(f332(f334(x60923),x60922),f332(f173(x60923),x60924))) % 172.78/172.49 [6111]~E(f332(f332(f79(a876),x61113),x61112),f332(f332(f79(a876),x61111),x61114))+~P102(f332(f332(f247(a876),x61113),x61114))+P102(f332(f332(f247(a876),x61111),x61112)) % 172.78/172.49 [6115]P34(x61151,x61152,x61153)+~P102(f332(x61152,x61154))+~P102(f332(f332(f334(x61151),x61154),f332(f173(x61151),x61153))) % 172.78/172.49 [6151]~P32(x61513,x61511,x61514)+P102(f332(x61511,x61512))+~P102(f332(f332(f334(x61513),x61512),f332(f173(x61513),x61514))) % 172.78/172.49 [6153]~E(f332(f136(x61531,x61532),x61533),f116(x61531))+~P102(f332(x61532,x61534))+~P102(f332(f332(f334(x61531),x61534),f332(f173(x61531),x61533))) % 172.78/172.49 [6154]~E(f178(x61543,x61541,x61544),x61544)+P102(f332(x61541,x61542))+~P102(f332(f332(f334(x61543),x61542),f332(f173(x61543),x61544))) % 172.78/172.49 [6183]~E(x61834,f195(f883(x61832,a871)))+~E(x61833,f195(f883(x61831,a871)))+E(f319(x61831,x61832,x61833,x61834),f195(f883(f881(x61831,x61832),a871))) % 172.78/172.49 [6328]P102(f332(x63281,x63282))+~P102(f332(f160(x63283,x63281),x63284))+~P102(f332(f332(f334(x63283),x63282),f332(f173(x63283),x63284))) % 172.78/172.49 [6595]~P71(x65951)+E(f332(f332(f6(a876,x65951),x65952),f303(a876,x65953,f332(a115,x65954))),f2(x65951))+~P102(f332(f332(f247(a876),f332(a115,x65954)),x65953)) % 172.78/172.49 [6736]~P104(x67361)+E(f332(f332(f22(f883(x67361,a871)),f332(f302(x67361,x67362),x67363)),f332(f302(x67361,x67362),x67364)),f332(f302(x67361,x67364),x67363))+~P102(f332(f332(f246(x67361),x67362),x67364)) % 172.78/172.49 [6808]~E(x68083,x68084)+E(x68081,f2(a876))+P102(f332(f332(f334(x68082),x68083),f332(f173(x68082),f170(x68082,x68081,x68084)))) % 172.78/172.49 [7090]~P102(f332(f332(f334(f877(x70901)),x70904),f161(x70901,x70903)))+P102(f332(f332(f334(x70901),x70902),x70903))+~P102(f332(f332(f334(x70901),x70902),f332(f173(x70901),x70904))) % 172.78/172.49 [7097]~P38(x70971,x70972)+P102(f332(f332(f334(x70971),f643(x70972,x70971,x70973)),x70973))+~P102(f332(f332(f334(x70971),x70974),x70973)) % 172.78/172.49 [7153]~P71(x71531)+E(f332(f332(f332(f65(x71531,x71532,f79(x71531)),x71533),f2(x71531)),x71534),f332(f332(f6(x71532,x71531),x71533),x71534))+~P102(f332(f61(x71532),x71534)) % 172.78/172.49 [7155]~P67(x71551)+E(f332(f332(f332(f65(x71551,x71552,f80(x71551)),x71553),f77(x71551)),x71554),f332(f332(f9(x71552,x71551),x71553),x71554))+~P102(f332(f61(x71552),x71554)) % 172.78/172.49 [7183]P20(x71831,x71832,x71833,x71834)+~E(f332(f37(x71832),f332(f311(x71831,x71832,x71833),x71834)),f332(f37(x71831),x71834))+~P102(f332(f61(x71831),x71834)) % 172.78/172.49 [7369]~P71(x73691)+E(f332(f332(f79(x73691),f332(x73692,x73693)),f332(f332(f6(a876,x73691),x73692),f305(a876,x73693,x73694))),f332(f332(f6(a876,x73691),x73692),f303(a876,x73693,x73694)))+~P102(f332(f332(f246(a876),x73693),x73694)) % 172.78/172.49 [7379]~P71(x73791)+~P20(x73792,x73791,x73793,x73794)+E(f332(f332(f6(x73791,x73791),f33(x73791)),f332(f311(x73792,x73791,x73793),x73794)),f332(f332(f6(x73792,x73791),x73793),x73794)) % 172.78/172.49 [7380]~P67(x73801)+~P20(x73802,x73801,x73803,x73804)+E(f332(f332(f9(x73801,x73801),f33(x73801)),f332(f311(x73802,x73801,x73803),x73804)),f332(f332(f9(x73802,x73801),x73803),x73804)) % 172.78/172.49 [7433]E(f332(f37(f881(x74331,x74332)),f319(x74331,x74332,x74333,x74334)),f332(f332(f79(a876),f332(f37(x74331),x74333)),f332(f37(x74332),x74334)))+~P102(f332(f61(x74332),x74334))+~P102(f332(f61(x74331),x74333)) % 172.78/172.49 [7520]E(x75201,x75202)+P102(f332(f332(f334(x75203),x75201),f332(f173(x75203),f171(x75203,x75202,x75204))))+~P102(f332(f332(f334(x75203),x75201),f332(f173(x75203),x75204))) % 172.78/172.49 [7748]~P71(x77481)+E(f332(f332(f79(x77481),f332(f332(f6(a876,x77481),x77482),f332(f302(a876,x77483),x77484))),f332(x77482,x77484)),f332(f332(f6(a876,x77481),x77482),f332(f302(a876,x77483),f332(a115,x77484))))+P102(f332(f332(f247(a876),x77484),x77483)) % 172.78/172.49 [7804]~P20(x78041,x78042,x78043,f255(f883(x78041,a871)))+~P102(f332(f61(x78042),x78044))+P102(f332(f61(x78041),f332(f312(x78041,x78042,x78043),x78044))) % 172.78/172.49 [7917]P102(f332(f332(f334(f877(x79171)),f332(f332(f151(x79171),x79172),x79173)),f161(x79171,x79174)))+~P102(f332(f332(f334(f877(x79171)),x79173),f161(x79171,x79174)))+~P102(f332(f332(f334(x79171),x79172),x79174)) % 172.78/172.49 [8009]~E(f332(f311(x80093,x80091,x80094),f255(f883(x80093,a871))),f255(f883(x80091,a871)))+P102(f332(f61(x80091),x80092))+~P102(f332(f61(x80093),f332(f312(x80093,x80091,x80094),x80092))) % 172.78/172.49 [8105]~P20(x81051,x81053,x81054,x81052)+P102(f332(f61(x81051),x81052))+~P102(f332(f61(x81053),f332(f311(x81051,x81053,x81054),x81052))) % 172.78/172.49 [8126]~E(x81262,x81263)+P102(f332(f332(f334(f882(x81261,x81261)),f332(f332(f267(x81261,x81261),x81262),x81263)),f264(x81261,x81264)))+~P102(f332(f332(f334(x81261),x81262),x81264)) % 172.78/172.49 [8165]~P71(x81651)+E(f332(f332(f79(x81651),f332(f332(f6(a876,x81651),x81652),f303(a876,x81653,x81654))),f332(x81652,f332(a115,x81654))),f332(f332(f6(a876,x81651),x81652),f303(a876,x81653,f332(a115,x81654))))+P102(f332(f332(f247(a876),f332(a115,x81654)),x81653)) % 172.78/172.49 [8229]P102(f332(x82291,x82292))+~P102(f332(x82291,f332(f332(f165(x82293),x82294),f683(x82291,x82294,x82293))))+~P102(f332(f332(f334(x82293),x82292),f332(f173(x82293),x82294))) % 172.78/172.49 [8368]~P102(f332(f332(f334(x83681),x83682),f321(x83681,x83684)))+P102(f332(f332(f334(f877(x83681)),f332(f332(f151(x83681),x83682),x83683)),f321(f877(x83681),f157(x83681,x83684))))+~P102(f332(f332(f334(f877(x83681)),x83683),f321(f877(x83681),f157(x83681,x83684)))) % 172.78/172.49 [8381]~P20(x83812,x83813,x83814,f646(x83814,x83813,x83812,x83811))+P20(x83812,x83813,x83814,f40(f883(x83812,a871),x83811))+E(x83811,f195(f883(f883(x83812,a871),a871))) % 172.78/172.49 [8653]E(x86531,x86532)+~P102(f332(f332(f334(f882(x86533,x86533)),f332(f332(f267(x86533,x86533),x86531),x86532)),f308(x86533,x86534)))+P102(f332(f332(f334(x86533),x86531),f332(f265(x86533,x86533),x86534))) % 172.78/172.49 [8918]E(x89181,f2(a876))+P102(f332(x89182,x89183))+P102(f332(f332(f334(x89184),f813(x89182,x89183,x89181,x89184)),f332(f173(x89184),f170(x89184,x89181,x89183)))) % 172.78/172.49 [8928]E(x89281,f2(a876))+~P102(f332(x89283,x89284))+P102(f332(f332(f334(x89282),f812(x89283,x89284,x89281,x89282)),f332(f173(x89282),f170(x89282,x89281,x89284)))) % 172.78/172.49 [8936]P20(x89362,x89363,x89364,f40(f883(x89362,a871),x89361))+E(x89361,f195(f883(f883(x89362,a871),a871)))+P102(f332(f332(f334(f883(x89362,a871)),f646(x89364,x89363,x89362,x89361)),x89361)) % 172.78/172.49 [9073]P102(f332(f61(x90731),x90732))+~P102(f332(f61(x90734),f332(f311(x90731,x90734,x90733),x90732)))+P102(f332(f332(f334(x90731),f436(x90733,x90734,x90732,x90731)),x90732)) % 172.78/172.49 [9165]~P27(x91652)+E(f332(f332(f64(x91651,x91652,f332(f332(f8(x91652,f883(x91652,x91652),x91651),f113(x91652)),x91653)),f195(x91652)),x91654),f332(f332(f41(x91651,x91652),x91654),x91653))+~P102(f332(f61(x91651),x91654)) % 172.78/172.49 [9166]~P27(x91662)+E(f332(f332(f64(x91661,x91662,f332(f332(f8(x91662,f883(x91662,x91662),x91661),f104(x91662)),x91663)),f255(x91662)),x91664),f332(f332(f42(x91661,x91662),x91664),x91663))+~P102(f332(f61(x91661),x91664)) % 172.78/172.49 [9249]P102(f332(x92491,x92492))+~P102(f332(x92491,f332(f332(f165(x92493),x92494),f738(x92492,x92491,x92494,x92493))))+~P102(f332(f332(f334(x92493),x92492),f332(f173(x92493),x92494))) % 172.78/172.49 [9269]E(x92691,x92692)+~P102(f332(f332(f334(f882(x92693,x92693)),f332(f332(f267(x92693,x92693),x92691),x92692)),f308(x92693,x92694)))+P102(f332(f332(f334(f882(x92693,x92693)),f332(f332(f267(x92693,x92693),x92691),x92692)),f332(f332(f289(x92693,x92693,x92693),x92694),f308(x92693,x92694)))) % 172.78/172.49 [9318]~E(f332(f196(f877(x93181)),x93182),f332(f196(f877(x93181)),x93183))+~P102(f332(f332(f334(f882(f877(x93181),f877(x93181))),f332(f332(f267(f877(x93181),f877(x93181)),x93182),x93183)),f147(x93181,x93184)))+P102(f332(f332(f334(f882(f877(x93181),f877(x93181))),f332(f332(f267(f877(x93181),f877(x93181)),x93182),x93183)),f145(x93181,x93184))) % 172.78/172.49 [9548]P32(x95481,f332(f332(f18(x95481,a871,a871),f332(f332(f8(a871,f883(a871,a871),x95481),a331),f332(f332(f8(a871,a871,x95481),a327),x95482))),f332(a329,x95483)),x95484)+~P102(f332(x95482,x95483))+~P36(x95481,x95482,f332(f332(f151(x95481),x95483),x95484)) % 172.78/172.49 [9709]~P32(x97091,f332(f332(f18(x97091,a871,a871),f332(f332(f8(a871,f883(a871,a871),x97091),a331),f332(f332(f8(a871,a871,x97091),a327),x97092))),f332(a329,x97093)),x97094)+~P102(f332(x97092,x97093))+P36(x97091,x97092,f332(f332(f151(x97091),x97093),x97094)) % 172.78/172.49 [9713]~P36(x97131,x97132,x97134)+~P32(x97131,f332(f332(f18(x97131,a871,a871),f332(f332(f8(a871,f883(a871,a871),x97131),a331),f332(f332(f8(a871,a871,x97131),a327),x97132))),f332(a329,x97133)),x97134)+P36(x97131,x97132,f332(f332(f151(x97131),x97133),x97134)) % 172.78/172.49 [9750]~P66(x97501)+E(f332(f332(f6(a876,x97501),f332(f332(f18(a876,x97501,x97501),f332(f332(f8(x97501,f883(x97501,x97501),a876),f22(x97501)),x97502)),f332(f332(f8(a876,x97501,a876),x97502),f332(f332(f7(a876,a876,a876),f79(a876)),f77(a876))))),f303(a876,x97503,x97504)),f2(x97501))+P102(f332(f332(f246(a876),x97503),x97504)) % 172.78/172.49 [9992]~P38(x99922,x99924)+~P20(x99922,x99921,x99923,f255(f883(x99922,a871)))+P38(x99921,f332(f311(f882(x99922,x99922),f882(x99921,x99921),f272(x99922,x99921,x99922,x99921,x99923,x99923)),x99924)) % 172.78/172.49 [10154]~E(f332(f196(f877(x101541)),x101543),f332(f196(f877(x101541)),x101542))+P102(f332(f332(f334(f882(f877(x101541),f877(x101541))),f332(f332(f267(f877(x101541),f877(x101541)),x101542),x101543)),f158(x101541,x101544)))+~P102(f332(f332(f271(x101541,x101541,a871),f332(f332(f7(x101541,f883(f882(x101541,x101541),a871),f883(x101541,a871)),f332(f332(f8(f883(x101541,f883(f883(f882(x101541,x101541),a871),a871)),f883(f883(f882(x101541,x101541),a871),f883(x101541,a871)),x101541),f7(x101541,f883(f882(x101541,x101541),a871),a871)),f332(f332(f8(f883(x101541,f882(x101541,x101541)),f883(x101541,f883(f883(f882(x101541,x101541),a871),a871)),x101541),f332(f8(f882(x101541,x101541),f883(f883(f882(x101541,x101541),a871),a871),x101541),f334(f882(x101541,x101541)))),f267(x101541,x101541)))),x101544)),f685(x101544,x101543,x101542,x101541))) % 172.78/172.49 [5984]~E(x59844,x59842)+P102(f332(x59841,x59842))+P102(f332(f332(f201(f31(x59841,x59843)),x59842),x59844)) % 172.78/172.49 [6076]~P25(x60761)+~E(x60762,f2(x60761))+E(f332(f332(f38(x60761),f332(f332(f80(x60761),x60762),x60763)),f332(f332(f80(x60761),x60762),x60764)),f2(x60761)) % 172.78/172.49 [6114]E(x61141,f116(x61142))+E(x61143,f332(f332(f22(a876),f332(f196(f877(x61142)),x61141)),f77(a876)))+E(f144(x61142,f332(f332(f159(x61142,x61141),x61143),x61144)),f144(x61142,x61141)) % 172.78/172.49 [6142]E(x61421,x61422)+P102(f332(x61423,x61422))+~P102(f332(f332(f332(f310(x61424),x61421),x61423),x61422)) % 172.78/172.49 [6158]~P71(x61581)+~P102(f332(f137(x61582),x61584))+E(f332(f166(x61581),f332(f332(f154(x61582,x61581),x61583),x61584)),f332(f332(f6(x61582,x61581),x61583),f332(f173(x61582),x61584))) % 172.78/172.49 [6176]~P67(x61762)+~P102(f332(f61(x61761),x61764))+E(f332(f332(f9(x61761,x61762),f332(f16(x61762,x61761),x61763)),x61764),f332(f332(f257(x61762),x61763),f332(f37(x61761),x61764))) % 172.78/172.49 [6231]~P57(x62312)+E(x62311,f2(x62312))+E(f332(f332(f290(x62312),f332(f332(f80(x62312),x62313),x62311)),f332(f332(f80(x62312),x62314),x62311)),f332(f332(f290(x62312),x62313),x62314)) % 172.78/172.49 [6232]~P57(x62322)+E(x62321,f2(x62322))+E(f332(f332(f290(x62322),f332(f332(f80(x62322),x62321),x62323)),f332(f332(f80(x62322),x62321),x62324)),f332(f332(f290(x62322),x62323),x62324)) % 172.78/172.49 [6233]~P25(x62332)+E(x62331,f2(x62332))+E(f332(f332(f38(x62332),f332(f332(f80(x62332),x62333),x62331)),f332(f332(f80(x62332),x62334),x62331)),f332(f332(f38(x62332),x62333),x62334)) % 172.78/172.49 [6235]~P25(x62352)+E(x62351,f2(x62352))+E(f332(f332(f38(x62352),f332(f332(f80(x62352),x62351),x62353)),f332(f332(f80(x62352),x62351),x62354)),f332(f332(f38(x62352),x62353),x62354)) % 172.78/172.49 [6298]P102(f332(x62981,x62982))+~E(x62983,f332(f332(f79(a876),x62984),x62982))+~P102(f332(x62981,f332(f332(f22(a876),x62983),x62984))) % 172.78/172.49 [6379]P22(x63791,x63792,x63793)+P30(x63791,f566(x63793,x63792,x63791),x63794)+~P102(f332(f332(f334(f875(x63791)),x63794),x63792)) % 172.78/172.49 [6381]~P102(f332(x63812,x63813))+~P102(f332(f160(x63811,x63812),x63814))+P102(f332(f160(x63811,x63812),f332(f332(f151(x63811),x63813),x63814))) % 172.78/172.49 [6421]E(x64211,f116(x64212))+~E(x64213,f332(f332(f22(a876),f332(f196(f877(x64212)),x64211)),f77(a876)))+E(f144(x64212,f332(f332(f159(x64212,x64211),x64213),x64214)),x64214) % 172.78/172.49 [6444]~P97(x64441)+~P102(f332(f332(f247(x64441),x64442),x64444))+P102(f332(f332(f247(x64441),x64442),f332(f332(f113(x64441),x64443),x64444))) % 172.78/172.49 [6445]~P97(x64451)+~P102(f332(f332(f247(x64451),x64452),x64453))+P102(f332(f332(f247(x64451),x64452),f332(f332(f113(x64451),x64453),x64454))) % 172.78/172.49 [6447]~P104(x64471)+~P102(f332(f332(f247(x64471),x64472),x64474))+P102(f332(f332(f247(x64471),x64472),f332(f332(f245(x64471),x64473),x64474))) % 172.78/172.49 [6449]~P104(x64491)+~P102(f332(f332(f247(x64491),x64492),x64493))+P102(f332(f332(f247(x64491),x64492),f332(f332(f245(x64491),x64493),x64494))) % 172.78/172.49 [6450]~P97(x64501)+~P102(f332(f332(f246(x64501),x64502),x64504))+P102(f332(f332(f246(x64501),x64502),f332(f332(f113(x64501),x64503),x64504))) % 172.78/172.49 [6451]~P97(x64511)+~P102(f332(f332(f246(x64511),x64512),x64513))+P102(f332(f332(f246(x64511),x64512),f332(f332(f113(x64511),x64513),x64514))) % 172.78/172.49 [6453]~P104(x64531)+~P102(f332(f332(f246(x64531),x64532),x64534))+P102(f332(f332(f246(x64531),x64532),f332(f332(f245(x64531),x64533),x64534))) % 172.78/172.49 [6455]~P104(x64551)+~P102(f332(f332(f246(x64551),x64552),x64553))+P102(f332(f332(f246(x64551),x64552),f332(f332(f245(x64551),x64553),x64554))) % 172.78/172.49 [6540]~E(f332(f332(f165(x65401),x65402),x65403),x65404)+E(f332(f332(f159(x65401,x65402),x65403),x65404),x65402)+~P102(f332(f332(f247(a876),x65403),f332(f196(f877(x65401)),x65402))) % 172.78/172.49 [6557]E(x65571,x65572)+P102(f332(x65573,x65571))+~P102(f332(f332(f201(f31(x65573,x65574)),x65571),x65572)) % 172.78/172.49 [6581]P102(f332(x65811,x65812))+~P102(f332(x65813,x65812))+~P102(f332(f332(f246(f883(x65814,a871)),x65813),x65811)) % 172.78/172.49 [6613]~E(f332(f332(f159(x66131,x66132),x66133),x66134),x66132)+E(f332(f332(f165(x66131),x66132),x66133),x66134)+~P102(f332(f332(f247(a876),x66133),f332(f196(f877(x66131)),x66132))) % 172.78/172.49 [6628]~P102(f332(f160(x66281,x66282),x66284))+~P102(f332(f160(x66281,x66282),x66283))+P102(f332(f160(x66281,x66282),f332(f332(f134(x66281),x66283),x66284))) % 172.78/172.49 [6724]P30(x67241,x67242,x67243)+~P30(x67241,f332(a115,x67242),f567(x67242,x67244,x67241))+~P102(f332(f332(f334(f875(x67241)),x67243),x67244)) % 172.78/172.49 [6733]E(x67331,f195(f883(x67332,a871)))+E(x67333,f195(f883(x67334,a871)))+~E(f332(f332(f269(x67334,x67332),x67333),f332(f16(f883(x67332,a871),x67334),x67331)),f195(f883(f882(x67334,x67332),a871))) % 172.78/172.49 [6752]E(x67521,x67522)+P102(f332(f332(f334(x67523),x67521),x67524))+~P102(f332(f332(f334(x67523),x67521),f332(f332(f310(x67523),x67522),x67524))) % 172.78/172.49 [6768]~P104(x67681)+P102(f332(f332(f247(x67681),x67682),x67683))+~P102(f332(f332(f247(x67681),x67682),f332(f332(f244(x67681),x67684),x67683))) % 172.78/172.49 [6769]~P104(x67691)+P102(f332(f332(f247(x67691),x67692),x67693))+~P102(f332(f332(f247(x67691),x67692),f332(f332(f244(x67691),x67693),x67694))) % 172.78/172.49 [6771]~P98(x67711)+P102(f332(f332(f246(x67711),x67712),x67713))+~P102(f332(f332(f246(x67711),x67712),f332(f332(f104(x67711),x67714),x67713))) % 172.78/172.49 [6773]~P98(x67731)+P102(f332(f332(f246(x67731),x67732),x67733))+~P102(f332(f332(f246(x67731),x67732),f332(f332(f104(x67731),x67733),x67734))) % 172.78/172.49 [6775]~P104(x67751)+P102(f332(f332(f246(x67751),x67752),x67753))+~P102(f332(f332(f246(x67751),x67752),f332(f332(f244(x67751),x67754),x67753))) % 172.78/172.49 [6777]~P104(x67771)+P102(f332(f332(f246(x67771),x67772),x67773))+~P102(f332(f332(f246(x67771),x67772),f332(f332(f244(x67771),x67773),x67774))) % 172.78/172.49 [6799]~E(f332(f332(f165(x67991),x67993),x67994),x67992)+P102(f332(f332(f334(x67991),x67992),f332(f173(x67991),x67993)))+~P102(f332(f332(f247(a876),x67994),f332(f196(f877(x67991)),x67993))) % 172.78/172.49 [6811]~P104(x68111)+~P29(x68111,f332(f332(f151(x68111),x68112),f332(f332(f151(x68111),x68113),x68114)))+P102(f332(f332(f246(x68111),x68112),x68113)) % 172.78/172.49 [6953]~P32(x69532,x69531,x69533)+P102(f332(x69531,f332(f332(f165(x69532),x69533),x69534)))+~P102(f332(f332(f247(a876),x69534),f332(f196(f877(x69532)),x69533))) % 172.78/172.49 [6972]E(x69721,f2(a1))+E(f332(f332(f38(a1),x69722),x69721),x69723)+~P102(f332(f48(x69722,x69721),f332(f332(f267(a1,a1),x69723),x69724))) % 172.78/172.49 [6993]E(f44(a1,x69932,x69931),x69933)+E(x69931,f2(a1))+~P102(f332(f48(x69932,x69931),f332(f332(f267(a1,a1),x69934),x69933))) % 172.78/172.49 [7111]P102(f332(f332(f334(x71111),x71112),x71113))+~P102(f332(f332(f334(x71111),x71112),x71114))+~P102(f332(f332(f247(f883(x71111,a871)),x71114),x71113)) % 172.78/172.49 [7115]P102(f332(f332(f334(x71151),x71152),x71153))+~P102(f332(f332(f334(x71151),x71152),x71154))+~P102(f332(f332(f246(f883(x71151,a871)),x71154),x71153)) % 172.78/172.49 [7223]P34(x72231,x72232,x72233)+~P102(f332(x72232,f332(f332(f165(x72231),x72233),x72234)))+~P102(f332(f332(f247(a876),x72234),f332(f196(f877(x72231)),x72233))) % 172.78/172.49 [7334]~P106(x73342)+~P102(f332(f332(f247(f883(x73341,x73342)),x73343),x73344))+P102(f332(f332(f246(f883(x73341,x73342)),x73343),x73344)) % 172.78/172.49 [7421]~P19(x74211,x74212,x74214)+P19(x74211,x74212,f332(f332(f310(f875(x74211)),x74213),x74214))+~P19(x74211,x74212,f332(f332(f310(f875(x74211)),x74213),f195(f883(f875(x74211),a871)))) % 172.78/172.49 [7466]~P102(f332(f332(f334(x74661),x74662),x74664))+P102(f332(f332(f334(x74661),x74662),f39(f883(x74661,a871),x74663)))+~P102(f332(f332(f334(f883(x74661,a871)),x74664),x74663)) % 172.78/172.49 [7478]P30(x74781,x74782,x74783)+P102(f332(f332(f334(f875(x74781)),f567(x74782,x74784,x74781)),x74784))+~P102(f332(f332(f334(f875(x74781)),x74783),x74784)) % 172.78/172.49 [7498]~P78(x74981)+~P102(f332(f332(f247(x74981),x74983),x74984))+P102(f332(f332(f247(x74981),f332(f332(f79(x74981),x74982),x74983)),f332(f332(f79(x74981),x74982),x74984))) % 172.78/172.49 [7499]~P82(x74991)+~P102(f332(f332(f247(x74991),x74993),x74994))+P102(f332(f332(f247(x74991),f332(f332(f79(x74991),x74992),x74993)),f332(f332(f79(x74991),x74992),x74994))) % 172.78/172.49 [7500]~P78(x75001)+~P102(f332(f332(f247(x75001),x75002),x75004))+P102(f332(f332(f247(x75001),f332(f332(f79(x75001),x75002),x75003)),f332(f332(f79(x75001),x75004),x75003))) % 172.78/172.49 [7501]~P82(x75011)+~P102(f332(f332(f247(x75011),x75012),x75014))+P102(f332(f332(f247(x75011),f332(f332(f79(x75011),x75012),x75013)),f332(f332(f79(x75011),x75014),x75013))) % 172.78/172.49 [7502]~P78(x75021)+~P102(f332(f332(f246(x75021),x75023),x75024))+P102(f332(f332(f246(x75021),f332(f332(f79(x75021),x75022),x75023)),f332(f332(f79(x75021),x75022),x75024))) % 172.78/172.49 [7503]~P80(x75031)+~P102(f332(f332(f246(x75031),x75033),x75034))+P102(f332(f332(f246(x75031),f332(f332(f79(x75031),x75032),x75033)),f332(f332(f79(x75031),x75032),x75034))) % 172.78/172.49 [7504]~P78(x75041)+~P102(f332(f332(f246(x75041),x75042),x75044))+P102(f332(f332(f246(x75041),f332(f332(f79(x75041),x75042),x75043)),f332(f332(f79(x75041),x75044),x75043))) % 172.78/172.49 [7505]~P80(x75051)+~P102(f332(f332(f246(x75051),x75052),x75054))+P102(f332(f332(f246(x75051),f332(f332(f79(x75051),x75052),x75053)),f332(f332(f79(x75051),x75054),x75053))) % 172.78/172.49 [7514]~P123(x75141)+~P90(x75141)+E(f332(f332(f22(x75141),f332(f332(f80(x75141),x75142),f332(f106(x75141),x75143))),f332(f332(f80(x75141),x75144),f332(f106(x75141),x75143))),f332(f332(f80(x75141),f332(f332(f22(x75141),x75142),x75144)),f332(f106(x75141),x75143))) % 172.78/172.49 [7515]~P122(x75151)+~P90(x75151)+E(f332(f332(f79(x75151),f332(f332(f80(x75151),x75152),f332(f106(x75151),x75153))),f332(f332(f80(x75151),x75154),f332(f106(x75151),x75153))),f332(f332(f80(x75151),f332(f332(f79(x75151),x75152),x75154)),f332(f106(x75151),x75153))) % 172.78/172.49 [7551]~P71(x75511)+E(f332(f332(f79(x75511),f332(x75512,x75513)),f332(f332(f6(a876,x75511),x75512),f303(a876,f332(a115,x75513),x75514))),f332(f332(f6(a876,x75511),x75512),f303(a876,x75513,x75514)))+~P102(f332(f332(f246(a876),x75513),x75514)) % 172.78/172.49 [7562]~P20(x75622,x75621,x75623,f332(f173(x75622),x75624))+~P102(f332(f137(x75622),x75624))+P102(f332(f137(x75621),f332(f332(f154(x75622,x75621),x75623),x75624))) % 172.78/172.49 [7611]~P102(f332(f332(f247(a876),x76112),x76114))+~P102(f332(f332(f247(a876),x76111),x76113))+P102(f332(f332(f247(a876),f332(f332(f79(a876),x76111),x76112)),f332(f332(f79(a876),x76113),x76114))) % 172.78/172.49 [7612]~P102(f332(f332(f247(a1),x76121),x76123))+~P102(f332(f332(f246(a1),x76122),x76124))+P102(f332(f332(f247(a1),f332(f332(f79(a1),x76121),x76122)),f332(f332(f79(a1),x76123),x76124))) % 172.78/172.49 [7613]~P102(f332(f332(f246(a876),x76132),x76134))+~P102(f332(f332(f246(a876),x76131),x76133))+P102(f332(f332(f246(a876),f332(f332(f80(a876),x76131),x76132)),f332(f332(f80(a876),x76133),x76134))) % 172.78/172.49 [7614]~P102(f332(f332(f246(a876),x76142),x76144))+~P102(f332(f332(f246(a876),x76141),x76143))+P102(f332(f332(f246(a876),f332(f332(f79(a876),x76141),x76142)),f332(f332(f79(a876),x76143),x76144))) % 172.78/172.49 [7662]P102(f332(f332(f334(x76621),x76622),x76623))+~P102(f332(f332(f334(x76621),x76622),f40(f883(x76621,a871),x76624)))+~P102(f332(f332(f334(f883(x76621,a871)),x76623),x76624)) % 172.78/172.49 [7678]~P102(f332(x76781,f680(x76781,x76783,x76782)))+P102(f332(x76781,f332(f332(f165(x76782),x76783),x76784)))+~P102(f332(f332(f247(a876),x76784),f332(f196(f877(x76782)),x76783))) % 172.78/172.49 [7684]P102(f332(x76841,x76842))+~P102(f332(f332(f334(x76844),x76842),f332(f173(x76844),x76843)))+P102(f332(f332(f247(a876),f683(x76841,x76843,x76844)),f332(f196(f877(x76844)),x76843))) % 172.83/172.49 [7704]~P102(f332(f332(f201(x77042),x77043),x77044))+~P102(f332(f332(f201(f31(x77041,x77042)),x77044),x77043))+P102(f332(f332(f201(f31(x77041,x77042)),x77043),x77043)) % 172.83/172.49 [7733]~P106(x77331)+~P102(f332(f332(f246(f883(x77332,x77331)),x77334),x77333))+~P102(f332(f332(f247(f883(x77332,x77331)),x77333),x77334)) % 172.83/172.49 [7781]~P102(f332(x77814,x77812))+~P102(f332(f332(f334(x77811),x77812),x77813))+P102(f332(f332(f334(x77811),x77812),f332(f332(f104(f883(x77811,a871)),x77813),f332(f252(x77811),x77814)))) % 172.83/172.49 [7926]~P102(f332(f332(f334(x79261),x79263),x79264))+~P102(f332(f332(f247(f883(x79261,a871)),x79262),x79264))+P102(f332(f332(f247(f883(x79261,a871)),x79262),f332(f332(f310(x79261),x79263),x79264))) % 172.83/172.49 [7928]E(f332(f332(f104(f883(x79281,a871)),x79282),x79283),f195(f883(x79281,a871)))+~E(f332(f332(f104(f883(x79281,a871)),f39(f883(x79281,a871),x79284)),x79283),f195(f883(x79281,a871)))+~P102(f332(f332(f334(f883(x79281,a871)),x79282),x79284)) % 172.83/172.49 [8005]P102(f332(f332(f334(x80051),x80052),x80053))+~P102(f332(f332(f246(f883(x80051,a871)),x80053),f332(f332(f310(x80051),x80052),x80054)))+P102(f332(f332(f246(f883(x80051,a871)),x80053),x80054)) % 172.83/172.49 [8027]P102(f332(f332(f334(x80272),f680(x80271,x80273,x80272)),f332(f173(x80272),x80273)))+P102(f332(x80271,f332(f332(f165(x80272),x80273),x80274)))+~P102(f332(f332(f247(a876),x80274),f332(f196(f877(x80272)),x80273))) % 172.83/172.49 [8035]~P102(f332(f332(f247(f883(x80351,a871)),x80352),x80354))+P102(f332(f332(f247(f883(x80351,a871)),x80352),x80353))+~P102(f332(f332(f247(f883(x80351,a871)),x80354),x80353)) % 172.83/172.49 [8036]~P102(f332(f332(f246(f883(x80361,a871)),x80362),x80364))+P102(f332(f332(f247(f883(x80361,a871)),x80362),x80363))+~P102(f332(f332(f247(f883(x80361,a871)),x80364),x80363)) % 172.83/172.49 [8037]~P102(f332(f332(f246(f883(x80371,a871)),x80374),x80373))+~P102(f332(f332(f247(f883(x80371,a871)),x80372),x80374))+P102(f332(f332(f247(f883(x80371,a871)),x80372),x80373)) % 172.83/172.49 [8038]~P102(f332(f332(f246(f883(x80381,a871)),x80382),x80384))+P102(f332(f332(f246(f883(x80381,a871)),x80382),x80383))+~P102(f332(f332(f246(f883(x80381,a871)),x80384),x80383)) % 172.83/172.49 [8078]~P102(f332(f332(f334(x80781),x80784),x80783))+~P102(f332(f332(f247(f883(x80781,a871)),x80782),f332(f332(f310(x80781),x80784),x80783)))+P102(f332(f332(f247(f883(x80781,a871)),x80782),x80783)) % 172.83/172.49 [8090]~P78(x80901)+P102(f332(f332(f247(x80901),x80902),x80903))+~P102(f332(f332(f247(x80901),f332(f332(f79(x80901),x80904),x80902)),f332(f332(f79(x80901),x80904),x80903))) % 172.83/172.49 [8092]~P78(x80921)+P102(f332(f332(f247(x80921),x80922),x80923))+~P102(f332(f332(f247(x80921),f332(f332(f79(x80921),x80922),x80924)),f332(f332(f79(x80921),x80923),x80924))) % 172.83/172.49 [8094]~P78(x80941)+P102(f332(f332(f246(x80941),x80942),x80943))+~P102(f332(f332(f246(x80941),f332(f332(f79(x80941),x80944),x80942)),f332(f332(f79(x80941),x80944),x80943))) % 172.83/172.49 [8096]~P78(x80961)+P102(f332(f332(f246(x80961),x80962),x80963))+~P102(f332(f332(f246(x80961),f332(f332(f79(x80961),x80962),x80964)),f332(f332(f79(x80961),x80963),x80964))) % 172.83/172.49 [8145]P102(f332(x81451,x81452))+~E(f332(f332(f138(x81453),f332(f196(f877(x81453)),f178(x81453,x81451,x81454))),x81454),f116(x81453))+~P102(f332(f332(f334(x81453),x81452),f332(f173(x81453),x81454))) % 172.83/172.49 [8271]P102(f332(x82711,x82712))+~P102(f332(f332(f334(x82713),x82712),f332(f173(x82713),x82714)))+P102(f332(f332(f247(a876),f332(f196(f877(x82713)),f332(f136(x82713,x82711),x82714))),f332(f196(f877(x82713)),x82714))) % 172.83/172.49 [8398]E(x83981,x83982)+P102(f332(f332(f201(x83983),x83981),f354(x83982,x83981,x83983,x83984)))+~P102(f332(f332(f201(f31(x83984,x83983)),x83981),x83982)) % 172.83/172.49 [8429]~P102(f332(x84294,x84292))+P102(f332(f332(f201(x84291),x84292),f354(x84293,x84292,x84291,x84294)))+~P102(f332(f332(f201(f31(x84294,x84291)),x84292),x84293)) % 172.83/172.49 [8745]~P102(f332(x87451,f782(x87451,x87453,x87452,x87454)))+P102(f332(x87451,f332(f332(f165(x87452),x87453),x87454)))+~P102(f332(f332(f247(a876),x87454),f332(f196(f877(x87452)),x87453))) % 172.83/172.49 [8768]~P20(x87684,x87683,x87681,f255(f883(x87684,a871)))+E(f332(x87681,f518(x87682,x87681,x87683,x87684)),x87682)+~P102(f332(f332(f334(x87683),x87682),f332(f311(x87684,x87683,x87681),f255(f883(x87684,a871))))) % 172.83/172.49 [8834]E(f178(x88341,x88342,x88343),f332(f332(f176(x88341),x88344),x88343))+P102(f332(f332(f247(a876),f759(x88342,x88343,x88341,x88344)),x88344))+P102(f332(f332(f247(a876),x88344),f332(f196(f877(x88341)),x88343))) % 172.83/172.49 [8837]E(f178(x88371,x88372,x88373),f332(f332(f176(x88371),x88374),x88373))+P102(f332(f332(f247(a876),f759(x88372,x88373,x88371,x88374)),x88374))+P102(f332(x88372,f332(f332(f165(x88371),x88373),x88374))) % 172.83/172.49 [8866]P102(f332(x88661,x88662))+~P102(f332(f332(f334(x88664),x88662),f332(f173(x88664),x88663)))+P102(f332(f332(f247(a876),f738(x88662,x88661,x88663,x88664)),f332(f196(f877(x88664)),x88663))) % 172.83/172.49 [8869]E(f178(x88691,x88692,x88693),f332(f332(f176(x88691),x88694),x88693))+P102(f332(f332(f247(a876),x88694),f332(f196(f877(x88691)),x88693)))+P102(f332(f332(f247(a876),f759(x88692,x88693,x88691,x88694)),f332(f196(f877(x88691)),x88693))) % 172.83/172.49 [8876]E(f178(x88761,x88762,x88763),f332(f332(f176(x88761),x88764),x88763))+P102(f332(x88762,f332(f332(f165(x88761),x88763),x88764)))+P102(f332(f332(f247(a876),f759(x88762,x88763,x88761,x88764)),f332(f196(f877(x88761)),x88763))) % 172.83/172.49 [8903]~P107(x89034)+P102(f332(f332(f334(x89031),f666(x89032,x89033,x89031,x89034)),x89033))+P102(f332(f332(f247(x89034),f2(x89034)),f332(f332(f9(x89031,x89034),x89032),x89033))) % 172.83/172.49 [8904]~P107(x89044)+P102(f332(f332(f334(x89041),f667(x89042,x89043,x89041,x89044)),x89043))+P102(f332(f332(f246(x89044),f2(x89044)),f332(f332(f9(x89041,x89044),x89042),x89043))) % 172.83/172.49 [8938]~P102(f332(f61(x89381),x89384))+P102(f332(f332(f334(x89381),f540(x89382,x89383,x89384,x89381)),x89384))+P102(f332(f61(f882(x89381,x89383)),f332(f332(f269(x89381,x89383),x89384),x89382))) % 172.83/172.49 [8972]P102(f332(f332(f334(x89722),f782(x89721,x89723,x89722,x89724)),f332(f173(x89722),x89723)))+P102(f332(x89721,f332(f332(f165(x89722),x89723),x89724)))+~P102(f332(f332(f247(a876),x89724),f332(f196(f877(x89722)),x89723))) % 172.83/172.49 [8987]E(x89871,x89872)+P102(f332(f332(f201(f31(x89873,x89874)),f354(x89871,x89872,x89874,x89873)),x89871))+~P102(f332(f332(f201(f31(x89873,x89874)),x89872),x89871)) % 172.83/172.49 [9007]~P102(f332(x90071,x90074))+P102(f332(f332(f201(f31(x90071,x90072)),f354(x90073,x90074,x90072,x90071)),x90073))+~P102(f332(f332(f201(f31(x90071,x90072)),x90074),x90073)) % 172.83/172.49 [9102]P102(f332(f332(f246(a876),x91024),f332(f196(f877(x91022)),f178(x91022,x91023,x91021))))+P102(f332(f332(f247(a876),f760(x91021,x91022,x91023,x91024)),x91024))+~P102(f332(f332(f246(a876),x91024),f332(f196(f877(x91022)),x91021))) % 172.83/172.49 [9206]~E(f332(f332(f179(x92061,x92062),x92063),f771(x92064,x92063,x92062,x92061)),f332(f332(f179(x92061,x92062),x92064),f771(x92064,x92063,x92062,x92061)))+E(f332(f179(x92061,x92062),x92063),f332(f179(x92061,x92062),x92064))+~E(f332(f173(x92061),f332(f332(f154(f882(x92061,x92062),x92061),f266(x92061,x92062)),x92063)),f332(f173(x92061),f332(f332(f154(f882(x92061,x92062),x92061),f266(x92061,x92062)),x92064))) % 172.83/172.49 [9252]E(f178(x92521,x92522,x92523),f332(f332(f176(x92521),x92524),x92523))+~P102(f332(x92522,f332(f332(f165(x92521),x92523),f759(x92522,x92523,x92521,x92524))))+P102(f332(f332(f247(a876),x92524),f332(f196(f877(x92521)),x92523))) % 172.83/172.49 [9256]E(f178(x92561,x92562,x92563),f332(f332(f176(x92561),x92564),x92563))+~P102(f332(x92562,f332(f332(f165(x92561),x92563),f759(x92562,x92563,x92561,x92564))))+P102(f332(x92562,f332(f332(f165(x92561),x92563),x92564))) % 172.83/172.49 [9263]~P102(f332(f61(x92631),x92633))+~P102(f332(f61(x92632),f332(x92634,f540(x92634,x92632,x92633,x92631))))+P102(f332(f61(f882(x92631,x92632)),f332(f332(f269(x92631,x92632),x92633),x92634))) % 172.83/172.49 [9271]~P107(x92711)+~P102(f332(f332(f247(x92711),f2(x92711)),f332(x92713,f666(x92713,x92714,x92712,x92711))))+P102(f332(f332(f247(x92711),f2(x92711)),f332(f332(f9(x92712,x92711),x92713),x92714))) % 172.83/172.49 [9272]~P107(x92721)+~P102(f332(f332(f246(x92721),f2(x92721)),f332(x92723,f667(x92723,x92724,x92722,x92721))))+P102(f332(f332(f246(x92721),f2(x92721)),f332(f332(f9(x92722,x92721),x92723),x92724))) % 172.83/172.49 [9278]~E(f332(f196(f877(x92784)),x92782),f332(f196(f877(x92784)),x92783))+P102(f332(f332(f334(f882(f877(x92784),f877(x92784))),f332(f332(f267(f877(x92784),f877(x92784)),x92783),x92782)),f158(x92784,x92781)))+P102(f332(f332(f247(a876),f670(x92781,x92782,x92783,x92784)),f332(f196(f877(x92784)),x92783))) % 172.83/172.49 [9332]~P102(f332(x93323,f332(f332(f165(x93322),x93324),f760(x93324,x93322,x93323,x93321))))+P102(f332(f332(f246(a876),x93321),f332(f196(f877(x93322)),f178(x93322,x93323,x93324))))+~P102(f332(f332(f246(a876),x93321),f332(f196(f877(x93322)),x93324))) % 172.83/172.49 [9409]E(f332(f332(f176(x94091),f681(x94092,x94093,x94094,x94091)),x94093),f332(f332(f176(x94091),f681(x94092,x94093,x94094,x94091)),x94094))+~P102(f332(f332(f334(f882(f877(x94091),f877(x94091))),f332(f332(f267(f877(x94091),f877(x94091)),x94094),x94093)),f147(x94091,x94092)))+P102(f332(f332(f247(a876),f332(f196(f877(x94091)),x94094)),f332(f196(f877(x94091)),x94093))) % 172.83/172.49 [9463]~P102(f332(f332(f247(a876),f2(a876)),x94633))+~P102(f332(f332(f247(a876),x94634),x94631))+P102(f332(f332(f247(a876),f332(f332(f79(a876),f332(f332(f80(a876),x94631),f44(a876,x94632,x94633))),x94634)),f332(f332(f80(a876),x94631),x94633))) % 172.83/172.49 [9654]~P106(x96542)+~P102(f332(f332(f246(x96542),f332(x96543,f836(x96544,x96543,x96541,x96542))),f332(x96544,f836(x96544,x96543,x96541,x96542))))+P102(f332(f332(f246(f883(x96541,x96542)),x96543),x96544)) % 172.83/172.49 [9757]~P66(x97571)+E(f332(f332(f6(a876,x97571),f332(f332(f18(a876,x97571,x97571),f332(f332(f8(x97571,f883(x97571,x97571),a876),f22(x97571)),x97572)),f332(f332(f8(a876,x97571,a876),x97572),f332(f332(f7(a876,a876,a876),f79(a876)),f77(a876))))),f303(a876,x97573,x97574)),f332(f332(f22(x97571),f332(x97572,x97573)),f332(x97572,f332(f332(f79(a876),x97574),f77(a876)))))+~P102(f332(f332(f246(a876),x97573),x97574)) % 172.83/172.49 [6803]E(f332(f332(f134(x68031),x68032),x68033),x68034)+~E(x68033,f332(f332(f138(x68031),f332(f196(f877(x68031)),x68032)),x68034))+~E(f332(f332(f176(x68031),f332(f196(f877(x68031)),x68032)),x68034),x68032) % 172.83/172.49 [6859]~P58(x68592)+E(x68591,f2(x68592))+E(f332(f332(f290(x68592),f332(f332(f257(x68592),x68593),x68594)),f332(f332(f257(x68592),x68591),x68594)),f332(f332(f257(x68592),f332(f332(f290(x68592),x68593),x68591)),x68594)) % 172.83/172.49 [6995]~E(f332(f196(f877(x69951)),x69953),f332(f196(f877(x69952)),x69954))+~P102(f332(f137(x69951),x69953))+E(f185(x69951,x69952,f332(f179(x69951,x69952),f332(f332(f183(x69951,x69952),x69953),x69954))),f332(f173(x69951),x69953)) % 172.83/172.49 [7014]~P98(x70141)+~P102(f332(f332(f247(x70141),x70143),x70144))+P102(f332(f332(f247(x70141),f332(f332(f104(x70141),x70142),x70143)),x70144)) % 172.83/172.49 [7015]~P98(x70151)+~P102(f332(f332(f247(x70151),x70152),x70154))+P102(f332(f332(f247(x70151),f332(f332(f104(x70151),x70152),x70153)),x70154)) % 172.83/172.49 [7017]~P104(x70171)+~P102(f332(f332(f247(x70171),x70173),x70174))+P102(f332(f332(f247(x70171),f332(f332(f244(x70171),x70172),x70173)),x70174)) % 172.83/172.49 [7019]~P104(x70191)+~P102(f332(f332(f247(x70191),x70192),x70194))+P102(f332(f332(f247(x70191),f332(f332(f244(x70191),x70192),x70193)),x70194)) % 172.83/172.49 [7020]~P98(x70201)+~P102(f332(f332(f246(x70201),x70203),x70204))+P102(f332(f332(f246(x70201),f332(f332(f104(x70201),x70202),x70203)),x70204)) % 172.83/172.49 [7021]~P98(x70211)+~P102(f332(f332(f246(x70211),x70212),x70214))+P102(f332(f332(f246(x70211),f332(f332(f104(x70211),x70212),x70213)),x70214)) % 172.83/172.49 [7023]~P104(x70231)+~P102(f332(f332(f246(x70231),x70233),x70234))+P102(f332(f332(f246(x70231),f332(f332(f244(x70231),x70232),x70233)),x70234)) % 172.83/172.49 [7025]~P104(x70251)+~P102(f332(f332(f246(x70251),x70252),x70254))+P102(f332(f332(f246(x70251),f332(f332(f244(x70251),x70252),x70253)),x70254)) % 172.83/172.49 [7045]~P102(f332(x70453,x70454))+~P102(f332(x70452,x70454))+P102(f332(f332(f332(f104(f883(x70451,a871)),x70452),x70453),x70454)) % 172.83/172.49 [7169]P19(x71691,x71692,x71693)+~P19(x71691,x71694,x71693)+~P102(f332(f332(f246(f883(f875(x71691),a871)),x71694),x71692)) % 172.83/172.49 [7170]P19(x71701,x71702,x71703)+~P19(x71701,x71702,x71704)+~P102(f332(f332(f246(f883(f875(x71701),a871)),x71703),x71704)) % 172.83/172.49 [7541]~P71(x75411)+E(f332(f332(f79(x75411),f332(x75412,x75413)),f332(f332(f6(a876,x75411),x75412),f332(f302(a876,f332(a115,x75413)),x75414))),f332(f332(f6(a876,x75411),x75412),f332(f302(a876,x75413),x75414)))+~P102(f332(f332(f247(a876),x75413),x75414)) % 172.83/172.49 [7569]~P104(x75691)+P102(f332(f332(f247(x75691),x75692),x75693))+~P102(f332(f332(f247(x75691),f332(f332(f245(x75691),x75694),x75692)),x75693)) % 172.83/172.49 [7570]~P104(x75701)+P102(f332(f332(f247(x75701),x75702),x75703))+~P102(f332(f332(f247(x75701),f332(f332(f245(x75701),x75702),x75704)),x75703)) % 172.83/172.49 [7572]~P97(x75721)+P102(f332(f332(f246(x75721),x75722),x75723))+~P102(f332(f332(f246(x75721),f332(f332(f113(x75721),x75724),x75722)),x75723)) % 172.83/172.49 [7574]~P97(x75741)+P102(f332(f332(f246(x75741),x75742),x75743))+~P102(f332(f332(f246(x75741),f332(f332(f113(x75741),x75742),x75744)),x75743)) % 172.83/172.49 [7576]~P104(x75761)+P102(f332(f332(f246(x75761),x75762),x75763))+~P102(f332(f332(f246(x75761),f332(f332(f245(x75761),x75764),x75762)),x75763)) % 172.83/172.49 [7578]~P104(x75781)+P102(f332(f332(f246(x75781),x75782),x75783))+~P102(f332(f332(f246(x75781),f332(f332(f245(x75781),x75782),x75784)),x75783)) % 172.83/172.49 [7654]~P102(f332(f332(f334(x76541),x76542),x76544))+P102(f332(f332(f334(x76541),x76542),x76543))+P102(f332(f332(f334(x76541),x76542),f332(f332(f22(f883(x76541,a871)),x76544),x76543))) % 172.83/172.49 [7740]P102(f332(x77401,x77402))+P102(f332(x77403,x77402))+~P102(f332(f332(f332(f113(f883(x77404,a871)),x77403),x77401),x77402)) % 172.83/172.49 [7751]~P102(f332(f332(f334(x77511),x77512),x77514))+~P102(f332(f332(f334(x77511),x77512),x77513))+P102(f332(f332(f334(x77511),x77512),f332(f332(f104(f883(x77511,a871)),x77513),x77514))) % 172.83/172.49 [7805]~P97(x78051)+~P102(f332(f61(x78051),x78054))+E(f332(f332(f64(x78051,x78051,f113(x78051)),x78052),f332(f332(f310(x78051),x78053),x78054)),f332(f332(f113(x78051),x78053),f332(f332(f64(x78051,x78051,f113(x78051)),x78052),x78054))) % 172.83/172.49 [7806]~P98(x78061)+~P102(f332(f61(x78061),x78064))+E(f332(f332(f64(x78061,x78061,f104(x78061)),x78062),f332(f332(f310(x78061),x78063),x78064)),f332(f332(f104(x78061),x78063),f332(f332(f64(x78061,x78061,f104(x78061)),x78062),x78064))) % 172.83/172.49 [7807]~P104(x78071)+~P102(f332(f61(x78071),x78074))+E(f332(f332(f64(x78071,x78071,f244(x78071)),x78072),f332(f332(f310(x78071),x78073),x78074)),f332(f332(f244(x78071),x78073),f332(f332(f64(x78071,x78071,f244(x78071)),x78072),x78074))) % 172.83/172.49 [7808]~P104(x78081)+~P102(f332(f61(x78081),x78084))+E(f332(f332(f64(x78081,x78081,f245(x78081)),x78082),f332(f332(f310(x78081),x78083),x78084)),f332(f332(f245(x78081),x78083),f332(f332(f64(x78081,x78081,f245(x78081)),x78082),x78084))) % 172.83/172.49 [7809]~P123(x78091)+~P90(x78091)+E(f332(f332(f22(x78091),f332(f332(f80(x78091),f332(f106(x78091),x78092)),x78093)),f332(f332(f80(x78091),f332(f106(x78091),x78092)),x78094)),f332(f332(f80(x78091),f332(f106(x78091),x78092)),f332(f332(f22(x78091),x78093),x78094))) % 172.83/172.49 [7810]~P122(x78101)+~P90(x78101)+E(f332(f332(f79(x78101),f332(f332(f80(x78101),f332(f106(x78101),x78102)),x78103)),f332(f332(f80(x78101),f332(f106(x78101),x78102)),x78104)),f332(f332(f80(x78101),f332(f106(x78101),x78102)),f332(f332(f79(x78101),x78103),x78104))) % 172.83/172.49 [7924]E(x79241,x79242)+P102(f332(f332(f334(x79243),x79241),f332(f173(x79243),x79244)))+~P102(f332(f332(f334(x79243),x79241),f332(f173(x79243),f332(f332(f151(x79243),x79242),x79244)))) % 172.83/172.49 [7949]~P56(x79491)+~E(f332(f196(f877(x79492)),x79493),f332(f196(f877(x79491)),f55(x79491)))+E(f332(f332(f179(x79491,x79492),f332(f332(f183(x79491,x79492),f55(x79491)),x79493)),x79494),f332(f239(x79492),f729(x79494,x79493,x79492,x79491))) % 172.83/172.49 [8103]P50(x81031,x81032,x81033)+~P50(x81031,x81032,x81034)+~P102(f332(f332(f246(f883(f882(x81031,x81032),a871)),x81033),x81034)) % 172.83/172.49 [8148]P102(f332(f332(f334(x81481),x81482),x81483))+P102(f332(f332(f334(x81481),x81482),x81484))+~P102(f332(f332(f334(x81481),x81482),f332(f332(f113(f883(x81481,a871)),x81484),x81483))) % 172.83/172.49 [8159]~P40(x81591,x81594,x81593)+~P102(f332(f332(f334(x81591),x81592),x81594))+P102(f332(f332(f334(f882(x81591,x81591)),f332(f332(f267(x81591,x81591),x81592),x81592)),x81593)) % 172.83/172.49 [8174]~P102(f332(f61(x81742),x81744))+~P102(f332(f61(x81741),x81743))+P102(f332(f61(f882(x81741,x81742)),f332(f332(f269(x81741,x81742),x81743),f332(f16(f883(x81742,a871),x81741),x81744)))) % 172.83/172.49 [8175]~P102(f332(f332(f334(x81751),x81752),x81754))+~P102(f332(f332(f246(f883(x81751,a871)),x81753),x81754))+P102(f332(f332(f246(f883(x81751,a871)),f332(f332(f310(x81751),x81752),x81753)),x81754)) % 172.83/172.49 [8183]~P67(x81832)+~P141(x81832)+E(f332(f332(f9(x81831,x81832),f332(f332(f8(a876,x81832,x81831),f103(x81832)),x81833)),x81834),f332(f103(x81832),f332(f332(f9(x81831,a876),x81833),x81834))) % 172.83/172.49 [8184]~P67(x81842)+~P137(x81842)+E(f332(f332(f9(x81841,x81842),f332(f332(f8(a1,x81842,x81841),f105(x81842)),x81843)),x81844),f332(f105(x81842),f332(f332(f9(x81841,a1),x81843),x81844))) % 172.83/172.49 [8210]E(f332(f332(f22(f883(x82101,a871)),x82102),f332(f332(f22(f883(x82101,a871)),x82103),x82104)),x82104)+~P102(f332(f332(f246(f883(x82101,a871)),x82102),x82103))+~P102(f332(f332(f246(f883(x82101,a871)),x82104),x82102)) % 172.83/172.49 [8305]~P102(f332(f61(x83051),x83054))+E(f332(f332(f22(a876),f332(f332(f6(x83051,a876),x83052),x83053)),f332(f332(f6(x83051,a876),x83052),x83054)),f332(f332(f6(x83051,a876),x83052),f332(f332(f22(f883(x83051,a871)),x83053),x83054)))+~P102(f332(f332(f246(f883(x83051,a871)),x83054),x83053)) % 172.83/172.49 [8463]~P3(x84631,x84634,x84633)+~P102(f332(f332(f334(x84631),x84632),x84634))+P102(f332(f332(f334(x84631),x84632),f332(f286(x84631,x84631,x84633),f332(f332(f310(x84631),x84632),f195(f883(x84631,a871)))))) % 172.83/172.49 [8525]~P102(f332(f332(f246(f883(x85251,a871)),x85252),x85253))+~P102(f332(f332(f246(f883(x85251,a871)),x85252),x85254))+P102(f332(f332(f246(f883(x85251,a871)),x85252),f332(f332(f104(f883(x85251,a871)),x85253),x85254))) % 172.83/172.49 [8621]E(x86211,f195(f883(x86212,a871)))+P102(f332(f61(x86213),x86214))+~P102(f332(f61(f882(x86213,x86212)),f332(f332(f269(x86213,x86212),x86214),f332(f16(f883(x86212,a871),x86213),x86211)))) % 172.83/172.49 [8622]E(x86221,f195(f883(x86222,a871)))+P102(f332(f61(x86223),x86224))+~P102(f332(f61(f882(x86222,x86223)),f332(f332(f269(x86222,x86223),x86221),f332(f16(f883(x86223,a871),x86222),x86224)))) % 172.83/172.49 [8688]P102(f332(f332(f334(x86881),x86882),f321(x86881,x86883)))+~P102(f332(f332(f334(x86881),x86884),f321(x86881,x86883)))+~P102(f332(f332(f334(f882(x86881,x86881)),f332(f332(f267(x86881,x86881),x86882),x86884)),x86883)) % 172.83/172.49 [8740]~P38(x87401,x87404)+P102(f332(f332(f334(f882(x87401,x87401)),f332(f332(f267(x87401,x87401),x87403),x87402)),f308(x87401,x87404)))+P38(x87401,f332(f332(f310(f882(x87401,x87401)),f332(f332(f267(x87401,x87401),x87402),x87403)),x87404)) % 172.83/172.49 [8741]~P53(x87411,x87414)+P102(f332(f332(f334(f882(x87411,x87411)),f332(f332(f267(x87411,x87411),x87413),x87412)),f308(x87411,x87414)))+P53(x87411,f332(f332(f310(f882(x87411,x87411)),f332(f332(f267(x87411,x87411),x87412),x87413)),x87414)) % 172.83/172.49 [8819]~E(x88192,x88193)+~P102(f332(f332(f334(x88191),x88192),f332(f173(x88191),x88194)))+P102(f332(f332(f334(f882(x88191,x88191)),f332(f332(f267(x88191,x88191),x88192),x88193)),f332(f173(f882(x88191,x88191)),f332(f332(f183(x88191,x88191),x88194),x88194)))) % 172.83/172.49 [8901]~E(x89013,x89014)+P102(f332(f332(f271(x89011,x89011,a871),a329),x89012))+~P102(f332(f332(f334(f882(x89011,x89011)),x89012),f332(f173(f882(x89011,x89011)),f332(f332(f183(x89011,x89011),x89013),x89014)))) % 172.83/172.49 [8929]~P102(f332(x89294,x89292))+P102(f332(f332(f332(f332(a203,x89291),x89292),x89293),f586(x89293,x89292,x89291,x89294)))+~P102(f332(f332(f332(f332(a203,f31(x89294,x89291)),x89292),x89293),x89292)) % 172.83/172.49 [8956]P102(f332(f332(f334(f882(f877(x89561),f877(x89561))),f332(f332(f267(f877(x89561),f877(x89561)),x89562),x89563)),f147(x89561,x89564)))+~E(f332(f332(f176(x89561),f332(f196(f877(x89561)),x89562)),x89563),x89562)+~P102(f332(f332(f247(a876),f332(f196(f877(x89561)),x89562)),f332(f196(f877(x89561)),x89563))) % 172.83/172.49 [9054]~P102(f332(f61(x90541),x90544))+P102(f332(f332(f334(x90541),f439(x90542,x90543,x90544,x90541)),x90544))+P102(f332(f61(x90543),f332(f332(f41(x90541,f883(x90543,a871)),x90544),x90542))) % 172.83/172.49 [9055]~P102(f332(f61(x90551),x90554))+P102(f332(f332(f334(x90551),f478(x90552,x90553,x90554,x90551)),x90554))+P102(f332(f61(x90553),f332(f332(f41(x90551,f883(x90553,a871)),x90554),x90552))) % 172.83/172.49 [9136]P102(f332(f332(f334(f882(x91361,x91361)),x91362),f332(f332(f289(x91361,x91361,x91361),x91363),f308(x91361,x91363))))+~P102(f332(f332(f247(a876),f2(a876)),x91364))+~P102(f332(f332(f334(f882(x91361,x91361)),x91362),f332(f332(f190(f882(x91361,x91361),a871),x91364),x91363))) % 172.83/172.49 [9144]~P38(x91441,x91442)+~P102(f332(f332(f334(f882(x91441,x91441)),f332(f332(f267(x91441,x91441),x91444),x91443)),x91442))+~P102(f332(f332(f334(f882(x91441,x91441)),f332(f332(f267(x91441,x91441),x91443),x91444)),x91442)) % 172.83/172.49 [9270]~P102(f332(f61(x92701),x92704))+E(f332(f332(f6(x92701,a876),f332(f332(f8(f883(x92702,a871),a876,x92701),f37(x92702)),x92703)),x92704),f332(f37(f882(x92701,x92702)),f332(f332(f269(x92701,x92702),x92704),x92703)))+P102(f332(f332(f334(x92701),f541(x92703,x92702,x92704,x92701)),x92704)) % 172.83/172.49 [9274]~P102(f332(f137(x92741),x92742))+P102(f332(f137(x92741),f332(f332(f159(x92741,x92742),x92743),x92744)))+P102(f332(f332(f334(x92741),x92744),f332(f332(f22(f883(x92741,a871)),f332(f173(x92741),x92742)),f332(f332(f310(x92741),f332(f332(f165(x92741),x92742),x92743)),f195(f883(x92741,a871)))))) % 172.83/172.49 [9290]~P102(f332(f61(x92902),x92903))+~P102(f332(f61(x92901),f332(x92904,f439(x92904,x92901,x92903,x92902))))+P102(f332(f61(x92901),f332(f332(f41(x92902,f883(x92901,a871)),x92903),x92904))) % 172.83/172.49 [9291]~P102(f332(f61(x92912),x92913))+~P102(f332(f61(x92911),f332(x92914,f478(x92914,x92911,x92913,x92912))))+P102(f332(f61(x92911),f332(f332(f41(x92912,f883(x92911,a871)),x92913),x92914))) % 172.83/172.49 [9370]~P102(f332(f332(f334(f882(x93701,x93701)),x93702),f332(f332(f289(x93701,x93701,x93701),x93704),f308(x93701,x93704))))+P102(f332(f332(f334(f882(x93701,x93701)),x93702),f332(f332(f289(x93701,x93701,x93701),x93703),f308(x93701,x93703))))+~P102(f332(f332(f246(f883(f882(x93701,x93701),a871)),x93704),x93703)) % 172.83/172.49 [9377]E(f332(f332(f176(x93771),f681(x93774,x93773,x93772,x93771)),x93773),f332(f332(f176(x93771),f681(x93774,x93773,x93772,x93771)),x93772))+~P102(f332(f332(f334(f882(f877(x93771),f877(x93771))),f332(f332(f267(f877(x93771),f877(x93771)),x93772),x93773)),f147(x93771,x93774)))+E(f332(f332(f176(x93771),f332(f196(f877(x93771)),x93772)),x93773),x93772) % 172.83/172.49 [9394]~P102(f332(f61(x93941),x93944))+E(f332(f332(f6(x93941,a876),f332(f332(f8(f883(x93942,a871),a876,x93941),f37(x93942)),x93943)),x93944),f332(f37(f882(x93941,x93942)),f332(f332(f269(x93941,x93942),x93944),x93943)))+~P102(f332(f61(x93942),f332(x93943,f541(x93943,x93942,x93944,x93941)))) % 172.83/172.49 [9398]~E(f332(f196(f877(x93981)),x93983),f332(f196(f877(x93981)),x93982))+P102(f332(f332(f334(f882(f877(x93981),f877(x93981))),f332(f332(f267(f877(x93981),f877(x93981)),x93982),x93983)),f158(x93981,x93984)))+P102(f332(f332(f334(f882(x93981,x93981)),f685(x93984,x93983,x93982,x93981)),f332(f173(f882(x93981,x93981)),f332(f332(f183(x93981,x93981),x93982),x93983)))) % 172.83/172.49 [9475]~P102(f332(f332(f334(f882(f877(x94751),f877(x94751))),f332(f332(f267(f877(x94751),f877(x94751)),x94752),x94753)),f147(x94751,x94754)))+E(f332(f332(f176(x94751),f332(f196(f877(x94751)),x94752)),x94753),x94752)+P102(f332(f332(f247(a876),f681(x94754,x94753,x94752,x94751)),f332(f332(f244(a876),f332(f196(f877(x94751)),x94752)),f332(f196(f877(x94751)),x94753)))) % 172.83/172.49 [9476]E(f332(f179(x94761,x94762),x94763),f332(f179(x94761,x94762),x94764))+~E(f332(f173(x94761),f332(f332(f154(f882(x94761,x94762),x94761),f266(x94761,x94762)),x94763)),f332(f173(x94761),f332(f332(f154(f882(x94761,x94762),x94761),f266(x94761,x94762)),x94764)))+P102(f332(f332(f334(x94761),f771(x94763,x94764,x94762,x94761)),f332(f173(x94761),f332(f332(f154(f882(x94761,x94762),x94761),f266(x94761,x94762)),x94764)))) % 172.83/172.49 [9492]~P102(f332(x94921,x94924))+P102(f332(f332(f332(f332(a203,f31(x94921,x94922)),f586(x94923,x94924,x94922,x94921)),x94923),x94924))+~P102(f332(f332(f332(f332(a203,f31(x94921,x94922)),x94924),x94923),x94924)) % 172.83/172.49 [9497]~P102(f332(f332(f334(f882(f877(x94971),f877(x94971))),f332(f332(f267(f877(x94971),f877(x94971)),x94972),x94973)),f147(x94971,x94974)))+P102(f332(f332(f247(a876),f332(f196(f877(x94971)),x94972)),f332(f196(f877(x94971)),x94973)))+P102(f332(f332(f247(a876),f681(x94974,x94973,x94972,x94971)),f332(f332(f244(a876),f332(f196(f877(x94971)),x94972)),f332(f196(f877(x94971)),x94973)))) % 172.83/172.49 [9794]~P102(f332(f332(f332(x97941,f731(x97941,x97944,x97943,x97942)),f732(x97941,x97944,x97943,x97942)),f733(x97941,x97944,x97943,x97942)))+P102(f332(f332(f332(x97941,x97942),x97943),x97944))+~P102(f332(f320(f882(f883(a1,f880(f877(a328))),f882(a1,a1)),a318),f332(f332(f267(f883(a1,f880(f877(a328))),f882(a1,a1)),x97942),f332(f332(f267(a1,a1),x97943),x97944)))) % 172.83/172.49 [9873]P102(f332(f332(f332(x98731,x98732),x98733),x98734))+P102(f332(f320(f882(f883(a1,f880(f877(a328))),f882(a1,a1)),a318),f332(f332(f267(f883(a1,f880(f877(a328))),f882(a1,a1)),f731(x98731,x98734,x98733,x98732)),f332(f332(f267(a1,a1),f732(x98731,x98734,x98733,x98732)),f733(x98731,x98734,x98733,x98732)))))+~P102(f332(f320(f882(f883(a1,f880(f877(a328))),f882(a1,a1)),a318),f332(f332(f267(f883(a1,f880(f877(a328))),f882(a1,a1)),x98732),f332(f332(f267(a1,a1),x98733),x98734)))) % 172.83/172.49 [9912]~P102(f332(f332(f334(f882(f877(x99121),f877(x99121))),f332(f332(f267(f877(x99121),f877(x99121)),x99122),x99123)),f147(x99121,x99124)))+E(f332(f332(f176(x99121),f332(f196(f877(x99121)),x99122)),x99123),x99122)+P102(f332(f332(f334(f882(x99121,x99121)),f332(f332(f267(x99121,x99121),f332(f332(f165(x99121),x99122),f681(x99124,x99123,x99122,x99121))),f332(f332(f165(x99121),x99123),f681(x99124,x99123,x99122,x99121)))),x99124)) % 172.83/172.49 [9913]~P102(f332(f332(f334(f882(f877(x99131),f877(x99131))),f332(f332(f267(f877(x99131),f877(x99131)),x99132),x99133)),f147(x99131,x99134)))+P102(f332(f332(f247(a876),f332(f196(f877(x99131)),x99132)),f332(f196(f877(x99131)),x99133)))+P102(f332(f332(f334(f882(x99131,x99131)),f332(f332(f267(x99131,x99131),f332(f332(f165(x99131),x99132),f681(x99134,x99133,x99132,x99131))),f332(f332(f165(x99131),x99133),f681(x99134,x99133,x99132,x99131)))),x99134)) % 172.83/172.49 [9970]~E(f332(f196(f877(x99701)),x99702),f332(f196(f877(x99701)),x99703))+P102(f332(f332(f334(f882(f877(x99701),f877(x99701))),f332(f332(f267(f877(x99701),f877(x99701)),x99702),x99703)),f158(x99701,x99704)))+~P102(f332(f332(f334(f882(x99701,x99701)),f332(f332(f267(x99701,x99701),f332(f332(f165(x99701),x99702),f670(x99704,x99703,x99702,x99701))),f332(f332(f165(x99701),x99703),f670(x99704,x99703,x99702,x99701)))),x99704)) % 172.83/172.49 [10106]~P71(x101061)+~P102(f332(f61(x101062),x101064))+E(f332(f166(x101061),f332(f332(f154(x101062,x101061),x101063),f89(f877(x101062),f332(f332(f18(f877(x101062),a871,a871),f332(f332(f8(a871,f883(a871,a871),f877(x101062)),a330),f332(f332(f7(f877(x101062),f883(x101062,a871),a871),f332(f332(f8(f883(x101062,a871),f883(f883(x101062,a871),a871),f877(x101062)),a329),f173(x101062))),x101064))),f137(x101062))))),f237(x101062,x101061,x101063,x101064)) % 172.83/172.49 [7381]~P57(x73812)+E(x73811,f2(x73812))+E(f332(f332(f290(x73812),f332(f332(f79(x73812),x73813),f332(f332(f80(x73812),x73814),x73811))),x73811),f332(f332(f79(x73812),x73814),f332(f332(f290(x73812),x73813),x73811))) % 172.83/172.49 [7382]~P25(x73822)+E(x73821,f2(x73822))+E(f332(f332(f38(x73822),f332(f332(f79(x73822),x73823),f332(f332(f80(x73822),x73824),x73821))),x73821),f332(f332(f79(x73822),x73824),f332(f332(f38(x73822),x73823),x73821))) % 172.83/172.49 [7383]~P25(x73832)+E(x73831,f2(x73832))+E(f332(f332(f38(x73832),f332(f332(f79(x73832),x73833),f332(f332(f80(x73832),x73831),x73834))),x73831),f332(f332(f79(x73832),x73834),f332(f332(f38(x73832),x73833),x73831))) % 172.83/172.49 [7617]~P58(x76172)+E(x76171,f2(x76172))+E(f332(f332(f290(x76172),f332(f332(f22(x76172),x76173),f332(f332(f80(x76172),x76171),x76174))),x76171),f332(f332(f22(x76172),f332(f332(f290(x76172),x76173),x76171)),x76174)) % 172.83/172.49 [7618]~P57(x76182)+E(x76181,f2(x76182))+E(f332(f332(f290(x76182),f332(f332(f79(x76182),x76183),f332(f332(f80(x76182),x76184),x76181))),x76181),f332(f332(f79(x76182),f332(f332(f290(x76182),x76183),x76181)),x76184)) % 172.83/172.49 [7619]~P58(x76192)+E(x76191,f2(x76192))+E(f332(f332(f290(x76192),f332(f332(f79(x76192),x76193),f332(f332(f80(x76192),x76191),x76194))),x76191),f332(f332(f79(x76192),f332(f332(f290(x76192),x76193),x76191)),x76194)) % 172.83/172.49 [8333]~P102(f332(f160(x83331,x83333),x83334))+~P102(f332(f160(x83331,x83332),x83334))+P102(f332(f160(x83331,f332(f332(f104(f883(x83331,a871)),x83332),x83333)),x83334)) % 172.83/172.49 [8702]~E(f332(f332(f289(x87021,x87021,x87021),x87022),x87024),f195(f883(f882(x87021,x87021),a871)))+~E(f332(f332(f289(x87021,x87021,x87021),x87022),x87023),f195(f883(f882(x87021,x87021),a871)))+E(f332(f332(f289(x87021,x87021,x87021),x87022),f332(f332(f113(f883(f882(x87021,x87021),a871)),x87023),x87024)),f195(f883(f882(x87021,x87021),a871))) % 172.83/172.49 [8820]~P102(f332(f332(f246(f883(x88201,a871)),x88203),x88204))+~P102(f332(f332(f246(f883(x88201,a871)),x88202),x88204))+P102(f332(f332(f246(f883(x88201,a871)),f332(f332(f113(f883(x88201,a871)),x88202),x88203)),x88204)) % 172.83/172.49 [9200]~P102(f332(f61(x92001),x92004))+~P102(f332(f61(x92001),x92003))+E(f332(f332(f22(a876),f332(f332(f79(a876),f332(f332(f6(x92001,a876),x92002),x92003)),f332(f332(f6(x92001,a876),x92002),x92004))),f332(f332(f6(x92001,a876),x92002),f332(f332(f104(f883(x92001,a871)),x92003),x92004))),f332(f332(f6(x92001,a876),x92002),f332(f332(f113(f883(x92001,a871)),x92003),x92004))) % 172.83/172.49 [9287]~P102(f332(f332(f334(x92871),x92873),x92872))+~P102(f332(f332(f246(f883(x92871,a871)),x92872),f332(f332(f310(x92871),x92873),x92874)))+P102(f332(f332(f246(f883(x92871,a871)),f332(f332(f22(f883(x92871,a871)),x92872),f332(f332(f310(x92871),x92873),f195(f883(x92871,a871))))),x92874)) % 172.83/172.49 [9447]~P102(f332(f332(f334(x94471),x94473),x94472))+P102(f332(f332(f246(f883(x94471,a871)),x94472),f332(f332(f310(x94471),x94473),x94474)))+~P102(f332(f332(f246(f883(x94471,a871)),f332(f332(f22(f883(x94471,a871)),x94472),f332(f332(f310(x94471),x94473),f195(f883(x94471,a871))))),x94474)) % 172.83/172.49 [9537]~P102(f332(f332(f247(a876),x95372),x95374))+~P102(f332(f332(f246(a876),x95371),x95373))+P102(f332(f332(f334(f882(f882(a876,a876),f882(a876,a876))),f332(f332(f267(f882(a876,a876),f882(a876,a876)),f332(f332(f267(a876,a876),x95371),x95372)),f332(f332(f267(a876,a876),x95373),x95374))),a34)) % 172.83/172.49 [9538]~P102(f332(f332(f246(a876),x95382),x95384))+~P102(f332(f332(f246(a876),x95381),x95383))+P102(f332(f332(f334(f882(f882(a876,a876),f882(a876,a876))),f332(f332(f267(f882(a876,a876),f882(a876,a876)),f332(f332(f267(a876,a876),x95381),x95382)),f332(f332(f267(a876,a876),x95383),x95384))),a69)) % 172.83/172.49 [9833]~P102(f332(f332(f334(f877(x98331)),x98334),f161(x98331,x98333)))+~P102(f332(f332(f334(f877(x98331)),x98334),f161(x98331,x98332)))+P102(f332(f160(x98331,f332(f332(f104(f883(x98331,a871)),f332(f332(f7(x98331,f883(x98331,a871),a871),f334(x98331)),x98332)),f332(f332(f7(x98331,f883(x98331,a871),a871),f334(x98331)),x98333))),x98334)) % 172.83/172.49 [9935]~P20(x99351,f883(f883(x99351,a871),a871),f332(f332(f7(x99351,f883(f882(x99351,x99351),a871),f883(f883(x99351,a871),a871)),f332(f332(f8(f883(x99351,a871),f883(f883(f882(x99351,x99351),a871),f883(f883(x99351,a871),a871)),x99351),f60(x99351)),f332(f332(f7(x99351,f883(x99351,a871),f883(x99351,a871)),f310(x99351)),f195(f883(x99351,a871))))),x99353),x99352)+~P102(f332(f332(f334(x99351),x99354),x99352))+E(f332(f332(f22(f883(f883(x99351,a871),a871)),f332(f332(f60(x99351),x99352),x99353)),f332(f332(f60(x99351),f332(f332(f310(x99351),x99354),f195(f883(x99351,a871)))),x99353)),f332(f332(f60(x99351),f332(f332(f22(f883(x99351,a871)),x99352),f332(f332(f310(x99351),x99354),f195(f883(x99351,a871))))),x99353)) % 172.83/172.49 [10070]~P40(x100701,x100702,x100704)+~P102(f332(f332(f334(f882(x100701,x100701)),x100703),x100704))+P102(f332(f332(f271(x100701,x100701,a871),f332(f332(f7(x100701,f883(x100701,a871),f883(x100701,a871)),f332(f332(f8(f883(a871,a871),f883(f883(x100701,a871),f883(x100701,a871)),x100701),f8(a871,a871,x100701)),f332(f332(f8(a871,f883(a871,a871),x100701),a330),f332(f332(f7(x100701,f883(x100701,a871),a871),f334(x100701)),x100702)))),f332(f332(f7(x100701,f883(x100701,a871),a871),f334(x100701)),x100702))),x100703)) % 172.83/172.49 [10082]P102(f332(f61(x100821),x100822))+~P102(f332(f61(x100823),f332(f311(x100821,x100823,x100824),x100822)))+~P102(f332(f61(x100821),f332(f252(x100821),f332(f332(f18(x100821,a871,a871),f332(f332(f8(a871,f883(a871,a871),x100821),a330),f332(f332(f7(x100821,f883(x100821,a871),a871),f334(x100821)),x100822))),f332(f332(f7(x100821,x100823,a871),f332(f332(f8(x100823,f883(x100823,a871),x100821),a329),x100824)),f332(x100824,f436(x100824,x100823,x100822,x100821))))))) % 172.83/172.49 [8085]~P58(x80852)+E(x80851,f2(x80852))+E(f332(f332(f290(x80852),f332(f332(f22(x80852),f332(f332(f80(x80852),x80851),x80853)),x80854)),x80851),f332(f332(f22(x80852),x80853),f332(f332(f290(x80852),x80854),x80851))) % 172.83/172.49 [8086]~P58(x80862)+E(x80861,f2(x80862))+E(f332(f332(f290(x80862),f332(f332(f79(x80862),f332(f332(f80(x80862),x80861),x80863)),x80864)),x80861),f332(f332(f79(x80862),x80863),f332(f332(f290(x80862),x80864),x80861))) % 172.83/172.49 [8986]~E(f332(f332(f289(x89861,x89861,x89861),x89863),x89864),f195(f883(f882(x89861,x89861),a871)))+~E(f332(f332(f289(x89861,x89861,x89861),x89862),x89864),f195(f883(f882(x89861,x89861),a871)))+E(f332(f332(f289(x89861,x89861,x89861),f332(f332(f113(f883(f882(x89861,x89861),a871)),x89862),x89863)),x89864),f195(f883(f882(x89861,x89861),a871))) % 172.83/172.49 [10012]~P142(x100121)+~P142(x100122)+E(f332(f332(f317(x100121),f332(f332(f7(x100121,a102,f880(f877(a328))),f332(f332(f8(f883(x100122,f880(f877(a328))),f883(a102,f880(f877(a328))),x100121),f317(x100122)),f332(f332(f8(f883(x100122,f882(x100121,x100122)),f883(x100122,f880(f877(a328))),x100121),f332(f8(f882(x100121,x100122),f880(f877(a328)),x100122),x100123)),f267(x100121,x100122)))),x100124)),x100124),f332(f332(f317(f882(x100121,x100122)),x100123),x100124)) % 172.83/172.49 [9742]~P102(f332(f160(x97421,x97423),x97424))+~P102(f332(f160(x97421,x97422),x97424))+P102(f332(f160(x97421,f332(f332(f18(x97421,a871,a871),f332(f332(f8(a871,f883(a871,a871),x97421),a330),x97422)),x97423)),x97424)) % 172.83/172.49 [10004]P102(f332(x100041,f437(x100042,x100043,x100041,x100044)))+~P102(f332(f61(x100044),f332(f252(x100044),x100041)))+P102(f332(f61(x100043),f332(f252(x100043),f332(f332(f8(f883(x100044,a871),a871,x100043),f86(x100044)),f332(f332(f8(f883(x100044,a871),f883(x100044,a871),x100043),f332(f18(x100044,a871,a871),f332(f332(f8(a871,f883(a871,a871),x100044),a330),x100041))),x100042))))) % 172.83/172.49 [10025]~P102(f332(f61(x100252),f332(f252(x100252),x100253)))+~P102(f332(f61(x100251),f332(f252(x100251),f332(f332(f7(x100251,x100252,a871),x100254),f437(x100254,x100251,x100253,x100252)))))+P102(f332(f61(x100251),f332(f252(x100251),f332(f332(f8(f883(x100252,a871),a871,x100251),f86(x100252)),f332(f332(f8(f883(x100252,a871),f883(x100252,a871),x100251),f332(f18(x100252,a871,a871),f332(f332(f8(a871,f883(a871,a871),x100252),a330),x100253))),x100254))))) % 172.83/172.49 [5035]~E(x50352,x50354)+E(f170(x50351,x50352,x50353),f170(x50351,x50354,x50355))+~E(x50352,f2(a876)) % 172.83/172.49 [5287]E(x52871,x52872)+~E(f170(x52874,x52873,x52871),f170(x52874,x52875,x52872))+E(x52873,f2(a876)) % 172.83/172.49 [6521]E(x65211,x65212)+~E(f332(x65213,x65211),f332(x65213,x65212))+~P20(x65214,x65215,x65213,f255(f883(x65214,a871))) % 172.83/172.49 [6681]~E(f332(x66813,x66815),f208(x66812))+~E(f332(x66814,x66815),f208(x66812))+E(f332(f186(x66811,x66812,x66813,x66814),x66815),f208(x66812)) % 172.83/172.49 [7416]E(x74161,x74162)+~P20(x74163,x74164,x74165,f255(f883(x74163,a871)))+~E(f332(f311(x74163,x74164,x74165),x74161),f332(f311(x74163,x74164,x74165),x74162)) % 172.83/172.49 [7671]P20(x76712,x76713,f508(x76714,x76713,x76712,x76711),x76711)+~E(f332(f311(x76713,x76712,x76715),x76714),x76711)+E(x76711,f195(f883(x76712,a871))) % 172.83/172.49 [8221]~P102(f332(f332(x82213,x82212),x82215))+~P102(f332(f332(x82213,x82214),x82212))+P102(f332(f332(f334(x82211),x82212),f296(x82211,x82213,x82214,x82215))) % 172.83/172.49 [8222]~P102(f332(f332(x82223,x82222),x82225))+~P102(f332(f332(x82223,x82224),x82222))+P102(f332(f332(f334(x82221),x82222),f299(x82221,x82223,x82224,x82225))) % 172.83/172.49 [8777]~P20(x87771,x87773,x87775,f255(f883(x87771,a871)))+~P20(x87773,x87772,x87774,f255(f883(x87773,a871)))+P20(x87771,x87772,f332(f72(x87773,x87772,x87771,x87774),x87775),f255(f883(x87771,a871))) % 172.83/172.49 [9346]P102(f332(f332(f334(f882(x93461,x93461)),f332(f332(f267(x93461,x93461),x93462),x93463)),f308(x93461,x93464)))+~P102(f332(f332(f334(f882(x93461,x93461)),f332(f332(f267(x93461,x93461),x93462),x93465)),f308(x93461,x93464)))+~P102(f332(f332(f334(f882(x93461,x93461)),f332(f332(f267(x93461,x93461),x93465),x93463)),f308(x93461,x93464))) % 172.83/172.49 [9384]~P104(x93842)+~P102(f332(f137(x93841),x93845))+P102(f332(f137(x93841),f149(x93841,x93842,x93843,x93844,x93845))) % 172.83/172.49 [5360]~E(x53602,f116(x53601))+E(f332(f332(f134(x53601),x53602),x53603),f332(f332(f151(x53601),x53604),x53605))+~E(x53603,f332(f332(f151(x53601),x53604),x53605)) % 172.83/172.49 [5361]~E(x53612,f116(x53611))+E(f332(f332(f134(x53611),x53612),x53613),f332(f332(f151(x53611),x53614),x53615))+~E(f332(f332(f151(x53611),x53614),x53615),x53613) % 172.83/172.49 [6478]~E(f332(f196(f877(x64781)),x64785),f332(f196(f877(x64782)),x64784))+E(f332(f332(f154(f882(x64781,x64782),x64782),f270(x64781,x64782)),x64783),x64784)+~E(f332(f332(f183(x64781,x64782),x64785),x64784),x64783) % 172.83/172.49 [6479]~E(f332(f196(f877(x64791)),x64794),f332(f196(f877(x64792)),x64795))+E(f332(f332(f154(f882(x64791,x64792),x64791),f266(x64791,x64792)),x64793),x64794)+~E(f332(f332(f183(x64791,x64792),x64794),x64795),x64793) % 172.83/172.49 [6954]~P104(x69541)+~P29(x69541,f332(f332(f154(x69542,x69541),x69543),x69545))+P29(x69541,f332(f332(f154(x69542,x69541),x69543),f332(f136(x69542,x69544),x69545))) % 172.83/172.49 [7001]~P102(f332(x70013,x70015))+~P102(f332(f332(x70012,x70014),x70015))+P102(f332(f332(f94(x70011,x70012,x70013),x70014),x70015)) % 172.83/172.49 [7098]~P104(x70981)+P29(x70981,f332(f332(f154(x70982,x70981),x70983),f171(x70982,x70984,x70985)))+~P29(x70981,f332(f332(f154(x70982,x70981),x70983),x70985)) % 172.83/172.49 [7121]~P50(x71213,x71212,x71215)+~P50(x71211,x71213,x71214)+P50(x71211,x71212,f332(f332(f289(x71211,x71213,x71212),x71214),x71215)) % 172.83/172.49 [7213]E(x72131,x72132)+~P20(x72133,x72134,x72135,f255(f883(x72133,a871)))+~E(f332(f332(f154(x72133,x72134),x72135),x72131),f332(f332(f154(x72133,x72134),x72135),x72132)) % 172.83/172.49 [7367]~P102(f332(f332(f247(a876),x73671),f332(x73673,x73675)))+P102(f332(f332(f247(a876),x73671),f155(x73672,x73673,x73674)))+~P102(f332(f332(f334(x73672),x73675),f332(f173(x73672),x73674))) % 172.83/172.49 [7368]~P102(f332(f332(f246(a876),x73681),f332(x73683,x73685)))+P102(f332(f332(f246(a876),x73681),f155(x73682,x73683,x73684)))+~P102(f332(f332(f334(x73682),x73685),f332(f173(x73682),x73684))) % 172.83/172.49 [7774]P102(f332(x77741,x77742))+~P102(f332(x77741,x77743))+~P102(f332(f332(f334(x77744),x77742),f332(f173(x77744),f170(x77744,x77745,x77743)))) % 172.83/172.49 [7775]P102(f332(x77751,x77752))+~P102(f332(x77751,x77753))+~P102(f332(f332(f334(x77754),x77753),f332(f173(x77754),f170(x77754,x77755,x77752)))) % 172.83/172.49 [7780]~P105(x77801)+P102(f332(f332(f246(f883(x77801,a871)),f303(x77801,x77802,x77803)),f303(x77801,x77804,x77805)))+P102(f332(f332(f246(x77801),x77802),x77803)) % 172.83/172.49 [7803]~P27(x78031)+P102(f332(f332(f246(x78031),f332(f332(f42(x78032,x78031),x78033),x78034)),f332(x78034,x78035)))+~P102(f332(f332(f334(x78032),x78035),x78033)) % 172.83/172.49 [7870]~P20(x78701,x78702,x78704,x78703)+E(f332(f76(x78701,x78702,x78703,x78704),f332(x78704,x78705)),x78705)+~P102(f332(f332(f334(x78701),x78705),x78703)) % 172.83/172.49 [8073]~P102(f332(x80731,x80735))+P102(f332(x80731,f427(x80731,x80732,x80733,x80734)))+~P102(f332(f332(f334(x80734),x80735),x80733)) % 172.83/172.49 [8074]~P102(f332(x80741,x80745))+P102(f332(x80741,f427(x80741,x80742,x80743,x80744)))+~P102(f332(f332(f334(x80744),x80745),x80742)) % 172.83/172.49 [8172]P102(f332(f61(x81721),x81722))+~P102(f332(f61(x81723),x81724))+~P102(f332(f332(f246(f883(x81721,a871)),x81722),f332(f311(x81723,x81721,x81725),x81724))) % 172.83/172.49 [8337]E(x83371,x83372)+~P20(x83373,x83374,x83375,f332(f332(f113(f883(x83373,a871)),f332(f173(x83373),x83371)),f332(f173(x83373),x83372)))+~E(f332(f332(f154(x83373,x83374),x83375),x83371),f332(f332(f154(x83373,x83374),x83375),x83372)) % 172.83/172.49 [8391]~P105(x83911)+~P102(f332(f332(f247(f883(x83911,a871)),f303(x83911,x83914,x83915)),f303(x83911,x83912,x83913)))+P102(f332(f332(f246(x83911),x83912),x83913)) % 172.83/172.49 [8461]~P20(x84611,x84614,x84615,f255(f883(x84611,a871)))+~P102(f332(f332(f334(x84614),f332(x84615,x84612)),f332(f311(x84611,x84614,x84615),x84613)))+P102(f332(f332(f334(x84611),x84612),x84613)) % 172.83/172.49 [8538]P102(f332(x85381,x85382))+~P102(f332(x85381,f435(x85381,x85383,x85384,x85385)))+~P102(f332(f332(f334(x85385),x85382),x85384)) % 172.83/172.49 [8539]P102(f332(x85391,x85392))+~P102(f332(x85391,f435(x85391,x85393,x85394,x85395)))+~P102(f332(f332(f334(x85395),x85392),x85393)) % 172.83/172.49 [8817]~P20(x88172,x88173,x88171,x88174)+E(f332(x88171,f332(f76(x88172,x88173,x88174,x88171),x88175)),x88175)+~P102(f332(f332(f334(x88173),x88175),f332(f311(x88172,x88173,x88171),x88174))) % 172.83/172.49 [8923]E(x89231,f116(x89232))+E(f332(f332(f151(x89232),x89233),f697(x89234,x89233,x89235,x89231,x89232)),x89231)+~E(f332(f332(f134(x89232),x89231),x89235),f332(f332(f151(x89232),x89233),x89234)) % 172.83/172.49 [8924]E(x89241,f116(x89242))+E(f332(f332(f151(x89242),x89243),f698(x89244,x89241,x89245,x89243,x89242)),x89241)+~E(f332(f332(f134(x89242),x89241),x89244),f332(f332(f151(x89242),x89243),x89245)) % 172.83/172.49 [8942]E(f332(f332(f151(x89422),x89423),f697(x89424,x89423,x89421,x89425,x89422)),x89425)+~E(f332(f332(f134(x89422),x89425),x89421),f332(f332(f151(x89422),x89423),x89424))+E(x89421,f332(f332(f151(x89422),x89423),x89424)) % 172.83/172.49 [8943]E(f332(f332(f151(x89431),x89432),f698(x89434,x89435,x89433,x89432,x89431)),x89435)+~E(f332(f332(f134(x89431),x89435),x89434),f332(f332(f151(x89431),x89432),x89433))+E(f332(f332(f151(x89431),x89432),x89433),x89434) % 172.83/172.49 [9024]~E(f332(f311(x90243,x90242,x90244),f255(f883(x90243,a871))),f255(f883(x90242,a871)))+~E(f332(f311(x90241,x90243,x90245),f255(f883(x90241,a871))),f255(f883(x90243,a871)))+E(f332(f311(x90241,x90242,f332(f72(x90243,x90242,x90241,x90244),x90245)),f255(f883(x90241,a871))),f255(f883(x90242,a871))) % 172.83/172.49 [9391]E(x93911,f116(x93912))+~E(f332(f332(f134(x93912),x93911),x93913),f332(f332(f151(x93912),x93915),x93914))+E(f332(f332(f134(x93912),f698(x93913,x93911,x93914,x93915,x93912)),x93913),x93914) % 172.83/172.49 [9392]E(x93921,f116(x93922))+~E(f332(f332(f134(x93922),x93921),x93925),f332(f332(f151(x93922),x93924),x93923))+E(f332(f332(f134(x93922),f697(x93923,x93924,x93925,x93921,x93922)),x93925),x93923) % 172.83/172.49 [9399]E(f332(f332(f134(x93992),f697(x93994,x93993,x93991,x93995,x93992)),x93991),x93994)+~E(f332(f332(f134(x93992),x93995),x93991),f332(f332(f151(x93992),x93993),x93994))+E(x93991,f332(f332(f151(x93992),x93993),x93994)) % 172.83/172.49 [9400]~E(f332(f332(f134(x94001),x94005),x94004),f332(f332(f151(x94001),x94002),x94003))+E(f332(f332(f134(x94001),f698(x94004,x94005,x94003,x94002,x94001)),x94004),x94003)+E(f332(f332(f151(x94001),x94002),x94003),x94004) % 172.83/172.49 [9401]E(f332(f332(f134(x94011),x94015),f700(x94013,x94012,x94014,x94015,x94011)),x94012)+E(f332(f332(f134(x94011),x94012),f699(x94013,x94012,x94014,x94015,x94011)),x94015)+~E(f332(f332(f134(x94011),x94015),x94014),f332(f332(f134(x94011),x94012),x94013)) % 172.83/172.49 [9433]~P104(x94331)+P29(x94331,f332(f332(f154(x94332,x94331),x94333),f149(x94332,x94331,x94333,x94334,x94335)))+~P29(x94331,f332(f332(f154(x94332,x94331),x94333),x94335)) % 172.83/172.49 [9444]~P54(x94445,x94441,x94444,x94443)+P102(f332(f332(x94441,x94442),f524(x94443,x94444,x94441,x94445,x94442)))+~P102(f332(f332(f334(x94445),x94442),x94444)) % 172.83/172.49 [9549]~P102(f332(f332(f334(f882(x95491,x95491)),f332(f332(f267(x95491,x95491),x95495),x95493)),f308(x95491,x95494)))+P102(f332(f332(f334(f882(x95491,x95491)),f332(f332(f267(x95491,x95491),x95492),x95493)),f332(f332(f289(x95491,x95491,x95491),x95494),f308(x95491,x95494))))+~P102(f332(f332(f334(f882(x95491,x95491)),f332(f332(f267(x95491,x95491),x95492),x95495)),f332(f332(f289(x95491,x95491,x95491),x95494),f308(x95491,x95494)))) % 172.83/172.49 [9550]~P102(f332(f332(f334(f882(x95501,x95501)),f332(f332(f267(x95501,x95501),x95502),x95505)),f308(x95501,x95504)))+P102(f332(f332(f334(f882(x95501,x95501)),f332(f332(f267(x95501,x95501),x95502),x95503)),f332(f332(f289(x95501,x95501,x95501),x95504),f308(x95501,x95504))))+~P102(f332(f332(f334(f882(x95501,x95501)),f332(f332(f267(x95501,x95501),x95505),x95503)),f332(f332(f289(x95501,x95501,x95501),x95504),f308(x95501,x95504)))) % 172.83/172.49 [9553]P102(f332(f332(f334(f882(f877(x95531),f877(x95531))),f332(f332(f267(f877(x95531),f877(x95531)),x95532),x95533)),f158(x95531,f308(x95531,x95534))))+~P102(f332(f332(f334(f882(f877(x95531),f877(x95531))),f332(f332(f267(f877(x95531),f877(x95531)),x95532),x95535)),f158(x95531,f308(x95531,x95534))))+~P102(f332(f332(f334(f882(f877(x95531),f877(x95531))),f332(f332(f267(f877(x95531),f877(x95531)),x95535),x95533)),f158(x95531,f308(x95531,x95534)))) % 172.83/172.49 [9557]E(f332(f332(f134(x95571),x95572),f699(x95573,x95572,x95574,x95575,x95571)),x95575)+E(f332(f332(f134(x95571),f700(x95573,x95572,x95574,x95575,x95571)),x95573),x95574)+~E(f332(f332(f134(x95571),x95572),x95573),f332(f332(f134(x95571),x95575),x95574)) % 172.83/172.49 [9558]E(f332(f332(f134(x95581),x95582),f700(x95583,x95584,x95585,x95582,x95581)),x95584)+E(f332(f332(f134(x95581),f699(x95583,x95584,x95585,x95582,x95581)),x95585),x95583)+~E(f332(f332(f134(x95581),x95582),x95585),f332(f332(f134(x95581),x95584),x95583)) % 172.83/172.49 [9612]P102(f332(f332(f334(f882(x96121,x96121)),f332(f332(f267(x96121,x96121),x96122),x96123)),f332(f332(f289(x96121,x96121,x96121),x96124),f308(x96121,x96124))))+~P102(f332(f332(f334(f882(x96121,x96121)),f332(f332(f267(x96121,x96121),x96122),x96125)),f332(f332(f289(x96121,x96121,x96121),x96124),f308(x96121,x96124))))+~P102(f332(f332(f334(f882(x96121,x96121)),f332(f332(f267(x96121,x96121),x96125),x96123)),f332(f332(f289(x96121,x96121,x96121),x96124),f308(x96121,x96124)))) % 172.83/172.49 [9639]P35(x96391,x96392,x96393,x96394,x96395)+~E(f332(f196(f877(x96391)),x96394),f332(f196(f877(x96392)),x96395))+~P102(f332(f332(f271(x96391,x96392,a871),x96393),f730(x96395,x96394,x96393,x96392,x96391))) % 172.83/172.49 [9640]P35(x96401,x96402,x96403,x96404,x96405)+~E(f332(f196(f877(x96401)),x96404),f332(f196(f877(x96402)),x96405))+~P102(f332(f332(f271(x96401,x96402,a871),x96403),f739(x96403,x96405,x96404,x96402,x96401))) % 172.83/172.49 [9645]E(f332(f332(f134(x96451),f699(x96452,x96453,x96454,x96455,x96451)),x96454),x96452)+~E(f332(f332(f134(x96451),x96453),x96452),f332(f332(f134(x96451),x96455),x96454))+E(f332(f332(f134(x96451),f700(x96452,x96453,x96454,x96455,x96451)),x96452),x96454) % 172.83/172.49 [9660]~P104(x96602)+E(f332(f332(f148(x96601,x96602,x96603),x96604),x96605),f332(f332(f151(x96601),x96604),x96605))+P102(f332(f332(f334(x96601),f785(x96604,x96603,x96605,x96601,x96602)),f332(f173(x96601),x96605))) % 172.83/172.49 [9665]~P54(x96651,x96654,x96653,x96652)+~P102(f332(f332(f334(x96651),x96655),x96653))+P102(f332(f332(f334(x96651),f524(x96652,x96653,x96654,x96651,x96655)),x96652)) % 172.83/172.49 [9785]~P102(f332(f332(f334(f882(f883(x97851,a871),f883(x97851,a871))),f332(f332(f267(f883(x97851,a871),f883(x97851,a871)),x97854),x97853)),f324(x97851,x97852)))+~P102(f332(f332(f334(x97851),x97855),x97854))+P102(f332(f332(f334(x97851),f589(x97852,x97853,x97854,x97851,x97855)),x97853)) % 172.83/172.49 [9797]~P104(x97972)+E(f332(f332(f148(x97971,x97972,x97973),x97974),x97975),f332(f332(f151(x97971),x97974),x97975))+~P102(f332(f332(f246(x97972),f332(x97973,x97974)),f332(x97973,f785(x97974,x97973,x97975,x97971,x97972)))) % 172.83/172.49 [9987]P35(x99871,x99872,x99873,x99874,x99875)+~E(f332(f196(f877(x99871)),x99874),f332(f196(f877(x99872)),x99875))+~P102(f332(f332(x99873,f332(f332(f165(x99871),x99874),f734(x99875,x99874,x99873,x99872,x99871))),f332(f332(f165(x99872),x99875),f734(x99875,x99874,x99873,x99872,x99871)))) % 172.83/172.49 [9988]P35(x99881,x99882,x99883,x99884,x99885)+~E(f332(f196(f877(x99881)),x99884),f332(f196(f877(x99882)),x99885))+~P102(f332(f332(x99883,f332(f332(f165(x99881),x99884),f775(x99883,x99885,x99882,x99884,x99881))),f332(f332(f165(x99882),x99885),f775(x99883,x99885,x99882,x99884,x99881)))) % 172.83/172.49 [6549]~P12(x65492,x65495,x65491)+~P102(f332(f61(x65492),x65494))+E(f332(x65491,f332(f332(f310(x65492),x65493),x65494)),f332(f332(f64(x65492,x65492,x65495),x65493),x65494)) % 172.83/172.49 [6550]~E(x65503,x65504)+~E(x65502,x65505)+E(f332(f332(f310(x65501),x65502),f332(f332(f310(x65501),x65503),f195(f883(x65501,a871)))),f332(f332(f310(x65501),x65504),f332(f332(f310(x65501),x65505),f195(f883(x65501,a871))))) % 172.83/172.49 [6561]P102(f332(x65612,x65615))+E(f178(x65611,x65612,f332(f332(f134(x65611),x65613),x65614)),f178(x65611,x65612,x65613))+~P102(f332(f332(f334(x65611),x65615),f332(f173(x65611),x65613))) % 172.83/172.49 [6598]E(f332(x65981,x65982),f195(f883(x65983,a871)))+~E(f332(f332(f41(x65984,f883(x65983,a871)),x65985),x65981),f195(f883(x65983,a871)))+~P102(f332(f332(f334(x65984),x65982),x65985)) % 172.83/172.49 [6599]E(f332(x65991,x65992),f255(f883(x65993,a871)))+~E(f332(f332(f42(x65994,f883(x65993,a871)),x65995),x65991),f255(f883(x65993,a871)))+~P102(f332(f332(f334(x65994),x65992),x65995)) % 172.83/172.49 [6903]~P102(f332(f332(f201(x69031),x69033),x69035))+~P102(f332(f332(f201(x69032),x69035),x69034))+P102(f332(f332(f201(f32(x69031,x69032)),x69033),x69034)) % 172.83/172.49 [7108]~E(x71082,x71084)+~P138(x71081)+E(f332(f332(f79(x71081),f332(f332(f80(x71081),x71082),x71083)),f332(f332(f80(x71081),x71084),x71085)),f332(f332(f79(x71081),f332(f332(f80(x71081),x71082),x71085)),f332(f332(f80(x71081),x71084),x71083))) % 172.83/172.49 [7168]~P27(x71681)+~P102(f332(f332(f334(x71684),x71683),x71685))+P102(f332(f332(f246(x71681),f332(x71682,x71683)),f332(f332(f41(x71684,x71681),x71685),x71682))) % 172.83/172.49 [7218]~P106(x72181)+P102(f332(f332(f246(x72181),f332(x72182,x72183)),f332(x72184,x72183)))+~P102(f332(f332(f246(f883(x72185,x72181)),x72182),x72184)) % 172.83/172.49 [7335]E(x73351,x73352)+E(x73353,x73351)+~E(f332(f332(f310(x73354),x73351),f332(f332(f310(x73354),x73355),f195(f883(x73354,a871)))),f332(f332(f310(x73354),x73352),f332(f332(f310(x73354),x73353),f195(f883(x73354,a871))))) % 172.83/172.49 [7336]E(x73361,x73362)+E(x73363,x73361)+~E(f332(f332(f310(x73364),x73363),f332(f332(f310(x73364),x73362),f195(f883(x73364,a871)))),f332(f332(f310(x73364),x73365),f332(f332(f310(x73364),x73361),f195(f883(x73364,a871))))) % 172.83/172.49 [7337]E(x73371,x73372)+E(x73371,x73373)+~E(f332(f332(f310(x73374),x73373),f332(f332(f310(x73374),x73372),f195(f883(x73374,a871)))),f332(f332(f310(x73374),x73375),f332(f332(f310(x73374),x73371),f195(f883(x73374,a871))))) % 172.83/172.49 [7338]E(x73381,x73382)+E(x73381,x73383)+~E(f332(f332(f310(x73384),x73381),f332(f332(f310(x73384),x73385),f195(f883(x73384,a871)))),f332(f332(f310(x73384),x73382),f332(f332(f310(x73384),x73383),f195(f883(x73384,a871))))) % 172.83/172.49 [7880]P20(x78801,x78802,x78803,x78804)+~P20(x78801,x78802,x78803,x78805)+~P102(f332(f332(f246(f883(x78801,a871)),x78804),x78805)) % 172.83/172.49 [7887]~P102(f332(f332(f246(a876),x78875),x78873))+~P102(f332(f332(f332(f332(a203,x78871),x78872),x78875),x78874))+P102(f332(f332(f332(f332(a203,x78871),x78872),x78873),x78874)) % 172.83/172.49 [7984]P102(f332(x79841,x79842))+~P102(f332(f332(f201(x79844),x79842),x79845))+P102(f332(f332(f201(f29(x79841,x79843,x79844)),x79842),x79845)) % 172.83/172.49 [8012]~P102(f332(x80121,x80124))+~P102(f332(f332(f201(x80122),x80124),x80125))+P102(f332(f332(f201(f29(x80121,x80122,x80123)),x80124),x80125)) % 172.83/172.49 [8063]E(x80631,x80632)+~E(f332(f311(x80633,x80634,x80635),x80631),f332(f311(x80633,x80634,x80635),x80632))+~P20(x80633,x80634,x80635,f332(f332(f113(f883(x80633,a871)),x80631),x80632)) % 172.83/172.49 [8137]P102(f332(x81372,x81374))+E(f332(f332(f138(x81371),f332(f196(f877(x81371)),f178(x81371,x81372,x81373))),x81373),f332(f332(f151(x81371),x81374),x81375))+~E(f332(f332(f134(x81371),f178(x81371,x81372,x81373)),f332(f332(f151(x81371),x81374),x81375)),x81373) % 172.83/172.49 [8169]~P20(x81691,x81692,x81693,x81695)+~P20(x81691,x81692,x81693,x81694)+P20(x81691,x81692,x81693,f332(f332(f104(f883(x81691,a871)),x81694),x81695)) % 172.83/172.49 [8278]~P71(x82781)+E(f332(f332(f79(x82781),f332(x82782,x82783)),f332(f166(x82781),f332(f332(f154(x82784,x82781),x82782),f171(x82784,x82783,x82785)))),f332(f166(x82781),f332(f332(f154(x82784,x82781),x82782),x82785)))+~P102(f332(f332(f334(x82784),x82783),f332(f173(x82784),x82785))) % 172.83/172.49 [8367]~P104(x83671)+~P29(x83671,f332(f332(f154(x83672,x83671),x83673),x83675))+P29(x83671,f332(f332(f154(x83672,x83671),x83673),f332(f332(f148(x83672,x83671,x83673),x83674),x83675))) % 172.83/172.49 [8446]P102(f332(x84461,x84462))+P102(f332(f332(f201(x84463),x84462),x84464))+~P102(f332(f332(f201(f29(x84461,x84465,x84463)),x84462),x84464)) % 172.83/172.49 [8457]~P27(x84571)+P102(f332(f332(f246(x84571),f332(f332(f41(x84572,x84571),x84573),x84574)),f332(f332(f41(x84572,x84571),x84575),x84574)))+~P102(f332(f332(f246(f883(x84572,a871)),x84573),x84575)) % 172.83/172.49 [8458]~P27(x84581)+P102(f332(f332(f246(x84581),f332(f332(f42(x84582,x84581),x84583),x84584)),f332(f332(f42(x84582,x84581),x84585),x84584)))+~P102(f332(f332(f246(f883(x84582,a871)),x84585),x84583)) % 172.83/172.49 [8469]~P102(f332(x84694,x84692))+P102(f332(f332(f201(x84691),x84692),x84693))+~P102(f332(f332(f201(f29(x84694,x84691,x84695)),x84692),x84693)) % 172.83/172.49 [8492]~P104(x84923)+P102(f332(f137(x84921),x84922))+~P102(f332(f137(x84921),f332(f332(f148(x84921,x84923,x84924),x84925),x84922))) % 172.83/172.49 [8502]P102(f332(f332(f201(x85021),x85022),x85023))+P102(f332(f332(f201(x85024),x85022),x85023))+~P102(f332(f332(f201(f29(x85025,x85021,x85024)),x85022),x85023)) % 172.83/172.49 [8632]~P104(x86321)+~P102(f332(f332(f334(x86322),x86323),f332(f173(x86322),x86324)))+~P102(f332(f137(x86322),f332(f332(f148(x86322,x86321,x86325),x86323),x86324))) % 172.83/172.49 [8712]~P104(x87121)+P29(x87121,f332(f332(f154(x87122,x87121),x87123),x87124))+~P29(x87121,f332(f332(f154(x87122,x87121),x87123),f332(f332(f148(x87122,x87121,x87123),x87125),x87124))) % 172.83/172.49 [8804]~P104(x88042)+E(f332(f332(f148(x88041,x88042,x88043),x88044),x88045),f149(x88041,x88042,x88043,x88044,x88045))+P102(f332(f332(f334(x88042),f332(x88043,x88044)),f332(f311(x88041,x88042,x88043),f332(f173(x88041),x88045)))) % 172.83/172.49 [8879]~P104(x88792)+E(f149(x88791,x88792,x88793,x88794,x88795),x88795)+~P102(f332(f332(f334(x88792),f332(x88793,x88794)),f332(f311(x88791,x88792,x88793),f332(f173(x88791),x88795)))) % 172.83/172.49 [8895]~P20(x88952,x88951,x88953,x88955)+P102(f332(f332(f247(f883(x88951,a871)),f332(f311(x88952,x88951,x88953),x88954)),f332(f311(x88952,x88951,x88953),x88955)))+~P102(f332(f332(f247(f883(x88952,a871)),x88954),x88955)) % 172.83/172.49 [9066]~P20(x90661,x90662,x90663,f255(f883(x90661,a871)))+~P102(f332(f332(f246(f883(x90662,a871)),x90664),f332(f311(x90661,x90662,x90663),x90665)))+P102(f332(f332(f246(f883(x90661,a871)),f332(f312(x90661,x90662,x90663),x90664)),x90665)) % 172.83/172.49 [9086]~E(f332(f311(x90863,x90861,x90864),f255(f883(x90863,a871))),f255(f883(x90861,a871)))+P102(f332(f332(f246(f883(x90861,a871)),x90862),f332(f311(x90863,x90861,x90864),x90865)))+~P102(f332(f332(f246(f883(x90863,a871)),f332(f312(x90863,x90861,x90864),x90862)),x90865)) % 172.83/172.49 [9110]~E(f332(f239(x91102),x91104),f332(f332(f179(x91101,x91102),x91105),x91103))+~P102(f332(f137(x91101),f332(f332(f154(f882(x91101,x91102),x91101),f266(x91101,x91102)),x91105)))+P102(f332(f332(f334(f882(x91101,x91102)),f332(f332(f267(x91101,x91102),x91103),x91104)),f332(f173(f882(x91101,x91102)),x91105))) % 172.83/172.49 [9192]~P20(x91921,x91924,x91925,f255(f883(x91921,a871)))+~P102(f332(f332(f246(f883(x91924,a871)),f332(f311(x91921,x91924,x91925),x91922)),f332(f311(x91921,x91924,x91925),x91923)))+P102(f332(f332(f246(f883(x91921,a871)),x91922),x91923)) % 172.83/172.49 [9257]E(f332(f239(x92571),x92572),f332(f332(f179(x92573,x92571),x92574),x92575))+~P102(f332(f137(x92573),f332(f332(f154(f882(x92573,x92571),x92573),f266(x92573,x92571)),x92574)))+~P102(f332(f332(f334(f882(x92573,x92571)),f332(f332(f267(x92573,x92571),x92575),x92572)),f332(f173(f882(x92573,x92571)),x92574))) % 172.83/172.49 [9259]E(f332(f332(f179(x92591,x92592),x92593),x92594),f332(f239(x92592),x92595))+~P102(f332(f137(x92591),f332(f332(f154(f882(x92591,x92592),x92591),f266(x92591,x92592)),x92593)))+~P102(f332(f332(f334(f882(x92591,x92592)),f332(f332(f267(x92591,x92592),x92594),x92595)),f332(f173(f882(x92591,x92592)),x92593))) % 172.83/172.49 [9314]~P76(x93141)+~E(f332(x93143,f755(x93143,x93144,x93145,x93142,x93141)),f2(x93141))+E(f332(f166(x93141),f332(f332(f154(x93142,x93141),x93143),f332(f136(x93142,x93144),x93145))),f332(f166(x93141),f332(f332(f154(x93142,x93141),x93143),x93145))) % 172.83/172.49 [9491]~P11(x94911,x94912,x94913)+~P102(f332(f61(x94911),x94915))+P102(f332(f66(x94911,x94912,x94913,x94914,x94915),f332(f332(f64(x94911,x94912,x94913),x94914),x94915))) % 172.83/172.49 [9570]P102(f332(x95701,f660(x95702,x95701,x95703,x95704,x95705)))+~P102(f332(f332(f246(f883(x95705,a871)),x95704),x95703))+P102(f332(f332(f246(f883(x95705,a871)),f332(f332(f104(f883(x95705,a871)),x95704),f332(f252(x95705),x95701))),f332(f332(f104(f883(x95705,a871)),x95703),f332(f252(x95705),x95702)))) % 172.83/172.49 [9584]~P76(x95841)+~P102(f332(x95844,f755(x95843,x95844,x95845,x95842,x95841)))+E(f332(f166(x95841),f332(f332(f154(x95842,x95841),x95843),f332(f136(x95842,x95844),x95845))),f332(f166(x95841),f332(f332(f154(x95842,x95841),x95843),x95845))) % 172.83/172.49 [9663]~P27(x96635)+P102(f332(f332(f334(x96631),f628(x96632,x96633,x96631,x96634,x96635)),x96633))+P102(f332(f332(f246(x96635),x96634),f332(f332(f42(x96631,x96635),x96633),x96632))) % 172.83/172.49 [9666]~P76(x96661)+E(f332(f166(x96661),f332(f332(f154(x96662,x96661),x96663),f332(f136(x96662,x96664),x96665))),f332(f166(x96661),f332(f332(f154(x96662,x96661),x96663),x96665)))+P102(f332(f332(f334(x96662),f755(x96663,x96664,x96665,x96662,x96661)),f332(f173(x96662),x96665))) % 172.83/172.49 [9676]~P102(f332(x96765,f660(x96765,x96763,x96764,x96762,x96761)))+~P102(f332(f332(f246(f883(x96761,a871)),x96762),x96764))+P102(f332(f332(f246(f883(x96761,a871)),f332(f332(f104(f883(x96761,a871)),x96762),f332(f252(x96761),x96763))),f332(f332(f104(f883(x96761,a871)),x96764),f332(f252(x96761),x96765)))) % 172.83/172.49 [9710]P35(x97101,x97102,x97103,x97104,x97105)+~E(f332(f196(f877(x97102)),x97105),f332(f196(f877(x97101)),x97104))+P102(f332(f332(f247(a876),f734(x97105,x97104,x97103,x97102,x97101)),f332(f196(f877(x97101)),x97104))) % 172.83/172.49 [9711]P35(x97111,x97112,x97113,x97114,x97115)+~E(f332(f196(f877(x97112)),x97115),f332(f196(f877(x97111)),x97114))+P102(f332(f332(f247(a876),f775(x97113,x97115,x97112,x97114,x97111)),f332(f196(f877(x97111)),x97114))) % 172.83/172.49 [9744]P102(f332(f332(f334(x97441),f660(x97442,x97443,x97444,x97445,x97441)),x97445))+~P102(f332(f332(f246(f883(x97441,a871)),x97445),x97444))+P102(f332(f332(f246(f883(x97441,a871)),f332(f332(f104(f883(x97441,a871)),x97445),f332(f252(x97441),x97443))),f332(f332(f104(f883(x97441,a871)),x97444),f332(f252(x97441),x97442)))) % 172.83/172.49 [9798]~P27(x97981)+~P102(f332(f332(f246(x97981),x97982),f332(x97985,f628(x97985,x97984,x97983,x97982,x97981))))+P102(f332(f332(f246(x97981),x97982),f332(f332(f42(x97983,x97981),x97984),x97985))) % 172.83/172.49 [9831]~P67(x98311)+~P102(f332(f61(x98312),x98315))+E(f332(f332(f332(f65(x98311,x98312,f80(x98311)),f332(f332(f18(x98312,x98311,x98311),f332(f332(f8(x98311,f883(x98311,x98311),x98312),f80(x98311)),x98313)),x98314)),f77(x98311)),x98315),f332(f332(f80(x98311),f332(f332(f332(f65(x98311,x98312,f80(x98311)),x98313),f77(x98311)),x98315)),f332(f332(f332(f65(x98311,x98312,f80(x98311)),x98314),f77(x98311)),x98315))) % 172.83/172.49 [9894]~P102(f332(f332(f334(f882(f883(x98941,a871),f883(x98941,a871))),f332(f332(f267(f883(x98941,a871),f883(x98941,a871)),x98945),x98944)),f324(x98941,x98943)))+~P102(f332(f332(f334(x98941),x98942),x98945))+P102(f332(f332(f334(f882(x98941,x98941)),f332(f332(f267(x98941,x98941),x98942),f589(x98943,x98944,x98945,x98941,x98942))),x98943)) % 172.83/172.49 [10022]~P102(f332(f332(f334(f882(f877(x100221),f877(x100221))),f332(f332(f267(f877(x100221),f877(x100221)),f332(f332(f134(x100221),x100225),x100222)),f332(f332(f134(x100221),x100225),x100223))),f147(x100221,x100224)))+P102(f332(f332(f334(f882(f877(x100221),f877(x100221))),f332(f332(f267(f877(x100221),f877(x100221)),x100222),x100223)),f147(x100221,x100224)))+P102(f332(f332(f334(f882(x100221,x100221)),f332(f332(f267(x100221,x100221),f706(x100224,x100223,x100222,x100225,x100221)),f706(x100224,x100223,x100222,x100225,x100221))),x100224)) % 172.83/172.49 [7148]~E(f332(f196(f877(x71481)),x71483),f332(f196(f877(x71482)),x71484))+E(f332(f332(f179(x71481,x71482),f332(f332(f183(x71481,x71482),x71483),x71484)),x71485),f208(x71482))+P102(f332(f332(f334(x71481),x71485),f332(f173(x71481),x71483))) % 172.83/172.49 [7221]~E(x72213,x72215)+E(f332(f332(f165(x72211),f332(f332(f159(x72211,x72212),x72213),x72214)),x72215),x72214)+~P102(f332(f332(f247(a876),x72213),f332(f196(f877(x72211)),x72212))) % 172.83/172.49 [7330]~E(f332(f332(f134(x73301),x73302),x73304),f332(f332(f134(x73301),x73303),x73305))+E(f332(f332(f176(x73301),f332(f196(f877(x73301)),x73302)),x73303),x73302)+P102(f332(f332(f246(a876),f332(f196(f877(x73301)),x73303)),f332(f196(f877(x73301)),x73302))) % 172.83/172.49 [7347]~E(x73475,x73472)+P102(f332(x73471,x73472))+P102(f332(f332(f332(f332(a203,f31(x73471,x73473)),x73472),x73474),x73475)) % 172.83/172.49 [7841]~E(f332(f332(f134(x78411),x78412),x78414),f332(f332(f134(x78411),x78413),x78415))+E(f332(f332(f176(x78411),f332(f196(f877(x78411)),x78412)),x78413),x78412)+~P102(f332(f332(f246(a876),f332(f196(f877(x78411)),x78412)),f332(f196(f877(x78411)),x78413))) % 172.83/172.49 [7865]~P102(f332(f61(x78651),f332(x78654,x78655)))+~P102(f332(f332(f334(x78652),x78655),x78653))+P102(f332(f61(x78651),f332(f332(f42(x78652,f883(x78651,a871)),x78653),x78654))) % 172.83/172.49 [7918]~E(f332(f196(f877(x79181)),x79182),f332(f196(f877(x79183)),x79184))+~E(f332(f332(f179(x79181,x79183),f332(f332(f183(x79181,x79183),x79182),x79184)),x79185),f208(x79183))+~P102(f332(f332(f334(x79181),x79185),f332(f173(x79181),x79182))) % 172.83/172.49 [8048]~P40(x80481,x80483,x80485)+~P40(x80481,x80482,x80484)+P40(x80481,f332(f332(f113(f883(x80481,a871)),x80482),x80483),f332(f332(f113(f883(f882(x80481,x80481),a871)),x80484),x80485)) % 172.83/172.49 [8049]~P40(x80491,x80493,x80495)+~P40(x80491,x80492,x80494)+P40(x80491,f332(f332(f104(f883(x80491,a871)),x80492),x80493),f332(f332(f104(f883(f882(x80491,x80491),a871)),x80494),x80495)) % 172.83/172.49 [8131]E(x81311,x81312)+P102(f332(x81313,x81311))+~P102(f332(f332(f332(f332(a203,f31(x81313,x81314)),x81311),x81315),x81312)) % 172.83/172.49 [8406]E(f332(f332(f267(x84061,x84062),f332(f332(f165(x84061),x84063),x84064)),f332(f332(f165(x84062),x84065),x84064)),f332(f332(f165(f882(x84061,x84062)),f332(f332(f183(x84061,x84062),x84063),x84065)),x84064))+~P102(f332(f332(f247(a876),x84064),f332(f196(f877(x84061)),x84063)))+~P102(f332(f332(f247(a876),x84064),f332(f196(f877(x84062)),x84065))) % 172.83/172.49 [8566]~P40(x85661,x85663,x85664)+P102(f332(f332(f334(x85661),x85662),x85663))+~P102(f332(f332(f334(f882(x85661,x85661)),f332(f332(f267(x85661,x85661),x85665),x85662)),x85664)) % 172.83/172.49 [8567]~P40(x85671,x85673,x85674)+P102(f332(f332(f334(x85671),x85672),x85673))+~P102(f332(f332(f334(f882(x85671,x85671)),f332(f332(f267(x85671,x85671),x85672),x85675)),x85674)) % 172.83/172.49 [8568]~P3(x85681,x85683,x85684)+P102(f332(f332(f334(x85681),x85682),x85683))+~P102(f332(f332(f334(f882(x85681,x85681)),f332(f332(f267(x85681,x85681),x85685),x85682)),x85684)) % 172.83/172.49 [8569]~P3(x85691,x85693,x85694)+P102(f332(f332(f334(x85691),x85692),x85693))+~P102(f332(f332(f334(f882(x85691,x85691)),f332(f332(f267(x85691,x85691),x85692),x85695)),x85694)) % 172.83/172.49 [8827]~P3(x88271,x88275,x88272)+E(f332(f286(x88271,x88271,x88272),f332(f332(f310(x88271),x88273),f195(f883(x88271,a871)))),f332(f286(x88271,x88271,x88272),f332(f332(f310(x88271),x88274),f195(f883(x88271,a871)))))+~P102(f332(f332(f334(f882(x88271,x88271)),f332(f332(f267(x88271,x88271),x88273),x88274)),x88272)) % 172.83/172.49 [8910]~P102(f332(f332(f332(f332(a203,x89102),x89103),x89104),x89105))+~P102(f332(f332(f332(f332(a203,f31(x89101,x89102)),x89105),x89104),x89103))+P102(f332(f332(f332(f332(a203,f31(x89101,x89102)),x89103),x89104),x89103)) % 172.83/172.49 [9021]P102(f332(x90211,x90212))+~P102(f332(f332(f334(x90213),x90212),x90215))+P102(f332(f332(f334(x90213),f435(x90211,x90214,x90215,x90213)),f332(f332(f113(f883(x90213,a871)),x90215),x90214))) % 172.83/172.49 [9022]P102(f332(x90221,x90222))+~P102(f332(f332(f334(x90223),x90222),x90224))+P102(f332(f332(f334(x90223),f435(x90221,x90224,x90225,x90223)),f332(f332(f113(f883(x90223,a871)),x90225),x90224))) % 172.83/172.49 [9030]~P102(f332(x90302,x90305))+~P102(f332(f332(f334(x90301),x90305),x90304))+P102(f332(f332(f334(x90301),f427(x90302,x90303,x90304,x90301)),f332(f332(f113(f883(x90301,a871)),x90304),x90303))) % 172.83/172.49 [9031]~P102(f332(x90312,x90315))+~P102(f332(f332(f334(x90311),x90315),x90313))+P102(f332(f332(f334(x90311),f427(x90312,x90313,x90314,x90311)),f332(f332(f113(f883(x90311,a871)),x90314),x90313))) % 172.83/172.49 [9046]~P102(f332(f332(f246(f883(x90461,a871)),x90463),x90465))+~P102(f332(f332(f246(f883(x90461,a871)),x90462),x90464))+P102(f332(f332(f246(f883(x90461,a871)),f332(f332(f113(f883(x90461,a871)),x90462),x90463)),f332(f332(f113(f883(x90461,a871)),x90464),x90465))) % 172.83/172.49 [9047]~P102(f332(f332(f246(f883(x90471,a871)),x90475),x90473))+~P102(f332(f332(f246(f883(x90471,a871)),x90472),x90474))+P102(f332(f332(f246(f883(x90471,a871)),f332(f332(f22(f883(x90471,a871)),x90472),x90473)),f332(f332(f22(f883(x90471,a871)),x90474),x90475))) % 172.83/172.49 [9048]~P102(f332(f332(f246(f883(x90481,a871)),x90483),x90485))+~P102(f332(f332(f246(f883(x90481,a871)),x90482),x90484))+P102(f332(f332(f246(f883(x90481,a871)),f332(f332(f104(f883(x90481,a871)),x90482),x90483)),f332(f332(f104(f883(x90481,a871)),x90484),x90485))) % 172.83/172.49 [9135]~E(f332(f196(f877(x91351)),x91353),f332(f196(f877(x91352)),x91354))+E(f332(f332(f179(x91351,x91352),f332(f332(f183(x91351,x91352),x91353),x91354)),x91355),f332(f239(x91352),f712(x91355,x91354,x91352,x91353,x91351)))+~P102(f332(f332(f334(x91351),x91355),f332(f173(x91351),x91353))) % 172.83/172.49 [9139]P102(f332(f332(f334(f882(x91391,x91391)),f332(f332(f267(x91391,x91391),x91392),x91393)),f326(x91391,x91394,x91395)))+~P102(f332(f332(f246(a876),f332(x91394,x91392)),f332(x91394,x91393)))+~P102(f332(f332(f334(f882(x91391,x91391)),f332(f332(f267(x91391,x91391),x91392),x91393)),x91395)) % 172.83/172.49 [9324]P102(f332(f332(f334(f882(x93241,x93241)),f332(f332(f267(x93241,x93241),x93242),x93243)),f308(x93241,x93244)))+~P102(f332(f332(f334(f882(x93241,x93241)),f332(f332(f267(x93241,x93241),x93242),x93245)),f308(x93241,x93244)))+~P102(f332(f332(f334(f882(x93241,x93241)),f332(f332(f267(x93241,x93241),x93245),x93243)),x93244)) % 172.83/172.49 [9325]P102(f332(f332(f334(f882(x93251,x93251)),f332(f332(f267(x93251,x93251),x93252),x93253)),f308(x93251,x93254)))+~P102(f332(f332(f334(f882(x93251,x93251)),f332(f332(f267(x93251,x93251),x93255),x93253)),f308(x93251,x93254)))+~P102(f332(f332(f334(f882(x93251,x93251)),f332(f332(f267(x93251,x93251),x93252),x93255)),x93254)) % 172.83/172.49 [9422]E(x94221,x94222)+E(f332(a115,f609(x94223,x94224,x94221,x94222,x94225)),x94224)+~P102(f332(f332(f334(f882(x94225,x94225)),f332(f332(f267(x94225,x94225),x94222),x94221)),f332(f332(f190(f882(x94225,x94225),a871),x94224),x94223))) % 172.83/172.49 [9423]E(x94231,x94232)+E(f332(a115,f612(x94233,x94234,x94231,x94232,x94235)),x94234)+~P102(f332(f332(f334(f882(x94235,x94235)),f332(f332(f267(x94235,x94235),x94232),x94231)),f332(f332(f190(f882(x94235,x94235),a871),x94234),x94233))) % 172.83/172.49 [9424]E(x94241,f2(a876))+E(f332(a115,f609(x94242,x94241,x94243,x94244,x94245)),x94241)+~P102(f332(f332(f334(f882(x94245,x94245)),f332(f332(f267(x94245,x94245),x94244),x94243)),f332(f332(f190(f882(x94245,x94245),a871),x94241),x94242))) % 172.83/172.49 [9425]E(x94251,f2(a876))+E(f332(a115,f612(x94252,x94251,x94253,x94254,x94255)),x94251)+~P102(f332(f332(f334(f882(x94255,x94255)),f332(f332(f267(x94255,x94255),x94254),x94253)),f332(f332(f190(f882(x94255,x94255),a871),x94251),x94252))) % 172.83/172.49 [9441]P102(f332(f332(f334(f882(x94411,x94411)),f332(f332(f267(x94411,x94411),x94412),x94413)),f332(f332(f289(x94411,x94411,x94411),x94414),f308(x94411,x94414))))+~P102(f332(f332(f334(f882(x94411,x94411)),f332(f332(f267(x94411,x94411),x94412),x94415)),x94414))+~P102(f332(f332(f334(f882(x94411,x94411)),f332(f332(f267(x94411,x94411),x94415),x94413)),x94414)) % 172.83/172.49 [9448]~P102(f332(f332(f334(f882(x94481,x94481)),f332(f332(f267(x94481,x94481),x94482),x94485)),f308(x94481,x94484)))+P102(f332(f332(f334(f882(x94481,x94481)),f332(f332(f267(x94481,x94481),x94482),x94483)),f332(f332(f289(x94481,x94481,x94481),x94484),f308(x94481,x94484))))+~P102(f332(f332(f334(f882(x94481,x94481)),f332(f332(f267(x94481,x94481),x94485),x94483)),x94484)) % 172.83/172.49 [9487]~P3(x94871,x94875,x94872)+~P102(f332(f332(f334(f882(x94871,x94871)),f332(f332(f267(x94871,x94871),x94873),x94874)),x94872))+P102(f332(f332(f246(f883(x94871,a871)),f332(f286(x94871,x94871,x94872),f332(f332(f310(x94871),x94873),f195(f883(x94871,a871))))),f332(f286(x94871,x94871,x94872),f332(f332(f310(x94871),x94874),f195(f883(x94871,a871)))))) % 172.83/172.49 [9509]E(x95091,x95092)+P102(f332(f332(f332(f332(a203,x95093),x95091),x95094),f580(x95092,x95094,x95091,x95093,x95095)))+~P102(f332(f332(f332(f332(a203,f31(x95095,x95093)),x95091),x95094),x95092)) % 172.83/172.49 [9513]~P102(f332(x95135,x95132))+P102(f332(f332(f332(f332(a203,x95131),x95132),x95133),f580(x95134,x95133,x95132,x95131,x95135)))+~P102(f332(f332(f332(f332(a203,f31(x95135,x95131)),x95132),x95133),x95134)) % 172.83/172.49 [9542]P102(f332(f332(f334(f882(x95421,x95421)),f332(f332(f267(x95421,x95421),x95422),x95423)),f332(f332(f289(x95421,x95421,x95421),x95424),f308(x95421,x95424))))+~P102(f332(f332(f334(f882(x95421,x95421)),f332(f332(f267(x95421,x95421),x95422),x95425)),f332(f332(f289(x95421,x95421,x95421),x95424),f308(x95421,x95424))))+~P102(f332(f332(f334(f882(x95421,x95421)),f332(f332(f267(x95421,x95421),x95425),x95423)),x95424)) % 172.83/172.49 [9543]P102(f332(f332(f334(f882(x95431,x95431)),f332(f332(f267(x95431,x95431),x95432),x95433)),f332(f332(f289(x95431,x95431,x95431),x95434),f308(x95431,x95434))))+~P102(f332(f332(f334(f882(x95431,x95431)),f332(f332(f267(x95431,x95431),x95435),x95433)),f332(f332(f289(x95431,x95431,x95431),x95434),f308(x95431,x95434))))+~P102(f332(f332(f334(f882(x95431,x95431)),f332(f332(f267(x95431,x95431),x95432),x95435)),x95434)) % 172.83/172.49 [9593]~P102(f332(f66(x95931,x95931,x95934,x95932,x95933),x95935))+P102(f332(f332(f334(x95931),x95932),x95933))+P102(f332(f62(x95931,x95934,f332(f332(f310(x95931),x95932),x95933)),x95935)) % 172.83/172.49 [9632]~E(f332(f311(x96323,x96322,x96325),x96324),x96321)+E(x96321,f195(f883(x96322,a871)))+P102(f332(f332(f246(f883(x96323,a871)),f332(f311(x96322,x96323,f508(x96324,x96323,x96322,x96321)),x96321)),x96324)) % 172.83/172.49 [9679]~P27(x96795)+P102(f332(f332(f334(x96791),f444(x96792,x96793,x96794,x96791,x96795)),x96794))+P102(f332(f332(f246(x96795),f332(f332(f41(x96791,x96795),x96794),x96793)),x96792)) % 172.83/172.49 [9730]P35(x97301,x97302,x97303,x97304,x97305)+~E(f332(f196(f877(x97301)),x97304),f332(f196(f877(x97302)),x97305))+P102(f332(f332(f334(f882(x97301,x97302)),f730(x97305,x97304,x97303,x97302,x97301)),f332(f173(f882(x97301,x97302)),f332(f332(f183(x97301,x97302),x97304),x97305)))) % 172.83/172.49 [9731]P35(x97311,x97312,x97313,x97314,x97315)+~E(f332(f196(f877(x97311)),x97314),f332(f196(f877(x97312)),x97315))+P102(f332(f332(f334(f882(x97311,x97312)),f739(x97313,x97315,x97314,x97312,x97311)),f332(f173(f882(x97311,x97312)),f332(f332(f183(x97311,x97312),x97314),x97315)))) % 172.83/172.49 [9861]E(x98611,x98612)+P102(f332(f332(f332(f332(a203,f31(x98613,x98614)),f580(x98611,x98615,x98612,x98614,x98613)),x98615),x98611))+~P102(f332(f332(f332(f332(a203,f31(x98613,x98614)),x98612),x98615),x98611)) % 172.83/172.49 [9863]~P102(f332(x98631,x98635))+P102(f332(f332(f332(f332(a203,f31(x98631,x98632)),f580(x98633,x98634,x98635,x98632,x98631)),x98634),x98633))+~P102(f332(f332(f332(f332(a203,f31(x98631,x98632)),x98635),x98634),x98633)) % 172.83/172.49 [9871]E(x98711,x98712)+P102(f332(f332(f334(f882(x98713,x98713)),f332(f332(f267(x98713,x98713),x98711),f613(x98714,x98715,x98712,x98711,x98713))),x98714))+~P102(f332(f332(f334(f882(x98713,x98713)),f332(f332(f267(x98713,x98713),x98711),x98712)),f332(f332(f190(f882(x98713,x98713),a871),x98715),x98714))) % 172.83/172.49 [9872]E(x98721,f2(a876))+P102(f332(f332(f334(f882(x98722,x98722)),f332(f332(f267(x98722,x98722),x98723),f613(x98724,x98721,x98725,x98723,x98722))),x98724))+~P102(f332(f332(f334(f882(x98722,x98722)),f332(f332(f267(x98722,x98722),x98723),x98725)),f332(f332(f190(f882(x98722,x98722),a871),x98721),x98724))) % 172.83/172.49 [9915]~P27(x99151)+~P102(f332(f332(f246(x99151),f332(x99154,f444(x99155,x99154,x99153,x99152,x99151))),x99155))+P102(f332(f332(f246(x99151),f332(f332(f41(x99152,x99151),x99153),x99154)),x99155)) % 172.83/172.49 [9957]E(x99571,x99572)+P102(f332(f332(f334(f882(x99573,x99573)),f332(f332(f267(x99573,x99573),f611(x99574,x99575,x99571,x99572,x99573)),x99571)),x99574))+~P102(f332(f332(f334(f882(x99573,x99573)),f332(f332(f267(x99573,x99573),x99572),x99571)),f332(f332(f190(f882(x99573,x99573),a871),x99575),x99574))) % 172.83/172.49 [9958]E(x99581,f2(a876))+P102(f332(f332(f334(f882(x99582,x99582)),f332(f332(f267(x99582,x99582),f611(x99583,x99581,x99584,x99585,x99582)),x99584)),x99583))+~P102(f332(f332(f334(f882(x99582,x99582)),f332(f332(f267(x99582,x99582),x99585),x99584)),f332(f332(f190(f882(x99582,x99582),a871),x99581),x99583))) % 172.83/172.49 [9962]E(x99621,x99622)+P102(f332(f332(f334(f882(x99623,x99623)),f332(f332(f267(x99623,x99623),x99621),f611(x99624,x99625,x99622,x99621,x99623))),f332(f332(f190(f882(x99623,x99623),a871),f609(x99624,x99625,x99622,x99621,x99623)),x99624)))+~P102(f332(f332(f334(f882(x99623,x99623)),f332(f332(f267(x99623,x99623),x99621),x99622)),f332(f332(f190(f882(x99623,x99623),a871),x99625),x99624))) % 172.83/172.49 [9963]E(x99631,f2(a876))+P102(f332(f332(f334(f882(x99632,x99632)),f332(f332(f267(x99632,x99632),x99633),f611(x99634,x99631,x99635,x99633,x99632))),f332(f332(f190(f882(x99632,x99632),a871),f609(x99634,x99631,x99635,x99633,x99632)),x99634)))+~P102(f332(f332(f334(f882(x99632,x99632)),f332(f332(f267(x99632,x99632),x99633),x99635)),f332(f332(f190(f882(x99632,x99632),a871),x99631),x99634))) % 172.83/172.49 [10013]E(x100131,x100132)+P102(f332(f332(f334(f882(x100133,x100133)),f332(f332(f267(x100133,x100133),f613(x100134,x100135,x100131,x100132,x100133)),x100131)),f332(f332(f190(f882(x100133,x100133),a871),f612(x100134,x100135,x100131,x100132,x100133)),x100134)))+~P102(f332(f332(f334(f882(x100133,x100133)),f332(f332(f267(x100133,x100133),x100132),x100131)),f332(f332(f190(f882(x100133,x100133),a871),x100135),x100134))) % 172.83/172.49 [10014]E(x100141,f2(a876))+P102(f332(f332(f334(f882(x100142,x100142)),f332(f332(f267(x100142,x100142),f613(x100143,x100141,x100144,x100145,x100142)),x100144)),f332(f332(f190(f882(x100142,x100142),a871),f612(x100143,x100141,x100144,x100145,x100142)),x100143)))+~P102(f332(f332(f334(f882(x100142,x100142)),f332(f332(f267(x100142,x100142),x100145),x100144)),f332(f332(f190(f882(x100142,x100142),a871),x100141),x100143))) % 172.83/172.49 [10048]~P71(x100482)+~P102(f332(f61(x100481),x100485))+E(f332(f332(f6(x100481,x100482),f332(f332(f7(x100481,x100482,x100482),f332(f332(f18(x100481,x100482,f883(x100482,x100482)),f332(f332(f8(a871,f883(x100482,f883(x100482,x100482)),x100481),f99(x100482)),f332(f332(f7(x100481,f883(x100481,a871),a871),f334(x100481)),x100483))),x100484)),f2(x100482))),x100485),f332(f332(f6(x100481,x100482),x100484),f332(f332(f104(f883(x100481,a871)),x100485),x100483))) % 172.83/172.49 [8629]~P71(x86291)+~P102(f332(f61(x86294),x86295))+E(f332(f332(f79(x86291),f332(x86292,x86293)),f332(f332(f6(x86294,x86291),x86292),f332(f332(f22(f883(x86294,a871)),x86295),f332(f332(f310(x86294),x86293),f195(f883(x86294,a871)))))),f332(f332(f6(x86294,x86291),x86292),f332(f332(f310(x86294),x86293),x86295))) % 172.83/172.49 [8630]~P67(x86301)+~P102(f332(f61(x86304),x86305))+E(f332(f332(f80(x86301),f332(x86302,x86303)),f332(f332(f9(x86304,x86301),x86302),f332(f332(f22(f883(x86304,a871)),x86305),f332(f332(f310(x86304),x86303),f195(f883(x86304,a871)))))),f332(f332(f9(x86304,x86301),x86302),f332(f332(f310(x86304),x86303),x86305))) % 172.83/172.49 [8951]~P104(x89512)+~P29(x89512,f332(f169(x89512),f332(f332(f154(x89511,x89512),x89514),x89515)))+E(f332(f136(x89511,f332(f332(f8(x89512,a871,x89511),f332(f247(x89512),x89513)),x89514)),x89515),f178(x89511,f332(f332(f8(x89512,a871,x89511),f332(f247(x89512),x89513)),x89514),x89515)) % 172.83/172.49 [8976]~P71(x89761)+E(f332(f332(f79(x89761),f332(f332(f6(a876,x89761),x89762),f303(a876,x89763,x89764))),f332(f332(f6(a876,x89761),x89762),f303(a876,f332(f332(f79(a876),x89764),f77(a876)),f332(f332(f79(a876),x89764),x89765)))),f332(f332(f6(a876,x89761),x89762),f303(a876,x89763,f332(f332(f79(a876),x89764),x89765))))+~P102(f332(f332(f246(a876),x89763),f332(f332(f79(a876),x89764),f77(a876)))) % 172.83/172.49 [8977]~P102(f332(f332(f334(x89771),x89774),x89775))+~P102(f332(f332(f246(f883(x89771,a871)),f332(f173(x89771),x89772)),x89775))+P102(f332(f332(f246(f883(x89771,a871)),f332(f173(x89771),f332(f332(f159(x89771,x89772),x89773),x89774))),x89775)) % 172.83/172.49 [9202]~P27(x92022)+~P102(f332(f61(x92021),x92025))+E(f332(f332(f64(x92021,x92022,f332(f332(f8(x92022,f883(x92022,x92022),x92021),f113(x92022)),x92023)),x92024),x92025),f332(f332(f113(x92022),x92024),f332(f332(f41(x92021,x92022),x92025),x92023))) % 172.83/172.49 [9203]~P27(x92032)+~P102(f332(f61(x92031),x92035))+E(f332(f332(f64(x92031,x92032,f332(f332(f8(x92032,f883(x92032,x92032),x92031),f104(x92032)),x92033)),x92034),x92035),f332(f332(f104(x92032),x92034),f332(f332(f42(x92031,x92032),x92035),x92033))) % 172.83/172.49 [9250]E(f332(x92501,x92502),f332(x92501,x92503))+P102(f332(f332(f247(a876),f332(x92501,x92502)),f332(x92501,x92503)))+~P102(f332(f332(f334(f882(x92504,x92504)),f332(f332(f267(x92504,x92504),x92502),x92503)),f153(x92504,f332(f332(f151(f883(x92504,a876)),x92501),x92505)))) % 172.83/172.49 [9281]~E(f332(x92814,x92812),f332(x92814,x92813))+~P102(f332(f332(f334(f882(x92811,x92811)),f332(f332(f267(x92811,x92811),x92812),x92813)),f153(x92811,x92815)))+P102(f332(f332(f334(f882(x92811,x92811)),f332(f332(f267(x92811,x92811),x92812),x92813)),f153(x92811,f332(f332(f151(f883(x92811,a876)),x92814),x92815)))) % 172.83/172.49 [9303]~P20(x93031,x93032,x93033,x93035)+P20(x93031,x93032,x93033,f332(f332(f310(x93031),x93034),x93035))+P102(f332(f332(f334(x93032),f332(x93033,x93034)),f332(f311(x93031,x93032,x93033),f332(f332(f22(f883(x93031,a871)),x93035),f332(f332(f310(x93031),x93034),f195(f883(x93031,a871))))))) % 172.83/172.49 [9307]P102(f332(x93072,x93075))+~P102(f332(f332(f334(x93071),x93075),f332(f173(x93071),x93073)))+E(f332(f332(f138(x93071),f332(f196(f877(x93071)),f178(x93071,x93072,f332(f332(f134(x93071),x93073),x93074)))),f332(f332(f134(x93071),x93073),x93074)),f332(f332(f134(x93071),f332(f332(f138(x93071),f332(f196(f877(x93071)),f178(x93071,x93072,x93073))),x93073)),x93074)) % 172.83/172.49 [9310]~P102(f332(f332(f334(f882(x93101,x93101)),f332(f332(f267(x93101,x93101),x93102),x93103)),f153(x93101,x93105)))+~P102(f332(f332(f246(a876),f332(x93104,x93102)),f332(x93104,x93103)))+P102(f332(f332(f334(f882(x93101,x93101)),f332(f332(f267(x93101,x93101),x93102),x93103)),f153(x93101,f332(f332(f151(f883(x93101,a876)),x93104),x93105)))) % 172.83/172.49 [9375]P102(f332(f332(f334(f882(x93754,x93754)),f332(f332(f267(x93754,x93754),x93752),x93753)),f153(x93754,x93755)))+P102(f332(f332(f247(a876),f332(x93751,x93752)),f332(x93751,x93753)))+~P102(f332(f332(f334(f882(x93754,x93754)),f332(f332(f267(x93754,x93754),x93752),x93753)),f153(x93754,f332(f332(f151(f883(x93754,a876)),x93751),x93755)))) % 172.83/172.49 [9516]~P102(f332(f332(f334(f882(f877(x95161),f877(x95161))),f332(f332(f267(f877(x95161),f877(x95161)),x95162),x95164)),f158(x95161,x95165)))+~P102(f332(f332(f247(a876),x95163),f332(f196(f877(x95161)),x95162)))+P102(f332(f332(f334(f882(x95161,x95161)),f332(f332(f267(x95161,x95161),f332(f332(f165(x95161),x95162),x95163)),f332(f332(f165(x95161),x95164),x95163))),x95165)) % 172.83/172.49 [9758]E(x97581,f2(a1))+~P102(f332(f48(x97583,x97581),f332(f332(f267(a1,a1),x97584),x97585)))+P102(f332(f48(f332(f332(f80(a1),x97582),x97583),x97581),f332(f332(f267(a1,a1),f332(f332(f79(a1),f332(f332(f80(a1),x97582),x97584)),f332(f332(f38(a1),f332(f332(f80(a1),x97582),x97585)),x97581))),f44(a1,f332(f332(f80(a1),x97582),x97585),x97581)))) % 172.83/172.49 [9760]~P102(f332(f332(f247(a876),f2(a876)),x97603))+~P102(f332(f47(x97602,x97603),f332(f332(f267(a876,a876),x97604),x97605)))+P102(f332(f47(f332(f332(f80(a876),x97601),x97602),x97603),f332(f332(f267(a876,a876),f332(f332(f79(a876),f332(f332(f80(a876),x97601),x97604)),f332(f332(f38(a876),f332(f332(f80(a876),x97601),x97605)),x97603))),f44(a876,f332(f332(f80(a876),x97601),x97605),x97603)))) % 172.83/172.49 [10071]~P71(x100712)+~P102(f332(f61(x100711),x100714))+E(f332(f332(f6(x100711,x100712),x100713),f332(f252(x100711),f332(f332(f18(x100711,a871,a871),f332(f332(f8(a871,f883(a871,a871),x100711),a330),f332(f332(f7(x100711,f883(x100711,a871),a871),f334(x100711)),x100714))),f332(f332(f7(x100711,f883(x100711,a871),a871),f334(x100711)),x100715)))),f332(f332(f6(x100711,x100712),f332(f332(f7(x100711,x100712,x100712),f332(f332(f18(x100711,x100712,f883(x100712,x100712)),f332(f332(f8(a871,f883(x100712,f883(x100712,x100712)),x100711),f99(x100712)),f332(f332(f7(x100711,f883(x100711,a871),a871),f334(x100711)),x100715))),x100713)),f2(x100712))),x100714)) % 172.83/172.49 [8260]~E(f332(f332(f134(x82601),x82602),x82605),f332(f332(f134(x82601),x82603),x82604))+E(f332(f332(f134(x82601),f332(f332(f138(x82601),f332(f196(f877(x82601)),x82602)),x82603)),x82604),x82605)+P102(f332(f332(f246(a876),f332(f196(f877(x82601)),x82603)),f332(f196(f877(x82601)),x82602))) % 172.83/172.49 [8460]~E(f332(f332(f134(x84602),x84603),x84601),f332(f332(f134(x84602),x84604),x84605))+E(x84601,f332(f332(f134(x84602),f332(f332(f138(x84602),f332(f196(f877(x84602)),x84603)),x84604)),x84605))+~P102(f332(f332(f246(a876),f332(f196(f877(x84602)),x84603)),f332(f196(f877(x84602)),x84604))) % 172.83/172.49 [8549]~E(f332(f332(f79(a876),f332(f332(f80(a876),x85493),x85494)),x85491),f332(f332(f79(a876),f332(f332(f80(a876),x85492),x85494)),x85495))+~P102(f332(f332(f246(a876),x85493),x85492))+E(x85491,f332(f332(f79(a876),f332(f332(f80(a876),f332(f332(f22(a876),x85492),x85493)),x85494)),x85495)) % 172.83/172.49 [8550]~E(f332(f332(f79(a876),f332(f332(f80(a876),x85501),x85503)),x85504),f332(f332(f79(a876),f332(f332(f80(a876),x85502),x85503)),x85505))+~P102(f332(f332(f246(a876),x85502),x85501))+E(f332(f332(f79(a876),f332(f332(f80(a876),f332(f332(f22(a876),x85501),x85502)),x85503)),x85504),x85505) % 172.83/172.49 [8705]E(f332(f332(f79(a876),f332(f332(f80(a876),x87051),x87052)),x87053),f332(f332(f79(a876),f332(f332(f80(a876),x87054),x87052)),x87055))+~P102(f332(f332(f246(a876),x87054),x87051))+~E(x87055,f332(f332(f79(a876),f332(f332(f80(a876),f332(f332(f22(a876),x87051),x87054)),x87052)),x87053)) % 172.83/172.49 [8706]E(f332(f332(f79(a876),f332(f332(f80(a876),x87061),x87062)),x87063),f332(f332(f79(a876),f332(f332(f80(a876),x87064),x87062)),x87065))+~P102(f332(f332(f246(a876),x87064),x87061))+~E(f332(f332(f79(a876),f332(f332(f80(a876),f332(f332(f22(a876),x87061),x87064)),x87062)),x87063),x87065) % 172.83/172.49 [9569]~P57(x95692)+~P102(f332(f61(x95691),x95695))+E(f332(f332(f9(x95691,x95692),f332(f332(f18(x95691,x95692,x95692),f332(f332(f8(x95692,f883(x95692,x95692),x95691),f290(x95692)),x95693)),x95694)),x95695),f332(f332(f290(x95692),f332(f332(f9(x95691,x95692),x95693),x95695)),f332(f332(f9(x95691,x95692),x95694),x95695))) % 172.83/172.49 [9694]~E(f614(x96945,x96944,x96943,x96942,x96941),f615(x96945,x96944,x96943,x96942,x96941))+P102(f332(f332(f334(f882(x96941,x96941)),f332(f332(f267(x96941,x96941),x96942),x96943)),f308(x96941,x96944)))+~P102(f332(f332(f334(f882(x96941,x96941)),f332(f332(f267(x96941,x96941),x96942),x96943)),f308(x96941,f332(f332(f113(f883(f882(x96941,x96941),a871)),x96944),x96945)))) % 172.83/172.49 [9695]~E(f616(x96955,x96954,x96953,x96952,x96951),f617(x96955,x96954,x96953,x96952,x96951))+P102(f332(f332(f334(f882(x96951,x96951)),f332(f332(f267(x96951,x96951),x96952),x96953)),f308(x96951,x96954)))+~P102(f332(f332(f334(f882(x96951,x96951)),f332(f332(f267(x96951,x96951),x96952),x96953)),f308(x96951,f332(f332(f113(f883(f882(x96951,x96951),a871)),x96954),x96955)))) % 172.83/172.49 [9905]P102(f332(f332(f334(f882(x99051,x99051)),f332(f332(f267(x99051,x99051),x99052),f615(x99055,x99054,x99053,x99052,x99051))),f308(x99051,x99054)))+P102(f332(f332(f334(f882(x99051,x99051)),f332(f332(f267(x99051,x99051),x99052),x99053)),f308(x99051,x99054)))+~P102(f332(f332(f334(f882(x99051,x99051)),f332(f332(f267(x99051,x99051),x99052),x99053)),f308(x99051,f332(f332(f113(f883(f882(x99051,x99051),a871)),x99054),x99055)))) % 172.83/172.49 [9984]P102(f332(f332(f334(f882(x99841,x99841)),f332(f332(f267(x99841,x99841),f617(x99845,x99844,x99843,x99842,x99841)),x99843)),f308(x99841,x99844)))+P102(f332(f332(f334(f882(x99841,x99841)),f332(f332(f267(x99841,x99841),x99842),x99843)),f308(x99841,x99844)))+~P102(f332(f332(f334(f882(x99841,x99841)),f332(f332(f267(x99841,x99841),x99842),x99843)),f308(x99841,f332(f332(f113(f883(f882(x99841,x99841),a871)),x99844),x99845)))) % 172.83/172.49 [10020]P102(f332(f332(f334(f882(x100201,x100201)),f332(f332(f267(x100201,x100201),x100202),x100203)),f308(x100201,x100204)))+P102(f332(f332(f334(f882(x100201,x100201)),f332(f332(f267(x100201,x100201),f615(x100205,x100204,x100203,x100202,x100201)),f614(x100205,x100204,x100203,x100202,x100201))),x100205))+~P102(f332(f332(f334(f882(x100201,x100201)),f332(f332(f267(x100201,x100201),x100202),x100203)),f308(x100201,f332(f332(f113(f883(f882(x100201,x100201),a871)),x100204),x100205)))) % 172.83/172.49 [10021]P102(f332(f332(f334(f882(x100211,x100211)),f332(f332(f267(x100211,x100211),x100212),x100213)),f308(x100211,x100214)))+P102(f332(f332(f334(f882(x100211,x100211)),f332(f332(f267(x100211,x100211),f616(x100215,x100214,x100213,x100212,x100211)),f617(x100215,x100214,x100213,x100212,x100211))),x100215))+~P102(f332(f332(f334(f882(x100211,x100211)),f332(f332(f267(x100211,x100211),x100212),x100213)),f308(x100211,f332(f332(f113(f883(f882(x100211,x100211),a871)),x100214),x100215)))) % 172.83/172.49 [10142]~P102(f332(f332(f334(f882(f877(x101421),f877(x101421))),f332(f332(f267(f877(x101421),f877(x101421)),x101424),x101425)),f158(x101421,x101422)))+~P102(f332(f332(f334(f882(x101421,x101421)),x101423),f332(f173(f882(x101421,x101421)),f332(f332(f183(x101421,x101421),x101424),x101425))))+P102(f332(f332(f271(x101421,x101421,a871),f332(f332(f7(x101421,f883(f882(x101421,x101421),a871),f883(x101421,a871)),f332(f332(f8(f883(x101421,f883(f883(f882(x101421,x101421),a871),a871)),f883(f883(f882(x101421,x101421),a871),f883(x101421,a871)),x101421),f7(x101421,f883(f882(x101421,x101421),a871),a871)),f332(f332(f8(f883(x101421,f882(x101421,x101421)),f883(x101421,f883(f883(f882(x101421,x101421),a871),a871)),x101421),f332(f8(f882(x101421,x101421),f883(f883(f882(x101421,x101421),a871),a871),x101421),f334(f882(x101421,x101421)))),f267(x101421,x101421)))),x101422)),x101423)) % 172.83/172.49 [9597]~P102(f332(f332(f246(a876),x95973),x95972))+~P102(f332(f332(f247(a876),f332(f332(f79(a876),f332(f332(f80(a876),x95973),x95974)),x95971)),f332(f332(f79(a876),f332(f332(f80(a876),x95972),x95974)),x95975)))+P102(f332(f332(f247(a876),x95971),f332(f332(f79(a876),f332(f332(f80(a876),f332(f332(f22(a876),x95972),x95973)),x95974)),x95975))) % 172.83/172.49 [9598]~P102(f332(f332(f246(a876),x95983),x95982))+~P102(f332(f332(f246(a876),f332(f332(f79(a876),f332(f332(f80(a876),x95983),x95984)),x95981)),f332(f332(f79(a876),f332(f332(f80(a876),x95982),x95984)),x95985)))+P102(f332(f332(f246(a876),x95981),f332(f332(f79(a876),f332(f332(f80(a876),f332(f332(f22(a876),x95982),x95983)),x95984)),x95985))) % 172.83/172.49 [9616]~P102(f332(f332(f246(a876),x96161),x96164))+P102(f332(f332(f247(a876),f332(f332(f79(a876),f332(f332(f80(a876),x96161),x96162)),x96163)),f332(f332(f79(a876),f332(f332(f80(a876),x96164),x96162)),x96165)))+~P102(f332(f332(f247(a876),x96163),f332(f332(f79(a876),f332(f332(f80(a876),f332(f332(f22(a876),x96164),x96161)),x96162)),x96165))) % 172.83/172.49 [9617]~P102(f332(f332(f246(a876),x96171),x96174))+P102(f332(f332(f246(a876),f332(f332(f79(a876),f332(f332(f80(a876),x96171),x96172)),x96173)),f332(f332(f79(a876),f332(f332(f80(a876),x96174),x96172)),x96175)))+~P102(f332(f332(f246(a876),x96173),f332(f332(f79(a876),f332(f332(f80(a876),f332(f332(f22(a876),x96174),x96171)),x96172)),x96175))) % 172.83/172.49 [9728]~P102(f332(f332(f246(a876),x97282),x97281))+~P102(f332(f332(f247(a876),f332(f332(f79(a876),f332(f332(f80(a876),x97281),x97283)),x97284)),f332(f332(f79(a876),f332(f332(f80(a876),x97282),x97283)),x97285)))+P102(f332(f332(f247(a876),f332(f332(f79(a876),f332(f332(f80(a876),f332(f332(f22(a876),x97281),x97282)),x97283)),x97284)),x97285)) % 172.83/172.49 [9729]~P102(f332(f332(f246(a876),x97292),x97291))+~P102(f332(f332(f246(a876),f332(f332(f79(a876),f332(f332(f80(a876),x97291),x97293)),x97294)),f332(f332(f79(a876),f332(f332(f80(a876),x97292),x97293)),x97295)))+P102(f332(f332(f246(a876),f332(f332(f79(a876),f332(f332(f80(a876),f332(f332(f22(a876),x97291),x97292)),x97293)),x97294)),x97295)) % 172.83/172.49 [9782]~P102(f332(f332(f246(a876),x97824),x97821))+P102(f332(f332(f247(a876),f332(f332(f79(a876),f332(f332(f80(a876),x97821),x97822)),x97823)),f332(f332(f79(a876),f332(f332(f80(a876),x97824),x97822)),x97825)))+~P102(f332(f332(f247(a876),f332(f332(f79(a876),f332(f332(f80(a876),f332(f332(f22(a876),x97821),x97824)),x97822)),x97823)),x97825)) % 172.83/172.49 [9783]~P102(f332(f332(f246(a876),x97834),x97831))+P102(f332(f332(f246(a876),f332(f332(f79(a876),f332(f332(f80(a876),x97831),x97832)),x97833)),f332(f332(f79(a876),f332(f332(f80(a876),x97834),x97832)),x97835)))+~P102(f332(f332(f246(a876),f332(f332(f79(a876),f332(f332(f80(a876),f332(f332(f22(a876),x97831),x97834)),x97832)),x97833)),x97835)) % 172.83/172.49 [10005]~P8(x100051,x100052,x100055,x100053)+~P102(f332(f332(f334(f882(x100051,x100051)),x100054),x100055))+P102(f332(f332(f271(x100051,x100051,a871),f332(f332(f7(x100051,f883(x100051,x100052),f883(x100051,a871)),f332(f332(f8(f883(x100052,a871),f883(f883(x100051,x100052),f883(x100051,a871)),x100051),f8(x100052,a871,x100051)),f332(f332(f8(x100052,f883(x100052,a871),x100051),a329),x100053))),x100053)),x100054)) % 172.83/172.49 [6791]~E(f332(x67914,x67915),f208(x67912))+E(f332(f186(x67911,x67912,x67913,x67914),x67915),f332(f239(x67912),x67916))+~E(f332(x67913,x67915),f332(f239(x67912),x67916)) % 172.83/172.49 [6892]~E(f332(x68923,x68926),f208(x68921))+E(f332(f241(f880(x68921),x68922,f208(x68921),x68923),f332(x68924,x68925)),f208(x68921))+~E(f332(x68924,x68925),f332(f239(x68922),x68926)) % 172.83/172.49 [7477]E(f332(x74771,x74772),f208(x74773))+~E(f332(f186(x74775,x74773,x74776,x74771),x74772),f332(f239(x74773),x74774))+E(f332(x74771,x74772),f332(f239(x74773),x74774)) % 172.83/172.49 [7513]~E(f332(f186(x75136,x75133,x75135,x75131),x75132),f332(f239(x75133),x75134))+E(f332(x75131,x75132),f332(f239(x75133),x75134))+E(f332(x75135,x75132),f332(f239(x75133),x75134)) % 172.83/172.49 [8419]~P14(x84196,x84191,x84192,x84194)+E(f332(f72(x84191,x84191,x84191,f332(x84192,x84193)),f332(x84194,x84195)),f332(f72(x84191,x84191,x84191,f332(x84194,x84195)),f332(x84192,x84193)))+~P102(f332(f61(x84196),x84195)) % 172.83/172.49 [8839]~P20(x88391,x88393,x88395,x88396)+~P20(x88393,x88392,x88394,f332(f311(x88391,x88393,x88395),x88396))+P20(x88391,x88392,f332(f72(x88393,x88392,x88391,x88394),x88395),x88396) % 172.83/172.49 [9407]~P102(f332(f332(x94073,x94072),x94076))+~P102(f332(f332(x94074,x94075),x94072))+P102(f332(f332(f334(x94071),x94072),f300(x94071,x94073,x94074,x94075,x94076))) % 172.83/172.49 [9408]~P102(f332(f332(x94084,x94082),x94086))+~P102(f332(f332(x94083,x94085),x94082))+P102(f332(f332(f334(x94081),x94082),f297(x94081,x94083,x94084,x94085,x94086))) % 172.83/172.49 [9517]E(x95171,x95172)+E(x95173,x95174)+~P102(f332(f332(f334(f882(f877(x95175),f877(x95175))),f332(f332(f267(f877(x95175),f877(x95175)),f332(f332(f151(x95175),x95173),x95171)),f332(f332(f151(x95175),x95174),x95172))),f157(x95175,x95176))) % 172.83/172.49 [9526]~E(x95262,x95264)+P102(f332(f332(f334(f882(f877(x95261),f877(x95261))),f332(f332(f267(f877(x95261),f877(x95261)),f332(f332(f151(x95261),x95262),x95263)),f332(f332(f151(x95261),x95264),x95265))),f145(x95261,x95266)))+~P102(f332(f332(f334(f882(f877(x95261),f877(x95261))),f332(f332(f267(f877(x95261),f877(x95261)),x95263),x95265)),f145(x95261,x95266))) % 172.83/172.49 [9527]~E(x95272,x95274)+P102(f332(f332(f334(f882(f877(x95271),f877(x95271))),f332(f332(f267(f877(x95271),f877(x95271)),f332(f332(f151(x95271),x95272),x95273)),f332(f332(f151(x95271),x95274),x95275))),f147(x95271,x95276)))+~P102(f332(f332(f334(f882(f877(x95271),f877(x95271))),f332(f332(f267(f877(x95271),f877(x95271)),x95273),x95275)),f147(x95271,x95276))) % 172.83/172.49 [9528]~E(x95282,x95284)+P102(f332(f332(f334(f882(f877(x95281),f877(x95281))),f332(f332(f267(f877(x95281),f877(x95281)),f332(f332(f151(x95281),x95282),x95283)),f332(f332(f151(x95281),x95284),x95285))),f157(x95281,x95286)))+~P102(f332(f332(f334(f882(f877(x95281),f877(x95281))),f332(f332(f267(f877(x95281),f877(x95281)),x95283),x95285)),f157(x95281,x95286))) % 172.83/172.49 [9529]~E(x95292,x95294)+P102(f332(f332(f334(f882(f877(x95291),f877(x95291))),f332(f332(f267(f877(x95291),f877(x95291)),f332(f332(f134(x95291),x95292),x95293)),f332(f332(f134(x95291),x95294),x95295))),f157(x95291,x95296)))+~P102(f332(f332(f334(f882(f877(x95291),f877(x95291))),f332(f332(f267(f877(x95291),f877(x95291)),x95293),x95295)),f157(x95291,x95296))) % 172.83/172.49 [9530]~E(x95303,x95305)+P102(f332(f332(f334(f882(f877(x95301),f877(x95301))),f332(f332(f267(f877(x95301),f877(x95301)),f332(f332(f134(x95301),x95302),x95303)),f332(f332(f134(x95301),x95304),x95305))),f157(x95301,x95306)))+~P102(f332(f332(f334(f882(f877(x95301),f877(x95301))),f332(f332(f267(f877(x95301),f877(x95301)),x95302),x95304)),f157(x95301,x95306))) % 172.83/172.49 [9585]E(x95851,x95852)+P102(f332(f332(f334(f882(f877(x95853),f877(x95853))),f332(f332(f267(f877(x95853),f877(x95853)),x95851),x95852)),f157(x95853,x95854)))+~P102(f332(f332(f334(f882(f877(x95853),f877(x95853))),f332(f332(f267(f877(x95853),f877(x95853)),f332(f332(f151(x95853),x95855),x95851)),f332(f332(f151(x95853),x95856),x95852))),f157(x95853,x95854))) % 172.83/172.49 [9732]~E(x97323,x97325)+P102(f332(f332(f334(f882(f877(x97321),f877(x97321))),f332(f332(f267(f877(x97321),f877(x97321)),f332(f332(f134(x97321),x97322),f332(f332(f151(x97321),x97323),f116(x97321)))),f332(f332(f134(x97321),x97324),f332(f332(f151(x97321),x97325),f116(x97321))))),f157(x97321,x97326)))+~P102(f332(f332(f334(f882(f877(x97321),f877(x97321))),f332(f332(f267(f877(x97321),f877(x97321)),x97322),x97324)),f157(x97321,x97326))) % 172.83/172.49 [9748]E(f332(x97481,x97482),f208(x97483))+~E(f332(f241(f880(x97486),x97483,f208(x97486),x97484),f332(x97481,x97482)),f208(x97486))+E(f332(x97484,f768(x97482,x97481,x97484,x97485,x97486,x97483)),f208(x97486)) % 172.83/172.49 [9749]E(f332(x97491,x97492),f208(x97493))+~E(f332(f241(f880(x97496),x97493,f208(x97496),x97494),f332(x97491,x97492)),f208(x97496))+E(f332(f239(x97493),f768(x97492,x97491,x97494,x97495,x97496,x97493)),f332(x97491,x97492)) % 172.83/172.49 [9786]E(x97861,x97862)+E(x97863,x97864)+~P102(f332(f332(f334(f882(f877(x97865),f877(x97865))),f332(f332(f267(f877(x97865),f877(x97865)),f332(f332(f134(x97865),x97863),f332(f332(f151(x97865),x97861),f116(x97865)))),f332(f332(f134(x97865),x97864),f332(f332(f151(x97865),x97862),f116(x97865))))),f157(x97865,x97866))) % 172.83/172.49 [9811]E(x98111,x98112)+~P102(f332(f332(f334(f882(f877(x98113),f877(x98113))),f332(f332(f267(f877(x98113),f877(x98113)),f332(f332(f134(x98113),x98111),f332(f332(f151(x98113),x98115),f116(x98113)))),f332(f332(f134(x98113),x98112),f332(f332(f151(x98113),x98116),f116(x98113))))),f157(x98113,x98114)))+P102(f332(f332(f334(f882(f877(x98113),f877(x98113))),f332(f332(f267(f877(x98113),f877(x98113)),x98111),x98112)),f157(x98113,x98114))) % 172.83/172.49 [9847]~P102(f332(f332(f334(f882(f883(x98471,a871),f883(x98471,a871))),f332(f332(f267(f883(x98471,a871),f883(x98471,a871)),x98472),x98474)),f324(x98471,x98476)))+~P102(f332(f332(f334(f882(f883(x98471,a871),f883(x98471,a871))),f332(f332(f267(f883(x98471,a871),f883(x98471,a871)),x98473),x98475)),f324(x98471,x98476)))+P102(f332(f332(f334(f882(f883(x98471,a871),f883(x98471,a871))),f332(f332(f267(f883(x98471,a871),f883(x98471,a871)),f332(f332(f113(f883(x98471,a871)),x98472),x98473)),f332(f332(f113(f883(x98471,a871)),x98474),x98475))),f324(x98471,x98476))) % 172.83/172.49 [5243]~E(f332(x52433,x52436),x52435)+~E(x52434,f332(f239(x52431),x52436))+E(f332(f332(f209(x52431,x52432),x52433),x52434),f332(f239(x52432),x52435)) % 172.83/172.49 [5661]~E(f332(f332(f134(x56611),x56616),x56613),x56615)+E(f332(f332(f134(x56611),x56612),x56613),f332(f332(f151(x56611),x56614),x56615))+~E(x56612,f332(f332(f151(x56611),x56614),x56616)) % 172.83/172.49 [5662]~E(f332(f332(f134(x56621),x56626),x56623),x56625)+E(f332(f332(f134(x56621),x56622),x56623),f332(f332(f134(x56621),x56624),x56625))+~E(x56622,f332(f332(f134(x56621),x56624),x56626)) % 172.83/172.49 [5664]E(f332(f332(f134(x56641),x56642),x56643),f332(f332(f151(x56641),x56644),x56645))+~E(f332(f332(f151(x56641),x56644),x56646),x56642)+~E(x56645,f332(f332(f134(x56641),x56646),x56643)) % 172.83/172.49 [5666]~E(f332(f332(f134(x56661),x56662),x56666),x56664)+E(f332(f332(f134(x56661),x56662),x56663),f332(f332(f134(x56661),x56664),x56665))+~E(x56663,f332(f332(f134(x56661),x56666),x56665)) % 172.83/172.49 [6785]E(f332(x67851,x67852),f332(x67853,x67852))+~E(f332(f332(f154(x67854,x67855),x67851),x67856),f332(f332(f154(x67854,x67855),x67853),x67856))+~P102(f332(f332(f334(x67854),x67852),f332(f173(x67854),x67856))) % 172.83/172.49 [7171]~P14(x71714,x71715,x71716,x71711)+E(f332(f332(x71711,x71712),x71713),f332(f332(f64(x71714,x71715,x71716),x71713),x71712))+~P102(f332(f61(x71714),x71712)) % 172.83/172.49 [7237]~E(x72372,f332(x72374,x72376))+~P102(f332(f332(f334(x72373),x72376),x72375))+P102(f332(f332(f334(x72371),x72372),f332(f311(x72373,x72371,x72374),x72375))) % 172.83/172.49 [7238]~E(f332(x72384,x72382),x72386)+~P102(f332(f332(f334(x72383),x72386),x72385))+P102(f332(f332(f334(x72381),x72382),f332(f312(x72381,x72383,x72384),x72385))) % 172.83/172.49 [7694]~P33(x76941,x76942,x76944,x76946)+P33(x76941,x76942,f332(f332(f151(x76941),x76943),x76944),f332(f332(f151(x76941),x76945),x76946))+~P102(f332(f332(x76942,x76943),x76945)) % 172.83/172.49 [8713]~P52(x87134,x87135,x87131,x87132,x87136)+E(f332(x87131,f332(x87132,x87133)),x87133)+~P102(f332(f332(f334(x87135),x87133),x87136)) % 172.83/172.49 [9519]E(x95191,x95192)+E(f332(f196(f877(x95193)),x95194),f332(f196(f877(x95193)),x95195))+~P102(f332(f332(f334(f882(f877(x95193),f877(x95193))),f332(f332(f267(f877(x95193),f877(x95193)),f332(f332(f151(x95193),x95191),x95194)),f332(f332(f151(x95193),x95192),x95195))),f145(x95193,x95196))) % 172.83/172.49 [9581]~P11(x95811,x95812,x95813)+E(f332(f332(f64(x95811,x95812,x95813),x95814),x95815),x95816)+~P102(f332(f66(x95811,x95812,x95813,x95814,x95815),x95816)) % 172.83/172.49 [9588]E(f332(f196(f877(x95881)),x95882),f332(f196(f877(x95881)),x95883))+P102(f332(f332(f334(f882(f877(x95881),f877(x95881))),f332(f332(f267(f877(x95881),f877(x95881)),x95882),x95883)),f145(x95881,x95884)))+~P102(f332(f332(f334(f882(f877(x95881),f877(x95881))),f332(f332(f267(f877(x95881),f877(x95881)),f332(f332(f151(x95881),x95885),x95882)),f332(f332(f151(x95881),x95886),x95883))),f145(x95881,x95884))) % 172.83/172.49 [9610]~P102(f332(f332(f334(f882(x96101,x96101)),f332(f332(f267(x96101,x96101),x96102),x96104)),f308(x96101,x96106)))+P102(f332(f332(f334(f882(f877(x96101),f877(x96101))),f332(f332(f267(f877(x96101),f877(x96101)),f332(f332(f151(x96101),x96102),x96103)),f332(f332(f151(x96101),x96104),x96105))),f308(f877(x96101),f157(x96101,x96106))))+~P102(f332(f332(f334(f882(f877(x96101),f877(x96101))),f332(f332(f267(f877(x96101),f877(x96101)),x96103),x96105)),f308(f877(x96101),f157(x96101,x96106)))) % 172.83/172.49 [9792]~P102(f332(x97922,x97926))+~E(f332(f136(x97921,x97922),x97923),f332(f332(f151(x97921),x97924),x97925))+~P102(f332(f332(f334(x97921),x97926),f332(f173(x97921),f784(x97925,x97924,x97923,x97922,x97921)))) % 172.83/172.49 [9793]~P102(f332(x97934,x97936))+~E(f332(f332(f151(x97931),x97932),x97933),f332(f136(x97931,x97934),x97935))+~P102(f332(f332(f334(x97931),x97936),f332(f173(x97931),f789(x97935,x97934,x97933,x97932,x97931)))) % 172.83/172.49 [10099]~P71(x100992)+E(f332(f332(f6(x100991,x100992),f332(f332(f8(f883(x100993,a871),x100992,x100991),f332(f6(x100993,x100992),x100994)),f332(f332(f8(f883(x100993,a871),f883(x100993,a871),x100991),f252(x100993)),f332(f332(f8(f883(x100993,a871),f883(x100993,a871),x100991),f332(f18(x100993,a871,a871),f332(f332(f8(a871,f883(a871,a871),x100993),a330),f332(f332(f7(x100993,f883(x100993,a871),a871),f334(x100993)),x100995)))),f332(f7(x100993,x100991,a871),f332(f332(f8(x100991,f883(x100991,a871),x100993),a329),x100996)))))),f332(f311(x100993,x100991,x100996),x100995)),f332(f332(f6(x100993,x100992),x100994),x100995))+~P102(f332(f61(x100993),x100995)) % 172.83/172.49 [6843]~P104(x68433)+P102(f332(x68432,x68435))+E(f332(f136(x68431,x68432),f332(f332(f148(x68431,x68433,x68434),x68435),x68436)),f332(f136(x68431,x68432),x68436)) % 172.83/172.49 [6845]P102(f332(x68451,x68452))+~E(f167(x68453,x68451,x68454),f332(f332(f267(f877(x68453),f877(x68453)),x68455),x68456))+~P102(f332(f332(f334(x68453),x68452),f332(f173(x68453),x68455))) % 172.83/172.49 [6889]~P102(f332(x68892,x68896))+~E(f167(x68891,x68892,x68893),f332(f332(f267(f877(x68891),f877(x68891)),x68894),x68895))+~P102(f332(f332(f334(x68891),x68896),f332(f173(x68891),x68895))) % 172.83/172.49 [7558]~P10(x75581,x75582,x75583)+~P102(f332(f61(x75581),x75586))+E(f332(f332(f64(x75581,x75582,x75583),x75584),f332(f332(f310(x75581),x75585),x75586)),f332(f332(f64(x75581,x75582,x75583),f332(f332(x75583,x75585),x75584)),x75586)) % 172.83/172.49 [7608]~P104(x76082)+~P102(f332(f332(f246(x76082),f332(x76083,x76084)),f332(x76083,x76085)))+E(f332(f332(f148(x76081,x76082,x76083),x76084),f332(f332(f151(x76081),x76085),x76086)),f332(f332(f151(x76081),x76084),f332(f332(f151(x76081),x76085),x76086))) % 172.83/172.49 [7725]E(x77251,x77252)+~E(f332(f332(f269(x77253,x77254),x77251),f332(f16(f883(x77254,a871),x77253),x77255)),f332(f332(f269(x77253,x77254),x77252),f332(f16(f883(x77254,a871),x77253),x77255)))+~P102(f332(f332(f334(x77254),x77256),x77255)) % 172.83/172.49 [7793]~P10(x77931,x77932,x77933)+~P102(f332(f61(x77931),x77936))+E(f332(f332(f64(x77931,x77932,x77933),x77934),f332(f332(f310(x77931),x77935),x77936)),f332(f332(x77933,x77935),f332(f332(f64(x77931,x77932,x77933),x77934),x77936))) % 172.83/172.49 [7910]~P11(x79101,x79102,x79103)+~P102(f332(f61(x79101),x79106))+E(f332(f332(f64(x79101,x79102,x79103),f332(f332(x79103,x79104),x79105)),x79106),f332(f332(x79103,x79104),f332(f332(f64(x79101,x79102,x79103),x79105),x79106))) % 172.83/172.49 [7980]~P15(x79802,x79805,x79806,x79801)+~P102(f332(f61(x79802),x79804))+E(f332(x79801,f332(f332(f310(x79802),x79803),x79804)),f332(f72(x79805,x79805,x79805,f332(x79801,x79804)),f332(x79806,x79803))) % 172.83/172.49 [8018]~P104(x80182)+P102(f332(f332(f246(x80182),f332(x80183,x80184)),f332(x80183,x80185)))+E(f332(f332(f148(x80181,x80182,x80183),x80184),f332(f332(f151(x80181),x80185),x80186)),f332(f332(f151(x80181),x80185),f332(f332(f148(x80181,x80182,x80183),x80184),x80186))) % 172.83/172.49 [8161]~E(f332(f196(f877(x81611)),x81615),f332(f196(f877(x81612)),x81616))+~E(f332(f196(f877(x81611)),x81613),f332(f196(f877(x81612)),x81614))+E(f332(f332(f134(f882(x81611,x81612)),f332(f332(f183(x81611,x81612),x81613),x81614)),f332(f332(f183(x81611,x81612),x81615),x81616)),f332(f332(f183(x81611,x81612),f332(f332(f134(x81611),x81613),x81615)),f332(f332(f134(x81612),x81614),x81616))) % 172.83/172.49 [8275]~E(x82752,f332(f311(x82753,x82751,x82754),x82756))+P102(f332(f332(f246(f883(x82751,a871)),x82752),f332(f311(x82753,x82751,x82754),x82755)))+~P102(f332(f332(f246(f883(x82753,a871)),x82756),x82755)) % 172.83/172.49 [8376]~P104(x83765)+E(f332(x83761,x83762),f332(x83761,x83763))+E(f332(f332(f148(x83764,x83765,x83761),x83762),f332(f332(f148(x83764,x83765,x83761),x83763),x83766)),f332(f332(f148(x83764,x83765,x83761),x83763),f332(f332(f148(x83764,x83765,x83761),x83762),x83766))) % 172.83/172.49 [8412]~P20(x84123,x84121,x84124,x84125)+P20(x84123,x84121,f332(f332(f332(f71(x84123,x84121),x84124),x84126),x84122),x84125)+P102(f332(f332(f334(x84121),x84122),f332(f311(x84123,x84121,x84124),x84125))) % 172.83/172.49 [8558]~P102(f332(f332(f334(x85582),x85584),f332(x85586,x85583)))+~P102(f332(f332(f334(x85581),x85583),x85585))+P102(f332(f332(f334(f882(x85581,x85582)),f332(f332(f267(x85581,x85582),x85583),x85584)),f332(f332(f269(x85581,x85582),x85585),x85586))) % 172.83/172.49 [9019]~P71(x90192)+~P20(x90194,x90191,x90195,x90196)+E(f332(f332(f6(x90191,x90192),x90193),f332(f311(x90194,x90191,x90195),x90196)),f332(f332(f6(x90194,x90192),f332(f72(x90191,x90192,x90194,x90193),x90195)),x90196)) % 172.83/172.49 [9020]~P67(x90202)+~P20(x90204,x90201,x90205,x90206)+E(f332(f332(f9(x90201,x90202),x90203),f332(f311(x90204,x90201,x90205),x90206)),f332(f332(f9(x90204,x90202),f332(f72(x90201,x90202,x90204,x90203),x90205)),x90206)) % 172.83/172.49 [9068]~P35(x90682,x90685,x90681,x90683,x90686)+P102(f332(f332(x90681,f332(f332(f165(x90682),x90683),x90684)),f332(f332(f165(x90685),x90686),x90684)))+~P102(f332(f332(f247(a876),x90684),f332(f196(f877(x90685)),x90686))) % 172.83/172.49 [9069]~P35(x90692,x90695,x90691,x90693,x90696)+P102(f332(f332(x90691,f332(f332(f165(x90692),x90693),x90694)),f332(f332(f165(x90695),x90696),x90694)))+~P102(f332(f332(f247(a876),x90694),f332(f196(f877(x90692)),x90693))) % 172.83/172.49 [9277]~P14(x92773,x92771,x92776,x92772)+~P102(f332(f61(x92773),x92774))+E(f332(f72(x92771,x92771,x92771,f332(x92772,f332(f332(f22(f883(x92773,a871)),x92774),f332(f332(f310(x92773),x92775),f195(f883(x92773,a871)))))),f332(x92776,x92775)),f332(x92772,f332(f332(f310(x92773),x92775),x92774))) % 172.83/172.49 [9885]~E(f332(f311(x98852,x98854,x98856),f255(f883(x98852,a871))),f255(f883(x98854,a871)))+~E(f332(f311(x98851,x98853,x98855),f255(f883(x98851,a871))),f255(f883(x98853,a871)))+E(f332(f311(f882(x98851,x98852),f882(x98853,x98854),f272(x98851,x98853,x98852,x98854,x98855,x98856)),f255(f883(f882(x98851,x98852),a871))),f255(f883(f882(x98853,x98854),a871))) % 172.83/172.49 [9933]~P20(x99333,x99334,x99335,f332(x99336,f648(x99336,x99335,x99334,x99333,x99332,x99331)))+P20(x99333,x99334,x99335,f332(f332(f42(x99332,f883(x99333,a871)),x99331),x99336))+E(x99331,f195(f883(x99332,a871))) % 172.83/172.49 [9991]P20(x99916,x99915,x99914,f332(f332(f42(x99912,f883(x99916,a871)),x99911),x99913))+E(x99911,f195(f883(x99912,a871)))+P102(f332(f332(f334(x99912),f648(x99913,x99914,x99915,x99916,x99912,x99911)),x99911)) % 172.83/172.49 [9996]P102(f332(f332(f334(x99961),f581(x99962,x99963,x99964,x99965,x99966,x99961)),x99966))+P102(f332(f332(f246(f883(f882(x99961,x99964),a871)),f332(f332(f269(x99961,x99964),x99966),x99963)),f332(f332(f269(x99961,x99964),x99965),x99962)))+~P102(f332(f332(f246(f883(x99961,a871)),x99966),x99965)) % 172.83/172.49 [10034]P19(x100346,x100345,f332(f332(f310(f875(x100346)),f332(f332(f332(f91(x100346),x100341),x100343),x100342)),f195(f883(f875(x100346),a871))))+~P19(x100346,x100345,f332(f332(f310(f875(x100346)),f332(f332(f332(f91(x100346),x100344),x100343),x100342)),f195(f883(f875(x100346),a871))))+P102(f332(f332(x100341,f786(x100341,x100342,x100343,x100344,x100345,x100346)),f832(x100341,x100342,x100343,x100344,x100345,x100346))) % 172.83/172.49 [10035]P19(x100356,x100355,f332(f332(f310(f875(x100356)),f332(f332(f332(f91(x100356),x100354),x100353),x100352)),f195(f883(f875(x100356),a871))))+~P19(x100356,x100355,f332(f332(f310(f875(x100356)),f332(f332(f332(f91(x100356),x100354),x100353),x100351)),f195(f883(f875(x100356),a871))))+P102(f332(f332(x100351,f846(x100352,x100351,x100353,x100354,x100355,x100356)),f851(x100352,x100351,x100353,x100354,x100355,x100356))) % 172.83/172.49 [10074]~P19(x100741,x100742,f332(f332(f310(f875(x100741)),f332(f332(f332(f91(x100741),x100743),x100744),x100746)),f195(f883(f875(x100741),a871))))+P19(x100741,x100742,f332(f332(f310(f875(x100741)),f332(f332(f332(f91(x100741),x100743),x100744),x100745)),f195(f883(f875(x100741),a871))))+~P102(f332(f332(x100745,f846(x100745,x100746,x100744,x100743,x100742,x100741)),f851(x100745,x100746,x100744,x100743,x100742,x100741))) % 172.83/172.49 [10075]~P19(x100751,x100752,f332(f332(f310(f875(x100751)),f332(f332(f332(f91(x100751),x100756),x100754),x100755)),f195(f883(f875(x100751),a871))))+P19(x100751,x100752,f332(f332(f310(f875(x100751)),f332(f332(f332(f91(x100751),x100753),x100754),x100755)),f195(f883(f875(x100751),a871))))+~P102(f332(f332(x100756,f786(x100753,x100755,x100754,x100756,x100752,x100751)),f832(x100753,x100755,x100754,x100756,x100752,x100751))) % 172.83/172.49 [10110]~P102(f332(f332(f246(f883(x101102,a871)),f332(x101104,f581(x101106,x101104,x101102,x101105,x101103,x101101))),f332(x101106,f581(x101106,x101104,x101102,x101105,x101103,x101101))))+~P102(f332(f332(f246(f883(x101101,a871)),x101103),x101105))+P102(f332(f332(f246(f883(f882(x101101,x101102),a871)),f332(f332(f269(x101101,x101102),x101103),x101104)),f332(f332(f269(x101101,x101102),x101105),x101106))) % 172.83/172.49 [7745]~P102(f332(x77451,x77455))+~P102(f332(x77456,x77454))+P102(f332(x77451,f332(f270(x77452,x77453),f332(f332(f267(x77452,x77453),x77454),x77455)))) % 172.83/172.49 [7746]~P102(f332(x77461,x77464))+~P102(f332(x77466,x77465))+P102(f332(x77461,f332(f266(x77462,x77463),f332(f332(f267(x77462,x77463),x77464),x77465)))) % 172.83/172.49 [7769]~E(f332(f196(f877(x77691)),x77693),f332(f196(f877(x77694)),x77695))+~E(f332(f332(f179(x77691,x77694),f332(f332(f183(x77691,x77694),x77693),x77695)),x77692),f332(f239(x77694),x77696))+P102(f332(f332(f334(x77691),x77692),f332(f173(x77691),x77693))) % 172.83/172.49 [7798]~P102(f332(f332(x77984,x77986),x77985))+~P102(f332(f332(f334(x77981),x77986),x77983))+P102(f332(f332(f332(f41(x77981,f883(x77982,a871)),x77983),x77984),x77985)) % 172.83/172.49 [8109]~P102(f332(f332(f334(x81091),x81092),f332(x81095,x81096)))+~P102(f332(f332(f334(x81093),x81096),x81094))+P102(f332(f332(f334(x81091),x81092),f332(f332(f41(x81093,f883(x81091,a871)),x81094),x81095))) % 172.83/172.49 [8153]P102(f332(f332(x81531,x81532),x81533))+~P102(f332(f332(x81534,x81532),x81533))+~P102(f332(f332(f246(f883(x81535,f883(x81536,a871))),x81534),x81531)) % 172.83/172.49 [8299]P102(f332(f332(x82991,x82992),x82993))+~P102(f332(f332(f334(x82994),x82992),x82995))+~P102(f332(f332(f332(f42(x82994,f883(x82996,a871)),x82995),x82991),x82993)) % 172.83/172.49 [8436]P102(f332(f332(f334(x84361),x84362),f332(x84363,x84364)))+~P102(f332(f332(f334(x84365),x84364),x84366))+~P102(f332(f332(f334(x84361),x84362),f332(f332(f42(x84365,f883(x84361,a871)),x84366),x84363))) % 172.83/172.49 [8626]~P102(f332(f332(f332(f332(a203,x86261),x86263),x86264),x86266))+~P102(f332(f332(f332(f332(a203,x86262),x86266),x86264),x86265))+P102(f332(f332(f332(f332(a203,f32(x86261,x86262)),x86263),x86264),x86265)) % 172.83/172.49 [8695]~P8(x86954,x86955,x86956,x86951)+E(f332(x86951,x86952),f332(x86951,x86953))+~P102(f332(f332(f334(f882(x86954,x86954)),f332(f332(f267(x86954,x86954),x86952),x86953)),x86956)) % 172.83/172.49 [8726]P102(f332(f332(f246(f883(x87261,a871)),x87262),f332(x87263,x87264)))+~P102(f332(f332(f334(x87265),x87264),x87266))+~P102(f332(f332(f246(f883(x87261,a871)),x87262),f332(f332(f42(x87265,f883(x87261,a871)),x87266),x87263))) % 172.83/172.49 [8754]~P50(x87543,x87544,f332(f287(x87544,x87543),x87545))+E(x87541,f195(f883(x87542,a871)))+E(f332(f332(f42(x87542,f883(x87543,a871)),x87541),f332(f332(f8(f883(x87544,a871),f883(x87543,a871),x87542),f286(x87544,x87543,x87545)),x87546)),f332(f286(x87544,x87543,x87545),f332(f332(f42(x87542,f883(x87544,a871)),x87541),x87546))) % 172.83/172.49 [8830]P102(f332(f332(f334(x88301),x88302),f332(f286(x88303,x88301,x88304),x88305)))+~P102(f332(f332(f334(x88303),x88306),x88305))+~P102(f332(f332(f334(f882(x88303,x88301)),f332(f332(f267(x88303,x88301),x88306),x88302)),x88304)) % 172.83/172.49 [8950]P102(f332(x89501,x89502))+~P102(f332(f332(f332(f332(a203,x89504),x89502),x89505),x89506))+P102(f332(f332(f332(f332(a203,f29(x89501,x89503,x89504)),x89502),x89505),x89506)) % 172.83/172.49 [8967]~P102(f332(x89671,x89674))+~P102(f332(f332(f332(f332(a203,x89672),x89674),x89675),x89676))+P102(f332(f332(f332(f332(a203,f29(x89671,x89672,x89673)),x89674),x89675),x89676)) % 172.83/172.49 [9141]P102(f332(f332(f246(f883(x91411,a871)),f332(f286(x91412,x91411,x91413),x91414)),f332(f286(x91412,x91411,x91415),x91416)))+~P102(f332(f332(f246(f883(x91412,a871)),x91414),x91416))+~P102(f332(f332(f246(f883(f882(x91412,x91411),a871)),x91413),x91415)) % 172.83/172.49 [9229]P102(f332(x92291,x92292))+P102(f332(f332(f332(f332(a203,x92293),x92292),x92294),x92295))+~P102(f332(f332(f332(f332(a203,f29(x92291,x92296,x92293)),x92292),x92294),x92295)) % 172.83/172.49 [9234]~P102(f332(x92345,x92342))+P102(f332(f332(f332(f332(a203,x92341),x92342),x92343),x92344))+~P102(f332(f332(f332(f332(a203,f29(x92345,x92341,x92346)),x92342),x92343),x92344)) % 172.83/172.49 [9284]P102(f332(f332(f332(f332(a203,x92841),x92842),x92843),x92844))+P102(f332(f332(f332(f332(a203,x92845),x92842),x92843),x92844))+~P102(f332(f332(f332(f332(a203,f29(x92846,x92841,x92845)),x92842),x92843),x92844)) % 172.83/172.49 [9326]~P102(f332(f332(f334(x93262),x93266),x93264))+~P102(f332(f332(f246(f883(x93261,a871)),x93263),x93265))+P102(f332(f332(f246(f883(f882(x93261,x93262),a871)),f332(f332(f269(x93261,x93262),x93263),f332(f16(f883(x93262,a871),x93261),x93264))),f332(f332(f269(x93261,x93262),x93265),f332(f16(f883(x93262,a871),x93261),x93264)))) % 172.83/172.49 [9339]~P35(x93391,x93392,x93393,x93395,x93396)+P102(f332(f332(f271(x93391,x93392,a871),x93393),x93394))+~P102(f332(f332(f334(f882(x93391,x93392)),x93394),f332(f173(f882(x93391,x93392)),f332(f332(f183(x93391,x93392),x93395),x93396)))) % 172.83/172.49 [9473]~E(x94733,x94735)+P102(f332(f332(f334(f882(f877(x94731),f877(x94731))),f332(f332(f267(f877(x94731),f877(x94731)),f332(f332(f151(x94731),x94732),x94733)),f332(f332(f151(x94731),x94734),x94735))),f157(x94731,x94736)))+~P102(f332(f332(f334(f882(x94731,x94731)),f332(f332(f267(x94731,x94731),x94732),x94734)),x94736)) % 172.83/172.49 [9479]~E(f332(f196(f877(x94791)),x94795),f332(f196(f877(x94792)),x94796))+E(f188(x94791,x94792,f189(x94791,x94792,x94793,f332(f332(f22(f883(x94791,a871)),x94794),f332(f173(x94791),x94795))),x94795,x94796),f189(x94791,x94792,f188(x94791,x94792,x94793,x94795,x94796),x94794))+~P102(f332(f332(f246(f883(x94791,a871)),f332(f173(x94791),x94795)),x94794)) % 172.83/172.49 [9480]~E(f332(f196(f877(x94801)),x94803),f332(f196(f877(x94801)),x94805))+P102(f332(f332(f334(f882(f877(x94801),f877(x94801))),f332(f332(f267(f877(x94801),f877(x94801)),f332(f332(f151(x94801),x94802),x94803)),f332(f332(f151(x94801),x94804),x94805))),f145(x94801,x94806)))+~P102(f332(f332(f334(f882(x94801,x94801)),f332(f332(f267(x94801,x94801),x94802),x94804)),x94806)) % 172.83/172.49 [9510]P102(f332(f332(f334(f882(x95101,x95101)),f332(f332(f267(x95101,x95101),x95102),x95103)),f332(f332(f190(f882(x95101,x95101),a871),f332(a115,x95104)),x95105)))+~P102(f332(f332(f334(f882(x95101,x95101)),f332(f332(f267(x95101,x95101),x95106),x95103)),x95105))+~P102(f332(f332(f334(f882(x95101,x95101)),f332(f332(f267(x95101,x95101),x95102),x95106)),f332(f332(f190(f882(x95101,x95101),a871),x95104),x95105))) % 172.83/172.49 [9511]P102(f332(f332(f334(f882(x95111,x95111)),f332(f332(f267(x95111,x95111),x95112),x95113)),f332(f332(f190(f882(x95111,x95111),a871),f332(a115,x95114)),x95115)))+~P102(f332(f332(f334(f882(x95111,x95111)),f332(f332(f267(x95111,x95111),x95112),x95116)),x95115))+~P102(f332(f332(f334(f882(x95111,x95111)),f332(f332(f267(x95111,x95111),x95116),x95113)),f332(f332(f190(f882(x95111,x95111),a871),x95114),x95115))) % 172.83/172.49 [9515]~P102(f332(f332(f334(x95154),x95155),x95156))+P102(f332(f332(f246(f883(x95151,a871)),x95152),x95153))+~P102(f332(f332(f246(f883(f882(x95151,x95154),a871)),f332(f332(f269(x95151,x95154),x95152),f332(f16(f883(x95154,a871),x95151),x95156))),f332(f332(f269(x95151,x95154),x95153),f332(f16(f883(x95154,a871),x95151),x95156)))) % 172.83/172.49 [9559]E(x95591,x95592)+~P102(f332(f332(f334(f882(f877(x95593),f877(x95593))),f332(f332(f267(f877(x95593),f877(x95593)),f332(f332(f151(x95593),x95591),x95595)),f332(f332(f151(x95593),x95592),x95596))),f145(x95593,x95594)))+P102(f332(f332(f334(f882(x95593,x95593)),f332(f332(f267(x95593,x95593),x95591),x95592)),x95594)) % 172.83/172.49 [9560]E(x95601,x95602)+~P102(f332(f332(f334(f882(f877(x95603),f877(x95603))),f332(f332(f267(f877(x95603),f877(x95603)),f332(f332(f151(x95603),x95601),x95605)),f332(f332(f151(x95603),x95602),x95606))),f147(x95603,x95604)))+P102(f332(f332(f334(f882(x95603,x95603)),f332(f332(f267(x95603,x95603),x95601),x95602)),x95604)) % 172.83/172.49 [9561]E(x95611,x95612)+~P102(f332(f332(f334(f882(f877(x95613),f877(x95613))),f332(f332(f267(f877(x95613),f877(x95613)),f332(f332(f151(x95613),x95611),x95615)),f332(f332(f151(x95613),x95612),x95616))),f157(x95613,x95614)))+P102(f332(f332(f334(f882(x95613,x95613)),f332(f332(f267(x95613,x95613),x95611),x95612)),x95614)) % 172.83/172.49 [9596]P102(f332(f332(f334(f882(f877(x95961),f877(x95961))),f332(f332(f267(f877(x95961),f877(x95961)),f332(f332(f151(x95961),x95962),x95963)),f332(f332(f151(x95961),x95964),x95965))),f158(x95961,x95966)))+~P102(f332(f332(f334(f882(f877(x95961),f877(x95961))),f332(f332(f267(f877(x95961),f877(x95961)),x95963),x95965)),f158(x95961,x95966)))+~P102(f332(f332(f334(f882(x95961,x95961)),f332(f332(f267(x95961,x95961),x95962),x95964)),x95966)) % 172.83/172.49 [9614]P102(f332(x96141,x96142))+~P102(f332(x96141,f441(x96141,x96143,x96144,x96145,x96146)))+~P102(f332(f332(f334(x96146),x96142),f332(f332(f41(x96145,f883(x96146,a871)),x96144),x96143))) % 172.83/172.49 [9619]~P102(f332(f332(f334(f882(f877(x96191),f877(x96191))),f332(f332(f267(f877(x96191),f877(x96191)),f332(f332(f151(x96191),x96192),x96195)),f332(f332(f151(x96191),x96193),x96196))),f145(x96191,x96194)))+P102(f332(f332(f334(f882(f877(x96191),f877(x96191))),f332(f332(f267(f877(x96191),f877(x96191)),x96195),x96196)),f145(x96191,x96194)))+P102(f332(f332(f334(f882(x96191,x96191)),f332(f332(f267(x96191,x96191),x96192),x96193)),x96194)) % 172.83/172.49 [9620]~P102(f332(f332(f334(f882(f877(x96201),f877(x96201))),f332(f332(f267(f877(x96201),f877(x96201)),f332(f332(f151(x96201),x96202),x96205)),f332(f332(f151(x96201),x96203),x96206))),f147(x96201,x96204)))+P102(f332(f332(f334(f882(f877(x96201),f877(x96201))),f332(f332(f267(f877(x96201),f877(x96201)),x96205),x96206)),f147(x96201,x96204)))+P102(f332(f332(f334(f882(x96201,x96201)),f332(f332(f267(x96201,x96201),x96202),x96203)),x96204)) % 172.83/172.49 [9621]~P102(f332(f332(f334(f882(f877(x96211),f877(x96211))),f332(f332(f267(f877(x96211),f877(x96211)),f332(f332(f151(x96211),x96212),x96215)),f332(f332(f151(x96211),x96213),x96216))),f157(x96211,x96214)))+P102(f332(f332(f334(f882(f877(x96211),f877(x96211))),f332(f332(f267(f877(x96211),f877(x96211)),x96215),x96216)),f157(x96211,x96214)))+P102(f332(f332(f334(f882(x96211,x96211)),f332(f332(f267(x96211,x96211),x96212),x96213)),x96214)) % 172.83/172.49 [9704]P102(f332(x97041,x97042))+P102(f332(f332(f334(x97043),f442(x97041,x97044,x97045,x97043,x97046)),x97045))+~P102(f332(f332(f334(x97046),x97042),f332(f332(f41(x97043,f883(x97046,a871)),x97045),x97044))) % 172.83/172.49 [9715]~E(x97152,x97154)+P102(f332(f332(f334(f882(f877(x97151),f877(x97151))),f332(f332(f267(f877(x97151),f877(x97151)),f332(f332(f134(x97151),x97152),f332(f332(f151(x97151),x97153),f116(x97151)))),f332(f332(f134(x97151),x97154),f332(f332(f151(x97151),x97155),f116(x97151))))),f157(x97151,x97156)))+~P102(f332(f332(f334(f882(x97151,x97151)),f332(f332(f267(x97151,x97151),x97153),x97155)),x97156)) % 172.83/172.49 [9802]E(x98021,x98022)+~P102(f332(f332(f334(f882(f877(x98023),f877(x98023))),f332(f332(f267(f877(x98023),f877(x98023)),f332(f332(f134(x98023),x98025),f332(f332(f151(x98023),x98021),f116(x98023)))),f332(f332(f134(x98023),x98026),f332(f332(f151(x98023),x98022),f116(x98023))))),f157(x98023,x98024)))+P102(f332(f332(f334(f882(x98023,x98023)),f332(f332(f267(x98023,x98023),x98021),x98022)),x98024)) % 172.83/172.49 [9830]~P102(f332(f332(f334(f882(f877(x98301),f877(x98301))),f332(f332(f267(f877(x98301),f877(x98301)),f332(f332(f134(x98301),x98305),f332(f332(f151(x98301),x98302),f116(x98301)))),f332(f332(f134(x98301),x98306),f332(f332(f151(x98301),x98303),f116(x98301))))),f157(x98301,x98304)))+P102(f332(f332(f334(f882(f877(x98301),f877(x98301))),f332(f332(f267(f877(x98301),f877(x98301)),x98305),x98306)),f157(x98301,x98304)))+P102(f332(f332(f334(f882(x98301,x98301)),f332(f332(f267(x98301,x98301),x98302),x98303)),x98304)) % 172.83/172.49 [9848]P102(f332(x98481,x98482))+P102(f332(f332(f334(x98483),f441(x98481,x98484,x98485,x98486,x98483)),f332(x98484,f442(x98481,x98484,x98485,x98486,x98483))))+~P102(f332(f332(f334(x98483),x98482),f332(f332(f41(x98486,f883(x98483,a871)),x98485),x98484))) % 172.83/172.49 [8845]~P11(x88453,x88454,x88451)+~P102(f332(f61(x88453),x88456))+E(f332(f332(x88451,x88452),f332(f332(f64(x88453,x88454,x88451),x88455),f332(f332(f22(f883(x88453,a871)),x88456),f332(f332(f310(x88453),x88452),f195(f883(x88453,a871)))))),f332(f332(f64(x88453,x88454,x88451),x88455),f332(f332(f310(x88453),x88452),x88456))) % 172.83/172.49 [8933]~E(f332(f332(f179(x89331,x89332),x89334),x89335),f332(f239(x89332),x89336))+~P102(f332(f332(x89333,x89335),x89336))+E(f332(f332(f179(x89331,x89332),f332(f136(f882(x89331,x89332),f332(f271(x89331,x89332,a871),x89333)),x89334)),x89335),f332(f239(x89332),x89336)) % 172.83/172.49 [9148]~P102(f332(f332(f334(x91485),x91483),x91486))+P102(f332(f332(f246(f883(x91481,a871)),f332(x91482,x91483)),x91484))+~P102(f332(f332(f246(f883(x91481,a871)),f332(f332(f41(x91485,f883(x91481,a871)),x91486),x91482)),x91484)) % 172.83/172.49 [9775]~P3(x97751,x97755,x97754)+P102(f332(f332(f334(f882(x97751,x97751)),f332(f332(f267(x97751,x97751),x97752),x97753)),x97754))+~P102(f332(f332(f334(x97751),x97756),f332(f332(f104(f883(x97751,a871)),f332(f286(x97751,x97751,x97754),f332(f332(f310(x97751),x97752),f195(f883(x97751,a871))))),f332(f286(x97751,x97751,x97754),f332(f332(f310(x97751),x97753),f195(f883(x97751,a871))))))) % 172.83/172.49 [8593]~P123(x85932)+~E(f332(f332(f79(x85932),f332(f332(f80(x85932),x85934),x85935)),x85931),f332(f332(f79(x85932),f332(f332(f80(x85932),x85933),x85935)),x85936))+E(x85931,f332(f332(f79(x85932),f332(f332(f80(x85932),f332(f332(f22(x85932),x85933),x85934)),x85935)),x85936)) % 172.83/172.49 [8594]~P123(x85941)+~E(f332(f332(f79(x85941),f332(f332(f80(x85941),x85942),x85944)),x85945),f332(f332(f79(x85941),f332(f332(f80(x85941),x85943),x85944)),x85946))+E(f332(f332(f79(x85941),f332(f332(f80(x85941),f332(f332(f22(x85941),x85942),x85943)),x85944)),x85945),x85946) % 172.83/172.49 [8757]~P123(x87571)+E(f332(f332(f79(x87571),f332(f332(f80(x87571),x87572),x87573)),x87574),f332(f332(f79(x87571),f332(f332(f80(x87571),x87575),x87573)),x87576))+~E(x87576,f332(f332(f79(x87571),f332(f332(f80(x87571),f332(f332(f22(x87571),x87572),x87575)),x87573)),x87574)) % 172.83/172.49 [8758]~P123(x87581)+E(f332(f332(f79(x87581),f332(f332(f80(x87581),x87582),x87583)),x87584),f332(f332(f79(x87581),f332(f332(f80(x87581),x87585),x87583)),x87586))+~E(f332(f332(f79(x87581),f332(f332(f80(x87581),f332(f332(f22(x87581),x87582),x87585)),x87583)),x87584),x87586) % 172.83/172.49 [9088]~P102(f332(f332(x90884,x90885),x90886))+~P102(f332(f332(x90883,x90885),x90886))+P102(f332(f332(f332(f332(f104(f883(x90881,f883(x90882,a871))),x90883),x90884),x90885),x90886)) % 172.83/172.49 [9347]P102(f332(f332(x93471,x93472),x93473))+P102(f332(f332(x93474,x93472),x93473))+~P102(f332(f332(f332(f332(f113(f883(x93475,f883(x93476,a871))),x93474),x93471),x93472),x93473)) % 172.83/172.49 [9634]~P124(x96341)+~P102(f332(f332(f247(x96341),f332(f332(f79(x96341),f332(f332(f80(x96341),x96344),x96345)),x96342)),f332(f332(f79(x96341),f332(f332(f80(x96341),x96343),x96345)),x96346)))+P102(f332(f332(f247(x96341),x96342),f332(f332(f79(x96341),f332(f332(f80(x96341),f332(f332(f22(x96341),x96343),x96344)),x96345)),x96346))) % 172.83/172.49 [9635]~P124(x96351)+~P102(f332(f332(f246(x96351),f332(f332(f79(x96351),f332(f332(f80(x96351),x96354),x96355)),x96352)),f332(f332(f79(x96351),f332(f332(f80(x96351),x96353),x96355)),x96356)))+P102(f332(f332(f246(x96351),x96352),f332(f332(f79(x96351),f332(f332(f80(x96351),f332(f332(f22(x96351),x96353),x96354)),x96355)),x96356))) % 172.83/172.49 [9658]~P124(x96581)+P102(f332(f332(f247(x96581),f332(f332(f79(x96581),f332(f332(f80(x96581),x96582),x96583)),x96584)),f332(f332(f79(x96581),f332(f332(f80(x96581),x96585),x96583)),x96586)))+~P102(f332(f332(f247(x96581),x96584),f332(f332(f79(x96581),f332(f332(f80(x96581),f332(f332(f22(x96581),x96585),x96582)),x96583)),x96586))) % 172.83/172.49 [9659]~P124(x96591)+P102(f332(f332(f246(x96591),f332(f332(f79(x96591),f332(f332(f80(x96591),x96592),x96593)),x96594)),f332(f332(f79(x96591),f332(f332(f80(x96591),x96595),x96593)),x96596)))+~P102(f332(f332(f246(x96591),x96594),f332(f332(f79(x96591),f332(f332(f80(x96591),f332(f332(f22(x96591),x96595),x96592)),x96593)),x96596))) % 172.83/172.49 [9763]~P124(x97631)+~P102(f332(f332(f247(x97631),f332(f332(f79(x97631),f332(f332(f80(x97631),x97632),x97634)),x97635)),f332(f332(f79(x97631),f332(f332(f80(x97631),x97633),x97634)),x97636)))+P102(f332(f332(f247(x97631),f332(f332(f79(x97631),f332(f332(f80(x97631),f332(f332(f22(x97631),x97632),x97633)),x97634)),x97635)),x97636)) % 172.83/172.49 [9764]~P124(x97641)+~P102(f332(f332(f246(x97641),f332(f332(f79(x97641),f332(f332(f80(x97641),x97642),x97644)),x97645)),f332(f332(f79(x97641),f332(f332(f80(x97641),x97643),x97644)),x97646)))+P102(f332(f332(f246(x97641),f332(f332(f79(x97641),f332(f332(f80(x97641),f332(f332(f22(x97641),x97642),x97643)),x97644)),x97645)),x97646)) % 172.83/172.49 [9813]~P124(x98131)+P102(f332(f332(f247(x98131),f332(f332(f79(x98131),f332(f332(f80(x98131),x98132),x98133)),x98134)),f332(f332(f79(x98131),f332(f332(f80(x98131),x98135),x98133)),x98136)))+~P102(f332(f332(f247(x98131),f332(f332(f79(x98131),f332(f332(f80(x98131),f332(f332(f22(x98131),x98132),x98135)),x98133)),x98134)),x98136)) % 172.83/172.49 [9814]~P124(x98141)+P102(f332(f332(f246(x98141),f332(f332(f79(x98141),f332(f332(f80(x98141),x98142),x98143)),x98144)),f332(f332(f79(x98141),f332(f332(f80(x98141),x98145),x98143)),x98146)))+~P102(f332(f332(f246(x98141),f332(f332(f79(x98141),f332(f332(f80(x98141),f332(f332(f22(x98141),x98142),x98145)),x98143)),x98144)),x98146)) % 172.83/172.49 [9985]~P71(x99852)+~P102(f332(f61(x99851),x99856))+E(f332(f332(f6(x99851,x99852),f332(f332(f18(x99851,x99852,x99852),f332(f332(f18(x99851,x99852,f883(x99852,x99852)),f332(f332(f8(a871,f883(x99852,f883(x99852,x99852)),x99851),f99(x99852)),x99853)),x99854)),x99855)),x99856),f332(f332(f79(x99852),f332(f332(f6(x99851,x99852),x99854),f332(f332(f104(f883(x99851,a871)),x99856),f332(f252(x99851),x99853)))),f332(f332(f6(x99851,x99852),x99855),f332(f332(f104(f883(x99851,a871)),x99856),f332(f78(f883(x99851,a871)),f332(f252(x99851),x99853)))))) % 172.83/172.49 [10044]P102(f332(f332(f334(x100442),x100444),x100446))+P102(f332(f332(f334(x100442),x100445),x100446))+E(f332(f312(x100441,x100442,f332(f332(f7(x100441,x100442,x100442),f332(f332(f7(x100441,x100442,f883(x100442,x100442)),f332(f332(f8(a871,f883(x100442,f883(x100442,x100442)),x100441),f99(x100442)),f332(f332(f7(x100441,f883(x100441,a871),a871),f334(x100441)),x100443))),x100444)),x100445)),x100446),f195(f883(x100441,a871))) % 172.83/172.49 [10045]P102(f332(f332(f334(x100452),x100455),x100456))+~P102(f332(f332(f334(x100452),x100454),x100456))+E(f332(f312(x100451,x100452,f332(f332(f7(x100451,x100452,x100452),f332(f332(f7(x100451,x100452,f883(x100452,x100452)),f332(f332(f8(a871,f883(x100452,f883(x100452,x100452)),x100451),f99(x100452)),f332(f332(f7(x100451,f883(x100451,a871),a871),f334(x100451)),x100453))),x100454)),x100455)),x100456),x100453) % 172.83/172.49 [10046]P102(f332(f332(f334(x100462),x100464),x100466))+~P102(f332(f332(f334(x100462),x100465),x100466))+E(f332(f312(x100461,x100462,f332(f332(f7(x100461,x100462,x100462),f332(f332(f7(x100461,x100462,f883(x100462,x100462)),f332(f332(f8(a871,f883(x100462,f883(x100462,x100462)),x100461),f99(x100462)),f332(f332(f7(x100461,f883(x100461,a871),a871),f334(x100461)),x100463))),x100464)),x100465)),x100466),f332(f78(f883(x100461,a871)),x100463)) % 172.83/172.49 [10047]~P102(f332(f332(f334(x100472),x100474),x100476))+~P102(f332(f332(f334(x100472),x100475),x100476))+E(f332(f312(x100471,x100472,f332(f332(f7(x100471,x100472,x100472),f332(f332(f7(x100471,x100472,f883(x100472,x100472)),f332(f332(f8(a871,f883(x100472,f883(x100472,x100472)),x100471),f99(x100472)),f332(f332(f7(x100471,f883(x100471,a871),a871),f334(x100471)),x100473))),x100474)),x100475)),x100476),f255(f883(x100471,a871))) % 172.83/172.49 [10176]P19(x101761,x101762,f332(f332(f310(f875(x101761)),f332(f332(f332(f91(x101761),f332(x101763,x101764)),f332(a25,x101764)),f332(x101765,x101764))),f195(f883(f875(x101761),a871))))+~P102(f332(f332(f334(a874),x101764),x101766))+~P19(x101761,f332(f332(f113(f883(f875(x101761),a871)),x101762),f332(f311(a874,f875(x101761),f332(f332(f18(a874,f883(x101761,f883(a872,a871)),f875(x101761)),f332(f332(f18(a874,a873,f883(f883(x101761,f883(a872,a871)),f875(x101761))),f332(f332(f8(f883(x101761,f883(a872,a871)),f883(a873,f883(f883(x101761,f883(a872,a871)),f875(x101761))),a874),f91(x101761)),x101763)),a25)),x101765)),x101766)),f332(f311(a874,f875(x101761),f332(f332(f18(a874,f883(x101761,f883(a872,a871)),f875(x101761)),f332(f332(f18(a874,a873,f883(f883(x101761,f883(a872,a871)),f875(x101761))),f332(f332(f8(f883(x101761,f883(a872,a871)),f883(a873,f883(f883(x101761,f883(a872,a871)),f875(x101761))),a874),f91(x101761)),x101763)),f332(f332(f8(f880(a873),a873,a874),f243(a873)),a27))),x101765)),x101766)) % 172.83/172.49 [8623]E(x86231,x86232)+~P52(x86234,x86235,x86233,x86236,x86237)+~E(f332(x86233,x86231),f332(x86233,x86232)) % 172.83/172.49 [6997]E(f332(f241(f880(x69971),x69972,f208(x69971),x69973),f332(x69974,x69975)),f332(f239(x69971),x69976))+~E(f332(x69974,x69975),f332(f239(x69972),x69977))+~E(f332(x69973,x69977),f332(f239(x69971),x69976)) % 172.83/172.49 [8651]~P5(x86516,x86515,x86517,x86514,x86511)+E(f332(f332(x86511,x86512),x86513),x86514)+P102(f332(f61(x86515),x86513)) % 172.83/172.49 [9500]P43(x95001,x95002,x95003,x95004,x95005,f332(f332(x95003,x95006),x95007))+~E(f332(f332(x95003,x95006),x95007),x95004)+~E(x95005,f195(f883(x95001,a871))) % 172.83/172.49 [9680]~P102(f332(x96806,x96803))+~P102(f332(f332(f334(f882(x96802,x96802)),f332(f332(f267(x96802,x96802),x96804),x96805)),f332(x96807,x96803)))+P102(f332(f332(f334(f882(f882(x96801,x96802),f882(x96801,x96802))),f332(f332(f267(f882(x96801,x96802),f882(x96801,x96802)),f332(f332(f267(x96801,x96802),x96803),x96804)),f332(f332(f267(x96801,x96802),x96803),x96805))),f284(x96801,x96802,x96806,x96807))) % 172.83/172.49 [10101]~P43(x101012,x101017,x101013,x101016,x101011,f332(f332(x101013,x101015),x101014))+E(f332(f332(x101013,f770(x101014,x101015,x101011,x101016,x101013,x101017,x101012)),f787(x101014,x101015,x101011,x101016,x101013,x101017,x101012)),f332(f332(x101013,x101015),x101014))+E(x101011,f195(f883(x101012,a871))) % 172.83/172.49 [10102]~P43(x101027,x101026,x101021,x101024,x101025,f332(f332(x101021,x101022),x101023))+E(f332(f332(x101021,f770(x101023,x101022,x101025,x101024,x101021,x101026,x101027)),f787(x101023,x101022,x101025,x101024,x101021,x101026,x101027)),f332(f332(x101021,x101022),x101023))+E(f332(f332(x101021,x101022),x101023),x101024) % 172.83/172.49 [9186]~P35(x91861,x91862,x91863,x91865,x91867)+P35(x91861,x91862,x91863,f332(f332(f151(x91861),x91864),x91865),f332(f332(f151(x91862),x91866),x91867))+~P102(f332(f332(x91863,x91864),x91866)) % 172.83/172.49 [9204]P35(x92041,x92042,x92043,x92044,x92045)+~P35(x92041,x92042,x92043,f332(f332(f134(x92041),x92046),x92044),f332(f332(f134(x92042),x92047),x92045))+~E(f332(f196(f877(x92041)),x92046),f332(f196(f877(x92042)),x92047)) % 172.83/172.49 [9205]P35(x92051,x92052,x92053,x92054,x92055)+~P35(x92051,x92052,x92053,f332(f332(f134(x92051),x92054),x92056),f332(f332(f134(x92052),x92055),x92057))+~E(f332(f196(f877(x92051)),x92054),f332(f196(f877(x92052)),x92055)) % 172.83/172.49 [9410]~P35(x94101,x94102,x94103,x94105,x94107)+~P35(x94101,x94102,x94103,x94104,x94106)+P35(x94101,x94102,x94103,f332(f332(f134(x94101),x94104),x94105),f332(f332(f134(x94102),x94106),x94107)) % 172.83/172.49 [9752]~P102(f332(f66(x97521,x97524,x97525,x97526,x97523),x97527))+P102(f332(f66(x97521,x97524,x97525,x97526,f332(f332(f310(x97521),x97522),x97523)),f332(f332(x97525,x97522),x97527)))+P102(f332(f332(f334(x97521),x97522),x97523)) % 172.83/172.49 [9883]~P20(x98833,x98831,x98834,f255(f883(x98833,a871)))+E(f332(f332(f179(x98831,x98832),f332(f332(f154(f882(x98833,x98832),f882(x98831,x98832)),f332(f271(x98833,x98832,f882(x98831,x98832)),f332(f332(f8(x98831,f883(x98832,f882(x98831,x98832)),x98833),f267(x98831,x98832)),x98834))),x98835)),f332(x98834,x98836)),f332(f239(x98832),x98837))+~E(f332(f332(f179(x98833,x98832),x98835),x98836),f332(f239(x98832),x98837)) % 172.83/172.49 [10122]~P43(x101222,x101227,x101226,x101225,x101221,f332(f332(x101226,x101224),x101223))+E(x101221,f195(f883(x101222,a871)))+P102(f332(f332(f334(x101222),f770(x101223,x101224,x101221,x101225,x101226,x101227,x101222)),x101221)) % 172.83/172.49 [10123]~P43(x101235,x101237,x101231,x101234,x101236,f332(f332(x101231,x101232),x101233))+E(f332(f332(x101231,x101232),x101233),x101234)+P102(f332(f332(f334(x101235),f770(x101233,x101232,x101236,x101234,x101231,x101237,x101235)),x101236)) % 172.83/172.49 [6784]~E(x67845,x67847)+~E(x67846,x67844)+E(f332(f332(f332(f332(f71(x67841,f880(x67842)),x67843),x67844),f332(f239(x67842),x67845)),x67846),f332(f239(x67842),x67847)) % 172.83/172.49 [6913]E(x69131,x69132)+~E(f332(x69135,x69131),f332(f239(x69134),x69137))+E(f332(f332(f332(f332(f71(x69133,f880(x69134)),x69135),x69132),f332(f239(x69134),x69136)),x69131),f332(f239(x69134),x69137)) % 172.83/172.49 [7633]E(x76331,x76332)+~E(x76333,x76334)+~E(f332(f332(f332(f332(f71(x76335,f880(x76336)),x76337),x76334),f332(f239(x76336),x76331)),x76333),f332(f239(x76336),x76332)) % 172.83/172.49 [7700]E(x77001,x77002)+E(f332(x77003,x77004),f332(f239(x77005),x77001))+~E(f332(f332(f332(f332(f71(x77006,f880(x77005)),x77003),x77007),f332(f239(x77005),x77002)),x77004),f332(f239(x77005),x77001)) % 172.83/172.49 [7701]E(x77011,x77012)+E(f332(x77013,x77011),f332(f239(x77014),x77015))+~E(f332(f332(f332(f332(f71(x77016,f880(x77014)),x77013),x77012),f332(f239(x77014),x77017)),x77011),f332(f239(x77014),x77015)) % 172.83/172.49 [8870]~P16(x88704,x88705,x88706,x88707,x88701)+~P102(f332(f61(x88705),x88703))+E(f332(f332(x88701,x88702),x88703),f332(f332(f332(f65(x88704,x88705,x88706),x88702),x88707),x88703)) % 172.83/172.49 [8871]~P5(x88714,x88715,x88716,x88717,x88711)+~P102(f332(f61(x88715),x88713))+E(f332(f332(x88711,x88712),x88713),f332(f332(f332(f65(x88714,x88715,x88716),x88712),x88717),x88713)) % 172.83/172.49 [9466]~P19(x94661,x94662,f332(f332(f310(f875(x94661)),f332(f332(f332(f91(x94661),x94663),x94664),x94667)),f195(f883(f875(x94661),a871))))+P19(x94661,x94662,f332(f332(f310(f875(x94661)),f332(f332(f332(f91(x94661),x94663),f32(x94664,x94665)),x94666)),f195(f883(f875(x94661),a871))))+~P19(x94661,x94662,f332(f332(f310(f875(x94661)),f332(f332(f332(f91(x94661),x94667),x94665),x94666)),f195(f883(f875(x94661),a871)))) % 172.83/172.49 [9653]~P18(x96533,x96534,x96535,x96537,x96536,x96531)+~P102(f332(f61(x96534),x96532))+E(f332(x96531,x96532),f332(f332(f332(f65(x96533,x96534,x96535),x96536),x96537),x96532)) % 172.83/172.49 [9808]P43(x98081,x98082,x98083,x98084,x98085,f332(f332(x98083,x98086),x98087))+~P43(x98081,x98082,x98083,x98084,f332(f332(f22(f883(x98081,a871)),x98085),f332(f332(f310(x98081),x98086),f195(f883(x98081,a871)))),x98087)+~P102(f332(f332(f334(x98081),x98086),x98085)) % 172.83/172.49 [10076]~P19(x100761,x100762,f332(f332(f310(f875(x100761)),f332(f332(f332(f91(x100761),f94(x100761,x100763,x100764)),x100765),x100767)),f195(f883(f875(x100761),a871))))+P19(x100761,x100762,f332(f332(f310(f875(x100761)),f332(f332(f332(f91(x100761),x100763),f29(x100764,x100765,x100766)),x100767)),f195(f883(f875(x100761),a871))))+~P19(x100761,x100762,f332(f332(f310(f875(x100761)),f332(f332(f332(f91(x100761),f94(x100761,x100763,f332(f72(a871,a871,a872,a327),x100764))),x100766),x100767)),f195(f883(f875(x100761),a871)))) % 172.83/172.49 [10147]~P43(x101472,x101473,x101474,x101475,x101471,f332(f332(x101474,x101477),x101476))+P43(x101472,x101473,x101474,x101475,f332(f332(f22(f883(x101472,a871)),x101471),f332(f332(f310(x101472),f770(x101476,x101477,x101471,x101475,x101474,x101473,x101472)),f195(f883(x101472,a871)))),f787(x101476,x101477,x101471,x101475,x101474,x101473,x101472))+E(x101471,f195(f883(x101472,a871))) % 172.83/172.49 [10148]~P43(x101485,x101486,x101481,x101484,x101487,f332(f332(x101481,x101482),x101483))+P43(x101485,x101486,x101481,x101484,f332(f332(f22(f883(x101485,a871)),x101487),f332(f332(f310(x101485),f770(x101483,x101482,x101487,x101484,x101481,x101486,x101485)),f195(f883(x101485,a871)))),f787(x101483,x101482,x101487,x101484,x101481,x101486,x101485))+E(f332(f332(x101481,x101482),x101483),x101484) % 172.83/172.49 [9193]E(f188(x91931,x91932,x91933,x91934,f332(f332(f159(x91932,x91935),x91936),x91937)),f188(x91931,x91932,x91933,x91934,x91935))+~P102(f332(f332(f247(a876),x91936),f332(f196(f877(x91932)),x91935)))+~P102(f332(f332(f246(a876),f332(f196(f877(x91931)),x91934)),x91936)) % 172.83/172.49 [9488]P102(f332(f332(f246(f883(f882(x94881,x94882),a871)),f332(f332(f289(x94881,x94883,x94882),x94884),x94885)),f332(f332(f289(x94881,x94883,x94882),x94886),x94887)))+~P102(f332(f332(f246(f883(f882(x94883,x94882),a871)),x94885),x94887))+~P102(f332(f332(f246(f883(f882(x94881,x94883),a871)),x94884),x94886)) % 172.83/172.49 [9819]~P102(f332(f332(f334(x98191),x98196),x98195))+P102(f332(f66(x98191,x98192,x98193,x98194,x98195),f332(f332(x98193,x98196),x98197)))+~P102(f332(f66(x98191,x98192,x98193,x98194,f332(f332(f22(f883(x98191,a871)),x98195),f332(f332(f310(x98191),x98196),f195(f883(x98191,a871))))),x98197)) % 172.83/172.49 [10207]~P139(x102071)+~P20(f882(x102072,x102073),x102071,f332(f271(x102072,x102073,x102071),f332(f332(f7(x102072,f883(x102073,x102071),f883(x102073,x102071)),f332(f332(f8(f883(x102071,x102071),f883(f883(x102073,x102071),f883(x102073,x102071)),x102072),f8(x102071,x102071,x102073)),f332(f332(f8(x102071,f883(x102071,x102071),x102072),f80(x102071)),x102074))),x102075)),f332(f332(f269(x102072,x102073),x102076),f332(f16(f883(x102073,a871),x102072),x102077)))+E(f332(f332(f6(x102071,x102071),f33(x102071)),f332(f252(x102071),f332(f332(f8(f883(x102072,a871),a871,x102071),f86(x102072)),f332(f332(f8(f883(x102072,f883(x102073,a871)),f883(x102072,a871),x102071),f332(f8(f883(x102073,a871),a871,x102072),f86(x102073))),f332(f332(f7(x102071,f883(x102072,f883(x102073,a871)),f883(x102072,f883(x102073,a871))),f332(f332(f8(f883(x102072,f883(f883(x102073,a871),f883(x102073,a871))),f883(f883(x102072,f883(x102073,a871)),f883(x102072,f883(x102073,a871))),x102071),f18(x102072,f883(x102073,a871),f883(x102073,a871))),f332(f332(f8(f883(x102072,f883(x102073,f883(a871,a871))),f883(x102072,f883(f883(x102073,a871),f883(x102073,a871))),x102071),f332(f8(f883(x102073,f883(a871,a871)),f883(f883(x102073,a871),f883(x102073,a871)),x102072),f18(x102073,a871,a871))),f332(f332(f8(f883(x102072,f883(x102073,a871)),f883(x102072,f883(x102073,f883(a871,a871))),x102071),f332(f8(f883(x102073,a871),f883(x102073,f883(a871,a871)),x102072),f332(f8(a871,f883(a871,a871),x102073),a330))),f332(f332(f7(x102071,f883(x102072,f883(x102073,x102071)),f883(x102072,f883(x102073,a871))),f332(f332(f8(f883(f883(x102073,x102071),f883(x102073,a871)),f883(f883(x102072,f883(x102073,x102071)),f883(x102072,f883(x102073,a871))),x102071),f8(f883(x102073,x102071),f883(x102073,a871),x102072)),f332(f332(f8(f883(x102071,a871),f883(f883(x102073,x102071),f883(x102073,a871)),x102071),f8(x102071,a871,x102073)),a329))),f332(f332(f7(x102072,f883(x102073,x102071),f883(x102073,x102071)),f332(f332(f8(f883(x102071,x102071),f883(f883(x102073,x102071),f883(x102073,x102071)),x102072),f8(x102071,x102071,x102073)),f332(f332(f8(x102071,f883(x102071,x102071),x102072),f80(x102071)),x102074))),x102075)))))),f332(f332(f7(x102072,f883(x102073,a871),f883(x102073,a871)),f332(f332(f8(f883(a871,a871),f883(f883(x102073,a871),f883(x102073,a871)),x102072),f8(a871,a871,x102073)),f332(f332(f8(a871,f883(a871,a871),x102072),a330),f332(f332(f7(x102072,f883(x102072,a871),a871),f334(x102072)),x102076)))),f332(f332(f7(x102073,f883(x102073,a871),a871),f334(x102073)),x102077))))))),f332(f332(f80(x102071),f332(f332(f6(x102072,x102071),x102074),x102076)),f332(f332(f6(x102073,x102071),x102075),x102077))) % 172.83/172.49 [9651]~P102(f332(f332(x96514,x96516),x96518))+~P102(f332(f332(x96515,x96518),x96517))+P102(f332(f332(f268(x96511,x96512,x96513,x96514,x96515),x96516),x96517)) % 172.83/172.49 [9254]~P14(x92548,x92541,x92543,x92545)+~P102(f332(f61(x92548),x92546))+E(f332(f72(x92541,x92541,x92542,f332(x92543,x92544)),f332(f72(x92541,x92541,x92542,f332(x92545,x92546)),x92547)),f332(f72(x92541,x92541,x92542,f332(x92545,x92546)),f332(f72(x92541,x92541,x92542,f332(x92543,x92544)),x92547))) % 172.83/172.49 [9641]~P17(x96417,x96412,x96415,x96418,x96416,x96411)+~P102(f332(f61(x96412),x96414))+E(f332(x96411,f332(f332(f310(x96412),x96413),x96414)),f332(f332(x96415,f332(x96416,x96413)),f332(x96411,x96414))) % 172.83/172.49 [9761]~P20(x97612,x97614,x97616,x97618)+~P20(x97611,x97613,x97615,x97617)+P20(f882(x97611,x97612),f882(x97613,x97614),f272(x97611,x97613,x97612,x97614,x97615,x97616),f332(f332(f269(x97611,x97612),x97617),f332(f16(f883(x97612,a871),x97611),x97618))) % 172.83/172.49 [9434]P102(f332(f332(f334(f882(x94341,x94342)),f332(f332(f267(x94341,x94342),x94343),x94344)),f332(f332(f289(x94341,x94345,x94342),x94346),x94347)))+~P102(f332(f332(f334(f882(x94341,x94345)),f332(f332(f267(x94341,x94345),x94343),x94348)),x94346))+~P102(f332(f332(f334(f882(x94345,x94342)),f332(f332(f267(x94345,x94342),x94348),x94344)),x94347)) % 172.83/172.49 [9622]~P102(f332(f332(f246(f883(f882(x96223,x96222),a871)),x96225),f332(f332(f269(x96223,x96222),x96228),f332(f16(f883(x96222,a871),x96223),x96227))))+~P102(f332(f332(f246(f883(f882(x96221,x96223),a871)),x96224),f332(f332(f269(x96221,x96223),x96226),f332(f16(f883(x96223,a871),x96221),x96228))))+P102(f332(f332(f246(f883(f882(x96221,x96222),a871)),f332(f332(f289(x96221,x96223,x96222),x96224),x96225)),f332(f332(f269(x96221,x96222),x96226),f332(f16(f883(x96222,a871),x96221),x96227)))) % 172.83/172.49 [9675]~E(x96753,x96755)+P102(f332(f332(f334(f882(f882(x96751,x96752),f882(x96751,x96752))),f332(f332(f267(f882(x96751,x96752),f882(x96751,x96752)),f332(f332(f267(x96751,x96752),x96753),x96754)),f332(f332(f267(x96751,x96752),x96755),x96756))),f325(x96751,x96752,x96757,x96758)))+~P102(f332(f332(f334(f882(x96752,x96752)),f332(f332(f267(x96752,x96752),x96754),x96756)),x96758)) % 172.83/172.49 [9784]E(x97841,x97842)+~P102(f332(f332(f334(f882(f882(x97843,x97845),f882(x97843,x97845))),f332(f332(f267(f882(x97843,x97845),f882(x97843,x97845)),f332(f332(f267(x97843,x97845),x97841),x97846)),f332(f332(f267(x97843,x97845),x97842),x97847))),f325(x97843,x97845,x97844,x97848)))+P102(f332(f332(f334(f882(x97843,x97843)),f332(f332(f267(x97843,x97843),x97841),x97842)),x97844)) % 172.83/172.49 [9801]~P102(f332(f332(f334(f882(f882(x98011,x98015),f882(x98011,x98015))),f332(f332(f267(f882(x98011,x98015),f882(x98011,x98015)),f332(f332(f267(x98011,x98015),x98012),x98016)),f332(f332(f267(x98011,x98015),x98013),x98017))),f325(x98011,x98015,x98014,x98018)))+P102(f332(f332(f334(f882(x98011,x98011)),f332(f332(f267(x98011,x98011),x98012),x98013)),x98014))+P102(f332(f332(f334(f882(x98015,x98015)),f332(f332(f267(x98015,x98015),x98016),x98017)),x98018)) % 172.83/172.49 [9705]~P18(x97057,x97055,x97051,x97058,x97052,x97054)+~P102(f332(f61(x97055),x97056))+E(f332(f332(x97051,f332(x97052,x97053)),f332(x97054,f332(f332(f22(f883(x97055,a871)),x97056),f332(f332(f310(x97055),x97053),f195(f883(x97055,a871)))))),f332(x97054,f332(f332(f310(x97055),x97053),x97056))) % 172.83/172.49 [9212]~P102(f332(f332(f332(x92125,x92128),x92126),x92127))+~P102(f332(f332(f334(x92121),x92128),x92124))+P102(f332(f332(f332(f332(f41(x92121,f883(x92122,f883(x92123,a871))),x92124),x92125),x92126),x92127)) % 172.83/172.49 [9421]P102(f332(f332(f332(x94211,x94212),x94213),x94214))+~P102(f332(f332(f334(x94215),x94212),x94216))+~P102(f332(f332(f332(f332(f42(x94215,f883(x94217,f883(x94218,a871))),x94216),x94211),x94213),x94214)) % 172.83/172.49 [9615]~P16(x96153,x96152,x96154,x96158,x96151)+~P102(f332(f61(x96152),x96157))+E(f332(f332(x96151,f332(f332(f18(x96152,x96153,x96153),f332(f332(f8(x96153,f883(x96153,x96153),x96152),x96154),x96155)),x96156)),x96157),f332(f332(x96154,f332(f332(x96151,x96155),x96157)),f332(f332(x96151,x96156),x96157))) % 172.83/172.49 [9891]~E(f332(f311(x98912,x98914,x98916),x98918),x989110)+~E(f332(f311(x98911,x98913,x98915),x98917),x98919)+E(f332(f311(f882(x98911,x98912),f882(x98913,x98914),f272(x98911,x98913,x98912,x98914,x98915,x98916)),f332(f332(f269(x98911,x98912),x98917),f332(f16(f883(x98912,a871),x98911),x98918))),f332(f332(f269(x98913,x98914),x98919),f332(f16(f883(x98914,a871),x98913),x989110))) % 172.83/172.49 [4844]~P104(x48442)+~P29(x48442,x48441)+P29(x48442,f117(x48442,x48441))+E(x48441,f116(x48442)) % 172.83/172.49 [4845]~P104(x48452)+~P29(x48452,x48451)+P29(x48452,f743(x48451,x48452))+E(x48451,f116(x48452)) % 172.83/172.49 [5077]~P27(x50772)+E(f10(x50772,x50771),f40(x50772,x50771))+E(x50771,f195(f883(x50772,a871)))+~P102(f332(f61(x50772),x50771)) % 172.83/172.49 [5078]~P27(x50782)+E(f13(x50782,x50781),f39(x50782,x50781))+E(x50781,f195(f883(x50782,a871)))+~P102(f332(f61(x50782),x50781)) % 172.83/172.49 [5231]~P104(x52312)+~P29(x52312,x52311)+E(x52311,f116(x52312))+E(f332(f332(f151(x52312),f762(x52311,x52312)),f743(x52311,x52312)),x52311) % 172.83/172.49 [6028]~P61(x60282)+E(x60281,f195(f883(x60282,a871)))+P102(f332(f332(f246(x60282),f10(x60282,x60281)),f13(x60282,x60281)))+~P102(f332(f61(x60282),x60281)) % 172.83/172.49 [6040]~P39(x60402)+~P39(x60401)+E(x60401,x60402)+~E(f332(f311(a1,a876,a107),x60401),f332(f311(a1,a876,a107),x60402)) % 172.83/172.49 [9070]~P113(x90701)+~P102(f332(f332(f334(x90701),x90702),f112(x90701)))+P102(f332(f332(f247(x90701),f332(f332(f79(x90701),f332(f332(f79(x90701),f77(x90701)),x90702)),x90702)),f2(x90701)))+~P102(f332(f332(f247(x90701),x90702),f2(x90701))) % 172.83/172.49 [9309]~P113(x93091)+~P102(f332(f332(f334(x93091),x93092),f112(x93091)))+~P102(f332(f332(f247(x93091),f332(f332(f79(x93091),f332(f332(f79(x93091),f77(x93091)),x93092)),x93092)),f2(x93091)))+P102(f332(f332(f247(x93091),x93092),f2(x93091))) % 172.83/172.49 [4900]~P139(x49002)+~P109(x49002)+E(x49001,f2(a876))+E(f332(f332(f257(x49002),f2(x49002)),x49001),f2(x49002)) % 172.83/172.49 [4904]~P139(x49041)+~P109(x49041)+~E(x49042,f2(a876))+E(f332(f332(f257(x49041),f2(x49041)),x49042),f77(x49041)) % 172.83/172.49 [5064]~P136(x50642)+E(x50641,f77(x50642))+E(x50641,f332(f78(x50642),f77(x50642)))+~E(f332(f332(f80(x50642),x50641),x50641),f77(x50642)) % 172.83/172.49 [5314]~P86(x53142)+E(x53141,f2(x53142))+E(f81(x53142,x53141),f332(f78(x53142),f77(x53142)))+P102(f332(f332(f247(x53142),f2(x53142)),x53141)) % 172.83/172.49 [5552]~P86(x55522)+E(f81(x55522,x55521),f77(x55522))+E(x55521,f2(x55522))+~P102(f332(f332(f247(x55522),f2(x55522)),x55521)) % 172.83/172.49 [5561]E(x55611,x55612)+~E(f332(f106(a876),x55611),f332(f106(a876),x55612))+P102(f332(a200,f332(f106(a1),x55612)))+P102(f332(a200,f332(f106(a1),x55611))) % 172.83/172.49 [5611]~P88(x56111)+~E(x56112,f2(x56111))+E(f332(f332(f79(x56111),x56112),x56112),f2(x56111))+~P102(f332(f332(f334(x56111),x56112),f112(x56111))) % 172.83/172.49 [5649]E(x56491,f2(a1))+~E(f332(f332(f38(a1),x56492),x56491),f2(a1))+P102(f332(f332(f247(a1),x56491),x56492))+P102(f332(f332(f247(a1),x56492),x56491)) % 172.83/172.49 [5680]E(x56801,f2(a1))+~E(f332(f332(f38(a1),x56802),x56801),f2(a1))+P102(f332(f332(f246(a1),x56802),f2(a1)))+P102(f332(f332(f247(a1),x56802),x56801)) % 172.83/172.49 [5714]E(x57141,f2(a1))+~E(f332(f332(f38(a1),x57142),x57141),f2(a1))+P102(f332(f332(f246(a1),f2(a1)),x57142))+P102(f332(f332(f247(a1),x57141),x57142)) % 172.83/172.49 [5748]~P88(x57482)+E(x57481,f2(x57482))+~E(f332(f332(f79(x57482),x57481),x57481),f2(x57482))+~P102(f332(f332(f334(x57482),x57481),f112(x57482))) % 172.83/172.49 [5808]E(f332(f106(a876),x58081),f332(f106(a876),x58082))+~E(f332(f106(a1),x58082),f2(a1))+P102(f332(a200,f332(f106(a1),x58082)))+~P102(f332(a200,f332(f106(a1),x58081))) % 172.83/172.49 [5835]~E(f332(f106(a876),x58352),f332(f106(a876),x58351))+E(f332(f106(a1),x58351),f2(a1))+P102(f332(a200,f332(f106(a1),x58351)))+~P102(f332(a200,f332(f106(a1),x58352))) % 172.83/172.49 [5844]~P104(x58442)+E(x58441,f195(f883(x58442,a871)))+~P102(f332(f61(x58442),x58441))+P102(f332(f332(f334(x58442),f14(x58442,x58441)),x58441)) % 172.83/172.49 [5845]~P104(x58452)+E(x58451,f195(f883(x58452,a871)))+~P102(f332(f61(x58452),x58451))+P102(f332(f332(f334(x58452),f15(x58452,x58451)),x58451)) % 172.83/172.49 [6008]~P113(x60081)+~P89(x60081)+P102(f332(f332(f247(x60081),f2(x60081)),f332(f106(x60081),x60082)))+~P102(f332(f332(f247(a1),a82),x60082)) % 172.83/172.49 [6009]~P113(x60091)+~P89(x60091)+P102(f332(f332(f246(x60091),f2(x60091)),f332(f106(x60091),x60092)))+~P102(f332(f332(f246(a1),a82),x60092)) % 172.83/172.49 [6027]~P113(x60271)+~P89(x60271)+E(f332(f74(x60271),f332(f106(x60271),x60272)),f332(f106(x60271),x60272))+P102(f332(f332(f247(x60271),f332(f106(x60271),x60272)),f2(x60271))) % 172.83/172.49 [6067]E(x60671,x60672)+~E(f332(a107,x60671),f332(a107,x60672))+~P102(f332(f332(f246(a1),f2(a1)),x60672))+~P102(f332(f332(f246(a1),f2(a1)),x60671)) % 172.83/172.49 [6258]~P89(x62582)+~P113(x62582)+~P102(f332(f332(f247(x62582),f2(x62582)),f332(f106(x62582),x62581)))+P102(f332(f332(f247(a1),a82),x62581)) % 172.83/172.49 [6259]~P89(x62592)+~P113(x62592)+~P102(f332(f332(f246(x62592),f2(x62592)),f332(f106(x62592),x62591)))+P102(f332(f332(f246(a1),a82),x62591)) % 172.83/172.49 [6264]~P113(x62641)+~P89(x62641)+P102(f332(f332(f247(x62641),f332(f106(x62641),x62642)),f2(x62641)))+~P102(f332(f332(f247(a1),x62642),a82)) % 172.83/172.49 [6265]~P113(x62651)+~P89(x62651)+P102(f332(f332(f246(x62651),f332(f106(x62651),x62652)),f2(x62651)))+~P102(f332(f332(f246(a1),x62652),a82)) % 172.83/172.49 [6572]~P89(x65722)+~P113(x65722)+~P102(f332(f332(f247(x65722),f332(f106(x65722),x65721)),f2(x65722)))+P102(f332(f332(f247(a1),x65721),a82)) % 172.83/172.49 [6573]~P89(x65732)+~P113(x65732)+~P102(f332(f332(f246(x65732),f332(f106(x65732),x65731)),f2(x65732)))+P102(f332(f332(f246(a1),x65731),a82)) % 172.83/172.49 [6664]~P113(x66641)+~P89(x66641)+E(f332(f74(x66641),f332(f106(x66641),x66642)),f332(f78(x66641),f332(f106(x66641),x66642)))+~P102(f332(f332(f247(x66641),f332(f106(x66641),x66642)),f2(x66641))) % 172.83/172.49 [6682]E(f332(f106(a876),x66821),f332(f106(a876),x66822))+~E(f332(f106(a1),x66822),f2(a1))+~P102(f332(f332(f246(a1),f332(f106(a1),x66821)),f2(a1)))+~P102(f332(a200,f332(f106(a1),x66821))) % 172.83/172.49 [7564]~P104(x75642)+E(x75641,f195(f883(x75642,a871)))+~P102(f332(f61(x75642),x75641))+P102(f332(f332(f246(x75642),f12(x75642,f244(x75642),x75641)),f11(x75642,f245(x75642),x75641))) % 172.83/172.49 [7886]~P28(x78861)+~P39(x78862)+P102(f332(f332(f334(a1),x78861),x78862))+~P102(f332(f332(f334(a876),f332(a107,x78861)),f332(f311(a1,a876,a107),x78862))) % 172.83/172.49 [8164]~P56(x81642)+P102(f332(x81641,f208(x81642)))+~P102(f332(f57(f880(x81642)),x81641))+P102(f332(f57(x81642),f332(f332(f8(f880(x81642),a871,x81642),x81641),f239(x81642)))) % 172.83/172.49 [8631]~P56(x86311)+~P102(f332(x86312,f208(x86311)))+P102(f332(f58(f880(x86311)),x86312))+~P102(f332(f58(x86311),f332(f332(f8(f880(x86311),a871,x86311),x86312),f239(x86311)))) % 172.83/172.49 [5841]~P137(x58412)+E(x58411,f2(a1))+E(f332(f78(x58412),f332(f105(x58412),f332(f78(a1),x58411))),f332(f105(x58412),x58411))+~P102(f332(f332(f247(a1),x58411),f2(a1))) % 172.83/172.49 [5912]~P88(x59121)+~P89(x59121)+~P31(x59121,f332(f106(x59121),x59122))+P31(x59121,f332(f106(x59121),f332(f332(f79(a1),x59122),x59122))) % 172.83/172.49 [6246]~P73(x62462)+E(x62461,f195(f883(x62462,a871)))+E(f15(x62462,f332(f311(x62462,x62462,f78(x62462)),x62461)),f332(f78(x62462),f14(x62462,x62461)))+~P102(f332(f61(x62462),x62461)) % 172.83/172.49 [6247]~P73(x62472)+E(x62471,f195(f883(x62472,a871)))+E(f14(x62472,f332(f311(x62472,x62472,f78(x62472)),x62471)),f332(f78(x62472),f15(x62472,x62471)))+~P102(f332(f61(x62472),x62471)) % 172.83/172.49 [6279]~P88(x62791)+~P89(x62791)+P31(x62791,f332(f106(x62791),x62792))+~P31(x62791,f332(f106(x62791),f332(f332(f79(a1),x62792),x62792))) % 172.83/172.49 [6368]E(x63681,f2(a1))+E(f332(a50,f49(f332(f78(a1),x63681),f332(f78(a1),x63682))),f45(x63681,x63682))+P102(f332(f332(f246(a1),f2(a1)),x63682))+~P102(f332(f332(f246(a1),f2(a1)),x63681)) % 172.83/172.49 [8674]~P39(x86742)+~P39(x86741)+P102(f332(f332(f247(f883(a876,a871)),f332(f311(a1,a876,a107),x86741)),f332(f311(a1,a876,a107),x86742)))+~P102(f332(f332(f247(f883(a1,a871)),x86741),x86742)) % 172.83/172.49 [8888]~E(f765(x88882,x88881),f766(x88882,x88881))+~P102(f332(f137(x88881),f767(x88882,x88881)))+~P102(f332(f137(f877(x88881)),x88882))+P102(f332(f137(x88881),f332(f142(f877(x88881),f877(x88881),f134(x88881),f116(x88881)),x88882))) % 172.83/172.49 [8988]~P39(x89882)+~P39(x89881)+~P102(f332(f332(f247(f883(a876,a871)),f332(f311(a1,a876,a107),x89881)),f332(f311(a1,a876,a107),x89882)))+P102(f332(f332(f247(f883(a1,a871)),x89881),x89882)) % 172.83/172.49 [8989]~P39(x89892)+~P39(x89891)+~P102(f332(f332(f246(f883(a876,a871)),f332(f311(a1,a876,a107),x89891)),f332(f311(a1,a876,a107),x89892)))+P102(f332(f332(f246(f883(a1,a871)),x89891),x89892)) % 172.83/172.49 [8995]~E(f765(x89952,x89951),f766(x89952,x89951))+~P102(f332(f137(f877(x89951)),x89952))+P102(f332(f137(x89951),f332(f142(f877(x89951),f877(x89951),f134(x89951),f116(x89951)),x89952)))+P102(f332(f332(f334(f877(x89951)),f767(x89952,x89951)),f332(f173(f877(x89951)),x89952))) % 172.83/172.49 [9037]~P102(f332(f137(x90371),f767(x90372,x90371)))+~P102(f332(f137(f877(x90371)),x90372))+P102(f332(f137(x90371),f332(f142(f877(x90371),f877(x90371),f134(x90371),f116(x90371)),x90372)))+P102(f332(f332(f334(f877(x90371)),f766(x90372,x90371)),f332(f173(f877(x90371)),x90372))) % 172.83/172.49 [9038]~P102(f332(f137(x90381),f767(x90382,x90381)))+~P102(f332(f137(f877(x90381)),x90382))+P102(f332(f137(x90381),f332(f142(f877(x90381),f877(x90381),f134(x90381),f116(x90381)),x90382)))+P102(f332(f332(f334(f877(x90381)),f765(x90382,x90381)),f332(f173(f877(x90381)),x90382))) % 172.83/172.49 [9113]~P102(f332(f137(f877(x91131)),x91132))+P102(f332(f137(x91131),f332(f142(f877(x91131),f877(x91131),f134(x91131),f116(x91131)),x91132)))+P102(f332(f332(f334(f877(x91131)),f766(x91132,x91131)),f332(f173(f877(x91131)),x91132)))+P102(f332(f332(f334(f877(x91131)),f767(x91132,x91131)),f332(f173(f877(x91131)),x91132))) % 172.83/172.49 [9114]~P102(f332(f137(f877(x91141)),x91142))+P102(f332(f137(x91141),f332(f142(f877(x91141),f877(x91141),f134(x91141),f116(x91141)),x91142)))+P102(f332(f332(f334(f877(x91141)),f765(x91142,x91141)),f332(f173(f877(x91141)),x91142)))+P102(f332(f332(f334(f877(x91141)),f767(x91142,x91141)),f332(f173(f877(x91141)),x91142))) % 172.83/172.49 [9127]~E(f332(f332(f104(f883(x91271,a871)),f332(f173(x91271),f766(x91272,x91271))),f332(f173(x91271),f765(x91272,x91271))),f195(f883(x91271,a871)))+~P102(f332(f137(x91271),f767(x91272,x91271)))+~P102(f332(f137(f877(x91271)),x91272))+P102(f332(f137(x91271),f332(f142(f877(x91271),f877(x91271),f134(x91271),f116(x91271)),x91272))) % 172.83/172.49 [9189]~E(f332(f332(f104(f883(x91891,a871)),f332(f173(x91891),f766(x91892,x91891))),f332(f173(x91891),f765(x91892,x91891))),f195(f883(x91891,a871)))+~P102(f332(f137(f877(x91891)),x91892))+P102(f332(f137(x91891),f332(f142(f877(x91891),f877(x91891),f134(x91891),f116(x91891)),x91892)))+P102(f332(f332(f334(f877(x91891)),f767(x91892,x91891)),f332(f173(f877(x91891)),x91892))) % 172.83/172.49 [9458]E(x94581,f2(a1))+E(x94582,f2(a1))+E(f332(f332(f85(a1,f882(a1,a1)),f332(f332(a228,x94582),x94581)),f332(f332(f18(a1,a1,f882(a1,a1)),f332(f332(f8(a1,f883(a1,f882(a1,a1)),a1),f267(a1,a1)),f332(f38(a1),x94582))),f332(f38(a1),x94581))),f226(x94582,x94581))+P102(f332(f332(f247(a1),x94581),f2(a1))) % 172.83/172.49 [8225]~P89(x82252)+~P113(x82252)+~P102(f332(f332(f247(x82252),f332(f106(x82252),x82251)),f77(x82252)))+P102(f332(f332(f247(a1),x82251),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100))) % 172.83/172.49 [8226]~P89(x82262)+~P113(x82262)+~P102(f332(f332(f246(x82262),f332(f106(x82262),x82261)),f77(x82262)))+P102(f332(f332(f246(a1),x82261),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100))) % 172.83/172.49 [8504]~P113(x85041)+~P89(x85041)+P102(f332(f332(f247(x85041),f332(f106(x85041),x85042)),f77(x85041)))+~P102(f332(f332(f247(a1),x85042),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100))) % 172.83/172.49 [8505]~P113(x85051)+~P89(x85051)+P102(f332(f332(f246(x85051),f332(f106(x85051),x85052)),f77(x85051)))+~P102(f332(f332(f246(a1),x85052),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100))) % 172.83/172.49 [8700]~P89(x87002)+~P113(x87002)+~P102(f332(f332(f247(x87002),f77(x87002)),f332(f106(x87002),x87001)))+P102(f332(f332(f247(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),x87001)) % 172.83/172.49 [8701]~P89(x87012)+~P113(x87012)+~P102(f332(f332(f246(x87012),f77(x87012)),f332(f106(x87012),x87011)))+P102(f332(f332(f246(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),x87011)) % 172.83/172.49 [9076]~P113(x90761)+~P89(x90761)+P102(f332(f332(f247(x90761),f77(x90761)),f332(f106(x90761),x90762)))+~P102(f332(f332(f247(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),x90762)) % 172.83/172.49 [9077]~P113(x90771)+~P89(x90771)+P102(f332(f332(f246(x90771),f77(x90771)),f332(f106(x90771),x90772)))+~P102(f332(f332(f246(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),x90772)) % 172.83/172.49 [9587]~P136(x95872)+E(x95871,f77(x95872))+E(x95871,f332(f78(x95872),f77(x95872)))+~E(f332(f332(f257(x95872),x95871),f332(f106(a876),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)))),f77(x95872)) % 172.83/172.49 [9859]~P59(x98591)+~P89(x98591)+~P102(f332(f332(f247(x98591),f2(x98591)),x98592))+P102(f332(f332(f247(x98591),f2(x98591)),f332(f332(f290(x98591),x98592),f332(f106(x98591),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)))))) % 172.83/172.49 [9921]~P59(x99211)+~P89(x99211)+P102(f332(f332(f247(x99211),f2(x99211)),x99212))+~P102(f332(f332(f247(x99211),f2(x99211)),f332(f332(f290(x99211),x99212),f332(f106(x99211),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)))))) % 172.83/172.49 [10175]~P137(x101752)+E(x101751,f2(a1))+P102(f332(f332(f247(a1),x101751),f2(a1)))+E(f332(f332(f271(a1,a1,x101752),f332(f332(f7(a1,f883(a1,f883(x101752,x101752)),f883(a1,x101752)),f332(f332(f8(f883(f883(x101752,x101752),x101752),f883(f883(a1,f883(x101752,x101752)),f883(a1,x101752)),a1),f8(f883(x101752,x101752),x101752,a1)),f332(f332(f8(x101752,f883(f883(x101752,x101752),x101752),a1),f85(x101752,x101752)),f105(x101752)))),f332(f332(f7(a1,f883(x101752,x101752),f883(x101752,x101752)),f332(f332(f8(f883(x101752,f883(x101752,x101752)),f883(f883(x101752,x101752),f883(x101752,x101752)),a1),f18(x101752,x101752,x101752)),f332(f332(f7(a1,f883(x101752,x101752),f883(x101752,f883(x101752,x101752))),f332(f332(f8(f883(x101752,f883(x101752,x101752)),f883(f883(x101752,x101752),f883(x101752,f883(x101752,x101752))),a1),f8(x101752,f883(x101752,x101752),x101752)),f332(f332(f8(a871,f883(x101752,f883(x101752,x101752)),a1),f99(x101752)),f332(f332(f7(a1,a1,a871),a329),f2(a1))))),f332(f332(f18(x101752,x101752,x101752),f79(x101752)),f5(x101752))))),f332(f332(f7(x101752,x101752,x101752),f332(f332(f8(x101752,f883(x101752,x101752),x101752),f79(x101752)),f332(f332(f18(x101752,x101752,x101752),f79(x101752)),f5(x101752)))),f77(x101752))))),f45(x101751,f332(f106(a1),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100))))),f332(f105(x101752),x101751)) % 172.83/172.49 [5226]~P56(x52263)+~P36(x52263,x52262,f55(x52263))+E(x52261,f777(x52262,x52263))+~P102(f332(x52262,x52261)) % 172.83/172.49 [5386]~P56(x53861)+P36(x53861,x53862,f55(x53861))+~E(f778(x53862,x53861,x53863),x53863)+~P102(f332(x53862,x53863)) % 172.83/172.49 [4871]~P88(x48713)+~P89(x48713)+E(x48711,x48712)+~E(f332(f106(x48713),x48711),f332(f106(x48713),x48712)) % 172.83/172.49 [6007]~P56(x60071)+P36(x60071,x60072,f55(x60071))+~P102(f332(x60072,x60073))+P102(f332(x60072,f778(x60072,x60071,x60073))) % 172.83/172.49 [6017]~P102(f332(x60171,x60172))+~P102(f332(x60171,x60173))+~P102(f332(f332(f246(a876),x60173),f863(x60172,x60171)))+P102(f332(x60171,f2(a876))) % 172.83/172.49 [6431]P144(x64312,x64313,x64311)+E(x64311,f2(a1))+P102(f332(f332(f246(a1),f2(a1)),f815(x64311,x64313,x64312)))+P102(f332(f332(f247(a1),x64311),f2(a1))) % 172.83/172.49 [6432]P143(x64322,x64323,x64321)+E(x64321,f2(a1))+P102(f332(f332(f246(a1),f2(a1)),f820(x64321,x64323,x64322)))+P102(f332(f332(f247(a1),x64321),f2(a1))) % 172.83/172.49 [6551]P143(x65511,x65512,x65513)+~P102(f332(x65511,x65512))+P102(f332(f332(f246(a1),f2(a1)),f820(x65513,x65512,x65511)))+P102(f332(f332(f247(a1),x65513),f2(a1))) % 172.83/172.49 [6578]P144(x65781,x65782,x65783)+P102(f332(f332(f246(a1),f2(a1)),f815(x65783,x65782,x65781)))+~P102(f332(x65781,f2(a1)))+P102(f332(f332(f247(a1),x65783),f2(a1))) % 172.83/172.49 [6606]P144(x66062,x66063,x66061)+E(x66061,f2(a1))+~P102(f332(x66062,f816(x66061,x66063,x66062)))+P102(f332(f332(f247(a1),x66061),f2(a1))) % 172.83/172.49 [6607]P143(x66072,x66073,x66071)+E(x66071,f2(a1))+~P102(f332(x66072,f820(x66071,x66073,x66072)))+P102(f332(f332(f247(a1),x66071),f2(a1))) % 172.83/172.49 [6707]~P104(x67071)+~P27(x67071)+~P102(f332(f332(f247(x67071),x67072),f39(x67071,x67073)))+P102(f332(f332(f247(x67071),x67072),f602(x67073,x67072,x67071))) % 172.83/172.49 [6716]P143(x67161,x67162,x67163)+~P102(f332(x67161,x67162))+~P102(f332(x67161,f820(x67163,x67162,x67161)))+P102(f332(f332(f247(a1),x67163),f2(a1))) % 172.83/172.49 [6748]P144(x67481,x67482,x67483)+~P102(f332(x67481,f816(x67483,x67482,x67481)))+~P102(f332(x67481,f2(a1)))+P102(f332(f332(f247(a1),x67483),f2(a1))) % 172.83/172.49 [7002]P144(x70022,x70023,x70021)+E(x70021,f2(a1))+P102(f332(f332(f246(a1),f2(a1)),f815(x70021,x70023,x70022)))+P102(f332(f332(f247(a1),x70021),f814(x70021,x70023,x70022))) % 172.83/172.49 [7003]P143(x70032,x70033,x70031)+E(x70031,f2(a1))+P102(f332(f332(f246(a1),f2(a1)),f820(x70031,x70033,x70032)))+P102(f332(f332(f247(a1),x70031),f819(x70031,x70033,x70032))) % 172.83/172.49 [7120]P143(x71201,x71202,x71203)+~P102(f332(x71201,x71202))+P102(f332(f332(f246(a1),f2(a1)),f820(x71203,x71202,x71201)))+P102(f332(f332(f247(a1),x71203),f819(x71203,x71202,x71201))) % 172.83/172.49 [7139]P144(x71391,x71392,x71393)+P102(f332(f332(f246(a1),f2(a1)),f815(x71393,x71392,x71391)))+P102(f332(f332(f247(a1),x71393),f814(x71393,x71392,x71391)))+~P102(f332(x71391,f2(a1))) % 172.83/172.49 [7172]P144(x71722,x71723,x71721)+E(x71721,f2(a1))+~P102(f332(x71722,f816(x71721,x71723,x71722)))+P102(f332(f332(f247(a1),x71721),f814(x71721,x71723,x71722))) % 172.83/172.49 [7173]P143(x71732,x71733,x71731)+E(x71731,f2(a1))+~P102(f332(x71732,f820(x71731,x71733,x71732)))+P102(f332(f332(f247(a1),x71731),f819(x71731,x71733,x71732))) % 172.83/172.49 [7214]P144(x72142,x72143,x72141)+E(x72141,f2(a1))+P102(f332(f332(f246(a1),f2(a1)),f815(x72141,x72143,x72142)))+~P102(f332(x72142,f818(x72141,x72143,x72142))) % 172.83/172.49 [7215]P143(x72152,x72153,x72151)+E(x72151,f2(a1))+P102(f332(f332(f246(a1),f2(a1)),f820(x72151,x72153,x72152)))+~P102(f332(x72152,f819(x72151,x72153,x72152))) % 172.83/172.49 [7303]P143(x73031,x73032,x73033)+~P102(f332(x73031,x73032))+~P102(f332(x73031,f820(x73033,x73032,x73031)))+P102(f332(f332(f247(a1),x73033),f819(x73033,x73032,x73031))) % 172.83/172.49 [7319]P144(x73191,x73192,x73193)+~P102(f332(x73191,f816(x73193,x73192,x73191)))+P102(f332(f332(f247(a1),x73193),f814(x73193,x73192,x73191)))+~P102(f332(x73191,f2(a1))) % 172.83/172.49 [7323]P143(x73231,x73232,x73233)+~P102(f332(x73231,x73232))+P102(f332(f332(f246(a1),f2(a1)),f820(x73233,x73232,x73231)))+~P102(f332(x73231,f819(x73233,x73232,x73231))) % 172.83/172.49 [7341]P144(x73411,x73412,x73413)+P102(f332(f332(f246(a1),f2(a1)),f815(x73413,x73412,x73411)))+~P102(f332(x73411,f818(x73413,x73412,x73411)))+~P102(f332(x73411,f2(a1))) % 172.83/172.49 [7365]P144(x73652,x73653,x73651)+E(x73651,f2(a1))+~P102(f332(x73652,f816(x73651,x73653,x73652)))+~P102(f332(x73652,f818(x73651,x73653,x73652))) % 172.83/172.49 [7366]P143(x73662,x73663,x73661)+E(x73661,f2(a1))+~P102(f332(x73662,f820(x73661,x73663,x73662)))+~P102(f332(x73662,f819(x73661,x73663,x73662))) % 172.83/172.49 [7458]P143(x74581,x74582,x74583)+~P102(f332(x74581,x74582))+~P102(f332(x74581,f820(x74583,x74582,x74581)))+~P102(f332(x74581,f819(x74583,x74582,x74581))) % 172.83/172.49 [7475]P144(x74751,x74752,x74753)+~P102(f332(x74751,f816(x74753,x74752,x74751)))+~P102(f332(x74751,f818(x74753,x74752,x74751)))+~P102(f332(x74751,f2(a1))) % 172.83/172.49 [7524]P144(x75242,x75243,x75241)+E(x75241,f2(a1))+P102(f332(f332(f246(a1),f2(a1)),f815(x75241,x75243,x75242)))+P102(f332(f332(f246(a1),f814(x75241,x75243,x75242)),f2(a1))) % 172.83/172.49 [7525]P143(x75252,x75253,x75251)+E(x75251,f2(a1))+P102(f332(f332(f246(a1),f2(a1)),f820(x75251,x75253,x75252)))+P102(f332(f332(f246(a1),f819(x75251,x75253,x75252)),f2(a1))) % 172.83/172.49 [7526]~P137(x75261)+~P102(f332(f332(f334(x75261),x75263),f112(x75261)))+~P102(f332(f332(f334(x75261),x75262),f112(x75261)))+P102(f332(f332(f334(x75261),f332(f332(f22(x75261),x75262),x75263)),f112(x75261))) % 172.83/172.49 [7527]~P137(x75271)+~P102(f332(f332(f334(x75271),x75273),f112(x75271)))+~P102(f332(f332(f334(x75271),x75272),f112(x75271)))+P102(f332(f332(f334(x75271),f332(f332(f80(x75271),x75272),x75273)),f112(x75271))) % 172.83/172.49 [7528]~P141(x75281)+~P102(f332(f332(f334(x75281),x75283),f193(x75281)))+~P102(f332(f332(f334(x75281),x75282),f193(x75281)))+P102(f332(f332(f334(x75281),f332(f332(f80(x75281),x75282),x75283)),f193(x75281))) % 172.83/172.49 [7529]~P137(x75291)+~P102(f332(f332(f334(x75291),x75293),f112(x75291)))+~P102(f332(f332(f334(x75291),x75292),f112(x75291)))+P102(f332(f332(f334(x75291),f332(f332(f79(x75291),x75292),x75293)),f112(x75291))) % 172.83/172.49 [7530]~P141(x75301)+~P102(f332(f332(f334(x75301),x75303),f193(x75301)))+~P102(f332(f332(f334(x75301),x75302),f193(x75301)))+P102(f332(f332(f334(x75301),f332(f332(f79(x75301),x75302),x75303)),f193(x75301))) % 172.83/172.49 [7531]~P84(x75311)+~P102(f332(f332(f247(x75311),x75313),f2(x75311)))+~P102(f332(f332(f247(x75311),x75312),f2(x75311)))+P102(f332(f332(f247(x75311),f332(f332(f79(x75311),x75312),x75313)),f2(x75311))) % 172.83/172.49 [7532]~P84(x75321)+~P102(f332(f332(f246(x75321),x75322),f2(x75321)))+~P102(f332(f332(f247(x75321),x75323),f2(x75321)))+P102(f332(f332(f247(x75321),f332(f332(f79(x75321),x75322),x75323)),f2(x75321))) % 172.83/172.49 [7533]~P84(x75331)+~P102(f332(f332(f246(x75331),x75333),f2(x75331)))+~P102(f332(f332(f247(x75331),x75332),f2(x75331)))+P102(f332(f332(f247(x75331),f332(f332(f79(x75331),x75332),x75333)),f2(x75331))) % 172.83/172.49 [7534]~P84(x75341)+~P102(f332(f332(f246(x75341),x75343),f2(x75341)))+~P102(f332(f332(f246(x75341),x75342),f2(x75341)))+P102(f332(f332(f246(x75341),f332(f332(f79(x75341),x75342),x75343)),f2(x75341))) % 172.83/172.49 [7560]P144(x75603,x75602,x75601)+E(x75601,f2(a1))+E(f332(f332(f79(a1),f332(f332(f80(a1),x75601),f816(x75601,x75602,x75603))),f815(x75601,x75602,x75603)),x75602)+P102(f332(f332(f247(a1),x75601),f2(a1))) % 172.83/172.49 [7561]P143(x75613,x75612,x75611)+E(x75611,f2(a1))+E(f332(f332(f79(a1),f332(f332(f80(a1),x75611),f821(x75611,x75612,x75613))),f820(x75611,x75612,x75613)),x75612)+P102(f332(f332(f247(a1),x75611),f2(a1))) % 172.83/172.49 [7643]P143(x76431,x76432,x76433)+~P102(f332(x76431,x76432))+P102(f332(f332(f246(a1),f2(a1)),f820(x76433,x76432,x76431)))+P102(f332(f332(f246(a1),f819(x76433,x76432,x76431)),f2(a1))) % 172.83/172.49 [7672]P144(x76721,x76722,x76723)+P102(f332(f332(f246(a1),f2(a1)),f815(x76723,x76722,x76721)))+~P102(f332(x76721,f2(a1)))+P102(f332(f332(f246(a1),f814(x76723,x76722,x76721)),f2(a1))) % 172.83/172.49 [7682]P143(x76823,x76822,x76821)+~P102(f332(x76823,x76822))+E(f332(f332(f79(a1),f332(f332(f80(a1),x76821),f821(x76821,x76822,x76823))),f820(x76821,x76822,x76823)),x76822)+P102(f332(f332(f247(a1),x76821),f2(a1))) % 172.83/172.49 [7689]P144(x76892,x76893,x76891)+E(x76891,f2(a1))+~P102(f332(x76892,f816(x76891,x76893,x76892)))+P102(f332(f332(f246(a1),f814(x76891,x76893,x76892)),f2(a1))) % 172.83/172.49 [7690]P143(x76902,x76903,x76901)+E(x76901,f2(a1))+~P102(f332(x76902,f820(x76901,x76903,x76902)))+P102(f332(f332(f246(a1),f819(x76901,x76903,x76902)),f2(a1))) % 172.83/172.49 [7695]P144(x76953,x76952,x76951)+E(f332(f332(f79(a1),f332(f332(f80(a1),x76951),f816(x76951,x76952,x76953))),f815(x76951,x76952,x76953)),x76952)+~P102(f332(x76953,f2(a1)))+P102(f332(f332(f247(a1),x76951),f2(a1))) % 172.83/172.49 [7752]P143(x77521,x77522,x77523)+~P102(f332(x77521,x77522))+~P102(f332(x77521,f820(x77523,x77522,x77521)))+P102(f332(f332(f246(a1),f819(x77523,x77522,x77521)),f2(a1))) % 172.83/172.49 [7756]P144(x77561,x77562,x77563)+~P102(f332(x77561,f816(x77563,x77562,x77561)))+~P102(f332(x77561,f2(a1)))+P102(f332(f332(f246(a1),f814(x77563,x77562,x77561)),f2(a1))) % 172.83/172.49 [7828]~P59(x78281)+~P102(f332(f332(f247(x78281),f332(f332(f290(x78281),x78283),x78282)),f2(x78281)))+P102(f332(f332(f247(x78281),x78282),f2(x78281)))+P102(f332(f332(f247(x78281),x78283),f2(x78281))) % 172.83/172.49 [7829]~P120(x78291)+~P102(f332(f332(f246(x78291),f332(f332(f80(x78291),x78293),x78292)),f2(x78291)))+P102(f332(f332(f246(x78291),x78292),f2(x78291)))+P102(f332(f332(f246(x78291),x78293),f2(x78291))) % 172.83/172.49 [7830]~P59(x78301)+~P102(f332(f332(f246(x78301),f332(f332(f290(x78301),x78303),x78302)),f2(x78301)))+P102(f332(f332(f246(x78301),x78302),f2(x78301)))+P102(f332(f332(f246(x78301),x78303),f2(x78301))) % 172.83/172.49 [7944]P144(x79443,x79442,x79441)+E(x79441,f2(a1))+E(f332(f332(f79(a1),f332(f332(f80(a1),x79441),f816(x79441,x79442,x79443))),f815(x79441,x79442,x79443)),x79442)+P102(f332(f332(f247(a1),x79441),f814(x79441,x79442,x79443))) % 172.83/172.49 [7945]P143(x79453,x79452,x79451)+E(x79451,f2(a1))+E(f332(f332(f79(a1),f332(f332(f80(a1),x79451),f821(x79451,x79452,x79453))),f820(x79451,x79452,x79453)),x79452)+P102(f332(f332(f247(a1),x79451),f819(x79451,x79452,x79453))) % 172.83/172.49 [7957]P144(x79573,x79572,x79571)+E(x79571,f2(a1))+E(f332(f332(f79(a1),f332(f332(f80(a1),x79571),f818(x79571,x79572,x79573))),f814(x79571,x79572,x79573)),x79572)+P102(f332(f332(f246(a1),f2(a1)),f815(x79571,x79572,x79573))) % 172.83/172.49 [7958]P143(x79583,x79582,x79581)+E(x79581,f2(a1))+E(f332(f332(f79(a1),f332(f332(f80(a1),x79581),f822(x79581,x79582,x79583))),f819(x79581,x79582,x79583)),x79582)+P102(f332(f332(f246(a1),f2(a1)),f820(x79581,x79582,x79583))) % 172.83/172.49 [8003]P143(x80033,x80032,x80031)+~P102(f332(x80033,x80032))+E(f332(f332(f79(a1),f332(f332(f80(a1),x80031),f821(x80031,x80032,x80033))),f820(x80031,x80032,x80033)),x80032)+P102(f332(f332(f247(a1),x80031),f819(x80031,x80032,x80033))) % 172.83/172.49 [8015]P144(x80153,x80152,x80151)+E(f332(f332(f79(a1),f332(f332(f80(a1),x80151),f816(x80151,x80152,x80153))),f815(x80151,x80152,x80153)),x80152)+P102(f332(f332(f247(a1),x80151),f814(x80151,x80152,x80153)))+~P102(f332(x80153,f2(a1))) % 172.83/172.49 [8021]P143(x80213,x80212,x80211)+~P102(f332(x80213,x80212))+E(f332(f332(f79(a1),f332(f332(f80(a1),x80211),f822(x80211,x80212,x80213))),f819(x80211,x80212,x80213)),x80212)+P102(f332(f332(f246(a1),f2(a1)),f820(x80211,x80212,x80213))) % 172.83/172.49 [8029]P144(x80293,x80292,x80291)+E(f332(f332(f79(a1),f332(f332(f80(a1),x80291),f818(x80291,x80292,x80293))),f814(x80291,x80292,x80293)),x80292)+P102(f332(f332(f246(a1),f2(a1)),f815(x80291,x80292,x80293)))+~P102(f332(x80293,f2(a1))) % 172.83/172.49 [8040]P144(x80403,x80402,x80401)+E(x80401,f2(a1))+E(f332(f332(f79(a1),f332(f332(f80(a1),x80401),f816(x80401,x80402,x80403))),f815(x80401,x80402,x80403)),x80402)+~P102(f332(x80403,f818(x80401,x80402,x80403))) % 172.83/172.49 [8041]P143(x80413,x80412,x80411)+E(x80411,f2(a1))+E(f332(f332(f79(a1),f332(f332(f80(a1),x80411),f821(x80411,x80412,x80413))),f820(x80411,x80412,x80413)),x80412)+~P102(f332(x80413,f819(x80411,x80412,x80413))) % 172.83/172.49 [8042]P144(x80423,x80422,x80421)+E(x80421,f2(a1))+E(f332(f332(f79(a1),f332(f332(f80(a1),x80421),f818(x80421,x80422,x80423))),f814(x80421,x80422,x80423)),x80422)+~P102(f332(x80423,f816(x80421,x80422,x80423))) % 172.83/172.49 [8043]P143(x80433,x80432,x80431)+E(x80431,f2(a1))+E(f332(f332(f79(a1),f332(f332(f80(a1),x80431),f822(x80431,x80432,x80433))),f819(x80431,x80432,x80433)),x80432)+~P102(f332(x80433,f820(x80431,x80432,x80433))) % 172.83/172.49 [8101]P143(x81013,x81012,x81011)+~P102(f332(x81013,x81012))+E(f332(f332(f79(a1),f332(f332(f80(a1),x81011),f821(x81011,x81012,x81013))),f820(x81011,x81012,x81013)),x81012)+~P102(f332(x81013,f819(x81011,x81012,x81013))) % 172.83/172.49 [8102]P143(x81023,x81022,x81021)+~P102(f332(x81023,x81022))+E(f332(f332(f79(a1),f332(f332(f80(a1),x81021),f822(x81021,x81022,x81023))),f819(x81021,x81022,x81023)),x81022)+~P102(f332(x81023,f820(x81021,x81022,x81023))) % 172.83/172.49 [8112]P144(x81123,x81122,x81121)+E(f332(f332(f79(a1),f332(f332(f80(a1),x81121),f816(x81121,x81122,x81123))),f815(x81121,x81122,x81123)),x81122)+~P102(f332(x81123,f818(x81121,x81122,x81123)))+~P102(f332(x81123,f2(a1))) % 172.83/172.49 [8113]P144(x81133,x81132,x81131)+E(f332(f332(f79(a1),f332(f332(f80(a1),x81131),f818(x81131,x81132,x81133))),f814(x81131,x81132,x81133)),x81132)+~P102(f332(x81133,f816(x81131,x81132,x81133)))+~P102(f332(x81133,f2(a1))) % 172.83/172.49 [8218]P144(x82183,x82182,x82181)+E(x82181,f2(a1))+E(f332(f332(f79(a1),f332(f332(f80(a1),x82181),f816(x82181,x82182,x82183))),f815(x82181,x82182,x82183)),x82182)+P102(f332(f332(f246(a1),f814(x82181,x82182,x82183)),f2(a1))) % 172.83/172.49 [8219]P143(x82193,x82192,x82191)+E(x82191,f2(a1))+E(f332(f332(f79(a1),f332(f332(f80(a1),x82191),f821(x82191,x82192,x82193))),f820(x82191,x82192,x82193)),x82192)+P102(f332(f332(f246(a1),f819(x82191,x82192,x82193)),f2(a1))) % 172.83/172.49 [8259]P143(x82593,x82592,x82591)+~P102(f332(x82593,x82592))+E(f332(f332(f79(a1),f332(f332(f80(a1),x82591),f821(x82591,x82592,x82593))),f820(x82591,x82592,x82593)),x82592)+P102(f332(f332(f246(a1),f819(x82591,x82592,x82593)),f2(a1))) % 172.83/172.49 [8264]P144(x82643,x82642,x82641)+E(f332(f332(f79(a1),f332(f332(f80(a1),x82641),f816(x82641,x82642,x82643))),f815(x82641,x82642,x82643)),x82642)+~P102(f332(x82643,f2(a1)))+P102(f332(f332(f246(a1),f814(x82641,x82642,x82643)),f2(a1))) % 172.83/172.49 [8393]P144(x83933,x83932,x83931)+E(x83931,f2(a1))+E(f332(f332(f79(a1),f332(f332(f80(a1),x83931),f818(x83931,x83932,x83933))),f814(x83931,x83932,x83933)),x83932)+E(f332(f332(f79(a1),f332(f332(f80(a1),x83931),f816(x83931,x83932,x83933))),f815(x83931,x83932,x83933)),x83932) % 172.83/172.49 [8394]P143(x83943,x83942,x83941)+E(x83941,f2(a1))+E(f332(f332(f79(a1),f332(f332(f80(a1),x83941),f822(x83941,x83942,x83943))),f819(x83941,x83942,x83943)),x83942)+E(f332(f332(f79(a1),f332(f332(f80(a1),x83941),f821(x83941,x83942,x83943))),f820(x83941,x83942,x83943)),x83942) % 172.83/172.49 [8418]P143(x84183,x84182,x84181)+~P102(f332(x84183,x84182))+E(f332(f332(f79(a1),f332(f332(f80(a1),x84181),f822(x84181,x84182,x84183))),f819(x84181,x84182,x84183)),x84182)+E(f332(f332(f79(a1),f332(f332(f80(a1),x84181),f821(x84181,x84182,x84183))),f820(x84181,x84182,x84183)),x84182) % 172.83/172.49 [8431]P144(x84313,x84312,x84311)+E(f332(f332(f79(a1),f332(f332(f80(a1),x84311),f818(x84311,x84312,x84313))),f814(x84311,x84312,x84313)),x84312)+E(f332(f332(f79(a1),f332(f332(f80(a1),x84311),f816(x84311,x84312,x84313))),f815(x84311,x84312,x84313)),x84312)+~P102(f332(x84313,f2(a1))) % 172.83/172.49 [9081]~P120(x90811)+~E(x90813,f2(x90811))+~E(x90812,f2(x90811))+P102(f332(f332(f246(x90811),f332(f332(f79(x90811),f332(f332(f80(x90811),x90812),x90812)),f332(f332(f80(x90811),x90813),x90813))),f2(x90811))) % 172.83/172.49 [10125]~P113(x101251)+~E(x101253,f2(x101251))+~E(x101252,f2(x101251))+P102(f332(f332(f246(x101251),f332(f332(f79(x101251),f332(f332(f257(x101251),x101252),f332(f106(a876),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100))))),f332(f332(f257(x101251),x101253),f332(f106(a876),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)))))),f2(x101251))) % 172.83/172.49 [4820]~E(x48203,x48201)+~P117(x48202)+E(x48201,f2(x48202))+E(f332(f332(f290(x48202),x48203),x48201),f77(x48202)) % 172.83/172.49 [4872]~P62(x48721)+~E(x48723,f195(x48721))+~E(x48722,f195(x48721))+E(f332(f332(f113(x48721),x48722),x48723),f195(x48721)) % 172.83/172.49 [4873]~P96(x48731)+~E(x48733,f255(x48731))+~E(x48732,f255(x48731))+E(f332(f332(f104(x48731),x48732),x48733),f255(x48731)) % 172.83/172.49 [4961]~P117(x49613)+E(x49611,x49612)+E(x49612,f2(x49613))+~E(f332(f332(f290(x49613),x49611),x49612),f77(x49613)) % 172.83/172.49 [4979]~P135(x49792)+E(x49791,f2(x49792))+E(x49793,f2(x49792))+~E(f332(f332(f80(x49792),x49793),x49791),f2(x49792)) % 172.83/172.49 [4981]~P130(x49812)+E(x49811,f2(x49812))+E(x49813,f2(x49812))+~E(f332(f332(f80(x49812),x49813),x49811),f2(x49812)) % 172.83/172.49 [5353]~P116(x53533)+E(x53531,x53532)+E(x53531,f332(f78(x53533),x53532))+~E(f332(f332(f80(x53533),x53531),x53531),f332(f332(f80(x53533),x53532),x53532)) % 172.83/172.49 [5393]~P92(x53931)+E(f332(f78(x53931),x53932),x53933)+~E(f332(f332(f113(x53931),x53932),x53933),f255(x53931))+~E(f332(f332(f104(x53931),x53932),x53933),f195(x53931)) % 172.83/172.49 [5472]~P113(x54723)+E(x54721,x54722)+P102(f332(f332(f247(x54723),x54722),x54721))+P102(f332(f332(f247(x54723),x54721),x54722)) % 172.83/172.49 [5473]~P104(x54733)+E(x54731,x54732)+P102(f332(f332(f247(x54733),x54732),x54731))+P102(f332(f332(f247(x54733),x54731),x54732)) % 172.83/172.49 [5474]~E(x54742,x54743)+~P104(x54741)+P102(f332(f332(f246(x54741),x54742),x54743))+P102(f332(f332(f247(x54741),x54742),x54743)) % 172.83/172.49 [5730]~P105(x57303)+E(x57301,x57302)+~P102(f332(f332(f246(x57303),x57302),x57301))+P102(f332(f332(f247(x57303),x57302),x57301)) % 172.83/172.49 [5732]~P104(x57323)+E(x57321,x57322)+~P102(f332(f332(f246(x57323),x57321),x57322))+P102(f332(f332(f247(x57323),x57321),x57322)) % 172.83/172.49 [5738]~P105(x57383)+E(x57381,x57382)+~P102(f332(f332(f246(x57383),x57381),x57382))+P102(f332(f332(f247(x57383),x57381),x57382)) % 172.83/172.49 [5838]P143(x58381,x58382,x58383)+~P102(f332(x58381,x58382))+P102(f332(f332(f247(a1),x58383),f2(a1)))+P102(f332(f332(f247(a1),f2(a1)),x58383)) % 172.83/172.49 [5885]P144(x58851,x58852,x58853)+~P102(f332(x58851,f2(a1)))+P102(f332(f332(f247(a1),x58853),f2(a1)))+P102(f332(f332(f247(a1),f2(a1)),x58853)) % 172.83/172.49 [5889]~P61(x58891)+E(f332(f332(f113(x58891),x58892),f10(x58891,x58893)),x58892)+~P102(f332(f61(x58891),x58893))+~P102(f332(f332(f334(x58891),x58892),x58893)) % 172.83/172.49 [5890]~P61(x58901)+E(f332(f332(f104(x58901),x58902),f13(x58901,x58903)),x58902)+~P102(f332(f61(x58901),x58903))+~P102(f332(f332(f334(x58901),x58902),x58903)) % 172.83/172.49 [5924]~P61(x59241)+E(f332(f332(f113(x59241),x59242),f13(x59241,x59243)),f13(x59241,x59243))+~P102(f332(f61(x59241),x59243))+~P102(f332(f332(f334(x59241),x59242),x59243)) % 172.83/172.49 [5925]~P61(x59251)+E(f332(f332(f104(x59251),x59252),f10(x59251,x59253)),f10(x59251,x59253))+~P102(f332(f61(x59251),x59253))+~P102(f332(f332(f334(x59251),x59252),x59253)) % 172.83/172.49 [5926]~P104(x59261)+E(f332(f332(f244(x59261),x59262),f15(x59261,x59263)),f15(x59261,x59263))+~P102(f332(f61(x59261),x59263))+~P102(f332(f332(f334(x59261),x59262),x59263)) % 172.83/172.49 [5927]~P104(x59271)+E(f332(f332(f245(x59271),x59272),f14(x59271,x59273)),f14(x59271,x59273))+~P102(f332(f61(x59271),x59273))+~P102(f332(f332(f334(x59271),x59272),x59273)) % 172.83/172.49 [5972]E(x59721,x59722)+~P105(x59723)+~P102(f332(f332(f246(x59723),x59722),x59721))+~P102(f332(f332(f246(x59723),x59721),x59722)) % 172.83/172.49 [6112]~P103(x61121)+P102(f332(f332(f246(x61121),x61123),x61122))+~P102(f332(f332(f246(x61121),x61122),x61123))+P102(f332(f332(f247(x61121),x61122),x61123)) % 172.83/172.49 [6133]~P104(x61331)+~P102(f332(f61(x61331),x61333))+P102(f332(f332(f246(x61331),x61332),f14(x61331,x61333)))+~P102(f332(f332(f334(x61331),x61332),x61333)) % 172.83/172.49 [6181]~P104(x61811)+E(f332(f332(f244(x61811),x61812),f11(x61811,f245(x61811),x61813)),x61812)+~P102(f332(f61(x61811),x61813))+~P102(f332(f332(f334(x61811),x61812),x61813)) % 172.83/172.49 [6182]~P104(x61821)+E(f332(f332(f245(x61821),x61822),f12(x61821,f244(x61821),x61823)),x61822)+~P102(f332(f61(x61821),x61823))+~P102(f332(f332(f334(x61821),x61822),x61823)) % 172.83/172.49 [6320]E(x63201,x63202)+~E(f332(f332(f22(a876),x63201),x63203),f332(f332(f22(a876),x63202),x63203))+~P102(f332(f332(f246(a876),x63203),x63201))+~P102(f332(f332(f246(a876),x63203),x63202)) % 172.83/172.49 [6347]~P104(x63471)+~P102(f332(f61(x63471),x63472))+~P102(f332(f332(f334(x63471),x63473),x63472))+P102(f332(f332(f246(x63471),f15(x63471,x63472)),x63473)) % 172.83/172.49 [6410]P144(x64102,x64103,x64101)+E(x64101,f2(a1))+P102(f332(f332(f247(a1),x64101),f814(x64101,x64103,x64102)))+P102(f332(f332(f247(a1),f2(a1)),x64101)) % 172.83/172.49 [6411]P143(x64112,x64113,x64111)+E(x64111,f2(a1))+P102(f332(f332(f247(a1),x64111),f819(x64111,x64113,x64112)))+P102(f332(f332(f247(a1),f2(a1)),x64111)) % 172.83/172.49 [6412]~P104(x64121)+E(f332(f332(f244(x64121),x64122),f12(x64121,f244(x64121),x64123)),f12(x64121,f244(x64121),x64123))+~P102(f332(f61(x64121),x64123))+~P102(f332(f332(f334(x64121),x64122),x64123)) % 172.83/172.49 [6413]~P104(x64131)+E(f332(f332(f245(x64131),x64132),f11(x64131,f245(x64131),x64133)),f11(x64131,f245(x64131),x64133))+~P102(f332(f61(x64131),x64133))+~P102(f332(f332(f334(x64131),x64132),x64133)) % 172.83/172.49 [6419]~P102(f332(x64191,x64192))+P102(f332(x64191,f480(x64192,x64191,x64193)))+P102(f332(x64191,f2(a876)))+~P102(f332(f332(f247(a876),x64192),x64193)) % 172.83/172.49 [6473]~P102(f332(x64731,x64732))+~P102(f332(f61(x64733),x64732))+P102(f332(x64731,f655(x64731,x64732,x64733)))+P102(f332(x64731,f195(f883(x64733,a871)))) % 172.83/172.49 [6486]~P113(x64861)+~P89(x64861)+P102(f332(f332(f247(x64861),f332(f106(x64861),x64862)),f332(f106(x64861),x64863)))+~P102(f332(f332(f247(a1),x64862),x64863)) % 172.83/172.49 [6487]~P113(x64871)+~P89(x64871)+P102(f332(f332(f246(x64871),f332(f106(x64871),x64872)),f332(f106(x64871),x64873)))+~P102(f332(f332(f246(a1),x64872),x64873)) % 172.83/172.49 [6490]~P102(f332(x64901,x64903))+~P102(f332(f61(x64902),x64903))+P102(f332(f61(x64902),f655(x64901,x64903,x64902)))+P102(f332(x64901,f195(f883(x64902,a871)))) % 172.83/172.49 [6523]P143(x65231,x65232,x65233)+~P102(f332(x65231,x65232))+P102(f332(f332(f247(a1),x65233),f819(x65233,x65232,x65231)))+P102(f332(f332(f247(a1),f2(a1)),x65233)) % 172.83/172.49 [6558]P144(x65581,x65582,x65583)+P102(f332(f332(f247(a1),x65583),f814(x65583,x65582,x65581)))+~P102(f332(x65581,f2(a1)))+P102(f332(f332(f247(a1),f2(a1)),x65583)) % 172.83/172.49 [6589]~P106(x65891)+~P90(x65891)+E(f332(f332(f244(x65891),f332(f106(x65891),x65892)),f332(f106(x65891),x65893)),f332(f106(x65891),x65893))+P102(f332(f332(f246(x65891),f332(f106(x65891),x65892)),f332(f106(x65891),x65893))) % 172.83/172.49 [6590]~P106(x65901)+~P90(x65901)+E(f332(f332(f245(x65901),f332(f106(x65901),x65902)),f332(f106(x65901),x65903)),f332(f106(x65901),x65902))+P102(f332(f332(f246(x65901),f332(f106(x65901),x65902)),f332(f106(x65901),x65903))) % 172.83/172.49 [6648]P144(x66482,x66483,x66481)+E(x66481,f2(a1))+~P102(f332(x66482,f818(x66481,x66483,x66482)))+P102(f332(f332(f247(a1),f2(a1)),x66481)) % 172.83/172.49 [6649]P143(x66492,x66493,x66491)+E(x66491,f2(a1))+~P102(f332(x66492,f819(x66491,x66493,x66492)))+P102(f332(f332(f247(a1),f2(a1)),x66491)) % 172.83/172.49 [6653]P102(f332(x66531,x66532))+~P102(f332(f61(x66533),x66532))+P102(f332(x66531,f555(x66531,x66532,x66533)))+~P102(f332(x66531,f195(f883(x66533,a871)))) % 172.83/172.49 [6672]P102(f332(x66721,x66722))+P102(f332(f61(x66723),f555(x66721,x66722,x66723)))+~P102(f332(f61(x66723),x66722))+~P102(f332(x66721,f195(f883(x66723,a871)))) % 172.83/172.49 [6737]P143(x67371,x67372,x67373)+~P102(f332(x67371,x67372))+~P102(f332(x67371,f819(x67373,x67372,x67371)))+P102(f332(f332(f247(a1),f2(a1)),x67373)) % 172.83/172.49 [6767]P144(x67671,x67672,x67673)+~P102(f332(x67671,f818(x67673,x67672,x67671)))+~P102(f332(x67671,f2(a1)))+P102(f332(f332(f247(a1),f2(a1)),x67673)) % 172.83/172.49 [6875]~P89(x68753)+~P113(x68753)+~P102(f332(f332(f247(x68753),f332(f106(x68753),x68751)),f332(f106(x68753),x68752)))+P102(f332(f332(f247(a1),x68751),x68752)) % 172.83/172.49 [6876]~P89(x68763)+~P113(x68763)+~P102(f332(f332(f246(x68763),f332(f106(x68763),x68761)),f332(f106(x68763),x68762)))+P102(f332(f332(f246(a1),x68761),x68762)) % 172.83/172.49 [6905]~P104(x69051)+~P29(x69051,x69053)+P29(x69051,f332(f332(f151(x69051),x69052),x69053))+~P102(f332(f332(f246(x69051),x69052),f746(x69053,x69052,x69051))) % 172.83/172.49 [6906]~P104(x69061)+~P29(x69061,x69063)+P29(x69061,f332(f332(f151(x69061),x69062),x69063))+~P102(f332(f332(f246(x69061),x69062),f749(x69063,x69062,x69061))) % 172.83/172.49 [6907]~P104(x69071)+~P29(x69071,x69073)+P29(x69071,f332(f332(f151(x69071),x69072),x69073))+~P102(f332(f332(f246(x69071),x69072),f780(x69072,x69073,x69071))) % 172.83/172.49 [6991]P144(x69912,x69913,x69911)+E(x69911,f2(a1))+P102(f332(f332(f247(a1),x69911),f2(a1)))+P102(f332(f332(f247(a1),f815(x69911,x69913,x69912)),x69911)) % 172.83/172.49 [6992]P143(x69922,x69923,x69921)+E(x69921,f2(a1))+P102(f332(f332(f247(a1),x69921),f2(a1)))+P102(f332(f332(f247(a1),f820(x69921,x69923,x69922)),x69921)) % 172.83/172.49 [7033]P144(x70332,x70333,x70331)+E(x70331,f2(a1))+P102(f332(f332(f246(a1),f814(x70331,x70333,x70332)),f2(a1)))+P102(f332(f332(f247(a1),f2(a1)),x70331)) % 172.83/172.49 [7034]P143(x70342,x70343,x70341)+E(x70341,f2(a1))+P102(f332(f332(f246(a1),f819(x70341,x70343,x70342)),f2(a1)))+P102(f332(f332(f247(a1),f2(a1)),x70341)) % 172.83/172.49 [7056]~P104(x70561)+~P29(x70561,x70563)+E(f332(f332(f148(x70561,x70561,f5(x70561)),x70562),f171(x70561,x70562,x70563)),x70563)+~P102(f332(f332(f334(x70561),x70562),f332(f173(x70561),x70563))) % 172.83/172.49 [7103]P143(x71031,x71032,x71033)+~P102(f332(x71031,x71032))+P102(f332(f332(f247(a1),x71033),f2(a1)))+P102(f332(f332(f247(a1),f820(x71033,x71032,x71031)),x71033)) % 172.83/172.49 [7109]~P106(x71091)+~P90(x71091)+E(f332(f332(f244(x71091),f332(f106(x71091),x71092)),f332(f106(x71091),x71093)),f332(f106(x71091),x71092))+~P102(f332(f332(f246(x71091),f332(f106(x71091),x71092)),f332(f106(x71091),x71093))) % 172.83/172.49 [7110]~P106(x71101)+~P90(x71101)+E(f332(f332(f245(x71101),f332(f106(x71101),x71102)),f332(f106(x71101),x71103)),f332(f106(x71101),x71103))+~P102(f332(f332(f246(x71101),f332(f106(x71101),x71102)),f332(f106(x71101),x71103))) % 172.83/172.49 [7124]P144(x71241,x71242,x71243)+~P102(f332(x71241,f2(a1)))+P102(f332(f332(f247(a1),x71243),f2(a1)))+P102(f332(f332(f247(a1),f815(x71243,x71242,x71241)),x71243)) % 172.83/172.49 [7132]P143(x71321,x71322,x71323)+~P102(f332(x71321,x71322))+P102(f332(f332(f246(a1),f819(x71323,x71322,x71321)),f2(a1)))+P102(f332(f332(f247(a1),f2(a1)),x71323)) % 172.83/172.49 [7156]P144(x71561,x71562,x71563)+~P102(f332(x71561,f2(a1)))+P102(f332(f332(f246(a1),f814(x71563,x71562,x71561)),f2(a1)))+P102(f332(f332(f247(a1),f2(a1)),x71563)) % 172.83/172.49 [7184]~P102(f332(x71841,x71842))+P102(f332(x71841,f2(a876)))+~P102(f332(f332(f247(a876),x71842),x71843))+P102(f332(f332(f247(a876),f480(x71842,x71841,x71843)),x71843)) % 172.83/172.49 [7201]~P104(x72011)+~P29(x72011,x72013)+P29(x72011,f332(f332(f151(x72011),x72012),x72013))+P102(f332(f332(f334(x72011),f746(x72013,x72012,x72011)),f332(f173(x72011),x72013))) % 172.83/172.49 [7202]~P104(x72021)+~P29(x72021,x72023)+P29(x72021,f332(f332(f151(x72021),x72022),x72023))+P102(f332(f332(f334(x72021),f749(x72023,x72022,x72021)),f332(f173(x72021),x72023))) % 172.83/172.49 [7203]~P104(x72031)+~P29(x72031,x72033)+P29(x72031,f332(f332(f151(x72031),x72032),x72033))+P102(f332(f332(f334(x72031),f780(x72032,x72033,x72031)),f332(f173(x72031),x72033))) % 172.83/172.49 [7307]~P104(x73071)+~P27(x73071)+~P102(f332(f332(f247(x73071),x73073),f39(x73071,x73072)))+P102(f332(f332(f334(x73071),f602(x73072,x73073,x73071)),x73072)) % 172.83/172.49 [7473]~P104(x74731)+~P27(x74731)+~P102(f332(f332(f247(x74731),f40(x74731,x74733)),x74732))+P102(f332(f332(f334(x74731),f634(x74732,x74733,x74731)),x74733)) % 172.83/172.49 [7474]~P104(x74741)+~P27(x74741)+~P102(f332(f332(f247(x74741),f40(x74741,x74743)),x74742))+P102(f332(f332(f247(x74741),f634(x74742,x74743,x74741)),x74742)) % 172.83/172.49 [7489]P144(x74892,x74893,x74891)+E(x74891,f2(a1))+P102(f332(f332(f247(a1),x74891),f814(x74891,x74893,x74892)))+P102(f332(f332(f247(a1),f815(x74891,x74893,x74892)),x74891)) % 172.83/172.49 [7490]P143(x74902,x74903,x74901)+E(x74901,f2(a1))+P102(f332(f332(f247(a1),x74901),f819(x74901,x74903,x74902)))+P102(f332(f332(f247(a1),f820(x74901,x74903,x74902)),x74901)) % 172.83/172.49 [7581]P144(x75813,x75812,x75811)+E(x75811,f2(a1))+E(f332(f332(f79(a1),f332(f332(f80(a1),x75811),f818(x75811,x75812,x75813))),f814(x75811,x75812,x75813)),x75812)+P102(f332(f332(f247(a1),f2(a1)),x75811)) % 172.83/172.49 [7582]P143(x75823,x75822,x75821)+E(x75821,f2(a1))+E(f332(f332(f79(a1),f332(f332(f80(a1),x75821),f822(x75821,x75822,x75823))),f819(x75821,x75822,x75823)),x75822)+P102(f332(f332(f247(a1),f2(a1)),x75821)) % 172.83/172.49 [7584]~P126(x75841)+~P102(f332(f332(f247(x75841),x75843),f2(x75841)))+P102(f332(f332(f247(x75841),f332(f332(f80(x75841),x75842),x75843)),f2(x75841)))+~P102(f332(f332(f247(x75841),f2(x75841)),x75842)) % 172.83/172.49 [7585]~P126(x75851)+~P102(f332(f332(f247(x75851),x75852),f2(x75851)))+P102(f332(f332(f247(x75851),f332(f332(f80(x75851),x75852),x75853)),f2(x75851)))+~P102(f332(f332(f247(x75851),f2(x75851)),x75853)) % 172.83/172.49 [7586]~P59(x75861)+~P102(f332(f332(f247(x75861),x75863),f2(x75861)))+P102(f332(f332(f247(x75861),f332(f332(f290(x75861),x75862),x75863)),f2(x75861)))+~P102(f332(f332(f247(x75861),f2(x75861)),x75862)) % 172.83/172.49 [7587]~P59(x75871)+~P102(f332(f332(f247(x75871),x75872),f2(x75871)))+P102(f332(f332(f247(x75871),f332(f332(f290(x75871),x75872),x75873)),f2(x75871)))+~P102(f332(f332(f247(x75871),f2(x75871)),x75873)) % 172.83/172.49 [7588]~P60(x75881)+~P102(f332(f332(f247(x75881),x75883),f2(x75881)))+P102(f332(f332(f247(x75881),f332(f332(f290(x75881),x75882),x75883)),f2(x75881)))+~P102(f332(f332(f247(x75881),f2(x75881)),x75882)) % 172.83/172.49 [7589]~P60(x75891)+~P102(f332(f332(f247(x75891),x75892),f2(x75891)))+P102(f332(f332(f247(x75891),f332(f332(f290(x75891),x75892),x75893)),f2(x75891)))+~P102(f332(f332(f247(x75891),f2(x75891)),x75893)) % 172.83/172.49 [7592]~P131(x75921)+~P102(f332(f332(f246(x75921),x75923),f2(x75921)))+P102(f332(f332(f246(x75921),f332(f332(f80(x75921),x75922),x75923)),f2(x75921)))+~P102(f332(f332(f246(x75921),f2(x75921)),x75922)) % 172.83/172.49 [7594]~P131(x75941)+~P102(f332(f332(f246(x75941),x75942),f2(x75941)))+P102(f332(f332(f246(x75941),f332(f332(f80(x75941),x75942),x75943)),f2(x75941)))+~P102(f332(f332(f246(x75941),f2(x75941)),x75943)) % 172.83/172.49 [7595]~P120(x75951)+~P102(f332(f332(f246(x75951),x75953),f2(x75951)))+P102(f332(f332(f246(x75951),f332(f332(f80(x75951),x75952),x75953)),f2(x75951)))+~P102(f332(f332(f246(x75951),f2(x75951)),x75952)) % 172.83/172.49 [7596]~P120(x75961)+~P102(f332(f332(f246(x75961),x75962),f2(x75961)))+P102(f332(f332(f246(x75961),f332(f332(f80(x75961),x75962),x75963)),f2(x75961)))+~P102(f332(f332(f246(x75961),f2(x75961)),x75963)) % 172.83/172.49 [7597]~P59(x75971)+~P102(f332(f332(f246(x75971),x75973),f2(x75971)))+P102(f332(f332(f246(x75971),f332(f332(f290(x75971),x75972),x75973)),f2(x75971)))+~P102(f332(f332(f246(x75971),f2(x75971)),x75972)) % 172.83/172.49 [7598]~P59(x75981)+~P102(f332(f332(f246(x75981),x75982),f2(x75981)))+P102(f332(f332(f246(x75981),f332(f332(f290(x75981),x75982),x75983)),f2(x75981)))+~P102(f332(f332(f246(x75981),f2(x75981)),x75983)) % 172.83/172.49 [7599]~P60(x75991)+~P102(f332(f332(f247(x75991),x75993),f2(x75991)))+P102(f332(f332(f246(x75991),f332(f332(f290(x75991),x75992),x75993)),f2(x75991)))+~P102(f332(f332(f246(x75991),f2(x75991)),x75992)) % 172.83/172.49 [7600]~P60(x76001)+~P102(f332(f332(f246(x76001),x76002),f2(x76001)))+P102(f332(f332(f246(x76001),f332(f332(f290(x76001),x76002),x76003)),f2(x76001)))+~P102(f332(f332(f247(x76001),f2(x76001)),x76003)) % 172.83/172.49 [7615]P143(x76151,x76152,x76153)+~P102(f332(x76151,x76152))+P102(f332(f332(f247(a1),x76153),f819(x76153,x76152,x76151)))+P102(f332(f332(f247(a1),f820(x76153,x76152,x76151)),x76153)) % 172.83/172.49 [7628]P144(x76281,x76282,x76283)+P102(f332(f332(f247(a1),x76283),f814(x76283,x76282,x76281)))+~P102(f332(x76281,f2(a1)))+P102(f332(f332(f247(a1),f815(x76283,x76282,x76281)),x76283)) % 172.83/172.49 [7679]P144(x76792,x76793,x76791)+E(x76791,f2(a1))+~P102(f332(x76792,f818(x76791,x76793,x76792)))+P102(f332(f332(f247(a1),f815(x76791,x76793,x76792)),x76791)) % 172.83/172.49 [7680]P143(x76802,x76803,x76801)+E(x76801,f2(a1))+~P102(f332(x76802,f819(x76801,x76803,x76802)))+P102(f332(f332(f247(a1),f820(x76801,x76803,x76802)),x76801)) % 172.83/172.49 [7692]P143(x76923,x76922,x76921)+~P102(f332(x76923,x76922))+E(f332(f332(f79(a1),f332(f332(f80(a1),x76921),f822(x76921,x76922,x76923))),f819(x76921,x76922,x76923)),x76922)+P102(f332(f332(f247(a1),f2(a1)),x76921)) % 172.83/172.49 [7710]P144(x77103,x77102,x77101)+E(f332(f332(f79(a1),f332(f332(f80(a1),x77101),f818(x77101,x77102,x77103))),f814(x77101,x77102,x77103)),x77102)+~P102(f332(x77103,f2(a1)))+P102(f332(f332(f247(a1),f2(a1)),x77101)) % 172.83/172.49 [7736]~P102(f332(x77361,x77363))+~P102(f332(f61(x77362),x77363))+P102(f332(f332(f334(x77362),f658(x77361,x77363,x77362)),f655(x77361,x77363,x77362)))+P102(f332(x77361,f195(f883(x77362,a871)))) % 172.83/172.49 [7747]P143(x77471,x77472,x77473)+~P102(f332(x77471,x77472))+~P102(f332(x77471,f819(x77473,x77472,x77471)))+P102(f332(f332(f247(a1),f820(x77473,x77472,x77471)),x77473)) % 172.83/172.49 [7753]P144(x77531,x77532,x77533)+~P102(f332(x77531,f818(x77533,x77532,x77531)))+~P102(f332(x77531,f2(a1)))+P102(f332(f332(f247(a1),f815(x77533,x77532,x77531)),x77533)) % 172.83/172.49 [7859]~P59(x78591)+~P102(f332(f332(f247(x78591),f332(f332(f290(x78591),x78593),x78592)),f2(x78591)))+P102(f332(f332(f247(x78591),x78592),f2(x78591)))+P102(f332(f332(f247(x78591),f2(x78591)),x78592)) % 172.83/172.49 [7860]~P59(x78601)+~P102(f332(f332(f247(x78601),f332(f332(f290(x78601),x78602),x78603)),f2(x78601)))+P102(f332(f332(f247(x78601),x78602),f2(x78601)))+P102(f332(f332(f247(x78601),f2(x78601)),x78602)) % 172.83/172.49 [7861]~P120(x78611)+~P102(f332(f332(f246(x78611),f332(f332(f80(x78611),x78613),x78612)),f2(x78611)))+P102(f332(f332(f246(x78611),x78612),f2(x78611)))+P102(f332(f332(f246(x78611),f2(x78611)),x78612)) % 172.83/172.49 [7862]~P120(x78621)+~P102(f332(f332(f246(x78621),f332(f332(f80(x78621),x78622),x78623)),f2(x78621)))+P102(f332(f332(f246(x78621),x78622),f2(x78621)))+P102(f332(f332(f246(x78621),f2(x78621)),x78622)) % 172.83/172.49 [7863]~P59(x78631)+~P102(f332(f332(f246(x78631),f332(f332(f290(x78631),x78633),x78632)),f2(x78631)))+P102(f332(f332(f246(x78631),x78632),f2(x78631)))+P102(f332(f332(f246(x78631),f2(x78631)),x78632)) % 172.83/172.49 [7864]~P59(x78641)+~P102(f332(f332(f246(x78641),f332(f332(f290(x78641),x78642),x78643)),f2(x78641)))+P102(f332(f332(f246(x78641),x78642),f2(x78641)))+P102(f332(f332(f246(x78641),f2(x78641)),x78642)) % 172.83/172.49 [7888]~P59(x78881)+~P102(f332(f332(f247(x78881),f332(f332(f290(x78881),x78882),x78883)),f2(x78881)))+P102(f332(f332(f247(x78881),f2(x78881)),x78882))+P102(f332(f332(f247(x78881),f2(x78881)),x78883)) % 172.83/172.49 [7889]~P120(x78891)+~P102(f332(f332(f246(x78891),f332(f332(f80(x78891),x78892),x78893)),f2(x78891)))+P102(f332(f332(f246(x78891),f2(x78891)),x78892))+P102(f332(f332(f246(x78891),f2(x78891)),x78893)) % 172.83/172.49 [7890]~P59(x78901)+~P102(f332(f332(f246(x78901),f332(f332(f290(x78901),x78902),x78903)),f2(x78901)))+P102(f332(f332(f246(x78901),f2(x78901)),x78902))+P102(f332(f332(f246(x78901),f2(x78901)),x78903)) % 172.83/172.49 [7911]P144(x79112,x79113,x79111)+E(x79111,f2(a1))+P102(f332(f332(f246(a1),f814(x79111,x79113,x79112)),f2(a1)))+P102(f332(f332(f247(a1),f815(x79111,x79113,x79112)),x79111)) % 172.83/172.49 [7912]P143(x79122,x79123,x79121)+E(x79121,f2(a1))+P102(f332(f332(f246(a1),f819(x79121,x79123,x79122)),f2(a1)))+P102(f332(f332(f247(a1),f820(x79121,x79123,x79122)),x79121)) % 172.83/172.49 [7919]~P107(x79191)+~P102(f332(f332(f247(x79191),x79192),f77(x79191)))+P102(f332(f332(f247(x79191),f332(f332(f257(x79191),x79192),f332(a115,x79193))),f77(x79191)))+~P102(f332(f332(f247(x79191),f2(x79191)),x79192)) % 172.83/172.49 [7974]~P104(x79741)+~E(x79743,f116(x79741))+~P29(x79741,f332(f169(x79741),x79743))+E(f332(f142(x79741,x79741,f332(f7(x79741,x79741,x79741),f245(x79741)),x79742),f332(f169(x79741),x79743)),x79742) % 172.83/172.49 [7977]P143(x79771,x79772,x79773)+~P102(f332(x79771,x79772))+P102(f332(f332(f246(a1),f819(x79773,x79772,x79771)),f2(a1)))+P102(f332(f332(f247(a1),f820(x79773,x79772,x79771)),x79773)) % 172.83/172.49 [7987]P144(x79871,x79872,x79873)+~P102(f332(x79871,f2(a1)))+P102(f332(f332(f246(a1),f814(x79873,x79872,x79871)),f2(a1)))+P102(f332(f332(f247(a1),f815(x79873,x79872,x79871)),x79873)) % 172.83/172.49 [8213]P144(x82133,x82132,x82131)+E(x82131,f2(a1))+E(f332(f332(f79(a1),f332(f332(f80(a1),x82131),f818(x82131,x82132,x82133))),f814(x82131,x82132,x82133)),x82132)+P102(f332(f332(f247(a1),f815(x82131,x82132,x82133)),x82131)) % 172.83/172.49 [8214]P143(x82143,x82142,x82141)+E(x82141,f2(a1))+E(f332(f332(f79(a1),f332(f332(f80(a1),x82141),f822(x82141,x82142,x82143))),f819(x82141,x82142,x82143)),x82142)+P102(f332(f332(f247(a1),f820(x82141,x82142,x82143)),x82141)) % 172.83/172.49 [8250]P143(x82503,x82502,x82501)+~P102(f332(x82503,x82502))+E(f332(f332(f79(a1),f332(f332(f80(a1),x82501),f822(x82501,x82502,x82503))),f819(x82501,x82502,x82503)),x82502)+P102(f332(f332(f247(a1),f820(x82501,x82502,x82503)),x82501)) % 172.83/172.49 [8251]~P67(x82511)+~P71(x82511)+~P39(x82513)+E(f332(f332(f6(a876,x82511),f332(f332(f8(a1,x82511,a876),x82512),f103(a1))),f332(f311(a1,a876,a107),x82513)),f332(f332(f6(a1,x82511),x82512),x82513)) % 172.83/172.49 [8252]~P67(x82521)+~P71(x82521)+~P39(x82523)+E(f332(f332(f9(a876,x82521),f332(f332(f8(a1,x82521,a876),x82522),f103(a1))),f332(f311(a1,a876,a107),x82523)),f332(f332(f9(a1,x82521),x82522),x82523)) % 172.83/172.49 [8261]P144(x82613,x82612,x82611)+E(f332(f332(f79(a1),f332(f332(f80(a1),x82611),f818(x82611,x82612,x82613))),f814(x82611,x82612,x82613)),x82612)+~P102(f332(x82613,f2(a1)))+P102(f332(f332(f247(a1),f815(x82611,x82612,x82613)),x82611)) % 172.83/172.49 [8280]~E(x82802,f2(a876))+~E(f332(f266(a876,a876),x82803),f2(a876))+~E(x82801,f332(f332(f79(a876),f332(f332(f80(a876),f332(f266(a876,a876),x82803)),x82802)),f332(f270(a876,a876),x82803)))+P102(f332(f47(x82801,x82802),x82803)) % 172.83/172.49 [8334]P102(f332(x83341,x83342))+~P102(f332(f332(f334(x83343),f539(x83341,x83342,x83343)),f555(x83341,x83342,x83343)))+~P102(f332(f61(x83343),x83342))+~P102(f332(x83341,f195(f883(x83343,a871)))) % 172.83/172.49 [8952]P102(f332(x89521,x89522))+~P102(f332(f61(x89523),x89522))+~P102(f332(x89521,f332(f332(f310(x89523),f539(x89521,x89522,x89523)),f555(x89521,x89522,x89523))))+~P102(f332(x89521,f195(f883(x89523,a871)))) % 172.83/172.49 [9185]P102(f332(f332(f246(a1),x91851),f2(a1)))+~P102(f332(f332(f247(a1),f332(f332(f79(a1),f332(f332(f80(a1),x91852),x91851)),x91853)),f2(a1)))+~P102(f332(f332(f247(a1),f2(a1)),x91852))+~P102(f332(f332(f246(a1),f2(a1)),x91853)) % 172.83/172.49 [5799]~P61(x57992)+E(x57991,f195(f883(x57992,a871)))+~P102(f332(f61(x57992),x57991))+E(f13(x57992,f332(f332(f310(x57992),x57993),x57991)),f332(f332(f113(x57992),x57993),f13(x57992,x57991))) % 172.83/172.49 [5800]~P61(x58002)+E(x58001,f195(f883(x58002,a871)))+~P102(f332(f61(x58002),x58001))+E(f10(x58002,f332(f332(f310(x58002),x58003),x58001)),f332(f332(f104(x58002),x58003),f10(x58002,x58001))) % 172.83/172.49 [5801]~P104(x58012)+E(x58011,f195(f883(x58012,a871)))+~P102(f332(f61(x58012),x58011))+E(f14(x58012,f332(f332(f310(x58012),x58013),x58011)),f332(f332(f245(x58012),x58013),f14(x58012,x58011))) % 172.83/172.49 [5802]~P104(x58022)+E(x58021,f195(f883(x58022,a871)))+~P102(f332(f61(x58022),x58021))+E(f15(x58022,f332(f332(f310(x58022),x58023),x58021)),f332(f332(f244(x58022),x58023),f15(x58022,x58021))) % 172.83/172.49 [6109]~P120(x61091)+~E(x61093,f2(x61091))+~E(x61092,f2(x61091))+E(f332(f332(f79(x61091),f332(f332(f80(x61091),x61092),x61092)),f332(f332(f80(x61091),x61093),x61093)),f2(x61091)) % 172.83/172.49 [6174]~P93(x61742)+E(x61741,f195(f883(x61742,a871)))+~P102(f332(f61(x61742),x61741))+E(f332(f63(x61742,f80(x61742)),f332(f332(f310(x61742),x61743),x61741)),f332(f332(f80(x61742),x61743),f332(f63(x61742,f80(x61742)),x61741))) % 172.83/172.49 [6299]~P104(x62992)+E(x62991,f195(f883(x62992,a871)))+~P102(f332(f61(x62992),x62991))+E(f11(x62992,f245(x62992),f332(f332(f310(x62992),x62993),x62991)),f332(f332(f245(x62992),x62993),f11(x62992,f245(x62992),x62991))) % 172.83/172.49 [6300]~P104(x63002)+E(x63001,f195(f883(x63002,a871)))+~P102(f332(f61(x63002),x63001))+E(f12(x63002,f244(x63002),f332(f332(f310(x63002),x63003),x63001)),f332(f332(f244(x63002),x63003),f12(x63002,f244(x63002),x63001))) % 172.83/172.49 [6802]~P64(x68021)+~P102(f332(f61(x68021),x68023))+E(f332(f63(x68021,f80(x68021)),f332(f332(f310(x68021),x68022),x68023)),f332(f332(f64(x68021,x68021,f80(x68021)),x68022),x68023))+P102(f332(f332(f334(x68021),x68022),x68023)) % 172.83/172.49 [6883]~E(f332(f332(f79(a1),x68832),f332(f332(f80(a1),x68833),x68831)),x68833)+~P102(f332(f332(f247(a1),f2(a1)),x68833))+P102(f332(f332(f246(a1),f77(a1)),x68831))+~P102(f332(f332(f247(a1),x68832),x68833)) % 172.83/172.49 [6912]~E(f332(f332(f79(a1),x69122),f332(f332(f80(a1),x69123),x69121)),x69123)+P102(f332(f332(f246(a1),x69121),f77(a1)))+~P102(f332(f332(f247(a1),f2(a1)),x69123))+~P102(f332(f332(f246(a1),f2(a1)),x69122)) % 172.83/172.49 [6928]E(x69281,f2(a876))+~P102(f332(f47(x69283,x69281),x69282))+~P102(f332(f332(f247(a876),f2(a876)),x69281))+P102(f332(f332(f247(a876),f332(f270(a876,a876),x69282)),x69281)) % 172.83/172.49 [6958]~P134(x69581)+~P102(f332(f332(f246(x69581),x69582),f2(x69581)))+~P102(f332(f332(f246(x69581),x69583),f2(x69581)))+E(f332(f332(f80(x69581),f332(f74(x69581),x69582)),f332(f74(x69581),x69583)),f332(f74(x69581),f332(f332(f80(x69581),x69582),x69583))) % 172.83/172.49 [7010]~P134(x70101)+~P102(f332(f332(f246(x70101),x70102),f2(x70101)))+E(f332(f332(f80(x70101),f332(f74(x70101),x70102)),f332(f74(x70101),x70103)),f332(f74(x70101),f332(f332(f80(x70101),x70102),x70103)))+~P102(f332(f332(f246(x70101),f2(x70101)),x70103)) % 172.83/172.49 [7011]~P134(x70111)+~P102(f332(f332(f246(x70111),x70113),f2(x70111)))+E(f332(f332(f80(x70111),f332(f74(x70111),x70112)),f332(f74(x70111),x70113)),f332(f74(x70111),f332(f332(f80(x70111),x70112),x70113)))+~P102(f332(f332(f246(x70111),f2(x70111)),x70112)) % 172.83/172.49 [7065]~P134(x70651)+E(f332(f332(f80(x70651),f332(f74(x70651),x70652)),f332(f74(x70651),x70653)),f332(f74(x70651),f332(f332(f80(x70651),x70652),x70653)))+~P102(f332(f332(f246(x70651),f2(x70651)),x70652))+~P102(f332(f332(f246(x70651),f2(x70651)),x70653)) % 172.83/172.49 [7081]~P120(x70811)+~P102(f332(f332(f247(x70811),x70813),f2(x70811)))+~P102(f332(f332(f247(x70811),x70812),f2(x70811)))+P102(f332(f332(f247(x70811),f2(x70811)),f332(f332(f80(x70811),x70812),x70813))) % 172.83/172.49 [7082]~P59(x70821)+~P102(f332(f332(f247(x70821),x70823),f2(x70821)))+~P102(f332(f332(f247(x70821),x70822),f2(x70821)))+P102(f332(f332(f247(x70821),f2(x70821)),f332(f332(f290(x70821),x70822),x70823))) % 172.83/172.49 [7083]~P60(x70831)+~P102(f332(f332(f247(x70831),x70833),f2(x70831)))+~P102(f332(f332(f247(x70831),x70832),f2(x70831)))+P102(f332(f332(f247(x70831),f2(x70831)),f332(f332(f290(x70831),x70832),x70833))) % 172.83/172.49 [7085]~P124(x70851)+~P102(f332(f332(f246(x70851),x70853),f2(x70851)))+~P102(f332(f332(f246(x70851),x70852),f2(x70851)))+P102(f332(f332(f246(x70851),f2(x70851)),f332(f332(f80(x70851),x70852),x70853))) % 172.83/172.49 [7086]~P120(x70861)+~P102(f332(f332(f246(x70861),x70863),f2(x70861)))+~P102(f332(f332(f246(x70861),x70862),f2(x70861)))+P102(f332(f332(f246(x70861),f2(x70861)),f332(f332(f80(x70861),x70862),x70863))) % 172.83/172.49 [7087]~P59(x70871)+~P102(f332(f332(f246(x70871),x70873),f2(x70871)))+~P102(f332(f332(f246(x70871),x70872),f2(x70871)))+P102(f332(f332(f246(x70871),f2(x70871)),f332(f332(f290(x70871),x70872),x70873))) % 172.83/172.49 [7088]~P60(x70881)+~P102(f332(f332(f247(x70881),x70883),f2(x70881)))+~P102(f332(f332(f246(x70881),x70882),f2(x70881)))+P102(f332(f332(f246(x70881),f2(x70881)),f332(f332(f290(x70881),x70882),x70883))) % 172.83/172.49 [7089]~P107(x70891)+~P102(f332(f332(f247(a876),f2(a876)),x70893))+~P102(f332(f332(f247(x70891),f77(x70891)),x70892))+P102(f332(f332(f247(x70891),f77(x70891)),f332(f332(f257(x70891),x70892),x70893))) % 172.83/172.49 [7185]~P107(x71851)+~P102(f332(f332(f247(x71851),f77(x71851)),x71853))+~P102(f332(f332(f247(x71851),f77(x71851)),x71852))+P102(f332(f332(f247(x71851),f77(x71851)),f332(f332(f80(x71851),x71852),x71853))) % 172.83/172.49 [7186]~P126(x71861)+~P102(f332(f332(f247(x71861),f2(x71861)),x71863))+~P102(f332(f332(f247(x71861),f2(x71861)),x71862))+P102(f332(f332(f247(x71861),f2(x71861)),f332(f332(f80(x71861),x71862),x71863))) % 172.83/172.49 [7187]~P84(x71871)+~P102(f332(f332(f247(x71871),f2(x71871)),x71873))+~P102(f332(f332(f247(x71871),f2(x71871)),x71872))+P102(f332(f332(f247(x71871),f2(x71871)),f332(f332(f79(x71871),x71872),x71873))) % 172.83/172.49 [7190]~P59(x71901)+~P102(f332(f332(f247(x71901),f2(x71901)),x71903))+~P102(f332(f332(f247(x71901),f2(x71901)),x71902))+P102(f332(f332(f247(x71901),f2(x71901)),f332(f332(f290(x71901),x71902),x71903))) % 172.83/172.49 [7191]~P60(x71911)+~P102(f332(f332(f247(x71911),f2(x71911)),x71913))+~P102(f332(f332(f247(x71911),f2(x71911)),x71912))+P102(f332(f332(f247(x71911),f2(x71911)),f332(f332(f290(x71911),x71912),x71913))) % 172.83/172.49 [7192]~P124(x71921)+~P102(f332(f332(f246(x71921),f2(x71921)),x71923))+~P102(f332(f332(f246(x71921),f2(x71921)),x71922))+P102(f332(f332(f246(x71921),f2(x71921)),f332(f332(f80(x71921),x71922),x71923))) % 172.83/172.49 [7193]~P131(x71931)+~P102(f332(f332(f246(x71931),f2(x71931)),x71933))+~P102(f332(f332(f246(x71931),f2(x71931)),x71932))+P102(f332(f332(f246(x71931),f2(x71931)),f332(f332(f80(x71931),x71932),x71933))) % 172.83/172.49 [7194]~P120(x71941)+~P102(f332(f332(f246(x71941),f2(x71941)),x71943))+~P102(f332(f332(f246(x71941),f2(x71941)),x71942))+P102(f332(f332(f246(x71941),f2(x71941)),f332(f332(f80(x71941),x71942),x71943))) % 172.83/172.49 [7196]~P59(x71961)+~P102(f332(f332(f246(x71961),f2(x71961)),x71963))+~P102(f332(f332(f246(x71961),f2(x71961)),x71962))+P102(f332(f332(f246(x71961),f2(x71961)),f332(f332(f290(x71961),x71962),x71963))) % 172.83/172.49 [7197]~P60(x71971)+~P102(f332(f332(f247(x71971),f2(x71971)),x71973))+~P102(f332(f332(f246(x71971),f2(x71971)),x71972))+P102(f332(f332(f246(x71971),f2(x71971)),f332(f332(f290(x71971),x71972),x71973))) % 172.83/172.49 [7268]~P61(x72681)+~P102(f332(f61(x72681),x72683))+E(f13(x72681,f332(f332(f310(x72681),x72682),x72683)),x72682)+~E(f332(f332(f22(f883(x72681,a871)),x72683),f332(f332(f310(x72681),x72682),f195(f883(x72681,a871)))),f195(f883(x72681,a871))) % 172.83/172.49 [7269]~P61(x72691)+~P102(f332(f61(x72691),x72693))+E(f10(x72691,f332(f332(f310(x72691),x72692),x72693)),x72692)+~E(f332(f332(f22(f883(x72691,a871)),x72693),f332(f332(f310(x72691),x72692),f195(f883(x72691,a871)))),f195(f883(x72691,a871))) % 172.83/172.49 [7270]~P104(x72701)+~P102(f332(f61(x72701),x72703))+E(f14(x72701,f332(f332(f310(x72701),x72702),x72703)),x72702)+~E(f332(f332(f22(f883(x72701,a871)),x72703),f332(f332(f310(x72701),x72702),f195(f883(x72701,a871)))),f195(f883(x72701,a871))) % 172.83/172.49 [7271]~P104(x72711)+~P102(f332(f61(x72711),x72713))+E(f15(x72711,f332(f332(f310(x72711),x72712),x72713)),x72712)+~E(f332(f332(f22(f883(x72711,a871)),x72713),f332(f332(f310(x72711),x72712),f195(f883(x72711,a871)))),f195(f883(x72711,a871))) % 172.83/172.49 [7272]~P59(x72721)+P102(f332(f332(f247(x72721),x72722),f2(x72721)))+P102(f332(f332(f247(x72721),f2(x72721)),x72723))+~P102(f332(f332(f247(x72721),f2(x72721)),f332(f332(f290(x72721),x72723),x72722))) % 172.83/172.49 [7273]~P59(x72731)+P102(f332(f332(f247(x72731),x72732),f2(x72731)))+P102(f332(f332(f247(x72731),f2(x72731)),x72733))+~P102(f332(f332(f247(x72731),f2(x72731)),f332(f332(f290(x72731),x72732),x72733))) % 172.83/172.49 [7274]~P59(x72741)+P102(f332(f332(f247(x72741),x72742),f2(x72741)))+P102(f332(f332(f247(x72741),f2(x72741)),x72742))+~P102(f332(f332(f247(x72741),f2(x72741)),f332(f332(f290(x72741),x72743),x72742))) % 172.83/172.49 [7275]~P59(x72751)+P102(f332(f332(f247(x72751),x72752),f2(x72751)))+P102(f332(f332(f247(x72751),f2(x72751)),x72752))+~P102(f332(f332(f247(x72751),f2(x72751)),f332(f332(f290(x72751),x72752),x72753))) % 172.83/172.49 [7276]~P120(x72761)+P102(f332(f332(f246(x72761),x72762),f2(x72761)))+P102(f332(f332(f246(x72761),f2(x72761)),x72763))+~P102(f332(f332(f246(x72761),f2(x72761)),f332(f332(f80(x72761),x72763),x72762))) % 172.83/172.49 [7277]~P120(x72771)+P102(f332(f332(f246(x72771),x72772),f2(x72771)))+P102(f332(f332(f246(x72771),f2(x72771)),x72773))+~P102(f332(f332(f246(x72771),f2(x72771)),f332(f332(f80(x72771),x72772),x72773))) % 172.83/172.49 [7278]~P59(x72781)+P102(f332(f332(f246(x72781),x72782),f2(x72781)))+P102(f332(f332(f246(x72781),f2(x72781)),x72783))+~P102(f332(f332(f246(x72781),f2(x72781)),f332(f332(f290(x72781),x72783),x72782))) % 172.83/172.49 [7279]~P59(x72791)+P102(f332(f332(f246(x72791),x72792),f2(x72791)))+P102(f332(f332(f246(x72791),f2(x72791)),x72793))+~P102(f332(f332(f246(x72791),f2(x72791)),f332(f332(f290(x72791),x72792),x72793))) % 172.83/172.49 [7280]~P120(x72801)+P102(f332(f332(f246(x72801),x72802),f2(x72801)))+P102(f332(f332(f246(x72801),f2(x72801)),x72802))+~P102(f332(f332(f246(x72801),f2(x72801)),f332(f332(f80(x72801),x72803),x72802))) % 172.83/172.49 [7281]~P120(x72811)+P102(f332(f332(f246(x72811),x72812),f2(x72811)))+P102(f332(f332(f246(x72811),f2(x72811)),x72812))+~P102(f332(f332(f246(x72811),f2(x72811)),f332(f332(f80(x72811),x72812),x72813))) % 172.83/172.49 [7282]~P59(x72821)+P102(f332(f332(f246(x72821),x72822),f2(x72821)))+P102(f332(f332(f246(x72821),f2(x72821)),x72822))+~P102(f332(f332(f246(x72821),f2(x72821)),f332(f332(f290(x72821),x72823),x72822))) % 172.83/172.49 [7283]~P59(x72831)+P102(f332(f332(f246(x72831),x72832),f2(x72831)))+P102(f332(f332(f246(x72831),f2(x72831)),x72832))+~P102(f332(f332(f246(x72831),f2(x72831)),f332(f332(f290(x72831),x72832),x72833))) % 172.83/172.49 [7373]~E(f332(f332(f104(f883(x73731,a871)),f332(f173(x73731),x73732)),f332(f173(x73731),x73733)),f195(f883(x73731,a871)))+~P102(f332(f137(x73731),x73733))+~P102(f332(f137(x73731),x73732))+P102(f332(f137(x73731),f332(f332(f134(x73731),x73732),x73733))) % 172.83/172.49 [7374]~P104(x73741)+~P102(f332(f61(x73741),x73743))+E(f11(x73741,f245(x73741),f332(f332(f310(x73741),x73742),x73743)),x73742)+~E(f332(f332(f22(f883(x73741,a871)),x73743),f332(f332(f310(x73741),x73742),f195(f883(x73741,a871)))),f195(f883(x73741,a871))) % 172.83/172.49 [7375]~P104(x73751)+~P102(f332(f61(x73751),x73753))+E(f12(x73751,f244(x73751),f332(f332(f310(x73751),x73752),x73753)),x73752)+~E(f332(f332(f22(f883(x73751,a871)),x73753),f332(f332(f310(x73751),x73752),f195(f883(x73751,a871)))),f195(f883(x73751,a871))) % 172.83/172.49 [7390]~P113(x73901)+~P102(f332(f332(f247(x73901),x73902),x73903))+~P102(f332(f332(f247(x73901),f332(f78(x73901),x73902)),x73903))+P102(f332(f332(f247(x73901),f332(f74(x73901),x73902)),x73903)) % 172.83/172.49 [7392]~P81(x73921)+~P102(f332(f332(f246(x73921),x73922),x73923))+~P102(f332(f332(f246(x73921),f332(f78(x73921),x73922)),x73923))+P102(f332(f332(f246(x73921),f332(f74(x73921),x73922)),x73923)) % 172.83/172.49 [7463]~P126(x74631)+P102(f332(f332(f247(x74631),f2(x74631)),x74632))+~P102(f332(f332(f247(x74631),f2(x74631)),x74633))+~P102(f332(f332(f247(x74631),f2(x74631)),f332(f332(f80(x74631),x74633),x74632))) % 172.83/172.49 [7464]~P126(x74641)+P102(f332(f332(f247(x74641),f2(x74641)),x74642))+~P102(f332(f332(f247(x74641),f2(x74641)),x74643))+~P102(f332(f332(f247(x74641),f2(x74641)),f332(f332(f80(x74641),x74642),x74643))) % 172.83/172.49 [7771]E(x77711,x77712)+~P102(f332(f61(x77713),x77711))+~P102(f332(f332(f246(a876),f332(f37(x77713),x77711)),f332(f37(x77713),x77712)))+~P102(f332(f332(f246(f883(x77713,a871)),x77712),x77711)) % 172.83/172.49 [7915]~P102(f332(f332(f247(a1),x79151),f2(a1)))+~P102(f332(f332(f247(a1),f2(a1)),x79152))+~P102(f332(f332(f246(a1),x79152),x79153))+P102(f332(f332(f246(a1),f332(f332(f38(a1),x79151),x79152)),f332(f332(f38(a1),x79151),x79153))) % 172.83/172.49 [7927]~P102(f332(f332(f247(a1),f2(a1)),x79273))+~P102(f332(f332(f246(a1),f2(a1)),x79271))+~P102(f332(f332(f246(a1),x79273),x79272))+P102(f332(f332(f246(a1),f332(f332(f38(a1),x79271),x79272)),f332(f332(f38(a1),x79271),x79273))) % 172.83/172.49 [8068]E(f332(x80681,f419(x80682,x80681,x80683)),x80682)+~P102(f332(f332(f246(a1),x80682),f332(x80681,x80683)))+P102(f332(f332(f247(a876),f420(x80682,x80681,x80683)),x80683))+~P102(f332(f332(f246(a1),f332(x80681,f2(a876))),x80682)) % 172.83/172.49 [8069]E(f332(x80691,f425(x80692,x80691,x80693)),x80692)+~P102(f332(f332(f246(a1),x80692),f332(x80691,x80693)))+P102(f332(f332(f247(a876),f426(x80692,x80691,x80693)),x80693))+~P102(f332(f332(f246(a1),f332(x80691,f2(a876))),x80692)) % 172.83/172.49 [8173]~P102(f332(f61(x81731),x81733))+~P102(f332(f332(f247(a876),f332(f37(x81731),x81732)),f332(f37(x81731),x81733)))+~P102(f332(f332(f246(f883(x81731,a871)),x81732),x81733))+P102(f332(f332(f247(f883(x81731,a871)),x81732),x81733)) % 172.83/172.49 [8202]E(f332(f332(f79(a1),f387(x82023,x82021,x82022)),f388(x82023,x82021,x82022)),x82021)+E(f332(f332(f22(a1),x82021),x82022),x82021)+~P102(f332(f332(f247(a1),f2(a1)),x82022))+~P102(f332(f332(f334(a1),f332(f332(f22(a1),x82021),f77(a1))),x82023)) % 172.83/172.49 [8203]E(f332(f332(f22(a1),f400(x82033,x82031,x82032)),f401(x82033,x82031,x82032)),x82031)+E(f332(f332(f79(a1),x82031),x82032),x82031)+~P102(f332(f332(f247(a1),f2(a1)),x82032))+~P102(f332(f332(f334(a1),f332(f332(f79(a1),x82031),f77(a1))),x82033)) % 172.83/172.49 [8256]~P102(f332(f332(f246(a876),x82563),x82561))+P102(f332(f332(f247(a876),x82561),x82562))+~P102(f332(f332(f246(a876),x82563),x82562))+~P102(f332(f332(f247(a876),f332(f332(f22(a876),x82561),x82563)),f332(f332(f22(a876),x82562),x82563))) % 172.83/172.49 [8257]~P102(f332(f332(f246(a876),x82573),x82571))+P102(f332(f332(f246(a876),x82571),x82572))+~P102(f332(f332(f246(a876),x82573),x82572))+~P102(f332(f332(f246(a876),f332(f332(f22(a876),x82571),x82573)),f332(f332(f22(a876),x82572),x82573))) % 172.83/172.49 [8273]~P104(x82732)+E(x82731,f116(x82732))+~P29(x82732,f332(f169(x82732),x82731))+E(f332(f142(x82732,x82732,f332(f7(x82732,x82732,x82732),f245(x82732)),x82733),f332(f169(x82732),x82731)),f332(f332(f245(x82732),f332(f332(f165(x82732),x82731),f2(a876))),x82733)) % 172.83/172.49 [8339]E(f332(f332(f22(a1),x83391),x83392),x83391)+~P102(f332(f332(f247(a1),f2(a1)),x83392))+P102(f332(f332(f334(a1),f387(x83393,x83391,x83392)),x83393))+~P102(f332(f332(f334(a1),f332(f332(f22(a1),x83391),f77(a1))),x83393)) % 172.83/172.49 [8340]E(f332(f332(f79(a1),x83401),x83402),x83401)+~P102(f332(f332(f247(a1),f2(a1)),x83402))+P102(f332(f332(f334(a1),f400(x83403,x83401,x83402)),x83403))+~P102(f332(f332(f334(a1),f332(f332(f79(a1),x83401),f77(a1))),x83403)) % 172.83/172.49 [8416]~P102(f332(f332(f246(a1),x84161),f332(x84162,x84163)))+P102(f332(f332(f246(a876),f419(x84161,x84162,x84163)),x84163))+P102(f332(f332(f247(a876),f420(x84161,x84162,x84163)),x84163))+~P102(f332(f332(f246(a1),f332(x84162,f2(a876))),x84161)) % 172.83/172.49 [8417]~P102(f332(f332(f246(a1),x84171),f332(x84172,x84173)))+P102(f332(f332(f246(a876),f425(x84171,x84172,x84173)),x84173))+P102(f332(f332(f247(a876),f426(x84171,x84172,x84173)),x84173))+~P102(f332(f332(f246(a1),f332(x84172,f2(a876))),x84171)) % 172.83/172.49 [8495]E(f332(f332(f22(a1),x84951),x84952),x84951)+~P102(f332(f332(f247(a1),f2(a1)),x84952))+P102(f332(f332(f334(a1),f388(x84953,x84951,x84952)),f303(a1,f77(a1),x84952)))+~P102(f332(f332(f334(a1),f332(f332(f22(a1),x84951),f77(a1))),x84953)) % 172.83/172.49 [8496]E(f332(f332(f79(a1),x84961),x84962),x84961)+~P102(f332(f332(f247(a1),f2(a1)),x84962))+P102(f332(f332(f334(a1),f401(x84963,x84961,x84962)),f303(a1,f77(a1),x84962)))+~P102(f332(f332(f334(a1),f332(f332(f79(a1),x84961),f77(a1))),x84963)) % 172.83/172.49 [8624]~P107(x86241)+~P102(f332(f332(f247(x86241),x86242),f77(x86241)))+~P102(f332(f332(f247(x86241),f2(x86241)),x86242))+P102(f332(f332(f247(x86241),f332(f332(f80(x86241),x86242),f332(f332(f257(x86241),x86242),x86243))),f332(f332(f257(x86241),x86242),x86243))) % 172.83/172.49 [8707]~P102(f332(x87071,x87072))+P102(f332(x87071,f2(a876)))+~P102(f332(f332(f247(a876),x87072),x87073))+~P102(f332(x87071,f44(a876,f332(a115,f480(x87072,x87071,x87073)),x87073))) % 172.83/172.49 [8846]E(f499(x88461,x88462,x88463),f2(a876))+P102(f332(f332(x88461,x88463),x88462))+P102(f332(f332(x88461,f499(x88461,x88462,x88463)),f44(a876,f498(x88461,x88462,x88463),f499(x88461,x88462,x88463))))+~P102(f332(f320(f882(a876,a876),a230),f332(f332(f267(a876,a876),x88463),x88462))) % 172.83/172.49 [8884]~P20(x88841,x88841,x88842,x88843)+E(f332(f311(x88841,x88841,x88842),x88843),x88843)+~P102(f332(f61(x88841),x88843))+~P102(f332(f332(f246(f883(x88841,a871)),f332(f311(x88841,x88841,x88842),x88843)),x88843)) % 172.83/172.49 [9126]P102(f332(f332(x91261,x91262),x91263))+~P102(f332(f332(f247(a1),f495(x91261,x91263,x91262)),f2(a1)))+P102(f332(f332(x91261,f332(f78(a1),f494(x91261,x91263,x91262))),f332(f78(a1),f495(x91261,x91263,x91262))))+~P102(f332(f320(f882(a1,a1),a235),f332(f332(f267(a1,a1),x91262),x91263))) % 172.83/172.49 [9313]P102(f332(f332(x93131,x93132),x93133))+P102(f332(f332(x93131,f332(f332(f79(a1),f694(x93131,x93133,x93132)),f77(a1))),f696(x93131,x93133,x93132)))+~P102(f332(f332(f246(a1),f694(x93131,x93133,x93132)),f696(x93131,x93133,x93132)))+~P102(f332(f320(f882(a1,a1),a184),f332(f332(f267(a1,a1),x93132),x93133))) % 172.83/172.49 [9737]~P56(x97372)+~P56(x97371)+~P102(f332(f57(f882(x97371,x97372)),x97373))+P102(f332(f57(x97371),f332(f332(f8(f883(x97372,a871),a871,x97371),f57(x97372)),f332(f332(f8(f883(x97372,f882(x97371,x97372)),f883(x97372,a871),x97371),f332(f8(f882(x97371,x97372),a871,x97372),x97373)),f267(x97371,x97372))))) % 172.83/172.49 [9738]~P56(x97382)+~P56(x97381)+~P102(f332(f58(f882(x97381,x97382)),x97383))+P102(f332(f58(x97381),f332(f332(f8(f883(x97382,a871),a871,x97381),f58(x97382)),f332(f332(f8(f883(x97382,f882(x97381,x97382)),f883(x97382,a871),x97381),f332(f8(f882(x97381,x97382),a871,x97382),x97383)),f267(x97381,x97382))))) % 172.83/172.49 [9840]~P56(x98402)+~P56(x98401)+P102(f332(f57(f882(x98401,x98402)),x98403))+~P102(f332(f57(x98401),f332(f332(f8(f883(x98402,a871),a871,x98401),f57(x98402)),f332(f332(f8(f883(x98402,f882(x98401,x98402)),f883(x98402,a871),x98401),f332(f8(f882(x98401,x98402),a871,x98402),x98403)),f267(x98401,x98402))))) % 172.83/172.49 [9841]~P56(x98412)+~P56(x98411)+P102(f332(f58(f882(x98411,x98412)),x98413))+~P102(f332(f58(x98411),f332(f332(f8(f883(x98412,a871),a871,x98411),f58(x98412)),f332(f332(f8(f883(x98412,f882(x98411,x98412)),f883(x98412,a871),x98411),f332(f8(f882(x98411,x98412),a871,x98412),x98413)),f267(x98411,x98412))))) % 172.83/172.49 [10010]E(f332(x100101,f419(x100102,x100101,x100103)),x100102)+~P102(f332(f332(f246(a1),x100102),f332(x100101,x100103)))+~P102(f332(f332(f246(a1),f332(f74(a1),f332(f332(f22(a1),f332(x100101,f332(f332(f79(a876),f420(x100102,x100101,x100103)),f77(a876)))),f332(x100101,f420(x100102,x100101,x100103))))),f77(a1)))+~P102(f332(f332(f246(a1),f332(x100101,f2(a876))),x100102)) % 172.83/172.49 [10011]E(f332(x100111,f425(x100112,x100111,x100113)),x100112)+~P102(f332(f332(f246(a1),x100112),f332(x100111,x100113)))+~P102(f332(f332(f246(a1),f332(f74(a1),f332(f332(f22(a1),f332(x100111,f332(f332(f79(a876),f426(x100112,x100111,x100113)),f77(a876)))),f332(x100111,f426(x100112,x100111,x100113))))),f77(a1)))+~P102(f332(f332(f246(a1),f332(x100111,f2(a876))),x100112)) % 172.83/172.49 [10015]~P102(f332(f332(f246(a1),x100151),f332(x100152,x100153)))+~P102(f332(f332(f246(a1),f332(f74(a1),f332(f332(f22(a1),f332(x100152,f332(f332(f79(a876),f420(x100151,x100152,x100153)),f77(a876)))),f332(x100152,f420(x100151,x100152,x100153))))),f77(a1)))+P102(f332(f332(f246(a876),f419(x100151,x100152,x100153)),x100153))+~P102(f332(f332(f246(a1),f332(x100152,f2(a876))),x100151)) % 172.83/172.49 [10016]~P102(f332(f332(f246(a1),x100161),f332(x100162,x100163)))+~P102(f332(f332(f246(a1),f332(f74(a1),f332(f332(f22(a1),f332(x100162,f332(f332(f79(a876),f426(x100161,x100162,x100163)),f77(a876)))),f332(x100162,f426(x100161,x100162,x100163))))),f77(a1)))+P102(f332(f332(f246(a876),f425(x100161,x100162,x100163)),x100163))+~P102(f332(f332(f246(a1),f332(x100162,f2(a876))),x100161)) % 172.83/172.49 [10072]E(x100721,x100722)+~E(f332(f142(f877(x100723),f877(x100723),f134(x100723),f116(x100723)),x100721),f332(f142(f877(x100723),f877(x100723),f134(x100723),f116(x100723)),x100722))+~E(f332(f196(f877(f877(x100723))),x100721),f332(f196(f877(f877(x100723))),x100722))+~P102(f332(f332(f271(f877(x100723),f877(x100723),a871),f332(f332(f7(f877(x100723),f883(f877(x100723),a876),f883(f877(x100723),a871)),f332(f332(f8(f883(a876,a871),f883(f883(f877(x100723),a876),f883(f877(x100723),a871)),f877(x100723)),f8(a876,a871,f877(x100723))),f332(f332(f8(a876,f883(a876,a871),f877(x100723)),a329),f196(f877(x100723))))),f196(f877(x100723)))),f741(x100722,x100721,x100723))) % 172.83/172.49 [10073]E(x100731,x100732)+~E(f332(f142(f877(x100733),f877(x100733),f134(x100733),f116(x100733)),x100731),f332(f142(f877(x100733),f877(x100733),f134(x100733),f116(x100733)),x100732))+~E(f332(f196(f877(f877(x100733))),x100731),f332(f196(f877(f877(x100733))),x100732))+~P102(f332(f332(f271(f877(x100733),f877(x100733),a871),f332(f332(f7(f877(x100733),f883(f877(x100733),a876),f883(f877(x100733),a871)),f332(f332(f8(f883(a876,a871),f883(f883(f877(x100733),a876),f883(f877(x100733),a871)),f877(x100733)),f8(a876,a871,f877(x100733))),f332(f332(f8(a876,f883(a876,a871),f877(x100733)),a329),f196(f877(x100733))))),f196(f877(x100733)))),f742(x100731,x100732,x100733))) % 172.83/172.49 [6789]~E(f77(a876),f2(a876))+~P102(f332(f61(x67891),x67893))+~P102(f332(f61(x67891),x67892))+E(f332(f332(f79(a876),f332(f37(x67891),x67892)),f332(f37(x67891),x67893)),f332(f37(x67891),f332(f332(f113(f883(x67891,a871)),x67892),x67893))) % 172.83/172.49 [7204]~P98(x72041)+~P102(f332(f61(x72041),x72042))+~P102(f332(f332(f334(x72041),x72043),x72042))+P102(f332(f332(f246(x72041),f332(f63(x72041,f104(x72041)),x72042)),x72043)) % 172.83/172.49 [7205]~P104(x72051)+~P102(f332(f61(x72051),x72052))+~P102(f332(f332(f334(x72051),x72053),x72052))+P102(f332(f332(f246(x72051),f332(f63(x72051,f244(x72051)),x72052)),x72053)) % 172.83/172.49 [7457]~P102(f332(f61(x74571),x74573))+~P102(f332(f61(x74571),x74572))+~E(f332(f332(f104(f883(x74571,a871)),x74572),x74573),f195(f883(x74571,a871)))+E(f332(f332(f79(a876),f332(f37(x74571),x74572)),f332(f37(x74571),x74573)),f332(f37(x74571),f332(f332(f113(f883(x74571,a871)),x74572),x74573))) % 172.83/172.49 [8262]~P38(x82621,x82623)+~P38(x82621,x82622)+~E(f332(f332(f104(f883(x82621,a871)),f332(f265(x82621,x82621),x82622)),f332(f263(x82621,x82621),x82623)),f195(f883(x82621,a871)))+P38(x82621,f332(f332(f113(f883(f882(x82621,x82621),a871)),x82622),x82623)) % 172.83/172.49 [8354]E(x83541,f332(f332(f38(a876),x83542),x83543))+~P102(f332(f332(f247(a876),f2(a876)),x83543))+~P102(f332(f332(f247(a876),x83542),f332(f332(f80(a876),x83543),f332(a115,x83541))))+~P102(f332(f332(f246(a876),f332(f332(f80(a876),x83543),x83541)),x83542)) % 172.83/172.49 [8493]~P102(f332(f61(x84931),x84932))+~P102(f332(f61(x84931),x84933))+E(f332(f332(f79(a876),f332(f37(x84931),x84932)),f332(f37(x84931),x84933)),f332(f37(x84931),f332(f332(f113(f883(x84931,a871)),x84932),x84933)))+P102(f332(f332(f334(x84931),f859(x84933,x84932,x84931)),f332(f332(f104(f883(x84931,a871)),x84932),x84933))) % 172.83/172.49 [8858]~P120(x88582)+~E(x88581,f2(x88582))+~E(x88583,f2(x88582))+~P102(f332(f332(f247(x88582),f2(x88582)),f332(f332(f79(x88582),f332(f332(f80(x88582),x88583),x88583)),f332(f332(f80(x88582),x88581),x88581)))) % 172.83/172.49 [9393]~P38(x93931,x93933)+~P38(x93931,x93932)+P38(x93931,f332(f332(f113(f883(f882(x93931,x93931),a871)),x93932),x93933))+~P102(f332(f332(f246(f883(f882(x93931,x93931),a871)),f332(f332(f289(x93931,x93931,x93931),x93932),x93933)),x93932)) % 172.83/172.49 [9518]~P102(f332(x95181,x95183))+~P102(f332(f61(x95182),x95183))+P102(f332(x95181,f195(f883(x95182,a871))))+~P102(f332(x95181,f332(f332(f22(f883(x95182,a871)),f655(x95181,x95183,x95182)),f332(f332(f310(x95182),f658(x95181,x95183,x95182)),f195(f883(x95182,a871)))))) % 172.83/172.49 [9767]~P56(x97671)+~P56(x97672)+P7(x97671,f332(f332(f8(f883(x97672,x97671),a871,f877(x97671)),x97673),f332(f332(f8(f883(x97672,f880(x97671)),f883(x97672,x97671),f877(x97671)),f72(f880(x97671),x97671,x97672,f243(x97671))),f332(f332(f8(f877(f882(x97672,x97671)),f883(x97672,f880(x97671)),f877(x97671)),f179(x97672,x97671)),f332(f183(x97672,x97671),f55(x97672))))),f332(f196(f877(x97672)),f55(x97672)))+~P102(f332(f58(f883(x97672,x97671)),x97673)) % 172.83/172.49 [9768]~P56(x97681)+~P56(x97682)+P6(x97681,f332(f332(f8(f883(x97682,x97681),a871,f877(x97681)),x97683),f332(f332(f8(f883(x97682,f880(x97681)),f883(x97682,x97681),f877(x97681)),f72(f880(x97681),x97681,x97682,f243(x97681))),f332(f332(f8(f877(f882(x97682,x97681)),f883(x97682,f880(x97681)),f877(x97681)),f179(x97682,x97681)),f332(f183(x97682,x97681),f55(x97682))))),f332(f196(f877(x97682)),f55(x97682)))+~P102(f332(f57(f883(x97682,x97681)),x97683)) % 172.83/172.49 [9864]~P56(x98641)+~P56(x98642)+~P6(x98642,f332(f332(f8(f883(x98641,x98642),a871,f877(x98642)),x98643),f332(f332(f8(f883(x98641,f880(x98642)),f883(x98641,x98642),f877(x98642)),f72(f880(x98642),x98642,x98641,f243(x98642))),f332(f332(f8(f877(f882(x98641,x98642)),f883(x98641,f880(x98642)),f877(x98642)),f179(x98641,x98642)),f332(f183(x98641,x98642),f55(x98641))))),f332(f196(f877(x98641)),f55(x98641)))+P102(f332(f57(f883(x98641,x98642)),x98643)) % 172.83/172.49 [9865]~P56(x98651)+~P56(x98652)+~P7(x98652,f332(f332(f8(f883(x98651,x98652),a871,f877(x98652)),x98653),f332(f332(f8(f883(x98651,f880(x98652)),f883(x98651,x98652),f877(x98652)),f72(f880(x98652),x98652,x98651,f243(x98652))),f332(f332(f8(f877(f882(x98651,x98652)),f883(x98651,f880(x98652)),f877(x98652)),f179(x98651,x98652)),f332(f183(x98651,x98652),f55(x98651))))),f332(f196(f877(x98651)),f55(x98651)))+P102(f332(f58(f883(x98651,x98652)),x98653)) % 172.83/172.49 [8659]~P102(f332(f332(f247(a1),f2(a1)),x86593))+P102(f332(f332(f246(a1),f2(a1)),x86591))+~P102(f332(f332(f247(a1),x86592),x86593))+~P102(f332(f332(f246(a1),f2(a1)),f332(f332(f79(a1),f332(f332(f80(a1),x86593),x86591)),x86592))) % 172.83/172.49 [8681]~P61(x86811)+~P102(f332(f61(x86811),x86812))+E(f332(f332(f22(f883(x86811,a871)),x86812),f332(f332(f310(x86811),x86813),f195(f883(x86811,a871)))),f195(f883(x86811,a871)))+E(f332(f332(f113(x86811),x86813),f13(x86811,f332(f332(f22(f883(x86811,a871)),x86812),f332(f332(f310(x86811),x86813),f195(f883(x86811,a871)))))),f13(x86811,f332(f332(f310(x86811),x86813),x86812))) % 172.83/172.49 [8682]~P61(x86821)+~P102(f332(f61(x86821),x86822))+E(f332(f332(f22(f883(x86821,a871)),x86822),f332(f332(f310(x86821),x86823),f195(f883(x86821,a871)))),f195(f883(x86821,a871)))+E(f332(f332(f104(x86821),x86823),f10(x86821,f332(f332(f22(f883(x86821,a871)),x86822),f332(f332(f310(x86821),x86823),f195(f883(x86821,a871)))))),f10(x86821,f332(f332(f310(x86821),x86823),x86822))) % 172.83/172.49 [8683]~P104(x86831)+~P102(f332(f61(x86831),x86832))+E(f332(f332(f22(f883(x86831,a871)),x86832),f332(f332(f310(x86831),x86833),f195(f883(x86831,a871)))),f195(f883(x86831,a871)))+E(f332(f332(f245(x86831),x86833),f14(x86831,f332(f332(f22(f883(x86831,a871)),x86832),f332(f332(f310(x86831),x86833),f195(f883(x86831,a871)))))),f14(x86831,f332(f332(f310(x86831),x86833),x86832))) % 172.83/172.49 [8684]~P104(x86841)+~P102(f332(f61(x86841),x86842))+E(f332(f332(f22(f883(x86841,a871)),x86842),f332(f332(f310(x86841),x86843),f195(f883(x86841,a871)))),f195(f883(x86841,a871)))+E(f332(f332(f244(x86841),x86843),f15(x86841,f332(f332(f22(f883(x86841,a871)),x86842),f332(f332(f310(x86841),x86843),f195(f883(x86841,a871)))))),f15(x86841,f332(f332(f310(x86841),x86843),x86842))) % 172.83/172.49 [8748]~P104(x87481)+~P102(f332(f61(x87481),x87482))+E(f332(f332(f22(f883(x87481,a871)),x87482),f332(f332(f310(x87481),x87483),f195(f883(x87481,a871)))),f195(f883(x87481,a871)))+E(f332(f332(f245(x87481),x87483),f11(x87481,f245(x87481),f332(f332(f22(f883(x87481,a871)),x87482),f332(f332(f310(x87481),x87483),f195(f883(x87481,a871)))))),f11(x87481,f245(x87481),f332(f332(f310(x87481),x87483),x87482))) % 172.83/172.49 [8749]~P104(x87491)+~P102(f332(f61(x87491),x87492))+E(f332(f332(f22(f883(x87491,a871)),x87492),f332(f332(f310(x87491),x87493),f195(f883(x87491,a871)))),f195(f883(x87491,a871)))+E(f332(f332(f244(x87491),x87493),f12(x87491,f244(x87491),f332(f332(f22(f883(x87491,a871)),x87492),f332(f332(f310(x87491),x87493),f195(f883(x87491,a871)))))),f12(x87491,f244(x87491),f332(f332(f310(x87491),x87493),x87492))) % 172.83/172.49 [9333]E(x93331,x93332)+~E(f332(f142(f877(x93333),f877(x93333),f134(x93333),f116(x93333)),x93331),f332(f142(f877(x93333),f877(x93333),f134(x93333),f116(x93333)),x93332))+~E(f332(f196(f877(f877(x93333))),x93331),f332(f196(f877(f877(x93333))),x93332))+P102(f332(f332(f334(f882(f877(x93333),f877(x93333))),f741(x93332,x93331,x93333)),f332(f173(f882(f877(x93333),f877(x93333))),f332(f332(f183(f877(x93333),f877(x93333)),x93331),x93332)))) % 172.83/172.49 [9334]E(x93341,x93342)+~E(f332(f142(f877(x93343),f877(x93343),f134(x93343),f116(x93343)),x93341),f332(f142(f877(x93343),f877(x93343),f134(x93343),f116(x93343)),x93342))+~E(f332(f196(f877(f877(x93343))),x93341),f332(f196(f877(f877(x93343))),x93342))+P102(f332(f332(f334(f882(f877(x93343),f877(x93343))),f742(x93341,x93342,x93343)),f332(f173(f882(f877(x93343),f877(x93343))),f332(f332(f183(f877(x93343),f877(x93343)),x93342),x93341)))) % 172.83/172.49 [10157]~P95(x101572)+E(x101571,f195(f883(x101572,a871)))+~P102(f332(f61(x101572),x101571))+E(f10(x101572,f332(f252(x101572),f332(f332(f8(f883(x101572,a871),a871,x101572),f86(x101572)),f332(f332(f7(x101572,f883(x101572,a871),f883(x101572,a871)),f332(f332(f8(f883(x101572,f883(a871,a871)),f883(f883(x101572,a871),f883(x101572,a871)),x101572),f18(x101572,a871,a871)),f332(f332(f8(f883(x101572,a871),f883(x101572,f883(a871,a871)),x101572),f332(f8(a871,f883(a871,a871),x101572),a330)),f332(f332(f7(x101572,f883(x101572,x101572),f883(x101572,a871)),f332(f332(f8(f883(x101572,a871),f883(f883(x101572,x101572),f883(x101572,a871)),x101572),f8(x101572,a871,x101572)),a329)),f332(f113(x101572),x101573))))),f332(f332(f7(x101572,f883(x101572,a871),a871),f334(x101572)),x101571))))),f332(f332(f113(x101572),x101573),f10(x101572,x101571))) % 172.83/172.49 [10158]~P95(x101582)+E(x101581,f195(f883(x101582,a871)))+~P102(f332(f61(x101582),x101581))+E(f13(x101582,f332(f252(x101582),f332(f332(f8(f883(x101582,a871),a871,x101582),f86(x101582)),f332(f332(f7(x101582,f883(x101582,a871),f883(x101582,a871)),f332(f332(f8(f883(x101582,f883(a871,a871)),f883(f883(x101582,a871),f883(x101582,a871)),x101582),f18(x101582,a871,a871)),f332(f332(f8(f883(x101582,a871),f883(x101582,f883(a871,a871)),x101582),f332(f8(a871,f883(a871,a871),x101582),a330)),f332(f332(f7(x101582,f883(x101582,x101582),f883(x101582,a871)),f332(f332(f8(f883(x101582,a871),f883(f883(x101582,x101582),f883(x101582,a871)),x101582),f8(x101582,a871,x101582)),a329)),f332(f104(x101582),x101583))))),f332(f332(f7(x101582,f883(x101582,a871),a871),f334(x101582)),x101581))))),f332(f332(f104(x101582),x101583),f13(x101582,x101581))) % 172.83/172.49 [10159]~P74(x101592)+E(x101591,f195(f883(x101592,a871)))+~P102(f332(f61(x101592),x101591))+E(f14(x101592,f332(f252(x101592),f332(f332(f8(f883(x101592,a871),a871,x101592),f86(x101592)),f332(f332(f7(x101592,f883(x101592,a871),f883(x101592,a871)),f332(f332(f8(f883(x101592,f883(a871,a871)),f883(f883(x101592,a871),f883(x101592,a871)),x101592),f18(x101592,a871,a871)),f332(f332(f8(f883(x101592,a871),f883(x101592,f883(a871,a871)),x101592),f332(f8(a871,f883(a871,a871),x101592),a330)),f332(f332(f7(x101592,f883(x101592,x101592),f883(x101592,a871)),f332(f332(f8(f883(x101592,a871),f883(f883(x101592,x101592),f883(x101592,a871)),x101592),f8(x101592,a871,x101592)),a329)),f332(f79(x101592),x101593))))),f332(f332(f7(x101592,f883(x101592,a871),a871),f334(x101592)),x101591))))),f332(f332(f79(x101592),x101593),f14(x101592,x101591))) % 172.83/172.49 [10160]~P74(x101602)+E(x101601,f195(f883(x101602,a871)))+~P102(f332(f61(x101602),x101601))+E(f15(x101602,f332(f252(x101602),f332(f332(f8(f883(x101602,a871),a871,x101602),f86(x101602)),f332(f332(f7(x101602,f883(x101602,a871),f883(x101602,a871)),f332(f332(f8(f883(x101602,f883(a871,a871)),f883(f883(x101602,a871),f883(x101602,a871)),x101602),f18(x101602,a871,a871)),f332(f332(f8(f883(x101602,a871),f883(x101602,f883(a871,a871)),x101602),f332(f8(a871,f883(a871,a871),x101602),a330)),f332(f332(f7(x101602,f883(x101602,x101602),f883(x101602,a871)),f332(f332(f8(f883(x101602,a871),f883(f883(x101602,x101602),f883(x101602,a871)),x101602),f8(x101602,a871,x101602)),a329)),f332(f79(x101602),x101603))))),f332(f332(f7(x101602,f883(x101602,a871),a871),f334(x101602)),x101601))))),f332(f332(f79(x101602),x101603),f15(x101602,x101601))) % 172.83/172.49 [10161]~P104(x101612)+E(x101611,f195(f883(x101612,a871)))+~P102(f332(f61(x101612),x101611))+E(f11(x101612,f245(x101612),f332(f252(x101612),f332(f332(f8(f883(x101612,a871),a871,x101612),f86(x101612)),f332(f332(f7(x101612,f883(x101612,a871),f883(x101612,a871)),f332(f332(f8(f883(x101612,f883(a871,a871)),f883(f883(x101612,a871),f883(x101612,a871)),x101612),f18(x101612,a871,a871)),f332(f332(f8(f883(x101612,a871),f883(x101612,f883(a871,a871)),x101612),f332(f8(a871,f883(a871,a871),x101612),a330)),f332(f332(f7(x101612,f883(x101612,x101612),f883(x101612,a871)),f332(f332(f8(f883(x101612,a871),f883(f883(x101612,x101612),f883(x101612,a871)),x101612),f8(x101612,a871,x101612)),a329)),f332(f244(x101612),x101613))))),f332(f332(f7(x101612,f883(x101612,a871),a871),f334(x101612)),x101611))))),f332(f332(f244(x101612),x101613),f11(x101612,f245(x101612),x101611))) % 172.83/172.49 [10162]~P104(x101622)+E(x101621,f195(f883(x101622,a871)))+~P102(f332(f61(x101622),x101621))+E(f12(x101622,f244(x101622),f332(f252(x101622),f332(f332(f8(f883(x101622,a871),a871,x101622),f86(x101622)),f332(f332(f7(x101622,f883(x101622,a871),f883(x101622,a871)),f332(f332(f8(f883(x101622,f883(a871,a871)),f883(f883(x101622,a871),f883(x101622,a871)),x101622),f18(x101622,a871,a871)),f332(f332(f8(f883(x101622,a871),f883(x101622,f883(a871,a871)),x101622),f332(f8(a871,f883(a871,a871),x101622),a330)),f332(f332(f7(x101622,f883(x101622,x101622),f883(x101622,a871)),f332(f332(f8(f883(x101622,a871),f883(f883(x101622,x101622),f883(x101622,a871)),x101622),f8(x101622,a871,x101622)),a329)),f332(f245(x101622),x101623))))),f332(f332(f7(x101622,f883(x101622,a871),a871),f334(x101622)),x101621))))),f332(f332(f245(x101622),x101623),f12(x101622,f244(x101622),x101621))) % 172.83/172.49 [9914]~P113(x99141)+~E(x99143,f2(x99141))+~E(x99142,f2(x99141))+E(f332(f332(f79(x99141),f332(f332(f257(x99141),x99142),f332(f106(a876),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100))))),f332(f332(f257(x99141),x99143),f332(f106(a876),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100))))),f2(x99141)) % 172.83/172.49 [10057]~P107(x100571)+~P102(f332(f332(f246(x100571),f2(x100571)),x100573))+P102(f332(f332(f246(x100571),x100572),x100573))+~P102(f332(f332(f246(x100571),f332(f332(f257(x100571),x100572),f332(f106(a876),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100))))),f332(f332(f257(x100571),x100573),f332(f106(a876),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)))))) % 172.83/172.49 [10103]~P113(x101032)+~E(x101031,f2(x101032))+~E(x101033,f2(x101032))+~P102(f332(f332(f247(x101032),f2(x101032)),f332(f332(f79(x101032),f332(f332(f257(x101032),x101033),f332(f106(a876),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100))))),f332(f332(f257(x101032),x101031),f332(f106(a876),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100))))))) % 172.83/172.49 [9295]E(x92951,x92952)+~E(f671(x92951,x92952,x92954,x92953),f673(x92951,x92952,x92954,x92953))+P102(f332(f332(f334(f882(f877(x92953),f877(x92953))),f332(f332(f267(f877(x92953),f877(x92953)),x92952),x92951)),f147(x92953,x92954)))+P102(f332(f332(f334(f882(f877(x92953),f877(x92953))),f332(f332(f267(f877(x92953),f877(x92953)),x92951),x92952)),f147(x92953,x92954))) % 172.83/172.49 [4858]~P57(x48582)+~E(x48584,f2(x48582))+~E(x48581,f2(x48582))+E(x48581,f332(f332(f290(x48582),x48583),x48584)) % 172.83/172.49 [4859]~P57(x48591)+~E(x48593,f2(x48591))+~E(x48594,f2(x48591))+E(f332(f332(f290(x48591),x48592),x48593),x48594) % 172.83/172.49 [4970]~P57(x49702)+E(x49701,f2(x49702))+~E(x49703,f2(x49702))+~E(x49701,f332(f332(f290(x49702),x49704),x49703)) % 172.83/172.49 [4971]~P57(x49712)+E(x49711,f2(x49712))+~E(x49713,f2(x49712))+~E(f332(f332(f290(x49712),x49714),x49713),x49711) % 172.83/172.49 [5146]~P117(x51462)+E(x51461,f2(x51462))+~E(f332(f332(f290(x51462),x51463),x51461),x51464)+E(x51463,f332(f332(f80(x51462),x51464),x51461)) % 172.83/172.49 [5148]~P117(x51482)+E(x51481,f2(x51482))+~E(f332(f332(f80(x51482),x51483),x51481),x51484)+E(x51483,f332(f332(f290(x51482),x51484),x51481)) % 172.83/172.49 [5149]~P57(x51492)+E(x51491,f2(x51492))+~E(f332(f332(f290(x51492),x51493),x51491),x51494)+E(x51493,f332(f332(f80(x51492),x51494),x51491)) % 172.83/172.49 [5150]~P57(x51502)+E(x51501,f2(x51502))+~E(f332(f332(f80(x51502),x51503),x51501),x51504)+E(x51503,f332(f332(f290(x51502),x51504),x51501)) % 172.83/172.49 [5151]~P117(x51512)+E(x51511,f2(x51512))+~E(x51513,f332(f332(f290(x51512),x51514),x51511))+E(f332(f332(f80(x51512),x51513),x51511),x51514) % 172.83/172.49 [5153]~P117(x51532)+E(x51531,f2(x51532))+~E(x51533,f332(f332(f80(x51532),x51534),x51531))+E(f332(f332(f290(x51532),x51533),x51531),x51534) % 172.83/172.49 [5154]~P57(x51542)+E(x51541,f2(x51542))+~E(x51543,f332(f332(f290(x51542),x51544),x51541))+E(f332(f332(f80(x51542),x51543),x51541),x51544) % 172.83/172.49 [5155]~P57(x51552)+E(x51551,f2(x51552))+~E(x51553,f332(f332(f80(x51552),x51554),x51551))+E(f332(f332(f290(x51552),x51553),x51551),x51554) % 172.83/172.49 [5180]~P57(x51802)+~E(x51801,f2(x51802))+~E(f332(f332(f80(x51802),x51801),x51804),x51803)+E(x51801,f332(f332(f290(x51802),x51803),x51804)) % 172.83/172.49 [5181]~P57(x51811)+~E(x51814,f2(x51811))+~E(x51812,f332(f332(f80(x51811),x51814),x51813))+E(f332(f332(f290(x51811),x51812),x51813),x51814) % 172.83/172.49 [5254]~E(x52543,x52544)+~E(x52542,x52543)+~P105(x52541)+E(f303(x52541,x52542,x52543),f332(f332(f310(x52541),x52544),f195(f883(x52541,a871)))) % 172.83/172.49 [5462]~E(f117(x54622,x54621),x54623)+~E(f144(x54622,x54621),x54624)+E(x54621,f116(x54622))+E(f332(f332(f134(x54622),x54623),f332(f332(f151(x54622),x54624),f116(x54622))),x54621) % 172.83/172.49 [6077]~P107(x60773)+E(x60771,x60772)+~E(f332(f332(f257(x60773),x60774),x60771),f332(f332(f257(x60773),x60774),x60772))+~P102(f332(f332(f247(x60773),f77(x60773)),x60774)) % 172.83/172.49 [6078]E(x60781,x60782)+~E(f332(f332(f310(x60783),x60784),x60781),f332(f332(f310(x60783),x60784),x60782))+P102(f332(f332(f334(x60783),x60784),x60782))+P102(f332(f332(f334(x60783),x60784),x60781)) % 172.83/172.49 [6116]E(f332(x61161,x61162),f77(a876))+~E(f332(f332(f9(x61163,a876),x61161),x61164),f77(a876))+~P102(f332(f61(x61163),x61164))+~P102(f332(f332(f334(x61163),x61162),x61164)) % 172.83/172.49 [6117]E(f332(x61171,x61172),f2(a876))+~E(f332(f332(f6(x61173,a876),x61171),x61174),f2(a876))+~P102(f332(f61(x61173),x61174))+~P102(f332(f332(f334(x61173),x61172),x61174)) % 172.83/172.49 [6332]~P105(x63321)+~P102(f332(f332(f247(x63321),x63324),x63323))+P102(f332(f332(f247(x63321),x63322),x63323))+~P102(f332(f332(f247(x63321),x63322),x63324)) % 172.83/172.49 [6333]~P105(x63331)+~P102(f332(f332(f246(x63331),x63334),x63333))+P102(f332(f332(f247(x63331),x63332),x63333))+~P102(f332(f332(f247(x63331),x63332),x63334)) % 172.83/172.49 [6334]~P105(x63341)+~P102(f332(f332(f246(x63341),x63342),x63344))+P102(f332(f332(f247(x63341),x63342),x63343))+~P102(f332(f332(f247(x63341),x63344),x63343)) % 172.83/172.49 [6335]~P103(x63351)+~P102(f332(f332(f247(x63351),x63352),x63354))+P102(f332(f332(f247(x63351),x63352),x63353))+~P102(f332(f332(f247(x63351),x63354),x63353)) % 172.83/172.49 [6336]~P103(x63361)+~P102(f332(f332(f246(x63361),x63362),x63364))+P102(f332(f332(f247(x63361),x63362),x63363))+~P102(f332(f332(f247(x63361),x63364),x63363)) % 172.83/172.49 [6337]~P103(x63371)+~P102(f332(f332(f246(x63371),x63374),x63373))+P102(f332(f332(f247(x63371),x63372),x63373))+~P102(f332(f332(f247(x63371),x63372),x63374)) % 172.83/172.49 [6338]~P105(x63381)+~P102(f332(f332(f246(x63381),x63384),x63383))+P102(f332(f332(f246(x63381),x63382),x63383))+~P102(f332(f332(f246(x63381),x63382),x63384)) % 172.83/172.49 [6339]~P103(x63391)+~P102(f332(f332(f246(x63391),x63392),x63394))+P102(f332(f332(f246(x63391),x63392),x63393))+~P102(f332(f332(f246(x63391),x63394),x63393)) % 172.83/172.49 [6420]~P36(x64204,x64203,x64202)+E(x64201,f809(x64202,x64203,x64204))+~P102(f332(x64203,x64201))+~P102(f332(f332(f334(x64204),x64201),f332(f173(x64204),x64202))) % 172.83/172.49 [6564]~P27(x65641)+~P102(f332(f332(f246(x65641),x65642),f40(x65641,x65644)))+P102(f332(f332(f246(x65641),x65642),x65643))+~P102(f332(f332(f334(x65641),x65643),x65644)) % 172.83/172.49 [6710]~P104(x67101)+~P29(x67101,f332(f332(f151(x67101),x67102),x67104))+~P102(f332(f332(f334(x67101),x67103),f332(f173(x67101),x67104)))+P102(f332(f332(f246(x67101),x67102),x67103)) % 172.83/172.49 [6800]~P27(x68001)+~P102(f332(f332(f246(x68001),f39(x68001,x68004)),x68003))+P102(f332(f332(f246(x68001),x68002),x68003))+~P102(f332(f332(f334(x68001),x68002),x68004)) % 172.83/172.49 [7207]~P104(x72071)+E(f332(f332(f113(f883(x72071,a871)),f332(f302(x72071,x72072),x72073)),f332(f302(x72071,x72073),x72074)),f332(f302(x72071,x72072),x72074))+~P102(f332(f332(f246(x72071),x72073),x72074))+~P102(f332(f332(f246(x72071),x72072),x72073)) % 172.83/172.49 [7244]P36(x72441,x72442,x72443)+~E(f811(x72443,x72442,x72441,x72444),x72444)+~P102(f332(x72442,x72444))+~P102(f332(f332(f334(x72441),x72444),f332(f173(x72441),x72443))) % 172.83/172.49 [7318]~P104(x73181)+E(f332(f332(f113(f883(x73181,a871)),f332(f302(x73181,x73182),x73183)),f303(x73181,x73183,x73184)),f303(x73181,x73182,x73184))+~P102(f332(f332(f246(x73181),x73183),x73184))+~P102(f332(f332(f246(x73181),x73182),x73183)) % 172.83/172.49 [7384]~P104(x73841)+E(f332(f332(f113(f883(x73841,a871)),f306(x73841,x73842,x73843)),f332(f302(x73841,x73843),x73844)),f306(x73841,x73842,x73844))+~P102(f332(f332(f247(x73841),x73842),x73843))+~P102(f332(f332(f246(x73841),x73843),x73844)) % 172.83/172.49 [7404]~P104(x74041)+E(f332(f332(f113(f883(x74041,a871)),f303(x74041,x74042,x74043)),f306(x74041,x74043,x74044)),f332(f302(x74041,x74042),x74044))+~P102(f332(f332(f247(x74041),x74043),x74044))+~P102(f332(f332(f246(x74041),x74042),x74043)) % 172.83/172.49 [7436]~P104(x74361)+E(f332(f332(f113(f883(x74361,a871)),f303(x74361,x74362,x74363)),f305(x74361,x74363,x74364)),f303(x74361,x74362,x74364))+~P102(f332(f332(f246(x74361),x74363),x74364))+~P102(f332(f332(f246(x74361),x74362),x74363)) % 172.83/172.49 [7437]~P104(x74371)+E(f332(f332(f113(f883(x74371,a871)),f306(x74371,x74372,x74373)),f303(x74371,x74373,x74374)),f305(x74371,x74372,x74374))+~P102(f332(f332(f247(x74371),x74372),x74373))+~P102(f332(f332(f246(x74371),x74373),x74374)) % 172.83/172.49 [7438]~P104(x74381)+E(f332(f332(f113(f883(x74381,a871)),f305(x74381,x74382,x74383)),f306(x74381,x74383,x74384)),f306(x74381,x74382,x74384))+~P102(f332(f332(f247(x74381),x74383),x74384))+~P102(f332(f332(f246(x74381),x74382),x74383)) % 172.83/172.49 [7439]~P104(x74391)+E(f332(f332(f113(f883(x74391,a871)),f305(x74391,x74392,x74393)),f305(x74391,x74393,x74394)),f305(x74391,x74392,x74394))+~P102(f332(f332(f246(x74391),x74393),x74394))+~P102(f332(f332(f246(x74391),x74392),x74393)) % 172.83/172.49 [8246]P20(x82461,x82462,f522(x82463,x82462,x82464,x82461),x82464)+~P102(f332(f61(x82462),x82463))+~P102(f332(f61(x82461),x82464))+~P102(f332(f332(f246(a876),f332(f37(x82461),x82464)),f332(f37(x82462),x82463))) % 172.83/172.49 [8267]P36(x82671,x82672,x82673)+~P102(f332(x82672,x82674))+P102(f332(x82672,f811(x82673,x82672,x82671,x82674)))+~P102(f332(f332(f334(x82671),x82674),f332(f173(x82671),x82673))) % 172.83/172.49 [8318]~P67(x83181)+~E(f332(x83183,f825(x83183,x83184,x83182,x83181)),f77(x83181))+E(f332(f332(f332(f65(x83181,x83182,f80(x83181)),x83183),f77(x83181)),x83184),f77(x83181))+~P102(f332(f61(x83182),x83184)) % 172.83/172.49 [8591]~P107(x85911)+~P102(f332(f332(f246(x85911),f2(x85911)),x85913))+P102(f332(f332(f246(x85911),x85912),x85913))+~P102(f332(f332(f246(x85911),f332(f332(f257(x85911),x85912),f332(a115,x85914))),f332(f332(f257(x85911),x85913),f332(a115,x85914)))) % 172.83/172.49 [8885]P36(x88851,x88852,x88853)+~P102(f332(x88852,x88854))+~P102(f332(f332(f334(x88851),x88854),f332(f173(x88851),x88853)))+P102(f332(f332(f334(x88851),f811(x88853,x88852,x88851,x88854)),f332(f173(x88851),x88853))) % 172.83/172.49 [8973]~P67(x89731)+E(f332(f332(f332(f65(x89731,x89732,f80(x89731)),x89733),f77(x89731)),x89734),f77(x89731))+~P102(f332(f61(x89732),x89734))+P102(f332(f332(f334(x89732),f825(x89733,x89734,x89732,x89731)),x89734)) % 172.83/172.49 [9459]~P102(f332(f332(f246(a1),x94594),f2(a1)))+P102(f332(f332(f246(a1),f332(f332(f79(a1),f332(f332(f80(a1),x94591),f44(a1,x94592,x94593))),x94594)),f2(a1)))+~P102(f332(f332(f247(a1),f2(a1)),x94593))+~P102(f332(f332(f247(a1),x94591),x94594)) % 172.83/172.49 [9907]~P102(f332(f61(x99071),x99072))+~P102(f332(f332(f334(x99071),x99074),x99072))+~P102(f332(f332(f334(x99071),x99073),x99072))+P102(f332(f332(f247(a876),f332(f37(x99071),f332(f332(f22(f883(x99071,a871)),f332(f332(f22(f883(x99071,a871)),x99072),f332(f332(f310(x99071),x99073),f195(f883(x99071,a871))))),f332(f332(f310(x99071),x99074),f195(f883(x99071,a871)))))),f332(f37(x99071),x99072))) % 172.83/172.49 [6915]~P104(x69151)+~P102(f332(f332(f247(x69151),x69152),x69154))+~P102(f332(f332(f247(x69151),x69152),x69153))+P102(f332(f332(f247(x69151),x69152),f332(f332(f244(x69151),x69153),x69154))) % 172.83/172.49 [6918]~P98(x69181)+~P102(f332(f332(f246(x69181),x69182),x69184))+~P102(f332(f332(f246(x69181),x69182),x69183))+P102(f332(f332(f246(x69181),x69182),f332(f332(f104(x69181),x69183),x69184))) % 172.83/172.49 [6921]~P104(x69211)+~P102(f332(f332(f246(x69211),x69212),x69214))+~P102(f332(f332(f246(x69211),x69212),x69213))+P102(f332(f332(f246(x69211),x69212),f332(f332(f244(x69211),x69213),x69214))) % 172.83/172.49 [6940]~P58(x69402)+E(x69401,f2(x69402))+E(f332(f332(f290(x69402),f332(f332(f257(x69402),x69401),x69403)),f332(f332(f257(x69402),x69401),x69404)),f332(f332(f257(x69402),x69401),f332(f332(f22(a876),x69403),x69404)))+~P102(f332(f332(f246(a876),x69404),x69403)) % 172.83/172.49 [6985]~P104(x69851)+~P29(x69851,f332(f332(f151(x69851),x69853),x69854))+P29(x69851,f332(f332(f151(x69851),x69852),f332(f332(f151(x69851),x69853),x69854)))+~P102(f332(f332(f246(x69851),x69852),x69853)) % 172.83/172.49 [7026]~P107(x70261)+~P102(f332(f332(f247(x70261),f2(x70261)),x70263))+~P102(f332(f332(f247(x70261),x70262),x70264))+P102(f332(f332(f247(x70261),x70262),f332(f332(f79(x70261),x70263),x70264))) % 172.83/172.49 [7027]~P84(x70271)+~P102(f332(f332(f246(x70271),f2(x70271)),x70273))+~P102(f332(f332(f247(x70271),x70272),x70274))+P102(f332(f332(f247(x70271),x70272),f332(f332(f79(x70271),x70273),x70274))) % 172.83/172.49 [7028]~P84(x70281)+~P102(f332(f332(f246(x70281),x70282),x70284))+~P102(f332(f332(f247(x70281),f2(x70281)),x70283))+P102(f332(f332(f247(x70281),x70282),f332(f332(f79(x70281),x70283),x70284))) % 172.83/172.49 [7029]~P84(x70291)+~P102(f332(f332(f246(x70291),f2(x70291)),x70294))+~P102(f332(f332(f246(x70291),x70292),x70293))+P102(f332(f332(f246(x70291),x70292),f332(f332(f79(x70291),x70293),x70294))) % 172.83/172.49 [7030]~P84(x70301)+~P102(f332(f332(f246(x70301),f2(x70301)),x70303))+~P102(f332(f332(f246(x70301),x70302),x70304))+P102(f332(f332(f246(x70301),x70302),f332(f332(f79(x70301),x70303),x70304))) % 172.83/172.49 [7069]~P104(x70691)+P102(f332(f332(f247(x70691),x70692),x70693))+P102(f332(f332(f247(x70691),x70692),x70694))+~P102(f332(f332(f247(x70691),x70692),f332(f332(f245(x70691),x70694),x70693))) % 172.83/172.49 [7070]~P104(x70701)+P102(f332(f332(f246(x70701),x70702),x70703))+P102(f332(f332(f246(x70701),x70702),x70704))+~P102(f332(f332(f246(x70701),x70702),f332(f332(f245(x70701),x70704),x70703))) % 172.83/172.49 [7357]~P105(x73572)+~P56(x73571)+~P102(f332(f332(f247(f883(x73571,x73572)),x73573),x73574))+P102(f332(f332(f246(f883(x73571,x73572)),x73573),x73574)) % 172.83/172.49 [7729]~P60(x77291)+~P102(f332(f332(f247(x77291),x77294),f2(x77291)))+~P102(f332(f332(f247(x77291),x77293),f332(f332(f290(x77291),x77292),x77294)))+P102(f332(f332(f247(x77291),x77292),f332(f332(f80(x77291),x77293),x77294))) % 172.83/172.49 [7730]~P60(x77301)+~P102(f332(f332(f247(x77301),x77304),f2(x77301)))+~P102(f332(f332(f247(x77301),x77303),f332(f332(f80(x77301),x77302),x77304)))+P102(f332(f332(f247(x77301),x77302),f332(f332(f290(x77301),x77303),x77304))) % 172.83/172.49 [7731]~P60(x77311)+~P102(f332(f332(f247(x77311),x77314),f2(x77311)))+~P102(f332(f332(f246(x77311),x77313),f332(f332(f290(x77311),x77312),x77314)))+P102(f332(f332(f246(x77311),x77312),f332(f332(f80(x77311),x77313),x77314))) % 172.83/172.49 [7732]~P60(x77321)+~P102(f332(f332(f247(x77321),x77324),f2(x77321)))+~P102(f332(f332(f246(x77321),x77323),f332(f332(f80(x77321),x77322),x77324)))+P102(f332(f332(f246(x77321),x77322),f332(f332(f290(x77321),x77323),x77324))) % 172.83/172.49 [7845]~P120(x78451)+~P102(f332(f332(f247(x78451),x78453),f2(x78451)))+~P102(f332(f332(f247(x78451),x78454),x78452))+P102(f332(f332(f247(x78451),f332(f332(f80(x78451),x78452),x78453)),f332(f332(f80(x78451),x78454),x78453))) % 172.83/172.49 [7846]~P120(x78461)+~P102(f332(f332(f247(x78461),x78462),f2(x78461)))+~P102(f332(f332(f247(x78461),x78464),x78463))+P102(f332(f332(f247(x78461),f332(f332(f80(x78461),x78462),x78463)),f332(f332(f80(x78461),x78462),x78464))) % 172.83/172.49 [7847]~P60(x78471)+~P102(f332(f332(f247(x78471),x78473),f2(x78471)))+~P102(f332(f332(f247(x78471),x78474),x78472))+P102(f332(f332(f247(x78471),f332(f332(f290(x78471),x78472),x78473)),f332(f332(f290(x78471),x78474),x78473))) % 172.83/172.49 [7848]~P124(x78481)+~P102(f332(f332(f246(x78481),x78482),f2(x78481)))+~P102(f332(f332(f246(x78481),x78484),x78483))+P102(f332(f332(f246(x78481),f332(f332(f80(x78481),x78482),x78483)),f332(f332(f80(x78481),x78482),x78484))) % 172.83/172.49 [7849]~P120(x78491)+~P102(f332(f332(f247(x78491),x78492),f2(x78491)))+~P102(f332(f332(f246(x78491),x78494),x78493))+P102(f332(f332(f246(x78491),f332(f332(f80(x78491),x78492),x78493)),f332(f332(f80(x78491),x78492),x78494))) % 172.83/172.49 [7850]~P124(x78501)+~P102(f332(f332(f246(x78501),x78503),f2(x78501)))+~P102(f332(f332(f246(x78501),x78504),x78502))+P102(f332(f332(f246(x78501),f332(f332(f80(x78501),x78502),x78503)),f332(f332(f80(x78501),x78504),x78503))) % 172.83/172.49 [7851]~P59(x78511)+~P102(f332(f332(f246(x78511),x78513),f2(x78511)))+~P102(f332(f332(f246(x78511),x78514),x78512))+P102(f332(f332(f246(x78511),f332(f332(f290(x78511),x78512),x78513)),f332(f332(f290(x78511),x78514),x78513))) % 172.83/172.49 [7853]~P107(x78531)+~P102(f332(f332(f247(x78531),f77(x78531)),x78532))+~P102(f332(f332(f247(a876),x78533),x78534))+P102(f332(f332(f247(x78531),f332(f332(f257(x78531),x78532),x78533)),f332(f332(f257(x78531),x78532),x78534))) % 172.83/172.49 [7854]~P107(x78541)+~P102(f332(f332(f247(x78541),f77(x78541)),x78542))+~P102(f332(f332(f246(a876),x78543),x78544))+P102(f332(f332(f246(x78541),f332(f332(f257(x78541),x78542),x78543)),f332(f332(f257(x78541),x78542),x78544))) % 172.83/172.49 [7855]~P107(x78551)+~P102(f332(f332(f246(x78551),f77(x78551)),x78552))+~P102(f332(f332(f246(a876),x78553),x78554))+P102(f332(f332(f246(x78551),f332(f332(f257(x78551),x78552),x78553)),f332(f332(f257(x78551),x78552),x78554))) % 172.83/172.49 [7882]P102(f332(f332(f247(a876),f2(a876)),f332(x78821,x78822)))+~P102(f332(f61(x78823),x78824))+~P102(f332(f332(f334(x78823),x78822),x78824))+~P102(f332(f332(f247(a876),f2(a876)),f332(f332(f9(x78823,a876),x78821),x78824))) % 172.83/172.49 [7892]~P115(x78921)+~P102(f332(f332(f247(x78921),x78923),x78924))+~P102(f332(f332(f247(x78921),f2(x78921)),x78922))+P102(f332(f332(f247(x78921),f332(f332(f80(x78921),x78922),x78923)),f332(f332(f80(x78921),x78922),x78924))) % 172.83/172.49 [7893]~P126(x78931)+~P102(f332(f332(f247(x78931),x78933),x78934))+~P102(f332(f332(f247(x78931),f2(x78931)),x78932))+P102(f332(f332(f247(x78931),f332(f332(f80(x78931),x78932),x78933)),f332(f332(f80(x78931),x78932),x78934))) % 172.83/172.49 [7894]~P120(x78941)+~P102(f332(f332(f247(x78941),x78942),x78944))+~P102(f332(f332(f247(x78941),f2(x78941)),x78943))+P102(f332(f332(f247(x78941),f332(f332(f80(x78941),x78942),x78943)),f332(f332(f80(x78941),x78944),x78943))) % 172.83/172.49 [7895]~P126(x78951)+~P102(f332(f332(f247(x78951),x78952),x78954))+~P102(f332(f332(f247(x78951),f2(x78951)),x78953))+P102(f332(f332(f247(x78951),f332(f332(f80(x78951),x78952),x78953)),f332(f332(f80(x78951),x78954),x78953))) % 172.83/172.49 [7896]~P120(x78961)+~P102(f332(f332(f247(x78961),x78963),x78964))+~P102(f332(f332(f247(x78961),f2(x78961)),x78962))+P102(f332(f332(f247(x78961),f332(f332(f80(x78961),x78962),x78963)),f332(f332(f80(x78961),x78962),x78964))) % 172.83/172.49 [7897]~P60(x78971)+~P102(f332(f332(f247(x78971),x78972),x78974))+~P102(f332(f332(f247(x78971),f2(x78971)),x78973))+P102(f332(f332(f247(x78971),f332(f332(f290(x78971),x78972),x78973)),f332(f332(f290(x78971),x78974),x78973))) % 172.83/172.49 [7898]~P133(x78981)+~P102(f332(f332(f246(x78981),x78983),x78984))+~P102(f332(f332(f246(x78981),f2(x78981)),x78982))+P102(f332(f332(f246(x78981),f332(f332(f80(x78981),x78982),x78983)),f332(f332(f80(x78981),x78982),x78984))) % 172.83/172.49 [7899]~P132(x78991)+~P102(f332(f332(f246(x78991),x78993),x78994))+~P102(f332(f332(f246(x78991),f2(x78991)),x78992))+P102(f332(f332(f246(x78991),f332(f332(f80(x78991),x78992),x78993)),f332(f332(f80(x78991),x78992),x78994))) % 172.83/172.49 [7900]~P120(x79001)+~P102(f332(f332(f247(x79001),f2(x79001)),x79002))+~P102(f332(f332(f246(x79001),x79003),x79004))+P102(f332(f332(f246(x79001),f332(f332(f80(x79001),x79002),x79003)),f332(f332(f80(x79001),x79002),x79004))) % 172.83/172.49 [7901]~P133(x79011)+~P102(f332(f332(f246(x79011),x79012),x79014))+~P102(f332(f332(f246(x79011),f2(x79011)),x79013))+P102(f332(f332(f246(x79011),f332(f332(f80(x79011),x79012),x79013)),f332(f332(f80(x79011),x79014),x79013))) % 172.83/172.49 [7902]~P107(x79021)+~P102(f332(f332(f246(x79021),x79022),x79024))+~P102(f332(f332(f246(x79021),f2(x79021)),x79022))+P102(f332(f332(f246(x79021),f332(f332(f257(x79021),x79022),x79023)),f332(f332(f257(x79021),x79024),x79023))) % 172.83/172.49 [7903]~P59(x79031)+~P102(f332(f332(f246(x79031),x79032),x79034))+~P102(f332(f332(f246(x79031),f2(x79031)),x79033))+P102(f332(f332(f246(x79031),f332(f332(f290(x79031),x79032),x79033)),f332(f332(f290(x79031),x79034),x79033))) % 172.83/172.49 [7946]~P106(x79462)+P102(f332(f332(f246(f883(x79461,x79462)),x79464),x79463))+~P102(f332(f332(f246(f883(x79461,x79462)),x79463),x79464))+P102(f332(f332(f247(f883(x79461,x79462)),x79463),x79464)) % 172.83/172.49 [7989]P102(f332(f332(f334(x79891),x79892),x79893))+P102(f332(f332(f334(x79891),x79892),x79894))+~P102(f332(f332(f246(f883(x79891,a871)),x79894),x79893))+P102(f332(f332(f247(f883(x79891,a871)),x79894),f332(f332(f310(x79891),x79892),x79893))) % 172.83/172.49 [8151]P102(f332(f332(f334(x81511),x81512),x81513))+P102(f332(f332(f334(x81511),x81512),x81514))+~P102(f332(f332(f247(f883(x81511,a871)),x81514),f332(f332(f310(x81511),x81512),x81513)))+P102(f332(f332(f246(f883(x81511,a871)),x81514),x81513)) % 172.83/172.49 [8160]~P56(x81601)+P6(x81601,x81602,x81603)+~P102(f332(x81602,x81604))+~P102(f332(f332(f334(f877(x81601)),x81604),f332(f173(f877(x81601)),f54(x81601,x81603,f55(x81601))))) % 172.83/172.49 [8170]~P7(x81703,x81701,x81704)+~P56(x81703)+P102(f332(x81701,x81702))+~P102(f332(f332(f334(f877(x81703)),x81702),f332(f173(f877(x81703)),f54(x81703,x81704,f55(x81703))))) % 172.83/172.49 [8223]~P120(x82231)+P102(f332(f332(f247(x82231),x82233),x82232))+P102(f332(f332(f247(x82231),x82232),x82233))+~P102(f332(f332(f247(x82231),f332(f332(f80(x82231),x82234),x82232)),f332(f332(f80(x82231),x82234),x82233))) % 172.83/172.49 [8224]~P120(x82241)+P102(f332(f332(f247(x82241),x82243),x82242))+P102(f332(f332(f247(x82241),x82242),x82243))+~P102(f332(f332(f247(x82241),f332(f332(f80(x82241),x82242),x82244)),f332(f332(f80(x82241),x82243),x82244))) % 172.83/172.49 [8235]~P120(x82351)+P102(f332(f332(f247(x82351),x82354),f2(x82351)))+P102(f332(f332(f247(x82351),x82352),x82353))+~P102(f332(f332(f247(x82351),f332(f332(f80(x82351),x82352),x82354)),f332(f332(f80(x82351),x82353),x82354))) % 172.83/172.49 [8236]~P120(x82361)+P102(f332(f332(f247(x82361),x82364),f2(x82361)))+P102(f332(f332(f247(x82361),x82362),x82363))+~P102(f332(f332(f247(x82361),f332(f332(f80(x82361),x82364),x82362)),f332(f332(f80(x82361),x82364),x82363))) % 172.83/172.49 [8240]~P120(x82401)+P102(f332(f332(f247(x82401),x82402),x82403))+P102(f332(f332(f247(x82401),f2(x82401)),x82404))+~P102(f332(f332(f247(x82401),f332(f332(f80(x82401),x82404),x82403)),f332(f332(f80(x82401),x82404),x82402))) % 172.83/172.49 [8241]~P120(x82411)+P102(f332(f332(f247(x82411),x82412),x82413))+P102(f332(f332(f247(x82411),f2(x82411)),x82414))+~P102(f332(f332(f247(x82411),f332(f332(f80(x82411),x82413),x82414)),f332(f332(f80(x82411),x82412),x82414))) % 172.83/172.49 [8254]~P120(x82541)+P102(f332(f332(f247(x82541),x82542),f2(x82541)))+P102(f332(f332(f247(x82541),f2(x82541)),x82542))+~P102(f332(f332(f247(x82541),f332(f332(f80(x82541),x82543),x82542)),f332(f332(f80(x82541),x82544),x82542))) % 172.83/172.49 [8255]~P120(x82551)+P102(f332(f332(f247(x82551),x82552),f2(x82551)))+P102(f332(f332(f247(x82551),f2(x82551)),x82552))+~P102(f332(f332(f247(x82551),f332(f332(f80(x82551),x82552),x82553)),f332(f332(f80(x82551),x82552),x82554))) % 172.83/172.49 [8281]~P120(x82811)+~P102(f332(f332(f247(x82811),x82814),f2(x82811)))+P102(f332(f332(f247(x82811),x82812),x82813))+~P102(f332(f332(f247(x82811),f332(f332(f80(x82811),x82814),x82813)),f332(f332(f80(x82811),x82814),x82812))) % 172.83/172.49 [8282]~P120(x82821)+~P102(f332(f332(f247(x82821),x82824),f2(x82821)))+P102(f332(f332(f246(x82821),x82822),x82823))+~P102(f332(f332(f246(x82821),f332(f332(f80(x82821),x82824),x82823)),f332(f332(f80(x82821),x82824),x82822))) % 172.83/172.49 [8294]~P107(x82943)+~P102(f332(f332(f247(x82943),f77(x82943)),x82944))+P102(f332(f332(f247(a876),x82941),x82942))+~P102(f332(f332(f247(x82943),f332(f332(f257(x82943),x82944),x82941)),f332(f332(f257(x82943),x82944),x82942))) % 172.83/172.49 [8296]~P107(x82963)+~P102(f332(f332(f247(x82963),f77(x82963)),x82964))+P102(f332(f332(f246(a876),x82961),x82962))+~P102(f332(f332(f246(x82963),f332(f332(f257(x82963),x82964),x82961)),f332(f332(f257(x82963),x82964),x82962))) % 172.83/172.49 [8306]~P120(x83061)+P102(f332(f332(f247(x83061),x83062),x83063))+~P102(f332(f332(f247(x83061),f2(x83061)),x83064))+~P102(f332(f332(f247(x83061),f332(f332(f80(x83061),x83064),x83062)),f332(f332(f80(x83061),x83064),x83063))) % 172.83/172.49 [8307]~P126(x83071)+P102(f332(f332(f247(x83071),x83072),x83073))+~P102(f332(f332(f246(x83071),f2(x83071)),x83074))+~P102(f332(f332(f247(x83071),f332(f332(f80(x83071),x83074),x83072)),f332(f332(f80(x83071),x83074),x83073))) % 172.83/172.49 [8308]~P127(x83081)+P102(f332(f332(f247(x83081),x83082),x83083))+~P102(f332(f332(f246(x83081),f2(x83081)),x83084))+~P102(f332(f332(f247(x83081),f332(f332(f80(x83081),x83084),x83082)),f332(f332(f80(x83081),x83084),x83083))) % 172.83/172.49 [8309]~P107(x83091)+~P102(f332(f332(f246(x83091),f2(x83091)),x83093))+P102(f332(f332(f247(x83091),x83092),x83093))+~P102(f332(f332(f247(x83091),f332(f332(f257(x83091),x83092),x83094)),f332(f332(f257(x83091),x83093),x83094))) % 172.83/172.49 [8310]~P126(x83101)+P102(f332(f332(f247(x83101),x83102),x83103))+~P102(f332(f332(f246(x83101),f2(x83101)),x83104))+~P102(f332(f332(f247(x83101),f332(f332(f80(x83101),x83102),x83104)),f332(f332(f80(x83101),x83103),x83104))) % 172.83/172.49 [8311]~P127(x83111)+P102(f332(f332(f247(x83111),x83112),x83113))+~P102(f332(f332(f246(x83111),f2(x83111)),x83114))+~P102(f332(f332(f247(x83111),f332(f332(f80(x83111),x83112),x83114)),f332(f332(f80(x83111),x83113),x83114))) % 172.83/172.49 [8312]~P120(x83121)+P102(f332(f332(f246(x83121),x83122),x83123))+~P102(f332(f332(f247(x83121),f2(x83121)),x83124))+~P102(f332(f332(f246(x83121),f332(f332(f80(x83121),x83124),x83122)),f332(f332(f80(x83121),x83124),x83123))) % 172.83/172.49 [8313]~P126(x83131)+P102(f332(f332(f246(x83131),x83132),x83133))+~P102(f332(f332(f247(x83131),f2(x83131)),x83134))+~P102(f332(f332(f246(x83131),f332(f332(f80(x83131),x83134),x83132)),f332(f332(f80(x83131),x83134),x83133))) % 172.83/172.49 [8314]~P126(x83141)+P102(f332(f332(f246(x83141),x83142),x83143))+~P102(f332(f332(f247(x83141),f2(x83141)),x83144))+~P102(f332(f332(f246(x83141),f332(f332(f80(x83141),x83142),x83144)),f332(f332(f80(x83141),x83143),x83144))) % 172.83/172.49 [8357]P102(f332(f332(f334(x83571),x83572),x83573))+~P102(f332(f332(f246(f883(x83571,a871)),x83573),x83574))+~P102(f332(f332(f247(f883(x83571,a871)),x83573),x83574))+P102(f332(f332(f247(f883(x83571,a871)),x83573),f332(f332(f310(x83571),x83572),x83574))) % 172.83/172.49 [8614]~P56(x86141)+~P91(x86142)+~E(f332(x86143,f805(x86144,x86143,x86141,x86142)),f332(x86144,f805(x86144,x86143,x86141,x86142)))+P102(f332(f332(f90(f883(x86141,x86142)),x86143),x86144)) % 172.83/172.49 [8728]E(f332(f332(f22(a1),f403(x87281,x87282,x87283,x87284)),f404(x87281,x87282,x87283,x87284)),x87284)+~P102(f332(f332(f247(a1),f2(a1)),x87283))+~P102(f332(f332(f246(a1),x87281),x87284))+P102(f332(f332(f246(a1),x87281),f332(f332(f79(a1),x87284),x87283))) % 172.83/172.49 [8729]E(f332(f332(f22(a1),f411(x87291,x87292,x87293,x87294)),f412(x87291,x87292,x87293,x87294)),x87294)+~P102(f332(f332(f247(a1),f2(a1)),x87293))+~P102(f332(f332(f247(a1),x87291),x87294))+P102(f332(f332(f247(a1),x87291),f332(f332(f79(a1),x87294),x87293))) % 172.83/172.49 [8865]~E(f332(f332(f165(x88651),x88653),f695(x88654,x88653,x88651,x88652)),f332(f332(f165(x88651),x88654),f695(x88654,x88653,x88651,x88652)))+E(f332(f332(f176(x88651),x88652),x88653),f332(f332(f176(x88651),x88652),x88654))+~P102(f332(f332(f246(a876),x88652),f332(f196(f877(x88651)),x88653)))+~P102(f332(f332(f246(a876),x88652),f332(f196(f877(x88651)),x88654))) % 172.83/172.49 [8939]~P102(f332(f332(f247(a1),f2(a1)),x89393))+~P102(f332(f332(f246(a1),x89391),x89394))+P102(f332(f332(f334(a1),f403(x89391,x89392,x89393,x89394)),x89392))+P102(f332(f332(f246(a1),x89391),f332(f332(f79(a1),x89394),x89393))) % 172.83/172.49 [8940]~P102(f332(f332(f247(a1),f2(a1)),x89403))+~P102(f332(f332(f247(a1),x89401),x89404))+P102(f332(f332(f334(a1),f411(x89401,x89402,x89403,x89404)),x89402))+P102(f332(f332(f247(a1),x89401),f332(f332(f79(a1),x89404),x89403))) % 172.83/172.49 [8982]~P98(x89821)+~P102(f332(f61(x89821),x89823))+~P102(f332(f332(f334(x89821),x89824),x89823))+P102(f332(f332(f246(x89821),f332(f332(f64(x89821,x89821,f104(x89821)),x89822),x89823)),f332(f332(f104(x89821),x89824),x89822))) % 172.83/172.49 [8983]~P104(x89831)+~P102(f332(f61(x89831),x89833))+~P102(f332(f332(f334(x89831),x89834),x89833))+P102(f332(f332(f246(x89831),f332(f332(f64(x89831,x89831,f244(x89831)),x89832),x89833)),f332(f332(f244(x89831),x89834),x89832))) % 172.83/172.49 [9029]E(f332(f332(f176(x90291),x90292),x90293),f332(f332(f176(x90291),x90292),x90294))+P102(f332(f332(f247(a876),f695(x90293,x90294,x90291,x90292)),x90292))+~P102(f332(f332(f246(a876),x90292),f332(f196(f877(x90291)),x90293)))+~P102(f332(f332(f246(a876),x90292),f332(f196(f877(x90291)),x90294))) % 172.83/172.49 [9034]~P102(f332(f332(f247(a1),f2(a1)),x90343))+~P102(f332(f332(f247(a1),x90341),x90342))+P102(f332(f332(f334(a1),f412(x90341,x90344,x90343,x90342)),f303(a1,f77(a1),x90343)))+P102(f332(f332(f247(a1),x90341),f332(f332(f79(a1),x90342),x90343))) % 172.83/172.49 [9035]~P102(f332(f332(f247(a1),f2(a1)),x90353))+~P102(f332(f332(f246(a1),x90351),x90352))+P102(f332(f332(f334(a1),f404(x90351,x90354,x90353,x90352)),f303(a1,f77(a1),x90353)))+P102(f332(f332(f246(a1),x90351),f332(f332(f79(a1),x90352),x90353))) % 172.83/172.49 [9198]~E(f332(f179(x91981,x91982),x91983),f332(f179(x91981,x91982),x91984))+E(f332(f173(f882(x91981,x91982)),x91983),f332(f173(f882(x91981,x91982)),x91984))+~P102(f332(f137(x91981),f332(f332(f154(f882(x91981,x91982),x91981),f266(x91981,x91982)),x91984)))+~P102(f332(f137(x91981),f332(f332(f154(f882(x91981,x91982),x91981),f266(x91981,x91982)),x91983))) % 172.83/172.49 [9210]E(f332(f179(x92101,x92102),x92103),f332(f179(x92101,x92102),x92104))+~E(f332(f173(f882(x92101,x92102)),x92103),f332(f173(f882(x92101,x92102)),x92104))+~P102(f332(f137(x92101),f332(f332(f154(f882(x92101,x92102),x92101),f266(x92101,x92102)),x92104)))+~P102(f332(f137(x92101),f332(f332(f154(f882(x92101,x92102),x92101),f266(x92101,x92102)),x92103))) % 172.83/172.49 [9353]~P104(x93531)+~P102(f332(f61(x93531),x93534))+P102(f332(f332(f334(x93531),f651(x93532,x93533,x93534,x93531)),x93534))+P102(f332(f332(f246(x93531),f332(f332(f64(x93531,x93531,f245(x93531)),x93532),x93534)),f332(f332(f245(x93531),x93533),x93532))) % 172.83/172.49 [9354]~P97(x93541)+~P102(f332(f61(x93541),x93544))+P102(f332(f332(f334(x93541),f653(x93542,x93543,x93544,x93541)),x93544))+P102(f332(f332(f246(x93541),f332(f332(f64(x93541,x93541,f113(x93541)),x93542),x93544)),f332(f332(f113(x93541),x93543),x93542))) % 172.83/172.49 [9477]~P97(x94771)+~P102(f332(f61(x94771),x94773))+~P102(f332(f332(f246(x94771),f653(x94772,x94774,x94773,x94771)),x94774))+P102(f332(f332(f246(x94771),f332(f332(f64(x94771,x94771,f113(x94771)),x94772),x94773)),f332(f332(f113(x94771),x94774),x94772))) % 172.83/172.49 [9478]~P104(x94781)+~P102(f332(f61(x94781),x94783))+~P102(f332(f332(f246(x94781),f651(x94782,x94784,x94783,x94781)),x94784))+P102(f332(f332(f246(x94781),f332(f332(f64(x94781,x94781,f245(x94781)),x94782),x94783)),f332(f332(f245(x94781),x94784),x94782))) % 172.83/172.49 [9481]~P102(f332(f332(f247(a1),f2(a1)),x94813))+~P102(f332(f332(f246(a1),f2(a1)),x94814))+~P102(f332(f332(f247(a1),x94814),x94811))+P102(f332(f332(f247(a1),f332(f332(f79(a1),f332(f332(f80(a1),x94811),f44(a1,x94812,x94813))),x94814)),f332(f332(f80(a1),x94811),x94813))) % 172.83/172.49 [9876]E(x98761,x98762)+P102(f332(f332(f334(f882(f877(x98763),f877(x98763))),f332(f332(f267(f877(x98763),f877(x98763)),x98762),x98761)),f147(x98763,x98764)))+P102(f332(f332(f334(f882(f877(x98763),f877(x98763))),f332(f332(f267(f877(x98763),f877(x98763)),x98761),x98762)),f147(x98763,x98764)))+~P102(f332(f332(f334(f882(x98763,x98763)),f332(f332(f267(x98763,x98763),f671(x98761,x98762,x98764,x98763)),f673(x98761,x98762,x98764,x98763))),x98764)) % 172.83/172.49 [9877]E(x98771,x98772)+P102(f332(f332(f334(f882(f877(x98773),f877(x98773))),f332(f332(f267(f877(x98773),f877(x98773)),x98772),x98771)),f147(x98773,x98774)))+P102(f332(f332(f334(f882(f877(x98773),f877(x98773))),f332(f332(f267(f877(x98773),f877(x98773)),x98771),x98772)),f147(x98773,x98774)))+~P102(f332(f332(f334(f882(x98773,x98773)),f332(f332(f267(x98773,x98773),f673(x98771,x98772,x98774,x98773)),f671(x98771,x98772,x98774,x98773))),x98774)) % 172.83/172.49 [7424]~P104(x74241)+~P102(f332(f332(f247(x74241),x74243),x74244))+~P102(f332(f332(f247(x74241),x74242),x74244))+P102(f332(f332(f247(x74241),f332(f332(f245(x74241),x74242),x74243)),x74244)) % 172.83/172.49 [7427]~P97(x74271)+~P102(f332(f332(f246(x74271),x74273),x74274))+~P102(f332(f332(f246(x74271),x74272),x74274))+P102(f332(f332(f246(x74271),f332(f332(f113(x74271),x74272),x74273)),x74274)) % 172.83/172.49 [7430]~P104(x74301)+~P102(f332(f332(f246(x74301),x74303),x74304))+~P102(f332(f332(f246(x74301),x74302),x74304))+P102(f332(f332(f246(x74301),f332(f332(f245(x74301),x74302),x74303)),x74304)) % 172.83/172.49 [7754]~E(x77541,x77543)+E(f139(a876,f332(f302(a876,x77541),x77542)),f332(f332(f151(a876),x77543),x77544))+~E(f139(a876,f332(f302(a876,f332(f332(f79(a876),x77541),f77(a876))),x77542)),x77544)+~P102(f332(f332(f247(a876),x77541),x77542)) % 172.83/172.49 [7765]~P104(x77651)+P102(f332(f332(f247(x77651),x77652),x77653))+P102(f332(f332(f247(x77651),x77654),x77653))+~P102(f332(f332(f247(x77651),f332(f332(f244(x77651),x77654),x77652)),x77653)) % 172.83/172.49 [7766]~P104(x77661)+P102(f332(f332(f246(x77661),x77662),x77663))+P102(f332(f332(f246(x77661),x77664),x77663))+~P102(f332(f332(f246(x77661),f332(f332(f244(x77661),x77664),x77662)),x77663)) % 172.83/172.49 [8050]~P59(x80501)+~P102(f332(f332(f247(x80501),f2(x80501)),x80503))+~P102(f332(f332(f247(x80501),x80502),f332(f332(f290(x80501),x80504),x80503)))+P102(f332(f332(f247(x80501),f332(f332(f80(x80501),x80502),x80503)),x80504)) % 172.83/172.49 [8051]~P60(x80511)+~P102(f332(f332(f247(x80511),f2(x80511)),x80513))+~P102(f332(f332(f247(x80511),x80512),f332(f332(f290(x80511),x80514),x80513)))+P102(f332(f332(f247(x80511),f332(f332(f80(x80511),x80512),x80513)),x80514)) % 172.83/172.49 [8052]~P59(x80521)+~P102(f332(f332(f247(x80521),f2(x80521)),x80523))+~P102(f332(f332(f247(x80521),x80522),f332(f332(f80(x80521),x80524),x80523)))+P102(f332(f332(f247(x80521),f332(f332(f290(x80521),x80522),x80523)),x80524)) % 172.83/172.49 [8054]~P60(x80541)+~P102(f332(f332(f247(x80541),f2(x80541)),x80543))+~P102(f332(f332(f247(x80541),x80542),f332(f332(f80(x80541),x80544),x80543)))+P102(f332(f332(f247(x80541),f332(f332(f290(x80541),x80542),x80543)),x80544)) % 172.83/172.49 [8055]~P59(x80551)+~P102(f332(f332(f247(x80551),f2(x80551)),x80553))+~P102(f332(f332(f246(x80551),x80552),f332(f332(f290(x80551),x80554),x80553)))+P102(f332(f332(f246(x80551),f332(f332(f80(x80551),x80552),x80553)),x80554)) % 172.83/172.49 [8056]~P60(x80561)+~P102(f332(f332(f247(x80561),f2(x80561)),x80563))+~P102(f332(f332(f246(x80561),x80562),f332(f332(f290(x80561),x80564),x80563)))+P102(f332(f332(f246(x80561),f332(f332(f80(x80561),x80562),x80563)),x80564)) % 172.83/172.49 [8057]~P59(x80571)+~P102(f332(f332(f247(x80571),f2(x80571)),x80573))+~P102(f332(f332(f246(x80571),x80572),f332(f332(f80(x80571),x80574),x80573)))+P102(f332(f332(f246(x80571),f332(f332(f290(x80571),x80572),x80573)),x80574)) % 172.83/172.49 [8059]~P60(x80591)+~P102(f332(f332(f247(x80591),f2(x80591)),x80593))+~P102(f332(f332(f246(x80591),x80592),f332(f332(f80(x80591),x80594),x80593)))+P102(f332(f332(f246(x80591),f332(f332(f290(x80591),x80592),x80593)),x80594)) % 172.83/172.49 [8192]~P59(x81921)+~P102(f332(f332(f247(x81921),f2(x81921)),x81924))+P102(f332(f332(f247(x81921),x81922),f332(f332(f80(x81921),x81923),x81924)))+~P102(f332(f332(f247(x81921),f332(f332(f290(x81921),x81922),x81924)),x81923)) % 172.83/172.49 [8193]~P59(x81931)+~P102(f332(f332(f247(x81931),f2(x81931)),x81934))+P102(f332(f332(f247(x81931),x81932),f332(f332(f290(x81931),x81933),x81934)))+~P102(f332(f332(f247(x81931),f332(f332(f80(x81931),x81932),x81934)),x81933)) % 172.83/172.49 [8195]~P60(x81951)+~P102(f332(f332(f247(x81951),f2(x81951)),x81954))+P102(f332(f332(f247(x81951),x81952),f332(f332(f80(x81951),x81953),x81954)))+~P102(f332(f332(f247(x81951),f332(f332(f290(x81951),x81952),x81954)),x81953)) % 172.83/172.49 [8196]~P60(x81961)+~P102(f332(f332(f247(x81961),f2(x81961)),x81964))+P102(f332(f332(f247(x81961),x81962),f332(f332(f290(x81961),x81963),x81964)))+~P102(f332(f332(f247(x81961),f332(f332(f80(x81961),x81962),x81964)),x81963)) % 172.83/172.49 [8197]~P59(x81971)+~P102(f332(f332(f247(x81971),f2(x81971)),x81974))+P102(f332(f332(f246(x81971),x81972),f332(f332(f80(x81971),x81973),x81974)))+~P102(f332(f332(f246(x81971),f332(f332(f290(x81971),x81972),x81974)),x81973)) % 172.83/172.49 [8198]~P59(x81981)+~P102(f332(f332(f247(x81981),f2(x81981)),x81984))+P102(f332(f332(f246(x81981),x81982),f332(f332(f290(x81981),x81983),x81984)))+~P102(f332(f332(f246(x81981),f332(f332(f80(x81981),x81982),x81984)),x81983)) % 172.83/172.49 [8200]~P60(x82001)+~P102(f332(f332(f247(x82001),f2(x82001)),x82004))+P102(f332(f332(f246(x82001),x82002),f332(f332(f80(x82001),x82003),x82004)))+~P102(f332(f332(f246(x82001),f332(f332(f290(x82001),x82002),x82004)),x82003)) % 172.83/172.49 [8201]~P60(x82011)+~P102(f332(f332(f247(x82011),f2(x82011)),x82014))+P102(f332(f332(f246(x82011),x82012),f332(f332(f290(x82011),x82013),x82014)))+~P102(f332(f332(f246(x82011),f332(f332(f80(x82011),x82012),x82014)),x82013)) % 172.83/172.49 [8361]~P60(x83611)+~P102(f332(f332(f247(x83611),x83613),f2(x83611)))+~P102(f332(f332(f247(x83611),f332(f332(f290(x83611),x83614),x83613)),x83612))+P102(f332(f332(f247(x83611),f332(f332(f80(x83611),x83612),x83613)),x83614)) % 172.83/172.49 [8362]~P60(x83621)+~P102(f332(f332(f247(x83621),x83623),f2(x83621)))+~P102(f332(f332(f247(x83621),f332(f332(f80(x83621),x83624),x83623)),x83622))+P102(f332(f332(f247(x83621),f332(f332(f290(x83621),x83622),x83623)),x83624)) % 172.83/172.49 [8363]~P60(x83631)+~P102(f332(f332(f247(x83631),x83633),f2(x83631)))+~P102(f332(f332(f246(x83631),f332(f332(f290(x83631),x83634),x83633)),x83632))+P102(f332(f332(f246(x83631),f332(f332(f80(x83631),x83632),x83633)),x83634)) % 172.83/172.49 [8364]~P60(x83641)+~P102(f332(f332(f247(x83641),x83643),f2(x83641)))+~P102(f332(f332(f246(x83641),f332(f332(f80(x83641),x83644),x83643)),x83642))+P102(f332(f332(f246(x83641),f332(f332(f290(x83641),x83642),x83643)),x83644)) % 172.83/172.49 [8374]~P102(f332(x83741,x83744))+~P102(f332(f332(f247(a876),x83742),f332(f332(f80(a876),x83743),f332(a115,x83744))))+P102(f332(x83741,f332(f332(f38(a876),x83742),x83743)))+~P102(f332(f332(f246(a876),f332(f332(f80(a876),x83743),x83744)),x83742)) % 172.83/172.49 [8588]~P97(x85881)+~P102(f332(f61(x85881),x85884))+~P102(f332(f332(f334(x85881),x85882),x85884))+P102(f332(f332(f246(x85881),f332(f332(f113(x85881),x85882),x85883)),f332(f332(f64(x85881,x85881,f113(x85881)),x85883),x85884))) % 172.83/172.49 [8589]~P104(x85891)+~P102(f332(f61(x85891),x85894))+~P102(f332(f332(f334(x85891),x85892),x85894))+P102(f332(f332(f246(x85891),f332(f332(f245(x85891),x85892),x85893)),f332(f332(f64(x85891,x85891,f245(x85891)),x85893),x85894))) % 172.83/172.49 [8730]~P102(f332(f61(x87301),x87302))+E(f332(f37(x87301),f332(f332(f22(f883(x87301,a871)),x87302),f332(f332(f310(x87301),x87303),x87304))),f332(f332(f22(a876),f332(f37(x87301),f332(f332(f22(f883(x87301,a871)),x87302),x87304))),f77(a876)))+P102(f332(f332(f334(x87301),x87303),x87304))+~P102(f332(f332(f334(x87301),x87303),x87302)) % 172.83/172.49 [8800]E(f332(f332(f79(a1),f405(x88001,x88002,x88003,x88004)),f406(x88001,x88002,x88003,x88004)),x88004)+~P102(f332(f332(f247(a1),f2(a1)),x88003))+~P102(f332(f332(f246(a1),x88004),x88001))+P102(f332(f332(f246(a1),f332(f332(f22(a1),x88004),x88003)),x88001)) % 172.83/172.49 [8801]E(f332(f332(f79(a1),f413(x88011,x88012,x88013,x88014)),f414(x88011,x88012,x88013,x88014)),x88014)+~P102(f332(f332(f247(a1),f2(a1)),x88013))+~P102(f332(f332(f247(a1),x88014),x88011))+P102(f332(f332(f247(a1),f332(f332(f22(a1),x88014),x88013)),x88011)) % 172.83/172.49 [9014]~P102(f332(f332(f247(a1),f2(a1)),x90143))+~P102(f332(f332(f246(a1),x90144),x90141))+P102(f332(f332(f334(a1),f405(x90141,x90142,x90143,x90144)),x90142))+P102(f332(f332(f246(a1),f332(f332(f22(a1),x90144),x90143)),x90141)) % 172.83/172.49 [9015]~P102(f332(f332(f247(a1),f2(a1)),x90153))+~P102(f332(f332(f247(a1),x90154),x90151))+P102(f332(f332(f334(a1),f413(x90151,x90152,x90153,x90154)),x90152))+P102(f332(f332(f247(a1),f332(f332(f22(a1),x90154),x90153)),x90151)) % 172.83/172.49 [9100]~P102(f332(f332(f247(a1),f2(a1)),x91002))+~P102(f332(f332(f247(a1),x91001),x91003))+P102(f332(f332(f334(a1),f414(x91003,x91004,x91002,x91001)),f303(a1,f77(a1),x91002)))+P102(f332(f332(f247(a1),f332(f332(f22(a1),x91001),x91002)),x91003)) % 172.83/172.49 [9101]~P102(f332(f332(f247(a1),f2(a1)),x91012))+~P102(f332(f332(f246(a1),x91011),x91013))+P102(f332(f332(f334(a1),f406(x91013,x91014,x91012,x91011)),f303(a1,f77(a1),x91012)))+P102(f332(f332(f246(a1),f332(f332(f22(a1),x91011),x91012)),x91013)) % 172.83/172.49 [9117]~P102(f332(f332(f247(a1),f2(a1)),x91173))+~P102(f332(f332(f246(a1),f2(a1)),x91174))+~P102(f332(f332(f247(a1),x91174),x91171))+P102(f332(f332(f246(a1),f2(a1)),f332(f332(f79(a1),f332(f332(f80(a1),x91171),f44(a1,x91172,x91173))),x91174))) % 172.83/172.49 [9181]~P98(x91811)+~P102(f332(f61(x91811),x91814))+~P102(f332(f332(f246(x91811),x91812),f652(x91813,x91812,x91814,x91811)))+P102(f332(f332(f246(x91811),f332(f332(f104(x91811),x91812),x91813)),f332(f332(f64(x91811,x91811,f104(x91811)),x91813),x91814))) % 172.83/172.49 [9182]~P104(x91821)+~P102(f332(f61(x91821),x91824))+~P102(f332(f332(f246(x91821),x91822),f650(x91823,x91822,x91824,x91821)))+P102(f332(f332(f246(x91821),f332(f332(f244(x91821),x91822),x91823)),f332(f332(f64(x91821,x91821,f244(x91821)),x91823),x91824))) % 172.83/172.49 [9197]~P102(f332(f332(f246(a1),x91974),f2(a1)))+~P102(f332(f332(f247(a1),f2(a1)),x91972))+~P102(f332(f332(f247(a1),x91971),x91974))+P102(f332(f332(f247(a1),f332(f332(f80(a1),x91971),x91972)),f332(f332(f79(a1),f332(f332(f80(a1),x91971),f44(a1,x91973,x91972))),x91974))) % 172.83/172.49 [9219]P102(f332(f61(x92191),x92192))+~P102(f332(f61(x92191),x92193))+~P102(f332(f332(f334(f883(x92191,a871)),x92192),f332(f332(f60(x92191),x92193),x92194)))+~P102(f332(f332(f246(f883(f882(x92191,x92191),a871)),x92194),f332(f332(f269(x92191,x92191),x92193),f332(f16(f883(x92191,a871),x92191),x92193)))) % 172.83/172.49 [9247]~P104(x92471)+~P102(f332(f61(x92471),x92474))+P102(f332(f332(f334(x92471),f650(x92472,x92473,x92474,x92471)),x92474))+P102(f332(f332(f246(x92471),f332(f332(f244(x92471),x92473),x92472)),f332(f332(f64(x92471,x92471,f244(x92471)),x92472),x92474))) % 172.83/172.49 [9248]~P98(x92481)+~P102(f332(f61(x92481),x92484))+P102(f332(f332(f334(x92481),f652(x92482,x92483,x92484,x92481)),x92484))+P102(f332(f332(f246(x92481),f332(f332(f104(x92481),x92483),x92482)),f332(f332(f64(x92481,x92481,f104(x92481)),x92482),x92484))) % 172.83/172.49 [9643]~P102(f332(f61(x96432),x96434))+~P102(f332(f61(x96431),x96433))+~P102(f332(f332(f246(a876),f332(f37(x96432),x96434)),f332(f37(x96431),x96433)))+P102(f332(f332(f246(f883(x96431,a871)),f332(f311(x96432,x96431,f522(x96433,x96431,x96434,x96432)),x96434)),x96433)) % 172.83/172.49 [9294]~P102(f332(f332(f334(x92941),x92942),x92944))+P102(f332(f332(f334(x92941),x92942),x92943))+~P102(f332(f332(f247(f883(x92941,a871)),x92944),f332(f332(f310(x92941),x92942),x92943)))+P102(f332(f332(f247(f883(x92941,a871)),f332(f332(f22(f883(x92941,a871)),x92944),f332(f332(f310(x92941),x92942),f195(f883(x92941,a871))))),x92943)) % 172.83/172.49 [9455]~P102(f332(f332(f334(x94551),x94552),x94554))+P102(f332(f332(f334(x94551),x94552),x94553))+P102(f332(f332(f247(f883(x94551,a871)),x94554),f332(f332(f310(x94551),x94552),x94553)))+~P102(f332(f332(f247(f883(x94551,a871)),f332(f332(f22(f883(x94551,a871)),x94554),f332(f332(f310(x94551),x94552),f195(f883(x94551,a871))))),x94553)) % 172.83/172.49 [9484]P102(f332(f332(f334(x94841),x94842),x94843))+~P102(f332(f332(f246(f883(x94841,a871)),x94844),x94843))+P102(f332(f332(f247(f883(x94841,a871)),x94844),f332(f332(f310(x94841),x94842),x94843)))+~P102(f332(f332(f247(f883(x94841,a871)),f332(f332(f22(f883(x94841,a871)),x94844),f332(f332(f310(x94841),x94842),f195(f883(x94841,a871))))),x94843)) % 172.83/172.49 [9489]~P102(f332(f332(f334(x94891),x94893),x94892))+~P102(f332(f332(f247(f883(x94891,a871)),x94892),x94894))+P102(f332(f332(f247(f883(x94891,a871)),x94892),f332(f332(f310(x94891),x94893),x94894)))+~P102(f332(f332(f247(f883(x94891,a871)),f332(f332(f22(f883(x94891,a871)),x94892),f332(f332(f310(x94891),x94893),f195(f883(x94891,a871))))),x94894)) % 172.83/172.49 [9502]~P102(f332(f332(f246(f883(x95021,a871)),x95022),x95024))+~P102(f332(f332(f247(f883(x95021,a871)),x95022),x95024))+P102(f332(f332(f247(f883(x95021,a871)),x95022),f332(f332(f310(x95021),x95023),x95024)))+~P102(f332(f332(f247(f883(x95021,a871)),f332(f332(f22(f883(x95021,a871)),x95022),f332(f332(f310(x95021),x95023),f195(f883(x95021,a871))))),x95024)) % 172.83/172.49 [9546]~P105(x95462)+~P56(x95461)+~P102(f332(f332(f246(f883(x95461,x95462)),x95463),x95464))+P102(f332(f58(x95461),f332(f332(f18(x95461,x95462,a871),f332(f332(f8(x95462,f883(x95462,a871),x95461),f246(x95462)),x95463)),x95464))) % 172.83/172.49 [9690]~P105(x96902)+~P56(x96901)+P102(f332(f332(f246(f883(x96901,x96902)),x96903),x96904))+~P102(f332(f58(x96901),f332(f332(f18(x96901,x96902,a871),f332(f332(f8(x96902,f883(x96902,a871),x96901),f246(x96902)),x96903)),x96904))) % 172.83/172.49 [9860]E(f332(f332(f165(x98601),f332(f332(f165(f877(x98601)),f181(x98601,x98602)),x98603)),x98604),f332(f332(f165(x98601),f332(f332(f165(f877(x98601)),x98602),x98604)),x98603))+~P102(f332(f332(f247(a876),x98603),f332(f196(f877(f877(x98601))),f181(x98601,x98602))))+~P29(a876,f332(f169(a876),f332(f332(f154(f877(x98601),a876),f196(f877(x98601))),x98602)))+~P102(f332(f332(f247(a876),x98604),f332(f196(f877(f877(x98601))),f332(f136(f877(x98601),f332(f332(f8(a876,a871,f877(x98601)),f332(f247(a876),x98603)),f196(f877(x98601)))),x98602)))) % 172.83/172.49 [9889]~P102(f332(f332(f334(f882(a876,a876)),x98894),x98891))+~P102(f332(f332(f334(f882(f882(a876,a876),f882(a876,a876))),f332(f332(f267(f882(a876,a876),f882(a876,a876)),x98894),x98892)),a34))+~P102(f332(f332(f334(f882(f883(f882(a876,a876),a871),f883(f882(a876,a876),a871))),f332(f332(f267(f883(f882(a876,a876),a871),f883(f882(a876,a876),a871)),x98891),x98893)),a35))+P102(f332(f332(f334(f882(f883(f882(a876,a876),a871),f883(f882(a876,a876),a871))),f332(f332(f267(f883(f882(a876,a876),a871),f883(f882(a876,a876),a871)),x98891),f332(f332(f310(f882(a876,a876)),x98892),x98893))),a35)) % 172.83/172.49 [9890]~P102(f332(f332(f334(f882(a876,a876)),x98904),x98901))+~P102(f332(f332(f334(f882(f882(a876,a876),f882(a876,a876))),f332(f332(f267(f882(a876,a876),f882(a876,a876)),x98904),x98902)),a69))+~P102(f332(f332(f334(f882(f883(f882(a876,a876),a871),f883(f882(a876,a876),a871))),f332(f332(f267(f883(f882(a876,a876),a871),f883(f882(a876,a876),a871)),x98901),x98903)),a70))+P102(f332(f332(f334(f882(f883(f882(a876,a876),a871),f883(f882(a876,a876),a871))),f332(f332(f267(f883(f882(a876,a876),a871),f883(f882(a876,a876),a871)),x98901),f332(f332(f310(f882(a876,a876)),x98902),x98903))),a70)) % 172.83/172.49 [9774]~P105(x97742)+~P56(x97741)+~P102(f332(f332(f247(f883(x97741,x97742)),x97743),x97744))+P102(f332(f57(x97741),f332(f332(f8(a871,a871,x97741),a327),f332(f332(f18(x97741,x97742,a871),f332(f332(f8(x97742,f883(x97742,a871),x97741),a329),x97743)),x97744)))) % 172.83/172.49 [9903]~P102(f332(f332(f334(f882(a876,a876)),x99034),x99033))+~P102(f332(f332(f334(f882(f882(a876,a876),f882(a876,a876))),f332(f332(f267(f882(a876,a876),f882(a876,a876)),x99031),x99034)),a69))+~P102(f332(f332(f334(f882(f883(f882(a876,a876),a871),f883(f882(a876,a876),a871))),f332(f332(f267(f883(f882(a876,a876),a871),f883(f882(a876,a876),a871)),x99032),x99033)),a68))+P102(f332(f332(f334(f882(f883(f882(a876,a876),a871),f883(f882(a876,a876),a871))),f332(f332(f267(f883(f882(a876,a876),a871),f883(f882(a876,a876),a871)),f332(f332(f310(f882(a876,a876)),x99031),x99032)),x99033)),a68)) % 172.83/172.49 [9904]~P102(f332(f332(f334(f882(a876,a876)),x99044),x99043))+~P102(f332(f332(f334(f882(f882(a876,a876),f882(a876,a876))),f332(f332(f267(f882(a876,a876),f882(a876,a876)),x99041),x99044)),a34))+~P102(f332(f332(f334(f882(f883(f882(a876,a876),a871),f883(f882(a876,a876),a871))),f332(f332(f267(f883(f882(a876,a876),a871),f883(f882(a876,a876),a871)),x99042),x99043)),a36))+P102(f332(f332(f334(f882(f883(f882(a876,a876),a871),f883(f882(a876,a876),a871))),f332(f332(f267(f883(f882(a876,a876),a871),f883(f882(a876,a876),a871)),f332(f332(f310(f882(a876,a876)),x99041),x99042)),x99043)),a36)) % 172.83/172.49 [6026]~P2(x60264,x60261)+~P102(f332(f332(x60261,x60262),x60265))+P102(f332(f332(x60261,x60262),x60263))+~P102(f332(f332(x60261,x60265),x60263)) % 172.83/172.49 [5286]~P66(x52865)+E(x52861,x52862)+~E(x52863,x52864)+~E(f332(f332(f22(x52865),x52863),x52864),f332(f332(f22(x52865),x52861),x52862)) % 172.83/172.49 [6134]~P12(x61345,x61341,x61343)+E(f332(f332(x61341,x61342),f332(x61343,x61344)),f332(x61343,x61344))+~P102(f332(f61(x61345),x61344))+~P102(f332(f332(f334(x61345),x61342),x61344)) % 172.83/172.49 [6323]~P79(x63231)+~E(f332(f332(f22(x63231),x63234),x63235),f332(f332(f22(x63231),x63232),x63233))+~P102(f332(f332(f247(x63231),x63234),x63235))+P102(f332(f332(f247(x63231),x63232),x63233)) % 172.83/172.49 [6325]~P79(x63251)+~E(f332(f332(f22(x63251),x63254),x63255),f332(f332(f22(x63251),x63252),x63253))+~P102(f332(f332(f246(x63251),x63254),x63255))+P102(f332(f332(f246(x63251),x63252),x63253)) % 172.83/172.49 [7285]~E(x72852,f332(f332(f151(x72851),x72854),x72855))+P102(f332(f332(f334(f877(x72851)),x72852),f161(x72851,x72853)))+~P102(f332(f332(f334(f877(x72851)),x72855),f161(x72851,x72853)))+~P102(f332(f332(f334(x72851),x72854),x72853)) % 172.83/172.49 [7705]~E(f332(f196(f877(x77051)),x77053),f332(f196(f877(x77052)),x77054))+~E(f332(f332(f154(f882(x77051,x77052),x77052),f270(x77051,x77052)),x77055),x77054)+~E(f332(f332(f154(f882(x77051,x77052),x77051),f266(x77051,x77052)),x77055),x77053)+E(f332(f332(f183(x77051,x77052),x77053),x77054),x77055) % 172.83/172.49 [8047]~P105(x80471)+P102(f332(f332(f247(f883(x80471,a871)),f303(x80471,x80472,x80473)),f303(x80471,x80474,x80475)))+~P102(f332(f332(f246(x80471),x80474),x80475))+P102(f332(f332(f246(x80471),x80472),x80473)) % 172.83/172.49 [8143]~P105(x81431)+P102(f332(f332(f246(f883(x81431,a871)),f303(x81431,x81432,x81433)),f303(x81431,x81434,x81435)))+~P102(f332(f332(f246(x81431),x81433),x81435))+~P102(f332(f332(f246(x81431),x81434),x81432)) % 172.83/172.49 [8269]~P104(x82691)+P102(f332(f332(f246(x82691),x82692),x82693))+P102(f332(f332(f246(x82691),x82694),x82693))+~P102(f332(f332(f246(f883(x82691,a871)),f332(f302(x82691,x82693),x82692)),f332(f302(x82691,x82694),x82695))) % 172.83/172.49 [8270]~P104(x82701)+P102(f332(f332(f246(x82701),x82702),x82703))+P102(f332(f332(f246(x82701),x82702),x82704))+~P102(f332(f332(f246(f883(x82701,a871)),f332(f302(x82701,x82703),x82702)),f332(f302(x82701,x82705),x82704))) % 172.83/172.49 [8510]~P105(x85101)+~P102(f332(f332(f247(f883(x85101,a871)),f303(x85101,x85104,x85102)),f303(x85101,x85105,x85103)))+P102(f332(f332(f246(x85101),x85102),x85103))+~P102(f332(f332(f246(x85101),x85104),x85102)) % 172.83/172.49 [8511]~P105(x85111)+~P102(f332(f332(f246(f883(x85111,a871)),f303(x85111,x85114,x85112)),f303(x85111,x85115,x85113)))+P102(f332(f332(f246(x85111),x85112),x85113))+~P102(f332(f332(f246(x85111),x85114),x85112)) % 172.83/172.49 [8512]~P105(x85121)+~P102(f332(f332(f247(f883(x85121,a871)),f303(x85121,x85123,x85124)),f303(x85121,x85122,x85125)))+P102(f332(f332(f246(x85121),x85122),x85123))+~P102(f332(f332(f246(x85121),x85123),x85124)) % 172.83/172.49 [8513]~P105(x85131)+~P102(f332(f332(f246(f883(x85131,a871)),f303(x85131,x85133,x85134)),f303(x85131,x85132,x85135)))+P102(f332(f332(f246(x85131),x85132),x85133))+~P102(f332(f332(f246(x85131),x85133),x85134)) % 172.83/172.49 [6025]~P12(x60252,x60255,x60253)+E(x60251,f195(f883(x60252,a871)))+~P102(f332(f61(x60252),x60251))+E(f332(x60253,f332(f332(f310(x60252),x60254),x60251)),f332(f332(x60255,x60254),f332(x60253,x60251))) % 172.83/172.49 [6787]~E(x67871,x67872)+~E(f332(f332(f104(f883(x67873,a871)),x67874),x67875),f195(f883(x67873,a871)))+~P102(f332(f332(f334(x67873),x67872),x67875))+~P102(f332(f332(f334(x67873),x67871),x67874)) % 172.83/172.49 [6869]~P13(x68692,x68695,x68691)+~P102(f332(f61(x68692),x68694))+E(f332(x68691,f332(f332(f310(x68692),x68693),x68694)),f332(f332(f64(x68692,x68692,x68695),x68693),x68694))+P102(f332(f332(f334(x68692),x68693),x68694)) % 172.83/172.49 [6936]~P71(x69362)+~P102(f332(f61(x69361),x69365))+E(f332(f332(f6(x69361,x69362),x69363),f332(f332(f310(x69361),x69364),x69365)),f332(f332(f79(x69362),f332(x69363,x69364)),f332(f332(f6(x69361,x69362),x69363),x69365)))+P102(f332(f332(f334(x69361),x69364),x69365)) % 172.83/172.49 [6938]~P67(x69382)+~P102(f332(f61(x69381),x69385))+E(f332(f332(f9(x69381,x69382),x69383),f332(f332(f310(x69381),x69384),x69385)),f332(f332(f80(x69382),f332(x69383,x69384)),f332(f332(f9(x69381,x69382),x69383),x69385)))+P102(f332(f332(f334(x69381),x69384),x69385)) % 172.83/172.50 [7442]~P13(x74422,x74425,x74421)+~P102(f332(f61(x74422),x74424))+E(f332(x74421,f332(f332(f310(x74422),x74423),x74424)),x74423)+~E(f332(f332(f22(f883(x74422,a871)),x74424),f332(f332(f310(x74422),x74423),f195(f883(x74422,a871)))),f195(f883(x74422,a871))) % 172.83/172.50 [7758]~P102(f332(x77581,x77583))+~P102(f332(f332(f201(x77582),x77583),x77585))+~P102(f332(f332(f201(f31(x77581,x77582)),x77585),x77584))+P102(f332(f332(f201(f31(x77581,x77582)),x77583),x77584)) % 172.83/172.50 [7812]~P82(x78121)+~P102(f332(f332(f247(x78121),x78123),x78125))+~P102(f332(f332(f247(x78121),x78122),x78124))+P102(f332(f332(f247(x78121),f332(f332(f79(x78121),x78122),x78123)),f332(f332(f79(x78121),x78124),x78125))) % 172.83/172.50 [7813]~P82(x78131)+~P102(f332(f332(f246(x78131),x78132),x78134))+~P102(f332(f332(f247(x78131),x78133),x78135))+P102(f332(f332(f247(x78131),f332(f332(f79(x78131),x78132),x78133)),f332(f332(f79(x78131),x78134),x78135))) % 172.83/172.50 [7814]~P82(x78141)+~P102(f332(f332(f246(x78141),x78143),x78145))+~P102(f332(f332(f247(x78141),x78142),x78144))+P102(f332(f332(f247(x78141),f332(f332(f79(x78141),x78142),x78143)),f332(f332(f79(x78141),x78144),x78145))) % 172.83/172.50 [7815]~P97(x78151)+~P102(f332(f332(f246(x78151),x78153),x78155))+~P102(f332(f332(f246(x78151),x78152),x78154))+P102(f332(f332(f246(x78151),f332(f332(f113(x78151),x78152),x78153)),f332(f332(f113(x78151),x78154),x78155))) % 172.83/172.50 [7816]~P98(x78161)+~P102(f332(f332(f246(x78161),x78163),x78165))+~P102(f332(f332(f246(x78161),x78162),x78164))+P102(f332(f332(f246(x78161),f332(f332(f104(x78161),x78162),x78163)),f332(f332(f104(x78161),x78164),x78165))) % 172.83/172.50 [7817]~P80(x78171)+~P102(f332(f332(f246(x78171),x78173),x78175))+~P102(f332(f332(f246(x78171),x78172),x78174))+P102(f332(f332(f246(x78171),f332(f332(f79(x78171),x78172),x78173)),f332(f332(f79(x78171),x78174),x78175))) % 172.83/172.50 [7818]~P104(x78181)+~P102(f332(f332(f246(x78181),x78183),x78185))+~P102(f332(f332(f246(x78181),x78182),x78184))+P102(f332(f332(f246(x78181),f332(f332(f244(x78181),x78182),x78183)),f332(f332(f244(x78181),x78184),x78185))) % 172.83/172.50 [7819]~P104(x78191)+~P102(f332(f332(f246(x78191),x78193),x78195))+~P102(f332(f332(f246(x78191),x78192),x78194))+P102(f332(f332(f246(x78191),f332(f332(f245(x78191),x78192),x78193)),f332(f332(f245(x78191),x78194),x78195))) % 172.83/172.50 [7956]~P138(x79565)+E(x79561,x79562)+E(x79563,x79564)+~E(f332(f332(f79(x79565),f332(f332(f80(x79565),x79563),x79561)),f332(f332(f80(x79565),x79564),x79562)),f332(f332(f79(x79565),f332(f332(f80(x79565),x79563),x79562)),f332(f332(f80(x79565),x79564),x79561))) % 172.83/172.50 [8098]P30(x80981,x80982,x80983)+~P22(x80981,x80984,x80985)+~P30(x80981,x80982,f570(x80985,x80984,x80981,x80982))+~P102(f332(f332(f334(f875(x80981)),x80983),x80985)) % 172.83/172.50 [8167]~P104(x81674)+~P102(f332(f137(x81671),x81673))+P102(f332(f332(f334(x81671),x81672),f332(f173(x81671),x81673)))+P102(f332(f137(x81671),f332(f332(f148(x81671,x81674,x81675),x81672),x81673))) % 172.83/172.50 [8315]~P66(x83151)+E(f332(f332(f22(x83151),f332(f332(f6(a876,x83151),x83152),f332(f302(a876,x83153),x83154))),f332(f332(f6(a876,x83151),x83152),f332(f302(a876,x83153),x83155))),f332(f332(f6(a876,x83151),x83152),f332(f302(a876,x83155),x83154)))+~P102(f332(f332(f246(a876),x83155),x83154))+~P102(f332(f332(f246(a876),x83153),x83155)) % 172.83/172.50 [8316]~P71(x83161)+E(f332(f332(f79(x83161),f332(f332(f6(a876,x83161),x83162),f332(f302(a876,x83163),x83164))),f332(f332(f6(a876,x83161),x83162),f332(f302(a876,x83164),x83165))),f332(f332(f6(a876,x83161),x83162),f332(f302(a876,x83163),x83165)))+~P102(f332(f332(f246(a876),x83164),x83165))+~P102(f332(f332(f246(a876),x83163),x83164)) % 172.83/172.50 [8645]~P58(x86452)+E(x86451,f2(x86452))+E(x86453,f2(x86452))+E(f332(f332(f290(x86452),f332(f332(f22(x86452),f332(f332(f80(x86452),x86454),x86451)),f332(f332(f80(x86452),x86455),x86453))),f332(f332(f80(x86452),x86453),x86451)),f332(f332(f22(x86452),f332(f332(f290(x86452),x86454),x86453)),f332(f332(f290(x86452),x86455),x86451))) % 172.83/172.50 [8646]~P58(x86462)+E(x86461,f2(x86462))+E(x86463,f2(x86462))+E(f332(f332(f290(x86462),f332(f332(f79(x86462),f332(f332(f80(x86462),x86464),x86461)),f332(f332(f80(x86462),x86465),x86463))),f332(f332(f80(x86462),x86463),x86461)),f332(f332(f79(x86462),f332(f332(f290(x86462),x86464),x86463)),f332(f332(f290(x86462),x86465),x86461))) % 172.83/172.50 [8655]~E(x86552,f332(x86553,x86551))+E(x86551,f518(x86552,x86553,x86554,x86555))+~P20(x86555,x86554,x86553,f255(f883(x86555,a871)))+~P102(f332(f332(f334(x86554),x86552),f332(f311(x86555,x86554,x86553),f255(f883(x86555,a871))))) % 172.83/172.50 [8850]~P113(x88501)+~P102(f332(f332(f247(x88501),f332(f74(x88501),x88502)),x88504))+P102(f332(f332(f247(x88501),f332(f332(f80(x88501),f332(f74(x88501),x88502)),f332(f74(x88501),x88503))),f332(f332(f80(x88501),x88504),x88505)))+~P102(f332(f332(f247(x88501),f332(f74(x88501),x88503)),x88505)) % 172.83/172.50 [8867]~P22(x88671,x88675,x88674)+P30(x88671,x88672,x88673)+P102(f332(f332(f334(f875(x88671)),f570(x88674,x88675,x88671,x88672)),x88675))+~P102(f332(f332(f334(f875(x88671)),x88673),x88674)) % 172.83/172.50 [8974]~P20(x89741,x89743,x89745,x89742)+~P102(f332(f61(x89743),x89744))+P102(f332(f332(f246(a876),f332(f37(x89741),x89742)),f332(f37(x89743),x89744)))+~P102(f332(f332(f246(f883(x89743,a871)),f332(f311(x89741,x89743,x89745),x89742)),x89744)) % 172.83/172.50 [9043]~P71(x90432)+~P20(x90431,x90431,x90434,x90435)+~P102(f332(f61(x90431),x90435))+E(f332(f332(f6(x90431,x90432),f332(f72(x90431,x90432,x90431,x90433),x90434)),x90435),f332(f332(f6(x90431,x90432),x90433),f332(f311(x90431,x90431,x90434),x90435))) % 172.83/172.50 [9044]~P67(x90442)+~P20(x90441,x90441,x90444,x90445)+~P102(f332(f61(x90441),x90445))+E(f332(f332(f9(x90441,x90442),f332(f72(x90441,x90442,x90441,x90443),x90444)),x90445),f332(f332(f9(x90441,x90442),x90443),f332(f311(x90441,x90441,x90444),x90445))) % 172.83/172.50 [9158]~P38(x91581,x91582)+~P102(f332(f332(f334(x91581),x91583),x91584))+~P102(f332(f332(f334(x91581),x91585),x91584))+~P102(f332(f332(f334(f882(x91581,x91581)),f332(f332(f267(x91581,x91581),x91585),f643(x91582,x91581,x91584))),x91582)) % 172.83/172.50 [9196]~P20(x91962,x91963,x91965,x91961)+E(x91961,f195(f883(x91962,a871)))+E(f332(f311(x91963,x91962,f520(x91964,x91963,x91962,x91961)),x91964),x91961)+~P102(f332(f332(f246(f883(x91963,a871)),f332(f311(x91962,x91963,x91965),x91961)),x91964)) % 172.83/172.50 [9672]~P104(x96725)+~P27(x96725)+P102(f332(f332(f334(x96721),f443(x96722,x96723,x96721,x96724,x96725)),x96723))+~P102(f332(f332(f247(x96725),x96724),f332(f332(f41(x96721,x96725),x96723),x96722))) % 172.83/172.50 [9677]~P104(x96771)+~P27(x96771)+P102(f332(f332(f247(x96771),x96772),f332(x96773,f443(x96773,x96774,x96775,x96772,x96771))))+~P102(f332(f332(f247(x96771),x96772),f332(f332(f41(x96775,x96771),x96774),x96773))) % 172.83/172.50 [9754]~P64(x97541)+~P102(f332(f66(x97541,x97541,f80(x97541),x97542,x97543),x97545))+P102(f332(f332(f334(x97541),x97542),x97543))+P102(f332(f66(x97541,x97541,f80(x97541),x97544,f332(f332(f310(x97541),x97542),x97543)),f332(f332(f80(x97541),x97544),x97545))) % 172.83/172.50 [9971]~P71(x99712)+~P102(f332(f61(x99711),x99715))+E(f332(f332(f6(x99711,x99712),f332(f332(f7(x99711,x99712,x99712),f332(f332(f18(x99711,x99712,f883(x99712,x99712)),f332(f332(f8(a871,f883(x99712,f883(x99712,x99712)),x99711),f99(x99712)),f332(a329,x99713))),x99714)),f2(x99712))),x99715),f2(x99712))+P102(f332(f332(f334(x99711),x99713),x99715)) % 172.83/172.50 [9972]~P67(x99722)+~P102(f332(f61(x99721),x99725))+E(f332(f332(f9(x99721,x99722),f332(f332(f7(x99721,x99722,x99722),f332(f332(f18(x99721,x99722,f883(x99722,x99722)),f332(f332(f8(a871,f883(x99722,f883(x99722,x99722)),x99721),f99(x99722)),f332(a329,x99723))),x99724)),f77(x99722))),x99725),f77(x99722))+P102(f332(f332(f334(x99721),x99723),x99725)) % 172.83/172.50 [9973]~P71(x99732)+~P102(f332(f61(x99731),x99735))+E(f332(f332(f6(x99731,x99732),f332(f332(f7(x99731,x99732,x99732),f332(f332(f18(x99731,x99732,f883(x99732,x99732)),f332(f332(f8(a871,f883(x99732,f883(x99732,x99732)),x99731),f99(x99732)),f332(a329,x99733))),x99734)),f2(x99732))),x99735),f332(x99734,x99733))+~P102(f332(f332(f334(x99731),x99733),x99735)) % 172.83/172.50 [9974]~P67(x99742)+~P102(f332(f61(x99741),x99745))+E(f332(f332(f9(x99741,x99742),f332(f332(f7(x99741,x99742,x99742),f332(f332(f18(x99741,x99742,f883(x99742,x99742)),f332(f332(f8(a871,f883(x99742,f883(x99742,x99742)),x99741),f99(x99742)),f332(a329,x99743))),x99744)),f77(x99742))),x99745),f332(x99744,x99743))+~P102(f332(f332(f334(x99741),x99743),x99745)) % 172.83/172.50 [10029]~P71(x100292)+~P102(f332(f61(x100291),x100295))+E(f332(f332(f6(x100291,x100292),f332(f332(f7(x100291,x100292,x100292),f332(f332(f18(x100291,x100292,f883(x100292,x100292)),f332(f332(f8(a871,f883(x100292,f883(x100292,x100292)),x100291),f99(x100292)),f332(f332(f7(x100291,x100291,a871),a329),x100293))),x100294)),f2(x100292))),x100295),f2(x100292))+P102(f332(f332(f334(x100291),x100293),x100295)) % 172.83/172.50 [10030]~P67(x100302)+~P102(f332(f61(x100301),x100305))+E(f332(f332(f9(x100301,x100302),f332(f332(f7(x100301,x100302,x100302),f332(f332(f18(x100301,x100302,f883(x100302,x100302)),f332(f332(f8(a871,f883(x100302,f883(x100302,x100302)),x100301),f99(x100302)),f332(f332(f7(x100301,x100301,a871),a329),x100303))),x100304)),f77(x100302))),x100305),f77(x100302))+P102(f332(f332(f334(x100301),x100303),x100305)) % 172.83/172.50 [10032]~P71(x100322)+~P102(f332(f61(x100321),x100325))+E(f332(f332(f6(x100321,x100322),f332(f332(f7(x100321,x100322,x100322),f332(f332(f18(x100321,x100322,f883(x100322,x100322)),f332(f332(f8(a871,f883(x100322,f883(x100322,x100322)),x100321),f99(x100322)),f332(f332(f7(x100321,x100321,a871),a329),x100323))),x100324)),f2(x100322))),x100325),f332(x100324,x100323))+~P102(f332(f332(f334(x100321),x100323),x100325)) % 172.83/172.50 [10033]~P67(x100332)+~P102(f332(f61(x100331),x100335))+E(f332(f332(f9(x100331,x100332),f332(f332(f7(x100331,x100332,x100332),f332(f332(f18(x100331,x100332,f883(x100332,x100332)),f332(f332(f8(a871,f883(x100332,f883(x100332,x100332)),x100331),f99(x100332)),f332(f332(f7(x100331,x100331,a871),a329),x100333))),x100334)),f77(x100332))),x100335),f332(x100334,x100333))+~P102(f332(f332(f334(x100331),x100333),x100335)) % 172.83/172.50 [7811]~P66(x78112)+~P102(f332(f61(x78111),x78114))+E(f332(f332(f6(x78111,x78112),x78113),f332(f332(f22(f883(x78111,a871)),x78114),f332(f332(f310(x78111),x78115),f195(f883(x78111,a871))))),f332(f332(f6(x78111,x78112),x78113),x78114))+P102(f332(f332(f334(x78111),x78115),x78114)) % 172.83/172.50 [8321]~P123(x83212)+~P102(f332(f61(x83211),x83214))+E(f332(f332(f6(x83211,x83212),x83213),f332(f332(f22(f883(x83211,a871)),x83214),f332(f332(f310(x83211),x83215),f195(f883(x83211,a871))))),f332(f332(f22(x83212),f332(f332(f6(x83211,x83212),x83213),x83214)),f332(x83213,x83215)))+~P102(f332(f332(f334(x83211),x83215),x83214)) % 172.83/172.50 [8322]~P66(x83222)+~P102(f332(f61(x83221),x83224))+E(f332(f332(f6(x83221,x83222),x83223),f332(f332(f22(f883(x83221,a871)),x83224),f332(f332(f310(x83221),x83225),f195(f883(x83221,a871))))),f332(f332(f22(x83222),f332(f332(f6(x83221,x83222),x83223),x83224)),f332(x83223,x83225)))+~P102(f332(f332(f334(x83221),x83225),x83224)) % 172.83/172.50 [8353]~P66(x83531)+~P102(f332(f61(x83532),x83534))+E(f332(f332(f22(x83531),f332(f332(f6(x83532,x83531),x83533),x83534)),f332(f332(f6(x83532,x83531),x83533),x83535)),f332(f332(f6(x83532,x83531),x83533),f332(f332(f22(f883(x83532,a871)),x83534),x83535)))+~P102(f332(f332(f246(f883(x83532,a871)),x83535),x83534)) % 172.83/172.50 [8373]P102(f332(f61(x83731),f332(x83732,x83733)))+~P102(f332(f61(x83734),x83735))+~P102(f332(f332(f334(x83734),x83733),x83735))+~P102(f332(f61(x83731),f332(f332(f41(x83734,f883(x83731,a871)),x83735),x83732))) % 172.83/172.50 [8813]~P3(x88131,x88135,x88134)+~E(f332(f286(x88131,x88131,x88134),f332(f332(f310(x88131),x88132),f195(f883(x88131,a871)))),f332(f286(x88131,x88131,x88134),f332(f332(f310(x88131),x88133),f195(f883(x88131,a871)))))+~P102(f332(f332(f334(x88131),x88133),x88135))+P102(f332(f332(f334(f882(x88131,x88131)),f332(f332(f267(x88131,x88131),x88132),x88133)),x88134)) % 172.83/172.50 [9115]~P102(f332(x91151,x91155))+P102(f332(x91151,f418(x91151,x91152,x91153,x91154)))+P102(f332(x91151,f409(x91151,x91152,x91153,x91154)))+~P102(f332(f332(f334(x91154),x91155),f332(f332(f113(f883(x91154,a871)),x91153),x91152))) % 172.83/172.50 [9299]~P102(f332(x92991,x92995))+P102(f332(x92991,f409(x92991,x92992,x92993,x92994)))+P102(f332(f332(f334(x92994),f418(x92991,x92992,x92993,x92994)),x92992))+~P102(f332(f332(f334(x92994),x92995),f332(f332(f113(f883(x92994,a871)),x92993),x92992))) % 172.83/172.50 [9300]~P102(f332(x93001,x93005))+P102(f332(x93001,f418(x93001,x93002,x93003,x93004)))+P102(f332(f332(f334(x93004),f409(x93001,x93002,x93003,x93004)),x93003))+~P102(f332(f332(f334(x93004),x93005),f332(f332(f113(f883(x93004,a871)),x93003),x93002))) % 172.83/172.50 [9306]P102(f332(x93061,x93062))+~P102(f332(x93061,f459(x93061,x93063,x93064,x93065)))+~P102(f332(x93061,f447(x93061,x93063,x93064,x93065)))+~P102(f332(f332(f334(x93065),x93062),f332(f332(f113(f883(x93065,a871)),x93064),x93063))) % 172.83/172.50 [9348]E(x93481,x93482)+~P102(f332(f332(f334(f882(x93483,x93483)),f332(f332(f267(x93483,x93483),x93481),x93482)),f308(x93483,x93485)))+P102(f332(f332(f334(x93483),x93481),x93484))+~P102(f332(f332(f246(f883(f882(x93483,x93483),a871)),x93485),f332(f332(f269(x93483,x93483),x93484),f332(f16(f883(x93483,a871),x93483),x93484)))) % 172.83/172.50 [9367]P102(f332(x93671,x93672))+~P102(f332(x93671,f447(x93671,x93674,x93675,x93673)))+P102(f332(f332(f334(x93673),f459(x93671,x93674,x93675,x93673)),x93674))+~P102(f332(f332(f334(x93673),x93672),f332(f332(f113(f883(x93673,a871)),x93675),x93674))) % 172.83/172.50 [9368]P102(f332(x93681,x93682))+~P102(f332(x93681,f459(x93681,x93684,x93685,x93683)))+P102(f332(f332(f334(x93683),f447(x93681,x93684,x93685,x93683)),x93685))+~P102(f332(f332(f334(x93683),x93682),f332(f332(f113(f883(x93683,a871)),x93685),x93684))) % 172.83/172.50 [9429]P102(f332(x94291,x94292))+P102(f332(f332(f334(x94293),f459(x94291,x94294,x94295,x94293)),x94294))+P102(f332(f332(f334(x94293),f447(x94291,x94294,x94295,x94293)),x94295))+~P102(f332(f332(f334(x94293),x94292),f332(f332(f113(f883(x94293,a871)),x94295),x94294))) % 172.83/172.50 [9431]~P102(f332(x94312,x94315))+P102(f332(f332(f334(x94311),f418(x94312,x94313,x94314,x94311)),x94313))+P102(f332(f332(f334(x94311),f409(x94312,x94313,x94314,x94311)),x94314))+~P102(f332(f332(f334(x94311),x94315),f332(f332(f113(f883(x94311,a871)),x94314),x94313))) % 172.83/172.50 [9579]~P3(x95791,x95795,x95794)+~P102(f332(f332(f334(x95791),x95793),x95795))+P102(f332(f332(f334(f882(x95791,x95791)),f332(f332(f267(x95791,x95791),x95792),x95793)),x95794))+~P102(f332(f332(f246(f883(x95791,a871)),f332(f286(x95791,x95791,x95794),f332(f332(f310(x95791),x95793),f195(f883(x95791,a871))))),f332(f286(x95791,x95791,x95794),f332(f332(f310(x95791),x95792),f195(f883(x95791,a871)))))) % 172.83/172.50 [9702]~P104(x97025)+~P27(x97025)+P102(f332(f332(f334(x97021),f631(x97022,x97023,x97024,x97021,x97025)),x97024))+~P102(f332(f332(f247(x97025),f332(f332(f42(x97021,x97025),x97024),x97023)),x97022)) % 172.83/172.50 [9734]~P80(x97345)+~P76(x97345)+P102(f332(f332(f334(x97341),f715(x97342,x97343,x97344,x97341,x97345)),f332(f173(x97341),x97344)))+P102(f332(f332(f246(x97345),f332(f166(x97345),f332(f332(f154(x97341,x97345),x97343),x97344))),f332(f166(x97345),f332(f332(f154(x97341,x97345),x97342),x97344)))) % 172.83/172.50 [9849]~P104(x98491)+~P27(x98491)+P102(f332(f332(f247(x98491),f332(x98492,f631(x98493,x98492,x98494,x98495,x98491))),x98493))+~P102(f332(f332(f247(x98491),f332(f332(f42(x98495,x98491),x98494),x98492)),x98493)) % 172.83/172.50 [9989]~P80(x99891)+~P76(x99891)+~P102(f332(f332(f246(x99891),f332(x99893,f715(x99895,x99893,x99894,x99892,x99891))),f332(x99895,f715(x99895,x99893,x99894,x99892,x99891))))+P102(f332(f332(f246(x99891),f332(f166(x99891),f332(f332(f154(x99892,x99891),x99893),x99894))),f332(f166(x99891),f332(f332(f154(x99892,x99891),x99895),x99894)))) % 172.83/172.50 [8663]~P71(x86631)+~P102(f332(f61(x86634),x86635))+~P102(f332(f332(f334(x86634),x86633),x86635))+E(f332(f332(f79(x86631),f332(x86632,x86633)),f332(f332(f6(x86634,x86631),x86632),f332(f332(f22(f883(x86634,a871)),x86635),f332(f332(f310(x86634),x86633),f195(f883(x86634,a871)))))),f332(f332(f6(x86634,x86631),x86632),x86635)) % 172.83/172.50 [8664]~P67(x86641)+~P102(f332(f61(x86644),x86645))+~P102(f332(f332(f334(x86644),x86643),x86645))+E(f332(f332(f80(x86641),f332(x86642,x86643)),f332(f332(f9(x86644,x86641),x86642),f332(f332(f22(f883(x86644,a871)),x86645),f332(f332(f310(x86644),x86643),f195(f883(x86644,a871)))))),f332(f332(f9(x86644,x86641),x86642),x86645)) % 172.83/172.50 [8719]~P13(x87191,x87194,x87195)+~P102(f332(f61(x87191),x87192))+E(f332(f332(f22(f883(x87191,a871)),x87192),f332(f332(f310(x87191),x87193),f195(f883(x87191,a871)))),f195(f883(x87191,a871)))+E(f332(f332(x87194,x87193),f332(x87195,f332(f332(f22(f883(x87191,a871)),x87192),f332(f332(f310(x87191),x87193),f195(f883(x87191,a871)))))),f332(x87195,f332(f332(f310(x87191),x87193),x87192))) % 172.83/172.50 [9096]~P67(x90961)+~P102(f332(f61(x90962),x90965))+~P102(f332(f61(x90962),x90964))+E(f332(f332(f80(x90961),f332(f332(f9(x90962,x90961),x90963),f332(f332(f113(f883(x90962,a871)),x90964),x90965))),f332(f332(f9(x90962,x90961),x90963),f332(f332(f104(f883(x90962,a871)),x90964),x90965))),f332(f332(f80(x90961),f332(f332(f9(x90962,x90961),x90963),x90964)),f332(f332(f9(x90962,x90961),x90963),x90965))) % 172.83/172.50 [9097]~P71(x90971)+~P102(f332(f61(x90972),x90975))+~P102(f332(f61(x90972),x90974))+E(f332(f332(f79(x90971),f332(f332(f6(x90972,x90971),x90973),f332(f332(f113(f883(x90972,a871)),x90974),x90975))),f332(f332(f6(x90972,x90971),x90973),f332(f332(f104(f883(x90972,a871)),x90974),x90975))),f332(f332(f79(x90971),f332(f332(f6(x90972,x90971),x90973),x90974)),f332(f332(f6(x90972,x90971),x90973),x90975))) % 172.83/172.50 [9238]~P66(x92381)+~P102(f332(f61(x92382),x92385))+~P102(f332(f61(x92382),x92384))+E(f332(f332(f22(x92381),f332(f332(f79(x92381),f332(f332(f6(x92382,x92381),x92383),x92384)),f332(f332(f6(x92382,x92381),x92383),x92385))),f332(f332(f6(x92382,x92381),x92383),f332(f332(f104(f883(x92382,a871)),x92384),x92385))),f332(f332(f6(x92382,x92381),x92383),f332(f332(f113(f883(x92382,a871)),x92384),x92385))) % 172.83/172.50 [9440]~P20(x94401,x94402,x94403,x94405)+~P20(x94401,x94402,x94403,x94404)+P20(x94401,x94402,x94403,f332(f332(f113(f883(x94401,a871)),x94404),x94405))+~E(f332(f332(f104(f883(x94402,a871)),f332(f311(x94401,x94402,x94403),f332(f332(f22(f883(x94401,a871)),x94404),x94405))),f332(f311(x94401,x94402,x94403),f332(f332(f22(f883(x94401,a871)),x94405),x94404))),f195(f883(x94402,a871))) % 172.83/172.50 [9554]E(x95541,f2(a1))+~P102(f332(f332(f247(a1),f2(a1)),x95543))+~P102(f332(f48(x95542,x95541),f332(f332(f267(a1,a1),x95544),x95545)))+P102(f332(f48(x95542,f332(f332(f80(a1),x95541),x95543)),f332(f332(f267(a1,a1),f332(f332(f38(a1),x95544),x95543)),f332(f332(f79(a1),f332(f332(f80(a1),x95541),f44(a1,x95544,x95543))),x95545)))) % 172.83/172.50 [9562]~P102(f332(f332(f247(a876),f2(a876)),x95623))+~P102(f332(f332(f247(a876),f2(a876)),x95622))+~P102(f332(f47(x95621,x95622),f332(f332(f267(a876,a876),x95624),x95625)))+P102(f332(f47(x95621,f332(f332(f80(a876),x95622),x95623)),f332(f332(f267(a876,a876),f332(f332(f38(a876),x95624),x95623)),f332(f332(f79(a876),f332(f332(f80(a876),x95622),f44(a876,x95624,x95623))),x95625)))) % 172.83/172.50 [9611]~P67(x96111)+~P102(f332(f61(x96112),x96115))+~P102(f332(f61(x96112),x96114))+E(f332(f332(f80(x96111),f332(f332(f332(f65(x96111,x96112,f80(x96111)),x96113),f77(x96111)),f332(f332(f113(f883(x96112,a871)),x96114),x96115))),f332(f332(f332(f65(x96111,x96112,f80(x96111)),x96113),f77(x96111)),f332(f332(f104(f883(x96112,a871)),x96114),x96115))),f332(f332(f80(x96111),f332(f332(f332(f65(x96111,x96112,f80(x96111)),x96113),f77(x96111)),x96114)),f332(f332(f332(f65(x96111,x96112,f80(x96111)),x96113),f77(x96111)),x96115))) % 172.83/172.50 [9613]~E(f332(f332(f176(x96131),x96135),x96132),f332(f332(f176(x96131),x96135),x96133))+P102(f332(f332(f334(f882(f877(x96131),f877(x96131))),f332(f332(f267(f877(x96131),f877(x96131)),x96132),x96133)),f147(x96131,x96134)))+~P102(f332(f332(f247(a876),x96135),f332(f332(f244(a876),f332(f196(f877(x96131)),x96132)),f332(f196(f877(x96131)),x96133))))+~P102(f332(f332(f334(f882(x96131,x96131)),f332(f332(f267(x96131,x96131),f332(f332(f165(x96131),x96132),x96135)),f332(f332(f165(x96131),x96133),x96135))),x96134)) % 172.83/172.50 [9722]~P80(x97225)+~P141(x97225)+P102(f332(f332(f334(x97221),f373(x97222,x97223,x97224,x97221,x97225)),x97224))+P102(f332(f332(f246(x97225),f332(f332(f6(x97221,x97225),x97223),x97224)),f332(f332(f80(x97225),f332(f103(x97225),f332(f37(x97221),x97224))),x97222))) % 172.83/172.50 [9917]~P80(x99171)+~P141(x99171)+~P102(f332(f332(f246(x99171),f332(x99173,f373(x99175,x99173,x99174,x99172,x99171))),x99175))+P102(f332(f332(f246(x99171),f332(f332(f6(x99172,x99171),x99173),x99174)),f332(f332(f80(x99171),f332(f103(x99171),f332(f37(x99172),x99174))),x99175))) % 172.83/172.50 [8691]E(f332(f332(f134(x86911),x86912),x86913),f332(f332(f134(x86911),x86914),x86915))+~E(f332(f332(f176(x86911),f332(f196(f877(x86911)),x86912)),x86914),x86912)+~E(f332(f332(f134(x86911),f332(f332(f138(x86911),f332(f196(f877(x86911)),x86912)),x86914)),x86915),x86913)+P102(f332(f332(f246(a876),f332(f196(f877(x86911)),x86914)),f332(f196(f877(x86911)),x86912))) % 172.83/172.50 [8811]E(f332(f332(f134(x88111),x88112),x88113),f332(f332(f134(x88111),x88114),x88115))+~E(f332(f332(f176(x88111),f332(f196(f877(x88111)),x88112)),x88114),x88112)+~E(x88113,f332(f332(f134(x88111),f332(f332(f138(x88111),f332(f196(f877(x88111)),x88112)),x88114)),x88115))+~P102(f332(f332(f246(a876),f332(f196(f877(x88111)),x88112)),f332(f196(f877(x88111)),x88114))) % 172.83/172.50 [10052]~P102(f332(x100525,x100524))+~P102(f332(f61(x100522),f332(f252(x100522),x100525)))+P102(f332(f61(x100521),f332(f252(x100521),f332(f332(f7(x100521,x100522,a871),x100523),x100524))))+~P102(f332(f61(x100521),f332(f252(x100521),f332(f332(f8(f883(x100522,a871),a871,x100521),f86(x100522)),f332(f332(f8(f883(x100522,a871),f883(x100522,a871),x100521),f332(f18(x100522,a871,a871),f332(f332(f8(a871,f883(a871,a871),x100522),a330),x100525))),x100523))))) % 172.83/172.50 [8488]~P14(x84885,x84881,x84886,x84882)+E(f332(f72(x84881,x84881,x84881,f332(x84882,x84883)),f332(x84882,x84884)),f332(f72(x84881,x84881,x84881,f332(x84882,x84884)),f332(x84882,x84883)))+~P102(f332(f61(x84885),x84884))+~P102(f332(f61(x84885),x84883)) % 172.83/172.50 [7867]~P20(x78671,x78672,x78674,x78673)+~E(f332(x78674,x78676),x78675)+E(f332(f76(x78671,x78672,x78673,x78674),x78675),x78676)+~P102(f332(f332(f334(x78671),x78676),x78673)) % 172.83/172.50 [8067]~P15(x80676,x80671,x80674,x80672)+E(f332(f72(x80671,x80671,x80671,f332(x80672,x80673)),f332(x80674,x80675)),f332(x80672,x80673))+~P102(f332(f61(x80676),x80673))+~P102(f332(f332(f334(x80676),x80675),x80673)) % 172.83/172.50 [9285]~P14(x92853,x92851,x92856,x92852)+E(f332(f72(x92851,x92851,x92851,f332(x92852,f332(f332(f22(f883(x92853,a871)),x92854),f332(f332(f310(x92853),x92855),f195(f883(x92853,a871)))))),f332(x92856,x92855)),f332(x92852,x92854))+~P102(f332(f61(x92853),x92854))+~P102(f332(f332(f334(x92853),x92855),x92854)) % 172.83/172.50 [6941]~P26(x69411)+~E(f44(x69411,x69413,x69414),f44(x69411,x69416,x69414))+~E(f44(x69411,x69412,x69414),f44(x69411,x69415,x69414))+E(f44(x69411,f332(f332(f22(x69411),x69412),x69413),x69414),f44(x69411,f332(f332(f22(x69411),x69415),x69416),x69414)) % 172.83/172.50 [6942]~P25(x69421)+~E(f44(x69421,x69423,x69424),f44(x69421,x69426,x69424))+~E(f44(x69421,x69422,x69424),f44(x69421,x69425,x69424))+E(f44(x69421,f332(f332(f80(x69421),x69422),x69423),x69424),f44(x69421,f332(f332(f80(x69421),x69425),x69426),x69424)) % 172.83/172.50 [6943]~P25(x69431)+~E(f44(x69431,x69433,x69434),f44(x69431,x69436,x69434))+~E(f44(x69431,x69432,x69434),f44(x69431,x69435,x69434))+E(f44(x69431,f332(f332(f79(x69431),x69432),x69433),x69434),f44(x69431,f332(f332(f79(x69431),x69435),x69436),x69434)) % 172.83/172.50 [7760]~P11(x77601,x77602,x77603)+~P102(f332(f61(x77601),x77606))+E(f332(f332(f64(x77601,x77602,x77603),x77604),f332(f332(f310(x77601),x77605),x77606)),f332(f332(f64(x77601,x77602,x77603),f332(f332(x77603,x77605),x77604)),x77606))+P102(f332(f332(f334(x77601),x77605),x77606)) % 172.83/172.50 [7825]~P27(x78251)+P102(f332(f332(f246(x78251),x78252),f332(x78253,x78254)))+~P102(f332(f332(f334(x78255),x78254),x78256))+~P102(f332(f332(f246(x78251),x78252),f332(f332(f42(x78255,x78251),x78256),x78253))) % 172.83/172.50 [7986]~P11(x79861,x79862,x79863)+~P102(f332(f61(x79861),x79866))+E(f332(f332(f64(x79861,x79862,x79863),x79864),f332(f332(f310(x79861),x79865),x79866)),f332(f332(x79863,x79865),f332(f332(f64(x79861,x79862,x79863),x79864),x79866)))+P102(f332(f332(f334(x79861),x79865),x79866)) % 172.83/172.50 [8083]~P104(x80833)+~P102(f332(x80832,x80835))+~P29(x80833,f332(f332(f154(x80831,x80833),x80834),x80836))+E(f332(f136(x80831,x80832),f332(f332(f148(x80831,x80833,x80834),x80835),x80836)),f332(f332(f148(x80831,x80833,x80834),x80835),f332(f136(x80831,x80832),x80836))) % 172.83/172.50 [8106]E(x81061,x81062)+E(x81063,f2(a1))+~P102(f332(f48(x81064,x81063),f332(f332(f267(a1,a1),x81065),x81062)))+~P102(f332(f48(x81064,x81063),f332(f332(f267(a1,a1),x81066),x81061))) % 172.83/172.50 [8107]E(x81071,x81072)+E(x81073,f2(a1))+~P102(f332(f48(x81074,x81073),f332(f332(f267(a1,a1),x81072),x81075)))+~P102(f332(f48(x81074,x81073),f332(f332(f267(a1,a1),x81071),x81076))) % 172.83/172.50 [8127]~P14(x81272,x81275,x81276,x81271)+~P102(f332(f61(x81272),x81274))+E(f332(x81271,f332(f332(f310(x81272),x81273),x81274)),f332(f72(x81275,x81275,x81275,f332(x81271,x81274)),f332(x81276,x81273)))+P102(f332(f332(f334(x81272),x81273),x81274)) % 172.83/172.50 [8356]~P15(x83565,x83561,x83566,x83562)+E(f332(f72(x83561,x83561,x83561,f332(x83562,x83563)),f332(x83562,x83564)),f332(x83562,x83563))+~P102(f332(f61(x83565),x83563))+~P102(f332(f332(f246(f883(x83565,a871)),x83564),x83563)) % 172.83/172.50 [9486]~P20(x94861,x94862,x94864,x94863)+~P102(f332(f332(f334(x94862),x94865),f332(f311(x94861,x94862,x94864),x94863)))+P102(f332(f332(f334(x94861),f332(f76(x94861,x94862,x94863,x94864),x94865)),x94866))+~P102(f332(f332(f246(f883(x94861,a871)),x94863),x94866)) % 172.83/172.50 [9862]~P71(x98622)+~E(f866(x98621,x98623,x98625,x98626,x98624,x98622),f867(x98621,x98623,x98625,x98626,x98624,x98622))+~P102(f332(f61(x98624),x98626))+E(f332(f332(f6(x98621,x98622),x98623),f332(f311(x98624,x98621,x98625),x98626)),f332(f332(f6(x98624,x98622),f332(f72(x98621,x98622,x98624,x98623),x98625)),x98626)) % 172.83/172.50 [9899]~P71(x98996)+E(f332(x98991,f866(x98992,x98993,x98991,x98994,x98995,x98996)),f332(x98991,f867(x98992,x98993,x98991,x98994,x98995,x98996)))+E(f332(f332(f6(x98992,x98996),x98993),f332(f311(x98995,x98992,x98991),x98994)),f332(f332(f6(x98995,x98996),f332(f72(x98992,x98996,x98995,x98993),x98991)),x98994))+~P102(f332(f61(x98995),x98994)) % 172.83/172.50 [9939]~P71(x99392)+~E(f332(x99393,f332(x99395,f867(x99391,x99393,x99395,x99396,x99394,x99392))),f2(x99392))+~P102(f332(f61(x99394),x99396))+E(f332(f332(f6(x99391,x99392),x99393),f332(f311(x99394,x99391,x99395),x99396)),f332(f332(f6(x99394,x99392),f332(f72(x99391,x99392,x99394,x99393),x99395)),x99396)) % 172.83/172.50 [9997]~P71(x99972)+~P102(f332(f61(x99974),x99976))+E(f332(f332(f6(x99971,x99972),x99973),f332(f311(x99974,x99971,x99975),x99976)),f332(f332(f6(x99974,x99972),f332(f72(x99971,x99972,x99974,x99973),x99975)),x99976))+P102(f332(f332(f334(x99974),f867(x99971,x99973,x99975,x99976,x99974,x99972)),x99976)) % 172.83/172.50 [9998]~P71(x99982)+~P102(f332(f61(x99984),x99986))+E(f332(f332(f6(x99981,x99982),x99983),f332(f311(x99984,x99981,x99985),x99986)),f332(f332(f6(x99984,x99982),f332(f72(x99981,x99982,x99984,x99983),x99985)),x99986))+P102(f332(f332(f334(x99984),f866(x99981,x99983,x99985,x99986,x99984,x99982)),x99986)) % 172.83/172.50 [10111]~P67(x101111)+~P102(f332(f61(x101112),x101116))+E(f332(f332(f332(f65(x101111,x101112,f80(x101111)),f332(f332(f18(x101112,f883(x101113,a871),x101111),f332(f332(f7(x101112,x101111,f883(f883(x101113,a871),x101111)),f332(f332(f8(f883(x101113,x101111),f883(x101111,f883(f883(x101113,a871),x101111)),x101112),f65(x101111,x101113,f80(x101111))),x101114)),f77(x101111))),x101115)),f77(x101111)),x101116),f332(f332(f332(f65(x101111,f882(x101112,x101113),f80(x101111)),f332(f271(x101112,x101113,x101111),x101114)),f77(x101111)),f332(f332(f269(x101112,x101113),x101116),x101115)))+P102(f332(f332(f334(x101112),f544(x101114,x101115,x101113,x101116,x101112,x101111)),x101116)) % 172.83/172.50 [10129]~P67(x101291)+~P102(f332(f61(x101292),x101296))+E(f332(f332(f332(f65(x101291,x101292,f80(x101291)),f332(f332(f18(x101292,f883(x101293,a871),x101291),f332(f332(f7(x101292,x101291,f883(f883(x101293,a871),x101291)),f332(f332(f8(f883(x101293,x101291),f883(x101291,f883(f883(x101293,a871),x101291)),x101292),f65(x101291,x101293,f80(x101291))),x101294)),f77(x101291))),x101295)),f77(x101291)),x101296),f332(f332(f332(f65(x101291,f882(x101292,x101293),f80(x101291)),f332(f271(x101292,x101293,x101291),x101294)),f77(x101291)),f332(f332(f269(x101292,x101293),x101296),x101295)))+~P102(f332(f61(x101293),f332(x101295,f544(x101294,x101295,x101293,x101296,x101292,x101291)))) % 172.83/172.50 [8268]~P15(x82682,x82685,x82686,x82681)+~P102(f332(f61(x82682),x82684))+~P102(f332(f61(x82682),x82683))+E(f332(x82681,f332(f332(f113(f883(x82682,a871)),x82683),x82684)),f332(f72(x82685,x82685,x82685,f332(x82681,x82683)),f332(x82681,x82684))) % 172.83/172.50 [8489]~P27(x84891)+P102(f332(f332(f246(x84891),f332(x84892,x84893)),x84894))+~P102(f332(f332(f334(x84895),x84893),x84896))+~P102(f332(f332(f246(x84891),f332(f332(f41(x84895,x84891),x84896),x84892)),x84894)) % 172.83/172.50 [8891]~P20(x88912,x88911,x88913,x88916)+E(f332(f332(f22(f883(x88911,a871)),f332(f311(x88912,x88911,x88913),x88914)),f332(f311(x88912,x88911,x88913),x88915)),f332(f311(x88912,x88911,x88913),f332(f332(f22(f883(x88912,a871)),x88914),x88915)))+~P102(f332(f332(f246(f883(x88912,a871)),x88915),x88916))+~P102(f332(f332(f246(f883(x88912,a871)),x88914),x88916)) % 172.83/172.50 [8892]~P20(x88922,x88921,x88923,x88926)+E(f332(f332(f104(f883(x88921,a871)),f332(f311(x88922,x88921,x88923),x88924)),f332(f311(x88922,x88921,x88923),x88925)),f332(f311(x88922,x88921,x88923),f332(f332(f104(f883(x88922,a871)),x88924),x88925)))+~P102(f332(f332(f246(f883(x88922,a871)),x88925),x88926))+~P102(f332(f332(f246(f883(x88922,a871)),x88924),x88926)) % 172.83/172.50 [8932]~P102(f332(x89321,x89323))+~P102(f332(f332(f332(f332(a203,x89322),x89323),x89324),x89326))+~P102(f332(f332(f332(f332(a203,f31(x89321,x89322)),x89326),x89324),x89325))+P102(f332(f332(f332(f332(a203,f31(x89321,x89322)),x89323),x89324),x89325)) % 172.83/172.50 [9160]E(x91601,x91602)+~P50(x91603,x91604,x91605)+~P102(f332(f332(f334(f882(x91603,x91604)),f332(f332(f267(x91603,x91604),x91606),x91602)),x91605))+~P102(f332(f332(f334(f882(x91603,x91604)),f332(f332(f267(x91603,x91604),x91606),x91601)),x91605)) % 172.83/172.50 [9934]~P64(x99341)+~E(f332(x99343,f481(x99344,x99346,x99343,x99345,x99342,x99341)),f332(x99346,f481(x99344,x99346,x99343,x99345,x99342,x99341)))+~P102(f332(f61(x99342),x99345))+E(f332(f332(f332(f65(x99341,x99342,f80(x99341)),x99343),x99344),x99345),f332(f332(f332(f65(x99341,x99342,f80(x99341)),x99346),x99344),x99345)) % 172.83/172.50 [9995]~P64(x99951)+~P102(f332(f61(x99952),x99955))+E(f332(f332(f332(f65(x99951,x99952,f80(x99951)),x99953),x99954),x99955),f332(f332(f332(f65(x99951,x99952,f80(x99951)),x99956),x99954),x99955))+P102(f332(f332(f334(x99952),f481(x99954,x99953,x99956,x99955,x99952,x99951)),x99955)) % 172.83/172.50 [8704]~P64(x87041)+~P102(f332(f61(x87042),x87046))+P102(f332(f332(f334(x87042),x87045),x87046))+E(f332(f332(f332(f65(x87041,x87042,f80(x87041)),x87043),x87044),f332(f332(f310(x87042),x87045),x87046)),f332(f332(f80(x87041),f332(x87043,x87045)),f332(f332(f332(f65(x87041,x87042,f80(x87041)),x87043),x87044),x87046))) % 172.83/172.50 [8750]~P3(x87501,x87506,x87503)+~P8(x87501,f883(x87502,a871),x87503,x87505)+~P102(f332(f332(f334(x87501),x87504),x87506))+E(f332(f332(f41(x87501,f883(x87502,a871)),f332(f286(x87501,x87501,x87503),f332(f332(f310(x87501),x87504),f195(f883(x87501,a871))))),x87505),f332(x87505,x87504)) % 172.83/172.50 [8868]~P11(x88683,x88684,x88681)+~P102(f332(f61(x88683),x88686))+~P102(f332(f332(f334(x88683),x88682),x88686))+E(f332(f332(x88681,x88682),f332(f332(f64(x88683,x88684,x88681),x88685),f332(f332(f22(f883(x88683,a871)),x88686),f332(f332(f310(x88683),x88682),f195(f883(x88683,a871)))))),f332(f332(f64(x88683,x88684,x88681),x88685),x88686)) % 172.83/172.50 [9173]~P14(x91733,x91731,x91736,x91732)+~P102(f332(f61(x91733),x91735))+~P102(f332(f61(x91733),x91734))+E(f332(f72(x91731,x91731,x91731,f332(x91732,f332(f332(f113(f883(x91733,a871)),x91734),x91735))),f332(x91732,f332(f332(f104(f883(x91733,a871)),x91734),x91735))),f332(f72(x91731,x91731,x91731,f332(x91732,x91734)),f332(x91732,x91735))) % 172.83/172.50 [9506]~E(x95063,f332(f332(f159(x95061,x95062),x95065),x95066))+P102(f332(f332(f334(f882(f877(x95061),f877(x95061))),f332(f332(f267(f877(x95061),f877(x95061)),x95062),x95063)),f157(x95061,x95064)))+~P102(f332(f332(f247(a876),x95065),f332(f196(f877(x95061)),x95062)))+~P102(f332(f332(f334(f882(x95061,x95061)),f332(f332(f267(x95061,x95061),f332(f332(f165(x95061),x95062),x95065)),x95066)),x95064)) % 172.83/172.50 [10008]~P71(x100082)+~P102(f332(f61(x100081),x100086))+P102(f332(f332(f334(x100081),f542(x100084,x100085,x100083,x100086,x100081,x100082)),x100086))+E(f332(f332(f6(x100081,x100082),f332(f332(f18(x100081,f883(x100083,a871),x100082),f332(f332(f8(f883(x100083,x100082),f883(f883(x100083,a871),x100082),x100081),f6(x100083,x100082)),x100084)),x100085)),x100086),f332(f332(f6(f882(x100081,x100083),x100082),f332(f271(x100081,x100083,x100082),x100084)),f332(f332(f269(x100081,x100083),x100086),x100085))) % 172.83/172.50 [10009]~P67(x100092)+~P102(f332(f61(x100091),x100096))+P102(f332(f332(f334(x100091),f543(x100094,x100095,x100093,x100096,x100091,x100092)),x100096))+E(f332(f332(f9(x100091,x100092),f332(f332(f18(x100091,f883(x100093,a871),x100092),f332(f332(f8(f883(x100093,x100092),f883(f883(x100093,a871),x100092),x100091),f9(x100093,x100092)),x100094)),x100095)),x100096),f332(f332(f9(f882(x100091,x100093),x100092),f332(f271(x100091,x100093,x100092),x100094)),f332(f332(f269(x100091,x100093),x100096),x100095))) % 172.83/172.50 [10049]~P71(x100492)+~P102(f332(f61(x100491),x100496))+~P102(f332(f61(x100493),f332(x100495,f542(x100494,x100495,x100493,x100496,x100491,x100492))))+E(f332(f332(f6(x100491,x100492),f332(f332(f18(x100491,f883(x100493,a871),x100492),f332(f332(f8(f883(x100493,x100492),f883(f883(x100493,a871),x100492),x100491),f6(x100493,x100492)),x100494)),x100495)),x100496),f332(f332(f6(f882(x100491,x100493),x100492),f332(f271(x100491,x100493,x100492),x100494)),f332(f332(f269(x100491,x100493),x100496),x100495))) % 172.83/172.50 [10050]~P67(x100502)+~P102(f332(f61(x100501),x100506))+~P102(f332(f61(x100503),f332(x100505,f543(x100504,x100505,x100503,x100506,x100501,x100502))))+E(f332(f332(f9(x100501,x100502),f332(f332(f18(x100501,f883(x100503,a871),x100502),f332(f332(f8(f883(x100503,x100502),f883(f883(x100503,a871),x100502),x100501),f9(x100503,x100502)),x100504)),x100505)),x100506),f332(f332(f9(f882(x100501,x100503),x100502),f332(f271(x100501,x100503,x100502),x100504)),f332(f332(f269(x100501,x100503),x100506),x100505))) % 172.83/172.50 [10031]~P67(x100312)+~P102(f332(f61(x100311),x100316))+P102(f332(f332(f334(x100311),x100313),x100316))+E(f332(f332(f9(x100311,x100312),f332(f332(f7(x100311,x100312,x100312),f332(f332(f18(x100311,x100312,f883(x100312,x100312)),f332(f332(f8(a871,f883(x100312,f883(x100312,x100312)),x100311),f99(x100312)),f332(f332(f7(x100311,x100311,a871),a329),x100313))),x100314)),x100315)),x100316),f332(f332(f257(x100312),x100315),f332(f37(x100311),x100316))) % 172.83/172.50 [10036]~P67(x100362)+~P102(f332(f61(x100361),x100366))+~P102(f332(f332(f334(x100361),x100363),x100366))+E(f332(f332(f9(x100361,x100362),f332(f332(f7(x100361,x100362,x100362),f332(f332(f18(x100361,x100362,f883(x100362,x100362)),f332(f332(f8(a871,f883(x100362,f883(x100362,x100362)),x100361),f99(x100362)),f332(f332(f7(x100361,x100361,a871),a329),x100363))),x100364)),x100365)),x100366),f332(f332(f80(x100362),f332(x100364,x100363)),f332(f332(f257(x100362),x100365),f332(f332(f22(a876),f332(f37(x100361),x100366)),f77(a876))))) % 172.83/172.50 [10104]~P102(f332(f61(x101041),x101045))+~P102(f332(f61(x101042),x101043))+P102(f332(f332(f334(x101042),f433(x101046,x101044,x101043,x101042,x101045,x101041)),x101043))+E(f332(f332(f6(x101041,a876),f332(f332(f8(f883(x101042,a871),a876,x101041),f37(x101042)),f332(f332(f8(f883(x101042,a871),f883(x101042,a871),x101041),f252(x101042)),f332(f332(f8(f883(x101042,a871),f883(x101042,a871),x101041),f332(f18(x101042,a871,a871),f332(f332(f8(a871,f883(a871,a871),x101042),a330),f332(f332(f7(x101042,f883(x101042,a871),a871),f334(x101042)),x101043)))),x101044)))),x101045),f332(f332(f80(a876),x101046),f332(f37(x101042),x101043))) % 172.83/172.50 [10105]~P102(f332(f61(x101051),x101055))+~P102(f332(f61(x101052),x101053))+P102(f332(f332(f334(x101052),f434(x101056,x101054,x101053,x101052,x101055,x101051)),x101053))+E(f332(f332(f6(x101051,a876),f332(f332(f8(f883(x101052,a871),a876,x101051),f37(x101052)),f332(f332(f8(f883(x101052,a871),f883(x101052,a871),x101051),f252(x101052)),f332(f332(f8(f883(x101052,a871),f883(x101052,a871),x101051),f332(f18(x101052,a871,a871),f332(f332(f8(a871,f883(a871,a871),x101052),a330),f332(f332(f7(x101052,f883(x101052,a871),a871),f334(x101052)),x101053)))),x101054)))),x101055),f332(f332(f6(x101052,a876),x101056),x101053)) % 172.83/172.50 [10135]~P102(f332(f61(x101352),x101353))+~P102(f332(f61(x101351),x101355))+~E(f332(f37(x101351),f332(f252(x101351),f332(f332(f18(x101351,a871,a871),f332(f332(f8(a871,f883(a871,a871),x101351),a330),f332(f332(f7(x101351,f883(x101351,a871),a871),f334(x101351)),x101355))),f332(f332(f7(x101351,x101352,a871),x101354),f433(x101356,x101354,x101353,x101352,x101355,x101351))))),x101356)+E(f332(f332(f6(x101351,a876),f332(f332(f8(f883(x101352,a871),a876,x101351),f37(x101352)),f332(f332(f8(f883(x101352,a871),f883(x101352,a871),x101351),f252(x101352)),f332(f332(f8(f883(x101352,a871),f883(x101352,a871),x101351),f332(f18(x101352,a871,a871),f332(f332(f8(a871,f883(a871,a871),x101352),a330),f332(f332(f7(x101352,f883(x101352,a871),a871),f334(x101352)),x101353)))),x101354)))),x101355),f332(f332(f80(a876),x101356),f332(f37(x101352),x101353))) % 172.83/172.50 [10137]~P102(f332(f61(x101372),x101373))+~P102(f332(f61(x101371),x101375))+~E(f332(f37(x101371),f332(f252(x101371),f332(f332(f18(x101371,a871,a871),f332(f332(f8(a871,f883(a871,a871),x101371),a330),f332(f332(f7(x101371,f883(x101371,a871),a871),f334(x101371)),x101375))),f332(f332(f7(x101371,x101372,a871),x101374),f434(x101376,x101374,x101373,x101372,x101375,x101371))))),f332(x101376,f434(x101376,x101374,x101373,x101372,x101375,x101371)))+E(f332(f332(f6(x101371,a876),f332(f332(f8(f883(x101372,a871),a876,x101371),f37(x101372)),f332(f332(f8(f883(x101372,a871),f883(x101372,a871),x101371),f252(x101372)),f332(f332(f8(f883(x101372,a871),f883(x101372,a871),x101371),f332(f18(x101372,a871,a871),f332(f332(f8(a871,f883(a871,a871),x101372),a330),f332(f332(f7(x101372,f883(x101372,a871),a871),f334(x101372)),x101373)))),x101374)))),x101375),f332(f332(f6(x101372,a876),x101376),x101373)) % 172.83/172.50 [9789]E(x97891,x97892)+~P11(x97893,x97894,x97895)+~P102(f332(f66(x97893,x97894,x97895,x97896,x97897),x97892))+~P102(f332(f66(x97893,x97894,x97895,x97896,x97897),x97891)) % 172.83/172.50 [9582]P102(f332(x95821,x95822))+~P102(f332(f332(f334(x95827),x95822),f332(x95826,x95824)))+~P102(f332(x95821,f440(x95821,x95826,x95825,x95823,x95827)))+~P102(f332(f332(f334(x95823),x95824),x95825)) % 172.83/172.50 [10023]~P11(x100237,x100236,x100231)+E(f332(f332(x100231,x100232),f626(x100232,x100233,x100234,x100235,x100231,x100236,x100237)),x100233)+~P102(f332(f66(x100237,x100236,x100231,x100235,x100234),x100233))+~P102(f332(f332(f334(x100237),x100232),x100234)) % 172.83/172.50 [10089]~P11(x100891,x100892,x100893)+~P102(f332(f66(x100891,x100892,x100893,x100894,x100895),x100897))+P102(f332(f66(x100891,x100892,x100893,x100894,f332(f332(f22(f883(x100891,a871)),x100895),f332(f332(f310(x100891),x100896),f195(f883(x100891,a871))))),f626(x100896,x100897,x100895,x100894,x100893,x100892,x100891)))+~P102(f332(f332(f334(x100891),x100896),x100895)) % 172.83/172.50 [9482]~P64(x94821)+~P20(x94825,x94822,x94826,x94827)+~P102(f332(f61(x94825),x94827))+E(f332(f332(f332(f65(x94821,x94822,f80(x94821)),x94823),x94824),f332(f311(x94825,x94822,x94826),x94827)),f332(f332(f332(f65(x94821,x94825,f80(x94821)),f332(f72(x94822,x94821,x94825,x94823),x94826)),x94824),x94827)) % 172.83/172.50 [9606]~E(f332(f332(f310(x96061),x96065),x96066),f332(f332(f310(x96061),x96062),x96063))+~P102(f332(f66(x96061,x96061,x96064,x96062,x96063),x96067))+P102(f332(f332(f334(x96061),x96062),x96063))+P102(f332(f62(x96061,x96064,f332(f332(f310(x96061),x96065),x96066)),x96067)) % 172.83/172.50 [9689]P102(f332(x96891,x96892))+~P102(f332(f332(f334(x96893),x96892),f332(x96894,x96897)))+~P102(f332(f332(f334(x96896),x96897),x96895))+P102(f332(f332(f334(x96893),f440(x96891,x96894,x96895,x96896,x96893)),f332(f332(f41(x96896,f883(x96893,a871)),x96895),x96894))) % 172.83/172.50 [9703]~P20(x97032,x97031,x97035,x97034)+~P20(x97031,x97033,x97036,f332(f311(x97032,x97031,x97035),x97034))+E(f332(f332(f72(x97031,x97032,x97033,f76(x97032,x97031,x97034,x97035)),f76(x97031,x97033,f332(f311(x97032,x97031,x97035),x97034),x97036)),x97037),f332(f76(x97032,x97033,x97034,f332(f72(x97031,x97033,x97032,x97036),x97035)),x97037))+~P102(f332(f332(f334(x97033),x97037),f332(f311(x97031,x97033,x97036),f332(f311(x97032,x97031,x97035),x97034)))) % 172.83/172.50 [10024]~P11(x100247,x100246,x100241)+E(f332(f332(x100241,x100242),f649(x100243,x100244,x100242,x100245,x100241,x100246,x100247)),x100243)+P102(f332(f332(f334(x100247),x100242),x100244))+~P102(f332(f66(x100247,x100246,x100241,x100245,f332(f332(f310(x100247),x100242),x100244)),x100243)) % 172.83/172.50 [10088]~P11(x100881,x100884,x100885)+P102(f332(f66(x100881,x100884,x100885,x100886,x100883),f649(x100887,x100883,x100882,x100886,x100885,x100884,x100881)))+P102(f332(f332(f334(x100881),x100882),x100883))+~P102(f332(f66(x100881,x100884,x100885,x100886,f332(f332(f310(x100881),x100882),x100883)),x100887)) % 172.83/172.50 [9771]E(x97711,f2(a1))+~P102(f332(f48(x97713,x97711),f332(f332(f267(a1,a1),x97715),x97717)))+~P102(f332(f48(x97712,x97711),f332(f332(f267(a1,a1),x97714),x97716)))+P102(f332(f48(f332(f332(f79(a1),x97712),x97713),x97711),f332(f332(f267(a1,a1),f332(f332(f79(a1),f332(f332(f79(a1),x97714),x97715)),f332(f332(f38(a1),f332(f332(f79(a1),x97716),x97717)),x97711))),f44(a1,f332(f332(f79(a1),x97716),x97717),x97711)))) % 172.83/172.50 [9773]~P102(f332(f332(f247(a876),f2(a876)),x97733))+~P102(f332(f47(x97732,x97733),f332(f332(f267(a876,a876),x97735),x97737)))+~P102(f332(f47(x97731,x97733),f332(f332(f267(a876,a876),x97734),x97736)))+P102(f332(f47(f332(f332(f79(a876),x97731),x97732),x97733),f332(f332(f267(a876,a876),f332(f332(f79(a876),f332(f332(f79(a876),x97734),x97735)),f332(f332(f38(a876),f332(f332(f79(a876),x97736),x97737)),x97733))),f44(a876,f332(f332(f79(a876),x97736),x97737),x97733)))) % 172.83/172.50 [10134]~P71(x101342)+~P102(f332(f61(x101343),x101345))+~P102(f332(f61(x101341),x101347))+E(f332(f332(f6(x101341,x101342),f332(f332(f18(x101341,f883(x101343,a871),x101342),f332(f332(f8(f883(x101343,x101342),f883(f883(x101343,a871),x101342),x101341),f6(x101343,x101342)),x101344)),f332(f332(f8(f883(x101343,a871),f883(x101343,a871),x101341),f252(x101343)),f332(f332(f8(f883(x101343,a871),f883(x101343,a871),x101341),f332(f18(x101343,a871,a871),f332(f332(f8(a871,f883(a871,a871),x101343),a330),f332(f332(f7(x101343,f883(x101343,a871),a871),f334(x101343)),x101345)))),x101346)))),x101347),f332(f332(f6(x101343,x101342),f332(f332(f18(x101343,f883(x101341,a871),x101342),f332(f332(f8(f883(x101341,x101342),f883(f883(x101341,a871),x101342),x101343),f6(x101341,x101342)),f332(f7(x101341,x101343,x101342),x101344))),f332(f332(f8(f883(x101341,a871),f883(x101341,a871),x101343),f252(x101341)),f332(f332(f8(f883(x101341,a871),f883(x101341,a871),x101343),f332(f18(x101341,a871,a871),f332(f332(f8(a871,f883(a871,a871),x101341),a330),f332(f332(f7(x101341,f883(x101341,a871),a871),f334(x101341)),x101347)))),f332(f7(x101341,x101343,a871),x101346))))),x101345)) % 172.83/172.50 [9642]~P17(x96427,x96426,x96421,x96428,x96422,x96424)+E(f332(f332(x96421,f332(x96422,x96423)),f332(x96424,x96425)),f332(x96424,x96425))+~P102(f332(f61(x96426),x96425))+~P102(f332(f332(f334(x96426),x96423),x96425)) % 172.83/172.50 [9646]~P9(x96466,x96461,x96462,x96468,x96463,x96464)+~P3(x96466,x96467,x96468)+P8(x96461,x96462,x96463,f332(x96464,x96465))+~P102(f332(f332(f334(x96466),x96465),x96467)) % 172.83/172.50 [8084]~P30(x80848,x80847,f332(f332(f332(f91(x80848),x80844),x80846),x80841))+P102(f332(f332(x80841,x80842),x80843))+~P102(f332(f332(x80844,x80842),x80845))+~P102(f332(f332(f332(f332(a203,x80846),x80845),x80847),x80843)) % 172.83/172.50 [9267]~P14(x92677,x92671,x92678,x92673)+~P102(f332(f61(x92677),x92675))+~P102(f332(f61(x92677),x92674))+E(f332(f72(x92671,x92671,x92672,f332(x92673,x92674)),f332(f72(x92671,x92671,x92672,f332(x92673,x92675)),x92676)),f332(f72(x92671,x92671,x92672,f332(x92673,x92675)),f332(f72(x92671,x92671,x92672,f332(x92673,x92674)),x92676))) % 172.83/172.50 [9275]~P35(x92751,x92752,x92753,x92754,x92757)+P35(x92751,x92752,x92753,f332(f332(f159(x92751,x92754),x92755),x92756),f332(f332(f159(x92752,x92757),x92755),x92758))+~P102(f332(f332(x92753,x92756),x92758))+~P102(f332(f332(f247(a876),x92755),f332(f196(f877(x92751)),x92754))) % 172.83/172.50 [9276]~P35(x92761,x92762,x92763,x92764,x92767)+P35(x92761,x92762,x92763,f332(f332(f159(x92761,x92764),x92765),x92766),f332(f332(f159(x92762,x92767),x92765),x92768))+~P102(f332(f332(x92763,x92766),x92768))+~P102(f332(f332(f247(a876),x92765),f332(f196(f877(x92762)),x92767))) % 172.83/172.50 [9355]~P20(x93552,x93552,x93555,x93556)+~P16(x93553,x93552,x93557,x93558,x93551)+~P102(f332(f61(x93552),x93556))+E(f332(f332(x93551,f332(f72(x93552,x93553,x93552,x93554),x93555)),x93556),f332(f332(x93551,x93554),f332(f311(x93552,x93552,x93555),x93556))) % 172.83/172.50 [9644]~P18(x96447,x96442,x96445,x96448,x96446,x96441)+~P102(f332(f61(x96442),x96444))+E(f332(x96441,f332(f332(f310(x96442),x96443),x96444)),f332(f332(x96445,f332(x96446,x96443)),f332(x96441,x96444)))+P102(f332(f332(f334(x96442),x96443),x96444)) % 172.83/172.50 [9655]~P17(x96556,x96555,x96551,x96557,x96558,x96552)+E(f332(f332(x96551,f332(x96552,x96553)),f332(x96552,x96554)),f332(x96552,x96554))+~P102(f332(f61(x96555),x96554))+~P102(f332(f332(f246(f883(x96555,a871)),x96553),x96554)) % 172.83/172.50 [9253]P102(f332(f332(f334(f882(f877(x92531),f877(x92531))),f332(f332(f267(f877(x92531),f877(x92531)),x92532),x92533)),f157(x92531,x92534)))+~E(x92533,f332(f332(f134(x92531),x92535),f332(f332(f151(x92531),x92536),x92537)))+~E(x92532,f332(f332(f134(x92531),x92535),f332(f332(f151(x92531),x92538),x92537)))+~P102(f332(f332(f334(f882(x92531,x92531)),f332(f332(f267(x92531,x92531),x92538),x92536)),x92534)) % 172.83/172.50 [9649]~P17(x96496,x96492,x96495,x96497,x96498,x96491)+~P102(f332(f61(x96492),x96494))+~P102(f332(f61(x96492),x96493))+E(f332(x96491,f332(f332(f113(f883(x96492,a871)),x96493),x96494)),f332(f332(x96495,f332(x96491,x96493)),f332(x96491,x96494))) % 172.83/172.50 [10172]~P20(x101724,x101722,x101725,x101728)+E(f332(f332(f42(x101721,f883(x101722,a871)),x101723),f332(f332(f8(f883(x101724,a871),f883(x101722,a871),x101721),f311(x101724,x101722,x101725)),x101726)),f332(f311(x101724,x101722,x101725),f332(f332(f42(x101721,f883(x101724,a871)),x101723),x101726)))+~P102(f332(f332(f334(x101721),x101727),x101723))+P102(f332(f332(f334(x101721),f640(x101727,x101726,x101723,x101721,x101728,x101725,x101722,x101724)),x101723)) % 172.83/172.50 [10196]~P20(x101964,x101962,x101965,x101967)+E(f332(f332(f42(x101961,f883(x101962,a871)),x101963),f332(f332(f8(f883(x101964,a871),f883(x101962,a871),x101961),f311(x101964,x101962,x101965)),x101966)),f332(f311(x101964,x101962,x101965),f332(f332(f42(x101961,f883(x101964,a871)),x101963),x101966)))+~P102(f332(f332(f334(x101961),x101968),x101963))+~P102(f332(f332(f246(f883(x101964,a871)),f332(x101966,f640(x101968,x101966,x101963,x101961,x101967,x101965,x101962,x101964))),x101967)) % 172.83/172.50 [9712]~P18(x97127,x97125,x97121,x97128,x97122,x97124)+~P102(f332(f61(x97125),x97126))+~P102(f332(f332(f334(x97125),x97123),x97126))+E(f332(f332(x97121,f332(x97122,x97123)),f332(x97124,f332(f332(f22(f883(x97125,a871)),x97126),f332(f332(f310(x97125),x97123),f195(f883(x97125,a871)))))),f332(x97124,x97126)) % 172.83/172.50 [9720]~P18(x97206,x97203,x97201,x97207,x97208,x97202)+~P102(f332(f61(x97203),x97205))+~P102(f332(f61(x97203),x97204))+E(f332(f332(x97201,f332(x97202,f332(f332(f113(f883(x97203,a871)),x97204),x97205))),f332(x97202,f332(f332(f104(f883(x97203,a871)),x97204),x97205))),f332(f332(x97201,f332(x97202,x97204)),f332(x97202,x97205))) % 172.83/172.50 [9812]P43(x98121,x98122,x98123,x98124,x98125,f332(f332(x98123,x98126),x98127))+~P43(x98121,x98122,x98123,x98124,f332(f332(f22(f883(x98121,a871)),x98125),f332(f332(f310(x98121),x98128),f195(f883(x98121,a871)))),x98129)+~E(f332(f332(x98123,x98126),x98127),f332(f332(x98123,x98128),x98129))+~P102(f332(f332(f334(x98121),x98128),x98125)) % 172.83/172.50 [10211]P19(x102111,x102112,f332(f332(f310(f875(x102111)),f332(f332(f332(f91(x102111),f332(x102113,f399(x102114,x102115,x102116,x102117,x102113,x102112,x102111,x102118,x102119))),f332(x102117,f399(x102114,x102115,x102116,x102117,x102113,x102112,x102111,x102118,x102119))),f332(x102116,f399(x102114,x102115,x102116,x102117,x102113,x102112,x102111,x102118,x102119)))),f195(f883(f875(x102111),a871))))+~P102(f332(f61(x102119),x102118))+~P19(x102111,x102112,f332(f311(x102119,f875(x102111),f332(f332(f18(x102119,f883(x102111,f883(a872,a871)),f875(x102111)),f332(f332(f18(x102119,a873,f883(f883(x102111,f883(a872,a871)),f875(x102111))),f332(f332(f8(f883(x102111,f883(a872,a871)),f883(a873,f883(f883(x102111,f883(a872,a871)),f875(x102111))),x102119),f91(x102111)),x102113)),x102117)),x102116)),x102118))+P19(x102111,x102112,f332(f311(x102119,f875(x102111),f332(f332(f18(x102119,f883(x102111,f883(a872,a871)),f875(x102111)),f332(f332(f18(x102119,a873,f883(f883(x102111,f883(a872,a871)),f875(x102111))),f332(f332(f8(f883(x102111,f883(a872,a871)),f883(a873,f883(f883(x102111,f883(a872,a871)),f875(x102111))),x102119),f91(x102111)),x102115)),x102117)),x102114)),x102118)) % 172.83/172.50 [10212]~P19(x102121,x102122,f332(f332(f310(f875(x102121)),f332(f332(f332(f91(x102121),f332(x102124,f399(x102126,x102124,x102128,x102125,x102129,x102122,x102121,x102127,x102123))),f332(x102125,f399(x102126,x102124,x102128,x102125,x102129,x102122,x102121,x102127,x102123))),f332(x102126,f399(x102126,x102124,x102128,x102125,x102129,x102122,x102121,x102127,x102123)))),f195(f883(f875(x102121),a871))))+~P102(f332(f61(x102123),x102127))+~P19(x102121,x102122,f332(f311(x102123,f875(x102121),f332(f332(f18(x102123,f883(x102121,f883(a872,a871)),f875(x102121)),f332(f332(f18(x102123,a873,f883(f883(x102121,f883(a872,a871)),f875(x102121))),f332(f332(f8(f883(x102121,f883(a872,a871)),f883(a873,f883(f883(x102121,f883(a872,a871)),f875(x102121))),x102123),f91(x102121)),x102129)),x102125)),x102128)),x102127))+P19(x102121,x102122,f332(f311(x102123,f875(x102121),f332(f332(f18(x102123,f883(x102121,f883(a872,a871)),f875(x102121)),f332(f332(f18(x102123,a873,f883(f883(x102121,f883(a872,a871)),f875(x102121))),f332(f332(f8(f883(x102121,f883(a872,a871)),f883(a873,f883(f883(x102121,f883(a872,a871)),f875(x102121))),x102123),f91(x102121)),x102124)),x102125)),x102126)),x102127)) % 172.83/172.50 [9746]~P9(x97466,x97467,x97468,x97469,x974610,x97461)+E(f332(f332(x97461,x97462),x97463),f332(f332(x97461,x97464),x97465))+~P102(f332(f332(f334(f882(x97467,x97467)),f332(f332(f267(x97467,x97467),x97463),x97465)),x974610))+~P102(f332(f332(f334(f882(x97466,x97466)),f332(f332(f267(x97466,x97466),x97462),x97464)),x97469)) % 172.83/172.50 [9357]~P61(x93572)+E(x93571,f195(f883(x93572,a871)))+~P102(f332(f61(x93572),x93571))+P102(f332(f332(f334(x93572),f13(x93572,x93571)),x93571))+~P102(f332(f332(f334(x93572),f332(f332(f113(x93572),f747(x93571,x93572)),f757(x93571,x93572))),f332(f332(f310(x93572),f747(x93571,x93572)),f332(f332(f310(x93572),f757(x93571,x93572)),f195(f883(x93572,a871)))))) % 172.83/172.50 [9358]~P61(x93582)+E(x93581,f195(f883(x93582,a871)))+~P102(f332(f61(x93582),x93581))+P102(f332(f332(f334(x93582),f10(x93582,x93581)),x93581))+~P102(f332(f332(f334(x93582),f332(f332(f104(x93582),f823(x93581,x93582)),f824(x93581,x93582))),f332(f332(f310(x93582),f823(x93581,x93582)),f332(f332(f310(x93582),f824(x93581,x93582)),f195(f883(x93582,a871)))))) % 172.83/172.50 [9390]~P64(x93902)+E(x93901,f195(f883(x93902,a871)))+~P102(f332(f61(x93902),x93901))+P102(f332(f332(f334(x93902),f332(f63(x93902,f80(x93902)),x93901)),x93901))+~P102(f332(f332(f334(x93902),f332(f332(f80(x93902),f829(x93901,x93902)),f831(x93901,x93902))),f332(f332(f310(x93902),f829(x93901,x93902)),f332(f332(f310(x93902),f831(x93901,x93902)),f195(f883(x93902,a871)))))) % 172.83/172.50 [9396]~P104(x93962)+E(x93961,f195(f883(x93962,a871)))+~P102(f332(f61(x93962),x93961))+P102(f332(f332(f334(x93962),f11(x93962,f245(x93962),x93961)),x93961))+~P102(f332(f332(f334(x93962),f332(f332(f245(x93962),f460(x93961,x93962)),f462(x93961,x93962))),f332(f332(f310(x93962),f460(x93961,x93962)),f332(f332(f310(x93962),f462(x93961,x93962)),f195(f883(x93962,a871)))))) % 172.83/172.50 [9397]~P104(x93972)+E(x93971,f195(f883(x93972,a871)))+~P102(f332(f61(x93972),x93971))+P102(f332(f332(f334(x93972),f12(x93972,f244(x93972),x93971)),x93971))+~P102(f332(f332(f334(x93972),f332(f332(f244(x93972),f466(x93971,x93972)),f467(x93971,x93972))),f332(f332(f310(x93972),f466(x93971,x93972)),f332(f332(f310(x93972),f467(x93971,x93972)),f195(f883(x93972,a871)))))) % 172.83/172.50 [6509]~P84(x65092)+E(x65091,f2(x65092))+~E(f332(f332(f79(x65092),x65093),x65091),f2(x65092))+~P102(f332(f332(f246(x65092),f2(x65092)),x65093))+~P102(f332(f332(f246(x65092),f2(x65092)),x65091)) % 172.83/172.50 [6510]~P84(x65102)+E(x65101,f2(x65102))+~E(f332(f332(f79(x65102),x65101),x65103),f2(x65102))+~P102(f332(f332(f246(x65102),f2(x65102)),x65103))+~P102(f332(f332(f246(x65102),f2(x65102)),x65101)) % 172.83/172.50 [7043]~P104(x70432)+~P29(x70432,x70431)+E(x70431,f116(x70432))+~P102(f332(f332(f334(x70432),x70433),f332(f173(x70432),f743(x70431,x70432))))+P102(f332(f332(f246(x70432),f762(x70431,x70432)),x70433)) % 172.83/172.50 [7209]~P104(x72091)+E(f15(x72091,x72092),x72093)+~P102(f332(f61(x72091),x72092))+~P102(f332(f332(f246(x72091),x72093),f483(x72093,x72092,x72091)))+~P102(f332(f332(f334(x72091),x72093),x72092)) % 172.83/172.50 [7240]~P104(x72401)+~P29(x72401,x72402)+~P29(x72401,x72403)+P29(x72401,f332(f332(f134(x72401),x72402),x72403))+P102(f332(f332(f334(x72401),f750(x72403,x72402,x72401)),f332(f173(x72401),x72402))) % 172.83/172.50 [7241]~P104(x72411)+~P29(x72411,x72412)+~P29(x72411,x72413)+P29(x72411,f332(f332(f134(x72411),x72412),x72413))+P102(f332(f332(f334(x72411),f751(x72413,x72412,x72411)),f332(f173(x72411),x72413))) % 172.83/172.50 [7297]~P104(x72971)+E(f14(x72971,x72972),x72973)+~P102(f332(f61(x72971),x72972))+P102(f332(f332(f334(x72971),f484(x72973,x72972,x72971)),x72972))+~P102(f332(f332(f334(x72971),x72973),x72972)) % 172.83/172.50 [7298]~P104(x72981)+E(f15(x72981,x72982),x72983)+~P102(f332(f61(x72981),x72982))+P102(f332(f332(f334(x72981),f483(x72983,x72982,x72981)),x72982))+~P102(f332(f332(f334(x72981),x72983),x72982)) % 172.83/172.50 [7885]~P104(x78851)+E(f14(x78851,x78852),x78853)+~P102(f332(f61(x78851),x78852))+~P102(f332(f332(f334(x78851),x78853),x78852))+~P102(f332(f332(f246(x78851),f484(x78853,x78852,x78851)),x78853)) % 172.83/172.50 [8216]~P104(x82161)+~P29(x82161,x82162)+~P29(x82161,x82163)+P29(x82161,f332(f332(f134(x82161),x82162),x82163))+~P102(f332(f332(f246(x82161),f750(x82163,x82162,x82161)),f751(x82163,x82162,x82161))) % 172.83/172.50 [8998]~P61(x89982)+E(x89981,f195(f883(x89982,a871)))+~E(f332(f332(f113(x89982),f332(x89983,f794(x89981,x89983,x89982))),f332(x89983,f804(x89981,x89983,x89982))),f332(x89983,f332(f332(f113(x89982),f794(x89981,x89983,x89982)),f804(x89981,x89983,x89982))))+E(f13(x89982,f332(f311(x89982,x89982,x89983),x89981)),f332(x89983,f13(x89982,x89981)))+~P102(f332(f61(x89982),x89981)) % 172.83/172.50 [8999]~P61(x89992)+E(x89991,f195(f883(x89992,a871)))+~E(f332(f332(f104(x89992),f332(x89993,f826(x89991,x89993,x89992))),f332(x89993,f827(x89991,x89993,x89992))),f332(x89993,f332(f332(f104(x89992),f826(x89991,x89993,x89992)),f827(x89991,x89993,x89992))))+E(f10(x89992,f332(f311(x89992,x89992,x89993),x89991)),f332(x89993,f10(x89992,x89991)))+~P102(f332(f61(x89992),x89991)) % 172.83/172.50 [9000]~P104(x90002)+E(x90001,f195(f883(x90002,a871)))+~E(f332(f332(f245(x90002),f332(x90003,f474(x90001,x90003,x90002))),f332(x90003,f475(x90001,x90003,x90002))),f332(x90003,f332(f332(f245(x90002),f474(x90001,x90003,x90002)),f475(x90001,x90003,x90002))))+E(f14(x90002,f332(f311(x90002,x90002,x90003),x90001)),f332(x90003,f14(x90002,x90001)))+~P102(f332(f61(x90002),x90001)) % 172.83/172.50 [9001]~P104(x90012)+E(x90011,f195(f883(x90012,a871)))+~E(f332(f332(f244(x90012),f332(x90013,f476(x90011,x90013,x90012))),f332(x90013,f477(x90011,x90013,x90012))),f332(x90013,f332(f332(f244(x90012),f476(x90011,x90013,x90012)),f477(x90011,x90013,x90012))))+E(f15(x90012,f332(f311(x90012,x90012,x90013),x90011)),f332(x90013,f15(x90012,x90011)))+~P102(f332(f61(x90012),x90011)) % 172.83/172.50 [9071]~P104(x90712)+E(x90711,f195(f883(x90712,a871)))+~E(f332(f332(f245(x90712),f332(x90713,f458(x90711,x90713,x90712))),f332(x90713,f469(x90711,x90713,x90712))),f332(x90713,f332(f332(f245(x90712),f458(x90711,x90713,x90712)),f469(x90711,x90713,x90712))))+E(f11(x90712,f245(x90712),f332(f311(x90712,x90712,x90713),x90711)),f332(x90713,f11(x90712,f245(x90712),x90711)))+~P102(f332(f61(x90712),x90711)) % 172.83/172.50 [9072]~P104(x90722)+E(x90721,f195(f883(x90722,a871)))+~E(f332(f332(f244(x90722),f332(x90723,f470(x90721,x90723,x90722))),f332(x90723,f471(x90721,x90723,x90722))),f332(x90723,f332(f332(f244(x90722),f470(x90721,x90723,x90722)),f471(x90721,x90723,x90722))))+E(f12(x90722,f244(x90722),f332(f311(x90722,x90722,x90723),x90721)),f332(x90723,f12(x90722,f244(x90722),x90721)))+~P102(f332(f61(x90722),x90721)) % 172.83/172.50 [6525]~P64(x65252)+E(x65251,f195(f883(x65252,a871)))+~P102(f332(f61(x65252),x65251))+E(f332(f63(x65252,f80(x65252)),f332(f332(f310(x65252),x65253),x65251)),f332(f332(f80(x65252),x65253),f332(f63(x65252,f80(x65252)),x65251)))+P102(f332(f332(f334(x65252),x65253),x65251)) % 172.83/172.50 [7049]~P61(x70492)+E(f332(f332(f113(x70492),f13(x70492,x70491)),f13(x70492,x70493)),f13(x70492,x70493))+E(x70491,f195(f883(x70492,a871)))+~P102(f332(f61(x70492),x70493))+~P102(f332(f332(f246(f883(x70492,a871)),x70491),x70493)) % 172.83/172.50 [7050]~P61(x70502)+E(f332(f332(f104(x70502),f10(x70502,x70501)),f10(x70502,x70503)),f10(x70502,x70503))+E(x70501,f195(f883(x70502,a871)))+~P102(f332(f61(x70502),x70503))+~P102(f332(f332(f246(f883(x70502,a871)),x70501),x70503)) % 172.83/172.50 [7051]~P104(x70512)+E(f332(f332(f244(x70512),f15(x70512,x70511)),f15(x70512,x70513)),f15(x70512,x70513))+E(x70511,f195(f883(x70512,a871)))+~P102(f332(f61(x70512),x70513))+~P102(f332(f332(f246(f883(x70512,a871)),x70511),x70513)) % 172.83/172.50 [7052]~P104(x70522)+E(f332(f332(f245(x70522),f14(x70522,x70521)),f14(x70522,x70523)),f14(x70522,x70523))+E(x70521,f195(f883(x70522,a871)))+~P102(f332(f61(x70522),x70523))+~P102(f332(f332(f246(f883(x70522,a871)),x70521),x70523)) % 172.83/172.50 [7349]~P104(x73492)+E(x73491,f195(f883(x73492,a871)))+~P102(f332(f61(x73492),x73493))+P102(f332(f332(f246(x73492),f14(x73492,x73491)),f14(x73492,x73493)))+~P102(f332(f332(f246(f883(x73492,a871)),x73491),x73493)) % 172.83/172.50 [7350]~P104(x73502)+E(x73501,f195(f883(x73502,a871)))+~P102(f332(f61(x73502),x73503))+P102(f332(f332(f246(x73502),f15(x73502,x73503)),f15(x73502,x73501)))+~P102(f332(f332(f246(f883(x73502,a871)),x73501),x73503)) % 172.83/172.50 [7408]~P61(x74081)+E(f13(x74081,x74082),x74083)+~P102(f332(f61(x74081),x74082))+~E(f332(f332(f22(f883(x74081,a871)),x74082),f332(f332(f310(x74081),x74083),f195(f883(x74081,a871)))),f195(f883(x74081,a871)))+~P102(f332(f332(f334(x74081),x74083),x74082)) % 172.83/172.50 [7409]~P61(x74091)+E(f10(x74091,x74092),x74093)+~P102(f332(f61(x74091),x74092))+~E(f332(f332(f22(f883(x74091,a871)),x74092),f332(f332(f310(x74091),x74093),f195(f883(x74091,a871)))),f195(f883(x74091,a871)))+~P102(f332(f332(f334(x74091),x74093),x74092)) % 172.83/172.50 [7410]~P104(x74101)+E(f14(x74101,x74102),x74103)+~P102(f332(f61(x74101),x74102))+~E(f332(f332(f22(f883(x74101,a871)),x74102),f332(f332(f310(x74101),x74103),f195(f883(x74101,a871)))),f195(f883(x74101,a871)))+~P102(f332(f332(f334(x74101),x74103),x74102)) % 172.83/172.50 [7411]~P104(x74111)+E(f15(x74111,x74112),x74113)+~P102(f332(f61(x74111),x74112))+~E(f332(f332(f22(f883(x74111,a871)),x74112),f332(f332(f310(x74111),x74113),f195(f883(x74111,a871)))),f195(f883(x74111,a871)))+~P102(f332(f332(f334(x74111),x74113),x74112)) % 172.83/172.50 [7510]~P104(x75101)+E(f11(x75101,f245(x75101),x75102),x75103)+~P102(f332(f61(x75101),x75102))+~E(f332(f332(f22(f883(x75101,a871)),x75102),f332(f332(f310(x75101),x75103),f195(f883(x75101,a871)))),f195(f883(x75101,a871)))+~P102(f332(f332(f334(x75101),x75103),x75102)) % 172.83/172.50 [7511]~P104(x75111)+E(f12(x75111,f244(x75111),x75112),x75113)+~P102(f332(f61(x75111),x75112))+~E(f332(f332(f22(f883(x75111,a871)),x75112),f332(f332(f310(x75111),x75113),f195(f883(x75111,a871)))),f195(f883(x75111,a871)))+~P102(f332(f332(f334(x75111),x75113),x75112)) % 172.83/172.50 [7548]~P104(x75482)+E(x75481,f195(f883(x75482,a871)))+~P102(f332(f61(x75482),x75481))+~P102(f332(f332(f247(x75482),x75483),f451(x75483,x75481,x75482)))+P102(f332(f332(f247(x75482),x75483),f332(f63(x75482,f244(x75482)),x75481))) % 172.83/172.50 [7549]~P98(x75492)+E(x75491,f195(f883(x75492,a871)))+~P102(f332(f61(x75492),x75491))+~P102(f332(f332(f246(x75492),x75493),f840(x75493,x75491,x75492)))+P102(f332(f332(f246(x75492),x75493),f332(f63(x75492,f104(x75492)),x75491))) % 172.83/172.50 [7550]~P104(x75502)+E(x75501,f195(f883(x75502,a871)))+~P102(f332(f61(x75502),x75501))+~P102(f332(f332(f246(x75502),x75503),f452(x75503,x75501,x75502)))+P102(f332(f332(f246(x75502),x75503),f332(f63(x75502,f244(x75502)),x75501))) % 172.83/172.50 [7635]~P98(x76352)+E(x76351,f195(f883(x76352,a871)))+~P102(f332(f61(x76352),x76351))+P102(f332(f332(f334(x76352),f840(x76353,x76351,x76352)),x76351))+P102(f332(f332(f246(x76352),x76353),f332(f63(x76352,f104(x76352)),x76351))) % 172.83/172.50 [7636]~P104(x76362)+E(x76361,f195(f883(x76362,a871)))+~P102(f332(f61(x76362),x76361))+P102(f332(f332(f334(x76362),f452(x76363,x76361,x76362)),x76361))+P102(f332(f332(f246(x76362),x76363),f332(f63(x76362,f244(x76362)),x76361))) % 172.83/172.50 [7637]~P104(x76372)+E(x76371,f195(f883(x76372,a871)))+~P102(f332(f61(x76372),x76371))+P102(f332(f332(f334(x76372),f451(x76373,x76371,x76372)),x76371))+P102(f332(f332(f247(x76372),x76373),f332(f63(x76372,f244(x76372)),x76371))) % 172.83/172.50 [7762]~P104(x77622)+E(x77621,f195(f883(x77622,a871)))+E(f332(f332(f244(x77622),f12(x77622,f244(x77622),x77621)),f12(x77622,f244(x77622),x77623)),f12(x77622,f244(x77622),x77623))+~P102(f332(f61(x77622),x77623))+~P102(f332(f332(f246(f883(x77622,a871)),x77621),x77623)) % 172.83/172.50 [7763]~P104(x77632)+E(x77631,f195(f883(x77632,a871)))+E(f332(f332(f245(x77632),f11(x77632,f245(x77632),x77631)),f11(x77632,f245(x77632),x77633)),f11(x77632,f245(x77632),x77633))+~P102(f332(f61(x77632),x77633))+~P102(f332(f332(f246(f883(x77632,a871)),x77631),x77633)) % 172.83/172.50 [7964]~E(f636(x79641,x79643,x79642),f637(x79641,x79643,x79642))+~E(f332(f37(x79642),f638(x79641,x79643,x79642)),x79641)+E(f332(f332(f80(a876),x79641),f332(f37(f883(x79642,a871)),x79643)),f332(f37(x79642),f39(f883(x79642,a871),x79643)))+~P102(f332(f61(x79642),f39(f883(x79642,a871),x79643)))+~P102(f332(f61(f883(x79642,a871)),x79643)) % 172.83/172.50 [8149]~P104(x81492)+E(x81491,f195(f883(x81492,a871)))+~P102(f332(f61(x81492),x81493))+P102(f332(f332(f246(x81492),f332(f63(x81492,f244(x81492)),x81493)),f332(f63(x81492,f244(x81492)),x81491)))+~P102(f332(f332(f246(f883(x81492,a871)),x81491),x81493)) % 172.83/172.50 [8459]~E(f636(x84591,x84593,x84592),f637(x84591,x84593,x84592))+E(f332(f332(f80(a876),x84591),f332(f37(f883(x84592,a871)),x84593)),f332(f37(x84592),f39(f883(x84592,a871),x84593)))+P102(f332(f332(f334(f883(x84592,a871)),f638(x84591,x84593,x84592)),x84593))+~P102(f332(f61(x84592),f39(f883(x84592,a871),x84593)))+~P102(f332(f61(f883(x84592,a871)),x84593)) % 172.83/172.50 [8485]~E(f332(f37(x84852),f638(x84851,x84853,x84852)),x84851)+E(f332(f332(f80(a876),x84851),f332(f37(f883(x84852,a871)),x84853)),f332(f37(x84852),f39(f883(x84852,a871),x84853)))+P102(f332(f332(f334(f883(x84852,a871)),f637(x84851,x84853,x84852)),x84853))+~P102(f332(f61(x84852),f39(f883(x84852,a871),x84853)))+~P102(f332(f61(f883(x84852,a871)),x84853)) % 172.83/172.50 [8486]~E(f332(f37(x84862),f638(x84861,x84863,x84862)),x84861)+E(f332(f332(f80(a876),x84861),f332(f37(f883(x84862,a871)),x84863)),f332(f37(x84862),f39(f883(x84862,a871),x84863)))+P102(f332(f332(f334(f883(x84862,a871)),f636(x84861,x84863,x84862)),x84863))+~P102(f332(f61(x84862),f39(f883(x84862,a871),x84863)))+~P102(f332(f61(f883(x84862,a871)),x84863)) % 172.83/172.50 [8514]~E(f332(f37(x85142),f638(x85141,x85143,x85142)),x85141)+~E(f332(f332(f104(f883(x85142,a871)),f637(x85141,x85143,x85142)),f636(x85141,x85143,x85142)),f195(f883(x85142,a871)))+E(f332(f332(f80(a876),x85141),f332(f37(f883(x85142,a871)),x85143)),f332(f37(x85142),f39(f883(x85142,a871),x85143)))+~P102(f332(f61(f883(x85142,a871)),x85143))+~P102(f332(f61(x85142),f39(f883(x85142,a871),x85143))) % 172.83/172.50 [8755]E(f332(f332(f80(a876),x87551),f332(f37(f883(x87552,a871)),x87553)),f332(f37(x87552),f39(f883(x87552,a871),x87553)))+P102(f332(f332(f334(f883(x87552,a871)),f638(x87551,x87553,x87552)),x87553))+P102(f332(f332(f334(f883(x87552,a871)),f637(x87551,x87553,x87552)),x87553))+~P102(f332(f61(f883(x87552,a871)),x87553))+~P102(f332(f61(x87552),f39(f883(x87552,a871),x87553))) % 172.83/172.50 [8756]E(f332(f332(f80(a876),x87561),f332(f37(f883(x87562,a871)),x87563)),f332(f37(x87562),f39(f883(x87562,a871),x87563)))+P102(f332(f332(f334(f883(x87562,a871)),f638(x87561,x87563,x87562)),x87563))+P102(f332(f332(f334(f883(x87562,a871)),f636(x87561,x87563,x87562)),x87563))+~P102(f332(f61(f883(x87562,a871)),x87563))+~P102(f332(f61(x87562),f39(f883(x87562,a871),x87563))) % 172.83/172.50 [8781]~E(f332(f332(f104(f883(x87812,a871)),f637(x87811,x87813,x87812)),f636(x87811,x87813,x87812)),f195(f883(x87812,a871)))+E(f332(f332(f80(a876),x87811),f332(f37(f883(x87812,a871)),x87813)),f332(f37(x87812),f39(f883(x87812,a871),x87813)))+~P102(f332(f61(f883(x87812,a871)),x87813))+P102(f332(f332(f334(f883(x87812,a871)),f638(x87811,x87813,x87812)),x87813))+~P102(f332(f61(x87812),f39(f883(x87812,a871),x87813))) % 172.83/172.50 [9045]~P93(x90452)+E(x90451,f195(f883(x90452,a871)))+~E(f332(f332(f80(x90452),f332(x90453,f828(x90451,x90453,x90452))),f332(x90453,f833(x90451,x90453,x90452))),f332(x90453,f332(f332(f80(x90452),f828(x90451,x90453,x90452)),f833(x90451,x90453,x90452))))+~P102(f332(f61(x90452),x90451))+E(f332(f63(x90452,f80(x90452)),f332(f311(x90452,x90452,x90453),x90451)),f332(x90453,f332(f63(x90452,f80(x90452)),x90451))) % 172.83/172.50 [9969]P102(f332(f332(x99691,x99692),x99693))+P102(f332(f332(f247(a1),f492(x99691,x99693,x99692)),f493(x99691,x99693,x99692)))+P102(f332(f332(f246(a1),f493(x99691,x99693,x99692)),f2(a1)))+P102(f332(f332(x99691,f492(x99691,x99693,x99692)),f332(f332(f80(a1),f332(f106(a1),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)))),f493(x99691,x99693,x99692))))+~P102(f332(f320(f882(a1,a1),a56),f332(f332(f267(a1,a1),x99692),x99693))) % 172.83/172.50 [9975]P102(f332(f332(x99751,x99752),x99753))+P102(f332(f332(f246(a1),f491(x99751,x99753,x99752)),f2(a1)))+P102(f332(f332(x99751,f487(x99751,x99753,x99752)),f332(f332(f80(a1),f332(f106(a1),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)))),f491(x99751,x99753,x99752))))+P102(f332(f332(f246(a1),f2(a1)),f332(f332(f79(a1),f487(x99751,x99753,x99752)),f491(x99751,x99753,x99752))))+~P102(f332(f320(f882(a1,a1),a51),f332(f332(f267(a1,a1),x99752),x99753))) % 172.83/172.50 [7935]~P113(x79351)+~P102(f332(f332(f246(x79351),x79352),f77(x79351)))+~P102(f332(f332(f246(x79351),f2(x79351)),x79352))+~P102(f332(f332(f246(x79351),f2(x79351)),x79353))+P102(f332(f332(f246(x79351),f332(f332(f80(x79351),x79352),x79353)),x79353)) % 172.83/172.50 [7936]~P113(x79361)+~P102(f332(f332(f246(x79361),x79363),f77(x79361)))+~P102(f332(f332(f246(x79361),f2(x79361)),x79363))+~P102(f332(f332(f246(x79361),f2(x79361)),x79362))+P102(f332(f332(f246(x79361),f332(f332(f80(x79361),x79362),x79363)),x79362)) % 172.83/172.50 [8300]~P104(x83002)+E(x83001,f195(f883(x83002,a871)))+~P102(f332(f61(x83002),x83001))+P102(f332(f332(f334(x83002),f456(x83003,x83001,x83002)),x83001))+~P102(f332(f332(f246(x83002),f332(f63(x83002,f244(x83002)),x83001)),x83003)) % 172.83/172.50 [8301]~P104(x83012)+E(x83011,f195(f883(x83012,a871)))+~P102(f332(f61(x83012),x83011))+P102(f332(f332(f334(x83012),f457(x83013,x83011,x83012)),x83011))+~P102(f332(f332(f247(x83012),f332(f63(x83012,f244(x83012)),x83011)),x83013)) % 172.83/172.50 [8302]~P104(x83022)+E(x83021,f195(f883(x83022,a871)))+~P102(f332(f61(x83022),x83021))+P102(f332(f332(f247(x83022),f457(x83023,x83021,x83022)),x83023))+~P102(f332(f332(f247(x83022),f332(f63(x83022,f244(x83022)),x83021)),x83023)) % 172.83/172.50 [8303]~P104(x83032)+E(x83031,f195(f883(x83032,a871)))+~P102(f332(f61(x83032),x83031))+P102(f332(f332(f246(x83032),f456(x83033,x83031,x83032)),x83033))+~P102(f332(f332(f246(x83032),f332(f63(x83032,f244(x83032)),x83031)),x83033)) % 172.83/172.50 [8387]~P102(f332(x83871,x83873))+P102(f332(x83871,f407(x83871,x83872)))+P102(f332(x83871,f402(x83871,x83872)))+~P102(f332(f332(f247(a1),f2(a1)),x83872))+P102(f332(x83871,f332(f332(f22(a1),f402(x83871,x83872)),f332(f332(f80(a1),f408(x83871,x83872)),x83872)))) % 172.83/172.50 [8608]~P102(f332(x86081,x86083))+P102(f332(x86081,f402(x86081,x86082)))+~P102(f332(f332(f247(a1),f2(a1)),x86082))+P102(f332(f332(f334(a1),f407(x86081,x86082)),f303(a1,f77(a1),x86082)))+P102(f332(x86081,f332(f332(f22(a1),f402(x86081,x86082)),f332(f332(f80(a1),f408(x86081,x86082)),x86082)))) % 172.83/172.50 [8803]~P102(f332(x88031,x88033))+~P102(f332(x88031,f402(x88031,x88032)))+P102(f332(x88031,f407(x88031,x88032)))+~P102(f332(f332(f247(a1),f2(a1)),x88032))+~P102(f332(x88031,f332(f332(f22(a1),f402(x88031,x88032)),f332(f332(f80(a1),f408(x88031,x88032)),x88032)))) % 172.83/172.50 [8930]~P102(f332(x89301,x89303))+~P102(f332(x89301,f402(x89301,x89302)))+~P102(f332(f332(f247(a1),f2(a1)),x89302))+P102(f332(f332(f334(a1),f407(x89301,x89302)),f303(a1,f77(a1),x89302)))+~P102(f332(x89301,f332(f332(f22(a1),f402(x89301,x89302)),f332(f332(f80(a1),f408(x89301,x89302)),x89302)))) % 172.83/172.50 [8715]~P61(x87151)+~P102(f332(f61(x87151),x87152))+E(f332(f332(f22(f883(x87151,a871)),x87152),f332(f332(f310(x87151),x87153),f195(f883(x87151,a871)))),f195(f883(x87151,a871)))+~P102(f332(f332(f334(x87151),x87153),x87152))+E(f332(f332(f113(x87151),x87153),f13(x87151,f332(f332(f22(f883(x87151,a871)),x87152),f332(f332(f310(x87151),x87153),f195(f883(x87151,a871)))))),f13(x87151,x87152)) % 172.83/172.50 [8716]~P61(x87161)+~P102(f332(f61(x87161),x87162))+E(f332(f332(f22(f883(x87161,a871)),x87162),f332(f332(f310(x87161),x87163),f195(f883(x87161,a871)))),f195(f883(x87161,a871)))+~P102(f332(f332(f334(x87161),x87163),x87162))+E(f332(f332(f104(x87161),x87163),f10(x87161,f332(f332(f22(f883(x87161,a871)),x87162),f332(f332(f310(x87161),x87163),f195(f883(x87161,a871)))))),f10(x87161,x87162)) % 172.83/172.50 [8717]~P104(x87171)+~P102(f332(f61(x87171),x87172))+E(f332(f332(f22(f883(x87171,a871)),x87172),f332(f332(f310(x87171),x87173),f195(f883(x87171,a871)))),f195(f883(x87171,a871)))+~P102(f332(f332(f334(x87171),x87173),x87172))+E(f332(f332(f245(x87171),x87173),f14(x87171,f332(f332(f22(f883(x87171,a871)),x87172),f332(f332(f310(x87171),x87173),f195(f883(x87171,a871)))))),f14(x87171,x87172)) % 172.83/172.50 [8718]~P104(x87181)+~P102(f332(f61(x87181),x87182))+E(f332(f332(f22(f883(x87181,a871)),x87182),f332(f332(f310(x87181),x87183),f195(f883(x87181,a871)))),f195(f883(x87181,a871)))+~P102(f332(f332(f334(x87181),x87183),x87182))+E(f332(f332(f244(x87181),x87183),f15(x87181,f332(f332(f22(f883(x87181,a871)),x87182),f332(f332(f310(x87181),x87183),f195(f883(x87181,a871)))))),f15(x87181,x87182)) % 172.83/172.50 [8775]~P104(x87751)+~P102(f332(f61(x87751),x87752))+E(f332(f332(f22(f883(x87751,a871)),x87752),f332(f332(f310(x87751),x87753),f195(f883(x87751,a871)))),f195(f883(x87751,a871)))+~P102(f332(f332(f334(x87751),x87753),x87752))+E(f332(f332(f245(x87751),x87753),f11(x87751,f245(x87751),f332(f332(f22(f883(x87751,a871)),x87752),f332(f332(f310(x87751),x87753),f195(f883(x87751,a871)))))),f11(x87751,f245(x87751),x87752)) % 172.83/172.50 [8776]~P104(x87761)+~P102(f332(f61(x87761),x87762))+E(f332(f332(f22(f883(x87761,a871)),x87762),f332(f332(f310(x87761),x87763),f195(f883(x87761,a871)))),f195(f883(x87761,a871)))+~P102(f332(f332(f334(x87761),x87763),x87762))+E(f332(f332(f244(x87761),x87763),f12(x87761,f244(x87761),f332(f332(f22(f883(x87761,a871)),x87762),f332(f332(f310(x87761),x87763),f195(f883(x87761,a871)))))),f12(x87761,f244(x87761),x87762)) % 172.83/172.50 [8790]~P61(x87901)+~P102(f332(f61(x87901),x87903))+~P102(f332(f61(x87901),x87902))+E(f332(f332(f104(f883(x87901,a871)),x87902),x87903),f195(f883(x87901,a871)))+E(f332(f332(f113(x87901),f13(x87901,f332(f332(f113(f883(x87901,a871)),x87902),x87903))),f13(x87901,f332(f332(f104(f883(x87901,a871)),x87902),x87903))),f332(f332(f113(x87901),f13(x87901,x87902)),f13(x87901,x87903))) % 172.83/172.50 [8791]~P61(x87911)+~P102(f332(f61(x87911),x87913))+~P102(f332(f61(x87911),x87912))+E(f332(f332(f104(f883(x87911,a871)),x87912),x87913),f195(f883(x87911,a871)))+E(f332(f332(f104(x87911),f10(x87911,f332(f332(f113(f883(x87911,a871)),x87912),x87913))),f10(x87911,f332(f332(f104(f883(x87911,a871)),x87912),x87913))),f332(f332(f104(x87911),f10(x87911,x87912)),f10(x87911,x87913))) % 172.83/172.50 [8792]~P104(x87921)+~P102(f332(f61(x87921),x87923))+~P102(f332(f61(x87921),x87922))+E(f332(f332(f104(f883(x87921,a871)),x87922),x87923),f195(f883(x87921,a871)))+E(f332(f332(f244(x87921),f15(x87921,f332(f332(f113(f883(x87921,a871)),x87922),x87923))),f15(x87921,f332(f332(f104(f883(x87921,a871)),x87922),x87923))),f332(f332(f244(x87921),f15(x87921,x87922)),f15(x87921,x87923))) % 172.83/172.50 [8793]~P104(x87931)+~P102(f332(f61(x87931),x87933))+~P102(f332(f61(x87931),x87932))+E(f332(f332(f104(f883(x87931,a871)),x87932),x87933),f195(f883(x87931,a871)))+E(f332(f332(f245(x87931),f14(x87931,f332(f332(f113(f883(x87931,a871)),x87932),x87933))),f14(x87931,f332(f332(f104(f883(x87931,a871)),x87932),x87933))),f332(f332(f245(x87931),f14(x87931,x87932)),f14(x87931,x87933))) % 172.83/172.50 [9017]~P104(x90171)+~P102(f332(f61(x90171),x90173))+~P102(f332(f61(x90171),x90172))+E(f332(f332(f104(f883(x90171,a871)),x90172),x90173),f195(f883(x90171,a871)))+E(f332(f332(f244(x90171),f12(x90171,f244(x90171),f332(f332(f113(f883(x90171,a871)),x90172),x90173))),f12(x90171,f244(x90171),f332(f332(f104(f883(x90171,a871)),x90172),x90173))),f332(f332(f244(x90171),f12(x90171,f244(x90171),x90172)),f12(x90171,f244(x90171),x90173))) % 172.83/172.50 [9018]~P104(x90181)+~P102(f332(f61(x90181),x90183))+~P102(f332(f61(x90181),x90182))+E(f332(f332(f104(f883(x90181,a871)),x90182),x90183),f195(f883(x90181,a871)))+E(f332(f332(f245(x90181),f11(x90181,f245(x90181),f332(f332(f113(f883(x90181,a871)),x90182),x90183))),f11(x90181,f245(x90181),f332(f332(f104(f883(x90181,a871)),x90182),x90183))),f332(f332(f245(x90181),f11(x90181,f245(x90181),x90182)),f11(x90181,f245(x90181),x90183))) % 172.83/172.50 [9809]~P107(x98093)+E(x98091,x98092)+~P102(f332(f332(f246(x98093),f2(x98093)),x98092))+~P102(f332(f332(f246(x98093),f2(x98093)),x98091))+~E(f332(f332(f257(x98093),x98091),f332(f106(a876),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)))),f332(f332(f257(x98093),x98092),f332(f106(a876),f332(f332(f79(a1),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100)),f332(f332(f22(a1),f332(f332(f79(a1),a82),a82)),a100))))) % 172.83/172.50 [6327]E(f849(x63271,x63272,x63273),x63274)+E(f332(x63271,x63274),f2(a876))+~E(f332(f332(f6(x63273,a876),x63271),x63272),f77(a876))+~P102(f332(f61(x63273),x63272))+~P102(f332(f332(f334(x63273),x63274),x63272)) % 172.83/172.50 [6389]E(f852(x63891,x63892,x63893),x63894)+E(f332(x63891,x63894),f2(a876))+~E(f332(f332(f6(x63893,a876),x63891),x63892),f332(a115,f2(a876)))+~P102(f332(f61(x63893),x63892))+~P102(f332(f332(f334(x63893),x63894),x63892)) % 172.83/172.50 [6494]~P104(x64941)+~P27(x64941)+P102(f332(f332(f247(x64941),x64942),f39(x64941,x64943)))+~P102(f332(f332(f247(x64941),x64942),x64944))+~P102(f332(f332(f334(x64941),x64944),x64943)) % 172.83/172.50 [6667]~P104(x66671)+~P27(x66671)+~P102(f332(f332(f247(x66671),x66674),x66673))+P102(f332(f332(f247(x66671),f40(x66671,x66672)),x66673))+~P102(f332(f332(f334(x66671),x66674),x66672)) % 172.83/172.50 [6927]~P107(x69273)+E(x69271,x69272)+~E(f332(f332(f257(x69273),x69271),f332(a115,x69274)),f332(f332(f257(x69273),x69272),f332(a115,x69274)))+~P102(f332(f332(f246(x69273),f2(x69273)),x69272))+~P102(f332(f332(f246(x69273),f2(x69273)),x69271)) % 172.83/172.50 [7138]~E(f857(x71382,x71383,x71381,x71384),x71384)+~E(f332(x71382,x71384),f77(a876))+E(f332(f332(f6(x71381,a876),x71382),x71383),f77(a876))+~P102(f332(f61(x71381),x71383))+~P102(f332(f332(f334(x71381),x71384),x71383)) % 172.83/172.50 [7145]~P114(x71454)+~P130(x71454)+E(f332(x71451,f839(x71451,x71452,x71453,x71454)),f2(x71454))+~E(f332(f332(f9(x71453,x71454),x71451),x71452),f2(x71454))+~P102(f332(f61(x71453),x71452)) % 172.83/172.50 [7231]~E(f855(x72312,x72313,x72311,x72314),x72314)+~E(f332(x72312,x72314),f332(a115,f2(a876)))+E(f332(f332(f6(x72311,a876),x72312),x72313),f332(a115,f2(a876)))+~P102(f332(f61(x72311),x72313))+~P102(f332(f332(f334(x72311),x72314),x72313)) % 172.83/172.50 [7976]~E(f332(x79762,x79764),f77(a876))+~E(f332(x79762,f857(x79762,x79763,x79761,x79764)),f2(a876))+E(f332(f332(f6(x79761,a876),x79762),x79763),f77(a876))+~P102(f332(f61(x79761),x79763))+~P102(f332(f332(f334(x79761),x79764),x79763)) % 172.83/172.50 [8020]~E(f332(x80202,x80204),f332(a115,f2(a876)))+~E(f332(x80202,f855(x80202,x80203,x80201,x80204)),f2(a876))+E(f332(f332(f6(x80201,a876),x80202),x80203),f332(a115,f2(a876)))+~P102(f332(f61(x80201),x80203))+~P102(f332(f332(f334(x80201),x80204),x80203)) % 172.83/172.50 [8578]~P104(x85781)+~P29(x85781,x85784)+P29(x85781,x85782)+~E(x85782,f332(f332(f151(x85781),x85783),x85784))+~P102(f332(f332(f246(x85781),x85783),f764(x85782,x85781,x85784,x85783))) % 172.83/172.50 [8612]E(x86121,x86122)+E(f332(f332(f22(a1),f389(x86123,x86122,x86124,x86121)),f390(x86123,x86122,x86124,x86121)),x86121)+~E(f332(f332(f79(a1),x86121),x86124),x86122)+~P102(f332(f332(f247(a1),f2(a1)),x86124))+~P102(f332(f332(f334(a1),x86122),x86123)) % 172.83/172.50 [8613]E(x86131,x86132)+E(f332(f332(f79(a1),f393(x86133,x86132,x86134,x86131)),f394(x86133,x86132,x86134,x86131)),x86131)+~E(f332(f332(f22(a1),x86131),x86134),x86132)+~P102(f332(f332(f247(a1),f2(a1)),x86134))+~P102(f332(f332(f334(a1),x86132),x86133)) % 172.83/172.50 [8788]E(f332(x87881,f623(x87882,x87881,x87883,x87884)),x87882)+P102(f332(f332(f246(a876),x87884),f624(x87882,x87881,x87883,x87884)))+~P102(f332(f332(f246(a1),x87882),f332(x87881,x87883)))+~P102(f332(f332(f247(a876),x87884),x87883))+~P102(f332(f332(f246(a1),f332(x87881,x87884)),x87882)) % 172.83/172.50 [8789]~P104(x87891)+~P29(x87891,x87893)+P29(x87891,x87892)+~E(x87892,f332(f332(f151(x87891),x87894),x87893))+P102(f332(f332(f334(x87891),f764(x87892,x87891,x87893,x87894)),f332(f173(x87891),x87893))) % 172.83/172.50 [8807]~P114(x88074)+~P130(x88074)+~E(f332(f332(f9(x88071,x88074),x88072),x88073),f2(x88074))+~P102(f332(f61(x88071),x88073))+P102(f332(f332(f334(x88071),f839(x88072,x88073,x88071,x88074)),x88073)) % 172.83/172.50 [8842]~E(f332(x88422,x88424),f77(a876))+E(f332(f332(f6(x88421,a876),x88422),x88423),f77(a876))+~P102(f332(f61(x88421),x88423))+~P102(f332(f332(f334(x88421),x88424),x88423))+P102(f332(f332(f334(x88421),f857(x88422,x88423,x88421,x88424)),x88423)) % 172.83/172.50 [8851]E(x88511,x88512)+~E(f332(f332(f79(a1),x88512),x88514),x88511)+~P102(f332(f332(f247(a1),f2(a1)),x88514))+~P102(f332(f332(f334(a1),x88511),x88513))+P102(f332(f332(f334(a1),f389(x88513,x88511,x88514,x88512)),x88513)) % 172.83/172.50 [8852]E(x88521,x88522)+~E(f332(f332(f22(a1),x88522),x88524),x88521)+~P102(f332(f332(f247(a1),f2(a1)),x88524))+~P102(f332(f332(f334(a1),x88521),x88523))+P102(f332(f332(f334(a1),f393(x88523,x88521,x88524,x88522)),x88523)) % 172.83/172.50 [8854]~E(f332(x88542,x88544),f332(a115,f2(a876)))+E(f332(f332(f6(x88541,a876),x88542),x88543),f332(a115,f2(a876)))+~P102(f332(f61(x88541),x88543))+~P102(f332(f332(f334(x88541),x88544),x88543))+P102(f332(f332(f334(x88541),f855(x88542,x88543,x88541,x88544)),x88543)) % 172.83/172.50 [8859]P54(x88592,x88593,x88594,x88591)+E(x88591,f195(f883(x88592,a871)))+~P102(f332(f61(x88592),x88594))+~P102(f332(f61(x88592),x88591))+P102(f332(f332(f334(x88592),f523(x88591,x88594,x88593,x88592)),x88594)) % 172.83/172.50 [8944]E(x89441,x89442)+~E(f332(f332(f79(a1),x89442),x89444),x89441)+~P102(f332(f332(f247(a1),f2(a1)),x89444))+~P102(f332(f332(f334(a1),x89441),x89443))+P102(f332(f332(f334(a1),f390(x89443,x89441,x89444,x89442)),f303(a1,f77(a1),x89444))) % 172.83/172.50 [8945]E(x89451,x89452)+~E(f332(f332(f22(a1),x89452),x89454),x89451)+~P102(f332(f332(f247(a1),f2(a1)),x89454))+~P102(f332(f332(f334(a1),x89451),x89453))+P102(f332(f332(f334(a1),f394(x89453,x89451,x89454,x89452)),f303(a1,f77(a1),x89454))) % 172.83/172.50 [9023]P102(f332(f332(f246(a876),x90231),f623(x90232,x90233,x90234,x90231)))+~P102(f332(f332(f246(a1),x90232),f332(x90233,x90234)))+P102(f332(f332(f246(a876),x90231),f624(x90232,x90233,x90234,x90231)))+~P102(f332(f332(f247(a876),x90231),x90234))+~P102(f332(f332(f246(a1),f332(x90233,x90231)),x90232)) % 172.83/172.50 [9133]E(f332(x91331,f623(x91332,x91331,x91333,x91334)),x91332)+~P102(f332(f332(f246(a1),x91332),f332(x91331,x91333)))+P102(f332(f332(f247(a876),f624(x91332,x91331,x91333,x91334)),x91333))+~P102(f332(f332(f247(a876),x91334),x91333))+~P102(f332(f332(f246(a1),f332(x91331,x91334)),x91332)) % 172.83/172.50 [9264]~P102(f332(f332(f246(a1),x92642),f332(x92643,x92644)))+P102(f332(f332(f246(a876),x92641),f624(x92642,x92643,x92644,x92641)))+P102(f332(f332(f246(a876),f623(x92642,x92643,x92644,x92641)),x92644))+~P102(f332(f332(f247(a876),x92641),x92644))+~P102(f332(f332(f246(a1),f332(x92643,x92641)),x92642)) % 172.83/172.50 [9265]~P102(f332(f332(f246(a1),x92652),f332(x92653,x92654)))+P102(f332(f332(f246(a876),x92651),f623(x92652,x92653,x92654,x92651)))+P102(f332(f332(f247(a876),f624(x92652,x92653,x92654,x92651)),x92654))+~P102(f332(f332(f247(a876),x92651),x92654))+~P102(f332(f332(f246(a1),f332(x92653,x92651)),x92652)) % 172.83/172.50 [9372]~P102(f332(f332(f246(a1),x93721),f332(x93722,x93723)))+P102(f332(f332(f246(a876),f623(x93721,x93722,x93723,x93724)),x93723))+~P102(f332(f332(f247(a876),x93724),x93723))+~P102(f332(f332(f246(a1),f332(x93722,x93724)),x93721))+P102(f332(f332(f247(a876),f624(x93721,x93722,x93723,x93724)),x93723)) % 172.83/172.50 [9450]E(x94501,f195(f883(x94502,a871)))+~P102(f332(f61(x94502),x94504))+~P102(f332(f61(x94502),x94501))+P102(f332(f332(f334(f882(f883(x94502,a871),f883(x94502,a871))),f332(f332(f267(f883(x94502,a871),f883(x94502,a871)),x94504),x94501)),f324(x94502,x94503)))+P102(f332(f332(f334(x94502),f527(x94503,x94501,x94504,x94502)),x94504)) % 172.83/172.50 [9451]E(x94511,f195(f883(x94512,a871)))+~P102(f332(f61(x94512),x94514))+~P102(f332(f61(x94512),x94511))+P102(f332(f332(f334(f882(f883(x94512,a871),f883(x94512,a871))),f332(f332(f267(f883(x94512,a871),f883(x94512,a871)),x94514),x94511)),f324(x94512,x94513)))+P102(f332(f332(f334(x94512),f588(x94513,x94511,x94514,x94512)),x94514)) % 172.83/172.50 [10112]E(f332(x101121,f623(x101122,x101121,x101123,x101124)),x101122)+~P102(f332(f332(f246(a1),x101122),f332(x101121,x101123)))+~P102(f332(f332(f246(a1),f332(f74(a1),f332(f332(f22(a1),f332(x101121,f332(f332(f79(a876),f624(x101122,x101121,x101123,x101124)),f77(a876)))),f332(x101121,f624(x101122,x101121,x101123,x101124))))),f77(a1)))+~P102(f332(f332(f247(a876),x101124),x101123))+~P102(f332(f332(f246(a1),f332(x101121,x101124)),x101122)) % 172.83/172.50 [10113]~P102(f332(f332(f246(a1),x101132),f332(x101133,x101134)))+P102(f332(f332(f246(a876),x101131),f623(x101132,x101133,x101134,x101131)))+~P102(f332(f332(f246(a1),f332(f74(a1),f332(f332(f22(a1),f332(x101133,f332(f332(f79(a876),f624(x101132,x101133,x101134,x101131)),f77(a876)))),f332(x101133,f624(x101132,x101133,x101134,x101131))))),f77(a1)))+~P102(f332(f332(f247(a876),x101131),x101134))+~P102(f332(f332(f246(a1),f332(x101133,x101131)),x101132)) % 172.83/172.50 [10114]~P102(f332(f332(f246(a1),x101141),f332(x101142,x101143)))+~P102(f332(f332(f246(a1),f332(f74(a1),f332(f332(f22(a1),f332(x101142,f332(f332(f79(a876),f624(x101141,x101142,x101143,x101144)),f77(a876)))),f332(x101142,f624(x101141,x101142,x101143,x101144))))),f77(a1)))+~P102(f332(f332(f247(a876),x101144),x101143))+~P102(f332(f332(f246(a1),f332(x101142,x101144)),x101141))+P102(f332(f332(f246(a876),f623(x101141,x101142,x101143,x101144)),x101143)) % 172.83/172.50 [7198]~P59(x71981)+P102(f332(f332(f247(x71981),x71982),f2(x71981)))+~P102(f332(f332(f247(x71981),x71983),f2(x71981)))+P102(f332(f332(f247(x71981),f2(x71981)),x71982))+P102(f332(f332(f247(x71981),x71983),f332(f332(f290(x71981),x71984),x71982))) % 172.83/172.50 [7199]~P59(x71991)+P102(f332(f332(f247(x71991),x71992),f2(x71991)))+~P102(f332(f332(f246(x71991),x71993),f2(x71991)))+P102(f332(f332(f247(x71991),f2(x71991)),x71992))+P102(f332(f332(f246(x71991),x71993),f332(f332(f290(x71991),x71994),x71992))) % 172.83/172.50 [7448]~P59(x74481)+P102(f332(f332(f247(x74481),x74482),f2(x74481)))+P102(f332(f332(f247(x74481),x74483),f2(x74481)))+P102(f332(f332(f247(x74481),f2(x74481)),x74483))+~P102(f332(f332(f247(x74481),x74482),f332(f332(f290(x74481),x74484),x74483))) % 172.83/172.50 [7449]~P59(x74491)+P102(f332(f332(f247(x74491),x74492),f2(x74491)))+P102(f332(f332(f246(x74491),x74493),f2(x74491)))+P102(f332(f332(f247(x74491),f2(x74491)),x74492))+~P102(f332(f332(f246(x74491),x74493),f332(f332(f290(x74491),x74494),x74492))) % 172.83/172.50 [7568]E(x75681,x75682)+~E(f332(f332(f165(x75683),x75684),x75681),f332(f332(f165(x75683),x75684),x75682))+~P102(f332(f137(x75683),x75684))+~P102(f332(f332(f247(a876),x75682),f332(f196(f877(x75683)),x75684)))+~P102(f332(f332(f247(a876),x75681),f332(f196(f877(x75683)),x75684))) % 172.83/172.50 [7937]~P59(x79371)+~P102(f332(f332(f247(x79371),x79373),f2(x79371)))+P102(f332(f332(f247(x79371),f2(x79371)),x79372))+~P102(f332(f332(f247(x79371),x79374),f332(f332(f80(x79371),x79373),x79372)))+P102(f332(f332(f247(x79371),x79373),f332(f332(f290(x79371),x79374),x79372))) % 172.83/172.50 [7938]~P59(x79381)+~P102(f332(f332(f246(x79381),x79383),f2(x79381)))+P102(f332(f332(f247(x79381),f2(x79381)),x79382))+~P102(f332(f332(f246(x79381),x79384),f332(f332(f80(x79381),x79383),x79382)))+P102(f332(f332(f246(x79381),x79383),f332(f332(f290(x79381),x79384),x79382))) % 172.83/172.50 [7939]~P59(x79391)+~P102(f332(f332(f247(x79391),x79392),f2(x79391)))+P102(f332(f332(f247(x79391),f2(x79391)),x79392))+~P102(f332(f332(f247(x79391),x79394),f332(f332(f80(x79391),x79393),x79392)))+P102(f332(f332(f247(x79391),x79393),f332(f332(f290(x79391),x79394),x79392))) % 172.83/172.50 [7940]~P59(x79401)+~P102(f332(f332(f247(x79401),x79402),f2(x79401)))+P102(f332(f332(f247(x79401),f2(x79401)),x79402))+~P102(f332(f332(f247(x79401),x79404),f332(f332(f290(x79401),x79403),x79402)))+P102(f332(f332(f247(x79401),x79403),f332(f332(f80(x79401),x79404),x79402))) % 172.83/172.50 [7941]~P59(x79411)+~P102(f332(f332(f247(x79411),x79412),f2(x79411)))+P102(f332(f332(f247(x79411),f2(x79411)),x79412))+~P102(f332(f332(f246(x79411),x79414),f332(f332(f80(x79411),x79413),x79412)))+P102(f332(f332(f246(x79411),x79413),f332(f332(f290(x79411),x79414),x79412))) % 172.83/172.50 [7942]~P59(x79421)+~P102(f332(f332(f247(x79421),x79422),f2(x79421)))+P102(f332(f332(f247(x79421),f2(x79421)),x79422))+~P102(f332(f332(f246(x79421),x79424),f332(f332(f290(x79421),x79423),x79422)))+P102(f332(f332(f246(x79421),x79423),f332(f332(f80(x79421),x79424),x79422))) % 172.83/172.50 [8088]~P104(x80881)+~P29(x80881,x80882)+~P102(f332(f332(f246(a876),x80883),x80884))+P102(f332(f332(f246(x80881),f332(f332(f165(x80881),x80882),x80883)),f332(f332(f165(x80881),x80882),x80884)))+~P102(f332(f332(f247(a876),x80884),f332(f196(f877(x80881)),x80882))) % 172.83/172.50 [8139]~P107(x81391)+~P102(f332(f332(f247(x81391),x81392),f77(x81391)))+~P102(f332(f332(f247(x81391),f2(x81391)),x81392))+~P102(f332(f332(f247(a876),x81394),x81393))+P102(f332(f332(f247(x81391),f332(f332(f257(x81391),x81392),x81393)),f332(f332(f257(x81391),x81392),x81394))) % 172.83/172.50 [8140]~P107(x81401)+~P102(f332(f332(f246(x81401),x81402),f77(x81401)))+~P102(f332(f332(f246(x81401),f2(x81401)),x81402))+~P102(f332(f332(f246(a876),x81404),x81403))+P102(f332(f332(f246(x81401),f332(f332(f257(x81401),x81402),x81403)),f332(f332(f257(x81401),x81402),x81404))) % 172.83/172.50 [8141]~P107(x81411)+~P102(f332(f332(f246(x81411),f2(x81411)),x81412))+~P102(f332(f332(f247(a876),f2(a876)),x81413))+~P102(f332(f332(f247(x81411),x81412),x81414))+P102(f332(f332(f247(x81411),f332(f332(f257(x81411),x81412),x81413)),f332(f332(f257(x81411),x81414),x81413))) % 172.83/172.50 [8162]~P104(x81621)+~P29(x81621,f332(f169(x81621),x81622))+~P102(f332(f332(f246(a876),x81624),x81623))+P102(f332(f332(f246(x81621),f332(f332(f165(x81621),x81622),x81623)),f332(f332(f165(x81621),x81622),x81624)))+~P102(f332(f332(f247(a876),x81623),f332(f196(f877(x81621)),x81622))) % 172.83/172.50 [8410]~P60(x84101)+~P102(f332(f332(f247(x84101),x84102),f2(x84101)))+~P102(f332(f332(f247(x84101),x84103),x84104))+~P102(f332(f332(f247(x84101),f2(x84101)),f332(f332(f80(x84101),x84103),x84104)))+P102(f332(f332(f247(x84101),f332(f332(f290(x84101),x84102),x84103)),f332(f332(f290(x84101),x84102),x84104))) % 172.83/172.50 [8411]~P59(x84111)+~P102(f332(f332(f246(x84111),x84112),f2(x84111)))+~P102(f332(f332(f246(x84111),x84113),x84114))+~P102(f332(f332(f247(x84111),f2(x84111)),f332(f332(f80(x84111),x84113),x84114)))+P102(f332(f332(f246(x84111),f332(f332(f290(x84111),x84112),x84113)),f332(f332(f290(x84111),x84112),x84114))) % 172.83/172.50 [8421]~P60(x84211)+~P102(f332(f332(f247(x84211),x84214),x84213))+~P102(f332(f332(f247(x84211),f2(x84211)),x84212))+~P102(f332(f332(f247(x84211),f2(x84211)),f332(f332(f80(x84211),x84213),x84214)))+P102(f332(f332(f247(x84211),f332(f332(f290(x84211),x84212),x84213)),f332(f332(f290(x84211),x84212),x84214))) % 172.83/172.50 [8422]~P60(x84221)+~P102(f332(f332(f246(x84221),x84224),x84223))+~P102(f332(f332(f246(x84221),f2(x84221)),x84222))+~P102(f332(f332(f247(x84221),f2(x84221)),f332(f332(f80(x84221),x84223),x84224)))+P102(f332(f332(f246(x84221),f332(f332(f290(x84221),x84222),x84223)),f332(f332(f290(x84221),x84222),x84224))) % 172.83/172.50 [8529]P102(f332(x85291,x85292))+~P102(f332(f61(x85294),x85292))+P102(f332(x85291,f842(x85291,x85293,x85292,x85294)))+~P102(f332(x85291,f195(f883(x85294,a871))))+~P102(f332(f332(f246(f883(x85294,a871)),x85292),x85293)) % 172.83/172.50 [8537]P102(f332(x85371,x85372))+P102(f332(f61(x85373),f842(x85371,x85374,x85372,x85373)))+~P102(f332(f61(x85373),x85372))+~P102(f332(x85371,f195(f883(x85373,a871))))+~P102(f332(f332(f246(f883(x85373,a871)),x85372),x85374)) % 172.83/172.50 [8783]E(f332(f332(f79(a1),f395(x87831,x87832,x87833,x87834)),f396(x87831,x87832,x87833,x87834)),x87834)+~P102(f332(f332(f247(a1),f2(a1)),x87833))+~P102(f332(f332(f247(a1),x87832),x87834))+~P102(f332(f332(f334(a1),x87832),x87831))+P102(f332(f332(f247(a1),x87832),f332(f332(f22(a1),x87834),x87833))) % 172.83/172.50 [9004]~P102(f332(f332(f247(a1),f2(a1)),x90043))+~P102(f332(f332(f247(a1),x90042),x90044))+~P102(f332(f332(f334(a1),x90042),x90041))+P102(f332(f332(f334(a1),f395(x90041,x90042,x90043,x90044)),x90041))+P102(f332(f332(f247(a1),x90042),f332(f332(f22(a1),x90044),x90043))) % 172.83/172.50 [9016]P102(f332(x90161,x90162))+~P102(f332(f61(x90163),x90162))+P102(f332(f332(f334(x90163),f843(x90161,x90164,x90162,x90163)),x90164))+~P102(f332(x90161,f195(f883(x90163,a871))))+~P102(f332(f332(f246(f883(x90163,a871)),x90162),x90164)) % 172.83/172.50 [9033]E(f332(f332(f79(a1),f391(x90331,x90332,x90333,x90334)),f392(x90331,x90332,x90333,x90334)),x90334)+~P102(f332(f332(f247(a1),f2(a1)),x90333))+~P102(f332(f332(f246(a1),x90332),x90334))+P102(f332(f332(f246(a1),x90332),f332(f332(f22(a1),x90334),x90333)))+~P102(f332(f332(f334(a1),f332(f332(f22(a1),x90332),f77(a1))),x90331)) % 172.83/172.50 [9085]~P102(f332(f332(f247(a1),f2(a1)),x90853))+~P102(f332(f332(f247(a1),x90851),x90852))+~P102(f332(f332(f334(a1),x90851),x90854))+P102(f332(f332(f334(a1),f396(x90854,x90851,x90853,x90852)),f303(a1,f77(a1),x90853)))+P102(f332(f332(f247(a1),x90851),f332(f332(f22(a1),x90852),x90853))) % 172.83/172.50 [9180]~P102(f332(f332(f247(a1),f2(a1)),x91803))+~P102(f332(f332(f246(a1),x91802),x91804))+P102(f332(f332(f334(a1),f391(x91801,x91802,x91803,x91804)),x91801))+P102(f332(f332(f246(a1),x91802),f332(f332(f22(a1),x91804),x91803)))+~P102(f332(f332(f334(a1),f332(f332(f22(a1),x91802),f77(a1))),x91801)) % 172.83/172.50 [9220]~P102(f332(f332(f247(a1),f2(a1)),x92203))+~P102(f332(f332(f246(a1),x92201),x92202))+P102(f332(f332(f334(a1),f392(x92204,x92201,x92203,x92202)),f303(a1,f77(a1),x92203)))+P102(f332(f332(f246(a1),x92201),f332(f332(f22(a1),x92202),x92203)))+~P102(f332(f332(f334(a1),f332(f332(f22(a1),x92201),f77(a1))),x92204)) % 172.83/172.50 [9453]P102(f332(x94531,x94532))+~P102(f332(f332(f334(x94533),f843(x94531,x94534,x94532,x94533)),f842(x94531,x94534,x94532,x94533)))+~P102(f332(f61(x94533),x94532))+~P102(f332(x94531,f195(f883(x94533,a871))))+~P102(f332(f332(f246(f883(x94533,a871)),x94532),x94534)) % 172.83/172.50 [9669]P102(f332(x96691,x96692))+~P102(f332(f61(x96693),x96692))+~P102(f332(x96691,f332(f332(f310(x96693),f843(x96691,x96694,x96692,x96693)),f842(x96691,x96694,x96692,x96693))))+~P102(f332(x96691,f195(f883(x96693,a871))))+~P102(f332(f332(f246(f883(x96693,a871)),x96692),x96694)) % 172.83/172.50 [7706]~P59(x77061)+P102(f332(f332(f247(x77061),x77062),f2(x77061)))+P102(f332(f332(f247(x77061),f2(x77061)),x77062))+~P102(f332(f332(f247(x77061),f2(x77061)),x77064))+P102(f332(f332(f247(x77061),f332(f332(f290(x77061),x77063),x77062)),x77064)) % 172.83/172.50 [7707]~P59(x77071)+P102(f332(f332(f247(x77071),x77072),f2(x77071)))+~P102(f332(f332(f246(x77071),f2(x77071)),x77074))+P102(f332(f332(f247(x77071),f2(x77071)),x77072))+P102(f332(f332(f246(x77071),f332(f332(f290(x77071),x77073),x77072)),x77074)) % 172.83/172.50 [7992]~P102(f332(f332(f246(a1),x79924),f2(a1)))+~E(x79922,f332(f332(f79(a1),f332(f332(f80(a1),x79921),x79923)),x79924))+P102(f332(f332(f247(a1),f2(a1)),x79921))+~P102(f332(f332(f247(a1),x79921),x79924))+P102(f332(f48(x79922,x79921),f332(f332(f267(a1,a1),x79923),x79924))) % 172.83/172.50 [8031]~P102(f332(x80311,x80314))+P102(f332(x80311,f371(x80312,x80311,x80313)))+~P102(f332(f332(f247(a1),f2(a1)),x80313))+~P102(f332(f332(f246(a1),f2(a1)),x80312))+P102(f332(x80311,f332(f332(f22(a1),x80314),f332(f332(f80(a1),x80312),x80313)))) % 172.83/172.50 [8032]~P102(f332(x80321,x80324))+P102(f332(x80321,f374(x80322,x80321,x80323)))+~P102(f332(f332(f247(a1),f2(a1)),x80323))+~P102(f332(f332(f246(a1),f2(a1)),x80322))+P102(f332(x80321,f332(f332(f79(a1),x80324),f332(f332(f80(a1),x80322),x80323)))) % 172.83/172.50 [8033]~P59(x80331)+P102(f332(f332(f247(x80331),x80332),f2(x80331)))+P102(f332(f332(f247(x80331),f2(x80331)),x80332))+P102(f332(f332(f247(x80331),f2(x80331)),x80333))+~P102(f332(f332(f247(x80331),f332(f332(f290(x80331),x80334),x80332)),x80333)) % 172.83/172.50 [8034]~P59(x80341)+P102(f332(f332(f247(x80341),x80342),f2(x80341)))+P102(f332(f332(f247(x80341),f2(x80341)),x80342))+P102(f332(f332(f246(x80341),f2(x80341)),x80343))+~P102(f332(f332(f246(x80341),f332(f332(f290(x80341),x80344),x80342)),x80343)) % 172.83/172.50 [8082]~E(x80821,f332(f332(f79(a1),f332(f332(f80(a1),x80822),x80823)),x80824))+~P102(f332(f332(f247(a1),f2(a1)),x80822))+~P102(f332(f332(f246(a1),f2(a1)),x80824))+~P102(f332(f332(f247(a1),x80824),x80822))+P102(f332(f48(x80821,x80822),f332(f332(f267(a1,a1),x80823),x80824))) % 172.83/172.50 [8206]~P59(x82061)+P102(f332(f332(f247(x82061),x82062),f2(x82061)))+~P102(f332(f332(f247(x82061),f2(x82061)),x82064))+~P102(f332(f332(f247(x82061),x82063),f332(f332(f80(x82061),x82064),x82062)))+P102(f332(f332(f247(x82061),f332(f332(f290(x82061),x82063),x82062)),x82064)) % 172.83/172.50 [8207]~P59(x82071)+P102(f332(f332(f247(x82071),x82072),f2(x82071)))+~P102(f332(f332(f246(x82071),f2(x82071)),x82074))+~P102(f332(f332(f246(x82071),x82073),f332(f332(f80(x82071),x82074),x82072)))+P102(f332(f332(f246(x82071),f332(f332(f290(x82071),x82073),x82072)),x82074)) % 172.83/172.50 [8288]~P59(x82881)+P102(f332(f332(f247(x82881),x82882),f2(x82881)))+~P102(f332(f332(f247(x82881),x82883),f2(x82881)))+P102(f332(f332(f247(x82881),x82883),f332(f332(f290(x82881),x82884),x82882)))+~P102(f332(f332(f247(x82881),f332(f332(f80(x82881),x82883),x82882)),x82884)) % 172.83/172.50 [8289]~P59(x82891)+P102(f332(f332(f247(x82891),x82892),f2(x82891)))+~P102(f332(f332(f246(x82891),x82893),f2(x82891)))+P102(f332(f332(f246(x82891),x82893),f332(f332(f290(x82891),x82894),x82892)))+~P102(f332(f332(f246(x82891),f332(f332(f80(x82891),x82893),x82892)),x82894)) % 172.83/172.50 [8448]~P59(x84481)+~P102(f332(f332(f247(x84481),x84482),f2(x84481)))+P102(f332(f332(f247(x84481),f2(x84481)),x84482))+~P102(f332(f332(f247(x84481),f332(f332(f290(x84481),x84484),x84482)),x84483))+P102(f332(f332(f247(x84481),f332(f332(f80(x84481),x84483),x84482)),x84484)) % 172.83/172.50 [8449]~P59(x84491)+~P102(f332(f332(f247(x84491),x84492),f2(x84491)))+P102(f332(f332(f247(x84491),f2(x84491)),x84492))+~P102(f332(f332(f247(x84491),f332(f332(f80(x84491),x84494),x84492)),x84493))+P102(f332(f332(f247(x84491),f332(f332(f290(x84491),x84493),x84492)),x84494)) % 172.83/172.50 [8450]~P59(x84501)+~P102(f332(f332(f247(x84501),x84502),f2(x84501)))+P102(f332(f332(f247(x84501),f2(x84501)),x84502))+~P102(f332(f332(f246(x84501),f332(f332(f290(x84501),x84504),x84502)),x84503))+P102(f332(f332(f246(x84501),f332(f332(f80(x84501),x84503),x84502)),x84504)) % 172.83/172.50 [8451]~P59(x84511)+~P102(f332(f332(f247(x84511),x84512),f2(x84511)))+P102(f332(f332(f247(x84511),f2(x84511)),x84512))+~P102(f332(f332(f246(x84511),f332(f332(f80(x84511),x84514),x84512)),x84513))+P102(f332(f332(f246(x84511),f332(f332(f290(x84511),x84513),x84512)),x84514)) % 172.83/172.50 [8472]~P59(x84721)+~P102(f332(f332(f247(x84721),f2(x84721)),x84724))+P102(f332(f332(f247(x84721),f2(x84721)),x84722))+~P102(f332(f332(f247(x84721),f332(f332(f80(x84721),x84724),x84722)),x84723))+P102(f332(f332(f247(x84721),f332(f332(f290(x84721),x84723),x84722)),x84724)) % 172.83/172.50 [8473]~P59(x84731)+~P102(f332(f332(f246(x84731),f2(x84731)),x84734))+P102(f332(f332(f247(x84731),f2(x84731)),x84732))+~P102(f332(f332(f246(x84731),f332(f332(f80(x84731),x84734),x84732)),x84733))+P102(f332(f332(f246(x84731),f332(f332(f290(x84731),x84733),x84732)),x84734)) % 172.83/172.50 [8545]~P59(x85451)+~P102(f332(f332(f247(x85451),x85454),f2(x85451)))+~P102(f332(f332(f247(x85451),x85453),f332(f332(f80(x85451),x85452),x85454)))+P102(f332(f332(f247(x85451),x85452),f332(f332(f290(x85451),x85453),x85454)))+~P102(f332(f332(f247(x85451),f332(f332(f80(x85451),x85452),x85454)),x85453)) % 172.83/172.50 [8546]~P59(x85461)+~P102(f332(f332(f247(x85461),x85462),f2(x85461)))+~P102(f332(f332(f247(x85461),x85463),f332(f332(f80(x85461),x85462),x85464)))+P102(f332(f332(f247(x85461),x85462),f332(f332(f290(x85461),x85463),x85464)))+~P102(f332(f332(f247(x85461),f332(f332(f80(x85461),x85462),x85464)),x85463)) % 172.83/172.50 [8547]~P59(x85471)+~P102(f332(f332(f247(x85471),x85474),f2(x85471)))+~P102(f332(f332(f246(x85471),x85473),f332(f332(f80(x85471),x85472),x85474)))+P102(f332(f332(f246(x85471),x85472),f332(f332(f290(x85471),x85473),x85474)))+~P102(f332(f332(f246(x85471),f332(f332(f80(x85471),x85472),x85474)),x85473)) % 172.83/172.50 [8548]~P59(x85481)+~P102(f332(f332(f246(x85481),x85482),f2(x85481)))+~P102(f332(f332(f246(x85481),x85483),f332(f332(f80(x85481),x85482),x85484)))+P102(f332(f332(f246(x85481),x85482),f332(f332(f290(x85481),x85483),x85484)))+~P102(f332(f332(f246(x85481),f332(f332(f80(x85481),x85482),x85484)),x85483)) % 172.83/172.50 [8660]~P59(x86601)+~P102(f332(f332(f247(x86601),x86603),f2(x86601)))+~P102(f332(f332(f247(x86601),x86602),f332(f332(f80(x86601),x86604),x86603)))+~P102(f332(f332(f247(x86601),f332(f332(f80(x86601),x86604),x86603)),x86602))+P102(f332(f332(f247(x86601),f332(f332(f290(x86601),x86602),x86603)),x86604)) % 172.83/172.50 [8661]~P59(x86611)+~P102(f332(f332(f247(x86611),x86613),f2(x86611)))+~P102(f332(f332(f246(x86611),x86612),f332(f332(f80(x86611),x86614),x86613)))+~P102(f332(f332(f246(x86611),f332(f332(f80(x86611),x86614),x86613)),x86612))+P102(f332(f332(f246(x86611),f332(f332(f290(x86611),x86612),x86613)),x86614)) % 172.83/172.50 [8676]~P59(x86761)+~P102(f332(f332(f247(x86761),f2(x86761)),x86764))+~P102(f332(f332(f247(x86761),x86762),f332(f332(f80(x86761),x86764),x86763)))+~P102(f332(f332(f247(x86761),f332(f332(f80(x86761),x86764),x86763)),x86762))+P102(f332(f332(f247(x86761),f332(f332(f290(x86761),x86762),x86763)),x86764)) % 172.83/172.50 [8677]~P59(x86771)+~P102(f332(f332(f246(x86771),f2(x86771)),x86774))+~P102(f332(f332(f246(x86771),x86772),f332(f332(f80(x86771),x86774),x86773)))+~P102(f332(f332(f246(x86771),f332(f332(f80(x86771),x86774),x86773)),x86772))+P102(f332(f332(f246(x86771),f332(f332(f290(x86771),x86772),x86773)),x86774)) % 172.83/172.50 [8844]E(f332(f332(f22(a1),f397(x88441,x88442,x88443,x88444)),f398(x88441,x88442,x88443,x88444)),x88444)+~P102(f332(f332(f247(a1),f2(a1)),x88443))+~P102(f332(f332(f334(a1),x88442),x88441))+~P102(f332(f332(f247(a1),x88444),x88442))+P102(f332(f332(f247(a1),f332(f332(f79(a1),x88444),x88443)),x88442)) % 172.83/172.50 [8925]~P102(f332(x89251,x89252))+~P102(f332(f332(f247(a1),f2(a1)),x89254))+~P102(f332(f332(f246(a1),f2(a1)),x89253))+~P102(f332(x89251,f332(f332(f22(a1),f371(x89253,x89251,x89254)),x89254)))+P102(f332(x89251,f332(f332(f22(a1),x89252),f332(f332(f80(a1),x89253),x89254)))) % 172.83/172.50 [8926]~P102(f332(x89261,x89262))+~P102(f332(f332(f247(a1),f2(a1)),x89264))+~P102(f332(f332(f246(a1),f2(a1)),x89263))+~P102(f332(x89261,f332(f332(f79(a1),f374(x89263,x89261,x89264)),x89264)))+P102(f332(x89261,f332(f332(f79(a1),x89262),f332(f332(f80(a1),x89263),x89264)))) % 172.83/172.50 [9079]~P102(f332(f332(f247(a1),f2(a1)),x90793))+~P102(f332(f332(f334(a1),x90792),x90791))+~P102(f332(f332(f247(a1),x90794),x90792))+P102(f332(f332(f334(a1),f397(x90791,x90792,x90793,x90794)),x90791))+P102(f332(f332(f247(a1),f332(f332(f79(a1),x90794),x90793)),x90792)) % 172.83/172.50 [9099]E(f332(f332(f22(a1),f385(x90991,x90992,x90993,x90994)),f386(x90991,x90992,x90993,x90994)),x90994)+~P102(f332(f332(f247(a1),f2(a1)),x90993))+~P102(f332(f332(f246(a1),x90994),x90992))+~P102(f332(f332(f334(a1),f332(f332(f79(a1),x90992),f77(a1))),x90991))+P102(f332(f332(f246(a1),f332(f332(f79(a1),x90994),x90993)),x90992)) % 172.83/172.50 [9125]~P102(f332(f332(f247(a1),f2(a1)),x91252))+~P102(f332(f332(f334(a1),x91253),x91254))+~P102(f332(f332(f247(a1),x91251),x91253))+P102(f332(f332(f334(a1),f398(x91254,x91253,x91252,x91251)),f303(a1,f77(a1),x91252)))+P102(f332(f332(f247(a1),f332(f332(f79(a1),x91251),x91252)),x91253)) % 172.83/172.50 [9215]~P102(f332(f332(f247(a1),f2(a1)),x92153))+~P102(f332(f332(f246(a1),x92154),x92152))+P102(f332(f332(f334(a1),f385(x92151,x92152,x92153,x92154)),x92151))+~P102(f332(f332(f334(a1),f332(f332(f79(a1),x92152),f77(a1))),x92151))+P102(f332(f332(f246(a1),f332(f332(f79(a1),x92154),x92153)),x92152)) % 172.83/172.50 [9260]~P102(f332(f332(f247(a1),f2(a1)),x92602))+~P102(f332(f332(f246(a1),x92601),x92603))+P102(f332(f332(f334(a1),f386(x92604,x92603,x92602,x92601)),f303(a1,f77(a1),x92602)))+~P102(f332(f332(f334(a1),f332(f332(f79(a1),x92603),f77(a1))),x92604))+P102(f332(f332(f246(a1),f332(f332(f79(a1),x92601),x92602)),x92603)) % 172.83/172.50 [9545]~P38(x95451,x95453)+~P21(x95451,x95454)+P38(x95451,f332(f332(f113(f883(f882(x95451,x95451),a871)),x95452),x95453))+~P102(f332(f332(f246(f883(f882(x95451,x95451),a871)),x95452),f332(f266(f883(f882(x95451,x95451),a871),f883(f882(x95451,x95451),a871)),x95454)))+~P102(f332(f332(f246(f883(f882(x95451,x95451),a871)),x95453),f332(f270(f883(f882(x95451,x95451),a871),f883(f882(x95451,x95451),a871)),x95454))) % 172.83/172.50 [9837]~E(f332(f731(x98371,x98374,x98373,x98372),f733(x98371,x98374,x98373,x98372)),f208(f877(a328)))+P102(f332(f332(f247(a1),f732(x98371,x98374,x98373,x98372)),f733(x98371,x98374,x98373,x98372)))+P102(f332(f332(f332(x98371,x98372),x98373),x98374))+P102(f332(f332(f332(x98371,f731(x98371,x98374,x98373,x98372)),f732(x98371,x98374,x98373,x98372)),f332(f332(f79(a1),f733(x98371,x98374,x98373,x98372)),f77(a1))))+~P102(f332(f320(f882(f883(a1,f880(f877(a328))),f882(a1,a1)),a318),f332(f332(f267(f883(a1,f880(f877(a328))),f882(a1,a1)),x98372),f332(f332(f267(a1,a1),x98373),x98374)))) % 172.83/172.50 [9938]~P13(x99382,x99384,x99383)+E(x99381,f195(f883(x99382,a871)))+~P102(f332(f61(x99382),x99381))+P102(f332(f332(f334(x99382),f332(x99383,x99381)),x99381))+~P102(f332(f332(f334(x99382),f332(f332(x99384,f505(x99381,x99383,x99384,x99382)),f516(x99381,x99383,x99384,x99382))),f332(f332(f310(x99382),f505(x99381,x99383,x99384,x99382)),f332(f332(f310(x99382),f516(x99381,x99383,x99384,x99382)),f195(f883(x99382,a871)))))) % 172.83/172.50 [9869]~P105(x98692)+~P56(x98691)+~P102(f332(f332(f246(f883(x98691,x98692)),x98693),x98694))+P102(f332(f332(f247(f883(x98691,x98692)),x98693),x98694))+~P102(f332(f57(x98691),f332(f332(f8(a871,a871,x98691),a327),f332(f332(f18(x98691,x98692,a871),f332(f332(f8(x98692,f883(x98692,a871),x98691),a329),x98693)),x98694)))) % 172.83/172.50 [9461]~P50(x94611,x94611,x94614)+P102(f332(f332(f334(f882(x94611,x94611)),f332(f332(f267(x94611,x94611),x94612),x94613)),f308(x94611,x94614)))+P102(f332(f332(f334(f882(x94611,x94611)),f332(f332(f267(x94611,x94611),x94613),x94612)),f308(x94611,x94614)))+~P102(f332(f332(f334(f882(x94611,x94611)),f332(f332(f267(x94611,x94611),x94615),x94612)),f308(x94611,x94614)))+~P102(f332(f332(f334(f882(x94611,x94611)),f332(f332(f267(x94611,x94611),x94615),x94613)),f308(x94611,x94614))) % 172.83/172.50 [5618]E(x56181,f2(a876))+~E(f332(f37(x56182),x56185),x56181)+E(f332(f37(x56182),x56183),f332(a115,x56181))+~E(x56183,f332(f332(f310(x56182),x56184),x56185))+P102(f332(f332(f334(x56182),x56184),x56185)) % 172.83/172.50 [5742]~P58(x57422)+E(x57421,f2(x57422))+E(x57423,f2(x57422))+~E(f332(f332(f290(x57422),x57424),x57423),f332(f332(f290(x57422),x57425),x57421))+E(f332(f332(f80(x57422),x57424),x57421),f332(f332(f80(x57422),x57425),x57423)) % 172.83/172.50 [5743]~P58(x57432)+E(x57431,f2(x57432))+E(x57433,f2(x57432))+~E(f332(f332(f80(x57432),x57434),x57433),f332(f332(f80(x57432),x57435),x57431))+E(f332(f332(f290(x57432),x57434),x57431),f332(f332(f290(x57432),x57435),x57433)) % 172.83/172.50 [5809]~E(f332(f37(x58091),x58095),x58093)+~E(x58095,f195(f883(x58091,a871)))+E(f332(f37(x58091),x58092),f332(a115,x58093))+~E(x58092,f332(f332(f310(x58091),x58094),x58095))+P102(f332(f332(f334(x58091),x58094),x58095)) % 172.83/172.50 [6035]~P114(x60352)+~E(f332(x60353,x60355),f2(x60352))+E(f332(f332(f9(x60351,x60352),x60353),x60354),f2(x60352))+~P102(f332(f61(x60351),x60354))+~P102(f332(f332(f334(x60351),x60355),x60354)) % 172.83/172.50 [6402]~P104(x64023)+E(x64021,x64022)+~E(f332(f302(x64023,x64024),x64021),f332(f302(x64023,x64025),x64022))+~P102(f332(f332(f247(x64023),x64025),x64022))+~P102(f332(f332(f247(x64023),x64024),x64021)) % 172.83/172.50 [6403]~P104(x64033)+E(x64031,x64032)+~E(f332(f302(x64033,x64031),x64034),f332(f302(x64033,x64032),x64035))+~P102(f332(f332(f247(x64033),x64032),x64035))+~P102(f332(f332(f247(x64033),x64031),x64034)) % 172.83/172.50 [7465]~P104(x74651)+~P29(x74651,f332(f332(f134(x74651),x74654),x74655))+~P102(f332(f332(f334(x74651),x74653),f332(f173(x74651),x74655)))+~P102(f332(f332(f334(x74651),x74652),f332(f173(x74651),x74654)))+P102(f332(f332(f246(x74651),x74652),x74653)) % 172.83/172.50 [8580]~P105(x85801)+~P102(f332(f332(f247(f883(x85801,a871)),f303(x85801,x85805,x85802)),f303(x85801,x85804,x85803)))+~P102(f332(f332(f246(x85801),x85805),x85802))+P102(f332(f332(f247(x85801),x85802),x85803))+P102(f332(f332(f247(x85801),x85804),x85805)) % 172.83/172.50 [9981]~P12(x99812,x99815,x99813)+E(x99811,f195(f883(x99812,a871)))+~E(f332(f332(x99815,f332(x99814,f526(x99811,x99814,x99813,x99815,x99812))),f332(x99814,f538(x99811,x99814,x99813,x99815,x99812))),f332(x99814,f332(f332(x99815,f526(x99811,x99814,x99813,x99815,x99812)),f538(x99811,x99814,x99813,x99815,x99812))))+E(f332(x99813,f332(f311(x99812,x99812,x99814),x99811)),f332(x99814,f332(x99813,x99811)))+~P102(f332(f61(x99812),x99811)) % 172.83/172.50 [6399]~P13(x63992,x63995,x63993)+E(x63991,f195(f883(x63992,a871)))+~P102(f332(f61(x63992),x63991))+E(f332(x63993,f332(f332(f310(x63992),x63994),x63991)),f332(f332(x63995,x63994),f332(x63993,x63991)))+P102(f332(f332(f334(x63992),x63994),x63991)) % 172.83/172.50 [7222]~P12(x72222,x72223,x72224)+E(f332(f332(x72223,f332(x72224,x72221)),f332(x72224,x72225)),f332(x72224,x72225))+E(x72221,f195(f883(x72222,a871)))+~P102(f332(f61(x72222),x72225))+~P102(f332(f332(f246(f883(x72222,a871)),x72221),x72225)) % 172.83/172.50 [7441]~P56(x74414)+~P91(x74415)+E(f332(x74411,x74412),f332(x74413,x74412))+~P102(f332(f332(f334(x74414),x74412),f332(f173(x74414),f55(x74414))))+~P102(f332(f332(f90(f883(x74414,x74415)),x74411),x74413)) % 172.83/172.50 [7601]~P13(x76014,x76015,x76011)+E(f332(x76011,x76012),x76013)+~P102(f332(f61(x76014),x76012))+~E(f332(f332(f22(f883(x76014,a871)),x76012),f332(f332(f310(x76014),x76013),f195(f883(x76014,a871)))),f195(f883(x76014,a871)))+~P102(f332(f332(f334(x76014),x76013),x76012)) % 172.83/172.50 [7688]E(x76881,x76882)+~E(f332(f196(f877(x76883)),x76882),f332(f196(f877(x76884)),x76885))+~E(f332(f196(f877(x76883)),x76881),f332(f196(f877(x76884)),x76885))+~E(f332(f179(x76884,x76883),f332(f332(f183(x76884,x76883),x76885),x76881)),f332(f179(x76884,x76883),f332(f332(f183(x76884,x76883),x76885),x76882)))+~P102(f332(f137(x76884),x76885)) % 172.83/172.50 [8552]E(x85521,x85522)+~P3(x85523,x85524,x85525)+E(f332(f332(f104(f883(x85523,a871)),x85521),x85522),f195(f883(x85523,a871)))+~P102(f332(f332(f334(f883(x85523,a871)),x85522),f332(f332(f60(x85523),x85524),x85525)))+~P102(f332(f332(f334(f883(x85523,a871)),x85521),f332(f332(f60(x85523),x85524),x85525))) % 172.83/172.50 [9342]~P71(x93422)+~E(f332(x93423,f345(x93423,x93424,x93425,x93421,x93422)),f2(x93422))+E(f332(f332(f6(x93421,x93422),x93423),x93424),f332(f332(f6(x93421,x93422),x93423),x93425))+~P102(f332(f61(x93421),x93425))+~P102(f332(f332(f246(f883(x93421,a871)),x93424),x93425)) % 172.83/172.50 [9343]~P71(x93432)+~E(f332(x93433,f346(x93433,x93434,x93435,x93431,x93432)),f2(x93432))+E(f332(f332(f6(x93431,x93432),x93433),x93434),f332(f332(f6(x93431,x93432),x93433),x93435))+~P102(f332(f61(x93431),x93435))+~P102(f332(f332(f246(f883(x93431,a871)),x93434),x93435)) % 172.83/172.50 [9344]~P67(x93442)+~E(f332(x93443,f844(x93443,x93444,x93445,x93441,x93442)),f77(x93442))+E(f332(f332(f9(x93441,x93442),x93443),x93444),f332(f332(f9(x93441,x93442),x93443),x93445))+~P102(f332(f61(x93441),x93445))+~P102(f332(f332(f246(f883(x93441,a871)),x93444),x93445)) % 172.83/172.50 [9345]~P67(x93452)+~E(f332(x93453,f848(x93453,x93454,x93455,x93451,x93452)),f77(x93452))+E(f332(f332(f9(x93451,x93452),x93453),x93454),f332(f332(f9(x93451,x93452),x93453),x93455))+~P102(f332(f61(x93451),x93455))+~P102(f332(f332(f246(f883(x93451,a871)),x93454),x93455)) % 172.83/172.50 [9817]~P84(x98171)+~P102(f332(f61(x98172),x98175))+~P102(f332(f332(f246(x98171),f2(x98171)),f332(x98173,f861(x98173,x98174,x98175,x98172,x98171))))+P102(f332(f332(f246(x98171),f332(f332(f6(x98172,x98171),x98173),x98174)),f332(f332(f6(x98172,x98171),x98173),x98175)))+~P102(f332(f332(f246(f883(x98172,a871)),x98174),x98175)) % 172.83/172.50 [7462]E(x74621,f2(a876))+P102(f332(x74622,x74623))+~E(x74624,f332(f332(f79(a876),f332(f332(f80(a876),x74621),x74623)),x74625))+~P102(f332(f332(f247(a876),x74625),x74621))+~P102(f332(x74622,f332(f332(f38(a876),x74624),x74621))) % 172.83/172.50 [7542]E(x75421,f2(a876))+P102(f332(x75422,x75423))+~P102(f332(x75422,f44(a876,x75424,x75421)))+~E(x75424,f332(f332(f79(a876),f332(f332(f80(a876),x75421),x75425)),x75423))+~P102(f332(f332(f247(a876),x75423),x75421)) % 172.83/172.50 [7838]~P58(x78383)+E(f332(x78381,x78382),f2(x78383))+~P102(f332(f61(x78384),x78385))+E(f332(f332(f9(x78384,x78383),x78381),f332(f332(f22(f883(x78384,a871)),x78385),f332(f332(f310(x78384),x78382),f195(f883(x78384,a871))))),f332(f332(f9(x78384,x78383),x78381),x78385))+P102(f332(f332(f334(x78384),x78382),x78385)) % 172.83/172.50 [8247]~P71(x82471)+~P102(f332(f61(x82472),x82475))+~P102(f332(f61(x82472),x82474))+~E(f332(f332(f104(f883(x82472,a871)),x82474),x82475),f195(f883(x82472,a871)))+E(f332(f332(f79(x82471),f332(f332(f6(x82472,x82471),x82473),x82474)),f332(f332(f6(x82472,x82471),x82473),x82475)),f332(f332(f6(x82472,x82471),x82473),f332(f332(f113(f883(x82472,a871)),x82474),x82475))) % 172.83/172.50 [8249]~P67(x82491)+~P102(f332(f61(x82492),x82495))+~P102(f332(f61(x82492),x82494))+~E(f332(f332(f104(f883(x82492,a871)),x82494),x82495),f195(f883(x82492,a871)))+E(f332(f332(f80(x82491),f332(f332(f9(x82492,x82491),x82493),x82494)),f332(f332(f9(x82492,x82491),x82493),x82495)),f332(f332(f9(x82492,x82491),x82493),f332(f332(f113(f883(x82492,a871)),x82494),x82495))) % 172.83/172.50 [8342]~P58(x83423)+E(f332(x83421,x83422),f2(x83423))+~P102(f332(f61(x83424),x83425))+E(f332(f332(f9(x83424,x83423),x83421),f332(f332(f22(f883(x83424,a871)),x83425),f332(f332(f310(x83424),x83422),f195(f883(x83424,a871))))),f332(f332(f290(x83423),f332(f332(f9(x83424,x83423),x83421),x83425)),f332(x83421,x83422)))+~P102(f332(f332(f334(x83424),x83422),x83425)) % 172.83/172.50 [9058]~P3(x90581,x90585,x90584)+~E(f332(f332(f60(x90581),f332(f332(f310(x90581),x90582),f195(f883(x90581,a871)))),x90584),f332(f332(f60(x90581),f332(f332(f310(x90581),x90583),f195(f883(x90581,a871)))),x90584))+~P102(f332(f332(f334(x90581),x90583),x90585))+~P102(f332(f332(f334(x90581),x90582),x90585))+P102(f332(f332(f334(f882(x90581,x90581)),f332(f332(f267(x90581,x90581),x90582),x90583)),x90584)) % 172.83/172.50 [9078]~P3(x90781,x90785,x90783)+E(f332(f332(f60(x90781),f332(f332(f310(x90781),x90782),f195(f883(x90781,a871)))),x90783),f332(f332(f60(x90781),f332(f332(f310(x90781),x90784),f195(f883(x90781,a871)))),x90783))+~P102(f332(f332(f334(x90781),x90784),x90785))+~P102(f332(f332(f334(x90781),x90782),x90785))+~P102(f332(f332(f334(f882(x90781,x90781)),f332(f332(f267(x90781,x90781),x90782),x90784)),x90783)) % 172.83/172.50 [9371]~P67(x93711)+~P102(f332(f61(x93712),x93715))+~P102(f332(f61(x93712),x93714))+~E(f332(f332(f104(f883(x93712,a871)),x93714),x93715),f195(f883(x93712,a871)))+E(f332(f332(f80(x93711),f332(f332(f332(f65(x93711,x93712,f80(x93711)),x93713),f77(x93711)),x93714)),f332(f332(f332(f65(x93711,x93712,f80(x93711)),x93713),f77(x93711)),x93715)),f332(f332(f332(f65(x93711,x93712,f80(x93711)),x93713),f77(x93711)),f332(f332(f113(f883(x93712,a871)),x93714),x93715))) % 172.83/172.50 [9380]~P71(x93801)+~E(f332(x93803,f860(x93803,x93805,x93804,x93802,x93801)),f2(x93801))+~P102(f332(f61(x93802),x93804))+~P102(f332(f61(x93802),x93805))+E(f332(f332(f79(x93801),f332(f332(f6(x93802,x93801),x93803),x93804)),f332(f332(f6(x93802,x93801),x93803),x93805)),f332(f332(f6(x93802,x93801),x93803),f332(f332(f113(f883(x93802,a871)),x93804),x93805))) % 172.83/172.50 [9381]~P71(x93811)+~E(f332(x93813,f862(x93813,x93815,x93814,x93812,x93811)),f2(x93811))+~P102(f332(f61(x93812),x93814))+~P102(f332(f61(x93812),x93815))+E(f332(f332(f79(x93811),f332(f332(f6(x93812,x93811),x93813),x93814)),f332(f332(f6(x93812,x93811),x93813),x93815)),f332(f332(f6(x93812,x93811),x93813),f332(f332(f113(f883(x93812,a871)),x93814),x93815))) % 172.83/172.50 [9382]~P67(x93821)+~E(f332(x93823,f845(x93823,x93825,x93824,x93822,x93821)),f77(x93821))+~P102(f332(f61(x93822),x93824))+~P102(f332(f61(x93822),x93825))+E(f332(f332(f80(x93821),f332(f332(f9(x93822,x93821),x93823),x93824)),f332(f332(f9(x93822,x93821),x93823),x93825)),f332(f332(f9(x93822,x93821),x93823),f332(f332(f113(f883(x93822,a871)),x93824),x93825))) % 172.83/172.50 [9383]~P67(x93831)+~E(f332(x93833,f847(x93833,x93835,x93834,x93832,x93831)),f77(x93831))+~P102(f332(f61(x93832),x93834))+~P102(f332(f61(x93832),x93835))+E(f332(f332(f80(x93831),f332(f332(f9(x93832,x93831),x93833),x93834)),f332(f332(f9(x93832,x93831),x93833),x93835)),f332(f332(f9(x93832,x93831),x93833),f332(f332(f113(f883(x93832,a871)),x93834),x93835))) % 172.83/172.50 [9589]~P67(x95891)+~E(f332(x95893,f817(x95893,x95895,x95894,x95892,x95891)),f77(x95891))+~P102(f332(f61(x95892),x95894))+~P102(f332(f61(x95892),x95895))+E(f332(f332(f80(x95891),f332(f332(f332(f65(x95891,x95892,f80(x95891)),x95893),f77(x95891)),x95894)),f332(f332(f332(f65(x95891,x95892,f80(x95891)),x95893),f77(x95891)),x95895)),f332(f332(f332(f65(x95891,x95892,f80(x95891)),x95893),f77(x95891)),f332(f332(f113(f883(x95892,a871)),x95894),x95895))) % 172.83/172.50 [9696]~P71(x96962)+E(f332(f332(f6(x96961,x96962),x96963),x96964),f332(f332(f6(x96961,x96962),x96963),x96965))+~P102(f332(f61(x96961),x96965))+~P102(f332(f332(f246(f883(x96961,a871)),x96964),x96965))+P102(f332(f332(f334(x96961),f345(x96963,x96964,x96965,x96961,x96962)),f332(f332(f22(f883(x96961,a871)),x96965),x96964))) % 172.83/172.50 [9697]~P71(x96972)+E(f332(f332(f6(x96971,x96972),x96973),x96974),f332(f332(f6(x96971,x96972),x96973),x96975))+~P102(f332(f61(x96971),x96975))+~P102(f332(f332(f246(f883(x96971,a871)),x96974),x96975))+P102(f332(f332(f334(x96971),f346(x96973,x96974,x96975,x96971,x96972)),f332(f332(f22(f883(x96971,a871)),x96975),x96974))) % 172.83/172.50 [9698]~P67(x96982)+E(f332(f332(f9(x96981,x96982),x96983),x96984),f332(f332(f9(x96981,x96982),x96983),x96985))+~P102(f332(f61(x96981),x96985))+~P102(f332(f332(f246(f883(x96981,a871)),x96984),x96985))+P102(f332(f332(f334(x96981),f844(x96983,x96984,x96985,x96981,x96982)),f332(f332(f22(f883(x96981,a871)),x96985),x96984))) % 172.83/172.50 [9699]~P67(x96992)+E(f332(f332(f9(x96991,x96992),x96993),x96994),f332(f332(f9(x96991,x96992),x96993),x96995))+~P102(f332(f61(x96991),x96995))+~P102(f332(f332(f246(f883(x96991,a871)),x96994),x96995))+P102(f332(f332(f334(x96991),f848(x96993,x96994,x96995,x96991,x96992)),f332(f332(f22(f883(x96991,a871)),x96995),x96994))) % 172.83/172.50 [9716]~P71(x97161)+~P102(f332(f61(x97162),x97164))+~P102(f332(f61(x97162),x97165))+E(f332(f332(f79(x97161),f332(f332(f6(x97162,x97161),x97163),x97164)),f332(f332(f6(x97162,x97161),x97163),x97165)),f332(f332(f6(x97162,x97161),x97163),f332(f332(f113(f883(x97162,a871)),x97164),x97165)))+P102(f332(f332(f334(x97162),f860(x97163,x97165,x97164,x97162,x97161)),f332(f332(f104(f883(x97162,a871)),x97164),x97165))) % 172.83/172.50 [9717]~P71(x97171)+~P102(f332(f61(x97172),x97174))+~P102(f332(f61(x97172),x97175))+E(f332(f332(f79(x97171),f332(f332(f6(x97172,x97171),x97173),x97174)),f332(f332(f6(x97172,x97171),x97173),x97175)),f332(f332(f6(x97172,x97171),x97173),f332(f332(f113(f883(x97172,a871)),x97174),x97175)))+P102(f332(f332(f334(x97172),f862(x97173,x97175,x97174,x97172,x97171)),f332(f332(f104(f883(x97172,a871)),x97174),x97175))) % 172.83/172.50 [9718]~P67(x97181)+~P102(f332(f61(x97182),x97184))+~P102(f332(f61(x97182),x97185))+E(f332(f332(f80(x97181),f332(f332(f9(x97182,x97181),x97183),x97184)),f332(f332(f9(x97182,x97181),x97183),x97185)),f332(f332(f9(x97182,x97181),x97183),f332(f332(f113(f883(x97182,a871)),x97184),x97185)))+P102(f332(f332(f334(x97182),f845(x97183,x97185,x97184,x97182,x97181)),f332(f332(f104(f883(x97182,a871)),x97184),x97185))) % 172.83/172.50 [9719]~P67(x97191)+~P102(f332(f61(x97192),x97194))+~P102(f332(f61(x97192),x97195))+E(f332(f332(f80(x97191),f332(f332(f9(x97192,x97191),x97193),x97194)),f332(f332(f9(x97192,x97191),x97193),x97195)),f332(f332(f9(x97192,x97191),x97193),f332(f332(f113(f883(x97192,a871)),x97194),x97195)))+P102(f332(f332(f334(x97192),f847(x97193,x97195,x97194,x97192,x97191)),f332(f332(f104(f883(x97192,a871)),x97194),x97195))) % 172.83/172.50 [9726]~P84(x97265)+~P102(f332(f61(x97261),x97264))+P102(f332(f332(f246(x97265),f332(f332(f6(x97261,x97265),x97262),x97263)),f332(f332(f6(x97261,x97265),x97262),x97264)))+~P102(f332(f332(f246(f883(x97261,a871)),x97263),x97264))+P102(f332(f332(f334(x97261),f861(x97262,x97263,x97264,x97261,x97265)),f332(f332(f22(f883(x97261,a871)),x97264),x97263))) % 172.83/172.50 [9780]~P67(x97801)+~P102(f332(f61(x97802),x97804))+~P102(f332(f61(x97802),x97805))+E(f332(f332(f80(x97801),f332(f332(f332(f65(x97801,x97802,f80(x97801)),x97803),f77(x97801)),x97804)),f332(f332(f332(f65(x97801,x97802,f80(x97801)),x97803),f77(x97801)),x97805)),f332(f332(f332(f65(x97801,x97802,f80(x97801)),x97803),f77(x97801)),f332(f332(f113(f883(x97802,a871)),x97804),x97805)))+P102(f332(f332(f334(x97802),f817(x97803,x97805,x97804,x97802,x97801)),f332(f332(f104(f883(x97802,a871)),x97804),x97805))) % 172.83/172.50 [8744]~P13(x87441,x87444,x87445)+~P102(f332(f61(x87441),x87442))+E(f332(f332(f22(f883(x87441,a871)),x87442),f332(f332(f310(x87441),x87443),f195(f883(x87441,a871)))),f195(f883(x87441,a871)))+~P102(f332(f332(f334(x87441),x87443),x87442))+E(f332(f332(x87444,x87443),f332(x87445,f332(f332(f22(f883(x87441,a871)),x87442),f332(f332(f310(x87441),x87443),f195(f883(x87441,a871)))))),f332(x87445,x87442)) % 172.83/172.50 [8818]~P13(x88181,x88184,x88185)+~P102(f332(f61(x88181),x88183))+~P102(f332(f61(x88181),x88182))+E(f332(f332(f104(f883(x88181,a871)),x88182),x88183),f195(f883(x88181,a871)))+E(f332(f332(x88184,f332(x88185,f332(f332(f113(f883(x88181,a871)),x88182),x88183))),f332(x88185,f332(f332(f104(f883(x88181,a871)),x88182),x88183))),f332(f332(x88184,f332(x88185,x88182)),f332(x88185,x88183))) % 172.83/172.50 [9385]~P102(f332(f332(f246(a1),x93854),f2(a1)))+~P102(f332(f332(f247(a1),x93853),x93855))+P102(f332(f332(f246(a1),x93851),x93852))+~P102(f332(f332(f247(a1),x93853),x93854))+~P102(f332(f332(f246(a1),f332(f332(f79(a1),f332(f332(f80(a1),x93853),x93852)),x93855)),f332(f332(f79(a1),f332(f332(f80(a1),x93853),x93851)),x93854))) % 172.83/172.50 [9387]~P102(f332(f332(f246(a1),f2(a1)),x93875))+P102(f332(f332(f246(a1),x93871),x93872))+~P102(f332(f332(f247(a1),x93873),x93874))+~P102(f332(f332(f247(a1),x93875),x93874))+~P102(f332(f332(f246(a1),f332(f332(f79(a1),f332(f332(f80(a1),x93874),x93871)),x93875)),f332(f332(f79(a1),f332(f332(f80(a1),x93874),x93872)),x93873))) % 172.83/172.50 [9498]~P58(x94985)+E(f332(x94981,f870(x94981,x94982,x94983,x94984,x94985)),f2(x94985))+~P102(f332(f61(x94984),x94983))+~P102(f332(f61(x94984),x94982))+E(f332(f332(f290(x94985),f332(f332(f80(x94985),f332(f332(f9(x94984,x94985),x94981),x94983)),f332(f332(f9(x94984,x94985),x94981),x94982))),f332(f332(f9(x94984,x94985),x94981),f332(f332(f104(f883(x94984,a871)),x94983),x94982))),f332(f332(f9(x94984,x94985),x94981),f332(f332(f113(f883(x94984,a871)),x94983),x94982))) % 172.83/172.50 [9772]~P58(x97721)+~P102(f332(f61(x97722),x97724))+~P102(f332(f61(x97722),x97725))+E(f332(f332(f290(x97721),f332(f332(f80(x97721),f332(f332(f9(x97722,x97721),x97723),x97724)),f332(f332(f9(x97722,x97721),x97723),x97725))),f332(f332(f9(x97722,x97721),x97723),f332(f332(f104(f883(x97722,a871)),x97724),x97725))),f332(f332(f9(x97722,x97721),x97723),f332(f332(f113(f883(x97722,a871)),x97724),x97725)))+P102(f332(f332(f334(x97722),f870(x97723,x97725,x97724,x97722,x97721)),f332(f332(f104(f883(x97722,a871)),x97724),x97725))) % 172.83/172.50 [9098]E(f332(f332(f134(x90981),x90982),x90983),f332(f332(f134(x90981),x90984),x90985))+~E(f332(f332(f176(x90981),f332(f196(f877(x90981)),x90984)),x90982),x90984)+~E(f332(f332(f176(x90981),f332(f196(f877(x90981)),x90982)),x90984),x90982)+~E(x90985,f332(f332(f134(x90981),f332(f332(f138(x90981),f332(f196(f877(x90981)),x90984)),x90982)),x90983))+~E(f332(f332(f134(x90981),f332(f332(f138(x90981),f332(f196(f877(x90981)),x90982)),x90984)),x90985),x90983) % 172.83/172.50 [9496]~P104(x94962)+E(f332(f332(f148(x94961,x94962,x94963),x94964),f171(x94961,x94964,x94965)),x94965)+~P29(x94962,f332(f332(f154(x94961,x94962),x94963),x94965))+~P102(f332(f332(f334(x94961),x94964),f332(f173(x94961),x94965)))+~E(f332(f141(x94961),f332(f136(x94961,f332(f332(f8(x94962,a871,x94961),f332(a329,f332(x94963,x94964))),x94963)),x94965)),x94964) % 172.83/172.50 [9834]~P64(x98341)+~P102(f332(f66(x98341,x98341,f80(x98341),x98342,x98343),x98345))+~P102(f332(f332(f334(x98341),x98344),x98343))+P102(f332(f332(f334(x98341),x98342),x98343))+P102(f332(f66(x98341,x98341,f80(x98341),x98344,f332(f332(f310(x98341),x98342),f332(f332(f22(f883(x98341,a871)),x98343),f332(f332(f310(x98341),x98344),f195(f883(x98341,a871)))))),x98345)) % 172.83/172.50 [7230]E(x72301,x72302)+~P20(x72304,x72305,x72303,x72306)+~E(f332(x72303,x72301),f332(x72303,x72302))+~P102(f332(f332(f334(x72304),x72302),x72306))+~P102(f332(f332(f334(x72304),x72301),x72306)) % 172.83/172.50 [6489]~P138(x64894)+E(x64891,x64892)+~E(x64895,x64896)+E(x64893,f2(x64894))+~E(f332(f332(f79(x64894),x64895),f332(f332(f80(x64894),x64893),x64891)),f332(f332(f79(x64894),x64896),f332(f332(f80(x64894),x64893),x64892))) % 172.83/172.50 [7522]~P104(x75221)+~P27(x75221)+~P102(f332(f332(f247(x75221),x75222),f332(x75225,x75226)))+~P102(f332(f332(f334(x75223),x75226),x75224))+P102(f332(f332(f247(x75221),x75222),f332(f332(f41(x75223,x75221),x75224),x75225))) % 172.83/172.50 [8217]~P104(x82171)+~P27(x82171)+~P102(f332(f332(f247(x82171),f332(x82174,x82176)),x82175))+~P102(f332(f332(f334(x82172),x82176),x82173))+P102(f332(f332(f247(x82171),f332(f332(f42(x82172,x82171),x82173),x82174)),x82175)) % 172.83/172.50 [8479]~P14(x84792,x84795,x84796,x84791)+~P102(f332(f61(x84792),x84794))+~P102(f332(f61(x84792),x84793))+~E(f332(f332(f104(f883(x84792,a871)),x84793),x84794),f195(f883(x84792,a871)))+E(f332(x84791,f332(f332(f113(f883(x84792,a871)),x84793),x84794)),f332(f72(x84795,x84795,x84795,f332(x84791,x84793)),f332(x84791,x84794))) % 172.83/172.50 [8787]E(x87871,x87872)+~P52(x87874,x87875,x87876,x87873,x87877)+~E(f332(x87873,x87871),f332(x87873,x87872))+~P102(f332(f332(f334(x87875),x87872),x87877))+~P102(f332(f332(f334(x87875),x87871),x87877)) % 172.83/172.50 [10080]~P102(f332(x100802,x100804))+~E(x100805,f332(f136(x100801,x100802),x100807))+E(f332(f136(x100801,x100802),x100803),f332(f332(f151(x100801),x100804),x100805))+~E(x100803,f332(f332(f134(x100801),x100806),f332(f332(f151(x100801),x100804),x100807)))+P102(f332(x100802,f790(x100805,x100804,x100803,x100802,x100801,x100806,x100807))) % 172.83/172.50 [10081]~P102(f332(x100814,x100812))+~E(x100813,f332(f136(x100811,x100814),x100817))+E(f332(f332(f151(x100811),x100812),x100813),f332(f136(x100811,x100814),x100815))+~E(x100815,f332(f332(f134(x100811),x100816),f332(f332(f151(x100811),x100812),x100817)))+P102(f332(x100814,f791(x100815,x100814,x100813,x100812,x100811,x100816,x100817))) % 172.83/172.50 [10115]~P102(f332(x101152,x101154))+~E(x101155,f332(f136(x101151,x101152),x101157))+E(f332(f136(x101151,x101152),x101153),f332(f332(f151(x101151),x101154),x101155))+~E(x101153,f332(f332(f134(x101151),x101156),f332(f332(f151(x101151),x101154),x101157)))+P102(f332(f332(f334(x101151),f790(x101155,x101154,x101153,x101152,x101151,x101156,x101157)),f332(f173(x101151),x101156))) % 172.83/172.50 [10116]~P102(f332(x101164,x101162))+~E(x101163,f332(f136(x101161,x101164),x101167))+E(f332(f332(f151(x101161),x101162),x101163),f332(f136(x101161,x101164),x101165))+~E(x101165,f332(f332(f134(x101161),x101166),f332(f332(f151(x101161),x101162),x101167)))+P102(f332(f332(f334(x101161),f791(x101165,x101164,x101163,x101162,x101161,x101166,x101167)),f332(f173(x101161),x101166))) % 172.83/172.50 [10119]~P3(x101191,x101197,x101196)+~P8(x101191,f883(x101195,a871),x101196,x101194)+P102(f332(f332(f334(x101191),f512(x101192,x101193,x101194,x101195,x101196,x101197,x101191)),x101197))+~P102(f332(f332(f334(f883(x101191,a871)),x101193),f332(f332(f60(x101191),x101197),x101196)))+P102(f332(f332(f334(f883(x101195,a871)),f332(f332(f41(x101191,f883(x101195,a871)),x101193),x101194)),x101192)) % 172.83/172.50 [10164]~P3(x101642,x101646,x101647)+~P8(x101642,f883(x101641,a871),x101647,x101644)+~P102(f332(f332(f334(f883(x101642,a871)),x101643),f332(f332(f60(x101642),x101646),x101647)))+~P102(f332(f332(f334(f883(x101641,a871)),f332(x101644,f512(x101645,x101643,x101644,x101641,x101647,x101646,x101642))),x101645))+P102(f332(f332(f334(f883(x101641,a871)),f332(f332(f41(x101642,f883(x101641,a871)),x101643),x101644)),x101645)) % 172.83/172.50 [8386]~P67(x83862)+~P20(x83861,x83865,x83868,x83864)+~E(x83863,f332(f72(x83865,x83862,x83861,x83866),x83868))+~E(x83867,f332(f311(x83861,x83865,x83868),x83864))+E(f332(f332(f9(x83861,x83862),x83863),x83864),f332(f332(f9(x83865,x83862),x83866),x83867)) % 172.83/172.50 [10168]~P67(x101682)+~P20(x101685,x101681,x101688,x101687)+~E(f332(x101686,f525(x101683,x101686,x101684,x101687,x101688,x101681,x101685,x101682)),f332(f332(f72(x101681,x101682,x101685,x101683),x101688),f525(x101683,x101686,x101684,x101687,x101688,x101681,x101685,x101682)))+~E(x101684,f332(f311(x101685,x101681,x101688),x101687))+E(f332(f332(f9(x101681,x101682),x101683),x101684),f332(f332(f9(x101685,x101682),x101686),x101687)) % 172.83/172.50 [10170]~P71(x101702)+~P20(x101701,x101705,x101708,x101704)+~E(x101707,f332(f311(x101701,x101705,x101708),x101704))+E(f332(f332(f6(x101701,x101702),x101703),x101704),f332(f332(f6(x101705,x101702),x101706),x101707))+P102(f332(f332(f334(x101701),f592(x101706,x101703,x101707,x101704,x101708,x101705,x101701,x101702)),x101704)) % 172.83/172.50 [10171]~P67(x101712)+~P20(x101711,x101715,x101718,x101714)+~E(x101717,f332(f311(x101711,x101715,x101718),x101714))+E(f332(f332(f9(x101711,x101712),x101713),x101714),f332(f332(f9(x101715,x101712),x101716),x101717))+P102(f332(f332(f334(x101711),f525(x101716,x101713,x101717,x101714,x101718,x101715,x101711,x101712)),x101714)) % 172.83/172.50 [10177]~P71(x101772)+~P20(x101775,x101771,x101778,x101777)+~E(x101774,f332(f311(x101775,x101771,x101778),x101777))+~E(f332(x101776,f592(x101773,x101776,x101774,x101777,x101778,x101771,x101775,x101772)),f332(x101773,f332(x101778,f592(x101773,x101776,x101774,x101777,x101778,x101771,x101775,x101772))))+E(f332(f332(f6(x101771,x101772),x101773),x101774),f332(f332(f6(x101775,x101772),x101776),x101777)) % 172.83/172.50 [9551]~E(f332(f196(f877(x95512)),x95515),f332(f196(f877(x95511)),x95513))+~E(f332(f196(f877(x95512)),x95514),f332(f196(f877(x95511)),x95513))+~E(f332(f332(f332(f71(x95511,f880(x95512)),f332(f179(x95511,x95512),f332(f332(f183(x95511,x95512),x95513),x95514))),x95516),f332(f239(x95512),x95517)),f332(f332(f332(f71(x95511,f880(x95512)),f332(f179(x95511,x95512),f332(f332(f183(x95511,x95512),x95513),x95515))),x95516),f332(f239(x95512),x95518)))+E(f332(f179(x95511,x95512),f332(f332(f183(x95511,x95512),x95513),x95514)),f332(f179(x95511,x95512),f332(f332(f183(x95511,x95512),x95513),x95515)))+P102(f332(f332(f334(x95511),x95516),f332(f173(x95511),x95513))) % 172.83/172.50 [9664]~P18(x96646,x96642,x96645,x96647,x96648,x96641)+~P102(f332(f61(x96642),x96644))+~P102(f332(f61(x96642),x96643))+~E(f332(f332(f104(f883(x96642,a871)),x96643),x96644),f195(f883(x96642,a871)))+E(f332(x96641,f332(f332(f113(f883(x96642,a871)),x96643),x96644)),f332(f332(x96645,f332(x96641,x96643)),f332(x96641,x96644))) % 172.83/172.50 [10067]~P18(x100678,x100672,x100675,x100677,x100676,x100671)+~E(f332(x100676,f830(x100674,x100673,x100671,x100676,x100677,x100675,x100672)),x100677)+~P102(f332(f61(x100672),x100673))+~P102(f332(f61(x100672),x100674))+E(f332(x100671,f332(f332(f113(f883(x100672,a871)),x100673),x100674)),f332(f332(x100675,f332(x100671,x100673)),f332(x100671,x100674))) % 172.83/172.50 [10124]~P18(x101248,x101242,x101245,x101247,x101246,x101241)+~P102(f332(f61(x101242),x101243))+~P102(f332(f61(x101242),x101244))+E(f332(x101241,f332(f332(f113(f883(x101242,a871)),x101243),x101244)),f332(f332(x101245,f332(x101241,x101243)),f332(x101241,x101244)))+P102(f332(f332(f334(x101242),f830(x101244,x101243,x101241,x101246,x101247,x101245,x101242)),f332(f332(f104(f883(x101242,a871)),x101243),x101244))) % 172.83/172.50 [9822]~P3(x98224,x98228,x98225)+~P3(x98221,x98229,x98223)+~P9(x98221,x98224,f883(x98222,a871),x98223,x98225,x98227)+P8(x98221,f883(x98222,a871),x98223,f332(f332(f8(f883(x98224,f883(x98222,a871)),f883(x98222,a871),x98221),f332(f41(x98224,f883(x98222,a871)),f332(f286(x98224,x98224,x98225),f332(f332(f310(x98224),x98226),f195(f883(x98224,a871)))))),x98227))+~P102(f332(f332(f334(x98224),x98226),x98228)) % 172.83/172.50 [5422]~P104(x54223)+~P29(x54223,x54221)+E(x54221,f761(x54222,x54223))+~E(f332(f173(x54223),x54221),x54222)+~P102(f332(f61(x54223),x54222))+~P102(f332(f137(x54223),x54221)) % 172.83/172.50 [5048]~P125(x50482)+~P130(x50482)+~P140(x50482)+~P109(x50482)+E(x50481,f2(x50482))+~E(f332(f332(f257(x50482),x50481),x50483),f2(x50482)) % 172.83/172.50 [5049]~P125(x50492)+~P130(x50492)+~P140(x50492)+~P109(x50492)+~E(x50491,f2(a876))+~E(f332(f332(f257(x50492),x50493),x50491),f2(x50492)) % 172.83/172.50 [6471]~P84(x64711)+~E(x64713,f2(x64711))+~E(x64712,f2(x64711))+E(f332(f332(f79(x64711),x64712),x64713),f2(x64711))+~P102(f332(f332(f246(x64711),f2(x64711)),x64713))+~P102(f332(f332(f246(x64711),f2(x64711)),x64712)) % 172.83/172.50 [8849]~E(f332(f266(a876,a876),x88493),f2(a876))+~E(x88491,f332(f332(f79(a876),f332(f332(f80(a876),f332(f266(a876,a876),x88493)),x88492)),f332(f270(a876,a876),x88493)))+P102(f332(f47(x88491,x88492),x88493))+~P102(f332(f332(f246(a876),f332(f270(a876,a876),x88493)),f2(a876)))+P102(f332(f332(f247(a876),f2(a876)),x88492))+~P102(f332(f332(f247(a876),x88492),f332(f270(a876,a876),x88493))) % 172.83/172.50 [8857]E(x88571,f2(a876))+~E(x88572,f332(f332(f79(a876),f332(f332(f80(a876),f332(f266(a876,a876),x88573)),x88571)),f332(f270(a876,a876),x88573)))+P102(f332(f47(x88572,x88571),x88573))+~P102(f332(f332(f247(a876),f2(a876)),x88571))+~P102(f332(f332(f246(a876),f2(a876)),f332(f270(a876,a876),x88573)))+~P102(f332(f332(f247(a876),f332(f270(a876,a876),x88573)),x88571)) % 172.83/172.50 [8875]~E(f332(f266(a876,a876),x88753),f2(a876))+~E(x88751,f332(f332(f79(a876),f332(f332(f80(a876),f332(f266(a876,a876),x88753)),x88752)),f332(f270(a876,a876),x88753)))+P102(f332(f47(x88751,x88752),x88753))+~P102(f332(f332(f247(a876),f2(a876)),x88752))+~P102(f332(f332(f246(a876),f2(a876)),f332(f270(a876,a876),x88753)))+~P102(f332(f332(f247(a876),f332(f270(a876,a876),x88753)),x88752)) % 172.83/172.50 [6853]~P61(x68532)+E(x68531,f195(f883(x68532,a871)))+E(x68533,f195(f883(x68532,a871)))+~P102(f332(f61(x68532),x68531))+~P102(f332(f61(x68532),x68533))+E(f13(x68532,f332(f332(f113(f883(x68532,a871)),x68533),x68531)),f332(f332(f113(x68532),f13(x68532,x68533)),f13(x68532,x68531))) % 172.83/172.50 [6854]~P61(x68542)+E(x68541,f195(f883(x68542,a871)))+E(x68543,f195(f883(x68542,a871)))+~P102(f332(f61(x68542),x68541))+~P102(f332(f61(x68542),x68543))+E(f10(x68542,f332(f332(f113(f883(x68542,a871)),x68543),x68541)),f332(f332(f104(x68542),f10(x68542,x68543)),f10(x68542,x68541))) % 172.83/172.50 [6855]~P104(x68552)+E(x68551,f195(f883(x68552,a871)))+E(x68553,f195(f883(x68552,a871)))+~P102(f332(f61(x68552),x68551))+~P102(f332(f61(x68552),x68553))+E(f14(x68552,f332(f332(f113(f883(x68552,a871)),x68553),x68551)),f332(f332(f245(x68552),f14(x68552,x68553)),f14(x68552,x68551))) % 172.83/172.50 [6856]~P104(x68562)+E(x68561,f195(f883(x68562,a871)))+E(x68563,f195(f883(x68562,a871)))+~P102(f332(f61(x68562),x68561))+~P102(f332(f61(x68562),x68563))+E(f15(x68562,f332(f332(f113(f883(x68562,a871)),x68563),x68561)),f332(f332(f244(x68562),f15(x68562,x68563)),f15(x68562,x68561))) % 172.83/172.50 [7497]~P93(x74972)+E(x74971,f195(f883(x74972,a871)))+E(x74973,f195(f883(x74972,a871)))+~P102(f332(f61(x74972),x74971))+~P102(f332(f61(x74972),x74973))+E(f332(f332(f80(x74972),f332(f63(x74972,f80(x74972)),x74973)),f332(f63(x74972,f80(x74972)),x74971)),f332(f63(x74972,f80(x74972)),f332(f332(f113(f883(x74972,a871)),x74973),x74971))) % 172.83/172.50 [7655]~P104(x76552)+E(x76551,f195(f883(x76552,a871)))+E(x76553,f195(f883(x76552,a871)))+~P102(f332(f61(x76552),x76551))+~P102(f332(f61(x76552),x76553))+E(f332(f332(f245(x76552),f11(x76552,f245(x76552),x76553)),f11(x76552,f245(x76552),x76551)),f11(x76552,f245(x76552),f332(f332(f113(f883(x76552,a871)),x76553),x76551))) % 172.83/172.50 [7656]~P104(x76562)+E(x76561,f195(f883(x76562,a871)))+E(x76563,f195(f883(x76562,a871)))+~P102(f332(f61(x76562),x76561))+~P102(f332(f61(x76562),x76563))+E(f332(f332(f244(x76562),f12(x76562,f244(x76562),x76563)),f12(x76562,f244(x76562),x76561)),f12(x76562,f244(x76562),f332(f332(f113(f883(x76562,a871)),x76563),x76561))) % 172.83/172.50 [8697]~P102(f332(x86971,x86973))+P102(f332(x86971,f410(x86971,x86972)))+P102(f332(x86971,f402(x86971,x86972)))+~P102(f332(f332(f247(a1),f2(a1)),x86972))+~P102(f332(f332(f334(a1),x86973),f303(a1,f77(a1),x86972)))+P102(f332(x86971,f332(f332(f22(a1),f402(x86971,x86972)),f332(f332(f80(a1),f408(x86971,x86972)),x86972)))) % 172.83/172.50 [8997]~P102(f332(x89971,x89973))+~P102(f332(x89971,f402(x89971,x89972)))+P102(f332(x89971,f410(x89971,x89972)))+~P102(f332(f332(f247(a1),f2(a1)),x89972))+~P102(f332(f332(f334(a1),x89973),f303(a1,f77(a1),x89972)))+~P102(f332(x89971,f332(f332(f22(a1),f402(x89971,x89972)),f332(f332(f80(a1),f408(x89971,x89972)),x89972)))) % 172.83/172.50 [10202]~P95(x102022)+E(x102021,f195(f883(x102022,a871)))+E(x102023,f195(f883(x102022,a871)))+~P102(f332(f61(x102022),x102021))+~P102(f332(f61(x102022),x102023))+E(f10(x102022,f332(f252(x102022),f332(f332(f8(f883(x102022,a871),a871,x102022),f86(x102022)),f332(f332(f8(f883(x102022,f883(x102022,a871)),f883(x102022,a871),x102022),f332(f8(f883(x102022,a871),a871,x102022),f86(x102022))),f332(f332(f7(x102022,f883(x102022,f883(x102022,a871)),f883(x102022,f883(x102022,a871))),f332(f332(f8(f883(x102022,f883(f883(x102022,a871),f883(x102022,a871))),f883(f883(x102022,f883(x102022,a871)),f883(x102022,f883(x102022,a871))),x102022),f18(x102022,f883(x102022,a871),f883(x102022,a871))),f332(f332(f8(f883(x102022,f883(x102022,f883(a871,a871))),f883(x102022,f883(f883(x102022,a871),f883(x102022,a871))),x102022),f332(f8(f883(x102022,f883(a871,a871)),f883(f883(x102022,a871),f883(x102022,a871)),x102022),f18(x102022,a871,a871))),f332(f332(f8(f883(x102022,f883(x102022,a871)),f883(x102022,f883(x102022,f883(a871,a871))),x102022),f332(f8(f883(x102022,a871),f883(x102022,f883(a871,a871)),x102022),f332(f8(a871,f883(a871,a871),x102022),a330))),f332(f332(f7(x102022,f883(x102022,f883(x102022,x102022)),f883(x102022,f883(x102022,a871))),f332(f332(f8(f883(f883(x102022,x102022),f883(x102022,a871)),f883(f883(x102022,f883(x102022,x102022)),f883(x102022,f883(x102022,a871))),x102022),f8(f883(x102022,x102022),f883(x102022,a871),x102022)),f332(f332(f8(f883(x102022,a871),f883(f883(x102022,x102022),f883(x102022,a871)),x102022),f8(x102022,a871,x102022)),a329))),f113(x102022)))))),f332(f332(f7(x102022,f883(x102022,a871),f883(x102022,a871)),f332(f332(f8(f883(a871,a871),f883(f883(x102022,a871),f883(x102022,a871)),x102022),f8(a871,a871,x102022)),f332(f332(f8(a871,f883(a871,a871),x102022),a330),f332(f332(f7(x102022,f883(x102022,a871),a871),f334(x102022)),x102023)))),f332(f332(f7(x102022,f883(x102022,a871),a871),f334(x102022)),x102021))))))),f332(f332(f113(x102022),f10(x102022,x102023)),f10(x102022,x102021))) % 172.83/172.50 [10203]~P95(x102032)+E(x102031,f195(f883(x102032,a871)))+E(x102033,f195(f883(x102032,a871)))+~P102(f332(f61(x102032),x102031))+~P102(f332(f61(x102032),x102033))+E(f13(x102032,f332(f252(x102032),f332(f332(f8(f883(x102032,a871),a871,x102032),f86(x102032)),f332(f332(f8(f883(x102032,f883(x102032,a871)),f883(x102032,a871),x102032),f332(f8(f883(x102032,a871),a871,x102032),f86(x102032))),f332(f332(f7(x102032,f883(x102032,f883(x102032,a871)),f883(x102032,f883(x102032,a871))),f332(f332(f8(f883(x102032,f883(f883(x102032,a871),f883(x102032,a871))),f883(f883(x102032,f883(x102032,a871)),f883(x102032,f883(x102032,a871))),x102032),f18(x102032,f883(x102032,a871),f883(x102032,a871))),f332(f332(f8(f883(x102032,f883(x102032,f883(a871,a871))),f883(x102032,f883(f883(x102032,a871),f883(x102032,a871))),x102032),f332(f8(f883(x102032,f883(a871,a871)),f883(f883(x102032,a871),f883(x102032,a871)),x102032),f18(x102032,a871,a871))),f332(f332(f8(f883(x102032,f883(x102032,a871)),f883(x102032,f883(x102032,f883(a871,a871))),x102032),f332(f8(f883(x102032,a871),f883(x102032,f883(a871,a871)),x102032),f332(f8(a871,f883(a871,a871),x102032),a330))),f332(f332(f7(x102032,f883(x102032,f883(x102032,x102032)),f883(x102032,f883(x102032,a871))),f332(f332(f8(f883(f883(x102032,x102032),f883(x102032,a871)),f883(f883(x102032,f883(x102032,x102032)),f883(x102032,f883(x102032,a871))),x102032),f8(f883(x102032,x102032),f883(x102032,a871),x102032)),f332(f332(f8(f883(x102032,a871),f883(f883(x102032,x102032),f883(x102032,a871)),x102032),f8(x102032,a871,x102032)),a329))),f104(x102032)))))),f332(f332(f7(x102032,f883(x102032,a871),f883(x102032,a871)),f332(f332(f8(f883(a871,a871),f883(f883(x102032,a871),f883(x102032,a871)),x102032),f8(a871,a871,x102032)),f332(f332(f8(a871,f883(a871,a871),x102032),a330),f332(f332(f7(x102032,f883(x102032,a871),a871),f334(x102032)),x102033)))),f332(f332(f7(x102032,f883(x102032,a871),a871),f334(x102032)),x102031))))))),f332(f332(f104(x102032),f13(x102032,x102033)),f13(x102032,x102031))) % 172.83/172.50 [10204]~P104(x102042)+E(x102041,f195(f883(x102042,a871)))+E(x102043,f195(f883(x102042,a871)))+~P102(f332(f61(x102042),x102041))+~P102(f332(f61(x102042),x102043))+E(f11(x102042,f245(x102042),f332(f252(x102042),f332(f332(f8(f883(x102042,a871),a871,x102042),f86(x102042)),f332(f332(f8(f883(x102042,f883(x102042,a871)),f883(x102042,a871),x102042),f332(f8(f883(x102042,a871),a871,x102042),f86(x102042))),f332(f332(f7(x102042,f883(x102042,f883(x102042,a871)),f883(x102042,f883(x102042,a871))),f332(f332(f8(f883(x102042,f883(f883(x102042,a871),f883(x102042,a871))),f883(f883(x102042,f883(x102042,a871)),f883(x102042,f883(x102042,a871))),x102042),f18(x102042,f883(x102042,a871),f883(x102042,a871))),f332(f332(f8(f883(x102042,f883(x102042,f883(a871,a871))),f883(x102042,f883(f883(x102042,a871),f883(x102042,a871))),x102042),f332(f8(f883(x102042,f883(a871,a871)),f883(f883(x102042,a871),f883(x102042,a871)),x102042),f18(x102042,a871,a871))),f332(f332(f8(f883(x102042,f883(x102042,a871)),f883(x102042,f883(x102042,f883(a871,a871))),x102042),f332(f8(f883(x102042,a871),f883(x102042,f883(a871,a871)),x102042),f332(f8(a871,f883(a871,a871),x102042),a330))),f332(f332(f7(x102042,f883(x102042,f883(x102042,x102042)),f883(x102042,f883(x102042,a871))),f332(f332(f8(f883(f883(x102042,x102042),f883(x102042,a871)),f883(f883(x102042,f883(x102042,x102042)),f883(x102042,f883(x102042,a871))),x102042),f8(f883(x102042,x102042),f883(x102042,a871),x102042)),f332(f332(f8(f883(x102042,a871),f883(f883(x102042,x102042),f883(x102042,a871)),x102042),f8(x102042,a871,x102042)),a329))),f244(x102042)))))),f332(f332(f7(x102042,f883(x102042,a871),f883(x102042,a871)),f332(f332(f8(f883(a871,a871),f883(f883(x102042,a871),f883(x102042,a871)),x102042),f8(a871,a871,x102042)),f332(f332(f8(a871,f883(a871,a871),x102042),a330),f332(f332(f7(x102042,f883(x102042,a871),a871),f334(x102042)),x102043)))),f332(f332(f7(x102042,f883(x102042,a871),a871),f334(x102042)),x102041))))))),f332(f332(f244(x102042),f11(x102042,f245(x102042),x102043)),f11(x102042,f245(x102042),x102041))) % 172.83/172.50 [10205]~P104(x102052)+E(x102051,f195(f883(x102052,a871)))+E(x102053,f195(f883(x102052,a871)))+~P102(f332(f61(x102052),x102051))+~P102(f332(f61(x102052),x102053))+E(f12(x102052,f244(x102052),f332(f252(x102052),f332(f332(f8(f883(x102052,a871),a871,x102052),f86(x102052)),f332(f332(f8(f883(x102052,f883(x102052,a871)),f883(x102052,a871),x102052),f332(f8(f883(x102052,a871),a871,x102052),f86(x102052))),f332(f332(f7(x102052,f883(x102052,f883(x102052,a871)),f883(x102052,f883(x102052,a871))),f332(f332(f8(f883(x102052,f883(f883(x102052,a871),f883(x102052,a871))),f883(f883(x102052,f883(x102052,a871)),f883(x102052,f883(x102052,a871))),x102052),f18(x102052,f883(x102052,a871),f883(x102052,a871))),f332(f332(f8(f883(x102052,f883(x102052,f883(a871,a871))),f883(x102052,f883(f883(x102052,a871),f883(x102052,a871))),x102052),f332(f8(f883(x102052,f883(a871,a871)),f883(f883(x102052,a871),f883(x102052,a871)),x102052),f18(x102052,a871,a871))),f332(f332(f8(f883(x102052,f883(x102052,a871)),f883(x102052,f883(x102052,f883(a871,a871))),x102052),f332(f8(f883(x102052,a871),f883(x102052,f883(a871,a871)),x102052),f332(f8(a871,f883(a871,a871),x102052),a330))),f332(f332(f7(x102052,f883(x102052,f883(x102052,x102052)),f883(x102052,f883(x102052,a871))),f332(f332(f8(f883(f883(x102052,x102052),f883(x102052,a871)),f883(f883(x102052,f883(x102052,x102052)),f883(x102052,f883(x102052,a871))),x102052),f8(f883(x102052,x102052),f883(x102052,a871),x102052)),f332(f332(f8(f883(x102052,a871),f883(f883(x102052,x102052),f883(x102052,a871)),x102052),f8(x102052,a871,x102052)),a329))),f245(x102052)))))),f332(f332(f7(x102052,f883(x102052,a871),f883(x102052,a871)),f332(f332(f8(f883(a871,a871),f883(f883(x102052,a871),f883(x102052,a871)),x102052),f8(a871,a871,x102052)),f332(f332(f8(a871,f883(a871,a871),x102052),a330),f332(f332(f7(x102052,f883(x102052,a871),a871),f334(x102052)),x102053)))),f332(f332(f7(x102052,f883(x102052,a871),a871),f334(x102052)),x102051))))))),f332(f332(f245(x102052),f12(x102052,f244(x102052),x102053)),f12(x102052,f244(x102052),x102051))) % 172.83/172.50 [7181]~P107(x71813)+E(x71811,x71812)+~E(f332(f332(f257(x71813),x71811),x71814),f332(f332(f257(x71813),x71812),x71814))+~P102(f332(f332(f246(x71813),f2(x71813)),x71812))+~P102(f332(f332(f246(x71813),f2(x71813)),x71811))+~P102(f332(f332(f247(a876),f2(a876)),x71814)) % 172.83/172.50 [7454]~P104(x74542)+E(x74541,f195(f883(x74542,a871)))+~P102(f332(f61(x74542),x74541))+~P102(f332(f332(f334(x74542),x74544),x74541))+P102(f332(f332(f247(x74542),x74543),x74544))+~P102(f332(f332(f247(x74542),x74543),f332(f63(x74542,f244(x74542)),x74541))) % 172.83/172.50 [7455]~P98(x74552)+E(x74551,f195(f883(x74552,a871)))+~P102(f332(f61(x74552),x74551))+~P102(f332(f332(f334(x74552),x74554),x74551))+P102(f332(f332(f246(x74552),x74553),x74554))+~P102(f332(f332(f246(x74552),x74553),f332(f63(x74552,f104(x74552)),x74551))) % 172.83/172.50 [7456]~P104(x74562)+E(x74561,f195(f883(x74562,a871)))+~P102(f332(f61(x74562),x74561))+~P102(f332(f332(f334(x74562),x74564),x74561))+P102(f332(f332(f246(x74562),x74563),x74564))+~P102(f332(f332(f246(x74562),x74563),f332(f63(x74562,f244(x74562)),x74561))) % 172.83/172.50 [7355]E(x73551,f2(a1))+E(f332(f332(f38(a1),x73552),x73551),x73553)+~P102(f332(f332(f246(a1),x73554),f2(a1)))+~E(x73552,f332(f332(f79(a1),f332(f332(f80(a1),x73551),x73553)),x73554))+P102(f332(f332(f247(a1),f2(a1)),x73551))+~P102(f332(f332(f247(a1),x73551),x73554)) % 172.83/172.50 [7370]E(f44(a1,x73702,x73701),x73703)+E(x73701,f2(a1))+~P102(f332(f332(f246(a1),x73703),f2(a1)))+~E(x73702,f332(f332(f79(a1),f332(f332(f80(a1),x73701),x73704)),x73703))+P102(f332(f332(f247(a1),f2(a1)),x73701))+~P102(f332(f332(f247(a1),x73701),x73703)) % 172.83/172.50 [7496]E(x74961,f2(a1))+E(f332(f332(f38(a1),x74962),x74961),x74963)+~E(x74962,f332(f332(f79(a1),f332(f332(f80(a1),x74961),x74963)),x74964))+~P102(f332(f332(f247(a1),f2(a1)),x74961))+~P102(f332(f332(f246(a1),f2(a1)),x74964))+~P102(f332(f332(f247(a1),x74964),x74961)) % 172.83/172.50 [7518]E(f44(a1,x75182,x75181),x75183)+E(x75181,f2(a1))+~E(x75182,f332(f332(f79(a1),f332(f332(f80(a1),x75181),x75184)),x75183))+~P102(f332(f332(f247(a1),f2(a1)),x75181))+~P102(f332(f332(f246(a1),f2(a1)),x75183))+~P102(f332(f332(f247(a1),x75183),x75181)) % 172.83/172.50 [7659]~P104(x76592)+E(x76591,f195(f883(x76592,a871)))+~P102(f332(f61(x76592),x76591))+~P102(f332(f332(f247(x76592),x76594),x76593))+~P102(f332(f332(f334(x76592),x76594),x76591))+P102(f332(f332(f247(x76592),f332(f63(x76592,f244(x76592)),x76591)),x76593)) % 172.83/172.50 [7660]~P104(x76602)+E(x76601,f195(f883(x76602,a871)))+~P102(f332(f61(x76602),x76601))+~P102(f332(f332(f246(x76602),x76604),x76603))+~P102(f332(f332(f334(x76602),x76604),x76601))+P102(f332(f332(f246(x76602),f332(f63(x76602,f244(x76602)),x76601)),x76603)) % 172.83/172.50 [8242]~P102(f332(f332(f246(a1),x82424),f2(a1)))+~E(x82421,f332(f332(f79(a1),f332(f332(f80(a1),x82422),x82423)),x82424))+~P102(f332(f332(f246(a1),f2(a1)),x82424))+~P102(f332(f332(f247(a1),x82424),x82422))+~P102(f332(f332(f247(a1),x82422),x82424))+P102(f332(f48(x82421,x82422),f332(f332(f267(a1,a1),x82423),x82424))) % 172.83/172.50 [9190]~P56(x91903)+~P56(x91904)+E(x91901,x91902)+~E(f332(f196(f877(x91903)),x91902),f332(f196(f877(x91904)),f55(x91904)))+~E(f332(f196(f877(x91903)),x91901),f332(f196(f877(x91904)),f55(x91904)))+~E(f332(f72(f880(x91903),x91903,x91904,f243(x91903)),f332(f179(x91904,x91903),f332(f332(f183(x91904,x91903),f55(x91904)),x91901))),f332(f72(f880(x91903),x91903,x91904,f243(x91903)),f332(f179(x91904,x91903),f332(f332(f183(x91904,x91903),f55(x91904)),x91902)))) % 172.83/172.50 [8407]~P105(x84071)+P102(f332(f332(f247(f883(x84071,a871)),f303(x84071,x84072,x84073)),f303(x84071,x84074,x84075)))+~P102(f332(f332(f247(x84071),x84073),x84075))+~P102(f332(f332(f246(x84071),x84074),x84072))+~P102(f332(f332(f246(x84071),x84074),x84075))+~P102(f332(f332(f246(x84071),x84073),x84075)) % 172.83/172.50 [8408]~P105(x84081)+P102(f332(f332(f247(f883(x84081,a871)),f303(x84081,x84082,x84083)),f303(x84081,x84084,x84085)))+~P102(f332(f332(f247(x84081),x84084),x84082))+~P102(f332(f332(f246(x84081),x84083),x84085))+~P102(f332(f332(f246(x84081),x84084),x84085))+~P102(f332(f332(f246(x84081),x84084),x84082)) % 172.83/172.50 [9255]P54(x92552,x92553,x92554,x92551)+E(x92551,f195(f883(x92552,a871)))+~P102(f332(f61(x92552),x92554))+~P102(f332(f61(x92552),x92551))+~P102(f332(f332(x92553,f523(x92551,x92554,x92553,x92552)),x92555))+~P102(f332(f332(f334(x92552),x92555),x92551)) % 172.83/172.50 [9404]~E(x94043,x94045)+~P67(x94041)+~P71(x94041)+~P39(x94043)+E(f332(f332(f6(a1,x94041),x94042),x94043),f332(f332(f6(a1,x94041),x94044),x94045))+P102(f332(f332(f246(a1),f2(a1)),f423(x94042,x94044,x94043,x94045,x94041))) % 172.83/172.50 [9405]~E(x94053,x94055)+~P67(x94051)+~P71(x94051)+~P39(x94053)+E(f332(f332(f9(a1,x94051),x94052),x94053),f332(f332(f9(a1,x94051),x94054),x94055))+P102(f332(f332(f246(a1),f2(a1)),f424(x94052,x94054,x94053,x94055,x94051))) % 172.83/172.50 [9572]~E(x95725,x95723)+~P67(x95721)+~P71(x95721)+~P39(x95725)+~E(f332(x95722,f423(x95724,x95722,x95725,x95723,x95721)),f332(x95724,f423(x95724,x95722,x95725,x95723,x95721)))+E(f332(f332(f6(a1,x95721),x95722),x95723),f332(f332(f6(a1,x95721),x95724),x95725)) % 172.83/172.50 [9573]~E(x95735,x95733)+~P67(x95731)+~P71(x95731)+~P39(x95735)+~E(f332(x95732,f424(x95734,x95732,x95735,x95733,x95731)),f332(x95734,f424(x95734,x95732,x95735,x95733,x95731)))+E(f332(f332(f9(a1,x95731),x95732),x95733),f332(f332(f9(a1,x95731),x95734),x95735)) % 172.83/172.50 [9661]~P79(x96613)+E(f332(x96611,x96612),f2(x96613))+~E(f332(f332(f6(x96614,x96613),x96611),x96615),f2(x96613))+~P102(f332(f61(x96614),x96615))+P102(f332(f332(f334(x96614),f864(x96612,x96611,x96615,x96614,x96613)),x96615))+~P102(f332(f332(f334(x96614),x96612),x96615)) % 172.83/172.50 [9796]~P79(x97963)+E(f332(x97961,x97962),f2(x97963))+~E(f332(f332(f6(x97964,x97963),x97961),x97965),f2(x97963))+~P102(f332(f61(x97964),x97965))+~P102(f332(f332(f334(x97964),x97962),x97965))+~P102(f332(f332(f246(x97963),f2(x97963)),f332(x97961,f864(x97962,x97961,x97965,x97964,x97963)))) % 172.83/172.50 [8323]~P126(x83231)+~P102(f332(f332(f246(x83231),f2(x83231)),x83233))+~P102(f332(f332(f247(x83231),x83233),x83235))+~P102(f332(f332(f247(x83231),x83232),x83234))+~P102(f332(f332(f247(x83231),f2(x83231)),x83234))+P102(f332(f332(f247(x83231),f332(f332(f80(x83231),x83232),x83233)),f332(f332(f80(x83231),x83234),x83235))) % 172.83/172.50 [8324]~P126(x83241)+~P102(f332(f332(f246(x83241),f2(x83241)),x83243))+~P102(f332(f332(f246(x83241),f2(x83241)),x83242))+~P102(f332(f332(f247(x83241),x83243),x83245))+~P102(f332(f332(f247(x83241),x83242),x83244))+P102(f332(f332(f247(x83241),f332(f332(f80(x83241),x83242),x83243)),f332(f332(f80(x83241),x83244),x83245))) % 172.83/172.50 [8325]~P126(x83251)+~P102(f332(f332(f246(x83251),x83252),x83254))+~P102(f332(f332(f246(x83251),f2(x83251)),x83253))+~P102(f332(f332(f247(x83251),x83253),x83255))+~P102(f332(f332(f247(x83251),f2(x83251)),x83252))+P102(f332(f332(f247(x83251),f332(f332(f80(x83251),x83252),x83253)),f332(f332(f80(x83251),x83254),x83255))) % 172.83/172.50 [8326]~P126(x83261)+~P102(f332(f332(f246(x83261),x83263),x83265))+~P102(f332(f332(f246(x83261),f2(x83261)),x83262))+~P102(f332(f332(f247(x83261),x83262),x83264))+~P102(f332(f332(f247(x83261),f2(x83261)),x83263))+P102(f332(f332(f247(x83261),f332(f332(f80(x83261),x83262),x83263)),f332(f332(f80(x83261),x83264),x83265))) % 172.83/172.50 [8327]~P60(x83271)+~P102(f332(f332(f246(x83271),x83272),x83274))+~P102(f332(f332(f247(x83271),x83275),x83273))+~P102(f332(f332(f247(x83271),f2(x83271)),x83275))+~P102(f332(f332(f247(x83271),f2(x83271)),x83272))+P102(f332(f332(f247(x83271),f332(f332(f290(x83271),x83272),x83273)),f332(f332(f290(x83271),x83274),x83275))) % 172.83/172.50 [8328]~P60(x83281)+~P102(f332(f332(f246(x83281),x83285),x83283))+~P102(f332(f332(f246(x83281),f2(x83281)),x83282))+~P102(f332(f332(f247(x83281),x83282),x83284))+~P102(f332(f332(f247(x83281),f2(x83281)),x83285))+P102(f332(f332(f247(x83281),f332(f332(f290(x83281),x83282),x83283)),f332(f332(f290(x83281),x83284),x83285))) % 172.83/172.50 [8329]~P133(x83291)+~P102(f332(f332(f246(x83291),x83293),x83295))+~P102(f332(f332(f246(x83291),x83292),x83294))+~P102(f332(f332(f246(x83291),f2(x83291)),x83293))+~P102(f332(f332(f246(x83291),f2(x83291)),x83294))+P102(f332(f332(f246(x83291),f332(f332(f80(x83291),x83292),x83293)),f332(f332(f80(x83291),x83294),x83295))) % 172.83/172.50 [8330]~P133(x83301)+~P102(f332(f332(f246(x83301),x83303),x83305))+~P102(f332(f332(f246(x83301),x83302),x83304))+~P102(f332(f332(f246(x83301),f2(x83301)),x83303))+~P102(f332(f332(f246(x83301),f2(x83301)),x83302))+P102(f332(f332(f246(x83301),f332(f332(f80(x83301),x83302),x83303)),f332(f332(f80(x83301),x83304),x83305))) % 172.83/172.50 [8331]~P60(x83311)+~P102(f332(f332(f247(x83311),f2(x83311)),x83315))+~P102(f332(f332(f246(x83311),x83315),x83313))+~P102(f332(f332(f246(x83311),x83312),x83314))+~P102(f332(f332(f246(x83311),f2(x83311)),x83312))+P102(f332(f332(f246(x83311),f332(f332(f290(x83311),x83312),x83313)),f332(f332(f290(x83311),x83314),x83315))) % 172.83/172.50 [9700]~P82(x97005)+~P71(x97005)+E(x97001,f195(f883(x97002,a871)))+~P102(f332(f61(x97002),x97001))+P102(f332(f332(f334(x97002),f834(x97003,x97004,x97001,x97002,x97005)),x97001))+P102(f332(f332(f247(x97005),f332(f332(f6(x97002,x97005),x97004),x97001)),f332(f332(f6(x97002,x97005),x97003),x97001))) % 172.83/172.50 [9818]~P71(x98181)+~P80(x98181)+~P102(f332(f61(x98182),x98185))+~P102(f332(f332(f246(x98181),f2(x98181)),f332(x98183,f865(x98183,x98184,x98185,x98182,x98181))))+P102(f332(f332(f246(x98181),f332(f332(f6(x98182,x98181),x98183),x98184)),f332(f332(f6(x98182,x98181),x98183),x98185)))+~P102(f332(f332(f246(f883(x98182,a871)),x98184),x98185)) % 172.83/172.50 [9986]~P82(x99863)+~P71(x99863)+E(x99861,f195(f883(x99862,a871)))+~P102(f332(f61(x99862),x99861))+~P102(f332(f332(f247(x99863),f332(x99864,f834(x99865,x99864,x99861,x99862,x99863))),f332(x99865,f834(x99865,x99864,x99861,x99862,x99863))))+P102(f332(f332(f247(x99863),f332(f332(f6(x99862,x99863),x99864),x99861)),f332(f332(f6(x99862,x99863),x99865),x99861))) % 172.83/172.50 [7040]~P12(x70402,x70405,x70404)+E(x70401,f195(f883(x70402,a871)))+E(x70403,f195(f883(x70402,a871)))+~P102(f332(f61(x70402),x70401))+~P102(f332(f61(x70402),x70403))+E(f332(x70404,f332(f332(f113(f883(x70402,a871)),x70403),x70401)),f332(f332(x70405,f332(x70404,x70403)),f332(x70404,x70401))) % 172.83/172.50 [7625]~P144(x76251,x76253,x76254)+P102(f332(x76251,x76252))+~P102(f332(f332(f247(a1),x76254),f2(a1)))+~P102(f332(f332(f246(a1),x76255),f2(a1)))+~E(x76253,f332(f332(f79(a1),f332(f332(f80(a1),x76254),x76252)),x76255))+~P102(f332(f332(f247(a1),x76254),x76255)) % 172.83/172.50 [7626]~P143(x76261,x76263,x76264)+P102(f332(x76261,x76262))+~P102(f332(f332(f247(a1),x76264),f2(a1)))+~P102(f332(f332(f246(a1),x76262),f2(a1)))+~E(x76263,f332(f332(f79(a1),f332(f332(f80(a1),x76264),x76265)),x76262))+~P102(f332(f332(f247(a1),x76264),x76262)) % 172.83/172.50 [7668]~P144(x76681,x76683,x76684)+P102(f332(x76681,x76682))+~E(x76683,f332(f332(f79(a1),f332(f332(f80(a1),x76684),x76682)),x76685))+~P102(f332(f332(f247(a1),f2(a1)),x76684))+~P102(f332(f332(f246(a1),f2(a1)),x76685))+~P102(f332(f332(f247(a1),x76685),x76684)) % 172.83/172.50 [7669]~P143(x76691,x76693,x76694)+P102(f332(x76691,x76692))+~E(x76693,f332(f332(f79(a1),f332(f332(f80(a1),x76694),x76695)),x76692))+~P102(f332(f332(f247(a1),f2(a1)),x76694))+~P102(f332(f332(f246(a1),f2(a1)),x76692))+~P102(f332(f332(f247(a1),x76692),x76694)) % 172.83/172.50 [8619]P102(f332(f332(x86191,x86192),x86193))+~P102(f332(f332(x86191,f332(f332(f38(a1),x86194),x86195)),f44(a1,x86194,x86195)))+~P102(f332(f332(f247(a1),x86195),f2(a1)))+~P102(f332(f332(f246(a1),x86193),f2(a1)))+~E(x86194,f332(f332(f79(a1),f332(f332(f80(a1),x86195),x86192)),x86193))+~P102(f332(f332(f247(a1),x86195),x86193)) % 172.83/172.50 [8628]P102(f332(f332(x86281,x86282),x86283))+~P102(f332(f332(x86281,f332(f332(f38(a1),x86284),x86285)),f44(a1,x86284,x86285)))+~E(x86284,f332(f332(f79(a1),f332(f332(f80(a1),x86285),x86282)),x86283))+~P102(f332(f332(f247(a1),f2(a1)),x86285))+~P102(f332(f332(f246(a1),f2(a1)),x86283))+~P102(f332(f332(f247(a1),x86283),x86285)) % 172.83/172.50 [8863]E(x88631,x88632)+~P51(x88633,x88635,x88634)+~P102(f332(f332(f334(x88633),x88632),x88635))+~P102(f332(f332(f334(x88633),x88631),x88635))+P102(f332(f332(f334(f882(x88633,x88633)),f332(f332(f267(x88633,x88633),x88631),x88632)),x88634))+P102(f332(f332(f334(f882(x88633,x88633)),f332(f332(f267(x88633,x88633),x88632),x88631)),x88634)) % 172.83/172.50 [9727]~P71(x97275)+~P80(x97275)+~P102(f332(f61(x97271),x97274))+P102(f332(f332(f246(x97275),f332(f332(f6(x97271,x97275),x97272),x97273)),f332(f332(f6(x97271,x97275),x97272),x97274)))+~P102(f332(f332(f246(f883(x97271,a871)),x97273),x97274))+P102(f332(f332(f334(x97271),f865(x97272,x97273,x97274,x97271,x97275)),f332(f332(f22(f883(x97271,a871)),x97274),x97273))) % 172.83/172.50 [9826]E(x98261,f195(f883(x98262,a871)))+~P102(f332(f61(x98262),x98263))+~P102(f332(f61(x98262),x98261))+P102(f332(f332(f334(f882(f883(x98262,a871),f883(x98262,a871))),f332(f332(f267(f883(x98262,a871),f883(x98262,a871)),x98263),x98261)),f324(x98262,x98264)))+~P102(f332(f332(f334(x98262),x98265),x98261))+~P102(f332(f332(f334(f882(x98262,x98262)),f332(f332(f267(x98262,x98262),f527(x98264,x98261,x98263,x98262)),x98265)),x98264)) % 172.83/172.50 [9827]E(x98271,f195(f883(x98272,a871)))+~P102(f332(f61(x98272),x98273))+~P102(f332(f61(x98272),x98271))+P102(f332(f332(f334(f882(f883(x98272,a871),f883(x98272,a871))),f332(f332(f267(f883(x98272,a871),f883(x98272,a871)),x98273),x98271)),f324(x98272,x98274)))+~P102(f332(f332(f334(x98272),x98275),x98271))+~P102(f332(f332(f334(f882(x98272,x98272)),f332(f332(f267(x98272,x98272),f588(x98274,x98271,x98273,x98272)),x98275)),x98274)) % 172.83/172.50 [9990]~P79(x99901)+~E(f332(f332(f6(x99905,x99901),x99902),x99906),x99904)+~P102(f332(f61(x99905),x99906))+P102(f332(f332(f334(x99905),f868(x99903,x99904,x99902,x99906,x99905,x99901)),x99906))+P102(f332(f332(f246(x99901),f332(x99902,x99903)),x99904))+~P102(f332(f332(f334(x99905),x99903),x99906)) % 172.83/172.50 [10037]~P79(x100371)+~E(f332(f332(f6(x100375,x100371),x100372),x100376),x100374)+~P102(f332(f61(x100375),x100376))+~P102(f332(f332(f334(x100375),x100373),x100376))+~P102(f332(f332(f246(x100371),f2(x100371)),f332(x100372,f868(x100373,x100374,x100372,x100376,x100375,x100371))))+P102(f332(f332(f246(x100371),f332(x100372,x100373)),x100374)) % 172.83/172.50 [10150]~E(x101505,x101508)+~E(x101504,x101507)+~P106(x101501)+~P71(x101502)+E(f332(f332(f6(x101501,x101502),x101503),f332(f302(x101501,x101504),x101505)),f332(f332(f6(x101501,x101502),x101506),f332(f302(x101501,x101507),x101508)))+P102(f332(f332(f246(x101501),x101504),f591(x101503,x101506,x101505,x101508,x101504,x101507,x101501,x101502))) % 172.83/172.50 [10167]~E(x101677,x101674)+~E(x101678,x101675)+~P106(x101671)+~P71(x101672)+~E(f332(x101673,f591(x101676,x101673,x101678,x101675,x101677,x101674,x101671,x101672)),f332(x101676,f591(x101676,x101673,x101678,x101675,x101677,x101674,x101671,x101672)))+E(f332(f332(f6(x101671,x101672),x101673),f332(f302(x101671,x101674),x101675)),f332(f332(f6(x101671,x101672),x101676),f332(f302(x101671,x101677),x101678))) % 172.83/172.50 [10169]~E(x101694,x101697)+~E(x101695,x101698)+~P106(x101691)+~P71(x101692)+E(f332(f332(f6(x101691,x101692),x101693),f332(f302(x101691,x101694),x101695)),f332(f332(f6(x101691,x101692),x101696),f332(f302(x101691,x101697),x101698)))+P102(f332(f332(f247(x101691),f591(x101693,x101696,x101695,x101698,x101694,x101697,x101691,x101692)),x101695)) % 172.83/172.50 [9832]~P3(x98325,x98329,x98326)+~P3(x98321,x983210,x98323)+~P9(x98321,x98325,f883(x98322,a871),x98323,x98326,x98328)+~P102(f332(f332(f334(x98325),x98327),x98329))+~P102(f332(f332(f334(x98321),x98324),x983210))+E(f332(f332(f41(x98321,f883(x98322,a871)),f332(f286(x98321,x98321,x98323),f332(f332(f310(x98321),x98324),f195(f883(x98321,a871))))),f332(f332(f8(f883(x98325,f883(x98322,a871)),f883(x98322,a871),x98321),f332(f41(x98325,f883(x98322,a871)),f332(f286(x98325,x98325,x98326),f332(f332(f310(x98325),x98327),f195(f883(x98325,a871)))))),x98328)),f332(f332(x98328,x98324),x98327)) % 172.83/172.50 [5591]~P104(x55913)+~P29(x55913,x55912)+~P29(x55913,x55911)+E(x55911,x55912)+~E(f332(f173(x55913),x55911),f332(f173(x55913),x55912))+~P102(f332(f137(x55913),x55912))+~P102(f332(f137(x55913),x55911)) % 172.83/172.50 [4933]~P125(x49332)+~P130(x49332)+~P140(x49332)+~P109(x49332)+~E(x49333,f2(x49332))+E(x49331,f2(a876))+E(f332(f332(f257(x49332),x49333),x49331),f2(x49332)) % 172.83/172.50 [9131]E(x91311,f2(a876))+~E(x91312,f332(f332(f79(a876),f332(f332(f80(a876),f332(f266(a876,a876),x91313)),x91311)),f332(f270(a876,a876),x91313)))+P102(f332(f47(x91312,x91311),x91313))+~P102(f332(f332(f246(a876),f332(f270(a876,a876),x91313)),f2(a876)))+~P102(f332(f332(f246(a876),f2(a876)),f332(f270(a876,a876),x91313)))+~P102(f332(f332(f247(a876),x91311),f332(f270(a876,a876),x91313)))+~P102(f332(f332(f247(a876),f332(f270(a876,a876),x91313)),x91311)) % 172.83/172.50 [9140]~E(f332(f266(a876,a876),x91403),f2(a876))+~E(x91401,f332(f332(f79(a876),f332(f332(f80(a876),f332(f266(a876,a876),x91403)),x91402)),f332(f270(a876,a876),x91403)))+P102(f332(f47(x91401,x91402),x91403))+~P102(f332(f332(f246(a876),f332(f270(a876,a876),x91403)),f2(a876)))+~P102(f332(f332(f246(a876),f2(a876)),f332(f270(a876,a876),x91403)))+~P102(f332(f332(f247(a876),x91402),f332(f270(a876,a876),x91403)))+~P102(f332(f332(f247(a876),f332(f270(a876,a876),x91403)),x91402)) % 172.83/172.50 [7988]~P64(x79882)+E(x79881,f195(f883(x79882,a871)))+E(x79883,f195(f883(x79882,a871)))+~P102(f332(f61(x79882),x79881))+~P102(f332(f61(x79882),x79883))+~E(f332(f332(f104(f883(x79882,a871)),x79883),x79881),f195(f883(x79882,a871)))+E(f332(f332(f80(x79882),f332(f63(x79882,f80(x79882)),x79883)),f332(f63(x79882,f80(x79882)),x79881)),f332(f63(x79882,f80(x79882)),f332(f332(f113(f883(x79882,a871)),x79883),x79881))) % 172.83/172.50 [7768]E(x77681,f2(a1))+E(f332(f332(f38(a1),x77682),x77681),x77683)+~P102(f332(f332(f246(a1),x77684),f2(a1)))+~E(x77682,f332(f332(f79(a1),f332(f332(f80(a1),x77681),x77683)),x77684))+~P102(f332(f332(f246(a1),f2(a1)),x77684))+~P102(f332(f332(f247(a1),x77684),x77681))+~P102(f332(f332(f247(a1),x77681),x77684)) % 172.83/172.50 [7777]E(f44(a1,x77772,x77771),x77773)+E(x77771,f2(a1))+~P102(f332(f332(f246(a1),x77773),f2(a1)))+~E(x77772,f332(f332(f79(a1),f332(f332(f80(a1),x77771),x77774)),x77773))+~P102(f332(f332(f246(a1),f2(a1)),x77773))+~P102(f332(f332(f247(a1),x77773),x77771))+~P102(f332(f332(f247(a1),x77771),x77773)) % 172.83/172.50 [7677]~P13(x76772,x76775,x76774)+E(x76771,f195(f883(x76772,a871)))+E(x76773,f195(f883(x76772,a871)))+~P102(f332(f61(x76772),x76771))+~P102(f332(f61(x76772),x76773))+~E(f332(f332(f104(f883(x76772,a871)),x76773),x76771),f195(f883(x76772,a871)))+E(f332(x76774,f332(f332(f113(f883(x76772,a871)),x76773),x76771)),f332(f332(x76775,f332(x76774,x76773)),f332(x76774,x76771))) % 172.83/172.50 [9376]~P20(x93763,x93761,x93765,x93764)+~P20(x93761,x93763,x93766,x93762)+E(f332(f37(x93761),x93762),f332(f37(x93763),x93764))+~P102(f332(f61(x93763),x93764))+~P102(f332(f61(x93761),x93762))+~P102(f332(f332(f246(f883(x93763,a871)),f332(f311(x93761,x93763,x93766),x93762)),x93764))+~P102(f332(f332(f246(f883(x93761,a871)),f332(f311(x93763,x93761,x93765),x93764)),x93762)) % 172.83/172.50 [9320]~P102(f332(f332(f247(a1),f332(f332(f79(a1),f332(f332(f80(a1),x93205),x93201)),x93206)),f2(a1)))+~E(f332(f332(f79(a1),f332(f332(f80(a1),x93203),x93202)),x93204),f332(f332(f79(a1),f332(f332(f80(a1),x93205),x93201)),x93206))+~P102(f332(f332(f247(a1),f2(a1)),x93205))+~P102(f332(f332(f246(a1),f2(a1)),x93206))+~P102(f332(f332(f247(a1),x93204),x93203))+~P102(f332(f332(f246(a1),x93205),x93203))+P102(f332(f332(f246(a1),x93201),x93202)) % 172.83/172.50 [9084]~E(f332(f332(f79(a1),f332(f332(f80(a1),x90843),x90841)),x90844),f332(f332(f79(a1),f332(f332(f80(a1),x90845),x90842)),x90846))+~P102(f332(f332(f247(a1),f2(a1)),x90845))+~P102(f332(f332(f246(a1),f2(a1)),x90844))+~P102(f332(f332(f247(a1),x90846),x90845))+~P102(f332(f332(f246(a1),x90845),x90843))+P102(f332(f332(f246(a1),x90841),x90842))+~P102(f332(f332(f246(a1),f2(a1)),f332(f332(f79(a1),f332(f332(f80(a1),x90845),x90842)),x90846))) % 172.83/172.50 [9261]~P129(x92611)+~E(f332(f332(f79(x92611),x92612),x92614),f77(x92611))+~P102(f332(f332(f246(x92611),f2(x92611)),x92614))+~P102(f332(f332(f246(x92611),f2(x92611)),x92612))+~P102(f332(f332(f247(x92611),x92615),x92616))+~P102(f332(f332(f247(x92611),x92613),x92616))+P102(f332(f332(f247(x92611),f332(f332(f79(x92611),f332(f332(f80(x92611),x92612),x92613)),f332(f332(f80(x92611),x92614),x92615))),x92616)) % 172.83/172.50 [9262]~P128(x92621)+~E(f332(f332(f79(x92621),x92622),x92624),f77(x92621))+~P102(f332(f332(f246(x92621),x92625),x92626))+~P102(f332(f332(f246(x92621),x92623),x92626))+~P102(f332(f332(f246(x92621),f2(x92621)),x92624))+~P102(f332(f332(f246(x92621),f2(x92621)),x92622))+P102(f332(f332(f246(x92621),f332(f332(f79(x92621),f332(f332(f80(x92621),x92622),x92623)),f332(f332(f80(x92621),x92624),x92625))),x92626)) % 172.83/172.50 [10083]~P3(x100837,x100836,x100835)+E(x100831,x100832)+~P8(x100837,f883(x100834,a871),x100835,x100833)+E(f332(x100833,f510(x100831,x100832,x100833,x100834,x100835,x100836,x100837)),f332(x100833,f511(x100831,x100832,x100833,x100834,x100835,x100836,x100837)))+~E(f332(f332(f41(x100837,f883(x100834,a871)),x100831),x100833),f332(f332(f41(x100837,f883(x100834,a871)),x100832),x100833))+~P102(f332(f332(f334(f883(x100837,a871)),x100832),f332(f332(f60(x100837),x100836),x100835)))+~P102(f332(f332(f334(f883(x100837,a871)),x100831),f332(f332(f60(x100837),x100836),x100835))) % 172.83/172.50 [10117]~P3(x101173,x101177,x101176)+E(x101171,x101172)+~P8(x101173,f883(x101175,a871),x101176,x101174)+~E(f332(f332(f41(x101173,f883(x101175,a871)),x101171),x101174),f332(f332(f41(x101173,f883(x101175,a871)),x101172),x101174))+P102(f332(f332(f334(x101173),f511(x101171,x101172,x101174,x101175,x101176,x101177,x101173)),x101177))+~P102(f332(f332(f334(f883(x101173,a871)),x101172),f332(f332(f60(x101173),x101177),x101176)))+~P102(f332(f332(f334(f883(x101173,a871)),x101171),f332(f332(f60(x101173),x101177),x101176))) % 172.83/172.50 [10118]~P3(x101183,x101187,x101186)+E(x101181,x101182)+~P8(x101183,f883(x101185,a871),x101186,x101184)+~E(f332(f332(f41(x101183,f883(x101185,a871)),x101181),x101184),f332(f332(f41(x101183,f883(x101185,a871)),x101182),x101184))+P102(f332(f332(f334(x101183),f510(x101181,x101182,x101184,x101185,x101186,x101187,x101183)),x101187))+~P102(f332(f332(f334(f883(x101183,a871)),x101182),f332(f332(f60(x101183),x101187),x101186)))+~P102(f332(f332(f334(f883(x101183,a871)),x101181),f332(f332(f60(x101183),x101187),x101186))) % 172.83/172.50 [10186]E(x101861,x101862)+~P3(x101863,x101866,x101867)+~P8(x101863,f883(x101864,a871),x101867,x101865)+~E(f332(f332(f41(x101863,f883(x101864,a871)),x101861),x101865),f332(f332(f41(x101863,f883(x101864,a871)),x101862),x101865))+~P102(f332(f332(f334(f882(x101863,x101863)),f332(f332(f267(x101863,x101863),f511(x101861,x101862,x101865,x101864,x101867,x101866,x101863)),f510(x101861,x101862,x101865,x101864,x101867,x101866,x101863))),x101867))+~P102(f332(f332(f334(f883(x101863,a871)),x101862),f332(f332(f60(x101863),x101866),x101867)))+~P102(f332(f332(f334(f883(x101863,a871)),x101861),f332(f332(f60(x101863),x101866),x101867))) % 172.83/172.50 [9083]~P3(x90831,x90837,x90834)+~E(x90835,x90836)+~P102(f332(f332(f334(x90831),x90833),x90836))+~P102(f332(f332(f334(x90831),x90832),x90835))+~P102(f332(f332(f334(f883(x90831,a871)),x90836),f332(f332(f60(x90831),x90837),x90834)))+~P102(f332(f332(f334(f883(x90831,a871)),x90835),f332(f332(f60(x90831),x90837),x90834)))+P102(f332(f332(f334(f882(x90831,x90831)),f332(f332(f267(x90831,x90831),x90832),x90833)),x90834)) % 172.83/172.50 [9218]E(x92181,x92182)+~P3(x92183,x92184,x92185)+~P102(f332(f332(f334(x92183),x92186),x92182))+~P102(f332(f332(f334(x92183),x92187),x92181))+~P102(f332(f332(f334(f883(x92183,a871)),x92182),f332(f332(f60(x92183),x92184),x92185)))+~P102(f332(f332(f334(f883(x92183,a871)),x92181),f332(f332(f60(x92183),x92184),x92185)))+~P102(f332(f332(f334(f882(x92183,x92183)),f332(f332(f267(x92183,x92183),x92187),x92186)),x92185)) % 172.83/172.50 [10209]~P3(x102099,x102098,x102097)+~P3(x102091,x1020911,x1020910)+~P9(x102091,x102099,f883(x102096,a871),x1020910,x102097,x102095)+P102(f332(f332(f334(x102091),f513(x102092,x102093,x102094,x102095,x102096,x102097,x102098,x102099,x1020910,x1020911,x102091)),x1020911))+~P102(f332(f332(f334(f883(x102099,a871)),x102093),f332(f332(f60(x102099),x102098),x102097)))+~P102(f332(f332(f334(f883(x102091,a871)),x102094),f332(f332(f60(x102091),x1020911),x1020910)))+P102(f332(f332(f334(f883(x102096,a871)),f332(f332(f41(x102091,f883(x102096,a871)),x102094),f332(f332(f8(f883(x102099,f883(x102096,a871)),f883(x102096,a871),x102091),f332(f41(x102099,f883(x102096,a871)),x102093)),x102095))),x102092)) % 172.83/172.50 [10210]~P3(x1021011,x1021010,x102109)+~P3(x102101,x102108,x102107)+~P9(x1021011,x102101,f883(x102106,a871),x102109,x102107,x102105)+P102(f332(f332(f334(x102101),f514(x102102,x102103,x102104,x102105,x102106,x102107,x102108,x102101,x102109,x1021010,x1021011)),x102108))+~P102(f332(f332(f334(f883(x1021011,a871)),x102104),f332(f332(f60(x1021011),x1021010),x102109)))+~P102(f332(f332(f334(f883(x102101,a871)),x102103),f332(f332(f60(x102101),x102108),x102107)))+P102(f332(f332(f334(f883(x102106,a871)),f332(f332(f41(x1021011,f883(x102106,a871)),x102104),f332(f332(f8(f883(x102101,f883(x102106,a871)),f883(x102106,a871),x1021011),f332(f41(x102101,f883(x102106,a871)),x102103)),x102105))),x102102)) % 172.83/172.50 [10213]~P3(x102132,x102138,x102139)+~P3(x102134,x1021310,x1021311)+~P9(x102132,x102134,f883(x102131,a871),x102139,x1021311,x102136)+~P102(f332(f332(f334(f883(x102132,a871)),x102133),f332(f332(f60(x102132),x102138),x102139)))+~P102(f332(f332(f334(f883(x102134,a871)),x102135),f332(f332(f60(x102134),x1021310),x1021311)))+~P102(f332(f332(f334(f883(x102131,a871)),f332(f332(x102136,f513(x102137,x102135,x102133,x102136,x102131,x1021311,x1021310,x102134,x102139,x102138,x102132)),f514(x102137,x102135,x102133,x102136,x102131,x1021311,x1021310,x102134,x102139,x102138,x102132))),x102137))+P102(f332(f332(f334(f883(x102131,a871)),f332(f332(f41(x102132,f883(x102131,a871)),x102133),f332(f332(f8(f883(x102134,f883(x102131,a871)),f883(x102131,a871),x102132),f332(f41(x102134,f883(x102131,a871)),x102135)),x102136))),x102137)) % 172.83/172.50 [9118]E(x91181,x91182)+~P104(x91184)+~P20(x91183,x91184,x91185,f332(f332(f113(f883(x91183,a871)),f332(f173(x91183),x91181)),f332(f173(x91183),x91182)))+~E(f332(f173(x91183),x91181),f332(f173(x91183),x91182))+~P29(x91184,f332(f332(f154(x91183,x91184),x91185),x91182))+~P29(x91184,f332(f332(f154(x91183,x91184),x91185),x91181))+~P102(f332(f137(x91184),f332(f332(f154(x91183,x91184),x91185),x91182)))+~P102(f332(f137(x91184),f332(f332(f154(x91183,x91184),x91185),x91181))) % 172.83/172.50 %EqnAxiom % 172.83/172.50 [1]E(x11,x11) % 172.83/172.50 [2]E(x22,x21)+~E(x21,x22) % 172.83/172.50 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 172.83/172.50 [4]~E(x41,x42)+E(f2(x41),f2(x42)) % 172.83/172.50 [5]~E(x51,x52)+E(f103(x51),f103(x52)) % 172.83/172.50 [6]~E(x61,x62)+E(f22(x61),f22(x62)) % 172.83/172.50 [7]~E(x71,x72)+E(f195(x71),f195(x72)) % 172.83/172.50 [8]~E(x81,x82)+E(f332(x81,x83),f332(x82,x83)) % 172.83/172.50 [9]~E(x91,x92)+E(f332(x93,x91),f332(x93,x92)) % 172.83/172.50 [10]~E(x101,x102)+E(f30(x101),f30(x102)) % 172.83/172.50 [11]~E(x111,x112)+E(f877(x111),f877(x112)) % 172.83/172.50 [12]~E(x121,x122)+E(f104(x121),f104(x122)) % 172.83/172.50 [13]~E(x131,x132)+E(f244(x131),f244(x132)) % 172.83/172.50 [14]~E(x141,x142)+E(f113(x141),f113(x142)) % 172.83/172.50 [15]~E(x151,x152)+E(f245(x151),f245(x152)) % 172.83/172.50 [16]~E(x161,x162)+E(f105(x161),f105(x162)) % 172.83/172.50 [17]~E(x171,x172)+E(f33(x171),f33(x172)) % 172.83/172.50 [18]~E(x181,x182)+E(f83(x181),f83(x182)) % 172.83/172.50 [19]~E(x191,x192)+E(f14(x191,x193),f14(x192,x193)) % 172.83/172.50 [20]~E(x201,x202)+E(f14(x203,x201),f14(x203,x202)) % 172.83/172.50 [21]~E(x211,x212)+E(f883(x211,x213),f883(x212,x213)) % 172.83/172.50 [22]~E(x221,x222)+E(f883(x223,x221),f883(x223,x222)) % 172.83/172.50 [23]~E(x231,x232)+E(f514(x231,x233,x234,x235,x236,x237,x238,x239,x2310,x2311,x2312),f514(x232,x233,x234,x235,x236,x237,x238,x239,x2310,x2311,x2312)) % 172.83/172.50 [24]~E(x241,x242)+E(f514(x243,x241,x244,x245,x246,x247,x248,x249,x2410,x2411,x2412),f514(x243,x242,x244,x245,x246,x247,x248,x249,x2410,x2411,x2412)) % 172.83/172.50 [25]~E(x251,x252)+E(f514(x253,x254,x251,x255,x256,x257,x258,x259,x2510,x2511,x2512),f514(x253,x254,x252,x255,x256,x257,x258,x259,x2510,x2511,x2512)) % 172.83/172.50 [26]~E(x261,x262)+E(f514(x263,x264,x265,x261,x266,x267,x268,x269,x2610,x2611,x2612),f514(x263,x264,x265,x262,x266,x267,x268,x269,x2610,x2611,x2612)) % 172.83/172.50 [27]~E(x271,x272)+E(f514(x273,x274,x275,x276,x271,x277,x278,x279,x2710,x2711,x2712),f514(x273,x274,x275,x276,x272,x277,x278,x279,x2710,x2711,x2712)) % 172.83/172.50 [28]~E(x281,x282)+E(f514(x283,x284,x285,x286,x287,x281,x288,x289,x2810,x2811,x2812),f514(x283,x284,x285,x286,x287,x282,x288,x289,x2810,x2811,x2812)) % 172.83/172.50 [29]~E(x291,x292)+E(f514(x293,x294,x295,x296,x297,x298,x291,x299,x2910,x2911,x2912),f514(x293,x294,x295,x296,x297,x298,x292,x299,x2910,x2911,x2912)) % 172.83/172.50 [30]~E(x301,x302)+E(f514(x303,x304,x305,x306,x307,x308,x309,x301,x3010,x3011,x3012),f514(x303,x304,x305,x306,x307,x308,x309,x302,x3010,x3011,x3012)) % 172.83/172.50 [31]~E(x311,x312)+E(f514(x313,x314,x315,x316,x317,x318,x319,x3110,x311,x3111,x3112),f514(x313,x314,x315,x316,x317,x318,x319,x3110,x312,x3111,x3112)) % 172.83/172.50 [32]~E(x321,x322)+E(f514(x323,x324,x325,x326,x327,x328,x329,x3210,x3211,x321,x3212),f514(x323,x324,x325,x326,x327,x328,x329,x3210,x3211,x322,x3212)) % 172.83/172.50 [33]~E(x331,x332)+E(f514(x333,x334,x335,x336,x337,x338,x339,x3310,x3311,x3312,x331),f514(x333,x334,x335,x336,x337,x338,x339,x3310,x3311,x3312,x332)) % 172.83/172.50 [34]~E(x341,x342)+E(f77(x341),f77(x342)) % 172.83/172.50 [35]~E(x351,x352)+E(f15(x351,x353),f15(x352,x353)) % 172.83/172.50 [36]~E(x361,x362)+E(f15(x363,x361),f15(x363,x362)) % 172.83/172.50 [37]~E(x371,x372)+E(f513(x371,x373,x374,x375,x376,x377,x378,x379,x3710,x3711,x3712),f513(x372,x373,x374,x375,x376,x377,x378,x379,x3710,x3711,x3712)) % 172.83/172.50 [38]~E(x381,x382)+E(f513(x383,x381,x384,x385,x386,x387,x388,x389,x3810,x3811,x3812),f513(x383,x382,x384,x385,x386,x387,x388,x389,x3810,x3811,x3812)) % 172.83/172.50 [39]~E(x391,x392)+E(f513(x393,x394,x391,x395,x396,x397,x398,x399,x3910,x3911,x3912),f513(x393,x394,x392,x395,x396,x397,x398,x399,x3910,x3911,x3912)) % 172.83/172.50 [40]~E(x401,x402)+E(f513(x403,x404,x405,x401,x406,x407,x408,x409,x4010,x4011,x4012),f513(x403,x404,x405,x402,x406,x407,x408,x409,x4010,x4011,x4012)) % 172.83/172.50 [41]~E(x411,x412)+E(f513(x413,x414,x415,x416,x411,x417,x418,x419,x4110,x4111,x4112),f513(x413,x414,x415,x416,x412,x417,x418,x419,x4110,x4111,x4112)) % 172.83/172.50 [42]~E(x421,x422)+E(f513(x423,x424,x425,x426,x427,x421,x428,x429,x4210,x4211,x4212),f513(x423,x424,x425,x426,x427,x422,x428,x429,x4210,x4211,x4212)) % 172.83/172.50 [43]~E(x431,x432)+E(f513(x433,x434,x435,x436,x437,x438,x431,x439,x4310,x4311,x4312),f513(x433,x434,x435,x436,x437,x438,x432,x439,x4310,x4311,x4312)) % 172.83/172.50 [44]~E(x441,x442)+E(f513(x443,x444,x445,x446,x447,x448,x449,x441,x4410,x4411,x4412),f513(x443,x444,x445,x446,x447,x448,x449,x442,x4410,x4411,x4412)) % 172.83/172.50 [45]~E(x451,x452)+E(f513(x453,x454,x455,x456,x457,x458,x459,x4510,x451,x4511,x4512),f513(x453,x454,x455,x456,x457,x458,x459,x4510,x452,x4511,x4512)) % 172.83/172.50 [46]~E(x461,x462)+E(f513(x463,x464,x465,x466,x467,x468,x469,x4610,x4611,x461,x4612),f513(x463,x464,x465,x466,x467,x468,x469,x4610,x4611,x462,x4612)) % 172.83/172.50 [47]~E(x471,x472)+E(f513(x473,x474,x475,x476,x477,x478,x479,x4710,x4711,x4712,x471),f513(x473,x474,x475,x476,x477,x478,x479,x4710,x4711,x4712,x472)) % 172.83/172.50 [48]~E(x481,x482)+E(f4(x481),f4(x482)) % 172.83/172.50 [49]~E(x491,x492)+E(f334(x491),f334(x492)) % 172.83/172.50 [50]~E(x501,x502)+E(f246(x501),f246(x502)) % 172.83/172.50 [51]~E(x511,x512)+E(f114(x511),f114(x512)) % 172.83/172.50 [52]~E(x521,x522)+E(f16(x521,x523),f16(x522,x523)) % 172.83/172.50 [53]~E(x531,x532)+E(f16(x533,x531),f16(x533,x532)) % 172.83/172.50 [54]~E(x541,x542)+E(f875(x541),f875(x542)) % 172.83/172.50 [55]~E(x551,x552)+E(f880(x551),f880(x552)) % 172.83/172.50 [56]~E(x561,x562)+E(f247(x561),f247(x562)) % 172.83/172.50 [57]~E(x571,x572)+E(f878(x571),f878(x572)) % 172.83/172.50 [58]~E(x581,x582)+E(f7(x581,x583,x584),f7(x582,x583,x584)) % 172.83/172.50 [59]~E(x591,x592)+E(f7(x593,x591,x594),f7(x593,x592,x594)) % 172.83/172.50 [60]~E(x601,x602)+E(f7(x603,x604,x601),f7(x603,x604,x602)) % 172.83/172.50 [61]~E(x611,x612)+E(f80(x611),f80(x612)) % 172.83/172.50 [62]~E(x621,x622)+E(f61(x621),f61(x622)) % 172.83/172.50 [63]~E(x631,x632)+E(f116(x631),f116(x632)) % 172.83/172.50 [64]~E(x641,x642)+E(f78(x641),f78(x642)) % 172.83/172.50 [65]~E(x651,x652)+E(f290(x651),f290(x652)) % 172.83/172.50 [66]~E(x661,x662)+E(f196(x661),f196(x662)) % 172.83/172.50 [67]~E(x671,x672)+E(f311(x671,x673,x674),f311(x672,x673,x674)) % 172.83/172.50 [68]~E(x681,x682)+E(f311(x683,x681,x684),f311(x683,x682,x684)) % 172.83/172.50 [69]~E(x691,x692)+E(f311(x693,x694,x691),f311(x693,x694,x692)) % 172.83/172.50 [70]~E(x701,x702)+E(f106(x701),f106(x702)) % 172.83/172.50 [71]~E(x711,x712)+E(f38(x711),f38(x712)) % 172.83/172.50 [72]~E(x721,x722)+E(f269(x721,x723),f269(x722,x723)) % 172.83/172.50 [73]~E(x731,x732)+E(f269(x733,x731),f269(x733,x732)) % 172.83/172.50 [74]~E(x741,x742)+E(f302(x741,x743),f302(x742,x743)) % 172.83/172.50 [75]~E(x751,x752)+E(f302(x753,x751),f302(x753,x752)) % 172.83/172.50 [76]~E(x761,x762)+E(f524(x761,x763,x764,x765,x766),f524(x762,x763,x764,x765,x766)) % 172.83/172.50 [77]~E(x771,x772)+E(f524(x773,x771,x774,x775,x776),f524(x773,x772,x774,x775,x776)) % 172.83/172.50 [78]~E(x781,x782)+E(f524(x783,x784,x781,x785,x786),f524(x783,x784,x782,x785,x786)) % 172.83/172.50 [79]~E(x791,x792)+E(f524(x793,x794,x795,x791,x796),f524(x793,x794,x795,x792,x796)) % 172.83/172.50 [80]~E(x801,x802)+E(f524(x803,x804,x805,x806,x801),f524(x803,x804,x805,x806,x802)) % 172.83/172.50 [81]~E(x811,x812)+E(f79(x811),f79(x812)) % 172.83/172.50 [82]~E(x821,x822)+E(f8(x821,x823,x824),f8(x822,x823,x824)) % 172.83/172.50 [83]~E(x831,x832)+E(f8(x833,x831,x834),f8(x833,x832,x834)) % 172.83/172.50 [84]~E(x841,x842)+E(f8(x843,x844,x841),f8(x843,x844,x842)) % 172.83/172.50 [85]~E(x851,x852)+E(f239(x851),f239(x852)) % 172.83/172.50 [86]~E(x861,x862)+E(f248(x861,x863),f248(x862,x863)) % 172.83/172.50 [87]~E(x871,x872)+E(f248(x873,x871),f248(x873,x872)) % 172.83/172.50 [88]~E(x881,x882)+E(f267(x881,x883),f267(x882,x883)) % 172.83/172.50 [89]~E(x891,x892)+E(f267(x893,x891),f267(x893,x892)) % 172.83/172.50 [90]~E(x901,x902)+E(f176(x901),f176(x902)) % 172.83/172.50 [91]~E(x911,x912)+E(f770(x911,x913,x914,x915,x916,x917,x918),f770(x912,x913,x914,x915,x916,x917,x918)) % 172.83/172.50 [92]~E(x921,x922)+E(f770(x923,x921,x924,x925,x926,x927,x928),f770(x923,x922,x924,x925,x926,x927,x928)) % 172.83/172.50 [93]~E(x931,x932)+E(f770(x933,x934,x931,x935,x936,x937,x938),f770(x933,x934,x932,x935,x936,x937,x938)) % 172.83/172.50 [94]~E(x941,x942)+E(f770(x943,x944,x945,x941,x946,x947,x948),f770(x943,x944,x945,x942,x946,x947,x948)) % 172.83/172.50 [95]~E(x951,x952)+E(f770(x953,x954,x955,x956,x951,x957,x958),f770(x953,x954,x955,x956,x952,x957,x958)) % 172.83/172.50 [96]~E(x961,x962)+E(f770(x963,x964,x965,x966,x967,x961,x968),f770(x963,x964,x965,x966,x967,x962,x968)) % 172.83/172.50 [97]~E(x971,x972)+E(f770(x973,x974,x975,x976,x977,x978,x971),f770(x973,x974,x975,x976,x977,x978,x972)) % 172.83/172.50 [98]~E(x981,x982)+E(f154(x981,x983),f154(x982,x983)) % 172.83/172.50 [99]~E(x991,x992)+E(f154(x993,x991),f154(x993,x992)) % 172.83/172.50 [100]~E(x1001,x1002)+E(f60(x1001),f60(x1002)) % 172.83/172.50 [101]~E(x1011,x1012)+E(f6(x1011,x1013),f6(x1012,x1013)) % 172.83/172.50 [102]~E(x1021,x1022)+E(f6(x1023,x1021),f6(x1023,x1022)) % 172.83/172.50 [103]~E(x1031,x1032)+E(f151(x1031),f151(x1032)) % 172.83/172.50 [104]~E(x1041,x1042)+E(f882(x1041,x1043),f882(x1042,x1043)) % 172.83/172.50 [105]~E(x1051,x1052)+E(f882(x1053,x1051),f882(x1053,x1052)) % 172.83/172.50 [106]~E(x1061,x1062)+E(f173(x1061),f173(x1062)) % 172.83/172.50 [107]~E(x1071,x1072)+E(f134(x1071),f134(x1072)) % 172.83/172.50 [108]~E(x1081,x1082)+E(f266(x1081,x1083),f266(x1082,x1083)) % 172.83/172.50 [109]~E(x1091,x1092)+E(f266(x1093,x1091),f266(x1093,x1092)) % 172.83/172.50 [110]~E(x1101,x1102)+E(f32(x1101,x1103),f32(x1102,x1103)) % 172.83/172.50 [111]~E(x1111,x1112)+E(f32(x1113,x1111),f32(x1113,x1112)) % 172.83/172.50 [112]~E(x1121,x1122)+E(f142(x1121,x1123,x1124,x1125),f142(x1122,x1123,x1124,x1125)) % 172.83/172.50 [113]~E(x1131,x1132)+E(f142(x1133,x1131,x1134,x1135),f142(x1133,x1132,x1134,x1135)) % 172.83/172.50 [114]~E(x1141,x1142)+E(f142(x1143,x1144,x1141,x1145),f142(x1143,x1144,x1142,x1145)) % 172.83/172.50 [115]~E(x1151,x1152)+E(f142(x1153,x1154,x1155,x1151),f142(x1153,x1154,x1155,x1152)) % 172.83/172.50 [116]~E(x1161,x1162)+E(f64(x1161,x1163,x1164),f64(x1162,x1163,x1164)) % 172.83/172.50 [117]~E(x1171,x1172)+E(f64(x1173,x1171,x1174),f64(x1173,x1172,x1174)) % 172.83/172.50 [118]~E(x1181,x1182)+E(f64(x1183,x1184,x1181),f64(x1183,x1184,x1182)) % 172.83/172.50 [119]~E(x1191,x1192)+E(f144(x1191,x1193),f144(x1192,x1193)) % 172.83/172.50 [120]~E(x1201,x1202)+E(f144(x1203,x1201),f144(x1203,x1202)) % 172.83/172.50 [121]~E(x1211,x1212)+E(f71(x1211,x1213),f71(x1212,x1213)) % 172.83/172.50 [122]~E(x1221,x1222)+E(f71(x1223,x1221),f71(x1223,x1222)) % 172.83/172.50 [123]~E(x1231,x1232)+E(f785(x1231,x1233,x1234,x1235,x1236),f785(x1232,x1233,x1234,x1235,x1236)) % 172.83/172.50 [124]~E(x1241,x1242)+E(f785(x1243,x1241,x1244,x1245,x1246),f785(x1243,x1242,x1244,x1245,x1246)) % 172.83/172.50 [125]~E(x1251,x1252)+E(f785(x1253,x1254,x1251,x1255,x1256),f785(x1253,x1254,x1252,x1255,x1256)) % 172.83/172.50 [126]~E(x1261,x1262)+E(f785(x1263,x1264,x1265,x1261,x1266),f785(x1263,x1264,x1265,x1262,x1266)) % 172.83/172.50 [127]~E(x1271,x1272)+E(f785(x1273,x1274,x1275,x1276,x1271),f785(x1273,x1274,x1275,x1276,x1272)) % 172.83/172.50 [128]~E(x1281,x1282)+E(f137(x1281),f137(x1282)) % 172.83/172.50 [129]~E(x1291,x1292)+E(f10(x1291,x1293),f10(x1292,x1293)) % 172.83/172.50 [130]~E(x1301,x1302)+E(f10(x1303,x1301),f10(x1303,x1302)) % 172.83/172.50 [131]~E(x1311,x1312)+E(f18(x1311,x1313,x1314),f18(x1312,x1313,x1314)) % 172.83/172.50 [132]~E(x1321,x1322)+E(f18(x1323,x1321,x1324),f18(x1323,x1322,x1324)) % 172.83/172.50 [133]~E(x1331,x1332)+E(f18(x1333,x1334,x1331),f18(x1333,x1334,x1332)) % 172.83/172.50 [134]~E(x1341,x1342)+E(f303(x1341,x1343,x1344),f303(x1342,x1343,x1344)) % 172.83/172.50 [135]~E(x1351,x1352)+E(f303(x1353,x1351,x1354),f303(x1353,x1352,x1354)) % 172.83/172.50 [136]~E(x1361,x1362)+E(f303(x1363,x1364,x1361),f303(x1363,x1364,x1362)) % 172.83/172.50 [137]~E(x1371,x1372)+E(f778(x1371,x1373,x1374),f778(x1372,x1373,x1374)) % 172.83/172.50 [138]~E(x1381,x1382)+E(f778(x1383,x1381,x1384),f778(x1383,x1382,x1384)) % 172.83/172.50 [139]~E(x1391,x1392)+E(f778(x1393,x1394,x1391),f778(x1393,x1394,x1392)) % 172.83/172.50 [140]~E(x1401,x1402)+E(f169(x1401),f169(x1402)) % 172.83/172.50 [141]~E(x1411,x1412)+E(f44(x1411,x1413,x1414),f44(x1412,x1413,x1414)) % 172.83/172.50 [142]~E(x1421,x1422)+E(f44(x1423,x1421,x1424),f44(x1423,x1422,x1424)) % 172.83/172.50 [143]~E(x1431,x1432)+E(f44(x1433,x1434,x1431),f44(x1433,x1434,x1432)) % 172.83/172.50 [144]~E(x1441,x1442)+E(f190(x1441,x1443),f190(x1442,x1443)) % 172.83/172.50 [145]~E(x1451,x1452)+E(f190(x1453,x1451),f190(x1453,x1452)) % 172.83/172.50 [146]~E(x1461,x1462)+E(f141(x1461),f141(x1462)) % 172.83/172.50 [147]~E(x1471,x1472)+E(f37(x1471),f37(x1472)) % 172.83/172.50 [148]~E(x1481,x1482)+E(f74(x1481),f74(x1482)) % 172.83/172.50 [149]~E(x1491,x1492)+E(f310(x1491),f310(x1492)) % 172.83/172.50 [150]~E(x1501,x1502)+E(f754(x1501,x1503,x1504),f754(x1502,x1503,x1504)) % 172.83/172.50 [151]~E(x1511,x1512)+E(f754(x1513,x1511,x1514),f754(x1513,x1512,x1514)) % 172.83/172.50 [152]~E(x1521,x1522)+E(f754(x1523,x1524,x1521),f754(x1523,x1524,x1522)) % 172.83/172.50 [153]~E(x1531,x1532)+E(f90(x1531),f90(x1532)) % 172.83/172.50 [154]~E(x1541,x1542)+E(f364(x1541,x1543,x1544,x1545),f364(x1542,x1543,x1544,x1545)) % 172.83/172.50 [155]~E(x1551,x1552)+E(f364(x1553,x1551,x1554,x1555),f364(x1553,x1552,x1554,x1555)) % 172.83/172.50 [156]~E(x1561,x1562)+E(f364(x1563,x1564,x1561,x1565),f364(x1563,x1564,x1562,x1565)) % 172.83/172.50 [157]~E(x1571,x1572)+E(f364(x1573,x1574,x1575,x1571),f364(x1573,x1574,x1575,x1572)) % 172.83/172.50 [158]~E(x1581,x1582)+E(f108(x1581),f108(x1582)) % 172.83/172.50 [159]~E(x1591,x1592)+E(f109(x1591),f109(x1592)) % 172.83/172.50 [160]~E(x1601,x1602)+E(f333(x1601),f333(x1602)) % 172.83/172.50 [161]~E(x1611,x1612)+E(f156(x1611,x1613,x1614,x1615),f156(x1612,x1613,x1614,x1615)) % 172.83/172.50 [162]~E(x1621,x1622)+E(f156(x1623,x1621,x1624,x1625),f156(x1623,x1622,x1624,x1625)) % 172.83/172.50 [163]~E(x1631,x1632)+E(f156(x1633,x1634,x1631,x1635),f156(x1633,x1634,x1632,x1635)) % 172.83/172.50 [164]~E(x1641,x1642)+E(f156(x1643,x1644,x1645,x1641),f156(x1643,x1644,x1645,x1642)) % 172.83/172.50 [165]~E(x1651,x1652)+E(f41(x1651,x1653),f41(x1652,x1653)) % 172.83/172.50 [166]~E(x1661,x1662)+E(f41(x1663,x1661),f41(x1663,x1662)) % 172.83/172.50 [167]~E(x1671,x1672)+E(f271(x1671,x1673,x1674),f271(x1672,x1673,x1674)) % 172.83/172.50 [168]~E(x1681,x1682)+E(f271(x1683,x1681,x1684),f271(x1683,x1682,x1684)) % 172.83/172.50 [169]~E(x1691,x1692)+E(f271(x1693,x1694,x1691),f271(x1693,x1694,x1692)) % 172.83/172.50 [170]~E(x1701,x1702)+E(f819(x1701,x1703,x1704),f819(x1702,x1703,x1704)) % 172.83/172.50 [171]~E(x1711,x1712)+E(f819(x1713,x1711,x1714),f819(x1713,x1712,x1714)) % 172.83/172.50 [172]~E(x1721,x1722)+E(f819(x1723,x1724,x1721),f819(x1723,x1724,x1722)) % 172.83/172.50 [173]~E(x1731,x1732)+E(f5(x1731),f5(x1732)) % 172.83/172.50 [174]~E(x1741,x1742)+E(f178(x1741,x1743,x1744),f178(x1742,x1743,x1744)) % 172.83/172.50 [175]~E(x1751,x1752)+E(f178(x1753,x1751,x1754),f178(x1753,x1752,x1754)) % 172.83/172.50 [176]~E(x1761,x1762)+E(f178(x1763,x1764,x1761),f178(x1763,x1764,x1762)) % 172.83/172.50 [177]~E(x1771,x1772)+E(f252(x1771),f252(x1772)) % 172.83/172.50 [178]~E(x1781,x1782)+E(f263(x1781,x1783),f263(x1782,x1783)) % 172.83/172.50 [179]~E(x1791,x1792)+E(f263(x1793,x1791),f263(x1793,x1792)) % 172.83/172.50 [180]~E(x1801,x1802)+E(f684(x1801,x1803,x1804),f684(x1802,x1803,x1804)) % 172.83/172.50 [181]~E(x1811,x1812)+E(f684(x1813,x1811,x1814),f684(x1813,x1812,x1814)) % 172.83/172.50 [182]~E(x1821,x1822)+E(f684(x1823,x1824,x1821),f684(x1823,x1824,x1822)) % 172.83/172.50 [183]~E(x1831,x1832)+E(f255(x1831),f255(x1832)) % 172.83/172.50 [184]~E(x1841,x1842)+E(f881(x1841,x1843),f881(x1842,x1843)) % 172.83/172.50 [185]~E(x1851,x1852)+E(f881(x1853,x1851),f881(x1853,x1852)) % 172.83/172.50 [186]~E(x1861,x1862)+E(f138(x1861),f138(x1862)) % 172.83/172.50 [187]~E(x1871,x1872)+E(f89(x1871,x1873),f89(x1872,x1873)) % 172.83/172.50 [188]~E(x1881,x1882)+E(f89(x1883,x1881),f89(x1883,x1882)) % 172.83/172.50 [189]~E(x1891,x1892)+E(f814(x1891,x1893,x1894),f814(x1892,x1893,x1894)) % 172.83/172.50 [190]~E(x1901,x1902)+E(f814(x1903,x1901,x1904),f814(x1903,x1902,x1904)) % 172.83/172.50 [191]~E(x1911,x1912)+E(f814(x1913,x1914,x1911),f814(x1913,x1914,x1912)) % 172.83/172.50 [192]~E(x1921,x1922)+E(f28(x1921,x1923,x1924),f28(x1922,x1923,x1924)) % 172.83/172.50 [193]~E(x1931,x1932)+E(f28(x1933,x1931,x1934),f28(x1933,x1932,x1934)) % 172.83/172.50 [194]~E(x1941,x1942)+E(f28(x1943,x1944,x1941),f28(x1943,x1944,x1942)) % 172.83/172.50 [195]~E(x1951,x1952)+E(f179(x1951,x1953),f179(x1952,x1953)) % 172.83/172.50 [196]~E(x1961,x1962)+E(f179(x1963,x1961),f179(x1963,x1962)) % 172.83/172.50 [197]~E(x1971,x1972)+E(f189(x1971,x1973,x1974,x1975),f189(x1972,x1973,x1974,x1975)) % 172.83/172.50 [198]~E(x1981,x1982)+E(f189(x1983,x1981,x1984,x1985),f189(x1983,x1982,x1984,x1985)) % 172.83/172.50 [199]~E(x1991,x1992)+E(f189(x1993,x1994,x1991,x1995),f189(x1993,x1994,x1992,x1995)) % 172.83/172.50 [200]~E(x2001,x2002)+E(f189(x2003,x2004,x2005,x2001),f189(x2003,x2004,x2005,x2002)) % 172.83/172.50 [201]~E(x2011,x2012)+E(f257(x2011),f257(x2012)) % 172.83/172.50 [202]~E(x2021,x2022)+E(f55(x2021),f55(x2022)) % 172.83/172.50 [203]~E(x2031,x2032)+E(f139(x2031,x2033),f139(x2032,x2033)) % 172.83/172.50 [204]~E(x2041,x2042)+E(f139(x2043,x2041),f139(x2043,x2042)) % 172.83/172.50 [205]~E(x2051,x2052)+E(f608(x2051,x2053,x2054,x2055),f608(x2052,x2053,x2054,x2055)) % 172.83/172.50 [206]~E(x2061,x2062)+E(f608(x2063,x2061,x2064,x2065),f608(x2063,x2062,x2064,x2065)) % 172.83/172.50 [207]~E(x2071,x2072)+E(f608(x2073,x2074,x2071,x2075),f608(x2073,x2074,x2072,x2075)) % 172.83/172.50 [208]~E(x2081,x2082)+E(f608(x2083,x2084,x2085,x2081),f608(x2083,x2084,x2085,x2082)) % 172.83/172.50 [209]~E(x2091,x2092)+E(f157(x2091,x2093),f157(x2092,x2093)) % 172.83/172.50 [210]~E(x2101,x2102)+E(f157(x2103,x2101),f157(x2103,x2102)) % 172.83/172.50 [211]~E(x2111,x2112)+E(f523(x2111,x2113,x2114,x2115),f523(x2112,x2113,x2114,x2115)) % 172.83/172.50 [212]~E(x2121,x2122)+E(f523(x2123,x2121,x2124,x2125),f523(x2123,x2122,x2124,x2125)) % 172.83/172.50 [213]~E(x2131,x2132)+E(f523(x2133,x2134,x2131,x2135),f523(x2133,x2134,x2132,x2135)) % 172.83/172.50 [214]~E(x2141,x2142)+E(f523(x2143,x2144,x2145,x2141),f523(x2143,x2144,x2145,x2142)) % 172.83/172.50 [215]~E(x2151,x2152)+E(f72(x2151,x2153,x2154,x2155),f72(x2152,x2153,x2154,x2155)) % 172.83/172.50 [216]~E(x2161,x2162)+E(f72(x2163,x2161,x2164,x2165),f72(x2163,x2162,x2164,x2165)) % 172.83/172.50 [217]~E(x2171,x2172)+E(f72(x2173,x2174,x2171,x2175),f72(x2173,x2174,x2172,x2175)) % 172.83/172.50 [218]~E(x2181,x2182)+E(f72(x2183,x2184,x2185,x2181),f72(x2183,x2184,x2185,x2182)) % 172.83/172.50 [219]~E(x2191,x2192)+E(f181(x2191,x2193),f181(x2192,x2193)) % 172.83/172.50 [220]~E(x2201,x2202)+E(f181(x2203,x2201),f181(x2203,x2202)) % 172.83/172.50 [221]~E(x2211,x2212)+E(f65(x2211,x2213,x2214),f65(x2212,x2213,x2214)) % 172.83/172.50 [222]~E(x2221,x2222)+E(f65(x2223,x2221,x2224),f65(x2223,x2222,x2224)) % 172.83/172.50 [223]~E(x2231,x2232)+E(f65(x2233,x2234,x2231),f65(x2233,x2234,x2232)) % 172.83/172.50 [224]~E(x2241,x2242)+E(f132(x2241,x2243),f132(x2242,x2243)) % 172.83/172.50 [225]~E(x2251,x2252)+E(f132(x2253,x2251),f132(x2253,x2252)) % 172.83/172.50 [226]~E(x2261,x2262)+E(f286(x2261,x2263,x2264),f286(x2262,x2263,x2264)) % 172.83/172.50 [227]~E(x2271,x2272)+E(f286(x2273,x2271,x2274),f286(x2273,x2272,x2274)) % 172.83/172.50 [228]~E(x2281,x2282)+E(f286(x2283,x2284,x2281),f286(x2283,x2284,x2282)) % 172.83/172.50 [229]~E(x2291,x2292)+E(f347(x2291,x2293,x2294),f347(x2292,x2293,x2294)) % 172.83/172.50 [230]~E(x2301,x2302)+E(f347(x2303,x2301,x2304),f347(x2303,x2302,x2304)) % 172.83/172.50 [231]~E(x2311,x2312)+E(f347(x2313,x2314,x2311),f347(x2313,x2314,x2312)) % 172.83/172.50 [232]~E(x2321,x2322)+E(f58(x2321),f58(x2322)) % 172.83/172.50 [233]~E(x2331,x2332)+E(f270(x2331,x2333),f270(x2332,x2333)) % 172.83/172.50 [234]~E(x2341,x2342)+E(f270(x2343,x2341),f270(x2343,x2342)) % 172.83/172.50 [235]~E(x2351,x2352)+E(f287(x2351,x2353),f287(x2352,x2353)) % 172.83/172.50 [236]~E(x2361,x2362)+E(f287(x2363,x2361),f287(x2363,x2362)) % 172.83/172.50 [237]~E(x2371,x2372)+E(f457(x2371,x2373,x2374),f457(x2372,x2373,x2374)) % 172.83/172.50 [238]~E(x2381,x2382)+E(f457(x2383,x2381,x2384),f457(x2383,x2382,x2384)) % 172.83/172.50 [239]~E(x2391,x2392)+E(f457(x2393,x2394,x2391),f457(x2393,x2394,x2392)) % 172.83/172.50 [240]~E(x2401,x2402)+E(f9(x2401,x2403),f9(x2402,x2403)) % 172.83/172.50 [241]~E(x2411,x2412)+E(f9(x2413,x2411),f9(x2413,x2412)) % 172.83/172.50 [242]~E(x2421,x2422)+E(f816(x2421,x2423,x2424),f816(x2422,x2423,x2424)) % 172.83/172.50 [243]~E(x2431,x2432)+E(f816(x2433,x2431,x2434),f816(x2433,x2432,x2434)) % 172.83/172.50 [244]~E(x2441,x2442)+E(f816(x2443,x2444,x2441),f816(x2443,x2444,x2442)) % 172.83/172.50 [245]~E(x2451,x2452)+E(f683(x2451,x2453,x2454),f683(x2452,x2453,x2454)) % 172.83/172.50 [246]~E(x2461,x2462)+E(f683(x2463,x2461,x2464),f683(x2463,x2462,x2464)) % 172.83/172.50 [247]~E(x2471,x2472)+E(f683(x2473,x2474,x2471),f683(x2473,x2474,x2472)) % 172.83/172.50 [248]~E(x2481,x2482)+E(f796(x2481,x2483,x2484),f796(x2482,x2483,x2484)) % 172.83/172.50 [249]~E(x2491,x2492)+E(f796(x2493,x2491,x2494),f796(x2493,x2492,x2494)) % 172.83/172.50 [250]~E(x2501,x2502)+E(f796(x2503,x2504,x2501),f796(x2503,x2504,x2502)) % 172.83/172.50 [251]~E(x2511,x2512)+E(f165(x2511),f165(x2512)) % 172.83/172.50 [252]~E(x2521,x2522)+E(f166(x2521),f166(x2522)) % 172.83/172.50 [253]~E(x2531,x2532)+E(f504(x2531,x2533,x2534,x2535,x2536),f504(x2532,x2533,x2534,x2535,x2536)) % 172.83/172.50 [254]~E(x2541,x2542)+E(f504(x2543,x2541,x2544,x2545,x2546),f504(x2543,x2542,x2544,x2545,x2546)) % 172.83/172.50 [255]~E(x2551,x2552)+E(f504(x2553,x2554,x2551,x2555,x2556),f504(x2553,x2554,x2552,x2555,x2556)) % 172.83/172.50 [256]~E(x2561,x2562)+E(f504(x2563,x2564,x2565,x2561,x2566),f504(x2563,x2564,x2565,x2562,x2566)) % 172.83/172.50 [257]~E(x2571,x2572)+E(f504(x2573,x2574,x2575,x2576,x2571),f504(x2573,x2574,x2575,x2576,x2572)) % 172.83/172.50 [258]~E(x2581,x2582)+E(f29(x2581,x2583,x2584),f29(x2582,x2583,x2584)) % 172.83/172.50 [259]~E(x2591,x2592)+E(f29(x2593,x2591,x2594),f29(x2593,x2592,x2594)) % 172.83/172.50 [260]~E(x2601,x2602)+E(f29(x2603,x2604,x2601),f29(x2603,x2604,x2602)) % 172.83/172.50 [261]~E(x2611,x2612)+E(f117(x2611,x2613),f117(x2612,x2613)) % 172.83/172.50 [262]~E(x2621,x2622)+E(f117(x2623,x2621),f117(x2623,x2622)) % 172.83/172.50 [263]~E(x2631,x2632)+E(f11(x2631,x2633,x2634),f11(x2632,x2633,x2634)) % 172.83/172.50 [264]~E(x2641,x2642)+E(f11(x2643,x2641,x2644),f11(x2643,x2642,x2644)) % 172.83/172.50 [265]~E(x2651,x2652)+E(f11(x2653,x2654,x2651),f11(x2653,x2654,x2652)) % 172.83/172.50 [266]~E(x2661,x2662)+E(f177(x2661,x2663,x2664),f177(x2662,x2663,x2664)) % 172.83/172.50 [267]~E(x2671,x2672)+E(f177(x2673,x2671,x2674),f177(x2673,x2672,x2674)) % 172.83/172.50 [268]~E(x2681,x2682)+E(f177(x2683,x2684,x2681),f177(x2683,x2684,x2682)) % 172.83/172.50 [269]~E(x2691,x2692)+E(f152(x2691,x2693),f152(x2692,x2693)) % 172.83/172.50 [270]~E(x2701,x2702)+E(f152(x2703,x2701),f152(x2703,x2702)) % 172.83/172.50 [271]~E(x2711,x2712)+E(f208(x2711),f208(x2712)) % 172.83/172.50 [272]~E(x2721,x2722)+E(f198(x2721),f198(x2722)) % 172.83/172.50 [273]~E(x2731,x2732)+E(f42(x2731,x2733),f42(x2732,x2733)) % 172.83/172.50 [274]~E(x2741,x2742)+E(f42(x2743,x2741),f42(x2743,x2742)) % 172.83/172.50 [275]~E(x2751,x2752)+E(f118(x2751),f118(x2752)) % 172.83/172.50 [276]~E(x2761,x2762)+E(f435(x2761,x2763,x2764,x2765),f435(x2762,x2763,x2764,x2765)) % 172.83/172.50 [277]~E(x2771,x2772)+E(f435(x2773,x2771,x2774,x2775),f435(x2773,x2772,x2774,x2775)) % 172.83/172.50 [278]~E(x2781,x2782)+E(f435(x2783,x2784,x2781,x2785),f435(x2783,x2784,x2782,x2785)) % 172.83/172.50 [279]~E(x2791,x2792)+E(f435(x2793,x2794,x2795,x2791),f435(x2793,x2794,x2795,x2792)) % 172.83/172.50 [280]~E(x2801,x2802)+E(f99(x2801),f99(x2802)) % 172.83/172.50 [281]~E(x2811,x2812)+E(f168(x2811),f168(x2812)) % 172.83/172.50 [282]~E(x2821,x2822)+E(f687(x2821,x2823),f687(x2822,x2823)) % 172.83/172.50 [283]~E(x2831,x2832)+E(f687(x2833,x2831),f687(x2833,x2832)) % 172.83/172.50 [284]~E(x2841,x2842)+E(f389(x2841,x2843,x2844,x2845),f389(x2842,x2843,x2844,x2845)) % 172.83/172.50 [285]~E(x2851,x2852)+E(f389(x2853,x2851,x2854,x2855),f389(x2853,x2852,x2854,x2855)) % 172.83/172.50 [286]~E(x2861,x2862)+E(f389(x2863,x2864,x2861,x2865),f389(x2863,x2864,x2862,x2865)) % 172.83/172.50 [287]~E(x2871,x2872)+E(f389(x2873,x2874,x2875,x2871),f389(x2873,x2874,x2875,x2872)) % 172.83/172.50 [288]~E(x2881,x2882)+E(f170(x2881,x2883,x2884),f170(x2882,x2883,x2884)) % 172.83/172.50 [289]~E(x2891,x2892)+E(f170(x2893,x2891,x2894),f170(x2893,x2892,x2894)) % 172.83/172.50 [290]~E(x2901,x2902)+E(f170(x2903,x2904,x2901),f170(x2903,x2904,x2902)) % 172.83/172.50 [291]~E(x2911,x2912)+E(f183(x2911,x2913),f183(x2912,x2913)) % 172.83/172.50 [292]~E(x2921,x2922)+E(f183(x2923,x2921),f183(x2923,x2922)) % 172.83/172.50 [293]~E(x2931,x2932)+E(f281(x2931,x2933,x2934,x2935),f281(x2932,x2933,x2934,x2935)) % 172.83/172.50 [294]~E(x2941,x2942)+E(f281(x2943,x2941,x2944,x2945),f281(x2943,x2942,x2944,x2945)) % 172.83/172.50 [295]~E(x2951,x2952)+E(f281(x2953,x2954,x2951,x2955),f281(x2953,x2954,x2952,x2955)) % 172.83/172.50 [296]~E(x2961,x2962)+E(f281(x2963,x2964,x2965,x2961),f281(x2963,x2964,x2965,x2962)) % 172.83/172.50 [297]~E(x2971,x2972)+E(f84(x2971,x2973),f84(x2972,x2973)) % 172.83/172.50 [298]~E(x2981,x2982)+E(f84(x2983,x2981),f84(x2983,x2982)) % 172.83/172.50 [299]~E(x2991,x2992)+E(f439(x2991,x2993,x2994,x2995),f439(x2992,x2993,x2994,x2995)) % 172.83/172.50 [300]~E(x3001,x3002)+E(f439(x3003,x3001,x3004,x3005),f439(x3003,x3002,x3004,x3005)) % 172.83/172.50 [301]~E(x3011,x3012)+E(f439(x3013,x3014,x3011,x3015),f439(x3013,x3014,x3012,x3015)) % 172.83/172.50 [302]~E(x3021,x3022)+E(f439(x3023,x3024,x3025,x3021),f439(x3023,x3024,x3025,x3022)) % 172.83/172.50 [303]~E(x3031,x3032)+E(f272(x3031,x3033,x3034,x3035,x3036,x3037),f272(x3032,x3033,x3034,x3035,x3036,x3037)) % 172.83/172.50 [304]~E(x3041,x3042)+E(f272(x3043,x3041,x3044,x3045,x3046,x3047),f272(x3043,x3042,x3044,x3045,x3046,x3047)) % 172.83/172.50 [305]~E(x3051,x3052)+E(f272(x3053,x3054,x3051,x3055,x3056,x3057),f272(x3053,x3054,x3052,x3055,x3056,x3057)) % 172.83/172.50 [306]~E(x3061,x3062)+E(f272(x3063,x3064,x3065,x3061,x3066,x3067),f272(x3063,x3064,x3065,x3062,x3066,x3067)) % 172.83/172.50 [307]~E(x3071,x3072)+E(f272(x3073,x3074,x3075,x3076,x3071,x3077),f272(x3073,x3074,x3075,x3076,x3072,x3077)) % 172.83/172.50 [308]~E(x3081,x3082)+E(f272(x3083,x3084,x3085,x3086,x3087,x3081),f272(x3083,x3084,x3085,x3086,x3087,x3082)) % 172.83/172.50 [309]~E(x3091,x3092)+E(f172(x3091),f172(x3092)) % 172.83/172.50 [310]~E(x3101,x3102)+E(f48(x3101,x3103),f48(x3102,x3103)) % 172.83/172.50 [311]~E(x3111,x3112)+E(f48(x3113,x3111),f48(x3113,x3112)) % 172.83/172.50 [312]~E(x3121,x3122)+E(f789(x3121,x3123,x3124,x3125,x3126),f789(x3122,x3123,x3124,x3125,x3126)) % 172.83/172.50 [313]~E(x3131,x3132)+E(f789(x3133,x3131,x3134,x3135,x3136),f789(x3133,x3132,x3134,x3135,x3136)) % 172.83/172.50 [314]~E(x3141,x3142)+E(f789(x3143,x3144,x3141,x3145,x3146),f789(x3143,x3144,x3142,x3145,x3146)) % 172.83/172.50 [315]~E(x3151,x3152)+E(f789(x3153,x3154,x3155,x3151,x3156),f789(x3153,x3154,x3155,x3152,x3156)) % 172.83/172.50 [316]~E(x3161,x3162)+E(f789(x3163,x3164,x3165,x3166,x3161),f789(x3163,x3164,x3165,x3166,x3162)) % 172.83/172.50 [317]~E(x3171,x3172)+E(f161(x3171,x3173),f161(x3172,x3173)) % 172.83/172.50 [318]~E(x3181,x3182)+E(f161(x3183,x3181),f161(x3183,x3182)) % 172.83/172.50 [319]~E(x3191,x3192)+E(f136(x3191,x3193),f136(x3192,x3193)) % 172.83/172.50 [320]~E(x3201,x3202)+E(f136(x3203,x3201),f136(x3203,x3202)) % 172.83/172.50 [321]~E(x3211,x3212)+E(f47(x3211,x3213),f47(x3212,x3213)) % 172.83/172.50 [322]~E(x3221,x3222)+E(f47(x3223,x3221),f47(x3223,x3222)) % 172.83/172.50 [323]~E(x3231,x3232)+E(f308(x3231,x3233),f308(x3232,x3233)) % 172.83/172.50 [324]~E(x3241,x3242)+E(f308(x3243,x3241),f308(x3243,x3242)) % 172.83/172.50 [325]~E(x3251,x3252)+E(f209(x3251,x3253),f209(x3252,x3253)) % 172.83/172.50 [326]~E(x3261,x3262)+E(f209(x3263,x3261),f209(x3263,x3262)) % 172.83/172.50 [327]~E(x3271,x3272)+E(f556(x3271),f556(x3272)) % 172.83/172.50 [328]~E(x3281,x3282)+E(f188(x3281,x3283,x3284,x3285,x3286),f188(x3282,x3283,x3284,x3285,x3286)) % 172.83/172.50 [329]~E(x3291,x3292)+E(f188(x3293,x3291,x3294,x3295,x3296),f188(x3293,x3292,x3294,x3295,x3296)) % 172.83/172.50 [330]~E(x3301,x3302)+E(f188(x3303,x3304,x3301,x3305,x3306),f188(x3303,x3304,x3302,x3305,x3306)) % 172.83/172.50 [331]~E(x3311,x3312)+E(f188(x3313,x3314,x3315,x3311,x3316),f188(x3313,x3314,x3315,x3312,x3316)) % 172.83/172.50 [332]~E(x3321,x3322)+E(f188(x3323,x3324,x3325,x3326,x3321),f188(x3323,x3324,x3325,x3326,x3322)) % 172.83/172.50 [333]~E(x3331,x3332)+E(f288(x3331,x3333),f288(x3332,x3333)) % 172.83/172.50 [334]~E(x3341,x3342)+E(f288(x3343,x3341),f288(x3343,x3342)) % 172.83/172.50 [335]~E(x3351,x3352)+E(f564(x3351),f564(x3352)) % 172.83/172.50 [336]~E(x3361,x3362)+E(f289(x3361,x3363,x3364),f289(x3362,x3363,x3364)) % 172.83/172.50 [337]~E(x3371,x3372)+E(f289(x3373,x3371,x3374),f289(x3373,x3372,x3374)) % 172.83/172.50 [338]~E(x3381,x3382)+E(f289(x3383,x3384,x3381),f289(x3383,x3384,x3382)) % 172.83/172.50 [339]~E(x3391,x3392)+E(f265(x3391,x3393),f265(x3392,x3393)) % 172.83/172.50 [340]~E(x3401,x3402)+E(f265(x3403,x3401),f265(x3403,x3402)) % 172.83/172.50 [341]~E(x3411,x3412)+E(f625(x3411,x3413,x3414,x3415,x3416),f625(x3412,x3413,x3414,x3415,x3416)) % 172.83/172.50 [342]~E(x3421,x3422)+E(f625(x3423,x3421,x3424,x3425,x3426),f625(x3423,x3422,x3424,x3425,x3426)) % 172.83/172.50 [343]~E(x3431,x3432)+E(f625(x3433,x3434,x3431,x3435,x3436),f625(x3433,x3434,x3432,x3435,x3436)) % 172.83/172.50 [344]~E(x3441,x3442)+E(f625(x3443,x3444,x3445,x3441,x3446),f625(x3443,x3444,x3445,x3442,x3446)) % 172.83/172.50 [345]~E(x3451,x3452)+E(f625(x3453,x3454,x3455,x3456,x3451),f625(x3453,x3454,x3455,x3456,x3452)) % 172.83/172.50 [346]~E(x3461,x3462)+E(f323(x3461,x3463),f323(x3462,x3463)) % 172.83/172.50 [347]~E(x3471,x3472)+E(f323(x3473,x3471),f323(x3473,x3472)) % 172.83/172.50 [348]~E(x3481,x3482)+E(f160(x3481,x3483),f160(x3482,x3483)) % 172.83/172.50 [349]~E(x3491,x3492)+E(f160(x3493,x3491),f160(x3493,x3492)) % 172.83/172.50 [350]~E(x3501,x3502)+E(f324(x3501,x3503),f324(x3502,x3503)) % 172.83/172.50 [351]~E(x3511,x3512)+E(f324(x3513,x3511),f324(x3513,x3512)) % 172.83/172.50 [352]~E(x3521,x3522)+E(f567(x3521,x3523,x3524),f567(x3522,x3523,x3524)) % 172.83/172.50 [353]~E(x3531,x3532)+E(f567(x3533,x3531,x3534),f567(x3533,x3532,x3534)) % 172.83/172.50 [354]~E(x3541,x3542)+E(f567(x3543,x3544,x3541),f567(x3543,x3544,x3542)) % 172.83/172.50 [355]~E(x3551,x3552)+E(f843(x3551,x3553,x3554,x3555),f843(x3552,x3553,x3554,x3555)) % 172.83/172.50 [356]~E(x3561,x3562)+E(f843(x3563,x3561,x3564,x3565),f843(x3563,x3562,x3564,x3565)) % 172.83/172.50 [357]~E(x3571,x3572)+E(f843(x3573,x3574,x3571,x3575),f843(x3573,x3574,x3572,x3575)) % 172.83/172.50 [358]~E(x3581,x3582)+E(f843(x3583,x3584,x3585,x3581),f843(x3583,x3584,x3585,x3582)) % 172.83/172.50 [359]~E(x3591,x3592)+E(f434(x3591,x3593,x3594,x3595,x3596,x3597),f434(x3592,x3593,x3594,x3595,x3596,x3597)) % 172.83/172.50 [360]~E(x3601,x3602)+E(f434(x3603,x3601,x3604,x3605,x3606,x3607),f434(x3603,x3602,x3604,x3605,x3606,x3607)) % 172.83/172.50 [361]~E(x3611,x3612)+E(f434(x3613,x3614,x3611,x3615,x3616,x3617),f434(x3613,x3614,x3612,x3615,x3616,x3617)) % 172.83/172.50 [362]~E(x3621,x3622)+E(f434(x3623,x3624,x3625,x3621,x3626,x3627),f434(x3623,x3624,x3625,x3622,x3626,x3627)) % 172.83/172.50 [363]~E(x3631,x3632)+E(f434(x3633,x3634,x3635,x3636,x3631,x3637),f434(x3633,x3634,x3635,x3636,x3632,x3637)) % 172.83/172.50 [364]~E(x3641,x3642)+E(f434(x3643,x3644,x3645,x3646,x3647,x3641),f434(x3643,x3644,x3645,x3646,x3647,x3642)) % 172.83/172.50 [365]~E(x3651,x3652)+E(f186(x3651,x3653,x3654,x3655),f186(x3652,x3653,x3654,x3655)) % 172.83/172.50 [366]~E(x3661,x3662)+E(f186(x3663,x3661,x3664,x3665),f186(x3663,x3662,x3664,x3665)) % 172.83/172.50 [367]~E(x3671,x3672)+E(f186(x3673,x3674,x3671,x3675),f186(x3673,x3674,x3672,x3675)) % 172.83/172.50 [368]~E(x3681,x3682)+E(f186(x3683,x3684,x3685,x3681),f186(x3683,x3684,x3685,x3682)) % 172.83/172.50 [369]~E(x3691,x3692)+E(f86(x3691),f86(x3692)) % 172.83/172.50 [370]~E(x3701,x3702)+E(f517(x3701,x3703,x3704,x3705),f517(x3702,x3703,x3704,x3705)) % 172.83/172.50 [371]~E(x3711,x3712)+E(f517(x3713,x3711,x3714,x3715),f517(x3713,x3712,x3714,x3715)) % 172.83/172.50 [372]~E(x3721,x3722)+E(f517(x3723,x3724,x3721,x3725),f517(x3723,x3724,x3722,x3725)) % 172.83/172.50 [373]~E(x3731,x3732)+E(f517(x3733,x3734,x3735,x3731),f517(x3733,x3734,x3735,x3732)) % 172.83/172.50 [374]~E(x3741,x3742)+E(f13(x3741,x3743),f13(x3742,x3743)) % 172.83/172.50 [375]~E(x3751,x3752)+E(f13(x3753,x3751),f13(x3753,x3752)) % 172.83/172.50 [376]~E(x3761,x3762)+E(f202(x3761,x3763),f202(x3762,x3763)) % 172.83/172.50 [377]~E(x3771,x3772)+E(f202(x3773,x3771),f202(x3773,x3772)) % 172.83/172.50 [378]~E(x3781,x3782)+E(f644(x3781,x3783,x3784),f644(x3782,x3783,x3784)) % 172.83/172.50 [379]~E(x3791,x3792)+E(f644(x3793,x3791,x3794),f644(x3793,x3792,x3794)) % 172.83/172.50 [380]~E(x3801,x3802)+E(f644(x3803,x3804,x3801),f644(x3803,x3804,x3802)) % 172.83/172.50 [381]~E(x3811,x3812)+E(f587(x3811,x3813),f587(x3812,x3813)) % 172.83/172.50 [382]~E(x3821,x3822)+E(f587(x3823,x3821),f587(x3823,x3822)) % 172.83/172.50 [383]~E(x3831,x3832)+E(f738(x3831,x3833,x3834,x3835),f738(x3832,x3833,x3834,x3835)) % 172.83/172.50 [384]~E(x3841,x3842)+E(f738(x3843,x3841,x3844,x3845),f738(x3843,x3842,x3844,x3845)) % 172.83/172.50 [385]~E(x3851,x3852)+E(f738(x3853,x3854,x3851,x3855),f738(x3853,x3854,x3852,x3855)) % 172.83/172.50 [386]~E(x3861,x3862)+E(f738(x3863,x3864,x3865,x3861),f738(x3863,x3864,x3865,x3862)) % 172.83/172.50 [387]~E(x3871,x3872)+E(f307(x3871),f307(x3872)) % 172.83/172.50 [388]~E(x3881,x3882)+E(f57(x3881),f57(x3882)) % 172.83/172.50 [389]~E(x3891,x3892)+E(f620(x3891,x3893,x3894,x3895,x3896),f620(x3892,x3893,x3894,x3895,x3896)) % 172.83/172.50 [390]~E(x3901,x3902)+E(f620(x3903,x3901,x3904,x3905,x3906),f620(x3903,x3902,x3904,x3905,x3906)) % 172.83/172.50 [391]~E(x3911,x3912)+E(f620(x3913,x3914,x3911,x3915,x3916),f620(x3913,x3914,x3912,x3915,x3916)) % 172.83/172.50 [392]~E(x3921,x3922)+E(f620(x3923,x3924,x3925,x3921,x3926),f620(x3923,x3924,x3925,x3922,x3926)) % 172.83/172.50 [393]~E(x3931,x3932)+E(f620(x3933,x3934,x3935,x3936,x3931),f620(x3933,x3934,x3935,x3936,x3932)) % 172.83/172.50 [394]~E(x3941,x3942)+E(f123(x3941,x3943,x3944,x3945),f123(x3942,x3943,x3944,x3945)) % 172.83/172.50 [395]~E(x3951,x3952)+E(f123(x3953,x3951,x3954,x3955),f123(x3953,x3952,x3954,x3955)) % 172.83/172.50 [396]~E(x3961,x3962)+E(f123(x3963,x3964,x3961,x3965),f123(x3963,x3964,x3962,x3965)) % 172.83/172.50 [397]~E(x3971,x3972)+E(f123(x3973,x3974,x3975,x3971),f123(x3973,x3974,x3975,x3972)) % 172.83/172.50 [398]~E(x3981,x3982)+E(f716(x3981,x3983,x3984,x3985,x3986),f716(x3982,x3983,x3984,x3985,x3986)) % 172.83/172.50 [399]~E(x3991,x3992)+E(f716(x3993,x3991,x3994,x3995,x3996),f716(x3993,x3992,x3994,x3995,x3996)) % 172.83/172.50 [400]~E(x4001,x4002)+E(f716(x4003,x4004,x4001,x4005,x4006),f716(x4003,x4004,x4002,x4005,x4006)) % 172.83/172.50 [401]~E(x4011,x4012)+E(f716(x4013,x4014,x4015,x4011,x4016),f716(x4013,x4014,x4015,x4012,x4016)) % 172.83/172.50 [402]~E(x4021,x4022)+E(f716(x4023,x4024,x4025,x4026,x4021),f716(x4023,x4024,x4025,x4026,x4022)) % 172.83/172.50 [403]~E(x4031,x4032)+E(f206(x4031,x4033,x4034,x4035),f206(x4032,x4033,x4034,x4035)) % 172.83/172.50 [404]~E(x4041,x4042)+E(f206(x4043,x4041,x4044,x4045),f206(x4043,x4042,x4044,x4045)) % 172.83/172.50 [405]~E(x4051,x4052)+E(f206(x4053,x4054,x4051,x4055),f206(x4053,x4054,x4052,x4055)) % 172.83/172.50 [406]~E(x4061,x4062)+E(f206(x4063,x4064,x4065,x4061),f206(x4063,x4064,x4065,x4062)) % 172.83/172.50 [407]~E(x4071,x4072)+E(f859(x4071,x4073,x4074),f859(x4072,x4073,x4074)) % 172.83/172.50 [408]~E(x4081,x4082)+E(f859(x4083,x4081,x4084),f859(x4083,x4082,x4084)) % 172.83/172.50 [409]~E(x4091,x4092)+E(f859(x4093,x4094,x4091),f859(x4093,x4094,x4092)) % 172.83/172.50 [410]~E(x4101,x4102)+E(f223(x4101),f223(x4102)) % 172.83/172.50 [411]~E(x4111,x4112)+E(f180(x4111,x4113),f180(x4112,x4113)) % 172.83/172.50 [412]~E(x4121,x4122)+E(f180(x4123,x4121),f180(x4123,x4122)) % 172.83/172.50 [413]~E(x4131,x4132)+E(f153(x4131,x4133),f153(x4132,x4133)) % 172.83/172.50 [414]~E(x4141,x4142)+E(f153(x4143,x4141),f153(x4143,x4142)) % 172.83/172.50 [415]~E(x4151,x4152)+E(f201(x4151),f201(x4152)) % 172.83/172.50 [416]~E(x4161,x4162)+E(f818(x4161,x4163,x4164),f818(x4162,x4163,x4164)) % 172.83/172.50 [417]~E(x4171,x4172)+E(f818(x4173,x4171,x4174),f818(x4173,x4172,x4174)) % 172.83/172.50 [418]~E(x4181,x4182)+E(f818(x4183,x4184,x4181),f818(x4183,x4184,x4182)) % 172.83/172.50 [419]~E(x4191,x4192)+E(f728(x4191,x4193,x4194),f728(x4192,x4193,x4194)) % 172.83/172.50 [420]~E(x4201,x4202)+E(f728(x4203,x4201,x4204),f728(x4203,x4202,x4204)) % 172.83/172.50 [421]~E(x4211,x4212)+E(f728(x4213,x4214,x4211),f728(x4213,x4214,x4212)) % 172.83/172.50 [422]~E(x4221,x4222)+E(f52(x4221,x4223),f52(x4222,x4223)) % 172.83/172.50 [423]~E(x4231,x4232)+E(f52(x4233,x4231),f52(x4233,x4232)) % 172.83/172.50 [424]~E(x4241,x4242)+E(f12(x4241,x4243,x4244),f12(x4242,x4243,x4244)) % 172.83/172.50 [425]~E(x4251,x4252)+E(f12(x4253,x4251,x4254),f12(x4253,x4252,x4254)) % 172.83/172.50 [426]~E(x4261,x4262)+E(f12(x4263,x4264,x4261),f12(x4263,x4264,x4262)) % 172.83/172.50 [427]~E(x4271,x4272)+E(f714(x4271,x4273,x4274,x4275,x4276),f714(x4272,x4273,x4274,x4275,x4276)) % 172.83/172.50 [428]~E(x4281,x4282)+E(f714(x4283,x4281,x4284,x4285,x4286),f714(x4283,x4282,x4284,x4285,x4286)) % 172.83/172.50 [429]~E(x4291,x4292)+E(f714(x4293,x4294,x4291,x4295,x4296),f714(x4293,x4294,x4292,x4295,x4296)) % 172.83/172.50 [430]~E(x4301,x4302)+E(f714(x4303,x4304,x4305,x4301,x4306),f714(x4303,x4304,x4305,x4302,x4306)) % 172.83/172.50 [431]~E(x4311,x4312)+E(f714(x4313,x4314,x4315,x4316,x4311),f714(x4313,x4314,x4315,x4316,x4312)) % 172.83/172.50 [432]~E(x4321,x4322)+E(f306(x4321,x4323,x4324),f306(x4322,x4323,x4324)) % 172.83/172.50 [433]~E(x4331,x4332)+E(f306(x4333,x4331,x4334),f306(x4333,x4332,x4334)) % 172.83/172.50 [434]~E(x4341,x4342)+E(f306(x4343,x4344,x4341),f306(x4343,x4344,x4342)) % 172.83/172.50 [435]~E(x4351,x4352)+E(f320(x4351,x4353),f320(x4352,x4353)) % 172.83/172.50 [436]~E(x4361,x4362)+E(f320(x4363,x4361),f320(x4363,x4362)) % 172.83/172.50 [437]~E(x4371,x4372)+E(f49(x4371,x4373),f49(x4372,x4373)) % 172.83/172.50 [438]~E(x4381,x4382)+E(f49(x4383,x4381),f49(x4383,x4382)) % 172.83/172.50 [439]~E(x4391,x4392)+E(f238(x4391,x4393),f238(x4392,x4393)) % 172.83/172.50 [440]~E(x4401,x4402)+E(f238(x4403,x4401),f238(x4403,x4402)) % 172.83/172.50 [441]~E(x4411,x4412)+E(f45(x4411,x4413),f45(x4412,x4413)) % 172.83/172.50 [442]~E(x4421,x4422)+E(f45(x4423,x4421),f45(x4423,x4422)) % 172.83/172.50 [443]~E(x4431,x4432)+E(f675(x4431,x4433,x4434,x4435,x4436),f675(x4432,x4433,x4434,x4435,x4436)) % 172.83/172.50 [444]~E(x4441,x4442)+E(f675(x4443,x4441,x4444,x4445,x4446),f675(x4443,x4442,x4444,x4445,x4446)) % 172.83/172.50 [445]~E(x4451,x4452)+E(f675(x4453,x4454,x4451,x4455,x4456),f675(x4453,x4454,x4452,x4455,x4456)) % 172.83/172.50 [446]~E(x4461,x4462)+E(f675(x4463,x4464,x4465,x4461,x4466),f675(x4463,x4464,x4465,x4462,x4466)) % 172.83/172.50 [447]~E(x4471,x4472)+E(f675(x4473,x4474,x4475,x4476,x4471),f675(x4473,x4474,x4475,x4476,x4472)) % 172.83/172.50 [448]~E(x4481,x4482)+E(f374(x4481,x4483,x4484),f374(x4482,x4483,x4484)) % 172.83/172.50 [449]~E(x4491,x4492)+E(f374(x4493,x4491,x4494),f374(x4493,x4492,x4494)) % 172.83/172.50 [450]~E(x4501,x4502)+E(f374(x4503,x4504,x4501),f374(x4503,x4504,x4502)) % 172.83/172.50 [451]~E(x4511,x4512)+E(f39(x4511,x4513),f39(x4512,x4513)) % 172.83/172.50 [452]~E(x4521,x4522)+E(f39(x4523,x4521),f39(x4523,x4522)) % 172.83/172.50 [453]~E(x4531,x4532)+E(f478(x4531,x4533,x4534,x4535),f478(x4532,x4533,x4534,x4535)) % 172.83/172.50 [454]~E(x4541,x4542)+E(f478(x4543,x4541,x4544,x4545),f478(x4543,x4542,x4544,x4545)) % 172.83/172.50 [455]~E(x4551,x4552)+E(f478(x4553,x4554,x4551,x4555),f478(x4553,x4554,x4552,x4555)) % 172.83/172.50 [456]~E(x4561,x4562)+E(f478(x4563,x4564,x4565,x4561),f478(x4563,x4564,x4565,x4562)) % 172.83/172.50 [457]~E(x4571,x4572)+E(f826(x4571,x4573,x4574),f826(x4572,x4573,x4574)) % 172.83/172.50 [458]~E(x4581,x4582)+E(f826(x4583,x4581,x4584),f826(x4583,x4582,x4584)) % 172.83/172.50 [459]~E(x4591,x4592)+E(f826(x4593,x4594,x4591),f826(x4593,x4594,x4592)) % 172.83/172.50 [460]~E(x4601,x4602)+E(f508(x4601,x4603,x4604,x4605),f508(x4602,x4603,x4604,x4605)) % 172.83/172.50 [461]~E(x4611,x4612)+E(f508(x4613,x4611,x4614,x4615),f508(x4613,x4612,x4614,x4615)) % 172.83/172.50 [462]~E(x4621,x4622)+E(f508(x4623,x4624,x4621,x4625),f508(x4623,x4624,x4622,x4625)) % 172.83/172.50 [463]~E(x4631,x4632)+E(f508(x4633,x4634,x4635,x4631),f508(x4633,x4634,x4635,x4632)) % 172.83/172.50 [464]~E(x4641,x4642)+E(f391(x4641,x4643,x4644,x4645),f391(x4642,x4643,x4644,x4645)) % 172.83/172.50 [465]~E(x4651,x4652)+E(f391(x4653,x4651,x4654,x4655),f391(x4653,x4652,x4654,x4655)) % 172.83/172.50 [466]~E(x4661,x4662)+E(f391(x4663,x4664,x4661,x4665),f391(x4663,x4664,x4662,x4665)) % 172.83/172.50 [467]~E(x4671,x4672)+E(f391(x4673,x4674,x4675,x4671),f391(x4673,x4674,x4675,x4672)) % 172.83/172.50 [468]~E(x4681,x4682)+E(f226(x4681,x4683),f226(x4682,x4683)) % 172.83/172.50 [469]~E(x4691,x4692)+E(f226(x4693,x4691),f226(x4693,x4692)) % 172.83/172.50 [470]~E(x4701,x4702)+E(f698(x4701,x4703,x4704,x4705,x4706),f698(x4702,x4703,x4704,x4705,x4706)) % 172.83/172.50 [471]~E(x4711,x4712)+E(f698(x4713,x4711,x4714,x4715,x4716),f698(x4713,x4712,x4714,x4715,x4716)) % 172.83/172.50 [472]~E(x4721,x4722)+E(f698(x4723,x4724,x4721,x4725,x4726),f698(x4723,x4724,x4722,x4725,x4726)) % 172.83/172.50 [473]~E(x4731,x4732)+E(f698(x4733,x4734,x4735,x4731,x4736),f698(x4733,x4734,x4735,x4732,x4736)) % 172.83/172.50 [474]~E(x4741,x4742)+E(f698(x4743,x4744,x4745,x4746,x4741),f698(x4743,x4744,x4745,x4746,x4742)) % 172.83/172.50 [475]~E(x4751,x4752)+E(f321(x4751,x4753),f321(x4752,x4753)) % 172.83/172.50 [476]~E(x4761,x4762)+E(f321(x4763,x4761),f321(x4763,x4762)) % 172.83/172.50 [477]~E(x4771,x4772)+E(f595(x4771,x4773,x4774),f595(x4772,x4773,x4774)) % 172.83/172.50 [478]~E(x4781,x4782)+E(f595(x4783,x4781,x4784),f595(x4783,x4782,x4784)) % 172.83/172.50 [479]~E(x4791,x4792)+E(f595(x4793,x4794,x4791),f595(x4793,x4794,x4792)) % 172.83/172.50 [480]~E(x4801,x4802)+E(f423(x4801,x4803,x4804,x4805,x4806),f423(x4802,x4803,x4804,x4805,x4806)) % 172.83/172.50 [481]~E(x4811,x4812)+E(f423(x4813,x4811,x4814,x4815,x4816),f423(x4813,x4812,x4814,x4815,x4816)) % 172.83/172.50 [482]~E(x4821,x4822)+E(f423(x4823,x4824,x4821,x4825,x4826),f423(x4823,x4824,x4822,x4825,x4826)) % 172.83/172.50 [483]~E(x4831,x4832)+E(f423(x4833,x4834,x4835,x4831,x4836),f423(x4833,x4834,x4835,x4832,x4836)) % 172.83/172.50 [484]~E(x4841,x4842)+E(f423(x4843,x4844,x4845,x4846,x4841),f423(x4843,x4844,x4845,x4846,x4842)) % 172.83/172.50 [485]~E(x4851,x4852)+E(f444(x4851,x4853,x4854,x4855,x4856),f444(x4852,x4853,x4854,x4855,x4856)) % 172.83/172.50 [486]~E(x4861,x4862)+E(f444(x4863,x4861,x4864,x4865,x4866),f444(x4863,x4862,x4864,x4865,x4866)) % 172.83/172.50 [487]~E(x4871,x4872)+E(f444(x4873,x4874,x4871,x4875,x4876),f444(x4873,x4874,x4872,x4875,x4876)) % 172.83/172.50 [488]~E(x4881,x4882)+E(f444(x4883,x4884,x4885,x4881,x4886),f444(x4883,x4884,x4885,x4882,x4886)) % 172.83/172.50 [489]~E(x4891,x4892)+E(f444(x4893,x4894,x4895,x4896,x4891),f444(x4893,x4894,x4895,x4896,x4892)) % 172.83/172.50 [490]~E(x4901,x4902)+E(f858(x4901,x4903,x4904,x4905),f858(x4902,x4903,x4904,x4905)) % 172.83/172.50 [491]~E(x4911,x4912)+E(f858(x4913,x4911,x4914,x4915),f858(x4913,x4912,x4914,x4915)) % 172.83/172.50 [492]~E(x4921,x4922)+E(f858(x4923,x4924,x4921,x4925),f858(x4923,x4924,x4922,x4925)) % 172.83/172.50 [493]~E(x4931,x4932)+E(f858(x4933,x4934,x4935,x4931),f858(x4933,x4934,x4935,x4932)) % 172.83/172.50 [494]~E(x4941,x4942)+E(f46(x4941,x4943),f46(x4942,x4943)) % 172.83/172.50 [495]~E(x4951,x4952)+E(f46(x4953,x4951),f46(x4953,x4952)) % 172.83/172.50 [496]~E(x4961,x4962)+E(f847(x4961,x4963,x4964,x4965,x4966),f847(x4962,x4963,x4964,x4965,x4966)) % 172.83/172.50 [497]~E(x4971,x4972)+E(f847(x4973,x4971,x4974,x4975,x4976),f847(x4973,x4972,x4974,x4975,x4976)) % 172.83/172.50 [498]~E(x4981,x4982)+E(f847(x4983,x4984,x4981,x4985,x4986),f847(x4983,x4984,x4982,x4985,x4986)) % 172.83/172.50 [499]~E(x4991,x4992)+E(f847(x4993,x4994,x4995,x4991,x4996),f847(x4993,x4994,x4995,x4992,x4996)) % 172.83/172.50 [500]~E(x5001,x5002)+E(f847(x5003,x5004,x5005,x5006,x5001),f847(x5003,x5004,x5005,x5006,x5002)) % 172.83/172.50 [501]~E(x5011,x5012)+E(f273(x5011,x5013,x5014,x5015),f273(x5012,x5013,x5014,x5015)) % 172.83/172.50 [502]~E(x5021,x5022)+E(f273(x5023,x5021,x5024,x5025),f273(x5023,x5022,x5024,x5025)) % 172.83/172.50 [503]~E(x5031,x5032)+E(f273(x5033,x5034,x5031,x5035),f273(x5033,x5034,x5032,x5035)) % 172.83/172.50 [504]~E(x5041,x5042)+E(f273(x5043,x5044,x5045,x5041),f273(x5043,x5044,x5045,x5042)) % 172.83/172.50 [505]~E(x5051,x5052)+E(f663(x5051,x5053,x5054,x5055,x5056,x5057),f663(x5052,x5053,x5054,x5055,x5056,x5057)) % 172.83/172.50 [506]~E(x5061,x5062)+E(f663(x5063,x5061,x5064,x5065,x5066,x5067),f663(x5063,x5062,x5064,x5065,x5066,x5067)) % 172.83/172.50 [507]~E(x5071,x5072)+E(f663(x5073,x5074,x5071,x5075,x5076,x5077),f663(x5073,x5074,x5072,x5075,x5076,x5077)) % 172.83/172.50 [508]~E(x5081,x5082)+E(f663(x5083,x5084,x5085,x5081,x5086,x5087),f663(x5083,x5084,x5085,x5082,x5086,x5087)) % 172.83/172.50 [509]~E(x5091,x5092)+E(f663(x5093,x5094,x5095,x5096,x5091,x5097),f663(x5093,x5094,x5095,x5096,x5092,x5097)) % 172.83/172.50 [510]~E(x5101,x5102)+E(f663(x5103,x5104,x5105,x5106,x5107,x5101),f663(x5103,x5104,x5105,x5106,x5107,x5102)) % 172.83/172.50 [511]~E(x5111,x5112)+E(f40(x5111,x5113),f40(x5112,x5113)) % 172.83/172.50 [512]~E(x5121,x5122)+E(f40(x5123,x5121),f40(x5123,x5122)) % 172.83/172.50 [513]~E(x5131,x5132)+E(f402(x5131,x5133),f402(x5132,x5133)) % 172.83/172.50 [514]~E(x5141,x5142)+E(f402(x5143,x5141),f402(x5143,x5142)) % 172.83/172.50 [515]~E(x5151,x5152)+E(f91(x5151),f91(x5152)) % 172.83/172.50 [516]~E(x5161,x5162)+E(f557(x5161,x5163,x5164),f557(x5162,x5163,x5164)) % 172.83/172.50 [517]~E(x5171,x5172)+E(f557(x5173,x5171,x5174),f557(x5173,x5172,x5174)) % 172.83/172.50 [518]~E(x5181,x5182)+E(f557(x5183,x5184,x5181),f557(x5183,x5184,x5182)) % 172.83/172.50 [519]~E(x5191,x5192)+E(f149(x5191,x5193,x5194,x5195,x5196),f149(x5192,x5193,x5194,x5195,x5196)) % 172.83/172.50 [520]~E(x5201,x5202)+E(f149(x5203,x5201,x5204,x5205,x5206),f149(x5203,x5202,x5204,x5205,x5206)) % 172.83/172.50 [521]~E(x5211,x5212)+E(f149(x5213,x5214,x5211,x5215,x5216),f149(x5213,x5214,x5212,x5215,x5216)) % 172.83/172.50 [522]~E(x5221,x5222)+E(f149(x5223,x5224,x5225,x5221,x5226),f149(x5223,x5224,x5225,x5222,x5226)) % 172.83/172.50 [523]~E(x5231,x5232)+E(f149(x5233,x5234,x5235,x5236,x5231),f149(x5233,x5234,x5235,x5236,x5232)) % 172.83/172.50 [524]~E(x5241,x5242)+E(f788(x5241,x5243,x5244,x5245,x5246),f788(x5242,x5243,x5244,x5245,x5246)) % 172.83/172.50 [525]~E(x5251,x5252)+E(f788(x5253,x5251,x5254,x5255,x5256),f788(x5253,x5252,x5254,x5255,x5256)) % 172.83/172.50 [526]~E(x5261,x5262)+E(f788(x5263,x5264,x5261,x5265,x5266),f788(x5263,x5264,x5262,x5265,x5266)) % 172.83/172.50 [527]~E(x5271,x5272)+E(f788(x5273,x5274,x5275,x5271,x5276),f788(x5273,x5274,x5275,x5272,x5276)) % 172.83/172.50 [528]~E(x5281,x5282)+E(f788(x5283,x5284,x5285,x5286,x5281),f788(x5283,x5284,x5285,x5286,x5282)) % 172.83/172.50 [529]~E(x5291,x5292)+E(f85(x5291,x5293),f85(x5292,x5293)) % 172.83/172.50 [530]~E(x5301,x5302)+E(f85(x5303,x5301),f85(x5303,x5302)) % 172.83/172.50 [531]~E(x5311,x5312)+E(f253(x5311),f253(x5312)) % 172.83/172.50 [532]~E(x5321,x5322)+E(f551(x5321,x5323,x5324,x5325,x5326,x5327,x5328,x5329),f551(x5322,x5323,x5324,x5325,x5326,x5327,x5328,x5329)) % 172.83/172.50 [533]~E(x5331,x5332)+E(f551(x5333,x5331,x5334,x5335,x5336,x5337,x5338,x5339),f551(x5333,x5332,x5334,x5335,x5336,x5337,x5338,x5339)) % 172.83/172.50 [534]~E(x5341,x5342)+E(f551(x5343,x5344,x5341,x5345,x5346,x5347,x5348,x5349),f551(x5343,x5344,x5342,x5345,x5346,x5347,x5348,x5349)) % 172.83/172.50 [535]~E(x5351,x5352)+E(f551(x5353,x5354,x5355,x5351,x5356,x5357,x5358,x5359),f551(x5353,x5354,x5355,x5352,x5356,x5357,x5358,x5359)) % 172.83/172.50 [536]~E(x5361,x5362)+E(f551(x5363,x5364,x5365,x5366,x5361,x5367,x5368,x5369),f551(x5363,x5364,x5365,x5366,x5362,x5367,x5368,x5369)) % 172.83/172.50 [537]~E(x5371,x5372)+E(f551(x5373,x5374,x5375,x5376,x5377,x5371,x5378,x5379),f551(x5373,x5374,x5375,x5376,x5377,x5372,x5378,x5379)) % 172.83/172.50 [538]~E(x5381,x5382)+E(f551(x5383,x5384,x5385,x5386,x5387,x5388,x5381,x5389),f551(x5383,x5384,x5385,x5386,x5387,x5388,x5382,x5389)) % 172.83/172.50 [539]~E(x5391,x5392)+E(f551(x5393,x5394,x5395,x5396,x5397,x5398,x5399,x5391),f551(x5393,x5394,x5395,x5396,x5397,x5398,x5399,x5392)) % 172.83/172.50 [540]~E(x5401,x5402)+E(f827(x5401,x5403,x5404),f827(x5402,x5403,x5404)) % 172.83/172.50 [541]~E(x5411,x5412)+E(f827(x5413,x5411,x5414),f827(x5413,x5412,x5414)) % 172.83/172.50 [542]~E(x5421,x5422)+E(f827(x5423,x5424,x5421),f827(x5423,x5424,x5422)) % 172.83/172.50 [543]~E(x5431,x5432)+E(f561(x5431,x5433),f561(x5432,x5433)) % 172.83/172.50 [544]~E(x5441,x5442)+E(f561(x5443,x5441),f561(x5443,x5442)) % 172.83/172.50 [545]~E(x5451,x5452)+E(f231(x5451,x5453),f231(x5452,x5453)) % 172.83/172.50 [546]~E(x5461,x5462)+E(f231(x5463,x5461),f231(x5463,x5462)) % 172.83/172.50 [547]~E(x5471,x5472)+E(f254(x5471),f254(x5472)) % 172.83/172.50 [548]~E(x5481,x5482)+E(f167(x5481,x5483,x5484),f167(x5482,x5483,x5484)) % 172.83/172.50 [549]~E(x5491,x5492)+E(f167(x5493,x5491,x5494),f167(x5493,x5492,x5494)) % 172.83/172.50 [550]~E(x5501,x5502)+E(f167(x5503,x5504,x5501),f167(x5503,x5504,x5502)) % 172.83/172.50 [551]~E(x5511,x5512)+E(f350(x5511,x5513,x5514),f350(x5512,x5513,x5514)) % 172.83/172.50 [552]~E(x5521,x5522)+E(f350(x5523,x5521,x5524),f350(x5523,x5522,x5524)) % 172.83/172.50 [553]~E(x5531,x5532)+E(f350(x5533,x5534,x5531),f350(x5533,x5534,x5532)) % 172.83/172.50 [554]~E(x5541,x5542)+E(f751(x5541,x5543,x5544),f751(x5542,x5543,x5544)) % 172.83/172.50 [555]~E(x5551,x5552)+E(f751(x5553,x5551,x5554),f751(x5553,x5552,x5554)) % 172.83/172.50 [556]~E(x5561,x5562)+E(f751(x5563,x5564,x5561),f751(x5563,x5564,x5562)) % 172.83/172.50 [557]~E(x5571,x5572)+E(f531(x5571,x5573,x5574),f531(x5572,x5573,x5574)) % 172.83/172.50 [558]~E(x5581,x5582)+E(f531(x5583,x5581,x5584),f531(x5583,x5582,x5584)) % 172.83/172.50 [559]~E(x5591,x5592)+E(f531(x5593,x5594,x5591),f531(x5593,x5594,x5592)) % 172.83/172.50 [560]~E(x5601,x5602)+E(f305(x5601,x5603,x5604),f305(x5602,x5603,x5604)) % 172.83/172.50 [561]~E(x5611,x5612)+E(f305(x5613,x5611,x5614),f305(x5613,x5612,x5614)) % 172.83/172.50 [562]~E(x5621,x5622)+E(f305(x5623,x5624,x5621),f305(x5623,x5624,x5622)) % 172.83/172.50 [563]~E(x5631,x5632)+E(f81(x5631,x5633),f81(x5632,x5633)) % 172.83/172.50 [564]~E(x5641,x5642)+E(f81(x5643,x5641),f81(x5643,x5642)) % 172.83/172.50 [565]~E(x5651,x5652)+E(f256(x5651,x5653,x5654),f256(x5652,x5653,x5654)) % 172.83/172.50 [566]~E(x5661,x5662)+E(f256(x5663,x5661,x5664),f256(x5663,x5662,x5664)) % 172.83/172.50 [567]~E(x5671,x5672)+E(f256(x5673,x5674,x5671),f256(x5673,x5674,x5672)) % 172.83/172.50 [568]~E(x5681,x5682)+E(f767(x5681,x5683),f767(x5682,x5683)) % 172.83/172.50 [569]~E(x5691,x5692)+E(f767(x5693,x5691),f767(x5693,x5692)) % 172.83/172.50 [570]~E(x5701,x5702)+E(f637(x5701,x5703,x5704),f637(x5702,x5703,x5704)) % 172.83/172.50 [571]~E(x5711,x5712)+E(f637(x5713,x5711,x5714),f637(x5713,x5712,x5714)) % 172.83/172.50 [572]~E(x5721,x5722)+E(f637(x5723,x5724,x5721),f637(x5723,x5724,x5722)) % 172.83/172.50 [573]~E(x5731,x5732)+E(f448(x5731,x5733,x5734,x5735,x5736),f448(x5732,x5733,x5734,x5735,x5736)) % 172.83/172.50 [574]~E(x5741,x5742)+E(f448(x5743,x5741,x5744,x5745,x5746),f448(x5743,x5742,x5744,x5745,x5746)) % 172.83/172.50 [575]~E(x5751,x5752)+E(f448(x5753,x5754,x5751,x5755,x5756),f448(x5753,x5754,x5752,x5755,x5756)) % 172.83/172.50 [576]~E(x5761,x5762)+E(f448(x5763,x5764,x5765,x5761,x5766),f448(x5763,x5764,x5765,x5762,x5766)) % 172.83/172.50 [577]~E(x5771,x5772)+E(f448(x5773,x5774,x5775,x5776,x5771),f448(x5773,x5774,x5775,x5776,x5772)) % 172.83/172.50 [578]~E(x5781,x5782)+E(f31(x5781,x5783),f31(x5782,x5783)) % 172.83/172.50 [579]~E(x5791,x5792)+E(f31(x5793,x5791),f31(x5793,x5792)) % 172.83/172.50 [580]~E(x5801,x5802)+E(f776(x5801,x5803,x5804),f776(x5802,x5803,x5804)) % 172.83/172.50 [581]~E(x5811,x5812)+E(f776(x5813,x5811,x5814),f776(x5813,x5812,x5814)) % 172.83/172.50 [582]~E(x5821,x5822)+E(f776(x5823,x5824,x5821),f776(x5823,x5824,x5822)) % 172.83/172.50 [583]~E(x5831,x5832)+E(f414(x5831,x5833,x5834,x5835),f414(x5832,x5833,x5834,x5835)) % 172.83/172.50 [584]~E(x5841,x5842)+E(f414(x5843,x5841,x5844,x5845),f414(x5843,x5842,x5844,x5845)) % 172.83/172.50 [585]~E(x5851,x5852)+E(f414(x5853,x5854,x5851,x5855),f414(x5853,x5854,x5852,x5855)) % 172.83/172.50 [586]~E(x5861,x5862)+E(f414(x5863,x5864,x5865,x5861),f414(x5863,x5864,x5865,x5862)) % 172.83/172.50 [587]~E(x5871,x5872)+E(f487(x5871,x5873,x5874),f487(x5872,x5873,x5874)) % 172.83/172.50 [588]~E(x5881,x5882)+E(f487(x5883,x5881,x5884),f487(x5883,x5882,x5884)) % 172.83/172.50 [589]~E(x5891,x5892)+E(f487(x5893,x5894,x5891),f487(x5893,x5894,x5892)) % 172.83/172.50 [590]~E(x5901,x5902)+E(f552(x5901,x5903),f552(x5902,x5903)) % 172.83/172.50 [591]~E(x5911,x5912)+E(f552(x5913,x5911),f552(x5913,x5912)) % 172.83/172.50 [592]~E(x5921,x5922)+E(f712(x5921,x5923,x5924,x5925,x5926),f712(x5922,x5923,x5924,x5925,x5926)) % 172.83/172.50 [593]~E(x5931,x5932)+E(f712(x5933,x5931,x5934,x5935,x5936),f712(x5933,x5932,x5934,x5935,x5936)) % 172.83/172.50 [594]~E(x5941,x5942)+E(f712(x5943,x5944,x5941,x5945,x5946),f712(x5943,x5944,x5942,x5945,x5946)) % 172.83/172.50 [595]~E(x5951,x5952)+E(f712(x5953,x5954,x5955,x5951,x5956),f712(x5953,x5954,x5955,x5952,x5956)) % 172.83/172.50 [596]~E(x5961,x5962)+E(f712(x5963,x5964,x5965,x5966,x5961),f712(x5963,x5964,x5965,x5966,x5962)) % 172.83/172.50 [597]~E(x5971,x5972)+E(f676(x5971,x5973,x5974,x5975,x5976),f676(x5972,x5973,x5974,x5975,x5976)) % 172.83/172.50 [598]~E(x5981,x5982)+E(f676(x5983,x5981,x5984,x5985,x5986),f676(x5983,x5982,x5984,x5985,x5986)) % 172.83/172.50 [599]~E(x5991,x5992)+E(f676(x5993,x5994,x5991,x5995,x5996),f676(x5993,x5994,x5992,x5995,x5996)) % 172.83/172.50 [600]~E(x6001,x6002)+E(f676(x6003,x6004,x6005,x6001,x6006),f676(x6003,x6004,x6005,x6002,x6006)) % 172.83/172.50 [601]~E(x6011,x6012)+E(f676(x6013,x6014,x6015,x6016,x6011),f676(x6013,x6014,x6015,x6016,x6012)) % 172.83/172.50 [602]~E(x6021,x6022)+E(f639(x6021,x6023,x6024,x6025),f639(x6022,x6023,x6024,x6025)) % 172.83/172.50 [603]~E(x6031,x6032)+E(f639(x6033,x6031,x6034,x6035),f639(x6033,x6032,x6034,x6035)) % 172.83/172.50 [604]~E(x6041,x6042)+E(f639(x6043,x6044,x6041,x6045),f639(x6043,x6044,x6042,x6045)) % 172.83/172.50 [605]~E(x6051,x6052)+E(f639(x6053,x6054,x6055,x6051),f639(x6053,x6054,x6055,x6052)) % 172.83/172.50 [606]~E(x6061,x6062)+E(f296(x6061,x6063,x6064,x6065),f296(x6062,x6063,x6064,x6065)) % 172.83/172.50 [607]~E(x6071,x6072)+E(f296(x6073,x6071,x6074,x6075),f296(x6073,x6072,x6074,x6075)) % 172.83/172.50 [608]~E(x6081,x6082)+E(f296(x6083,x6084,x6081,x6085),f296(x6083,x6084,x6082,x6085)) % 172.83/172.50 [609]~E(x6091,x6092)+E(f296(x6093,x6094,x6095,x6091),f296(x6093,x6094,x6095,x6092)) % 172.83/172.50 [610]~E(x6101,x6102)+E(f112(x6101),f112(x6102)) % 172.83/172.50 [611]~E(x6111,x6112)+E(f433(x6111,x6113,x6114,x6115,x6116,x6117),f433(x6112,x6113,x6114,x6115,x6116,x6117)) % 172.83/172.50 [612]~E(x6121,x6122)+E(f433(x6123,x6121,x6124,x6125,x6126,x6127),f433(x6123,x6122,x6124,x6125,x6126,x6127)) % 172.83/172.50 [613]~E(x6131,x6132)+E(f433(x6133,x6134,x6131,x6135,x6136,x6137),f433(x6133,x6134,x6132,x6135,x6136,x6137)) % 172.83/172.50 [614]~E(x6141,x6142)+E(f433(x6143,x6144,x6145,x6141,x6146,x6147),f433(x6143,x6144,x6145,x6142,x6146,x6147)) % 172.83/172.50 [615]~E(x6151,x6152)+E(f433(x6153,x6154,x6155,x6156,x6151,x6157),f433(x6153,x6154,x6155,x6156,x6152,x6157)) % 172.83/172.50 [616]~E(x6161,x6162)+E(f433(x6163,x6164,x6165,x6166,x6167,x6161),f433(x6163,x6164,x6165,x6166,x6167,x6162)) % 172.83/172.50 [617]~E(x6171,x6172)+E(f63(x6171,x6173),f63(x6172,x6173)) % 172.83/172.50 [618]~E(x6181,x6182)+E(f63(x6183,x6181),f63(x6183,x6182)) % 172.83/172.50 [619]~E(x6191,x6192)+E(f319(x6191,x6193,x6194,x6195),f319(x6192,x6193,x6194,x6195)) % 172.83/172.50 [620]~E(x6201,x6202)+E(f319(x6203,x6201,x6204,x6205),f319(x6203,x6202,x6204,x6205)) % 172.83/172.50 [621]~E(x6211,x6212)+E(f319(x6213,x6214,x6211,x6215),f319(x6213,x6214,x6212,x6215)) % 172.83/172.50 [622]~E(x6221,x6222)+E(f319(x6223,x6224,x6225,x6221),f319(x6223,x6224,x6225,x6222)) % 172.83/172.50 [623]~E(x6231,x6232)+E(f408(x6231,x6233),f408(x6232,x6233)) % 172.83/172.50 [624]~E(x6241,x6242)+E(f408(x6243,x6241),f408(x6243,x6242)) % 172.83/172.50 [625]~E(x6251,x6252)+E(f654(x6251,x6253,x6254),f654(x6252,x6253,x6254)) % 172.83/172.50 [626]~E(x6261,x6262)+E(f654(x6263,x6261,x6264),f654(x6263,x6262,x6264)) % 172.83/172.50 [627]~E(x6271,x6272)+E(f654(x6273,x6274,x6271),f654(x6273,x6274,x6272)) % 172.83/172.50 [628]~E(x6281,x6282)+E(f409(x6281,x6283,x6284,x6285),f409(x6282,x6283,x6284,x6285)) % 172.83/172.50 [629]~E(x6291,x6292)+E(f409(x6293,x6291,x6294,x6295),f409(x6293,x6292,x6294,x6295)) % 172.83/172.50 [630]~E(x6301,x6302)+E(f409(x6303,x6304,x6301,x6305),f409(x6303,x6304,x6302,x6305)) % 172.83/172.50 [631]~E(x6311,x6312)+E(f409(x6313,x6314,x6315,x6311),f409(x6313,x6314,x6315,x6312)) % 172.83/172.50 [632]~E(x6321,x6322)+E(f159(x6321,x6323),f159(x6322,x6323)) % 172.83/172.50 [633]~E(x6331,x6332)+E(f159(x6333,x6331),f159(x6333,x6332)) % 172.83/172.50 [634]~E(x6341,x6342)+E(f314(x6341,x6343,x6344),f314(x6342,x6343,x6344)) % 172.83/172.50 [635]~E(x6351,x6352)+E(f314(x6353,x6351,x6354),f314(x6353,x6352,x6354)) % 172.83/172.50 [636]~E(x6361,x6362)+E(f314(x6363,x6364,x6361),f314(x6363,x6364,x6362)) % 172.83/172.50 [637]~E(x6371,x6372)+E(f171(x6371,x6373,x6374),f171(x6372,x6373,x6374)) % 172.83/172.50 [638]~E(x6381,x6382)+E(f171(x6383,x6381,x6384),f171(x6383,x6382,x6384)) % 172.83/172.50 [639]~E(x6391,x6392)+E(f171(x6393,x6394,x6391),f171(x6393,x6394,x6392)) % 172.83/172.50 [640]~E(x6401,x6402)+E(f397(x6401,x6403,x6404,x6405),f397(x6402,x6403,x6404,x6405)) % 172.83/172.50 [641]~E(x6411,x6412)+E(f397(x6413,x6411,x6414,x6415),f397(x6413,x6412,x6414,x6415)) % 172.83/172.50 [642]~E(x6421,x6422)+E(f397(x6423,x6424,x6421,x6425),f397(x6423,x6424,x6422,x6425)) % 172.83/172.50 [643]~E(x6431,x6432)+E(f397(x6433,x6434,x6435,x6431),f397(x6433,x6434,x6435,x6432)) % 172.83/172.50 [644]~E(x6441,x6442)+E(f309(x6441),f309(x6442)) % 172.83/172.50 [645]~E(x6451,x6452)+E(f317(x6451),f317(x6452)) % 172.83/172.50 [646]~E(x6461,x6462)+E(f385(x6461,x6463,x6464,x6465),f385(x6462,x6463,x6464,x6465)) % 172.83/172.50 [647]~E(x6471,x6472)+E(f385(x6473,x6471,x6474,x6475),f385(x6473,x6472,x6474,x6475)) % 172.83/172.50 [648]~E(x6481,x6482)+E(f385(x6483,x6484,x6481,x6485),f385(x6483,x6484,x6482,x6485)) % 172.83/172.50 [649]~E(x6491,x6492)+E(f385(x6493,x6494,x6495,x6491),f385(x6493,x6494,x6495,x6492)) % 172.83/172.50 [650]~E(x6501,x6502)+E(f746(x6501,x6503,x6504),f746(x6502,x6503,x6504)) % 172.83/172.50 [651]~E(x6511,x6512)+E(f746(x6513,x6511,x6514),f746(x6513,x6512,x6514)) % 172.83/172.50 [652]~E(x6521,x6522)+E(f746(x6523,x6524,x6521),f746(x6523,x6524,x6522)) % 172.83/172.50 [653]~E(x6531,x6532)+E(f187(x6531,x6533,x6534),f187(x6532,x6533,x6534)) % 172.83/172.50 [654]~E(x6541,x6542)+E(f187(x6543,x6541,x6544),f187(x6543,x6542,x6544)) % 172.83/172.50 [655]~E(x6551,x6552)+E(f187(x6553,x6554,x6551),f187(x6553,x6554,x6552)) % 172.83/172.50 [656]~E(x6561,x6562)+E(f668(x6561,x6563),f668(x6562,x6563)) % 172.83/172.50 [657]~E(x6571,x6572)+E(f668(x6573,x6571),f668(x6573,x6572)) % 172.83/172.50 [658]~E(x6581,x6582)+E(f823(x6581,x6583),f823(x6582,x6583)) % 172.83/172.50 [659]~E(x6591,x6592)+E(f823(x6593,x6591),f823(x6593,x6592)) % 172.83/172.50 [660]~E(x6601,x6602)+E(f312(x6601,x6603,x6604),f312(x6602,x6603,x6604)) % 172.83/172.50 [661]~E(x6611,x6612)+E(f312(x6613,x6611,x6614),f312(x6613,x6612,x6614)) % 172.83/172.50 [662]~E(x6621,x6622)+E(f312(x6623,x6624,x6621),f312(x6623,x6624,x6622)) % 172.83/172.50 [663]~E(x6631,x6632)+E(f730(x6631,x6633,x6634,x6635,x6636),f730(x6632,x6633,x6634,x6635,x6636)) % 172.83/172.50 [664]~E(x6641,x6642)+E(f730(x6643,x6641,x6644,x6645,x6646),f730(x6643,x6642,x6644,x6645,x6646)) % 172.83/172.50 [665]~E(x6651,x6652)+E(f730(x6653,x6654,x6651,x6655,x6656),f730(x6653,x6654,x6652,x6655,x6656)) % 172.83/172.50 [666]~E(x6661,x6662)+E(f730(x6663,x6664,x6665,x6661,x6666),f730(x6663,x6664,x6665,x6662,x6666)) % 172.83/172.50 [667]~E(x6671,x6672)+E(f730(x6673,x6674,x6675,x6676,x6671),f730(x6673,x6674,x6675,x6676,x6672)) % 172.83/172.50 [668]~E(x6681,x6682)+E(f731(x6681,x6683,x6684,x6685),f731(x6682,x6683,x6684,x6685)) % 172.83/172.50 [669]~E(x6691,x6692)+E(f731(x6693,x6691,x6694,x6695),f731(x6693,x6692,x6694,x6695)) % 172.83/172.50 [670]~E(x6701,x6702)+E(f731(x6703,x6704,x6701,x6705),f731(x6703,x6704,x6702,x6705)) % 172.83/172.50 [671]~E(x6711,x6712)+E(f731(x6713,x6714,x6715,x6711),f731(x6713,x6714,x6715,x6712)) % 172.83/172.50 [672]~E(x6721,x6722)+E(f147(x6721,x6723),f147(x6722,x6723)) % 172.83/172.50 [673]~E(x6731,x6732)+E(f147(x6733,x6731),f147(x6733,x6732)) % 172.83/172.50 [674]~E(x6741,x6742)+E(f820(x6741,x6743,x6744),f820(x6742,x6743,x6744)) % 172.83/172.50 [675]~E(x6751,x6752)+E(f820(x6753,x6751,x6754),f820(x6753,x6752,x6754)) % 172.83/172.50 [676]~E(x6761,x6762)+E(f820(x6763,x6764,x6761),f820(x6763,x6764,x6762)) % 172.83/172.50 [677]~E(x6771,x6772)+E(f185(x6771,x6773,x6774),f185(x6772,x6773,x6774)) % 172.83/172.50 [678]~E(x6781,x6782)+E(f185(x6783,x6781,x6784),f185(x6783,x6782,x6784)) % 172.83/172.50 [679]~E(x6791,x6792)+E(f185(x6793,x6794,x6791),f185(x6793,x6794,x6792)) % 172.83/172.50 [680]~E(x6801,x6802)+E(f525(x6801,x6803,x6804,x6805,x6806,x6807,x6808,x6809),f525(x6802,x6803,x6804,x6805,x6806,x6807,x6808,x6809)) % 172.83/172.50 [681]~E(x6811,x6812)+E(f525(x6813,x6811,x6814,x6815,x6816,x6817,x6818,x6819),f525(x6813,x6812,x6814,x6815,x6816,x6817,x6818,x6819)) % 172.83/172.50 [682]~E(x6821,x6822)+E(f525(x6823,x6824,x6821,x6825,x6826,x6827,x6828,x6829),f525(x6823,x6824,x6822,x6825,x6826,x6827,x6828,x6829)) % 172.83/172.50 [683]~E(x6831,x6832)+E(f525(x6833,x6834,x6835,x6831,x6836,x6837,x6838,x6839),f525(x6833,x6834,x6835,x6832,x6836,x6837,x6838,x6839)) % 172.83/172.50 [684]~E(x6841,x6842)+E(f525(x6843,x6844,x6845,x6846,x6841,x6847,x6848,x6849),f525(x6843,x6844,x6845,x6846,x6842,x6847,x6848,x6849)) % 172.83/172.50 [685]~E(x6851,x6852)+E(f525(x6853,x6854,x6855,x6856,x6857,x6851,x6858,x6859),f525(x6853,x6854,x6855,x6856,x6857,x6852,x6858,x6859)) % 172.83/172.50 [686]~E(x6861,x6862)+E(f525(x6863,x6864,x6865,x6866,x6867,x6868,x6861,x6869),f525(x6863,x6864,x6865,x6866,x6867,x6868,x6862,x6869)) % 172.83/172.50 [687]~E(x6871,x6872)+E(f525(x6873,x6874,x6875,x6876,x6877,x6878,x6879,x6871),f525(x6873,x6874,x6875,x6876,x6877,x6878,x6879,x6872)) % 172.83/172.50 [688]~E(x6881,x6882)+E(f623(x6881,x6883,x6884,x6885),f623(x6882,x6883,x6884,x6885)) % 172.83/172.50 [689]~E(x6891,x6892)+E(f623(x6893,x6891,x6894,x6895),f623(x6893,x6892,x6894,x6895)) % 172.83/172.50 [690]~E(x6901,x6902)+E(f623(x6903,x6904,x6901,x6905),f623(x6903,x6904,x6902,x6905)) % 172.83/172.50 [691]~E(x6911,x6912)+E(f623(x6913,x6914,x6915,x6911),f623(x6913,x6914,x6915,x6912)) % 172.83/172.50 [692]~E(x6921,x6922)+E(f54(x6921,x6923,x6924),f54(x6922,x6923,x6924)) % 172.83/172.50 [693]~E(x6931,x6932)+E(f54(x6933,x6931,x6934),f54(x6933,x6932,x6934)) % 172.83/172.50 [694]~E(x6941,x6942)+E(f54(x6943,x6944,x6941),f54(x6943,x6944,x6942)) % 172.83/172.50 [695]~E(x6951,x6952)+E(f199(x6951,x6953),f199(x6952,x6953)) % 172.83/172.50 [696]~E(x6961,x6962)+E(f199(x6963,x6961),f199(x6963,x6962)) % 172.83/172.50 [697]~E(x6971,x6972)+E(f75(x6971,x6973,x6974,x6975,x6976),f75(x6972,x6973,x6974,x6975,x6976)) % 172.83/172.50 [698]~E(x6981,x6982)+E(f75(x6983,x6981,x6984,x6985,x6986),f75(x6983,x6982,x6984,x6985,x6986)) % 172.83/172.50 [699]~E(x6991,x6992)+E(f75(x6993,x6994,x6991,x6995,x6996),f75(x6993,x6994,x6992,x6995,x6996)) % 172.83/172.50 [700]~E(x7001,x7002)+E(f75(x7003,x7004,x7005,x7001,x7006),f75(x7003,x7004,x7005,x7002,x7006)) % 172.83/172.50 [701]~E(x7011,x7012)+E(f75(x7013,x7014,x7015,x7016,x7011),f75(x7013,x7014,x7015,x7016,x7012)) % 172.83/172.50 [702]~E(x7021,x7022)+E(f294(x7021,x7023,x7024),f294(x7022,x7023,x7024)) % 172.83/172.50 [703]~E(x7031,x7032)+E(f294(x7033,x7031,x7034),f294(x7033,x7032,x7034)) % 172.83/172.50 [704]~E(x7041,x7042)+E(f294(x7043,x7044,x7041),f294(x7043,x7044,x7042)) % 172.83/172.50 [705]~E(x7051,x7052)+E(f842(x7051,x7053,x7054,x7055),f842(x7052,x7053,x7054,x7055)) % 172.83/172.50 [706]~E(x7061,x7062)+E(f842(x7063,x7061,x7064,x7065),f842(x7063,x7062,x7064,x7065)) % 172.83/172.50 [707]~E(x7071,x7072)+E(f842(x7073,x7074,x7071,x7075),f842(x7073,x7074,x7072,x7075)) % 172.83/172.50 [708]~E(x7081,x7082)+E(f842(x7083,x7084,x7085,x7081),f842(x7083,x7084,x7085,x7082)) % 172.83/172.50 [709]~E(x7091,x7092)+E(f148(x7091,x7093,x7094),f148(x7092,x7093,x7094)) % 172.83/172.50 [710]~E(x7101,x7102)+E(f148(x7103,x7101,x7104),f148(x7103,x7102,x7104)) % 172.83/172.50 [711]~E(x7111,x7112)+E(f148(x7113,x7114,x7111),f148(x7113,x7114,x7112)) % 172.83/172.50 [712]~E(x7121,x7122)+E(f313(x7121,x7123),f313(x7122,x7123)) % 172.83/172.50 [713]~E(x7131,x7132)+E(f313(x7133,x7131),f313(x7133,x7132)) % 172.83/172.50 [714]~E(x7141,x7142)+E(f158(x7141,x7143),f158(x7142,x7143)) % 172.83/172.50 [715]~E(x7151,x7152)+E(f158(x7153,x7151),f158(x7153,x7152)) % 172.83/172.50 [716]~E(x7161,x7162)+E(f815(x7161,x7163,x7164),f815(x7162,x7163,x7164)) % 172.83/172.50 [717]~E(x7171,x7172)+E(f815(x7173,x7171,x7174),f815(x7173,x7172,x7174)) % 172.83/172.50 [718]~E(x7181,x7182)+E(f815(x7183,x7184,x7181),f815(x7183,x7184,x7182)) % 172.83/172.50 [719]~E(x7191,x7192)+E(f671(x7191,x7193,x7194,x7195),f671(x7192,x7193,x7194,x7195)) % 172.83/172.50 [720]~E(x7201,x7202)+E(f671(x7203,x7201,x7204,x7205),f671(x7203,x7202,x7204,x7205)) % 172.83/172.50 [721]~E(x7211,x7212)+E(f671(x7213,x7214,x7211,x7215),f671(x7213,x7214,x7212,x7215)) % 172.83/172.50 [722]~E(x7221,x7222)+E(f671(x7223,x7224,x7225,x7221),f671(x7223,x7224,x7225,x7222)) % 172.83/172.50 [723]~E(x7231,x7232)+E(f797(x7231,x7233,x7234),f797(x7232,x7233,x7234)) % 172.83/172.50 [724]~E(x7241,x7242)+E(f797(x7243,x7241,x7244),f797(x7243,x7242,x7244)) % 172.83/172.50 [725]~E(x7251,x7252)+E(f797(x7253,x7254,x7251),f797(x7253,x7254,x7252)) % 172.83/172.50 [726]~E(x7261,x7262)+E(f862(x7261,x7263,x7264,x7265,x7266),f862(x7262,x7263,x7264,x7265,x7266)) % 172.83/172.50 [727]~E(x7271,x7272)+E(f862(x7273,x7271,x7274,x7275,x7276),f862(x7273,x7272,x7274,x7275,x7276)) % 172.83/172.50 [728]~E(x7281,x7282)+E(f862(x7283,x7284,x7281,x7285,x7286),f862(x7283,x7284,x7282,x7285,x7286)) % 172.83/172.50 [729]~E(x7291,x7292)+E(f862(x7293,x7294,x7295,x7291,x7296),f862(x7293,x7294,x7295,x7292,x7296)) % 172.83/172.50 [730]~E(x7301,x7302)+E(f862(x7303,x7304,x7305,x7306,x7301),f862(x7303,x7304,x7305,x7306,x7302)) % 172.83/172.50 [731]~E(x7311,x7312)+E(f822(x7311,x7313,x7314),f822(x7312,x7313,x7314)) % 172.83/172.50 [732]~E(x7321,x7322)+E(f822(x7323,x7321,x7324),f822(x7323,x7322,x7324)) % 172.83/172.50 [733]~E(x7331,x7332)+E(f822(x7333,x7334,x7331),f822(x7333,x7334,x7332)) % 172.83/172.50 [734]~E(x7341,x7342)+E(f87(x7341),f87(x7342)) % 172.83/172.50 [735]~E(x7351,x7352)+E(f443(x7351,x7353,x7354,x7355,x7356),f443(x7352,x7353,x7354,x7355,x7356)) % 172.83/172.50 [736]~E(x7361,x7362)+E(f443(x7363,x7361,x7364,x7365,x7366),f443(x7363,x7362,x7364,x7365,x7366)) % 172.83/172.50 [737]~E(x7371,x7372)+E(f443(x7373,x7374,x7371,x7375,x7376),f443(x7373,x7374,x7372,x7375,x7376)) % 172.83/172.50 [738]~E(x7381,x7382)+E(f443(x7383,x7384,x7385,x7381,x7386),f443(x7383,x7384,x7385,x7382,x7386)) % 172.83/172.50 [739]~E(x7391,x7392)+E(f443(x7393,x7394,x7395,x7396,x7391),f443(x7393,x7394,x7395,x7396,x7392)) % 172.83/172.50 [740]~E(x7401,x7402)+E(f427(x7401,x7403,x7404,x7405),f427(x7402,x7403,x7404,x7405)) % 172.83/172.50 [741]~E(x7411,x7412)+E(f427(x7413,x7411,x7414,x7415),f427(x7413,x7412,x7414,x7415)) % 172.83/172.50 [742]~E(x7421,x7422)+E(f427(x7423,x7424,x7421,x7425),f427(x7423,x7424,x7422,x7425)) % 172.83/172.50 [743]~E(x7431,x7432)+E(f427(x7433,x7434,x7435,x7431),f427(x7433,x7434,x7435,x7432)) % 172.83/172.50 [744]~E(x7441,x7442)+E(f191(x7441,x7443,x7444),f191(x7442,x7443,x7444)) % 172.83/172.50 [745]~E(x7451,x7452)+E(f191(x7453,x7451,x7454),f191(x7453,x7452,x7454)) % 172.83/172.50 [746]~E(x7461,x7462)+E(f191(x7463,x7464,x7461),f191(x7463,x7464,x7462)) % 172.83/172.50 [747]~E(x7471,x7472)+E(f92(x7471,x7473,x7474),f92(x7472,x7473,x7474)) % 172.83/172.50 [748]~E(x7481,x7482)+E(f92(x7483,x7481,x7484),f92(x7483,x7482,x7484)) % 172.83/172.50 [749]~E(x7491,x7492)+E(f92(x7493,x7494,x7491),f92(x7493,x7494,x7492)) % 172.83/172.50 [750]~E(x7501,x7502)+E(f431(x7501,x7503),f431(x7502,x7503)) % 172.83/172.50 [751]~E(x7511,x7512)+E(f431(x7513,x7511),f431(x7513,x7512)) % 172.83/172.50 [752]~E(x7521,x7522)+E(f66(x7521,x7523,x7524,x7525,x7526),f66(x7522,x7523,x7524,x7525,x7526)) % 172.83/172.50 [753]~E(x7531,x7532)+E(f66(x7533,x7531,x7534,x7535,x7536),f66(x7533,x7532,x7534,x7535,x7536)) % 172.83/172.50 [754]~E(x7541,x7542)+E(f66(x7543,x7544,x7541,x7545,x7546),f66(x7543,x7544,x7542,x7545,x7546)) % 172.83/172.50 [755]~E(x7551,x7552)+E(f66(x7553,x7554,x7555,x7551,x7556),f66(x7553,x7554,x7555,x7552,x7556)) % 172.83/172.50 [756]~E(x7561,x7562)+E(f66(x7563,x7564,x7565,x7566,x7561),f66(x7563,x7564,x7565,x7566,x7562)) % 172.83/172.50 [757]~E(x7571,x7572)+E(f67(x7571,x7573,x7574),f67(x7572,x7573,x7574)) % 172.83/172.50 [758]~E(x7581,x7582)+E(f67(x7583,x7581,x7584),f67(x7583,x7582,x7584)) % 172.83/172.50 [759]~E(x7591,x7592)+E(f67(x7593,x7594,x7591),f67(x7593,x7594,x7592)) % 172.83/172.50 [760]~E(x7601,x7602)+E(f867(x7601,x7603,x7604,x7605,x7606,x7607),f867(x7602,x7603,x7604,x7605,x7606,x7607)) % 172.83/172.50 [761]~E(x7611,x7612)+E(f867(x7613,x7611,x7614,x7615,x7616,x7617),f867(x7613,x7612,x7614,x7615,x7616,x7617)) % 172.83/172.50 [762]~E(x7621,x7622)+E(f867(x7623,x7624,x7621,x7625,x7626,x7627),f867(x7623,x7624,x7622,x7625,x7626,x7627)) % 172.83/172.50 [763]~E(x7631,x7632)+E(f867(x7633,x7634,x7635,x7631,x7636,x7637),f867(x7633,x7634,x7635,x7632,x7636,x7637)) % 172.83/172.50 [764]~E(x7641,x7642)+E(f867(x7643,x7644,x7645,x7646,x7641,x7647),f867(x7643,x7644,x7645,x7646,x7642,x7647)) % 172.83/172.50 [765]~E(x7651,x7652)+E(f867(x7653,x7654,x7655,x7656,x7657,x7651),f867(x7653,x7654,x7655,x7656,x7657,x7652)) % 172.83/172.50 [766]~E(x7661,x7662)+E(f121(x7661,x7663,x7664),f121(x7662,x7663,x7664)) % 172.83/172.50 [767]~E(x7671,x7672)+E(f121(x7673,x7671,x7674),f121(x7673,x7672,x7674)) % 172.83/172.50 [768]~E(x7681,x7682)+E(f121(x7683,x7684,x7681),f121(x7683,x7684,x7682)) % 172.83/172.50 [769]~E(x7691,x7692)+E(f750(x7691,x7693,x7694),f750(x7692,x7693,x7694)) % 172.83/172.50 [770]~E(x7701,x7702)+E(f750(x7703,x7701,x7704),f750(x7703,x7702,x7704)) % 172.83/172.50 [771]~E(x7711,x7712)+E(f750(x7713,x7714,x7711),f750(x7713,x7714,x7712)) % 172.83/172.50 [772]~E(x7721,x7722)+E(f456(x7721,x7723,x7724),f456(x7722,x7723,x7724)) % 172.83/172.50 [773]~E(x7731,x7732)+E(f456(x7733,x7731,x7734),f456(x7733,x7732,x7734)) % 172.83/172.50 [774]~E(x7741,x7742)+E(f456(x7743,x7744,x7741),f456(x7743,x7744,x7742)) % 172.83/172.50 [775]~E(x7751,x7752)+E(f175(x7751,x7753,x7754),f175(x7752,x7753,x7754)) % 172.83/172.50 [776]~E(x7761,x7762)+E(f175(x7763,x7761,x7764),f175(x7763,x7762,x7764)) % 172.83/172.50 [777]~E(x7771,x7772)+E(f175(x7773,x7774,x7771),f175(x7773,x7774,x7772)) % 172.83/172.50 [778]~E(x7781,x7782)+E(f43(x7781),f43(x7782)) % 172.83/172.50 [779]~E(x7791,x7792)+E(f628(x7791,x7793,x7794,x7795,x7796),f628(x7792,x7793,x7794,x7795,x7796)) % 172.83/172.50 [780]~E(x7801,x7802)+E(f628(x7803,x7801,x7804,x7805,x7806),f628(x7803,x7802,x7804,x7805,x7806)) % 172.83/172.50 [781]~E(x7811,x7812)+E(f628(x7813,x7814,x7811,x7815,x7816),f628(x7813,x7814,x7812,x7815,x7816)) % 172.83/172.50 [782]~E(x7821,x7822)+E(f628(x7823,x7824,x7825,x7821,x7826),f628(x7823,x7824,x7825,x7822,x7826)) % 172.83/172.50 [783]~E(x7831,x7832)+E(f628(x7833,x7834,x7835,x7836,x7831),f628(x7833,x7834,x7835,x7836,x7832)) % 172.83/172.50 [784]~E(x7841,x7842)+E(f649(x7841,x7843,x7844,x7845,x7846,x7847,x7848),f649(x7842,x7843,x7844,x7845,x7846,x7847,x7848)) % 172.83/172.50 [785]~E(x7851,x7852)+E(f649(x7853,x7851,x7854,x7855,x7856,x7857,x7858),f649(x7853,x7852,x7854,x7855,x7856,x7857,x7858)) % 172.83/172.50 [786]~E(x7861,x7862)+E(f649(x7863,x7864,x7861,x7865,x7866,x7867,x7868),f649(x7863,x7864,x7862,x7865,x7866,x7867,x7868)) % 172.83/172.50 [787]~E(x7871,x7872)+E(f649(x7873,x7874,x7875,x7871,x7876,x7877,x7878),f649(x7873,x7874,x7875,x7872,x7876,x7877,x7878)) % 172.83/172.50 [788]~E(x7881,x7882)+E(f649(x7883,x7884,x7885,x7886,x7881,x7887,x7888),f649(x7883,x7884,x7885,x7886,x7882,x7887,x7888)) % 172.83/172.50 [789]~E(x7891,x7892)+E(f649(x7893,x7894,x7895,x7896,x7897,x7891,x7898),f649(x7893,x7894,x7895,x7896,x7897,x7892,x7898)) % 172.83/172.50 [790]~E(x7901,x7902)+E(f649(x7903,x7904,x7905,x7906,x7907,x7908,x7901),f649(x7903,x7904,x7905,x7906,x7907,x7908,x7902)) % 172.83/172.50 [791]~E(x7911,x7912)+E(f243(x7911),f243(x7912)) % 172.83/172.50 [792]~E(x7921,x7922)+E(f119(x7921,x7923,x7924),f119(x7922,x7923,x7924)) % 172.83/172.50 [793]~E(x7931,x7932)+E(f119(x7933,x7931,x7934),f119(x7933,x7932,x7934)) % 172.83/172.50 [794]~E(x7941,x7942)+E(f119(x7943,x7944,x7941),f119(x7943,x7944,x7942)) % 172.83/172.50 [795]~E(x7951,x7952)+E(f565(x7951,x7953),f565(x7952,x7953)) % 172.83/172.50 [796]~E(x7961,x7962)+E(f565(x7963,x7961),f565(x7963,x7962)) % 172.83/172.50 [797]~E(x7971,x7972)+E(f598(x7971,x7973,x7974),f598(x7972,x7973,x7974)) % 172.83/172.50 [798]~E(x7981,x7982)+E(f598(x7983,x7981,x7984),f598(x7983,x7982,x7984)) % 172.83/172.50 [799]~E(x7991,x7992)+E(f598(x7993,x7994,x7991),f598(x7993,x7994,x7992)) % 172.83/172.50 [800]~E(x8001,x8002)+E(f494(x8001,x8003,x8004),f494(x8002,x8003,x8004)) % 172.83/172.50 [801]~E(x8011,x8012)+E(f494(x8013,x8011,x8014),f494(x8013,x8012,x8014)) % 172.83/172.50 [802]~E(x8021,x8022)+E(f494(x8023,x8024,x8021),f494(x8023,x8024,x8022)) % 172.83/172.50 [803]~E(x8031,x8032)+E(f695(x8031,x8033,x8034,x8035),f695(x8032,x8033,x8034,x8035)) % 172.83/172.50 [804]~E(x8041,x8042)+E(f695(x8043,x8041,x8044,x8045),f695(x8043,x8042,x8044,x8045)) % 172.83/172.50 [805]~E(x8051,x8052)+E(f695(x8053,x8054,x8051,x8055),f695(x8053,x8054,x8052,x8055)) % 172.83/172.50 [806]~E(x8061,x8062)+E(f695(x8063,x8064,x8065,x8061),f695(x8063,x8064,x8065,x8062)) % 172.83/172.50 [807]~E(x8071,x8072)+E(f454(x8071,x8073,x8074,x8075),f454(x8072,x8073,x8074,x8075)) % 172.83/172.50 [808]~E(x8081,x8082)+E(f454(x8083,x8081,x8084,x8085),f454(x8083,x8082,x8084,x8085)) % 172.83/172.50 [809]~E(x8091,x8092)+E(f454(x8093,x8094,x8091,x8095),f454(x8093,x8094,x8092,x8095)) % 172.83/172.50 [810]~E(x8101,x8102)+E(f454(x8103,x8104,x8105,x8101),f454(x8103,x8104,x8105,x8102)) % 172.83/172.50 [811]~E(x8111,x8112)+E(f615(x8111,x8113,x8114,x8115,x8116),f615(x8112,x8113,x8114,x8115,x8116)) % 172.83/172.50 [812]~E(x8121,x8122)+E(f615(x8123,x8121,x8124,x8125,x8126),f615(x8123,x8122,x8124,x8125,x8126)) % 172.83/172.50 [813]~E(x8131,x8132)+E(f615(x8133,x8134,x8131,x8135,x8136),f615(x8133,x8134,x8132,x8135,x8136)) % 172.83/172.50 [814]~E(x8141,x8142)+E(f615(x8143,x8144,x8145,x8141,x8146),f615(x8143,x8144,x8145,x8142,x8146)) % 172.83/172.50 [815]~E(x8151,x8152)+E(f615(x8153,x8154,x8155,x8156,x8151),f615(x8153,x8154,x8155,x8156,x8152)) % 172.83/172.50 [816]~E(x8161,x8162)+E(f657(x8161,x8163,x8164),f657(x8162,x8163,x8164)) % 172.83/172.50 [817]~E(x8171,x8172)+E(f657(x8173,x8171,x8174),f657(x8173,x8172,x8174)) % 172.83/172.50 [818]~E(x8181,x8182)+E(f657(x8183,x8184,x8181),f657(x8183,x8184,x8182)) % 172.83/172.50 [819]~E(x8191,x8192)+E(f411(x8191,x8193,x8194,x8195),f411(x8192,x8193,x8194,x8195)) % 172.83/172.50 [820]~E(x8201,x8202)+E(f411(x8203,x8201,x8204,x8205),f411(x8203,x8202,x8204,x8205)) % 172.83/172.50 [821]~E(x8211,x8212)+E(f411(x8213,x8214,x8211,x8215),f411(x8213,x8214,x8212,x8215)) % 172.83/172.50 [822]~E(x8221,x8222)+E(f411(x8223,x8224,x8225,x8221),f411(x8223,x8224,x8225,x8222)) % 172.83/172.50 [823]~E(x8231,x8232)+E(f583(x8231,x8233,x8234),f583(x8232,x8233,x8234)) % 172.83/172.50 [824]~E(x8241,x8242)+E(f583(x8243,x8241,x8244),f583(x8243,x8242,x8244)) % 172.83/172.50 [825]~E(x8251,x8252)+E(f583(x8253,x8254,x8251),f583(x8253,x8254,x8252)) % 172.83/172.50 [826]~E(x8261,x8262)+E(f426(x8261,x8263,x8264),f426(x8262,x8263,x8264)) % 172.83/172.50 [827]~E(x8271,x8272)+E(f426(x8273,x8271,x8274),f426(x8273,x8272,x8274)) % 172.83/172.50 [828]~E(x8281,x8282)+E(f426(x8283,x8284,x8281),f426(x8283,x8284,x8282)) % 172.83/172.50 [829]~E(x8291,x8292)+E(f377(x8291,x8293),f377(x8292,x8293)) % 172.83/172.50 [830]~E(x8301,x8302)+E(f377(x8303,x8301),f377(x8303,x8302)) % 172.83/172.50 [831]~E(x8311,x8312)+E(f304(x8311),f304(x8312)) % 172.83/172.50 [832]~E(x8321,x8322)+E(f279(x8321,x8323),f279(x8322,x8323)) % 172.83/172.50 [833]~E(x8331,x8332)+E(f279(x8333,x8331),f279(x8333,x8332)) % 172.83/172.50 [834]~E(x8341,x8342)+E(f855(x8341,x8343,x8344,x8345),f855(x8342,x8343,x8344,x8345)) % 172.83/172.50 [835]~E(x8351,x8352)+E(f855(x8353,x8351,x8354,x8355),f855(x8353,x8352,x8354,x8355)) % 172.83/172.50 [836]~E(x8361,x8362)+E(f855(x8363,x8364,x8361,x8365),f855(x8363,x8364,x8362,x8365)) % 172.83/172.50 [837]~E(x8371,x8372)+E(f855(x8373,x8374,x8375,x8371),f855(x8373,x8374,x8375,x8372)) % 172.83/172.50 [838]~E(x8381,x8382)+E(f611(x8381,x8383,x8384,x8385,x8386),f611(x8382,x8383,x8384,x8385,x8386)) % 172.83/172.50 [839]~E(x8391,x8392)+E(f611(x8393,x8391,x8394,x8395,x8396),f611(x8393,x8392,x8394,x8395,x8396)) % 172.83/172.50 [840]~E(x8401,x8402)+E(f611(x8403,x8404,x8401,x8405,x8406),f611(x8403,x8404,x8402,x8405,x8406)) % 172.83/172.50 [841]~E(x8411,x8412)+E(f611(x8413,x8414,x8415,x8411,x8416),f611(x8413,x8414,x8415,x8412,x8416)) % 172.83/172.50 [842]~E(x8421,x8422)+E(f611(x8423,x8424,x8425,x8426,x8421),f611(x8423,x8424,x8425,x8426,x8422)) % 172.83/172.50 [843]~E(x8431,x8432)+E(f372(x8431,x8433,x8434),f372(x8432,x8433,x8434)) % 172.83/172.50 [844]~E(x8441,x8442)+E(f372(x8443,x8441,x8444),f372(x8443,x8442,x8444)) % 172.83/172.50 [845]~E(x8451,x8452)+E(f372(x8453,x8454,x8451),f372(x8453,x8454,x8452)) % 172.83/172.50 [846]~E(x8461,x8462)+E(f503(x8461,x8463,x8464,x8465),f503(x8462,x8463,x8464,x8465)) % 172.83/172.50 [847]~E(x8471,x8472)+E(f503(x8473,x8471,x8474,x8475),f503(x8473,x8472,x8474,x8475)) % 172.83/172.50 [848]~E(x8481,x8482)+E(f503(x8483,x8484,x8481,x8485),f503(x8483,x8484,x8482,x8485)) % 172.83/172.50 [849]~E(x8491,x8492)+E(f503(x8493,x8494,x8495,x8491),f503(x8493,x8494,x8495,x8492)) % 172.83/172.50 [850]~E(x8501,x8502)+E(f363(x8501,x8503,x8504),f363(x8502,x8503,x8504)) % 172.83/172.50 [851]~E(x8511,x8512)+E(f363(x8513,x8511,x8514),f363(x8513,x8512,x8514)) % 172.83/172.50 [852]~E(x8521,x8522)+E(f363(x8523,x8524,x8521),f363(x8523,x8524,x8522)) % 172.83/172.50 [853]~E(x8531,x8532)+E(f577(x8531,x8533,x8534,x8535,x8536,x8537),f577(x8532,x8533,x8534,x8535,x8536,x8537)) % 172.83/172.50 [854]~E(x8541,x8542)+E(f577(x8543,x8541,x8544,x8545,x8546,x8547),f577(x8543,x8542,x8544,x8545,x8546,x8547)) % 172.83/172.50 [855]~E(x8551,x8552)+E(f577(x8553,x8554,x8551,x8555,x8556,x8557),f577(x8553,x8554,x8552,x8555,x8556,x8557)) % 172.83/172.50 [856]~E(x8561,x8562)+E(f577(x8563,x8564,x8565,x8561,x8566,x8567),f577(x8563,x8564,x8565,x8562,x8566,x8567)) % 172.83/172.50 [857]~E(x8571,x8572)+E(f577(x8573,x8574,x8575,x8576,x8571,x8577),f577(x8573,x8574,x8575,x8576,x8572,x8577)) % 172.83/172.50 [858]~E(x8581,x8582)+E(f577(x8583,x8584,x8585,x8586,x8587,x8581),f577(x8583,x8584,x8585,x8586,x8587,x8582)) % 172.83/172.50 [859]~E(x8591,x8592)+E(f262(x8591,x8593,x8594),f262(x8592,x8593,x8594)) % 172.83/172.50 [860]~E(x8601,x8602)+E(f262(x8603,x8601,x8604),f262(x8603,x8602,x8604)) % 172.83/172.50 [861]~E(x8611,x8612)+E(f262(x8613,x8614,x8611),f262(x8613,x8614,x8612)) % 172.83/172.50 [862]~E(x8621,x8622)+E(f495(x8621,x8623,x8624),f495(x8622,x8623,x8624)) % 172.83/172.50 [863]~E(x8631,x8632)+E(f495(x8633,x8631,x8634),f495(x8633,x8632,x8634)) % 172.83/172.50 [864]~E(x8641,x8642)+E(f495(x8643,x8644,x8641),f495(x8643,x8644,x8642)) % 172.83/172.50 [865]~E(x8651,x8652)+E(f299(x8651,x8653,x8654,x8655),f299(x8652,x8653,x8654,x8655)) % 172.83/172.50 [866]~E(x8661,x8662)+E(f299(x8663,x8661,x8664,x8665),f299(x8663,x8662,x8664,x8665)) % 172.83/172.50 [867]~E(x8671,x8672)+E(f299(x8673,x8674,x8671,x8675),f299(x8673,x8674,x8672,x8675)) % 172.83/172.50 [868]~E(x8681,x8682)+E(f299(x8683,x8684,x8685,x8681),f299(x8683,x8684,x8685,x8682)) % 172.83/172.50 [869]~E(x8691,x8692)+E(f591(x8691,x8693,x8694,x8695,x8696,x8697,x8698,x8699),f591(x8692,x8693,x8694,x8695,x8696,x8697,x8698,x8699)) % 172.83/172.50 [870]~E(x8701,x8702)+E(f591(x8703,x8701,x8704,x8705,x8706,x8707,x8708,x8709),f591(x8703,x8702,x8704,x8705,x8706,x8707,x8708,x8709)) % 172.83/172.50 [871]~E(x8711,x8712)+E(f591(x8713,x8714,x8711,x8715,x8716,x8717,x8718,x8719),f591(x8713,x8714,x8712,x8715,x8716,x8717,x8718,x8719)) % 172.83/172.50 [872]~E(x8721,x8722)+E(f591(x8723,x8724,x8725,x8721,x8726,x8727,x8728,x8729),f591(x8723,x8724,x8725,x8722,x8726,x8727,x8728,x8729)) % 172.83/172.50 [873]~E(x8731,x8732)+E(f591(x8733,x8734,x8735,x8736,x8731,x8737,x8738,x8739),f591(x8733,x8734,x8735,x8736,x8732,x8737,x8738,x8739)) % 172.83/172.50 [874]~E(x8741,x8742)+E(f591(x8743,x8744,x8745,x8746,x8747,x8741,x8748,x8749),f591(x8743,x8744,x8745,x8746,x8747,x8742,x8748,x8749)) % 172.83/172.50 [875]~E(x8751,x8752)+E(f591(x8753,x8754,x8755,x8756,x8757,x8758,x8751,x8759),f591(x8753,x8754,x8755,x8756,x8757,x8758,x8752,x8759)) % 172.83/172.50 [876]~E(x8761,x8762)+E(f591(x8763,x8764,x8765,x8766,x8767,x8768,x8769,x8761),f591(x8763,x8764,x8765,x8766,x8767,x8768,x8769,x8762)) % 172.83/172.50 [877]~E(x8771,x8772)+E(f484(x8771,x8773,x8774),f484(x8772,x8773,x8774)) % 172.83/172.50 [878]~E(x8781,x8782)+E(f484(x8783,x8781,x8784),f484(x8783,x8782,x8784)) % 172.83/172.50 [879]~E(x8791,x8792)+E(f484(x8793,x8794,x8791),f484(x8793,x8794,x8792)) % 172.83/172.50 [880]~E(x8801,x8802)+E(f506(x8801),f506(x8802)) % 172.83/172.50 [881]~E(x8811,x8812)+E(f325(x8811,x8813,x8814,x8815),f325(x8812,x8813,x8814,x8815)) % 172.83/172.50 [882]~E(x8821,x8822)+E(f325(x8823,x8821,x8824,x8825),f325(x8823,x8822,x8824,x8825)) % 172.83/172.50 [883]~E(x8831,x8832)+E(f325(x8833,x8834,x8831,x8835),f325(x8833,x8834,x8832,x8835)) % 172.83/172.50 [884]~E(x8841,x8842)+E(f325(x8843,x8844,x8845,x8841),f325(x8843,x8844,x8845,x8842)) % 172.83/172.50 [885]~E(x8851,x8852)+E(f550(x8851,x8853,x8854,x8855,x8856,x8857,x8858,x8859),f550(x8852,x8853,x8854,x8855,x8856,x8857,x8858,x8859)) % 172.83/172.50 [886]~E(x8861,x8862)+E(f550(x8863,x8861,x8864,x8865,x8866,x8867,x8868,x8869),f550(x8863,x8862,x8864,x8865,x8866,x8867,x8868,x8869)) % 172.83/172.50 [887]~E(x8871,x8872)+E(f550(x8873,x8874,x8871,x8875,x8876,x8877,x8878,x8879),f550(x8873,x8874,x8872,x8875,x8876,x8877,x8878,x8879)) % 172.83/172.50 [888]~E(x8881,x8882)+E(f550(x8883,x8884,x8885,x8881,x8886,x8887,x8888,x8889),f550(x8883,x8884,x8885,x8882,x8886,x8887,x8888,x8889)) % 172.83/172.50 [889]~E(x8891,x8892)+E(f550(x8893,x8894,x8895,x8896,x8891,x8897,x8898,x8899),f550(x8893,x8894,x8895,x8896,x8892,x8897,x8898,x8899)) % 172.83/172.50 [890]~E(x8901,x8902)+E(f550(x8903,x8904,x8905,x8906,x8907,x8901,x8908,x8909),f550(x8903,x8904,x8905,x8906,x8907,x8902,x8908,x8909)) % 172.83/172.50 [891]~E(x8911,x8912)+E(f550(x8913,x8914,x8915,x8916,x8917,x8918,x8911,x8919),f550(x8913,x8914,x8915,x8916,x8917,x8918,x8912,x8919)) % 172.83/172.50 [892]~E(x8921,x8922)+E(f550(x8923,x8924,x8925,x8926,x8927,x8928,x8929,x8921),f550(x8923,x8924,x8925,x8926,x8927,x8928,x8929,x8922)) % 172.83/172.50 [893]~E(x8931,x8932)+E(f150(x8931,x8933,x8934,x8935),f150(x8932,x8933,x8934,x8935)) % 172.83/172.50 [894]~E(x8941,x8942)+E(f150(x8943,x8941,x8944,x8945),f150(x8943,x8942,x8944,x8945)) % 172.83/172.50 [895]~E(x8951,x8952)+E(f150(x8953,x8954,x8951,x8955),f150(x8953,x8954,x8952,x8955)) % 172.83/172.50 [896]~E(x8961,x8962)+E(f150(x8963,x8964,x8965,x8961),f150(x8963,x8964,x8965,x8962)) % 172.83/172.50 [897]~E(x8971,x8972)+E(f624(x8971,x8973,x8974,x8975),f624(x8972,x8973,x8974,x8975)) % 172.83/172.50 [898]~E(x8981,x8982)+E(f624(x8983,x8981,x8984,x8985),f624(x8983,x8982,x8984,x8985)) % 172.83/172.50 [899]~E(x8991,x8992)+E(f624(x8993,x8994,x8991,x8995),f624(x8993,x8994,x8992,x8995)) % 172.83/172.50 [900]~E(x9001,x9002)+E(f624(x9003,x9004,x9005,x9001),f624(x9003,x9004,x9005,x9002)) % 172.83/172.50 [901]~E(x9011,x9012)+E(f94(x9011,x9013,x9014),f94(x9012,x9013,x9014)) % 172.83/172.50 [902]~E(x9021,x9022)+E(f94(x9023,x9021,x9024),f94(x9023,x9022,x9024)) % 172.83/172.50 [903]~E(x9031,x9032)+E(f94(x9033,x9034,x9031),f94(x9033,x9034,x9032)) % 172.83/172.50 [904]~E(x9041,x9042)+E(f285(x9041),f285(x9042)) % 172.83/172.50 [905]~E(x9051,x9052)+E(f851(x9051,x9053,x9054,x9055,x9056,x9057),f851(x9052,x9053,x9054,x9055,x9056,x9057)) % 172.83/172.50 [906]~E(x9061,x9062)+E(f851(x9063,x9061,x9064,x9065,x9066,x9067),f851(x9063,x9062,x9064,x9065,x9066,x9067)) % 172.83/172.50 [907]~E(x9071,x9072)+E(f851(x9073,x9074,x9071,x9075,x9076,x9077),f851(x9073,x9074,x9072,x9075,x9076,x9077)) % 172.83/172.50 [908]~E(x9081,x9082)+E(f851(x9083,x9084,x9085,x9081,x9086,x9087),f851(x9083,x9084,x9085,x9082,x9086,x9087)) % 172.83/172.50 [909]~E(x9091,x9092)+E(f851(x9093,x9094,x9095,x9096,x9091,x9097),f851(x9093,x9094,x9095,x9096,x9092,x9097)) % 172.83/172.50 [910]~E(x9101,x9102)+E(f851(x9103,x9104,x9105,x9106,x9107,x9101),f851(x9103,x9104,x9105,x9106,x9107,x9102)) % 172.83/172.50 [911]~E(x9111,x9112)+E(f589(x9111,x9113,x9114,x9115,x9116),f589(x9112,x9113,x9114,x9115,x9116)) % 172.83/172.50 [912]~E(x9121,x9122)+E(f589(x9123,x9121,x9124,x9125,x9126),f589(x9123,x9122,x9124,x9125,x9126)) % 172.83/172.50 [913]~E(x9131,x9132)+E(f589(x9133,x9134,x9131,x9135,x9136),f589(x9133,x9134,x9132,x9135,x9136)) % 172.83/172.50 [914]~E(x9141,x9142)+E(f589(x9143,x9144,x9145,x9141,x9146),f589(x9143,x9144,x9145,x9142,x9146)) % 172.83/172.50 [915]~E(x9151,x9152)+E(f589(x9153,x9154,x9155,x9156,x9151),f589(x9153,x9154,x9155,x9156,x9152)) % 172.83/172.50 [916]~E(x9161,x9162)+E(f700(x9161,x9163,x9164,x9165,x9166),f700(x9162,x9163,x9164,x9165,x9166)) % 172.83/172.50 [917]~E(x9171,x9172)+E(f700(x9173,x9171,x9174,x9175,x9176),f700(x9173,x9172,x9174,x9175,x9176)) % 172.83/172.50 [918]~E(x9181,x9182)+E(f700(x9183,x9184,x9181,x9185,x9186),f700(x9183,x9184,x9182,x9185,x9186)) % 172.83/172.50 [919]~E(x9191,x9192)+E(f700(x9193,x9194,x9195,x9191,x9196),f700(x9193,x9194,x9195,x9192,x9196)) % 172.83/172.50 [920]~E(x9201,x9202)+E(f700(x9203,x9204,x9205,x9206,x9201),f700(x9203,x9204,x9205,x9206,x9202)) % 172.83/172.50 [921]~E(x9211,x9212)+E(f588(x9211,x9213,x9214,x9215),f588(x9212,x9213,x9214,x9215)) % 172.83/172.50 [922]~E(x9221,x9222)+E(f588(x9223,x9221,x9224,x9225),f588(x9223,x9222,x9224,x9225)) % 172.83/172.50 [923]~E(x9231,x9232)+E(f588(x9233,x9234,x9231,x9235),f588(x9233,x9234,x9232,x9235)) % 172.83/172.50 [924]~E(x9241,x9242)+E(f588(x9243,x9244,x9245,x9241),f588(x9243,x9244,x9245,x9242)) % 172.83/172.50 [925]~E(x9251,x9252)+E(f679(x9251,x9253,x9254),f679(x9252,x9253,x9254)) % 172.83/172.50 [926]~E(x9261,x9262)+E(f679(x9263,x9261,x9264),f679(x9263,x9262,x9264)) % 172.83/172.50 [927]~E(x9271,x9272)+E(f679(x9273,x9274,x9271),f679(x9273,x9274,x9272)) % 172.83/172.50 [928]~E(x9281,x9282)+E(f775(x9281,x9283,x9284,x9285,x9286),f775(x9282,x9283,x9284,x9285,x9286)) % 172.83/172.50 [929]~E(x9291,x9292)+E(f775(x9293,x9291,x9294,x9295,x9296),f775(x9293,x9292,x9294,x9295,x9296)) % 172.83/172.50 [930]~E(x9301,x9302)+E(f775(x9303,x9304,x9301,x9305,x9306),f775(x9303,x9304,x9302,x9305,x9306)) % 172.83/172.50 [931]~E(x9311,x9312)+E(f775(x9313,x9314,x9315,x9311,x9316),f775(x9313,x9314,x9315,x9312,x9316)) % 172.83/172.50 [932]~E(x9321,x9322)+E(f775(x9323,x9324,x9325,x9326,x9321),f775(x9323,x9324,x9325,x9326,x9322)) % 172.83/172.50 [933]~E(x9331,x9332)+E(f122(x9331,x9333),f122(x9332,x9333)) % 172.83/172.50 [934]~E(x9341,x9342)+E(f122(x9343,x9341),f122(x9343,x9342)) % 172.83/172.50 [935]~E(x9351,x9352)+E(f53(x9351,x9353),f53(x9352,x9353)) % 172.83/172.50 [936]~E(x9361,x9362)+E(f53(x9363,x9361),f53(x9363,x9362)) % 172.83/172.50 [937]~E(x9371,x9372)+E(f688(x9371,x9373,x9374,x9375),f688(x9372,x9373,x9374,x9375)) % 172.83/172.50 [938]~E(x9381,x9382)+E(f688(x9383,x9381,x9384,x9385),f688(x9383,x9382,x9384,x9385)) % 172.83/172.50 [939]~E(x9391,x9392)+E(f688(x9393,x9394,x9391,x9395),f688(x9393,x9394,x9392,x9395)) % 172.83/172.50 [940]~E(x9401,x9402)+E(f688(x9403,x9404,x9405,x9401),f688(x9403,x9404,x9405,x9402)) % 172.83/172.50 [941]~E(x9411,x9412)+E(f425(x9411,x9413,x9414),f425(x9412,x9413,x9414)) % 172.83/172.50 [942]~E(x9421,x9422)+E(f425(x9423,x9421,x9424),f425(x9423,x9422,x9424)) % 172.83/172.50 [943]~E(x9431,x9432)+E(f425(x9433,x9434,x9431),f425(x9433,x9434,x9432)) % 172.83/172.50 [944]~E(x9441,x9442)+E(f739(x9441,x9443,x9444,x9445,x9446),f739(x9442,x9443,x9444,x9445,x9446)) % 172.83/172.50 [945]~E(x9451,x9452)+E(f739(x9453,x9451,x9454,x9455,x9456),f739(x9453,x9452,x9454,x9455,x9456)) % 172.83/172.50 [946]~E(x9461,x9462)+E(f739(x9463,x9464,x9461,x9465,x9466),f739(x9463,x9464,x9462,x9465,x9466)) % 172.83/172.50 [947]~E(x9471,x9472)+E(f739(x9473,x9474,x9475,x9471,x9476),f739(x9473,x9474,x9475,x9472,x9476)) % 172.83/172.50 [948]~E(x9481,x9482)+E(f739(x9483,x9484,x9485,x9486,x9481),f739(x9483,x9484,x9485,x9486,x9482)) % 172.83/172.50 [949]~E(x9491,x9492)+E(f362(x9491,x9493,x9494),f362(x9492,x9493,x9494)) % 172.83/172.50 [950]~E(x9501,x9502)+E(f362(x9503,x9501,x9504),f362(x9503,x9502,x9504)) % 172.83/172.50 [951]~E(x9511,x9512)+E(f362(x9513,x9514,x9511),f362(x9513,x9514,x9512)) % 172.83/172.50 [952]~E(x9521,x9522)+E(f480(x9521,x9523,x9524),f480(x9522,x9523,x9524)) % 172.83/172.50 [953]~E(x9531,x9532)+E(f480(x9533,x9531,x9534),f480(x9533,x9532,x9534)) % 172.83/172.50 [954]~E(x9541,x9542)+E(f480(x9543,x9544,x9541),f480(x9543,x9544,x9542)) % 172.83/172.50 [955]~E(x9551,x9552)+E(f351(x9551,x9553,x9554),f351(x9552,x9553,x9554)) % 172.83/172.50 [956]~E(x9561,x9562)+E(f351(x9563,x9561,x9564),f351(x9563,x9562,x9564)) % 172.83/172.50 [957]~E(x9571,x9572)+E(f351(x9573,x9574,x9571),f351(x9573,x9574,x9572)) % 172.83/172.50 [958]~E(x9581,x9582)+E(f545(x9581,x9583,x9584,x9585),f545(x9582,x9583,x9584,x9585)) % 172.83/172.50 [959]~E(x9591,x9592)+E(f545(x9593,x9591,x9594,x9595),f545(x9593,x9592,x9594,x9595)) % 172.83/172.50 [960]~E(x9601,x9602)+E(f545(x9603,x9604,x9601,x9605),f545(x9603,x9604,x9602,x9605)) % 172.83/172.50 [961]~E(x9611,x9612)+E(f545(x9613,x9614,x9615,x9611),f545(x9613,x9614,x9615,x9612)) % 172.83/172.50 [962]~E(x9621,x9622)+E(f276(x9621,x9623),f276(x9622,x9623)) % 172.83/172.50 [963]~E(x9631,x9632)+E(f276(x9633,x9631),f276(x9633,x9632)) % 172.83/172.50 [964]~E(x9641,x9642)+E(f732(x9641,x9643,x9644,x9645),f732(x9642,x9643,x9644,x9645)) % 172.83/172.50 [965]~E(x9651,x9652)+E(f732(x9653,x9651,x9654,x9655),f732(x9653,x9652,x9654,x9655)) % 172.83/172.50 [966]~E(x9661,x9662)+E(f732(x9663,x9664,x9661,x9665),f732(x9663,x9664,x9662,x9665)) % 172.83/172.50 [967]~E(x9671,x9672)+E(f732(x9673,x9674,x9675,x9671),f732(x9673,x9674,x9675,x9672)) % 172.83/172.50 [968]~E(x9681,x9682)+E(f733(x9681,x9683,x9684,x9685),f733(x9682,x9683,x9684,x9685)) % 172.83/172.50 [969]~E(x9691,x9692)+E(f733(x9693,x9691,x9694,x9695),f733(x9693,x9692,x9694,x9695)) % 172.83/172.50 [970]~E(x9701,x9702)+E(f733(x9703,x9704,x9701,x9705),f733(x9703,x9704,x9702,x9705)) % 172.83/172.50 [971]~E(x9711,x9712)+E(f733(x9713,x9714,x9715,x9711),f733(x9713,x9714,x9715,x9712)) % 172.83/172.50 [972]~E(x9721,x9722)+E(f727(x9721,x9723),f727(x9722,x9723)) % 172.83/172.50 [973]~E(x9731,x9732)+E(f727(x9733,x9731),f727(x9733,x9732)) % 172.83/172.50 [974]~E(x9741,x9742)+E(f127(x9741,x9743,x9744),f127(x9742,x9743,x9744)) % 172.83/172.50 [975]~E(x9751,x9752)+E(f127(x9753,x9751,x9754),f127(x9753,x9752,x9754)) % 172.83/172.50 [976]~E(x9761,x9762)+E(f127(x9763,x9764,x9761),f127(x9763,x9764,x9762)) % 172.83/172.50 [977]~E(x9771,x9772)+E(f757(x9771,x9773),f757(x9772,x9773)) % 172.83/172.50 [978]~E(x9781,x9782)+E(f757(x9783,x9781),f757(x9783,x9782)) % 172.83/172.50 [979]~E(x9791,x9792)+E(f192(x9791,x9793,x9794,x9795),f192(x9792,x9793,x9794,x9795)) % 172.83/172.50 [980]~E(x9801,x9802)+E(f192(x9803,x9801,x9804,x9805),f192(x9803,x9802,x9804,x9805)) % 172.83/172.50 [981]~E(x9811,x9812)+E(f192(x9813,x9814,x9811,x9815),f192(x9813,x9814,x9812,x9815)) % 172.83/172.50 [982]~E(x9821,x9822)+E(f192(x9823,x9824,x9825,x9821),f192(x9823,x9824,x9825,x9822)) % 172.83/172.50 [983]~E(x9831,x9832)+E(f143(x9831,x9833),f143(x9832,x9833)) % 172.83/172.50 [984]~E(x9841,x9842)+E(f143(x9843,x9841),f143(x9843,x9842)) % 172.83/172.50 [985]~E(x9851,x9852)+E(f737(x9851,x9853),f737(x9852,x9853)) % 172.83/172.50 [986]~E(x9861,x9862)+E(f737(x9863,x9861),f737(x9863,x9862)) % 172.83/172.50 [987]~E(x9871,x9872)+E(f856(x9871,x9873,x9874),f856(x9872,x9873,x9874)) % 172.83/172.50 [988]~E(x9881,x9882)+E(f856(x9883,x9881,x9884),f856(x9883,x9882,x9884)) % 172.83/172.50 [989]~E(x9891,x9892)+E(f856(x9893,x9894,x9891),f856(x9893,x9894,x9892)) % 172.83/172.50 [990]~E(x9901,x9902)+E(f699(x9901,x9903,x9904,x9905,x9906),f699(x9902,x9903,x9904,x9905,x9906)) % 172.83/172.50 [991]~E(x9911,x9912)+E(f699(x9913,x9911,x9914,x9915,x9916),f699(x9913,x9912,x9914,x9915,x9916)) % 172.83/172.50 [992]~E(x9921,x9922)+E(f699(x9923,x9924,x9921,x9925,x9926),f699(x9923,x9924,x9922,x9925,x9926)) % 172.83/172.50 [993]~E(x9931,x9932)+E(f699(x9933,x9934,x9935,x9931,x9936),f699(x9933,x9934,x9935,x9932,x9936)) % 172.83/172.50 [994]~E(x9941,x9942)+E(f699(x9943,x9944,x9945,x9946,x9941),f699(x9943,x9944,x9945,x9946,x9942)) % 172.83/172.50 [995]~E(x9951,x9952)+E(f612(x9951,x9953,x9954,x9955,x9956),f612(x9952,x9953,x9954,x9955,x9956)) % 172.83/172.50 [996]~E(x9961,x9962)+E(f612(x9963,x9961,x9964,x9965,x9966),f612(x9963,x9962,x9964,x9965,x9966)) % 172.83/172.50 [997]~E(x9971,x9972)+E(f612(x9973,x9974,x9971,x9975,x9976),f612(x9973,x9974,x9972,x9975,x9976)) % 172.83/172.50 [998]~E(x9981,x9982)+E(f612(x9983,x9984,x9985,x9981,x9986),f612(x9983,x9984,x9985,x9982,x9986)) % 172.83/172.50 [999]~E(x9991,x9992)+E(f612(x9993,x9994,x9995,x9996,x9991),f612(x9993,x9994,x9995,x9996,x9992)) % 172.83/172.50 [1000]~E(x10001,x10002)+E(f126(x10001),f126(x10002)) % 172.83/172.50 [1001]~E(x10011,x10012)+E(f670(x10011,x10013,x10014,x10015),f670(x10012,x10013,x10014,x10015)) % 172.83/172.50 [1002]~E(x10021,x10022)+E(f670(x10023,x10021,x10024,x10025),f670(x10023,x10022,x10024,x10025)) % 172.83/172.50 [1003]~E(x10031,x10032)+E(f670(x10033,x10034,x10031,x10035),f670(x10033,x10034,x10032,x10035)) % 172.83/172.50 [1004]~E(x10041,x10042)+E(f670(x10043,x10044,x10045,x10041),f670(x10043,x10044,x10045,x10042)) % 172.83/172.50 [1005]~E(x10051,x10052)+E(f568(x10051,x10053),f568(x10052,x10053)) % 172.83/172.50 [1006]~E(x10061,x10062)+E(f568(x10063,x10061),f568(x10063,x10062)) % 172.83/172.50 [1007]~E(x10071,x10072)+E(f301(x10071),f301(x10072)) % 172.83/172.50 [1008]~E(x10081,x10082)+E(f618(x10081,x10083,x10084,x10085,x10086),f618(x10082,x10083,x10084,x10085,x10086)) % 172.83/172.50 [1009]~E(x10091,x10092)+E(f618(x10093,x10091,x10094,x10095,x10096),f618(x10093,x10092,x10094,x10095,x10096)) % 172.83/172.50 [1010]~E(x10101,x10102)+E(f618(x10103,x10104,x10101,x10105,x10106),f618(x10103,x10104,x10102,x10105,x10106)) % 172.83/172.50 [1011]~E(x10111,x10112)+E(f618(x10113,x10114,x10115,x10111,x10116),f618(x10113,x10114,x10115,x10112,x10116)) % 172.83/172.50 [1012]~E(x10121,x10122)+E(f618(x10123,x10124,x10125,x10126,x10121),f618(x10123,x10124,x10125,x10126,x10122)) % 172.83/172.50 [1013]~E(x10131,x10132)+E(f810(x10131,x10133,x10134),f810(x10132,x10133,x10134)) % 172.83/172.50 [1014]~E(x10141,x10142)+E(f810(x10143,x10141,x10144),f810(x10143,x10142,x10144)) % 172.83/172.50 [1015]~E(x10151,x10152)+E(f810(x10153,x10154,x10151),f810(x10153,x10154,x10152)) % 172.83/172.50 [1016]~E(x10161,x10162)+E(f459(x10161,x10163,x10164,x10165),f459(x10162,x10163,x10164,x10165)) % 172.83/172.50 [1017]~E(x10171,x10172)+E(f459(x10173,x10171,x10174,x10175),f459(x10173,x10172,x10174,x10175)) % 172.83/172.50 [1018]~E(x10181,x10182)+E(f459(x10183,x10184,x10181,x10185),f459(x10183,x10184,x10182,x10185)) % 172.83/172.50 [1019]~E(x10191,x10192)+E(f459(x10193,x10194,x10195,x10191),f459(x10193,x10194,x10195,x10192)) % 172.83/172.50 [1020]~E(x10201,x10202)+E(f455(x10201,x10203,x10204,x10205),f455(x10202,x10203,x10204,x10205)) % 172.83/172.50 [1021]~E(x10211,x10212)+E(f455(x10213,x10211,x10214,x10215),f455(x10213,x10212,x10214,x10215)) % 172.83/172.50 [1022]~E(x10221,x10222)+E(f455(x10223,x10224,x10221,x10225),f455(x10223,x10224,x10222,x10225)) % 172.83/172.50 [1023]~E(x10231,x10232)+E(f455(x10233,x10234,x10235,x10231),f455(x10233,x10234,x10235,x10232)) % 172.83/172.50 [1024]~E(x10241,x10242)+E(f284(x10241,x10243,x10244,x10245),f284(x10242,x10243,x10244,x10245)) % 172.83/172.50 [1025]~E(x10251,x10252)+E(f284(x10253,x10251,x10254,x10255),f284(x10253,x10252,x10254,x10255)) % 172.83/172.50 [1026]~E(x10261,x10262)+E(f284(x10263,x10264,x10261,x10265),f284(x10263,x10264,x10262,x10265)) % 172.83/172.50 [1027]~E(x10271,x10272)+E(f284(x10273,x10274,x10275,x10271),f284(x10273,x10274,x10275,x10272)) % 172.83/172.50 [1028]~E(x10281,x10282)+E(f580(x10281,x10283,x10284,x10285,x10286),f580(x10282,x10283,x10284,x10285,x10286)) % 172.83/172.50 [1029]~E(x10291,x10292)+E(f580(x10293,x10291,x10294,x10295,x10296),f580(x10293,x10292,x10294,x10295,x10296)) % 172.83/172.50 [1030]~E(x10301,x10302)+E(f580(x10303,x10304,x10301,x10305,x10306),f580(x10303,x10304,x10302,x10305,x10306)) % 172.83/172.50 [1031]~E(x10311,x10312)+E(f580(x10313,x10314,x10315,x10311,x10316),f580(x10313,x10314,x10315,x10312,x10316)) % 172.83/172.50 [1032]~E(x10321,x10322)+E(f580(x10323,x10324,x10325,x10326,x10321),f580(x10323,x10324,x10325,x10326,x10322)) % 172.83/172.50 [1033]~E(x10331,x10332)+E(f677(x10331,x10333,x10334,x10335,x10336),f677(x10332,x10333,x10334,x10335,x10336)) % 172.83/172.50 [1034]~E(x10341,x10342)+E(f677(x10343,x10341,x10344,x10345,x10346),f677(x10343,x10342,x10344,x10345,x10346)) % 172.83/172.50 [1035]~E(x10351,x10352)+E(f677(x10353,x10354,x10351,x10355,x10356),f677(x10353,x10354,x10352,x10355,x10356)) % 172.83/172.50 [1036]~E(x10361,x10362)+E(f677(x10363,x10364,x10365,x10361,x10366),f677(x10363,x10364,x10365,x10362,x10366)) % 172.83/172.50 [1037]~E(x10371,x10372)+E(f677(x10373,x10374,x10375,x10376,x10371),f677(x10373,x10374,x10375,x10376,x10372)) % 172.83/172.50 [1038]~E(x10381,x10382)+E(f780(x10381,x10383,x10384),f780(x10382,x10383,x10384)) % 172.83/172.50 [1039]~E(x10391,x10392)+E(f780(x10393,x10391,x10394),f780(x10393,x10392,x10394)) % 172.83/172.50 [1040]~E(x10401,x10402)+E(f780(x10403,x10404,x10401),f780(x10403,x10404,x10402)) % 172.83/172.50 [1041]~E(x10411,x10412)+E(f355(x10411,x10413,x10414),f355(x10412,x10413,x10414)) % 172.83/172.50 [1042]~E(x10421,x10422)+E(f355(x10423,x10421,x10424),f355(x10423,x10422,x10424)) % 172.83/172.50 [1043]~E(x10431,x10432)+E(f355(x10433,x10434,x10431),f355(x10433,x10434,x10432)) % 172.83/172.50 [1044]~E(x10441,x10442)+E(f241(x10441,x10443,x10444,x10445),f241(x10442,x10443,x10444,x10445)) % 172.83/172.50 [1045]~E(x10451,x10452)+E(f241(x10453,x10451,x10454,x10455),f241(x10453,x10452,x10454,x10455)) % 172.83/172.50 [1046]~E(x10461,x10462)+E(f241(x10463,x10464,x10461,x10465),f241(x10463,x10464,x10462,x10465)) % 172.83/172.50 [1047]~E(x10471,x10472)+E(f241(x10473,x10474,x10475,x10471),f241(x10473,x10474,x10475,x10472)) % 172.83/172.50 [1048]~E(x10481,x10482)+E(f546(x10481,x10483,x10484,x10485,x10486),f546(x10482,x10483,x10484,x10485,x10486)) % 172.83/172.50 [1049]~E(x10491,x10492)+E(f546(x10493,x10491,x10494,x10495,x10496),f546(x10493,x10492,x10494,x10495,x10496)) % 172.83/172.50 [1050]~E(x10501,x10502)+E(f546(x10503,x10504,x10501,x10505,x10506),f546(x10503,x10504,x10502,x10505,x10506)) % 172.83/172.50 [1051]~E(x10511,x10512)+E(f546(x10513,x10514,x10515,x10511,x10516),f546(x10513,x10514,x10515,x10512,x10516)) % 172.83/172.50 [1052]~E(x10521,x10522)+E(f546(x10523,x10524,x10525,x10526,x10521),f546(x10523,x10524,x10525,x10526,x10522)) % 172.83/172.50 [1053]~E(x10531,x10532)+E(f559(x10531,x10533,x10534),f559(x10532,x10533,x10534)) % 172.83/172.50 [1054]~E(x10541,x10542)+E(f559(x10543,x10541,x10544),f559(x10543,x10542,x10544)) % 172.83/172.50 [1055]~E(x10551,x10552)+E(f559(x10553,x10554,x10551),f559(x10553,x10554,x10552)) % 172.83/172.50 [1056]~E(x10561,x10562)+E(f460(x10561,x10563),f460(x10562,x10563)) % 172.83/172.50 [1057]~E(x10571,x10572)+E(f460(x10573,x10571),f460(x10573,x10572)) % 172.83/172.50 [1058]~E(x10581,x10582)+E(f348(x10581,x10583,x10584),f348(x10582,x10583,x10584)) % 172.83/172.50 [1059]~E(x10591,x10592)+E(f348(x10593,x10591,x10594),f348(x10593,x10592,x10594)) % 172.83/172.50 [1060]~E(x10601,x10602)+E(f348(x10603,x10604,x10601),f348(x10603,x10604,x10602)) % 172.83/172.50 [1061]~E(x10611,x10612)+E(f641(x10611,x10613,x10614),f641(x10612,x10613,x10614)) % 172.83/172.50 [1062]~E(x10621,x10622)+E(f641(x10623,x10621,x10624),f641(x10623,x10622,x10624)) % 172.83/172.50 [1063]~E(x10631,x10632)+E(f641(x10633,x10634,x10631),f641(x10633,x10634,x10632)) % 172.83/172.50 [1064]~E(x10641,x10642)+E(f469(x10641,x10643,x10644),f469(x10642,x10643,x10644)) % 172.83/172.50 [1065]~E(x10651,x10652)+E(f469(x10653,x10651,x10654),f469(x10653,x10652,x10654)) % 172.83/172.50 [1066]~E(x10661,x10662)+E(f469(x10663,x10664,x10661),f469(x10663,x10664,x10662)) % 172.83/172.50 [1067]~E(x10671,x10672)+E(f120(x10671,x10673,x10674),f120(x10672,x10673,x10674)) % 172.83/172.50 [1068]~E(x10681,x10682)+E(f120(x10683,x10681,x10684),f120(x10683,x10682,x10684)) % 172.83/172.50 [1069]~E(x10691,x10692)+E(f120(x10693,x10694,x10691),f120(x10693,x10694,x10692)) % 172.83/172.50 [1070]~E(x10701,x10702)+E(f638(x10701,x10703,x10704),f638(x10702,x10703,x10704)) % 172.83/172.50 [1071]~E(x10711,x10712)+E(f638(x10713,x10711,x10714),f638(x10713,x10712,x10714)) % 172.83/172.50 [1072]~E(x10721,x10722)+E(f638(x10723,x10724,x10721),f638(x10723,x10724,x10722)) % 172.83/172.50 [1073]~E(x10731,x10732)+E(f837(x10731,x10733),f837(x10732,x10733)) % 172.83/172.50 [1074]~E(x10741,x10742)+E(f837(x10743,x10741),f837(x10743,x10742)) % 172.83/172.50 [1075]~E(x10751,x10752)+E(f791(x10751,x10753,x10754,x10755,x10756,x10757,x10758),f791(x10752,x10753,x10754,x10755,x10756,x10757,x10758)) % 172.83/172.50 [1076]~E(x10761,x10762)+E(f791(x10763,x10761,x10764,x10765,x10766,x10767,x10768),f791(x10763,x10762,x10764,x10765,x10766,x10767,x10768)) % 172.83/172.50 [1077]~E(x10771,x10772)+E(f791(x10773,x10774,x10771,x10775,x10776,x10777,x10778),f791(x10773,x10774,x10772,x10775,x10776,x10777,x10778)) % 172.83/172.50 [1078]~E(x10781,x10782)+E(f791(x10783,x10784,x10785,x10781,x10786,x10787,x10788),f791(x10783,x10784,x10785,x10782,x10786,x10787,x10788)) % 172.83/172.50 [1079]~E(x10791,x10792)+E(f791(x10793,x10794,x10795,x10796,x10791,x10797,x10798),f791(x10793,x10794,x10795,x10796,x10792,x10797,x10798)) % 172.83/172.50 [1080]~E(x10801,x10802)+E(f791(x10803,x10804,x10805,x10806,x10807,x10801,x10808),f791(x10803,x10804,x10805,x10806,x10807,x10802,x10808)) % 172.83/172.50 [1081]~E(x10811,x10812)+E(f791(x10813,x10814,x10815,x10816,x10817,x10818,x10811),f791(x10813,x10814,x10815,x10816,x10817,x10818,x10812)) % 172.83/172.50 [1082]~E(x10821,x10822)+E(f375(x10821),f375(x10822)) % 172.83/172.50 [1083]~E(x10831,x10832)+E(f762(x10831,x10833),f762(x10832,x10833)) % 172.83/172.50 [1084]~E(x10841,x10842)+E(f762(x10843,x10841),f762(x10843,x10842)) % 172.83/172.50 [1085]~E(x10851,x10852)+E(f590(x10851,x10853,x10854),f590(x10852,x10853,x10854)) % 172.83/172.50 [1086]~E(x10861,x10862)+E(f590(x10863,x10861,x10864),f590(x10863,x10862,x10864)) % 172.83/172.50 [1087]~E(x10871,x10872)+E(f590(x10873,x10874,x10871),f590(x10873,x10874,x10872)) % 172.83/172.50 [1088]~E(x10881,x10882)+E(f723(x10881,x10883,x10884),f723(x10882,x10883,x10884)) % 172.83/172.50 [1089]~E(x10891,x10892)+E(f723(x10893,x10891,x10894),f723(x10893,x10892,x10894)) % 172.83/172.50 [1090]~E(x10901,x10902)+E(f723(x10903,x10904,x10901),f723(x10903,x10904,x10902)) % 172.83/172.50 [1091]~E(x10911,x10912)+E(f396(x10911,x10913,x10914,x10915),f396(x10912,x10913,x10914,x10915)) % 172.83/172.50 [1092]~E(x10921,x10922)+E(f396(x10923,x10921,x10924,x10925),f396(x10923,x10922,x10924,x10925)) % 172.83/172.50 [1093]~E(x10931,x10932)+E(f396(x10933,x10934,x10931,x10935),f396(x10933,x10934,x10932,x10935)) % 172.83/172.50 [1094]~E(x10941,x10942)+E(f396(x10943,x10944,x10945,x10941),f396(x10943,x10944,x10945,x10942)) % 172.83/172.50 [1095]~E(x10951,x10952)+E(f207(x10951,x10953,x10954,x10955),f207(x10952,x10953,x10954,x10955)) % 172.83/172.50 [1096]~E(x10961,x10962)+E(f207(x10963,x10961,x10964,x10965),f207(x10963,x10962,x10964,x10965)) % 172.83/172.50 [1097]~E(x10971,x10972)+E(f207(x10973,x10974,x10971,x10975),f207(x10973,x10974,x10972,x10975)) % 172.83/172.50 [1098]~E(x10981,x10982)+E(f207(x10983,x10984,x10985,x10981),f207(x10983,x10984,x10985,x10982)) % 172.83/172.50 [1099]~E(x10991,x10992)+E(f614(x10991,x10993,x10994,x10995,x10996),f614(x10992,x10993,x10994,x10995,x10996)) % 172.83/172.50 [1100]~E(x11001,x11002)+E(f614(x11003,x11001,x11004,x11005,x11006),f614(x11003,x11002,x11004,x11005,x11006)) % 172.83/172.50 [1101]~E(x11011,x11012)+E(f614(x11013,x11014,x11011,x11015,x11016),f614(x11013,x11014,x11012,x11015,x11016)) % 172.83/172.50 [1102]~E(x11021,x11022)+E(f614(x11023,x11024,x11025,x11021,x11026),f614(x11023,x11024,x11025,x11022,x11026)) % 172.83/172.50 [1103]~E(x11031,x11032)+E(f614(x11033,x11034,x11035,x11036,x11031),f614(x11033,x11034,x11035,x11036,x11032)) % 172.83/172.50 [1104]~E(x11041,x11042)+E(f419(x11041,x11043,x11044),f419(x11042,x11043,x11044)) % 172.83/172.50 [1105]~E(x11051,x11052)+E(f419(x11053,x11051,x11054),f419(x11053,x11052,x11054)) % 172.83/172.50 [1106]~E(x11061,x11062)+E(f419(x11063,x11064,x11061),f419(x11063,x11064,x11062)) % 172.83/172.50 [1107]~E(x11071,x11072)+E(f585(x11071,x11073,x11074),f585(x11072,x11073,x11074)) % 172.83/172.50 [1108]~E(x11081,x11082)+E(f585(x11083,x11081,x11084),f585(x11083,x11082,x11084)) % 172.83/172.50 [1109]~E(x11091,x11092)+E(f585(x11093,x11094,x11091),f585(x11093,x11094,x11092)) % 172.83/172.50 [1110]~E(x11101,x11102)+E(f647(x11101,x11103,x11104,x11105),f647(x11102,x11103,x11104,x11105)) % 172.83/172.50 [1111]~E(x11111,x11112)+E(f647(x11113,x11111,x11114,x11115),f647(x11113,x11112,x11114,x11115)) % 172.83/172.50 [1112]~E(x11121,x11122)+E(f647(x11123,x11124,x11121,x11125),f647(x11123,x11124,x11122,x11125)) % 172.83/172.50 [1113]~E(x11131,x11132)+E(f647(x11133,x11134,x11135,x11131),f647(x11133,x11134,x11135,x11132)) % 172.83/172.50 [1114]~E(x11141,x11142)+E(f742(x11141,x11143,x11144),f742(x11142,x11143,x11144)) % 172.83/172.50 [1115]~E(x11151,x11152)+E(f742(x11153,x11151,x11154),f742(x11153,x11152,x11154)) % 172.83/172.50 [1116]~E(x11161,x11162)+E(f742(x11163,x11164,x11161),f742(x11163,x11164,x11162)) % 172.83/172.50 [1117]~E(x11171,x11172)+E(f388(x11171,x11173,x11174),f388(x11172,x11173,x11174)) % 172.83/172.50 [1118]~E(x11181,x11182)+E(f388(x11183,x11181,x11184),f388(x11183,x11182,x11184)) % 172.83/172.50 [1119]~E(x11191,x11192)+E(f388(x11193,x11194,x11191),f388(x11193,x11194,x11192)) % 172.83/172.50 [1120]~E(x11201,x11202)+E(f162(x11201,x11203),f162(x11202,x11203)) % 172.83/172.50 [1121]~E(x11211,x11212)+E(f162(x11213,x11211),f162(x11213,x11212)) % 172.83/172.50 [1122]~E(x11221,x11222)+E(f704(x11221,x11223,x11224,x11225,x11226),f704(x11222,x11223,x11224,x11225,x11226)) % 172.83/172.50 [1123]~E(x11231,x11232)+E(f704(x11233,x11231,x11234,x11235,x11236),f704(x11233,x11232,x11234,x11235,x11236)) % 172.83/172.50 [1124]~E(x11241,x11242)+E(f704(x11243,x11244,x11241,x11245,x11246),f704(x11243,x11244,x11242,x11245,x11246)) % 172.83/172.50 [1125]~E(x11251,x11252)+E(f704(x11253,x11254,x11255,x11251,x11256),f704(x11253,x11254,x11255,x11252,x11256)) % 172.83/172.50 [1126]~E(x11261,x11262)+E(f704(x11263,x11264,x11265,x11266,x11261),f704(x11263,x11264,x11265,x11266,x11262)) % 172.83/172.50 [1127]~E(x11271,x11272)+E(f164(x11271,x11273,x11274,x11275),f164(x11272,x11273,x11274,x11275)) % 172.83/172.50 [1128]~E(x11281,x11282)+E(f164(x11283,x11281,x11284,x11285),f164(x11283,x11282,x11284,x11285)) % 172.83/172.50 [1129]~E(x11291,x11292)+E(f164(x11293,x11294,x11291,x11295),f164(x11293,x11294,x11292,x11295)) % 172.83/172.50 [1130]~E(x11301,x11302)+E(f164(x11303,x11304,x11305,x11301),f164(x11303,x11304,x11305,x11302)) % 172.83/172.50 [1131]~E(x11311,x11312)+E(f834(x11311,x11313,x11314,x11315,x11316),f834(x11312,x11313,x11314,x11315,x11316)) % 172.83/172.50 [1132]~E(x11321,x11322)+E(f834(x11323,x11321,x11324,x11325,x11326),f834(x11323,x11322,x11324,x11325,x11326)) % 172.83/172.50 [1133]~E(x11331,x11332)+E(f834(x11333,x11334,x11331,x11335,x11336),f834(x11333,x11334,x11332,x11335,x11336)) % 172.83/172.50 [1134]~E(x11341,x11342)+E(f834(x11343,x11344,x11345,x11341,x11346),f834(x11343,x11344,x11345,x11342,x11346)) % 172.83/172.50 [1135]~E(x11351,x11352)+E(f834(x11353,x11354,x11355,x11356,x11351),f834(x11353,x11354,x11355,x11356,x11352)) % 172.83/172.50 [1136]~E(x11361,x11362)+E(f498(x11361,x11363,x11364),f498(x11362,x11363,x11364)) % 172.83/172.50 [1137]~E(x11371,x11372)+E(f498(x11373,x11371,x11374),f498(x11373,x11372,x11374)) % 172.83/172.50 [1138]~E(x11381,x11382)+E(f498(x11383,x11384,x11381),f498(x11383,x11384,x11382)) % 172.83/172.50 [1139]~E(x11391,x11392)+E(f356(x11391,x11393,x11394,x11395),f356(x11392,x11393,x11394,x11395)) % 172.83/172.50 [1140]~E(x11401,x11402)+E(f356(x11403,x11401,x11404,x11405),f356(x11403,x11402,x11404,x11405)) % 172.83/172.50 [1141]~E(x11411,x11412)+E(f356(x11413,x11414,x11411,x11415),f356(x11413,x11414,x11412,x11415)) % 172.83/172.50 [1142]~E(x11421,x11422)+E(f356(x11423,x11424,x11425,x11421),f356(x11423,x11424,x11425,x11422)) % 172.83/172.50 [1143]~E(x11431,x11432)+E(f353(x11431,x11433,x11434),f353(x11432,x11433,x11434)) % 172.83/172.50 [1144]~E(x11441,x11442)+E(f353(x11443,x11441,x11444),f353(x11443,x11442,x11444)) % 172.83/172.50 [1145]~E(x11451,x11452)+E(f353(x11453,x11454,x11451),f353(x11453,x11454,x11452)) % 172.83/172.50 [1146]~E(x11461,x11462)+E(f584(x11461,x11463,x11464),f584(x11462,x11463,x11464)) % 172.83/172.50 [1147]~E(x11471,x11472)+E(f584(x11473,x11471,x11474),f584(x11473,x11472,x11474)) % 172.83/172.50 [1148]~E(x11481,x11482)+E(f584(x11483,x11484,x11481),f584(x11483,x11484,x11482)) % 172.83/172.50 [1149]~E(x11491,x11492)+E(f382(x11491,x11493),f382(x11492,x11493)) % 172.83/172.50 [1150]~E(x11501,x11502)+E(f382(x11503,x11501),f382(x11503,x11502)) % 172.83/172.50 [1151]~E(x11511,x11512)+E(f474(x11511,x11513,x11514),f474(x11512,x11513,x11514)) % 172.83/172.50 [1152]~E(x11521,x11522)+E(f474(x11523,x11521,x11524),f474(x11523,x11522,x11524)) % 172.83/172.50 [1153]~E(x11531,x11532)+E(f474(x11533,x11534,x11531),f474(x11533,x11534,x11532)) % 172.83/172.50 [1154]~E(x11541,x11542)+E(f745(x11541,x11543),f745(x11542,x11543)) % 172.83/172.50 [1155]~E(x11551,x11552)+E(f745(x11553,x11551),f745(x11553,x11552)) % 172.83/172.50 [1156]~E(x11561,x11562)+E(f492(x11561,x11563,x11564),f492(x11562,x11563,x11564)) % 172.83/172.50 [1157]~E(x11571,x11572)+E(f492(x11573,x11571,x11574),f492(x11573,x11572,x11574)) % 172.83/172.50 [1158]~E(x11581,x11582)+E(f492(x11583,x11584,x11581),f492(x11583,x11584,x11582)) % 172.83/172.50 [1159]~E(x11591,x11592)+E(f692(x11591,x11593),f692(x11592,x11593)) % 172.83/172.50 [1160]~E(x11601,x11602)+E(f692(x11603,x11601),f692(x11603,x11602)) % 172.83/172.50 [1161]~E(x11611,x11612)+E(f260(x11611,x11613),f260(x11612,x11613)) % 172.83/172.50 [1162]~E(x11621,x11622)+E(f260(x11623,x11621),f260(x11623,x11622)) % 172.83/172.50 [1163]~E(x11631,x11632)+E(f529(x11631,x11633,x11634,x11635),f529(x11632,x11633,x11634,x11635)) % 172.83/172.50 [1164]~E(x11641,x11642)+E(f529(x11643,x11641,x11644,x11645),f529(x11643,x11642,x11644,x11645)) % 172.83/172.50 [1165]~E(x11651,x11652)+E(f529(x11653,x11654,x11651,x11655),f529(x11653,x11654,x11652,x11655)) % 172.83/172.50 [1166]~E(x11661,x11662)+E(f529(x11663,x11664,x11665,x11661),f529(x11663,x11664,x11665,x11662)) % 172.83/172.50 [1167]~E(x11671,x11672)+E(f653(x11671,x11673,x11674,x11675),f653(x11672,x11673,x11674,x11675)) % 172.83/172.50 [1168]~E(x11681,x11682)+E(f653(x11683,x11681,x11684,x11685),f653(x11683,x11682,x11684,x11685)) % 172.83/172.50 [1169]~E(x11691,x11692)+E(f653(x11693,x11694,x11691,x11695),f653(x11693,x11694,x11692,x11695)) % 172.83/172.50 [1170]~E(x11701,x11702)+E(f653(x11703,x11704,x11705,x11701),f653(x11703,x11704,x11705,x11702)) % 172.83/172.50 [1171]~E(x11711,x11712)+E(f393(x11711,x11713,x11714,x11715),f393(x11712,x11713,x11714,x11715)) % 172.83/172.50 [1172]~E(x11721,x11722)+E(f393(x11723,x11721,x11724,x11725),f393(x11723,x11722,x11724,x11725)) % 172.83/172.50 [1173]~E(x11731,x11732)+E(f393(x11733,x11734,x11731,x11735),f393(x11733,x11734,x11732,x11735)) % 172.83/172.50 [1174]~E(x11741,x11742)+E(f393(x11743,x11744,x11745,x11741),f393(x11743,x11744,x11745,x11742)) % 172.83/172.50 [1175]~E(x11751,x11752)+E(f125(x11751,x11753),f125(x11752,x11753)) % 172.83/172.50 [1176]~E(x11761,x11762)+E(f125(x11763,x11761),f125(x11763,x11762)) % 172.83/172.50 [1177]~E(x11771,x11772)+E(f336(x11771,x11773,x11774,x11775),f336(x11772,x11773,x11774,x11775)) % 172.83/172.50 [1178]~E(x11781,x11782)+E(f336(x11783,x11781,x11784,x11785),f336(x11783,x11782,x11784,x11785)) % 172.83/172.50 [1179]~E(x11791,x11792)+E(f336(x11793,x11794,x11791,x11795),f336(x11793,x11794,x11792,x11795)) % 172.83/172.50 [1180]~E(x11801,x11802)+E(f336(x11803,x11804,x11805,x11801),f336(x11803,x11804,x11805,x11802)) % 172.83/172.50 [1181]~E(x11811,x11812)+E(f59(x11811,x11813,x11814,x11815),f59(x11812,x11813,x11814,x11815)) % 172.83/172.50 [1182]~E(x11821,x11822)+E(f59(x11823,x11821,x11824,x11825),f59(x11823,x11822,x11824,x11825)) % 172.83/172.50 [1183]~E(x11831,x11832)+E(f59(x11833,x11834,x11831,x11835),f59(x11833,x11834,x11832,x11835)) % 172.83/172.50 [1184]~E(x11841,x11842)+E(f59(x11843,x11844,x11845,x11841),f59(x11843,x11844,x11845,x11842)) % 172.83/172.50 [1185]~E(x11851,x11852)+E(f216(x11851,x11853,x11854,x11855),f216(x11852,x11853,x11854,x11855)) % 172.83/172.50 [1186]~E(x11861,x11862)+E(f216(x11863,x11861,x11864,x11865),f216(x11863,x11862,x11864,x11865)) % 172.83/172.50 [1187]~E(x11871,x11872)+E(f216(x11873,x11874,x11871,x11875),f216(x11873,x11874,x11872,x11875)) % 172.83/172.50 [1188]~E(x11881,x11882)+E(f216(x11883,x11884,x11885,x11881),f216(x11883,x11884,x11885,x11882)) % 172.83/172.50 [1189]~E(x11891,x11892)+E(f593(x11891,x11893,x11894,x11895,x11896),f593(x11892,x11893,x11894,x11895,x11896)) % 172.83/172.50 [1190]~E(x11901,x11902)+E(f593(x11903,x11901,x11904,x11905,x11906),f593(x11903,x11902,x11904,x11905,x11906)) % 172.83/172.50 [1191]~E(x11911,x11912)+E(f593(x11913,x11914,x11911,x11915,x11916),f593(x11913,x11914,x11912,x11915,x11916)) % 172.83/172.50 [1192]~E(x11921,x11922)+E(f593(x11923,x11924,x11925,x11921,x11926),f593(x11923,x11924,x11925,x11922,x11926)) % 172.83/172.50 [1193]~E(x11931,x11932)+E(f593(x11933,x11934,x11935,x11936,x11931),f593(x11933,x11934,x11935,x11936,x11932)) % 172.83/172.50 [1194]~E(x11941,x11942)+E(f540(x11941,x11943,x11944,x11945),f540(x11942,x11943,x11944,x11945)) % 172.83/172.50 [1195]~E(x11951,x11952)+E(f540(x11953,x11951,x11954,x11955),f540(x11953,x11952,x11954,x11955)) % 172.83/172.50 [1196]~E(x11961,x11962)+E(f540(x11963,x11964,x11961,x11965),f540(x11963,x11964,x11962,x11965)) % 172.83/172.50 [1197]~E(x11971,x11972)+E(f540(x11973,x11974,x11975,x11971),f540(x11973,x11974,x11975,x11972)) % 172.83/172.50 [1198]~E(x11981,x11982)+E(f227(x11981,x11983),f227(x11982,x11983)) % 172.83/172.50 [1199]~E(x11991,x11992)+E(f227(x11993,x11991),f227(x11993,x11992)) % 172.83/172.50 [1200]~E(x12001,x12002)+E(f155(x12001,x12003,x12004),f155(x12002,x12003,x12004)) % 172.83/172.50 [1201]~E(x12011,x12012)+E(f155(x12013,x12011,x12014),f155(x12013,x12012,x12014)) % 172.83/172.50 [1202]~E(x12021,x12022)+E(f155(x12023,x12024,x12021),f155(x12023,x12024,x12022)) % 172.83/172.50 [1203]~E(x12031,x12032)+E(f821(x12031,x12033,x12034),f821(x12032,x12033,x12034)) % 172.83/172.50 [1204]~E(x12041,x12042)+E(f821(x12043,x12041,x12044),f821(x12043,x12042,x12044)) % 172.83/172.50 [1205]~E(x12051,x12052)+E(f821(x12053,x12054,x12051),f821(x12053,x12054,x12052)) % 172.83/172.50 [1206]~E(x12061,x12062)+E(f753(x12061,x12063,x12064),f753(x12062,x12063,x12064)) % 172.83/172.50 [1207]~E(x12071,x12072)+E(f753(x12073,x12071,x12074),f753(x12073,x12072,x12074)) % 172.83/172.50 [1208]~E(x12081,x12082)+E(f753(x12083,x12084,x12081),f753(x12083,x12084,x12082)) % 172.83/172.50 [1209]~E(x12091,x12092)+E(f467(x12091,x12093),f467(x12092,x12093)) % 172.83/172.50 [1210]~E(x12101,x12102)+E(f467(x12103,x12101),f467(x12103,x12102)) % 172.83/172.50 [1211]~E(x12111,x12112)+E(f866(x12111,x12113,x12114,x12115,x12116,x12117),f866(x12112,x12113,x12114,x12115,x12116,x12117)) % 172.83/172.50 [1212]~E(x12121,x12122)+E(f866(x12123,x12121,x12124,x12125,x12126,x12127),f866(x12123,x12122,x12124,x12125,x12126,x12127)) % 172.83/172.50 [1213]~E(x12131,x12132)+E(f866(x12133,x12134,x12131,x12135,x12136,x12137),f866(x12133,x12134,x12132,x12135,x12136,x12137)) % 172.83/172.50 [1214]~E(x12141,x12142)+E(f866(x12143,x12144,x12145,x12141,x12146,x12147),f866(x12143,x12144,x12145,x12142,x12146,x12147)) % 172.83/172.50 [1215]~E(x12151,x12152)+E(f866(x12153,x12154,x12155,x12156,x12151,x12157),f866(x12153,x12154,x12155,x12156,x12152,x12157)) % 172.83/172.50 [1216]~E(x12161,x12162)+E(f866(x12163,x12164,x12165,x12166,x12167,x12161),f866(x12163,x12164,x12165,x12166,x12167,x12162)) % 172.83/172.50 [1217]~E(x12171,x12172)+E(f539(x12171,x12173,x12174),f539(x12172,x12173,x12174)) % 172.83/172.50 [1218]~E(x12181,x12182)+E(f539(x12183,x12181,x12184),f539(x12183,x12182,x12184)) % 172.83/172.50 [1219]~E(x12191,x12192)+E(f539(x12193,x12194,x12191),f539(x12193,x12194,x12192)) % 172.83/172.50 [1220]~E(x12201,x12202)+E(f337(x12201),f337(x12202)) % 172.83/172.50 [1221]~E(x12211,x12212)+E(f610(x12211,x12213,x12214,x12215,x12216),f610(x12212,x12213,x12214,x12215,x12216)) % 172.83/172.50 [1222]~E(x12221,x12222)+E(f610(x12223,x12221,x12224,x12225,x12226),f610(x12223,x12222,x12224,x12225,x12226)) % 172.83/172.50 [1223]~E(x12231,x12232)+E(f610(x12233,x12234,x12231,x12235,x12236),f610(x12233,x12234,x12232,x12235,x12236)) % 172.83/172.50 [1224]~E(x12241,x12242)+E(f610(x12243,x12244,x12245,x12241,x12246),f610(x12243,x12244,x12245,x12242,x12246)) % 172.83/172.50 [1225]~E(x12251,x12252)+E(f610(x12253,x12254,x12255,x12256,x12251),f610(x12253,x12254,x12255,x12256,x12252)) % 172.83/172.50 [1226]~E(x12261,x12262)+E(f640(x12261,x12263,x12264,x12265,x12266,x12267,x12268,x12269),f640(x12262,x12263,x12264,x12265,x12266,x12267,x12268,x12269)) % 172.83/172.50 [1227]~E(x12271,x12272)+E(f640(x12273,x12271,x12274,x12275,x12276,x12277,x12278,x12279),f640(x12273,x12272,x12274,x12275,x12276,x12277,x12278,x12279)) % 172.83/172.50 [1228]~E(x12281,x12282)+E(f640(x12283,x12284,x12281,x12285,x12286,x12287,x12288,x12289),f640(x12283,x12284,x12282,x12285,x12286,x12287,x12288,x12289)) % 172.83/172.50 [1229]~E(x12291,x12292)+E(f640(x12293,x12294,x12295,x12291,x12296,x12297,x12298,x12299),f640(x12293,x12294,x12295,x12292,x12296,x12297,x12298,x12299)) % 172.83/172.50 [1230]~E(x12301,x12302)+E(f640(x12303,x12304,x12305,x12306,x12301,x12307,x12308,x12309),f640(x12303,x12304,x12305,x12306,x12302,x12307,x12308,x12309)) % 172.83/172.50 [1231]~E(x12311,x12312)+E(f640(x12313,x12314,x12315,x12316,x12317,x12311,x12318,x12319),f640(x12313,x12314,x12315,x12316,x12317,x12312,x12318,x12319)) % 172.83/172.50 [1232]~E(x12321,x12322)+E(f640(x12323,x12324,x12325,x12326,x12327,x12328,x12321,x12329),f640(x12323,x12324,x12325,x12326,x12327,x12328,x12322,x12329)) % 172.83/172.50 [1233]~E(x12331,x12332)+E(f640(x12333,x12334,x12335,x12336,x12337,x12338,x12339,x12331),f640(x12333,x12334,x12335,x12336,x12337,x12338,x12339,x12332)) % 172.83/172.50 [1234]~E(x12341,x12342)+E(f358(x12341,x12343),f358(x12342,x12343)) % 172.83/172.50 [1235]~E(x12351,x12352)+E(f358(x12353,x12351),f358(x12353,x12352)) % 172.83/172.50 [1236]~E(x12361,x12362)+E(f76(x12361,x12363,x12364,x12365),f76(x12362,x12363,x12364,x12365)) % 172.83/172.50 [1237]~E(x12371,x12372)+E(f76(x12373,x12371,x12374,x12375),f76(x12373,x12372,x12374,x12375)) % 172.83/172.50 [1238]~E(x12381,x12382)+E(f76(x12383,x12384,x12381,x12385),f76(x12383,x12384,x12382,x12385)) % 172.83/172.50 [1239]~E(x12391,x12392)+E(f76(x12393,x12394,x12395,x12391),f76(x12393,x12394,x12395,x12392)) % 172.83/172.50 [1240]~E(x12401,x12402)+E(f210(x12401,x12403),f210(x12402,x12403)) % 172.83/172.50 [1241]~E(x12411,x12412)+E(f210(x12413,x12411),f210(x12413,x12412)) % 172.83/172.50 [1242]~E(x12421,x12422)+E(f163(x12421,x12423,x12424,x12425),f163(x12422,x12423,x12424,x12425)) % 172.83/172.50 [1243]~E(x12431,x12432)+E(f163(x12433,x12431,x12434,x12435),f163(x12433,x12432,x12434,x12435)) % 172.83/172.50 [1244]~E(x12441,x12442)+E(f163(x12443,x12444,x12441,x12445),f163(x12443,x12444,x12442,x12445)) % 172.83/172.50 [1245]~E(x12451,x12452)+E(f163(x12453,x12454,x12455,x12451),f163(x12453,x12454,x12455,x12452)) % 172.83/172.50 [1246]~E(x12461,x12462)+E(f558(x12461,x12463,x12464),f558(x12462,x12463,x12464)) % 172.83/172.50 [1247]~E(x12471,x12472)+E(f558(x12473,x12471,x12474),f558(x12473,x12472,x12474)) % 172.83/172.50 [1248]~E(x12481,x12482)+E(f558(x12483,x12484,x12481),f558(x12483,x12484,x12482)) % 172.83/172.50 [1249]~E(x12491,x12492)+E(f338(x12491),f338(x12492)) % 172.83/172.50 [1250]~E(x12501,x12502)+E(f475(x12501,x12503,x12504),f475(x12502,x12503,x12504)) % 172.83/172.50 [1251]~E(x12511,x12512)+E(f475(x12513,x12511,x12514),f475(x12513,x12512,x12514)) % 172.83/172.50 [1252]~E(x12521,x12522)+E(f475(x12523,x12524,x12521),f475(x12523,x12524,x12522)) % 172.83/172.50 [1253]~E(x12531,x12532)+E(f518(x12531,x12533,x12534,x12535),f518(x12532,x12533,x12534,x12535)) % 172.83/172.50 [1254]~E(x12541,x12542)+E(f518(x12543,x12541,x12544,x12545),f518(x12543,x12542,x12544,x12545)) % 172.83/172.50 [1255]~E(x12551,x12552)+E(f518(x12553,x12554,x12551,x12555),f518(x12553,x12554,x12552,x12555)) % 172.83/172.50 [1256]~E(x12561,x12562)+E(f518(x12563,x12564,x12565,x12561),f518(x12563,x12564,x12565,x12562)) % 172.83/172.50 [1257]~E(x12571,x12572)+E(f840(x12571,x12573,x12574),f840(x12572,x12573,x12574)) % 172.83/172.50 [1258]~E(x12581,x12582)+E(f840(x12583,x12581,x12584),f840(x12583,x12582,x12584)) % 172.83/172.50 [1259]~E(x12591,x12592)+E(f840(x12593,x12594,x12591),f840(x12593,x12594,x12592)) % 172.83/172.50 [1260]~E(x12601,x12602)+E(f140(x12601,x12603,x12604),f140(x12602,x12603,x12604)) % 172.83/172.50 [1261]~E(x12611,x12612)+E(f140(x12613,x12611,x12614),f140(x12613,x12612,x12614)) % 172.83/172.50 [1262]~E(x12621,x12622)+E(f140(x12623,x12624,x12621),f140(x12623,x12624,x12622)) % 172.83/172.50 [1263]~E(x12631,x12632)+E(f802(x12631,x12633,x12634),f802(x12632,x12633,x12634)) % 172.83/172.50 [1264]~E(x12641,x12642)+E(f802(x12643,x12641,x12644),f802(x12643,x12642,x12644)) % 172.83/172.50 [1265]~E(x12651,x12652)+E(f802(x12653,x12654,x12651),f802(x12653,x12654,x12652)) % 172.83/172.50 [1266]~E(x12661,x12662)+E(f234(x12661,x12663,x12664),f234(x12662,x12663,x12664)) % 172.83/172.50 [1267]~E(x12671,x12672)+E(f234(x12673,x12671,x12674),f234(x12673,x12672,x12674)) % 172.83/172.50 [1268]~E(x12681,x12682)+E(f234(x12683,x12684,x12681),f234(x12683,x12684,x12682)) % 172.83/172.50 [1269]~E(x12691,x12692)+E(f491(x12691,x12693,x12694),f491(x12692,x12693,x12694)) % 172.83/172.50 [1270]~E(x12701,x12702)+E(f491(x12703,x12701,x12704),f491(x12703,x12702,x12704)) % 172.83/172.50 [1271]~E(x12711,x12712)+E(f491(x12713,x12714,x12711),f491(x12713,x12714,x12712)) % 172.83/172.50 [1272]~E(x12721,x12722)+E(f664(x12721,x12723,x12724,x12725,x12726,x12727),f664(x12722,x12723,x12724,x12725,x12726,x12727)) % 172.83/172.50 [1273]~E(x12731,x12732)+E(f664(x12733,x12731,x12734,x12735,x12736,x12737),f664(x12733,x12732,x12734,x12735,x12736,x12737)) % 172.83/172.50 [1274]~E(x12741,x12742)+E(f664(x12743,x12744,x12741,x12745,x12746,x12747),f664(x12743,x12744,x12742,x12745,x12746,x12747)) % 172.83/172.50 [1275]~E(x12751,x12752)+E(f664(x12753,x12754,x12755,x12751,x12756,x12757),f664(x12753,x12754,x12755,x12752,x12756,x12757)) % 172.83/172.50 [1276]~E(x12761,x12762)+E(f664(x12763,x12764,x12765,x12766,x12761,x12767),f664(x12763,x12764,x12765,x12766,x12762,x12767)) % 172.83/172.50 [1277]~E(x12771,x12772)+E(f664(x12773,x12774,x12775,x12776,x12777,x12771),f664(x12773,x12774,x12775,x12776,x12777,x12772)) % 172.83/172.50 [1278]~E(x12781,x12782)+E(f718(x12781,x12783),f718(x12782,x12783)) % 172.83/172.50 [1279]~E(x12791,x12792)+E(f718(x12793,x12791),f718(x12793,x12792)) % 172.83/172.50 [1280]~E(x12801,x12802)+E(f665(x12801,x12803,x12804,x12805,x12806,x12807),f665(x12802,x12803,x12804,x12805,x12806,x12807)) % 172.83/172.50 [1281]~E(x12811,x12812)+E(f665(x12813,x12811,x12814,x12815,x12816,x12817),f665(x12813,x12812,x12814,x12815,x12816,x12817)) % 172.83/172.50 [1282]~E(x12821,x12822)+E(f665(x12823,x12824,x12821,x12825,x12826,x12827),f665(x12823,x12824,x12822,x12825,x12826,x12827)) % 172.83/172.50 [1283]~E(x12831,x12832)+E(f665(x12833,x12834,x12835,x12831,x12836,x12837),f665(x12833,x12834,x12835,x12832,x12836,x12837)) % 172.83/172.50 [1284]~E(x12841,x12842)+E(f665(x12843,x12844,x12845,x12846,x12841,x12847),f665(x12843,x12844,x12845,x12846,x12842,x12847)) % 172.83/172.50 [1285]~E(x12851,x12852)+E(f665(x12853,x12854,x12855,x12856,x12857,x12851),f665(x12853,x12854,x12855,x12856,x12857,x12852)) % 172.83/172.50 [1286]~E(x12861,x12862)+E(f646(x12861,x12863,x12864,x12865),f646(x12862,x12863,x12864,x12865)) % 172.83/172.50 [1287]~E(x12871,x12872)+E(f646(x12873,x12871,x12874,x12875),f646(x12873,x12872,x12874,x12875)) % 172.83/172.50 [1288]~E(x12881,x12882)+E(f646(x12883,x12884,x12881,x12885),f646(x12883,x12884,x12882,x12885)) % 172.83/172.50 [1289]~E(x12891,x12892)+E(f646(x12893,x12894,x12895,x12891),f646(x12893,x12894,x12895,x12892)) % 172.83/172.50 [1290]~E(x12901,x12902)+E(f62(x12901,x12903,x12904),f62(x12902,x12903,x12904)) % 172.83/172.50 [1291]~E(x12911,x12912)+E(f62(x12913,x12911,x12914),f62(x12913,x12912,x12914)) % 172.83/172.50 [1292]~E(x12921,x12922)+E(f62(x12923,x12924,x12921),f62(x12923,x12924,x12922)) % 172.83/172.50 [1293]~E(x12931,x12932)+E(f174(x12931,x12933,x12934),f174(x12932,x12933,x12934)) % 172.83/172.50 [1294]~E(x12941,x12942)+E(f174(x12943,x12941,x12944),f174(x12943,x12942,x12944)) % 172.83/172.50 [1295]~E(x12951,x12952)+E(f174(x12953,x12954,x12951),f174(x12953,x12954,x12952)) % 172.83/172.50 [1296]~E(x12961,x12962)+E(f519(x12961,x12963,x12964,x12965,x12966),f519(x12962,x12963,x12964,x12965,x12966)) % 172.83/172.50 [1297]~E(x12971,x12972)+E(f519(x12973,x12971,x12974,x12975,x12976),f519(x12973,x12972,x12974,x12975,x12976)) % 172.83/172.50 [1298]~E(x12981,x12982)+E(f519(x12983,x12984,x12981,x12985,x12986),f519(x12983,x12984,x12982,x12985,x12986)) % 172.83/172.50 [1299]~E(x12991,x12992)+E(f519(x12993,x12994,x12995,x12991,x12996),f519(x12993,x12994,x12995,x12992,x12996)) % 172.83/172.50 [1300]~E(x13001,x13002)+E(f519(x13003,x13004,x13005,x13006,x13001),f519(x13003,x13004,x13005,x13006,x13002)) % 172.83/172.50 [1301]~E(x13011,x13012)+E(f522(x13011,x13013,x13014,x13015),f522(x13012,x13013,x13014,x13015)) % 172.83/172.50 [1302]~E(x13021,x13022)+E(f522(x13023,x13021,x13024,x13025),f522(x13023,x13022,x13024,x13025)) % 172.83/172.50 [1303]~E(x13031,x13032)+E(f522(x13033,x13034,x13031,x13035),f522(x13033,x13034,x13032,x13035)) % 172.83/172.50 [1304]~E(x13041,x13042)+E(f522(x13043,x13044,x13045,x13041),f522(x13043,x13044,x13045,x13042)) % 172.83/172.50 [1305]~E(x13051,x13052)+E(f852(x13051,x13053,x13054),f852(x13052,x13053,x13054)) % 172.83/172.50 [1306]~E(x13061,x13062)+E(f852(x13063,x13061,x13064),f852(x13063,x13062,x13064)) % 172.83/172.50 [1307]~E(x13071,x13072)+E(f852(x13073,x13074,x13071),f852(x13073,x13074,x13072)) % 172.83/172.50 [1308]~E(x13081,x13082)+E(f661(x13081,x13083,x13084,x13085),f661(x13082,x13083,x13084,x13085)) % 172.83/172.50 [1309]~E(x13091,x13092)+E(f661(x13093,x13091,x13094,x13095),f661(x13093,x13092,x13094,x13095)) % 172.83/172.50 [1310]~E(x13101,x13102)+E(f661(x13103,x13104,x13101,x13105),f661(x13103,x13104,x13102,x13105)) % 172.83/172.50 [1311]~E(x13111,x13112)+E(f661(x13113,x13114,x13115,x13111),f661(x13113,x13114,x13115,x13112)) % 172.83/172.50 [1312]~E(x13121,x13122)+E(f825(x13121,x13123,x13124,x13125),f825(x13122,x13123,x13124,x13125)) % 172.83/172.50 [1313]~E(x13131,x13132)+E(f825(x13133,x13131,x13134,x13135),f825(x13133,x13132,x13134,x13135)) % 172.83/172.50 [1314]~E(x13141,x13142)+E(f825(x13143,x13144,x13141,x13145),f825(x13143,x13144,x13142,x13145)) % 172.83/172.50 [1315]~E(x13151,x13152)+E(f825(x13153,x13154,x13155,x13151),f825(x13153,x13154,x13155,x13152)) % 172.83/172.50 [1316]~E(x13161,x13162)+E(f678(x13161,x13163,x13164),f678(x13162,x13163,x13164)) % 172.83/172.50 [1317]~E(x13171,x13172)+E(f678(x13173,x13171,x13174),f678(x13173,x13172,x13174)) % 172.83/172.50 [1318]~E(x13181,x13182)+E(f678(x13183,x13184,x13181),f678(x13183,x13184,x13182)) % 172.83/172.50 [1319]~E(x13191,x13192)+E(f792(x13191,x13193,x13194),f792(x13192,x13193,x13194)) % 172.83/172.50 [1320]~E(x13201,x13202)+E(f792(x13203,x13201,x13204),f792(x13203,x13202,x13204)) % 172.83/172.50 [1321]~E(x13211,x13212)+E(f792(x13213,x13214,x13211),f792(x13213,x13214,x13212)) % 172.83/172.50 [1322]~E(x13221,x13222)+E(f722(x13221,x13223,x13224),f722(x13222,x13223,x13224)) % 172.83/172.50 [1323]~E(x13231,x13232)+E(f722(x13233,x13231,x13234),f722(x13233,x13232,x13234)) % 172.83/172.50 [1324]~E(x13241,x13242)+E(f722(x13243,x13244,x13241),f722(x13243,x13244,x13242)) % 172.83/172.50 [1325]~E(x13251,x13252)+E(f258(x13251,x13253,x13254),f258(x13252,x13253,x13254)) % 172.83/172.50 [1326]~E(x13261,x13262)+E(f258(x13263,x13261,x13264),f258(x13263,x13262,x13264)) % 172.83/172.50 [1327]~E(x13271,x13272)+E(f258(x13273,x13274,x13271),f258(x13273,x13274,x13272)) % 172.83/172.50 [1328]~E(x13281,x13282)+E(f752(x13281,x13283),f752(x13282,x13283)) % 172.83/172.50 [1329]~E(x13291,x13292)+E(f752(x13293,x13291),f752(x13293,x13292)) % 172.83/172.50 [1330]~E(x13301,x13302)+E(f844(x13301,x13303,x13304,x13305,x13306),f844(x13302,x13303,x13304,x13305,x13306)) % 172.83/172.50 [1331]~E(x13311,x13312)+E(f844(x13313,x13311,x13314,x13315,x13316),f844(x13313,x13312,x13314,x13315,x13316)) % 172.83/172.50 [1332]~E(x13321,x13322)+E(f844(x13323,x13324,x13321,x13325,x13326),f844(x13323,x13324,x13322,x13325,x13326)) % 172.83/172.50 [1333]~E(x13331,x13332)+E(f844(x13333,x13334,x13335,x13331,x13336),f844(x13333,x13334,x13335,x13332,x13336)) % 172.83/172.50 [1334]~E(x13341,x13342)+E(f844(x13343,x13344,x13345,x13346,x13341),f844(x13343,x13344,x13345,x13346,x13342)) % 172.83/172.50 [1335]~E(x13351,x13352)+E(f368(x13351),f368(x13352)) % 172.83/172.50 [1336]~E(x13361,x13362)+E(f404(x13361,x13363,x13364,x13365),f404(x13362,x13363,x13364,x13365)) % 172.83/172.50 [1337]~E(x13371,x13372)+E(f404(x13373,x13371,x13374,x13375),f404(x13373,x13372,x13374,x13375)) % 172.83/172.50 [1338]~E(x13381,x13382)+E(f404(x13383,x13384,x13381,x13385),f404(x13383,x13384,x13382,x13385)) % 172.83/172.50 [1339]~E(x13391,x13392)+E(f404(x13393,x13394,x13395,x13391),f404(x13393,x13394,x13395,x13392)) % 172.83/172.50 [1340]~E(x13401,x13402)+E(f741(x13401,x13403,x13404),f741(x13402,x13403,x13404)) % 172.83/172.50 [1341]~E(x13411,x13412)+E(f741(x13413,x13411,x13414),f741(x13413,x13412,x13414)) % 172.83/172.50 [1342]~E(x13421,x13422)+E(f741(x13423,x13424,x13421),f741(x13423,x13424,x13422)) % 172.83/172.50 [1343]~E(x13431,x13432)+E(f613(x13431,x13433,x13434,x13435,x13436),f613(x13432,x13433,x13434,x13435,x13436)) % 172.83/172.50 [1344]~E(x13441,x13442)+E(f613(x13443,x13441,x13444,x13445,x13446),f613(x13443,x13442,x13444,x13445,x13446)) % 172.83/172.50 [1345]~E(x13451,x13452)+E(f613(x13453,x13454,x13451,x13455,x13456),f613(x13453,x13454,x13452,x13455,x13456)) % 172.83/172.50 [1346]~E(x13461,x13462)+E(f613(x13463,x13464,x13465,x13461,x13466),f613(x13463,x13464,x13465,x13462,x13466)) % 172.83/172.50 [1347]~E(x13471,x13472)+E(f613(x13473,x13474,x13475,x13476,x13471),f613(x13473,x13474,x13475,x13476,x13472)) % 172.83/172.50 [1348]~E(x13481,x13482)+E(f21(x13481,x13483),f21(x13482,x13483)) % 172.83/172.50 [1349]~E(x13491,x13492)+E(f21(x13493,x13491),f21(x13493,x13492)) % 172.83/172.50 [1350]~E(x13501,x13502)+E(f242(x13501,x13503,x13504,x13505,x13506),f242(x13502,x13503,x13504,x13505,x13506)) % 172.83/172.50 [1351]~E(x13511,x13512)+E(f242(x13513,x13511,x13514,x13515,x13516),f242(x13513,x13512,x13514,x13515,x13516)) % 172.83/172.50 [1352]~E(x13521,x13522)+E(f242(x13523,x13524,x13521,x13525,x13526),f242(x13523,x13524,x13522,x13525,x13526)) % 172.83/172.50 [1353]~E(x13531,x13532)+E(f242(x13533,x13534,x13535,x13531,x13536),f242(x13533,x13534,x13535,x13532,x13536)) % 172.83/172.50 [1354]~E(x13541,x13542)+E(f242(x13543,x13544,x13545,x13546,x13541),f242(x13543,x13544,x13545,x13546,x13542)) % 172.83/172.50 [1355]~E(x13551,x13552)+E(f744(x13551,x13553),f744(x13552,x13553)) % 172.83/172.50 [1356]~E(x13561,x13562)+E(f744(x13563,x13561),f744(x13563,x13562)) % 172.83/172.50 [1357]~E(x13571,x13572)+E(f424(x13571,x13573,x13574,x13575,x13576),f424(x13572,x13573,x13574,x13575,x13576)) % 172.83/172.50 [1358]~E(x13581,x13582)+E(f424(x13583,x13581,x13584,x13585,x13586),f424(x13583,x13582,x13584,x13585,x13586)) % 172.83/172.50 [1359]~E(x13591,x13592)+E(f424(x13593,x13594,x13591,x13595,x13596),f424(x13593,x13594,x13592,x13595,x13596)) % 172.83/172.50 [1360]~E(x13601,x13602)+E(f424(x13603,x13604,x13605,x13601,x13606),f424(x13603,x13604,x13605,x13602,x13606)) % 172.83/172.50 [1361]~E(x13611,x13612)+E(f424(x13613,x13614,x13615,x13616,x13611),f424(x13613,x13614,x13615,x13616,x13612)) % 172.83/172.50 [1362]~E(x13621,x13622)+E(f749(x13621,x13623,x13624),f749(x13622,x13623,x13624)) % 172.83/172.50 [1363]~E(x13631,x13632)+E(f749(x13633,x13631,x13634),f749(x13633,x13632,x13634)) % 172.83/172.50 [1364]~E(x13641,x13642)+E(f749(x13643,x13644,x13641),f749(x13643,x13644,x13642)) % 172.83/172.50 [1365]~E(x13651,x13652)+E(f384(x13651,x13653),f384(x13652,x13653)) % 172.83/172.50 [1366]~E(x13661,x13662)+E(f384(x13663,x13661),f384(x13663,x13662)) % 172.83/172.50 [1367]~E(x13671,x13672)+E(f429(x13671,x13673),f429(x13672,x13673)) % 172.83/172.50 [1368]~E(x13681,x13682)+E(f429(x13683,x13681),f429(x13683,x13682)) % 172.83/172.50 [1369]~E(x13691,x13692)+E(f803(x13691,x13693,x13694),f803(x13692,x13693,x13694)) % 172.83/172.50 [1370]~E(x13701,x13702)+E(f803(x13703,x13701,x13704),f803(x13703,x13702,x13704)) % 172.83/172.50 [1371]~E(x13711,x13712)+E(f803(x13713,x13714,x13711),f803(x13713,x13714,x13712)) % 172.83/172.50 [1372]~E(x13721,x13722)+E(f468(x13721,x13723),f468(x13722,x13723)) % 172.83/172.50 [1373]~E(x13731,x13732)+E(f468(x13733,x13731),f468(x13733,x13732)) % 172.83/172.50 [1374]~E(x13741,x13742)+E(f674(x13741,x13743,x13744,x13745,x13746),f674(x13742,x13743,x13744,x13745,x13746)) % 172.83/172.50 [1375]~E(x13751,x13752)+E(f674(x13753,x13751,x13754,x13755,x13756),f674(x13753,x13752,x13754,x13755,x13756)) % 172.83/172.50 [1376]~E(x13761,x13762)+E(f674(x13763,x13764,x13761,x13765,x13766),f674(x13763,x13764,x13762,x13765,x13766)) % 172.83/172.50 [1377]~E(x13771,x13772)+E(f674(x13773,x13774,x13775,x13771,x13776),f674(x13773,x13774,x13775,x13772,x13776)) % 172.83/172.50 [1378]~E(x13781,x13782)+E(f674(x13783,x13784,x13785,x13786,x13781),f674(x13783,x13784,x13785,x13786,x13782)) % 172.83/172.50 [1379]~E(x13791,x13792)+E(f378(x13791,x13793),f378(x13792,x13793)) % 172.83/172.50 [1380]~E(x13801,x13802)+E(f378(x13803,x13801),f378(x13803,x13802)) % 172.83/172.50 [1381]~E(x13811,x13812)+E(f682(x13811,x13813,x13814,x13815,x13816),f682(x13812,x13813,x13814,x13815,x13816)) % 172.83/172.50 [1382]~E(x13821,x13822)+E(f682(x13823,x13821,x13824,x13825,x13826),f682(x13823,x13822,x13824,x13825,x13826)) % 172.83/172.50 [1383]~E(x13831,x13832)+E(f682(x13833,x13834,x13831,x13835,x13836),f682(x13833,x13834,x13832,x13835,x13836)) % 172.83/172.50 [1384]~E(x13841,x13842)+E(f682(x13843,x13844,x13845,x13841,x13846),f682(x13843,x13844,x13845,x13842,x13846)) % 172.83/172.50 [1385]~E(x13851,x13852)+E(f682(x13853,x13854,x13855,x13856,x13851),f682(x13853,x13854,x13855,x13856,x13852)) % 172.83/172.50 [1386]~E(x13861,x13862)+E(f563(x13861,x13863,x13864,x13865),f563(x13862,x13863,x13864,x13865)) % 172.83/172.50 [1387]~E(x13871,x13872)+E(f563(x13873,x13871,x13874,x13875),f563(x13873,x13872,x13874,x13875)) % 172.83/172.50 [1388]~E(x13881,x13882)+E(f563(x13883,x13884,x13881,x13885),f563(x13883,x13884,x13882,x13885)) % 172.83/172.50 [1389]~E(x13891,x13892)+E(f563(x13893,x13894,x13895,x13891),f563(x13893,x13894,x13895,x13892)) % 172.83/172.50 [1390]~E(x13901,x13902)+E(f768(x13901,x13903,x13904,x13905,x13906,x13907),f768(x13902,x13903,x13904,x13905,x13906,x13907)) % 172.83/172.50 [1391]~E(x13911,x13912)+E(f768(x13913,x13911,x13914,x13915,x13916,x13917),f768(x13913,x13912,x13914,x13915,x13916,x13917)) % 172.83/172.50 [1392]~E(x13921,x13922)+E(f768(x13923,x13924,x13921,x13925,x13926,x13927),f768(x13923,x13924,x13922,x13925,x13926,x13927)) % 172.83/172.50 [1393]~E(x13931,x13932)+E(f768(x13933,x13934,x13935,x13931,x13936,x13937),f768(x13933,x13934,x13935,x13932,x13936,x13937)) % 172.83/172.50 [1394]~E(x13941,x13942)+E(f768(x13943,x13944,x13945,x13946,x13941,x13947),f768(x13943,x13944,x13945,x13946,x13942,x13947)) % 172.83/172.50 [1395]~E(x13951,x13952)+E(f768(x13953,x13954,x13955,x13956,x13957,x13951),f768(x13953,x13954,x13955,x13956,x13957,x13952)) % 172.83/172.50 [1396]~E(x13961,x13962)+E(f416(x13961,x13963),f416(x13962,x13963)) % 172.83/172.50 [1397]~E(x13971,x13972)+E(f416(x13973,x13971),f416(x13973,x13972)) % 172.83/172.50 [1398]~E(x13981,x13982)+E(f869(x13981,x13983,x13984),f869(x13982,x13983,x13984)) % 172.83/172.50 [1399]~E(x13991,x13992)+E(f869(x13993,x13991,x13994),f869(x13993,x13992,x13994)) % 172.83/172.50 [1400]~E(x14001,x14002)+E(f869(x14003,x14004,x14001),f869(x14003,x14004,x14002)) % 172.83/172.50 [1401]~E(x14011,x14012)+E(f713(x14011,x14013,x14014,x14015,x14016),f713(x14012,x14013,x14014,x14015,x14016)) % 172.83/172.50 [1402]~E(x14021,x14022)+E(f713(x14023,x14021,x14024,x14025,x14026),f713(x14023,x14022,x14024,x14025,x14026)) % 172.83/172.50 [1403]~E(x14031,x14032)+E(f713(x14033,x14034,x14031,x14035,x14036),f713(x14033,x14034,x14032,x14035,x14036)) % 172.83/172.50 [1404]~E(x14041,x14042)+E(f713(x14043,x14044,x14045,x14041,x14046),f713(x14043,x14044,x14045,x14042,x14046)) % 172.83/172.50 [1405]~E(x14051,x14052)+E(f713(x14053,x14054,x14055,x14056,x14051),f713(x14053,x14054,x14055,x14056,x14052)) % 172.83/172.50 [1406]~E(x14061,x14062)+E(f553(x14061,x14063,x14064),f553(x14062,x14063,x14064)) % 172.83/172.50 [1407]~E(x14071,x14072)+E(f553(x14073,x14071,x14074),f553(x14073,x14072,x14074)) % 172.83/172.50 [1408]~E(x14081,x14082)+E(f553(x14083,x14084,x14081),f553(x14083,x14084,x14082)) % 172.83/172.50 [1409]~E(x14091,x14092)+E(f261(x14091,x14093,x14094),f261(x14092,x14093,x14094)) % 172.83/172.50 [1410]~E(x14101,x14102)+E(f261(x14103,x14101,x14104),f261(x14103,x14102,x14104)) % 172.83/172.50 [1411]~E(x14111,x14112)+E(f261(x14113,x14114,x14111),f261(x14113,x14114,x14112)) % 172.83/172.50 [1412]~E(x14121,x14122)+E(f681(x14121,x14123,x14124,x14125),f681(x14122,x14123,x14124,x14125)) % 172.83/172.50 [1413]~E(x14131,x14132)+E(f681(x14133,x14131,x14134,x14135),f681(x14133,x14132,x14134,x14135)) % 172.83/172.50 [1414]~E(x14141,x14142)+E(f681(x14143,x14144,x14141,x14145),f681(x14143,x14144,x14142,x14145)) % 172.83/172.50 [1415]~E(x14151,x14152)+E(f681(x14153,x14154,x14155,x14151),f681(x14153,x14154,x14155,x14152)) % 172.83/172.50 [1416]~E(x14161,x14162)+E(f277(x14161),f277(x14162)) % 172.83/172.50 [1417]~E(x14171,x14172)+E(f527(x14171,x14173,x14174,x14175),f527(x14172,x14173,x14174,x14175)) % 172.83/172.50 [1418]~E(x14181,x14182)+E(f527(x14183,x14181,x14184,x14185),f527(x14183,x14182,x14184,x14185)) % 172.83/172.50 [1419]~E(x14191,x14192)+E(f527(x14193,x14194,x14191,x14195),f527(x14193,x14194,x14192,x14195)) % 172.83/172.50 [1420]~E(x14201,x14202)+E(f527(x14203,x14204,x14205,x14201),f527(x14203,x14204,x14205,x14202)) % 172.83/172.50 [1421]~E(x14211,x14212)+E(f801(x14211,x14213,x14214),f801(x14212,x14213,x14214)) % 172.83/172.50 [1422]~E(x14221,x14222)+E(f801(x14223,x14221,x14224),f801(x14223,x14222,x14224)) % 172.83/172.50 [1423]~E(x14231,x14232)+E(f801(x14233,x14234,x14231),f801(x14233,x14234,x14232)) % 172.83/172.50 [1424]~E(x14241,x14242)+E(f734(x14241,x14243,x14244,x14245,x14246),f734(x14242,x14243,x14244,x14245,x14246)) % 172.83/172.50 [1425]~E(x14251,x14252)+E(f734(x14253,x14251,x14254,x14255,x14256),f734(x14253,x14252,x14254,x14255,x14256)) % 172.83/172.50 [1426]~E(x14261,x14262)+E(f734(x14263,x14264,x14261,x14265,x14266),f734(x14263,x14264,x14262,x14265,x14266)) % 172.83/172.50 [1427]~E(x14271,x14272)+E(f734(x14273,x14274,x14275,x14271,x14276),f734(x14273,x14274,x14275,x14272,x14276)) % 172.83/172.50 [1428]~E(x14281,x14282)+E(f734(x14283,x14284,x14285,x14286,x14281),f734(x14283,x14284,x14285,x14286,x14282)) % 172.83/172.50 [1429]~E(x14291,x14292)+E(f220(x14291,x14293,x14294,x14295),f220(x14292,x14293,x14294,x14295)) % 172.83/172.50 [1430]~E(x14301,x14302)+E(f220(x14303,x14301,x14304,x14305),f220(x14303,x14302,x14304,x14305)) % 172.83/172.50 [1431]~E(x14311,x14312)+E(f220(x14313,x14314,x14311,x14315),f220(x14313,x14314,x14312,x14315)) % 172.83/172.50 [1432]~E(x14321,x14322)+E(f220(x14323,x14324,x14325,x14321),f220(x14323,x14324,x14325,x14322)) % 172.83/172.50 [1433]~E(x14331,x14332)+E(f394(x14331,x14333,x14334,x14335),f394(x14332,x14333,x14334,x14335)) % 172.83/172.50 [1434]~E(x14341,x14342)+E(f394(x14343,x14341,x14344,x14345),f394(x14343,x14342,x14344,x14345)) % 172.83/172.50 [1435]~E(x14351,x14352)+E(f394(x14353,x14354,x14351,x14355),f394(x14353,x14354,x14352,x14355)) % 172.83/172.50 [1436]~E(x14361,x14362)+E(f394(x14363,x14364,x14365,x14361),f394(x14363,x14364,x14365,x14362)) % 172.83/172.50 [1437]~E(x14371,x14372)+E(f743(x14371,x14373),f743(x14372,x14373)) % 172.83/172.50 [1438]~E(x14381,x14382)+E(f743(x14383,x14381),f743(x14383,x14382)) % 172.83/172.50 [1439]~E(x14391,x14392)+E(f482(x14391,x14393,x14394),f482(x14392,x14393,x14394)) % 172.83/172.50 [1440]~E(x14401,x14402)+E(f482(x14403,x14401,x14404),f482(x14403,x14402,x14404)) % 172.83/172.50 [1441]~E(x14411,x14412)+E(f482(x14413,x14414,x14411),f482(x14413,x14414,x14412)) % 172.83/172.50 [1442]~E(x14421,x14422)+E(f592(x14421,x14423,x14424,x14425,x14426,x14427,x14428,x14429),f592(x14422,x14423,x14424,x14425,x14426,x14427,x14428,x14429)) % 172.83/172.50 [1443]~E(x14431,x14432)+E(f592(x14433,x14431,x14434,x14435,x14436,x14437,x14438,x14439),f592(x14433,x14432,x14434,x14435,x14436,x14437,x14438,x14439)) % 172.83/172.50 [1444]~E(x14441,x14442)+E(f592(x14443,x14444,x14441,x14445,x14446,x14447,x14448,x14449),f592(x14443,x14444,x14442,x14445,x14446,x14447,x14448,x14449)) % 172.83/172.50 [1445]~E(x14451,x14452)+E(f592(x14453,x14454,x14455,x14451,x14456,x14457,x14458,x14459),f592(x14453,x14454,x14455,x14452,x14456,x14457,x14458,x14459)) % 172.83/172.50 [1446]~E(x14461,x14462)+E(f592(x14463,x14464,x14465,x14466,x14461,x14467,x14468,x14469),f592(x14463,x14464,x14465,x14466,x14462,x14467,x14468,x14469)) % 172.83/172.50 [1447]~E(x14471,x14472)+E(f592(x14473,x14474,x14475,x14476,x14477,x14471,x14478,x14479),f592(x14473,x14474,x14475,x14476,x14477,x14472,x14478,x14479)) % 172.83/172.50 [1448]~E(x14481,x14482)+E(f592(x14483,x14484,x14485,x14486,x14487,x14488,x14481,x14489),f592(x14483,x14484,x14485,x14486,x14487,x14488,x14482,x14489)) % 172.83/172.50 [1449]~E(x14491,x14492)+E(f592(x14493,x14494,x14495,x14496,x14497,x14498,x14499,x14491),f592(x14493,x14494,x14495,x14496,x14497,x14498,x14499,x14492)) % 172.83/172.50 [1450]~E(x14501,x14502)+E(f95(x14501,x14503,x14504,x14505),f95(x14502,x14503,x14504,x14505)) % 172.83/172.50 [1451]~E(x14511,x14512)+E(f95(x14513,x14511,x14514,x14515),f95(x14513,x14512,x14514,x14515)) % 172.83/172.50 [1452]~E(x14521,x14522)+E(f95(x14523,x14524,x14521,x14525),f95(x14523,x14524,x14522,x14525)) % 172.83/172.50 [1453]~E(x14531,x14532)+E(f95(x14533,x14534,x14535,x14531),f95(x14533,x14534,x14535,x14532)) % 172.83/172.50 [1454]~E(x14541,x14542)+E(f696(x14541,x14543,x14544),f696(x14542,x14543,x14544)) % 172.83/172.50 [1455]~E(x14551,x14552)+E(f696(x14553,x14551,x14554),f696(x14553,x14552,x14554)) % 172.83/172.50 [1456]~E(x14561,x14562)+E(f696(x14563,x14564,x14561),f696(x14563,x14564,x14562)) % 172.83/172.50 [1457]~E(x14571,x14572)+E(f511(x14571,x14573,x14574,x14575,x14576,x14577,x14578),f511(x14572,x14573,x14574,x14575,x14576,x14577,x14578)) % 172.83/172.50 [1458]~E(x14581,x14582)+E(f511(x14583,x14581,x14584,x14585,x14586,x14587,x14588),f511(x14583,x14582,x14584,x14585,x14586,x14587,x14588)) % 172.83/172.50 [1459]~E(x14591,x14592)+E(f511(x14593,x14594,x14591,x14595,x14596,x14597,x14598),f511(x14593,x14594,x14592,x14595,x14596,x14597,x14598)) % 172.83/172.50 [1460]~E(x14601,x14602)+E(f511(x14603,x14604,x14605,x14601,x14606,x14607,x14608),f511(x14603,x14604,x14605,x14602,x14606,x14607,x14608)) % 172.83/172.50 [1461]~E(x14611,x14612)+E(f511(x14613,x14614,x14615,x14616,x14611,x14617,x14618),f511(x14613,x14614,x14615,x14616,x14612,x14617,x14618)) % 172.83/172.50 [1462]~E(x14621,x14622)+E(f511(x14623,x14624,x14625,x14626,x14627,x14621,x14628),f511(x14623,x14624,x14625,x14626,x14627,x14622,x14628)) % 172.83/172.50 [1463]~E(x14631,x14632)+E(f511(x14633,x14634,x14635,x14636,x14637,x14638,x14631),f511(x14633,x14634,x14635,x14636,x14637,x14638,x14632)) % 172.83/172.50 [1464]~E(x14641,x14642)+E(f297(x14641,x14643,x14644,x14645,x14646),f297(x14642,x14643,x14644,x14645,x14646)) % 172.83/172.50 [1465]~E(x14651,x14652)+E(f297(x14653,x14651,x14654,x14655,x14656),f297(x14653,x14652,x14654,x14655,x14656)) % 172.83/172.50 [1466]~E(x14661,x14662)+E(f297(x14663,x14664,x14661,x14665,x14666),f297(x14663,x14664,x14662,x14665,x14666)) % 172.83/172.50 [1467]~E(x14671,x14672)+E(f297(x14673,x14674,x14675,x14671,x14676),f297(x14673,x14674,x14675,x14672,x14676)) % 172.83/172.50 [1468]~E(x14681,x14682)+E(f297(x14683,x14684,x14685,x14686,x14681),f297(x14683,x14684,x14685,x14686,x14682)) % 172.83/172.50 [1469]~E(x14691,x14692)+E(f658(x14691,x14693,x14694),f658(x14692,x14693,x14694)) % 172.83/172.50 [1470]~E(x14701,x14702)+E(f658(x14703,x14701,x14704),f658(x14703,x14702,x14704)) % 172.83/172.50 [1471]~E(x14711,x14712)+E(f658(x14713,x14714,x14711),f658(x14713,x14714,x14712)) % 172.83/172.50 [1472]~E(x14721,x14722)+E(f240(x14721,x14723,x14724),f240(x14722,x14723,x14724)) % 172.83/172.50 [1473]~E(x14731,x14732)+E(f240(x14733,x14731,x14734),f240(x14733,x14732,x14734)) % 172.83/172.50 [1474]~E(x14741,x14742)+E(f240(x14743,x14744,x14741),f240(x14743,x14744,x14742)) % 172.83/172.50 [1475]~E(x14751,x14752)+E(f399(x14751,x14753,x14754,x14755,x14756,x14757,x14758,x14759,x147510),f399(x14752,x14753,x14754,x14755,x14756,x14757,x14758,x14759,x147510)) % 172.83/172.50 [1476]~E(x14761,x14762)+E(f399(x14763,x14761,x14764,x14765,x14766,x14767,x14768,x14769,x147610),f399(x14763,x14762,x14764,x14765,x14766,x14767,x14768,x14769,x147610)) % 172.83/172.50 [1477]~E(x14771,x14772)+E(f399(x14773,x14774,x14771,x14775,x14776,x14777,x14778,x14779,x147710),f399(x14773,x14774,x14772,x14775,x14776,x14777,x14778,x14779,x147710)) % 172.83/172.50 [1478]~E(x14781,x14782)+E(f399(x14783,x14784,x14785,x14781,x14786,x14787,x14788,x14789,x147810),f399(x14783,x14784,x14785,x14782,x14786,x14787,x14788,x14789,x147810)) % 172.83/172.50 [1479]~E(x14791,x14792)+E(f399(x14793,x14794,x14795,x14796,x14791,x14797,x14798,x14799,x147910),f399(x14793,x14794,x14795,x14796,x14792,x14797,x14798,x14799,x147910)) % 172.83/172.50 [1480]~E(x14801,x14802)+E(f399(x14803,x14804,x14805,x14806,x14807,x14801,x14808,x14809,x148010),f399(x14803,x14804,x14805,x14806,x14807,x14802,x14808,x14809,x148010)) % 172.83/172.50 [1481]~E(x14811,x14812)+E(f399(x14813,x14814,x14815,x14816,x14817,x14818,x14811,x14819,x148110),f399(x14813,x14814,x14815,x14816,x14817,x14818,x14812,x14819,x148110)) % 172.83/172.50 [1482]~E(x14821,x14822)+E(f399(x14823,x14824,x14825,x14826,x14827,x14828,x14829,x14821,x148210),f399(x14823,x14824,x14825,x14826,x14827,x14828,x14829,x14822,x148210)) % 172.83/172.50 [1483]~E(x14831,x14832)+E(f399(x14833,x14834,x14835,x14836,x14837,x14838,x14839,x148310,x14831),f399(x14833,x14834,x14835,x14836,x14837,x14838,x14839,x148310,x14832)) % 172.83/172.50 [1484]~E(x14841,x14842)+E(f341(x14841),f341(x14842)) % 172.83/172.50 [1485]~E(x14851,x14852)+E(f685(x14851,x14853,x14854,x14855),f685(x14852,x14853,x14854,x14855)) % 172.83/172.50 [1486]~E(x14861,x14862)+E(f685(x14863,x14861,x14864,x14865),f685(x14863,x14862,x14864,x14865)) % 172.83/172.50 [1487]~E(x14871,x14872)+E(f685(x14873,x14874,x14871,x14875),f685(x14873,x14874,x14872,x14875)) % 172.83/172.50 [1488]~E(x14881,x14882)+E(f685(x14883,x14884,x14885,x14881),f685(x14883,x14884,x14885,x14882)) % 172.83/172.50 [1489]~E(x14891,x14892)+E(f772(x14891,x14893,x14894,x14895,x14896),f772(x14892,x14893,x14894,x14895,x14896)) % 172.83/172.50 [1490]~E(x14901,x14902)+E(f772(x14903,x14901,x14904,x14905,x14906),f772(x14903,x14902,x14904,x14905,x14906)) % 172.83/172.50 [1491]~E(x14911,x14912)+E(f772(x14913,x14914,x14911,x14915,x14916),f772(x14913,x14914,x14912,x14915,x14916)) % 172.83/172.50 [1492]~E(x14921,x14922)+E(f772(x14923,x14924,x14925,x14921,x14926),f772(x14923,x14924,x14925,x14922,x14926)) % 172.83/172.50 [1493]~E(x14931,x14932)+E(f772(x14933,x14934,x14935,x14936,x14931),f772(x14933,x14934,x14935,x14936,x14932)) % 172.83/172.50 [1494]~E(x14941,x14942)+E(f725(x14941,x14943,x14944,x14945),f725(x14942,x14943,x14944,x14945)) % 172.83/172.50 [1495]~E(x14951,x14952)+E(f725(x14953,x14951,x14954,x14955),f725(x14953,x14952,x14954,x14955)) % 172.83/172.50 [1496]~E(x14961,x14962)+E(f725(x14963,x14964,x14961,x14965),f725(x14963,x14964,x14962,x14965)) % 172.83/172.50 [1497]~E(x14971,x14972)+E(f725(x14973,x14974,x14975,x14971),f725(x14973,x14974,x14975,x14972)) % 172.83/172.50 [1498]~E(x14981,x14982)+E(f452(x14981,x14983,x14984),f452(x14982,x14983,x14984)) % 172.83/172.50 [1499]~E(x14991,x14992)+E(f452(x14993,x14991,x14994),f452(x14993,x14992,x14994)) % 172.83/172.50 [1500]~E(x15001,x15002)+E(f452(x15003,x15004,x15001),f452(x15003,x15004,x15002)) % 172.83/172.50 [1501]~E(x15011,x15012)+E(f447(x15011,x15013,x15014,x15015),f447(x15012,x15013,x15014,x15015)) % 172.83/172.50 [1502]~E(x15021,x15022)+E(f447(x15023,x15021,x15024,x15025),f447(x15023,x15022,x15024,x15025)) % 172.83/172.50 [1503]~E(x15031,x15032)+E(f447(x15033,x15034,x15031,x15035),f447(x15033,x15034,x15032,x15035)) % 172.83/172.50 [1504]~E(x15041,x15042)+E(f447(x15043,x15044,x15045,x15041),f447(x15043,x15044,x15045,x15042)) % 172.83/172.50 [1505]~E(x15051,x15052)+E(f436(x15051,x15053,x15054,x15055),f436(x15052,x15053,x15054,x15055)) % 172.83/172.50 [1506]~E(x15061,x15062)+E(f436(x15063,x15061,x15064,x15065),f436(x15063,x15062,x15064,x15065)) % 172.83/172.50 [1507]~E(x15071,x15072)+E(f436(x15073,x15074,x15071,x15075),f436(x15073,x15074,x15072,x15075)) % 172.83/172.50 [1508]~E(x15081,x15082)+E(f436(x15083,x15084,x15085,x15081),f436(x15083,x15084,x15085,x15082)) % 172.83/172.50 [1509]~E(x15091,x15092)+E(f594(x15091,x15093,x15094),f594(x15092,x15093,x15094)) % 172.83/172.50 [1510]~E(x15101,x15102)+E(f594(x15103,x15101,x15104),f594(x15103,x15102,x15104)) % 172.83/172.50 [1511]~E(x15111,x15112)+E(f594(x15113,x15114,x15111),f594(x15113,x15114,x15112)) % 172.83/172.50 [1512]~E(x15121,x15122)+E(f193(x15121),f193(x15122)) % 172.83/172.50 [1513]~E(x15131,x15132)+E(f794(x15131,x15133,x15134),f794(x15132,x15133,x15134)) % 172.83/172.50 [1514]~E(x15141,x15142)+E(f794(x15143,x15141,x15144),f794(x15143,x15142,x15144)) % 172.83/172.50 [1515]~E(x15151,x15152)+E(f794(x15153,x15154,x15151),f794(x15153,x15154,x15152)) % 172.83/172.50 [1516]~E(x15161,x15162)+E(f470(x15161,x15163,x15164),f470(x15162,x15163,x15164)) % 172.83/172.50 [1517]~E(x15171,x15172)+E(f470(x15173,x15171,x15174),f470(x15173,x15172,x15174)) % 172.83/172.50 [1518]~E(x15181,x15182)+E(f470(x15183,x15184,x15181),f470(x15183,x15184,x15182)) % 172.83/172.50 [1519]~E(x15191,x15192)+E(f761(x15191,x15193),f761(x15192,x15193)) % 172.83/172.50 [1520]~E(x15201,x15202)+E(f761(x15203,x15201),f761(x15203,x15202)) % 172.83/172.50 [1521]~E(x15211,x15212)+E(f850(x15211,x15213,x15214),f850(x15212,x15213,x15214)) % 172.83/172.50 [1522]~E(x15221,x15222)+E(f850(x15223,x15221,x15224),f850(x15223,x15222,x15224)) % 172.83/172.50 [1523]~E(x15231,x15232)+E(f850(x15233,x15234,x15231),f850(x15233,x15234,x15232)) % 172.83/172.50 [1524]~E(x15241,x15242)+E(f766(x15241,x15243),f766(x15242,x15243)) % 172.83/172.50 [1525]~E(x15251,x15252)+E(f766(x15253,x15251),f766(x15253,x15252)) % 172.83/172.50 [1526]~E(x15261,x15262)+E(f606(x15261,x15263),f606(x15262,x15263)) % 172.83/172.50 [1527]~E(x15271,x15272)+E(f606(x15273,x15271),f606(x15273,x15272)) % 172.83/172.50 [1528]~E(x15281,x15282)+E(f597(x15281,x15283),f597(x15282,x15283)) % 172.83/172.50 [1529]~E(x15291,x15292)+E(f597(x15293,x15291),f597(x15293,x15292)) % 172.83/172.50 [1530]~E(x15301,x15302)+E(f129(x15301,x15303),f129(x15302,x15303)) % 172.83/172.50 [1531]~E(x15311,x15312)+E(f129(x15313,x15311),f129(x15313,x15312)) % 172.83/172.50 [1532]~E(x15321,x15322)+E(f865(x15321,x15323,x15324,x15325,x15326),f865(x15322,x15323,x15324,x15325,x15326)) % 172.83/172.50 [1533]~E(x15331,x15332)+E(f865(x15333,x15331,x15334,x15335,x15336),f865(x15333,x15332,x15334,x15335,x15336)) % 172.83/172.50 [1534]~E(x15341,x15342)+E(f865(x15343,x15344,x15341,x15345,x15346),f865(x15343,x15344,x15342,x15345,x15346)) % 172.83/172.50 [1535]~E(x15351,x15352)+E(f865(x15353,x15354,x15355,x15351,x15356),f865(x15353,x15354,x15355,x15352,x15356)) % 172.83/172.50 [1536]~E(x15361,x15362)+E(f865(x15363,x15364,x15365,x15366,x15361),f865(x15363,x15364,x15365,x15366,x15362)) % 172.83/172.50 [1537]~E(x15371,x15372)+E(f135(x15371),f135(x15372)) % 172.83/172.50 [1538]~E(x15381,x15382)+E(f182(x15381),f182(x15382)) % 172.83/172.50 [1539]~E(x15391,x15392)+E(f870(x15391,x15393,x15394,x15395,x15396),f870(x15392,x15393,x15394,x15395,x15396)) % 172.83/172.50 [1540]~E(x15401,x15402)+E(f870(x15403,x15401,x15404,x15405,x15406),f870(x15403,x15402,x15404,x15405,x15406)) % 172.83/172.50 [1541]~E(x15411,x15412)+E(f870(x15413,x15414,x15411,x15415,x15416),f870(x15413,x15414,x15412,x15415,x15416)) % 172.83/172.50 [1542]~E(x15421,x15422)+E(f870(x15423,x15424,x15425,x15421,x15426),f870(x15423,x15424,x15425,x15422,x15426)) % 172.83/172.50 [1543]~E(x15431,x15432)+E(f870(x15433,x15434,x15435,x15436,x15431),f870(x15433,x15434,x15435,x15436,x15432)) % 172.83/172.50 [1544]~E(x15441,x15442)+E(f786(x15441,x15443,x15444,x15445,x15446,x15447),f786(x15442,x15443,x15444,x15445,x15446,x15447)) % 172.83/172.50 [1545]~E(x15451,x15452)+E(f786(x15453,x15451,x15454,x15455,x15456,x15457),f786(x15453,x15452,x15454,x15455,x15456,x15457)) % 172.83/172.50 [1546]~E(x15461,x15462)+E(f786(x15463,x15464,x15461,x15465,x15466,x15467),f786(x15463,x15464,x15462,x15465,x15466,x15467)) % 172.83/172.50 [1547]~E(x15471,x15472)+E(f786(x15473,x15474,x15475,x15471,x15476,x15477),f786(x15473,x15474,x15475,x15472,x15476,x15477)) % 172.83/172.50 [1548]~E(x15481,x15482)+E(f786(x15483,x15484,x15485,x15486,x15481,x15487),f786(x15483,x15484,x15485,x15486,x15482,x15487)) % 172.83/172.50 [1549]~E(x15491,x15492)+E(f786(x15493,x15494,x15495,x15496,x15497,x15491),f786(x15493,x15494,x15495,x15496,x15497,x15492)) % 172.83/172.50 [1550]~E(x15501,x15502)+E(f264(x15501,x15503),f264(x15502,x15503)) % 172.83/172.50 [1551]~E(x15511,x15512)+E(f264(x15513,x15511),f264(x15513,x15512)) % 172.83/172.50 [1552]~E(x15521,x15522)+E(f501(x15521),f501(x15522)) % 172.83/172.50 [1553]~E(x15531,x15532)+E(f145(x15531,x15533),f145(x15532,x15533)) % 172.83/172.50 [1554]~E(x15541,x15542)+E(f145(x15543,x15541),f145(x15543,x15542)) % 172.83/172.50 [1555]~E(x15551,x15552)+E(f386(x15551,x15553,x15554,x15555),f386(x15552,x15553,x15554,x15555)) % 172.83/172.50 [1556]~E(x15561,x15562)+E(f386(x15563,x15561,x15564,x15565),f386(x15563,x15562,x15564,x15565)) % 172.83/172.50 [1557]~E(x15571,x15572)+E(f386(x15573,x15574,x15571,x15575),f386(x15573,x15574,x15572,x15575)) % 172.83/172.50 [1558]~E(x15581,x15582)+E(f386(x15583,x15584,x15585,x15581),f386(x15583,x15584,x15585,x15582)) % 172.83/172.50 [1559]~E(x15591,x15592)+E(f407(x15591,x15593),f407(x15592,x15593)) % 172.83/172.50 [1560]~E(x15601,x15602)+E(f407(x15603,x15601),f407(x15603,x15602)) % 172.83/172.50 [1561]~E(x15611,x15612)+E(f759(x15611,x15613,x15614,x15615),f759(x15612,x15613,x15614,x15615)) % 172.83/172.50 [1562]~E(x15621,x15622)+E(f759(x15623,x15621,x15624,x15625),f759(x15623,x15622,x15624,x15625)) % 172.83/172.50 [1563]~E(x15631,x15632)+E(f759(x15633,x15634,x15631,x15635),f759(x15633,x15634,x15632,x15635)) % 172.83/172.50 [1564]~E(x15641,x15642)+E(f759(x15643,x15644,x15645,x15641),f759(x15643,x15644,x15645,x15642)) % 172.83/172.50 [1565]~E(x15651,x15652)+E(f680(x15651,x15653,x15654),f680(x15652,x15653,x15654)) % 172.83/172.50 [1566]~E(x15661,x15662)+E(f680(x15663,x15661,x15664),f680(x15663,x15662,x15664)) % 172.83/172.50 [1567]~E(x15671,x15672)+E(f680(x15673,x15674,x15671),f680(x15673,x15674,x15672)) % 172.83/172.50 [1568]~E(x15681,x15682)+E(f609(x15681,x15683,x15684,x15685,x15686),f609(x15682,x15683,x15684,x15685,x15686)) % 172.83/172.50 [1569]~E(x15691,x15692)+E(f609(x15693,x15691,x15694,x15695,x15696),f609(x15693,x15692,x15694,x15695,x15696)) % 172.83/172.50 [1570]~E(x15701,x15702)+E(f609(x15703,x15704,x15701,x15705,x15706),f609(x15703,x15704,x15702,x15705,x15706)) % 172.83/172.50 [1571]~E(x15711,x15712)+E(f609(x15713,x15714,x15715,x15711,x15716),f609(x15713,x15714,x15715,x15712,x15716)) % 172.83/172.50 [1572]~E(x15721,x15722)+E(f609(x15723,x15724,x15725,x15726,x15721),f609(x15723,x15724,x15725,x15726,x15722)) % 172.83/172.50 [1573]~E(x15731,x15732)+E(f659(x15731,x15733),f659(x15732,x15733)) % 172.83/172.50 [1574]~E(x15741,x15742)+E(f659(x15743,x15741),f659(x15743,x15742)) % 172.83/172.50 [1575]~E(x15751,x15752)+E(f706(x15751,x15753,x15754,x15755,x15756),f706(x15752,x15753,x15754,x15755,x15756)) % 172.83/172.50 [1576]~E(x15761,x15762)+E(f706(x15763,x15761,x15764,x15765,x15766),f706(x15763,x15762,x15764,x15765,x15766)) % 172.83/172.50 [1577]~E(x15771,x15772)+E(f706(x15773,x15774,x15771,x15775,x15776),f706(x15773,x15774,x15772,x15775,x15776)) % 172.83/172.50 [1578]~E(x15781,x15782)+E(f706(x15783,x15784,x15785,x15781,x15786),f706(x15783,x15784,x15785,x15782,x15786)) % 172.83/172.50 [1579]~E(x15791,x15792)+E(f706(x15793,x15794,x15795,x15796,x15791),f706(x15793,x15794,x15795,x15796,x15792)) % 172.83/172.50 [1580]~E(x15801,x15802)+E(f560(x15801,x15803,x15804,x15805,x15806),f560(x15802,x15803,x15804,x15805,x15806)) % 172.83/172.50 [1581]~E(x15811,x15812)+E(f560(x15813,x15811,x15814,x15815,x15816),f560(x15813,x15812,x15814,x15815,x15816)) % 172.83/172.50 [1582]~E(x15821,x15822)+E(f560(x15823,x15824,x15821,x15825,x15826),f560(x15823,x15824,x15822,x15825,x15826)) % 172.83/172.50 [1583]~E(x15831,x15832)+E(f560(x15833,x15834,x15835,x15831,x15836),f560(x15833,x15834,x15835,x15832,x15836)) % 172.83/172.50 [1584]~E(x15841,x15842)+E(f560(x15843,x15844,x15845,x15846,x15841),f560(x15843,x15844,x15845,x15846,x15842)) % 172.83/172.50 [1585]~E(x15851,x15852)+E(f464(x15851,x15853),f464(x15852,x15853)) % 172.83/172.50 [1586]~E(x15861,x15862)+E(f464(x15863,x15861),f464(x15863,x15862)) % 172.83/172.50 [1587]~E(x15871,x15872)+E(f544(x15871,x15873,x15874,x15875,x15876,x15877),f544(x15872,x15873,x15874,x15875,x15876,x15877)) % 172.83/172.50 [1588]~E(x15881,x15882)+E(f544(x15883,x15881,x15884,x15885,x15886,x15887),f544(x15883,x15882,x15884,x15885,x15886,x15887)) % 172.83/172.50 [1589]~E(x15891,x15892)+E(f544(x15893,x15894,x15891,x15895,x15896,x15897),f544(x15893,x15894,x15892,x15895,x15896,x15897)) % 172.83/172.50 [1590]~E(x15901,x15902)+E(f544(x15903,x15904,x15905,x15901,x15906,x15907),f544(x15903,x15904,x15905,x15902,x15906,x15907)) % 172.83/172.50 [1591]~E(x15911,x15912)+E(f544(x15913,x15914,x15915,x15916,x15911,x15917),f544(x15913,x15914,x15915,x15916,x15912,x15917)) % 172.83/172.50 [1592]~E(x15921,x15922)+E(f544(x15923,x15924,x15925,x15926,x15927,x15921),f544(x15923,x15924,x15925,x15926,x15927,x15922)) % 172.83/172.50 [1593]~E(x15931,x15932)+E(f420(x15931,x15933,x15934),f420(x15932,x15933,x15934)) % 172.83/172.50 [1594]~E(x15941,x15942)+E(f420(x15943,x15941,x15944),f420(x15943,x15942,x15944)) % 172.83/172.50 [1595]~E(x15951,x15952)+E(f420(x15953,x15954,x15951),f420(x15953,x15954,x15952)) % 172.83/172.50 [1596]~E(x15961,x15962)+E(f515(x15961,x15963,x15964,x15965),f515(x15962,x15963,x15964,x15965)) % 172.83/172.50 [1597]~E(x15971,x15972)+E(f515(x15973,x15971,x15974,x15975),f515(x15973,x15972,x15974,x15975)) % 172.83/172.50 [1598]~E(x15981,x15982)+E(f515(x15983,x15984,x15981,x15985),f515(x15983,x15984,x15982,x15985)) % 172.83/172.50 [1599]~E(x15991,x15992)+E(f515(x15993,x15994,x15995,x15991),f515(x15993,x15994,x15995,x15992)) % 172.83/172.50 [1600]~E(x16001,x16002)+E(f472(x16001),f472(x16002)) % 172.83/172.50 [1601]~E(x16011,x16012)+E(f672(x16011,x16013,x16014,x16015,x16016),f672(x16012,x16013,x16014,x16015,x16016)) % 172.83/172.50 [1602]~E(x16021,x16022)+E(f672(x16023,x16021,x16024,x16025,x16026),f672(x16023,x16022,x16024,x16025,x16026)) % 172.83/172.50 [1603]~E(x16031,x16032)+E(f672(x16033,x16034,x16031,x16035,x16036),f672(x16033,x16034,x16032,x16035,x16036)) % 172.83/172.50 [1604]~E(x16041,x16042)+E(f672(x16043,x16044,x16045,x16041,x16046),f672(x16043,x16044,x16045,x16042,x16046)) % 172.83/172.50 [1605]~E(x16051,x16052)+E(f672(x16053,x16054,x16055,x16056,x16051),f672(x16053,x16054,x16055,x16056,x16052)) % 172.83/172.50 [1606]~E(x16061,x16062)+E(f437(x16061,x16063,x16064,x16065),f437(x16062,x16063,x16064,x16065)) % 172.83/172.50 [1607]~E(x16071,x16072)+E(f437(x16073,x16071,x16074,x16075),f437(x16073,x16072,x16074,x16075)) % 172.83/172.50 [1608]~E(x16081,x16082)+E(f437(x16083,x16084,x16081,x16085),f437(x16083,x16084,x16082,x16085)) % 172.83/172.50 [1609]~E(x16091,x16092)+E(f437(x16093,x16094,x16095,x16091),f437(x16093,x16094,x16095,x16092)) % 172.83/172.50 [1610]~E(x16101,x16102)+E(f836(x16101,x16103,x16104,x16105),f836(x16102,x16103,x16104,x16105)) % 172.83/172.50 [1611]~E(x16111,x16112)+E(f836(x16113,x16111,x16114,x16115),f836(x16113,x16112,x16114,x16115)) % 172.83/172.50 [1612]~E(x16121,x16122)+E(f836(x16123,x16124,x16121,x16125),f836(x16123,x16124,x16122,x16125)) % 172.83/172.50 [1613]~E(x16131,x16132)+E(f836(x16133,x16134,x16135,x16131),f836(x16133,x16134,x16135,x16132)) % 172.83/172.50 [1614]~E(x16141,x16142)+E(f555(x16141,x16143,x16144),f555(x16142,x16143,x16144)) % 172.83/172.50 [1615]~E(x16151,x16152)+E(f555(x16153,x16151,x16154),f555(x16153,x16152,x16154)) % 172.83/172.50 [1616]~E(x16161,x16162)+E(f555(x16163,x16164,x16161),f555(x16163,x16164,x16162)) % 172.83/172.50 [1617]~E(x16171,x16172)+E(f485(x16171,x16173,x16174),f485(x16172,x16173,x16174)) % 172.83/172.50 [1618]~E(x16181,x16182)+E(f485(x16183,x16181,x16184),f485(x16183,x16182,x16184)) % 172.83/172.50 [1619]~E(x16191,x16192)+E(f485(x16193,x16194,x16191),f485(x16193,x16194,x16192)) % 172.83/172.50 [1620]~E(x16201,x16202)+E(f131(x16201,x16203,x16204,x16205),f131(x16202,x16203,x16204,x16205)) % 172.83/172.50 [1621]~E(x16211,x16212)+E(f131(x16213,x16211,x16214,x16215),f131(x16213,x16212,x16214,x16215)) % 172.83/172.50 [1622]~E(x16221,x16222)+E(f131(x16223,x16224,x16221,x16225),f131(x16223,x16224,x16222,x16225)) % 172.83/172.50 [1623]~E(x16231,x16232)+E(f131(x16233,x16234,x16235,x16231),f131(x16233,x16234,x16235,x16232)) % 172.83/172.50 [1624]~E(x16241,x16242)+E(f345(x16241,x16243,x16244,x16245,x16246),f345(x16242,x16243,x16244,x16245,x16246)) % 172.83/172.50 [1625]~E(x16251,x16252)+E(f345(x16253,x16251,x16254,x16255,x16256),f345(x16253,x16252,x16254,x16255,x16256)) % 172.83/172.50 [1626]~E(x16261,x16262)+E(f345(x16263,x16264,x16261,x16265,x16266),f345(x16263,x16264,x16262,x16265,x16266)) % 172.83/172.50 [1627]~E(x16271,x16272)+E(f345(x16273,x16274,x16275,x16271,x16276),f345(x16273,x16274,x16275,x16272,x16276)) % 172.83/172.50 [1628]~E(x16281,x16282)+E(f345(x16283,x16284,x16285,x16286,x16281),f345(x16283,x16284,x16285,x16286,x16282)) % 172.83/172.50 [1629]~E(x16291,x16292)+E(f406(x16291,x16293,x16294,x16295),f406(x16292,x16293,x16294,x16295)) % 172.83/172.50 [1630]~E(x16301,x16302)+E(f406(x16303,x16301,x16304,x16305),f406(x16303,x16302,x16304,x16305)) % 172.83/172.50 [1631]~E(x16311,x16312)+E(f406(x16313,x16314,x16311,x16315),f406(x16313,x16314,x16312,x16315)) % 172.83/172.50 [1632]~E(x16321,x16322)+E(f406(x16323,x16324,x16325,x16321),f406(x16323,x16324,x16325,x16322)) % 172.83/172.50 [1633]~E(x16331,x16332)+E(f643(x16331,x16333,x16334),f643(x16332,x16333,x16334)) % 172.83/172.50 [1634]~E(x16341,x16342)+E(f643(x16343,x16341,x16344),f643(x16343,x16342,x16344)) % 172.83/172.50 [1635]~E(x16351,x16352)+E(f643(x16353,x16354,x16351),f643(x16353,x16354,x16352)) % 172.83/172.50 [1636]~E(x16361,x16362)+E(f268(x16361,x16363,x16364,x16365,x16366),f268(x16362,x16363,x16364,x16365,x16366)) % 172.83/172.50 [1637]~E(x16371,x16372)+E(f268(x16373,x16371,x16374,x16375,x16376),f268(x16373,x16372,x16374,x16375,x16376)) % 172.83/172.50 [1638]~E(x16381,x16382)+E(f268(x16383,x16384,x16381,x16385,x16386),f268(x16383,x16384,x16382,x16385,x16386)) % 172.83/172.50 [1639]~E(x16391,x16392)+E(f268(x16393,x16394,x16395,x16391,x16396),f268(x16393,x16394,x16395,x16392,x16396)) % 172.83/172.50 [1640]~E(x16401,x16402)+E(f268(x16403,x16404,x16405,x16406,x16401),f268(x16403,x16404,x16405,x16406,x16402)) % 172.83/172.50 [1641]~E(x16411,x16412)+E(f736(x16411,x16413,x16414),f736(x16412,x16413,x16414)) % 172.83/172.50 [1642]~E(x16421,x16422)+E(f736(x16423,x16421,x16424),f736(x16423,x16422,x16424)) % 172.83/172.50 [1643]~E(x16431,x16432)+E(f736(x16433,x16434,x16431),f736(x16433,x16434,x16432)) % 172.83/172.50 [1644]~E(x16441,x16442)+E(f354(x16441,x16443,x16444,x16445),f354(x16442,x16443,x16444,x16445)) % 172.83/172.50 [1645]~E(x16451,x16452)+E(f354(x16453,x16451,x16454,x16455),f354(x16453,x16452,x16454,x16455)) % 172.83/172.50 [1646]~E(x16461,x16462)+E(f354(x16463,x16464,x16461,x16465),f354(x16463,x16464,x16462,x16465)) % 172.83/172.50 [1647]~E(x16471,x16472)+E(f354(x16473,x16474,x16475,x16471),f354(x16473,x16474,x16475,x16472)) % 172.83/172.50 [1648]~E(x16481,x16482)+E(f726(x16481,x16483),f726(x16482,x16483)) % 172.83/172.50 [1649]~E(x16491,x16492)+E(f726(x16493,x16491),f726(x16493,x16492)) % 172.83/172.50 [1650]~E(x16501,x16502)+E(f387(x16501,x16503,x16504),f387(x16502,x16503,x16504)) % 172.83/172.50 [1651]~E(x16511,x16512)+E(f387(x16513,x16511,x16514),f387(x16513,x16512,x16514)) % 172.83/172.50 [1652]~E(x16521,x16522)+E(f387(x16523,x16524,x16521),f387(x16523,x16524,x16522)) % 172.83/172.50 [1653]~E(x16531,x16532)+E(f755(x16531,x16533,x16534,x16535,x16536),f755(x16532,x16533,x16534,x16535,x16536)) % 172.83/172.50 [1654]~E(x16541,x16542)+E(f755(x16543,x16541,x16544,x16545,x16546),f755(x16543,x16542,x16544,x16545,x16546)) % 172.83/172.50 [1655]~E(x16551,x16552)+E(f755(x16553,x16554,x16551,x16555,x16556),f755(x16553,x16554,x16552,x16555,x16556)) % 172.83/172.50 [1656]~E(x16561,x16562)+E(f755(x16563,x16564,x16565,x16561,x16566),f755(x16563,x16564,x16565,x16562,x16566)) % 172.83/172.50 [1657]~E(x16571,x16572)+E(f755(x16573,x16574,x16575,x16576,x16571),f755(x16573,x16574,x16575,x16576,x16572)) % 172.83/172.50 [1658]~E(x16581,x16582)+E(f693(x16581,x16583),f693(x16582,x16583)) % 172.83/172.50 [1659]~E(x16591,x16592)+E(f693(x16593,x16591),f693(x16593,x16592)) % 172.83/172.50 [1660]~E(x16601,x16602)+E(f130(x16601,x16603,x16604,x16605,x16606),f130(x16602,x16603,x16604,x16605,x16606)) % 172.83/172.50 [1661]~E(x16611,x16612)+E(f130(x16613,x16611,x16614,x16615,x16616),f130(x16613,x16612,x16614,x16615,x16616)) % 172.83/172.50 [1662]~E(x16621,x16622)+E(f130(x16623,x16624,x16621,x16625,x16626),f130(x16623,x16624,x16622,x16625,x16626)) % 172.83/172.50 [1663]~E(x16631,x16632)+E(f130(x16633,x16634,x16635,x16631,x16636),f130(x16633,x16634,x16635,x16632,x16636)) % 172.83/172.50 [1664]~E(x16641,x16642)+E(f130(x16643,x16644,x16645,x16646,x16641),f130(x16643,x16644,x16645,x16646,x16642)) % 172.83/172.50 [1665]~E(x16651,x16652)+E(f845(x16651,x16653,x16654,x16655,x16656),f845(x16652,x16653,x16654,x16655,x16656)) % 172.83/172.50 [1666]~E(x16661,x16662)+E(f845(x16663,x16661,x16664,x16665,x16666),f845(x16663,x16662,x16664,x16665,x16666)) % 172.83/172.50 [1667]~E(x16671,x16672)+E(f845(x16673,x16674,x16671,x16675,x16676),f845(x16673,x16674,x16672,x16675,x16676)) % 172.83/172.50 [1668]~E(x16681,x16682)+E(f845(x16683,x16684,x16685,x16681,x16686),f845(x16683,x16684,x16685,x16682,x16686)) % 172.83/172.50 [1669]~E(x16691,x16692)+E(f845(x16693,x16694,x16695,x16696,x16691),f845(x16693,x16694,x16695,x16696,x16692)) % 172.83/172.50 [1670]~E(x16701,x16702)+E(f662(x16701,x16703,x16704,x16705),f662(x16702,x16703,x16704,x16705)) % 172.83/172.50 [1671]~E(x16711,x16712)+E(f662(x16713,x16711,x16714,x16715),f662(x16713,x16712,x16714,x16715)) % 172.83/172.50 [1672]~E(x16721,x16722)+E(f662(x16723,x16724,x16721,x16725),f662(x16723,x16724,x16722,x16725)) % 172.83/172.50 [1673]~E(x16731,x16732)+E(f662(x16733,x16734,x16735,x16731),f662(x16733,x16734,x16735,x16732)) % 172.83/172.50 [1674]~E(x16741,x16742)+E(f805(x16741,x16743,x16744,x16745),f805(x16742,x16743,x16744,x16745)) % 172.83/172.50 [1675]~E(x16751,x16752)+E(f805(x16753,x16751,x16754,x16755),f805(x16753,x16752,x16754,x16755)) % 172.83/172.50 [1676]~E(x16761,x16762)+E(f805(x16763,x16764,x16761,x16765),f805(x16763,x16764,x16762,x16765)) % 172.83/172.50 [1677]~E(x16771,x16772)+E(f805(x16773,x16774,x16775,x16771),f805(x16773,x16774,x16775,x16772)) % 172.83/172.50 [1678]~E(x16781,x16782)+E(f774(x16781,x16783,x16784,x16785),f774(x16782,x16783,x16784,x16785)) % 172.83/172.50 [1679]~E(x16791,x16792)+E(f774(x16793,x16791,x16794,x16795),f774(x16793,x16792,x16794,x16795)) % 172.83/172.50 [1680]~E(x16801,x16802)+E(f774(x16803,x16804,x16801,x16805),f774(x16803,x16804,x16802,x16805)) % 172.83/172.50 [1681]~E(x16811,x16812)+E(f774(x16813,x16814,x16815,x16811),f774(x16813,x16814,x16815,x16812)) % 172.83/172.50 [1682]~E(x16821,x16822)+E(f493(x16821,x16823,x16824),f493(x16822,x16823,x16824)) % 172.83/172.50 [1683]~E(x16831,x16832)+E(f493(x16833,x16831,x16834),f493(x16833,x16832,x16834)) % 172.83/172.50 [1684]~E(x16841,x16842)+E(f493(x16843,x16844,x16841),f493(x16843,x16844,x16842)) % 172.83/172.50 [1685]~E(x16851,x16852)+E(f656(x16851,x16853,x16854),f656(x16852,x16853,x16854)) % 172.83/172.50 [1686]~E(x16861,x16862)+E(f656(x16863,x16861,x16864),f656(x16863,x16862,x16864)) % 172.83/172.50 [1687]~E(x16871,x16872)+E(f656(x16873,x16874,x16871),f656(x16873,x16874,x16872)) % 172.83/172.50 [1688]~E(x16881,x16882)+E(f838(x16881,x16883,x16884),f838(x16882,x16883,x16884)) % 172.83/172.50 [1689]~E(x16891,x16892)+E(f838(x16893,x16891,x16894),f838(x16893,x16892,x16894)) % 172.83/172.50 [1690]~E(x16901,x16902)+E(f838(x16903,x16904,x16901),f838(x16903,x16904,x16902)) % 172.83/172.50 [1691]~E(x16911,x16912)+E(f617(x16911,x16913,x16914,x16915,x16916),f617(x16912,x16913,x16914,x16915,x16916)) % 172.83/172.50 [1692]~E(x16921,x16922)+E(f617(x16923,x16921,x16924,x16925,x16926),f617(x16923,x16922,x16924,x16925,x16926)) % 172.83/172.50 [1693]~E(x16931,x16932)+E(f617(x16933,x16934,x16931,x16935,x16936),f617(x16933,x16934,x16932,x16935,x16936)) % 172.83/172.50 [1694]~E(x16941,x16942)+E(f617(x16943,x16944,x16945,x16941,x16946),f617(x16943,x16944,x16945,x16942,x16946)) % 172.83/172.50 [1695]~E(x16951,x16952)+E(f617(x16953,x16954,x16955,x16956,x16951),f617(x16953,x16954,x16955,x16956,x16952)) % 172.83/172.50 [1696]~E(x16961,x16962)+E(f798(x16961,x16963,x16964),f798(x16962,x16963,x16964)) % 172.83/172.50 [1697]~E(x16971,x16972)+E(f798(x16973,x16971,x16974),f798(x16973,x16972,x16974)) % 172.83/172.50 [1698]~E(x16981,x16982)+E(f798(x16983,x16984,x16981),f798(x16983,x16984,x16982)) % 172.83/172.50 [1699]~E(x16991,x16992)+E(f702(x16991,x16993,x16994,x16995),f702(x16992,x16993,x16994,x16995)) % 172.83/172.50 [1700]~E(x17001,x17002)+E(f702(x17003,x17001,x17004,x17005),f702(x17003,x17002,x17004,x17005)) % 172.83/172.50 [1701]~E(x17011,x17012)+E(f702(x17013,x17014,x17011,x17015),f702(x17013,x17014,x17012,x17015)) % 172.83/172.50 [1702]~E(x17021,x17022)+E(f702(x17023,x17024,x17025,x17021),f702(x17023,x17024,x17025,x17022)) % 172.83/172.50 [1703]~E(x17031,x17032)+E(f691(x17031,x17033,x17034,x17035,x17036),f691(x17032,x17033,x17034,x17035,x17036)) % 172.83/172.50 [1704]~E(x17041,x17042)+E(f691(x17043,x17041,x17044,x17045,x17046),f691(x17043,x17042,x17044,x17045,x17046)) % 172.83/172.50 [1705]~E(x17051,x17052)+E(f691(x17053,x17054,x17051,x17055,x17056),f691(x17053,x17054,x17052,x17055,x17056)) % 172.83/172.50 [1706]~E(x17061,x17062)+E(f691(x17063,x17064,x17065,x17061,x17066),f691(x17063,x17064,x17065,x17062,x17066)) % 172.83/172.50 [1707]~E(x17071,x17072)+E(f691(x17073,x17074,x17075,x17076,x17071),f691(x17073,x17074,x17075,x17076,x17072)) % 172.83/172.50 [1708]~E(x17081,x17082)+E(f340(x17081),f340(x17082)) % 172.83/172.50 [1709]~E(x17091,x17092)+E(f756(x17091,x17093),f756(x17092,x17093)) % 172.83/172.50 [1710]~E(x17101,x17102)+E(f756(x17103,x17101),f756(x17103,x17102)) % 172.83/172.50 [1711]~E(x17111,x17112)+E(f488(x17111,x17113),f488(x17112,x17113)) % 172.83/172.50 [1712]~E(x17121,x17122)+E(f488(x17123,x17121),f488(x17123,x17122)) % 172.83/172.50 [1713]~E(x17131,x17132)+E(f398(x17131,x17133,x17134,x17135),f398(x17132,x17133,x17134,x17135)) % 172.83/172.50 [1714]~E(x17141,x17142)+E(f398(x17143,x17141,x17144,x17145),f398(x17143,x17142,x17144,x17145)) % 172.83/172.50 [1715]~E(x17151,x17152)+E(f398(x17153,x17154,x17151,x17155),f398(x17153,x17154,x17152,x17155)) % 172.83/172.50 [1716]~E(x17161,x17162)+E(f398(x17163,x17164,x17165,x17161),f398(x17163,x17164,x17165,x17162)) % 172.83/172.50 [1717]~E(x17171,x17172)+E(f292(x17171,x17173),f292(x17172,x17173)) % 172.83/172.50 [1718]~E(x17181,x17182)+E(f292(x17183,x17181),f292(x17183,x17182)) % 172.83/172.50 [1719]~E(x17191,x17192)+E(f520(x17191,x17193,x17194,x17195),f520(x17192,x17193,x17194,x17195)) % 172.83/172.50 [1720]~E(x17201,x17202)+E(f520(x17203,x17201,x17204,x17205),f520(x17203,x17202,x17204,x17205)) % 172.83/172.50 [1721]~E(x17211,x17212)+E(f520(x17213,x17214,x17211,x17215),f520(x17213,x17214,x17212,x17215)) % 172.83/172.50 [1722]~E(x17221,x17222)+E(f520(x17223,x17224,x17225,x17221),f520(x17223,x17224,x17225,x17222)) % 172.83/172.50 [1723]~E(x17231,x17232)+E(f400(x17231,x17233,x17234),f400(x17232,x17233,x17234)) % 172.83/172.50 [1724]~E(x17241,x17242)+E(f400(x17243,x17241,x17244),f400(x17243,x17242,x17244)) % 172.83/172.50 [1725]~E(x17251,x17252)+E(f400(x17253,x17254,x17251),f400(x17253,x17254,x17252)) % 172.83/172.50 [1726]~E(x17261,x17262)+E(f339(x17261),f339(x17262)) % 172.83/172.50 [1727]~E(x17271,x17272)+E(f445(x17271,x17273,x17274,x17275,x17276),f445(x17272,x17273,x17274,x17275,x17276)) % 172.83/172.50 [1728]~E(x17281,x17282)+E(f445(x17283,x17281,x17284,x17285,x17286),f445(x17283,x17282,x17284,x17285,x17286)) % 172.83/172.50 [1729]~E(x17291,x17292)+E(f445(x17293,x17294,x17291,x17295,x17296),f445(x17293,x17294,x17292,x17295,x17296)) % 172.83/172.50 [1730]~E(x17301,x17302)+E(f445(x17303,x17304,x17305,x17301,x17306),f445(x17303,x17304,x17305,x17302,x17306)) % 172.83/172.50 [1731]~E(x17311,x17312)+E(f445(x17313,x17314,x17315,x17316,x17311),f445(x17313,x17314,x17315,x17316,x17312)) % 172.83/172.50 [1732]~E(x17321,x17322)+E(f326(x17321,x17323,x17324),f326(x17322,x17323,x17324)) % 172.83/172.50 [1733]~E(x17331,x17332)+E(f326(x17333,x17331,x17334),f326(x17333,x17332,x17334)) % 172.83/172.50 [1734]~E(x17341,x17342)+E(f326(x17343,x17344,x17341),f326(x17343,x17344,x17342)) % 172.83/172.50 [1735]~E(x17351,x17352)+E(f708(x17351,x17353,x17354),f708(x17352,x17353,x17354)) % 172.83/172.50 [1736]~E(x17361,x17362)+E(f708(x17363,x17361,x17364),f708(x17363,x17362,x17364)) % 172.83/172.50 [1737]~E(x17371,x17372)+E(f708(x17373,x17374,x17371),f708(x17373,x17374,x17372)) % 172.83/172.50 [1738]~E(x17381,x17382)+E(f346(x17381,x17383,x17384,x17385,x17386),f346(x17382,x17383,x17384,x17385,x17386)) % 172.83/172.50 [1739]~E(x17391,x17392)+E(f346(x17393,x17391,x17394,x17395,x17396),f346(x17393,x17392,x17394,x17395,x17396)) % 172.83/172.50 [1740]~E(x17401,x17402)+E(f346(x17403,x17404,x17401,x17405,x17406),f346(x17403,x17404,x17402,x17405,x17406)) % 172.83/172.50 [1741]~E(x17411,x17412)+E(f346(x17413,x17414,x17415,x17411,x17416),f346(x17413,x17414,x17415,x17412,x17416)) % 172.83/172.50 [1742]~E(x17421,x17422)+E(f346(x17423,x17424,x17425,x17426,x17421),f346(x17423,x17424,x17425,x17426,x17422)) % 172.83/172.50 [1743]~E(x17431,x17432)+E(f579(x17431,x17433),f579(x17432,x17433)) % 172.83/172.50 [1744]~E(x17441,x17442)+E(f579(x17443,x17441),f579(x17443,x17442)) % 172.83/172.50 [1745]~E(x17451,x17452)+E(f817(x17451,x17453,x17454,x17455,x17456),f817(x17452,x17453,x17454,x17455,x17456)) % 172.83/172.50 [1746]~E(x17461,x17462)+E(f817(x17463,x17461,x17464,x17465,x17466),f817(x17463,x17462,x17464,x17465,x17466)) % 172.83/172.50 [1747]~E(x17471,x17472)+E(f817(x17473,x17474,x17471,x17475,x17476),f817(x17473,x17474,x17472,x17475,x17476)) % 172.83/172.50 [1748]~E(x17481,x17482)+E(f817(x17483,x17484,x17485,x17481,x17486),f817(x17483,x17484,x17485,x17482,x17486)) % 172.83/172.50 [1749]~E(x17491,x17492)+E(f817(x17493,x17494,x17495,x17496,x17491),f817(x17493,x17494,x17495,x17496,x17492)) % 172.83/172.50 [1750]~E(x17501,x17502)+E(f237(x17501,x17503,x17504,x17505),f237(x17502,x17503,x17504,x17505)) % 172.83/172.50 [1751]~E(x17511,x17512)+E(f237(x17513,x17511,x17514,x17515),f237(x17513,x17512,x17514,x17515)) % 172.83/172.50 [1752]~E(x17521,x17522)+E(f237(x17523,x17524,x17521,x17525),f237(x17523,x17524,x17522,x17525)) % 172.83/172.50 [1753]~E(x17531,x17532)+E(f237(x17533,x17534,x17535,x17531),f237(x17533,x17534,x17535,x17532)) % 172.83/172.50 [1754]~E(x17541,x17542)+E(f343(x17541,x17543),f343(x17542,x17543)) % 172.83/172.50 [1755]~E(x17551,x17552)+E(f343(x17553,x17551),f343(x17553,x17552)) % 172.83/172.50 [1756]~E(x17561,x17562)+E(f96(x17561,x17563,x17564),f96(x17562,x17563,x17564)) % 172.83/172.50 [1757]~E(x17571,x17572)+E(f96(x17573,x17571,x17574),f96(x17573,x17572,x17574)) % 172.83/172.50 [1758]~E(x17581,x17582)+E(f96(x17583,x17584,x17581),f96(x17583,x17584,x17582)) % 172.83/172.50 [1759]~E(x17591,x17592)+E(f603(x17591,x17593,x17594),f603(x17592,x17593,x17594)) % 172.83/172.50 [1760]~E(x17601,x17602)+E(f603(x17603,x17601,x17604),f603(x17603,x17602,x17604)) % 172.83/172.50 [1761]~E(x17611,x17612)+E(f603(x17613,x17614,x17611),f603(x17613,x17614,x17612)) % 172.83/172.50 [1762]~E(x17621,x17622)+E(f280(x17621,x17623),f280(x17622,x17623)) % 172.83/172.50 [1763]~E(x17631,x17632)+E(f280(x17633,x17631),f280(x17633,x17632)) % 172.83/172.50 [1764]~E(x17641,x17642)+E(f787(x17641,x17643,x17644,x17645,x17646,x17647,x17648),f787(x17642,x17643,x17644,x17645,x17646,x17647,x17648)) % 172.83/172.50 [1765]~E(x17651,x17652)+E(f787(x17653,x17651,x17654,x17655,x17656,x17657,x17658),f787(x17653,x17652,x17654,x17655,x17656,x17657,x17658)) % 172.83/172.50 [1766]~E(x17661,x17662)+E(f787(x17663,x17664,x17661,x17665,x17666,x17667,x17668),f787(x17663,x17664,x17662,x17665,x17666,x17667,x17668)) % 172.83/172.50 [1767]~E(x17671,x17672)+E(f787(x17673,x17674,x17675,x17671,x17676,x17677,x17678),f787(x17673,x17674,x17675,x17672,x17676,x17677,x17678)) % 172.83/172.50 [1768]~E(x17681,x17682)+E(f787(x17683,x17684,x17685,x17686,x17681,x17687,x17688),f787(x17683,x17684,x17685,x17686,x17682,x17687,x17688)) % 172.83/172.50 [1769]~E(x17691,x17692)+E(f787(x17693,x17694,x17695,x17696,x17697,x17691,x17698),f787(x17693,x17694,x17695,x17696,x17697,x17692,x17698)) % 172.83/172.50 [1770]~E(x17701,x17702)+E(f787(x17703,x17704,x17705,x17706,x17707,x17708,x17701),f787(x17703,x17704,x17705,x17706,x17707,x17708,x17702)) % 172.83/172.50 [1771]~E(x17711,x17712)+E(f383(x17711,x17713),f383(x17712,x17713)) % 172.83/172.50 [1772]~E(x17721,x17722)+E(f383(x17723,x17721),f383(x17723,x17722)) % 172.83/172.50 [1773]~E(x17731,x17732)+E(f800(x17731,x17733,x17734),f800(x17732,x17733,x17734)) % 172.83/172.50 [1774]~E(x17741,x17742)+E(f800(x17743,x17741,x17744),f800(x17743,x17742,x17744)) % 172.83/172.50 [1775]~E(x17751,x17752)+E(f800(x17753,x17754,x17751),f800(x17753,x17754,x17752)) % 172.83/172.50 [1776]~E(x17761,x17762)+E(f278(x17761,x17763),f278(x17762,x17763)) % 172.83/172.50 [1777]~E(x17771,x17772)+E(f278(x17773,x17771),f278(x17773,x17772)) % 172.83/172.50 [1778]~E(x17781,x17782)+E(f197(x17781,x17783,x17784,x17785),f197(x17782,x17783,x17784,x17785)) % 172.83/172.50 [1779]~E(x17791,x17792)+E(f197(x17793,x17791,x17794,x17795),f197(x17793,x17792,x17794,x17795)) % 172.83/172.50 [1780]~E(x17801,x17802)+E(f197(x17803,x17804,x17801,x17805),f197(x17803,x17804,x17802,x17805)) % 172.83/172.50 [1781]~E(x17811,x17812)+E(f197(x17813,x17814,x17815,x17811),f197(x17813,x17814,x17815,x17812)) % 172.83/172.50 [1782]~E(x17821,x17822)+E(f412(x17821,x17823,x17824,x17825),f412(x17822,x17823,x17824,x17825)) % 172.83/172.50 [1783]~E(x17831,x17832)+E(f412(x17833,x17831,x17834,x17835),f412(x17833,x17832,x17834,x17835)) % 172.83/172.50 [1784]~E(x17841,x17842)+E(f412(x17843,x17844,x17841,x17845),f412(x17843,x17844,x17842,x17845)) % 172.83/172.50 [1785]~E(x17851,x17852)+E(f412(x17853,x17854,x17855,x17851),f412(x17853,x17854,x17855,x17852)) % 172.83/172.50 [1786]~E(x17861,x17862)+E(f586(x17861,x17863,x17864,x17865),f586(x17862,x17863,x17864,x17865)) % 172.83/172.50 [1787]~E(x17871,x17872)+E(f586(x17873,x17871,x17874,x17875),f586(x17873,x17872,x17874,x17875)) % 172.83/172.50 [1788]~E(x17881,x17882)+E(f586(x17883,x17884,x17881,x17885),f586(x17883,x17884,x17882,x17885)) % 172.83/172.50 [1789]~E(x17891,x17892)+E(f586(x17893,x17894,x17895,x17891),f586(x17893,x17894,x17895,x17892)) % 172.83/172.50 [1790]~E(x17901,x17902)+E(f839(x17901,x17903,x17904,x17905),f839(x17902,x17903,x17904,x17905)) % 172.83/172.50 [1791]~E(x17911,x17912)+E(f839(x17913,x17911,x17914,x17915),f839(x17913,x17912,x17914,x17915)) % 172.83/172.50 [1792]~E(x17921,x17922)+E(f839(x17923,x17924,x17921,x17925),f839(x17923,x17924,x17922,x17925)) % 172.83/172.50 [1793]~E(x17931,x17932)+E(f839(x17933,x17934,x17935,x17931),f839(x17933,x17934,x17935,x17932)) % 172.83/172.50 [1794]~E(x17941,x17942)+E(f710(x17941,x17943,x17944),f710(x17942,x17943,x17944)) % 172.83/172.50 [1795]~E(x17951,x17952)+E(f710(x17953,x17951,x17954),f710(x17953,x17952,x17954)) % 172.83/172.50 [1796]~E(x17961,x17962)+E(f710(x17963,x17964,x17961),f710(x17963,x17964,x17962)) % 172.83/172.50 [1797]~E(x17971,x17972)+E(f418(x17971,x17973,x17974,x17975),f418(x17972,x17973,x17974,x17975)) % 172.83/172.50 [1798]~E(x17981,x17982)+E(f418(x17983,x17981,x17984,x17985),f418(x17983,x17982,x17984,x17985)) % 172.83/172.50 [1799]~E(x17991,x17992)+E(f418(x17993,x17994,x17991,x17995),f418(x17993,x17994,x17992,x17995)) % 172.83/172.50 [1800]~E(x18001,x18002)+E(f418(x18003,x18004,x18005,x18001),f418(x18003,x18004,x18005,x18002)) % 172.83/172.50 [1801]~E(x18011,x18012)+E(f548(x18011,x18013,x18014,x18015,x18016),f548(x18012,x18013,x18014,x18015,x18016)) % 172.83/172.50 [1802]~E(x18021,x18022)+E(f548(x18023,x18021,x18024,x18025,x18026),f548(x18023,x18022,x18024,x18025,x18026)) % 172.83/172.50 [1803]~E(x18031,x18032)+E(f548(x18033,x18034,x18031,x18035,x18036),f548(x18033,x18034,x18032,x18035,x18036)) % 172.83/172.50 [1804]~E(x18041,x18042)+E(f548(x18043,x18044,x18045,x18041,x18046),f548(x18043,x18044,x18045,x18042,x18046)) % 172.83/172.50 [1805]~E(x18051,x18052)+E(f548(x18053,x18054,x18055,x18056,x18051),f548(x18053,x18054,x18055,x18056,x18052)) % 172.83/172.50 [1806]~E(x18061,x18062)+E(f453(x18061,x18063,x18064),f453(x18062,x18063,x18064)) % 172.83/172.50 [1807]~E(x18071,x18072)+E(f453(x18073,x18071,x18074),f453(x18073,x18072,x18074)) % 172.83/172.50 [1808]~E(x18081,x18082)+E(f453(x18083,x18084,x18081),f453(x18083,x18084,x18082)) % 172.83/172.50 [1809]~E(x18091,x18092)+E(f124(x18091),f124(x18092)) % 172.83/172.50 [1810]~E(x18101,x18102)+E(f811(x18101,x18103,x18104,x18105),f811(x18102,x18103,x18104,x18105)) % 172.83/172.50 [1811]~E(x18111,x18112)+E(f811(x18113,x18111,x18114,x18115),f811(x18113,x18112,x18114,x18115)) % 172.83/172.50 [1812]~E(x18121,x18122)+E(f811(x18123,x18124,x18121,x18125),f811(x18123,x18124,x18122,x18125)) % 172.83/172.50 [1813]~E(x18131,x18132)+E(f811(x18133,x18134,x18135,x18131),f811(x18133,x18134,x18135,x18132)) % 172.83/172.50 [1814]~E(x18141,x18142)+E(f631(x18141,x18143,x18144,x18145,x18146),f631(x18142,x18143,x18144,x18145,x18146)) % 172.83/172.50 [1815]~E(x18151,x18152)+E(f631(x18153,x18151,x18154,x18155,x18156),f631(x18153,x18152,x18154,x18155,x18156)) % 172.83/172.50 [1816]~E(x18161,x18162)+E(f631(x18163,x18164,x18161,x18165,x18166),f631(x18163,x18164,x18162,x18165,x18166)) % 172.83/172.50 [1817]~E(x18171,x18172)+E(f631(x18173,x18174,x18175,x18171,x18176),f631(x18173,x18174,x18175,x18172,x18176)) % 172.83/172.50 [1818]~E(x18181,x18182)+E(f631(x18183,x18184,x18185,x18186,x18181),f631(x18183,x18184,x18185,x18186,x18182)) % 172.83/172.50 [1819]~E(x18191,x18192)+E(f621(x18191,x18193,x18194,x18195),f621(x18192,x18193,x18194,x18195)) % 172.83/172.50 [1820]~E(x18201,x18202)+E(f621(x18203,x18201,x18204,x18205),f621(x18203,x18202,x18204,x18205)) % 172.83/172.50 [1821]~E(x18211,x18212)+E(f621(x18213,x18214,x18211,x18215),f621(x18213,x18214,x18212,x18215)) % 172.83/172.50 [1822]~E(x18221,x18222)+E(f621(x18223,x18224,x18225,x18221),f621(x18223,x18224,x18225,x18222)) % 172.83/172.50 [1823]~E(x18231,x18232)+E(f630(x18231,x18233,x18234,x18235,x18236),f630(x18232,x18233,x18234,x18235,x18236)) % 172.83/172.50 [1824]~E(x18241,x18242)+E(f630(x18243,x18241,x18244,x18245,x18246),f630(x18243,x18242,x18244,x18245,x18246)) % 172.83/172.50 [1825]~E(x18251,x18252)+E(f630(x18253,x18254,x18251,x18255,x18256),f630(x18253,x18254,x18252,x18255,x18256)) % 172.83/172.50 [1826]~E(x18261,x18262)+E(f630(x18263,x18264,x18265,x18261,x18266),f630(x18263,x18264,x18265,x18262,x18266)) % 172.83/172.50 [1827]~E(x18271,x18272)+E(f630(x18273,x18274,x18275,x18276,x18271),f630(x18273,x18274,x18275,x18276,x18272)) % 172.83/172.50 [1828]~E(x18281,x18282)+E(f438(x18281,x18283,x18284,x18285,x18286),f438(x18282,x18283,x18284,x18285,x18286)) % 172.83/172.50 [1829]~E(x18291,x18292)+E(f438(x18293,x18291,x18294,x18295,x18296),f438(x18293,x18292,x18294,x18295,x18296)) % 172.83/172.50 [1830]~E(x18301,x18302)+E(f438(x18303,x18304,x18301,x18305,x18306),f438(x18303,x18304,x18302,x18305,x18306)) % 172.83/172.50 [1831]~E(x18311,x18312)+E(f438(x18313,x18314,x18315,x18311,x18316),f438(x18313,x18314,x18315,x18312,x18316)) % 172.83/172.50 [1832]~E(x18321,x18322)+E(f438(x18323,x18324,x18325,x18326,x18321),f438(x18323,x18324,x18325,x18326,x18322)) % 172.83/172.50 [1833]~E(x18331,x18332)+E(f771(x18331,x18333,x18334,x18335),f771(x18332,x18333,x18334,x18335)) % 172.83/172.50 [1834]~E(x18341,x18342)+E(f771(x18343,x18341,x18344,x18345),f771(x18343,x18342,x18344,x18345)) % 172.83/172.50 [1835]~E(x18351,x18352)+E(f771(x18353,x18354,x18351,x18355),f771(x18353,x18354,x18352,x18355)) % 172.83/172.50 [1836]~E(x18361,x18362)+E(f771(x18363,x18364,x18365,x18361),f771(x18363,x18364,x18365,x18362)) % 172.83/172.50 [1837]~E(x18371,x18372)+E(f500(x18371,x18373,x18374,x18375,x18376),f500(x18372,x18373,x18374,x18375,x18376)) % 172.83/172.50 [1838]~E(x18381,x18382)+E(f500(x18383,x18381,x18384,x18385,x18386),f500(x18383,x18382,x18384,x18385,x18386)) % 172.83/172.50 [1839]~E(x18391,x18392)+E(f500(x18393,x18394,x18391,x18395,x18396),f500(x18393,x18394,x18392,x18395,x18396)) % 172.83/172.50 [1840]~E(x18401,x18402)+E(f500(x18403,x18404,x18405,x18401,x18406),f500(x18403,x18404,x18405,x18402,x18406)) % 172.83/172.50 [1841]~E(x18411,x18412)+E(f500(x18413,x18414,x18415,x18416,x18411),f500(x18413,x18414,x18415,x18416,x18412)) % 172.83/172.50 [1842]~E(x18421,x18422)+E(f17(x18421,x18423,x18424,x18425),f17(x18422,x18423,x18424,x18425)) % 172.83/172.50 [1843]~E(x18431,x18432)+E(f17(x18433,x18431,x18434,x18435),f17(x18433,x18432,x18434,x18435)) % 172.83/172.50 [1844]~E(x18441,x18442)+E(f17(x18443,x18444,x18441,x18445),f17(x18443,x18444,x18442,x18445)) % 172.83/172.50 [1845]~E(x18451,x18452)+E(f17(x18453,x18454,x18455,x18451),f17(x18453,x18454,x18455,x18452)) % 172.83/172.50 [1846]~E(x18461,x18462)+E(f543(x18461,x18463,x18464,x18465,x18466,x18467),f543(x18462,x18463,x18464,x18465,x18466,x18467)) % 172.83/172.50 [1847]~E(x18471,x18472)+E(f543(x18473,x18471,x18474,x18475,x18476,x18477),f543(x18473,x18472,x18474,x18475,x18476,x18477)) % 172.83/172.50 [1848]~E(x18481,x18482)+E(f543(x18483,x18484,x18481,x18485,x18486,x18487),f543(x18483,x18484,x18482,x18485,x18486,x18487)) % 172.83/172.50 [1849]~E(x18491,x18492)+E(f543(x18493,x18494,x18495,x18491,x18496,x18497),f543(x18493,x18494,x18495,x18492,x18496,x18497)) % 172.83/172.50 [1850]~E(x18501,x18502)+E(f543(x18503,x18504,x18505,x18506,x18501,x18507),f543(x18503,x18504,x18505,x18506,x18502,x18507)) % 172.83/172.50 [1851]~E(x18511,x18512)+E(f543(x18513,x18514,x18515,x18516,x18517,x18511),f543(x18513,x18514,x18515,x18516,x18517,x18512)) % 172.83/172.50 [1852]~E(x18521,x18522)+E(f249(x18521,x18523),f249(x18522,x18523)) % 172.83/172.50 [1853]~E(x18531,x18532)+E(f249(x18533,x18531),f249(x18533,x18532)) % 172.83/172.50 [1854]~E(x18541,x18542)+E(f215(x18541),f215(x18542)) % 172.83/172.50 [1855]~E(x18551,x18552)+E(f532(x18551,x18553,x18554,x18555),f532(x18552,x18553,x18554,x18555)) % 172.83/172.50 [1856]~E(x18561,x18562)+E(f532(x18563,x18561,x18564,x18565),f532(x18563,x18562,x18564,x18565)) % 172.83/172.50 [1857]~E(x18571,x18572)+E(f532(x18573,x18574,x18571,x18575),f532(x18573,x18574,x18572,x18575)) % 172.83/172.50 [1858]~E(x18581,x18582)+E(f532(x18583,x18584,x18585,x18581),f532(x18583,x18584,x18585,x18582)) % 172.83/172.50 [1859]~E(x18591,x18592)+E(f853(x18591,x18593,x18594),f853(x18592,x18593,x18594)) % 172.83/172.50 [1860]~E(x18601,x18602)+E(f853(x18603,x18601,x18604),f853(x18603,x18602,x18604)) % 172.83/172.50 [1861]~E(x18611,x18612)+E(f853(x18613,x18614,x18611),f853(x18613,x18614,x18612)) % 172.83/172.50 [1862]~E(x18621,x18622)+E(f600(x18621,x18623),f600(x18622,x18623)) % 172.83/172.50 [1863]~E(x18631,x18632)+E(f600(x18633,x18631),f600(x18633,x18632)) % 172.83/172.50 [1864]~E(x18641,x18642)+E(f578(x18641,x18643,x18644,x18645,x18646,x18647),f578(x18642,x18643,x18644,x18645,x18646,x18647)) % 172.83/172.50 [1865]~E(x18651,x18652)+E(f578(x18653,x18651,x18654,x18655,x18656,x18657),f578(x18653,x18652,x18654,x18655,x18656,x18657)) % 172.83/172.50 [1866]~E(x18661,x18662)+E(f578(x18663,x18664,x18661,x18665,x18666,x18667),f578(x18663,x18664,x18662,x18665,x18666,x18667)) % 172.83/172.50 [1867]~E(x18671,x18672)+E(f578(x18673,x18674,x18675,x18671,x18676,x18677),f578(x18673,x18674,x18675,x18672,x18676,x18677)) % 172.83/172.50 [1868]~E(x18681,x18682)+E(f578(x18683,x18684,x18685,x18686,x18681,x18687),f578(x18683,x18684,x18685,x18686,x18682,x18687)) % 172.83/172.50 [1869]~E(x18691,x18692)+E(f578(x18693,x18694,x18695,x18696,x18697,x18691),f578(x18693,x18694,x18695,x18696,x18697,x18692)) % 172.83/172.50 [1870]~E(x18701,x18702)+E(f636(x18701,x18703,x18704),f636(x18702,x18703,x18704)) % 172.83/172.50 [1871]~E(x18711,x18712)+E(f636(x18713,x18711,x18714),f636(x18713,x18712,x18714)) % 172.83/172.50 [1872]~E(x18721,x18722)+E(f636(x18723,x18724,x18721),f636(x18723,x18724,x18722)) % 172.83/172.50 [1873]~E(x18731,x18732)+E(f421(x18731,x18733,x18734),f421(x18732,x18733,x18734)) % 172.83/172.50 [1874]~E(x18741,x18742)+E(f421(x18743,x18741,x18744),f421(x18743,x18742,x18744)) % 172.83/172.50 [1875]~E(x18751,x18752)+E(f421(x18753,x18754,x18751),f421(x18753,x18754,x18752)) % 172.83/172.50 [1876]~E(x18761,x18762)+E(f711(x18761,x18763,x18764,x18765,x18766),f711(x18762,x18763,x18764,x18765,x18766)) % 172.83/172.50 [1877]~E(x18771,x18772)+E(f711(x18773,x18771,x18774,x18775,x18776),f711(x18773,x18772,x18774,x18775,x18776)) % 172.83/172.50 [1878]~E(x18781,x18782)+E(f711(x18783,x18784,x18781,x18785,x18786),f711(x18783,x18784,x18782,x18785,x18786)) % 172.83/172.50 [1879]~E(x18791,x18792)+E(f711(x18793,x18794,x18795,x18791,x18796),f711(x18793,x18794,x18795,x18792,x18796)) % 172.83/172.50 [1880]~E(x18801,x18802)+E(f711(x18803,x18804,x18805,x18806,x18801),f711(x18803,x18804,x18805,x18806,x18802)) % 172.83/172.50 [1881]~E(x18811,x18812)+E(f205(x18811,x18813,x18814,x18815),f205(x18812,x18813,x18814,x18815)) % 172.83/172.50 [1882]~E(x18821,x18822)+E(f205(x18823,x18821,x18824,x18825),f205(x18823,x18822,x18824,x18825)) % 172.83/172.50 [1883]~E(x18831,x18832)+E(f205(x18833,x18834,x18831,x18835),f205(x18833,x18834,x18832,x18835)) % 172.83/172.50 [1884]~E(x18841,x18842)+E(f205(x18843,x18844,x18845,x18841),f205(x18843,x18844,x18845,x18842)) % 172.83/172.50 [1885]~E(x18851,x18852)+E(f283(x18851,x18853),f283(x18852,x18853)) % 172.83/172.50 [1886]~E(x18861,x18862)+E(f283(x18863,x18861),f283(x18863,x18862)) % 172.83/172.50 [1887]~E(x18871,x18872)+E(f390(x18871,x18873,x18874,x18875),f390(x18872,x18873,x18874,x18875)) % 172.83/172.50 [1888]~E(x18881,x18882)+E(f390(x18883,x18881,x18884,x18885),f390(x18883,x18882,x18884,x18885)) % 172.83/172.50 [1889]~E(x18891,x18892)+E(f390(x18893,x18894,x18891,x18895),f390(x18893,x18894,x18892,x18895)) % 172.83/172.50 [1890]~E(x18901,x18902)+E(f390(x18903,x18904,x18905,x18901),f390(x18903,x18904,x18905,x18902)) % 172.83/172.50 [1891]~E(x18911,x18912)+E(f783(x18911,x18913,x18914,x18915,x18916),f783(x18912,x18913,x18914,x18915,x18916)) % 172.83/172.50 [1892]~E(x18921,x18922)+E(f783(x18923,x18921,x18924,x18925,x18926),f783(x18923,x18922,x18924,x18925,x18926)) % 172.83/172.50 [1893]~E(x18931,x18932)+E(f783(x18933,x18934,x18931,x18935,x18936),f783(x18933,x18934,x18932,x18935,x18936)) % 172.83/172.50 [1894]~E(x18941,x18942)+E(f783(x18943,x18944,x18945,x18941,x18946),f783(x18943,x18944,x18945,x18942,x18946)) % 172.83/172.50 [1895]~E(x18951,x18952)+E(f783(x18953,x18954,x18955,x18956,x18951),f783(x18953,x18954,x18955,x18956,x18952)) % 172.83/172.50 [1896]~E(x18961,x18962)+E(f765(x18961,x18963),f765(x18962,x18963)) % 172.83/172.50 [1897]~E(x18971,x18972)+E(f765(x18973,x18971),f765(x18973,x18972)) % 172.83/172.50 [1898]~E(x18981,x18982)+E(f804(x18981,x18983,x18984),f804(x18982,x18983,x18984)) % 172.83/172.50 [1899]~E(x18991,x18992)+E(f804(x18993,x18991,x18994),f804(x18993,x18992,x18994)) % 172.83/172.50 [1900]~E(x19001,x19002)+E(f804(x19003,x19004,x19001),f804(x19003,x19004,x19002)) % 172.83/172.50 [1901]~E(x19011,x19012)+E(f481(x19011,x19013,x19014,x19015,x19016,x19017),f481(x19012,x19013,x19014,x19015,x19016,x19017)) % 172.83/172.50 [1902]~E(x19021,x19022)+E(f481(x19023,x19021,x19024,x19025,x19026,x19027),f481(x19023,x19022,x19024,x19025,x19026,x19027)) % 172.83/172.50 [1903]~E(x19031,x19032)+E(f481(x19033,x19034,x19031,x19035,x19036,x19037),f481(x19033,x19034,x19032,x19035,x19036,x19037)) % 172.83/172.50 [1904]~E(x19041,x19042)+E(f481(x19043,x19044,x19045,x19041,x19046,x19047),f481(x19043,x19044,x19045,x19042,x19046,x19047)) % 172.83/172.50 [1905]~E(x19051,x19052)+E(f481(x19053,x19054,x19055,x19056,x19051,x19057),f481(x19053,x19054,x19055,x19056,x19052,x19057)) % 172.83/172.50 [1906]~E(x19061,x19062)+E(f481(x19063,x19064,x19065,x19066,x19067,x19061),f481(x19063,x19064,x19065,x19066,x19067,x19062)) % 172.83/172.50 [1907]~E(x19071,x19072)+E(f779(x19071,x19073,x19074),f779(x19072,x19073,x19074)) % 172.83/172.50 [1908]~E(x19081,x19082)+E(f779(x19083,x19081,x19084),f779(x19083,x19082,x19084)) % 172.83/172.50 [1909]~E(x19091,x19092)+E(f779(x19093,x19094,x19091),f779(x19093,x19094,x19092)) % 172.83/172.50 [1910]~E(x19101,x19102)+E(f538(x19101,x19103,x19104,x19105,x19106),f538(x19102,x19103,x19104,x19105,x19106)) % 172.83/172.50 [1911]~E(x19111,x19112)+E(f538(x19113,x19111,x19114,x19115,x19116),f538(x19113,x19112,x19114,x19115,x19116)) % 172.83/172.50 [1912]~E(x19121,x19122)+E(f538(x19123,x19124,x19121,x19125,x19126),f538(x19123,x19124,x19122,x19125,x19126)) % 172.83/172.50 [1913]~E(x19131,x19132)+E(f538(x19133,x19134,x19135,x19131,x19136),f538(x19133,x19134,x19135,x19132,x19136)) % 172.83/172.50 [1914]~E(x19141,x19142)+E(f538(x19143,x19144,x19145,x19146,x19141),f538(x19143,x19144,x19145,x19146,x19142)) % 172.83/172.50 [1915]~E(x19151,x19152)+E(f146(x19151,x19153),f146(x19152,x19153)) % 172.83/172.50 [1916]~E(x19161,x19162)+E(f146(x19163,x19161),f146(x19163,x19162)) % 172.83/172.50 [1917]~E(x19171,x19172)+E(f582(x19171,x19173,x19174),f582(x19172,x19173,x19174)) % 172.83/172.50 [1918]~E(x19181,x19182)+E(f582(x19183,x19181,x19184),f582(x19183,x19182,x19184)) % 172.83/172.50 [1919]~E(x19191,x19192)+E(f582(x19193,x19194,x19191),f582(x19193,x19194,x19192)) % 172.83/172.50 [1920]~E(x19201,x19202)+E(f360(x19201,x19203),f360(x19202,x19203)) % 172.83/172.50 [1921]~E(x19211,x19212)+E(f360(x19213,x19211),f360(x19213,x19212)) % 172.83/172.50 [1922]~E(x19221,x19222)+E(f652(x19221,x19223,x19224,x19225),f652(x19222,x19223,x19224,x19225)) % 172.83/172.50 [1923]~E(x19231,x19232)+E(f652(x19233,x19231,x19234,x19235),f652(x19233,x19232,x19234,x19235)) % 172.83/172.50 [1924]~E(x19241,x19242)+E(f652(x19243,x19244,x19241,x19245),f652(x19243,x19244,x19242,x19245)) % 172.83/172.50 [1925]~E(x19251,x19252)+E(f652(x19253,x19254,x19255,x19251),f652(x19253,x19254,x19255,x19252)) % 172.83/172.50 [1926]~E(x19261,x19262)+E(f573(x19261,x19263,x19264),f573(x19262,x19263,x19264)) % 172.83/172.50 [1927]~E(x19271,x19272)+E(f573(x19273,x19271,x19274),f573(x19273,x19272,x19274)) % 172.83/172.50 [1928]~E(x19281,x19282)+E(f573(x19283,x19284,x19281),f573(x19283,x19284,x19282)) % 172.83/172.50 [1929]~E(x19291,x19292)+E(f697(x19291,x19293,x19294,x19295,x19296),f697(x19292,x19293,x19294,x19295,x19296)) % 172.83/172.50 [1930]~E(x19301,x19302)+E(f697(x19303,x19301,x19304,x19305,x19306),f697(x19303,x19302,x19304,x19305,x19306)) % 172.83/172.50 [1931]~E(x19311,x19312)+E(f697(x19313,x19314,x19311,x19315,x19316),f697(x19313,x19314,x19312,x19315,x19316)) % 172.83/172.50 [1932]~E(x19321,x19322)+E(f697(x19323,x19324,x19325,x19321,x19326),f697(x19323,x19324,x19325,x19322,x19326)) % 172.83/172.50 [1933]~E(x19331,x19332)+E(f697(x19333,x19334,x19335,x19336,x19331),f697(x19333,x19334,x19335,x19336,x19332)) % 172.83/172.50 [1934]~E(x19341,x19342)+E(f720(x19341,x19343),f720(x19342,x19343)) % 172.83/172.50 [1935]~E(x19351,x19352)+E(f720(x19353,x19351),f720(x19353,x19352)) % 172.83/172.50 [1936]~E(x19361,x19362)+E(f541(x19361,x19363,x19364,x19365),f541(x19362,x19363,x19364,x19365)) % 172.83/172.50 [1937]~E(x19371,x19372)+E(f541(x19373,x19371,x19374,x19375),f541(x19373,x19372,x19374,x19375)) % 172.83/172.50 [1938]~E(x19381,x19382)+E(f541(x19383,x19384,x19381,x19385),f541(x19383,x19384,x19382,x19385)) % 172.83/172.50 [1939]~E(x19391,x19392)+E(f541(x19393,x19394,x19395,x19391),f541(x19393,x19394,x19395,x19392)) % 172.83/172.50 [1940]~E(x19401,x19402)+E(f432(x19401,x19403),f432(x19402,x19403)) % 172.83/172.50 [1941]~E(x19411,x19412)+E(f432(x19413,x19411),f432(x19413,x19412)) % 172.83/172.50 [1942]~E(x19421,x19422)+E(f530(x19421,x19423),f530(x19422,x19423)) % 172.83/172.50 [1943]~E(x19431,x19432)+E(f530(x19433,x19431),f530(x19433,x19432)) % 172.83/172.50 [1944]~E(x19441,x19442)+E(f673(x19441,x19443,x19444,x19445),f673(x19442,x19443,x19444,x19445)) % 172.83/172.50 [1945]~E(x19451,x19452)+E(f673(x19453,x19451,x19454,x19455),f673(x19453,x19452,x19454,x19455)) % 172.83/172.50 [1946]~E(x19461,x19462)+E(f673(x19463,x19464,x19461,x19465),f673(x19463,x19464,x19462,x19465)) % 172.83/172.50 [1947]~E(x19471,x19472)+E(f673(x19473,x19474,x19475,x19471),f673(x19473,x19474,x19475,x19472)) % 172.83/172.50 [1948]~E(x19481,x19482)+E(f619(x19481,x19483,x19484,x19485,x19486),f619(x19482,x19483,x19484,x19485,x19486)) % 172.83/172.50 [1949]~E(x19491,x19492)+E(f619(x19493,x19491,x19494,x19495,x19496),f619(x19493,x19492,x19494,x19495,x19496)) % 172.83/172.50 [1950]~E(x19501,x19502)+E(f619(x19503,x19504,x19501,x19505,x19506),f619(x19503,x19504,x19502,x19505,x19506)) % 172.83/172.50 [1951]~E(x19511,x19512)+E(f619(x19513,x19514,x19515,x19511,x19516),f619(x19513,x19514,x19515,x19512,x19516)) % 172.83/172.50 [1952]~E(x19521,x19522)+E(f619(x19523,x19524,x19525,x19526,x19521),f619(x19523,x19524,x19525,x19526,x19522)) % 172.83/172.50 [1953]~E(x19531,x19532)+E(f534(x19531,x19533),f534(x19532,x19533)) % 172.83/172.50 [1954]~E(x19541,x19542)+E(f534(x19543,x19541),f534(x19543,x19542)) % 172.83/172.50 [1955]~E(x19551,x19552)+E(f616(x19551,x19553,x19554,x19555,x19556),f616(x19552,x19553,x19554,x19555,x19556)) % 172.83/172.50 [1956]~E(x19561,x19562)+E(f616(x19563,x19561,x19564,x19565,x19566),f616(x19563,x19562,x19564,x19565,x19566)) % 172.83/172.50 [1957]~E(x19571,x19572)+E(f616(x19573,x19574,x19571,x19575,x19576),f616(x19573,x19574,x19572,x19575,x19576)) % 172.83/172.50 [1958]~E(x19581,x19582)+E(f616(x19583,x19584,x19585,x19581,x19586),f616(x19583,x19584,x19585,x19582,x19586)) % 172.83/172.50 [1959]~E(x19591,x19592)+E(f616(x19593,x19594,x19595,x19596,x19591),f616(x19593,x19594,x19595,x19596,x19592)) % 172.83/172.50 [1960]~E(x19601,x19602)+E(f581(x19601,x19603,x19604,x19605,x19606,x19607),f581(x19602,x19603,x19604,x19605,x19606,x19607)) % 172.83/172.50 [1961]~E(x19611,x19612)+E(f581(x19613,x19611,x19614,x19615,x19616,x19617),f581(x19613,x19612,x19614,x19615,x19616,x19617)) % 172.83/172.50 [1962]~E(x19621,x19622)+E(f581(x19623,x19624,x19621,x19625,x19626,x19627),f581(x19623,x19624,x19622,x19625,x19626,x19627)) % 172.83/172.50 [1963]~E(x19631,x19632)+E(f581(x19633,x19634,x19635,x19631,x19636,x19637),f581(x19633,x19634,x19635,x19632,x19636,x19637)) % 172.83/172.50 [1964]~E(x19641,x19642)+E(f581(x19643,x19644,x19645,x19646,x19641,x19647),f581(x19643,x19644,x19645,x19646,x19642,x19647)) % 172.83/172.50 [1965]~E(x19651,x19652)+E(f581(x19653,x19654,x19655,x19656,x19657,x19651),f581(x19653,x19654,x19655,x19656,x19657,x19652)) % 172.83/172.50 [1966]~E(x19661,x19662)+E(f476(x19661,x19663,x19664),f476(x19662,x19663,x19664)) % 172.83/172.50 [1967]~E(x19671,x19672)+E(f476(x19673,x19671,x19674),f476(x19673,x19672,x19674)) % 172.83/172.50 [1968]~E(x19681,x19682)+E(f476(x19683,x19684,x19681),f476(x19683,x19684,x19682)) % 172.83/172.50 [1969]~E(x19691,x19692)+E(f128(x19691),f128(x19692)) % 172.83/172.50 [1970]~E(x19701,x19702)+E(f222(x19701,x19703,x19704,x19705,x19706,x19707,x19708),f222(x19702,x19703,x19704,x19705,x19706,x19707,x19708)) % 172.83/172.50 [1971]~E(x19711,x19712)+E(f222(x19713,x19711,x19714,x19715,x19716,x19717,x19718),f222(x19713,x19712,x19714,x19715,x19716,x19717,x19718)) % 172.83/172.50 [1972]~E(x19721,x19722)+E(f222(x19723,x19724,x19721,x19725,x19726,x19727,x19728),f222(x19723,x19724,x19722,x19725,x19726,x19727,x19728)) % 172.83/172.50 [1973]~E(x19731,x19732)+E(f222(x19733,x19734,x19735,x19731,x19736,x19737,x19738),f222(x19733,x19734,x19735,x19732,x19736,x19737,x19738)) % 172.83/172.50 [1974]~E(x19741,x19742)+E(f222(x19743,x19744,x19745,x19746,x19741,x19747,x19748),f222(x19743,x19744,x19745,x19746,x19742,x19747,x19748)) % 172.83/172.50 [1975]~E(x19751,x19752)+E(f222(x19753,x19754,x19755,x19756,x19757,x19751,x19758),f222(x19753,x19754,x19755,x19756,x19757,x19752,x19758)) % 172.83/172.50 [1976]~E(x19761,x19762)+E(f222(x19763,x19764,x19765,x19766,x19767,x19768,x19761),f222(x19763,x19764,x19765,x19766,x19767,x19768,x19762)) % 172.83/172.50 [1977]~E(x19771,x19772)+E(f604(x19771,x19773,x19774,x19775),f604(x19772,x19773,x19774,x19775)) % 172.83/172.50 [1978]~E(x19781,x19782)+E(f604(x19783,x19781,x19784,x19785),f604(x19783,x19782,x19784,x19785)) % 172.83/172.50 [1979]~E(x19791,x19792)+E(f604(x19793,x19794,x19791,x19795),f604(x19793,x19794,x19792,x19795)) % 172.83/172.50 [1980]~E(x19801,x19802)+E(f604(x19803,x19804,x19805,x19801),f604(x19803,x19804,x19805,x19802)) % 172.83/172.50 [1981]~E(x19811,x19812)+E(f380(x19811,x19813),f380(x19812,x19813)) % 172.83/172.50 [1982]~E(x19821,x19822)+E(f380(x19823,x19821),f380(x19823,x19822)) % 172.83/172.50 [1983]~E(x19831,x19832)+E(f864(x19831,x19833,x19834,x19835,x19836),f864(x19832,x19833,x19834,x19835,x19836)) % 172.83/172.50 [1984]~E(x19841,x19842)+E(f864(x19843,x19841,x19844,x19845,x19846),f864(x19843,x19842,x19844,x19845,x19846)) % 172.83/172.50 [1985]~E(x19851,x19852)+E(f864(x19853,x19854,x19851,x19855,x19856),f864(x19853,x19854,x19852,x19855,x19856)) % 172.83/172.50 [1986]~E(x19861,x19862)+E(f864(x19863,x19864,x19865,x19861,x19866),f864(x19863,x19864,x19865,x19862,x19866)) % 172.83/172.50 [1987]~E(x19871,x19872)+E(f864(x19873,x19874,x19875,x19876,x19871),f864(x19873,x19874,x19875,x19876,x19872)) % 172.83/172.50 [1988]~E(x19881,x19882)+E(f602(x19881,x19883,x19884),f602(x19882,x19883,x19884)) % 172.83/172.50 [1989]~E(x19891,x19892)+E(f602(x19893,x19891,x19894),f602(x19893,x19892,x19894)) % 172.83/172.50 [1990]~E(x19901,x19902)+E(f602(x19903,x19904,x19901),f602(x19903,x19904,x19902)) % 172.83/172.50 [1991]~E(x19911,x19912)+E(f829(x19911,x19913),f829(x19912,x19913)) % 172.83/172.50 [1992]~E(x19921,x19922)+E(f829(x19923,x19921),f829(x19923,x19922)) % 172.83/172.50 [1993]~E(x19931,x19932)+E(f212(x19931),f212(x19932)) % 172.83/172.50 [1994]~E(x19941,x19942)+E(f509(x19941,x19943,x19944),f509(x19942,x19943,x19944)) % 172.83/172.50 [1995]~E(x19951,x19952)+E(f509(x19953,x19951,x19954),f509(x19953,x19952,x19954)) % 172.83/172.50 [1996]~E(x19961,x19962)+E(f509(x19963,x19964,x19961),f509(x19963,x19964,x19962)) % 172.83/172.50 [1997]~E(x19971,x19972)+E(f477(x19971,x19973,x19974),f477(x19972,x19973,x19974)) % 172.83/172.50 [1998]~E(x19981,x19982)+E(f477(x19983,x19981,x19984),f477(x19983,x19982,x19984)) % 172.83/172.50 [1999]~E(x19991,x19992)+E(f477(x19993,x19994,x19991),f477(x19993,x19994,x19992)) % 172.83/172.50 [2000]~E(x20001,x20002)+E(f773(x20001,x20003,x20004,x20005,x20006,x20007,x20008,x20009),f773(x20002,x20003,x20004,x20005,x20006,x20007,x20008,x20009)) % 172.83/172.50 [2001]~E(x20011,x20012)+E(f773(x20013,x20011,x20014,x20015,x20016,x20017,x20018,x20019),f773(x20013,x20012,x20014,x20015,x20016,x20017,x20018,x20019)) % 172.83/172.50 [2002]~E(x20021,x20022)+E(f773(x20023,x20024,x20021,x20025,x20026,x20027,x20028,x20029),f773(x20023,x20024,x20022,x20025,x20026,x20027,x20028,x20029)) % 172.83/172.50 [2003]~E(x20031,x20032)+E(f773(x20033,x20034,x20035,x20031,x20036,x20037,x20038,x20039),f773(x20033,x20034,x20035,x20032,x20036,x20037,x20038,x20039)) % 172.83/172.50 [2004]~E(x20041,x20042)+E(f773(x20043,x20044,x20045,x20046,x20041,x20047,x20048,x20049),f773(x20043,x20044,x20045,x20046,x20042,x20047,x20048,x20049)) % 172.83/172.50 [2005]~E(x20051,x20052)+E(f773(x20053,x20054,x20055,x20056,x20057,x20051,x20058,x20059),f773(x20053,x20054,x20055,x20056,x20057,x20052,x20058,x20059)) % 172.83/172.50 [2006]~E(x20061,x20062)+E(f773(x20063,x20064,x20065,x20066,x20067,x20068,x20061,x20069),f773(x20063,x20064,x20065,x20066,x20067,x20068,x20062,x20069)) % 172.83/172.50 [2007]~E(x20071,x20072)+E(f773(x20073,x20074,x20075,x20076,x20077,x20078,x20079,x20071),f773(x20073,x20074,x20075,x20076,x20077,x20078,x20079,x20072)) % 172.83/172.50 [2008]~E(x20081,x20082)+E(f213(x20081,x20083),f213(x20082,x20083)) % 172.83/172.50 [2009]~E(x20091,x20092)+E(f213(x20093,x20091),f213(x20093,x20092)) % 172.83/172.50 [2010]~E(x20101,x20102)+E(f848(x20101,x20103,x20104,x20105,x20106),f848(x20102,x20103,x20104,x20105,x20106)) % 172.83/172.50 [2011]~E(x20111,x20112)+E(f848(x20113,x20111,x20114,x20115,x20116),f848(x20113,x20112,x20114,x20115,x20116)) % 172.83/172.50 [2012]~E(x20121,x20122)+E(f848(x20123,x20124,x20121,x20125,x20126),f848(x20123,x20124,x20122,x20125,x20126)) % 172.83/172.50 [2013]~E(x20131,x20132)+E(f848(x20133,x20134,x20135,x20131,x20136),f848(x20133,x20134,x20135,x20132,x20136)) % 172.83/172.50 [2014]~E(x20141,x20142)+E(f848(x20143,x20144,x20145,x20146,x20141),f848(x20143,x20144,x20145,x20146,x20142)) % 172.83/172.50 [2015]~E(x20151,x20152)+E(f357(x20151),f357(x20152)) % 172.83/172.50 [2016]~E(x20161,x20162)+E(f542(x20161,x20163,x20164,x20165,x20166,x20167),f542(x20162,x20163,x20164,x20165,x20166,x20167)) % 172.83/172.50 [2017]~E(x20171,x20172)+E(f542(x20173,x20171,x20174,x20175,x20176,x20177),f542(x20173,x20172,x20174,x20175,x20176,x20177)) % 172.83/172.50 [2018]~E(x20181,x20182)+E(f542(x20183,x20184,x20181,x20185,x20186,x20187),f542(x20183,x20184,x20182,x20185,x20186,x20187)) % 172.83/172.50 [2019]~E(x20191,x20192)+E(f542(x20193,x20194,x20195,x20191,x20196,x20197),f542(x20193,x20194,x20195,x20192,x20196,x20197)) % 172.83/172.50 [2020]~E(x20201,x20202)+E(f542(x20203,x20204,x20205,x20206,x20201,x20207),f542(x20203,x20204,x20205,x20206,x20202,x20207)) % 172.83/172.50 [2021]~E(x20211,x20212)+E(f542(x20213,x20214,x20215,x20216,x20217,x20211),f542(x20213,x20214,x20215,x20216,x20217,x20212)) % 172.83/172.50 [2022]~E(x20221,x20222)+E(f458(x20221,x20223,x20224),f458(x20222,x20223,x20224)) % 172.83/172.50 [2023]~E(x20231,x20232)+E(f458(x20233,x20231,x20234),f458(x20233,x20232,x20234)) % 172.83/172.50 [2024]~E(x20241,x20242)+E(f458(x20243,x20244,x20241),f458(x20243,x20244,x20242)) % 172.83/172.50 [2025]~E(x20251,x20252)+E(f717(x20251,x20253),f717(x20252,x20253)) % 172.83/172.50 [2026]~E(x20261,x20262)+E(f717(x20263,x20261),f717(x20263,x20262)) % 172.83/172.50 [2027]~E(x20271,x20272)+E(f666(x20271,x20273,x20274,x20275),f666(x20272,x20273,x20274,x20275)) % 172.83/172.50 [2028]~E(x20281,x20282)+E(f666(x20283,x20281,x20284,x20285),f666(x20283,x20282,x20284,x20285)) % 172.83/172.50 [2029]~E(x20291,x20292)+E(f666(x20293,x20294,x20291,x20295),f666(x20293,x20294,x20292,x20295)) % 172.83/172.50 [2030]~E(x20301,x20302)+E(f666(x20303,x20304,x20305,x20301),f666(x20303,x20304,x20305,x20302)) % 172.83/172.50 [2031]~E(x20311,x20312)+E(f854(x20311,x20313,x20314),f854(x20312,x20313,x20314)) % 172.83/172.50 [2032]~E(x20321,x20322)+E(f854(x20323,x20321,x20324),f854(x20323,x20322,x20324)) % 172.83/172.50 [2033]~E(x20331,x20332)+E(f854(x20333,x20334,x20331),f854(x20333,x20334,x20332)) % 172.83/172.50 [2034]~E(x20341,x20342)+E(f634(x20341,x20343,x20344),f634(x20342,x20343,x20344)) % 172.83/172.50 [2035]~E(x20351,x20352)+E(f634(x20353,x20351,x20354),f634(x20353,x20352,x20354)) % 172.83/172.50 [2036]~E(x20361,x20362)+E(f634(x20363,x20364,x20361),f634(x20363,x20364,x20362)) % 172.83/172.50 [2037]~E(x20371,x20372)+E(f214(x20371,x20373,x20374),f214(x20372,x20373,x20374)) % 172.83/172.50 [2038]~E(x20381,x20382)+E(f214(x20383,x20381,x20384),f214(x20383,x20382,x20384)) % 172.83/172.50 [2039]~E(x20391,x20392)+E(f214(x20393,x20394,x20391),f214(x20393,x20394,x20392)) % 172.83/172.50 [2040]~E(x20401,x20402)+E(f392(x20401,x20403,x20404,x20405),f392(x20402,x20403,x20404,x20405)) % 172.83/172.50 [2041]~E(x20411,x20412)+E(f392(x20413,x20411,x20414,x20415),f392(x20413,x20412,x20414,x20415)) % 172.83/172.50 [2042]~E(x20421,x20422)+E(f392(x20423,x20424,x20421,x20425),f392(x20423,x20424,x20422,x20425)) % 172.83/172.50 [2043]~E(x20431,x20432)+E(f392(x20433,x20434,x20435,x20431),f392(x20433,x20434,x20435,x20432)) % 172.83/172.50 [2044]~E(x20441,x20442)+E(f703(x20441,x20443,x20444,x20445),f703(x20442,x20443,x20444,x20445)) % 172.83/172.50 [2045]~E(x20451,x20452)+E(f703(x20453,x20451,x20454,x20455),f703(x20453,x20452,x20454,x20455)) % 172.83/172.50 [2046]~E(x20461,x20462)+E(f703(x20463,x20464,x20461,x20465),f703(x20463,x20464,x20462,x20465)) % 172.83/172.50 [2047]~E(x20471,x20472)+E(f703(x20473,x20474,x20475,x20471),f703(x20473,x20474,x20475,x20472)) % 172.83/172.50 [2048]~E(x20481,x20482)+E(f422(x20481,x20483,x20484),f422(x20482,x20483,x20484)) % 172.83/172.50 [2049]~E(x20491,x20492)+E(f422(x20493,x20491,x20494),f422(x20493,x20492,x20494)) % 172.83/172.50 [2050]~E(x20501,x20502)+E(f422(x20503,x20504,x20501),f422(x20503,x20504,x20502)) % 172.83/172.50 [2051]~E(x20511,x20512)+E(f549(x20511,x20513,x20514,x20515),f549(x20512,x20513,x20514,x20515)) % 172.83/172.50 [2052]~E(x20521,x20522)+E(f549(x20523,x20521,x20524,x20525),f549(x20523,x20522,x20524,x20525)) % 172.83/172.50 [2053]~E(x20531,x20532)+E(f549(x20533,x20534,x20531,x20535),f549(x20533,x20534,x20532,x20535)) % 172.83/172.50 [2054]~E(x20541,x20542)+E(f549(x20543,x20544,x20545,x20541),f549(x20543,x20544,x20545,x20542)) % 172.83/172.50 [2055]~E(x20551,x20552)+E(f505(x20551,x20553,x20554,x20555),f505(x20552,x20553,x20554,x20555)) % 172.83/172.50 [2056]~E(x20561,x20562)+E(f505(x20563,x20561,x20564,x20565),f505(x20563,x20562,x20564,x20565)) % 172.83/172.50 [2057]~E(x20571,x20572)+E(f505(x20573,x20574,x20571,x20575),f505(x20573,x20574,x20572,x20575)) % 172.83/172.50 [2058]~E(x20581,x20582)+E(f505(x20583,x20584,x20585,x20581),f505(x20583,x20584,x20585,x20582)) % 172.83/172.50 [2059]~E(x20591,x20592)+E(f569(x20591,x20593,x20594),f569(x20592,x20593,x20594)) % 172.83/172.50 [2060]~E(x20601,x20602)+E(f569(x20603,x20601,x20604),f569(x20603,x20602,x20604)) % 172.83/172.50 [2061]~E(x20611,x20612)+E(f569(x20613,x20614,x20611),f569(x20613,x20614,x20612)) % 172.83/172.50 [2062]~E(x20621,x20622)+E(f73(x20621,x20623),f73(x20622,x20623)) % 172.83/172.50 [2063]~E(x20631,x20632)+E(f73(x20633,x20631),f73(x20633,x20632)) % 172.83/172.50 [2064]~E(x20641,x20642)+E(f831(x20641,x20643),f831(x20642,x20643)) % 172.83/172.50 [2065]~E(x20651,x20652)+E(f831(x20653,x20651),f831(x20653,x20652)) % 172.83/172.50 [2066]~E(x20661,x20662)+E(f441(x20661,x20663,x20664,x20665,x20666),f441(x20662,x20663,x20664,x20665,x20666)) % 172.83/172.50 [2067]~E(x20671,x20672)+E(f441(x20673,x20671,x20674,x20675,x20676),f441(x20673,x20672,x20674,x20675,x20676)) % 172.83/172.50 [2068]~E(x20681,x20682)+E(f441(x20683,x20684,x20681,x20685,x20686),f441(x20683,x20684,x20682,x20685,x20686)) % 172.83/172.50 [2069]~E(x20691,x20692)+E(f441(x20693,x20694,x20695,x20691,x20696),f441(x20693,x20694,x20695,x20692,x20696)) % 172.83/172.50 [2070]~E(x20701,x20702)+E(f441(x20703,x20704,x20705,x20706,x20701),f441(x20703,x20704,x20705,x20706,x20702)) % 172.83/172.50 [2071]~E(x20711,x20712)+E(f729(x20711,x20713,x20714,x20715),f729(x20712,x20713,x20714,x20715)) % 172.83/172.50 [2072]~E(x20721,x20722)+E(f729(x20723,x20721,x20724,x20725),f729(x20723,x20722,x20724,x20725)) % 172.83/172.50 [2073]~E(x20731,x20732)+E(f729(x20733,x20734,x20731,x20735),f729(x20733,x20734,x20732,x20735)) % 172.83/172.50 [2074]~E(x20741,x20742)+E(f729(x20743,x20744,x20745,x20741),f729(x20743,x20744,x20745,x20742)) % 172.83/172.50 [2075]~E(x20751,x20752)+E(f295(x20751,x20753,x20754),f295(x20752,x20753,x20754)) % 172.83/172.50 [2076]~E(x20761,x20762)+E(f295(x20763,x20761,x20764),f295(x20763,x20762,x20764)) % 172.83/172.50 [2077]~E(x20771,x20772)+E(f295(x20773,x20774,x20771),f295(x20773,x20774,x20772)) % 172.83/172.50 [2078]~E(x20781,x20782)+E(f229(x20781,x20783),f229(x20782,x20783)) % 172.83/172.50 [2079]~E(x20791,x20792)+E(f229(x20793,x20791),f229(x20793,x20792)) % 172.83/172.50 [2080]~E(x20801,x20802)+E(f627(x20801,x20803,x20804,x20805),f627(x20802,x20803,x20804,x20805)) % 172.83/172.50 [2081]~E(x20811,x20812)+E(f627(x20813,x20811,x20814,x20815),f627(x20813,x20812,x20814,x20815)) % 172.83/172.50 [2082]~E(x20821,x20822)+E(f627(x20823,x20824,x20821,x20825),f627(x20823,x20824,x20822,x20825)) % 172.83/172.50 [2083]~E(x20831,x20832)+E(f627(x20833,x20834,x20835,x20831),f627(x20833,x20834,x20835,x20832)) % 172.83/172.50 [2084]~E(x20841,x20842)+E(f782(x20841,x20843,x20844,x20845),f782(x20842,x20843,x20844,x20845)) % 172.83/172.50 [2085]~E(x20851,x20852)+E(f782(x20853,x20851,x20854,x20855),f782(x20853,x20852,x20854,x20855)) % 172.83/172.50 [2086]~E(x20861,x20862)+E(f782(x20863,x20864,x20861,x20865),f782(x20863,x20864,x20862,x20865)) % 172.83/172.50 [2087]~E(x20871,x20872)+E(f782(x20873,x20874,x20875,x20871),f782(x20873,x20874,x20875,x20872)) % 172.83/172.50 [2088]~E(x20881,x20882)+E(f526(x20881,x20883,x20884,x20885,x20886),f526(x20882,x20883,x20884,x20885,x20886)) % 172.83/172.50 [2089]~E(x20891,x20892)+E(f526(x20893,x20891,x20894,x20895,x20896),f526(x20893,x20892,x20894,x20895,x20896)) % 172.83/172.50 [2090]~E(x20901,x20902)+E(f526(x20903,x20904,x20901,x20905,x20906),f526(x20903,x20904,x20902,x20905,x20906)) % 172.83/172.50 [2091]~E(x20911,x20912)+E(f526(x20913,x20914,x20915,x20911,x20916),f526(x20913,x20914,x20915,x20912,x20916)) % 172.83/172.50 [2092]~E(x20921,x20922)+E(f526(x20923,x20924,x20925,x20926,x20921),f526(x20923,x20924,x20925,x20926,x20922)) % 172.83/172.50 [2093]~E(x20931,x20932)+E(f466(x20931,x20933),f466(x20932,x20933)) % 172.83/172.50 [2094]~E(x20941,x20942)+E(f466(x20943,x20941),f466(x20943,x20942)) % 172.83/172.50 [2095]~E(x20951,x20952)+E(f689(x20951,x20953,x20954,x20955),f689(x20952,x20953,x20954,x20955)) % 172.83/172.50 [2096]~E(x20961,x20962)+E(f689(x20963,x20961,x20964,x20965),f689(x20963,x20962,x20964,x20965)) % 172.83/172.50 [2097]~E(x20971,x20972)+E(f689(x20973,x20974,x20971,x20975),f689(x20973,x20974,x20972,x20975)) % 172.83/172.50 [2098]~E(x20981,x20982)+E(f689(x20983,x20984,x20985,x20981),f689(x20983,x20984,x20985,x20982)) % 172.83/172.50 [2099]~E(x20991,x20992)+E(f572(x20991,x20993,x20994),f572(x20992,x20993,x20994)) % 172.83/172.50 [2100]~E(x21001,x21002)+E(f572(x21003,x21001,x21004),f572(x21003,x21002,x21004)) % 172.83/172.50 [2101]~E(x21011,x21012)+E(f572(x21013,x21014,x21011),f572(x21013,x21014,x21012)) % 172.83/172.50 [2102]~E(x21021,x21022)+E(f715(x21021,x21023,x21024,x21025,x21026),f715(x21022,x21023,x21024,x21025,x21026)) % 172.83/172.50 [2103]~E(x21031,x21032)+E(f715(x21033,x21031,x21034,x21035,x21036),f715(x21033,x21032,x21034,x21035,x21036)) % 172.83/172.50 [2104]~E(x21041,x21042)+E(f715(x21043,x21044,x21041,x21045,x21046),f715(x21043,x21044,x21042,x21045,x21046)) % 172.83/172.50 [2105]~E(x21051,x21052)+E(f715(x21053,x21054,x21055,x21051,x21056),f715(x21053,x21054,x21055,x21052,x21056)) % 172.83/172.50 [2106]~E(x21061,x21062)+E(f715(x21063,x21064,x21065,x21066,x21061),f715(x21063,x21064,x21065,x21066,x21062)) % 172.83/172.50 [2107]~E(x21071,x21072)+E(f601(x21071,x21073),f601(x21072,x21073)) % 172.83/172.50 [2108]~E(x21081,x21082)+E(f601(x21083,x21081),f601(x21083,x21082)) % 172.83/172.50 [2109]~E(x21091,x21092)+E(f824(x21091,x21093),f824(x21092,x21093)) % 172.83/172.50 [2110]~E(x21101,x21102)+E(f824(x21103,x21101),f824(x21103,x21102)) % 172.83/172.50 [2111]~E(x21111,x21112)+E(f747(x21111,x21113),f747(x21112,x21113)) % 172.83/172.50 [2112]~E(x21121,x21122)+E(f747(x21123,x21121),f747(x21123,x21122)) % 172.83/172.50 [2113]~E(x21131,x21132)+E(f430(x21131,x21133,x21134,x21135),f430(x21132,x21133,x21134,x21135)) % 172.83/172.50 [2114]~E(x21141,x21142)+E(f430(x21143,x21141,x21144,x21145),f430(x21143,x21142,x21144,x21145)) % 172.83/172.50 [2115]~E(x21151,x21152)+E(f430(x21153,x21154,x21151,x21155),f430(x21153,x21154,x21152,x21155)) % 172.83/172.50 [2116]~E(x21161,x21162)+E(f430(x21163,x21164,x21165,x21161),f430(x21163,x21164,x21165,x21162)) % 172.83/172.50 [2117]~E(x21171,x21172)+E(f566(x21171,x21173,x21174),f566(x21172,x21173,x21174)) % 172.83/172.50 [2118]~E(x21181,x21182)+E(f566(x21183,x21181,x21184),f566(x21183,x21182,x21184)) % 172.83/172.50 [2119]~E(x21191,x21192)+E(f566(x21193,x21194,x21191),f566(x21193,x21194,x21192)) % 172.83/172.50 [2120]~E(x21201,x21202)+E(f629(x21201,x21203,x21204,x21205,x21206),f629(x21202,x21203,x21204,x21205,x21206)) % 172.83/172.50 [2121]~E(x21211,x21212)+E(f629(x21213,x21211,x21214,x21215,x21216),f629(x21213,x21212,x21214,x21215,x21216)) % 172.83/172.50 [2122]~E(x21221,x21222)+E(f629(x21223,x21224,x21221,x21225,x21226),f629(x21223,x21224,x21222,x21225,x21226)) % 172.83/172.50 [2123]~E(x21231,x21232)+E(f629(x21233,x21234,x21235,x21231,x21236),f629(x21233,x21234,x21235,x21232,x21236)) % 172.83/172.50 [2124]~E(x21241,x21242)+E(f629(x21243,x21244,x21245,x21246,x21241),f629(x21243,x21244,x21245,x21246,x21242)) % 172.83/172.50 [2125]~E(x21251,x21252)+E(f576(x21251,x21253,x21254,x21255,x21256,x21257),f576(x21252,x21253,x21254,x21255,x21256,x21257)) % 172.83/172.50 [2126]~E(x21261,x21262)+E(f576(x21263,x21261,x21264,x21265,x21266,x21267),f576(x21263,x21262,x21264,x21265,x21266,x21267)) % 172.83/172.50 [2127]~E(x21271,x21272)+E(f576(x21273,x21274,x21271,x21275,x21276,x21277),f576(x21273,x21274,x21272,x21275,x21276,x21277)) % 172.83/172.50 [2128]~E(x21281,x21282)+E(f576(x21283,x21284,x21285,x21281,x21286,x21287),f576(x21283,x21284,x21285,x21282,x21286,x21287)) % 172.83/172.50 [2129]~E(x21291,x21292)+E(f576(x21293,x21294,x21295,x21296,x21291,x21297),f576(x21293,x21294,x21295,x21296,x21292,x21297)) % 172.83/172.50 [2130]~E(x21301,x21302)+E(f576(x21303,x21304,x21305,x21306,x21307,x21301),f576(x21303,x21304,x21305,x21306,x21307,x21302)) % 172.83/172.50 [2131]~E(x21311,x21312)+E(f868(x21311,x21313,x21314,x21315,x21316,x21317),f868(x21312,x21313,x21314,x21315,x21316,x21317)) % 172.83/172.50 [2132]~E(x21321,x21322)+E(f868(x21323,x21321,x21324,x21325,x21326,x21327),f868(x21323,x21322,x21324,x21325,x21326,x21327)) % 172.83/172.50 [2133]~E(x21331,x21332)+E(f868(x21333,x21334,x21331,x21335,x21336,x21337),f868(x21333,x21334,x21332,x21335,x21336,x21337)) % 172.83/172.50 [2134]~E(x21341,x21342)+E(f868(x21343,x21344,x21345,x21341,x21346,x21347),f868(x21343,x21344,x21345,x21342,x21346,x21347)) % 172.83/172.50 [2135]~E(x21351,x21352)+E(f868(x21353,x21354,x21355,x21356,x21351,x21357),f868(x21353,x21354,x21355,x21356,x21352,x21357)) % 172.83/172.50 [2136]~E(x21361,x21362)+E(f868(x21363,x21364,x21365,x21366,x21367,x21361),f868(x21363,x21364,x21365,x21366,x21367,x21362)) % 172.83/172.50 [2137]~E(x21371,x21372)+E(f442(x21371,x21373,x21374,x21375,x21376),f442(x21372,x21373,x21374,x21375,x21376)) % 172.83/172.50 [2138]~E(x21381,x21382)+E(f442(x21383,x21381,x21384,x21385,x21386),f442(x21383,x21382,x21384,x21385,x21386)) % 172.83/172.50 [2139]~E(x21391,x21392)+E(f442(x21393,x21394,x21391,x21395,x21396),f442(x21393,x21394,x21392,x21395,x21396)) % 172.83/172.50 [2140]~E(x21401,x21402)+E(f442(x21403,x21404,x21405,x21401,x21406),f442(x21403,x21404,x21405,x21402,x21406)) % 172.83/172.50 [2141]~E(x21411,x21412)+E(f442(x21413,x21414,x21415,x21416,x21411),f442(x21413,x21414,x21415,x21416,x21412)) % 172.83/172.50 [2142]~E(x21421,x21422)+E(f795(x21421,x21423,x21424),f795(x21422,x21423,x21424)) % 172.83/172.50 [2143]~E(x21431,x21432)+E(f795(x21433,x21431,x21434),f795(x21433,x21432,x21434)) % 172.83/172.50 [2144]~E(x21441,x21442)+E(f795(x21443,x21444,x21441),f795(x21443,x21444,x21442)) % 172.83/172.50 [2145]~E(x21451,x21452)+E(f607(x21451,x21453,x21454),f607(x21452,x21453,x21454)) % 172.83/172.50 [2146]~E(x21461,x21462)+E(f607(x21463,x21461,x21464),f607(x21463,x21462,x21464)) % 172.83/172.50 [2147]~E(x21471,x21472)+E(f607(x21473,x21474,x21471),f607(x21473,x21474,x21472)) % 172.83/172.50 [2148]~E(x21481,x21482)+E(f635(x21481,x21483,x21484),f635(x21482,x21483,x21484)) % 172.83/172.50 [2149]~E(x21491,x21492)+E(f635(x21493,x21491,x21494),f635(x21493,x21492,x21494)) % 172.83/172.50 [2150]~E(x21501,x21502)+E(f635(x21503,x21504,x21501),f635(x21503,x21504,x21502)) % 172.83/172.50 [2151]~E(x21511,x21512)+E(f381(x21511,x21513),f381(x21512,x21513)) % 172.83/172.50 [2152]~E(x21521,x21522)+E(f381(x21523,x21521),f381(x21523,x21522)) % 172.83/172.50 [2153]~E(x21531,x21532)+E(f417(x21531),f417(x21532)) % 172.83/172.50 [2154]~E(x21541,x21542)+E(f473(x21541,x21543,x21544),f473(x21542,x21543,x21544)) % 172.83/172.50 [2155]~E(x21551,x21552)+E(f473(x21553,x21551,x21554),f473(x21553,x21552,x21554)) % 172.83/172.50 [2156]~E(x21561,x21562)+E(f473(x21563,x21564,x21561),f473(x21563,x21564,x21562)) % 172.83/172.50 [2157]~E(x21571,x21572)+E(f626(x21571,x21573,x21574,x21575,x21576,x21577,x21578),f626(x21572,x21573,x21574,x21575,x21576,x21577,x21578)) % 172.83/172.50 [2158]~E(x21581,x21582)+E(f626(x21583,x21581,x21584,x21585,x21586,x21587,x21588),f626(x21583,x21582,x21584,x21585,x21586,x21587,x21588)) % 172.83/172.50 [2159]~E(x21591,x21592)+E(f626(x21593,x21594,x21591,x21595,x21596,x21597,x21598),f626(x21593,x21594,x21592,x21595,x21596,x21597,x21598)) % 172.83/172.50 [2160]~E(x21601,x21602)+E(f626(x21603,x21604,x21605,x21601,x21606,x21607,x21608),f626(x21603,x21604,x21605,x21602,x21606,x21607,x21608)) % 172.83/172.50 [2161]~E(x21611,x21612)+E(f626(x21613,x21614,x21615,x21616,x21611,x21617,x21618),f626(x21613,x21614,x21615,x21616,x21612,x21617,x21618)) % 172.83/172.50 [2162]~E(x21621,x21622)+E(f626(x21623,x21624,x21625,x21626,x21627,x21621,x21628),f626(x21623,x21624,x21625,x21626,x21627,x21622,x21628)) % 172.83/172.50 [2163]~E(x21631,x21632)+E(f626(x21633,x21634,x21635,x21636,x21637,x21638,x21631),f626(x21633,x21634,x21635,x21636,x21637,x21638,x21632)) % 172.83/172.50 [2164]~E(x21641,x21642)+E(f528(x21641,x21643,x21644,x21645),f528(x21642,x21643,x21644,x21645)) % 172.83/172.50 [2165]~E(x21651,x21652)+E(f528(x21653,x21651,x21654,x21655),f528(x21653,x21652,x21654,x21655)) % 172.83/172.50 [2166]~E(x21661,x21662)+E(f528(x21663,x21664,x21661,x21665),f528(x21663,x21664,x21662,x21665)) % 172.83/172.50 [2167]~E(x21671,x21672)+E(f528(x21673,x21674,x21675,x21671),f528(x21673,x21674,x21675,x21672)) % 172.83/172.50 [2168]~E(x21681,x21682)+E(f655(x21681,x21683,x21684),f655(x21682,x21683,x21684)) % 172.83/172.50 [2169]~E(x21691,x21692)+E(f655(x21693,x21691,x21694),f655(x21693,x21692,x21694)) % 172.83/172.50 [2170]~E(x21701,x21702)+E(f655(x21703,x21704,x21701),f655(x21703,x21704,x21702)) % 172.83/172.50 [2171]~E(x21711,x21712)+E(f225(x21711,x21713),f225(x21712,x21713)) % 172.83/172.50 [2172]~E(x21721,x21722)+E(f225(x21723,x21721),f225(x21723,x21722)) % 172.83/172.50 [2173]~E(x21731,x21732)+E(f533(x21731,x21733,x21734,x21735),f533(x21732,x21733,x21734,x21735)) % 172.83/172.50 [2174]~E(x21741,x21742)+E(f533(x21743,x21741,x21744,x21745),f533(x21743,x21742,x21744,x21745)) % 172.83/172.50 [2175]~E(x21751,x21752)+E(f533(x21753,x21754,x21751,x21755),f533(x21753,x21754,x21752,x21755)) % 172.83/172.50 [2176]~E(x21761,x21762)+E(f533(x21763,x21764,x21765,x21761),f533(x21763,x21764,x21765,x21762)) % 172.83/172.50 [2177]~E(x21771,x21772)+E(f232(x21771,x21773,x21774),f232(x21772,x21773,x21774)) % 172.83/172.50 [2178]~E(x21781,x21782)+E(f232(x21783,x21781,x21784),f232(x21783,x21782,x21784)) % 172.83/172.50 [2179]~E(x21791,x21792)+E(f232(x21793,x21794,x21791),f232(x21793,x21794,x21792)) % 172.83/172.50 [2180]~E(x21801,x21802)+E(f349(x21801,x21803,x21804),f349(x21802,x21803,x21804)) % 172.83/172.50 [2181]~E(x21811,x21812)+E(f349(x21813,x21811,x21814),f349(x21813,x21812,x21814)) % 172.83/172.50 [2182]~E(x21821,x21822)+E(f349(x21823,x21824,x21821),f349(x21823,x21824,x21822)) % 172.83/172.50 [2183]~E(x21831,x21832)+E(f648(x21831,x21833,x21834,x21835,x21836,x21837),f648(x21832,x21833,x21834,x21835,x21836,x21837)) % 172.83/172.50 [2184]~E(x21841,x21842)+E(f648(x21843,x21841,x21844,x21845,x21846,x21847),f648(x21843,x21842,x21844,x21845,x21846,x21847)) % 172.83/172.50 [2185]~E(x21851,x21852)+E(f648(x21853,x21854,x21851,x21855,x21856,x21857),f648(x21853,x21854,x21852,x21855,x21856,x21857)) % 172.83/172.50 [2186]~E(x21861,x21862)+E(f648(x21863,x21864,x21865,x21861,x21866,x21867),f648(x21863,x21864,x21865,x21862,x21866,x21867)) % 172.83/172.51 [2187]~E(x21871,x21872)+E(f648(x21873,x21874,x21875,x21876,x21871,x21877),f648(x21873,x21874,x21875,x21876,x21872,x21877)) % 172.83/172.51 [2188]~E(x21881,x21882)+E(f648(x21883,x21884,x21885,x21886,x21887,x21881),f648(x21883,x21884,x21885,x21886,x21887,x21882)) % 172.83/172.51 [2189]~E(x21891,x21892)+E(f764(x21891,x21893,x21894,x21895),f764(x21892,x21893,x21894,x21895)) % 172.83/172.51 [2190]~E(x21901,x21902)+E(f764(x21903,x21901,x21904,x21905),f764(x21903,x21902,x21904,x21905)) % 172.83/172.51 [2191]~E(x21911,x21912)+E(f764(x21913,x21914,x21911,x21915),f764(x21913,x21914,x21912,x21915)) % 172.83/172.51 [2192]~E(x21921,x21922)+E(f764(x21923,x21924,x21925,x21921),f764(x21923,x21924,x21925,x21922)) % 172.83/172.51 [2193]~E(x21931,x21932)+E(f275(x21931,x21933,x21934,x21935,x21936),f275(x21932,x21933,x21934,x21935,x21936)) % 172.83/172.51 [2194]~E(x21941,x21942)+E(f275(x21943,x21941,x21944,x21945,x21946),f275(x21943,x21942,x21944,x21945,x21946)) % 172.83/172.51 [2195]~E(x21951,x21952)+E(f275(x21953,x21954,x21951,x21955,x21956),f275(x21953,x21954,x21952,x21955,x21956)) % 172.83/172.51 [2196]~E(x21961,x21962)+E(f275(x21963,x21964,x21965,x21961,x21966),f275(x21963,x21964,x21965,x21962,x21966)) % 172.83/172.51 [2197]~E(x21971,x21972)+E(f275(x21973,x21974,x21975,x21976,x21971),f275(x21973,x21974,x21975,x21976,x21972)) % 172.83/172.51 [2198]~E(x21981,x21982)+E(f497(x21981,x21983),f497(x21982,x21983)) % 172.83/172.51 [2199]~E(x21991,x21992)+E(f497(x21993,x21991),f497(x21993,x21992)) % 172.83/172.51 [2200]~E(x22001,x22002)+E(f633(x22001,x22003,x22004),f633(x22002,x22003,x22004)) % 172.83/172.51 [2201]~E(x22011,x22012)+E(f633(x22013,x22011,x22014),f633(x22013,x22012,x22014)) % 172.83/172.51 [2202]~E(x22021,x22022)+E(f633(x22023,x22024,x22021),f633(x22023,x22024,x22022)) % 172.83/172.51 [2203]~E(x22031,x22032)+E(f366(x22031),f366(x22032)) % 172.83/172.51 [2204]~E(x22041,x22042)+E(f812(x22041,x22043,x22044,x22045),f812(x22042,x22043,x22044,x22045)) % 172.83/172.51 [2205]~E(x22051,x22052)+E(f812(x22053,x22051,x22054,x22055),f812(x22053,x22052,x22054,x22055)) % 172.83/172.51 [2206]~E(x22061,x22062)+E(f812(x22063,x22064,x22061,x22065),f812(x22063,x22064,x22062,x22065)) % 172.83/172.51 [2207]~E(x22071,x22072)+E(f812(x22073,x22074,x22075,x22071),f812(x22073,x22074,x22075,x22072)) % 172.83/172.51 [2208]~E(x22081,x22082)+E(f694(x22081,x22083,x22084),f694(x22082,x22083,x22084)) % 172.83/172.51 [2209]~E(x22091,x22092)+E(f694(x22093,x22091,x22094),f694(x22093,x22092,x22094)) % 172.83/172.51 [2210]~E(x22101,x22102)+E(f694(x22103,x22104,x22101),f694(x22103,x22104,x22102)) % 172.83/172.51 [2211]~E(x22111,x22112)+E(f574(x22111,x22113,x22114),f574(x22112,x22113,x22114)) % 172.83/172.51 [2212]~E(x22121,x22122)+E(f574(x22123,x22121,x22124),f574(x22123,x22122,x22124)) % 172.83/172.51 [2213]~E(x22131,x22132)+E(f574(x22133,x22134,x22131),f574(x22133,x22134,x22132)) % 172.83/172.51 [2214]~E(x22141,x22142)+E(f446(x22141,x22143,x22144,x22145),f446(x22142,x22143,x22144,x22145)) % 172.83/172.51 [2215]~E(x22151,x22152)+E(f446(x22153,x22151,x22154,x22155),f446(x22153,x22152,x22154,x22155)) % 172.83/172.51 [2216]~E(x22161,x22162)+E(f446(x22163,x22164,x22161,x22165),f446(x22163,x22164,x22162,x22165)) % 172.83/172.51 [2217]~E(x22171,x22172)+E(f446(x22173,x22174,x22175,x22171),f446(x22173,x22174,x22175,x22172)) % 172.83/172.51 [2218]~E(x22181,x22182)+E(f660(x22181,x22183,x22184,x22185,x22186),f660(x22182,x22183,x22184,x22185,x22186)) % 172.83/172.51 [2219]~E(x22191,x22192)+E(f660(x22193,x22191,x22194,x22195,x22196),f660(x22193,x22192,x22194,x22195,x22196)) % 172.83/172.51 [2220]~E(x22201,x22202)+E(f660(x22203,x22204,x22201,x22205,x22206),f660(x22203,x22204,x22202,x22205,x22206)) % 172.83/172.51 [2221]~E(x22211,x22212)+E(f660(x22213,x22214,x22215,x22211,x22216),f660(x22213,x22214,x22215,x22212,x22216)) % 172.83/172.51 [2222]~E(x22221,x22222)+E(f660(x22223,x22224,x22225,x22226,x22221),f660(x22223,x22224,x22225,x22226,x22222)) % 172.83/172.51 [2223]~E(x22231,x22232)+E(f669(x22231,x22233,x22234),f669(x22232,x22233,x22234)) % 172.83/172.51 [2224]~E(x22241,x22242)+E(f669(x22243,x22241,x22244),f669(x22243,x22242,x22244)) % 172.83/172.51 [2225]~E(x22251,x22252)+E(f669(x22253,x22254,x22251),f669(x22253,x22254,x22252)) % 172.83/172.51 [2226]~E(x22261,x22262)+E(f373(x22261,x22263,x22264,x22265,x22266),f373(x22262,x22263,x22264,x22265,x22266)) % 172.83/172.51 [2227]~E(x22271,x22272)+E(f373(x22273,x22271,x22274,x22275,x22276),f373(x22273,x22272,x22274,x22275,x22276)) % 172.83/172.51 [2228]~E(x22281,x22282)+E(f373(x22283,x22284,x22281,x22285,x22286),f373(x22283,x22284,x22282,x22285,x22286)) % 172.83/172.51 [2229]~E(x22291,x22292)+E(f373(x22293,x22294,x22295,x22291,x22296),f373(x22293,x22294,x22295,x22292,x22296)) % 172.83/172.51 [2230]~E(x22301,x22302)+E(f373(x22303,x22304,x22305,x22306,x22301),f373(x22303,x22304,x22305,x22306,x22302)) % 172.83/172.51 [2231]~E(x22311,x22312)+E(f405(x22311,x22313,x22314,x22315),f405(x22312,x22313,x22314,x22315)) % 172.83/172.51 [2232]~E(x22321,x22322)+E(f405(x22323,x22321,x22324,x22325),f405(x22323,x22322,x22324,x22325)) % 172.83/172.51 [2233]~E(x22331,x22332)+E(f405(x22333,x22334,x22331,x22335),f405(x22333,x22334,x22332,x22335)) % 172.83/172.51 [2234]~E(x22341,x22342)+E(f405(x22343,x22344,x22345,x22341),f405(x22343,x22344,x22345,x22342)) % 172.83/172.51 [2235]~E(x22351,x22352)+E(f233(x22351,x22353,x22354,x22355),f233(x22352,x22353,x22354,x22355)) % 172.83/172.51 [2236]~E(x22361,x22362)+E(f233(x22363,x22361,x22364,x22365),f233(x22363,x22362,x22364,x22365)) % 172.83/172.51 [2237]~E(x22371,x22372)+E(f233(x22373,x22374,x22371,x22375),f233(x22373,x22374,x22372,x22375)) % 172.83/172.51 [2238]~E(x22381,x22382)+E(f233(x22383,x22384,x22385,x22381),f233(x22383,x22384,x22385,x22382)) % 172.83/172.51 [2239]~E(x22391,x22392)+E(f701(x22391,x22393,x22394,x22395),f701(x22392,x22393,x22394,x22395)) % 172.83/172.51 [2240]~E(x22401,x22402)+E(f701(x22403,x22401,x22404,x22405),f701(x22403,x22402,x22404,x22405)) % 172.83/172.51 [2241]~E(x22411,x22412)+E(f701(x22413,x22414,x22411,x22415),f701(x22413,x22414,x22412,x22415)) % 172.83/172.51 [2242]~E(x22421,x22422)+E(f701(x22423,x22424,x22425,x22421),f701(x22423,x22424,x22425,x22422)) % 172.83/172.51 [2243]~E(x22431,x22432)+E(f748(x22431,x22433,x22434),f748(x22432,x22433,x22434)) % 172.83/172.51 [2244]~E(x22441,x22442)+E(f748(x22443,x22441,x22444),f748(x22443,x22442,x22444)) % 172.83/172.51 [2245]~E(x22451,x22452)+E(f748(x22453,x22454,x22451),f748(x22453,x22454,x22452)) % 172.83/172.51 [2246]~E(x22461,x22462)+E(f769(x22461,x22463,x22464,x22465,x22466,x22467,x22468),f769(x22462,x22463,x22464,x22465,x22466,x22467,x22468)) % 172.83/172.51 [2247]~E(x22471,x22472)+E(f769(x22473,x22471,x22474,x22475,x22476,x22477,x22478),f769(x22473,x22472,x22474,x22475,x22476,x22477,x22478)) % 172.83/172.51 [2248]~E(x22481,x22482)+E(f769(x22483,x22484,x22481,x22485,x22486,x22487,x22488),f769(x22483,x22484,x22482,x22485,x22486,x22487,x22488)) % 172.83/172.51 [2249]~E(x22491,x22492)+E(f769(x22493,x22494,x22495,x22491,x22496,x22497,x22498),f769(x22493,x22494,x22495,x22492,x22496,x22497,x22498)) % 172.83/172.51 [2250]~E(x22501,x22502)+E(f769(x22503,x22504,x22505,x22506,x22501,x22507,x22508),f769(x22503,x22504,x22505,x22506,x22502,x22507,x22508)) % 172.83/172.51 [2251]~E(x22511,x22512)+E(f769(x22513,x22514,x22515,x22516,x22517,x22511,x22518),f769(x22513,x22514,x22515,x22516,x22517,x22512,x22518)) % 172.83/172.51 [2252]~E(x22521,x22522)+E(f769(x22523,x22524,x22525,x22526,x22527,x22528,x22521),f769(x22523,x22524,x22525,x22526,x22527,x22528,x22522)) % 172.83/172.51 [2253]~E(x22531,x22532)+E(f490(x22531,x22533,x22534),f490(x22532,x22533,x22534)) % 172.83/172.51 [2254]~E(x22541,x22542)+E(f490(x22543,x22541,x22544),f490(x22543,x22542,x22544)) % 172.83/172.51 [2255]~E(x22551,x22552)+E(f490(x22553,x22554,x22551),f490(x22553,x22554,x22552)) % 172.83/172.51 [2256]~E(x22561,x22562)+E(f98(x22561,x22563,x22564,x22565),f98(x22562,x22563,x22564,x22565)) % 172.83/172.51 [2257]~E(x22571,x22572)+E(f98(x22573,x22571,x22574,x22575),f98(x22573,x22572,x22574,x22575)) % 172.83/172.51 [2258]~E(x22581,x22582)+E(f98(x22583,x22584,x22581,x22585),f98(x22583,x22584,x22582,x22585)) % 172.83/172.51 [2259]~E(x22591,x22592)+E(f98(x22593,x22594,x22595,x22591),f98(x22593,x22594,x22595,x22592)) % 172.83/172.51 [2260]~E(x22601,x22602)+E(f376(x22601,x22603),f376(x22602,x22603)) % 172.83/172.51 [2261]~E(x22611,x22612)+E(f376(x22613,x22611),f376(x22613,x22612)) % 172.83/172.51 [2262]~E(x22621,x22622)+E(f650(x22621,x22623,x22624,x22625),f650(x22622,x22623,x22624,x22625)) % 172.83/172.51 [2263]~E(x22631,x22632)+E(f650(x22633,x22631,x22634,x22635),f650(x22633,x22632,x22634,x22635)) % 172.83/172.51 [2264]~E(x22641,x22642)+E(f650(x22643,x22644,x22641,x22645),f650(x22643,x22644,x22642,x22645)) % 172.83/172.51 [2265]~E(x22651,x22652)+E(f650(x22653,x22654,x22655,x22651),f650(x22653,x22654,x22655,x22652)) % 172.83/172.51 [2266]~E(x22661,x22662)+E(f379(x22661,x22663),f379(x22662,x22663)) % 172.83/172.51 [2267]~E(x22671,x22672)+E(f379(x22673,x22671),f379(x22673,x22672)) % 172.83/172.51 [2268]~E(x22681,x22682)+E(f724(x22681,x22683,x22684),f724(x22682,x22683,x22684)) % 172.83/172.51 [2269]~E(x22691,x22692)+E(f724(x22693,x22691,x22694),f724(x22693,x22692,x22694)) % 172.83/172.51 [2270]~E(x22701,x22702)+E(f724(x22703,x22704,x22701),f724(x22703,x22704,x22702)) % 172.83/172.51 [2271]~E(x22711,x22712)+E(f218(x22711,x22713,x22714,x22715,x22716,x22717,x22718),f218(x22712,x22713,x22714,x22715,x22716,x22717,x22718)) % 172.83/172.51 [2272]~E(x22721,x22722)+E(f218(x22723,x22721,x22724,x22725,x22726,x22727,x22728),f218(x22723,x22722,x22724,x22725,x22726,x22727,x22728)) % 172.83/172.51 [2273]~E(x22731,x22732)+E(f218(x22733,x22734,x22731,x22735,x22736,x22737,x22738),f218(x22733,x22734,x22732,x22735,x22736,x22737,x22738)) % 172.83/172.51 [2274]~E(x22741,x22742)+E(f218(x22743,x22744,x22745,x22741,x22746,x22747,x22748),f218(x22743,x22744,x22745,x22742,x22746,x22747,x22748)) % 172.83/172.51 [2275]~E(x22751,x22752)+E(f218(x22753,x22754,x22755,x22756,x22751,x22757,x22758),f218(x22753,x22754,x22755,x22756,x22752,x22757,x22758)) % 172.83/172.51 [2276]~E(x22761,x22762)+E(f218(x22763,x22764,x22765,x22766,x22767,x22761,x22768),f218(x22763,x22764,x22765,x22766,x22767,x22762,x22768)) % 172.83/172.51 [2277]~E(x22771,x22772)+E(f218(x22773,x22774,x22775,x22776,x22777,x22778,x22771),f218(x22773,x22774,x22775,x22776,x22777,x22778,x22772)) % 172.83/172.51 [2278]~E(x22781,x22782)+E(f365(x22781,x22783),f365(x22782,x22783)) % 172.83/172.51 [2279]~E(x22791,x22792)+E(f365(x22793,x22791),f365(x22793,x22792)) % 172.83/172.51 [2280]~E(x22801,x22802)+E(f352(x22801,x22803,x22804),f352(x22802,x22803,x22804)) % 172.83/172.51 [2281]~E(x22811,x22812)+E(f352(x22813,x22811,x22814),f352(x22813,x22812,x22814)) % 172.83/172.51 [2282]~E(x22821,x22822)+E(f352(x22823,x22824,x22821),f352(x22823,x22824,x22822)) % 172.83/172.51 [2283]~E(x22831,x22832)+E(f833(x22831,x22833,x22834),f833(x22832,x22833,x22834)) % 172.83/172.51 [2284]~E(x22841,x22842)+E(f833(x22843,x22841,x22844),f833(x22843,x22842,x22844)) % 172.83/172.51 [2285]~E(x22851,x22852)+E(f833(x22853,x22854,x22851),f833(x22853,x22854,x22852)) % 172.83/172.51 [2286]~E(x22861,x22862)+E(f861(x22861,x22863,x22864,x22865,x22866),f861(x22862,x22863,x22864,x22865,x22866)) % 172.83/172.51 [2287]~E(x22871,x22872)+E(f861(x22873,x22871,x22874,x22875,x22876),f861(x22873,x22872,x22874,x22875,x22876)) % 172.83/172.51 [2288]~E(x22881,x22882)+E(f861(x22883,x22884,x22881,x22885,x22886),f861(x22883,x22884,x22882,x22885,x22886)) % 172.83/172.51 [2289]~E(x22891,x22892)+E(f861(x22893,x22894,x22895,x22891,x22896),f861(x22893,x22894,x22895,x22892,x22896)) % 172.83/172.51 [2290]~E(x22901,x22902)+E(f861(x22903,x22904,x22905,x22906,x22901),f861(x22903,x22904,x22905,x22906,x22902)) % 172.83/172.51 [2291]~E(x22911,x22912)+E(f651(x22911,x22913,x22914,x22915),f651(x22912,x22913,x22914,x22915)) % 172.83/172.51 [2292]~E(x22921,x22922)+E(f651(x22923,x22921,x22924,x22925),f651(x22923,x22922,x22924,x22925)) % 172.83/172.51 [2293]~E(x22931,x22932)+E(f651(x22933,x22934,x22931,x22935),f651(x22933,x22934,x22932,x22935)) % 172.83/172.51 [2294]~E(x22941,x22942)+E(f651(x22943,x22944,x22945,x22941),f651(x22943,x22944,x22945,x22942)) % 172.83/172.51 [2295]~E(x22951,x22952)+E(f781(x22951,x22953,x22954,x22955),f781(x22952,x22953,x22954,x22955)) % 172.83/172.51 [2296]~E(x22961,x22962)+E(f781(x22963,x22961,x22964,x22965),f781(x22963,x22962,x22964,x22965)) % 172.83/172.51 [2297]~E(x22971,x22972)+E(f781(x22973,x22974,x22971,x22975),f781(x22973,x22974,x22972,x22975)) % 172.83/172.51 [2298]~E(x22981,x22982)+E(f781(x22983,x22984,x22985,x22981),f781(x22983,x22984,x22985,x22982)) % 172.83/172.51 [2299]~E(x22991,x22992)+E(f863(x22991,x22993),f863(x22992,x22993)) % 172.83/172.51 [2300]~E(x23001,x23002)+E(f863(x23003,x23001),f863(x23003,x23002)) % 172.83/172.51 [2301]~E(x23011,x23012)+E(f486(x23011,x23013,x23014,x23015),f486(x23012,x23013,x23014,x23015)) % 172.83/172.51 [2302]~E(x23021,x23022)+E(f486(x23023,x23021,x23024,x23025),f486(x23023,x23022,x23024,x23025)) % 172.83/172.51 [2303]~E(x23031,x23032)+E(f486(x23033,x23034,x23031,x23035),f486(x23033,x23034,x23032,x23035)) % 172.83/172.51 [2304]~E(x23041,x23042)+E(f486(x23043,x23044,x23045,x23041),f486(x23043,x23044,x23045,x23042)) % 172.83/172.51 [2305]~E(x23051,x23052)+E(f667(x23051,x23053,x23054,x23055),f667(x23052,x23053,x23054,x23055)) % 172.83/172.51 [2306]~E(x23061,x23062)+E(f667(x23063,x23061,x23064,x23065),f667(x23063,x23062,x23064,x23065)) % 172.83/172.51 [2307]~E(x23071,x23072)+E(f667(x23073,x23074,x23071,x23075),f667(x23073,x23074,x23072,x23075)) % 172.83/172.51 [2308]~E(x23081,x23082)+E(f667(x23083,x23084,x23085,x23081),f667(x23083,x23084,x23085,x23082)) % 172.83/172.51 [2309]~E(x23091,x23092)+E(f512(x23091,x23093,x23094,x23095,x23096,x23097,x23098),f512(x23092,x23093,x23094,x23095,x23096,x23097,x23098)) % 172.83/172.51 [2310]~E(x23101,x23102)+E(f512(x23103,x23101,x23104,x23105,x23106,x23107,x23108),f512(x23103,x23102,x23104,x23105,x23106,x23107,x23108)) % 172.83/172.51 [2311]~E(x23111,x23112)+E(f512(x23113,x23114,x23111,x23115,x23116,x23117,x23118),f512(x23113,x23114,x23112,x23115,x23116,x23117,x23118)) % 172.83/172.51 [2312]~E(x23121,x23122)+E(f512(x23123,x23124,x23125,x23121,x23126,x23127,x23128),f512(x23123,x23124,x23125,x23122,x23126,x23127,x23128)) % 172.83/172.51 [2313]~E(x23131,x23132)+E(f512(x23133,x23134,x23135,x23136,x23131,x23137,x23138),f512(x23133,x23134,x23135,x23136,x23132,x23137,x23138)) % 172.83/172.51 [2314]~E(x23141,x23142)+E(f512(x23143,x23144,x23145,x23146,x23147,x23141,x23148),f512(x23143,x23144,x23145,x23146,x23147,x23142,x23148)) % 172.83/172.51 [2315]~E(x23151,x23152)+E(f512(x23153,x23154,x23155,x23156,x23157,x23158,x23151),f512(x23153,x23154,x23155,x23156,x23157,x23158,x23152)) % 172.83/172.51 [2316]~E(x23161,x23162)+E(f461(x23161,x23163,x23164,x23165,x23166,x23167,x23168),f461(x23162,x23163,x23164,x23165,x23166,x23167,x23168)) % 172.83/172.51 [2317]~E(x23171,x23172)+E(f461(x23173,x23171,x23174,x23175,x23176,x23177,x23178),f461(x23173,x23172,x23174,x23175,x23176,x23177,x23178)) % 172.83/172.51 [2318]~E(x23181,x23182)+E(f461(x23183,x23184,x23181,x23185,x23186,x23187,x23188),f461(x23183,x23184,x23182,x23185,x23186,x23187,x23188)) % 172.83/172.51 [2319]~E(x23191,x23192)+E(f461(x23193,x23194,x23195,x23191,x23196,x23197,x23198),f461(x23193,x23194,x23195,x23192,x23196,x23197,x23198)) % 172.83/172.51 [2320]~E(x23201,x23202)+E(f461(x23203,x23204,x23205,x23206,x23201,x23207,x23208),f461(x23203,x23204,x23205,x23206,x23202,x23207,x23208)) % 172.83/172.51 [2321]~E(x23211,x23212)+E(f461(x23213,x23214,x23215,x23216,x23217,x23211,x23218),f461(x23213,x23214,x23215,x23216,x23217,x23212,x23218)) % 172.83/172.51 [2322]~E(x23221,x23222)+E(f461(x23223,x23224,x23225,x23226,x23227,x23228,x23221),f461(x23223,x23224,x23225,x23226,x23227,x23228,x23222)) % 172.83/172.51 [2323]~E(x23231,x23232)+E(f499(x23231,x23233,x23234),f499(x23232,x23233,x23234)) % 172.83/172.51 [2324]~E(x23241,x23242)+E(f499(x23243,x23241,x23244),f499(x23243,x23242,x23244)) % 172.83/172.51 [2325]~E(x23251,x23252)+E(f499(x23253,x23254,x23251),f499(x23253,x23254,x23252)) % 172.83/172.51 [2326]~E(x23261,x23262)+E(f236(x23261,x23263,x23264),f236(x23262,x23263,x23264)) % 172.83/172.51 [2327]~E(x23271,x23272)+E(f236(x23273,x23271,x23274),f236(x23273,x23272,x23274)) % 172.83/172.51 [2328]~E(x23281,x23282)+E(f236(x23283,x23284,x23281),f236(x23283,x23284,x23282)) % 172.83/172.51 [2329]~E(x23291,x23292)+E(f790(x23291,x23293,x23294,x23295,x23296,x23297,x23298),f790(x23292,x23293,x23294,x23295,x23296,x23297,x23298)) % 172.83/172.51 [2330]~E(x23301,x23302)+E(f790(x23303,x23301,x23304,x23305,x23306,x23307,x23308),f790(x23303,x23302,x23304,x23305,x23306,x23307,x23308)) % 172.83/172.51 [2331]~E(x23311,x23312)+E(f790(x23313,x23314,x23311,x23315,x23316,x23317,x23318),f790(x23313,x23314,x23312,x23315,x23316,x23317,x23318)) % 172.83/172.51 [2332]~E(x23321,x23322)+E(f790(x23323,x23324,x23325,x23321,x23326,x23327,x23328),f790(x23323,x23324,x23325,x23322,x23326,x23327,x23328)) % 172.83/172.51 [2333]~E(x23331,x23332)+E(f790(x23333,x23334,x23335,x23336,x23331,x23337,x23338),f790(x23333,x23334,x23335,x23336,x23332,x23337,x23338)) % 172.83/172.51 [2334]~E(x23341,x23342)+E(f790(x23343,x23344,x23345,x23346,x23347,x23341,x23348),f790(x23343,x23344,x23345,x23346,x23347,x23342,x23348)) % 172.83/172.51 [2335]~E(x23351,x23352)+E(f790(x23353,x23354,x23355,x23356,x23357,x23358,x23351),f790(x23353,x23354,x23355,x23356,x23357,x23358,x23352)) % 172.83/172.51 [2336]~E(x23361,x23362)+E(f605(x23361,x23363,x23364,x23365),f605(x23362,x23363,x23364,x23365)) % 172.83/172.51 [2337]~E(x23371,x23372)+E(f605(x23373,x23371,x23374,x23375),f605(x23373,x23372,x23374,x23375)) % 172.83/172.51 [2338]~E(x23381,x23382)+E(f605(x23383,x23384,x23381,x23385),f605(x23383,x23384,x23382,x23385)) % 172.83/172.51 [2339]~E(x23391,x23392)+E(f605(x23393,x23394,x23395,x23391),f605(x23393,x23394,x23395,x23392)) % 172.83/172.51 [2340]~E(x23401,x23402)+E(f300(x23401,x23403,x23404,x23405,x23406),f300(x23402,x23403,x23404,x23405,x23406)) % 172.83/172.51 [2341]~E(x23411,x23412)+E(f300(x23413,x23411,x23414,x23415,x23416),f300(x23413,x23412,x23414,x23415,x23416)) % 172.83/172.51 [2342]~E(x23421,x23422)+E(f300(x23423,x23424,x23421,x23425,x23426),f300(x23423,x23424,x23422,x23425,x23426)) % 172.83/172.51 [2343]~E(x23431,x23432)+E(f300(x23433,x23434,x23435,x23431,x23436),f300(x23433,x23434,x23435,x23432,x23436)) % 172.83/172.51 [2344]~E(x23441,x23442)+E(f300(x23443,x23444,x23445,x23446,x23441),f300(x23443,x23444,x23445,x23446,x23442)) % 172.83/172.51 [2345]~E(x23451,x23452)+E(f451(x23451,x23453,x23454),f451(x23452,x23453,x23454)) % 172.83/172.51 [2346]~E(x23461,x23462)+E(f451(x23463,x23461,x23464),f451(x23463,x23462,x23464)) % 172.83/172.51 [2347]~E(x23471,x23472)+E(f451(x23473,x23474,x23471),f451(x23473,x23474,x23472)) % 172.83/172.51 [2348]~E(x23481,x23482)+E(f835(x23481,x23483,x23484,x23485,x23486),f835(x23482,x23483,x23484,x23485,x23486)) % 172.83/172.51 [2349]~E(x23491,x23492)+E(f835(x23493,x23491,x23494,x23495,x23496),f835(x23493,x23492,x23494,x23495,x23496)) % 172.83/172.51 [2350]~E(x23501,x23502)+E(f835(x23503,x23504,x23501,x23505,x23506),f835(x23503,x23504,x23502,x23505,x23506)) % 172.83/172.51 [2351]~E(x23511,x23512)+E(f835(x23513,x23514,x23515,x23511,x23516),f835(x23513,x23514,x23515,x23512,x23516)) % 172.83/172.51 [2352]~E(x23521,x23522)+E(f835(x23523,x23524,x23525,x23526,x23521),f835(x23523,x23524,x23525,x23526,x23522)) % 172.83/172.51 [2353]~E(x23531,x23532)+E(f316(x23531,x23533,x23534),f316(x23532,x23533,x23534)) % 172.83/172.51 [2354]~E(x23541,x23542)+E(f316(x23543,x23541,x23544),f316(x23543,x23542,x23544)) % 172.83/172.51 [2355]~E(x23551,x23552)+E(f316(x23553,x23554,x23551),f316(x23553,x23554,x23552)) % 172.83/172.51 [2356]~E(x23561,x23562)+E(f857(x23561,x23563,x23564,x23565),f857(x23562,x23563,x23564,x23565)) % 172.83/172.51 [2357]~E(x23571,x23572)+E(f857(x23573,x23571,x23574,x23575),f857(x23573,x23572,x23574,x23575)) % 172.83/172.51 [2358]~E(x23581,x23582)+E(f857(x23583,x23584,x23581,x23585),f857(x23583,x23584,x23582,x23585)) % 172.83/172.51 [2359]~E(x23591,x23592)+E(f857(x23593,x23594,x23595,x23591),f857(x23593,x23594,x23595,x23592)) % 172.83/172.51 [2360]~E(x23601,x23602)+E(f642(x23601,x23603,x23604),f642(x23602,x23603,x23604)) % 172.83/172.51 [2361]~E(x23611,x23612)+E(f642(x23613,x23611,x23614),f642(x23613,x23612,x23614)) % 172.83/172.51 [2362]~E(x23621,x23622)+E(f642(x23623,x23624,x23621),f642(x23623,x23624,x23622)) % 172.83/172.51 [2363]~E(x23631,x23632)+E(f760(x23631,x23633,x23634,x23635),f760(x23632,x23633,x23634,x23635)) % 172.83/172.51 [2364]~E(x23641,x23642)+E(f760(x23643,x23641,x23644,x23645),f760(x23643,x23642,x23644,x23645)) % 172.83/172.51 [2365]~E(x23651,x23652)+E(f760(x23653,x23654,x23651,x23655),f760(x23653,x23654,x23652,x23655)) % 172.83/172.51 [2366]~E(x23661,x23662)+E(f760(x23663,x23664,x23665,x23661),f760(x23663,x23664,x23665,x23662)) % 172.83/172.51 [2367]~E(x23671,x23672)+E(f758(x23671,x23673,x23674),f758(x23672,x23673,x23674)) % 172.83/172.51 [2368]~E(x23681,x23682)+E(f758(x23683,x23681,x23684),f758(x23683,x23682,x23684)) % 172.83/172.51 [2369]~E(x23691,x23692)+E(f758(x23693,x23694,x23691),f758(x23693,x23694,x23692)) % 172.83/172.51 [2370]~E(x23701,x23702)+E(f799(x23701,x23703,x23704),f799(x23702,x23703,x23704)) % 172.83/172.51 [2371]~E(x23711,x23712)+E(f799(x23713,x23711,x23714),f799(x23713,x23712,x23714)) % 172.83/172.51 [2372]~E(x23721,x23722)+E(f799(x23723,x23724,x23721),f799(x23723,x23724,x23722)) % 172.83/172.51 [2373]~E(x23731,x23732)+E(f830(x23731,x23733,x23734,x23735,x23736,x23737,x23738),f830(x23732,x23733,x23734,x23735,x23736,x23737,x23738)) % 172.83/172.51 [2374]~E(x23741,x23742)+E(f830(x23743,x23741,x23744,x23745,x23746,x23747,x23748),f830(x23743,x23742,x23744,x23745,x23746,x23747,x23748)) % 172.83/172.51 [2375]~E(x23751,x23752)+E(f830(x23753,x23754,x23751,x23755,x23756,x23757,x23758),f830(x23753,x23754,x23752,x23755,x23756,x23757,x23758)) % 172.83/172.51 [2376]~E(x23761,x23762)+E(f830(x23763,x23764,x23765,x23761,x23766,x23767,x23768),f830(x23763,x23764,x23765,x23762,x23766,x23767,x23768)) % 172.83/172.51 [2377]~E(x23771,x23772)+E(f830(x23773,x23774,x23775,x23776,x23771,x23777,x23778),f830(x23773,x23774,x23775,x23776,x23772,x23777,x23778)) % 172.83/172.51 [2378]~E(x23781,x23782)+E(f830(x23783,x23784,x23785,x23786,x23787,x23781,x23788),f830(x23783,x23784,x23785,x23786,x23787,x23782,x23788)) % 172.83/172.51 [2379]~E(x23791,x23792)+E(f830(x23793,x23794,x23795,x23796,x23797,x23798,x23791),f830(x23793,x23794,x23795,x23796,x23797,x23798,x23792)) % 172.83/172.51 [2380]~E(x23801,x23802)+E(f707(x23801,x23803,x23804),f707(x23802,x23803,x23804)) % 172.83/172.51 [2381]~E(x23811,x23812)+E(f707(x23813,x23811,x23814),f707(x23813,x23812,x23814)) % 172.83/172.51 [2382]~E(x23821,x23822)+E(f707(x23823,x23824,x23821),f707(x23823,x23824,x23822)) % 172.83/172.51 [2383]~E(x23831,x23832)+E(f293(x23831,x23833,x23834),f293(x23832,x23833,x23834)) % 172.83/172.51 [2384]~E(x23841,x23842)+E(f293(x23843,x23841,x23844),f293(x23843,x23842,x23844)) % 172.83/172.51 [2385]~E(x23851,x23852)+E(f293(x23853,x23854,x23851),f293(x23853,x23854,x23852)) % 172.83/172.51 [2386]~E(x23861,x23862)+E(f554(x23861,x23863,x23864),f554(x23862,x23863,x23864)) % 172.83/172.51 [2387]~E(x23871,x23872)+E(f554(x23873,x23871,x23874),f554(x23873,x23872,x23874)) % 172.83/172.51 [2388]~E(x23881,x23882)+E(f554(x23883,x23884,x23881),f554(x23883,x23884,x23882)) % 172.83/172.51 [2389]~E(x23891,x23892)+E(f274(x23891,x23893,x23894,x23895,x23896),f274(x23892,x23893,x23894,x23895,x23896)) % 172.83/172.51 [2390]~E(x23901,x23902)+E(f274(x23903,x23901,x23904,x23905,x23906),f274(x23903,x23902,x23904,x23905,x23906)) % 172.83/172.51 [2391]~E(x23911,x23912)+E(f274(x23913,x23914,x23911,x23915,x23916),f274(x23913,x23914,x23912,x23915,x23916)) % 172.83/172.51 [2392]~E(x23921,x23922)+E(f274(x23923,x23924,x23925,x23921,x23926),f274(x23923,x23924,x23925,x23922,x23926)) % 172.83/172.51 [2393]~E(x23931,x23932)+E(f274(x23933,x23934,x23935,x23936,x23931),f274(x23933,x23934,x23935,x23936,x23932)) % 172.83/172.51 [2394]~E(x23941,x23942)+E(f471(x23941,x23943,x23944),f471(x23942,x23943,x23944)) % 172.83/172.51 [2395]~E(x23951,x23952)+E(f471(x23953,x23951,x23954),f471(x23953,x23952,x23954)) % 172.83/172.51 [2396]~E(x23961,x23962)+E(f471(x23963,x23964,x23961),f471(x23963,x23964,x23962)) % 172.83/172.51 [2397]~E(x23971,x23972)+E(f298(x23971,x23973,x23974),f298(x23972,x23973,x23974)) % 172.83/172.51 [2398]~E(x23981,x23982)+E(f298(x23983,x23981,x23984),f298(x23983,x23982,x23984)) % 172.83/172.51 [2399]~E(x23991,x23992)+E(f298(x23993,x23994,x23991),f298(x23993,x23994,x23992)) % 172.83/172.51 [2400]~E(x24001,x24002)+E(f440(x24001,x24003,x24004,x24005,x24006),f440(x24002,x24003,x24004,x24005,x24006)) % 172.83/172.51 [2401]~E(x24011,x24012)+E(f440(x24013,x24011,x24014,x24015,x24016),f440(x24013,x24012,x24014,x24015,x24016)) % 172.83/172.51 [2402]~E(x24021,x24022)+E(f440(x24023,x24024,x24021,x24025,x24026),f440(x24023,x24024,x24022,x24025,x24026)) % 172.83/172.51 [2403]~E(x24031,x24032)+E(f440(x24033,x24034,x24035,x24031,x24036),f440(x24033,x24034,x24035,x24032,x24036)) % 172.83/172.51 [2404]~E(x24041,x24042)+E(f440(x24043,x24044,x24045,x24046,x24041),f440(x24043,x24044,x24045,x24046,x24042)) % 172.83/172.51 [2405]~E(x24051,x24052)+E(f483(x24051,x24053,x24054),f483(x24052,x24053,x24054)) % 172.83/172.51 [2406]~E(x24061,x24062)+E(f483(x24063,x24061,x24064),f483(x24063,x24062,x24064)) % 172.83/172.51 [2407]~E(x24071,x24072)+E(f483(x24073,x24074,x24071),f483(x24073,x24074,x24072)) % 172.83/172.51 [2408]~E(x24081,x24082)+E(f410(x24081,x24083),f410(x24082,x24083)) % 172.83/172.51 [2409]~E(x24091,x24092)+E(f410(x24093,x24091),f410(x24093,x24092)) % 172.83/172.51 [2410]~E(x24101,x24102)+E(f370(x24101,x24103),f370(x24102,x24103)) % 172.83/172.51 [2411]~E(x24111,x24112)+E(f370(x24113,x24111),f370(x24113,x24112)) % 172.83/172.51 [2412]~E(x24121,x24122)+E(f536(x24121,x24123),f536(x24122,x24123)) % 172.83/172.51 [2413]~E(x24131,x24132)+E(f536(x24133,x24131),f536(x24133,x24132)) % 172.83/172.51 [2414]~E(x24141,x24142)+E(f259(x24141,x24143,x24144),f259(x24142,x24143,x24144)) % 172.83/172.51 [2415]~E(x24151,x24152)+E(f259(x24153,x24151,x24154),f259(x24153,x24152,x24154)) % 172.83/172.51 [2416]~E(x24161,x24162)+E(f259(x24163,x24164,x24161),f259(x24163,x24164,x24162)) % 172.83/172.51 [2417]~E(x24171,x24172)+E(f690(x24171,x24173,x24174,x24175),f690(x24172,x24173,x24174,x24175)) % 172.83/172.51 [2418]~E(x24181,x24182)+E(f690(x24183,x24181,x24184,x24185),f690(x24183,x24182,x24184,x24185)) % 172.83/172.51 [2419]~E(x24191,x24192)+E(f690(x24193,x24194,x24191,x24195),f690(x24193,x24194,x24192,x24195)) % 172.83/172.51 [2420]~E(x24201,x24202)+E(f690(x24203,x24204,x24205,x24201),f690(x24203,x24204,x24205,x24202)) % 172.83/172.51 [2421]~E(x24211,x24212)+E(f705(x24211,x24213,x24214,x24215),f705(x24212,x24213,x24214,x24215)) % 172.83/172.51 [2422]~E(x24221,x24222)+E(f705(x24223,x24221,x24224,x24225),f705(x24223,x24222,x24224,x24225)) % 172.83/172.51 [2423]~E(x24231,x24232)+E(f705(x24233,x24234,x24231,x24235),f705(x24233,x24234,x24232,x24235)) % 172.83/172.51 [2424]~E(x24241,x24242)+E(f705(x24243,x24244,x24245,x24241),f705(x24243,x24244,x24245,x24242)) % 172.83/172.51 [2425]~E(x24251,x24252)+E(f219(x24251),f219(x24252)) % 172.83/172.51 [2426]~E(x24261,x24262)+E(f450(x24261,x24263),f450(x24262,x24263)) % 172.83/172.51 [2427]~E(x24271,x24272)+E(f450(x24273,x24271),f450(x24273,x24272)) % 172.83/172.51 [2428]~E(x24281,x24282)+E(f632(x24281,x24283,x24284,x24285,x24286,x24287,x24288),f632(x24282,x24283,x24284,x24285,x24286,x24287,x24288)) % 172.83/172.51 [2429]~E(x24291,x24292)+E(f632(x24293,x24291,x24294,x24295,x24296,x24297,x24298),f632(x24293,x24292,x24294,x24295,x24296,x24297,x24298)) % 172.83/172.51 [2430]~E(x24301,x24302)+E(f632(x24303,x24304,x24301,x24305,x24306,x24307,x24308),f632(x24303,x24304,x24302,x24305,x24306,x24307,x24308)) % 172.83/172.51 [2431]~E(x24311,x24312)+E(f632(x24313,x24314,x24315,x24311,x24316,x24317,x24318),f632(x24313,x24314,x24315,x24312,x24316,x24317,x24318)) % 172.83/172.51 [2432]~E(x24321,x24322)+E(f632(x24323,x24324,x24325,x24326,x24321,x24327,x24328),f632(x24323,x24324,x24325,x24326,x24322,x24327,x24328)) % 172.83/172.51 [2433]~E(x24331,x24332)+E(f632(x24333,x24334,x24335,x24336,x24337,x24331,x24338),f632(x24333,x24334,x24335,x24336,x24337,x24332,x24338)) % 172.83/172.51 [2434]~E(x24341,x24342)+E(f632(x24343,x24344,x24345,x24346,x24347,x24348,x24341),f632(x24343,x24344,x24345,x24346,x24347,x24348,x24342)) % 172.83/172.51 [2435]~E(x24351,x24352)+E(f344(x24351,x24353,x24354),f344(x24352,x24353,x24354)) % 172.83/172.51 [2436]~E(x24361,x24362)+E(f344(x24363,x24361,x24364),f344(x24363,x24362,x24364)) % 172.83/172.51 [2437]~E(x24371,x24372)+E(f344(x24373,x24374,x24371),f344(x24373,x24374,x24372)) % 172.83/172.51 [2438]~E(x24381,x24382)+E(f371(x24381,x24383,x24384),f371(x24382,x24383,x24384)) % 172.83/172.51 [2439]~E(x24391,x24392)+E(f371(x24393,x24391,x24394),f371(x24393,x24392,x24394)) % 172.83/172.51 [2440]~E(x24401,x24402)+E(f371(x24403,x24404,x24401),f371(x24403,x24404,x24402)) % 172.83/172.51 [2441]~E(x24411,x24412)+E(f846(x24411,x24413,x24414,x24415,x24416,x24417),f846(x24412,x24413,x24414,x24415,x24416,x24417)) % 172.83/172.51 [2442]~E(x24421,x24422)+E(f846(x24423,x24421,x24424,x24425,x24426,x24427),f846(x24423,x24422,x24424,x24425,x24426,x24427)) % 172.83/172.51 [2443]~E(x24431,x24432)+E(f846(x24433,x24434,x24431,x24435,x24436,x24437),f846(x24433,x24434,x24432,x24435,x24436,x24437)) % 172.83/172.51 [2444]~E(x24441,x24442)+E(f846(x24443,x24444,x24445,x24441,x24446,x24447),f846(x24443,x24444,x24445,x24442,x24446,x24447)) % 172.83/172.51 [2445]~E(x24451,x24452)+E(f846(x24453,x24454,x24455,x24456,x24451,x24457),f846(x24453,x24454,x24455,x24456,x24452,x24457)) % 172.83/172.51 [2446]~E(x24461,x24462)+E(f846(x24463,x24464,x24465,x24466,x24467,x24461),f846(x24463,x24464,x24465,x24466,x24467,x24462)) % 172.83/172.51 [2447]~E(x24471,x24472)+E(f502(x24471),f502(x24472)) % 172.83/172.51 [2448]~E(x24481,x24482)+E(f809(x24481,x24483,x24484),f809(x24482,x24483,x24484)) % 172.83/172.51 [2449]~E(x24491,x24492)+E(f809(x24493,x24491,x24494),f809(x24493,x24492,x24494)) % 172.83/172.51 [2450]~E(x24501,x24502)+E(f809(x24503,x24504,x24501),f809(x24503,x24504,x24502)) % 172.83/172.51 [2451]~E(x24511,x24512)+E(f735(x24511,x24513,x24514),f735(x24512,x24513,x24514)) % 172.83/172.51 [2452]~E(x24521,x24522)+E(f735(x24523,x24521,x24524),f735(x24523,x24522,x24524)) % 172.83/172.51 [2453]~E(x24531,x24532)+E(f735(x24533,x24534,x24531),f735(x24533,x24534,x24532)) % 172.83/172.51 [2454]~E(x24541,x24542)+E(f369(x24541,x24543),f369(x24542,x24543)) % 172.83/172.51 [2455]~E(x24551,x24552)+E(f369(x24553,x24551),f369(x24553,x24552)) % 172.83/172.51 [2456]~E(x24561,x24562)+E(f645(x24561,x24563,x24564),f645(x24562,x24563,x24564)) % 172.83/172.51 [2457]~E(x24571,x24572)+E(f645(x24573,x24571,x24574),f645(x24573,x24572,x24574)) % 172.83/172.51 [2458]~E(x24581,x24582)+E(f645(x24583,x24584,x24581),f645(x24583,x24584,x24582)) % 172.83/172.51 [2459]~E(x24591,x24592)+E(f849(x24591,x24593,x24594),f849(x24592,x24593,x24594)) % 172.83/172.51 [2460]~E(x24601,x24602)+E(f849(x24603,x24601,x24604),f849(x24603,x24602,x24604)) % 172.83/172.51 [2461]~E(x24611,x24612)+E(f849(x24613,x24614,x24611),f849(x24613,x24614,x24612)) % 172.83/172.51 [2462]~E(x24621,x24622)+E(f403(x24621,x24623,x24624,x24625),f403(x24622,x24623,x24624,x24625)) % 172.83/172.51 [2463]~E(x24631,x24632)+E(f403(x24633,x24631,x24634,x24635),f403(x24633,x24632,x24634,x24635)) % 172.83/172.51 [2464]~E(x24641,x24642)+E(f403(x24643,x24644,x24641,x24645),f403(x24643,x24644,x24642,x24645)) % 172.83/172.51 [2465]~E(x24651,x24652)+E(f403(x24653,x24654,x24655,x24651),f403(x24653,x24654,x24655,x24652)) % 172.83/172.51 [2466]~E(x24661,x24662)+E(f521(x24661,x24663,x24664),f521(x24662,x24663,x24664)) % 172.83/172.51 [2467]~E(x24671,x24672)+E(f521(x24673,x24671,x24674),f521(x24673,x24672,x24674)) % 172.83/172.51 [2468]~E(x24681,x24682)+E(f521(x24683,x24684,x24681),f521(x24683,x24684,x24682)) % 172.83/172.51 [2469]~E(x24691,x24692)+E(f571(x24691,x24693,x24694),f571(x24692,x24693,x24694)) % 172.83/172.51 [2470]~E(x24701,x24702)+E(f571(x24703,x24701,x24704),f571(x24703,x24702,x24704)) % 172.83/172.51 [2471]~E(x24711,x24712)+E(f571(x24713,x24714,x24711),f571(x24713,x24714,x24712)) % 172.83/172.51 [2472]~E(x24721,x24722)+E(f516(x24721,x24723,x24724,x24725),f516(x24722,x24723,x24724,x24725)) % 172.83/172.51 [2473]~E(x24731,x24732)+E(f516(x24733,x24731,x24734,x24735),f516(x24733,x24732,x24734,x24735)) % 172.83/172.51 [2474]~E(x24741,x24742)+E(f516(x24743,x24744,x24741,x24745),f516(x24743,x24744,x24742,x24745)) % 172.83/172.51 [2475]~E(x24751,x24752)+E(f516(x24753,x24754,x24755,x24751),f516(x24753,x24754,x24755,x24752)) % 172.83/172.51 [2476]~E(x24761,x24762)+E(f462(x24761,x24763),f462(x24762,x24763)) % 172.83/172.51 [2477]~E(x24771,x24772)+E(f462(x24773,x24771),f462(x24773,x24772)) % 172.83/172.51 [2478]~E(x24781,x24782)+E(f860(x24781,x24783,x24784,x24785,x24786),f860(x24782,x24783,x24784,x24785,x24786)) % 172.83/172.51 [2479]~E(x24791,x24792)+E(f860(x24793,x24791,x24794,x24795,x24796),f860(x24793,x24792,x24794,x24795,x24796)) % 172.83/172.51 [2480]~E(x24801,x24802)+E(f860(x24803,x24804,x24801,x24805,x24806),f860(x24803,x24804,x24802,x24805,x24806)) % 172.83/172.51 [2481]~E(x24811,x24812)+E(f860(x24813,x24814,x24815,x24811,x24816),f860(x24813,x24814,x24815,x24812,x24816)) % 172.83/172.51 [2482]~E(x24821,x24822)+E(f860(x24823,x24824,x24825,x24826,x24821),f860(x24823,x24824,x24825,x24826,x24822)) % 172.83/172.51 [2483]~E(x24831,x24832)+E(f596(x24831,x24833,x24834),f596(x24832,x24833,x24834)) % 172.83/172.51 [2484]~E(x24841,x24842)+E(f596(x24843,x24841,x24844),f596(x24843,x24842,x24844)) % 172.83/172.51 [2485]~E(x24851,x24852)+E(f596(x24853,x24854,x24851),f596(x24853,x24854,x24852)) % 172.83/172.51 [2486]~E(x24861,x24862)+E(f367(x24861),f367(x24862)) % 172.83/172.51 [2487]~E(x24871,x24872)+E(f841(x24871,x24873,x24874),f841(x24872,x24873,x24874)) % 172.83/172.51 [2488]~E(x24881,x24882)+E(f841(x24883,x24881,x24884),f841(x24883,x24882,x24884)) % 172.83/172.51 [2489]~E(x24891,x24892)+E(f841(x24893,x24894,x24891),f841(x24893,x24894,x24892)) % 172.83/172.51 [2490]~E(x24901,x24902)+E(f211(x24901),f211(x24902)) % 172.83/172.51 [2491]~E(x24911,x24912)+E(f401(x24911,x24913,x24914),f401(x24912,x24913,x24914)) % 172.83/172.51 [2492]~E(x24921,x24922)+E(f401(x24923,x24921,x24924),f401(x24923,x24922,x24924)) % 172.83/172.51 [2493]~E(x24931,x24932)+E(f401(x24933,x24934,x24931),f401(x24933,x24934,x24932)) % 172.83/172.51 [2494]~E(x24941,x24942)+E(f217(x24941,x24943,x24944,x24945),f217(x24942,x24943,x24944,x24945)) % 172.83/172.51 [2495]~E(x24951,x24952)+E(f217(x24953,x24951,x24954,x24955),f217(x24953,x24952,x24954,x24955)) % 172.83/172.51 [2496]~E(x24961,x24962)+E(f217(x24963,x24964,x24961,x24965),f217(x24963,x24964,x24962,x24965)) % 172.83/172.51 [2497]~E(x24971,x24972)+E(f217(x24973,x24974,x24975,x24971),f217(x24973,x24974,x24975,x24972)) % 172.83/172.51 [2498]~E(x24981,x24982)+E(f547(x24981,x24983,x24984,x24985),f547(x24982,x24983,x24984,x24985)) % 172.83/172.51 [2499]~E(x24991,x24992)+E(f547(x24993,x24991,x24994,x24995),f547(x24993,x24992,x24994,x24995)) % 172.83/172.51 [2500]~E(x25001,x25002)+E(f547(x25003,x25004,x25001,x25005),f547(x25003,x25004,x25002,x25005)) % 172.83/172.51 [2501]~E(x25011,x25012)+E(f547(x25013,x25014,x25015,x25011),f547(x25013,x25014,x25015,x25012)) % 172.83/172.51 [2502]~E(x25021,x25022)+E(f828(x25021,x25023,x25024),f828(x25022,x25023,x25024)) % 172.83/172.51 [2503]~E(x25031,x25032)+E(f828(x25033,x25031,x25034),f828(x25033,x25032,x25034)) % 172.83/172.51 [2504]~E(x25041,x25042)+E(f828(x25043,x25044,x25041),f828(x25043,x25044,x25042)) % 172.83/172.51 [2505]~E(x25051,x25052)+E(f575(x25051,x25053,x25054,x25055,x25056,x25057),f575(x25052,x25053,x25054,x25055,x25056,x25057)) % 172.83/172.51 [2506]~E(x25061,x25062)+E(f575(x25063,x25061,x25064,x25065,x25066,x25067),f575(x25063,x25062,x25064,x25065,x25066,x25067)) % 172.83/172.51 [2507]~E(x25071,x25072)+E(f575(x25073,x25074,x25071,x25075,x25076,x25077),f575(x25073,x25074,x25072,x25075,x25076,x25077)) % 172.83/172.51 [2508]~E(x25081,x25082)+E(f575(x25083,x25084,x25085,x25081,x25086,x25087),f575(x25083,x25084,x25085,x25082,x25086,x25087)) % 172.83/172.51 [2509]~E(x25091,x25092)+E(f575(x25093,x25094,x25095,x25096,x25091,x25097),f575(x25093,x25094,x25095,x25096,x25092,x25097)) % 172.83/172.51 [2510]~E(x25101,x25102)+E(f575(x25103,x25104,x25105,x25106,x25107,x25101),f575(x25103,x25104,x25105,x25106,x25107,x25102)) % 172.83/172.51 [2511]~E(x25111,x25112)+E(f570(x25111,x25113,x25114,x25115),f570(x25112,x25113,x25114,x25115)) % 172.83/172.51 [2512]~E(x25121,x25122)+E(f570(x25123,x25121,x25124,x25125),f570(x25123,x25122,x25124,x25125)) % 172.83/172.51 [2513]~E(x25131,x25132)+E(f570(x25133,x25134,x25131,x25135),f570(x25133,x25134,x25132,x25135)) % 172.83/172.51 [2514]~E(x25141,x25142)+E(f570(x25143,x25144,x25145,x25141),f570(x25143,x25144,x25145,x25142)) % 172.83/172.51 [2515]~E(x25151,x25152)+E(f507(x25151,x25153),f507(x25152,x25153)) % 172.83/172.51 [2516]~E(x25161,x25162)+E(f507(x25163,x25161),f507(x25163,x25162)) % 172.83/172.51 [2517]~E(x25171,x25172)+E(f535(x25171,x25173),f535(x25172,x25173)) % 172.83/172.51 [2518]~E(x25181,x25182)+E(f535(x25183,x25181),f535(x25183,x25182)) % 172.83/172.51 [2519]~E(x25191,x25192)+E(f740(x25191,x25193),f740(x25192,x25193)) % 172.83/172.51 [2520]~E(x25201,x25202)+E(f740(x25203,x25201),f740(x25203,x25202)) % 172.83/172.51 [2521]~E(x25211,x25212)+E(f93(x25211),f93(x25212)) % 172.83/172.51 [2522]~E(x25221,x25222)+E(f777(x25221,x25223),f777(x25222,x25223)) % 172.83/172.51 [2523]~E(x25231,x25232)+E(f777(x25233,x25231),f777(x25233,x25232)) % 172.83/172.51 [2524]~E(x25241,x25242)+E(f282(x25241,x25243,x25244),f282(x25242,x25243,x25244)) % 172.83/172.51 [2525]~E(x25251,x25252)+E(f282(x25253,x25251,x25254),f282(x25253,x25252,x25254)) % 172.83/172.51 [2526]~E(x25261,x25262)+E(f282(x25263,x25264,x25261),f282(x25263,x25264,x25262)) % 172.83/172.51 [2527]~E(x25271,x25272)+E(f413(x25271,x25273,x25274,x25275),f413(x25272,x25273,x25274,x25275)) % 172.83/172.51 [2528]~E(x25281,x25282)+E(f413(x25283,x25281,x25284,x25285),f413(x25283,x25282,x25284,x25285)) % 172.83/172.51 [2529]~E(x25291,x25292)+E(f413(x25293,x25294,x25291,x25295),f413(x25293,x25294,x25292,x25295)) % 172.83/172.51 [2530]~E(x25301,x25302)+E(f413(x25303,x25304,x25305,x25301),f413(x25303,x25304,x25305,x25302)) % 172.83/172.51 [2531]~E(x25311,x25312)+E(f763(x25311,x25313,x25314),f763(x25312,x25313,x25314)) % 172.83/172.51 [2532]~E(x25321,x25322)+E(f763(x25323,x25321,x25324),f763(x25323,x25322,x25324)) % 172.83/172.51 [2533]~E(x25331,x25332)+E(f763(x25333,x25334,x25331),f763(x25333,x25334,x25332)) % 172.83/172.51 [2534]~E(x25341,x25342)+E(f793(x25341,x25343,x25344),f793(x25342,x25343,x25344)) % 172.83/172.51 [2535]~E(x25351,x25352)+E(f793(x25353,x25351,x25354),f793(x25353,x25352,x25354)) % 172.83/172.51 [2536]~E(x25361,x25362)+E(f793(x25363,x25364,x25361),f793(x25363,x25364,x25362)) % 172.83/172.51 [2537]~E(x25371,x25372)+E(f709(x25371,x25373,x25374),f709(x25372,x25373,x25374)) % 172.83/172.51 [2538]~E(x25381,x25382)+E(f709(x25383,x25381,x25384),f709(x25383,x25382,x25384)) % 172.83/172.51 [2539]~E(x25391,x25392)+E(f709(x25393,x25394,x25391),f709(x25393,x25394,x25392)) % 172.83/172.51 [2540]~E(x25401,x25402)+E(f489(x25401,x25403,x25404),f489(x25402,x25403,x25404)) % 172.83/172.51 [2541]~E(x25411,x25412)+E(f489(x25413,x25411,x25414),f489(x25413,x25412,x25414)) % 172.83/172.51 [2542]~E(x25421,x25422)+E(f489(x25423,x25424,x25421),f489(x25423,x25424,x25422)) % 172.83/172.51 [2543]~E(x25431,x25432)+E(f463(x25431,x25433),f463(x25432,x25433)) % 172.83/172.51 [2544]~E(x25441,x25442)+E(f463(x25443,x25441),f463(x25443,x25442)) % 172.83/172.51 [2545]~E(x25451,x25452)+E(f291(x25451,x25453),f291(x25452,x25453)) % 172.83/172.51 [2546]~E(x25461,x25462)+E(f291(x25463,x25461),f291(x25463,x25462)) % 172.83/172.51 [2547]~E(x25471,x25472)+E(f832(x25471,x25473,x25474,x25475,x25476,x25477),f832(x25472,x25473,x25474,x25475,x25476,x25477)) % 172.83/172.51 [2548]~E(x25481,x25482)+E(f832(x25483,x25481,x25484,x25485,x25486,x25487),f832(x25483,x25482,x25484,x25485,x25486,x25487)) % 172.83/172.51 [2549]~E(x25491,x25492)+E(f832(x25493,x25494,x25491,x25495,x25496,x25497),f832(x25493,x25494,x25492,x25495,x25496,x25497)) % 172.83/172.51 [2550]~E(x25501,x25502)+E(f832(x25503,x25504,x25505,x25501,x25506,x25507),f832(x25503,x25504,x25505,x25502,x25506,x25507)) % 172.83/172.51 [2551]~E(x25511,x25512)+E(f832(x25513,x25514,x25515,x25516,x25511,x25517),f832(x25513,x25514,x25515,x25516,x25512,x25517)) % 172.83/172.51 [2552]~E(x25521,x25522)+E(f832(x25523,x25524,x25525,x25526,x25527,x25521),f832(x25523,x25524,x25525,x25526,x25527,x25522)) % 172.83/172.51 [2553]~E(x25531,x25532)+E(f808(x25531,x25533),f808(x25532,x25533)) % 172.83/172.51 [2554]~E(x25541,x25542)+E(f808(x25543,x25541),f808(x25543,x25542)) % 172.83/172.51 [2555]~E(x25551,x25552)+E(f537(x25551,x25553),f537(x25552,x25553)) % 172.83/172.51 [2556]~E(x25561,x25562)+E(f537(x25563,x25561),f537(x25563,x25562)) % 172.83/172.51 [2557]~E(x25571,x25572)+E(f465(x25571,x25573),f465(x25572,x25573)) % 172.83/172.51 [2558]~E(x25581,x25582)+E(f465(x25583,x25581),f465(x25583,x25582)) % 172.83/172.51 [2559]~E(x25591,x25592)+E(f449(x25591,x25593),f449(x25592,x25593)) % 172.83/172.51 [2560]~E(x25601,x25602)+E(f449(x25603,x25601),f449(x25603,x25602)) % 172.83/172.51 [2561]~E(x25611,x25612)+E(f806(x25611),f806(x25612)) % 172.83/172.51 [2562]~E(x25621,x25622)+E(f395(x25621,x25623,x25624,x25625),f395(x25622,x25623,x25624,x25625)) % 172.83/172.51 [2563]~E(x25631,x25632)+E(f395(x25633,x25631,x25634,x25635),f395(x25633,x25632,x25634,x25635)) % 172.83/172.51 [2564]~E(x25641,x25642)+E(f395(x25643,x25644,x25641,x25645),f395(x25643,x25644,x25642,x25645)) % 172.83/172.51 [2565]~E(x25651,x25652)+E(f395(x25653,x25654,x25655,x25651),f395(x25653,x25654,x25655,x25652)) % 172.83/172.51 [2566]~E(x25661,x25662)+E(f510(x25661,x25663,x25664,x25665,x25666,x25667,x25668),f510(x25662,x25663,x25664,x25665,x25666,x25667,x25668)) % 172.83/172.51 [2567]~E(x25671,x25672)+E(f510(x25673,x25671,x25674,x25675,x25676,x25677,x25678),f510(x25673,x25672,x25674,x25675,x25676,x25677,x25678)) % 172.83/172.51 [2568]~E(x25681,x25682)+E(f510(x25683,x25684,x25681,x25685,x25686,x25687,x25688),f510(x25683,x25684,x25682,x25685,x25686,x25687,x25688)) % 172.83/172.51 [2569]~E(x25691,x25692)+E(f510(x25693,x25694,x25695,x25691,x25696,x25697,x25698),f510(x25693,x25694,x25695,x25692,x25696,x25697,x25698)) % 172.83/172.51 [2570]~E(x25701,x25702)+E(f510(x25703,x25704,x25705,x25706,x25701,x25707,x25708),f510(x25703,x25704,x25705,x25706,x25702,x25707,x25708)) % 172.83/172.51 [2571]~E(x25711,x25712)+E(f510(x25713,x25714,x25715,x25716,x25717,x25711,x25718),f510(x25713,x25714,x25715,x25716,x25717,x25712,x25718)) % 172.83/172.51 [2572]~E(x25721,x25722)+E(f510(x25723,x25724,x25725,x25726,x25727,x25728,x25721),f510(x25723,x25724,x25725,x25726,x25727,x25728,x25722)) % 172.83/172.51 [2573]~E(x25731,x25732)+E(f622(x25731,x25733,x25734,x25735),f622(x25732,x25733,x25734,x25735)) % 172.83/172.51 [2574]~E(x25741,x25742)+E(f622(x25743,x25741,x25744,x25745),f622(x25743,x25742,x25744,x25745)) % 172.83/172.51 [2575]~E(x25751,x25752)+E(f622(x25753,x25754,x25751,x25755),f622(x25753,x25754,x25752,x25755)) % 172.83/172.51 [2576]~E(x25761,x25762)+E(f622(x25763,x25764,x25765,x25761),f622(x25763,x25764,x25765,x25762)) % 172.83/172.51 [2577]~E(x25771,x25772)+E(f479(x25771,x25773),f479(x25772,x25773)) % 172.83/172.51 [2578]~E(x25781,x25782)+E(f479(x25783,x25781),f479(x25783,x25782)) % 172.83/172.51 [2579]~E(x25791,x25792)+E(f221(x25791,x25793,x25794,x25795),f221(x25792,x25793,x25794,x25795)) % 172.83/172.51 [2580]~E(x25801,x25802)+E(f221(x25803,x25801,x25804,x25805),f221(x25803,x25802,x25804,x25805)) % 172.83/172.51 [2581]~E(x25811,x25812)+E(f221(x25813,x25814,x25811,x25815),f221(x25813,x25814,x25812,x25815)) % 172.83/172.51 [2582]~E(x25821,x25822)+E(f221(x25823,x25824,x25825,x25821),f221(x25823,x25824,x25825,x25822)) % 172.83/172.51 [2583]~E(x25831,x25832)+E(f807(x25831,x25833),f807(x25832,x25833)) % 172.83/172.51 [2584]~E(x25841,x25842)+E(f807(x25843,x25841),f807(x25843,x25842)) % 172.83/172.51 [2585]~E(x25851,x25852)+E(f562(x25851),f562(x25852)) % 172.83/172.51 [2586]~E(x25861,x25862)+E(f204(x25861,x25863,x25864,x25865),f204(x25862,x25863,x25864,x25865)) % 172.83/172.51 [2587]~E(x25871,x25872)+E(f204(x25873,x25871,x25874,x25875),f204(x25873,x25872,x25874,x25875)) % 172.83/172.51 [2588]~E(x25881,x25882)+E(f204(x25883,x25884,x25881,x25885),f204(x25883,x25884,x25882,x25885)) % 172.83/172.51 [2589]~E(x25891,x25892)+E(f204(x25893,x25894,x25895,x25891),f204(x25893,x25894,x25895,x25892)) % 172.83/172.51 [2590]~E(x25901,x25902)+E(f415(x25901),f415(x25902)) % 172.83/172.51 [2591]~E(x25911,x25912)+E(f97(x25911,x25913,x25914,x25915),f97(x25912,x25913,x25914,x25915)) % 172.83/172.51 [2592]~E(x25921,x25922)+E(f97(x25923,x25921,x25924,x25925),f97(x25923,x25922,x25924,x25925)) % 172.83/172.51 [2593]~E(x25931,x25932)+E(f97(x25933,x25934,x25931,x25935),f97(x25933,x25934,x25932,x25935)) % 172.83/172.51 [2594]~E(x25941,x25942)+E(f97(x25943,x25944,x25945,x25941),f97(x25943,x25944,x25945,x25942)) % 172.83/172.51 [2595]~E(x25951,x25952)+E(f428(x25951),f428(x25952)) % 172.83/172.51 [2596]~E(x25961,x25962)+E(f784(x25961,x25963,x25964,x25965,x25966),f784(x25962,x25963,x25964,x25965,x25966)) % 172.83/172.51 [2597]~E(x25971,x25972)+E(f784(x25973,x25971,x25974,x25975,x25976),f784(x25973,x25972,x25974,x25975,x25976)) % 172.83/172.51 [2598]~E(x25981,x25982)+E(f784(x25983,x25984,x25981,x25985,x25986),f784(x25983,x25984,x25982,x25985,x25986)) % 172.83/172.51 [2599]~E(x25991,x25992)+E(f784(x25993,x25994,x25995,x25991,x25996),f784(x25993,x25994,x25995,x25992,x25996)) % 172.83/172.51 [2600]~E(x26001,x26002)+E(f784(x26003,x26004,x26005,x26006,x26001),f784(x26003,x26004,x26005,x26006,x26002)) % 172.83/172.51 [2601]~E(x26011,x26012)+E(f813(x26011,x26013,x26014,x26015),f813(x26012,x26013,x26014,x26015)) % 172.83/172.51 [2602]~E(x26021,x26022)+E(f813(x26023,x26021,x26024,x26025),f813(x26023,x26022,x26024,x26025)) % 172.83/172.51 [2603]~E(x26031,x26032)+E(f813(x26033,x26034,x26031,x26035),f813(x26033,x26034,x26032,x26035)) % 172.83/172.51 [2604]~E(x26041,x26042)+E(f813(x26043,x26044,x26045,x26041),f813(x26043,x26044,x26045,x26042)) % 172.83/172.51 [2605]~E(x26051,x26052)+E(f719(x26051,x26053),f719(x26052,x26053)) % 172.83/172.51 [2606]~E(x26061,x26062)+E(f719(x26063,x26061),f719(x26063,x26062)) % 172.83/172.51 [2607]~E(x26071,x26072)+E(f359(x26071),f359(x26072)) % 172.83/172.51 [2608]~E(x26081,x26082)+E(f721(x26081,x26083,x26084),f721(x26082,x26083,x26084)) % 172.83/172.51 [2609]~E(x26091,x26092)+E(f721(x26093,x26091,x26094),f721(x26093,x26092,x26094)) % 172.83/172.51 [2610]~E(x26101,x26102)+E(f721(x26103,x26104,x26101),f721(x26103,x26104,x26102)) % 172.83/172.51 [2611]~E(x26111,x26112)+E(f496(x26111,x26113,x26114),f496(x26112,x26113,x26114)) % 172.83/172.51 [2612]~E(x26121,x26122)+E(f496(x26123,x26121,x26124),f496(x26123,x26122,x26124)) % 172.83/172.51 [2613]~E(x26131,x26132)+E(f496(x26133,x26134,x26131),f496(x26133,x26134,x26132)) % 172.83/172.51 [2614]~E(x26141,x26142)+E(f315(x26141,x26143,x26144),f315(x26142,x26143,x26144)) % 172.83/172.51 [2615]~E(x26151,x26152)+E(f315(x26153,x26151,x26154),f315(x26153,x26152,x26154)) % 172.83/172.51 [2616]~E(x26161,x26162)+E(f315(x26163,x26164,x26161),f315(x26163,x26164,x26162)) % 172.83/172.51 [2617]~E(x26171,x26172)+E(f599(x26171,x26173),f599(x26172,x26173)) % 172.83/172.51 [2618]~E(x26181,x26182)+E(f599(x26183,x26181),f599(x26183,x26182)) % 172.83/172.51 [2619]~E(x26191,x26192)+E(f686(x26191,x26193),f686(x26192,x26193)) % 172.83/172.51 [2620]~E(x26201,x26202)+E(f686(x26203,x26201),f686(x26203,x26202)) % 172.83/172.51 [2621]~E(x26211,x26212)+E(f342(x26211,x26213),f342(x26212,x26213)) % 172.83/172.51 [2622]~E(x26221,x26222)+E(f342(x26223,x26221),f342(x26223,x26222)) % 172.83/172.51 [2623]~E(x26231,x26232)+E(f361(x26231),f361(x26232)) % 172.83/172.51 [2624]~P1(x26241)+P1(x26242)+~E(x26241,x26242) % 172.83/172.51 [2625]~P23(x26251)+P23(x26252)+~E(x26251,x26252) % 172.83/172.51 [2626]~P102(x26261)+P102(x26262)+~E(x26261,x26262) % 172.83/172.51 [2627]P19(x26272,x26273,x26274)+~E(x26271,x26272)+~P19(x26271,x26273,x26274) % 172.83/172.51 [2628]P19(x26283,x26282,x26284)+~E(x26281,x26282)+~P19(x26283,x26281,x26284) % 172.83/172.51 [2629]P19(x26293,x26294,x26292)+~E(x26291,x26292)+~P19(x26293,x26294,x26291) % 172.83/172.51 [2630]~P24(x26301)+P24(x26302)+~E(x26301,x26302) % 172.83/172.51 [2631]~P104(x26311)+P104(x26312)+~E(x26311,x26312) % 172.83/172.51 [2632]~P61(x26321)+P61(x26322)+~E(x26321,x26322) % 172.83/172.51 [2633]~P92(x26331)+P92(x26332)+~E(x26331,x26332) % 172.83/172.51 [2634]P144(x26342,x26343,x26344)+~E(x26341,x26342)+~P144(x26341,x26343,x26344) % 172.83/172.51 [2635]P144(x26353,x26352,x26354)+~E(x26351,x26352)+~P144(x26353,x26351,x26354) % 172.83/172.51 [2636]P144(x26363,x26364,x26362)+~E(x26361,x26362)+~P144(x26363,x26364,x26361) % 172.83/172.51 [2637]~P62(x26371)+P62(x26372)+~E(x26371,x26372) % 172.83/172.51 [2638]~P97(x26381)+P97(x26382)+~E(x26381,x26382) % 172.83/172.51 [2639]P29(x26392,x26393)+~E(x26391,x26392)+~P29(x26391,x26393) % 172.83/172.51 [2640]P29(x26403,x26402)+~E(x26401,x26402)+~P29(x26403,x26401) % 172.83/172.51 [2641]~P81(x26411)+P81(x26412)+~E(x26411,x26412) % 172.83/172.51 [2642]~P63(x26421)+P63(x26422)+~E(x26421,x26422) % 172.83/172.51 [2643]~P27(x26431)+P27(x26432)+~E(x26431,x26432) % 172.83/172.51 [2644]P11(x26442,x26443,x26444)+~E(x26441,x26442)+~P11(x26441,x26443,x26444) % 172.83/172.51 [2645]P11(x26453,x26452,x26454)+~E(x26451,x26452)+~P11(x26453,x26451,x26454) % 172.83/172.51 [2646]P11(x26463,x26464,x26462)+~E(x26461,x26462)+~P11(x26463,x26464,x26461) % 172.83/172.51 [2647]P143(x26472,x26473,x26474)+~E(x26471,x26472)+~P143(x26471,x26473,x26474) % 172.83/172.51 [2648]P143(x26483,x26482,x26484)+~E(x26481,x26482)+~P143(x26483,x26481,x26484) % 172.83/172.51 [2649]P143(x26493,x26494,x26492)+~E(x26491,x26492)+~P143(x26493,x26494,x26491) % 172.83/172.51 [2650]~P64(x26501)+P64(x26502)+~E(x26501,x26502) % 172.83/172.51 [2651]~P137(x26511)+P137(x26512)+~E(x26511,x26512) % 172.83/172.51 [2652]P31(x26522,x26523)+~E(x26521,x26522)+~P31(x26521,x26523) % 172.83/172.51 [2653]P31(x26533,x26532)+~E(x26531,x26532)+~P31(x26533,x26531) % 172.83/172.51 [2654]~P98(x26541)+P98(x26542)+~E(x26541,x26542) % 172.83/172.51 [2655]~P114(x26551)+P114(x26552)+~E(x26551,x26552) % 172.83/172.51 [2656]~P73(x26561)+P73(x26562)+~E(x26561,x26562) % 172.83/172.51 [2657]~P95(x26571)+P95(x26572)+~E(x26571,x26572) % 172.83/172.51 [2658]~P56(x26581)+P56(x26582)+~E(x26581,x26582) % 172.83/172.51 [2659]P14(x26592,x26593,x26594,x26595)+~E(x26591,x26592)+~P14(x26591,x26593,x26594,x26595) % 172.83/172.51 [2660]P14(x26603,x26602,x26604,x26605)+~E(x26601,x26602)+~P14(x26603,x26601,x26604,x26605) % 172.83/172.51 [2661]P14(x26613,x26614,x26612,x26615)+~E(x26611,x26612)+~P14(x26613,x26614,x26611,x26615) % 172.83/172.51 [2662]P14(x26623,x26624,x26625,x26622)+~E(x26621,x26622)+~P14(x26623,x26624,x26625,x26621) % 172.83/172.51 [2663]~P103(x26631)+P103(x26632)+~E(x26631,x26632) % 172.83/172.51 [2664]P10(x26642,x26643,x26644)+~E(x26641,x26642)+~P10(x26641,x26643,x26644) % 172.83/172.51 [2665]P10(x26653,x26652,x26654)+~E(x26651,x26652)+~P10(x26653,x26651,x26654) % 172.83/172.51 [2666]P10(x26663,x26664,x26662)+~E(x26661,x26662)+~P10(x26663,x26664,x26661) % 172.83/172.51 [2667]~P120(x26671)+P120(x26672)+~E(x26671,x26672) % 172.83/172.51 [2668]~P59(x26681)+P59(x26682)+~E(x26681,x26682) % 172.83/172.51 [2669]P13(x26692,x26693,x26694)+~E(x26691,x26692)+~P13(x26691,x26693,x26694) % 172.83/172.51 [2670]P13(x26703,x26702,x26704)+~E(x26701,x26702)+~P13(x26703,x26701,x26704) % 172.83/172.51 [2671]P13(x26713,x26714,x26712)+~E(x26711,x26712)+~P13(x26713,x26714,x26711) % 172.83/172.51 [2672]~P113(x26721)+P113(x26722)+~E(x26721,x26722) % 172.83/172.51 [2673]~P89(x26731)+P89(x26732)+~E(x26731,x26732) % 172.83/172.51 [2674]~P105(x26741)+P105(x26742)+~E(x26741,x26742) % 172.83/172.51 [2675]~P25(x26751)+P25(x26752)+~E(x26751,x26752) % 172.83/172.51 [2676]P20(x26762,x26763,x26764,x26765)+~E(x26761,x26762)+~P20(x26761,x26763,x26764,x26765) % 172.83/172.51 [2677]P20(x26773,x26772,x26774,x26775)+~E(x26771,x26772)+~P20(x26773,x26771,x26774,x26775) % 172.83/172.51 [2678]P20(x26783,x26784,x26782,x26785)+~E(x26781,x26782)+~P20(x26783,x26784,x26781,x26785) % 172.83/172.51 [2679]P20(x26793,x26794,x26795,x26792)+~E(x26791,x26792)+~P20(x26793,x26794,x26795,x26791) % 172.83/172.51 [2680]~P71(x26801)+P71(x26802)+~E(x26801,x26802) % 172.83/172.51 [2681]~P106(x26811)+P106(x26812)+~E(x26811,x26812) % 172.83/172.51 [2682]~P90(x26821)+P90(x26822)+~E(x26821,x26822) % 172.83/172.51 [2683]P35(x26832,x26833,x26834,x26835,x26836)+~E(x26831,x26832)+~P35(x26831,x26833,x26834,x26835,x26836) % 172.83/172.51 [2684]P35(x26843,x26842,x26844,x26845,x26846)+~E(x26841,x26842)+~P35(x26843,x26841,x26844,x26845,x26846) % 172.83/172.51 [2685]P35(x26853,x26854,x26852,x26855,x26856)+~E(x26851,x26852)+~P35(x26853,x26854,x26851,x26855,x26856) % 172.83/172.51 [2686]P35(x26863,x26864,x26865,x26862,x26866)+~E(x26861,x26862)+~P35(x26863,x26864,x26865,x26861,x26866) % 172.83/172.51 [2687]P35(x26873,x26874,x26875,x26876,x26872)+~E(x26871,x26872)+~P35(x26873,x26874,x26875,x26876,x26871) % 172.83/172.51 [2688]P32(x26882,x26883,x26884)+~E(x26881,x26882)+~P32(x26881,x26883,x26884) % 172.83/172.51 [2689]P32(x26893,x26892,x26894)+~E(x26891,x26892)+~P32(x26893,x26891,x26894) % 172.83/172.51 [2690]P32(x26903,x26904,x26902)+~E(x26901,x26902)+~P32(x26903,x26904,x26901) % 172.83/172.51 [2691]~P67(x26911)+P67(x26912)+~E(x26911,x26912) % 172.83/172.51 [2692]P40(x26922,x26923,x26924)+~E(x26921,x26922)+~P40(x26921,x26923,x26924) % 172.83/172.51 [2693]P40(x26933,x26932,x26934)+~E(x26931,x26932)+~P40(x26933,x26931,x26934) % 172.83/172.51 [2694]P40(x26943,x26944,x26942)+~E(x26941,x26942)+~P40(x26943,x26944,x26941) % 172.83/172.51 [2695]P38(x26952,x26953)+~E(x26951,x26952)+~P38(x26951,x26953) % 172.83/172.51 [2696]P38(x26963,x26962)+~E(x26961,x26962)+~P38(x26963,x26961) % 172.83/172.51 [2697]~P107(x26971)+P107(x26972)+~E(x26971,x26972) % 172.83/172.51 [2698]~P115(x26981)+P115(x26982)+~E(x26981,x26982) % 172.83/172.51 [2699]~P123(x26991)+P123(x26992)+~E(x26991,x26992) % 172.83/172.51 [2700]~P108(x27001)+P108(x27002)+~E(x27001,x27002) % 172.83/172.51 [2701]~P93(x27011)+P93(x27012)+~E(x27011,x27012) % 172.83/172.51 [2702]~P39(x27021)+P39(x27022)+~E(x27021,x27022) % 172.83/172.51 [2703]~P122(x27031)+P122(x27032)+~E(x27031,x27032) % 172.83/172.51 [2704]~P57(x27041)+P57(x27042)+~E(x27041,x27042) % 172.83/172.51 [2705]~P80(x27051)+P80(x27052)+~E(x27051,x27052) % 172.83/172.51 [2706]~P76(x27061)+P76(x27062)+~E(x27061,x27062) % 172.83/172.51 [2707]~P124(x27071)+P124(x27072)+~E(x27071,x27072) % 172.83/172.51 [2708]P52(x27082,x27083,x27084,x27085,x27086)+~E(x27081,x27082)+~P52(x27081,x27083,x27084,x27085,x27086) % 172.83/172.51 [2709]P52(x27093,x27092,x27094,x27095,x27096)+~E(x27091,x27092)+~P52(x27093,x27091,x27094,x27095,x27096) % 172.83/172.51 [2710]P52(x27103,x27104,x27102,x27105,x27106)+~E(x27101,x27102)+~P52(x27103,x27104,x27101,x27105,x27106) % 172.83/172.51 [2711]P52(x27113,x27114,x27115,x27112,x27116)+~E(x27111,x27112)+~P52(x27113,x27114,x27115,x27111,x27116) % 172.83/172.51 [2712]P52(x27123,x27124,x27125,x27126,x27122)+~E(x27121,x27122)+~P52(x27123,x27124,x27125,x27126,x27121) % 172.83/172.51 [2713]P30(x27132,x27133,x27134)+~E(x27131,x27132)+~P30(x27131,x27133,x27134) % 172.83/172.51 [2714]P30(x27143,x27142,x27144)+~E(x27141,x27142)+~P30(x27143,x27141,x27144) % 172.83/172.51 [2715]P30(x27153,x27154,x27152)+~E(x27151,x27152)+~P30(x27153,x27154,x27151) % 172.83/172.51 [2716]P53(x27162,x27163)+~E(x27161,x27162)+~P53(x27161,x27163) % 172.83/172.51 [2717]P53(x27173,x27172)+~E(x27171,x27172)+~P53(x27173,x27171) % 172.83/172.51 [2718]P55(x27182,x27183)+~E(x27181,x27182)+~P55(x27181,x27183) % 172.83/172.51 [2719]P55(x27193,x27192)+~E(x27191,x27192)+~P55(x27193,x27191) % 172.83/172.51 [2720]~P75(x27201)+P75(x27202)+~E(x27201,x27202) % 172.83/172.51 [2721]~P136(x27211)+P136(x27212)+~E(x27211,x27212) % 172.83/172.51 [2722]P3(x27222,x27223,x27224)+~E(x27221,x27222)+~P3(x27221,x27223,x27224) % 172.83/172.51 [2723]P3(x27233,x27232,x27234)+~E(x27231,x27232)+~P3(x27233,x27231,x27234) % 172.83/172.51 [2724]P3(x27243,x27244,x27242)+~E(x27241,x27242)+~P3(x27243,x27244,x27241) % 172.83/172.51 [2725]~P68(x27251)+P68(x27252)+~E(x27251,x27252) % 172.83/172.51 [2726]~P126(x27261)+P126(x27262)+~E(x27261,x27262) % 172.83/172.51 [2727]~P58(x27271)+P58(x27272)+~E(x27271,x27272) % 172.83/172.51 [2728]~P69(x27281)+P69(x27282)+~E(x27281,x27282) % 172.83/172.51 [2729]P5(x27292,x27293,x27294,x27295,x27296)+~E(x27291,x27292)+~P5(x27291,x27293,x27294,x27295,x27296) % 172.83/172.51 [2730]P5(x27303,x27302,x27304,x27305,x27306)+~E(x27301,x27302)+~P5(x27303,x27301,x27304,x27305,x27306) % 172.83/172.51 [2731]P5(x27313,x27314,x27312,x27315,x27316)+~E(x27311,x27312)+~P5(x27313,x27314,x27311,x27315,x27316) % 172.83/172.51 [2732]P5(x27323,x27324,x27325,x27322,x27326)+~E(x27321,x27322)+~P5(x27323,x27324,x27325,x27321,x27326) % 172.83/172.51 [2733]P5(x27333,x27334,x27335,x27336,x27332)+~E(x27331,x27332)+~P5(x27333,x27334,x27335,x27336,x27331) % 172.83/172.51 [2734]P7(x27342,x27343,x27344)+~E(x27341,x27342)+~P7(x27341,x27343,x27344) % 172.83/172.51 [2735]P7(x27353,x27352,x27354)+~E(x27351,x27352)+~P7(x27353,x27351,x27354) % 172.83/172.51 [2736]P7(x27363,x27364,x27362)+~E(x27361,x27362)+~P7(x27363,x27364,x27361) % 172.83/172.51 [2737]~P65(x27371)+P65(x27372)+~E(x27371,x27372) % 172.83/172.51 [2738]P43(x27382,x27383,x27384,x27385,x27386,x27387)+~E(x27381,x27382)+~P43(x27381,x27383,x27384,x27385,x27386,x27387) % 172.83/172.51 [2739]P43(x27393,x27392,x27394,x27395,x27396,x27397)+~E(x27391,x27392)+~P43(x27393,x27391,x27394,x27395,x27396,x27397) % 172.83/172.51 [2740]P43(x27403,x27404,x27402,x27405,x27406,x27407)+~E(x27401,x27402)+~P43(x27403,x27404,x27401,x27405,x27406,x27407) % 172.83/172.51 [2741]P43(x27413,x27414,x27415,x27412,x27416,x27417)+~E(x27411,x27412)+~P43(x27413,x27414,x27415,x27411,x27416,x27417) % 172.83/172.51 [2742]P43(x27423,x27424,x27425,x27426,x27422,x27427)+~E(x27421,x27422)+~P43(x27423,x27424,x27425,x27426,x27421,x27427) % 172.83/172.51 [2743]P43(x27433,x27434,x27435,x27436,x27437,x27432)+~E(x27431,x27432)+~P43(x27433,x27434,x27435,x27436,x27437,x27431) % 172.83/172.51 [2744]~P70(x27441)+P70(x27442)+~E(x27441,x27442) % 172.83/172.51 [2745]~P66(x27451)+P66(x27452)+~E(x27451,x27452) % 172.83/172.51 [2746]~P77(x27461)+P77(x27462)+~E(x27461,x27462) % 172.83/172.51 [2747]P34(x27472,x27473,x27474)+~E(x27471,x27472)+~P34(x27471,x27473,x27474) % 172.83/172.51 [2748]P34(x27483,x27482,x27484)+~E(x27481,x27482)+~P34(x27483,x27481,x27484) % 172.83/172.51 [2749]P34(x27493,x27494,x27492)+~E(x27491,x27492)+~P34(x27493,x27494,x27491) % 172.83/172.51 [2750]~P109(x27501)+P109(x27502)+~E(x27501,x27502) % 172.83/172.51 [2751]~P78(x27511)+P78(x27512)+~E(x27511,x27512) % 172.83/172.51 [2752]~P111(x27521)+P111(x27522)+~E(x27521,x27522) % 172.83/172.51 [2753]P2(x27532,x27533)+~E(x27531,x27532)+~P2(x27531,x27533) % 172.83/172.51 [2754]P2(x27543,x27542)+~E(x27541,x27542)+~P2(x27543,x27541) % 172.83/172.51 [2755]~P82(x27551)+P82(x27552)+~E(x27551,x27552) % 172.83/172.51 [2756]~P88(x27561)+P88(x27562)+~E(x27561,x27562) % 172.83/172.51 [2757]~P141(x27571)+P141(x27572)+~E(x27571,x27572) % 172.83/172.51 [2758]~P79(x27581)+P79(x27582)+~E(x27581,x27582) % 172.83/172.51 [2759]~P138(x27591)+P138(x27592)+~E(x27591,x27592) % 172.83/172.51 [2760]~P37(x27601)+P37(x27602)+~E(x27601,x27602) % 172.83/172.51 [2761]~P72(x27611)+P72(x27612)+~E(x27611,x27612) % 172.83/172.51 [2762]~P135(x27621)+P135(x27622)+~E(x27621,x27622) % 172.83/172.51 [2763]~P139(x27631)+P139(x27632)+~E(x27631,x27632) % 172.83/172.51 [2764]P6(x27642,x27643,x27644)+~E(x27641,x27642)+~P6(x27641,x27643,x27644) % 172.83/172.51 [2765]P6(x27653,x27652,x27654)+~E(x27651,x27652)+~P6(x27653,x27651,x27654) % 172.83/172.51 [2766]P6(x27663,x27664,x27662)+~E(x27661,x27662)+~P6(x27663,x27664,x27661) % 172.83/172.51 [2767]~P131(x27671)+P131(x27672)+~E(x27671,x27672) % 172.83/172.51 [2768]P44(x27682,x27683)+~E(x27681,x27682)+~P44(x27681,x27683) % 172.83/172.51 [2769]P44(x27693,x27692)+~E(x27691,x27692)+~P44(x27693,x27691) % 172.83/172.51 [2770]P50(x27702,x27703,x27704)+~E(x27701,x27702)+~P50(x27701,x27703,x27704) % 172.83/172.51 [2771]P50(x27713,x27712,x27714)+~E(x27711,x27712)+~P50(x27713,x27711,x27714) % 172.83/172.51 [2772]P50(x27723,x27724,x27722)+~E(x27721,x27722)+~P50(x27723,x27724,x27721) % 172.83/172.51 [2773]~P117(x27731)+P117(x27732)+~E(x27731,x27732) % 172.83/172.51 [2774]~P28(x27741)+P28(x27742)+~E(x27741,x27742) % 172.83/172.51 [2775]~P112(x27751)+P112(x27752)+~E(x27751,x27752) % 172.83/172.51 [2776]~P83(x27761)+P83(x27762)+~E(x27761,x27762) % 172.83/172.51 [2777]~P130(x27771)+P130(x27772)+~E(x27771,x27772) % 172.83/172.51 [2778]P21(x27782,x27783)+~E(x27781,x27782)+~P21(x27781,x27783) % 172.83/172.51 [2779]P21(x27793,x27792)+~E(x27791,x27792)+~P21(x27793,x27791) % 172.83/172.51 [2780]~P85(x27801)+P85(x27802)+~E(x27801,x27802) % 172.83/172.51 [2781]~P26(x27811)+P26(x27812)+~E(x27811,x27812) % 172.83/172.51 [2782]~P84(x27821)+P84(x27822)+~E(x27821,x27822) % 172.83/172.51 [2783]P33(x27832,x27833,x27834,x27835)+~E(x27831,x27832)+~P33(x27831,x27833,x27834,x27835) % 172.83/172.51 [2784]P33(x27843,x27842,x27844,x27845)+~E(x27841,x27842)+~P33(x27843,x27841,x27844,x27845) % 172.83/172.51 [2785]P33(x27853,x27854,x27852,x27855)+~E(x27851,x27852)+~P33(x27853,x27854,x27851,x27855) % 172.83/172.51 [2786]P33(x27863,x27864,x27865,x27862)+~E(x27861,x27862)+~P33(x27863,x27864,x27865,x27861) % 172.83/172.51 [2787]~P125(x27871)+P125(x27872)+~E(x27871,x27872) % 172.83/172.51 [2788]P22(x27882,x27883,x27884)+~E(x27881,x27882)+~P22(x27881,x27883,x27884) % 172.83/172.51 [2789]P22(x27893,x27892,x27894)+~E(x27891,x27892)+~P22(x27893,x27891,x27894) % 172.83/172.51 [2790]P22(x27903,x27904,x27902)+~E(x27901,x27902)+~P22(x27903,x27904,x27901) % 172.83/172.51 [2791]~P132(x27911)+P132(x27912)+~E(x27911,x27912) % 172.83/172.51 [2792]~P142(x27921)+P142(x27922)+~E(x27921,x27922) % 172.83/172.51 [2793]~P91(x27931)+P91(x27932)+~E(x27931,x27932) % 172.83/172.51 [2794]P36(x27942,x27943,x27944)+~E(x27941,x27942)+~P36(x27941,x27943,x27944) % 172.83/172.51 [2795]P36(x27953,x27952,x27954)+~E(x27951,x27952)+~P36(x27953,x27951,x27954) % 172.83/172.51 [2796]P36(x27963,x27964,x27962)+~E(x27961,x27962)+~P36(x27963,x27964,x27961) % 172.83/172.51 [2797]P17(x27972,x27973,x27974,x27975,x27976,x27977)+~E(x27971,x27972)+~P17(x27971,x27973,x27974,x27975,x27976,x27977) % 172.83/172.51 [2798]P17(x27983,x27982,x27984,x27985,x27986,x27987)+~E(x27981,x27982)+~P17(x27983,x27981,x27984,x27985,x27986,x27987) % 172.83/172.51 [2799]P17(x27993,x27994,x27992,x27995,x27996,x27997)+~E(x27991,x27992)+~P17(x27993,x27994,x27991,x27995,x27996,x27997) % 172.83/172.51 [2800]P17(x28003,x28004,x28005,x28002,x28006,x28007)+~E(x28001,x28002)+~P17(x28003,x28004,x28005,x28001,x28006,x28007) % 172.83/172.51 [2801]P17(x28013,x28014,x28015,x28016,x28012,x28017)+~E(x28011,x28012)+~P17(x28013,x28014,x28015,x28016,x28011,x28017) % 172.83/172.51 [2802]P17(x28023,x28024,x28025,x28026,x28027,x28022)+~E(x28021,x28022)+~P17(x28023,x28024,x28025,x28026,x28027,x28021) % 172.83/172.51 [2803]~P140(x28031)+P140(x28032)+~E(x28031,x28032) % 172.83/172.51 [2804]~P110(x28041)+P110(x28042)+~E(x28041,x28042) % 172.83/172.51 [2805]~P60(x28051)+P60(x28052)+~E(x28051,x28052) % 172.83/172.51 [2806]P9(x28062,x28063,x28064,x28065,x28066,x28067)+~E(x28061,x28062)+~P9(x28061,x28063,x28064,x28065,x28066,x28067) % 172.83/172.51 [2807]P9(x28073,x28072,x28074,x28075,x28076,x28077)+~E(x28071,x28072)+~P9(x28073,x28071,x28074,x28075,x28076,x28077) % 172.83/172.51 [2808]P9(x28083,x28084,x28082,x28085,x28086,x28087)+~E(x28081,x28082)+~P9(x28083,x28084,x28081,x28085,x28086,x28087) % 172.83/172.51 [2809]P9(x28093,x28094,x28095,x28092,x28096,x28097)+~E(x28091,x28092)+~P9(x28093,x28094,x28095,x28091,x28096,x28097) % 172.83/172.51 [2810]P9(x28103,x28104,x28105,x28106,x28102,x28107)+~E(x28101,x28102)+~P9(x28103,x28104,x28105,x28106,x28101,x28107) % 172.83/172.51 [2811]P9(x28113,x28114,x28115,x28116,x28117,x28112)+~E(x28111,x28112)+~P9(x28113,x28114,x28115,x28116,x28117,x28111) % 172.83/172.51 [2812]~P134(x28121)+P134(x28122)+~E(x28121,x28122) % 172.83/172.51 [2813]P8(x28132,x28133,x28134,x28135)+~E(x28131,x28132)+~P8(x28131,x28133,x28134,x28135) % 172.83/172.51 [2814]P8(x28143,x28142,x28144,x28145)+~E(x28141,x28142)+~P8(x28143,x28141,x28144,x28145) % 172.83/172.51 [2815]P8(x28153,x28154,x28152,x28155)+~E(x28151,x28152)+~P8(x28153,x28154,x28151,x28155) % 172.83/172.51 [2816]P8(x28163,x28164,x28165,x28162)+~E(x28161,x28162)+~P8(x28163,x28164,x28165,x28161) % 172.83/172.51 [2817]P51(x28172,x28173,x28174)+~E(x28171,x28172)+~P51(x28171,x28173,x28174) % 172.83/172.51 [2818]P51(x28183,x28182,x28184)+~E(x28181,x28182)+~P51(x28183,x28181,x28184) % 172.83/172.51 [2819]P51(x28193,x28194,x28192)+~E(x28191,x28192)+~P51(x28193,x28194,x28191) % 172.83/172.51 [2820]P16(x28202,x28203,x28204,x28205,x28206)+~E(x28201,x28202)+~P16(x28201,x28203,x28204,x28205,x28206) % 172.83/172.51 [2821]P16(x28213,x28212,x28214,x28215,x28216)+~E(x28211,x28212)+~P16(x28213,x28211,x28214,x28215,x28216) % 172.83/172.51 [2822]P16(x28223,x28224,x28222,x28225,x28226)+~E(x28221,x28222)+~P16(x28223,x28224,x28221,x28225,x28226) % 172.83/172.51 [2823]P16(x28233,x28234,x28235,x28232,x28236)+~E(x28231,x28232)+~P16(x28233,x28234,x28235,x28231,x28236) % 172.83/172.51 [2824]P16(x28243,x28244,x28245,x28246,x28242)+~E(x28241,x28242)+~P16(x28243,x28244,x28245,x28246,x28241) % 172.83/172.51 [2825]P18(x28252,x28253,x28254,x28255,x28256,x28257)+~E(x28251,x28252)+~P18(x28251,x28253,x28254,x28255,x28256,x28257) % 172.83/172.51 [2826]P18(x28263,x28262,x28264,x28265,x28266,x28267)+~E(x28261,x28262)+~P18(x28263,x28261,x28264,x28265,x28266,x28267) % 172.83/172.51 [2827]P18(x28273,x28274,x28272,x28275,x28276,x28277)+~E(x28271,x28272)+~P18(x28273,x28274,x28271,x28275,x28276,x28277) % 172.83/172.51 [2828]P18(x28283,x28284,x28285,x28282,x28286,x28287)+~E(x28281,x28282)+~P18(x28283,x28284,x28285,x28281,x28286,x28287) % 172.83/172.51 [2829]P18(x28293,x28294,x28295,x28296,x28292,x28297)+~E(x28291,x28292)+~P18(x28293,x28294,x28295,x28296,x28291,x28297) % 172.83/172.51 [2830]P18(x28303,x28304,x28305,x28306,x28307,x28302)+~E(x28301,x28302)+~P18(x28303,x28304,x28305,x28306,x28307,x28301) % 172.83/172.51 [2831]~P133(x28311)+P133(x28312)+~E(x28311,x28312) % 172.83/172.51 [2832]~P100(x28321)+P100(x28322)+~E(x28321,x28322) % 172.83/172.51 [2833]P4(x28332,x28333,x28334)+~E(x28331,x28332)+~P4(x28331,x28333,x28334) % 172.83/172.51 [2834]P4(x28343,x28342,x28344)+~E(x28341,x28342)+~P4(x28343,x28341,x28344) % 172.83/172.51 [2835]P4(x28353,x28354,x28352)+~E(x28351,x28352)+~P4(x28353,x28354,x28351) % 172.83/172.51 [2836]~P118(x28361)+P118(x28362)+~E(x28361,x28362) % 172.83/172.51 [2837]~P121(x28371)+P121(x28372)+~E(x28371,x28372) % 172.83/172.51 [2838]P15(x28382,x28383,x28384,x28385)+~E(x28381,x28382)+~P15(x28381,x28383,x28384,x28385) % 172.83/172.51 [2839]P15(x28393,x28392,x28394,x28395)+~E(x28391,x28392)+~P15(x28393,x28391,x28394,x28395) % 172.83/172.51 [2840]P15(x28403,x28404,x28402,x28405)+~E(x28401,x28402)+~P15(x28403,x28404,x28401,x28405) % 172.83/172.51 [2841]P15(x28413,x28414,x28415,x28412)+~E(x28411,x28412)+~P15(x28413,x28414,x28415,x28411) % 172.83/172.51 [2842]P42(x28422,x28423)+~E(x28421,x28422)+~P42(x28421,x28423) % 172.83/172.51 [2843]P42(x28433,x28432)+~E(x28431,x28432)+~P42(x28433,x28431) % 172.83/172.51 [2844]P12(x28442,x28443,x28444)+~E(x28441,x28442)+~P12(x28441,x28443,x28444) % 172.83/172.51 [2845]P12(x28453,x28452,x28454)+~E(x28451,x28452)+~P12(x28453,x28451,x28454) % 172.83/172.51 [2846]P12(x28463,x28464,x28462)+~E(x28461,x28462)+~P12(x28463,x28464,x28461) % 172.83/172.51 [2847]~P96(x28471)+P96(x28472)+~E(x28471,x28472) % 172.83/172.51 [2848]~P86(x28481)+P86(x28482)+~E(x28481,x28482) % 172.83/172.51 [2849]P54(x28492,x28493,x28494,x28495)+~E(x28491,x28492)+~P54(x28491,x28493,x28494,x28495) % 172.83/172.51 [2850]P54(x28503,x28502,x28504,x28505)+~E(x28501,x28502)+~P54(x28503,x28501,x28504,x28505) % 172.83/172.51 [2851]P54(x28513,x28514,x28512,x28515)+~E(x28511,x28512)+~P54(x28513,x28514,x28511,x28515) % 172.83/172.51 [2852]P54(x28523,x28524,x28525,x28522)+~E(x28521,x28522)+~P54(x28523,x28524,x28525,x28521) % 172.83/172.51 [2853]~P119(x28531)+P119(x28532)+~E(x28531,x28532) % 172.83/172.51 [2854]~P99(x28541)+P99(x28542)+~E(x28541,x28542) % 172.83/172.51 [2855]~P101(x28551)+P101(x28552)+~E(x28551,x28552) % 172.83/172.51 [2856]~P127(x28561)+P127(x28562)+~E(x28561,x28562) % 172.83/172.51 [2857]P46(x28572,x28573)+~E(x28571,x28572)+~P46(x28571,x28573) % 172.83/172.51 [2858]P46(x28583,x28582)+~E(x28581,x28582)+~P46(x28583,x28581) % 172.83/172.51 [2859]~P94(x28591)+P94(x28592)+~E(x28591,x28592) % 172.83/172.51 [2860]~P128(x28601)+P128(x28602)+~E(x28601,x28602) % 172.83/172.51 [2861]~P129(x28611)+P129(x28612)+~E(x28611,x28612) % 172.83/172.51 [2862]P48(x28622,x28623,x28624)+~E(x28621,x28622)+~P48(x28621,x28623,x28624) % 172.83/172.51 [2863]P48(x28633,x28632,x28634)+~E(x28631,x28632)+~P48(x28633,x28631,x28634) % 172.83/172.51 [2864]P48(x28643,x28644,x28642)+~E(x28641,x28642)+~P48(x28643,x28644,x28641) % 172.83/172.51 [2865]~P45(x28651)+P45(x28652)+~E(x28651,x28652) % 172.83/172.51 [2866]~P87(x28661)+P87(x28662)+~E(x28661,x28662) % 172.83/172.51 [2867]P49(x28672,x28673)+~E(x28671,x28672)+~P49(x28671,x28673) % 172.83/172.51 [2868]P49(x28683,x28682)+~E(x28681,x28682)+~P49(x28683,x28681) % 172.83/172.51 [2869]P47(x28692,x28693,x28694)+~E(x28691,x28692)+~P47(x28691,x28693,x28694) % 172.83/172.51 [2870]P47(x28703,x28702,x28704)+~E(x28701,x28702)+~P47(x28703,x28701,x28704) % 172.83/172.51 [2871]P47(x28713,x28714,x28712)+~E(x28711,x28712)+~P47(x28713,x28714,x28711) % 172.83/172.51 [2872]~P74(x28721)+P74(x28722)+~E(x28721,x28722) % 172.83/172.51 [2873]~P116(x28731)+P116(x28732)+~E(x28731,x28732) % 172.83/172.51 [2874]P41(x28742,x28743,x28744,x28745)+~E(x28741,x28742)+~P41(x28741,x28743,x28744,x28745) % 172.83/172.51 [2875]P41(x28753,x28752,x28754,x28755)+~E(x28751,x28752)+~P41(x28753,x28751,x28754,x28755) % 172.83/172.51 [2876]P41(x28763,x28764,x28762,x28765)+~E(x28761,x28762)+~P41(x28763,x28764,x28761,x28765) % 172.83/172.51 [2877]P41(x28773,x28774,x28775,x28772)+~E(x28771,x28772)+~P41(x28773,x28774,x28775,x28771) % 172.83/172.51 % 172.83/172.51 %------------------------------------------- % 172.88/172.54 cnf(10217,plain, % 172.88/172.54 (~E(f332(a115,x102171),x102171)), % 172.88/172.54 inference(rename_variables,[],[4480])). % 172.88/172.54 cnf(10220,plain, % 172.88/172.54 (E(f332(f263(x102201,x102201),f264(x102201,x102202)),x102202)), % 172.88/172.54 inference(rename_variables,[],[3246])). % 172.88/172.54 cnf(10227,plain, % 172.88/172.54 (~E(f332(a115,x102271),x102271)), % 172.88/172.54 inference(rename_variables,[],[4480])). % 172.88/172.54 cnf(10240,plain, % 172.88/172.54 (~E(f332(a115,x102401),x102401)), % 172.88/172.54 inference(rename_variables,[],[4480])). % 172.88/172.54 cnf(10245,plain, % 172.88/172.54 (~P102(f332(f62(x102451,x102452,f195(f883(x102451,a871))),x102453))), % 172.88/172.54 inference(rename_variables,[],[4565])). % 172.88/172.54 cnf(10248,plain, % 172.88/172.54 (~P102(f332(f62(x102481,x102482,f195(f883(x102481,a871))),x102483))), % 172.88/172.54 inference(rename_variables,[],[4565])). % 172.88/172.54 cnf(10251,plain, % 172.88/172.54 (~E(f332(a115,x102511),x102511)), % 172.88/172.54 inference(rename_variables,[],[4480])). % 172.88/172.54 cnf(10254,plain, % 172.88/172.54 (~E(f332(a115,x102541),x102541)), % 172.88/172.54 inference(rename_variables,[],[4480])). % 172.88/172.54 cnf(10257,plain, % 172.88/172.54 (~P102(f332(f332(f247(a876),x102571),f2(a876)))), % 172.88/172.54 inference(rename_variables,[],[4545])). % 172.88/172.54 cnf(10260,plain, % 172.88/172.54 (~P102(f332(f332(f247(a876),x102601),f2(a876)))), % 172.88/172.54 inference(rename_variables,[],[4545])). % 172.88/172.54 cnf(10277,plain, % 172.88/172.54 (~P102(f332(f332(f246(a876),f332(a115,x102771)),x102771))), % 172.88/172.54 inference(rename_variables,[],[4550])). % 172.88/172.54 cnf(10280,plain, % 172.88/172.54 (~E(f332(f332(f151(x102801),x102802),x102803),x102803)), % 172.88/172.54 inference(rename_variables,[],[4505])). % 172.88/172.54 cnf(10286,plain, % 172.88/172.54 (~P102(f332(f332(f247(a876),x102861),f2(a876)))), % 172.88/172.54 inference(rename_variables,[],[4545])). % 172.88/172.54 cnf(10288,plain, % 172.88/172.54 (E(f44(a876,f332(f263(x102881,x102881),f264(x102881,f332(f332(f80(a876),x102882),x102883))),x102882),f2(a876))), % 172.88/172.54 inference(scs_inference,[],[4480,10217,10227,10240,10251,3078,3246,10220,3121,3180,3147,3128,4505,3272,4545,10257,10260,4542,4500,4550,4548,3263,4535,4565,10245,4569,4590,4616,4665,4667,4698,4715,4722,4723,4759,4764,4794,4800,4884,4909,4910,4925,4947,4972,4973,4995,4996,5009,5013,5036,5042,5058,5061,5062,5063,5068])). % 172.88/172.54 cnf(10289,plain, % 172.88/172.54 (E(f332(f263(x102891,x102891),f264(x102891,x102892)),x102892)), % 172.88/172.54 inference(rename_variables,[],[3246])). % 172.88/172.54 cnf(10292,plain, % 172.88/172.54 (E(f332(f263(x102921,x102921),f264(x102921,x102922)),x102922)), % 172.88/172.54 inference(rename_variables,[],[3246])). % 172.88/172.54 cnf(10299,plain, % 172.88/172.54 (~P102(f332(f332(f247(a876),f332(f332(f79(a876),x102991),x102992)),x102992))), % 172.88/172.54 inference(rename_variables,[],[4567])). % 172.88/172.54 cnf(10302,plain, % 172.88/172.54 (~P102(f332(f332(f247(a876),f332(f332(f79(a876),x103021),x103022)),x103022))), % 172.88/172.54 inference(rename_variables,[],[4567])). % 172.88/172.54 cnf(10323,plain, % 172.88/172.54 (~P102(f332(f332(f247(a876),x103231),x103231))), % 172.88/172.54 inference(rename_variables,[],[4541])). % 172.88/172.54 cnf(10326,plain, % 172.88/172.54 (P102(f332(f332(f246(a876),f44(a876,x103261,x103262)),x103261))), % 172.88/172.54 inference(rename_variables,[],[3756])). % 172.88/172.54 cnf(10349,plain, % 172.88/172.54 (E(f332(f37(a876),f332(f253(a876),x103491)),x103491)), % 172.88/172.54 inference(rename_variables,[],[3177])). % 172.88/172.54 cnf(10357,plain, % 172.88/172.54 (~E(f332(a115,x103571),x103571)), % 172.88/172.54 inference(rename_variables,[],[4480])). % 172.88/172.54 cnf(10360,plain, % 172.88/172.54 (~E(f332(a115,x103601),x103601)), % 172.88/172.54 inference(rename_variables,[],[4480])). % 172.88/172.54 cnf(10363,plain, % 172.88/172.54 (~E(f332(a115,x103631),x103631)), % 172.88/172.54 inference(rename_variables,[],[4480])). % 172.88/172.54 cnf(10368,plain, % 172.88/172.54 (P102(f332(f332(f247(a876),x103681),f332(a115,x103681)))), % 172.88/172.54 inference(rename_variables,[],[3359])). % 172.88/172.54 cnf(10377,plain, % 172.88/172.54 (P102(f332(f332(f201(a24),x103771),x103771))), % 172.88/172.54 inference(rename_variables,[],[3289])). % 172.88/172.54 cnf(10384,plain, % 172.88/172.54 (E(f332(f263(x103841,x103841),f264(x103841,x103842)),x103842)), % 172.88/172.54 inference(rename_variables,[],[3246])). % 172.88/172.54 cnf(10387,plain, % 172.88/172.54 (E(f332(f263(x103871,x103871),f264(x103871,x103872)),x103872)), % 172.88/172.54 inference(rename_variables,[],[3246])). % 172.88/172.54 cnf(10406,plain, % 172.88/172.54 (P102(f332(f332(f246(a1),x104061),x104061))), % 172.88/172.54 inference(rename_variables,[],[3291])). % 172.88/172.54 cnf(10415,plain, % 172.88/172.54 (~P102(f332(f332(f247(a876),x104151),x104151))), % 172.88/172.54 inference(rename_variables,[],[4541])). % 172.88/172.54 cnf(10420,plain, % 172.88/172.54 (~E(f332(f332(f332(f71(x104201,f880(x104202)),x104203),x104204),f332(f239(x104202),x104205)),f332(f16(f880(x104202),x104201),f208(x104202)))), % 172.88/172.54 inference(rename_variables,[],[4562])). % 172.88/172.54 cnf(10447,plain, % 172.88/172.54 (~E(f332(f332(f151(x104471),x104472),x104473),x104473)), % 172.88/172.54 inference(rename_variables,[],[4505])). % 172.88/172.54 cnf(10450,plain, % 172.88/172.54 (~E(f332(a25,x104501),f32(x104502,x104503))), % 172.88/172.54 inference(rename_variables,[],[4495])). % 172.88/172.54 cnf(10461,plain, % 172.88/172.54 (P102(f332(f332(f246(a1),x104611),x104611))), % 172.88/172.54 inference(rename_variables,[],[3291])). % 172.88/172.54 cnf(10466,plain, % 172.88/172.54 (~E(f332(a115,x104661),x104661)), % 172.88/172.54 inference(rename_variables,[],[4480])). % 172.88/172.54 cnf(10473,plain, % 172.88/172.54 (P102(f332(f332(f201(a24),x104731),x104731))), % 172.88/172.54 inference(rename_variables,[],[3289])). % 172.88/172.54 cnf(10486,plain, % 172.88/172.54 (P102(f332(f332(f247(a876),x104861),f332(a115,x104861)))), % 172.88/172.54 inference(rename_variables,[],[3359])). % 172.88/172.54 cnf(10507,plain, % 172.88/172.54 (~P102(f332(f62(x105071,x105072,f195(f883(x105071,a871))),x105073))), % 172.88/172.54 inference(rename_variables,[],[4565])). % 172.88/172.54 cnf(10526,plain, % 172.88/172.54 (~P102(f332(f332(f247(a876),x105261),x105261))), % 172.88/172.54 inference(rename_variables,[],[4541])). % 172.88/172.54 cnf(10541,plain, % 172.88/172.54 (~E(f332(a25,x105411),f32(x105412,x105413))), % 172.88/172.54 inference(rename_variables,[],[4495])). % 172.88/172.54 cnf(10550,plain, % 172.88/172.54 (~P102(f332(f332(f247(a876),x105501),x105501))), % 172.88/172.54 inference(rename_variables,[],[4541])). % 172.88/172.54 cnf(10555,plain, % 172.88/172.54 (P102(f332(f332(f247(a876),x105551),f332(a115,x105551)))), % 172.88/172.54 inference(rename_variables,[],[3359])). % 172.88/172.54 cnf(10558,plain, % 172.88/172.54 (~P102(f332(f62(x105581,x105582,f195(f883(x105581,a871))),x105583))), % 172.88/172.54 inference(rename_variables,[],[4565])). % 172.88/172.54 cnf(10561,plain, % 172.88/172.54 (~P102(f332(f62(x105611,x105612,f195(f883(x105611,a871))),x105613))), % 172.88/172.54 inference(rename_variables,[],[4565])). % 172.88/172.54 cnf(10566,plain, % 172.88/172.54 (~P102(f332(f62(x105661,x105662,f195(f883(x105661,a871))),x105663))), % 172.88/172.54 inference(rename_variables,[],[4565])). % 172.88/172.54 cnf(10576,plain, % 172.88/172.54 (~E(f332(f169(x105761),f332(a115,f332(f332(f134(x105761),f332(f169(x105761),x105762)),f332(f332(f151(x105761),x105763),f116(x105761))))),f332(f332(f151(x105761),x105763),x105762))), % 172.88/172.54 inference(scs_inference,[],[4480,10217,10227,10240,10251,10254,10357,10360,10363,10466,4495,10450,3078,3246,10220,10289,10292,10384,3121,3180,3147,3128,3771,3216,4562,4505,10280,3177,4087,4575,3198,3661,3359,10368,10486,10555,3272,4545,10257,10260,10286,4557,3738,3890,3318,3319,3293,4542,4500,4040,3289,10377,3290,3291,10406,3292,4541,10323,10415,10526,3385,3820,3756,10326,4550,10277,4131,4548,4531,3263,3264,4532,4535,4536,4565,10245,10248,10507,10558,10561,4569,3780,4567,10299,4590,4616,4665,4667,4698,4715,4722,4723,4759,4764,4794,4800,4884,4909,4910,4925,4947,4972,4973,4995,4996,5009,5013,5036,5042,5058,5061,5062,5063,5068,5069,5091,5116,5117,5127,5132,5138,5175,5176,5184,5193,5198,5200,5211,5213,5219,5223,5224,5237,5244,5247,5248,5249,5253,5289,5302,5310,5312,5313,5317,5318,5319,5327,5330,5335,5336,5337,5344,5348,5349,5350,5359,5363,5364,5365,5370,5383,5392,5404,5406,5414,5415,5419,5423,5448,5454,5464,5465,5480,5493,5515,5521,5539,5540,5543,5562,5570,5571,5576,5577,5587,5589,5601,5605,5614,5615,5617,5632,5637,5647,5648,5660,5667,5681,5685,5688,5694,5695,5696,5699,5704,5740,5741,5744,5746,5749,5750,5751,5753,5755,5757,5762,5769,5784,5798,5803,5804,5817,5818,5823,5827,5829,5834,5875,5887,5896,5900,5909,5913,5914,5922,5936,5942,5960,5963,5975,6002])). % 172.88/172.54 cnf(10577,plain, % 172.88/172.54 (~E(f332(a115,x105771),x105771)), % 172.88/172.54 inference(rename_variables,[],[4480])). % 172.88/172.54 cnf(10602,plain, % 172.88/172.54 (P102(f332(f332(f201(a24),x106021),x106021))), % 172.88/172.54 inference(rename_variables,[],[3289])). % 172.88/172.54 cnf(10605,plain, % 172.88/172.54 (P102(f332(f332(f247(a876),x106051),f332(a115,f332(f332(f79(a876),x106052),x106051))))), % 172.88/172.54 inference(rename_variables,[],[3749])). % 172.88/172.54 cnf(10608,plain, % 172.88/172.54 (P102(f332(f332(f246(a876),x106081),f332(f332(f80(a876),x106081),x106081)))), % 172.88/172.54 inference(rename_variables,[],[3560])). % 172.88/172.54 cnf(10611,plain, % 172.88/172.54 (P102(f332(f332(f246(a876),x106111),f332(f332(f80(a876),x106111),x106111)))), % 172.88/172.54 inference(rename_variables,[],[3560])). % 172.88/172.54 cnf(10616,plain, % 172.88/172.54 (P102(f332(f332(f247(a876),x106161),f332(a115,x106161)))), % 172.88/172.54 inference(rename_variables,[],[3359])). % 172.88/172.54 cnf(10619,plain, % 172.88/172.54 (P102(f332(f332(f247(a876),x106191),f332(a115,x106191)))), % 172.88/172.54 inference(rename_variables,[],[3359])). % 172.88/172.54 cnf(10622,plain, % 172.88/172.54 (P102(f332(f332(f334(x106221),x106222),f255(f883(x106221,a871))))), % 172.88/172.54 inference(rename_variables,[],[3449])). % 172.88/172.54 cnf(10641,plain, % 172.88/172.54 (~P102(f332(f332(f247(a876),f332(f332(f79(a876),x106411),x106412)),x106412))), % 172.88/172.54 inference(rename_variables,[],[4567])). % 172.88/172.54 cnf(10644,plain, % 172.88/172.54 (~P102(f332(f332(f247(a876),f332(f332(f79(a876),x106441),x106442)),x106442))), % 172.88/172.54 inference(rename_variables,[],[4567])). % 172.88/172.54 cnf(10647,plain, % 172.88/172.54 (~P102(f332(f332(f246(a876),f332(a115,x106471)),x106471))), % 172.88/172.54 inference(rename_variables,[],[4550])). % 172.88/172.54 cnf(10650,plain, % 172.88/172.54 (~P102(f332(f332(f246(a876),f332(a115,x106501)),x106501))), % 172.88/172.54 inference(rename_variables,[],[4550])). % 172.88/172.54 cnf(10653,plain, % 172.88/172.54 (P102(f332(f255(f883(x106531,a871)),x106532))), % 172.88/172.54 inference(rename_variables,[],[3352])). % 172.88/172.54 cnf(10656,plain, % 172.88/172.54 (E(f332(f37(a876),f332(f253(a876),x106561)),x106561)), % 172.88/172.54 inference(rename_variables,[],[3177])). % 172.88/172.54 cnf(10659,plain, % 172.88/172.54 (P102(f332(f332(f247(a876),x106591),f332(a115,x106591)))), % 172.88/172.54 inference(rename_variables,[],[3359])). % 172.88/172.54 cnf(10666,plain, % 172.88/172.54 (P102(f332(f332(f201(a24),x106661),x106661))), % 172.88/172.54 inference(rename_variables,[],[3289])). % 172.88/172.54 cnf(10671,plain, % 172.88/172.54 (P102(f332(f332(f246(a1),x106711),x106711))), % 172.88/172.54 inference(rename_variables,[],[3291])). % 172.88/172.54 cnf(10680,plain, % 172.88/172.54 (E(f332(f263(x106801,x106801),f264(x106801,x106802)),x106802)), % 172.88/172.54 inference(rename_variables,[],[3246])). % 172.88/172.54 cnf(10683,plain, % 172.88/172.54 (P102(f332(f255(f883(x106831,a871)),x106832))), % 172.88/172.54 inference(rename_variables,[],[3352])). % 172.88/172.54 cnf(10686,plain, % 172.88/172.54 (P102(f332(f332(f246(a876),f2(a876)),x106861))), % 172.88/172.54 inference(rename_variables,[],[3312])). % 172.88/172.54 cnf(10689,plain, % 172.88/172.54 (P102(f332(f332(f246(f883(x106891,a871)),f195(f883(x106891,a871))),x106892))), % 172.88/172.54 inference(rename_variables,[],[3747])). % 172.88/172.54 cnf(10692,plain, % 172.88/172.54 (P102(f332(f255(f883(x106921,a871)),x106922))), % 172.88/172.54 inference(rename_variables,[],[3352])). % 172.88/172.54 cnf(10694,plain, % 172.88/172.54 (~P102(f332(f332(f246(a876),f332(f332(f80(a876),f332(a115,x106941)),f332(a115,x106941))),x106941))), % 172.88/172.54 inference(scs_inference,[],[4480,10217,10227,10240,10251,10254,10357,10360,10363,10466,4495,10450,3078,3246,10220,10289,10292,10384,10387,3121,3180,3147,3128,3771,3216,4562,4505,10280,3177,10349,4087,4575,3198,3661,3598,3359,10368,10486,10555,10616,10619,3751,3272,4545,10257,10260,10286,4557,3738,3504,3890,3318,3319,3293,4542,4500,4040,3289,10377,10473,10602,3290,3291,10406,10461,3292,4541,10323,10415,10526,3449,3352,10653,10683,3385,3820,3756,10326,4550,10277,10647,3312,4131,4548,4531,3263,3264,4532,4535,4536,4565,10245,10248,10507,10558,10561,4573,3747,3560,10608,10611,4569,3780,4567,10299,10302,10641,3749,4590,4616,4665,4667,4698,4715,4722,4723,4759,4764,4794,4800,4884,4909,4910,4925,4947,4972,4973,4995,4996,5009,5013,5036,5042,5058,5061,5062,5063,5068,5069,5091,5116,5117,5127,5132,5138,5175,5176,5184,5193,5198,5200,5211,5213,5219,5223,5224,5237,5244,5247,5248,5249,5253,5289,5302,5310,5312,5313,5317,5318,5319,5327,5330,5335,5336,5337,5344,5348,5349,5350,5359,5363,5364,5365,5370,5383,5392,5404,5406,5414,5415,5419,5423,5448,5454,5464,5465,5480,5493,5515,5521,5539,5540,5543,5562,5570,5571,5576,5577,5587,5589,5601,5605,5614,5615,5617,5632,5637,5647,5648,5660,5667,5681,5685,5688,5694,5695,5696,5699,5704,5740,5741,5744,5746,5749,5750,5751,5753,5755,5757,5762,5769,5784,5798,5803,5804,5817,5818,5823,5827,5829,5834,5875,5887,5896,5900,5909,5913,5914,5922,5936,5942,5960,5963,5975,6002,6016,6041,6061,6062,6065,6080,6082,6083,6085,6098,6099,6102,6104,6107,6108,6120,6126,6127,6128,6130,6132,6169,6170,6175,6178,6184,6188,6224,6226,6228,6230,6239,6241,6243,6249,6251,6257,6260,6268,6275,6276,6277,6282,6304,6305,6306,6308,6314])). % 172.88/172.54 cnf(10695,plain, % 172.88/172.54 (P102(f332(f332(f246(a876),x106951),f332(f332(f80(a876),x106951),x106951)))), % 172.88/172.54 inference(rename_variables,[],[3560])). % 172.88/172.54 cnf(10712,plain, % 172.88/172.54 (~P102(f332(f332(f246(a876),f332(a115,f332(a115,f332(f332(f79(a876),x107121),x107122)))),f332(a115,x107122)))), % 172.88/172.54 inference(scs_inference,[],[4480,10217,10227,10240,10251,10254,10357,10360,10363,10466,4495,10450,3078,3246,10220,10289,10292,10384,10387,3223,3121,3180,3147,3128,3771,3216,4562,4505,10280,3177,10349,4087,4575,3198,3661,3598,3359,10368,10486,10555,10616,10619,10659,3751,3272,4545,10257,10260,10286,4557,3738,3504,3890,3318,3319,3293,4542,4500,4040,3289,10377,10473,10602,3290,3291,10406,10461,3292,4541,10323,10415,10526,3449,3352,10653,10683,3385,3820,3756,10326,4550,10277,10647,3312,4131,4548,4531,4533,3263,3264,4532,4535,4536,4565,10245,10248,10507,10558,10561,4573,3747,3560,10608,10611,4569,3780,4567,10299,10302,10641,3749,4590,4616,4665,4667,4698,4715,4722,4723,4759,4764,4794,4800,4884,4909,4910,4925,4947,4972,4973,4995,4996,5009,5013,5036,5042,5058,5061,5062,5063,5068,5069,5091,5116,5117,5127,5132,5138,5175,5176,5184,5193,5198,5200,5211,5213,5219,5223,5224,5237,5244,5247,5248,5249,5253,5289,5302,5310,5312,5313,5317,5318,5319,5327,5330,5335,5336,5337,5344,5348,5349,5350,5359,5363,5364,5365,5370,5383,5392,5404,5406,5414,5415,5419,5423,5448,5454,5464,5465,5480,5493,5515,5521,5539,5540,5543,5562,5570,5571,5576,5577,5587,5589,5601,5605,5614,5615,5617,5632,5637,5647,5648,5660,5667,5681,5685,5688,5694,5695,5696,5699,5704,5740,5741,5744,5746,5749,5750,5751,5753,5755,5757,5762,5769,5784,5798,5803,5804,5817,5818,5823,5827,5829,5834,5875,5887,5896,5900,5909,5913,5914,5922,5936,5942,5960,5963,5975,6002,6016,6041,6061,6062,6065,6080,6082,6083,6085,6098,6099,6102,6104,6107,6108,6120,6126,6127,6128,6130,6132,6169,6170,6175,6178,6184,6188,6224,6226,6228,6230,6239,6241,6243,6249,6251,6257,6260,6268,6275,6276,6277,6282,6304,6305,6306,6308,6314,6319,6353,6354,6358,6359,6360,6361,6362])). % 172.88/172.54 cnf(10735,plain, % 172.88/172.54 (P102(f332(f332(f246(a876),x107351),x107351))), % 172.88/172.54 inference(rename_variables,[],[3290])). % 172.88/172.54 cnf(10746,plain, % 172.88/172.54 (~P102(f332(f332(f195(f883(x107461,f883(x107462,a871))),x107463),x107464))), % 172.88/172.54 inference(rename_variables,[],[4570])). % 172.88/172.54 cnf(10753,plain, % 172.88/172.54 (P102(f332(f332(f247(a876),x107531),f332(a115,x107531)))), % 172.88/172.54 inference(rename_variables,[],[3359])). % 172.88/172.54 cnf(10755,plain, % 172.88/172.54 (P102(f332(f332(f247(a1),f332(f332(f22(a1),x107551),f77(a1))),x107551))), % 172.88/172.54 inference(scs_inference,[],[4480,10217,10227,10240,10251,10254,10357,10360,10363,10466,4495,10450,3078,3246,10220,10289,10292,10384,10387,3223,3121,3180,3147,3128,3771,3216,4562,4505,10280,3177,10349,4087,3942,4575,3198,3661,3598,3359,10368,10486,10555,10616,10619,10659,3751,3272,4545,10257,10260,10286,4557,3738,3504,3890,3318,3319,3293,4542,4500,4040,3289,10377,10473,10602,3290,10735,3291,10406,10461,10671,3292,4541,10323,10415,10526,3449,4553,3352,10653,10683,3385,3820,3756,10326,4550,10277,10647,10650,3312,4131,4548,4531,4533,3263,3264,4532,4535,4536,4565,10245,10248,10507,10558,10561,4573,3747,3560,10608,10611,4569,4570,3780,4567,10299,10302,10641,3749,4590,4616,4665,4667,4698,4715,4722,4723,4759,4764,4794,4800,4884,4909,4910,4925,4947,4972,4973,4995,4996,5009,5013,5036,5042,5058,5061,5062,5063,5068,5069,5091,5116,5117,5127,5132,5138,5175,5176,5184,5193,5198,5200,5211,5213,5219,5223,5224,5237,5244,5247,5248,5249,5253,5289,5302,5310,5312,5313,5317,5318,5319,5327,5330,5335,5336,5337,5344,5348,5349,5350,5359,5363,5364,5365,5370,5383,5392,5404,5406,5414,5415,5419,5423,5448,5454,5464,5465,5480,5493,5515,5521,5539,5540,5543,5562,5570,5571,5576,5577,5587,5589,5601,5605,5614,5615,5617,5632,5637,5647,5648,5660,5667,5681,5685,5688,5694,5695,5696,5699,5704,5740,5741,5744,5746,5749,5750,5751,5753,5755,5757,5762,5769,5784,5798,5803,5804,5817,5818,5823,5827,5829,5834,5875,5887,5896,5900,5909,5913,5914,5922,5936,5942,5960,5963,5975,6002,6016,6041,6061,6062,6065,6080,6082,6083,6085,6098,6099,6102,6104,6107,6108,6120,6126,6127,6128,6130,6132,6169,6170,6175,6178,6184,6188,6224,6226,6228,6230,6239,6241,6243,6249,6251,6257,6260,6268,6275,6276,6277,6282,6304,6305,6306,6308,6314,6319,6353,6354,6358,6359,6360,6361,6362,6363,6364,6371,6404,6405,6414,6435,6436,6456,6458,6469,6470,6476,6506,6508,6522,6560,6562,6563,6616])). % 172.88/172.54 cnf(10756,plain, % 172.88/172.54 (P102(f332(f332(f246(a1),x107561),x107561))), % 172.88/172.54 inference(rename_variables,[],[3291])). % 172.88/172.54 cnf(10761,plain, % 172.88/172.54 (~P102(f332(f332(f247(a876),x107611),f2(a876)))), % 172.88/172.54 inference(rename_variables,[],[4545])). % 172.88/172.54 cnf(10774,plain, % 172.88/172.54 (~P102(f332(f332(f247(a876),x107741),f2(a876)))), % 172.88/172.54 inference(rename_variables,[],[4545])). % 172.88/172.54 cnf(10777,plain, % 172.88/172.54 (~P102(f332(f332(f247(f883(x107771,a871)),x107772),f195(f883(x107771,a871))))), % 172.88/172.54 inference(rename_variables,[],[4563])). % 172.88/172.54 cnf(10780,plain, % 172.88/172.54 (P102(f332(f332(f246(a876),x107801),x107801))), % 172.88/172.54 inference(rename_variables,[],[3290])). % 172.88/172.54 cnf(10783,plain, % 172.88/172.54 (P102(f332(f332(f246(a876),x107831),x107831))), % 172.88/172.54 inference(rename_variables,[],[3290])). % 172.88/172.54 cnf(10798,plain, % 172.88/172.54 (~P102(f332(f332(f247(a876),x107981),x107981))), % 172.88/172.54 inference(rename_variables,[],[4541])). % 172.88/172.54 cnf(10807,plain, % 172.88/172.54 (~P102(f332(f332(f334(x108071),x108072),f195(f883(x108071,a871))))), % 172.88/172.54 inference(rename_variables,[],[4553])). % 172.88/172.54 cnf(10816,plain, % 172.88/172.54 (P102(f332(f332(f246(a876),x108161),x108161))), % 172.88/172.54 inference(rename_variables,[],[3290])). % 172.88/172.54 cnf(10819,plain, % 172.88/172.54 (~P102(f332(f332(f334(x108191),x108192),f195(f883(x108191,a871))))), % 172.88/172.54 inference(rename_variables,[],[4553])). % 172.88/172.54 cnf(10822,plain, % 172.88/172.54 (P102(f332(f332(f246(f883(x108221,a871)),f332(f311(x108222,x108221,x108223),f332(f312(x108222,x108221,x108223),x108224))),x108224))), % 172.88/172.54 inference(rename_variables,[],[4191])). % 172.88/172.54 cnf(10829,plain, % 172.88/172.54 (P102(f332(f332(f246(f883(x108291,a871)),f332(f173(x108291),f332(f136(x108291,x108292),x108293))),f332(f173(x108291),x108293)))), % 172.88/172.54 inference(rename_variables,[],[3952])). % 172.88/172.54 cnf(10832,plain, % 172.88/172.54 (E(f332(f311(x108321,x108321,f5(x108321)),x108322),x108322)), % 172.88/172.54 inference(rename_variables,[],[3348])). % 172.88/172.54 cnf(10839,plain, % 172.88/172.54 (P102(f332(f332(f246(a876),f2(a876)),x108391))), % 172.88/172.54 inference(rename_variables,[],[3312])). % 172.88/172.54 cnf(10842,plain, % 172.88/172.54 (P102(f332(f332(f246(a876),x108421),x108421))), % 172.88/172.54 inference(rename_variables,[],[3290])). % 172.88/172.54 cnf(10845,plain, % 172.88/172.54 (~P102(f332(f332(f247(a876),x108451),x108451))), % 172.88/172.54 inference(rename_variables,[],[4541])). % 172.88/172.54 cnf(10848,plain, % 172.88/172.54 (~P102(f332(f332(f195(f883(x108481,f883(x108482,a871))),x108483),x108484))), % 172.88/172.54 inference(rename_variables,[],[4570])). % 172.88/172.54 cnf(10855,plain, % 172.88/172.54 (~P102(f332(f332(f247(a876),x108551),x108551))), % 172.88/172.54 inference(rename_variables,[],[4541])). % 172.88/172.54 cnf(10866,plain, % 172.88/172.54 (P102(f332(f332(f247(a876),x108661),f332(a115,f332(f332(f79(a876),x108662),x108661))))), % 172.88/172.54 inference(rename_variables,[],[3749])). % 172.88/172.54 cnf(10869,plain, % 172.88/172.54 (P102(f332(f332(f246(a876),x108691),f332(f332(f80(a876),x108691),x108691)))), % 172.88/172.54 inference(rename_variables,[],[3560])). % 172.88/172.54 cnf(10879,plain, % 172.88/172.54 (P102(f332(f332(f246(a876),x108791),x108791))), % 172.88/172.54 inference(rename_variables,[],[3290])). % 172.88/172.54 cnf(10882,plain, % 172.88/172.54 (P102(f332(f332(f246(a1),x108821),x108821))), % 172.88/172.54 inference(rename_variables,[],[3291])). % 172.88/172.54 cnf(10885,plain, % 172.88/172.54 (~E(f332(a115,x108851),x108851)), % 172.88/172.54 inference(rename_variables,[],[4480])). % 172.88/172.54 cnf(10890,plain, % 172.88/172.54 (P102(f332(f332(f334(x108901),x108902),f255(f883(x108901,a871))))), % 172.88/172.54 inference(rename_variables,[],[3449])). % 172.88/172.54 cnf(10895,plain, % 172.88/172.54 (~P102(f332(f332(f247(a876),x108951),f2(a876)))), % 172.88/172.54 inference(rename_variables,[],[4545])). % 172.88/172.54 cnf(10910,plain, % 172.88/172.54 (P102(f332(f332(f246(a876),f2(a876)),x109101))), % 172.88/172.54 inference(rename_variables,[],[3312])). % 172.88/172.54 cnf(10917,plain, % 172.88/172.54 (P102(f332(f332(f246(a876),x109171),x109171))), % 172.88/172.54 inference(rename_variables,[],[3290])). % 172.88/172.54 cnf(10926,plain, % 172.88/172.54 (~P102(f332(f332(f334(x109261),x109262),f195(f883(x109261,a871))))), % 172.88/172.54 inference(rename_variables,[],[4553])). % 172.88/172.54 cnf(10930,plain, % 172.88/172.54 (E(f332(f332(f104(f883(x109301,a871)),f332(f332(f104(f883(x109301,a871)),x109302),f332(f78(f883(x109301,a871)),x109303))),x109303),f195(f883(x109301,a871)))), % 172.88/172.54 inference(scs_inference,[],[4572,4480,10217,10227,10240,10251,10254,10357,10360,10363,10466,10577,4495,10450,3078,3246,10220,10289,10292,10384,10387,3223,3121,3180,3147,3128,3771,3348,3216,4562,4505,10280,3177,10349,4087,3942,4575,3198,3495,3661,3598,3816,3359,10368,10486,10555,10616,10619,10659,10753,3751,3272,4545,10257,10260,10286,10761,10774,4557,3738,3504,3890,3318,3319,3293,4542,4500,4051,3952,10829,3662,4040,4563,3289,10377,10473,10602,3290,10735,10780,10783,10816,10842,10879,3291,10406,10461,10671,10756,3292,4541,10323,10415,10526,10550,10798,10845,3449,10622,10890,4553,10807,10819,3352,10653,10683,3385,3820,3756,10326,4550,10277,10647,10650,3312,10686,10839,4131,4548,3828,4531,4533,3263,3264,4532,4535,4536,4565,10245,10248,10507,10558,10561,4573,3747,3560,10608,10611,10695,10869,4569,4570,10746,4191,3780,4567,10299,10302,10641,3749,10605,4024,4590,4616,4665,4667,4698,4715,4722,4723,4759,4764,4794,4800,4884,4909,4910,4925,4947,4972,4973,4995,4996,5009,5013,5036,5042,5058,5061,5062,5063,5068,5069,5091,5116,5117,5127,5132,5138,5175,5176,5184,5193,5198,5200,5211,5213,5219,5223,5224,5237,5244,5247,5248,5249,5253,5289,5302,5310,5312,5313,5317,5318,5319,5327,5330,5335,5336,5337,5344,5348,5349,5350,5359,5363,5364,5365,5370,5383,5392,5404,5406,5414,5415,5419,5423,5448,5454,5464,5465,5480,5493,5515,5521,5539,5540,5543,5562,5570,5571,5576,5577,5587,5589,5601,5605,5614,5615,5617,5632,5637,5647,5648,5660,5667,5681,5685,5688,5694,5695,5696,5699,5704,5740,5741,5744,5746,5749,5750,5751,5753,5755,5757,5762,5769,5784,5798,5803,5804,5817,5818,5823,5827,5829,5834,5875,5887,5896,5900,5909,5913,5914,5922,5936,5942,5960,5963,5975,6002,6016,6041,6061,6062,6065,6080,6082,6083,6085,6098,6099,6102,6104,6107,6108,6120,6126,6127,6128,6130,6132,6169,6170,6175,6178,6184,6188,6224,6226,6228,6230,6239,6241,6243,6249,6251,6257,6260,6268,6275,6276,6277,6282,6304,6305,6306,6308,6314,6319,6353,6354,6358,6359,6360,6361,6362,6363,6364,6371,6404,6405,6414,6435,6436,6456,6458,6469,6470,6476,6506,6508,6522,6560,6562,6563,6616,6641,6683,6703,6712,6713,6714,6715,6734,6735,6741,6754,6757,6759,6761,6762,6763,6765,6779,6790,6792,6793,6806,6810,6861,6872,6874,6878,6895,6896,6932,6944,6975,6994,7009,7063,7091,7146,7167,7176,7179,7234,7242,7300,7302,7317,7325,7328,7329,7348,7354,7356,7405,7415,7418,7434,7486,7487,7491,7535,7536,7554,7621,7640,7663,7687,7702,7718,7728,7737,7738,7767,7770,7772])). % 172.88/172.54 cnf(10934,plain, % 172.88/172.54 (P102(f332(f332(f334(x109341),x109342),f255(f883(x109341,a871))))), % 172.88/172.54 inference(rename_variables,[],[3449])). % 172.88/172.54 cnf(10937,plain, % 172.88/172.54 (~P102(f332(f332(f334(f882(f877(x109371),f877(x109371))),f332(f332(f267(f877(x109371),f877(x109371)),x109372),f116(x109371))),f145(x109371,x109373)))), % 172.88/172.54 inference(rename_variables,[],[4575])). % 172.88/172.54 cnf(10943,plain, % 172.88/172.54 (~P102(f332(f332(f334(f882(x109431,x109431)),x109432),f264(x109431,f195(f883(x109431,a871)))))), % 172.88/172.54 inference(scs_inference,[],[4572,4480,10217,10227,10240,10251,10254,10357,10360,10363,10466,10577,4495,10450,3078,3246,10220,10289,10292,10384,10387,3223,3121,3180,3147,3128,3771,3348,3216,4562,4505,10280,3177,10349,4087,3942,4575,3198,3495,3661,3598,3816,3359,10368,10486,10555,10616,10619,10659,10753,3751,3272,4545,10257,10260,10286,10761,10774,4557,3738,3504,3890,3318,3319,3293,4542,4500,4051,3952,10829,3662,4040,4563,3289,10377,10473,10602,3290,10735,10780,10783,10816,10842,10879,3291,10406,10461,10671,10756,3292,4541,10323,10415,10526,10550,10798,10845,3449,10622,10890,4553,10807,10819,10926,3352,10653,10683,3385,3820,3756,10326,4550,10277,10647,10650,3312,10686,10839,4131,4548,3828,4531,4533,3263,3264,4532,4535,4536,4565,10245,10248,10507,10558,10561,4573,3747,3560,10608,10611,10695,10869,4569,4570,10746,4191,3780,4567,10299,10302,10641,3749,10605,4024,4590,4616,4665,4667,4698,4715,4722,4723,4759,4764,4794,4800,4884,4909,4910,4925,4947,4972,4973,4995,4996,5009,5013,5036,5042,5058,5061,5062,5063,5068,5069,5091,5116,5117,5127,5132,5138,5175,5176,5184,5193,5198,5200,5211,5213,5219,5223,5224,5237,5244,5247,5248,5249,5253,5289,5302,5310,5312,5313,5317,5318,5319,5327,5330,5335,5336,5337,5344,5348,5349,5350,5359,5363,5364,5365,5370,5383,5392,5404,5406,5414,5415,5419,5423,5448,5454,5464,5465,5480,5493,5515,5521,5539,5540,5543,5562,5570,5571,5576,5577,5587,5589,5601,5605,5614,5615,5617,5632,5637,5647,5648,5660,5667,5681,5685,5688,5694,5695,5696,5699,5704,5740,5741,5744,5746,5749,5750,5751,5753,5755,5757,5762,5769,5784,5798,5803,5804,5817,5818,5823,5827,5829,5834,5875,5887,5896,5900,5909,5913,5914,5922,5936,5942,5960,5963,5975,6002,6016,6041,6061,6062,6065,6080,6082,6083,6085,6098,6099,6102,6104,6107,6108,6120,6126,6127,6128,6130,6132,6169,6170,6175,6178,6184,6188,6224,6226,6228,6230,6239,6241,6243,6249,6251,6257,6260,6268,6275,6276,6277,6282,6304,6305,6306,6308,6314,6319,6353,6354,6358,6359,6360,6361,6362,6363,6364,6371,6404,6405,6414,6435,6436,6456,6458,6469,6470,6476,6506,6508,6522,6560,6562,6563,6616,6641,6683,6703,6712,6713,6714,6715,6734,6735,6741,6754,6757,6759,6761,6762,6763,6765,6779,6790,6792,6793,6806,6810,6861,6872,6874,6878,6895,6896,6932,6944,6975,6994,7009,7063,7091,7146,7167,7176,7179,7234,7242,7300,7302,7317,7325,7328,7329,7348,7354,7356,7405,7415,7418,7434,7486,7487,7491,7535,7536,7554,7621,7640,7663,7687,7702,7718,7728,7737,7738,7767,7770,7772,7782,7820,7831,7856,7914])). % 172.88/172.54 cnf(10944,plain, % 172.88/172.54 (~P102(f332(f332(f334(x109441),x109442),f195(f883(x109441,a871))))), % 172.88/172.54 inference(rename_variables,[],[4553])). % 172.88/172.54 cnf(10946,plain, % 172.88/172.54 (~P102(f332(f332(f334(x109461),x109462),f332(f312(x109461,x109463,x109464),f195(f883(x109463,a871)))))), % 172.88/172.54 inference(scs_inference,[],[4572,4480,10217,10227,10240,10251,10254,10357,10360,10363,10466,10577,4495,10450,3078,3246,10220,10289,10292,10384,10387,3223,3121,3180,3147,3128,3771,3348,3216,4562,4505,10280,3177,10349,4087,3942,4575,3198,3495,3661,3598,3816,3359,10368,10486,10555,10616,10619,10659,10753,3751,3272,4545,10257,10260,10286,10761,10774,4557,3738,3504,3890,3318,3319,3293,4542,4500,4051,3952,10829,3662,4040,4563,3289,10377,10473,10602,3290,10735,10780,10783,10816,10842,10879,3291,10406,10461,10671,10756,3292,4541,10323,10415,10526,10550,10798,10845,3449,10622,10890,4553,10807,10819,10926,10944,3352,10653,10683,3385,3820,3756,10326,4550,10277,10647,10650,3312,10686,10839,4131,4548,3828,4531,4533,3263,3264,4532,4535,4536,4565,10245,10248,10507,10558,10561,4573,3747,3560,10608,10611,10695,10869,4569,4570,10746,4191,3780,4567,10299,10302,10641,3749,10605,4024,4590,4616,4665,4667,4698,4715,4722,4723,4759,4764,4794,4800,4884,4909,4910,4925,4947,4972,4973,4995,4996,5009,5013,5036,5042,5058,5061,5062,5063,5068,5069,5091,5116,5117,5127,5132,5138,5175,5176,5184,5193,5198,5200,5211,5213,5219,5223,5224,5237,5244,5247,5248,5249,5253,5289,5302,5310,5312,5313,5317,5318,5319,5327,5330,5335,5336,5337,5344,5348,5349,5350,5359,5363,5364,5365,5370,5383,5392,5404,5406,5414,5415,5419,5423,5448,5454,5464,5465,5480,5493,5515,5521,5539,5540,5543,5562,5570,5571,5576,5577,5587,5589,5601,5605,5614,5615,5617,5632,5637,5647,5648,5660,5667,5681,5685,5688,5694,5695,5696,5699,5704,5740,5741,5744,5746,5749,5750,5751,5753,5755,5757,5762,5769,5784,5798,5803,5804,5817,5818,5823,5827,5829,5834,5875,5887,5896,5900,5909,5913,5914,5922,5936,5942,5960,5963,5975,6002,6016,6041,6061,6062,6065,6080,6082,6083,6085,6098,6099,6102,6104,6107,6108,6120,6126,6127,6128,6130,6132,6169,6170,6175,6178,6184,6188,6224,6226,6228,6230,6239,6241,6243,6249,6251,6257,6260,6268,6275,6276,6277,6282,6304,6305,6306,6308,6314,6319,6353,6354,6358,6359,6360,6361,6362,6363,6364,6371,6404,6405,6414,6435,6436,6456,6458,6469,6470,6476,6506,6508,6522,6560,6562,6563,6616,6641,6683,6703,6712,6713,6714,6715,6734,6735,6741,6754,6757,6759,6761,6762,6763,6765,6779,6790,6792,6793,6806,6810,6861,6872,6874,6878,6895,6896,6932,6944,6975,6994,7009,7063,7091,7146,7167,7176,7179,7234,7242,7300,7302,7317,7325,7328,7329,7348,7354,7356,7405,7415,7418,7434,7486,7487,7491,7535,7536,7554,7621,7640,7663,7687,7702,7718,7728,7737,7738,7767,7770,7772,7782,7820,7831,7856,7914,7948])). % 172.88/172.54 cnf(10947,plain, % 172.88/172.54 (~P102(f332(f332(f334(x109471),x109472),f195(f883(x109471,a871))))), % 172.88/172.54 inference(rename_variables,[],[4553])). % 172.88/172.54 cnf(10950,plain, % 172.88/172.54 (P102(f332(f332(f246(f883(x109501,a871)),x109502),f332(f332(f310(x109501),x109503),x109502)))), % 172.88/172.54 inference(rename_variables,[],[3745])). % 172.88/172.54 cnf(10953,plain, % 172.88/172.54 (P102(f332(f332(f246(a876),x109531),x109531))), % 172.88/172.54 inference(rename_variables,[],[3290])). % 172.88/172.54 cnf(10956,plain, % 172.88/172.54 (P102(f332(f332(f246(f883(x109561,a871)),x109562),f332(f332(f310(x109561),x109563),x109562)))), % 172.88/172.54 inference(rename_variables,[],[3745])). % 172.88/172.54 cnf(10971,plain, % 172.88/172.54 (P102(f332(f332(f246(f883(x109711,a871)),x109712),f332(f332(f310(x109711),x109713),x109712)))), % 172.88/172.54 inference(rename_variables,[],[3745])). % 172.88/172.54 cnf(10976,plain, % 172.88/172.54 (~P102(f332(f62(x109761,x109762,f195(f883(x109761,a871))),x109763))), % 172.88/172.54 inference(rename_variables,[],[4565])). % 172.88/172.54 cnf(10989,plain, % 172.88/172.54 (P102(f332(f332(f247(a876),x109891),f332(a115,x109891)))), % 172.88/172.54 inference(rename_variables,[],[3359])). % 172.88/172.54 cnf(10999,plain, % 172.88/172.54 (~E(f332(f311(x109991,f883(x109991,a871),x109992),x109993),f332(f309(x109991),x109993))), % 172.88/172.54 inference(rename_variables,[],[4551])). % 172.88/172.54 cnf(11002,plain, % 172.88/172.54 (~P102(f332(f332(f334(x110021),x110022),f195(f883(x110021,a871))))), % 172.88/172.54 inference(rename_variables,[],[4553])). % 172.88/172.54 cnf(11005,plain, % 172.88/172.54 (P102(f332(f332(f334(f882(x110051,x110051)),f332(f332(f267(x110051,x110051),x110052),x110052)),f308(x110051,x110053)))), % 172.88/172.54 inference(rename_variables,[],[3942])). % 172.88/172.54 cnf(11008,plain, % 172.88/172.54 (P102(f332(f332(f246(f883(x110081,a871)),f332(f173(x110081),f177(x110081,x110082,x110083))),f332(f173(x110081),x110082)))), % 172.88/172.54 inference(rename_variables,[],[4003])). % 172.88/172.54 cnf(11011,plain, % 172.88/172.54 (P102(f332(f332(f246(f883(x110111,a871)),x110112),f255(f883(x110111,a871))))), % 172.88/172.54 inference(rename_variables,[],[3680])). % 172.88/172.54 cnf(11027,plain, % 172.88/172.54 (P102(f332(f332(f246(f883(x110271,a871)),f195(f883(x110271,a871))),x110272))), % 172.88/172.54 inference(rename_variables,[],[3747])). % 172.88/172.54 cnf(11038,plain, % 172.88/172.54 (~P102(f332(f332(f334(f882(f877(x110381),f877(x110381))),f332(f332(f267(f877(x110381),f877(x110381)),x110382),f116(x110381))),f147(x110381,x110383)))), % 172.88/172.54 inference(rename_variables,[],[4576])). % 172.88/172.54 cnf(11049,plain, % 172.88/172.54 (~E(f332(a115,x110491),x110491)), % 172.88/172.54 inference(rename_variables,[],[4480])). % 172.88/172.54 cnf(11052,plain, % 172.88/172.54 (~E(f332(a115,x110521),x110521)), % 172.88/172.54 inference(rename_variables,[],[4480])). % 172.88/172.54 cnf(11064,plain, % 172.88/172.54 (P20(x110641,x110641,f5(x110641),x110642)), % 172.88/172.54 inference(rename_variables,[],[3534])). % 172.88/172.54 cnf(11069,plain, % 172.88/172.54 (~E(f332(f311(x110691,f883(x110691,a871),x110692),x110693),f332(f309(x110691),x110693))), % 172.88/172.54 inference(rename_variables,[],[4551])). % 172.88/172.54 cnf(11074,plain, % 172.88/172.54 (P102(f332(f332(f246(f883(x110741,a871)),x110742),f255(f883(x110741,a871))))), % 172.88/172.54 inference(rename_variables,[],[3680])). % 172.88/172.54 cnf(11088,plain, % 172.88/172.54 (~P102(f332(f332(f334(x110881),x110882),f195(f883(x110881,a871))))), % 172.88/172.54 inference(rename_variables,[],[4553])). % 172.88/172.54 cnf(11091,plain, % 172.88/172.54 (~P102(f332(f332(f246(a876),f332(a115,x110911)),x110911))), % 172.88/172.54 inference(rename_variables,[],[4550])). % 172.88/172.54 cnf(11096,plain, % 172.88/172.54 (~P102(f332(f332(f334(x110961),x110962),f195(f883(x110961,a871))))), % 172.88/172.54 inference(rename_variables,[],[4553])). % 172.88/172.54 cnf(11109,plain, % 172.88/172.54 (~P102(f332(f332(f246(a876),f332(a115,x111091)),x111091))), % 172.88/172.54 inference(rename_variables,[],[4550])). % 172.88/172.54 cnf(11112,plain, % 172.88/172.54 (~P102(f332(f332(f334(x111121),x111122),f195(f883(x111121,a871))))), % 172.88/172.54 inference(rename_variables,[],[4553])). % 172.88/172.54 cnf(11131,plain, % 172.88/172.54 (P102(f332(f332(f334(f882(x111311,x111311)),f332(f332(f267(x111311,x111311),x111312),x111312)),f308(x111311,x111313)))), % 172.88/172.54 inference(rename_variables,[],[3942])). % 172.88/172.54 cnf(11136,plain, % 172.88/172.54 (~P102(f332(f332(f334(f882(f877(x111361),f877(x111361))),f332(f332(f267(f877(x111361),f877(x111361)),x111362),f116(x111361))),f145(x111361,x111363)))), % 172.88/172.54 inference(rename_variables,[],[4575])). % 172.88/172.54 cnf(11139,plain, % 172.88/172.54 (~P102(f332(f332(f334(f882(f877(x111391),f877(x111391))),f332(f332(f267(f877(x111391),f877(x111391)),x111392),f116(x111391))),f147(x111391,x111393)))), % 172.88/172.54 inference(rename_variables,[],[4576])). % 172.88/172.54 cnf(11142,plain, % 172.88/172.54 (~P102(f332(f332(f334(f882(f877(x111421),f877(x111421))),f332(f332(f267(f877(x111421),f877(x111421)),x111422),f116(x111421))),f157(x111421,x111423)))), % 172.88/172.54 inference(rename_variables,[],[4577])). % 172.88/172.54 cnf(11147,plain, % 172.88/172.54 (~P102(f332(f332(f247(f883(x111471,a871)),x111472),f195(f883(x111471,a871))))), % 172.88/172.54 inference(rename_variables,[],[4563])). % 172.88/172.54 cnf(11150,plain, % 172.88/172.54 (~P102(f332(f332(f334(x111501),x111502),f195(f883(x111501,a871))))), % 172.88/172.54 inference(rename_variables,[],[4553])). % 172.88/172.54 cnf(11155,plain, % 172.88/172.54 (P102(f332(f332(f246(f883(x111551,a871)),x111552),f255(f883(x111551,a871))))), % 172.88/172.54 inference(rename_variables,[],[3680])). % 172.88/172.54 cnf(11158,plain, % 172.88/172.54 (~P102(f332(f332(f195(f883(x111581,f883(x111582,a871))),x111583),x111584))), % 172.88/172.54 inference(rename_variables,[],[4570])). % 172.88/172.54 cnf(11167,plain, % 172.88/172.54 (~P102(f332(f332(f334(x111671),x111672),f195(f883(x111671,a871))))), % 172.88/172.54 inference(rename_variables,[],[4553])). % 172.88/172.54 cnf(11170,plain, % 172.88/172.54 (~P102(f332(f332(f334(f882(x111701,x111701)),f332(f332(f267(x111701,x111701),x111702),x111703)),f153(x111701,f116(f883(x111701,a876)))))), % 172.88/172.54 inference(rename_variables,[],[4573])). % 172.88/172.54 cnf(11173,plain, % 172.88/172.54 (P102(f332(f332(f246(f883(x111731,a871)),x111732),x111732))), % 172.88/172.54 inference(rename_variables,[],[3594])). % 172.88/172.54 cnf(11176,plain, % 172.88/172.54 (~P102(f332(f332(f334(x111761),x111762),f195(f883(x111761,a871))))), % 172.88/172.54 inference(rename_variables,[],[4553])). % 172.88/172.54 cnf(11178,plain, % 172.88/172.54 (P102(f332(f332(f246(f883(x111781,a871)),f332(f286(x111782,x111781,f195(f883(f882(x111782,x111781),a871))),x111783)),x111784))), % 172.88/172.54 inference(scs_inference,[],[4572,3534,4480,10217,10227,10240,10251,10254,10357,10360,10363,10466,10577,10885,11049,4495,10450,10541,3078,3131,3246,10220,10289,10292,10384,10387,3223,3758,3121,3180,3147,3128,3771,3348,3216,3395,4562,3940,4505,10280,4551,10999,3396,3177,10349,4087,3942,11005,4575,10937,11136,4576,11038,4577,3198,3495,3661,3598,3816,3359,10368,10486,10555,10616,10619,10659,10753,10989,3751,3272,4545,10257,10260,10286,10761,10774,10895,4557,3738,3504,3890,3318,3319,3293,4542,4500,4051,3952,10829,4003,3662,4040,3680,11011,11074,4563,10777,3289,10377,10473,10602,3290,10735,10780,10783,10816,10842,10879,10917,3291,10406,10461,10671,10756,3292,4541,10323,10415,10526,10550,10798,10845,3449,10622,10890,10934,4553,10807,10819,10926,10944,10947,11002,11088,11096,11112,11150,11167,3352,10653,10683,3385,3820,3756,10326,4550,10277,10647,10650,11091,3312,10686,10839,4131,4548,3828,4531,4533,3263,3264,4532,4535,4536,4565,10245,10248,10507,10558,10561,10566,4573,3907,3745,10950,10956,3594,3747,10689,11027,3560,10608,10611,10695,10869,4569,4570,10746,10848,4191,3780,4567,10299,10302,10641,3749,10605,4024,4590,4616,4665,4667,4698,4715,4722,4723,4759,4764,4794,4800,4884,4909,4910,4925,4947,4972,4973,4995,4996,5009,5013,5036,5042,5058,5061,5062,5063,5068,5069,5091,5116,5117,5127,5132,5138,5175,5176,5184,5193,5198,5200,5211,5213,5219,5223,5224,5237,5244,5247,5248,5249,5253,5289,5302,5310,5312,5313,5317,5318,5319,5327,5330,5335,5336,5337,5344,5348,5349,5350,5359,5363,5364,5365,5370,5383,5392,5404,5406,5414,5415,5419,5423,5448,5454,5464,5465,5480,5493,5515,5521,5539,5540,5543,5562,5570,5571,5576,5577,5587,5589,5601,5605,5614,5615,5617,5632,5637,5647,5648,5660,5667,5681,5685,5688,5694,5695,5696,5699,5704,5740,5741,5744,5746,5749,5750,5751,5753,5755,5757,5762,5769,5784,5798,5803,5804,5817,5818,5823,5827,5829,5834,5875,5887,5896,5900,5909,5913,5914,5922,5936,5942,5960,5963,5975,6002,6016,6041,6061,6062,6065,6080,6082,6083,6085,6098,6099,6102,6104,6107,6108,6120,6126,6127,6128,6130,6132,6169,6170,6175,6178,6184,6188,6224,6226,6228,6230,6239,6241,6243,6249,6251,6257,6260,6268,6275,6276,6277,6282,6304,6305,6306,6308,6314,6319,6353,6354,6358,6359,6360,6361,6362,6363,6364,6371,6404,6405,6414,6435,6436,6456,6458,6469,6470,6476,6506,6508,6522,6560,6562,6563,6616,6641,6683,6703,6712,6713,6714,6715,6734,6735,6741,6754,6757,6759,6761,6762,6763,6765,6779,6790,6792,6793,6806,6810,6861,6872,6874,6878,6895,6896,6932,6944,6975,6994,7009,7063,7091,7146,7167,7176,7179,7234,7242,7300,7302,7317,7325,7328,7329,7348,7354,7356,7405,7415,7418,7434,7486,7487,7491,7535,7536,7554,7621,7640,7663,7687,7702,7718,7728,7737,7738,7767,7770,7772,7782,7820,7831,7856,7914,7948,7981,8028,8044,8060,8061,8136,8190,8209,8233,8253,8277,8375,8377,8383,8400,8404,8420,8443,8454,8456,8471,8476,8480,8503,8517,8518,8534,8535,8540,8541,8542,8543,8544,8562,8563,8564,8572,8585,8587,8599,8603,8605,8606,8607,8615,8620,8647,8648,8679,8692,8696,8714,8736,8737,8738,8739,8751,8752,8774,8784,8794,8795,8796,8797,8799,8821,8822,8833,8877,8883,8889,8902,8907,8909,8912,8913,8917,8927,9009,9040,9041,9042,9057,9074,9080,9108,9109,9150,9153,9179,9224,9225,9226,9241,9266,9280])). % 172.88/172.54 cnf(11179,plain, % 172.88/172.54 (P102(f332(f332(f246(f883(x111791,a871)),f195(f883(x111791,a871))),x111792))), % 172.88/172.54 inference(rename_variables,[],[3747])). % 172.88/172.54 cnf(11182,plain, % 172.88/172.54 (P102(f332(f332(f334(f882(x111821,x111821)),f332(f332(f267(x111821,x111821),x111822),x111822)),f308(x111821,x111823)))), % 172.88/172.54 inference(rename_variables,[],[3942])). % 172.88/172.54 cnf(11184,plain, % 172.88/172.54 (~P35(x111841,x111842,x111843,f332(f332(f154(x111844,x111841),x111845),f332(a115,f116(x111844))),f116(x111842))), % 172.88/172.54 inference(scs_inference,[],[4572,3534,4480,10217,10227,10240,10251,10254,10357,10360,10363,10466,10577,10885,11049,4495,10450,10541,3078,3131,3246,10220,10289,10292,10384,10387,3223,3758,3121,3180,3147,3128,3771,3348,3216,3395,4562,3940,4505,10280,4551,10999,3396,3177,10349,4087,3942,11005,11131,4575,10937,11136,4576,11038,4577,3198,3495,3661,3598,3816,3359,10368,10486,10555,10616,10619,10659,10753,10989,3751,3272,4545,10257,10260,10286,10761,10774,10895,4557,3738,3504,3890,3318,3319,3293,4542,4500,4051,3952,10829,4003,3662,4040,3680,11011,11074,4563,10777,3289,10377,10473,10602,3290,10735,10780,10783,10816,10842,10879,10917,3291,10406,10461,10671,10756,3292,4541,10323,10415,10526,10550,10798,10845,3449,10622,10890,10934,4553,10807,10819,10926,10944,10947,11002,11088,11096,11112,11150,11167,3352,10653,10683,3385,3820,3756,10326,4550,10277,10647,10650,11091,3312,10686,10839,4131,4548,3828,4531,4533,3263,3264,4532,4535,4536,4565,10245,10248,10507,10558,10561,10566,4573,3907,3745,10950,10956,3594,3747,10689,11027,3560,10608,10611,10695,10869,4569,4570,10746,10848,4191,3780,4567,10299,10302,10641,3749,10605,4024,4590,4616,4665,4667,4698,4715,4722,4723,4759,4764,4794,4800,4884,4909,4910,4925,4947,4972,4973,4995,4996,5009,5013,5036,5042,5058,5061,5062,5063,5068,5069,5091,5116,5117,5127,5132,5138,5175,5176,5184,5193,5198,5200,5211,5213,5219,5223,5224,5237,5244,5247,5248,5249,5253,5289,5302,5310,5312,5313,5317,5318,5319,5327,5330,5335,5336,5337,5344,5348,5349,5350,5359,5363,5364,5365,5370,5383,5392,5404,5406,5414,5415,5419,5423,5448,5454,5464,5465,5480,5493,5515,5521,5539,5540,5543,5562,5570,5571,5576,5577,5587,5589,5601,5605,5614,5615,5617,5632,5637,5647,5648,5660,5667,5681,5685,5688,5694,5695,5696,5699,5704,5740,5741,5744,5746,5749,5750,5751,5753,5755,5757,5762,5769,5784,5798,5803,5804,5817,5818,5823,5827,5829,5834,5875,5887,5896,5900,5909,5913,5914,5922,5936,5942,5960,5963,5975,6002,6016,6041,6061,6062,6065,6080,6082,6083,6085,6098,6099,6102,6104,6107,6108,6120,6126,6127,6128,6130,6132,6169,6170,6175,6178,6184,6188,6224,6226,6228,6230,6239,6241,6243,6249,6251,6257,6260,6268,6275,6276,6277,6282,6304,6305,6306,6308,6314,6319,6353,6354,6358,6359,6360,6361,6362,6363,6364,6371,6404,6405,6414,6435,6436,6456,6458,6469,6470,6476,6506,6508,6522,6560,6562,6563,6616,6641,6683,6703,6712,6713,6714,6715,6734,6735,6741,6754,6757,6759,6761,6762,6763,6765,6779,6790,6792,6793,6806,6810,6861,6872,6874,6878,6895,6896,6932,6944,6975,6994,7009,7063,7091,7146,7167,7176,7179,7234,7242,7300,7302,7317,7325,7328,7329,7348,7354,7356,7405,7415,7418,7434,7486,7487,7491,7535,7536,7554,7621,7640,7663,7687,7702,7718,7728,7737,7738,7767,7770,7772,7782,7820,7831,7856,7914,7948,7981,8028,8044,8060,8061,8136,8190,8209,8233,8253,8277,8375,8377,8383,8400,8404,8420,8443,8454,8456,8471,8476,8480,8503,8517,8518,8534,8535,8540,8541,8542,8543,8544,8562,8563,8564,8572,8585,8587,8599,8603,8605,8606,8607,8615,8620,8647,8648,8679,8692,8696,8714,8736,8737,8738,8739,8751,8752,8774,8784,8794,8795,8796,8797,8799,8821,8822,8833,8877,8883,8889,8902,8907,8909,8912,8913,8917,8927,9009,9040,9041,9042,9057,9074,9080,9108,9109,9150,9153,9179,9224,9225,9226,9241,9266,9280,9286,9289])). % 172.88/172.54 cnf(11193,plain, % 172.88/172.54 (~P102(f332(f332(f334(f882(f877(x111931),f877(x111931))),f332(f332(f267(f877(x111931),f877(x111931)),x111932),f116(x111931))),f157(x111931,x111933)))), % 172.88/172.54 inference(rename_variables,[],[4577])). % 172.88/172.54 cnf(11196,plain, % 172.88/172.54 (~P102(f332(f332(f334(f882(f877(x111961),f877(x111961))),f332(f332(f267(f877(x111961),f877(x111961)),f116(x111961)),x111962)),f145(x111961,x111963)))), % 172.88/172.54 inference(rename_variables,[],[4578])). % 172.88/172.54 cnf(11204,plain, % 172.88/172.54 (P102(f332(f332(f334(x112041),x112042),f255(f883(x112041,a871))))), % 172.88/172.54 inference(rename_variables,[],[3449])). % 172.88/172.54 cnf(11209,plain, % 172.88/172.54 (P102(f332(f332(f246(f883(x112091,a871)),f195(f883(x112091,a871))),x112092))), % 172.88/172.54 inference(rename_variables,[],[3747])). % 172.88/172.54 cnf(11212,plain, % 172.88/172.54 (~P102(f332(f332(f334(x112121),x112122),f195(f883(x112121,a871))))), % 172.88/172.54 inference(rename_variables,[],[4553])). % 172.88/172.54 cnf(11215,plain, % 172.88/172.54 (P102(f332(f332(f246(f883(x112151,a871)),x112152),f255(f883(x112151,a871))))), % 172.88/172.54 inference(rename_variables,[],[3680])). % 172.88/172.54 cnf(11220,plain, % 172.88/172.54 (P102(f332(f332(f246(f883(x112201,a871)),f195(f883(x112201,a871))),x112202))), % 172.88/172.54 inference(rename_variables,[],[3747])). % 172.88/172.54 cnf(11233,plain, % 172.88/172.54 (P102(f332(f255(f883(x112331,a871)),x112332))), % 172.88/172.54 inference(rename_variables,[],[3352])). % 172.88/172.54 cnf(11241,plain, % 172.88/172.54 (~P102(f332(f332(f334(f882(f877(x112411),f877(x112411))),f332(f332(f267(f877(x112411),f877(x112411)),x112412),f116(x112411))),f145(x112411,x112413)))), % 172.88/172.54 inference(rename_variables,[],[4575])). % 172.88/172.54 cnf(11244,plain, % 172.88/172.54 (~P102(f332(f332(f334(f882(f877(x112441),f877(x112441))),f332(f332(f267(f877(x112441),f877(x112441)),x112442),f116(x112441))),f147(x112441,x112443)))), % 172.88/172.54 inference(rename_variables,[],[4576])). % 172.88/172.54 cnf(11247,plain, % 172.88/172.54 (~E(f332(f332(f151(x112471),x112472),x112473),x112473)), % 172.88/172.54 inference(rename_variables,[],[4505])). % 172.88/172.54 cnf(11250,plain, % 172.88/172.54 (~E(f332(a115,x112501),x112501)), % 172.88/172.54 inference(rename_variables,[],[4480])). % 172.88/172.54 cnf(11253,plain, % 172.88/172.54 (~P102(f332(f332(f334(x112531),x112532),f195(f883(x112531,a871))))), % 172.88/172.54 inference(rename_variables,[],[4553])). % 172.88/172.54 cnf(11258,plain, % 172.88/172.54 (P102(f332(f332(f334(f882(f877(x112581),f877(x112581))),f332(f332(f267(f877(x112581),f877(x112581)),x112582),x112582)),f158(x112581,f308(x112581,x112583))))), % 172.88/172.54 inference(rename_variables,[],[4081])). % 172.88/172.54 cnf(11263,plain, % 172.88/172.54 (~P102(f332(f332(f334(f882(f877(x112631),f877(x112631))),f332(f332(f267(f877(x112631),f877(x112631)),x112632),f116(x112631))),f145(x112631,x112633)))), % 172.88/172.54 inference(rename_variables,[],[4575])). % 172.88/172.54 cnf(11273,plain, % 172.88/172.54 (~P102(f332(f332(f334(x112731),x112732),f195(f883(x112731,a871))))), % 172.88/172.54 inference(rename_variables,[],[4553])). % 172.88/172.54 cnf(11276,plain, % 172.88/172.54 (~P102(f332(f332(f334(x112761),x112762),f195(f883(x112761,a871))))), % 172.88/172.54 inference(rename_variables,[],[4553])). % 172.88/172.54 cnf(11279,plain, % 172.88/172.54 (~P102(f332(f332(f334(x112791),x112792),f195(f883(x112791,a871))))), % 172.88/172.54 inference(rename_variables,[],[4553])). % 172.88/172.54 cnf(11282,plain, % 172.88/172.54 (P102(f332(f332(f334(x112821),x112822),f255(f883(x112821,a871))))), % 172.88/172.54 inference(rename_variables,[],[3449])). % 172.88/172.54 cnf(11285,plain, % 172.88/172.54 (~P102(f332(f332(f247(a876),x112851),f2(a876)))), % 172.88/172.54 inference(rename_variables,[],[4545])). % 172.88/172.54 cnf(11290,plain, % 172.88/172.54 (~P102(f332(f332(f334(f882(x112901,x112901)),f332(f332(f267(x112901,x112901),x112902),x112903)),f153(x112901,f116(f883(x112901,a876)))))), % 172.88/172.54 inference(rename_variables,[],[4573])). % 172.88/172.54 cnf(11293,plain, % 172.88/172.54 (~E(f332(f311(x112931,f883(x112931,a871),x112932),x112933),f332(f309(x112931),x112933))), % 172.88/172.54 inference(rename_variables,[],[4551])). % 172.88/172.54 cnf(11296,plain, % 172.88/172.54 (~E(f332(f311(x112961,f883(x112961,a871),x112962),x112963),f332(f309(x112961),x112963))), % 172.88/172.54 inference(rename_variables,[],[4551])). % 172.88/172.54 cnf(11301,plain, % 172.88/172.54 (~P102(f332(f332(f334(f882(f877(x113011),f877(x113011))),f332(f332(f267(f877(x113011),f877(x113011)),x113012),f116(x113011))),f145(x113011,x113013)))), % 172.88/172.54 inference(rename_variables,[],[4575])). % 172.88/172.54 cnf(11307,plain, % 172.88/172.54 (~P102(f332(f332(f334(f882(f877(x113071),f877(x113071))),f332(f332(f267(f877(x113071),f877(x113071)),x113072),f116(x113071))),f145(x113071,x113073)))), % 172.88/172.54 inference(rename_variables,[],[4575])). % 172.88/172.54 cnf(11310,plain, % 172.88/172.54 (~P102(f332(f332(f334(x113101),x113102),f195(f883(x113101,a871))))), % 172.88/172.54 inference(rename_variables,[],[4553])). % 172.88/172.54 cnf(11317,plain, % 172.88/172.54 (~P102(f332(f332(f334(x113171),x113172),f195(f883(x113171,a871))))), % 172.88/172.54 inference(rename_variables,[],[4553])). % 172.88/172.54 cnf(11320,plain, % 172.88/172.54 (~P102(f332(f332(f334(x113201),x113202),f195(f883(x113201,a871))))), % 172.88/172.54 inference(rename_variables,[],[4553])). % 172.88/172.54 cnf(11323,plain, % 172.88/172.54 (P102(f332(f332(f334(x113231),f332(x113232,x113233)),f332(f311(x113234,x113231,x113232),f255(f883(x113234,a871)))))), % 172.88/172.54 inference(rename_variables,[],[3907])). % 172.88/172.54 cnf(11326,plain, % 172.88/172.54 (~P102(f332(f332(f334(f882(x113261,x113261)),f332(f332(f267(x113261,x113261),x113262),x113263)),f153(x113261,f116(f883(x113261,a876)))))), % 172.88/172.54 inference(rename_variables,[],[4573])). % 172.88/172.54 cnf(11334,plain, % 172.88/172.54 (E(f117(x113341,f116(x113341)),f116(x113341))), % 172.88/172.54 inference(rename_variables,[],[3131])). % 172.88/172.54 cnf(11337,plain, % 172.88/172.54 (~E(f332(a115,x113371),x113371)), % 172.88/172.54 inference(rename_variables,[],[4480])). % 172.88/172.54 cnf(11344,plain, % 172.88/172.54 (~E(f332(a115,x113441),x113441)), % 172.88/172.54 inference(rename_variables,[],[4480])). % 172.88/172.54 cnf(11349,plain, % 172.88/172.54 (E(f332(f263(x113491,x113491),f264(x113491,x113492)),x113492)), % 172.88/172.54 inference(rename_variables,[],[3246])). % 172.88/172.54 cnf(11352,plain, % 172.88/172.54 (E(f332(f263(x113521,x113521),f264(x113521,x113522)),x113522)), % 172.88/172.54 inference(rename_variables,[],[3246])). % 172.88/172.54 cnf(11358,plain, % 172.88/172.54 (~E(f332(a115,x113581),x113581)), % 172.88/172.54 inference(rename_variables,[],[4480])). % 172.88/172.54 cnf(11365,plain, % 172.88/172.54 (~E(f332(f332(f79(a1),x113651),x113651),a100)), % 172.88/172.54 inference(rename_variables,[],[4503])). % 172.88/172.54 cnf(11374,plain, % 172.88/172.54 (E(f332(f332(f22(a876),f2(a876)),x113741),f2(a876))), % 172.88/172.54 inference(rename_variables,[],[3199])). % 172.88/172.54 cnf(11377,plain, % 172.88/172.54 (~P102(f332(f332(f247(a876),x113771),f2(a876)))), % 172.88/172.54 inference(rename_variables,[],[4545])). % 172.88/172.54 cnf(11384,plain, % 172.88/172.54 (E(f332(f332(f79(a1),f332(f332(f80(a1),x113841),f332(f332(f38(a1),x113842),x113841))),f44(a1,x113842,x113841)),x113842)), % 172.88/172.54 inference(rename_variables,[],[3853])). % 172.88/172.54 cnf(11410,plain, % 172.88/172.54 (~E(f332(a115,x114101),x114101)), % 172.88/172.54 inference(rename_variables,[],[4480])). % 172.88/172.54 cnf(11413,plain, % 172.88/172.54 (~E(f332(a115,x114131),x114131)), % 172.88/172.54 inference(rename_variables,[],[4480])). % 172.88/172.54 cnf(11439,plain, % 172.88/172.54 (~P102(f332(f62(x114391,x114392,f195(f883(x114391,a871))),x114393))), % 172.88/172.54 inference(rename_variables,[],[4565])). % 172.88/172.54 cnf(11442,plain, % 172.88/172.54 (~P102(f332(f332(f195(f883(x114421,f883(x114422,a871))),x114423),x114424))), % 172.88/172.54 inference(rename_variables,[],[4570])). % 172.88/172.54 cnf(11445,plain, % 172.88/172.54 (P102(f332(f332(f334(x114451),x114452),f255(f883(x114451,a871))))), % 172.88/172.54 inference(rename_variables,[],[3449])). % 172.88/172.54 cnf(11457,plain, % 172.88/172.54 (~E(f332(a115,x114571),x114571)), % 172.88/172.54 inference(rename_variables,[],[4480])). % 172.88/172.54 cnf(11460,plain, % 172.88/172.54 (P102(f332(f332(f201(a24),x114601),x114601))), % 172.88/172.54 inference(rename_variables,[],[3289])). % 172.88/172.54 cnf(11467,plain, % 172.88/172.54 (P102(f332(f66(x114671,x114672,x114673,x114674,f195(f883(x114671,a871))),x114674))), % 172.88/172.54 inference(rename_variables,[],[4231])). % 172.88/172.54 cnf(11468,plain, % 172.88/172.54 (E(f332(f263(x114681,x114681),f264(x114681,x114682)),x114682)), % 172.88/172.54 inference(rename_variables,[],[3246])). % 172.88/172.54 cnf(11473,plain, % 172.88/172.54 (~P102(f332(f332(f195(f883(x114731,f883(x114732,a871))),x114733),x114734))), % 172.88/172.54 inference(rename_variables,[],[4570])). % 172.88/172.54 cnf(11484,plain, % 172.88/172.54 (~P102(f332(f332(f247(a876),f332(f332(f79(a876),x114841),x114842)),x114842))), % 172.88/172.54 inference(rename_variables,[],[4567])). % 172.88/172.54 cnf(11487,plain, % 172.88/172.54 (~P102(f332(f332(f247(a1),f332(f103(a1),x114871)),f2(a1)))), % 172.88/172.54 inference(rename_variables,[],[4557])). % 172.88/172.54 cnf(11505,plain, % 172.88/172.54 (~E(f332(f332(f104(a876),f332(a115,x115051)),x115051),f332(a115,x115051))), % 172.88/172.54 inference(scs_inference,[],[4572,3534,4480,10217,10227,10240,10251,10254,10357,10360,10363,10466,10577,10885,11049,11052,11250,11337,11344,11358,11410,11413,4495,10450,10541,3203,2888,2892,2902,2909,2911,2915,2916,2922,2936,2943,2952,2963,2964,2965,2966,2981,3021,3030,3031,3046,3056,3062,3078,4476,3131,11334,3246,10220,10289,10292,10384,10387,10680,11349,11352,3223,3758,3121,3853,11384,3180,3147,3128,3771,3348,3216,3395,4562,3940,4505,10280,10447,4551,10999,11069,11293,11296,3396,3177,10349,10656,3178,3100,3199,11374,4087,3942,11005,11131,11182,4575,10937,11136,11241,11263,11301,11307,4576,11038,11139,11244,4577,11142,4578,11196,4579,3198,3495,3661,4503,3598,3816,3359,10368,10486,10555,10616,10619,10659,10753,10989,3751,3272,4545,10257,10260,10286,10761,10774,10895,11285,11377,4557,3738,3504,3890,3318,3319,3293,4542,4500,3487,4558,4081,11258,3619,4051,3952,10829,4003,3662,4040,3680,11011,11074,11155,4563,10777,11147,3289,10377,10473,10602,10666,3290,10735,10780,10783,10816,10842,10879,10917,3291,10406,10461,10671,10756,3292,4541,10323,10415,10526,10550,10798,10845,3449,10622,10890,10934,11204,11282,4553,10807,10819,10926,10944,10947,11002,11088,11096,11112,11150,11167,11176,11212,11253,11273,11276,11279,11310,11317,3352,10653,10683,10692,3385,3820,3756,10326,4550,10277,10647,10650,11091,11109,3312,10686,10839,4131,4548,3828,4531,4533,3263,3264,4532,4535,4536,4231,4565,10245,10248,10507,10558,10561,10566,10976,4573,11170,11290,3907,3745,10950,10956,3594,3747,10689,11027,11179,11209,3560,10608,10611,10695,10869,4569,4559,4570,10746,10848,11158,11442,4191,4092,3780,4567,10299,10302,10641,10644,3749,10605,4024,4590,4616,4665,4667,4698,4715,4722,4723,4759,4764,4794,4800,4884,4909,4910,4925,4947,4972,4973,4995,4996,5009,5013,5036,5042,5058,5061,5062,5063,5068,5069,5091,5116,5117,5127,5132,5138,5175,5176,5184,5193,5198,5200,5211,5213,5219,5223,5224,5237,5244,5247,5248,5249,5253,5289,5302,5310,5312,5313,5317,5318,5319,5327,5330,5335,5336,5337,5344,5348,5349,5350,5359,5363,5364,5365,5370,5383,5392,5404,5406,5414,5415,5419,5423,5448,5454,5464,5465,5480,5493,5515,5521,5539,5540,5543,5562,5570,5571,5576,5577,5587,5589,5601,5605,5614,5615,5617,5632,5637,5647,5648,5660,5667,5681,5685,5688,5694,5695,5696,5699,5704,5740,5741,5744,5746,5749,5750,5751,5753,5755,5757,5762,5769,5784,5798,5803,5804,5817,5818,5823,5827,5829,5834,5875,5887,5896,5900,5909,5913,5914,5922,5936,5942,5960,5963,5975,6002,6016,6041,6061,6062,6065,6080,6082,6083,6085,6098,6099,6102,6104,6107,6108,6120,6126,6127,6128,6130,6132,6169,6170,6175,6178,6184,6188,6224,6226,6228,6230,6239,6241,6243,6249,6251,6257,6260,6268,6275,6276,6277,6282,6304,6305,6306,6308,6314,6319,6353,6354,6358,6359,6360,6361,6362,6363,6364,6371,6404,6405,6414,6435,6436,6456,6458,6469,6470,6476,6506,6508,6522,6560,6562,6563,6616,6641,6683,6703,6712,6713,6714,6715,6734,6735,6741,6754,6757,6759,6761,6762,6763,6765,6779,6790,6792,6793,6806,6810,6861,6872,6874,6878,6895,6896,6932,6944,6975,6994,7009,7063,7091,7146,7167,7176,7179,7234,7242,7300,7302,7317,7325,7328,7329,7348,7354,7356,7405,7415,7418,7434,7486,7487,7491,7535,7536,7554,7621,7640,7663,7687,7702,7718,7728,7737,7738,7767,7770,7772,7782,7820,7831,7856,7914,7948,7981,8028,8044,8060,8061,8136,8190,8209,8233,8253,8277,8375,8377,8383,8400,8404,8420,8443,8454,8456,8471,8476,8480,8503,8517,8518,8534,8535,8540,8541,8542,8543,8544,8562,8563,8564,8572,8585,8587,8599,8603,8605,8606,8607,8615,8620,8647,8648,8679,8692,8696,8714,8736,8737,8738,8739,8751,8752,8774,8784,8794,8795,8796,8797,8799,8821,8822,8833,8877,8883,8889,8902,8907,8909,8912,8913,8917,8927,9009,9040,9041,9042,9057,9074,9080,9108,9109,9150,9153,9179,9224,9225,9226,9241,9266,9280,9286,9289,9311,9312,9340,9402,9437,9438,9439,9464,9465,9483,9501,9507,9521,9544,9566,9574,9575,9576,9577,9592,9594,9599,9630,9631,9637,9638,9682,9683,9714,9723,9733,9735,9736,9745,9759,9762,9790,9823,9825,9829,9886,9927,9928,9930,9940,9941,9961,9966,10007,10059,10131,10132,10185,10201,2,8,9,4603,4604,4622,4653,4655,4656,4684,4690,4691,4702,4751,4753,4785,4799,4829,4926,4927,4940,4960,5016,5017,5020,5021,5023,5025,5026,5035,5038,5039,5047,5059,5060,5066,5086,5087,5104,5109,5110,5111,5112,5115,5123,5126,5133,5190,5196,5197,5205,5234,5245,5251,5267,5287,5288,5295,5296,5297,5306,5316,5323,5325,5326,5332,5340,5341,5351,5355,5356,5357,5358,5360,5361,5366,5367])). % 172.88/172.54 cnf(11512,plain, % 172.88/172.54 (E(f332(f263(x115121,x115121),f264(x115121,x115122)),x115122)), % 172.88/172.54 inference(rename_variables,[],[3246])). % 172.88/172.54 cnf(11517,plain, % 172.88/172.54 (E(f332(f263(x115171,x115171),f264(x115171,x115172)),x115172)), % 172.88/172.54 inference(rename_variables,[],[3246])). % 172.88/172.54 cnf(11520,plain, % 172.88/172.54 (~P102(f332(f332(f247(a1),f332(f103(a1),x115201)),f2(a1)))), % 172.88/172.54 inference(rename_variables,[],[4557])). % 172.88/172.54 cnf(11525,plain, % 172.88/172.54 (~E(f332(a115,x115251),x115251)), % 172.88/172.54 inference(rename_variables,[],[4480])). % 172.88/172.54 cnf(11529,plain, % 172.88/172.54 (P102(f332(f332(f246(a1),f2(a1)),a82))), % 172.88/172.54 inference(scs_inference,[],[4572,3534,4480,10217,10227,10240,10251,10254,10357,10360,10363,10466,10577,10885,11049,11052,11250,11337,11344,11358,11410,11413,11457,4495,10450,10541,3203,2888,2892,2902,2909,2911,2912,2915,2916,2922,2936,2943,2952,2963,2964,2965,2966,2981,3021,3030,3031,3046,3056,3062,3078,4476,3131,11334,3246,10220,10289,10292,10384,10387,10680,11349,11352,11468,11512,3223,3758,3121,3853,11384,3180,3147,3142,3128,3129,3771,3348,3216,3395,4562,3940,4505,10280,10447,4551,10999,11069,11293,11296,3396,3177,10349,10656,3178,3100,3199,11374,4087,3942,11005,11131,11182,4575,10937,11136,11241,11263,11301,11307,4576,11038,11139,11244,4577,11142,4578,11196,4579,3198,3495,3661,4503,3598,3816,3359,10368,10486,10555,10616,10619,10659,10753,10989,3751,3272,4545,10257,10260,10286,10761,10774,10895,11285,11377,4557,11487,11520,3738,3504,3890,3318,3319,3293,4542,4500,3487,4558,4081,11258,3619,4051,3952,10829,4003,3662,4040,3680,11011,11074,11155,4563,10777,11147,3289,10377,10473,10602,10666,3290,10735,10780,10783,10816,10842,10879,10917,3291,10406,10461,10671,10756,3292,4541,10323,10415,10526,10550,10798,10845,3449,10622,10890,10934,11204,11282,4553,10807,10819,10926,10944,10947,11002,11088,11096,11112,11150,11167,11176,11212,11253,11273,11276,11279,11310,11317,3352,10653,10683,10692,3391,3385,3820,3756,10326,4550,10277,10647,10650,11091,11109,3312,10686,10839,4131,4548,3828,4531,4533,3263,3264,4532,4535,4536,4231,4565,10245,10248,10507,10558,10561,10566,10976,4573,11170,11290,3907,3745,10950,10956,3594,3747,10689,11027,11179,11209,3560,10608,10611,10695,10869,4569,4559,4570,10746,10848,11158,11442,4191,4092,3780,4567,10299,10302,10641,10644,3749,10605,4024,4590,4616,4665,4667,4698,4715,4722,4723,4759,4764,4794,4800,4884,4909,4910,4925,4947,4972,4973,4995,4996,5009,5013,5036,5042,5058,5061,5062,5063,5068,5069,5091,5116,5117,5127,5132,5138,5175,5176,5184,5193,5198,5200,5211,5213,5219,5223,5224,5237,5244,5247,5248,5249,5253,5289,5302,5310,5312,5313,5317,5318,5319,5327,5330,5335,5336,5337,5344,5348,5349,5350,5359,5363,5364,5365,5370,5383,5392,5404,5406,5414,5415,5419,5423,5448,5454,5464,5465,5480,5493,5515,5521,5539,5540,5543,5562,5570,5571,5576,5577,5587,5589,5601,5605,5614,5615,5617,5632,5637,5647,5648,5660,5667,5681,5685,5688,5694,5695,5696,5699,5704,5740,5741,5744,5746,5749,5750,5751,5753,5755,5757,5762,5769,5784,5798,5803,5804,5817,5818,5823,5827,5829,5834,5875,5887,5896,5900,5909,5913,5914,5922,5936,5942,5960,5963,5975,6002,6016,6041,6061,6062,6065,6080,6082,6083,6085,6098,6099,6102,6104,6107,6108,6120,6126,6127,6128,6130,6132,6169,6170,6175,6178,6184,6188,6224,6226,6228,6230,6239,6241,6243,6249,6251,6257,6260,6268,6275,6276,6277,6282,6304,6305,6306,6308,6314,6319,6353,6354,6358,6359,6360,6361,6362,6363,6364,6371,6404,6405,6414,6435,6436,6456,6458,6469,6470,6476,6506,6508,6522,6560,6562,6563,6616,6641,6683,6703,6712,6713,6714,6715,6734,6735,6741,6754,6757,6759,6761,6762,6763,6765,6779,6790,6792,6793,6806,6810,6861,6872,6874,6878,6895,6896,6932,6944,6975,6994,7009,7063,7091,7146,7167,7176,7179,7234,7242,7300,7302,7317,7325,7328,7329,7348,7354,7356,7405,7415,7418,7434,7486,7487,7491,7535,7536,7554,7621,7640,7663,7687,7702,7718,7728,7737,7738,7767,7770,7772,7782,7820,7831,7856,7914,7948,7981,8028,8044,8060,8061,8136,8190,8209,8233,8253,8277,8375,8377,8383,8400,8404,8420,8443,8454,8456,8471,8476,8480,8503,8517,8518,8534,8535,8540,8541,8542,8543,8544,8562,8563,8564,8572,8585,8587,8599,8603,8605,8606,8607,8615,8620,8647,8648,8679,8692,8696,8714,8736,8737,8738,8739,8751,8752,8774,8784,8794,8795,8796,8797,8799,8821,8822,8833,8877,8883,8889,8902,8907,8909,8912,8913,8917,8927,9009,9040,9041,9042,9057,9074,9080,9108,9109,9150,9153,9179,9224,9225,9226,9241,9266,9280,9286,9289,9311,9312,9340,9402,9437,9438,9439,9464,9465,9483,9501,9507,9521,9544,9566,9574,9575,9576,9577,9592,9594,9599,9630,9631,9637,9638,9682,9683,9714,9723,9733,9735,9736,9745,9759,9762,9790,9823,9825,9829,9886,9927,9928,9930,9940,9941,9961,9966,10007,10059,10131,10132,10185,10201,2,8,9,4603,4604,4622,4653,4655,4656,4684,4690,4691,4702,4751,4753,4785,4799,4829,4926,4927,4940,4960,5016,5017,5020,5021,5023,5025,5026,5035,5038,5039,5047,5059,5060,5066,5086,5087,5104,5109,5110,5111,5112,5115,5123,5126,5133,5190,5196,5197,5205,5234,5245,5251,5267,5287,5288,5295,5296,5297,5306,5316,5323,5325,5326,5332,5340,5341,5351,5355,5356,5357,5358,5360,5361,5366,5367,5368,5369,5400,5401,5402,5410,5411,5412,5413,5459])). % 172.88/172.54 cnf(11534,plain, % 172.88/172.54 (~P102(f332(f332(f247(a876),x115341),x115341))), % 172.88/172.54 inference(rename_variables,[],[4541])). % 172.88/172.54 cnf(11555,plain, % 172.88/172.54 (~P102(f332(f332(f247(a1),f332(f103(a1),x115551)),f2(a1)))), % 172.88/172.54 inference(rename_variables,[],[4557])). % 172.88/172.54 cnf(11568,plain, % 172.88/172.54 (P102(f332(f332(f246(a1),x115681),x115681))), % 172.88/172.54 inference(rename_variables,[],[3291])). % 172.88/172.54 cnf(11571,plain, % 172.88/172.54 (~P102(f332(f332(f246(a876),f332(a115,x115711)),x115711))), % 172.88/172.54 inference(rename_variables,[],[4550])). % 172.88/172.54 cnf(11572,plain, % 172.88/172.54 (~E(f332(a115,x115721),x115721)), % 172.88/172.54 inference(rename_variables,[],[4480])). % 172.88/172.54 cnf(11582,plain, % 172.88/172.54 (~P102(f332(f332(f247(a876),f332(f332(f79(a876),x115821),x115822)),x115821))), % 172.88/172.54 inference(rename_variables,[],[4568])). % 172.88/172.54 cnf(11585,plain, % 172.88/172.54 (~P102(f332(f332(f247(a1),f332(f103(a1),x115851)),f2(a1)))), % 172.88/172.54 inference(rename_variables,[],[4557])). % 172.88/172.54 cnf(11588,plain, % 172.88/172.54 (~E(f332(a115,x115881),x115881)), % 172.88/172.54 inference(rename_variables,[],[4480])). % 172.88/172.54 cnf(11601,plain, % 172.88/172.54 (P102(f332(f332(f334(x116011),x116012),f332(f332(f310(x116011),x116012),x116013)))), % 172.88/172.54 inference(rename_variables,[],[3609])). % 172.88/172.54 cnf(11602,plain, % 172.88/172.54 (~P102(f332(f332(f246(a1),f2(a1)),f332(f78(a1),f332(f103(a1),f332(a115,x116021)))))), % 172.88/172.54 inference(rename_variables,[],[4569])). % 172.88/172.54 cnf(11605,plain, % 172.88/172.54 (P102(f332(f332(f247(a876),f332(f332(f22(a876),x116051),x116052)),f332(a115,x116051)))), % 172.88/172.54 inference(rename_variables,[],[3751])). % 172.88/172.54 cnf(11608,plain, % 172.88/172.54 (P102(f332(f332(f246(a876),f44(a876,x116081,x116082)),x116081))), % 172.88/172.54 inference(rename_variables,[],[3756])). % 172.88/172.54 cnf(11614,plain, % 172.88/172.54 (E(f332(f263(x116141,x116141),f264(x116141,x116142)),x116142)), % 172.88/172.54 inference(rename_variables,[],[3246])). % 172.88/172.54 cnf(11619,plain, % 172.88/172.54 (E(f332(f332(f134(x116191),f170(x116191,x116192,x116193)),f170(x116191,x116194,x116193)),f332(f332(f134(x116191),f170(x116191,x116194,x116193)),f170(x116191,x116192,x116193)))), % 172.88/172.54 inference(rename_variables,[],[3868])). % 172.88/172.54 cnf(11624,plain, % 172.88/172.54 (~P102(f332(f332(f246(a876),f332(a115,x116241)),x116241))), % 172.88/172.54 inference(rename_variables,[],[4550])). % 172.88/172.54 cnf(11633,plain, % 172.88/172.54 (~P102(f332(f332(f247(a876),x116331),x116331))), % 172.88/172.54 inference(rename_variables,[],[4541])). % 172.88/172.54 cnf(11636,plain, % 172.88/172.54 (P102(f332(f332(f246(a876),f44(a876,x116361,x116362)),x116361))), % 172.88/172.54 inference(rename_variables,[],[3756])). % 172.88/172.54 cnf(11637,plain, % 172.88/172.54 (P102(f332(f332(f246(a876),f2(a876)),x116371))), % 172.88/172.54 inference(rename_variables,[],[3312])). % 172.88/172.54 cnf(11654,plain, % 172.88/172.54 (~P102(f332(f332(f247(a876),x116541),x116541))), % 172.88/172.54 inference(rename_variables,[],[4541])). % 172.88/172.54 cnf(11657,plain, % 172.88/172.54 (~P102(f332(f332(f247(a876),x116571),x116571))), % 172.88/172.54 inference(rename_variables,[],[4541])). % 172.88/172.54 cnf(11660,plain, % 172.88/172.54 (~P102(f332(f332(f247(a876),x116601),x116601))), % 172.88/172.54 inference(rename_variables,[],[4541])). % 172.88/172.54 cnf(11663,plain, % 172.88/172.54 (P102(f332(f332(f334(x116631),f332(x116632,x116633)),f332(f311(x116634,x116631,x116632),f255(f883(x116634,a871)))))), % 172.88/172.54 inference(rename_variables,[],[3907])). % 172.88/172.54 cnf(11664,plain, % 172.88/172.54 (~P102(f332(f332(f247(a876),f332(f332(f79(a876),x116641),x116642)),x116642))), % 172.88/172.54 inference(rename_variables,[],[4567])). % 172.88/172.54 cnf(11667,plain, % 172.88/172.54 (P102(f332(f332(f334(x116671),f332(x116672,x116673)),f332(f311(x116674,x116671,x116672),f255(f883(x116674,a871)))))), % 172.88/172.54 inference(rename_variables,[],[3907])). % 172.88/172.54 cnf(11668,plain, % 172.88/172.54 (~P102(f332(f332(f246(a876),f332(a115,x116681)),x116681))), % 172.88/172.54 inference(rename_variables,[],[4550])). % 172.88/172.54 cnf(11673,plain, % 172.88/172.54 (~P102(f332(f332(f247(a876),f332(f332(f79(a876),x116731),x116732)),x116731))), % 172.88/172.54 inference(rename_variables,[],[4568])). % 172.88/172.54 cnf(11676,plain, % 172.88/172.54 (~P102(f332(f332(f247(a876),x116761),x116761))), % 172.88/172.54 inference(rename_variables,[],[4541])). % 172.88/172.54 cnf(11679,plain, % 172.88/172.54 (P102(f332(f332(f201(a24),x116791),x116791))), % 172.88/172.54 inference(rename_variables,[],[3289])). % 172.88/172.54 cnf(11685,plain, % 172.88/172.54 (~P36(x116851,x116852,f116(x116851))), % 172.88/172.54 inference(rename_variables,[],[4514])). % 172.88/172.54 cnf(11688,plain, % 172.88/172.54 (P102(f332(f332(f334(x116881),x116882),f255(f883(x116881,a871))))), % 172.88/172.54 inference(rename_variables,[],[3449])). % 172.88/172.54 cnf(11689,plain, % 172.88/172.54 (~P102(f332(f332(f246(a876),f332(a115,x116891)),x116891))), % 172.88/172.54 inference(rename_variables,[],[4550])). % 172.88/172.54 cnf(11692,plain, % 172.88/172.54 (~P102(f332(f62(x116921,x116922,f195(f883(x116921,a871))),x116923))), % 172.88/172.54 inference(rename_variables,[],[4565])). % 172.88/172.54 cnf(11705,plain, % 172.88/172.54 (~P102(f332(f332(f334(x117051),x117052),f195(f883(x117051,a871))))), % 172.88/172.54 inference(rename_variables,[],[4553])). % 172.88/172.54 cnf(11708,plain, % 172.88/172.54 (E(f332(f332(f16(x117081,x117082),x117083),x117084),x117083)), % 172.88/172.54 inference(rename_variables,[],[3279])). % 172.88/172.54 cnf(11711,plain, % 172.88/172.54 (E(f332(f332(f16(x117111,x117112),x117113),x117114),x117113)), % 172.88/172.54 inference(rename_variables,[],[3279])). % 172.88/172.54 cnf(11723,plain, % 172.88/172.54 (P102(f332(f332(f247(a876),f2(a876)),f332(a115,x117231)))), % 172.88/172.54 inference(rename_variables,[],[3371])). % 172.88/172.54 cnf(11726,plain, % 172.88/172.54 (P102(f332(f332(f201(a24),x117261),x117261))), % 172.88/172.54 inference(rename_variables,[],[3289])). % 172.88/172.54 cnf(11729,plain, % 172.88/172.54 (P102(f332(f332(f334(x117291),f332(x117292,x117293)),f332(f311(x117294,x117291,x117292),f255(f883(x117294,a871)))))), % 172.88/172.54 inference(rename_variables,[],[3907])). % 172.88/172.54 cnf(11732,plain, % 172.88/172.54 (P102(f332(f61(x117321),f332(f173(x117321),x117322)))), % 172.88/172.54 inference(rename_variables,[],[3331])). % 172.88/172.54 cnf(11735,plain, % 172.88/172.54 (P102(f332(f61(x117351),f332(f173(x117351),x117352)))), % 172.88/172.54 inference(rename_variables,[],[3331])). % 172.88/172.54 cnf(11738,plain, % 172.88/172.54 (P102(f332(f332(f246(a1),f332(f78(a1),f332(f103(a1),x117381))),f332(f103(a1),x117382)))), % 172.88/172.54 inference(rename_variables,[],[3781])). % 172.88/172.54 cnf(11741,plain, % 172.88/172.54 (~P102(f332(f332(f334(x117411),x117412),f195(f883(x117411,a871))))), % 172.88/172.54 inference(rename_variables,[],[4553])). % 172.88/172.54 cnf(11753,plain, % 172.88/172.54 (~P102(f332(f332(f334(a876),x117531),f332(f253(a876),f2(a876))))), % 172.88/172.54 inference(scs_inference,[],[4572,3534,4513,4514,4480,10217,10227,10240,10251,10254,10357,10360,10363,10466,10577,10885,11049,11052,11250,11337,11344,11358,11410,11413,11457,11525,11572,4495,10450,10541,3203,2888,2892,2893,2902,2903,2908,2909,2911,2912,2915,2916,2919,2922,2936,2943,2952,2963,2964,2965,2966,2981,3021,3030,3031,3033,3040,3046,3056,3062,3078,4476,3868,11619,3131,11334,3246,10220,10289,10292,10384,10387,10680,11349,11352,11468,11512,11517,3223,3758,3121,3497,3853,11384,3180,3147,3142,3128,3129,3771,3348,3216,3395,4562,3940,4505,10280,10447,3279,11708,4551,10999,11069,11293,11296,3396,3177,10349,10656,3178,3454,3100,3199,11374,4087,3942,11005,11131,11182,4575,10937,11136,11241,11263,11301,11307,4576,11038,11139,11244,4577,11142,4578,11196,4579,3198,3495,3661,4371,4372,4503,3598,3816,3359,10368,10486,10555,10616,10619,10659,10753,10989,3751,11605,3272,3371,4545,10257,10260,10286,10761,10774,10895,11285,11377,4557,11487,11520,11555,3738,3504,3890,3318,3319,3293,4542,4500,3487,4558,4081,11258,3619,3331,11732,4051,3952,10829,4003,3662,4040,3680,11011,11074,11155,4563,10777,11147,3289,10377,10473,10602,10666,11460,11679,3290,10735,10780,10783,10816,10842,10879,10917,3291,10406,10461,10671,10756,10882,3292,3367,4541,10323,10415,10526,10550,10798,10845,10855,11534,11633,11654,11657,11660,3449,10622,10890,10934,11204,11282,11445,4553,10807,10819,10926,10944,10947,11002,11088,11096,11112,11150,11167,11176,11212,11253,11273,11276,11279,11310,11317,11320,11705,3352,10653,10683,10692,3391,3385,3820,3756,10326,11608,4550,10277,10647,10650,11091,11109,11571,11624,11668,3312,10686,10839,10910,3781,4131,4548,3828,4531,4533,3263,3264,4532,4535,4536,3609,4231,4565,10245,10248,10507,10558,10561,10566,10976,11439,4573,11170,11290,4017,3907,11323,11663,11667,3745,10950,10956,3594,3747,10689,11027,11179,11209,3560,10608,10611,10695,10869,4569,11602,4559,4570,10746,10848,11158,11442,4191,4092,3780,3724,4567,10299,10302,10641,10644,11484,4568,11582,3749,10605,4024,4590,4616,4665,4667,4698,4715,4722,4723,4759,4764,4794,4800,4884,4909,4910,4925,4947,4972,4973,4995,4996,5009,5013,5036,5042,5058,5061,5062,5063,5068,5069,5091,5116,5117,5127,5132,5138,5175,5176,5184,5193,5198,5200,5211,5213,5219,5223,5224,5237,5244,5247,5248,5249,5253,5289,5302,5310,5312,5313,5317,5318,5319,5327,5330,5335,5336,5337,5344,5348,5349,5350,5359,5363,5364,5365,5370,5383,5392,5404,5406,5414,5415,5419,5423,5448,5454,5464,5465,5480,5493,5515,5521,5539,5540,5543,5562,5570,5571,5576,5577,5587,5589,5601,5605,5614,5615,5617,5632,5637,5647,5648,5660,5667,5681,5685,5688,5694,5695,5696,5699,5704,5740,5741,5744,5746,5749,5750,5751,5753,5755,5757,5762,5769,5784,5798,5803,5804,5817,5818,5823,5827,5829,5834,5875,5887,5896,5900,5909,5913,5914,5922,5936,5942,5960,5963,5975,6002,6016,6041,6061,6062,6065,6080,6082,6083,6085,6098,6099,6102,6104,6107,6108,6120,6126,6127,6128,6130,6132,6169,6170,6175,6178,6184,6188,6224,6226,6228,6230,6239,6241,6243,6249,6251,6257,6260,6268,6275,6276,6277,6282,6304,6305,6306,6308,6314,6319,6353,6354,6358,6359,6360,6361,6362,6363,6364,6371,6404,6405,6414,6435,6436,6456,6458,6469,6470,6476,6506,6508,6522,6560,6562,6563,6616,6641,6683,6703,6712,6713,6714,6715,6734,6735,6741,6754,6757,6759,6761,6762,6763,6765,6779,6790,6792,6793,6806,6810,6861,6872,6874,6878,6895,6896,6932,6944,6975,6994,7009,7063,7091,7146,7167,7176,7179,7234,7242,7300,7302,7317,7325,7328,7329,7348,7354,7356,7405,7415,7418,7434,7486,7487,7491,7535,7536,7554,7621,7640,7663,7687,7702,7718,7728,7737,7738,7767,7770,7772,7782,7820,7831,7856,7914,7948,7981,8028,8044,8060,8061,8136,8190,8209,8233,8253,8277,8375,8377,8383,8400,8404,8420,8443,8454,8456,8471,8476,8480,8503,8517,8518,8534,8535,8540,8541,8542,8543,8544,8562,8563,8564,8572,8585,8587,8599,8603,8605,8606,8607,8615,8620,8647,8648,8679,8692,8696,8714,8736,8737,8738,8739,8751,8752,8774,8784,8794,8795,8796,8797,8799,8821,8822,8833,8877,8883,8889,8902,8907,8909,8912,8913,8917,8927,9009,9040,9041,9042,9057,9074,9080,9108,9109,9150,9153,9179,9224,9225,9226,9241,9266,9280,9286,9289,9311,9312,9340,9402,9437,9438,9439,9464,9465,9483,9501,9507,9521,9544,9566,9574,9575,9576,9577,9592,9594,9599,9630,9631,9637,9638,9682,9683,9714,9723,9733,9735,9736,9745,9759,9762,9790,9823,9825,9829,9886,9927,9928,9930,9940,9941,9961,9966,10007,10059,10131,10132,10185,10201,2,8,9,4603,4604,4622,4653,4655,4656,4684,4690,4691,4702,4751,4753,4785,4799,4829,4926,4927,4940,4960,5016,5017,5020,5021,5023,5025,5026,5035,5038,5039,5047,5059,5060,5066,5086,5087,5104,5109,5110,5111,5112,5115,5123,5126,5133,5190,5196,5197,5205,5234,5245,5251,5267,5287,5288,5295,5296,5297,5306,5316,5323,5325,5326,5332,5340,5341,5351,5355,5356,5357,5358,5360,5361,5366,5367,5368,5369,5400,5401,5402,5410,5411,5412,5413,5459,5461,5463,5500,5502,5503,5505,5506,5508,5509,5511,5520,5525,5527,5528,5529,5530,5531,5532,5541,5551,5554,5565,5581,5582,5585,5595,5597,5598,5599,5624,5634,5650,5651,5661,5662,5664,5666,5671,5706,5711,5713,5771,5805,5806,5810,5816,5819,5820,5821,5822,5828,5839,5840,5842,5843,5851,5872,5901,5917,5920,5921,5923,5932,5953,5954,5955,5958,5959,5977,5988,5989,6018,6019,6023,6043,6046,6050,6069,6074,6075,6100,6103,6111,6119,6125,6129,6136,6137])). % 172.88/172.54 cnf(11760,plain, % 172.88/172.54 (P102(f332(f332(f201(a24),x117601),x117601))), % 172.88/172.54 inference(rename_variables,[],[3289])). % 172.88/172.54 cnf(11763,plain, % 172.88/172.54 (P102(f332(f332(f246(a1),x117631),x117631))), % 172.88/172.54 inference(rename_variables,[],[3291])). % 172.88/172.54 cnf(11772,plain, % 172.88/172.54 (~P102(f332(f332(f247(a876),x117721),f2(a876)))), % 172.88/172.54 inference(rename_variables,[],[4545])). % 172.88/172.54 cnf(11775,plain, % 172.88/172.54 (P102(f332(f332(f246(a1),x117751),x117751))), % 172.88/172.54 inference(rename_variables,[],[3291])). % 172.88/172.54 cnf(11780,plain, % 172.88/172.54 (~P102(f332(f332(f247(a876),x117801),f2(a876)))), % 172.88/172.54 inference(rename_variables,[],[4545])). % 172.88/172.54 cnf(11787,plain, % 172.88/172.54 (P102(f332(f255(f883(x117871,a871)),x117872))), % 172.88/172.54 inference(rename_variables,[],[3352])). % 172.88/172.54 cnf(11792,plain, % 172.88/172.54 (P102(f332(f332(f246(a876),f2(a876)),x117921))), % 172.88/172.54 inference(rename_variables,[],[3312])). % 172.88/172.54 cnf(11793,plain, % 172.88/172.54 (~P102(f332(f332(f246(a876),f332(a115,x117931)),x117931))), % 172.88/172.54 inference(rename_variables,[],[4550])). % 172.88/172.54 cnf(11796,plain, % 172.88/172.54 (~P102(f332(f62(x117961,x117962,f195(f883(x117961,a871))),x117963))), % 172.88/172.54 inference(rename_variables,[],[4565])). % 172.88/172.54 cnf(11818,plain, % 172.88/172.54 (~P102(f332(f332(f247(a876),x118181),x118181))), % 172.88/172.54 inference(rename_variables,[],[4541])). % 172.88/172.54 cnf(11821,plain, % 172.88/172.54 (~P102(f332(f332(f247(a876),x118211),x118211))), % 172.88/172.54 inference(rename_variables,[],[4541])). % 172.88/172.54 cnf(11824,plain, % 172.88/172.54 (~P102(f332(f332(f247(a876),x118241),x118241))), % 172.88/172.54 inference(rename_variables,[],[4541])). % 172.88/172.54 cnf(11827,plain, % 172.88/172.54 (~P102(f332(f332(f247(a876),x118271),x118271))), % 172.88/172.54 inference(rename_variables,[],[4541])). % 172.88/172.54 cnf(11830,plain, % 172.88/172.54 (~P102(f332(f332(f246(a876),f332(a115,x118301)),x118301))), % 172.88/172.54 inference(rename_variables,[],[4550])). % 172.88/172.54 cnf(11833,plain, % 172.88/172.54 (~P102(f332(f332(f246(a876),f332(a115,x118331)),x118331))), % 172.88/172.54 inference(rename_variables,[],[4550])). % 172.88/172.54 cnf(11836,plain, % 172.88/172.54 (~P102(f332(f332(f246(a876),f332(a115,x118361)),x118361))), % 172.88/172.54 inference(rename_variables,[],[4550])). % 172.88/172.54 cnf(11839,plain, % 172.88/172.54 (~P102(f332(f332(f246(a876),f332(a115,x118391)),x118391))), % 172.88/172.54 inference(rename_variables,[],[4550])). % 172.88/172.54 cnf(11856,plain, % 172.88/172.54 (P102(f332(f332(f201(a24),x118561),x118561))), % 172.88/172.54 inference(rename_variables,[],[3289])). % 172.88/172.54 cnf(11862,plain, % 172.88/172.54 (P102(f332(f332(f246(a1),x118621),x118621))), % 172.88/172.54 inference(rename_variables,[],[3291])). % 172.88/172.54 cnf(11873,plain, % 172.88/172.54 (P102(f332(f332(f246(a1),x118731),x118731))), % 172.88/172.54 inference(rename_variables,[],[3291])). % 172.88/172.54 cnf(11876,plain, % 172.88/172.54 (P102(f332(f332(f246(f883(f882(f877(x118761),f877(x118761)),a871)),f158(x118761,x118762)),f308(f877(x118761),f157(x118761,x118762))))), % 172.88/172.54 inference(rename_variables,[],[4008])). % 172.88/172.54 cnf(11883,plain, % 172.88/172.54 (P102(f332(f332(f247(a876),x118831),f332(a115,x118831)))), % 172.88/172.54 inference(rename_variables,[],[3359])). % 172.88/172.54 cnf(11886,plain, % 172.88/172.54 (P102(f332(f332(f334(f883(x118861,a871)),x118862),f332(f309(x118861),x118862)))), % 172.88/172.54 inference(rename_variables,[],[3662])). % 172.88/172.54 cnf(11887,plain, % 172.88/172.54 (~E(f332(a115,x118871),x118871)), % 172.88/172.54 inference(rename_variables,[],[4480])). % 172.88/172.54 cnf(11894,plain, % 172.88/172.54 (P102(f332(f332(f246(a1),x118941),x118941))), % 172.88/172.54 inference(rename_variables,[],[3291])). % 172.88/172.54 cnf(11899,plain, % 172.88/172.54 (P102(f332(f332(f246(a1),x118991),x118991))), % 172.88/172.54 inference(rename_variables,[],[3291])). % 172.88/172.54 cnf(11908,plain, % 172.88/172.54 (P102(f332(f332(f246(f883(x119081,a871)),x119082),f332(f332(f310(x119081),x119083),x119082)))), % 172.88/172.54 inference(rename_variables,[],[3745])). % 172.88/172.54 cnf(11911,plain, % 172.88/172.54 (P102(f332(f332(f201(a24),x119111),x119111))), % 172.88/172.54 inference(rename_variables,[],[3289])). % 172.88/172.54 cnf(11912,plain, % 172.88/172.54 (~E(f332(a115,x119121),x119121)), % 172.88/172.54 inference(rename_variables,[],[4480])). % 172.88/172.54 cnf(11923,plain, % 172.88/172.54 (~P102(f332(f332(f247(a876),x119231),x119231))), % 172.88/172.54 inference(rename_variables,[],[4541])). % 172.88/172.54 cnf(11924,plain, % 172.88/172.54 (~E(f332(a115,x119241),x119241)), % 172.88/172.54 inference(rename_variables,[],[4480])). % 172.88/172.54 cnf(11927,plain, % 172.88/172.54 (P102(f332(f332(f246(a876),x119271),x119271))), % 172.88/172.54 inference(rename_variables,[],[3290])). % 172.88/172.54 cnf(11930,plain, % 172.88/172.54 (P102(f332(f332(f246(a876),x119301),x119301))), % 172.88/172.54 inference(rename_variables,[],[3290])). % 172.88/172.54 cnf(11933,plain, % 172.88/172.54 (P102(f332(f332(f246(a876),x119331),x119331))), % 172.88/172.54 inference(rename_variables,[],[3290])). % 172.88/172.54 cnf(11936,plain, % 172.88/172.54 (P102(f332(f332(f246(a876),x119361),x119361))), % 172.88/172.54 inference(rename_variables,[],[3290])). % 172.88/172.54 cnf(11939,plain, % 172.88/172.54 (P102(f332(f332(f246(a1),x119391),x119391))), % 172.88/172.54 inference(rename_variables,[],[3291])). % 172.88/172.54 cnf(11942,plain, % 172.88/172.54 (~P102(f332(f332(f247(a876),x119421),x119421))), % 172.88/172.54 inference(rename_variables,[],[4541])). % 172.88/172.54 cnf(11945,plain, % 172.88/172.54 (~P102(f332(f332(f247(a876),x119451),x119451))), % 172.88/172.54 inference(rename_variables,[],[4541])). % 172.88/172.54 cnf(11946,plain, % 172.88/172.54 (P102(f332(f332(f247(a876),x119461),f332(a115,x119461)))), % 172.88/172.54 inference(rename_variables,[],[3359])). % 172.88/172.54 cnf(11953,plain, % 172.88/172.54 (~E(f332(a115,x119531),x119531)), % 172.88/172.54 inference(rename_variables,[],[4480])). % 172.88/172.54 cnf(11958,plain, % 172.88/172.54 (~P102(f332(f332(f247(a876),x119581),x119581))), % 172.88/172.54 inference(rename_variables,[],[4541])). % 172.88/172.54 cnf(11959,plain, % 172.88/172.54 (~E(f332(a115,x119591),x119591)), % 172.88/172.54 inference(rename_variables,[],[4480])). % 172.88/172.54 cnf(11964,plain, % 172.88/172.54 (P102(f332(f332(f246(a1),x119641),x119641))), % 172.88/172.54 inference(rename_variables,[],[3291])). % 172.88/172.54 cnf(11979,plain, % 172.88/172.54 (P102(f332(f332(f246(a1),x119791),x119791))), % 172.88/172.54 inference(rename_variables,[],[3291])). % 172.88/172.54 cnf(11984,plain, % 172.88/172.54 (P102(f332(f332(f246(a876),f2(a876)),x119841))), % 172.88/172.54 inference(rename_variables,[],[3312])). % 172.88/172.54 cnf(12001,plain, % 172.88/172.54 (~P102(f332(f332(f247(a876),x120011),f2(a876)))), % 172.88/172.54 inference(rename_variables,[],[4545])). % 172.88/172.54 cnf(12004,plain, % 172.88/172.54 (~P102(f332(f332(f247(a876),x120041),f2(a876)))), % 172.88/172.54 inference(rename_variables,[],[4545])). % 172.88/172.54 cnf(12007,plain, % 172.88/172.54 (~P102(f332(f332(f334(x120071),x120072),f195(f883(x120071,a871))))), % 172.88/172.54 inference(rename_variables,[],[4553])). % 172.88/172.54 cnf(12010,plain, % 172.88/172.54 (~P102(f332(f332(f334(x120101),x120102),f195(f883(x120101,a871))))), % 172.88/172.54 inference(rename_variables,[],[4553])). % 172.88/172.54 cnf(12013,plain, % 172.88/172.54 (~P102(f332(f332(f247(a876),x120131),x120131))), % 172.88/172.54 inference(rename_variables,[],[4541])). % 172.88/172.54 cnf(12015,plain, % 172.88/172.54 (~P102(f332(f332(f247(a876),x120151),f332(f332(f104(a876),x120151),x120152)))), % 172.88/172.54 inference(scs_inference,[],[4572,3534,4513,4514,4480,10217,10227,10240,10251,10254,10357,10360,10363,10466,10577,10885,11049,11052,11250,11337,11344,11358,11410,11413,11457,11525,11572,11588,11887,11912,11924,11953,4495,10450,10541,3503,3203,2888,2892,2893,2902,2903,2908,2909,2911,2912,2915,2916,2919,2922,2925,2936,2943,2952,2962,2963,2964,2965,2966,2981,3021,3030,3031,3033,3040,3046,3048,3056,3062,3078,4476,3868,11619,3131,11334,3246,10220,10289,10292,10384,10387,10680,11349,11352,11468,11512,11517,3223,3231,3758,4000,3121,3497,3853,11384,3180,3147,3142,3128,3129,3771,3348,3216,3395,4562,3940,4505,10280,10447,3279,11708,4551,10999,11069,11293,11296,3396,3177,10349,10656,3178,3454,3100,3199,11374,4087,3942,11005,11131,11182,4575,10937,11136,11241,11263,11301,11307,4576,11038,11139,11244,4577,11142,4578,11196,4579,3198,3495,3661,4371,4372,4503,3598,3816,3359,10368,10486,10555,10616,10619,10659,10753,10989,11883,3751,11605,3272,3371,4545,10257,10260,10286,10761,10774,10895,11285,11377,11772,11780,12001,4557,11487,11520,11555,11585,3738,3504,3890,3318,3319,3293,4542,4500,3487,4558,4081,11258,3619,3331,11732,4051,4008,3952,10829,4003,3662,4040,3680,11011,11074,11155,4563,10777,11147,3289,10377,10473,10602,10666,11460,11679,11726,11760,11856,3290,10735,10780,10783,10816,10842,10879,10917,10953,11927,11930,11933,11936,3291,10406,10461,10671,10756,10882,11568,11763,11775,11862,11873,11894,11899,11939,11964,3292,3367,4541,10323,10415,10526,10550,10798,10845,10855,11534,11633,11654,11657,11660,11676,11818,11821,11824,11827,11923,11942,11945,11958,12013,3449,10622,10890,10934,11204,11282,11445,4553,10807,10819,10926,10944,10947,11002,11088,11096,11112,11150,11167,11176,11212,11253,11273,11276,11279,11310,11317,11320,11705,11741,12007,3352,10653,10683,10692,11233,3391,3385,3820,3756,10326,11608,11636,4550,10277,10647,10650,11091,11109,11571,11624,11668,11689,11793,11830,11833,11836,11839,3312,10686,10839,10910,11637,11792,3781,4131,4548,3792,3828,4531,4533,3263,3264,4532,4535,4536,3799,3609,4231,4565,10245,10248,10507,10558,10561,10566,10976,11439,11692,11796,4573,11170,11290,4017,3907,11323,11663,11667,3745,10950,10956,10971,3594,3747,10689,11027,11179,11209,3560,10608,10611,10695,10869,4569,11602,4559,4570,10746,10848,11158,11442,4191,4092,3780,3724,4567,10299,10302,10641,10644,11484,4568,11582,3749,10605,4024,4590,4616,4665,4667,4698,4715,4722,4723,4759,4764,4794,4800,4884,4909,4910,4925,4947,4972,4973,4995,4996,5009,5013,5036,5042,5058,5061,5062,5063,5068,5069,5091,5116,5117,5127,5132,5138,5175,5176,5184,5193,5198,5200,5211,5213,5219,5223,5224,5237,5244,5247,5248,5249,5253,5289,5302,5310,5312,5313,5317,5318,5319,5327,5330,5335,5336,5337,5344,5348,5349,5350,5359,5363,5364,5365,5370,5383,5392,5404,5406,5414,5415,5419,5423,5448,5454,5464,5465,5480,5493,5515,5521,5539,5540,5543,5562,5570,5571,5576,5577,5587,5589,5601,5605,5614,5615,5617,5632,5637,5647,5648,5660,5667,5681,5685,5688,5694,5695,5696,5699,5704,5740,5741,5744,5746,5749,5750,5751,5753,5755,5757,5762,5769,5784,5798,5803,5804,5817,5818,5823,5827,5829,5834,5875,5887,5896,5900,5909,5913,5914,5922,5936,5942,5960,5963,5975,6002,6016,6041,6061,6062,6065,6080,6082,6083,6085,6098,6099,6102,6104,6107,6108,6120,6126,6127,6128,6130,6132,6169,6170,6175,6178,6184,6188,6224,6226,6228,6230,6239,6241,6243,6249,6251,6257,6260,6268,6275,6276,6277,6282,6304,6305,6306,6308,6314,6319,6353,6354,6358,6359,6360,6361,6362,6363,6364,6371,6404,6405,6414,6435,6436,6456,6458,6469,6470,6476,6506,6508,6522,6560,6562,6563,6616,6641,6683,6703,6712,6713,6714,6715,6734,6735,6741,6754,6757,6759,6761,6762,6763,6765,6779,6790,6792,6793,6806,6810,6861,6872,6874,6878,6895,6896,6932,6944,6975,6994,7009,7063,7091,7146,7167,7176,7179,7234,7242,7300,7302,7317,7325,7328,7329,7348,7354,7356,7405,7415,7418,7434,7486,7487,7491,7535,7536,7554,7621,7640,7663,7687,7702,7718,7728,7737,7738,7767,7770,7772,7782,7820,7831,7856,7914,7948,7981,8028,8044,8060,8061,8136,8190,8209,8233,8253,8277,8375,8377,8383,8400,8404,8420,8443,8454,8456,8471,8476,8480,8503,8517,8518,8534,8535,8540,8541,8542,8543,8544,8562,8563,8564,8572,8585,8587,8599,8603,8605,8606,8607,8615,8620,8647,8648,8679,8692,8696,8714,8736,8737,8738,8739,8751,8752,8774,8784,8794,8795,8796,8797,8799,8821,8822,8833,8877,8883,8889,8902,8907,8909,8912,8913,8917,8927,9009,9040,9041,9042,9057,9074,9080,9108,9109,9150,9153,9179,9224,9225,9226,9241,9266,9280,9286,9289,9311,9312,9340,9402,9437,9438,9439,9464,9465,9483,9501,9507,9521,9544,9566,9574,9575,9576,9577,9592,9594,9599,9630,9631,9637,9638,9682,9683,9714,9723,9733,9735,9736,9745,9759,9762,9790,9823,9825,9829,9886,9927,9928,9930,9940,9941,9961,9966,10007,10059,10131,10132,10185,10201,2,8,9,4603,4604,4622,4653,4655,4656,4684,4690,4691,4702,4751,4753,4785,4799,4829,4926,4927,4940,4960,5016,5017,5020,5021,5023,5025,5026,5035,5038,5039,5047,5059,5060,5066,5086,5087,5104,5109,5110,5111,5112,5115,5123,5126,5133,5190,5196,5197,5205,5234,5245,5251,5267,5287,5288,5295,5296,5297,5306,5316,5323,5325,5326,5332,5340,5341,5351,5355,5356,5357,5358,5360,5361,5366,5367,5368,5369,5400,5401,5402,5410,5411,5412,5413,5459,5461,5463,5500,5502,5503,5505,5506,5508,5509,5511,5520,5525,5527,5528,5529,5530,5531,5532,5541,5551,5554,5565,5581,5582,5585,5595,5597,5598,5599,5624,5634,5650,5651,5661,5662,5664,5666,5671,5706,5711,5713,5771,5805,5806,5810,5816,5819,5820,5821,5822,5828,5839,5840,5842,5843,5851,5872,5901,5917,5920,5921,5923,5932,5953,5954,5955,5958,5959,5977,5988,5989,6018,6019,6023,6043,6046,6050,6069,6074,6075,6100,6103,6111,6119,6125,6129,6136,6137,6138,6139,6172,6189,6242,6278,6280,6301,6302,6307,6310,6311,6315,6321,6330,6346,6366,6367,6372,6382,6397,6417,6423,6425,6440,6441,6444,6445,6447,6449,6450,6451,6453,6455,6457,6463,6464,6465,6466,6472,6474,6516,6521,6536,6537,6538,6539,6574,6579,6581,6586,6587,6595,6599,6612,6637,6638,6639,6640,6651,6657,6673,6677,6696,6729,6730,6731,6736,6750,6771,6773,6775,6777,6780,6786,6788,6803,6808,6811,6847,6850,6851,6864,6865,6866,6867,6886,6887,6904,6930,6952,6963,6965,6966,6968,6970,6971,7006,7007,7012,7013,7014,7015])). % 172.88/172.54 cnf(12016,plain, % 172.88/172.54 (~P102(f332(f332(f247(a876),x120161),x120161))), % 172.88/172.54 inference(rename_variables,[],[4541])). % 172.88/172.54 cnf(12019,plain, % 172.88/172.54 (~P102(f332(f332(f247(a876),x120191),x120191))), % 172.88/172.54 inference(rename_variables,[],[4541])). % 172.88/172.54 cnf(12022,plain, % 172.88/172.54 (~P102(f332(f332(f247(a876),x120221),x120221))), % 172.88/172.54 inference(rename_variables,[],[4541])). % 172.88/172.54 cnf(12025,plain, % 172.88/172.54 (P102(f332(f332(f247(a876),x120251),f332(a115,x120251)))), % 172.88/172.54 inference(rename_variables,[],[3359])). % 172.88/172.54 cnf(12032,plain, % 172.88/172.54 (P102(f332(f332(f334(f883(x120321,a871)),x120322),f332(f309(x120321),x120322)))), % 172.88/172.54 inference(rename_variables,[],[3662])). % 172.88/172.54 cnf(12037,plain, % 172.88/172.54 (P102(f332(f332(f246(f883(x120371,a871)),x120372),f332(f332(f310(x120371),x120373),x120372)))), % 172.88/172.54 inference(rename_variables,[],[3745])). % 172.88/172.54 cnf(12044,plain, % 172.88/172.54 (~P102(f332(f332(f334(x120441),x120442),f195(f883(x120441,a871))))), % 172.88/172.54 inference(rename_variables,[],[4553])). % 172.88/172.54 cnf(12053,plain, % 172.88/172.54 (P102(f332(f332(f246(f883(x120531,a871)),x120532),f255(f883(x120531,a871))))), % 172.88/172.54 inference(rename_variables,[],[3680])). % 172.88/172.54 cnf(12054,plain, % 172.88/172.54 (~E(f332(a115,x120541),x120541)), % 172.88/172.54 inference(rename_variables,[],[4480])). % 172.88/172.54 cnf(12057,plain, % 172.88/172.54 (P102(f332(f332(f246(f883(x120571,a871)),f195(f883(x120571,a871))),x120572))), % 172.88/172.54 inference(rename_variables,[],[3747])). % 172.88/172.54 cnf(12060,plain, % 172.88/172.54 (P102(f332(f332(f246(f883(x120601,a871)),f332(f173(x120601),f332(f136(x120601,x120602),x120603))),f332(f173(x120601),x120603)))), % 172.88/172.54 inference(rename_variables,[],[3952])). % 172.88/172.54 cnf(12066,plain, % 172.88/172.54 (P102(f332(f332(f247(a876),x120661),f332(a115,x120661)))), % 172.88/172.54 inference(rename_variables,[],[3359])). % 172.88/172.54 cnf(12075,plain, % 172.88/172.54 (E(f332(f263(x120751,x120751),f264(x120751,x120752)),x120752)), % 172.88/172.54 inference(rename_variables,[],[3246])). % 172.88/172.54 cnf(12086,plain, % 172.88/172.54 (P102(f332(f61(x120861),f195(f883(x120861,a871))))), % 172.88/172.54 inference(rename_variables,[],[3367])). % 172.88/172.54 cnf(12087,plain, % 172.88/172.54 (~P102(f332(f332(f334(x120871),x120872),f195(f883(x120871,a871))))), % 172.88/172.54 inference(rename_variables,[],[4553])). % 172.88/172.54 cnf(12092,plain, % 172.88/172.54 (~P102(f332(f332(f247(a876),x120921),f2(a876)))), % 172.88/172.54 inference(rename_variables,[],[4545])). % 172.88/172.54 cnf(12093,plain, % 172.88/172.54 (~P102(f332(f332(f247(a876),x120931),x120931))), % 172.88/172.54 inference(rename_variables,[],[4541])). % 172.88/172.54 cnf(12098,plain, % 172.88/172.54 (P102(f332(f332(f246(f883(x120981,a871)),f332(f173(x120981),f177(x120981,x120982,x120983))),f332(f173(x120981),x120982)))), % 172.88/172.54 inference(rename_variables,[],[4003])). % 172.88/172.54 cnf(12101,plain, % 172.88/172.54 (P20(x121011,x121011,f5(x121011),x121012)), % 172.88/172.54 inference(rename_variables,[],[3534])). % 172.88/172.54 cnf(12106,plain, % 172.88/172.54 (P102(f332(f332(f334(f883(x121061,a871)),x121062),f332(f309(x121061),x121062)))), % 172.88/172.54 inference(rename_variables,[],[3662])). % 172.88/172.54 cnf(12113,plain, % 172.88/172.54 (P102(f332(f332(f201(a24),x121131),x121131))), % 172.88/172.54 inference(rename_variables,[],[3289])). % 172.88/172.54 cnf(12116,plain, % 172.88/172.54 (~P102(f332(f332(f334(x121161),x121162),f195(f883(x121161,a871))))), % 172.88/172.54 inference(rename_variables,[],[4553])). % 172.88/172.54 cnf(12119,plain, % 172.88/172.54 (P102(f332(f332(f246(f883(x121191,a871)),x121192),f332(f332(f310(x121191),x121193),x121192)))), % 172.88/172.54 inference(rename_variables,[],[3745])). % 172.88/172.54 cnf(12120,plain, % 172.88/172.54 (P102(f332(f332(f246(f883(x121201,a871)),x121202),f255(f883(x121201,a871))))), % 172.88/172.54 inference(rename_variables,[],[3680])). % 172.88/172.54 cnf(12127,plain, % 172.88/172.54 (P102(f332(f332(f247(a876),x121271),f332(a115,x121271)))), % 172.88/172.54 inference(rename_variables,[],[3359])). % 172.88/172.54 cnf(12130,plain, % 172.88/172.54 (P102(f332(f332(f247(a876),x121301),f332(a115,x121301)))), % 172.88/172.54 inference(rename_variables,[],[3359])). % 172.88/172.54 cnf(12133,plain, % 172.88/172.54 (P102(f332(f332(f246(a876),x121331),x121331))), % 172.88/172.54 inference(rename_variables,[],[3290])). % 172.88/172.54 cnf(12136,plain, % 172.88/172.54 (P102(f332(f332(f246(a876),x121361),x121361))), % 172.88/172.54 inference(rename_variables,[],[3290])). % 172.88/172.54 cnf(12139,plain, % 172.88/172.54 (P102(f332(f332(f246(a876),x121391),x121391))), % 172.88/172.54 inference(rename_variables,[],[3290])). % 172.88/172.54 cnf(12142,plain, % 172.88/172.54 (P102(f332(f332(f246(a876),x121421),x121421))), % 172.88/172.54 inference(rename_variables,[],[3290])). % 172.88/172.54 cnf(12145,plain, % 172.88/172.54 (P102(f332(f332(f246(f883(x121451,a871)),x121452),x121452))), % 172.88/172.54 inference(rename_variables,[],[3594])). % 172.88/172.54 cnf(12152,plain, % 172.88/172.54 (P102(f332(f332(f334(f883(x121521,a871)),x121522),f332(f309(x121521),x121522)))), % 172.88/172.54 inference(rename_variables,[],[3662])). % 172.88/172.54 cnf(12156,plain, % 172.88/172.54 (~P102(f332(f332(f247(a1),f332(f332(f79(a1),a82),a82)),f2(a1)))), % 172.88/172.54 inference(scs_inference,[],[4572,3534,11064,4513,4514,4480,10217,10227,10240,10251,10254,10357,10360,10363,10466,10577,10885,11049,11052,11250,11337,11344,11358,11410,11413,11457,11525,11572,11588,11887,11912,11924,11953,11959,4495,10450,10541,3503,3203,2888,2892,2893,2902,2903,2908,2909,2911,2912,2914,2915,2916,2918,2919,2922,2925,2936,2943,2952,2962,2963,2964,2965,2966,2981,3021,3030,3031,3033,3040,3046,3048,3056,3062,3078,4476,3868,11619,3131,11334,3246,10220,10289,10292,10384,10387,10680,11349,11352,11468,11512,11517,11614,3223,3231,3758,4000,3121,3497,3853,11384,3180,3147,3142,3128,3129,3771,3348,3216,3395,4562,3940,4505,10280,10447,3279,11708,4551,10999,11069,11293,11296,3396,3177,10349,10656,3178,3454,3100,3199,11374,4087,3942,11005,11131,11182,4575,10937,11136,11241,11263,11301,11307,4576,11038,11139,11244,4577,11142,4578,11196,4579,3198,3495,3661,4371,4372,4503,3598,3816,3480,3740,3359,10368,10486,10555,10616,10619,10659,10753,10989,11883,11946,12025,12066,12127,3751,11605,3272,3371,3559,4545,10257,10260,10286,10761,10774,10895,11285,11377,11772,11780,12001,12004,4557,11487,11520,11555,11585,3738,3504,3890,3318,3319,3293,4542,4500,3487,4558,4081,11258,3619,3331,11732,11735,4051,4008,3952,10829,4003,11008,3662,11886,12032,12106,4040,3680,11011,11074,11155,11215,12053,4563,10777,11147,3289,10377,10473,10602,10666,11460,11679,11726,11760,11856,11911,3290,10735,10780,10783,10816,10842,10879,10917,10953,11927,11930,11933,11936,12133,12136,12139,3291,10406,10461,10671,10756,10882,11568,11763,11775,11862,11873,11894,11899,11939,11964,3292,3367,12086,4541,10323,10415,10526,10550,10798,10845,10855,11534,11633,11654,11657,11660,11676,11818,11821,11824,11827,11923,11942,11945,11958,12013,12016,12019,12022,3449,10622,10890,10934,11204,11282,11445,4553,10807,10819,10926,10944,10947,11002,11088,11096,11112,11150,11167,11176,11212,11253,11273,11276,11279,11310,11317,11320,11705,11741,12007,12010,12044,12087,3352,10653,10683,10692,11233,3391,3385,3820,3756,10326,11608,11636,4550,10277,10647,10650,11091,11109,11571,11624,11668,11689,11793,11830,11833,11836,11839,3312,10686,10839,10910,11637,11792,3781,4131,4548,3792,3828,4531,4533,3263,3264,4532,4535,4536,3799,3609,4231,4565,10245,10248,10507,10558,10561,10566,10976,11439,11692,11796,4573,11170,11290,4017,3907,11323,11663,11667,3745,10950,10956,10971,11908,12037,3594,11173,3747,10689,11027,11179,11209,11220,3560,10608,10611,10695,10869,4569,11602,4559,4570,10746,10848,11158,11442,4191,4092,3780,3724,4567,10299,10302,10641,10644,11484,4568,11582,3749,10605,4024,4590,4616,4665,4667,4698,4715,4722,4723,4759,4764,4794,4800,4884,4909,4910,4925,4947,4972,4973,4995,4996,5009,5013,5036,5042,5058,5061,5062,5063,5068,5069,5091,5116,5117,5127,5132,5138,5175,5176,5184,5193,5198,5200,5211,5213,5219,5223,5224,5237,5244,5247,5248,5249,5253,5289,5302,5310,5312,5313,5317,5318,5319,5327,5330,5335,5336,5337,5344,5348,5349,5350,5359,5363,5364,5365,5370,5383,5392,5404,5406,5414,5415,5419,5423,5448,5454,5464,5465,5480,5493,5515,5521,5539,5540,5543,5562,5570,5571,5576,5577,5587,5589,5601,5605,5614,5615,5617,5632,5637,5647,5648,5660,5667,5681,5685,5688,5694,5695,5696,5699,5704,5740,5741,5744,5746,5749,5750,5751,5753,5755,5757,5762,5769,5784,5798,5803,5804,5817,5818,5823,5827,5829,5834,5875,5887,5896,5900,5909,5913,5914,5922,5936,5942,5960,5963,5975,6002,6016,6041,6061,6062,6065,6080,6082,6083,6085,6098,6099,6102,6104,6107,6108,6120,6126,6127,6128,6130,6132,6169,6170,6175,6178,6184,6188,6224,6226,6228,6230,6239,6241,6243,6249,6251,6257,6260,6268,6275,6276,6277,6282,6304,6305,6306,6308,6314,6319,6353,6354,6358,6359,6360,6361,6362,6363,6364,6371,6404,6405,6414,6435,6436,6456,6458,6469,6470,6476,6506,6508,6522,6560,6562,6563,6616,6641,6683,6703,6712,6713,6714,6715,6734,6735,6741,6754,6757,6759,6761,6762,6763,6765,6779,6790,6792,6793,6806,6810,6861,6872,6874,6878,6895,6896,6932,6944,6975,6994,7009,7063,7091,7146,7167,7176,7179,7234,7242,7300,7302,7317,7325,7328,7329,7348,7354,7356,7405,7415,7418,7434,7486,7487,7491,7535,7536,7554,7621,7640,7663,7687,7702,7718,7728,7737,7738,7767,7770,7772,7782,7820,7831,7856,7914,7948,7981,8028,8044,8060,8061,8136,8190,8209,8233,8253,8277,8375,8377,8383,8400,8404,8420,8443,8454,8456,8471,8476,8480,8503,8517,8518,8534,8535,8540,8541,8542,8543,8544,8562,8563,8564,8572,8585,8587,8599,8603,8605,8606,8607,8615,8620,8647,8648,8679,8692,8696,8714,8736,8737,8738,8739,8751,8752,8774,8784,8794,8795,8796,8797,8799,8821,8822,8833,8877,8883,8889,8902,8907,8909,8912,8913,8917,8927,9009,9040,9041,9042,9057,9074,9080,9108,9109,9150,9153,9179,9224,9225,9226,9241,9266,9280,9286,9289,9311,9312,9340,9402,9437,9438,9439,9464,9465,9483,9501,9507,9521,9544,9566,9574,9575,9576,9577,9592,9594,9599,9630,9631,9637,9638,9682,9683,9714,9723,9733,9735,9736,9745,9759,9762,9790,9823,9825,9829,9886,9927,9928,9930,9940,9941,9961,9966,10007,10059,10131,10132,10185,10201,2,8,9,4603,4604,4622,4653,4655,4656,4684,4690,4691,4702,4751,4753,4785,4799,4829,4926,4927,4940,4960,5016,5017,5020,5021,5023,5025,5026,5035,5038,5039,5047,5059,5060,5066,5086,5087,5104,5109,5110,5111,5112,5115,5123,5126,5133,5190,5196,5197,5205,5234,5245,5251,5267,5287,5288,5295,5296,5297,5306,5316,5323,5325,5326,5332,5340,5341,5351,5355,5356,5357,5358,5360,5361,5366,5367,5368,5369,5400,5401,5402,5410,5411,5412,5413,5459,5461,5463,5500,5502,5503,5505,5506,5508,5509,5511,5520,5525,5527,5528,5529,5530,5531,5532,5541,5551,5554,5565,5581,5582,5585,5595,5597,5598,5599,5624,5634,5650,5651,5661,5662,5664,5666,5671,5706,5711,5713,5771,5805,5806,5810,5816,5819,5820,5821,5822,5828,5839,5840,5842,5843,5851,5872,5901,5917,5920,5921,5923,5932,5953,5954,5955,5958,5959,5977,5988,5989,6018,6019,6023,6043,6046,6050,6069,6074,6075,6100,6103,6111,6119,6125,6129,6136,6137,6138,6139,6172,6189,6242,6278,6280,6301,6302,6307,6310,6311,6315,6321,6330,6346,6366,6367,6372,6382,6397,6417,6423,6425,6440,6441,6444,6445,6447,6449,6450,6451,6453,6455,6457,6463,6464,6465,6466,6472,6474,6516,6521,6536,6537,6538,6539,6574,6579,6581,6586,6587,6595,6599,6612,6637,6638,6639,6640,6651,6657,6673,6677,6696,6729,6730,6731,6736,6750,6771,6773,6775,6777,6780,6786,6788,6803,6808,6811,6847,6850,6851,6864,6865,6866,6867,6886,6887,6904,6930,6952,6963,6965,6966,6968,6970,6971,7006,7007,7012,7013,7014,7015,7017,7019,7044,7053,7054,7066,7076,7115,7125,7129,7136,7147,7153,7155,7161,7169,7170,7183,7200,7218,7220,7237,7286,7288,7289,7290,7296,7301,7324,7369,7402,7416,7433,7466,7469,7495,7519,7537,7540,7541,7551,7569,7570,7572,7574,7576,7578,7604,7629,7630,7662,7664,7665])). % 172.88/172.54 cnf(12161,plain, % 172.88/172.54 (~E(f332(a115,x121611),x121611)), % 172.88/172.54 inference(rename_variables,[],[4480])). % 172.88/172.54 cnf(12162,plain, % 172.88/172.54 (E(f332(f311(x121621,x121621,f5(x121621)),x121622),x121622)), % 172.88/172.54 inference(rename_variables,[],[3348])). % 172.88/172.54 cnf(12165,plain, % 172.88/172.54 (P33(x121651,x121652,f116(x121651),f116(x121651))), % 172.88/172.54 inference(rename_variables,[],[3543])). % 172.88/172.54 cnf(12168,plain, % 172.88/172.54 (~E(f332(a115,x121681),x121681)), % 172.88/172.54 inference(rename_variables,[],[4480])). % 172.88/172.54 cnf(12171,plain, % 172.88/172.54 (P102(f332(f332(f246(f883(x121711,a871)),f332(f173(x121711),f177(x121711,x121712,x121713))),f332(f173(x121711),x121712)))), % 172.88/172.54 inference(rename_variables,[],[4003])). % 172.88/172.54 cnf(12172,plain, % 172.88/172.54 (P102(f332(f61(x121721),f332(f173(x121721),x121722)))), % 172.88/172.54 inference(rename_variables,[],[3331])). % 172.88/172.54 cnf(12183,plain, % 172.88/172.54 (~P102(f332(f332(f247(a876),x121831),x121831))), % 172.88/172.54 inference(rename_variables,[],[4541])). % 172.88/172.54 cnf(12186,plain, % 172.88/172.54 (~P102(f332(f332(f247(a876),x121861),x121861))), % 172.88/172.54 inference(rename_variables,[],[4541])). % 172.88/172.54 cnf(12195,plain, % 172.88/172.54 (P29(a876,f332(f169(a876),f332(f332(f154(f877(x121951),a876),f196(f877(x121951))),f181(x121951,x121952))))), % 172.88/172.54 inference(rename_variables,[],[3863])). % 172.88/172.54 cnf(12198,plain, % 172.88/172.54 (P20(x121981,x121981,f5(x121981),x121982)), % 172.88/172.54 inference(rename_variables,[],[3534])). % 172.88/172.54 cnf(12201,plain, % 172.88/172.54 (P102(f332(f332(f334(f877(x122011)),f116(x122011)),f161(x122011,x122012)))), % 172.88/172.54 inference(rename_variables,[],[3495])). % 172.88/172.54 cnf(12204,plain, % 172.88/172.54 (~P102(f332(f332(f195(f883(x122041,f883(x122042,a871))),x122043),x122044))), % 172.88/172.54 inference(rename_variables,[],[4570])). % 172.88/172.54 cnf(12209,plain, % 172.88/172.54 (P102(f332(f332(f246(a876),x122091),x122091))), % 172.88/172.54 inference(rename_variables,[],[3290])). % 172.88/172.54 cnf(12210,plain, % 172.88/172.54 (P102(f332(f332(f246(a876),f2(a876)),x122101))), % 172.88/172.54 inference(rename_variables,[],[3312])). % 172.88/172.54 cnf(12213,plain, % 172.88/172.54 (~P102(f332(f332(f195(f883(x122131,f883(x122132,a871))),x122133),x122134))), % 172.88/172.54 inference(rename_variables,[],[4570])). % 172.88/172.54 cnf(12216,plain, % 172.88/172.54 (P102(f332(f332(f246(f883(f882(f877(x122161),f877(x122161)),a871)),f158(x122161,x122162)),f308(f877(x122161),f157(x122161,x122162))))), % 172.88/172.54 inference(rename_variables,[],[4008])). % 172.88/172.54 cnf(12222,plain, % 172.88/172.54 (P102(f332(f332(f246(f883(x122221,a871)),f195(f883(x122221,a871))),x122222))), % 172.88/172.54 inference(rename_variables,[],[3747])). % 172.88/172.54 cnf(12225,plain, % 172.88/172.54 (P102(f332(f332(f246(f883(x122251,a871)),f332(f311(x122252,x122251,x122253),f332(f312(x122252,x122251,x122253),x122254))),x122254))), % 172.88/172.54 inference(rename_variables,[],[4191])). % 172.88/172.54 cnf(12228,plain, % 172.88/172.54 (P102(f332(f332(f246(f883(x122281,a871)),f332(f173(x122281),f177(x122281,x122282,x122283))),f332(f173(x122281),x122282)))), % 172.88/172.54 inference(rename_variables,[],[4003])). % 172.88/172.54 cnf(12229,plain, % 172.88/172.54 (P102(f332(f332(f246(f883(x122291,a871)),f332(f173(x122291),f332(f136(x122291,x122292),x122293))),f332(f173(x122291),x122293)))), % 172.88/172.54 inference(rename_variables,[],[3952])). % 172.88/172.54 cnf(12232,plain, % 172.88/172.54 (P20(x122321,f880(x122321),f239(x122321),x122322)), % 172.88/172.54 inference(rename_variables,[],[3544])). % 172.88/172.54 cnf(12237,plain, % 172.88/172.54 (P102(f332(f332(f246(f883(x122371,a871)),f332(f311(x122372,x122371,x122373),f332(f312(x122372,x122371,x122373),x122374))),x122374))), % 172.88/172.54 inference(rename_variables,[],[4191])). % 172.88/172.54 cnf(12240,plain, % 172.88/172.54 (P102(f332(f61(f880(x122401)),f332(f311(x122402,f880(x122401),f332(f179(x122402,x122401),x122403)),f255(f883(x122402,a871)))))), % 172.88/172.54 inference(rename_variables,[],[4017])). % 172.88/172.54 cnf(12245,plain, % 172.88/172.54 (P102(f332(f332(f334(f877(x122451)),f116(x122451)),f161(x122451,x122452)))), % 172.88/172.54 inference(rename_variables,[],[3495])). % 172.88/172.54 cnf(12248,plain, % 172.88/172.54 (~P102(f332(f332(f334(f882(f877(x122481),f877(x122481))),f332(f332(f267(f877(x122481),f877(x122481)),x122482),f116(x122481))),f145(x122481,x122483)))), % 172.88/172.54 inference(rename_variables,[],[4575])). % 172.88/172.54 cnf(12251,plain, % 172.88/172.54 (~P102(f332(f332(f247(a876),x122511),f2(a876)))), % 172.88/172.54 inference(rename_variables,[],[4545])). % 172.88/172.54 cnf(12253,plain, % 172.88/172.54 (~P102(f332(f61(x122531),f255(f883(x122531,a871))))), % 172.88/172.54 inference(scs_inference,[],[4572,3534,11064,12101,3543,3544,3257,4513,4514,3156,4498,4480,10217,10227,10240,10251,10254,10357,10360,10363,10466,10577,10885,11049,11052,11250,11337,11344,11358,11410,11413,11457,11525,11572,11588,11887,11912,11924,11953,11959,12054,12161,4495,10450,10541,3503,3203,2888,2892,2893,2902,2903,2908,2909,2911,2912,2914,2915,2916,2918,2919,2922,2925,2936,2943,2952,2956,2962,2963,2964,2965,2966,2981,3021,3030,3031,3033,3040,3046,3048,3056,3062,3078,4476,3868,11619,3131,11334,3246,10220,10289,10292,10384,10387,10680,11349,11352,11468,11512,11517,11614,3223,3231,3758,4000,3121,3497,3853,11384,3180,3147,3142,3128,3129,3771,3162,3348,10832,3216,3395,4562,3940,4505,10280,10447,3279,11708,4551,10999,11069,11293,11296,3396,3177,10349,10656,3178,3454,3100,3199,11374,4087,3942,11005,11131,11182,4575,10937,11136,11241,11263,11301,11307,4576,11038,11139,11244,4577,11142,4578,11196,4579,3198,3495,12201,12245,3661,4371,4372,4503,3598,3816,3863,3480,3740,3359,10368,10486,10555,10616,10619,10659,10753,10989,11883,11946,12025,12066,12127,3751,11605,3272,3371,3559,4545,10257,10260,10286,10761,10774,10895,11285,11377,11772,11780,12001,12004,12092,4557,11487,11520,11555,11585,3738,3504,3890,3318,3319,3293,4542,4500,3487,4558,4081,11258,3619,3331,11732,11735,4051,4008,11876,12216,3952,10829,12060,4003,11008,12098,12171,3662,11886,12032,12106,12152,4040,3680,11011,11074,11155,11215,12053,4563,10777,11147,3289,10377,10473,10602,10666,11460,11679,11726,11760,11856,11911,3290,10735,10780,10783,10816,10842,10879,10917,10953,11927,11930,11933,11936,12133,12136,12139,12142,3291,10406,10461,10671,10756,10882,11568,11763,11775,11862,11873,11894,11899,11939,11964,3292,3367,12086,4541,10323,10415,10526,10550,10798,10845,10855,11534,11633,11654,11657,11660,11676,11818,11821,11824,11827,11923,11942,11945,11958,12013,12016,12019,12022,12093,12183,3449,10622,10890,10934,11204,11282,11445,11688,4553,10807,10819,10926,10944,10947,11002,11088,11096,11112,11150,11167,11176,11212,11253,11273,11276,11279,11310,11317,11320,11705,11741,12007,12010,12044,12087,3352,10653,10683,10692,11233,3391,3385,3820,3756,10326,11608,11636,4550,10277,10647,10650,11091,11109,11571,11624,11668,11689,11793,11830,11833,11836,11839,3312,10686,10839,10910,11637,11792,11984,3781,4131,4548,3792,3828,4531,4533,3263,3264,4532,4535,4536,3799,3609,4231,4565,10245,10248,10507,10558,10561,10566,10976,11439,11692,11796,4573,11170,11290,4017,3907,11323,11663,11667,3745,10950,10956,10971,11908,12037,3594,11173,12145,3747,10689,11027,11179,11209,11220,12057,3560,10608,10611,10695,10869,4569,11602,4559,4570,10746,10848,11158,11442,11473,12204,4191,10822,12225,4092,3780,3724,4567,10299,10302,10641,10644,11484,4568,11582,3749,10605,4024,4590,4616,4665,4667,4698,4715,4722,4723,4759,4764,4794,4800,4884,4909,4910,4925,4947,4972,4973,4995,4996,5009,5013,5036,5042,5058,5061,5062,5063,5068,5069,5091,5116,5117,5127,5132,5138,5175,5176,5184,5193,5198,5200,5211,5213,5219,5223,5224,5237,5244,5247,5248,5249,5253,5289,5302,5310,5312,5313,5317,5318,5319,5327,5330,5335,5336,5337,5344,5348,5349,5350,5359,5363,5364,5365,5370,5383,5392,5404,5406,5414,5415,5419,5423,5448,5454,5464,5465,5480,5493,5515,5521,5539,5540,5543,5562,5570,5571,5576,5577,5587,5589,5601,5605,5614,5615,5617,5632,5637,5647,5648,5660,5667,5681,5685,5688,5694,5695,5696,5699,5704,5740,5741,5744,5746,5749,5750,5751,5753,5755,5757,5762,5769,5784,5798,5803,5804,5817,5818,5823,5827,5829,5834,5875,5887,5896,5900,5909,5913,5914,5922,5936,5942,5960,5963,5975,6002,6016,6041,6061,6062,6065,6080,6082,6083,6085,6098,6099,6102,6104,6107,6108,6120,6126,6127,6128,6130,6132,6169,6170,6175,6178,6184,6188,6224,6226,6228,6230,6239,6241,6243,6249,6251,6257,6260,6268,6275,6276,6277,6282,6304,6305,6306,6308,6314,6319,6353,6354,6358,6359,6360,6361,6362,6363,6364,6371,6404,6405,6414,6435,6436,6456,6458,6469,6470,6476,6506,6508,6522,6560,6562,6563,6616,6641,6683,6703,6712,6713,6714,6715,6734,6735,6741,6754,6757,6759,6761,6762,6763,6765,6779,6790,6792,6793,6806,6810,6861,6872,6874,6878,6895,6896,6932,6944,6975,6994,7009,7063,7091,7146,7167,7176,7179,7234,7242,7300,7302,7317,7325,7328,7329,7348,7354,7356,7405,7415,7418,7434,7486,7487,7491,7535,7536,7554,7621,7640,7663,7687,7702,7718,7728,7737,7738,7767,7770,7772,7782,7820,7831,7856,7914,7948,7981,8028,8044,8060,8061,8136,8190,8209,8233,8253,8277,8375,8377,8383,8400,8404,8420,8443,8454,8456,8471,8476,8480,8503,8517,8518,8534,8535,8540,8541,8542,8543,8544,8562,8563,8564,8572,8585,8587,8599,8603,8605,8606,8607,8615,8620,8647,8648,8679,8692,8696,8714,8736,8737,8738,8739,8751,8752,8774,8784,8794,8795,8796,8797,8799,8821,8822,8833,8877,8883,8889,8902,8907,8909,8912,8913,8917,8927,9009,9040,9041,9042,9057,9074,9080,9108,9109,9150,9153,9179,9224,9225,9226,9241,9266,9280,9286,9289,9311,9312,9340,9402,9437,9438,9439,9464,9465,9483,9501,9507,9521,9544,9566,9574,9575,9576,9577,9592,9594,9599,9630,9631,9637,9638,9682,9683,9714,9723,9733,9735,9736,9745,9759,9762,9790,9823,9825,9829,9886,9927,9928,9930,9940,9941,9961,9966,10007,10059,10131,10132,10185,10201,2,8,9,4603,4604,4622,4653,4655,4656,4684,4690,4691,4702,4751,4753,4785,4799,4829,4926,4927,4940,4960,5016,5017,5020,5021,5023,5025,5026,5035,5038,5039,5047,5059,5060,5066,5086,5087,5104,5109,5110,5111,5112,5115,5123,5126,5133,5190,5196,5197,5205,5234,5245,5251,5267,5287,5288,5295,5296,5297,5306,5316,5323,5325,5326,5332,5340,5341,5351,5355,5356,5357,5358,5360,5361,5366,5367,5368,5369,5400,5401,5402,5410,5411,5412,5413,5459,5461,5463,5500,5502,5503,5505,5506,5508,5509,5511,5520,5525,5527,5528,5529,5530,5531,5532,5541,5551,5554,5565,5581,5582,5585,5595,5597,5598,5599,5624,5634,5650,5651,5661,5662,5664,5666,5671,5706,5711,5713,5771,5805,5806,5810,5816,5819,5820,5821,5822,5828,5839,5840,5842,5843,5851,5872,5901,5917,5920,5921,5923,5932,5953,5954,5955,5958,5959,5977,5988,5989,6018,6019,6023,6043,6046,6050,6069,6074,6075,6100,6103,6111,6119,6125,6129,6136,6137,6138,6139,6172,6189,6242,6278,6280,6301,6302,6307,6310,6311,6315,6321,6330,6346,6366,6367,6372,6382,6397,6417,6423,6425,6440,6441,6444,6445,6447,6449,6450,6451,6453,6455,6457,6463,6464,6465,6466,6472,6474,6516,6521,6536,6537,6538,6539,6574,6579,6581,6586,6587,6595,6599,6612,6637,6638,6639,6640,6651,6657,6673,6677,6696,6729,6730,6731,6736,6750,6771,6773,6775,6777,6780,6786,6788,6803,6808,6811,6847,6850,6851,6864,6865,6866,6867,6886,6887,6904,6930,6952,6963,6965,6966,6968,6970,6971,7006,7007,7012,7013,7014,7015,7017,7019,7044,7053,7054,7066,7076,7115,7125,7129,7136,7147,7153,7155,7161,7169,7170,7183,7200,7218,7220,7237,7286,7288,7289,7290,7296,7301,7324,7369,7402,7416,7433,7466,7469,7495,7519,7537,7540,7541,7551,7569,7570,7572,7574,7576,7578,7604,7629,7630,7662,7664,7665,7666,7671,7694,7703,7714,7719,7725,7727,7733,7745,7746,7748,7780,7803,7869,7870,7917,7925,7926,7950,7951,7968,7969,8036,8037,8038,8063,8096,8103,8105,8114,8126,8159,8165,8172])). % 172.88/172.54 cnf(12254,plain, % 172.88/172.54 (P102(f332(f332(f246(f883(x122541,a871)),x122542),x122542))), % 172.88/172.54 inference(rename_variables,[],[3594])). % 172.88/172.54 cnf(12257,plain, % 172.88/172.54 (~P102(f332(f332(f334(x122571),x122572),f195(f883(x122571,a871))))), % 172.88/172.54 inference(rename_variables,[],[4553])). % 172.88/172.54 cnf(12260,plain, % 172.88/172.54 (~P102(f332(f332(f195(f883(x122601,f883(x122602,a871))),x122603),x122604))), % 172.88/172.54 inference(rename_variables,[],[4570])). % 172.88/172.54 cnf(12263,plain, % 172.88/172.54 (P102(f332(f332(f246(f883(x122631,a871)),f332(f311(x122632,x122631,x122633),f332(f312(x122632,x122631,x122633),x122634))),x122634))), % 172.88/172.54 inference(rename_variables,[],[4191])). % 172.88/172.54 cnf(12264,plain, % 172.88/172.54 (P102(f332(f332(f246(f883(x122641,a871)),x122642),x122642))), % 172.88/172.54 inference(rename_variables,[],[3594])). % 172.88/172.54 cnf(12269,plain, % 172.88/172.54 (E(f332(f263(x122691,x122691),f264(x122691,x122692)),x122692)), % 172.88/172.54 inference(rename_variables,[],[3246])). % 172.88/172.54 cnf(12272,plain, % 172.88/172.54 (P102(f332(f332(f246(f883(x122721,a871)),f332(f173(x122721),f177(x122721,x122722,x122723))),f332(f173(x122721),x122722)))), % 172.88/172.54 inference(rename_variables,[],[4003])). % 172.88/172.54 cnf(12273,plain, % 172.88/172.54 (P102(f332(f61(x122731),f332(f173(x122731),x122732)))), % 172.88/172.54 inference(rename_variables,[],[3331])). % 172.88/172.54 cnf(12279,plain, % 172.88/172.54 (~P102(f332(f332(f247(a876),x122791),x122791))), % 172.88/172.54 inference(rename_variables,[],[4541])). % 172.88/172.54 cnf(12282,plain, % 172.88/172.54 (~P102(f332(f332(f247(a876),x122821),x122821))), % 172.88/172.54 inference(rename_variables,[],[4541])). % 172.88/172.54 cnf(12293,plain, % 172.88/172.54 (P20(x122931,x122931,f5(x122931),x122932)), % 172.88/172.54 inference(rename_variables,[],[3534])). % 172.88/172.54 cnf(12298,plain, % 172.88/172.54 (~P102(f332(f332(f334(x122981),x122982),f195(f883(x122981,a871))))), % 172.88/172.54 inference(rename_variables,[],[4553])). % 172.88/172.54 cnf(12301,plain, % 172.88/172.54 (P102(f332(f332(f334(f882(x123011,x123011)),f332(f332(f267(x123011,x123011),x123012),x123012)),f308(x123011,x123013)))), % 172.88/172.54 inference(rename_variables,[],[3942])). % 172.88/172.54 cnf(12304,plain, % 172.88/172.54 (~P102(f332(f332(f334(x123041),x123042),f195(f883(x123041,a871))))), % 172.88/172.54 inference(rename_variables,[],[4553])). % 172.88/172.54 cnf(12307,plain, % 172.88/172.54 (P102(f332(f332(f334(f882(x123071,x123071)),f332(f332(f267(x123071,x123071),x123072),x123072)),f308(x123071,x123073)))), % 172.88/172.54 inference(rename_variables,[],[3942])). % 172.88/172.54 cnf(12317,plain, % 172.88/172.54 (~E(f332(f332(f151(x123171),x123172),x123173),x123173)), % 172.88/172.54 inference(rename_variables,[],[4505])). % 172.88/172.54 cnf(12320,plain, % 172.88/172.54 (P102(f332(f332(f334(x123201),x123202),f255(f883(x123201,a871))))), % 172.88/172.54 inference(rename_variables,[],[3449])). % 172.88/172.54 cnf(12321,plain, % 172.88/172.54 (~E(f332(a115,x123211),x123211)), % 172.88/172.54 inference(rename_variables,[],[4480])). % 172.88/172.54 cnf(12324,plain, % 172.88/172.54 (P102(f332(f332(f334(f877(x123241)),f116(x123241)),f161(x123241,x123242)))), % 172.88/172.54 inference(rename_variables,[],[3495])). % 172.88/172.54 cnf(12325,plain, % 172.88/172.54 (~E(f332(f332(f151(x123251),x123252),x123253),f116(x123251))), % 172.88/172.54 inference(rename_variables,[],[4512])). % 172.88/172.54 cnf(12328,plain, % 172.88/172.54 (P102(f332(f332(f334(x123281),f332(x123282,x123283)),f332(f311(x123284,x123281,x123282),f255(f883(x123284,a871)))))), % 172.88/172.54 inference(rename_variables,[],[3907])). % 172.88/172.54 cnf(12329,plain, % 172.88/172.54 (P20(x123291,x123291,f5(x123291),x123292)), % 172.88/172.54 inference(rename_variables,[],[3534])). % 172.88/172.54 cnf(12332,plain, % 172.88/172.54 (P102(f332(f332(f246(f883(x123321,a871)),f195(f883(x123321,a871))),x123322))), % 172.88/172.54 inference(rename_variables,[],[3747])). % 172.88/172.54 cnf(12333,plain, % 172.88/172.54 (P102(f332(f332(f246(f883(x123331,a871)),x123332),x123332))), % 172.88/172.54 inference(rename_variables,[],[3594])). % 172.88/172.54 cnf(12336,plain, % 172.88/172.54 (P102(f332(f332(f334(x123361),f332(x123362,x123363)),f332(f311(x123364,x123361,x123362),f255(f883(x123364,a871)))))), % 172.88/172.54 inference(rename_variables,[],[3907])). % 172.88/172.54 cnf(12337,plain, % 172.88/172.54 (P20(x123371,x123371,f5(x123371),x123372)), % 172.88/172.54 inference(rename_variables,[],[3534])). % 172.88/172.54 cnf(12340,plain, % 172.88/172.54 (P102(f332(f332(f334(f882(f877(x123401),f877(x123401))),f332(f332(f267(f877(x123401),f877(x123401)),f116(x123401)),f116(x123401))),f158(x123401,x123402)))), % 172.88/172.54 inference(rename_variables,[],[4087])). % 172.88/172.54 cnf(12343,plain, % 172.88/172.54 (~P102(f332(f332(f247(a876),x123431),x123431))), % 172.88/172.54 inference(rename_variables,[],[4541])). % 172.88/172.54 cnf(12344,plain, % 172.88/172.54 (~P102(f332(f332(f247(a876),x123441),f2(a876)))), % 172.88/172.54 inference(rename_variables,[],[4545])). % 172.88/172.54 cnf(12350,plain, % 172.88/172.54 (P20(x123501,x123501,f5(x123501),x123502)), % 172.88/172.54 inference(rename_variables,[],[3534])). % 172.88/172.54 cnf(12353,plain, % 172.88/172.54 (E(f332(f332(f134(x123531),x123532),f116(x123531)),x123532)), % 172.88/172.54 inference(rename_variables,[],[3217])). % 172.88/172.54 cnf(12354,plain, % 172.88/172.54 (~E(f332(f332(f151(x123541),x123542),x123543),x123543)), % 172.88/172.54 inference(rename_variables,[],[4505])). % 172.88/172.54 cnf(12357,plain, % 172.88/172.54 (E(f332(f332(f134(x123571),x123572),f116(x123571)),x123572)), % 172.88/172.54 inference(rename_variables,[],[3217])). % 172.88/172.54 cnf(12358,plain, % 172.88/172.54 (~E(f332(f332(f151(x123581),x123582),x123583),x123583)), % 172.88/172.54 inference(rename_variables,[],[4505])). % 172.88/172.54 cnf(12361,plain, % 172.88/172.54 (E(f332(f332(f134(x123611),x123612),f116(x123611)),x123612)), % 172.88/172.54 inference(rename_variables,[],[3217])). % 172.88/172.54 cnf(12370,plain, % 172.88/172.54 (P102(f332(f332(f246(f883(x123701,a871)),x123702),f255(f883(x123701,a871))))), % 172.88/172.54 inference(rename_variables,[],[3680])). % 172.88/172.54 cnf(12374,plain, % 172.88/172.54 (~P102(f332(f332(f247(a876),x123741),x123741))), % 172.88/172.54 inference(rename_variables,[],[4541])). % 172.88/172.54 cnf(12375,plain, % 172.88/172.54 (~E(f332(a115,x123751),x123751)), % 172.88/172.54 inference(rename_variables,[],[4480])). % 172.88/172.54 cnf(12378,plain, % 172.88/172.54 (P102(f332(f332(f246(f883(x123781,a871)),f195(f883(x123781,a871))),x123782))), % 172.88/172.54 inference(rename_variables,[],[3747])). % 172.88/172.54 cnf(12381,plain, % 172.88/172.54 (P102(f332(f332(f246(a876),x123811),x123811))), % 172.88/172.54 inference(rename_variables,[],[3290])). % 172.88/172.54 cnf(12384,plain, % 172.88/172.54 (P102(f332(f332(f246(f883(x123841,a871)),x123842),x123842))), % 172.88/172.54 inference(rename_variables,[],[3594])). % 172.88/172.54 cnf(12389,plain, % 172.88/172.54 (P102(f332(f332(f246(f883(x123891,a871)),x123892),f332(f332(f310(x123891),x123893),x123892)))), % 172.88/172.54 inference(rename_variables,[],[3745])). % 172.88/172.54 cnf(12392,plain, % 172.88/172.54 (P102(f332(f332(f246(f883(x123921,a871)),x123922),x123922))), % 172.88/172.54 inference(rename_variables,[],[3594])). % 172.88/172.54 cnf(12393,plain, % 172.88/172.54 (~P102(f332(f332(f334(x123931),x123932),f195(f883(x123931,a871))))), % 172.88/172.54 inference(rename_variables,[],[4553])). % 172.88/172.54 cnf(12396,plain, % 172.88/172.54 (~P102(f332(f332(f334(x123961),x123962),f195(f883(x123961,a871))))), % 172.88/172.54 inference(rename_variables,[],[4553])). % 172.88/172.54 cnf(12405,plain, % 172.88/172.54 (P20(x124051,x124051,f5(x124051),x124052)), % 172.88/172.54 inference(rename_variables,[],[3534])). % 172.88/172.54 cnf(12408,plain, % 172.88/172.54 (E(f332(f196(f877(x124081)),f170(x124081,x124082,x124083)),x124082)), % 172.88/172.54 inference(rename_variables,[],[3358])). % 172.88/172.54 cnf(12411,plain, % 172.88/172.54 (~P102(f332(f332(f247(a876),x124111),x124111))), % 172.88/172.54 inference(rename_variables,[],[4541])). % 172.88/172.54 cnf(12412,plain, % 172.88/172.54 (P102(f332(f255(f883(x124121,a871)),x124122))), % 172.88/172.54 inference(rename_variables,[],[3352])). % 172.88/172.54 cnf(12415,plain, % 172.88/172.54 (~P102(f332(f332(f334(x124151),x124152),f195(f883(x124151,a871))))), % 172.88/172.54 inference(rename_variables,[],[4553])). % 172.88/172.54 cnf(12418,plain, % 172.88/172.54 (P102(f332(f332(f334(x124181),f332(x124182,x124183)),f332(f311(x124184,x124181,x124182),f255(f883(x124184,a871)))))), % 172.88/172.54 inference(rename_variables,[],[3907])). % 172.88/172.54 cnf(12419,plain, % 172.88/172.54 (P102(f332(f332(f334(f882(x124191,x124191)),f332(f332(f267(x124191,x124191),x124192),x124192)),f308(x124191,x124193)))), % 172.88/172.54 inference(rename_variables,[],[3942])). % 172.88/172.54 cnf(12422,plain, % 172.88/172.54 (P102(f332(f332(f334(f882(x124221,x124221)),f332(f332(f267(x124221,x124221),x124222),x124222)),f308(x124221,x124223)))), % 172.88/172.54 inference(rename_variables,[],[3942])). % 172.88/172.54 cnf(12425,plain, % 172.88/172.54 (P102(f332(f332(f246(a876),x124251),x124251))), % 172.88/172.54 inference(rename_variables,[],[3290])). % 172.88/172.54 cnf(12426,plain, % 172.88/172.54 (P102(f332(f255(f883(x124261,a871)),x124262))), % 172.88/172.54 inference(rename_variables,[],[3352])). % 172.88/172.54 cnf(12429,plain, % 172.88/172.54 (P102(f332(f61(x124291),f332(f173(x124291),x124292)))), % 172.88/172.54 inference(rename_variables,[],[3331])). % 172.88/172.54 cnf(12439,plain, % 172.88/172.54 (~P102(f332(f332(f195(f883(x124391,f883(x124392,a871))),x124393),x124394))), % 172.88/172.54 inference(rename_variables,[],[4570])). % 172.88/172.54 cnf(12442,plain, % 172.88/172.54 (P102(f332(f332(f246(f883(x124421,a871)),x124422),f255(f883(x124421,a871))))), % 172.88/172.54 inference(rename_variables,[],[3680])). % 172.88/172.54 cnf(12445,plain, % 172.88/172.54 (P102(f332(f332(f334(f882(x124451,x124451)),f332(f332(f267(x124451,x124451),x124452),x124452)),f308(x124451,x124453)))), % 172.88/172.54 inference(rename_variables,[],[3942])). % 172.88/172.54 cnf(12448,plain, % 172.88/172.54 (~P102(f332(f332(f247(a876),f332(f332(f79(a876),x124481),x124482)),x124482))), % 172.88/172.54 inference(rename_variables,[],[4567])). % 172.88/172.54 cnf(12449,plain, % 172.88/172.54 (P102(f332(f332(f247(a876),x124491),f332(a115,x124491)))), % 172.88/172.54 inference(rename_variables,[],[3359])). % 172.88/172.54 cnf(12452,plain, % 172.88/172.54 (P102(f332(f332(f246(f883(x124521,a871)),f332(f173(x124521),f332(f136(x124521,x124522),x124523))),f332(f173(x124521),x124523)))), % 172.88/172.54 inference(rename_variables,[],[3952])). % 172.88/172.54 cnf(12455,plain, % 172.88/172.54 (P102(f332(f332(f246(f883(x124551,a871)),x124552),f255(f883(x124551,a871))))), % 172.88/172.54 inference(rename_variables,[],[3680])). % 172.88/172.54 cnf(12458,plain, % 172.88/172.54 (E(f332(f263(x124581,x124581),f264(x124581,x124582)),x124582)), % 172.88/172.54 inference(rename_variables,[],[3246])). % 172.88/172.54 cnf(12469,plain, % 172.88/172.54 (~P102(f332(f332(f334(x124691),x124692),f195(f883(x124691,a871))))), % 172.88/172.54 inference(rename_variables,[],[4553])). % 172.88/172.54 cnf(12470,plain, % 172.88/172.54 (P102(f332(f332(f334(f882(f877(x124701),f877(x124701))),f332(f332(f267(f877(x124701),f877(x124701)),f116(x124701)),f116(x124701))),f158(x124701,x124702)))), % 172.88/172.54 inference(rename_variables,[],[4087])). % 172.88/172.54 cnf(12475,plain, % 172.88/172.54 (~P102(f332(f332(f334(x124751),x124752),f195(f883(x124751,a871))))), % 172.88/172.54 inference(rename_variables,[],[4553])). % 172.88/172.54 cnf(12478,plain, % 172.88/172.54 (P32(x124781,x124782,f116(x124781))), % 172.88/172.54 inference(rename_variables,[],[3222])). % 172.88/172.54 cnf(12481,plain, % 172.88/172.54 (E(f332(f196(f877(x124811)),f170(x124811,x124812,x124813)),x124812)), % 172.88/172.54 inference(rename_variables,[],[3358])). % 172.88/172.54 cnf(12484,plain, % 172.88/172.54 (~P102(f332(f332(f334(x124841),x124842),f195(f883(x124841,a871))))), % 172.88/172.54 inference(rename_variables,[],[4553])). % 172.88/172.54 cnf(12488,plain, % 172.88/172.54 (~P102(f332(f332(f334(f882(f877(x124881),f877(x124881))),f332(f332(f267(f877(x124881),f877(x124881)),x124882),x124882)),f147(x124881,f153(x124881,f116(f883(x124881,a876))))))), % 172.88/172.54 inference(scs_inference,[],[4572,3534,11064,12101,12198,12293,12329,12337,12350,3543,3544,3257,3222,4513,4514,3156,4498,4480,10217,10227,10240,10251,10254,10357,10360,10363,10466,10577,10885,11049,11052,11250,11337,11344,11358,11410,11413,11457,11525,11572,11588,11887,11912,11924,11953,11959,12054,12161,12168,12321,4495,10450,10541,3347,3503,3203,2888,2892,2893,2902,2903,2908,2909,2911,2912,2914,2915,2916,2918,2919,2922,2925,2934,2936,2943,2952,2956,2962,2963,2964,2965,2966,2981,3021,3030,3031,3033,3040,3046,3048,3056,3062,3078,4476,3635,3868,11619,3131,11334,3246,10220,10289,10292,10384,10387,10680,11349,11352,11468,11512,11517,11614,12075,12269,3217,12353,12357,12361,3223,3231,3758,3358,12408,4000,3121,4492,3497,3853,11384,3180,3147,3142,3128,3129,3771,3162,3348,10832,12162,3215,3216,3395,4562,3940,4505,10280,10447,11247,12317,12354,4512,12325,3279,11708,4551,10999,11069,11293,11296,3396,3177,10349,10656,3178,3454,3100,3199,11374,4087,12340,12470,3942,11005,11131,11182,12301,12307,12419,12422,12445,4575,10937,11136,11241,11263,11301,11307,12248,4576,11038,11139,11244,4577,11142,4578,11196,4579,3198,3495,12201,12245,12324,3661,4371,4372,4503,11365,3598,3816,3863,3480,3740,3359,10368,10486,10555,10616,10619,10659,10753,10989,11883,11946,12025,12066,12127,12130,3751,11605,3272,3371,3559,4545,10257,10260,10286,10761,10774,10895,11285,11377,11772,11780,12001,12004,12092,12251,4557,11487,11520,11555,11585,3738,3504,3890,3318,3319,3293,4542,4500,3689,4225,3487,4558,4081,11258,3619,3331,11732,11735,12172,12273,4051,4008,11876,12216,3952,10829,12060,12229,4003,11008,12098,12171,12228,12272,3662,11886,12032,12106,12152,4040,3680,11011,11074,11155,11215,12053,12120,12370,12442,4563,10777,11147,3289,10377,10473,10602,10666,11460,11679,11726,11760,11856,11911,12113,3290,10735,10780,10783,10816,10842,10879,10917,10953,11927,11930,11933,11936,12133,12136,12139,12142,12209,12381,3291,10406,10461,10671,10756,10882,11568,11763,11775,11862,11873,11894,11899,11939,11964,3292,3367,12086,4541,10323,10415,10526,10550,10798,10845,10855,11534,11633,11654,11657,11660,11676,11818,11821,11824,11827,11923,11942,11945,11958,12013,12016,12019,12022,12093,12183,12186,12279,12282,12343,12374,12411,3449,10622,10890,10934,11204,11282,11445,11688,4553,10807,10819,10926,10944,10947,11002,11088,11096,11112,11150,11167,11176,11212,11253,11273,11276,11279,11310,11317,11320,11705,11741,12007,12010,12044,12087,12116,12257,12298,12304,12393,12396,12415,12469,12475,3352,10653,10683,10692,11233,11787,12412,3391,3385,3820,3756,10326,11608,11636,4550,10277,10647,10650,11091,11109,11571,11624,11668,11689,11793,11830,11833,11836,11839,3312,10686,10839,10910,11637,11792,11984,3781,4131,4548,3792,3828,4531,4533,3263,3264,4532,4535,4536,3799,3609,4231,11467,4565,10245,10248,10507,10558,10561,10566,10976,11439,11692,11796,4573,11170,11290,11326,4017,3907,11323,11663,11667,11729,12328,12336,3745,10950,10956,10971,11908,12037,12119,3594,11173,12145,12254,12264,12333,12384,4085,3747,10689,11027,11179,11209,11220,12057,12222,12332,3560,10608,10611,10695,10869,4569,11602,4559,4570,10746,10848,11158,11442,11473,12204,12213,12260,4191,10822,12225,12237,4092,3780,3724,4567,10299,10302,10641,10644,11484,11664,4568,11582,3749,10605,4024,4590,4616,4665,4667,4698,4715,4722,4723,4759,4764,4794,4800,4884,4909,4910,4925,4947,4972,4973,4995,4996,5009,5013,5036,5042,5058,5061,5062,5063,5068,5069,5091,5116,5117,5127,5132,5138,5175,5176,5184,5193,5198,5200,5211,5213,5219,5223,5224,5237,5244,5247,5248,5249,5253,5289,5302,5310,5312,5313,5317,5318,5319,5327,5330,5335,5336,5337,5344,5348,5349,5350,5359,5363,5364,5365,5370,5383,5392,5404,5406,5414,5415,5419,5423,5448,5454,5464,5465,5480,5493,5515,5521,5539,5540,5543,5562,5570,5571,5576,5577,5587,5589,5601,5605,5614,5615,5617,5632,5637,5647,5648,5660,5667,5681,5685,5688,5694,5695,5696,5699,5704,5740,5741,5744,5746,5749,5750,5751,5753,5755,5757,5762,5769,5784,5798,5803,5804,5817,5818,5823,5827,5829,5834,5875,5887,5896,5900,5909,5913,5914,5922,5936,5942,5960,5963,5975,6002,6016,6041,6061,6062,6065,6080,6082,6083,6085,6098,6099,6102,6104,6107,6108,6120,6126,6127,6128,6130,6132,6169,6170,6175,6178,6184,6188,6224,6226,6228,6230,6239,6241,6243,6249,6251,6257,6260,6268,6275,6276,6277,6282,6304,6305,6306,6308,6314,6319,6353,6354,6358,6359,6360,6361,6362,6363,6364,6371,6404,6405,6414,6435,6436,6456,6458,6469,6470,6476,6506,6508,6522,6560,6562,6563,6616,6641,6683,6703,6712,6713,6714,6715,6734,6735,6741,6754,6757,6759,6761,6762,6763,6765,6779,6790,6792,6793,6806,6810,6861,6872,6874,6878,6895,6896,6932,6944,6975,6994,7009,7063,7091,7146,7167,7176,7179,7234,7242,7300,7302,7317,7325,7328,7329,7348,7354,7356,7405,7415,7418,7434,7486,7487,7491,7535,7536,7554,7621,7640,7663,7687,7702,7718,7728,7737,7738,7767,7770,7772,7782,7820,7831,7856,7914,7948,7981,8028,8044,8060,8061,8136,8190,8209,8233,8253,8277,8375,8377,8383,8400,8404,8420,8443,8454,8456,8471,8476,8480,8503,8517,8518,8534,8535,8540,8541,8542,8543,8544,8562,8563,8564,8572,8585,8587,8599,8603,8605,8606,8607,8615,8620,8647,8648,8679,8692,8696,8714,8736,8737,8738,8739,8751,8752,8774,8784,8794,8795,8796,8797,8799,8821,8822,8833,8877,8883,8889,8902,8907,8909,8912,8913,8917,8927,9009,9040,9041,9042,9057,9074,9080,9108,9109,9150,9153,9179,9224,9225,9226,9241,9266,9280,9286,9289,9311,9312,9340,9402,9437,9438,9439,9464,9465,9483,9501,9507,9521,9544,9566,9574,9575,9576,9577,9592,9594,9599,9630,9631,9637,9638,9682,9683,9714,9723,9733,9735,9736,9745,9759,9762,9790,9823,9825,9829,9886,9927,9928,9930,9940,9941,9961,9966,10007,10059,10131,10132,10185,10201,2,8,9,4603,4604,4622,4653,4655,4656,4684,4690,4691,4702,4751,4753,4785,4799,4829,4926,4927,4940,4960,5016,5017,5020,5021,5023,5025,5026,5035,5038,5039,5047,5059,5060,5066,5086,5087,5104,5109,5110,5111,5112,5115,5123,5126,5133,5190,5196,5197,5205,5234,5245,5251,5267,5287,5288,5295,5296,5297,5306,5316,5323,5325,5326,5332,5340,5341,5351,5355,5356,5357,5358,5360,5361,5366,5367,5368,5369,5400,5401,5402,5410,5411,5412,5413,5459,5461,5463,5500,5502,5503,5505,5506,5508,5509,5511,5520,5525,5527,5528,5529,5530,5531,5532,5541,5551,5554,5565,5581,5582,5585,5595,5597,5598,5599,5624,5634,5650,5651,5661,5662,5664,5666,5671,5706,5711,5713,5771,5805,5806,5810,5816,5819,5820,5821,5822,5828,5839,5840,5842,5843,5851,5872,5901,5917,5920,5921,5923,5932,5953,5954,5955,5958,5959,5977,5988,5989,6018,6019,6023,6043,6046,6050,6069,6074,6075,6100,6103,6111,6119,6125,6129,6136,6137,6138,6139,6172,6189,6242,6278,6280,6301,6302,6307,6310,6311,6315,6321,6330,6346,6366,6367,6372,6382,6397,6417,6423,6425,6440,6441,6444,6445,6447,6449,6450,6451,6453,6455,6457,6463,6464,6465,6466,6472,6474,6516,6521,6536,6537,6538,6539,6574,6579,6581,6586,6587,6595,6599,6612,6637,6638,6639,6640,6651,6657,6673,6677,6696,6729,6730,6731,6736,6750,6771,6773,6775,6777,6780,6786,6788,6803,6808,6811,6847,6850,6851,6864,6865,6866,6867,6886,6887,6904,6930,6952,6963,6965,6966,6968,6970,6971,7006,7007,7012,7013,7014,7015,7017,7019,7044,7053,7054,7066,7076,7115,7125,7129,7136,7147,7153,7155,7161,7169,7170,7183,7200,7218,7220,7237,7286,7288,7289,7290,7296,7301,7324,7369,7402,7416,7433,7466,7469,7495,7519,7537,7540,7541,7551,7569,7570,7572,7574,7576,7578,7604,7629,7630,7662,7664,7665,7666,7671,7694,7703,7714,7719,7725,7727,7733,7745,7746,7748,7780,7803,7869,7870,7917,7925,7926,7950,7951,7968,7969,8036,8037,8038,8063,8096,8103,8105,8114,8126,8159,8165,8172,8185,8204,8210,8232,8275,8305,8317,8335,8338,8368,8391,8457,8458,8461,8463,8566,8567,8568,8569,8594,8623,8651,8695,8713,8768,8814,8817,8830,8837,8874,8895,8923,8924,8942,8943,9082,9086,9106,9116,9139,9141,9144,9148,9151,9152,9165,9166,9186,9192,9204,9252,9270,9324,9325,9332,9394,9399,9434,9441,9444,9447,9448,9463,9479,9488,9500,9510,9511,9514,9516,9542,9665,9709,9710,9752,9797,9913])). % 172.88/172.55 cnf(12490,plain, % 172.88/172.55 (~P102(f332(f332(f247(a876),x124901),x124901))), % 172.88/172.55 inference(rename_variables,[],[4541])). % 172.88/172.55 cnf(12493,plain, % 172.88/172.55 (P102(f332(f332(f334(x124931),x124932),f255(f883(x124931,a871))))), % 172.88/172.55 inference(rename_variables,[],[3449])). % 172.88/172.55 cnf(12500,plain, % 172.88/172.55 (P102(f332(f332(f246(f883(x125001,a871)),x125002),x125002))), % 172.88/172.55 inference(rename_variables,[],[3594])). % 172.88/172.55 cnf(12503,plain, % 172.88/172.55 (~P102(f332(f332(f334(x125031),x125032),f195(f883(x125031,a871))))), % 172.88/172.55 inference(rename_variables,[],[4553])). % 172.88/172.55 cnf(12506,plain, % 172.88/172.55 (P102(f332(f332(f246(a1),f2(a1)),f332(f332(f257(a1),f332(f74(a1),x125061)),x125062)))), % 172.88/172.55 inference(rename_variables,[],[3780])). % 172.88/172.55 cnf(12509,plain, % 172.88/172.55 (~E(f332(a115,x125091),x125091)), % 172.88/172.55 inference(rename_variables,[],[4480])). % 172.88/172.55 cnf(12511,plain, % 172.88/172.55 (E(f332(f263(x125111,x125111),f264(x125111,x125112)),x125112)), % 172.88/172.55 inference(rename_variables,[],[3246])). % 172.88/172.55 cnf(12513,plain, % 172.88/172.55 (P19(x125131,x125132,f195(f883(f875(x125131),a871)))), % 172.88/172.55 inference(rename_variables,[],[3346])). % 172.88/172.55 cnf(12519,plain, % 172.88/172.55 (E(f332(f263(x125191,x125191),f264(x125191,x125192)),x125192)), % 172.88/172.55 inference(rename_variables,[],[3246])). % 172.88/172.55 cnf(12526,plain, % 172.88/172.55 (E(f332(f263(x125261,x125261),f264(x125261,x125262)),x125262)), % 172.88/172.55 inference(rename_variables,[],[3246])). % 172.88/172.55 cnf(12532,plain, % 172.88/172.55 (P10(x125321,f883(x125321,a871),f310(x125321))), % 172.88/172.55 inference(rename_variables,[],[3260])). % 172.88/172.55 cnf(12536,plain, % 172.88/172.55 (E(f332(f263(x125361,x125361),f264(x125361,x125362)),x125362)), % 172.88/172.55 inference(rename_variables,[],[3246])). % 172.88/172.55 cnf(12538,plain, % 172.88/172.55 (P20(x125381,x125381,f5(x125381),x125382)), % 172.88/172.55 inference(rename_variables,[],[3534])). % 172.88/172.55 cnf(12540,plain, % 172.88/172.55 (P20(x125401,x125401,f5(x125401),x125402)), % 172.88/172.55 inference(rename_variables,[],[3534])). % 172.88/172.55 cnf(12554,plain, % 172.88/172.55 (P40(x125541,x125542,f264(x125541,x125542))), % 172.88/172.55 inference(rename_variables,[],[3256])). % 172.88/172.55 cnf(12556,plain, % 172.88/172.55 (P40(x125561,x125562,f264(x125561,x125562))), % 172.88/172.55 inference(rename_variables,[],[3256])). % 172.88/172.55 cnf(12560,plain, % 172.88/172.55 (P38(x125601,f153(x125601,x125602))), % 172.88/172.55 inference(rename_variables,[],[3156])). % 172.88/172.55 cnf(12564,plain, % 172.88/172.55 (E(f332(f263(x125641,x125641),f264(x125641,x125642)),x125642)), % 172.88/172.55 inference(rename_variables,[],[3246])). % 172.88/172.55 cnf(12568,plain, % 172.88/172.55 (P30(x125681,f2(a876),f332(f332(f332(f91(x125681),x125682),f332(a25,x125683)),x125684))), % 172.88/172.55 inference(rename_variables,[],[3673])). % 172.88/172.55 cnf(12578,plain, % 172.88/172.55 (E(f195(f883(f882(x125781,x125781),a871)),f264(x125781,f195(f883(x125781,a871))))), % 172.88/172.55 inference(rename_variables,[],[3362])). % 172.88/172.55 cnf(12580,plain, % 172.88/172.55 (P43(x125801,x125802,x125803,x125804,f195(f883(x125801,a871)),x125804)), % 172.88/172.55 inference(rename_variables,[],[4255])). % 172.88/172.55 cnf(12583,plain, % 172.88/172.55 (P43(x125831,x125832,x125833,x125834,f195(f883(x125831,a871)),x125834)), % 172.88/172.55 inference(rename_variables,[],[4255])). % 172.88/172.55 cnf(12587,plain, % 172.88/172.55 (E(f332(f263(x125871,x125871),f264(x125871,x125872)),x125872)), % 172.88/172.55 inference(rename_variables,[],[3246])). % 172.88/172.55 cnf(12591,plain, % 172.88/172.55 (E(f332(f263(x125911,x125911),f264(x125911,x125912)),x125912)), % 172.88/172.55 inference(rename_variables,[],[3246])). % 172.88/172.55 cnf(12593,plain, % 172.88/172.55 (E(f332(f263(x125931,x125931),f264(x125931,x125932)),x125932)), % 172.88/172.55 inference(rename_variables,[],[3246])). % 172.88/172.55 cnf(12595,plain, % 172.88/172.55 (P50(x125951,x125951,f264(x125951,x125952))), % 172.88/172.55 inference(rename_variables,[],[3257])). % 172.88/172.55 cnf(12601,plain, % 172.88/172.55 (E(f332(f263(x126011,x126011),f264(x126011,x126012)),x126012)), % 172.88/172.55 inference(rename_variables,[],[3246])). % 172.88/172.55 cnf(12603,plain, % 172.88/172.55 (P33(x126031,x126032,f116(x126031),f116(x126031))), % 172.88/172.55 inference(rename_variables,[],[3543])). % 172.88/172.55 cnf(12605,plain, % 172.88/172.55 (P33(x126051,x126052,f116(x126051),f116(x126051))), % 172.88/172.55 inference(rename_variables,[],[3543])). % 172.88/172.55 cnf(12614,plain, % 172.88/172.55 (E(f332(f263(x126141,x126141),f264(x126141,x126142)),x126142)), % 172.88/172.55 inference(rename_variables,[],[3246])). % 172.88/172.55 cnf(12618,plain, % 172.88/172.55 (P51(x126181,f195(f883(x126181,a871)),x126182)), % 172.88/172.55 inference(rename_variables,[],[3310])). % 172.88/172.55 cnf(12626,plain, % 172.88/172.55 (P102(f332(f332(f247(a876),f2(a876)),f332(a115,x126261)))), % 172.88/172.55 inference(rename_variables,[],[3371])). % 172.88/172.55 cnf(12627,plain, % 172.88/172.55 (~E(f332(a115,x126271),x126271)), % 172.88/172.55 inference(rename_variables,[],[4480])). % 172.88/172.55 cnf(12633,plain, % 172.88/172.55 (P102(f332(f332(f247(a876),x126331),f332(a115,x126331)))), % 172.88/172.55 inference(rename_variables,[],[3359])). % 172.88/172.55 cnf(12638,plain, % 172.88/172.55 (~P102(f332(f332(f247(a876),x126381),f2(a876)))), % 172.88/172.55 inference(rename_variables,[],[4545])). % 172.88/172.55 cnf(12641,plain, % 172.88/172.55 (~P102(f332(f332(f247(a876),x126411),f2(a876)))), % 172.88/172.55 inference(rename_variables,[],[4545])). % 172.88/172.55 cnf(12648,plain, % 172.88/172.55 (~P102(f332(f332(f247(a1),f332(f103(a1),x126481)),f332(f78(a1),f332(f103(a1),x126482))))), % 172.88/172.55 inference(rename_variables,[],[4564])). % 172.88/172.55 cnf(12658,plain, % 172.88/172.55 (~P102(f332(f332(f247(a876),x126581),f2(a876)))), % 172.88/172.55 inference(rename_variables,[],[4545])). % 172.88/172.55 cnf(12661,plain, % 172.88/172.55 (~P102(f332(f332(f247(a876),x126611),f2(a876)))), % 172.88/172.55 inference(rename_variables,[],[4545])). % 172.88/172.55 cnf(12664,plain, % 172.88/172.55 (P102(f332(f61(a876),f305(a876,x126641,x126642)))), % 172.88/172.55 inference(rename_variables,[],[3506])). % 172.88/172.55 cnf(12667,plain, % 172.88/172.55 (P102(f332(f61(a876),f305(a876,x126671,x126672)))), % 172.88/172.55 inference(rename_variables,[],[3506])). % 172.88/172.55 cnf(12670,plain, % 172.88/172.55 (P102(f332(f61(a876),f305(a876,x126701,x126702)))), % 172.88/172.55 inference(rename_variables,[],[3506])). % 172.88/172.55 cnf(12673,plain, % 172.88/172.55 (P102(f332(f61(a876),f305(a876,x126731,x126732)))), % 172.88/172.55 inference(rename_variables,[],[3506])). % 172.88/172.55 cnf(12680,plain, % 172.88/172.55 (P102(f332(f332(f246(a1),f332(f78(a1),f332(f103(a1),x126801))),f332(f103(a1),x126802)))), % 172.88/172.55 inference(rename_variables,[],[3781])). % 172.88/172.55 cnf(12683,plain, % 172.88/172.55 (~P102(f332(f332(f247(a876),x126831),f2(a876)))), % 172.88/172.55 inference(rename_variables,[],[4545])). % 172.88/172.55 cnf(12684,plain, % 172.88/172.55 (P102(f332(f332(f246(a876),x126841),x126841))), % 172.88/172.55 inference(rename_variables,[],[3290])). % 172.88/172.55 cnf(12691,plain, % 172.88/172.55 (P102(f332(f332(f247(a876),x126911),f332(a115,x126911)))), % 172.88/172.55 inference(rename_variables,[],[3359])). % 172.88/172.55 cnf(12694,plain, % 172.88/172.55 (P102(f332(f332(f334(x126941),f332(x126942,x126943)),f332(f311(x126944,x126941,x126942),f255(f883(x126944,a871)))))), % 172.88/172.55 inference(rename_variables,[],[3907])). % 172.88/172.55 cnf(12695,plain, % 172.88/172.55 (~E(f332(a115,x126951),f2(a876))), % 172.88/172.55 inference(rename_variables,[],[4490])). % 172.88/172.55 cnf(12697,plain, % 172.88/172.55 (~P102(f332(f332(f247(a1),f2(a1)),f332(f106(a1),f2(a1))))), % 172.88/172.55 inference(scs_inference,[],[4572,3534,11064,12101,12198,12293,12329,12337,12350,12405,12538,3543,12165,12603,12605,3544,12232,3256,12554,12556,3257,12595,3222,12478,4513,4514,11685,4255,12580,12583,3260,12532,3099,3156,12560,4498,3596,4480,10217,10227,10240,10251,10254,10357,10360,10363,10466,10577,10885,11049,11052,11250,11337,11344,11358,11410,11413,11457,11525,11572,11588,11887,11912,11924,11953,11959,12054,12161,12168,12321,12375,12509,4495,10450,10541,3347,3310,12618,3503,3203,4490,2888,2892,2893,2902,2903,2908,2909,2911,2912,2914,2915,2916,2918,2919,2922,2925,2934,2936,2943,2952,2956,2962,2963,2964,2965,2966,2981,3021,3030,3031,3033,3040,3046,3047,3048,3056,3062,4475,3078,3155,4476,3635,3868,11619,3131,11334,3270,3243,3246,10220,10289,10292,10384,10387,10680,11349,11352,11468,11512,11517,11614,12075,12269,12458,12511,12519,12526,12536,12564,12587,12591,12593,12601,3217,12353,12357,12361,3223,3231,3758,3358,12408,12481,4000,3121,4492,3497,3853,11384,3346,12513,3180,3147,3673,12568,3142,3974,3678,3128,3129,3109,3771,3162,3348,10832,12162,3215,3216,3395,4562,10420,3940,4505,10280,10447,11247,12317,12354,4512,12325,3279,11708,4551,10999,11069,11293,11296,3698,3396,3620,3362,12578,3177,10349,10656,3178,3454,3170,3100,3199,11374,4087,12340,12470,3942,11005,11131,11182,12301,12307,12419,12422,12445,4575,10937,11136,11241,11263,11301,11307,12248,4576,11038,11139,11244,4577,11142,4578,11196,4579,3198,3495,12201,12245,12324,3661,4371,4372,4503,11365,3598,3638,3816,3863,3480,3740,3359,10368,10486,10555,10616,10619,10659,10753,10989,11883,11946,12025,12066,12127,12130,12449,12633,3751,11605,3272,3371,11723,3559,4545,10257,10260,10286,10761,10774,10895,11285,11377,11772,11780,12001,12004,12092,12251,12344,12638,12641,12658,12661,4557,11487,11520,11555,11585,3738,3504,3506,12664,12667,12670,3890,3318,3319,3293,4542,3176,4500,3689,4225,4009,3487,4558,4081,11258,3619,3331,11732,11735,12172,12273,4051,4008,11876,12216,3952,10829,12060,12229,4003,11008,12098,12171,12228,12272,3662,11886,12032,12106,12152,4040,3680,11011,11074,11155,11215,12053,12120,12370,12442,12455,4563,10777,11147,3289,10377,10473,10602,10666,11460,11679,11726,11760,11856,11911,12113,3290,10735,10780,10783,10816,10842,10879,10917,10953,11927,11930,11933,11936,12133,12136,12139,12142,12209,12381,12425,3291,10406,10461,10671,10756,10882,11568,11763,11775,11862,11873,11894,11899,11939,11964,3292,3367,12086,4541,10323,10415,10526,10550,10798,10845,10855,11534,11633,11654,11657,11660,11676,11818,11821,11824,11827,11923,11942,11945,11958,12013,12016,12019,12022,12093,12183,12186,12279,12282,12343,12374,12411,3449,10622,10890,10934,11204,11282,11445,11688,12320,4553,10807,10819,10926,10944,10947,11002,11088,11096,11112,11150,11167,11176,11212,11253,11273,11276,11279,11310,11317,11320,11705,11741,12007,12010,12044,12087,12116,12257,12298,12304,12393,12396,12415,12469,12475,12484,3352,10653,10683,10692,11233,11787,12412,3391,3385,3820,3756,10326,11608,11636,4550,10277,10647,10650,11091,11109,11571,11624,11668,11689,11793,11830,11833,11836,11839,3312,10686,10839,10910,11637,11792,11984,3781,11738,4131,3510,4548,3792,3828,4531,4533,4534,3263,3264,4532,4535,4536,3799,3609,4231,11467,4565,10245,10248,10507,10558,10561,10566,10976,11439,11692,11796,4573,11170,11290,11326,4017,12240,3907,11323,11663,11667,11729,12328,12336,12418,3745,10950,10956,10971,11908,12037,12119,3594,11173,12145,12254,12264,12333,12384,12392,4085,3747,10689,11027,11179,11209,11220,12057,12222,12332,3560,10608,10611,10695,10869,3562,4569,11602,4559,4564,12648,4570,10746,10848,11158,11442,11473,12204,12213,12260,12439,4191,10822,12225,12237,4092,3780,3724,3725,4567,10299,10302,10641,10644,11484,11664,4568,11582,3749,10605,4024,4590,4616,4665,4667,4698,4715,4722,4723,4759,4764,4794,4800,4884,4909,4910,4925,4947,4972,4973,4995,4996,5009,5013,5036,5042,5058,5061,5062,5063,5068,5069,5091,5116,5117,5127,5132,5138,5175,5176,5184,5193,5198,5200,5211,5213,5219,5223,5224,5237,5244,5247,5248,5249,5253,5289,5302,5310,5312,5313,5317,5318,5319,5327,5330,5335,5336,5337,5344,5348,5349,5350,5359,5363,5364,5365,5370,5383,5392,5404,5406,5414,5415,5419,5423,5448,5454,5464,5465,5480,5493,5515,5521,5539,5540,5543,5562,5570,5571,5576,5577,5587,5589,5601,5605,5614,5615,5617,5632,5637,5647,5648,5660,5667,5681,5685,5688,5694,5695,5696,5699,5704,5740,5741,5744,5746,5749,5750,5751,5753,5755,5757,5762,5769,5784,5798,5803,5804,5817,5818,5823,5827,5829,5834,5875,5887,5896,5900,5909,5913,5914,5922,5936,5942,5960,5963,5975,6002,6016,6041,6061,6062,6065,6080,6082,6083,6085,6098,6099,6102,6104,6107,6108,6120,6126,6127,6128,6130,6132,6169,6170,6175,6178,6184,6188,6224,6226,6228,6230,6239,6241,6243,6249,6251,6257,6260,6268,6275,6276,6277,6282,6304,6305,6306,6308,6314,6319,6353,6354,6358,6359,6360,6361,6362,6363,6364,6371,6404,6405,6414,6435,6436,6456,6458,6469,6470,6476,6506,6508,6522,6560,6562,6563,6616,6641,6683,6703,6712,6713,6714,6715,6734,6735,6741,6754,6757,6759,6761,6762,6763,6765,6779,6790,6792,6793,6806,6810,6861,6872,6874,6878,6895,6896,6932,6944,6975,6994,7009,7063,7091,7146,7167,7176,7179,7234,7242,7300,7302,7317,7325,7328,7329,7348,7354,7356,7405,7415,7418,7434,7486,7487,7491,7535,7536,7554,7621,7640,7663,7687,7702,7718,7728,7737,7738,7767,7770,7772,7782,7820,7831,7856,7914,7948,7981,8028,8044,8060,8061,8136,8190,8209,8233,8253,8277,8375,8377,8383,8400,8404,8420,8443,8454,8456,8471,8476,8480,8503,8517,8518,8534,8535,8540,8541,8542,8543,8544,8562,8563,8564,8572,8585,8587,8599,8603,8605,8606,8607,8615,8620,8647,8648,8679,8692,8696,8714,8736,8737,8738,8739,8751,8752,8774,8784,8794,8795,8796,8797,8799,8821,8822,8833,8877,8883,8889,8902,8907,8909,8912,8913,8917,8927,9009,9040,9041,9042,9057,9074,9080,9108,9109,9150,9153,9179,9224,9225,9226,9241,9266,9280,9286,9289,9311,9312,9340,9402,9437,9438,9439,9464,9465,9483,9501,9507,9521,9544,9566,9574,9575,9576,9577,9592,9594,9599,9630,9631,9637,9638,9682,9683,9714,9723,9733,9735,9736,9745,9759,9762,9790,9823,9825,9829,9886,9927,9928,9930,9940,9941,9961,9966,10007,10059,10131,10132,10185,10201,2,8,9,4603,4604,4622,4653,4655,4656,4684,4690,4691,4702,4751,4753,4785,4799,4829,4926,4927,4940,4960,5016,5017,5020,5021,5023,5025,5026,5035,5038,5039,5047,5059,5060,5066,5086,5087,5104,5109,5110,5111,5112,5115,5123,5126,5133,5190,5196,5197,5205,5234,5245,5251,5267,5287,5288,5295,5296,5297,5306,5316,5323,5325,5326,5332,5340,5341,5351,5355,5356,5357,5358,5360,5361,5366,5367,5368,5369,5400,5401,5402,5410,5411,5412,5413,5459,5461,5463,5500,5502,5503,5505,5506,5508,5509,5511,5520,5525,5527,5528,5529,5530,5531,5532,5541,5551,5554,5565,5581,5582,5585,5595,5597,5598,5599,5624,5634,5650,5651,5661,5662,5664,5666,5671,5706,5711,5713,5771,5805,5806,5810,5816,5819,5820,5821,5822,5828,5839,5840,5842,5843,5851,5872,5901,5917,5920,5921,5923,5932,5953,5954,5955,5958,5959,5977,5988,5989,6018,6019,6023,6043,6046,6050,6069,6074,6075,6100,6103,6111,6119,6125,6129,6136,6137,6138,6139,6172,6189,6242,6278,6280,6301,6302,6307,6310,6311,6315,6321,6330,6346,6366,6367,6372,6382,6397,6417,6423,6425,6440,6441,6444,6445,6447,6449,6450,6451,6453,6455,6457,6463,6464,6465,6466,6472,6474,6516,6521,6536,6537,6538,6539,6574,6579,6581,6586,6587,6595,6599,6612,6637,6638,6639,6640,6651,6657,6673,6677,6696,6729,6730,6731,6736,6750,6771,6773,6775,6777,6780,6786,6788,6803,6808,6811,6847,6850,6851,6864,6865,6866,6867,6886,6887,6904,6930,6952,6963,6965,6966,6968,6970,6971,7006,7007,7012,7013,7014,7015,7017,7019,7044,7053,7054,7066,7076,7115,7125,7129,7136,7147,7153,7155,7161,7169,7170,7183,7200,7218,7220,7237,7286,7288,7289,7290,7296,7301,7324,7369,7402,7416,7433,7466,7469,7495,7519,7537,7540,7541,7551,7569,7570,7572,7574,7576,7578,7604,7629,7630,7662,7664,7665,7666,7671,7694,7703,7714,7719,7725,7727,7733,7745,7746,7748,7780,7803,7869,7870,7917,7925,7926,7950,7951,7968,7969,8036,8037,8038,8063,8096,8103,8105,8114,8126,8159,8165,8172,8185,8204,8210,8232,8275,8305,8317,8335,8338,8368,8391,8457,8458,8461,8463,8566,8567,8568,8569,8594,8623,8651,8695,8713,8768,8814,8817,8830,8837,8874,8895,8923,8924,8942,8943,9082,9086,9106,9116,9139,9141,9144,9148,9151,9152,9165,9166,9186,9192,9204,9252,9270,9324,9325,9332,9394,9399,9434,9441,9444,9447,9448,9463,9479,9488,9500,9510,9511,9514,9516,9542,9665,9709,9710,9752,9797,9913,9970,10035,10110,10123,10128,3,2626,2627,2628,2629,2630,2634,2635,2636,2640,2643,2647,2648,2649,2653,2664,2666,2672,2676,2677,2678,2679,2683,2684,2686,2687,2688,2689,2690,2692,2693,2694,2695,2696,2702,2710,2711,2713,2714,2715,2718,2722,2723,2724,2738,2741,2742,2743,2745,2754,2758,2761,2770,2771,2772,2774,2783,2785,2786,2788,2794,2795,2796,2804,2813,2815,2817,2818,2842,2843,2857,5226,5286,5386,5472,5473,5474,5552,5649,5680,5714,5730,5732,5738,5799,5800,5801,5802,5808,5841,5972,6017,6040,6077,6117,6258])). % 172.88/172.55 cnf(12700,plain, % 172.88/172.55 (P102(f332(f332(f246(a1),x127001),x127001))), % 172.88/172.55 inference(rename_variables,[],[3291])). % 172.88/172.55 cnf(12703,plain, % 172.88/172.55 (P102(f332(f61(a876),f305(a876,x127031,x127032)))), % 172.88/172.55 inference(rename_variables,[],[3506])). % 172.88/172.55 cnf(12706,plain, % 172.88/172.55 (P102(f332(f61(a876),f305(a876,x127061,x127062)))), % 172.88/172.55 inference(rename_variables,[],[3506])). % 172.88/172.55 cnf(12709,plain, % 172.88/172.55 (P102(f332(f332(f246(a876),x127091),x127091))), % 172.88/172.55 inference(rename_variables,[],[3290])). % 172.88/172.55 cnf(12722,plain, % 172.88/172.55 (P102(f332(f332(f247(a876),x127221),f332(a115,x127221)))), % 172.88/172.55 inference(rename_variables,[],[3359])). % 172.88/172.55 cnf(12727,plain, % 172.88/172.55 (P102(f332(f332(f246(a876),f44(a876,x127271,x127272)),x127271))), % 172.88/172.55 inference(rename_variables,[],[3756])). % 172.88/172.55 cnf(12734,plain, % 172.88/172.55 (P102(f332(f332(f247(a876),x127341),f332(a115,x127341)))), % 172.88/172.55 inference(rename_variables,[],[3359])). % 172.88/172.55 cnf(12735,plain, % 172.88/172.55 (~P102(f332(f332(f247(a876),x127351),f2(a876)))), % 172.88/172.55 inference(rename_variables,[],[4545])). % 172.88/172.55 cnf(12744,plain, % 172.88/172.55 (~P102(f332(f332(f247(a1),f332(f103(a1),x127441)),f2(a1)))), % 172.88/172.55 inference(rename_variables,[],[4557])). % 172.88/172.55 cnf(12745,plain, % 172.88/172.55 (P102(f332(f255(f883(x127451,a871)),x127452))), % 172.88/172.55 inference(rename_variables,[],[3352])). % 172.88/172.55 cnf(12748,plain, % 172.88/172.55 (~P102(f332(f332(f247(a1),f332(f103(a1),x127481)),f2(a1)))), % 172.88/172.55 inference(rename_variables,[],[4557])). % 172.88/172.55 cnf(12749,plain, % 172.88/172.55 (P102(f332(f255(f883(x127491,a871)),x127492))), % 172.88/172.55 inference(rename_variables,[],[3352])). % 172.88/172.55 cnf(12752,plain, % 172.88/172.55 (P102(f332(f255(f883(x127521,a871)),x127522))), % 172.88/172.55 inference(rename_variables,[],[3352])). % 172.88/172.55 cnf(12763,plain, % 172.88/172.55 (~P102(f332(f332(f334(x127631),x127632),f195(f883(x127631,a871))))), % 172.88/172.55 inference(rename_variables,[],[4553])). % 172.88/172.55 cnf(12764,plain, % 172.88/172.55 (P102(f332(f61(x127641),f195(f883(x127641,a871))))), % 172.88/172.55 inference(rename_variables,[],[3367])). % 172.88/172.55 cnf(12773,plain, % 172.88/172.55 (P102(f332(f332(f246(a876),f2(a876)),x127731))), % 172.88/172.55 inference(rename_variables,[],[3312])). % 172.88/172.55 cnf(12776,plain, % 172.88/172.55 (~P102(f332(f332(f334(x127761),x127762),f195(f883(x127761,a871))))), % 172.88/172.55 inference(rename_variables,[],[4553])). % 172.88/172.55 cnf(12779,plain, % 172.88/172.55 (~P102(f332(f332(f334(x127791),x127792),f195(f883(x127791,a871))))), % 172.88/172.55 inference(rename_variables,[],[4553])). % 172.88/172.55 cnf(12782,plain, % 172.88/172.55 (P102(f332(f332(f246(a876),x127821),x127821))), % 172.88/172.55 inference(rename_variables,[],[3290])). % 172.88/172.55 cnf(12789,plain, % 172.88/172.55 (P102(f332(f332(f246(a876),x127891),x127891))), % 172.88/172.55 inference(rename_variables,[],[3290])). % 172.88/172.55 cnf(12793,plain, % 172.88/172.55 (P102(f332(f332(f247(a876),x127931),f332(a115,x127931)))), % 172.88/172.55 inference(rename_variables,[],[3359])). % 172.88/172.55 cnf(12796,plain, % 172.88/172.55 (P102(f332(f332(f246(a876),x127961),x127961))), % 172.88/172.55 inference(rename_variables,[],[3290])). % 172.88/172.55 cnf(12801,plain, % 172.88/172.55 (P102(f332(f332(f246(a876),x128011),x128011))), % 172.88/172.55 inference(rename_variables,[],[3290])). % 172.88/172.55 cnf(12804,plain, % 172.88/172.55 (P102(f332(f332(f246(a876),x128041),x128041))), % 172.88/172.55 inference(rename_variables,[],[3290])). % 172.88/172.55 cnf(12807,plain, % 172.88/172.55 (P102(f332(f332(f246(a876),x128071),x128071))), % 172.88/172.55 inference(rename_variables,[],[3290])). % 172.88/172.55 cnf(12810,plain, % 172.88/172.55 (E(f332(f332(f22(f883(x128101,a871)),f195(f883(x128101,a871))),x128102),f195(f883(x128101,a871)))), % 172.88/172.55 inference(rename_variables,[],[3565])). % 172.88/172.55 cnf(12811,plain, % 172.88/172.55 (P102(f332(f61(x128111),f195(f883(x128111,a871))))), % 172.88/172.55 inference(rename_variables,[],[3367])). % 172.88/172.55 cnf(12814,plain, % 172.88/172.55 (E(f332(f332(f22(f883(x128141,a871)),f195(f883(x128141,a871))),x128142),f195(f883(x128141,a871)))), % 172.88/172.55 inference(rename_variables,[],[3565])). % 172.88/172.55 cnf(12815,plain, % 172.88/172.55 (P102(f332(f61(x128151),f195(f883(x128151,a871))))), % 172.88/172.55 inference(rename_variables,[],[3367])). % 172.88/172.55 cnf(12818,plain, % 172.88/172.55 (E(f332(f332(f22(f883(x128181,a871)),f195(f883(x128181,a871))),x128182),f195(f883(x128181,a871)))), % 172.88/172.55 inference(rename_variables,[],[3565])). % 172.88/172.55 cnf(12819,plain, % 172.88/172.55 (P102(f332(f61(x128191),f195(f883(x128191,a871))))), % 172.88/172.55 inference(rename_variables,[],[3367])). % 172.88/172.55 cnf(12822,plain, % 172.88/172.55 (E(f332(f332(f22(f883(x128221,a871)),f195(f883(x128221,a871))),x128222),f195(f883(x128221,a871)))), % 172.88/172.55 inference(rename_variables,[],[3565])). % 172.88/172.55 cnf(12823,plain, % 172.88/172.55 (P102(f332(f61(x128231),f195(f883(x128231,a871))))), % 172.88/172.55 inference(rename_variables,[],[3367])). % 172.88/172.55 cnf(12827,plain, % 172.88/172.55 (E(f332(f263(x128271,x128271),f264(x128271,x128272)),x128272)), % 172.88/172.55 inference(rename_variables,[],[3246])). % 172.88/172.55 cnf(12832,plain, % 172.88/172.55 (E(f332(f332(f22(f883(x128321,a871)),f195(f883(x128321,a871))),x128322),f195(f883(x128321,a871)))), % 172.88/172.55 inference(rename_variables,[],[3565])). % 172.88/172.55 cnf(12833,plain, % 172.88/172.55 (P102(f332(f61(x128331),f195(f883(x128331,a871))))), % 172.88/172.55 inference(rename_variables,[],[3367])). % 172.88/172.55 cnf(12837,plain, % 172.88/172.55 (P102(f332(f61(x128371),f195(f883(x128371,a871))))), % 172.88/172.55 inference(rename_variables,[],[3367])). % 172.88/172.55 cnf(12840,plain, % 172.88/172.55 (P102(f332(f332(f246(a876),x128401),x128401))), % 172.88/172.55 inference(rename_variables,[],[3290])). % 172.88/172.55 cnf(12846,plain, % 172.88/172.55 (P102(f332(f332(f246(a1),x128461),x128461))), % 172.88/172.55 inference(rename_variables,[],[3291])). % 172.88/172.55 cnf(12849,plain, % 172.88/172.55 (P102(f332(f332(f247(a876),x128491),f332(a115,x128491)))), % 172.88/172.55 inference(rename_variables,[],[3359])). % 172.88/172.55 cnf(12854,plain, % 172.88/172.55 (P102(f332(f332(f246(a876),x128541),x128541))), % 172.88/172.55 inference(rename_variables,[],[3290])). % 172.88/172.55 cnf(12857,plain, % 172.88/172.55 (P102(f332(f332(f247(a876),x128571),f332(a115,x128571)))), % 172.88/172.55 inference(rename_variables,[],[3359])). % 172.88/172.55 cnf(12870,plain, % 172.88/172.55 (P102(f332(f332(f246(a1),x128701),x128701))), % 172.88/172.55 inference(rename_variables,[],[3291])). % 172.88/172.55 cnf(12875,plain, % 172.88/172.55 (~P102(f332(f332(f334(x128751),x128752),f195(f883(x128751,a871))))), % 172.88/172.55 inference(rename_variables,[],[4553])). % 172.88/172.55 cnf(12886,plain, % 172.88/172.55 (P102(f332(f332(f334(x128861),x128862),f255(f883(x128861,a871))))), % 172.88/172.55 inference(rename_variables,[],[3449])). % 172.88/172.55 cnf(12892,plain, % 172.88/172.55 (P102(f332(f332(f246(f883(x128921,a871)),x128922),x128922))), % 172.88/172.55 inference(rename_variables,[],[3594])). % 172.88/172.55 cnf(12898,plain, % 172.88/172.55 (~P102(f332(f332(f247(a876),x128981),f2(a876)))), % 172.88/172.55 inference(rename_variables,[],[4545])). % 172.88/172.55 cnf(12899,plain, % 172.88/172.55 (P102(f332(f332(f246(a1),x128991),x128991))), % 172.88/172.55 inference(rename_variables,[],[3291])). % 172.88/172.55 cnf(12903,plain, % 172.88/172.55 (~P102(f332(f332(f247(a876),x129031),f2(a876)))), % 172.88/172.55 inference(rename_variables,[],[4545])). % 172.88/172.55 cnf(12904,plain, % 172.88/172.55 (P102(f332(f332(f246(a1),x129041),x129041))), % 172.88/172.55 inference(rename_variables,[],[3291])). % 172.88/172.55 cnf(12913,plain, % 172.88/172.55 (P102(f332(f332(f246(a876),x129131),x129131))), % 172.88/172.55 inference(rename_variables,[],[3290])). % 172.88/172.55 cnf(12920,plain, % 172.88/172.55 (E(f332(f332(f16(x129201,x129202),x129203),x129204),x129203)), % 172.88/172.55 inference(rename_variables,[],[3279])). % 172.88/172.55 cnf(12923,plain, % 172.88/172.55 (P102(f332(f332(f246(f883(x129231,a871)),f332(f173(x129231),f177(x129231,x129232,x129233))),f332(f173(x129231),x129232)))), % 172.88/172.55 inference(rename_variables,[],[4003])). % 172.88/172.55 cnf(12927,plain, % 172.88/172.55 (~P102(f332(f332(f247(a876),x129271),f2(a876)))), % 172.88/172.55 inference(rename_variables,[],[4545])). % 172.88/172.55 cnf(12928,plain, % 172.88/172.55 (P102(f332(f332(f246(a1),x129281),x129281))), % 172.88/172.55 inference(rename_variables,[],[3291])). % 172.88/172.55 cnf(12932,plain, % 172.88/172.55 (~P102(f332(f332(f247(a876),x129321),f2(a876)))), % 172.88/172.55 inference(rename_variables,[],[4545])). % 172.88/172.55 cnf(12933,plain, % 172.88/172.55 (P102(f332(f332(f246(a1),x129331),x129331))), % 172.88/172.55 inference(rename_variables,[],[3291])). % 172.88/172.55 cnf(12938,plain, % 172.88/172.55 (P102(f332(f332(f246(a876),x129381),x129381))), % 172.88/172.55 inference(rename_variables,[],[3290])). % 172.88/172.55 cnf(12941,plain, % 172.88/172.55 (P102(f332(f332(f246(a876),x129411),x129411))), % 172.88/172.55 inference(rename_variables,[],[3290])). % 172.88/172.55 cnf(12944,plain, % 172.88/172.55 (~P102(f332(f332(f246(a876),f332(a115,x129441)),x129441))), % 172.88/172.55 inference(rename_variables,[],[4550])). % 172.88/172.55 cnf(12950,plain, % 172.88/172.55 (P102(f332(f332(f334(x129501),f332(x129502,x129503)),f332(f311(x129504,x129501,x129502),f255(f883(x129504,a871)))))), % 172.88/172.55 inference(rename_variables,[],[3907])). % 172.88/172.55 cnf(12951,plain, % 172.88/172.55 (P20(x129511,x129511,f5(x129511),x129512)), % 172.88/172.55 inference(rename_variables,[],[3534])). % 172.88/172.55 cnf(12955,plain, % 172.88/172.55 (P102(f332(f332(f334(x129551),x129552),f255(f883(x129551,a871))))), % 172.88/172.55 inference(rename_variables,[],[3449])). % 172.88/172.55 cnf(12956,plain, % 172.88/172.55 (~P102(f332(f332(f334(x129561),x129562),f195(f883(x129561,a871))))), % 172.88/172.55 inference(rename_variables,[],[4553])). % 172.88/172.55 cnf(12960,plain, % 172.88/172.55 (P102(f332(f332(f246(f883(x129601,a871)),x129602),f255(f883(x129601,a871))))), % 172.88/172.55 inference(rename_variables,[],[3680])). % 172.88/172.55 cnf(12961,plain, % 172.88/172.55 (P20(x129611,x129611,f5(x129611),x129612)), % 172.88/172.55 inference(rename_variables,[],[3534])). % 172.88/172.55 cnf(12965,plain, % 172.88/172.55 (P102(f332(f332(f246(f883(x129651,a871)),x129652),f255(f883(x129651,a871))))), % 172.88/172.55 inference(rename_variables,[],[3680])). % 172.88/172.55 cnf(12966,plain, % 172.88/172.55 (P20(x129661,x129661,f5(x129661),x129662)), % 172.88/172.55 inference(rename_variables,[],[3534])). % 172.88/172.55 cnf(12970,plain, % 172.88/172.55 (P20(x129701,x129701,f5(x129701),x129702)), % 172.88/172.55 inference(rename_variables,[],[3534])). % 172.88/172.55 cnf(12973,plain, % 172.88/172.55 (~P102(f332(f332(f247(f883(x129731,a871)),x129732),f195(f883(x129731,a871))))), % 172.88/172.55 inference(rename_variables,[],[4563])). % 172.88/172.55 cnf(12976,plain, % 172.88/172.55 (P20(x129761,x129761,f5(x129761),x129762)), % 172.88/172.55 inference(rename_variables,[],[3534])). % 172.88/172.55 cnf(12979,plain, % 172.88/172.55 (P20(x129791,x129791,f5(x129791),x129792)), % 172.88/172.55 inference(rename_variables,[],[3534])). % 172.88/172.55 cnf(12990,plain, % 172.88/172.55 (P102(f332(f332(f246(f883(x129901,a871)),f195(f883(x129901,a871))),x129902))), % 172.88/172.55 inference(rename_variables,[],[3747])). % 172.88/172.55 cnf(12994,plain, % 172.88/172.55 (E(f332(f263(x129941,x129941),f264(x129941,x129942)),x129942)), % 172.88/172.55 inference(rename_variables,[],[3246])). % 172.88/172.55 cnf(12998,plain, % 172.88/172.55 (~P102(f332(f332(f334(x129981),x129982),f195(f883(x129981,a871))))), % 172.88/172.55 inference(rename_variables,[],[4553])). % 172.88/172.55 cnf(13002,plain, % 172.88/172.55 (P102(f332(f332(f334(x130021),f332(x130022,x130023)),f332(f311(x130024,x130021,x130022),f255(f883(x130024,a871)))))), % 172.88/172.55 inference(rename_variables,[],[3907])). % 172.88/172.55 cnf(13003,plain, % 172.88/172.55 (P20(x130031,x130031,f5(x130031),x130032)), % 172.88/172.55 inference(rename_variables,[],[3534])). % 172.88/172.55 cnf(13006,plain, % 172.88/172.55 (P102(f332(f332(f334(x130061),x130062),f255(f883(x130061,a871))))), % 172.88/172.55 inference(rename_variables,[],[3449])). % 172.88/172.55 cnf(13013,plain, % 172.88/172.55 (~P102(f332(f332(f334(x130131),x130132),f195(f883(x130131,a871))))), % 172.88/172.55 inference(rename_variables,[],[4553])). % 172.88/172.55 cnf(13016,plain, % 172.88/172.55 (~P102(f332(f332(f334(x130161),x130162),f195(f883(x130161,a871))))), % 172.88/172.55 inference(rename_variables,[],[4553])). % 172.88/172.55 cnf(13020,plain, % 172.88/172.55 (E(f332(f332(f16(x130201,x130202),x130203),x130204),x130203)), % 172.88/172.55 inference(rename_variables,[],[3279])). % 172.88/172.55 cnf(13023,plain, % 172.88/172.55 (P102(f332(f332(f247(a876),x130231),f332(a115,x130231)))), % 172.88/172.55 inference(rename_variables,[],[3359])). % 172.88/172.55 cnf(13024,plain, % 172.88/172.55 (~E(f332(a115,x130241),x130241)), % 172.88/172.55 inference(rename_variables,[],[4480])). % 172.88/172.55 cnf(13027,plain, % 172.88/172.55 (P102(f332(f332(f247(a876),x130271),f332(a115,f332(f332(f79(a876),x130272),x130271))))), % 172.88/172.55 inference(rename_variables,[],[3749])). % 172.88/172.55 cnf(13028,plain, % 172.88/172.55 (P102(f332(f332(f247(a876),x130281),f332(a115,x130281)))), % 172.88/172.55 inference(rename_variables,[],[3359])). % 172.88/172.55 cnf(13030,plain, % 172.88/172.55 (~E(f332(f332(f80(a876),f332(a115,f2(a876))),f32(x130301,x130302)),f332(f332(f80(a876),f332(a115,f2(a876))),f31(x130303,x130304)))), % 172.88/172.55 inference(scs_inference,[],[4572,3534,11064,12101,12198,12293,12329,12337,12350,12405,12538,12540,12951,12961,12966,12970,12976,12979,3543,12165,12603,12605,3544,12232,3256,12554,12556,3257,12595,3222,12478,4513,4514,11685,4255,12580,12583,3260,12532,3099,3156,12560,4498,3596,4480,10217,10227,10240,10251,10254,10357,10360,10363,10466,10577,10885,11049,11052,11250,11337,11344,11358,11410,11413,11457,11525,11572,11588,11887,11912,11924,11953,11959,12054,12161,12168,12321,12375,12509,12627,13024,4495,10450,10541,3347,3310,12618,3503,3203,4490,2887,2888,2892,2893,2898,2902,2903,2908,2909,2911,2912,2914,2915,2916,2918,2919,2922,2925,2934,2936,2937,2943,2952,2956,2959,2962,2963,2964,2965,2966,2981,2992,2996,3004,3010,3021,3030,3031,3033,3034,3040,3046,3047,3048,3049,3056,3062,4475,3078,3155,4476,3635,3868,11619,3131,11334,3270,3243,3246,10220,10289,10292,10384,10387,10680,11349,11352,11468,11512,11517,11614,12075,12269,12458,12511,12519,12526,12536,12564,12587,12591,12593,12601,12614,12827,3881,3217,12353,12357,12361,3223,3231,3758,3358,12408,12481,4000,3120,3121,4492,3497,3853,11384,3346,12513,3180,3147,3673,12568,3142,3974,3163,3678,3128,3129,3109,3771,3162,3348,10832,12162,3215,3216,3395,4562,10420,3940,4505,10280,10447,11247,12317,12354,12358,4512,12325,3279,11708,11711,12920,4551,10999,11069,11293,11296,3698,3276,3396,3620,3362,12578,3177,10349,10656,3178,4539,3454,3170,3100,3199,11374,4087,12340,12470,3942,11005,11131,11182,12301,12307,12419,12422,12445,4575,10937,11136,11241,11263,11301,11307,12248,4576,11038,11139,11244,4577,11142,11193,4578,11196,4579,3198,3495,12201,12245,12324,3661,4371,4372,4503,11365,3598,3638,3816,3565,12810,12814,12818,12822,12832,3863,12195,3480,3740,3359,10368,10486,10555,10616,10619,10659,10753,10989,11883,11946,12025,12066,12127,12130,12449,12633,12691,12722,12734,12793,12849,12857,13023,3751,11605,3272,3371,11723,3559,4545,10257,10260,10286,10761,10774,10895,11285,11377,11772,11780,12001,12004,12092,12251,12344,12638,12641,12658,12661,12683,12735,12898,12903,12927,4557,11487,11520,11555,11585,12744,12748,3738,3504,3506,12664,12667,12670,12673,12703,3890,3318,3319,3293,4542,3176,4500,3689,4225,4009,3487,4558,4081,11258,3619,3331,11732,11735,12172,12273,12429,4051,4008,11876,12216,3952,10829,12060,12229,4003,11008,12098,12171,12228,12272,3662,11886,12032,12106,12152,4040,3680,11011,11074,11155,11215,12053,12120,12370,12442,12455,12960,12965,4563,10777,11147,12973,3289,10377,10473,10602,10666,11460,11679,11726,11760,11856,11911,12113,3290,10735,10780,10783,10816,10842,10879,10917,10953,11927,11930,11933,11936,12133,12136,12139,12142,12209,12381,12425,12684,12709,12782,12789,12796,12801,12804,12807,12840,12854,12913,12938,12941,3291,10406,10461,10671,10756,10882,11568,11763,11775,11862,11873,11894,11899,11939,11964,11979,12700,12846,12870,12899,12904,12928,3292,3367,12086,12764,12811,12815,12819,12823,12833,12837,4541,10323,10415,10526,10550,10798,10845,10855,11534,11633,11654,11657,11660,11676,11818,11821,11824,11827,11923,11942,11945,11958,12013,12016,12019,12022,12093,12183,12186,12279,12282,12343,12374,12411,12490,3449,10622,10890,10934,11204,11282,11445,11688,12320,12493,12886,12955,4553,10807,10819,10926,10944,10947,11002,11088,11096,11112,11150,11167,11176,11212,11253,11273,11276,11279,11310,11317,11320,11705,11741,12007,12010,12044,12087,12116,12257,12298,12304,12393,12396,12415,12469,12475,12484,12503,12763,12776,12779,12875,12956,12998,13013,3352,10653,10683,10692,11233,11787,12412,12426,12745,12749,12752,3391,3385,3820,3756,10326,11608,11636,12727,4550,10277,10647,10650,11091,11109,11571,11624,11668,11689,11793,11830,11833,11836,11839,12944,3312,10686,10839,10910,11637,11792,11984,12210,3781,11738,12680,4131,3510,4548,3792,3828,4531,4533,4534,3263,3264,4532,4535,4536,3799,3609,11601,4231,11467,4565,10245,10248,10507,10558,10561,10566,10976,11439,11692,11796,4573,11170,11290,11326,4017,12240,3907,11323,11663,11667,11729,12328,12336,12418,12694,12950,13002,3745,10950,10956,10971,11908,12037,12119,12389,3594,11173,12145,12254,12264,12333,12384,12392,12500,3633,4085,3747,10689,11027,11179,11209,11220,12057,12222,12332,12378,3560,10608,10611,10695,10869,3562,4569,11602,4559,4564,12648,4570,10746,10848,11158,11442,11473,12204,12213,12260,12439,4191,10822,12225,12237,12263,4092,3780,12506,3724,3725,4567,10299,10302,10641,10644,11484,11664,12448,4568,11582,11673,3749,10605,10866,4024,4590,4616,4665,4667,4698,4715,4722,4723,4759,4764,4794,4800,4884,4909,4910,4925,4947,4972,4973,4995,4996,5009,5013,5036,5042,5058,5061,5062,5063,5068,5069,5091,5116,5117,5127,5132,5138,5175,5176,5184,5193,5198,5200,5211,5213,5219,5223,5224,5237,5244,5247,5248,5249,5253,5289,5302,5310,5312,5313,5317,5318,5319,5327,5330,5335,5336,5337,5344,5348,5349,5350,5359,5363,5364,5365,5370,5383,5392,5404,5406,5414,5415,5419,5423,5448,5454,5464,5465,5480,5493,5515,5521,5539,5540,5543,5562,5570,5571,5576,5577,5587,5589,5601,5605,5614,5615,5617,5632,5637,5647,5648,5660,5667,5681,5685,5688,5694,5695,5696,5699,5704,5740,5741,5744,5746,5749,5750,5751,5753,5755,5757,5762,5769,5784,5798,5803,5804,5817,5818,5823,5827,5829,5834,5875,5887,5896,5900,5909,5913,5914,5922,5936,5942,5960,5963,5975,6002,6016,6041,6061,6062,6065,6080,6082,6083,6085,6098,6099,6102,6104,6107,6108,6120,6126,6127,6128,6130,6132,6169,6170,6175,6178,6184,6188,6224,6226,6228,6230,6239,6241,6243,6249,6251,6257,6260,6268,6275,6276,6277,6282,6304,6305,6306,6308,6314,6319,6353,6354,6358,6359,6360,6361,6362,6363,6364,6371,6404,6405,6414,6435,6436,6456,6458,6469,6470,6476,6506,6508,6522,6560,6562,6563,6616,6641,6683,6703,6712,6713,6714,6715,6734,6735,6741,6754,6757,6759,6761,6762,6763,6765,6779,6790,6792,6793,6806,6810,6861,6872,6874,6878,6895,6896,6932,6944,6975,6994,7009,7063,7091,7146,7167,7176,7179,7234,7242,7300,7302,7317,7325,7328,7329,7348,7354,7356,7405,7415,7418,7434,7486,7487,7491,7535,7536,7554,7621,7640,7663,7687,7702,7718,7728,7737,7738,7767,7770,7772,7782,7820,7831,7856,7914,7948,7981,8028,8044,8060,8061,8136,8190,8209,8233,8253,8277,8375,8377,8383,8400,8404,8420,8443,8454,8456,8471,8476,8480,8503,8517,8518,8534,8535,8540,8541,8542,8543,8544,8562,8563,8564,8572,8585,8587,8599,8603,8605,8606,8607,8615,8620,8647,8648,8679,8692,8696,8714,8736,8737,8738,8739,8751,8752,8774,8784,8794,8795,8796,8797,8799,8821,8822,8833,8877,8883,8889,8902,8907,8909,8912,8913,8917,8927,9009,9040,9041,9042,9057,9074,9080,9108,9109,9150,9153,9179,9224,9225,9226,9241,9266,9280,9286,9289,9311,9312,9340,9402,9437,9438,9439,9464,9465,9483,9501,9507,9521,9544,9566,9574,9575,9576,9577,9592,9594,9599,9630,9631,9637,9638,9682,9683,9714,9723,9733,9735,9736,9745,9759,9762,9790,9823,9825,9829,9886,9927,9928,9930,9940,9941,9961,9966,10007,10059,10131,10132,10185,10201,2,8,9,4603,4604,4622,4653,4655,4656,4684,4690,4691,4702,4751,4753,4785,4799,4829,4926,4927,4940,4960,5016,5017,5020,5021,5023,5025,5026,5035,5038,5039,5047,5059,5060,5066,5086,5087,5104,5109,5110,5111,5112,5115,5123,5126,5133,5190,5196,5197,5205,5234,5245,5251,5267,5287,5288,5295,5296,5297,5306,5316,5323,5325,5326,5332,5340,5341,5351,5355,5356,5357,5358,5360,5361,5366,5367,5368,5369,5400,5401,5402,5410,5411,5412,5413,5459,5461,5463,5500,5502,5503,5505,5506,5508,5509,5511,5520,5525,5527,5528,5529,5530,5531,5532,5541,5551,5554,5565,5581,5582,5585,5595,5597,5598,5599,5624,5634,5650,5651,5661,5662,5664,5666,5671,5706,5711,5713,5771,5805,5806,5810,5816,5819,5820,5821,5822,5828,5839,5840,5842,5843,5851,5872,5901,5917,5920,5921,5923,5932,5953,5954,5955,5958,5959,5977,5988,5989,6018,6019,6023,6043,6046,6050,6069,6074,6075,6100,6103,6111,6119,6125,6129,6136,6137,6138,6139,6172,6189,6242,6278,6280,6301,6302,6307,6310,6311,6315,6321,6330,6346,6366,6367,6372,6382,6397,6417,6423,6425,6440,6441,6444,6445,6447,6449,6450,6451,6453,6455,6457,6463,6464,6465,6466,6472,6474,6516,6521,6536,6537,6538,6539,6574,6579,6581,6586,6587,6595,6599,6612,6637,6638,6639,6640,6651,6657,6673,6677,6696,6729,6730,6731,6736,6750,6771,6773,6775,6777,6780,6786,6788,6803,6808,6811,6847,6850,6851,6864,6865,6866,6867,6886,6887,6904,6930,6952,6963,6965,6966,6968,6970,6971,7006,7007,7012,7013,7014,7015,7017,7019,7044,7053,7054,7066,7076,7115,7125,7129,7136,7147,7153,7155,7161,7169,7170,7183,7200,7218,7220,7237,7286,7288,7289,7290,7296,7301,7324,7369,7402,7416,7433,7466,7469,7495,7519,7537,7540,7541,7551,7569,7570,7572,7574,7576,7578,7604,7629,7630,7662,7664,7665,7666,7671,7694,7703,7714,7719,7725,7727,7733,7745,7746,7748,7780,7803,7869,7870,7917,7925,7926,7950,7951,7968,7969,8036,8037,8038,8063,8096,8103,8105,8114,8126,8159,8165,8172,8185,8204,8210,8232,8275,8305,8317,8335,8338,8368,8391,8457,8458,8461,8463,8566,8567,8568,8569,8594,8623,8651,8695,8713,8768,8814,8817,8830,8837,8874,8895,8923,8924,8942,8943,9082,9086,9106,9116,9139,9141,9144,9148,9151,9152,9165,9166,9186,9192,9204,9252,9270,9324,9325,9332,9394,9399,9434,9441,9444,9447,9448,9463,9479,9488,9500,9510,9511,9514,9516,9542,9665,9709,9710,9752,9797,9913,9970,10035,10110,10123,10128,3,2626,2627,2628,2629,2630,2634,2635,2636,2640,2643,2647,2648,2649,2653,2664,2666,2672,2676,2677,2678,2679,2683,2684,2686,2687,2688,2689,2690,2692,2693,2694,2695,2696,2702,2710,2711,2713,2714,2715,2718,2722,2723,2724,2738,2741,2742,2743,2745,2754,2758,2761,2770,2771,2772,2774,2783,2785,2786,2788,2794,2795,2796,2804,2813,2815,2817,2818,2842,2843,2857,5226,5286,5386,5472,5473,5474,5552,5649,5680,5714,5730,5732,5738,5799,5800,5801,5802,5808,5841,5972,6017,6040,6077,6117,6258,6265,6299,6300,6320,6323,6325,6332,6333,6334,6335,6336,6337,6338,6339,6419,6486,6487,6572,6606,6607,6648,6649,6787,6802,6875,6876,6883,6905,6936,6938,6985,7010,7011,7027,7028,7029,7065,7109,7110,7207,7268,7269,7270,7271,7285,7318,7374,7375,7384,7390,7392,7404,7436,7437,7438,7439,7584,7585,7592,7594,7595,7596,7811,7813,7814,7829,7867,7946,7989,8047,8068,8069,8084,8143,8246,8315,8316,8318,8353,8416,8417,8489,8510,8511,8512,8513,8655,8867,8891,8892,8974,8988,9043,9044,9160,9196,9219,9253,9294,9486,9746,9939,9995,9997,6035,6402,6403,6489])). % 172.88/172.55 cnf(13037,plain, % 172.88/172.55 (P102(f332(f332(f246(a1),f2(a1)),f332(f103(a1),x130371)))), % 172.88/172.55 inference(rename_variables,[],[3391])). % 172.88/172.55 cnf(13040,plain, % 172.88/172.55 (P102(f332(f332(f246(a876),f2(a876)),x130401))), % 172.88/172.55 inference(rename_variables,[],[3312])). % 172.88/172.55 cnf(13041,plain, % 172.88/172.55 (P102(f332(f332(f246(a876),x130411),x130411))), % 172.88/172.55 inference(rename_variables,[],[3290])). % 172.88/172.55 cnf(13044,plain, % 172.88/172.55 (~E(f332(a115,x130441),f2(a876))), % 172.88/172.55 inference(rename_variables,[],[4490])). % 172.88/172.55 cnf(13057,plain, % 172.88/172.55 (~P102(f332(f332(f334(x130571),x130572),f195(f883(x130571,a871))))), % 172.88/172.55 inference(rename_variables,[],[4553])). % 172.88/172.55 cnf(13060,plain, % 172.88/172.55 (P102(f332(f61(a876),f305(a876,x130601,x130602)))), % 172.88/172.55 inference(rename_variables,[],[3506])). % 172.88/172.55 cnf(13061,plain, % 172.88/172.55 (E(f332(f332(f245(a876),f332(a115,x130611)),f332(a115,x130612)),f332(a115,f332(f332(f245(a876),x130611),x130612)))), % 172.88/172.55 inference(rename_variables,[],[3467])). % 172.88/172.55 cnf(13064,plain, % 172.88/172.55 (P102(f332(f61(a876),f305(a876,x130641,x130642)))), % 172.88/172.55 inference(rename_variables,[],[3506])). % 172.88/172.55 cnf(13065,plain, % 172.88/172.55 (E(f332(f332(f244(a876),f332(a115,x130651)),f332(a115,x130652)),f332(a115,f332(f332(f244(a876),x130651),x130652)))), % 172.88/172.55 inference(rename_variables,[],[3466])). % 172.88/172.55 cnf(13068,plain, % 172.88/172.55 (P102(f332(f61(a876),f305(a876,x130681,x130682)))), % 172.88/172.55 inference(rename_variables,[],[3506])). % 172.88/172.55 cnf(13076,plain, % 172.88/172.55 (P102(f332(f332(f246(f883(x130761,a871)),f332(f173(x130761),f332(f136(x130761,x130762),x130763))),f332(f173(x130761),x130763)))), % 172.88/172.55 inference(rename_variables,[],[3952])). % 172.88/172.55 cnf(13077,plain, % 172.88/172.55 (E(f332(f332(f16(x130771,x130772),x130773),x130774),x130773)), % 172.88/172.55 inference(rename_variables,[],[3279])). % 172.88/172.55 cnf(13080,plain, % 172.88/172.55 (P102(f332(f332(f246(f883(x130801,a871)),f332(f173(x130801),f332(f332(f176(x130801),x130802),x130803))),f332(f173(x130801),x130803)))), % 172.88/172.55 inference(rename_variables,[],[3997])). % 172.88/172.55 cnf(13081,plain, % 172.88/172.55 (E(f332(f332(f16(x130811,x130812),x130813),x130814),x130813)), % 172.88/172.55 inference(rename_variables,[],[3279])). % 172.88/172.55 cnf(13085,plain, % 172.88/172.55 (E(f332(f332(f16(x130851,x130852),x130853),x130854),x130853)), % 172.88/172.55 inference(rename_variables,[],[3279])). % 172.88/172.55 cnf(13098,plain, % 172.88/172.55 (P102(f332(f332(f246(a1),f2(a1)),f332(f103(a1),x130981)))), % 172.88/172.55 inference(rename_variables,[],[3391])). % 172.88/172.55 cnf(13101,plain, % 172.88/172.55 (~P102(f332(f332(f334(x131011),x131012),f195(f883(x131011,a871))))), % 172.88/172.55 inference(rename_variables,[],[4553])). % 172.88/172.55 cnf(13104,plain, % 172.88/172.55 (~P102(f332(f332(f334(x131041),x131042),f195(f883(x131041,a871))))), % 172.88/172.55 inference(rename_variables,[],[4553])). % 172.88/172.55 cnf(13105,plain, % 172.88/172.55 (E(f332(f263(x131051,x131051),f264(x131051,x131052)),x131052)), % 172.88/172.55 inference(rename_variables,[],[3246])). % 172.88/172.55 cnf(13106,plain, % 172.88/172.55 (P20(x131061,x131061,f5(x131061),x131062)), % 172.88/172.55 inference(rename_variables,[],[3534])). % 172.88/172.55 cnf(13110,plain, % 172.88/172.55 (E(f332(f263(x131101,x131101),f264(x131101,x131102)),x131102)), % 172.88/172.55 inference(rename_variables,[],[3246])). % 172.88/172.55 cnf(13116,plain, % 172.88/172.55 (P102(f332(f332(f247(a876),x131161),f332(a115,x131161)))), % 172.88/172.55 inference(rename_variables,[],[3359])). % 172.88/172.55 cnf(13118,plain, % 172.88/172.55 (P102(f332(f332(f246(a876),x131181),x131181))), % 172.88/172.55 inference(rename_variables,[],[3290])). % 172.88/172.55 cnf(13119,plain, % 172.88/172.55 (P102(f332(f332(f246(a876),f2(a876)),x131191))), % 172.88/172.55 inference(rename_variables,[],[3312])). % 172.88/172.55 cnf(13122,plain, % 172.88/172.55 (P102(f332(f332(f247(a876),x131221),f332(a115,x131221)))), % 172.88/172.55 inference(rename_variables,[],[3359])). % 172.88/172.55 cnf(13125,plain, % 172.88/172.55 (P102(f332(f332(f246(a876),f2(a876)),x131251))), % 172.88/172.55 inference(rename_variables,[],[3312])). % 172.88/172.55 cnf(13129,plain, % 172.88/172.55 (P102(f332(f332(f246(a876),f2(a876)),x131291))), % 172.88/172.55 inference(rename_variables,[],[3312])). % 172.88/172.55 cnf(13130,plain, % 172.88/172.55 (P102(f332(f332(f247(a876),f2(a876)),f332(a115,x131301)))), % 172.88/172.55 inference(rename_variables,[],[3371])). % 172.88/172.55 cnf(13131,plain, % 172.88/172.55 (E(f332(f263(x131311,x131311),f264(x131311,x131312)),x131312)), % 172.88/172.55 inference(rename_variables,[],[3246])). % 172.88/172.55 cnf(13204,plain, % 172.88/172.55 (P102(f332(f332(f247(a1),f2(a1)),f332(f74(a1),f77(a1))))), % 172.88/172.55 inference(scs_inference,[],[4572,3534,11064,12101,12198,12293,12329,12337,12350,12405,12538,12540,12951,12961,12966,12970,12976,12979,13003,13106,3543,12165,12603,12605,3544,12232,3256,12554,12556,3257,12595,3222,12478,4513,4514,11685,4255,12580,12583,3260,12532,3099,3156,12560,4498,3596,4480,10217,10227,10240,10251,10254,10357,10360,10363,10466,10577,10885,11049,11052,11250,11337,11344,11358,11410,11413,11457,11525,11572,11588,11887,11912,11924,11953,11959,12054,12161,12168,12321,12375,12509,12627,13024,4495,10450,10541,3347,3310,12618,3503,3203,4490,12695,13044,2887,2888,2892,2893,2898,2902,2903,2908,2909,2911,2912,2914,2915,2916,2918,2919,2922,2925,2934,2936,2937,2943,2952,2956,2959,2962,2963,2964,2965,2966,2967,2973,2981,2986,2992,2993,2996,3004,3010,3021,3030,3031,3033,3034,3040,3046,3047,3048,3049,3056,3062,4475,3078,3155,4476,3635,3868,11619,3131,11334,3270,3243,3246,10220,10289,10292,10384,10387,10680,11349,11352,11468,11512,11517,11614,12075,12269,12458,12511,12519,12526,12536,12564,12587,12591,12593,12601,12614,12827,12994,13105,13110,13131,3881,3217,12353,12357,12361,3223,3231,3758,3358,12408,12481,4000,3120,3121,4492,3497,3853,11384,3346,12513,3180,3147,3673,12568,3142,3974,3163,3678,3128,3129,3109,3771,3162,3348,10832,12162,3215,3216,3395,4562,10420,3940,4505,10280,10447,11247,12317,12354,12358,4512,12325,3279,11708,11711,12920,13020,13077,13081,13085,4551,10999,11069,11293,11296,3698,3276,3396,3620,3388,3362,12578,3177,10349,10656,3178,4539,3454,3170,3100,3284,3199,11374,4087,12340,12470,3942,11005,11131,11182,12301,12307,12419,12422,12445,4575,10937,11136,11241,11263,11301,11307,12248,4576,11038,11139,11244,4577,11142,11193,4578,11196,4579,3198,3495,12201,12245,12324,3661,4371,4372,3477,4503,11365,3598,3638,3816,3565,12810,12814,12818,12822,12832,3863,12195,3480,3740,3359,10368,10486,10555,10616,10619,10659,10753,10989,11883,11946,12025,12066,12127,12130,12449,12633,12691,12722,12734,12793,12849,12857,13023,13028,13116,13122,3751,11605,3272,3371,11723,12626,13130,3559,4545,10257,10260,10286,10761,10774,10895,11285,11377,11772,11780,12001,12004,12092,12251,12344,12638,12641,12658,12661,12683,12735,12898,12903,12927,12932,4557,11487,11520,11555,11585,12744,12748,3738,3504,3506,12664,12667,12670,12673,12703,12706,13060,13064,13068,3507,3890,3466,13065,3467,13061,3318,3319,3293,4542,3176,4500,3689,4225,4009,3487,4558,4081,11258,3619,3331,11732,11735,12172,12273,12429,4051,4008,11876,12216,3952,10829,12060,12229,12452,13076,3997,13080,4003,11008,12098,12171,12228,12272,12923,4004,3662,11886,12032,12106,12152,4040,3680,11011,11074,11155,11215,12053,12120,12370,12442,12455,12960,12965,4563,10777,11147,12973,3289,10377,10473,10602,10666,11460,11679,11726,11760,11856,11911,12113,3290,10735,10780,10783,10816,10842,10879,10917,10953,11927,11930,11933,11936,12133,12136,12139,12142,12209,12381,12425,12684,12709,12782,12789,12796,12801,12804,12807,12840,12854,12913,12938,12941,13041,13118,3291,10406,10461,10671,10756,10882,11568,11763,11775,11862,11873,11894,11899,11939,11964,11979,12700,12846,12870,12899,12904,12928,12933,3292,3367,12086,12764,12811,12815,12819,12823,12833,12837,4541,10323,10415,10526,10550,10798,10845,10855,11534,11633,11654,11657,11660,11676,11818,11821,11824,11827,11923,11942,11945,11958,12013,12016,12019,12022,12093,12183,12186,12279,12282,12343,12374,12411,12490,3449,10622,10890,10934,11204,11282,11445,11688,12320,12493,12886,12955,13006,4553,10807,10819,10926,10944,10947,11002,11088,11096,11112,11150,11167,11176,11212,11253,11273,11276,11279,11310,11317,11320,11705,11741,12007,12010,12044,12087,12116,12257,12298,12304,12393,12396,12415,12469,12475,12484,12503,12763,12776,12779,12875,12956,12998,13013,13016,13057,13101,13104,3352,10653,10683,10692,11233,11787,12412,12426,12745,12749,12752,3391,13037,13098,3385,3820,3756,10326,11608,11636,12727,4550,10277,10647,10650,11091,11109,11571,11624,11668,11689,11793,11830,11833,11836,11839,12944,3312,10686,10839,10910,11637,11792,11984,12210,12773,13040,13119,13125,13129,3781,11738,12680,4131,3510,4548,3792,3828,4531,4533,4534,3263,3264,4532,4535,4536,4308,3799,3609,11601,4231,11467,4565,10245,10248,10507,10558,10561,10566,10976,11439,11692,11796,4573,11170,11290,11326,4017,12240,3907,11323,11663,11667,11729,12328,12336,12418,12694,12950,13002,3745,10950,10956,10971,11908,12037,12119,12389,3594,11173,12145,12254,12264,12333,12384,12392,12500,12892,3633,4085,3747,10689,11027,11179,11209,11220,12057,12222,12332,12378,12990,3560,10608,10611,10695,10869,3562,4569,11602,4559,4564,12648,4570,10746,10848,11158,11442,11473,12204,12213,12260,12439,4191,10822,12225,12237,12263,4092,3780,12506,3724,3725,4567,10299,10302,10641,10644,11484,11664,12448,4568,11582,11673,3749,10605,10866,13027,4024,4590,4616,4665,4667,4698,4715,4722,4723,4759,4764,4794,4800,4884,4909,4910,4925,4947,4972,4973,4995,4996,5009,5013,5036,5042,5058,5061,5062,5063,5068,5069,5091,5116,5117,5127,5132,5138,5175,5176,5184,5193,5198,5200,5211,5213,5219,5223,5224,5237,5244,5247,5248,5249,5253,5289,5302,5310,5312,5313,5317,5318,5319,5327,5330,5335,5336,5337,5344,5348,5349,5350,5359,5363,5364,5365,5370,5383,5392,5404,5406,5414,5415,5419,5423,5448,5454,5464,5465,5480,5493,5515,5521,5539,5540,5543,5562,5570,5571,5576,5577,5587,5589,5601,5605,5614,5615,5617,5632,5637,5647,5648,5660,5667,5681,5685,5688,5694,5695,5696,5699,5704,5740,5741,5744,5746,5749,5750,5751,5753,5755,5757,5762,5769,5784,5798,5803,5804,5817,5818,5823,5827,5829,5834,5875,5887,5896,5900,5909,5913,5914,5922,5936,5942,5960,5963,5975,6002,6016,6041,6061,6062,6065,6080,6082,6083,6085,6098,6099,6102,6104,6107,6108,6120,6126,6127,6128,6130,6132,6169,6170,6175,6178,6184,6188,6224,6226,6228,6230,6239,6241,6243,6249,6251,6257,6260,6268,6275,6276,6277,6282,6304,6305,6306,6308,6314,6319,6353,6354,6358,6359,6360,6361,6362,6363,6364,6371,6404,6405,6414,6435,6436,6456,6458,6469,6470,6476,6506,6508,6522,6560,6562,6563,6616,6641,6683,6703,6712,6713,6714,6715,6734,6735,6741,6754,6757,6759,6761,6762,6763,6765,6779,6790,6792,6793,6806,6810,6861,6872,6874,6878,6895,6896,6932,6944,6975,6994,7009,7063,7091,7146,7167,7176,7179,7234,7242,7300,7302,7317,7325,7328,7329,7348,7354,7356,7405,7415,7418,7434,7486,7487,7491,7535,7536,7554,7621,7640,7663,7687,7702,7718,7728,7737,7738,7767,7770,7772,7782,7820,7831,7856,7914,7948,7981,8028,8044,8060,8061,8136,8190,8209,8233,8253,8277,8375,8377,8383,8400,8404,8420,8443,8454,8456,8471,8476,8480,8503,8517,8518,8534,8535,8540,8541,8542,8543,8544,8562,8563,8564,8572,8585,8587,8599,8603,8605,8606,8607,8615,8620,8647,8648,8679,8692,8696,8714,8736,8737,8738,8739,8751,8752,8774,8784,8794,8795,8796,8797,8799,8821,8822,8833,8877,8883,8889,8902,8907,8909,8912,8913,8917,8927,9009,9040,9041,9042,9057,9074,9080,9108,9109,9150,9153,9179,9224,9225,9226,9241,9266,9280,9286,9289,9311,9312,9340,9402,9437,9438,9439,9464,9465,9483,9501,9507,9521,9544,9566,9574,9575,9576,9577,9592,9594,9599,9630,9631,9637,9638,9682,9683,9714,9723,9733,9735,9736,9745,9759,9762,9790,9823,9825,9829,9886,9927,9928,9930,9940,9941,9961,9966,10007,10059,10131,10132,10185,10201,2,8,9,4603,4604,4622,4653,4655,4656,4684,4690,4691,4702,4751,4753,4785,4799,4829,4926,4927,4940,4960,5016,5017,5020,5021,5023,5025,5026,5035,5038,5039,5047,5059,5060,5066,5086,5087,5104,5109,5110,5111,5112,5115,5123,5126,5133,5190,5196,5197,5205,5234,5245,5251,5267,5287,5288,5295,5296,5297,5306,5316,5323,5325,5326,5332,5340,5341,5351,5355,5356,5357,5358,5360,5361,5366,5367,5368,5369,5400,5401,5402,5410,5411,5412,5413,5459,5461,5463,5500,5502,5503,5505,5506,5508,5509,5511,5520,5525,5527,5528,5529,5530,5531,5532,5541,5551,5554,5565,5581,5582,5585,5595,5597,5598,5599,5624,5634,5650,5651,5661,5662,5664,5666,5671,5706,5711,5713,5771,5805,5806,5810,5816,5819,5820,5821,5822,5828,5839,5840,5842,5843,5851,5872,5901,5917,5920,5921,5923,5932,5953,5954,5955,5958,5959,5977,5988,5989,6018,6019,6023,6043,6046,6050,6069,6074,6075,6100,6103,6111,6119,6125,6129,6136,6137,6138,6139,6172,6189,6242,6278,6280,6301,6302,6307,6310,6311,6315,6321,6330,6346,6366,6367,6372,6382,6397,6417,6423,6425,6440,6441,6444,6445,6447,6449,6450,6451,6453,6455,6457,6463,6464,6465,6466,6472,6474,6516,6521,6536,6537,6538,6539,6574,6579,6581,6586,6587,6595,6599,6612,6637,6638,6639,6640,6651,6657,6673,6677,6696,6729,6730,6731,6736,6750,6771,6773,6775,6777,6780,6786,6788,6803,6808,6811,6847,6850,6851,6864,6865,6866,6867,6886,6887,6904,6930,6952,6963,6965,6966,6968,6970,6971,7006,7007,7012,7013,7014,7015,7017,7019,7044,7053,7054,7066,7076,7115,7125,7129,7136,7147,7153,7155,7161,7169,7170,7183,7200,7218,7220,7237,7286,7288,7289,7290,7296,7301,7324,7369,7402,7416,7433,7466,7469,7495,7519,7537,7540,7541,7551,7569,7570,7572,7574,7576,7578,7604,7629,7630,7662,7664,7665,7666,7671,7694,7703,7714,7719,7725,7727,7733,7745,7746,7748,7780,7803,7869,7870,7917,7925,7926,7950,7951,7968,7969,8036,8037,8038,8063,8096,8103,8105,8114,8126,8159,8165,8172,8185,8204,8210,8232,8275,8305,8317,8335,8338,8368,8391,8457,8458,8461,8463,8566,8567,8568,8569,8594,8623,8651,8695,8713,8768,8814,8817,8830,8837,8874,8895,8923,8924,8942,8943,9082,9086,9106,9116,9139,9141,9144,9148,9151,9152,9165,9166,9186,9192,9204,9252,9270,9324,9325,9332,9394,9399,9434,9441,9444,9447,9448,9463,9479,9488,9500,9510,9511,9514,9516,9542,9665,9709,9710,9752,9797,9913,9970,10035,10110,10123,10128,3,2626,2627,2628,2629,2630,2634,2635,2636,2640,2643,2647,2648,2649,2653,2664,2666,2672,2676,2677,2678,2679,2683,2684,2686,2687,2688,2689,2690,2692,2693,2694,2695,2696,2702,2710,2711,2713,2714,2715,2718,2722,2723,2724,2738,2741,2742,2743,2745,2754,2758,2761,2770,2771,2772,2774,2783,2785,2786,2788,2794,2795,2796,2804,2813,2815,2817,2818,2842,2843,2857,5226,5286,5386,5472,5473,5474,5552,5649,5680,5714,5730,5732,5738,5799,5800,5801,5802,5808,5841,5972,6017,6040,6077,6117,6258,6265,6299,6300,6320,6323,6325,6332,6333,6334,6335,6336,6337,6338,6339,6419,6486,6487,6572,6606,6607,6648,6649,6787,6802,6875,6876,6883,6905,6936,6938,6985,7010,7011,7027,7028,7029,7065,7109,7110,7207,7268,7269,7270,7271,7285,7318,7374,7375,7384,7390,7392,7404,7436,7437,7438,7439,7584,7585,7592,7594,7595,7596,7811,7813,7814,7829,7867,7946,7989,8047,8068,8069,8084,8143,8246,8315,8316,8318,8353,8416,8417,8489,8510,8511,8512,8513,8655,8867,8891,8892,8974,8988,9043,9044,9160,9196,9219,9253,9294,9486,9746,9939,9995,9997,6035,6402,6403,6489,6509,6510,6927,7145,8303,8580,8613,8807,9000,9001,9071,9072,9342,9343,9344,9345,9545,9817,10119,10170,10171,6471,8407,8408,8857,8875,9818,10169,4657,4659,4660,4716,4724,4862,4878,4879,4901,4907,4908,4939,4994,5054,5113,5163,5183,5220,5222,5229,5230,5256,5331,5354,5489,5557,5558,5559,5676])). % 172.88/172.55 cnf(13228,plain, % 172.88/172.55 (~P102(f332(f61(x132281),f39(f883(x132281,a871),f255(f883(f883(x132281,a871),a871)))))), % 172.88/172.55 inference(scs_inference,[],[4572,3534,11064,12101,12198,12293,12329,12337,12350,12405,12538,12540,12951,12961,12966,12970,12976,12979,13003,13106,3543,12165,12603,12605,3544,12232,3256,12554,12556,3257,12595,3222,12478,4513,4514,11685,4255,12580,12583,3260,12532,3099,3156,12560,4498,3596,4480,10217,10227,10240,10251,10254,10357,10360,10363,10466,10577,10885,11049,11052,11250,11337,11344,11358,11410,11413,11457,11525,11572,11588,11887,11912,11924,11953,11959,12054,12161,12168,12321,12375,12509,12627,13024,4495,10450,10541,3347,3310,12618,3503,3203,4490,12695,13044,2887,2888,2892,2893,2898,2902,2903,2908,2909,2911,2912,2914,2915,2916,2918,2919,2922,2925,2934,2936,2937,2943,2952,2956,2959,2962,2963,2964,2965,2966,2967,2973,2981,2986,2992,2993,2996,3004,3010,3021,3030,3031,3033,3034,3040,3046,3047,3048,3049,3056,3062,4475,3078,3155,4476,3635,3868,11619,3131,11334,3270,3243,3246,10220,10289,10292,10384,10387,10680,11349,11352,11468,11512,11517,11614,12075,12269,12458,12511,12519,12526,12536,12564,12587,12591,12593,12601,12614,12827,12994,13105,13110,13131,3881,3217,12353,12357,12361,3223,3231,3758,3358,12408,12481,4000,3120,3121,4492,3497,3853,11384,3346,12513,3180,3147,3673,12568,3142,3974,3163,3678,3128,3129,3109,3771,3162,3348,10832,12162,3215,3216,3395,4562,10420,3940,4505,10280,10447,11247,12317,12354,12358,4512,12325,3279,11708,11711,12920,13020,13077,13081,13085,4551,10999,11069,11293,11296,3698,3276,3396,3620,3388,3362,12578,3177,10349,10656,3178,4539,3454,3170,3100,3284,3199,11374,4087,12340,12470,3942,11005,11131,11182,12301,12307,12419,12422,12445,4575,10937,11136,11241,11263,11301,11307,12248,4576,11038,11139,11244,4577,11142,11193,4578,11196,4579,3198,3495,12201,12245,12324,3661,4371,4372,3477,4503,11365,3598,3638,3816,3565,12810,12814,12818,12822,12832,3863,12195,3480,3740,3359,10368,10486,10555,10616,10619,10659,10753,10989,11883,11946,12025,12066,12127,12130,12449,12633,12691,12722,12734,12793,12849,12857,13023,13028,13116,13122,3751,11605,3272,3371,11723,12626,13130,3559,4545,10257,10260,10286,10761,10774,10895,11285,11377,11772,11780,12001,12004,12092,12251,12344,12638,12641,12658,12661,12683,12735,12898,12903,12927,12932,4557,11487,11520,11555,11585,12744,12748,3738,3504,3506,12664,12667,12670,12673,12703,12706,13060,13064,13068,3507,3890,3466,13065,3467,13061,3318,3319,3293,4542,3176,4500,3689,4225,4009,3487,4558,4081,11258,3619,3331,11732,11735,12172,12273,12429,4051,4008,11876,12216,3952,10829,12060,12229,12452,13076,3997,13080,4003,11008,12098,12171,12228,12272,12923,4004,3662,11886,12032,12106,12152,4040,3680,11011,11074,11155,11215,12053,12120,12370,12442,12455,12960,12965,4563,10777,11147,12973,3289,10377,10473,10602,10666,11460,11679,11726,11760,11856,11911,12113,3290,10735,10780,10783,10816,10842,10879,10917,10953,11927,11930,11933,11936,12133,12136,12139,12142,12209,12381,12425,12684,12709,12782,12789,12796,12801,12804,12807,12840,12854,12913,12938,12941,13041,13118,3291,10406,10461,10671,10756,10882,11568,11763,11775,11862,11873,11894,11899,11939,11964,11979,12700,12846,12870,12899,12904,12928,12933,3292,3367,12086,12764,12811,12815,12819,12823,12833,12837,4541,10323,10415,10526,10550,10798,10845,10855,11534,11633,11654,11657,11660,11676,11818,11821,11824,11827,11923,11942,11945,11958,12013,12016,12019,12022,12093,12183,12186,12279,12282,12343,12374,12411,12490,3449,10622,10890,10934,11204,11282,11445,11688,12320,12493,12886,12955,13006,4553,10807,10819,10926,10944,10947,11002,11088,11096,11112,11150,11167,11176,11212,11253,11273,11276,11279,11310,11317,11320,11705,11741,12007,12010,12044,12087,12116,12257,12298,12304,12393,12396,12415,12469,12475,12484,12503,12763,12776,12779,12875,12956,12998,13013,13016,13057,13101,13104,3352,10653,10683,10692,11233,11787,12412,12426,12745,12749,12752,3391,13037,13098,3385,3820,3756,10326,11608,11636,12727,4550,10277,10647,10650,11091,11109,11571,11624,11668,11689,11793,11830,11833,11836,11839,12944,3312,10686,10839,10910,11637,11792,11984,12210,12773,13040,13119,13125,13129,3781,11738,12680,4131,3510,4548,3792,3828,4531,4533,4534,3263,3264,4532,4535,4536,4308,3799,3609,11601,4231,11467,4565,10245,10248,10507,10558,10561,10566,10976,11439,11692,11796,4573,11170,11290,11326,4017,12240,3907,11323,11663,11667,11729,12328,12336,12418,12694,12950,13002,3745,10950,10956,10971,11908,12037,12119,12389,3594,11173,12145,12254,12264,12333,12384,12392,12500,12892,3633,4085,3747,10689,11027,11179,11209,11220,12057,12222,12332,12378,12990,3560,10608,10611,10695,10869,3562,4569,11602,4559,4564,12648,4570,10746,10848,11158,11442,11473,12204,12213,12260,12439,4191,10822,12225,12237,12263,4092,3780,12506,3724,3725,4567,10299,10302,10641,10644,11484,11664,12448,4568,11582,11673,3749,10605,10866,13027,4024,4590,4616,4665,4667,4698,4715,4722,4723,4759,4764,4794,4800,4884,4909,4910,4925,4947,4972,4973,4995,4996,5009,5013,5036,5042,5058,5061,5062,5063,5068,5069,5091,5116,5117,5127,5132,5138,5175,5176,5184,5193,5198,5200,5211,5213,5219,5223,5224,5237,5244,5247,5248,5249,5253,5289,5302,5310,5312,5313,5317,5318,5319,5327,5330,5335,5336,5337,5344,5348,5349,5350,5359,5363,5364,5365,5370,5383,5392,5404,5406,5414,5415,5419,5423,5448,5454,5464,5465,5480,5493,5515,5521,5539,5540,5543,5562,5570,5571,5576,5577,5587,5589,5601,5605,5614,5615,5617,5632,5637,5647,5648,5660,5667,5681,5685,5688,5694,5695,5696,5699,5704,5740,5741,5744,5746,5749,5750,5751,5753,5755,5757,5762,5769,5784,5798,5803,5804,5817,5818,5823,5827,5829,5834,5875,5887,5896,5900,5909,5913,5914,5922,5936,5942,5960,5963,5975,6002,6016,6041,6061,6062,6065,6080,6082,6083,6085,6098,6099,6102,6104,6107,6108,6120,6126,6127,6128,6130,6132,6169,6170,6175,6178,6184,6188,6224,6226,6228,6230,6239,6241,6243,6249,6251,6257,6260,6268,6275,6276,6277,6282,6304,6305,6306,6308,6314,6319,6353,6354,6358,6359,6360,6361,6362,6363,6364,6371,6404,6405,6414,6435,6436,6456,6458,6469,6470,6476,6506,6508,6522,6560,6562,6563,6616,6641,6683,6703,6712,6713,6714,6715,6734,6735,6741,6754,6757,6759,6761,6762,6763,6765,6779,6790,6792,6793,6806,6810,6861,6872,6874,6878,6895,6896,6932,6944,6975,6994,7009,7063,7091,7146,7167,7176,7179,7234,7242,7300,7302,7317,7325,7328,7329,7348,7354,7356,7405,7415,7418,7434,7486,7487,7491,7535,7536,7554,7621,7640,7663,7687,7702,7718,7728,7737,7738,7767,7770,7772,7782,7820,7831,7856,7914,7948,7981,8028,8044,8060,8061,8136,8190,8209,8233,8253,8277,8375,8377,8383,8400,8404,8420,8443,8454,8456,8471,8476,8480,8503,8517,8518,8534,8535,8540,8541,8542,8543,8544,8562,8563,8564,8572,8585,8587,8599,8603,8605,8606,8607,8615,8620,8647,8648,8679,8692,8696,8714,8736,8737,8738,8739,8751,8752,8774,8784,8794,8795,8796,8797,8799,8821,8822,8833,8877,8883,8889,8902,8907,8909,8912,8913,8917,8927,9009,9040,9041,9042,9057,9074,9080,9108,9109,9150,9153,9179,9224,9225,9226,9241,9266,9280,9286,9289,9311,9312,9340,9402,9437,9438,9439,9464,9465,9483,9501,9507,9521,9544,9566,9574,9575,9576,9577,9592,9594,9599,9630,9631,9637,9638,9682,9683,9714,9723,9733,9735,9736,9745,9759,9762,9790,9823,9825,9829,9886,9927,9928,9930,9940,9941,9961,9966,10007,10059,10131,10132,10185,10201,2,8,9,4603,4604,4622,4653,4655,4656,4684,4690,4691,4702,4751,4753,4785,4799,4829,4926,4927,4940,4960,5016,5017,5020,5021,5023,5025,5026,5035,5038,5039,5047,5059,5060,5066,5086,5087,5104,5109,5110,5111,5112,5115,5123,5126,5133,5190,5196,5197,5205,5234,5245,5251,5267,5287,5288,5295,5296,5297,5306,5316,5323,5325,5326,5332,5340,5341,5351,5355,5356,5357,5358,5360,5361,5366,5367,5368,5369,5400,5401,5402,5410,5411,5412,5413,5459,5461,5463,5500,5502,5503,5505,5506,5508,5509,5511,5520,5525,5527,5528,5529,5530,5531,5532,5541,5551,5554,5565,5581,5582,5585,5595,5597,5598,5599,5624,5634,5650,5651,5661,5662,5664,5666,5671,5706,5711,5713,5771,5805,5806,5810,5816,5819,5820,5821,5822,5828,5839,5840,5842,5843,5851,5872,5901,5917,5920,5921,5923,5932,5953,5954,5955,5958,5959,5977,5988,5989,6018,6019,6023,6043,6046,6050,6069,6074,6075,6100,6103,6111,6119,6125,6129,6136,6137,6138,6139,6172,6189,6242,6278,6280,6301,6302,6307,6310,6311,6315,6321,6330,6346,6366,6367,6372,6382,6397,6417,6423,6425,6440,6441,6444,6445,6447,6449,6450,6451,6453,6455,6457,6463,6464,6465,6466,6472,6474,6516,6521,6536,6537,6538,6539,6574,6579,6581,6586,6587,6595,6599,6612,6637,6638,6639,6640,6651,6657,6673,6677,6696,6729,6730,6731,6736,6750,6771,6773,6775,6777,6780,6786,6788,6803,6808,6811,6847,6850,6851,6864,6865,6866,6867,6886,6887,6904,6930,6952,6963,6965,6966,6968,6970,6971,7006,7007,7012,7013,7014,7015,7017,7019,7044,7053,7054,7066,7076,7115,7125,7129,7136,7147,7153,7155,7161,7169,7170,7183,7200,7218,7220,7237,7286,7288,7289,7290,7296,7301,7324,7369,7402,7416,7433,7466,7469,7495,7519,7537,7540,7541,7551,7569,7570,7572,7574,7576,7578,7604,7629,7630,7662,7664,7665,7666,7671,7694,7703,7714,7719,7725,7727,7733,7745,7746,7748,7780,7803,7869,7870,7917,7925,7926,7950,7951,7968,7969,8036,8037,8038,8063,8096,8103,8105,8114,8126,8159,8165,8172,8185,8204,8210,8232,8275,8305,8317,8335,8338,8368,8391,8457,8458,8461,8463,8566,8567,8568,8569,8594,8623,8651,8695,8713,8768,8814,8817,8830,8837,8874,8895,8923,8924,8942,8943,9082,9086,9106,9116,9139,9141,9144,9148,9151,9152,9165,9166,9186,9192,9204,9252,9270,9324,9325,9332,9394,9399,9434,9441,9444,9447,9448,9463,9479,9488,9500,9510,9511,9514,9516,9542,9665,9709,9710,9752,9797,9913,9970,10035,10110,10123,10128,3,2626,2627,2628,2629,2630,2634,2635,2636,2640,2643,2647,2648,2649,2653,2664,2666,2672,2676,2677,2678,2679,2683,2684,2686,2687,2688,2689,2690,2692,2693,2694,2695,2696,2702,2710,2711,2713,2714,2715,2718,2722,2723,2724,2738,2741,2742,2743,2745,2754,2758,2761,2770,2771,2772,2774,2783,2785,2786,2788,2794,2795,2796,2804,2813,2815,2817,2818,2842,2843,2857,5226,5286,5386,5472,5473,5474,5552,5649,5680,5714,5730,5732,5738,5799,5800,5801,5802,5808,5841,5972,6017,6040,6077,6117,6258,6265,6299,6300,6320,6323,6325,6332,6333,6334,6335,6336,6337,6338,6339,6419,6486,6487,6572,6606,6607,6648,6649,6787,6802,6875,6876,6883,6905,6936,6938,6985,7010,7011,7027,7028,7029,7065,7109,7110,7207,7268,7269,7270,7271,7285,7318,7374,7375,7384,7390,7392,7404,7436,7437,7438,7439,7584,7585,7592,7594,7595,7596,7811,7813,7814,7829,7867,7946,7989,8047,8068,8069,8084,8143,8246,8315,8316,8318,8353,8416,8417,8489,8510,8511,8512,8513,8655,8867,8891,8892,8974,8988,9043,9044,9160,9196,9219,9253,9294,9486,9746,9939,9995,9997,6035,6402,6403,6489,6509,6510,6927,7145,8303,8580,8613,8807,9000,9001,9071,9072,9342,9343,9344,9345,9545,9817,10119,10170,10171,6471,8407,8408,8857,8875,9818,10169,4657,4659,4660,4716,4724,4862,4878,4879,4901,4907,4908,4939,4994,5054,5113,5163,5183,5220,5222,5229,5230,5256,5331,5354,5489,5557,5558,5559,5676,5677,5703,5707,5765,5767,5776,5782,5854,5930,6058,6081,6245])). % 172.88/172.55 cnf(13414,plain, % 172.88/172.55 (P102(f332(f332(f246(f883(x134141,a871)),x134142),x134142))), % 172.88/172.55 inference(rename_variables,[],[3594])). % 172.88/172.55 cnf(13417,plain, % 172.88/172.55 (~P102(f332(f332(f334(a876),x134171),f332(f253(a876),f2(a876))))), % 172.88/172.55 inference(rename_variables,[],[11753])). % 172.88/172.55 cnf(13420,plain, % 172.88/172.55 (~P102(f332(f332(f334(a876),x134201),f332(f253(a876),f2(a876))))), % 172.88/172.55 inference(rename_variables,[],[11753])). % 172.88/172.55 cnf(13437,plain, % 172.88/172.55 (~P35(x134371,x134372,x134373,f332(f332(f154(x134374,x134371),x134375),f332(a115,f116(x134374))),f116(x134372))), % 172.88/172.55 inference(rename_variables,[],[11184])). % 172.88/172.55 cnf(13480,plain, % 172.88/172.55 (P102(f332(f332(f246(a876),x134801),f332(f332(f79(a876),x134801),x134802)))), % 172.88/172.55 inference(rename_variables,[],[3562])). % 172.88/172.55 cnf(13487,plain, % 172.88/172.55 ($false), % 172.88/172.55 inference(scs_inference,[],[3890,4087,3078,4569,3385,3751,4553,3371,4003,3907,3756,3312,3594,13414,3562,13480,3246,3217,4550,11505,13030,10576,13204,11529,10755,11178,10288,10930,10712,12156,12253,11753,13417,13420,12697,10943,10946,10694,12015,12488,13228,11184,13437,2885,2,8,9,5558,9042,5515,5963,6308,6268,5784,5909,6080,8692,4759,5068,5746,5975,7738,8233,8799,9521,8795,8815,6245,6470,7767,8456,8752,9745,9308,6721,7354,5249,8045,5589,6099,6363,6506,7234,7981,6230,6306,5900,8794,5036,6314,6178,7328,4698]), % 172.88/172.55 ['proof']). % 172.88/172.55 % SZS output end Proof % 172.88/172.55 % Total time :146.890000s %------------------------------------------------------------------------------